ISBN:378-26-138420-0240
INTERNATIONAL CONFERENCE ON CIVIL AND MECHANICAL ENGINEERING, ICCME-2014
LOAD AREA FREQUENCY CONTROL FOR MULTI AREA POWER SYSYTEM HAVING COMMINICATION DELAYS P. MAHESH P.G scholar ABSTRACT Load frequency control (LFC) has been used as an effective ancillary service in power systems for many years . An effective power system market highly needs an open communication infrastructure to support the increasing decentralized property of control services. Normally there exist usually unreliable factors in open communication links, such as time delays and communication failures. When open communication, infrastructures are embedded into modern power system to support vast amounts of data exchange, it becomes more challenging to keep the complex power system reliable and stable. In specific, we consider a general case that there exist time varying delays in two channels. One is the feed-forward channel in which control centers send control signals to remote terminal units (RTUs). The other one is the feedback channel where measurement signals are transmitted from RTUs to the control centers. The state space models of LFC including two channel time varying delays are presented. INTRODUCTION Load frequency control basic objective is to restore the balance between load and generation in each control area. With the deregulation of power industry, the monitoring and operation of power system among interconnected areas are becoming much more challenging than ever before. Several large blackouts happened for lack of system level of situation awareness, such as the well-known 2003 North American and European blackouts. To support the vast amounts of information exchange in realtime power system, the rapidly developed high speed open communication infrastructures are urgently needed to be implemented in large scale power system. While the advanced open communication
DR.K.RAMASUDHA Professor links can be used to support the large amount of remote data transmission, they bring in new challenges in reliability and stability issues for next generation intelligent power system. As it is well known that communication networks, especially wireless networks, are unreliable because time delays and packet losses are unavoidable. These network-associated problems will degrade the dynamic performance of power system and even make it instable. In conventional LFC schemes, dedicated communication channels are used for transmission of measurements to the control center and control signals from the control center to the generator unit. The open communication infrastructure will also allow a bilateral market for the provision of load following and third party frequency control. Under this case, a certain part of generator units will receive a control signal to increase or reduce the power output, from either a control center or from the customer side directly. With the introduction of open communication channel, both constant delay and time-varying delay will be arisen in LFC problem. The operation of frequency control is fundamental in determining the way in which the frequency will change when load changes happen. When open communication links are embedded in power system, new control strategies are also necessarily needed to keep LFC performance robust to unreliable factors such as time delays and communication failures. MODEL OF LFC WITH TIME VARYING DELAYS In this section, the classical model of LFC is extended to include time varying delays existing in both states and control inputs for multi-area interconnected power systems.
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT 34
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ISBN:378-26-138420-0241
