Acta Energetica Electrical Power Engineering Quarterly no. 02/2011 by ENERGA SA

act

nergetica

02/2011

number 7/year 3

Electrical Power Engineering Quarterly

3XEOLVKHU ENERGA SA

3DWURQDJH

3ROLWHFKQLND *GDñVND

ENERGA SA

$FDGHPLF &RQVXOWDQWV -DQXV] %LDïHN 0LHF]\VïDZ %UG\Ă 0LURVïDZ &]DSLHZVNL $QWRQL 'PRZVNL 0LFKDï 'XG]LDN ,VWYDQ (UOLFK $QGU]HM *UDF]\N 3LRWU .DFHMNR 7DGHXV] .DF]RUHN 0DULDQ .DěPLHUNRZVNL -DQ .LFLñVNL .ZDQJ < /HH =ELJQLHZ /XERĂQ\ -DQ 0DFKRZVNL 2P 0DOLN -RYLFD 0LODQRYLF -DQ 3RSF]\N =ELJQLHZ 6]F]HUED 0DUFLQ 6]SDN * .XPDU 9HQD\DJDPRRUWK\ -DFHN :DñNRZLF]

5HYLHZHUV 6WDQLVïDZ &]DSS $QGU]HM *UDF]\N 3LRWU .DFHMNR -DQ .LFLñVNL =ELJQLHZ /XERĂQ\ -DQ 0DFKRZVNL -ö]HI 3DVND -DQ 3RSF]\N 'HVLUH 'DXSKLQ 5DVRORPDPSLRQRQD 6\OZHVWHU 5REDN 0DULDQ 6RELHUDMVNL 3DZHï 6RZD =ELJQLHZ 6]F]HUED $UWXU :LOF]\ñVNL

(GLWRU LQ &KLHI =ELJQLHZ /XERĂQ\ 9LFH (GLWRU LQ &KLHI 5DIDï +\U]\ñVNL &RS\ (GLWRUV .DWDU]\QD ¿HOD]HN %HUQDUG -DFNVRQ 7RSLF (GLWRUV -DFHN .OXF]QLN -HU]\ 0DMHZVNL 6HEDVWLDQ 1RMHN 6WDWLVWLFDO (GLWRU 3DZHï 6]DZïRZVNL (GLWRULDO DVVLVWDQW -DNXE 6NRQLHF]Q\ 3URRIUHDGLQJ 0LURVïDZ :öMFLN *UDSKLF GHVLJQ 0LURVïDZ 0LïRJURG]NL 7\SHVHWWLQJ 5\V]DUG .XěPD 7UDQVODWLRQ 6NULYDQHN 6S ] R R 3ULQW *UDğ[ &HQWUXP 3ROLJUDğL 'LVSDWFK SUHSDUDWLRQ (1(5*$ 2EVïXJD L 6SU]HGDĝ 6S ] R R (GLWRULDO 6WDII 2IğFH $FWD (QHUJHWLFD XO 0LNRïDMD 5HMD *GDñVN 32/$1' WHO ID[ H PDLO UHGDNFMD#DFWDHQHUJHWLFD RUJ www.actaenergetica.org

(OHFWURQLF 0HGLD $QQD )LEDN &RS\ (GLWRU

3DZHï %DQDV]DN 7HFKQLFDO (GLWRU

,QIRUPDWLRQ DERXW WKH 7KH SDSHU HGLWLRQ RI $FWD (QHUJHWLFD LV WKH RULJLQDO YHUVLRQ RI WKH MRXUQDO RULJLQDO YHUVLRQ 7KH MRXUQDO LV DOVR DYDLODEOH RQ WKH ZHEVLWH ZZZ DFWDHQHUJHWLFD RUJ ,661

featuring 4

COUNTERING THE VOLTAGE FAILURE DEVELOPMENT WITH SVC SYSTEMS Robert Kowalak

INDUCTION ALGORITHMS FOR OPTIMISATION OF REACTIVE POWER COMPENSATION MEASURES IN POWER GRID Robert Lis, Grzegorz Błajszczak

THE OPERATION OF THE EXCITATION AND VOLTAGE CONTROL SYSTEM OF A SYNCHRONOUS GENERATOR IN ASYMMETRICAL STATES Krzysztof Madajewski, Robert Rink

THE POSSIBILITIES OF ASSESSING THE CURRENT ESP STABILITY DERIVATIVES INSTEAD OF CHARACTERISTICS Kazimierz Ozięblewski, Ksawery Opala

ASSESMENT OF THE POWER SYSTEM ANGULAR STABILITY BASED ON ANALYSIS OF SELECTED DISTURBANCE STATES Stefan Paszek, Piotr Pruski

THE METHOD OF LINEAR OPTIMISATION OF THE PERMISSIBLE WIND POWER GENERATION IN THE TRANSMISSION GRID NODES Marian Sobierajski, Wilhelm Rojewski, Sebastian Słabosz

APPLICATION OF THE TABU SEARCH ALGORITHM FOR SPECIFYING LOCATION OF CAPACITOR BANKS IN A POWER GRID Paweł Wicher, Kazimierz Wilkosz

THE EFFECT OF DISTURBANCES IN THE ELECTRICAL POWER SYSTEM ON TORQUE MOMENTS OF THE HIGH-POWER TURBINE SET SHAFT Józef Wiśniewski

THE APPLICATION OF THE CIM FORMAT IN THE MODELLING OF AN ELECTRICAL POWER SYSTEM IN THE SYNDIS-PLANS SYSTEM Zbigniew Zdun, Marek Wawrzyniak

Stability is one of the basic concepts of dynamic systems. It is related to the capacity of a system to restore its state of balance once it is disrupted. In this sense, stability determines the ability of a system for operation. The following types of stability are identified in electrical power systems: local, global and voltage; however, other terms are also used. Depending on the electrical power system type, i.e. the structure and parameters of the grid, the type and locations of energy source regulating systems (i.e. objects with regulators) and the type and locations of power loads (consumers), the system stability reserve – defined as the distance of the current operating point from the operating state in which stability is lost – is different in each of the aforementioned stability types. The problem of local and global stability in the national power system is currently not drawing any particular attention of the system operator. Large power generation units driven by steam turbines, which dominate in this system, are equipped in system stabilisers that ensure suitable attenuation of electromechanical oscillation. The effect of small energy sources on local and global stability is negligible. However, one must expect that the territorial development of the West European synchronous area, in which the Polish system is located, as well as the change of the structure of generating sources in this area (i.e. the increase of dispersed power generation) will most likely change this condition. The problem of local and global stability will then become valid. Note that this problem persists in island systems. Among the problems which have the attention of the national system operators (and of other systems as well) is the problem of voltage stability. It is largely related to the insufficient investments into the structures of electrical power systems. In this case, and opposite to the aforementioned problems of local and global stability, an increase in the saturation of the electrical power system with energy sources can stiffen the voltages at the system nodes and hence increase the voltage stability margin. It will depend to a great extent on the characteristics of such energy sources with respect to reactive power generation and on the applied control mode. The operation of the said energy sources in the voltage regulation mode or their switching to the supervisory voltage control systems of the nodes should result in the best positive results (i.e. the highest increase of the voltage stability). The operation of these sources in the mode of regulating the power factor of cos φ = 1, which is currently practised in the case of small (dispersed) energy sources, will provide the least effect. This issue is dedicated to the problems of electrical power system stability and their related problems of control of the elements of such systems. Enjoy reading. Zbigniew Lubośny Editor-in-Chief of Acta Energetica

Robert Kowalak / Gdańsk University of Technology

Authors / Biographies

Robert Kowalak Gdańsk / Poland Graduated from the Faculty of Electrical and Control Engineering at Gdańsk University of Technology (2000). Obtained PhD in technology at this faculty (2005). Currently employed as a lecturer at the Power Engineering Department of the Faculty of Electrical and Control Engineering at Gdańsk University of Technology. Areas of interest: high-voltage power electronics systems (FACTS, HVDC), modelling the operation of power electronics systems in a power system, cooperation of power supply systems with traction power systems.

Countering the Voltage Failure Development with SVC Systems

COUNTERING THE VOLTAGE FAILURE DEVELOPMENT WITH SVC SYSTEMS Robert Kowalak / Gdańsk University of Technology

1. INTRODUCTION In recent years, the Polish National Power System has suffered from several failures which were primarily characterised by problems in maintaining correct voltage levels. There is much evidence that the main cause of the problem was a significant deficit in reactive power. A reactive power deficit in the system can be initiated by switching on a large number of loads (consumers) in the given system area and/or shutdown of at least one power supply network element due to its shorting or damage. One possibility of limiting the risk of a reactive power deficit (and thus limiting the voltage failure development) is to introduce additional sources of reactive power into the power supply system – these sources are compensators. The most widely used compensators of the NPS are static shunting compensators, which consist of condensers and reactors activated by electromechanical switching devices. One of their drawbacks is that they do not allow regulation in fast transient states. This is not the case with the currently most advanced shunting compensators used throughout the world, i.e. the SVC (Static Var Compensator) systems, STATCOM (Static Compensator) and STATCOM-based SVCs. All of these types belong to the FACTS family (Flexible Alternating Current Transmission Systems). Among the listed modern compensator systems, the SVC systems are probably the prime type used in the NPS. This paper presents the results of model tests of the operation of SVC systems as obtained through the research [4, 5, 6] in the effect of power electronic static compensators on the operation of the electrical power system during a voltage failure. The tests have been completed in DIgSILENT PowerFactory 13.2.

2. SVC SYSTEMS The world’s ﬁrst SVC system rated at more than 100 kV was commissioned in 1977. It was designed to regulate voltage of 138 kV buses [2]. The structure of these systems include the following reactive elements: condensers and reactors switched on-line by semiconductor switching devices. The complementary feature is higher harmonic ﬁlters, which are necessary for certain SVC variants to operate. The standard feature of systems switched on high-voltage networks are step-down transformers. Fig. 1 shows an example of the SVC system structure.

Abstract The article presents the results of the model tests which study the behaviour of SVC’s in the electrical power system. The basic state analysed has been the behaviour of the compensators installed in selected nodes of

the system during a voltage failure. The article presents the selected results of the tests completed during the research [4, 5, 6].

Robert Kowalak / Gdańsk University of Technology

WN UT Ik

SN Filters Filtry

TCR

UTz

TSC

USS

activated zał. wył. desactivated α

Fig. 1. Example of SVC structure based on TCR-TSC-FC system: USS – susceptance control system, RU – voltage regulator, TR – HV/MV transformer, a-kat of TCR thyristor ﬁring, U – preset voltage, UT – controlled voltage, Ik – condenser current

The SVC systems have a modular design which enables different variants of system configuration. Several variations of the systems are used. The name of each variant is related to the modules installed [1, 3, 7, 8, 9, 10, 11]. The most generalized breakdown of the systems allows grouping them as discrete control systems and continuous control systems. One of the simplest configuration variants of SVC is the TSC system. TSC is a thyristor switched capacitor. The TSC -SVC includes at least one TSC section; the maximum number of sections is below ten and in the multisection configuration, its members are interdependent. Each TSC section is activated and deactivated depending on the reactive power value to be supplied by the system. These systems can effectively replace the traditional capacitor banks used for reactive power compensation and triggered by electromechanical switching devices. The second variant includes TSR-SVC and TCR-SVC systems. TSR is a thyristor switched reactor and TCR is a thyristor controlled reactor. The section structures of these systems are similar; however, their control methods are different. These compensator types usually include one or several three-phase sections. In the TSR-SVC systems, the thyristor switches of each section are switched on and off depending on the reactive power to be picked up by the SVC. This system only provides incremental regulation of reactive power. The TCR system provides continuous regulation of reactive power consumption by controlling the firing angle of the thyristors included in each stage. The TSR-SVC systems can effectively replace the traditional reactors (equipped with electromechanical switching devices) for compensation of reactive power. The TCR-SVC systems are not used for stand-alone operation since these systems induce higher harmonics in the power supply systems; instead, they are the components of other SVC variants. Another SVC variant is the TCR-FC system. This system comprises two types of components: TCRs and FCs (Fixed Capacitors), which also include capacitative high harmonic filters, necessary for the elimination of noise generated by TCR operation. The reactive power of this system is the resultant of the filter power values and the reactor power value. It is also continuously regulated. These systems are most frequently used for limiting the impact of those consumers who introduce voltage disturbances – due to the high dynamics of the power consumption variations – and higher harmonics into the electrical power system. The most critical SVC variant to the power supply system is the TCR-TSC -FC system. It includes TCRs, TSC banks and FC filter systems. The structure of this system is presented in Fig. 1. The reactive power of this system as an entire SVC is the resultant of the power of the TCR stages in operation and the power of the switched on TSC stages and high harmonic filters. These systems have been primarily used for regulation of voltage and reactive power levels in high voltage grids. The last SVC variant is the TSR-TCR systems which include TSR stages and TSC stages. These systems have been used for regulation of voltage levels and reactive power in high voltage grids.

Countering the Voltage Failure Development with SVC Systems

3. EFFECTS OF SVC IN SIMPLE POWER SUPPLY SYSTEMS

SEE

L2a

L1a

L2b

L1b

Power_Plant (A)/425

Power_Plant (A)/415

CompIStation /425

Station 1/415

Comp_Station /415

In order to determine the effects of installing an SVC in relatively simple power supply systems on the course of a voltage failure, simulation tests have been completed on the system presented in Fig. 2. Adoption of this network structure has allowed obtaining several connection setups created by switching compensators and loads on different buses and by closing and opening speciﬁc bus couples in a given node.

TB1 G1

El. A

TB2

TS1

TS2 TB3

Comp.

El. B

TB4

Load.

Power_Plant (B)/225

Power_Plant (B)/215

Fig. 2. Conﬁguration of modelled system

The presented tested system assumes that the short-circuit power of the power system is 7000 MVA, the lines are 100 km long each, the power plant generators work at the load range of 80-100% of their rated active power (200 MW) and the power plant preset voltages are selected to keep the generators loaded with similar reactive power magnitudes when the active power is generated at 90% of the rated power. The system models the operation of SVCs with the power of +100/-30 MVA and +200/-60 MVA, where each of the two SVCs consists of a single TCR stage and four TSC stages. The voltage failure is modelled as the power system voltage decrease by 100-60% of the rated voltage at a rate of 0.1%/s (0.4 kV/s). The tests were started with an analysis of the power system performance, with the configuration shown in Fig. 2, during the voltage failure. The system performance was tests without SVC and with SVCs rated at 100 MVA and 200 MVA. The obtained simulation results shown in Fig. 3 and 4 are represented by the courses obtained for the assumed power plant generation at 90% of its rated active power. Fig. 3 shows the voltage changes occurring at specific nodes of the tested system. Fig. 4 shows the changes in the reactive power of the power plant generators and compensator. The successive curves from left to right were obtained for a non-compensated system, for the 100 MVA SVC and for the 200 MVA SVC. In the presented case, the generators lose synchronisation when the voltage reaches 72% of the rated value. When the smaller compensator is present in the system, the latter can operate until the system voltage is 69.9% Un; in the case of the bigger compenser, the system performs until the voltage is 67.6% Un. The rotor current limiters are activated after a longer time in the case of generators with a compensator, which is shown on the generator reactive power curves. The presented figures show slight disturbances caused by the incremental switching on of successive TSC sections. As expected, the least severe impact was caused by the compensator operated in the improvement mode during the voltage failure on a system node. Moreover, the compensator in question is the system element which is the first one to exhaust the voltage regulating capacities – this results from the preset voltage and droop but first of all, it is due to the location of the SVC in relation to the failure location. From the perspective of the power plant, first the reactive power is loaded on the generators closer to the failure location, i.e. the generators which work with the 400 kV buses. A larger number of analyses have been performed during the testing process. The impact of non-uniform loading of generators with active power has also been investigated. It has been discovered that non-uniform

Robert Kowalak / Gdańsk University of Technology

and uniform loading of specific generators at the identical active power generated by the power plant leads to premature desynchronisation during the voltage failure. This is caused by the fact that the generators loaded with higher active power have desynchronised more quickly and other units have followed suit. The active power loading ratio of the generators also determines the reactive power level a generator can provide. The higher the margin of reactive power is in the generators, the more capable a power plant is of maintaining operation at increasingly lower voltage of the power system. This implies that one of the possible courses of action to increase the power plant safety against the risk of generator desynchronisation upon a voltage failure would relieve the plant with active power. The completed tests have also shown the impact of the compensator location in relation to the power plant and the failure location upon a voltage failure. The research has shown that the closer the compensator is to the failure location, the less it was capable of mitigate the failure effects. However, the closer the SVC system is to the power plant, the lower is the voltage at which the plant can operate. The tests have also confirmed that the SVC droop is relevant only in the initial phase of the failure, when the system is still capable of regulation. The SVC droop is insignificant to the power plant, because when the power plant regulating capacity ends, the SVC systems in the power supply system either have already lost their regulating capacity or their location causes the power plant to take the reactive power load first, so the effect of the compensator is considerably limited. a)

1.10

0.98

0.86

0.74

0.62

0.50 0.0000

70.000

140.00

Station_1\415: U [p.u.] - w/o comp. Station_1\415: U [p.u.] - SVC 100MVA Station_1\415: U [p.u.] - SVC 200MVA

210.00

280.00

[s]

350.00

0.50 0.0000

140.00

210.00

140.00

210.00

280.00

[s]

350.00

1.10

1.15

0.98

1.02

0.86

0.89

0.74

0.76

0.62

0.63

0.50 0.0000

70.000

Comp_Station\415: U [p.u.] - w/o comp. Comp_Station\415: U [p.u.] - SVC 100MVA Comp_Station\415: U [p.u.] - SVC 200MVA

70.000

140.00

Power_plant(A)\415: U [p.u.] - w/o comp. Power_plant(A)\415: U [p.u.] - SVC 100MVA Power_plant(A)\415: U [p.u.] - SVC 200MVA

210.00

280.00

[s]

350.00

0.50 0.0000

70.000

Power_plant(B)\215: U [p.u.] - w/o comp. Power_plant(B)\215: U [p.u.] - SVC 100MVA Power_plant(B)\215: U [p.u.] - SVC 200MVA

280.00

[s]

350.00

Fig. 3. Voltage courses: (a) EPS connection node; (b) Station busbars w/compensator; (c) Power plant 400 kV buses; (d) Power plant 220 kV buses

Countering the Voltage Failure Development with SVC Systems

120.

96.0

72.0

48.0

24.0

0.00 0.0000

70.000 140.00 G1: Q [MVAr] - w/o comp.. G2: Q [MVAr] - w/o comp. G1: Q [MVAr] - SVC 100MVA G2: Q [MVAr] - SVC 100MVA G1: Q [MVAr] - SVC 200MVA G2: Q [MVAr] - SVC 200MVA

210.00

280.00

[s]

350.00

0.00 0.0000

70.000 140.00 G3: Q [MVAr] - w/o comp. G4: Q [MVAr] - w/o comp. G3: Q [MVAr] - SVC 100MVA G4: Q [MVAr] - SVC 100MVA G3: Q [MVAr] - SVC 200MVA G4: Q [MVAr] - SVC 200MVA

210.00

280.00

[s]

350.00

c) 240.

190.

140.

Fig. 4 Courses of reactive power: (a) Generators G1 and G2; (b) Generators G3 and G4; (c) Compensator

90.0

40.0

-10.0 0.0000

70.000 140.00 210.00 TR 120MVA 420kV/15.75kV: Q [MVAr] - SVC 100MVA TR 240MVA 420kV/15.75kV: Q [MVAr] - SVC 200MVA

280.00

[s]

350.00

4. PERFORMANCE OF SVC SYSTEM IN NPS In order to investigate the effect of SVC systems of the power system performance during a voltage failure, an NPS model has been developed in DIgSILENT PowerFactory, based on the data made available for the research [4, 5, 6]. Based on the analysis of voltage changes during normal operation in the nodes in various system loading states, and following the determination of voltage susceptibility of the nodes to the reactive power load increase, nodes have been selected where installation of compensators is recommended. Based on the parameters of these nodes and the range of voltage changes occurring therein, the power ratings of the SVC systems have been selected. Tab. 1 lists the nodes and the powers of adopted SVC systems. Tab. 1. List of parameters of selected compensators Node M0R211 PLE214 GRU215 MKR212 GDA215 NAR411 OLM415 LES114 GZC114 N0T114 CSK115 REC124 ZLC115

Uzad [p.u.] 1.025 1.021 1.042 1.072 1.039 1.011 1.015 1.071 1.064 1.047 1.045 1.084 1.045

Qind [MVAr] -250 -155 -135 -45 -100 -65 -70 -10 -10 -15 -15 -5 -5

Qpoj[MVAr] 250 185 185 115 100 85 70 60 50 30 25 20 10

Robert Kowalak / Gdańsk University of Technology

During the testing process, voltage failures have been modelled in specific areas of the NPS. The failure is forced by the incremental increase of the reactive power consumed by loads in the specific area. The test has been performed for several areas, but only example results are presented below as obtained for the model voltage failure in the area of Warsaw. The first of the figures (Fig. 5) shows the voltage changes in the node MOR near Warsaw. As the obtained courses indicate, the installation of compensators improves the voltage conditions. This is shown by the time during which the voltage in the analysed grid reaches the lowest of analysed values, i.e. 50% of Un (calculation end). It is also evident that the voltage in its final phase achieves higher values with the compensator working in the node in question. The voltages in the system achieve higher values at the same reactive power consumption by the loads.

1.10

1.00

0.90

0.80

0.70

0.60 0.00

100.00 MOR211: Voltage, Magnitude in p.u. MOR111: Voltage, Magnitude in p.u. MOR121: Voltage, Magnitude in p.u.

200.00

300.00

[s]

400.00

0.60 0.00

100.00 MOR211: Voltage, Magnitude in p.u. MOR111: Voltage, Magnitude in p.u. MOR121: Voltage, Magnitude in p.u.

200.00

300.00

[s]

400.00

Fig. 5. Voltage levels at Station MOR: (a) System w/o SVC; (b) System w/SVC

During a voltage failure, the power plant performance is important. The power plants closest to Warsaw are located in Kozienice, Ostrołęka (Station OST), Bełchatów, Pątnów and Konin. Fig. 6 shows the voltage changes over the Station OST buses; Fig. 7 shows the development of the reactive power loads of the generators in this node. The two smallest units quickly achieve the reactive power limit. In the case of the remaining units, they exhibit a signiﬁcantly lower rate of loading with reactive power in the systems with SVCs. The power plants at Ostrołęka and Kozienice are loaded with reactive power at the fastest rates and highest magnitudes than other facilities.

1.08

1.0800

1.0640

1.06

1.0480

1.04 1.0320

1.02

1.00 0.00

1.0160

100.00 OST211: Voltage, Magnitude in p.u. OST111: Voltage, Magnitude in p.u.

200.00

300.00

[s]

400.00

1.0000 0.00

Fig. 6. Voltage levels at Station OST: a) System w/o SVC; b) System w/SVC

100.00 OST211: Voltage, Magnitude in p.u. OST111: Voltage, Magnitude in p.u.

200.00

300.00

[s]

400.00

Countering the Voltage Failure Development with SVC Systems

160.00

120.00

80.00

40.00

0.00

-40.00 0.00

100.00 200.00 G_OSB_1_03: Reactive Power in Mvar G_OSB_2_01: Reactive Power in Mvar G_OSB_2_02: Reactive Power in Mvar GS_OST111: Reactive Power in p.u. GS_OST121: Reactive Power in p.u.

300.00

[s]

400.00

-40.00 0.00

100.00 200.00 G_OSB_1_03: Reactive Power in Mvar G_OSB_2_01: Reactive Power in Mvar G_OSB_2_02: Reactive Power in Mvar GS_OST111: Reactive Power in p.u. GS_OST121: Reactive Power in p.u.

300.00

[s]

400.00

Fig. 7. Reactive power levels at Station OST: (a) System w/o SVC; (b) System w/SVC

When analysing the performance of the power plants, it must be noted that they are loaded with reactive power at a slower rate when SVCs are operated in the system. This is related to the distribution of reactive power generation between the power plants and the compensators.

