Second International Conference on Electrical Engineering 25-26 March 2008

University of Engineering and Technology, Lahore (Pakistan)

978-1-4244-2293-7/08/$25.00 ©2008 IEEE.

Abstract—In this paper a new lead-lag supplementary damping controller is introduced for damping power system oscillations using SVC, which it's gain is controlled with a mamdani type fuzzy logic controller. Here the global signals are used as the input of damping controller, because some of the oscillating modes aren't seen in the local signals. The residue index function method is used to select this input signal. The phase compensation method is used to design the lead-lag controller parameters. To validate this controller, some computer simulations are used on a 4-machine 2-area test system. The results show the effectiveness of applying the fuzzy gain in damping controller.

I. INTRODUCTION ower systems are often subject to low frequency electro-mechanical oscillations resulting from electrical

disturbances. Interarea low frequency oscillation may arise as a result of lack of damping torque when there are weakly coupled transmission lines carrying large energy exchange between two areas. Oscillation between two areas becomes the main reason that constrains the power transmission capability, and the serious oscillation can even cause cascading failure.

The oscillations of one or more generators in an area with respect to the rest of the system are called local modes, which can be damped by traditional method such as power system stabilizers. Generally, power system stabilizers are designed to provide damping against this kind of oscillations. However, damping in the system is not enough for the oscillation between two areas, which becomes the main restriction of the power that can be transmitted. Due to the large size of modern power systems, the number of oscillation modes, both local and inter-area, experienced by a single generator can be large; and the number of generators actively participating in an interarea mode can also be large. In addition, the system operating points may vary much from day to day due to the market oriented operation structure.

Continuous advances in power electronic technologies have made the application of FACTS devices very popular in power systems. SVC is the most widely used FACTS devices. It is well known for providing dynamic voltage support and reactive power compensation [1]. However, it does not necessarily improve system damping. Once installed, a supplementary control signal could be introduced into the voltage-summing junction of the SVC and a supplementary damping controller could be designed in order to improve damping of system oscillation [2,3]. Although the local control signals are easy to get, they may not contain the inter-

area oscillation modes. So, local signals are not as highly controllable and observable as wide area signals for the inter-area oscillation modes [4].

Fuzzy logic (FL) control approach has been emerging as a promising tool for solving complicated problems dealing with systems whose behavior is very complicated to model [5,6]. In our proposed approach, Lead-Lag optimal controllers and fuzzy logic are used jointly to provide (1) easiness in design and (2) adaptiveness against changes in the operating condition. In this approach, optimal controllers are designed and then a fuzzy logic tuning mechanism is constructed to generate a single control signal.

In this paper we first try to find the best choice of global signal input for supplementary controller, and then design a proper lead-lag supplementary controller, based on needed compensation. Global input signals are selected based on residue index function method [7]. Eigenvalues and residues are obtained by test signal method [8], and supplementary controller, is designed by phase compensation procedure [9,10]. At last, a fuzzy adaptive controller is employed to obtain supplementary controller's gain (KPSDC). Some computer simulations are performed to validate this method by MATLAB/SIMULINK. The results show the effectiveness of damping controller using fuzzy logic obtained gain.

II. STRUCTURE OF SVC APPLICATION CONTROL Since the SVCs are employed primarily for voltage control,

their contributions to the damping of system oscillations resulting from voltage regulation alone are usually small. The following shows the structure of an SVC with supplementary control, which can improve the electrical damping of the power system clearly. The block diagram of SVC with control loop is shown in Fig. 1, where Vt is the voltage at SVC bus; BSVC denotes the susceptance and VPSDC is the supplementary modulation signal for damping control. Y is used as the input for the damping controller.

When the open loop transfer functions for the power system and the damping controller are represented by G(s) and HPSDC(s), respectively, the overall block diagram of the closed loop system can be obtained as shown in Fig. 2.

III. SVC PSDC BASED ON WIDE AREA SIGNALS

A. Selection of input signal based on synthetic residue index The state-space equations of the open-loop system can be

written as

Employing Fuzzy Logic in Damping Power System Oscillations Using SVC

Mahmood Joorabian, Morteza Razzaz, Mazdak Ebadi, Mahmood Moghaddasian Department of Electrical Engineering, Ahvaz 61355, Iran

Tel: (98) 611 3337010, Fax: (98) 6113336642 Email: mazdakebadi@yahoo.com

P

2

⎩⎨⎧

=+=xCyBuAxx

jj (1)

Here B is the input column-vector, yi some output signal, and Cj is the output row-vector corresponding to yi. The transfer function between input u and output yi can be expressed in terms of the residues and eigenvalues as:

⎪⎪⎩

⎪⎪⎨

⎧

=

λ−=∑

=

BvtCR

sR

)s(G

iijij

n

1i i

ijj (2)

where λi (i =1,2,...n) is the eigenvalues of the open-loop system Gj(s); ti and vi denote the right and left eigenvectors, respectively; Rij is the residue associated with eigenvalue λi and it is an index containing the controllability and the observability information.