INTERNATIONAL CONFERENCE ON CIVIL AND MECHANICAL ENGINEERING, ICCME-2014
For LFC studies, all the generators in each area are represented equivalently by one single machine. In the following models in this paper, we omit the time ݐin every variable for convenience, such as ( )ݐis written as ݔ. For area i, the dynamics of LFC are described by 1 1 1 − Di ∆f i• = ∆f i + ∆P mi − ∆P ij ∆P Li tie − Mi Mi Mi Mi −1 1 ∆P •mi = ∆P mi + ∆P vi T chi T chi −1 1 1 ∆ P •vi = ∆f i − ∆P vi + ∆P ci R i T gi T gi T gi P ij tie = T ij (∆P i − ∆P j)
where ∆ f i frequency deviation
∆pmi generator mechanical power deviation ∆Pvi turbine valve position deviation ∆Pci load reference set-point
∆Pij tie tie-line power flow between area i and j load deviation M i moment of inertia of generator i; D i damping coefficient of generator i;
∆P Li
T gi time constant of governor i T chi time constant of turbine i T ij stiffness constant Ri speed droop coefficient N x•i . = Ai xi + Bi ui + ∑ Aij x j + F i ∆P Li j =1, j ≠i
− Di Mi 0 Ai = −1 Ri T gi N ∑ T ij − j =1, j ≠i
[
xi = ∆f
−1 Mi
1 Mi
0
−1 T chi 0
1 T chi −1 T gi
0
0
∆Pmi ∆Pvi ∆Pij
]
0 0 0
0 0 Aij = 0 T ij
0 0 0
0 0 0 0 0 0 0 0 0
Bi = 0 0
−1
Fi =
Mi
1 T gi
0
0 0 0
The ACE signal in a multi-area LFC scheme is defined as follows: ACEi = Bi ∆f i + ∆Ptiei . For the whole multi-area power system, an linear time invariant(LTI) interconnected model is given by • x = Ax + Bu + F ∆P L Moreover, we consider two time varying bounded delays ݀1()ݐ, ݀2( )ݐexisting in states x and control input u. The two delays satisfy the following conditions: 0 ≤ ݀1(ˆ݀ ≤ )ݐ1, 0 ≤ ݀2(ˆ݀ ≤ )ݐ2; ݀1˙(ߩ ≤ )ݐ1 ≤ 1, ݀2˙(ߩ ≤ )ݐ2 ≤ 1. The LFC model with states and control inputs delays is given by • x = Ax + Ad x(t − d1 (t )) + Bu + B d _ u (t − d 2 (t )) + F ∆P L where T Ad = diag {Ad1 Ad 2 Adn} T Bd = diag{Bd1 Bd 2 Bdn} − Di −1 0 0 Mi Mi 0 0 0 Adi = 0 0 0 0 0
0
Bdi = 0 0
0 0
0
1 0 T gi
i tie INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT 35
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ISBN:378-26-138420-0242
INTERNATIONAL CONFERENCE ON CIVIL AND MECHANICAL ENGINEERING, ICCME-2014
DELAY DEPENDANT CONTROLLER FOR LFC In this section, we proposed the following delay dependant full state feedback controller for power system: u = Kx . After combining system with the above controller, the closed–loop system is given by • x = Acl x + Ad x(t − d1 (t )) + B d Kx (t − d 2 (t )) + F ∆P L
Acl = A + BK CASE STUDIES In this section, the two-area model shown in Fig.1 is used to evaluate the proposed control method. The generators in each area are modeled as single equivalent generator. In order to illustrate the effectiveness of the designed controller, comparisons are conducted with conventional PI controller used in LFC. Matlab/Simulink is chosen as the simulation environment. The variable transport delay elements in Matlab/Simulink are used to simulate the effects of the time delays. Here, two time varying delays are considered, existing in both the feed-forward channel (control set-points sent from control center to remote terminal units (RTUs)) and feed-back channel (measurements from
remote terminal units (RTUs) to control center) in power system. The varying rates of the two time varying delays satisfy ߩ1 ≤ 0.2, ߩ2 ≤ 0.2 x1• = A1 x1 + Ad1 x1 (t − d1 (t )) + B1 u1 + B d1 u1 (t − d 2 (t )) + A12 x 2 + F1 ∆P L1 • x 2 = A2 x 2 + Ad 2 x 2 (t − d1 (t )) + B 2 u 2 + Bd 2 u 2 (t − d 2 (t )) + A21 x 2 + F 2 ∆P L2
All the parameters are given in appendices. In this study, we use 100MVA base unit as the for per unit (p.u) calculations. The two ∆P1 = 0.2 p.u ∆P2 = 0.1p.u The transfer function of the conventional PI controller for 0. 5 each area is 0.5 + s Two cases are studied in this paper case 1: the conventional PI load frequency control with time-varying communication delays existing in two channels case 2: the proposed delay dependent load control with time-varying communication delays existing in two channels