5. SUMMARY The SVCs are follow-up systems. As the research has shown, their effect during a voltage failure can be quite signiﬁcant to the electrical power safety of the system. Their additional feature, which is also signiﬁcant to the system, is the capability of regulation in the states of higher dynamics of changes. Every additional source of reactive power is valuable during a voltage failure. The presence of such sources allows increasing the voltage value in relation to the situation where no compensators are present; it can also protect the power plants in operation from instability and subsequently from desynchronisation of generation units with the grid.

REFERENCES 1. Faruque M.O., Dinahavi V., Santoso S., Adapa R., Review of Electromagnetic Transient Models for Non-VSC FACTS, IEEETransactions on Power Delivery, vol. 20, no. 2, April 2005. 2. Hingorani N. G., Flexible ac transmission, IEEE SPECTRUM, April 1993. 3. Kodsi S.K.M., Canizares CA., Kazerani M., Reactive current control through SVC for load power factor correction, Electric Power System Research 76, 2006. 4. Kowalak R., Badania wpływu kompensatorów statycznych zainstalowanych w określonych punktach systemu na roz wój awarii napięciowej, ORDERED RESEARCH PROJECT NO. PBZ-MEiN-1/2/2006 „BEZPIECZEŃSTWO ELEKTROENER GETYCZNE KRAJU” Consortium of the Gdańsk, Silesian, Warsaw and Wrocław Universities of Technology, report on the fulfilment of task 6.1.1.C2, 2009 (unpublished). 5. Kowalak R., Model systemu elektroenergetycznego z elementami energoelektronicznymi, ORDERED RESEARCH PROJECT NO. PBZ-MEiN-1/2/2006 „BEZPIECZEŃSTWO ELEKTROENERGETYCZNE KRAJU’; Consortium of the Gdańsk, Silesian, Warsaw and Wrocław Universities of Technology, report on the fulfilment of task 3.14, 2008 (unpublished). 6. Kowalak R., Współpraca układów kompensatorów statycznych z jednostkami wytwórczymi w czasie lawiny napięciowej, ORDERED RESEARCH PROJECT NO. PBZ-MEiN-1/2/2006 „BEZPIECZEŃSTWO ELEKTROENERGETYCZNE KRAJU’’, Consortium of the Gdańsk, Silesian, Warsaw and Wrocław Universities of Technology, report on the fulfilment of task 6.1.1.C2, 2009 (unpublished). 7. Reference information: AMSCTM SVC Static Var Compensator, American Superconductor Corporation, 2008. 8. Reference information: Modelling of SVC in Power System Studies, ABB Power Systems AB, information NR 500026E April 1996. 9. Reference information: Power Transmission and Distribution, Discover the World of FACTS Technology, Technical Compendium, SIEMENS AG Power Transmission and Distribution High Voltage Division, no. E50001-U131-A99-X-7600. 10. Reference information: SVC Configuration Optimisation, Nokian Capacitors Ltd., EN-TH18-03/2007, 2007 11. Reference information: Utility Static Var Compensator (SVC), Nokian Capacitors Ltd., EN-CS08-03/2007, 2007

Robert Lis / Wrocław University of Technology Grzegorz Błajszczak / Polskie Sieci Elektroenergetyczne Operator SA

Authors / Biographies

Robert Lis Wrocław / Poland

Grzegorz Błajszczak Warszawa / Poland

Lecturer at the Institute of Electrical Power Engineering of the Wrocław University of Technology. Deals with scientiﬁc problems related to planning and control of electrical power engineering systems. Published around 90 papers, mainly on probabilistic power distribution, voltage stability, local stability and artiﬁcial intelligence. His recent papers are primarily dedicated to the methods of estimation of power transmission over high voltage grids, modelling and computer simulation of transient states (Matlab) and cooperation of dispersed power generation with the electrical power system.

In 1984-1994: research staff member of Warsaw University of Technology, Budapest Technical University and Rand Afrikaans University in Johannesburg. Foreign relation manager at Energoprojekt-Warszawa SA (1994-1995), Manager for Drives and Power Reserve at Schneider Electric Poland (1995-1996), Vice Director for Training and Applications at Westinghouse Electric, European Process Control Division (1996-1999). From 1999, employed at PSE Operator SA (Polish Power Grid and Transmission System Operator), where his areas were ancillary services and international power exchange; currently involved in implementation of new technologies, power quality and reactive power management. A member of: IEEE, Polish IEE, CIGRE, Eurelectric, Polish Standard Committee, Committee for Energy Management, Polish Committee on Quality and Effective Use of Electric Power. An expert in electrical power quality and author of over 100 scientiﬁc and technical papers.

Induction Algorithms for Optimisation of Reactive Power Compensation Measures in Power Grid

INDUCTION ALGORITHMS FOR OPTIMISATION OF REACTIVE POWER COMPENSATION MEASURES IN POWER GRID Robert Lis / Wrocław University of Technology Grzegorz Błajszczak / Polskie Sieci Elektroenergetyczne Operator SA

1. INTRODUCTION The proper management of reactive power distribution is a priority task of the transmission and distribution systems operators due to the national energy reliability demands [1]. The purpose of compensation is usually to decrease reactive power transmissions and thus mitigating the transmission loses in the grid. This most often translates into the introduction of new sources (capacitor banks) to the grid to achieve the established goal (reactors are not installed so often). It is the so-called artificial compensation of reactive power. In specific actual grid cases, at least some part of the effects obtained through artificial compensation of reactive power can be naturally created by the following: selection of the appropriate network system, proper usage of charging power (e.g. cables), use (control) of reactive power of synchronous machine (generators and motors). One special type of reactive power compensation is the follow-up compensation performed by non-linear consumers (e.g. steel works). The compensation of reactive power, including the installation of new sources (loads) and power control of all reactive power sources in the power grid is performed as regulated by operating instructions and numerous papers. The methods defined in these documents allow determining the losses of power and energy, as well as the costs of power transmission over the grid before and after compensation. The actual power grid is complex, multi-node and multi-voltage, hence the power losses depend on numerous factors: • the network systems in use and the parameters of its elements • the transmitted active and reactive powers • the voltage levels maintained • the transformer voltage ratio regulation. This paper discusses an algorithm for optimisation of artificial measures of reactive power compensation, which uses induction algorithms – decision trees [1]. The decision trees are the basic method of induction education of machines, which is due to the high effectiveness of this method and the capability of a simple programming implementation. This method of knowledge acquisition consists in an analysis of examples, where each example needs to be defined by a set of attributes and where each attribute can have different values. Knowledge discovery in databases is a process of discovery of new correlations, patterns and trends based on large data volumes stored in repositories; the process uses pattern recognition technologies. The critical stage of this process is data mining and the use of a proper algorithm to find the dependences and sequences in the prepared data set. The technique described here allows discovery of weak nodes in all possible power grid and grouping them in the so-called VCAs (Voltage Control Areas) on the basis of significant similarities in the postshutdown states [3].

Abstract The paper characterises the issues related to compensation of reactive power measures which protect the transmission grid from the loss of voltage stability. Slower forms of voltage instability are analysed with power distribution simulations. The simulations represent the behaviour of the system after preset shutdowns; P-U and Q-U charts are drawn to assess the voltage stability reserve in the given time. The purpose of the compensation is to decrease the reactive power transmission and the

losses on the transmission grid related to this power. This most often translates into introduction of new sources to achieve the established goal. This paper explains the algorithm for optimisation of artiﬁcial measures of reactive power compensation with the use of decision trees which are the primary method of induction education of machines due to their high effectiveness and the capability of a simple programming implementation.

Robert Lis / Wrocław University of Technology Grzegorz Błajszczak / Polskie Sieci Elektroenergetyczne Operator SA

2. DETERMINATION OF VOLTAGE STABILITY RESERVE IN TRANSMISSION SYSTEMS In references concerning the subject being discussed [4, 5], certain global trends can be identified regarding the determination of reactive power reserves and safe limits of node voltages in terms of voltage stability: • the reactive power reserves and the permissible voltage limits are determined mainly to ensure safe performance of electrical power systems • the purpose of the reactive power reserve control in system management is to prevent voltage avalanches and to maintain the voltage changes in safe ranges • the main difficulties in modelling of electric power systems in relation to the subject under discussion apply to modelling of loads (consumers), which is why a conservative hypothesis on constant node power values is usually adopted. The majority of electrical power engineering systems of the world features systematic analyses of transmission grid voltage stability by using power distribution software or programs for voltage optimisation and reactive power distribution, as well as specialist stability testing software products. The analyses are performed annually, monthly, weekly and daily for transmission grids. They use exact models of transmission systems and less precise models of lower voltage networks (where only those parts of distribution systems are modelled which have a significant impact on voltage changes in transmission systems; the smallest generators are often not modelled at all). In most electrical power systems, generators are modelled with power unit transformers. The permissible operating point of a generator is determined for the operation requirements and based on the actual voltage value U on terminals and the active power P being generated; the determination method uses the formulas (1-3), whereas under normal operating conditions, the permissible operating point of the generator must account for the limitations due to the maximum permissible voltage on terminals. In the case of voltage stability investigations, especially for the operational control of a transmission grid, it is recommended to model the generator more precisely. The permissible reactive power value of the generator is not only conditioned by the permissible values of the stator winding current Imax and of the rotor winding current ifmax, but also by the actual active power P and the voltage U on the terminals. emax is the maximum emf value of the rotor, which corresponds to the maximum rotor winding current i. If Xd = X, i.e. E = e, the permissible reactive power of the generator is calculated with the following dependency:

Q f max

 UE   q max  Xd

 U2   P 2  Xd 

(1)

where: U is the preset voltage modulus on generator terminals; E is the maximum emf value of the rotor, corresponds to the permissible rotor current /max P is the preset active power of the generator. The generator reactive power must respect the limitations which result from the permissible stator current value: qmax

Qs max  (UI max ) 2  P 2

(2)

Hence the permissible value of the power output from the generator to the transmission grid must be the smaller of the two maximum values: Qmax  min Qgs max , Q f max

(3)

In the long-term planning stage, the limits used are in the form of constant power values (Qmax and Qmin), irrespective of the generator operating point deﬁned by the power distribution. It is a conservative hypothesis which implies an additional, hidden voltage reserve which protects against a voltage avalanche. The capacitor banks, including those with mechanical switching devices, and reactors should be modelled with respect to the relation of their power to the voltage square. Qshunt  BU 2

where: B is the transverse susceptance of the capacitor.

(4)

Induction Algorithms for Optimisation of Reactive Power Compensation Measures in Power Grid

3. REACTIVE POWER COMPENSATION MEASURES There are different ways to determine the reactive power reserves in the planning process. In most electrical power systems, a safe reactive power reserve is deﬁned as the distance from the base operating point to the voltage avalanche point. The statistical analysis construes the voltage avalanche point (VAP) as the point in which the convergence of the iteration process in the power distribution program (Fig. 1) is lost after a small increase in the power of loads. �

��

�

��

Fig. 1. PU nose curve under normal conditions and upon critical emergency shutdown.

The reactive power compensation in electric power systems is intended for improving the reactive power management. It consists in properly selecting the capacitor battery power and its distribution in the grid. The optimisation criterion is also a result of economic considerations, i.e. the minimum total of annual costs. The distribution of the banks connected to EHV buses of the stations rated at 15-45 Mvar are optimised (the power might be higher if necessary). PSE Operator SA has been successively rebuilding the required reactive power reserve in the power grid by installing capacitor banks in selected 400/110 kV stations and 220/110 kV stations. The capacitor banks are connected to the compensation windings of the grid autotransformers at the example stations listed in table 1. Tab. 1. Example locations and powers of installed banks Location

TR/ATR

SC power [Mvar]

ES Gdańsk Błonia 400/110/31.5 kV

TR1

2x25

ES Grudziądz 400/110/15 kV

AT5

4x15

ES Olsztyn Matki 400/110/15 kV

AT2

4x15

ES Jasiniec 220/110/15 kV

ATI

3x15

ES Miłosna 220/110/15 kV

ATI

3x15

ES Ełk 220/110/15 kV

AT2

3x15

ES Mory 220/110/15 kV

AT1, AT2

2x15

3.1. Optimisation of compensation measures in MV networks The issue of compensation optimisation in MV networks consists in the following: • the power of compensators • the locations of compensators.

Robert Lis / Wrocław University of Technology Grzegorz Błajszczak / Polskie Sieci Elektroenergetyczne Operator SA

Power of compensators Depending on the actual local conditions, low-power condenser batteries are installed in LV lines (max. 300 kvar of power). The MV and LV banks are installed at the consumers to improve the power factor (tgφ = 0.4). The power of such a bank is determined in the following way: Qbat  Ptg�1  tg� 2 

(5)

where: P is the consumed active power and tgφ1, tgφ1 are the tgφ values before and after the compensation, respectively. In the case of an individual compensation, the capacitor bank power Qk is limited:

Qk  0,9Q0

(6)

where: Q0 is the reactive power of the induction motor in idle. This compensation measure is justified in the case of motors rated at more than 30 kW. Distribution of compensators In references concerning the subject being discussed [6, 7], several of the most important methods can be identified which are used for planning the distribution of various elements of reactive power artificial compensation: • the Polish Energy Regulatory Authority compliant method • the estimate method • the dynamic programming method.

3.1.1. The regulatory compliant method The compensated power Q on the LV side can be derived with the following formula: Qkn  Q 

240U 2 ( K kn  K kw ) K pTk ( RTr  RS )

(7)

Q is the reactive power demand; U is the rated voltage on LV and MV sides; Kkn, Kkw are the unit costs of transformation at low/medium voltage; K is the unit cost of power loss; Tk is the usage time of a capacitor bank; RTr, Rs is the transformer and grid resistances, respectively, expressed for LV. It is a simpliﬁed method which gives good results at the natural power factor cosφ ≥ 0.83. where:

3.1.2. The estimate method This method comes down to the following rules: • the power factor on the LV side during the load peak must not exceed 0.87-0.90 (this does not apply if the HV bank power would be less than 600 kvar, which is when the total reactive power must be compensated on the LV side); • the optimum LV reactive power fed from a single bay is 900-1200 kvar. 3.1.3. The dynamic programming method It applies to radial networks. The peak powers in the speciﬁc radii of the network are: Si = Pi +jQi, for i = the number of MV/LV stations

(8)

The transformation losses at the main transformation station (MTS) are:

STr  PTr jQTr

(9)

Induction Algorithms for Optimisation of Reactive Power Compensation Measures in Power Grid

The peak power of the entire large facility is the total of all these powers (accounting for time-varied loading):

Sobl  Pobl  Qobl

(10)

Qs is the maximum reactive power which can be picked up from the network, however:

Qs  Qobl

(11)

The power at the facility must be compensated using the following formula:

Qk  Qobl  Qs

(12)

This can be done in the following points of the facility network: • each transformer station, at the LV side • the MTS, at the MV side. The problem of the optimum location for the capacitor bank consists in the distribution of powers Qkl ..., Qkn, which satisﬁes the condition Qkl + ... + Qkn = Q , where the total annual costs of the network, banks and other devices is the lowest. This problem is solved by dynamic programming [3].

3.2. Optimisation of compensation measures in EHV grids In order to determine the U-Q curves, the reactive power generation at the specific node is increased (all other n ode powers are assumed to be constant) from high values of induction power to high values of capacitative power; the node voltage is monitored. The point at which the dQ/dU derivative is zero determines the limits of voltage stability. The right-hand area in which dQ/dU > 0 is the area of stable voltages, since the increase of the reactive power generation in the node increases the node’s voltage. The left-hand area in which dQ/dU < 0 is the area of unstable voltages, since the increase of the reactive power generation in the node reduces the node’s voltage. In the case of a node group (VCAs), the installation site of reactive power compensation systems usually depends on technical and economic considerations. PSE Operator S.A. has undertaken investment operations to decrease local deficits of reactive power. The company has identified VCA areas, i.e. the areas at risk of stability loss. For example, a considerable investment task is the installation of an SVC controlled reactive power source in a 400 kV transmission line: Gdańsk Błonia - Grudziądz - Płock - Miłosna - Mościska - Rogowiec. The constant current cable under the Baltic Sea allows a variable import/export of several hundred MWs, which causes high variations in the power flows at the NorthSouth section and poses a risk of destabilisation of the power grid.

Fig. 2 VCA identiﬁcation stages

Robert Lis / Wrocław University of Technology Grzegorz Błajszczak / Polskie Sieci Elektroenergetyczne Operator SA

The identification of VCAs involves the following stages (see Fig. 2): • Selection of the nodes for VCA identification: a modal analysis is applied for all previously defined shutdowns and upon its results the list of nodes is generated. Then the nodes with the highest own value share ratio (WDA) are selected. • Grouping of type N-1 and N-2 shutdowns based on their similarity: the program identifies the similar results of power distribution caused by different shutdowns. Only different shutdown groups are included in the identification of specific VCAs in stages 6 and 7. • Normalisation of the share ratio WDA for the recognised generator nodes (where Qmax, Qmin, the maximum and minimum reactive powers generated in the node is defined). • Selection of generating nodes in the group (cluster) Ck: the share ration of the generation node in the group is calculated for each identified shutdown group Ck. • Grouping of the clusters Ck by the similarities of their coefficients Gens: in this stage, only the clusters C in which the same or similar generator nodes exist are grouped again. • VCAs identification – finding the consumer nodes: the frequency of occurrence of each node is investigated for each VCAm. • VCAs identification – finding the generating nodes: the frequency of occurrence of each node is investigated for each Genm. Only those nodes are selected which occur more frequently than the defined criterion states.

3.2.1. Use of induction algorithm – decision trees Knowledge discovery in databases is a process of discovery of new correlations, patterns and trends based on large data volumes stored in repositories; the process uses pattern recognition technologies. The knowledge discovery process involves the following stages [1]: • creation of a training set, in which dependences, rules and connections are sought; • selection of the algorithm for data mining; • search of data patterns; • interpretation and verification of found patterns – report for users. The critical stage of this process is data mining (see fig. 3) and the use of a proper induction algorithm [1] to find the dependences and sequences in the prepared data set.

Induction Algorithms for Optimisation of Reactive Power Compensation Measures in Power Grid

Fig. 3. Based on the decision table (a) a decision tree (b) is generated, the nodes of which are the speciﬁc attributes, the branches are the values corresponding to these attributes and the leafs are the speciﬁc decisions. Part (b) shows the structure of database records used for generation of the decision tree for the given VCAs

Decision trees are a form of representing the discovered knowledge (see Fig. 3a). They are a graphical method of aiding the decision process applied in the theory of decisions. The algorithm of decision trees is used in machines to acquire knowledge based on examples. It is a diagram with the structure of a decision tree and its possible consequences. The purpose of decision trees is to identify the correct VCA based on numerous, branching variants of power flows in the power grid. Classification consists in finding the way to represent the data in a set of predefined classes, i.e. variant power flows. Based on the database content a model is built (i.e. classification tree) which is used to quickly identify the proper VCAs. In this case, the discriminating variable is the qualitative variable Pgen. In order to determine the reactive power value Qres, which is required due to the safety of the studied VCA type C, a regressive tree structure is used where a quantitative variable, i.e. selected parameters of power distribution, is the discriminating variable. An example of the program code (i.e. induction algorithm) written in an arbitrary programming language is shown below. The parameter φ denotes the probability index of attributes. Compute B=number of elements in base Compute R=number of elements in set-i Compute maximum number of elements M=max(B,R) Compute threshold for common elements T=cpM Compute number of common elements between base and set-i C=common elements If C>=T then base and set-i are similar If C<T then: Denote the set (base or set-i) with the lowest number of elements by S. If all elements in this smallest set are included in the largest set then sets are similar; otherwise sets are not similar

Robert Lis / Wrocław University of Technology Grzegorz Błajszczak / Polskie Sieci Elektroenergetyczne Operator SA

20 4. SUMMARY

The paper describes the method for identification of power grid areas susceptible to losses of voltage stability during operation of the grid under special (difficult) conditions. These areas susceptible to instability caused by the lack of reactive power reserve are called VCAs (Voltage Control Areas). The method is based on the combination of an analysis of P-U curves and a modal analysis. The VCAs are identified by methods of heuristic grouping. Regarding the investigated scenarios and sets of unforeseeable operating conditions within PSE Operator’s system, two VCAs have been identified. The following have been defined for each of the identified VCAs: the generator group with additional sources which, upon depletion of their reactive power reserve, result in instability in the VCA. The distribution of the required reactive power reserve among the generators, as well as the locations and magnitude of new reactive power sources which control the studied VCA have been obtained by applying linear programming and an algorithm of decision trees.

REFERENCES 1. Lis R., Wiszniewski A., Ocena projektu EPRI „Development of a Method forthe Identiﬁcation of Critical Voltage Areas and Determination of Required Reactive Reserves” pod względem możliwości wdrożenia jego wyników w PSE Operator SA, Report of the Institute of Electrical Power Engineering, Wrocław University of Technology, SPR series on. 09/2008, Wrocław 2008. 2. Zhong J., Nobile E., Bose A., Bhattacharya K., Localized Reactive Power Markets Using the Concept of Voltage Control Areas, IEEE Trans. Power Syst, vol. 19, pp. 1555-1561, August 2004. 3. Sobierajski M., Rojewski W., Badanie stabilności napięciowej sieci przesyłowych, Energetyka, 2007 subject book no. 10, pp. 13-19. 4. Taylor CW., Power system voltage stability, McGraw-Hill, 1994. 5. Bourgin F, Testud G., Heilbronn B., Verseille J., Present practices and trends on the French Power System to prevent voltage collapse, IEEE Trans, on Power Systems, vol. 8, no. 3, August 1993, pp. 778-787.

Krzysztof Madajewski / Institute of Power Engineering Department, Gdańsk Division Robert Rink / Institute of Power Engineering, Gdańsk Division

Authors / Biographies

Krzysztof Madajewski Gdańsk / Poland

Robert Rink Gdańsk / Poland

Electrical and automatic control engineer. Graduated from the Electrical Engineering Faculty at Gdańsk University of Technology. Obtained his PhD by defending a thesis on the dynamics of electrical power systems (1983) and then presented his habilitation paper on direct current transmission systems (2004). Since 2010, he has had the full professor degree of Gdańsk University of Technology. 1974-1988 – employed at the Institute of Power Systems Automation Gdańsk Division, since 1988 – employed in the Institute of Power Engineering Gdańsk Division. He has been the manager of the facility since 1990. A specialist in control and regulation of electrical power systems. Participated for years in the R&D work of EURELECTRIC. Currently engaged in the activities of the CIGRE Study Committe (Committee C2, System Control and Operation) and of the EERA (European Energy Research Alliance), in the Smart Grid and WIND groups. A Polish representative in the EEGI (European Electric Grid Initiative) which deals with the grids, especially the EU-level Smart Grid. Has been a head of numerous research and implementation projects commissioned by the Polish electrical power engineering industry, EPRI and UCTE (currently ENTSO-E). Author and co-author of more than forty scientiﬁc publications.

Electronic engineer specialised in automatic control, graduated from the Faculty of Electronics, Gdańsk University of Technology. Employed at the Institute of Power Engineering from 1991. His professional activities focus on two areas: excitation regulators and electronic voltage regulators of synchronous generators; design, commissioning, modelling and simulation of frequency start-up systems; performance analyses of the Polish Power Grid, including those related to the development of wind power engineering. Co-author of ten-plus publications.