The controllability of mode i is given by:

BvK Tic = (3)

The observability of mode i from yi can be shown as:

ijo tCK = (4)

The concept of synthetic residue index is introduced to extend this single signal analysis to combination of signals:

( )k,ij,ii OOjk,O K,KfEK = (5)

This means the observability of mode i from the combination signals of signal j and signal k can be expressed as some function of the single signal observability Koi,j and Koi,k , which provides a method to evaluate the control effect of the combination of several wide area signals. Accordingly the synthetic residue index (SR) is derived as:

jk,iOcjk,i EKKSR = (5)

The traditional residue-based index is designed to select the most effective feedback signal. However it is not suitable for choosing the combination of signals that may include several wide area signals. Considering the different dimensions of dif-ferent signals, we choose the synthetic residue index ratio to be the index for selection of the input signal. The index is known as:

0

nSRSR

=ρ (6)

where |SRn| is the module of the synthetic residue index at one operating condition n; |SR0| is the module of the synthetic residue index at some base operating condition. If the synthetic residue index ratio associated with one optional input signal changes less than other signals under different operating conditions, it means that this signal is more robust and effective than others if it is selected as the input signal of SVC PSDC controller.

Thus, in this paper, the control input signal is chosen based on the synthetic residue index ratioρ .

B. Parameter design of SVC PSDC The SVC PSDC controller includes a measurement block

and several lead-lag blocks. It may be represented as the block diagram of Fig. 3.

The transfer function of the damping controller can be written as:

( ) ( )sHKsH PSDCPSDC = (7)

2

111

sTsTKsvc +

+

111sT+

PowerSystem

PSDC

maxB

minB

Bsvc

tV

PSDCVrefV

Y-

+

+

Fig. 1. Block diagram of SVC model with PSDC

)s(HPSDC

YΔ

refVΔ

PSDCVΔ

Fig. 2. Block diagram of the closed loop system

Fig. 3. Block diagram of SVC PSDC

3

The eigenvalue associated with the interarea mode needs to be changed to the left half complex plane, so it is evident that the phase angle φ of H(λi) should satisfy )Rarg(180 ij

o −=φ .

Here φ represents the phase to be compensated. So the SVC PSDC controller can be designed by residue phase compensation method.

According to Fig. 3, the transfer function of SVC PSDC controller is

( )m

3

2

w

w

1PSDCPSDC sT1

sT1sT1

sTsT1

1KsH ⎟⎟⎠

⎞⎜⎜⎝

⎛++

++= (8)

Parameters of the lead–lag blocks can be calculated from the following equations:

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

α=αω

=

φ+φ−

==α

−=φ

23

i2

2

3

ijo

TT

1T

)m/sin(1)m/sin(1

TT

)Rarg(180

(9)

where Rij is the residue and ωi is the frequency of the inter-area oscillation mode.

IV. FUZZY LOGIC CONTROLLER DESIGN Fuzzy logic is a good mean to control the parameters when

there isn't any direct and exact relation between input and output of the system, and we only have some linguistic relations in the If-Then form. In the mamdani type fuzzy logic controller that is used here, first, the inputs are changed from numerical form into linguistic space (fuzzification). Then fuzzy inference is performed by linguistic rules, and output is derived. At the end, this output is changed back into the numerical form (defuzzification) and is fed to the system as the control signal. The followings are the main parts of the fuzzy controller used here. A. Fuzzification

Fuzzification is the process that changes the inputs from numerical onto linguistic space. The input signals are these:

)1(x)2(xy)1(x&=

= (10)

Where y is the input of the damping supplementary controller. These signals are fuzzified through three membership functions : P(positive)-Z(zero)-N(negative). The output signal should always be positive, three other membership functions are used for the output signal: Z(zero)-M(positive medium)-B(positive big). Fig. 4 show the membership functions for both input and output signals. B. Fuzzy inference

Output of the fuzzy logic is made by some linguistic decisions like: If x(1) is P and x(2) is P then u is B

Table I shows the rule base of the fuzzy logic controller. To determine the degree of memberships of output variables, the min-max aggregation is applied.