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ISBN:378-26-138420-0243
INTERNATIONAL CONFERENCE ON CIVIL AND MECHANICAL ENGINEERING, ICCME-2014
CONCLUSION This paper considers the modeling and delay dependent stabilization problems of LFC for power system with both feed-forward feed and feedback time varying communication delays. The state space models of LFC are presented, including the two-channel channel time varying delays. In case studies, two-area area LFC model is built to evaluate the effectiveness of the proposed method. With the comparison to the conventional PI controller, it is shown that the proposed controller can keep the power system robustly stable and good convergence rate when there exist time varying delays in i two channels. Fig(2) for area2
Fig(3) for area 1
REFERENCES [1] Shichao liu,Xiaping P.Liu,”Load frequency control for wide area monitoring and control system in power system with communication links”,IEEE transaction 2012. [2]G.Anderson,P.Donalek et.al,”Causes of the 2003 major grid blockouts lockouts in North America and Europe,and recommended means to improve system dynamic performance”,IEEE Transcationspowersystems,vol.20,n0.4,pp.19 22-1928,2005 [3] D. Karlsson, M. Hemmingsson and S. Lindahl, “Wide area system monitoring and control: terminology, ogy, phenomena, and solution implementationstrategies ,” IEEE Power and Energy Magazine,, vol. 2, no. 5, pp. 68-76, 2004. [4]] J. Machovski, J. W. Blalek, and J. R. Bumby, “Power system dynamics and stability,” John Wiley & Sons, 1998. [5] S. Bhovmik, K. Tomsovic, and A. Bose, “Communication models for third party load frequency control,” IEEE Transactions on PowerSystems PowerSystems, vol. 19, no. 1, pp. 543-548, 2004 [6] L. Jiang, W. Yao, Q. H. Wu et. al, “Delay-dependent dependent stability for load
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ISBN:378-26-138420-0244
INTERNATIONAL CONFERENCE ON CIVIL AND MECHANICAL ENGINEERING, ICCME-2014
frequency control with constant and timevarying delays,” in Power and Energy Society General Meeting, 2009. PES ’09. IEEE , Calgary, AB, Canada, 2009 [7] S. Xu, J. Lam, and Y. Zou,“improved conditions for delay-dependant robust stability and stabilization of uncertain discrete time delay systems,”Asian J. Control, vol. 7, no. 3, pp. 344-348, 2005 [8] L. E. Ghaoui, F. Oustry, and M. Aitrami, “A cone complementary linearization algorithm for static outputfeedback and related problems,” IEEE Transactions on Autom. Control, vol. 19, no. 3, pp. 1508-1515, 2004. [9] V.C. Gungor, and F.C. Lambert, “A survey on communication networks for electric system automation,” Computer Networks, vol. 50, no. 7, pp. 877-897, 2006 [10] P. Kundar, Power system stability and control, Stateplace, New York: McGraw-Hill, 1994. APPENDIX A Two–area power system parameters are shown as follows Area 1: T ch1 = 0.17 s, T g1 = 0.4s, R1 = 0.05, D1 = 1.5, M 1 = 12, 1 B1 = + D1 = 41.5 R1 Area 2: T ch2 = 0.2s, T g 2 = 0.35s, R2 = 0.05, D 2 = 1.8, M 2 = 12, 1 + D2 = 61.8 B2 = R2
APPENDIX B Area 2 − 0.15 0 A1 = − 57.1429 0. 5 0 0 0 0 A21 = 0 0 0.5 0
0.0833
0
− 0.0833
−5
5
0
0
− 2.8571
0
0
0
0
0 0
0 0 0 0
0 0
T B2 = [0 0 2.8571 0] − 0.15 0 0 − 0.0833 Ad 2 =
0
0 0
0
0
0 0
0
0
0 0
0 T Bd 2 = [0 0 2.88571 0] T F 2 = [− 0.0833 0 0 0] AREA1 − 0.125 A1 =
0
0.0833
− 0.0833
0
− 5.8824 5.8824
0
− 50
0
− 2.5
0
0.5
0
0
0
0 0 A12 = 0 0.5
0 0 0
0 0 0
0 0 0 0 0 0
− 0.125 0 Ad1 = 0 0
0 0 − 0.0833 0 0
0
0 0
0
0 0 T B1 = [0 0 2.5 0] T Bd1 = [0 0 2.5 0]
0
T F1 = [− 0.833 0 0 0]
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