The Operation of the Excitation and Voltage Control System of a Synchronous Generator in Asymmetrical States

THE OPERATION OF THE EXCITATION AND VOLTAGE CONTROL SYSTEM OF A SYNCHRONOUS GENERATOR IN ASYMMETRICAL STATES Krzysztof Madajewski / Institute of Power Engineering, Gdańsk Division Robert Rink / Institute of Power Engineering Department, Gdańsk Division

1. INTRODUCTION Traditionally, the excitation voltage of static models of thyristor excitation and control systems is described with an equation of the external characteristics of an excitation rectifier with the use of mean values. This method is applied in system analysis. The voltage regulator is selected from the standard IEEE models or custom-designed to meet the goal of the research. The input signals of the voltage regulator, such as currents, voltages and powers are derived directly from the generator model and do not account for the problems related to measurements, digital processing and imperfection of the algorithms adopted for determination of useful current, voltage and power signals. The synchronous generator model is by default the Park model, which includes the components of rotation, but no components of transformation. As a consequence, there are only aperiodic components in the excitation current during disturbances, and no oscillation components are present. The models of the grid infrastructure elements are described with the values for compliant components. These models of excitation and voltage regulation systems, and of the EPS, are tested, widely used and they have proven to be useful in the investigation of symmetrical states, including symmetrical faults. The calculations of this type are completed quickly even in the case of large EPSs. However, these models are not useful in the investigation of states with various asymmetrical disturbances. Building a model that enables analyses of asymmetrical states incurs numerous difficulties and significantly increases the time of calculations. Simulation research environment The simulation research uses the Matlab-Simulink environment. The developed model is in the class of the so-called rigid systems. On one hand, the time constants of a synchronous generator amount to seconds, while on the other, the processes related to the modelling of an excitation rectifiers require integration counted in tenths of microseconds. In many points of the model, it is necessary to cyclically determine precise times of zero crossing of voltages or to sample signals with defined frequencies. Another complication is that it is necessary to achieve a steady state prior to the introduction of disturbances to the model and repeatedly calculate from the same initial state. All of these problems are solved, while the average calculation time for one second of the simulation process requires approximately two minutes of real time.

Abstract This paper concerns the analysis of performance of static thyristor excitation and voltage regulation control systems of a high-power synchronous generator in asymmetrical operating states. Presented results were obtained from the model that reflects instantaneous processes both in the grid and in the excitation and voltage control system. The model of the synchronous generator includes the components of transformation. The rectifier model is based on a detailed thyristor model in the circuit of three-phase six-pulse thyristor converter, instead of simplified block model with defined external characteristics, as it is usual. It enables to monitor instantaneous

values of rectiﬁer voltages. The input signals for the voltage regulator model are not derived from the generator model the control system model includes digital measurement units of generator signals. The described model enables precise analysis of a synchronous generator with an excitation and voltage control system during disturbances and asymmetric operation in the grid. Such modelling is essential for analysis of novel solutions of excitation systems with digital controllers. This kind of analysis is not feasible using simpliﬁed models based on mean signals values and external characteristics of excitation systems.

Krzysztof Madajewski / Institute of Power Engineering Department, Gdańsk Division Robert Rink / Institute of Power Engineering, Gdańsk Division

2. DESCRIPTION OF THE MODEL FOR ASYMMETRICAL STATES The basic elements of the model of a synchronous generator with a static thyristor excitation and voltage control system for asymmetrical states are presented in Fig. 1.

Fig. 1. The model of the generator with the excitation and voltage control system used in the investigation of asymmetrical states (legend: G – generator, TB – power unit transformer, WT, WS – circuit breakers, LINIA – substitute transmission line, TW – excitation transformer, PR – excitation rectiﬁer, ZP – controlled current source, REG – voltage regulator, UWT – thyristor tripping system, A, B – locations of investigated faults)

2.1. Models of grid infrastructure elements The basic structure of the model is the high-power generator which cooperates through the power unit transformer and the supplementary transmission line to feed power to a rigid grid. It is a three-phase model with explicit representation of the three phases. The generator model uses the Park model, which accounts for the components of rotation and transformation. The generator works with the isolated neutral point, which is a typical solution [1]. The model of the substitute transmission line is presented in Fig. 2. The model includes the grid impedance parameters for the compliant and zero components.

Fig. 2. The model of the substitute transmission line for asymmetrical states

The parameters of the line are deﬁned by these dependences:

2 R1  R0 (2.1) 3 R  R1 (2.3) Rm  0 3

RS 

Cp  C1

(2.5)

2 L1  L0 3 L  L1 Lm  0 3 3C1C0 Cg  C1  C0 LS 

(2.2) (2. 4) (2.6)

The power unit transformer adopts the Ynd11 group with the earthed star point.

The Operation of the Excitation and Voltage Control System of a Synchronous Generator in Asymmetrical States

2.2. Excitation system model In the investigated model, both the rectifier (PR) and the tripping system (UWT) are modelled to represent with a high accuracy the phenomena which actually occur. The rectifier is the model of a six-pulse converter controlled by the pulses from the tripping system. The output voltage of the rectifier, after adaptation of the units, is fed to the input which corresponds to the excitation voltage in the generator model. The converter is loaded by a current source the output current of which corresponds to the excitation current of the generator. The current source is controlled by the excitation current received from the synchronous generator model. The converter is powered from the excitation transformer which has the Yd connection group. The transformer impedance is responsible for the switching processes of the converter. The rectifier supply voltage is used in the basic variant of the model to synchronise the tripping pulses for the thyristors. Another variant is also investigated, in which the pulses are synchronised with the signal from the generator voltage transformers. 2.3. Voltage regulator model The regulating system model included the primary voltage regulating loop at the generator terminals, the system stabiliser with the signal from the active power and the current compensation stage. The regulation limiters are not modelled. The measurement stages at the generator stator terminals use the signals of phase voltages and currents from the converters. The signals are sampled at the sampling time of one millisecond and the calculations are performed to determine the signals of voltage, active power, reactive power and frequency. 2. 4. Thyristor tripping system model. The model of the thyristor tripping system is presented in Fig. 3.

Fig. 3. Schematic diagram of the thyristor tripping system (TW – excitation transformer, PR – excitation rectiﬁer, TRsyn – synchronisation transformers, REG – voltage regulator, UWT – thyristor tripping system)

The input signals for the tripping system (UWT) are: the trip angle α from the regulator and the synchronisation voltages from the synchronisation transformers (TR) connected to the supply power of the excitation rectifier. The connection system of the synchronisation transformers and the filter transmittance are selected in the way which allows reception of sinusoidal signals without practically any interferences, and which are required to determine the moment of zero crossing of the converted supply voltages. The filter is selected to ensure a phase shift by -90° for the component with the fundamental frequency. This is accounted for in the selection of the connection group for the synchronisation transformers by shifting the voltage by +90°. The combined effects of the filter and of the transformer connection group enables near complete elimination of disturbance of the voltage used to synchronise the tripping pulses, caused by switching dips. The output signals of the tripping systems are the control pulses for the tripping of the converter thyristors, sent individually to each of the six thyristors. The pulses are sent in pairs – the activating pulse and the sustain pulse, just as in the case of real systems.

Krzysztof Madajewski / Institute of Power Engineering Department, Gdańsk Division Robert Rink / Institute of Power Engineering, Gdańsk Division

�

P�

U�

2.5. Model verification The correctness of the developed model is verified by comparing the simulation results to the model built in one of the professional system dynamics testing tools (DSATools). Analogous symmetrical disturbances are introduced to both models and the time courses are compared. Fig. 4 presents the courses for a three-phase fault at point B (see Fig. 1), while Fig. 5 presents the courses for the incremental change of the preset voltage value. The courses of both models show a good compliance. The models of voltage regulating systems used by the Institute of Power Engineering, Gdańsk Division in the investigations in system dynamics are repeatedly verified by comparing them to the actual courses in the EPS [2, 3]. �

�

��

�� Tested �� Stand.

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

I�

� � � � � � �

∆ω

��

�

��

t�� Fig. 4. The courses of the components of the generator voltage and power (Ug, Pg, Qg), of the excitation voltage and current (Uf, If) and of the generator rotational speed deviation (Δω) for the tested model and for the standard model in the DSATools simulation software during a three-phase fault at point B

U�

� ��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

�� Tested Stand. ��

��

�

t��

Fig. 5. The courses of the components of the generator voltage and power (Ug, Pg, Q ) and of the excitation voltage (Uf) for the tested model and for the standard model in the DSATools simulation software after the step change of the preset voltage by 5%

The Operation of the Excitation and Voltage Control System of a Synchronous Generator in Asymmetrical States

3. THE RESULTS OF SIMULATING THE ASYMMETRICAL STATES The paper presents the results of the model testing for the following: • a two-phase earth fault on the generator voltage at point A (see Fig. 1) • a two-phase earth fault in the 400 kV grid at point B (see Fig. 1) • the loss of one of the synchronising signals in the thyristor tripping system. The investigations also included the effect of changing the signal source for thyristor tripping (converter supply voltage or generator voltage transformers).

3.1. The two-phase earth fault on the generator voltage at point A In the steady state of operation at the rated power, a two-phase earth fault is effected with the duration of 400 ms at point A. The ﬁgures present the courses of the symmetrical components of voltages and currents at the generator terminals and at the EHV side of the power unit transformer (Fig. 6), as well as the instantaneous courses of the excitation voltage and of the excitation transformer currents (Fig. 7). The generator remains stable under the tested conditions. The courses of the excitation voltage and of the excitation transformer currents (see Fig. 7) show that upon the fault only those thyristors work, which are powered from the two voltage phases from the excitation transformer (a and c); the instantaneous excitation voltage value changes almost symmetrically from the maximum value (ca. +1000 V) to the minimum value (ca. -1000 V), which means that the mean value is close to zero. �

��

�

��

I��

��

I��

��

�

U��

��

U�� U��

��

�

��

U��

I��

��

I�� I��

��

�� t��

��

�

Fig. 6. The two-phase earth fault (tfault = 400 ms) at point A. The courses of the symmetrical components� of voltage and current at the generator terminals (Ug1, Ug2, Ug0, Ig1, Ig2, Ig0) and at the PV of the power unit transformer (Us1, Us2, Us0, Is1, Is2, Is0) �

�

��

I��

��

I�� I��

�

� ��

�

��

�� t��

��

Fig. 7. The two-phase earth fault at point A. The courses of the excitation transformer currents (Iwa, Iwb, Iwc) and of the instantaneous excitation voltage (Uf)

Krzysztof Madajewski / Institute of Power Engineering Department, Gdańsk Division Robert Rink / Institute of Power Engineering, Gdańsk Division

3.2. The two-phase earth fault in the 400 kV grid at point B In the steady state of operation at the rated power, a two-phase earth fault is effected with the duration of 400 ms at point B. Fig. 8 presents the courses of the symmetrical components of voltages and currents at the generator terminals and at the EHV side of the power unit transformer. Fig. 9 and 10 present the instantaneous courses of the excitation voltage and of the excitation transformer currents (Fig. 9 – for the synchronisation of the tripping system by the converter supply voltages, Fig. 10 – for the synchronisation by the generator voltage transformers). As implied by Fig. 8, in the tested conditions the generator becomes unstable. The fault limit duration, after which the system resumes stable operation, is ca. 370 ms. �

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

Fig. 8. The two-phase earth fault (tfault = 400 ms) at point B. The courses of the symmetrical components of voltage and current at the generator terminals (Ug1, Ug2, Ug0, Ig1, Ig2, Ig0) and at the PV of the power unit transformer (Us1, Us2, Us0, Is1, Is2, Is0) �

�

��

�

��

�

��

�

��

�

��

Fig. 9. The two-phase earth fault at point B. The courses of the excitation transformer currents (Iwa, Iwb, Iwc) and of the instantaneous excitation voltage (Uf). The tripping system is synchronised by the supply voltages of the converter

The Operation of the Excitation and Voltage Control System of a Synchronous Generator in Asymmetrical States

-5

Iwc

[k A ]

wa wb

[V ]

1000 0 -1 0 0 0 0

0 .0 2

0 .0 6 t [s ]

0 .0 4

0 .0 8

0 .1 2

0 .1 0

Fig. 10. The two-phase earth fault in point B. The courses of the excitation transformer currents (Iwa, Iwb, Iwc) and of the instantaneous excitation voltage (Uf). The tripping system is synchronised from the generator voltage transformers

During the fault, all thyristors conduct electricity, but each of them does it in a different manner. The detailed analysis of the conduction time and of the current values is critical to assess the threats to safe operation of the converter. The courses of the excitation voltage indicate the complex nature of the tripping process under these operating conditions. By comparing the excitation voltage courses of both synchronisation variants (see Fig. 9 and 10), it is concluded that in the investigated cases the thyristor converter works more smoothly when the thyristor tripping system is synchronised by the signals from the generator voltage transformers.

3.3. The loss of one of the synchronising signals Fig. 11 and 12 show the behaviour of the model upon the loss of one of the generated synchronising signals(signal Sa in Fig. 3). The emergency loss of the synchronising signal Saresults in the loss of the tripping pulses of two thyristors at the converter, and as a consequence, their lock-up (see Fig. 12). The regulator maintains the preset generator voltage value by changing the thyristor tripping angle a from 60° to approx. 30° – the thyristors in operation take over the current from the two locked thyristors. The disturbance of the mean excita� of 0.97 pu and returns to the tion current value lasts for approx. 1 s. The generator voltage drops a maximum value prior to the disturbance in approx. 10 s.

��

�

��

�

��

�

��

�

��

U��

��

� t��

��

�

Fig. 11. The loss of one of the synchronising signals. The courses of the generator voltage from the measurement system of the regulator (Ug), of the set angle of the rectiﬁer thyristor (α) and of the mean excitation voltage value (Ufs)

Krzysztof Madajewski / Institute of Power Engineering Department, Gdańsk Division Robert Rink / Institute of Power Engineering, Gdańsk Division

�

��

I��

��

�

��

U�

��

t��

��

Fig. 12. The loss of one of the synchronising signals. The courses of the excitation transformer currents (Iwa, Iwb, Iwc) and of the instantaneous excitation voltage (Uf)

4. SUMMARY The developed model of the generator with the excitation and voltage regulation systems allows testing and analysing any asymmetrical states of the generator and of the excitation system. It is a novel design that has not been applied to the research of excitation systems. The authors have applied a discrete model of the regulating system with real-time sampling and complete representation of measurement systems. The developed model of the thyristor tripping system allows representing the actual courses in excitation systems. The model will be applied in the development of excitation and voltage regulation systems, in the analysis of complex asymmetrical states of the system and in training.

REFERENCES 1. Kacejko P, Machowski J., Zwarcia w systemach elektroenergetycznych, WNT, Warsaw 2002. 2. Madajewski K., Sobczak B., Trębski R., Praca ograniczników w układach regulacji generatorów synchronicznych w wa runkach niskich napięć w systemie elektroenergetycznym, Archiwum Energetyki, numer specjalny, 13th Scientiﬁc Conference ΑΡΕ 2007, Gdańsk 2007. 3. Madajewski K., Sobczak B., Dynamiczne aspekty utraty stabilności napięciowej, Archiwum Energetyki, tom XXXIX (2009), no. 1, 29-46 - ΑΡΕ 2009, Gdańsk 2009.

Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

Authors / Biographies

Kazimierz Oziemblewski Katowice / Poland

Ksawery Opala Gdańsk / Poland

Graduated from the Faculty of Electrical Engineering, Wrocław University of Technology (1961). Obtained his PhD at the Faculty of Electrical Engineering, Gliwice University of Technology. 1961-2003 – employed in the District Power Control Centre in Katowice. 1977-1982 – delegated to the Central Power Control Authority of the Council for Mutual Economic Assistance in Prague (Czech Republic). A member of the Association of Polish Electrical Engineers (SEP). The author of papers and published works on optimisation of network systems, compensation of reactive power and stability of the electrical power system.

Graduated from the Faculty of Electrical and Control Engineering at Gdańsk University of Technology (2001). Presently employed at the Gdańsk Branch of the Power Engineering Department as a doctoral student. Areas of scientiﬁc interest: ARNE and ARST automatic control engineering, area voltage and reactive power control, electrical power system operation state analysis and power distribution calculations.

The Possibilities of Assessing the Current ESP Stability Derivatives Instead of Characteristics

THE POSSIBILITIES OF ASSESSING THE CURRENT EPS STABILITY DERIVATIVES INSTEAD OF CHARACTERISTICS Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

1. INTRODUCTION In the normal operating states of the electrical power system the answer to the following question is sought in order to find a way of optimising the system performance: how do the system operating parameters, e.g. node powers, node voltages and transformation ratios affect the magnitude of transmission losses? The question relating to the states of hazard is how these parameters affect the conditions of the safe system operation, i.e. primarily its stability – the answer is needed to find a way to prevent failures. The problems of optimising the power distributions are solved by the curves (characteristics) of active power losses (and rarely reactive power) determined as the function of node powers and transformation ratios. More specifically, it is not the loss curves which are pertinent here, but their relative increments (derivatives), calculated for the independent variables in the system. This results from the popular and general solutions of this problem [2, 11]. The traditional approach to solving problems of the system operating stability is to investigate the system’s response to small (local stability) or large (global stability) input functions of the following types: shutdown of grid transmission elements, shutdown of generating devices and in-grid shorting [3, 9, 10]. These types of research are relatively difficult, costly and performed sporadically – only when justified by circumstances. The incongruence of the iterative process in the power distribution calculation program is a certain signal of a threat of stability loss in the system; yet it is still only a signal. Apart from the traditional methods, there are also simplified methods of voltage stability testing (and rarely angular stability testing) [3, 4, 5, 9, 10, 22]. These methods investigate the characteristic courses of transmitted and received active/reactive power as a function of modulus (and rarely of angle) of the voltage vector in a power system node, or vice versa: the focus is on the dependence of voltage on the powers consumed at the node(s) of the grid. Due to the fact that the dependences which occur in the system between the operating parameters (e.g. power, voltage, etc.) are confounded non-linear dependences, these characteristics have not been translated so far into an explicit analytical form. Hence for their analysis, their courses are drawn and the parameters of their successive points are calculated step by step in the power distribution calculation program. The descriptions of formulation of V-Q, P-V and δ-P characteristics and their use are the subject of many published papers and as such they are not explained here. The assessments of conditions (defined here as the stability) of the system operation based on the characteristic charts for network nodes are time-consuming, but they can be performed as a part of the system operation planning [5]. These assessments provide information on the properties of the planned network system, especially concerning the tested directions of power transmissions. However, a planned network system is not always performed during operation. Random shutdowns of the system devices may significantly change the conditions under which the system stability was assessed during the planning process. The operator is not capable of repeating the calculations in real time and hence has absolutely no information on the system stability state (reserve).

Abstract A solution of problems concerning optimisation of power distributions consists in investigating the curves of grid losses as the function of system operating parameters. The solution of a speciﬁc group of problems in system stability consists in investigating the curves (characteristics) of active and reactive power transmissions as the function of the same system operating parameters.

The node powers and the power losses are equal physical categories; in total, they form the power balance of a system. The authors of this paper attempt to demonstrate that the methods and tools for testing the courses of loss curves and power transmission characteristics can be approximated.

Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

In this paper the authors consider the propositions of stability state analyses performance not solely based on the characteristics of transmitted powers, but on their derivatives (or relative increments). The derivatives provide correct information about the course of investigated curves, especially when the curves satisfy speciﬁc conditions of regularity. Calculations of these derivatives include all grid/network nodes can be performed offline, for the assumed system data, and in real-time as based on the actual network topology and current measurement data [13, 14, 17, 25].

2. SYSTEM STABILITY PROBLEM The authors believe that investigation or testing of system stability has to include at least three groups of characteristic phenomena observed in a system. The first group relates to the behaviour of loads (consumers). Generally speaking, the loads with the (active and reactive) power consumption that decreases significantly with the decrease of the power supply grid voltage do not affect (or do, but to a small extent) the development of a stability loss related system failure. The constant power consumption which is independent of the voltage (which is the case until the voltage regulating range of the receiving transformers is depleted), and especially the increase of power consumption at a reduced system voltage favour the development of a system failure. Example: an increase in the power consumption (reactive power) mainly by induction motors when the supply voltage decreases may cause a voltage avalanche [3, 5, 9, 10, 21]. The stable operation of the system can possibly be interrupted. The protection from voltage avalanches is to maintain a suitably high voltage, even at the cost of limiting the power supply. The characteristics of loads (consumers) are explained in more detail in the reference material [21]. The second group relates to the behaviour of power sources, primarily generators, within the system [3, 5, 9, 10, 23]. In the case of this group, the interactions between the generators and the grid are important. This paper does not analyse these problems. The authors share the opinion that random (but also not necessarily random) events in the system, the generator connections (i.e. a power plant) may be weakened compared to their normal state, which makes the network less rigid and react with significant parameter changes to small (normal) disturbances caused e.g. by the action of power regulators or voltage regulators at the generators. In the normal operating states of the system, the relatively constant grid parameters are the reference base for the generator power and voltage regulators. In all states other than normal, the same yet changing grid operating parameters fail to perform as reference parameters. This results in wobbling of power and generators. The point (parameters) of operation of the system in which power wobbling occurs is called the Hopf point. The third group relates to the behaviour of the grid/network and its rigidity, as well as its capacity of transmitting the demanded power to each grid node. This subject is covered here in more detail. The concept of a rigid network has been adopted in the literature and in real life, since it simplifies the analyses of the conditions of cooperation of technical devices with the system, including power plant generators and consumer devices. It also simplifies the selection of operating rules for their safety, control and regulating systems. The popularization of the rigid network term has been supported by the notion that operation of a single device in the grid/network cannot significantly affect the parameters of the system if the power of this device is much lower than the power of the entire system. The system, however, is not a „copper bar” – it is a set of individual generating and consumer devices which cooperate through transmission lines which can have great lengths and limited power-carrying capacities. Hence, the facts are different. In reality, a rigid network does not exist. Every grid/network is flexible (elastic or susceptible) and responds to any input function by changing its operating parameters. It depends solely on the magnitude and the application point of the input function whether the change of parameters is barely observable, significant or disruptive to the system. The undesirably high network voltage susceptibility to the reactive power load changes of the power units at the Ostrołęka power plant during the disturbance of June 26 2006 caused shutdown of the power units and threatened a system failure [18]. The unconscious weakening of the transmission capacity of the UCTE system grid by shutting down the 380 kV double-circuit line on November 4 2006 resulted in partitioning of the system and threatened a colossal system failure [19]. The paper [23] highlights and justifies the need for a change in the currently applied generator regulating systems to prevent such events.

The Possibilities of Assessing the Current ESP Stability Derivatives Instead of Characteristics

The flexibility (susceptibility) of the network depends on the system structure (i.e. the grid structure, power of sources, regulating methods of sources, etc.) and its operating parameters (voltage level, power of sources, etc.). The system operating parameters are the function of local power balances and of the power transmissions dependent on these balances. The problem of local balancing of the power in the system, including the characteristics of consumer power and generators is discussed in the paper [21], generally in relation to reactive power. The paper justly presents the balance of reactive power as the factor which affects the voltage stability state within the system. Likewise it pertains to the active power balance, although it has been customary to assume that it is the reactive power distribution which affects the vector moduli of node voltages, while the angle flare of this vectors depends on the active power distribution. What followed this approach is the term „angular stability”: scientific research has been conducted on this subject, while the current measurements of voltage phasors has been proposed for a more complex system protection [8]. The more specific considerations of the behaviour of the stable EPS operation indicate that the assessment of the stability state (reserve) requires consideration of node voltage vectors (moduli and angles) which are the effect of active and reactive power distributions [2, 11, 17, 25]. When investigating high power transmissions, it is evident that simultaneous association of voltage levels with transmission of reactive power only and of these voltage vector flare angles with transmission of active power only is incorrect. Sometimes the simplifications assumed a priori do not simplify the production of results but only complicate it or even make it absolutely impossible.

