Design of a Hierarchical Fuzzy Logic PSS - advantech greece

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DESIGN OF A HIERARCHICAL FUZZY LOGIC PSS FOR A MULTI-MACHINE POWER SYSTEM T. Hussein , A. L. Elshafei , A. Bahgat Electrical Power and Machines Department, Cairo University, Gama Street, Giza, Egypt Abstract - The performance of fuzzy-logic power system stabilizer (FPSS), which is tuned automatically as the operating conditions of power system change, is investigated by applying it to a multi-machine power system. FPSS is developed using speed deviation and the derivative of speed deviation as the controller inputs variables. Two scaling parameters are introduced to tune the FPSS. These scaling parameters are the output of another fuzzy-logic system (FLS), which gets its inputs from the operating condition of the power system. The proposed scheme is referred to as the self tuning fuzzy power system stabilizer (TFPSS). This mechanism of tuning the FPSS makes it adaptive to changes in the operating condition. The response of the system with three power system stabilizers (PSSs), namely CPSS, FPSS and self tuned FPSS, are compared. It is shown that the tuned FPSS is superior to both CPSS and fixed-parameter FPSS. The effect of the defuzzification methods on the control signal response is also shown in this paper. Keyword: power system stabilizer, multi-machine system, fuzzy logic control, supervisory control. I. INTRODUCTION

E

lectro-mechanical oscillation between interconnected synchronous generators is phenomena inherent to power systems. The damping of these oscillations is of vital concern, and is a prerequisite for secure system operation. Power system stabilizers (PSSs) can provide supplementary control signal to the excitation system to damp these oscillations and to improve dynamic performance [9]. Most PSSs in use in electric power systems employ the linear control theory approach based on a linear model of a fixed configuration of the power system and thus tuned at a certain operating condition. Such fixed parameter PSS, called conventional PSS (CPSS), is widely used in power systems, it often does not provide satisfactory results over a wide range of operating conditions. In recent years, fuzzy logic has emerged as a powerful tool and is starting to be used in various power system applications [2]. Fuzzy logic can be an alternative to classical control. It allows one to design a controller using linguistic rules without knowing the mathematical model of the plant. This makes fuzzy-logic controller very attractive systems with uncertain parameters. The linguistic rule necessary for designing a fuzzy-logic controller may be obtained directly from the operator who has enough knowledge of the response of the system under various operating conditions. The inference mechanism of the fuzzy-logic controller is represented by a decision table, which is consists of linguistic IF-THEN rule. It is assumed that an exact model of the plant is not available and it is difficult to extract the exact parameters of the power plant. Therefore, the design procedure cannot be based on an exact model. However the fuzzylogic approach makes the design of a controller possible

without knowing the mathematical (exact) model of the plant. The fuzzy logic implementation of power system stabilizer (PSS) has been reported in a number of publications [1], [12]. As with conventional power system stabilizer (CPSSs), the performance of FPSSs depends on the operating conditions of the system however, they are less sensitive to changing operating conditions than CPSSs. Further improvement can be achieved by the TFPSS as the operating conditions of the power system changed. In this paper a rule-based FPSS is designed. Its parameters are tuned by another fuzzy logic system, making it adaptable to changes in operating conditions [4]. It is then used to stabilize a synchronous machine, which is part of a multi-machine power system. The power system stabilizers (PSSs) are implementation at each machine. Response of the machines subjected to three-phase to ground fault are studied. System responses with tuned fuzzy-logic power system stabilizer (TFPSS) for different operating conditions are then compared with a CPSS and fixed parameter FPSS. II. FUZZY-LOGIC PSS (FPSS) A FLC is a kind of a state variable controller governed by a family of rule and a fuzzy inference mechanism. The FLC algorithm can be implementation using heuristic strategies, defined by linguistically describe statements. The fuzzy logic control algorithm reflects the mechanism of control implemented by people, without using a mathematical model the controlled object, and without an analytical description of the control algorithm. The main FLC processes are fuzzifier, knowledge base, the inference engine and defuzzifier as in Fig. 1.

