Iaetsd improvement of dynamic and steady state by Iaetsd Iaetsd

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Improvement of Dynamic and Steady State Responses in Combined Model of LFC and AVR Loops of One-Area Power System using PSS 1

1,2

Anil Kumar Sappa, 2Prof.Shyam Mohan S.Palli Dept. of EEE, Sir C R Reddy College of Engg., Andhra Pradesh, India

Abstractâ&#x20AC;&#x201D;This paper describes the improvement in stability by reducing the damping oscillations in one area power system using a power system stabilizer. A power system model, which includes both LFC and AVR loops, is considered. Low-frequency oscillation studies are made.PSS is designed to improve the stability of the system. The simulation results obtained indicate that, adding a PSS to a combined model of LFC and AVR improves the dynamic stability by reducing the low-frequency oscillations.

LFC since many years [7]-[8], but these researches gave little attention to AVR effects on the results. In fact, in LFC power system control literature there is a lack of stability analysis for AVR effects or the mutual effects between these loops. Usually, these studies are based on the assumption that there is no interaction between the power/frequency and the reactivepower/voltage control loops. But in practical systems some interactions between these control channels do exist during dynamic perturbations [9]. Also by neglecting the effect of voltage deviation on load demand, an important interaction in LFC systems is ignored. A combined model with LFC and AVR loops and their mutual effects is considered. In this paper the power system is designed by adding a PSS to a combined model of LFC and AVR loops in order to improve for more dynamic stability. The interaction of coupling effects between LFC and AVR loops are shown [3] and also the performance of proposed model is shown with simulations. The results of the proposed method with PSS are compared with a combined model without adding PSS and also by separate models of LFC and AVR loops without any interaction between those loops. The simulations are shown by adding a PSS to a combined model of LFC and AVR loops. It is observed that this proposed model can improve the dynamic stability of a complete power system by reducing the damping oscillations.

Index Termsâ&#x20AC;&#x201D; Automatic Voltage Regulator, Power System, Load Frequency control, Power system stabilizer, voltage, deviations, stability.

I. INTRODUCTION The change in operating conditions of a power system leads to low frequency oscillations of small magnitude that may exist for long periods of time. In some cases these oscillations will limit the amount of power transmitted through interconnecting lines. So a power system stabilizer is designed to provide an additional input signal to the excitation system in order to damp these power system oscillations [1]. The interconnected power system model for low frequency oscillation studies should be composed of mechanical and electrical loops. These oscillations can be damped by varying the exciter and speed-governor control parameters [2]. Furthermore, it has been shown that the load-voltage characteristic of the power system has a significant effect on its dynamic responses, and suggestions have been made for the proper representation of these characteristics in simulation studies [3]-[5].For economic and reliable operation of a power system, the two main control loops are required. The Load Frequency Controller loop (LFC) and Automatic Voltage Regulator loop (AVR) as shown in Figure 1. The turbine is fed by speed governor whose steam rate can be controlled by varying the internal parameters. Automatic Generation Control method deals with frequency through the LFC loop and with voltage through the AVR loop. The main purpose of these two loops is to maintain frequency and voltage at permissible levels [6]. Lot of studies have been made about

Fig 1. Automatic generation control with LFC and AVR loops.

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Fig 2. Block diagram model of Load Frequency Control (LFC).

comprises of excitation control mechanism and its main aim is to control the field current of the synchronous machine. Here the controlling of field current is to regulate the voltage generation by the machine. The maximum permissible limit for voltage is about 5  6% .

II. LOAD FREQUENCY CONTROL Load Frequency Control (LFC) loop is the basic control mechanism loop in the operation of power system. As the active power demand changes continuously with respect to load changes ,steam input to turbo-generators (water input to hydro-generators) must be continuously regulated in order to maintain the constant active power demand, failing which the machine speed changes with consequent change in frequency which may be highly undesirable. The maximum permissible change in power frequency is about ± 0.5Hz. Hence continuous regulation is to be provided by the LFC system to the generator turbine. At the time of Load change, the deviation from the nominal frequency is referred as frequency error (∆f), This symbol indicates that there is a mismatch and it can be used to send the appropriate command to change the generation by altering the LFC system [6].From Figure 2, it is seen that there are two control loops, one is primary control loop and the other one is secondary control loop. With primary control loop, if there is any change in system load, it will result in to a steady-state frequency deviation, which depends on the governor speed regulation. To nullify the frequency deviation, we should provide a reset action. The reset action is accomplished by secondary control loop which introduces an integral controller to act on the load reference setting in order to change the speed at the desirable operating point. Here the integral controller increases the system type by 1 which forces and makes the final frequency deviation to zero. Thus by using integral controller action in LFC system a zero steady state frequency error and a fast dynamic response will be achieved. The gain of the integral controller should be adjusted such that its transient response is satisfactory. The negative sign for gain of integral controller shown in Figure 2 is to provide a negative or reduced command signal for a positive frequency error.