3. GRADIENT OF LOSSES AND DOUBLE POWER DISTRIBUTION METHOD The gradient of losses is a vector the coordinates of which are the partial derivatives of losses calculated for the independent variables within the system. The gradient of losses has been determined by applying the Lagrange method with the Kuhn-Tucker conditions; this method allows searching for the extremes of complex functions of several variables when the variables are subjected to limits defined in the form of equalities and inequalities [2, 11]. This paper presents this method in a largely simplified form, i.e. without inequality limits, which significantly reduces the notation of the investigated mode. Moreover, the paper does not contain transformations of specific formulas; only their final forms are presented. The extremum [function f(x) min] is sought by applying the Lagrange method: L(x, λ) = f(x) + ∑i λi [ bi – hi(x) ]

(1)

the conditions of limitation are as follows: bi – hi(x) = 0 for x ∈ W1 , i ∈ N The Lagrange (target) function including the equations of power and the equations of power distribution denoted by Cartesian coordinates is listed by this expression (2): L = – ∑i Pi + ∆P + ∑i λi { Pi – ( Ui Ji – Vi Ii ) } + ∑i µi { Qi – ( Ui Ii + Vi Ji ) } + + ∑i ξi { Ui – U0 – ∑k ( Rik Jk + Xik Ik ) } + ∑i ψi { Vi– V0 – ∑k ( Xik Jk – Rik Ik ) }

(2)

Si = Pi +j Qi – complex apparent power of node Ui = Ui +j Vi – complex voltage of node Ji = Ji - j Ii – complex current of node Zik = Rik +jXik – expression of complex matrix of node impedances λi, μi, ξi, ψί – indeterminate Lagrange factors The partial derivatives of the function L calculated for all variables in the system allow determining the gradient coordinates of the function of losses ΔΡ: Designations:

Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

By equating the expressions of speciﬁc partial derivatives to zero: dL/dxi = 0 the result is as follows: (a) the partial derivatives of the function L for node powers: ∂ L / ∂Pi = – 1 + ∂ (∆P) / ∂Pi + λi = 0 ∂ L / ∂Qi = 0 + ∂ (∆P) / ∂Qi + µi = 0

(3)

and hence the expressions which deﬁne the indeterminate Lagrange expressions λi and μi and simultaneously the components of the operator by T. Szostek [2, 11]: T = λi + j µi

(4)

or: Ti = 1 – ∂ (∆P) / ∂Pi – j ∂ (∆P) / ∂Qi

(5)

Determination of the complex operator T leads directly to the determination of the partial derivatives of active power losses in the system, calculated for active and reactive powers of the nodes, where the derivatives constitute the coordinates of the gradient of losses. (b) the partial derivatives of the function L for node voltages: ∂ L / ∂Ui = – λi Ji – µi Ii + ξi = 0 ∂ L / ∂Vi = λi Ii – µi Ji + ψi = 0

(6)

The function L expresses the active power balance. The partial derivatives of active power, calculated for the real component Ui and the imaginary component Vi of the complex node voltage can be recognized as the components of a certain (dual) node current Jd,i. This current is expressed as follows: Jd,i = – (ξi + j ψi )

(7)

or Jd,i = – conjg (Ti * Ji )

(8)

(c) the partial derivatives of the function L for node currents: ∂L / ∂Ji = UB – λi Ui – µi Vi – ∑k ( ri,k ξk + xik ψk ) = 0 ∂L / ∂Ii = VB + λi Vi – µi Ui – ∑k ( xi,k ξk – rik ψk ) = 0

(9)

In analogy to the aforementioned function L derivative calculated for the components of the node current Ji, these partial derivatives can be recognized as the components of a (dual) node voltage Ud,i. Ud,i = Ti conjg ( Ui )

(10)

Once the formulas which describe the dual node voltage and the dual node current are known, it is possible to determine the dual node power: Sd,i = Ti *Ti conjg ( Si )

(11)

The node currents, voltages and powers satisfy the original power distribution. The dual node currents, voltages and powers satisfy the dual power distribution. The ratio of the node voltage vector from the dual distri-

The Possibilities of Assessing the Current ESP Stability Derivatives Instead of Characteristics

bution to the node voltage conjugate vector from the original distribution enables the calculation of coordinates for the vector T in any node of the grid/network. Ti = Ud,i / conjg (Ui )

(12)

The complex gradient of losses ρ, the coordinates of which are the partial derivatives of active power losses calculated for active and reactive powers of nodes: ρi = ∂ (∆P) / ∂Pi + j ∂ (∆P) / ∂Qi

(13)

can be determined directly from the vector T as follows: ρ = 1 – T

(14)

Until now, the designations λi and µi denoted the indeterminate Lagrange factors and constituted the complex components of the vector T. The same designations are sometimes used to directly denote the partial derivatives of active power losses: λi = ∂ (∆ P) / ∂ ( Pi)

and

µi = ∂ (∆ P) / ∂ ( Pi)

(15)

they are used as such further in this work, as the complex components of the vector ρ.

4. DERIVATIVES OF CHARACTERISTICS OF POWERS FED TO NODES The balances of active and reactive powers in the system are satisﬁed. The total of the powers generated in the system (ΣPG, ΣQG) equals the total of consumed powers (ΣPO, ΣQO) plus the network losses (ΔΡ, ΔQ) as follows: ∑ PG = ∑ PO + ∆P ,

∑ QG = ∑QO + ∆Q

(16)

The power balance equations are used in the following analyses. For the purpose of these analyses the authors assume that the independent variables are the node active and reactive powers, as well as the longitudinal and transverse transformation ratios, i.e. the physical magnitudes which can be directly regulated in the system (switching on and off, power regulation, transformation ratio regulation). All other electrical magnitudes, like node currents, node voltages etc. are the dependent variables expressed as the functions of independent variables. The types of dependency are irrelevant. These usually are confounded non-linear dependences. Many loads (consumers) feature power consumption characteristics which depend on the voltage. All of these dependences, provided that they are known, can be stored in the grid model and accounted for in the calculations of power distribution (both original and dual), in the economy analyses or in the analyses of the system stability state. The factors important to the investigation in the state (reserve) of system stability are the characteristic courses of active and reactive powers transmitted (fed to the grid nodes). The authors attempt to assess the courses of these characteristics by using their derivatives calculated in the grid nodes on the basis of current operating parameters of the system [13, 15, 25]. The rationale for this proceeding is very concisely explained below. First focus on the characteristics of the active power fed to the nodes. The power picked up at the grid node is expressed as the product of the consumed current and voltage in this node. If the consumed/picked up current value rises from zero to the shorting current value, the voltage in the node drops from a certain initial value to zero. The chart of the consumed active power as the function of the current J is represented by the curve P in Fig. 1. The point Pex in Fig. 1 denotes the maximum power transmittable in the system. The chart of the active power losses caused by the power transmission in the grid is represented by the curve ΔΡ, while the chart of the derivative of these losses, calculated for the picked-up active power, is represented by the curve λ. The derivative of losses λ expresses the ratio of the active power losses increment ΔΡ in the grid to the increment of the active power P fed to the grid node, where both values are referenced in the ﬁgure to the unit change of the node load current.

Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

Fig. 1. The courses of active power P , power losses ΔP and derivative λ curves

The increments of the function P in Fig. 2 for small and large grid loads are represented by sections a and c, while the increments of the function ΔP are represented by sections b and d. The relative increment (derivative λ) of active power losses in the grid, calculated for the power fed to the grid node (construed here as the ratio of section b to section a in Fig. 2) will be equal to the following at the low grid load: λa = b/a, or as the ratio of section d to section c at the large grid load: λc = d/c. These dependences directly present the important information included in the derivative λ. The author discuss them below.

Fig. 2. Graphical aid for interpretation of derivative of losses

The deﬁnition of λ, which is the derivative of the power losses function, calculated for the power fed to the node and which expresses the mutual interrelation of the characteristics of power losses ΔP and of the power P fed to the grid node, is an expression of the ratio of relative increments (derivatives) of these characteristics. As such, it carries the information about the course of the curve of losses ΔP and of the curve of active power P fed to the node. This implies a statement which is critical to these considerations: the derivative of the active power losses, calculated for the active power of any grid node λ, can be used to assess the characteristic course of the active power fed to the grid in the function of system operating parameters.

The Possibilities of Assessing the Current ESP Stability Derivatives Instead of Characteristics

The curve λ in Fig. 1 grows asymptotically to infinity when the node load P grows to the value Pex. This is not due to a certain considerable change of the grid losses in the neighbourhood of the point P = Pex. The losses indeed rise with the load current square, but these increments are nowhere this rapid. This course of the curve (derivative) λ in the neighbourhood of the point P = Pex are defined by the increments of the power P fed to the investigated node, which decrease to zero and which are in the denominator of the λ definition formula. The sum of the power ΣPG generated in the grid equals the sum of powers of the loads (consumers) ΣPO plus the losses ΔΡ. The unit change of the consumer power in the defined grid node ∂(P) causes a corresponding change of the generated power and of the transmission losses: ( ∑ PG) / ∂ ( P) = 1 + λ

(17)

The growth rate of the λ must be met with the same growth rate of the power generated in the grid to satisfy the increment of demand by a unit. Provided that λ = 1, two power units have to be generated in the grid to cover the unit increment of demand and losses. The more the operating point approximates to the point Pex, the faster the depletion of capacities for power generation and transmission in the grid is, and hence the closer a loss of stability in the grid is. The growing λ values mean that the curving of the characteristic of the power fed grows and that the extremum becomes closer. In other words, the growing values of λ translate into the shrinking stability reserve at the given point (node) of the grid. Apart from the active power P, the reactive power Q is also sent over the system grids. The transmission of reactive power affects the magnitude of the ﬂowing current modulus and hence it affects the active power losses in the grid. The change of the active power losses ΔΡ in the grid as the function of the transmitted reactive power Q is expressed by a derivative of these losses calculated for the reactive power [2, 11, 13, 17]: μ = ∂ (∆ P) / ∂ (Q)

(18)

Similar analyses completed for the derivative λ and for the derivative μ lead to similar conclusions. The derivative of the active power losses, calculated for the reactive power of the node, provides information on the course of the characteristics of the reactive power fed to this node in the function of system operating parameters. Moreover, both derivatives (λ and μ) approach inﬁnity at the same point (i.e. at the same parameters) of system operation. This logic is obvious. If, in any power transmission direction in the system, the capacity (natural ability) for active power transmission is depleted, reactive power cannot be transmitted any more. And vice versa: if the reactive power transmission capacities of the grid are depleted, it is impossible to transmit more active power. Do simultaneous excess transmissions of both powers lead to the loss of stability in the grid, or only one of the powers or which power is this the result of? The answers to these questions are the derivatives λ and μ alone. Transmission of the power, for which the calculated derivative of losses has the higher numerical value, brings the system increasingly closer to the point of stability loss. The higher the value of the derivative, the closer it is to the point of extremum. This is additional information critical to the system operator. In the case of a failure threat, this information indicates the power balance (reactive or active) which must be corrected ﬁrst. The derivatives λ and μ of the grid losses are calculated as the component of the complex vector ρ of grid losses gradient 1: ρ =λ+ jμ

(19)

Similarly, the derivatives α and β of grid losses, calculated for the longitudinal (α) and transverse (β) transformation ratios, are determined as the components of another complex vector κ of grid losses gradient 2: κ=α+jβ

(20)

The formula above applies to all transformers in the grid, irrespective of whether they are transversely controlled, diagonally controlled or only longitudinally controlled. In the case of the transformers with a longitudinal transformation ratio control only, the calculations are based on the assumption that the transverse transformation ratio (i.e. the independent variable) is zero. The coordinates of the vectors ρ and κ are the derivatives

Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

of the grid active power losses in the grid, calculated respectively for the active and reactive powers of all grid nodes, and for the longitudinal and transverse transformation ratios of all grid transformers. Hence both vectors ρ and κ constitute the complete gradient of grid losses with the coordinates referenced to all independent variables in the system. The coordinates of this gradient also carry the information on the characteristics of the reactive and active powers fed to all grid nodes. The practical use of the value λ or µ in the optimisation of power distribution and simultaneously for the assessment of the stability reserve of the grid can be of little convenience. The closer the point of extreme is, the faster their absolute values rise. This is why the values of other functions can be used to assess the stability state, i.e. Фp or Фq, as shown in Fig. 3, which can be determined directly from the functions λ and μ as their converses, or as a ratio of the increment of the active or reactive power fed to the node to the increment of the power generated in the grid.

Fig. 3. The dependence of stability reserve as the function of node load

Ρ is the curve of the active power fed to the node; Q is the curve of the reactive power fed to the node; Φp is the curve of the stability reserve as the function of node active load; Φq is the curve of the stability reserve as the function of node reactive load.

The stable operation limits of the system depend on the current condition of the grid (i.e. its natural transmission capacity) and of the active and reactive powers transmitted simultaneously. The purpose of the analyses of EPS grid operating states performed during the planning of grid traffic, is to prepare (schedule) and commission a system which meets the defined requirements for its reliability and operating safety. The purpose of similar analyses, albeit performed in real time, is the optimisation of grid performance (more specifically, the optimisation of voltages and reactive power distribution in the grid) on the one hand, while on the other – early detection of states which threaten a system-wide failure within the grid. The system operator should continuously receive information about the system state of stability. The knowledge of the operator about this state must be comprehensive enough to allow undertaking steps which are correct for each case of the actions intended to restore the required (sufficient) state of the EPS stability. In the case of random events within the system, which violate the conditions of stable operation of the EPS, the system defence automatic control must be immediately activated to effect system partitioning, limitations of power supply, generation regulation, etc., depending on the boundary conditions.

The Possibilities of Assessing the Current ESP Stability Derivatives Instead of Characteristics

5. SUMMARY The characteristic trait of the EPS is the continuous variation of its operating conditions. The safe maintenance of the system requires continuous and correct assessment of the grid stability state (reserve), irrespective of the events which occur in the grid. The information about the current stability reserve in each point of the system should be known well and available in the EMS, just like other operating parameters of the system. The disturbances of stable operation of power systems result from insufficient recognition of a state of threat before the disturbance ensues and from the limited capacities of system defence from a cascading development of a failure, after the disturbance which initiates the failure occurs. In theoretical terms, the system loses its stability when the physical capacity of the grid is depleted on one of the power transmission directions. This state can be caused by the following: • lack of sufficient reserves in the transmission system • weakening of the grid due to random shutdown of transmission elements or power sources • unfavourable characteristics of consumers, which cause voltage avalanches at a reduced voltage in the grid. The condition of safe operation of any system is the maintenance of defined local balances of active and reactive power. Free transmission of any magnitudes of power at every distance is not possible. There are natural limits of transmission capacity in many directions of power transmission of the grid, which are conditioned by the laws of physics. Any attempt at breaking these limits results in the loss of stability. The purpose of the EPS operating optimisation and investigation of the EPS stability can be performed in real time with the use of the same measurement data and with similar programming tools. The algorithm for calculation of the gradient of losses is used in both cases. The additional advantage of this method is that it produces results in relative numbers which have the same meaning (interpretation) for all grid nodes and different operating states of the grid. Once defined, the critical values are valid for different network systems (i.e. standard or repair) and grid operating states, including emergency states. The coordinates of the vector Φ carry important information about the EPS stability state – they serve as the basis for testing of network systems planned for commissioning, for operator’s decisions or for the performance of quick automated actions intended to protect the EPS from instability.

Kazimierz Oziemblewski / Coal Basin Branch, Association of Polish Electrical Engineers (SEP) Ksawery Opala / Power Engineering Department, Research Institute, Gdańsk Branch

REFERENCES 1. Findeisen W., Szymanowski J., Wierzbicki A., Metody obliczeniowe optymalizacji, WPW, Warsaw 1972. 2. Szostek T., Algorytm optymalizacji poziomów napięcia w sieciach elektroenergetycznych oparty na metodzie dwóch rozpływów mocy, Energetyka, no. 2, 1975. 3. Kremens Z., Sobierajski M., Analiza systemów elektroenergetycznych, NWT, Warsaw 1996. 4. On-line, Voltage Stability Assessment of Power System - An Aproach of Black - box Modeling, Tampere University of Technology 2001. 5. Final Report on the August 14, 2003 Blackout in the United States and Canada. Causes and Recommendations. U.S. - Canada Power System Outage Task Force, April 2004. 6. Final Report of the Investigation Committee on the 28 September 2003 Blackout in Italy, UCTE, Apirl 2004. 7. Kasprzyk S., Bezpieczeństwo pracy polskiego systemu elektroenergetycznego, Ogólnopolskie seminarium „Blackout a krajowy system elektroenergetyczny” Poznań, 2004, in: Energetyka, subject book no. II, 2004. 8. Machowski J., Zastosowanie rozległych systemów pomiarowych w automatyce przeciwawaryjnej systemu elektroenergetycznego, Electrical Power Institute, Warszaw University of Technology, 2005. 9. Machowski J., Regulacja i stabilność systemu elektroenergetycznego, Warsaw University of Technology Publishing House, Warsaw 2007. 10. Machowski J., Białek J.W., Bumby J.R., Power System Dynamics Stability end Control, John Wiley and Sons, Ltd. 2008. 11. Oziemblewski K., Optymalizacja napięć w węzłach dla celów prowadzenia ruchu systemu elektroenergetycznego, a doctoral dissertation, Silesian University of Technology, Gliwice, 1975. 12. Oziemblewski K., Największe awarie systemowe w 2003 roku, Śląskie Wiadomości Elektryczne, 1, 2005. 13. Oziemblewski K., O możliwościach oceny warunków pracy SE w stanach zagrożenia, Energetyka, 8, 2006. 14. Gładyś H., Orzechowski A., Oziemblewski K., O konferencji CIGRE 2006 i zagrożeniach w pracy systemu elektroenergetycznego, SER Seminary, PSE SA Monthly Bulletin, 11, 2006. 15. Oziemblewski K., Regulacja napięcia a stabilność pracy sieci systemu elektroenergetycznego, Automatyka Elektroenergetyczna, 2, 2007. 16. Oziemblewski K., Koordynacja poziomów regulacji napięcia w KSE, seminarium ’07, Działania automatyki elektro energetycznej w warunkach awaryjnych systemu, Bielsko-Biała 2007. 17 Oziemblewski K., Naturalna zdolność przesyłowa sieci jako kryterium oceny stabilności systemu elektroenergetycznego, Wiadomości Elektrotechniczne, no. 9, 2007. 18. Weryﬁkacja raportu wstępnego z analizy awarii napięciowej w KSE, 26 czerwca 2006, Institute of Electrical Power Engineering, Wrocław University of Technology, Wrocław, September/October 2006. 19. System Failure of November 4 2006. Final Report. UCTE, 2007. 20. Voltage Stability Improvement Using Static Var Compensator in Power System, Leonardo Journal of Science, I-VI 2009. 21. Sobierajski M., Rojewski W., Wpływ strat mocy biernej na wystąpienie lawiny napięcia w sieci przesyłowej, APE ’09, Jurata 3-5.06.2009. 22. Madajewski K., Sobczak B., Trębski R., Dynamiczne aspekty utraty stabilności napięciowej, APE ’09, Jurata 35.06.2009. 23. Klucznik M., Małkowski R., Szczeciński P., Zajczyk R., Wpływ obecnie stosowanych układów regulacji generatorów na możliwości pogłębienia awarii napięciowej. APE ’09, Jurata 3-5.06.2009. 24. Krebs R., Styczyński Z.A., SiGuard system do zapobiegania blackoutom ze szczególnym uwzględnieniem analizy działań zabezpieczających w warunkach utraty stabilności napięciowej. Elektroenergetyka Współczesność i Rozwój, no. 2-3, 2010. 25. Program Q-5 monitorowania pracy sieci dla potrzeb systemu SORN w ODM Bydgoszcz, Power Engineering Department, Gdańsk Branch, 2010.

Stefan Paszek / Silesian University of Technology Piotr Pruski / Silesian University of Technology

Authors / Biographies

Stefan Paszek Gliwice / Poland

Piotr Pruski Gliwice / Poland

Graduate of the Faculty of Automatic Control, Electronics and Computer Science at the Silesian University of Technology in Gliwice (1978). Areas of scientific interest: analysis of the power system in transient states, angular stability of the power system, optimisation and poly-optimisation of system stabilisers and synchronous generator voltage regulators, estimation of parameters of the PS generating set models, new models of synchronous generators with the application of artificial neural network technologies, application of fuzzy logic regulators in regulating systems of electrical power machines. Author and co-author of 118 publications, including two monographs. Co-author of three academic handbooks. Thesis supervisor of two completed and three open conferment procedures for doctoral degrees in the field of electrical power engineering. Reviewer of five doctoral dissertations and one habilitation thesis.

Graduated with distinction from (2009) and is currently a doctoral student at the Faculty of Electrical Engineering at the Silesian University of Technology. Areas of interest: analytical problems of operation of the power system. Co-author of twelve articles and papers published in Poland and abroad on the assessment of the angular stability of power systems and estimations of parameters of the mathematical models of PS generating set components. Since the beginning of his doctoral studies, has participated in the work under a grant by the Ministry of Science and Higher Education.

Assesment of the Power System Angular Stability Based on Analysis of Selected Disturbance States

ASSESMENT OF THE POWER SYSTEM ANGULAR STABILITY BASED ON ANALYSIS OF SELECTED DISTURBANCE STATES Stefan Paszek / Silesian University of Technology Piotr Pruski / Silesian University of Technology

1. INTRODUCTION The basic issue regarding the improvement of the power system (PS) angular stability is to develop a method to assess this stability. There are many methods which can be used for assessing the angular stability which are based on mathematical modelling of the PS and analysis of the PS state matrix eigenvalues. The eigenvalues calculated from the state equations depend on the values of the system state matrix elements; they also – indirectly – depend on the assumed system models and their uncertain parameters. The eigenvalues can also be calculated with good accuracy from analysis of the actual disturbance waveforms occurring in the PS after various disturbances. In this case, the calculation results are not affected by the assumed PS model and its parameters, but by the actual operating conditions of the system. The knowledge of the PS state matrix eigenvalues allows determining the PS stability factors [1] and the PS stability margin. The purpose of this paper is to assess the calculation accuracy of the PS state matrix electromechanical eigenvalues on the basis of the instantaneous power disturbance waveforms (often called the active power waveforms) in generating units, depending on the complexity of the analysed PS and the damping coefﬁcient of instantaneous power waveforms.

2. LINEARISED PS MODEL The PS model linearised around the operating point is described by the state and input equations [2]:

  AX  BU X

(1)

�Y  CX  DU

(2)

where: ΔX, ΔU, ΔY – are the deviations of the vector of state variables, inputs and output variables, respectively. Coefﬁcients of matrices A, B, C and D of the PS state and input equations are calculated for a steady operating point. The waveforms of input quantities of the linearised system model can be calculated directly by integrating the state equation, or by using the eigenvalues and eigenvectors of the state matrix A [2]. The waveform of the given input value is a superposition of the modal components which depend on the eigenvalues and eigenvectors of the state matrix. Example: in the case of a disturbance being a Dirac pulse of the input value ΔU(t) = ΔUδ(t), the i-th input value (at D = 0) is [2]:

Abstract This paper presents the method for assessing the angular stability of a multi-machine electrical power system based on the analysis of selected disturbance states. For the assessment of the angular stability there were used the electromechanical eigenvalues calculated from the instantaneous power disturbance waveforms in particular generating units after the occurrence of a disturbance in the form of a square pulse with a determined length, introduced into the voltage regulation system of one of the generating units. The inﬂuence of the pulse duration time on the accuracy of eigenvalue calcula-

tions and the amplitude of instantaneous power swings is analysed in the paper. The analysis was performed for various values of the system stabilizer gain coefﬁcients in particular generating units, which corresponded to different damping of instantaneous power swings in the power system. The eigenvalues were calculated with a hybrid algorithm, which combined a genetic algorithm with a gradient algorithm. A statistical analysis of the accuracy of electromechanical eigenvalue calculations was performed for selected cases.

Stefan Paszek / Silesian University of Technology Piotr Pruski / Silesian University of Technology

46 n

Yi   Fih e  h t U

(3)

h 1

where: λh is the h-th eigenvalue of the state matrix; Fih is the participation factor of the h-th eigenvalue in the i-th input value waveform. In the case of the instantaneous power swing waveforms in the PS, the so-called electromechanical eigenvalues related to the movement of rotors in the generating units play a decisive role. They are complex conjugate eigenvalues with imaginary parts, which correspond to the frequency range (0.1-2 Hz), hence their imaginary parts fall into the range (0.63-12.6 rad/s). The electromechanical eigenvalues intervene in different ways in the instantaneous power waveforms of particular generating units, which is related to the different values of their participation factors.