TABLE I RULE BASE OF THE FUZZY LOGIC CONTROLLER

C. Defuzzification

Since the output signals of rules may be very small sometimes, then the centroid formula for defuzzification may doesn't work properly, then the Bisector method is used here.

V. CASE STUDY

A. Inter-area oscillation analysis and input signal selection The one line diagram of the two-area, four-machine test

system [11] is shown in Fig. 5.The input signal of the controller will be selected from the following ones: speed deviations of generators G1 and G3, active power in tie-line A, and the phase angle deviation between generators G1 and G3. By changing the loads at buses 7 and 9, three different operating conditions are obtained in which the active power in tie-line A are 200, 100 and −200 MW, respectively.

If the combination of speed deviations of generator 1 and generator 3 is selected as the input signal, the synthetic residue index is calculated as follows:

Fig. 4. Membership functions for: (a) input signal, (b) output signal

Fig. 5. 4-machine, 2-area test system

4

⎪⎪⎩

⎪⎪⎨

⎧

ω=

−=−=ω

ω−ω=ω

cjkojk,i

ikjikijjko

kjjk

K)(EKSR

t)CC(tCtC)(EK

Δ

Δ

ΔΔΔ (11)

The synthetic residue index ratio under different operating conditions is summarized in Table II. It is clear that the synthetic residue index ratio of speed deviation is always bigger than that of the angle difference. By comparing the synthetic residue index ratio, speed deviation of generators 1 and 3 are selected as the input signals.

TABLE II THE SYNTHETIC RESIDUE INDEX RATIO UNDER DIFFERENT OPERATING

CONDITIONS

B. Parameters of PSDC controller and system analysis

The transfer function G(s) is obtained based on the test signal method described above. From Table 2 we can calculate the phase lead compensation is 82◦ for the speed difference and 88◦ for the angle difference. The parameters of the SVC PSDC controller are obtained as: T1 = 0.05, Tw =3, T2 = 0.65, T2 = 0.13, m = 2 for the speed difference.

C. Time domain simulation To validate the proposed SVC supplementary controller

based on wide area signal under extreme conditions, time domain simulation is performed on the system with a three-phase fault applied at the receiving end of the circuit between buses 8 and 9 that is cleared 0.08 s later. The resulting responses of the system are shown in Figs. 6–9.

As illustrated in Figs. 6–9, the SVC PSDC controller per-forms satisfactorily under different operating conditions, which shows its high robustness. And it is clear that employing fuzzy logic to determine the KPSDC will increase the damping widely. The synthetic residue index ratio is effective criterion to be adopted to choose the wide area feedback signal.

VI. CONCLUSION In this paper we showed the effect of adding a

supplementary damping controller on damping subsynchronous oscillations. Then a method was proposed to improve the performance of damping controller. In proposed method a mamdani type fuzzy logic controller was used to obtain the gain of damping controller KPSDC. Computer simulations showed the advantage of this method.

Fig. 6. Effect of damping controller (with constant gain) on phase angle deviation for generators G1-G4

Fig. 7. Effect of damping controller (with constant gain) on active power of line C)

Fig. 8. Effect of fuzzy gain on phase angel deviation G1-G4 (comparing the fixed gain)

5

ACKNOWLEDGMENTS The authors wish to express their gratitude to the Khuzestan Power Utilities Company-Research Council for their support.

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[3] E. Lerch, D. Povh and L.Xu, “Advanced SVC control for damping power system oscillations” IEEE Trans. Power Syst.6 (2) (1991)458-465.

[4] U. P. Mhaskar and A. M. Kulkarni, “Power Oscillation Damping Using FACTS Devices: Modal Controllability, Observability in Local Signals, and Location of Transfer Function Zeros” IEEE Transaction on Power Systems, Vol. 21, No. 1, February 2006.

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[9] Z. Xu, W. Shao and C. Zhou, “Power system small signal stability analysis based on test signal” Proc. Int. Conf. on Power System Computation Conference (PSCC), Sevilla, Spain, June 24–28, 2002.

[10] IEEE Special Stability Controls Working Group, “Static var compensator models for power flow and dynamic performance simulation” IEEE Trans. Power Syst. 19 (1) (1994) 229–240.

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[12] P. Kundur, "Power System Stability and Control", McGraw-Hill, 1994, Example 12.6, p.813.

Fig. 9. Effect of fuzzy gain on active power of line C (comparing the fixed gain)