Fig 3. Block diagram model of AVR system.

The Amplifier and Exciter block shown in Figure 3 regulates and amplifies input control signals to an appropriate level which is convenient to provide DC power to the generator field winding. This block must be expandable if the excitation system has rotating exciter and voltage regulator [2]. Depending upon how the DC supply is given to the generator field winding, the excitation systems are classified as DC, AC, and Static excitation systems [1]. IV. MATHEMATICAL MODELLING OF POWER SYSTEM In order to improve the dynamic stability of overall system, modeling of major components of power system is required. The study of low frequency oscillation studies is completely based on a single machine connected to an infinite bus system [2]. The single machine connected to an infinite bus system through transmission lines with a local load is shown in Figure 4. Here Z is the series impedance of transmission line and Y is the shunt admittance representing the local load.

III. AUTOMATIC VOLTAGE REGULATOR The basic mechanism of Automatic Voltage Regulator (AVR) is to regulate the system voltage magnitude. The AVR

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Iq 

Vd Xq

ISBN: 378 - 26 - 138420 - 5

(5)

Eq   Vq  X d  I d

(6)

To determine the values of V0 and δ0.From the definition of torque angle (δ0) which is the angle between the infinite-bus voltage (V0) and the internal voltage (Eq ′) [2], we have

Fig 4. Single machine connected to an infinite bus model of a power system.

A. Combined model of LFC and AVR of one-area power system A Combined model of LFC and AVR of one-area power system with PI controller is shown in figure5 .The PI controller used in figure 6 produce an output signal with a combination of proportional and integral controllers and the transfer function of that signal consists of a proportional gain (KP) which is proportional to the error signal and the term consisting of integral time constant (Ti) which is proportional to the integral of error signal [10]. Transfer function of PI controller = K 1  1  p    Ti s 

(1)

The block diagram shown in Figure 5 shows the coupling effects between LFC and AVR loops [9].Here the gain constants K1, K2, K3, K4, K5 and K6 are calculated using the equations (2)-(27) [2]. Where K1 is the change in electrical power for a change in rotor angle with constant flux linkages in the d-axis, K2 is change in electrical power for a change in the direct axis flux linkages with constant rotor angle, K3 is an impedance factor, K4 is the demagnetizing effect of a change in rotor angle, K5 is the change in terminal voltage with change in rotor angle for constant Eq′ and K6 is the change in terminal voltage with change in Eq′ for constant rotor angle.

  Vt 2  2  Vd  PV P  Q   e t e  e X   q   

   

1/2

V0 d  C1Vd  C2Vq  Rx I d  XI q

(7)

V0 q  C2Vd – C1Vq  XI d  Rx I q

(8)

V  0  tan 1  0d  V0q 

(9)

  

V0  (V0 d 2  V0 q 2 )1/2

(10)

R1  Rx  C2 X d 

(11)

R2  Rx  C2 X q

(12)

X 1  X  C1 X q

(13)

X 2  X  C1 X d 

(14)

Z e 2  R1 R2  X 1 X 2

(15)

C1  1  Rx G  XB

(16)

C2  XG  Rx B

(17)

Yd 

C1 X 1 – C2 R2 Ze2

(18)

Yq 

C1 R1  C2 X 2 Ze2

(19)

Fd 

V0 ( R2 cos 0  X 1sin 0 ) Ze2

(20)

Fq 

V0 ( X 2cos 0  R1sin 0 ) Ze2

(21)

(2)

1/ 2

Vq  Vt 2  Vd 2  Id 

Pe  I qVq Vd

(3)

(4)

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Fig 5. PSS with combined LFC and AVR.