3. EXAMPLES OF CALCULATIONS The method for calculations of electromechanical eigenvalues used in investigations consists in approximation of instantaneous power waveforms in particular generating units with use of the expression (3). The electromechanical eigenvalues and participation factors of speciﬁc modal components are the unknown parameters of this approximation. In the approximation process, these parameters are iteratively selected to minimise the value of the objective function deﬁned as a mean square error between the approximated and approximating waveform: n



 w �� F   Pi ( m )  Pi ( a ) �� F i 1



(4)

where: λ is the vector of electromechanical eigenvalues; F is the vector of participation factors; the index m denotes the approximated waveform, while the index a the approximating waveform of the instantaneous power P, calculated from the searched eigenvalues and participation factors. The objective function (4) is minimised by a hybrid algorithm which is a serial combination of a genetic algorithm with a gradient algorithm. The results of the genetic algorithm are the starting point of the gradient algorithm. The genetic algorithm seeks the global minimum of the objective function in the given interval of the parameters being determined. The starting point is sampled from the search interval, so it is not necessary to deﬁne it precisely. However, the algorithm is slowly convergent. The gradient algorithm is more quickly convergent, but it seeks the local minimum of the objective function, due to which the initial parameter values must be carefully selected to obtain correct results. The serial combination of genetic and gradient algorithms eliminates their basic disadvantages [3]. For the purpose of calculations, the input data (approximated during the calculation) is the measured instantaneous power waveforms, but in order to verify the calculation method, the instantaneous power waveforms obtained from simulations with use of the PS model are used for now. The eigenvalues and participation factors calculated from the assumed structure and parameters of the model are assumed to be the reference point. The example calculations are made for a 7-machine Cigre PS and a 4-machine PS (see Fig. 1). The 4-machine PS was obtained by modifying the 7-machine PS in such a way that three generating units were treated as the load nodes.

Assesment of the Power System Angular Stability Based on Analysis of Selected Disturbance States

L1 2

L1 0

1 L1

2 L7

2 L1

1 L1

L1 0

L13

Fig. 1. Analysed PS: 7-machine (a) and 4-machine (b)

The model of the analysed PS is developed in the Matlab-Simulink environment. Each generating unit in the modelled system consists of conﬁgurable subsystem units which allow selecting the models of the generator, excitation system, turbine and power system stabilizer (PSS). The calculations presented in this paper consider the following models: a synchronous generator GENROU with a non-linear magnetizing characteristics [4, 5], a static excitation system operating in the Polish PS, a steam turbine IEEEG1 [4, 6] and a power system stabilizer PSS3B [4]. The assumed disturbance is a square pulse of the voltage regulator reference voltage in one of generating units. The system response to an input in the form of a short square pulse with a suitably selected height and length is close to that to a Dirac pulse.

3.1. Analysis of square pulse length on instantaneous power swing amplitude and accuracy of eigenvalue calculations

��

�

��

The right selection of the height and length of the square pulse on the voltage regulator reference voltage is an important factor which determines the accuracy of calculations. The amplitude of instantaneous power swings must be sufficiently high to separate these swings from the recorded waveforms of phase currents and voltages in individual system nodes. The amplitude increases with the increase in the pulse surface of the voltage regulator reference voltage. The pulse height, however, must be limited to avoid a significant impact of nonlinearity and limits on the instantaneous power waveforms. The calculations assume a square pulse with a height equal to 5% of the steady value of the voltage regulator reference voltage. The square pulse duration must also be limited, since its significant lengthening results in increasing differences in the system responses to the square and Dirac pulse, which can decrease the accuracy of determining electromechanical eigenvalues. Fig. 2 shows the waveforms of phase currents of the generator armature in the generating unit G4 of the 4-machine PS following a disturbance in this generating unit in the form of square pulse 50 ms and 300 ms long. The gain coefficient of all system stabilizers is KS1 = 0.1 [4], which corresponds to the relatively low damping of electromechanical swings.

��

�

��

�

Fig. 2. The waveforms of phase currents of the generator armature in generating unit G4 for disturbance in the form of a square pulse 50 ms (a) and 300 ms (b) long

Stefan Paszek / Silesian University of Technology Piotr Pruski / Silesian University of Technology

Fig. 2 shows that increase in the pulse duration from 50 ms to 300 ms causes signiﬁcant changes in the phase currents of the generator armature and, hence, it increases the amplitude of instantaneous power swings. The analysis focuses on the effect of lengthening the square pulse duration on the calculation accuracy of electromechanical eigenvalues of the analysed 4-machine PS. Table 1 presents the electromechanical eigenvalues λ and the moduli of participation factors |F| of these eigenvalues in the unit G4 instantaneous power waveform. They were calculated directly from the PS model in Matlab-Simulink. Further in this paper, the electromechanical eigenvalues are referred to as “original eigenvalues”. Table 1 lists the relative moduli of participation factors in relation to the largest modulus of participation factor in the given waveform. Tab. 1. The original eigenvalues of the analysed 4-machine PS and their participation factors in the instantaneous power waveform of the unit G4 Item no.

-0.758 ± j10.176

-0.608 ± j10.346

-0. 478 ± j9.435

-0.0985 ± j5.311

|F| p.u.

0.0094

0.0548

0. 469

The participation factor modulus value determines the given modal component amplitude in the instantaneous power waveform and, hence, determines the inﬂuence of this moda l component on the objective function value (4). Due to the low values of the participation factor moduli of the eigenvalues λ1 and λ2 in the analysed instantaneous power waveform, those eigenvalues were not calculated on the basis of that waveform. Due to the existence of the objective function local minima in which the optimisation algorithm may freeze, the eigenvalues were calculated repeatedly based on the same waveform. If the objective function values were higher than a certain assumed limit, the results were rejected. The adopted ﬁnal result of the calculations of real and imaginary parts of the particular eigenvalues were the arithmetic means from the real and imaginary parts, respectively, of the eigenvalues obtained from the results not rejected in further calculations. Fig. 3 shows the disturbance waveforms of the generating unit G4 instantaneous power obtained from simulations (continuous line) and recovered from the original eigenvalues (broken line) for the pulse duration of 50 and 300 ms. It is evident that lengthening the pulse duration increases the differences between the waveform from simulations and that recovered from the original eigenvalues. a)

��

� ��

��

�

��

� ��

��

�

��

�

��

�

Fig. 3. The disturbance waveforms of the generating unit G4 instantaneous power for disturbance in the form of a square pulse 50 ms (a) and 300 ms (b) long

Assesment of the Power System Angular Stability Based on Analysis of Selected Disturbance States

Fig. 4 presents the histograms of the real and imaginary parts of the eigenvalue � determined from analysis of the disturbance waveforms for the pulse duration of 50 ms and 300 ms. The red bars show the results included in further analysis, while the green ones show the results rejected. The thin vertical lines in the centre of the histograms correspond to the original eigenvalues. a) ��

��

�

��

�

��

��  � � ��

��

��  � � ��

��

�

b) ��

��

�

��

�

��

�� � ��

��

�� � ��

��

�

Fig. 4. The histograms of the real and imaginary parts of the eigenvalue λ3 calculated from the instantaneous power waveforms for disturbance in the form of a square pulse 50 ms (a) and 300 ms (b) long

In Table 2 there are given the calculation errors for the eigenvalues λ3 and λ4 for several duration times of the pulse timp. Tab. 2. The calculation errors for the eigenvalues λ3 and λ4 for different duration of the pulse timp 200 ms

300 ms

Δλ3

(-18.3±j9.9) × 10-3

(-3.35±j1.09) × 10-2

(-125

Δλ4

(-4.7±j1.24) × 10-3

(-2.06±j2. 49) × 10-3

(-2.29±j6,62) × 10-3

j6.14) × 10-3

400 ms -0.384

50 ms

j0.112

(-1.28±j1,66) × 10-2

500 ms -1.589

timp

j0.675

(-3. 4±j3.06) × 10-2

The errors of the eigenvalue calculations increase with the increase in the pulse duration.

3.2. Calculations of eigenvalues of the 7-machine PS for low damping of swings Tables 3, 4 and 5 list the electromechanical eigenvalues of the analysed 7-machine PS, the relative moduli of their participation factors and the absolute errors of calculation for the gain coefﬁcient of all stabilizers, KS1 = 0.1. The relative moduli of the eigenvalue share factors are in bold – the moduli are calculated from the instantaneous power waveform of the given generating unit. The calculation of eigenvalues involved two stages. First, there were calculated the eigenvalues λ3 - λ6 having higher values of the real parts (i.e. smaller moduli of the real parts), corresponding to the less damped modes, when neglecting the eigenvalues λ1 and λ2 of lower values of the real parts of. In the second stage, there were calculated the eigenvalues with the lower values of the real parts, when taking into account the known eigenvalues λ3 - λ6.

Stefan Paszek / Silesian University of Technology Piotr Pruski / Silesian University of Technology

Tab. 3. Original electromechanical eigenvalues of the 7-machine PS for KS1 = 0.1 Lp.

-0.781 ± j10.177

-0.602 ± j10.507

-0.498 ± j9. 476

-0.327 ± j8.642

-0.251 ± j7.895

-0.0091 ± j6.540

Tab. 4. The relative participation factor moduli of the 7-machine PS eigenvalues for the gain coefﬁcient KS1 = 0.1 of all stabilizers Generating unit G1 G2 G3 G4 G5 G6

|F1|p.u.

0.0038

0.0212

0.0194

0.1005

0.0848

0.2260

0.0084

|F2|p.u.

0.0041

0.2026

0.1591

0.0923

0.2404

0.0585

|F3|p.u.

0.0210

0.5278

0.2858

0.7884

|F4|p.u.

0. 4289

0.5829

0.0416

0.0300

0.0068

0.00032

0.0219

|F5|p.u.

0.1079

0.0932

0.1995

0.2106

0.0996

0.3650

|F6|p.u.

0.1972

0.2508

0.1222

0.0921

0.1849

Tab. 5. Absolute calculation errors for eigenvalues of the 7-machine PS for KS1 = 0.1 Generating unit G1

Δλ1

–

Δλ2

–

-0.618

j3.402

-0.016 ± j0.118

0.021

j0.062

Δλ3

–

-0.309 ± j0.331

-0.179 ± j0.182

-0.003 ± j0.088

Δλ4

-0.006 ± j0.034

-0.053 ± j0.083

–

Δλ5

-0.013

j0.078

–

-0.002 ± j0.009

–

0.001

Δλ6

-0.001

j0.001

–

0.003 ± j0.001

0.058 ± j0.258

–

-0.087 ± j0.184

0.031

–

0.008 ± j0.011

0.032 ±j 0.004

-0.012

j0.249

–

j1.067

-0.031 ± j0.016

– j0.001

– ±

j0.003

0.002

j0.003

± ±

0.001

–

0.002

–

0.003 ± j0.001

j0.003

3.3. Calculations of eigenvalues of the 7-machine PS for higher damping of swings This subsection analyses the 7-machine PS for higher damping of electromechanical swings. The increase in swing damping was realized by increasing the gain coefﬁcients of all power system stabilizers (of type PSS3B) up to KS1 = 0.7. Tables 6, 7 and 8 list the electromechanical eigenvalues of the analysed PS, the relative moduli of their participation factors and the calculation errors. Tab. 6. Original electromechanical eigenvalues of the 7-machine PS for KS1 = 0.7 Item no

-1.393 ± j10.075

-1.262 ± j11.161

-1.091 ± j10.680

-0.9576 ± j8.993

-0.765 ± j7.803

-0.571 ± j6.536

Assesment of the Power System Angular Stability Based on Analysis of Selected Disturbance States

Tab. 7. The relative participation factor modulus of the 7-machine PS eigenvalues for the gain coefﬁcient KS1 = 0.7 of all stabilizers Generating unit G1

|F1|p.u.

0.1398

0.8164

0.3621

|F2|p.u.

0.0022

0.0392

0.0226

0.1128

0.0222

0.3458

0.0081

|F3|p.u.

0.0189

0.3735

0.2111

0.7727

0.1842

0.3630

0.0867

|F4|p.u.

0.5154

0.8520

0.0275

0.0248

0.0249

0.0166

0.0235

|F5|p.u.

0.2792

0.1373

0.1329

0.1999

0.1711

0.2258

|F6|p.u.

0.2526

0.1410

0.0850

0.0977

0.1105

-0.152 ± j0.006

-0.070 ± j0.089

-0.195±j0.228

–

Tab. 8. Absolute calculation errors for eigenvalues of the 7-machine PS for KS1 = 0.7 Generating unit G3

Δλ1

–

-1.584 ± j0.683

-0.379 ± j0.168

-0.088

Δλ2

–

0.105

Δλ3

–

-1.582 ± j4.000

-0.077 ± j0.099

0.007 ± j0.017

–

0.012

j0.007

j0.025

0.013 ± j0.085

-0.077

j0.159

-0.002 ± j0.119

0.010

-0.018

–

j0.061

0.159

j0.143

–

-0.139 ± j1.229

–

0.034

-0.021

Δλ6

j0.059

j2.563

± ±

-0.031 j0.053

0.007

-0.228

–

0.021 ± j0.150

Δλ5

j0.207

j0.314

-0.128

Δλ4

j1. 424

j0.062

j0.033

3. 4. Calculations of eigenvalues of the 4-machine PS for low damping of swings In order to investigate the effect of complexity of the analysed PS on the calculation accuracy of eigenvalues, the eigenvalues were calculated for the 4-machine PS for the gain KS1 = 0.1 (as in subsection 3.2.) for all stabilizers. Table 9 lists the calculation errors of electromechanical eigenvalues. In this case, the determination of eigenvalues was also performed in two stages. First, the eigenvalues λ3 and λ4 were determined and, once they were known, the eigenvalues λ1 and λ2 were calculated. Tab. 9. Absolute calculation errors for eigenvalues of the 4-machine PS for KS1 = 0.1 Generating unit G3

Δλ1

0.17080

Δλ2

0.00072

Δλ3

0.01658 ± j0.01057

0.01838

Δλ4

0.00094 ± j0.00135

-0.00061 ± j0.00231

j0.75264

-0.85943

j0.02339

-0.19605 ± j0.05164

j1.41602

j0.00047

-0.16195±j0.32636 -0.12014

j0.06776

– –

0.02593 ± j0.08586

-0.01605 ± j0.00962

-0.00097 ± j0.00105

0.00850

j0.01901

± ±

Stefan Paszek / Silesian University of Technology Piotr Pruski / Silesian University of Technology

4. SUMMARY The investigations performed allow to draw the following conclusions: • Lengthening the pulse duration time in the waveform of the generator voltage regulator reference voltage causes significant changes of the generator armature phase currents, hence an increase of the instantaneous power swing amplitude. However, the longer the pulse duration time is, the higher the errors of the eigenvalues calculated from the instantaneous power waveforms are. This requires a suitable compromise. It can be assumed with a certain approximation that the calculation accuracy for eigenvalues is still satisfactory when the pulse duration time does not exceed 300 ms. • Repeated calculations of eigenvalues with the hybrid algorithm, at different starting points sampled at each calculation from the seek range, eliminates the problem of algorithm freezing at local minima of the objective function. The calculation accuracy is increased by comparing the eigenvalues calculated from the instantaneous power waveforms of various generating units. • The two-stage estimation increases the accuracy of eigenvalue calculations. The optimisation algorithm performs more efficiently when the number of optimisation parameters is lower. The eigenvalues which correspond to more damped modes can be rejected in the first estimation stage since they intervene in the instantaneous power waveform only within a short time following the occurrence of a disturbance. The second stage consists in calculating the eigenvalues which correspond to more damped modes. • The calculation results of eigenvalues are more accurate for a system with the lower damping of electromechanical swings. • The calculation accuracy of eigenvalues for more and less complex PSs is comparable. In the case of the 4-machine PS, the accuracy was better for the eigenvalues which corresponded to less damped modes, while in the case of the 7-machine PS the accuracy was better for the eigenvalues which corresponded to highly damped modes.

REFERENCES 1. Paszek S., Nocoń A., The method for determining angular stability factors based on power waveforms, AT&P Journal Plus2, Power System Modelling and Control, Bratislava, Slovak Republic 2008, pp. 71-74. 2. Paszek S., Pruski P, Porównanie przebiegów nieustalonych w nieliniowym i zlinearyzowanym modelu zespołu wytwórczego pracującego w systemie elektroenergetycznym, Inter. Symp. on Electrical Machines, SME 2010, Gliwice - Ustroń, 2010, Proc. sum., pp. 181-185. 3. Nocoń A., Paszek S., Polioptymalizacja regulatorów napięcia zespołów prądotwórczych z generatorami synchronicznymi, a monograph, Silesian University of Technology Publishing, Gliwice 2008. 4. Paszek S., Pawłowski A., Optymalizacja parametrów dwuwejściowego stabilizatora systemowego PSS3B w jednomaszynowym systemie elektroenergetycznym generator - sieć sztywna, Zeszyty Naukowe Politechniki Śląskiej no. 1633, series: ‚Elektryka’; Gliwice 2004, pp. 115-124. 5. De Mello F, Hannett L. H., Representation of Saturation in Synchronous Machines. IEEE Transactions on Power Systems, vol. PWRS-1, no. 4, 1986, pp. 8-18. 6. IEEE Committee Report: Dynamic models for Steam and Hydro Turbines in Power System Studies, IEEE Transactions on Power Apparatus and Systems, vol. PAS-92, November (1973), no. 6, pp. 1904-1915.

Marian Sobierajski, Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

Authors / Biographies

Marian Sobierajski Wrocław / Poland

Wilhelm Rojewski Wrocław / Poland

Full professor at Wrocław University of Technology. Deals with scientiﬁc problems related to planning and control of electrical power engineering systems. Published about 180 papers, mainly on probabilistic power distribution, voltage stability, local stability and quality of electrical power. His recent papers are primarily related to the methods of estimation of power transmission over extrahigh voltage grids, modelling and computer simulation of transient states (Matlab) and cooperation of local power plants with the electrical power system.

Graduated from the Faculty of Electrical Engineering, Wrocław University of Technology (1973). Obtained his PhD of sciences at the Institute of Electrical Power Engineering of his alma mater (1977) where he is currently employed as a lecturer. Deals with electrical power engineering safety automation, control and regulation in electrical power systems and with the conditions of cooperation of dispersed energy sources and wind farms with the electrical power system.

Sebastian Słabosz Wrocław / Poland Graduated from the Faculty of Electrical Engineering, Wrocław University of Technology (2009), a student doctor at the Faculty of Electrical Engineering, Wrocław University of Technology, Facility of Electrical Power Grids and Systems at the Institute of Electrical Power Engineering. Areas of scientiﬁc interest: optimisation of dispersed power generation in electrical power systems.

The Method of Linear optimisation of ohe Permissible Wind Power Generation in the Transmission Grid Nodes

THE METHOD OF LINEAR OPTIMISATION OF THE PERMISSIBLE WIND POWER GENERATION IN THE TRANSMISSION GRID NODES Marian Sobierajski / Wrocław University of Technology Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

1. INTRODUCTION According to the plan for development of renewable energy sources adopted in Poland, the share of these sources in the ﬁnal power balance has to increase to 15% in 2020 and to 16% in 2030. In the document by the Ministry of Economy entitled „Polish Energy Policy for the Year 2030” [2], a deﬁned level was adopted to cover the forecast electrical power demand with renewable energy sources (RES), where the largest share is estimated to be on the part of wind power plants. Tab. 1. Power output of wind power plants acc. to „Polish Energy Policy for the Year 2030” Forecast demand and production of electrical power

Year 2010

Year 2015

Year 2020

Year 2030

Planned gross electrical power production of wind power plants (GWh)

2,023.6

7,349.0

13,704.8

17,793.9

Planned power output of wind power plants (MW)

976

3396

6089

7867

The adopted mean annual use of wind power plants in Poland (h)

2073

2164

2251

2262

Planned installed power of power plants in the NPS (MW)

36,280

40,007

44, 464

51, 412

The share of wind power plants in the installed power of the NPS (%)

2.7

8.5

13.7

15.3

Gross electrical power demand in the NPS (GWh)

141,100

152,800

169,300

217, 400

The planned share of wind power plants in the production of electrical power in the NPS (%)

1.4

4.8

8.1

8.2

Tab. 1 lists the planned power magnitudes of wind generation in the years 2010-2030 [2]. It is evident that the power of wind power plants in 2010 should amount to ca. 1000 MW and ca. 8000 MW after the following 20 years, i.e. in 2030. The planned introduction of wind generation to the NPS as a large share in the coverage of electrical power demand requires investigation into the potential of electrical power system operating safety violations. Fig. 1 presents the diagram of interfaces between the EHV grid with the 110 kV and MV grids. The system power plants generate the power which is transformed from the generator voltage level into 400 kV or 220 kV (where power unit transformers are accounted for) and then transmitted to the EHV/110 kV station.

Abstract This article presents the mathematical model of node optimisation for wind generation in the transmission grid. The target function is the maximum summary wind generation with compliance with the following bounds the

permissible load of lines and transformers, the permissible foreign exchange balance, the minimum technical regulating power at conventional power plants. The considerations are illustrated by an example calculation.

Marian Sobierajski, Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

��

Power plants ��

��

Power plants ��

Power plants � ��

��

�� 400/220 kV transmission grid

EHV/110 kV stations ��

110/SN stations ��

�� 110/SN stations�

110/SN stations� ��

��

MV �� grid with �� consumers�

��

Fig. 1. Interfaces of the 110 kV and MV grids to the 400/220 kV grid and to the system power plants and wind farms

Wind farms can be connected to the NPS nodes following this rule: the higher the power of the wind farm, the higher the rated voltage should be at the connection node. The limit values (maximum and minimum) result from the strategy of the transmission system operator. In the case of 110 kV and MV grids, the power of connected wind farms should be consumed at the local level. Introduction of a large wind power generation into the NPS entails the necessity of decreasing the generation magnitude in thermal power stations. This changes the power distribution and the voltage levels in the 400/220 kV transmission grid, which may result in three basic hazards: overloading of the lines and transformers in the national 400/220 kV grid, overloading of the foreign exchange line, decrease of power generation in thermal power plants below the minimum technical values. The estimation of the permissible wind power generation should be the result of an optimizing problem with bounds. This problem can be formulated in many different ways. It is critical that none of the bounds related to the said hazards is violated at full power generation by the wind farms. The development strategy for the NPS indicates that wind farms can only be connected at specific nodes. Nevertheless, the optimising problem dimension is so large that the NPS model requires simplification (reduction). The applied simplification should provide a decision margin, i.e. give pessimistic results, which means that they must be worse than in the complete model. Considering the aforementioned, the analysis of distribution of wind farms can be limited to selected 400 and 220 kV, and to 110 kV buses downstream of EHV/110 kV transformers. Fig. 2 presents a schematic diagram of such a model reduction, where the 110 kV lines, which connect EHV/110 kV stations and relieve the transmission grid, are omitted. As a consequence, the power flows increase in the 400/200 kV grid, which is significant, especially in the states N-1. Note that this approach is very common in system analysis. The substitute power magnitudes over the 110 kV buses are determined for the planned demand based on the power distribution calculated in the complete model of the 400/220/110 kV grid. Due to the dimension of the optimisation problem and the fact that the optimisation pertains to the planned wind power generation and to the forecast operating conditions of the NPS, it is necessary to adopt certain assumptions which specify the problem and simplify the mathematical model. Assumptions for the optimisation problem 1. The summary power of connected wind farms should be as high as possible. 2. The wind power generation cannot overload the lines and/or the transformers. 3. The synchronous exchange balance must be close to the value which was present before the connection of wind farms.

The Method of Linear optimisation of ohe Permissible Wind Power Generation in the Transmission Grid Nodes

4. The wind power generation being connected must not violate the technical minimum of the system which results from the characteristics of the power generating units and from the requirements of frequency control 5. The wind power generation being connected must not violate the technical minimum of the system which results from the characteristics of the power generating units and from the requirements of frequency control. 6. The power magnitudes of the wind farms connected to a node of a certain rated voltage should be within an interval deﬁned for the given voltage level by the operator.

2. THE LINEAR MODEL OF ACTIVE POWER DISTRIBUTION IN THE TRANSMISSION GRID The problems related to the estimation of the permissible power of wind farms in the 400/220/110 kV grid can be brought down to the optimisation of reactive power distributions in a simplified model which includes the 400/220 kV grids, the EHV/110 kV transformers and the substitute consumers connected to 110 kV buses downstream of these transformers. Formulation of the problem of linear optimisation requires detailed simplifying assumptions [3]. Simplifying assumptions for the linear model 1. The planning considers the steady states with a safe reserve of stability, i.e. small angular flares of the voltages at the ends of individual branches, which means that sin(δi - δj) ≈ (δi - δj) and cos (δi - Sj) ≈ 1. 2. The voltage drops in the lines and in the transformers are insignificant, which means that the values of node voltages are approximately equal to the rated values Ui ≈ UN and Uj ≈ UN. A reference node must be identified in the analysed electrical system. This node must be a balancing node. Usually the node with the highest number is adopted. With these assumptions, the power distribution is defined by a linear matrix equation: P = Bδ

lub

δ = B-1 P = X P

(1)

where: Ρ is the vector of node active powers in independent nodes; Β is the matrix of node susceptances; X is the matrix of node reactances; δ is the vector of angles of node voltages. Both generated and picked up / consumed power can occur in a transmission grid node. The node power is the difference of the power generated and the power picked up at the grid nodes, hence: P = Pg – Pd

(2)

where: Ρg is the vector of generated node powers; Ρd is the vector of picked up (demanded) node powers. The magnitudes of branch powers can be calculated directly from the node powers: Pb = diag(b) Cδ = Cb XP = HP

(3)

where: Η = CbX is the transfer matrix of node powers; Cb = diag(b) C is the admittance matrix of branch-node connections; C is the binary matrix of branch-node connections, b is the vector of branch susceptances.

3. THE PROBLEM OF LINEAR OPTIMISATION OF WIND POWER GENERATION The problem of linear optimisation of the wind farms connected to the transmission grid nodes can be formulated as a problem of maximising the summary power of wind farms in compliance with equality and inequatily bounds.

Marian Sobierajski, Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

The system power plants exist only in a part of the grid nodes; hence in a similar manner, wind farms can only be connected to the nodes identiﬁed by the operator. For this reason the vector of node powers should be divided into two subvectors:

Px   Pgx  Pdx  P   Py  Pgy  Pdy 

(4)

where: Ρ is the vector of power in the nodes with optimised generated powers; Ρ is the vector of optimised generated powers; Pdx is the vector of powers picked up at the nodes with optimised generated powers, Ρy is the vector of power in the nodes without optimised generated powers, Ρgy is the vector of non-optimised generated powers, Ρdy is the vector of powers picked up at the nodes without optimised generated powers. Generally speaking, among the components of the vector of optimised generated powers components can be identiﬁed which correspond to new sources (FW – wind farms) and those which correspond to the existing conventional sources (EC – system thermal power plants): χ

PgxFW  Pgx     PgxEC 

(5)

The components of the vector of optimised powers in the nodes with the new sources (wind farms) are assigned with indexes 1, ..., nxFW, while the components with the existing sources (system power plants) are assigned with indexes nxFW +1, ..., nx + nxEC. Between the number of the components and the problem dimension, the relation exists: nx = nxFW + nxEC. The optimised wind farm powers relate both to the existing farms in the NPS model and all other potentially connectible at the nodes identiﬁed by the Operator. In the case of the existing farms, it is assumed that their minimum power equals the planned power featured in the NPS model, which means, that the optimised power of an existing wind farm may only be higher than the planned farm power in the NPS model. Among the few considered functions, the target function is selected which ensures maximisation of the total power of wind farms at the identiﬁed nodes of the transmission grid. The adopted target function has the following form:



F  e TxFW

PgxFW  e TxEC   e TxFWEC Pgx   PgxEC 



(6)

T where: exFW = [1 1... 1] is the transposed vector of ones which correspond to the powers of the wind farms T being connected; exEC = [0 0... 0] is the transposed vector of zeroes which correspond to the powers of system power plants. T T The vector exFWEC = [exFW exEC ] zeroes the powers of system power plants, PgxEC, allowing the full dimension of the matrix Pgx. The vector of node powers PgxEC is optimised since it exists in the inequality limitations of the optimisation problem. The equality bounds are always satisﬁed in the problem of linear optimisation of wind power generation, since the increase of the total node power decreases the power in the balancing node, and vice versa.

System technical minimum The maximum and minimum powers of electrical power sources result from the power generation technologies and their share in the frequency regulation: Pgx ≤ Pgxmax and Pgx ≥ Pgxmin

(7)

In the case of system power plants (EC), the minimum and maximum values primarily result from the share in the frequency regulation. In the case of wind farms (FW), the upper and lower limit of a farm’s power is arbitrarily deﬁned by the operator, depending on the level of the rated voltage at the connection point.

The Method of Linear optimisation of ohe Permissible Wind Power Generation in the Transmission Grid Nodes

Permissible branch powers The inequality bounds, resulting from the permissible branch powers, are functional bounds and can be noted in the form of the following matrix inequality: H(Pg – Pd) ≤ Smax or HPg ≤ Smax + HPd

(8)

Consider the fact that a change of generated powers can change the power ﬂow direction, i.e. change the power sign. This is why the inequalities for the changed directions of branch powers must also be noted: – H(Pg – Pd) ≤ Smax or – HPg ≤ Smax + HPd

(9)

The inequalities which account for the changes of branch power directions may be combined in a matrix notation:

S max  HPd  H   P g S  HP   H    d  max

D b Pg  d b

(10)

where:

 H  Db    – is the generalized transfer matrix of generated powers;  H S  HPd  d b   max  – is the vector of right sides of inequality bounds. S max  HPd  Considering the division of the vector of generated powers into two subvectors, the following is produced: Dbx Pgx ≤ db – DbyPgy

(11)

Generally, the formula is: Dbxx ≤ dbx

(12)

where:

 H  D bx   x  ,  H x 

d bx  d b  D by Pgy

 Hy  D by    ,  H y 

S  HPd  d b   max  S max  HPd 

(12a)

(12b)

Synchronous power exchange balance The balance of synchronous foreign exchange, following the introduction of new sources, should be close or equal to the permissible exchange balance before the connection of these sources at the preset accuracy of +/- dPsaldo, e.g. +/-5 MW. Supplying a wider interval of accuracy will most likely result in an export increase, since it increases the target function value.

Marian Sobierajski, Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

Psaldodop – Psaldowym ≤ dPsaldo lub Psaldodop – Psaldowym ≥ – dPsaldo

(13)

The branch powers in the exchange sources, following the separation of the nodes into those with and those without optimised generation are expressed by a matrix equation: Pbwym = Hxwym Pgx – Hxwym Pdx + Hywym Py

(14)

Hxwym Pgx = Pbwym + Hxwym Pdx – Hywym Py

(15)

where: Ηxwym is the power transfer submatrix, corresponding to the exchange branches and to the nodes with optimised sources; Ηywym is the power transfer submatrix, corresponding to the exchange branches and to the nodes without optimised power generation. The balance of synchronous power exchange equals the algebraic sum of powers in the exchange lines: Psaldowym = eTbwym Pbwym

(16)

where: ebwym = [1 1 ... 1] is the transposed vector of ones which correspond to the powers of synchronous exchange. After the substitution of dependences for exchange powers, the following results: T

Psaldowym = ebwym (Hxwym Pgx – Hxwym Pdx + Hywym Py)

(17)

The difference between the permissible exchange balance and the actual exchange balance must be less than the preset accuracy: T

Psaldodop – ebwym Hxwym Pgx – eTbwym (– Hxwym Pdx + Hywym Py ) ≤ dPsaldo

(17a)

T T – ebwym Hxwym Pgx ≤ – Psaldodop + ebwym (– Hxwym Pdx + Hywym Py ) + dPsaldo

(17b)

and T

T Hxwym Pgx – ebwym (– Hxwym Pdx + Hywym Py ) ≥ – dPsaldo Psaldodop – ebwym

T ebwym Hxwym Pgx ≤ Psaldodop – ebwym (– Hxwym Pdx + Hywym Py ) + dPsaldo

(17c) (17d)

The inequalities which account for the upper and lower accuracies of the balance can be combined in a matrix notation:

 e Tbwym H xwym  dPsaldo  Ssaldodop  eTbwym ( H xwym Pdx  H ywym Py ) P   T  gx   T  e bwym H xwym  dPsaldo  Ssaldodop  e bwym ( H xwym Pdx  H ywym Py )

(18)

In general, the inequalities resulting from the power exchange balance have the following form: Dwym x ≤ dwym

(19)

The Method of Linear optimisation of ohe Permissible Wind Power Generation in the Transmission Grid Nodes

where:

 e T H  D wym   Tbwym xwym   e bwym H xwym  T dP  Psaldowym  e bwym ( H xwym Pdx  H ywym Py ) d wym   saldo  T dPsaldo  Psaldowym  e bwym ( H xwym Pdx  H ywym Py )

(19a)

(19b)

The power bounds in the balancing node If the exchange lines are connected to a balancing node, then the exchange balance bounds are also the power bounds in the balancing node. Otherwise the technical limitations of the power in the balancing node must be accounted for, which are expressed by the following inequality: Pn ≤ Pnmax

oraz Pn ≥ Pnmin

(20)

The power value in the balancing node results from the power values in the branches connected to this node. The matrix notation is as follows: Pbn = Hxn Px + Hyn Py

(20a)

Pbn = Hxn Pgx – Hxn Pdx + Hyn Py

(20b)

Hx Pgx = Pbn + Hxn Pdx – Hyn Py

(20c)

where: Ηxn is the transfer power submatrix which corresponds to the branches connected to this balancing node and to the nodes with optimised power generation; Ηyn is the transfer power submatrix which corresponds to the branches connected to this balancing node and to the nodes without optimised power generation. According to Kirchhoff’s current law, the sum of power in the node is zero which implies that the power in the balancing node is as follows: Pn = eTbn Pbn

(21)

T = [1 1 ... 1] – is the transposed vector of ones corresponding to the branches which connect where: ebwym to the balancing node. After substituting the dependences for the power in the balancing node, a matrix equation is given which makes this power value dependent on the node powers.

Pn = – eTbn (Hxn Pgx – Hxn Pdx + HynPy )

(22)

For the lowest permissible power value in the balancing mode, the following applies: Pn min ≤ – eTbn (Hxn Pgx – Hxn Pdx + HynPy )

(22a)

eTbn Hxn Pgx ≤ – Pn min – eTbn (– Hxn Pdx + HynPy )

(22b)

For the highest permissible power value in the balancing mode, the following applies: – eTbn Hxn Pgx ≤ Pn max + eTbn (– Hxn Pdx + HynPy )

(22c)

In general, the inequalities resulting from the power limitations in the balancing node are:

Marian Sobierajski, Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

62 Dnx ≤ dn

(23)

where:

 e Tbn H xn  Dn   T    e bn H xn 

 P  e T (  H xn Pdx  H yn Py ) d n   n min Tbn   Pn max  e bn ( H xn Pdx  H yn Py ) 

(23a)

General optimisation problems The Matlab software requires the target function and all functional bounds of inequality to be noted as matrices. T

min exWFEC x

(24)

When the following bounds are satisﬁed: Ax ≤ b

(24a)

x ≤ xmax

(24b)

– x ≤ – xmin

(24c)

where:

x  Pgx

 D bx    , A  D wym  ,  D n 

 d bx  b  d wym  , x  P   min gx min  d n 

, x max  Pgx max

(24d)

4. AN EXAMPLE OF WIND POWER GENERATION OPTIMISATION In order to illustrate the linear optimisation of wind power generation in the electrical power system, an exemplary calculation is performed for the 4-node grid (see Fig. 2). The rated voltage of the grid is UN = 400 kV and the base power Sb = 100 MVA. As a consequence, the base impedance is Zb = 1600 Ω. This example considers the connection of wind farms in nodes 1 and 2. They are to cover the power demand in node 3 at the value 30 expressed in relative units where the inter-systemic synchronous exchange rate is -12.5. The permissible branch powers are: Samax = 15, Sbmax, = 15, Scmax = 10, Sdmax = 15, Semax = 20. Prior to optimisation, wind farm powers are selected arbitrarily where their values are Ρ1 = 12, P2 = 3. As a consequence, the permissible load of the branch c is exceeded (Pc = 12 > Scmax = 10) and the synchronous exchange too (P wym = -15 < P wymdop = -12.5).

The Method of Linear optimisation of ohe Permissible Wind Power Generation in the Transmission Grid Nodes

��

� ��

��

Fig. 2. The power distribution in the example grid before and after optimisation of wind power generation; the brackets indicate the postoptimisation values

The speciﬁc matrices which describe the transmission grid are as follows:

z branch

 z a  0,0192   z   0,0096   b    z c   0,0048      z d  0,0192   z e  0,0038 

j 0,0962  b a  10   y a   2  j10  b  20  y    j 0,0481  b    b   4  j20  j 0,0240 , y branch   y c    8  j40  , b branch   b c   40 ,          j 0,0962 b d  10   y d   2  j10   b e  50  y  10  j50 j 0,0192   e 

 70  20  40 0,0293 0,0242 0,0141   1 B   20 30  10  , X  B  0,0242 0,0545 0,0152 ,    40  10 100   0,0141 0,0152 0,0172

 0,1010 1  1  0,1010  1 0  0  1 , H  diag(b branch )CX   0,6061   0 0  0,2929  0,7071 0 1   3   0   P1   12        P  P2    3  , P  HP   12  b    P3   30  0   15

0  1  C1  1  0

0,3939  0,0202 0,6061 0,0202  0,3636  0,1212  ,  0,2424 0,1414  0,7576 0,8586 

(26)

Marian Sobierajski, Wilhelm Rojewski / Wrocław University of Technology Sebastian Słabosz / Wrocław University of Technology

before opt.

balance

post opt.

Fig. 3. The results of wind power generation optimisation in the example transmission grid

The matrices related to optimisation are given in the following forms:

 P1   12   P1   Px   Pgx  Pdx        P  P2    3  , P        P2  , P P P  y gy dy  P      P3   30  3 P  0  Pgx   1  , Pdx    , P  0 gy P2  0

(27)

Pdy  30

The optimisation is performed in Matlab with the use of the linprog function. The optimisation results are speciﬁed in Fig. 3. In order to remove the violation of bounds, the wind farm powers are radically changed. Residuals:

Primal Dual Upper Duality Total Infeas Infeas Bounds Gap Rel A*x-b A’*y+z-w-f {x}+s-ub x’*z+s’*w Error ------------------------------------------------------------Iter 0: 4.72e+002 8.66e+000 1.00e+002 4.20e+003 7.16e+000 Iter 1: 1.53e+001 7.54e-001 3.24e+000 4.89e+002 9.38e-001 Iter 2: 6.53e+000 2.23e-001 1.38e+000 1.71e+002 8.63e-001 Iter 3: 5.04e-001 1.78e-014 1.07e-001 1.66e+001 4.39e-001 Iter 4: 2.31e-014 1.34e-015 1.42e-014 9.12e-002 5.18e-003 Iter 5: 2.04e-010 3.63e-015 2.84e-014 4.41e-003 2.52e-004 Optimization terminated. Fval0 = -15, Fval = -17.5, Pgxopt = [0.0000; 17.5000] Pgalopt = [7.5; 10; 10; 0; -12.5], Pwymopt = -12.5

The Method of Linear optimisation of ohe Permissible Wind Power Generation in the Transmission Grid Nodes

5. SUMMARY Wind power generation changes the power distributions, which may result in exceeding the permissible power-carrying capacities of lines and transformers, as well as of the permissible synchronous exchange with other power systems. Moreover, the value of wind power generation must not decrease the conventional power generation magnitudes below the permissible technical minimum. This problem can be formulated and solved as a problem of linear optimisation. This work presents the mathematical model of this problem. The considerations are illustrated by an example calculation.

REFERENCES 1. Kremens Z., Sobierajski M., Analiza systemów elektroenergetycznych, WNT, Warsaw 1996. 2. Polish Energy Policy for the Year 2030, online version: http://www.mg.gov.pl/Gospodarka/Energetyka/ Polityka+energetyczna. 3. Sobierajski M., Słabosz S., Rojewski W., Optimal interconnecting wind generation into Polish power system, Modern Electric Power Systems, MEPS‚ 10, September, 20-22, 2010, Wrocław, Institute of Electrical Power Engineering. Wrocław University of Technology.

Paweł Wicher / Wrocław University of Technology Kazimierz Wilkosz / Wrocław University of Technology

Authors / Biographies

Paweł Wicher Wrocław / Poland

Kazimierz Wilkosz Wrocław / Poland

Obtained Master’s degree at the Faculty of Electrical Engineering, Wrocław University of Technology. Currently PhD student at the same faculty. Works at the Wrocław department of the company EnergiaPro, part of Tauron Polska Energia SA holding. Interested in power system protection and smart processing of measurement data from a power system.

Obtained his MSc, PhD and DSc degrees at the Wrocław University of Technology. After completing doctoral studies at the Institute of Electrical Power Engineering, Wrocław University of Technology he was employed at that institute. Currently holds position of Associate Professor. Member of Association of Polish Electrical Engineers SEP, and CIGRE. Scientiﬁc secretary of the Power Systems Section of the Committee on Electrical Engineering, Polish Academy of Sciences. Member of scientiﬁc committees of multiple national and international conferences. Reviewer of papers submitted to several journals (including IEEE Transactions on Power Delivery, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering) and conferences (e.g. PSCC, ICHQP, EPQU). Particularly interested in power system analysis and application of information technologies in electrical power engineering.

Application of the Tabu Search Algorithm for Localization of Capacitor Banks in a Power System

APPLICATION OF THE TABU SEARCH ALGORITHM FOR LOCALIZATION OF CAPACITOR BANKS IN A POWER SYSTEM Paweł Wicher / Wrocław University of Technology Kazimierz Wilkosz / Wrocław University of Technology

1. INTRODUCTION One of the important issues which need to be addressed when operating a power grid is excess flow of reactive power. Such flows cause increased active power losses, increased effective voltage differences between the grid nodes and decreased transmission capacity of the grid. Therefore an effort is being made to restrict the excessive reactive power flows. This objective may be achieved through the installation of capacitor banks [1]. The process of finding the most favourable location for a capacitor bank is a combinatorial optimisation task, and it is quite a complex one. It needs to be pointed out that capacitor banks are characterised by parameters with discrete values. Values which characterise the condition of a power grid (voltages at grid nodes) on the other hand are continuous. Mathematical programming methods have been proposed for solving the optimisation task [1]; however, results of this approach have proven unsatisfactory due to insufficient accuracy and excessive computational power requirements. An interesting method for solving the capacitor bank localisation issue is the application of metaheuristics. The selected metaheuristic iteratively leads toward a solution close to the global extreme, not a local extreme, which is a significant difference when compared to the mathematical programming [4]. This paper discusses the application of a Tabu Search (TS) algorithm metaheuristic [4]. The aim of this paper is to present results of a comparative analysis of methods for determining a capacitor bank location using the TS algorithm. In conclusion the most important properties of investigated methods are summarised.

2. GENERAL DESCIRIPTION OF THE TS ALGORITHM The TS algorithm is a modern heuristic optimisation algorithm [5, 6]. It may be used to solve combinatorial optimisation tasks. It is an iterative solution search algorithm. It belongs to the single search thread class and uses a local search improvements method. It also uses a principle of weakening selection rule. This means that each current solution is replaced with the best solution in its neighbourhood, even if this deteriorates solution quality. Proper functioning of the algorithm depends on deﬁning the following elements: moves (between individual solutions), tabu list, aspiration criterion, stopping criterion and – in the case of searching for the optimal capacitor bank location – rules for evaluating location quality. a. Moves Correct functioning of the TS algorithm depends on deﬁning a set of actions that allow generating moves into new solutions which improve the quality of the investigated target function. In some situations, when it is not possible to improve solution quality, the algorithm will select a move which deteriorates solution quality to the smallest degree.

Abstract The paper discusses the process of ﬁnding the most optimal locations for capacitor banks within a power network. After general presenting the solution of this task, the authors focused on the application of the tabu search algorithm. A further part of the paper presents rules for

applying the tabu search algorithm to the considered task, and various methods for ﬁnding the optimal capacitor bank locations using that algorithm are presented. Finally, the previously presented methods for ﬁnding the optimal capacitor bank locations are compared.

Paweł Wicher / Wrocław University of Technology Kazimierz Wilkosz / Wrocław University of Technology

b. Tabu list The tabu list is a list of prohibited moves. The aim of creating a tabu list is to prevent cyclic moves and returns to a local minimum, from which the previous move was made. Here we assume (and so it will be assumed further on if not specified otherwise), that the previously mentioned target function must be minimised. The tabu list plays a very significant role when searching for a solution. It allows restricting the search space, thus shortening calculation time. c. Aspiration criterion The aspiration criterion allows overriding prohibition of a move as a result of this move being included in the tabu list. Often the aspiration criterion is defined in such a way that overriding prohibition occurs when the move in question allows decreasing the value of the target function, i.e. f(Sk*+ tabu_move) < f(Sk*), where f(-) is the target function, tabu_move is a move towards the next solution, Sk* is the best solution already known, Sk* is the solution from which the tabu_move leads to another solution characterised by a lower target function value than that for the Sk* solution. The aspiration criterion allows enhancing tabu search flexibility by directing the search process towards more attractive moves. d. Stopping criterion The stopping criterion, defining conditions for ending the search process, often assumes that at least one of the following conditions must be fulfilled: 1. Number of iterations since finding the best known solution exceeds a predetermined value 2. Total number of iterations exceeds a predetermined value.

3. CHARACTERISTICS OF CAPACITOR BANK LOCALIZATION METHODS USING TABU SEARCH ALGORITHM 3.1. Yang, Huang and Huang method The Yang, Huang and Huang method [7] assumes that the most favourable location of a capacitor bank will be found by minimising function: KE_str + KI

(1)

with the following constraints: g(X, Qz) = 0

(2)

Vi, min ≤ Vi ≤ Vi, max, 1 ≤ i ≤ n, 0 ≤ QBi, j ≤ QBi, max, 1 ≤ i ≤ nB, 1 ≤ j ≤ l,

(3)

where: KE_str is the cost of losses in the power network, KI is the capacitor bank installation cost, g(•) = 0 is the equation of power ﬂows in the power network, x is the nodal voltage vector, Qz is the vector of outputs of additional reactive power sources installed in the power network nodes, Vi is the effective voltage at the nodes i, n is the number of nodes, Vi_min and Vi_max are minimum and maximum voltage modules respectively, QBi,max and QBi,j are nominal powers of the i-th capacitor bank – maximal and for the j-th load level respectively, nb is the number of capacitor banks and l is the number of load levels. In this method additional sources of reactive power are capacitor banks. In the process of minimising function (1), values of power QBi,max and QBi,j are determined. During the initial stage of the optimisation procedure, operational experience is used to deﬁne the potential placement of capacitor banks. Then sensitivity analysis results are used to reach the previously determined objective. The main part of the optimisation process is carried out with a classic TS algorithm. The method was tested on a 69-node test system.

Application of the Tabu Search Algorithm for Localization of Capacitor Banks in a Power System

3.2. Gan, Qu and Cai method The Gan, Qu and Cai method [9] uses the target function (1) which is minimised with constraints (2), as well as: KTi min ≤ KTi ≤ KTi max, 1 ≤ i ≤ t, QGi min ≤ QGi ≤ QGi max, 1 ≤ i ≤ g,

(4)

.0 ≤ QDi, j ≤ QDi, max, 1 ≤ i ≤ nD, 1 ≤ j ≤ l,

(5)

where KTi, KTi,min and KTi,max are voltage ratios of the i-th transformer – actual, minimal and maximal respectively, t is the number of transformers, QGi, QGi,min and QGi,max are reactive power outputs of the i-th generator – actual, minimal and maximal respectively, g is the number of generators, QDi,max and QDi,j are nominal capacities of the i-th shunt reactor – maximal and for the j-th load level respectively, nD is the number of shunt reactors. This method searches for optimal locations and parameters of additional reactive power sources within the network using the TS algorithm. The paper [9] presents a solution of the problem when the optimisation task includes continuous values together with discrete ones. One of the factors which determine the effectiveness of the TS algorithm is efﬁcient realisation of moves towards new solutions. In the paper [9], the authors have presented an original method for evaluating solutions from the neighbourhood of the current solution, which assures such realisation of moves. This method was tested on a 200-node real-life power system. The tests highlight the considerably higher computational efﬁciency of the TS algorithm when compared to a simulated annealing.