B. Combined LFC-AVR model with PSS

Finally, the constants K1 to K6 can be represented as

K1  Fd  X q – X d  I q  Fq  Eq   X q – X d   I d 

The proposed model of combined LFC and AVR with PSS is shown in figure 5 for dynamic improvement of overall system response.



K 2  I q  Yd  X q  X d   I q  Yq  Eq    X q  X d   I d 

(24)

K3 

1 1   X d  X d   Yd 

(24)

K4 

Xd  Xd  Fd

(25)

 ( X d Vq )   X qVd  K 5  Fd    Fq    Vt   Vt  K6 

 ( X d Vq )   X qVd   Yd    Yq   Vt  Vt   Vt 

The basic function of a power system stabilizer (PSS) is to provide an additional input signal to the regulator to damp the Power System oscillations. This can be achieved by modulating the generator excitation in order to produce a component of electrical torque in phase with the rotor speed deviations. Some of the commonly used input signals are rotor speed deviation, accelerating power, and frequency deviation. A block diagram model of PSS is shown in Figure 6.

(23)

(26)

(27) Fig 6. Block diagram model of PSS.

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The frequency deviation (∆f) is used as input signal for PSS. Here the PSS will generate a pure damping torque at all frequencies that is the phase characteristics of PSS must balance the phase characteristics of GEP(s) at all frequencies. As this is not practicable, the time constants of PSS are to be adjusted in order to produce the phase compensation characteristic which shows the best performance [11]. The model of PSS shown in Figure 6 consists of three blocks, phase compensation block, washout filter block and gain block. The phase compensation block provides a suitable phase-lead characteristic to compensate the phase lag between the input of the exciter and the machine electric torque. The transfer function GEP(s) of the block shown with dashed lines in in figure 5 which represents the characteristics of the generator excitation and power system is given by [11]

GEP  s  

K a K3 K 2 (1  sTa )(1  sK 3Td 0 )  K a K 3 K 6

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From the simulations results shown in Figures 7-10 it can be observed that, by using PSS the settling time is reduced with a better dynamic stability. Hence desirable damping for low frequency oscillations in overall single-area power system is achieved.

(28)

The washout block acts as a high-pass filter. For local mode of oscillations, the washout time constant should be in between 1 to 2s for desirable operating point [12]. The PSS gain is chosen such that it is fraction of gain corresponding to instability [11].The PSS complete transfer function is given by

 sTW PSS (s)   1  sTW

  KS 

 1  sT1    1  sT2 

Fig 7.Frequency deviations in a single-area power system in pu.

(29)

Where GEP(s) is the plant transfer function through which the stabilizer must provide compensation. TW is washout time constant. KS is the gain of the stabilizer. T1 and T2 are the time constants of phase compensator. An optimal stabilizer is obtained by the proper selection of the time constants and gain of the PSS. V. SIMULATION RESULTS In this paper a power system stabilizer is designed to show the improvement in dynamic response for combined model of LFC and AVR. In this study the performance of the proposed model of PSS with combined LFC and AVR is compared with combined model of LFC and AVR loops and also with classic model of load frequency control system by separating AVR loop (i.e. excitation system). The simulations shown in this paper are carried out using MATLAB platform. The simulations results shown in this paper are performed by assuming real power as 0.9 pu, reactive power as 0.61 pu and the machine terminal voltage as 0.91 pu.

Fig 8.Turbine output power deviations in a singlearea power system in pu.

Turbine and Governor System Parameters are given in table-I, One Machine-Infinite Bus System Parameters are given in table-II and AVR and Local parameters are given in tableIII. The calculated gain parameter constants in AVR system for load change in real power at 10% for LFC is given in Table IV.

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TABLE III.

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AVR AND LOCAL LOAD PARAMETERS IN PER UNIT VALUE.

0.05

0.89

0.862

TABLE IV.

CALCULATED GAIN PARAMETER CONSTANTS IN AVR SYSTEM IN P ER UNIT VALUE.

0.40

1.85

0.38

0.22

0.07

1.02

VI. CONCLUSION In this paper the Load Frequency Control loop and Automatic Voltage Regulator loop are combined to show the mutual effects between these two loops in a one-area power system. A Power System Stabilizer is designed to improve the dynamic and steady state responses for one-area power system. Finally it is observed that a better dynamic stability is accessed by using a PSS to the combined LFC-AVR model.