3.3. Mori and Ogita method The Mori and Ogita method [10] uses the target function (1) and constraints (2). In order to increase searching efficiency understood as the time needed to find the solution as well as its quality, this method uses a concept of parallel tabu searches. With this approach a decomposed solution neighbourhood is investigated. This allows decomposing the search for the best solutions into identified network areas. The best of the identified solutions is finally selected. Such an approach allows reducing the calculation time. It also assumes multiplication of tabu lists, supposed to ensure greater diversity of solutions and more effective selection of betterquality solutions. This also increases search reliability. Sensitivity of the search process to the initial conditions is greatly limited. This method was tested on 27- and 69-node distribution systems. 3. 4. Chang and Lern method The Chang and Lern method [11] solves the task by maximising the value of the target function: max (ZΔP_str + ZΔE_str – K1) qi

(6)

where: ZΔP_str and ZΔE_str are incomes resulting from restricting the peak power losses and energy losses in the power network respectively. Optimal capacitor bank placement and parameters are determined for each speciﬁed load level of the power network. The search of the optimal capacitor bank placement and parameters uses the TS algorithm. The procedure is divided into three stages. Each of them consists of multiple iterations, during which new capacitor placement solutions are found. Division of the procedure into three stages is assumed to restrict the optimal solution found in each stage so that the total capacity of considered capacitor banks does not exceed a certain determined value. This value is different for each stage. It is deﬁned randomly, just like the number of capacitor banks in the preliminary solution. This method was tested on a 34-node distribution system.

Paweł Wicher / Wrocław University of Technology Kazimierz Wilkosz / Wrocław University of Technology

3.5. Gallego, Monticelli and Romero method The Gallego, Monticelli and Romero method [12] is a hybrid method utilising the tabu search concept as well as taking into account some concepts of the combinatorial approach used in the genetic algorithms, simulated annealing and practical heuristic approach (sensitivity analysis). The target function is the function (1) and it is minimised. The task of finding the best locations for a capacitor bank is solved with constraints (2), (3). In fact, this method has two stages: a heuristic search for capacitor bank location phase and a tabu search phase. The first stage provides a set of multiple (not necessarily optimal) locations for capacitor banks, which are then used as an initial point for further search for the best location. In this phase the locations are proposed as a result of using sensitivity analysis. The paper [12] shows how different settings of sensitivity parameters result in different capacitor bank locations. During the second stage, a tabu search is performed. If all locations identified so far have already been taken into account, new locations are generated by recombination, Path Relinking strategy and elite configurations. The authors predict that locations may be found for various network loads, in particular, for peak loads. This method was tested on test systems proposed by literature, with 9 and 69 nodes, as well as a 135node real-life system. 3.6. Zhang, Liu and Liu method The Zhang, Liu and Liu method [13] allows not only to search for optimal placement of capacitive reactive power sources (capacitor banks), but also inductive reactive power sources (shunt reactors). When searching for optimal locations for reactive power sources, high, intermediate and low load conditions are defined according to the engineering experience. The paper [13] states that in high load conditions it is necessary to supply capacitive reactive power to the network, while at low loads, inductive reactive power should be delivered. In the case of high loads it is assumed to use the target function (1), which is minimised with constraints (2)–(5) and the additional constraint SLi ≤ SLi,max, 1 ≤ i ≤ m, where: SLi, SLi,max are apparent power values for a power line i – actual and maximal respectively, m is the number of power lines. The term Ki in the target function represents the cost of capacitor banks installation. For low loads the KI term represents the cost of shunt reactors installation. For average loads the KI term is deleted. For high loads the condition 0 ≤ QBi,j ≤ QBi,max, 1 ≤ i ≤ nB, 1 ≤ j ≤ l is replaced by the condition 0 ≤ QBi, 1 ≤ i ≤ nB, while for low loads, except for the condition 0 ≤ QBi,j ≤ QBi,max, 1 ≤ i ≤ nB, 1 ≤ j ≤ l there is also the requirement 0 ≤ QDi, 1 ≤ i ≤ nD. Each defined load case is investigated separately. The process of searching for optimal placement of reactive power sources uses a modified TS algorithm. Preliminary solutions are stated according to operational experience and sensitivity analysis. This method was tested on a 137-node real-life (Chinese) power system. A method very similar to the Zhang, Liu and Liu method is presented in the paper [14]. It has been ascertained that when compared to the normal algorithm, the modified TS algorithm (with modification of preliminary solutions according to the operational experience and sensitivity analysis) allows achieving a lower value of the target function in a shorter time. 3.7. Pires, Martins and Antunes method The Pires, Martins and Antunes method [15] was developed to solve the task of multi-criteria optimisation of number, locations, parameters and switching times of capacitor banks within a distribution network. The method uses two target functions: active power losses (PΣ_str) and the cost of introducing capacitor banks into the network (Kl,B). The following constraints are taken into account: (2), (3) and a condition that no more than one capacitor bank shall be installed in one node. The method utilises the TS algorithm. The initial solution is determined randomly. The tabu search process is used to find a small area of non-dominant solutions. Selection of the ultimate solution is left to the operator. The method was tested on a 94-node real-life (Portugal) distribution system.

Application of the Tabu Search Algorithm for Localization of Capacitor Banks in a Power System

3.8. Mori and Tsunokawa method The Mori and Tsunokawa method [16] uses the target function (1) and constraints (2), (3). It combines the tabu search method with a variable neighbourhood search. Use of a variable neighbourhood search allows achieving greater diversity of potential solutions and thus improves the quality of the ﬁnal results. This method enables a more effective search of global solution than other methods. This method was tested on a 32-node distribution sytem. It has been noted that the standard deviation of the target function was 25% lower in the case of this method than in the case of a method without the variable neighbourhood search. 3.9. Summary Table 1 presents a summary of characteristic features of the presented methods. Tab. 1. Summary of characteristic features of presented methods. Method

Target function

Initial solution identiﬁcation

Movement area

Papers

Publishing year

Yang, Huang & Huang

KE_str+KIB

Operational experience Sensitivity analysis

Neighbourhood

7, 8

1995, 1996

Gan, Qu & Cai

KE_str+KIB +KID

Random

Neighbourhood

1996

Mori & Ogita

KE_str+KIB

Random

Decomposed neighbourhood

(1999) 2000

Chang & Lern

Z∆P_str+ Z∆E_str– KIB

Random

Neighbourhood

2000

Gallego, Monticelli & Romeor

KE_str+KIB

Sensitivity analysis

Exactly deﬁned

2001

Zhang, Liu & Liu

KE_str+KIB +KID

Operational experience Sensitivity analysis

Neighbourhood

2002 (2010)

Random

Neighbourhood

2005

No capacitor banks

Variable neighbourhood

2005

Pires, Martins & Antunes PΣ str, KIB Mori & Tsunokawa

KE_str+KIB

The methods discussed in this paper have been proposed quite recently. Most of the analysed methods utilise a target function being a sum of energy losses costs and cost of capacitor installation in the network. Significant differences between individual methods lie in the method for defining the initial solution and movements between the solutions. In three of the methods: the Yang, Huang and Huang method, Gallego, Monticelli and Romero method, and Zhang, Liu and Liu method – the initial solution is determined according to the results of a sensitivity analysis. Two of the others utilise operational experience, and one starts investigation from the situation without any capacitors in the network. In all others, the initial solution is defined randomly. Several methods focus on definition of movement area between individual solutions. In the Mori and Ogita method the neighbourhood of current solution is decomposed. In one of the later methods – Gallego, Monticelli and Romero – the solution area is initially defined according to the sensitivity analysis, and then changed using recombination, Path Relinking strategy and elite configurations. A different approach to determining the solution area can be found in the Mori and Tsunokawa method. Two solution (movement) areas are defined in the neighbourhood of the current solution. If no better solution than the current one is found in one of them, the search continues in the other.

Paweł Wicher / Wrocław University of Technology Kazimierz Wilkosz / Wrocław University of Technology

4. FINAL REMARKS The interest in using the TS algorithm for optimising placement of capacitor banks results from the general trend to find the most favourable– in terms of result accuracy and solution time – method possible for solving this task. The task in question is not an easy one. It requires finding the extreme value of a certain function in a discrete multi-dimensional space with many permissible points. Generally, the target function has multiple extremes. The TS algorithm provides a mechanism which allows finding the global extreme in a relatively short time.. It should be noted that the heuristic approach – which is also used when the TS algorithm is applied – allows to better reflect the real conditions. In many cases analytical methods are based on unrealistic assumptions, e.g. uniform load distribution or load invariability, while in the heuristic approach such assumptions are not needed. The TS algorithm is one of the more effective metaheuristics. It has a deterministic character. It is also simpler than other algorithms searching for the solution in a determined solution area. Its advantages are beneficial from the point of view of combinatorial optimisation, which occurs when searching for the best – according to the assumed criterion – location of reactive power sources. It has been determined [17] that the effects of using standard TS algorithm for finding the optimal location of capacitor banks – without taking into account calculation time – are comparable to the effects obtained with a genetic algorithm or simulated annealing. It was also discovered, however [10], that both genetic algorithms and simulated annealing are less accurate and more time-consuming when compared to the TS as long as the neighbourhood of the current solution is decomposed. This conclusion is particularly valid for larger power networks. The paper [18] proposes a combination of a standard TS algorithm and a genetic algorithm. It turns out that results obtained in this way are better than in case of using the TS algorithm only. In many cases, when optimisation methods for localization of reactive power sources using the TS algorithm are being developed, attention is paid to definition of the initial solution of the task and appropriate definition of the area of movement between individual solutions (solution area). Papers highlight the significant impact of those factors on the results of the optimisation process.

Application of the Tabu Search Algorithm for Localization of Capacitor Banks in a Power System

REFERENCES 1. Ng H.N., Salama M.M.A., Chikhani AY, Classification of Capacitor Allocation Techniques. IEEE Trans, on PD, 2000, vol. 15, no. 1, pp. 387–392. 2. Zhang W., Tolbert L.M., Survey of reactive power planning methods. IEEE PES General Meeting, 2005, pp. 1430– 1440. 3. Zhang W., Fangxing L., Tolbert L.M., Review of Reactive Power Planning: Objectives, Constraints, and Algorithms. IEEE Trans, on PS, 2007 vol. 22, no. 4, pp. 2177–2186. 4. Glover F., Future Paths for Integer Programming and Links to Artificial Intelligence. Computation & Operations Research, 1986, vol. 13, no. 5, pp. 533–549. 5. Glover F., Tabu Search – Part I, ORSA J. on Computing, 1989, vol. 1, no. 3, pp. 190–206. 6. Glover F, Tabu Search – Part II, ORSA J. on Computing, 1990, vol. 2, no. 1, pp. 4–32. 7. Yang HrT., Huang Y-Ch., Huang ChrL., Solution to Capacitor Placement Problem in a Radial Distribution System Using Tabu Search Method. Inter. Conf. on Energy Management and Power Delivery, 1995, vol. 1, pp. 388–393. 8. Huang Y-Ch., Yang H.-T, Huang ChrL., Solving the capacitor placement problem in a radial distribution system using Tabu Search approach. IEEE Trans, on PS, 1996, vol. 11, no. 4, pp. 1868–1873. 9. Gan D., Qu Z., Cai H., Large Scale Var Optimization and Planning by Tabu Search. Electric Power Systems Research, 1996, vol. 39, no. 3, pp. 195–204. 10. Mori H., Ogita Y., Parallel Tabu Search for Capacitor Placement in Radial Distribution Systems. IEEE PES Winter Meeting, 2000, vol. 4, pp. 2334–2339. 11. Chang CS., Lern L.P., Application of Tabu Search Strategy in Solving Non-Differentiable Savings Function for the Calculation of Optimum Savings due to Shunt Capacitor Installation in a Radial Distribution System. IEEE PES Winter Meeting, 2000, vol. 4, pp. 2323–2338. 12. Gallego R.A., Monticelli A.J., Romero R., Optimal Capacitor Placement in Radial Distribution Networks. IEEE Trans, on PS, 2001, vol. 16, no. 4, pp. 630–637. 13. Zhang W., Liu Y., Liu Y., Optimal VAr Planning in Area Power System. Inter. Conf. on Power System Technology, 2002, vol. 4, pp. 2072–2075. 14. Zou Y., Optimal Reactive Power Planning Based on Improved Tabu Search Algorithm. Inter. Conf. on Electrical and Control Engg 2010, Wuhan, pp. 3945–3948. 15. Pires D.F, Martins A.G., Antunes C.H., A Multiobjective Model for VAR Planning in Radial Distribution Networks Based on Tabu Search. IEEE Trans, on PS, 2005, vol. 20, no. 2, pp. 1089–1094. 16. Mori H., Tsunokawa S., Variable Neighborhood Tabu Search for Capacitor Placement in Distribution Systems. IEEE Inter. Symp. on Circuits and Systems, 2005, pp. 4747–4750. 17. Al-Mohammed A.H., Elamin I., Capacitor placement in distribution systems using artificial intelligent techniques. IEEE PowerTech, 2003, Bologna, Italy, vol. 4, s. 1-7 18. Nikoukar J., Gandomkar M., Capacitor Placement In Distribution Systems Using Genetic Algorithms and Tabu Search. The 4th WSEAS Inter. Conf. on Applications of Electrical Engineering, 2005, Prague, Czech Republic, pp. 354–358.

Józef Wiśniewski / Technical University of Łódź

Authors / Biographies

Józef Wiśniewski Łódź / Poland Graduated from Łódź University of Technology (1973). Obtained his PhD of sciences in electrical power engineering at the Faculty of Electrical Engineering, Technical University of Łódź. Currently a lecturer at the Institute of Electrical Power Engineering of his alma mater. Deals in the problems of modelling and simulation of transient states in electrical power systems and electrical power safety systems. A member of the Association of Polish Electrical Engineers (SEP).

The Effect of Disturbances in the Electrical Power System on Torque Moments of The High-power Turbine Set Shaft

THE EFFECT OF DISTURBANCES IN THE ELECTRICAL POWER SYSTEM ON TORQUE MOMENTS OF THE HIGH-POWER TURBINE SET SHAFT Józef Wiśniewski / Technical University of Łódź

The results presented in this paper have been obtained through research co-ﬁnanced by the National Centre for Research and Development (NCBiR) as a part of the contract SP/E/1/67484/10, The Strategic Research Program – Advanced Technologies of Power Acquisition: Development of technologies for high-performance, zero-emission coal power units integrated with ﬂue gas CO2 capture.

1. INTRODUCTION There are plans to introduce power units of approx. 1000 MW into the National Power System in the near future. These power units will operate at super-critical mean-temperature parameters and with the following steam parameters: temperature – 560-580°C, pressure – 25.8 MPa. The switch from the traditional parameters of 535°C and 18 MPa leads to an increase in the efficiency of electrical power generation by approx. 1.5-1.7 percentage points. The nearest goal seems to be the power unit efficiency of 50% (the 50+ Program). The new power unit designs carry new problems regarding the cooperation of power units with the electrical power system [1]. This paper presents the problem of modelling a rotating system of masses of turbines and of a generator. The purpose of this modelling is to calculate the torque moments in the shafts which couple individual system components during disturbances in the electrical power system. The calculations are performed with the EMTP/ ATP software [2]. The turbine set components are coupled by shafts with a determined mechanical strength which can be exceeded upon specific failures. The rotating system of the turbine set is characterised by intrinsic vibration frequencies. Calculation of these frequencies and preventing the system from working upon their presence is a critical condition of proper operation of the turbine set. This paper presents the model of a 1000 MW turbine set mechanical rotating system and the results of modal calculations of intrinsic vibration frequencies for the components of this system. The work considers the cases of disturbances in the electrical power system which increase the torque moments of the shaft. These are symmetrical and asymmetrical faults within the grid, action of the single-phase automatic reclosing system, improper synchronisation and the effect of grid harmonics in the generator current on the rotor, which may result in resonance vibrations. The threat to the shaft strength depends on the torque moment value upon a failure and also on the number and frequency of oscillation, as well as on the shaft overload history. For reasons of simplification, the paper adopts the value of the torque moment amplitude in the shaft of 3 p.u. as the permissible momentary limit value under the conditions of disturbance.

Abstract Mechanical parameters are determined for a set of turbines and power generator of 1000 MW of the reference power unit operated at super-critical parameters. The modal method is used to calculate the frequencies of intrinsic vibrations of the vibrating systems. The paper investigates the values of torqu moments which may occur

in the sections of shafts upon disturbances in the electrical power system, e.g. near faults, action of automatic reclosing systems, synchronisation or interaction of electromagnetic moments from the grid side which introduce the system into resonance vibration.

Józef Wiśniewski / Technical University of Łódź

2. DEVELOPMENT OF THE REFERENCE POWER UNIT MODEL The turbines. The design of the turbine system in high-power units is diverse. High and intermediate pressure turbines are usually designed as single-flow turbines, while intermediate-pressure turbines for the electrical power of more than 500 MW and low-pressure turbines are double-flow units. The number and arrangement of turbines, as well as their share in the total driving power are explained in the references [1]. This article assumes a turbine set system with five turbines and one generator (see Fig. 1). ��

� ��

��

� ��

��

Fig. 1. The structure of the turbine set in the 1000 MW adopted reference power unit

Power output Due to the limits of transport, the power unit output system precludes the use of a single three-phase transformer rated at more than 1000 MVA. The manufacturers of large transformers consider the use of a system with two transformers operating in parallel or a system which ensures higher reliability of the system, equipped in three single-phase transformers (plus one backup transformer) with the total power corresponding to that of the power unit (see Fig. 2). � � a)

���

��

���

��

Fig. 2. The solutions for the high power generator power output: a) traditional, b) the system with two three-phase transformers; c) the system with three single-phase transformers

Reference power unit data. The planned power unit of super-critical parameters will be rated at 1000 MW of power at least. No such power unit currently exists in Poland. The reference literature on this subject has been reviewed to obtain the predicted mechanical data for a power unit of similar magnitude. There are considerable amounts of such data in the publications from the 1980s, when units of similar magnitudes were commissioned – usually at nuclear power plants. The list of turbine set mechanical parameters is based on several publications [e.g. 3 to 7]. Fig. 3 shows the constants of generator inertia Hgen for the unit power range of 500-1100 MVA, in the units [p.u.*s], the mean value Hgen_mean of these constants (ca. 0.82 p.u.*s), as well as the totals of the inertia constants for all turbines, Hturb_sum, which power the generator, and ﬁnally the mean value Hturb_sum_mean of these totals (ca 2.96 p.u.*s). The constants of inertia H allow the calculation of moments of inertia J. �6 5

H gen

��

H turb sum H gen_mean

H turb_sum_mean

3 2 1

��

0 500

600

700

800

900

1000

1100

1200

Fig. 3. The constants of inertia Hgen of generators, the totals of inertia constants Hturb_sum of turbines and the means of these values, Hgen_mean and Hturb_sum_mean for power units of various power magnitudes

�

The Effect of Disturbances in the Electrical Power System on Torque Moments of The High-power Turbine Set Shaft

Fig. 4 shows – depending on the power of the unit – the averaged values of the coefﬁcients of ﬂexibility Kmean for the shafts which couple the turbines and the generator, expressed in the units [p.u./rad] and the average of these values, Kmean_average (approx. 83.5 p.u./rad). � 250 200

K mean

� ��

K mean_average

150 100 50 � ��

0 500

600

700

800

900

1000

1100

1200

Fig. 4. The average values of the coefﬁcients of ﬂexibility, Kmean, of the shafts which couple the turbines and the generator, and the average of these values, Kmean_average

Reference power unit parameters Based on the assessment of parameters of high-power units available in the reference literature or in the processing characteristics of power plant, the power unit with the following parameters is adopted in further calculations: • Generator: n = 2, f = 50 Hz, Pn_gen =1000 MW, Sn_gen = 1176 MVxA, Un_gen = 27 kV • Impedances (p.u.): Xd = 2.5, Xd’ = 0.3, Xd” = 0.26, XL = 0.23, Ra = 0.003, Xq = 2.2, Xq’= 0.5, Xq” = 0.25 • Time constants (s): Tdo’ =6, Tdo “= 0.04, Tqo’ = 0.6, Tqo “= 0.03 • The share of the turbines in the driving moment (%): HP = 30, IP = 22, LP1 = 16, LP2 = 16, LP3 = 16 • Constants of inertia (p.u.*s): HP = 0.17, IP = 0.4, LP1 = 0.6, LP2 = 0.6, LP3 = 0.6, GEN = 0.8 • Attenuation rates (p.u.*s/rad): HP = 0.0002, IP = 0.0002, LP1 = 0.0002, LP2 = 0.0002, LP3 = 0.0002, GEN = 0.0001 • Coefﬁcients of ﬂexibility (p.u./rad): HP-IP = 150, IP-LP1 = 200, LP1-LP2 = 250, LP2-LP3 = 300, LP3-GEN = 350.

3. MODEL PARAMETERS The EMTP/ATP software [ 2] allows simulating the dynamics of turbine systems with any number of separate rotating masses on a single shaft. Each mass is rigid and ﬂexibly connected to the adjacent masses. Each mass is assigned with the driving power which can be constant or change due to the action of regulating systems. The electrical part of the turbine generator model The three-phase synchronous generator model applied in the EMTP/ATP software is shown in Fig. 5. The model consists of the following: three phase windings of the stator, connected to the grid; the excitation winding producing a ﬂux in axis d, the substitute winding attenuating in axis d, the substitute winding which represents the effect of eddy currents and the substitute winding attenuating in axis q. �

� ��

��

� ��

��

Fig. 5. The substitute electrical diagram of the generator

Józef Wiśniewski / Technical University of Łódź

The generator model is described by two sets of equations: • the voltage equations:

u  R  i 

d � dt

(1)

• the ﬂux-current equations:

�  Li

(2)

where: u, R, L, i, λ are, respectively, the vectors of the following: voltages on the windings, resistances of the windings, inductances of the windings, currents of the windings and ﬂuxes in the windings. The input data for the generator modelling can be the resistances and inductances of the windings, or the data obtained through standard measurements from the generator manufacturer, which is more convenient. The mechanical part of the model. The mechanical system presented in Fig. 1 is adopted as a linear system, so the ﬂexibly coupled rotating masses can be described with Newton’s second law, according to this equation:

J

d2 d �  D  �  K  �  Tturb  Tgen dt dt 2

(3)

where the matrices are designated as follows: δ are the angular positions of the rotating masses; J are the moments of inertia of the rotating masses; D are the attenuation rates; K are the coefficients of flexibility of the couplings between the rotating masses; Tturb are the driving moments of the turbine, Tgen is the electromagnetic moment of the generator. The modal analysis [2, 3, 5]. By assuming a matrix of modal transformation Q, where its columns are the intrinsic vectors of the product J x K, the equation (3) is converted into the modal form. Its solution allows finding the modal frequencies of the system vibrations. In the case of the system being considered, these frequencies are: f = [1.44 13.37 23.77 32.98 38.17 44.9] Hz. Fig. 6 presents the shape of the specific moduli (the normalised values of the intrinsic vector components of the transformation matrix Q). The shape of the modes represents the reciprocal shifts of individual rotating masses upon a resonance at the given modal frequency. �

��

1 0 -1 11 0 -1 1 1 0 -1

1 1 0 -1

Fig. 6. The shape of the speciﬁc moduli (the normalised values of the intrinsic vector components of the transformation matrix Q

The Effect of Disturbances in the Electrical Power System on Torque Moments of The High-power Turbine Set Shaft

Fig. 7 shows the dependence of the maximum torque moments Ti (referenced to the rated moments of the shafts) at the specific sections of the shafts as the function of the external sinusoidal input function frequency from the grid side, at the amplitude of 1% of the rated moment Tn_gen acting on the generator rotor. The chart displays a strong amplification of the input function signal at the frequencies of the system intrinsic vibrations; the amplification manifests in the values of the torque moments, which exceed the ratings. �

T1 T2 T3 T4 T5

��

0.1

Fig. 7. The dependence of the maximum torque moments at the speciﬁc sections of the shafts as the function of the external sinusoidal input function frequency, at the amplitude of 1% of Tn_gen acting on the generator rotor

0.01

f [Hz]

0.001 0

Note that even at such small excitation of the rotor with the disturbing moment, the torque moments exceed the ratings of these shafts at certain resonance frequencies.