Fig 9.Internal electrical power deviations in a singlearea power system in pu.

NOMENCLATURE

Fig 10.Terminal voltage deviations in a single-area power system in pu.

TABLE I.

T URBINE AND GOVERNOR SYSTEM PARAMETERS FOR LFC IN PER UNIT VALUE.

102

0.32

0.06

1.7

TABLE II.

ONE MACHINE-INFINITE B US SYSTEM PARAMETERS IN P ER UNIT VALUE.

X d'

Td 0 '

1.973

0.82

0.1

7.76

0.004

0.74

R Ka

The overall gain of excitation system

The overall time constant of excitation system

Pm

Turbine output power deviation

PL

Load disturbance

The equivalent overall gain of a power system

Speed regulation due to governor action

The equivalent time constant of a power system

The equivalent gain of a sensor

The equivalent time constant of a turbine

The equivalent time constant of a governor

E q '

Deviation of internal voltage

 Td 0 '

Deviation of torque angle Transient time constant of generator field

Synchronous reactance of d-axis

Xd '

Transient reactance of d-axis

Vref

Reference input voltage

Infinite bus voltage

Terminal voltage

Stabilizer output

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[7] E.Rakshani and J.Sadeh,”A Reduced-Order control with prescribed degree of stability for Two-Area LFC System in a deregulated environment”, Proceeding 2009 IEEE PES Power Systems Conference and Exhibition (PSCE09). [8] J.Sadeh and E.Rakshani,”Multi-area load frequency control in a deregulated power system using optimal output feedback method, “International conf. on European Electricity Market, pp.1-6, May 2008. [9] Haadi Saadat, Power system analysis, Tata McGraw-Hill Edition 2002, pp.528. [10] K.Ogata, Modern Control Systems, 5th edition, Prentice Hall Publications, 2002, pp.669-674. [11] E.V.Larsen and D.A.Swan,”Applying power system stabilizers parts I, II and III”, IEEE Trans. On Power Apparatus and Systems, Vol.PAS-100, June-1981, pp.3017-3046. [12] P.Kundur, M.Klein, G.J.Rogers and M.S.Zywno,”Application of power system stabilizers for enhancement of overall system stability”, IEEE Trans. on Power systems, Vol.4, No.2, May 1989, pp.614-626.

REFERENCES [1] P.Kundur, Power System Stability and Control, McGraw-Hill Inc., 1994, pp.766-770. [2] Yau-NaN yu, Electrical Power System Dynamics, London Academic Press, 1983, pp.66-72. [3] E.Rakhshani, K.Rouzehi, S.Sadeh, “A New Combined Model for Simulation of Mutual Effects between LFC and AVR Loops”, Proceeding on Asia-Pacific Power and Energy Engineering, Wuhan, China, 2009. [4] S.C.Tripathy, N.D.Rao, and L.Roy,”Optimization of exciter and speed governor control parameters in stabilizing intersystem oscillations with voltage dependent load characteristics. “Electric power and energy systems, vol.3, pp.127-133, July 1981. [5] K.Yamashita and H.Miyagi,”Multivariable self-tuning regulator for load frequency control system with interaction of voltage on load demand”, IEEE Preceeedings-D, Vol.138, No.2, March 1991. [6] D.P.Kothari, I.J.Nagrath “Modern Power System Analysis”, Third Edition, pp.290-300

Authors Biography –

Anil Kumar Sappa received his B.Tech degree in Electrical and Electronics Engineering from JNTUK, Andhra Pradesh in 2011. He is currently pursuing M.E degree in Power Systems and Automation from Sir C R Reddy college of Engineering affiliated to A.U Visakhapatnam, Andhra Pradesh. His areas of interests include Power Systems.

Prof Shyam Mohan S Palli received his B.Tech degree in Electrical and Electronics Engineering from JNTU Kakinada in 1978; M.Tech degree in Power systems from same institute in 1980. He joined in teaching profession in 1981. He has put up an experience of 33 years in teaching as lecturer, Asst. Professor, Professor. Presently he is working as Professor and HOD, EEE of Sir C.R. Reddy college of Engineering, Andhra Pradesh. He is author of Circuits and Networks, Electrical Machines Published by TMG New Delhi. He published many papers in referred journals and conferences. His areas of interests include Machines and Power Systems.

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