4. CALCULATING THE TORQUE MOMENTS ACTING ON THE TURBINE SET SHAFTS The impact of the grid on the rotor. The rotating system is tested for the susceptibility to the action of a disturbance signal at the frequency close to the frequency of intrinsic vibrations. This disturbance may originate from the electrical power system as the generator loading current which contains a component with the suitable frequency. The increasing numbers of electronic power devices in the grid favours this situation. The calculations assume the presence of a disturbing sinusoidal moment at the frequency equal to the resonance frequency and at the amplitude equal to 1% of the rated moment. The EMTP/ATP software is used for simulation calculations of torque moments for the generator in two states: at the rated load and synchronised and operated without any load. The shaft sections exhibited signiﬁcant values of torque moments; their values were higher for the generator at the rated load. The modelled generator power output system is presented in Fig. 8. � ��

��

Fig. 8. The modelled generator power output system

Fig. 9 shows the amplitudes of the torque moments expressed in relative units (p.u.) and referenced to the rated moments of all shaft sections when the disturbing moment is applied to the generator rotor. The generator is loaded with full power. �

5 4

T1max

� ��

T2max T3max T4max

T5max

2 1 0

13.4

23.8

33.0

38.2

44.9

fres[Hz]

Fig. 9. The amplitudes of torque moments for the disturbing moment acting on the generator rotor at the amplitude equal to 1% of the rated moment Tn_gen

�

Józef Wiśniewski / Technical University of Łódź

Faults in the electrical power system Fig. 10 shows the values of the maximum torque moments in the rotating system shafts during the following disturbances (A to E): �

��

T1max T2max

T3max T4max T5max

4 3

�

Fig. 10. The maximum torque moment values in the shafts of the rotating system upon faults near the generator

1 0

fault A

fault B

fault C

fault D

fault E

A – Three-phase fault at the generator voltage buses. The generator cut-off switch Q1 breaks after 100 ms. After the following 500 ms the steam cut-off valves are actuated. The generator is loaded with full power. B – The fault is the same as in the scenario A. The generator is not loaded. C – Three-phase fault at the HV terminals of the transformer TB. The generator cut-off switch Q1 breaks after 100 ms. After the following 500 ms the steam cut-off valves are actuated. The generator is loaded with full power. D – The fault is the same as in the scenario C. The generator is not loaded. E – Single-phase fault at the power unit 400 kV line. The automatic control of the successful single-phase automatic reclosing is triggered in 0. 4 s. The generator is loaded with full power. The calculations indicate that the torque moments signiﬁcantly exceed the permissible value. Fig. 11 shows the courses of the torque moments in the shaft sections with the rotational speeds of the turbines and of the generator during a three-phase fault at the generator voltage buses, isolated after 100 ms, when the generator is running at full load. � 5.0 2.5

�3060

��

3030

0.0

3000

-2.5 -5.0 4.98

5.00

5.02

(f ile 1000MW.pl4; x-v ar t) t: T1

t: T2

5.06

5.04 t: T3

t: T4

5.08

5.10

5.12 [s] 5.14

t: T5

2970 4.98

5.00

�

5.06

5.04

5.02

(f ile 1000MW.pl4; x-v ar t) t: VEL_1

t: VEL_2

t: VEL_3

5.08

t: VEL_4

t: VEL_5

5.10

�5.12 [s] 5.14

�

t: VEL_6

Fig. 11. The courses of the torque moments and rotational speeds of the turbines and of the generator during a three-phase fault at the generator voltage buses

Synchronisation of the generator The courses of the torque moments in the turbine shafts are calculated for the synchronisation with the switch Q1 (see Fig. 8). The calculations were performed for the frequency difference between the generator and the grid, Δf = 0.1 Hz and for the difference of phase angles ΔΦ at the interval of 0°-180°. Fig. 12 shows the courses of the rumbling voltage and torque moments in the shaft sections during synchronisation, where the synchronisation exhibits a phase discordance ΔΦ = 5°. � 0.6

� 12 6 0

0.3

��

0.0

-6 -12 0.0

��

0.2

(f ile 1000MW.pl4; x-v ar t) t: DUD

0.4

0.6

0.8

1.0

[s]

1.2

-0.3 0.95

1.00

(f ile 1000MW.pl4; x-v ar t) t: T1

�

t: T2

1.10

1.05 t: T3

t: T4

�

1.15

[s] 1.20

t: T5

Fig. 12. The courses of the rumbling voltage and torque moments synchronisation, where the synchronisation at the phase discordance ΔΦ = 5°

The Effect of Disturbances in the Electrical Power System on Torque Moments of The High-power Turbine Set Shaft

The dependence of the maximum magnitudes of torque moments Ti in the successive sections of the shaft during synchronisation on the difference of phase angles ΔΦ is shown in Fig. 13. � 10

�� 8

�

T1max T2max T3max

T4max T5max 0

100

�� 150

Fig. 13. The dependence of the maximum torque moments during synchronisation on the difference of phase angles ΔΦ

The calculations imply that in the case of the investigated turbine set, the maximum torque moment values for different shaft sections occur when synchronisation is performed at the difference of phase angles ΔΦ within the interval of 110°-130°. The voltage phase upon voltage closing does not affect the magnitude of torque moments on the shaft.

5. SUMMARY • Calculating the intrinsic vibration frequencies of the rotating system of the turbine and generator masses is an important part of programming the turbine set operation. It allows avoiding operation in states of hazard and occurrence of oscillation vibrations caused by an external input function. • The calculations of the magnitudes of torque moments during external disturbances may be useful in the investigations into the causes of shaft damage, in the application of countermeasures and in the determination of operating rules for generators. • The considered cases of faults, synchronisation and external effects on the generator rotor caused by an electromagnetic moment at the resonance frequency display considerable values of the torque moments, which exceed the approved safe level.

REFERENCES 1.Zagadnienia projektowania i eksploatacji kotłów i turbin do nadkrytycznych bloków węglowych, a collective work, Silesian University of Technology Publishing, Gliwice 2010. 2. EMTP Rule Book and Theory Book, Bonneville Power Administration, 1987. 3. Machowski J., Białek J., Bumby J., Power System Dynamics and Stability, John Wiley & Sons Ltd., 1997. 4. Jennings G., Harley R., New index parameter for rapid evaluation of turbo-generator subsynchronous resonance susceptibility, Electric Power Systems Research, 37,1996. 5. Jose A., Castillo J., Turbo-generator torsional behavior using the participation factors and considering the static loads model. Transmission and Distribution Conference and Exposition: Latin America, IEEE/PES, 2008. 6. Maljkovic Z., Stegic M., Kuterovac L, Torsional oscillations of the turbine-generator due to network faults, 14th International Power Electronics and Motion Control Conference, EPE-PEMC, 2010. 7. Tsai J., A new single-pole switching technique for suppressing turbine-generator torsional vibrations and enhancing power stability and continuity, IET Gener. Transm. Distrib., 5, 2007.

Zbigniew Zdun / PLANS, Mikronika Marek Wawrzyniak / Mikronika

Authors / Biographies

Zbigniew Zdun Warszawa / Poland

Marek Wawrzyniak Poznań / Poland

Graduated from the Faculty of Electrical Engineering, Warsaw University of Technology (1972) and obtained his PhD of sciences (1978). From 1972 to 2008, employed as a university teacher at the Facility of Electrical Power Grids and Systems at the Institute of Electrical Power Engineering, Warsaw University of Technology. In his scientiﬁc work, he has been dealing in the methods of determination and analysis of the states of electrical power transmission systems. Author and co-author of over thirty works published in journals and conference materials, two academic handbooks and over one hundred papers commissioned by the national electrical power engineering industry, many of which have been implemented. Established the PLANS company in 1993, which conducts R&D in technical sciences and programming. The developer of the PLANS package for the determination of power distributions in the transmission grids; the suite is used at PSE Operator S.A., national power distribution companies and also at the enterprises which operate on behalf of the national electrical power industry. In cooperation with Mikronika, he developed a calculation system for the operating states of EHV grids which works in real time with the SCADA-EMS (SyndisRV – PlansRVS) measurement system, which has been implemented in EC_Nowa (Mittla Steel Works), EnergiaPro (Wrocław) and KIB-TEK (Cyprus).

Graduated as a Master Engineer of mathematics (numerical methods) from Poznań University of Technology in 1995. Since 1995, employed at BRSPMSA Mikronika as programmer and project manager. Since 2005 – the IT and Software Manager at the company.

The Application of the Cim Format in the Modelling of an Electrical Power System in the Syndis-plans System

THE APPLICATION OF THE CIM FORMAT IN THE MODELLING OF AN ELECTRICAL POWER SYSTEM IN THE SYNDIS-PLANS SYSTEM Zbigniew Zdun / PLANS, Mikronika Marek Wawrzyniak / Mikronika

1. THE CIM MODEL The enterprises which operate multiple complex systems increasingly stress the cooperation between these systems. An interesting proposition with respect to this subject is the package of the standards IEC 61968 and IEC 61970, which are collectively referred to as the CIM (Common Information Model). These standards form the basis for its Polish counterparts, PN-EN 61969 and PN-EN 61907. The purpose of the CIM is to introduce a standard of data exchange between various computer systems over a common abstract model of data. Each program usually utilizes its own data model. When information needs to be exchanged between different programs, usually one of them features a special driver for the data from the other program (see Fig. 1). The exchange of messages in the CIM format between various IT applications should provide essential information for all other applications which share the same common data model. The classes (types) of the CIM model are the representation of the electrical power system objects, their states and connections; they include attributes which describe their properties and relations which describe the relations between the classes. The classes are hierarchically deﬁned, which means the grouping of the same attributes and relations in sets and their representation as an abstract base of classes from which other, more detailed ones are derived.

EMS Data warehouse

SCADA

Work management

GIS

Portal

Fig. 1. Current data exchange (without CIM)

Abstract This paper presents the application of the CIM standard in the modelling of a transmission grid in the SYNDIS-PLANS system. The SYNDIS system is a SCADA type environment and has been integrated with the PLANS package, which is widely used in the NPS for calculation and analysis of power distribution. The electrical power engineering industry uses various programs the work of which is based on their proprietary data models. The data exchange between different packages is difﬁcult. Hence there was a need for developing a common data model which greatly simpliﬁes the data exchange between applications. The development work on the common

deﬁnition of the electrical power system was conducted at EPRI and resulted in the standard system/grid description, i.e the CIM (Common Information Model). This paper presents the basic rules of modelling in compliance with the CIM standard, including the description of basic CIM classes used in the modelling of the transmission grid in SYNDIS-PLANS, supplemented by a description of the electrical power system elements browser. This article also describes the method of integrating the PLANS power distribution calculation package with the SYNDIS system. A list of SYNDIS-PLANS application in electrical power engineering is also provided.

Zbigniew Zdun / PLANS, Mikronika Marek Wawrzyniak / Mikronika

mapping to model

The common model signiﬁcantly simpliﬁes the data exchange between the applications.

Application 1

Application 2

Fig. 2. Communication between applications acc. to CIM

Below is an abbreviated presentation of the set of basic CIM model classes used in SYNDIS-PLANS. Substation

represents a power switching substation

BusbarSection

is a busbar section

Bay

is a bay at the switching substation

Breaker

is a breaker (switch)

Disconnector

is the class which represents disconnectors

Terminal

is an electrical connection point of a conductor device

ConnectivityNode

is a node of connection

GroundDisconnector

is an earthing switch

PowerTransformer

is the class which represents transformers

TransformerWinding

is a transformer winding, where each winding is represented by a separate element of the TransformerWinding class

TapChanger

is a changer of the transformer taps

ACLineSegment

is a section of an alternating current line

Junction

is a point where devices are connected by zero resistance

Unit

is the magnitude measured a system, e.g. A, MWh, kV

MeasurementType

is the measurement type

Discrete

is the measurement of discrete values

Analog

is an analog measurement

ConductorType

is a type of a conductor; describes the electrical parameters of cables and conductors

WireArrangement

conﬁguration, spacing, identiﬁcation of conductors of the ConductorType class

WireType

is a type of electric conductor

Example: An abstract type, ProtectedSwitch, exists in the CIM standard, which receives attributes and relations from the Switch class. The Breaker and Disconnector classes are derived from the ProtectedSwitch type. Breaker and Disconnector contain the attributes and relations from the Switch and ProtectedSwitch classes; they also add their own speciﬁc attributes, which are not visible to the Switch and ProtectedSwitch classes. The attributes and relations added in the Breaker class are not visible in Disconnector, while the attributes added in the Disconnector class are not visible in Breaker. Some devices are modelled as built from several components, e.g. the transformer is represented by the PowerTransformer class, with its windings modelled separately by

The Application of the Cim Format in the Modelling of an Electrical Power System in the Syndis-plans System

the TransformerWinding class, including the tap changer of the TapChanger class. Fig. 3 presents an example of a substation bay. Fig. 3. An example of the line ﬁeld in a two-circuit substation

The ﬁgure presents the Bay bay which is connected with two BusbarSection busbar sections. This connection is effected by the nodes (ConnectivityNode class) cn1 and cn2, which connect to the terminals related to the busbar sections and to the disconnectors d1 and d2. The disconnectors d1 and d2 are connected at the node cn3, by its terminals. The node cn3 is also connected to a ground disconnector via the terminals (Terminal class) t1 and t2, and to the breaker b1, also via a terminal. The breaker b1 is also connected to the disconnector d3, over the node cn4 and the terminals. This disconnector is connected to the ground disconnector and the line segment via the terminals at node cn5. All objects of the Disconnector, Breaker and GroundDisconnector classes are located in the Bay bay.

2. CIM IN SYNDIS The electrical power system is modelled in SYNDIS in accordance with the CIM, which means that the elements of this system are represented in the structure of classes of this model. Each element has a unique numerical identiﬁer, Sid, which explicitly deﬁnes its element in the SYNDIS database. The system features a browser which is used to display the elements of the electrical power system modelled in the CIM system. An example of the diagram of a two-circuit substation is shown in Fig. 4. It is a two-circuit 110 kV substantions with two line bays, two 110 kV/MV transformer bays and one coupler bay.

Zbigniew Zdun / PLANS, Mikronika Marek Wawrzyniak / Mikronika

The tabulated view used in the edition of power line elements is shown in Fig. 5.

Fig. 5. The editing dialogue window of electrical power line elements

Upon switching to the topological view, a wheel chart is displayed (see Fig. 6), which presents the connections between the individual elements. The elements browser features a module for the validation of element deďŹ nitions and model correction; it also features a separate programming module, IEC 61970 Expert, for viewing the CIM standard.

The Application of the Cim Format in the Modelling of an Electrical Power System in the Syndis-plans System

Fig. 6. An example of the topological view

3. CIM MODELLING Changing a CIM grid model is quite complicated, since they require great expertise and skill in the use of the standard classes. The system features the following three wizards which facilitate editing the model: • New Substation • Line Tap-in or Tap-out • Connect Substation with Line • New Line Bay • New Bay with Power Generation • New Transformer (Load) Bay.

Fig. 7. Line Tap-in Wizard

Zbigniew Zdun / PLANS, Mikronika Marek Wawrzyniak / Mikronika

A special operating mode has been prepared for power distribution analysis. This mode allows performing analysis irrespective of edition and maintenance. The operator can easily perform calculations with the supplemented grid model by basing on current or historic data; the operator can also manually correct the states of all elements and change any of their electrical parameters.

4. SYNDIS-PLANS The SYNDIS system has been integrated with the PLANS package to enable simulations from measurement data of the electrical power system states on the level of a power distribution company or a group which cover a certain isolated and coherent fragment of the 110 kV grid. When simulating the states of an isolated 110 kV subgrid, the EHV transmission grid must also be accounted for, along with a certain part of the 110 kV grid, i.e. of adjacent power companies. Hence, it is possible to isolate an internal grid for which measurements from the SYNDIS are available, and an external grid in a static state. The assumed input database is the NPS model in a normal network system. Based on the grid model in a normal network system, the CIM of the internal grid is built as monitored in SYNDIS. The external grid is always loaded from the NPS base model. The internal grid model is defined by a list of interface nodes between the CIM-modelled grid and the remaining part of the grid in the NPS model. Note that the NPS model includes much more data than the CIM standard, yet the CIM enables generating additional classes which have not been defined in the standard. Hence additional objects are introduced to retain the integrity of the SYNDIS CIM data with the data in the NPS models. The NPS model can be dynamically substituted. A model from the normal system is assumed at first, but also a daily model (DACF) can be assumed.

Fig. 8. The main screen with the grid topology

The SYNDIS system operation is based on a cyclic development of an internal grid from the CIM and measurement data. This model is then transferred to the PLANS package. The PLANS package loads the complete NPS model, then the internal grid is removed and the subgrid is loaded from SYNDIS. Based on such a model structure, estimation of the state vector can be calculated, following which the simulation calculations are launched in the PLANS package. By default, the SYNDIS-PLANS package displays the grid state – the actual connection conﬁguration and the measurement data; it also presents the calculation data from PLANS in the same graphical diagrams. Fig. 8 and 9 present an example of the screen with measurement and calculation data.

The Application of the Cim Format in the Modelling of an Electrical Power System in the Syndis-plans System

During the simulation, the grid model is built for the given time point and then it is possible to simulate various grid operating conditions and calculate the following: power distribution, N-1 analysis, voltage stability, losses, optimisation, faults, and safety system settings. The simulations can also be performed for historical states in the retrospective mode.

Fig. 9. The view of a substation on the map with measurement and calculation data

5. IMPLEMENTATION Integration of SYNDIS and PLANS was, at first, a pilot installation for the testing of voltage stability in the north-eastern part of the National Power System at PSE Północ. The NPS model has been corrected based on the measurement data acquired by SYNDIS from the parts of the 110 kV grid. The voltage stability reserves have been determined for selected nodes; it has also been possible to calculate the voltage stability reserve for the entire power system. The use of electrical grid modelling in CIM has been used during the SYNDIS-PLANS deployment at the Energia-Pro power control centre in Wrocław. SYNDIS collects measurement data from five branches of Energia-Pro (the former five ZE – power facilities); SYNDIS calculates the power distribution and faults, considering the full NPS grid – it is also possible to calculate the fault safety setting cards of 110 kV lines. The SYNDIS-PLANS has been installed in Nicosia, Cyprus, for the monitoring and control of the grid in northern Cyprus. The 132 kV and 66 kV grids have been fully modelled in the CIM standard, while the residual external network has been built for the purpose of a potential connection of the northern and southern parts of the grid. The package uses modules for power distribution calculations, faults calculations and optimisation; additionally, an estimator of the state vector has been tested. Another installation which uses the CIM modelling is the operating states simulator for substation dispatcher training, installed in PSE Zachód. The selected HV power substations of the NPS have been modelled in the CIM standard, while the users can monitor the changes in the power distribution in real time while switching at their substations.

Zbigniew Zdun / PLANS, Mikronika Marek Wawrzyniak / Mikronika

90 6. SUMMARY

SYNDIS-PLANS is a modern system designed for real-time monitoring and analysis of the electrical power system stated. It enables observation of the grid operating state directly from the measurement data and from the calculation data with respect to the state vector estimation or directly following power distribution calculations. It is also possible to simulate the scheduled states of the grid, e.g. shutting down of lines, transformers, generators, etc. The power distribution calculations enable the monitoring of the electrical power system safety. Integration of PLANS with SYNDIS has uniﬁed the GUI. The grid state, based on both measurements and simulations, is presented on the same graphical diagrams and with the use of one user interface.

REFERENCES 1. Zdun Z., Wykonanie programu PLANS PSE w wersji dla systemu operacyjnego Windows NT z uwzględnieniem roz szerzonej struktury danych oraz wprowadzenia makropoleceń, a work commissioned by PSE SA, 2000. 2. Zdun Z., Zdun T., Wawrzyniak M., Wronek P, Wykorzystanie systemu SYNDIS-PLANS do oceny stabilności napięcio wej w wybranych obszarach Krajowego Systemu Energetycznego, III Konferencja Naukowo-Techniczna „Blackout” Poznań, 2008. 3. IEC 61970 Energy management system application program interface (EMS-API) - Part 301: Common information model (CIM) base, IEC, edition no. 2.0, 2009. 4. IEC61968 Application integration at electric Utilities - System interfaces for distribution management - Part 1: Interface architecture and general requirements, IEC, edition no. 1.0, 2010. 5. Conference reference material from the CIM Users Group Meeting of Genval (Belgium), 2009, available at: http:// mug.ucaiug.org/Meetings/Genval2009/Presentations.

,1)250$7,21 )25 $87+256 :H DFFHSW RQO\ WKH DUWLFOHV WKDW KDYH QHYHU EHHQ SXEOLVKHG EHIRUH (DFK WH[W VHQW WR $FWD (QHUJHWLFD LV VXEMHFW WR VFLHQWLğF UHYLHZ 7KH HGLWRULDO PHHWLQJ GHFLGHV ZKHQ WKH WH[WV DUH SXEOLVKHG :H GR QRW VHQG WKH WH[WV EDFNV WR WKH DXWKRUV 3OHDVH VHQG WKH PDWHULDOV ZKLFK PXVW FRQVLVW RI WKH HQWLUH SDFNDJH RI IRXU FRPSRQHQWV DUWLFOH DEVWUDFW ELEOLRJUDSKLFDO QRWH SKRWRJUDSK RI WKH DXWKRU HOHFWURQLFDOO\ WR WKH IROORZLQJ DGGUHVV UHGDNFMD#DFWDHQHUJHWLFD RUJ NOTE! ( PDLO FRQWHQW PXVW LQFOXGH FRQWDFW GDWD JLYHQ QDPH DQG VXUQDPH GHJUHH WHOHSKRQH QXPEHU VWDWLRQDU\ DQG PRELOH DQG H PDLO DGGUHVV 1. ARTICLE ľ 7H[W OHQJWK 1RW PRUH WKDQ VWDQGDUG SDJHV FKDUDFWHUV VL]H LQWHUOLQHV FROXPQ ľ )RUPDW :25' ğOH DQG 3') DV D PXVW ľ )RUPXOD SDWWHUQV 3OHDVH EH YHU\ FDUHIXO ZLWK SXQFWXDWLRQ VWDQGDUGV ķ×” LV XVHG DV D VLJQ RI multiplication ([DPSOHV

ľ )RRWQRWHV $W WKH ERWWRP RI HDFK SDJH ([DPSOHV -RXUQDO RI ODZV 1R SRV RI 2FWREHU 7KH H[DPSOHV DUH GHDOW ZLWK LQ WKH ERRN )LHGRU % *UDF]\N $ -DNXEF]\N = 5\QHN SR]ZROHñ QD HPL VMÚ ]DQLHF]\V]F]Hñ QD SU]\NïDG]LH 62 Z HQHUJHW\FH SROVNLHM >3ROOXWLRQ (PLVVLRQ $OORZDQFHV 0DUNHW LQ 3ROLVK 3RZHU (QJLQHHULQJ RQ WKH ([DPSOH RI 62 @ :\GDZQLFWZR (NRQRPLD L ¥URGRZLVNR %LDï\VWRN SS ļ ľ /LWHUDWXUH $W WKH HQG RI WKH WH[W ([DPSOHV /DUVHQ ( 9 6ZDQQ ' $ $SSO\LQJ 3RZHU 6\VWHP 6WDELOL]HU ,((( 7UDQV 3RZHU $SSDU 6\VW YRO SS ļ 0DGDMHZVNL . 6REF]DN % 7UÚEVNL 5 3UDFD RJUDQLF]QLNöZ Z XNïDGDFK UHJXODFML JHQHUDWRUöZ V\QFKUR QLF]Q\FK Z ZDUXQNDFK QLVNLFK QDSLÚÊ Z V\VWHPLH HOHNWURHQHUJHW\F]Q\P PDWHULDï\ NRQIHUHQF\MQH $3( ĳ *GDñVN

2. ABSTRACT ľ 7H[W OHQJWK 1RW PRUH WKDQ FKDUDFWHUV ZLWKRXW VSDFHV ľ )RUPDW :25' ğOH DQG 3') DV D PXVW %,%/,2*5$3+,&$/ 127( ľ 7H[W OHQJWK &D FKDUDFWHUV ZLWKRXW VSDFHV ľ )RUPDW :25' ğOH DQG 3') DV D PXVW 3+272*5$3+ ľ )RUPDW &RORXU RU EODFN DQG ZKLWH SKRWRJUDSK MSJ RU WLII GSL

etica.org

energ www. acta