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The inference engine maps the input values into fuzzy value using normalized membership functions and input gain. The fuzzy-logic inference engine deduces the proper control action based on the available rule base. The fuzzy control action is translated to the proper crisp value through the defuzzifier using normalized membership functions and the output gain. The output control signal from FPSS is injected to the summing point of the AVR. In this paper, inputs are fuzzified using normalized triangle membership functions. Knowledge Base Data Base

Crisp

Rule Base

Crisp

Fuzzy Fuzzification

Inference Engine

Fuzzy Fuzzy Defuzzification

Fig. 1: The basic structure of the fuzzy controller LN

MN

SN

Z

SP

MP

LP

III.

SELF TUNING OF FPSS (TFPSS)

In order to tune the FPSS, two scaling factors are used to adjust the range of inputs as the operating conditions of the system change, the speed deviation is scaled with ∆ω ′ = k p ∆ω and the derivative of speed deviation is scaled with ∆ω ′ = k d ∆ω . Also, the output of the FPSS ( K u ) is scaled with a fixed scaling factor, which is chosen by the designer based on the system requirement. For the system under study this scaling factor is chosen to be equal to (6.8). The FPSS is tuned by computing optimum input scaling factors, using another FLS [4]. The electrical active power and reactive power of each generator are selected for input signals to represent the operating conditions of each machine. The FLS with two inputs (Pe, Q) and two outputs (scaling factors) designed this way is referred to as the tuner. For brevity only one rule base from four rule bases for (FLS) are shown bellow: 1. If (input1 is PB1) and (input2 is PB2) then (output1 is PVVB3) (output2 is PVVB4)

X min

2. If (input1 is PS1) and (input2 is PM2) then (output1 is PB3) (output2 is PB4)

X max

X range

Fig. 2: Fuzzy variable, Xi, seven membership function

3. If (input1 is PS1) and (input2 is PS2) then (output1 is PM3) (output2 is PM4)

The bisector method is used for defuzzification. Triangle membership functions are used for defuzzification of the output. For each input variable seven labels are defined as shown in Fig. 2 Table 1: Fuzzy-logic PSS rules ∆ώ LN MN ∆ω LN MN SN Z SP MP LP

LN LN LN MN MN SN Z

LN LN MN MN SN Z SP

SN LN MN MN SN Z SP MP

Z LN MN SN Z SP MP LP

SP MN SN Z SP MP MP LP

MP SN Z SP MP MP LP LP

LP Z SP MP MP LP LP LP

LN, MN, SN, Z, SP, MP and LP stand for large negative, medium negative, small negative, zero, small positive, medium positive, large positive. The value x max and x min represent maximum and minimum variation of the input and output signals. The values are selected based on simulation information. A decision table is constructed consisting of 49 rules. An example of the ith rule is: If

∆ ω is SN and ∆ ώ is MP then U is SP

A symmetrical fuzzy rule set is used to describe the FPSS behavior as shown in table 1. The procedure to design a FLC can be found in [1].

4. If (input1 is PB1) and (input2 is PM2) then (output1 is PVVB3) (output2 is PS4) 5. If (input1 is PB1) and (input2 is PS2) then (output1 is PVVB3) (output2 is PVVB4) For the inputs, trapezoidal membership functions are used and for the outputs, triangle membership functions are used. By nonlinear simulation with three phases to ground fault, the optimum scaling factors are chosen. The rule base for the FLS is derived from the operating conditions of the generators on line (as the machine are operating) and calculates the scaling factors for the FPSS. The whole stabilizer obtained is referred to as the tuner fuzzy power system stabilizer (TFPSS). The block diagram for TFPSS is shown in Fig. 3. ω

Ke

ω ref

d/dt

Kė

Rule table+ defuz zifier

Ku

Rule table +defu zzifier

Fig. 3: Tuning FPSS

Pe Qe

Gen. and exciter

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IV. FOUR MACHINES TWO AREA SYSTEM Brk1

In fuzzy logic toolbox (GUI) we have five different defuzzification methods. Our purpose is to select the best one that suits our application.

Brk2

G1

In this work we tested them and we found that:

G3

L1

Area 1

L2

1. The (mom, lom, som) defuzzification methods have fixed small oscillation in the steady state, and that is clear from the surfaces in Figure 5.

Area 2

G2

G4

2. The centroid defuzzification method, the results is a very slow simulation and stops.

Fig. 4: Multi-machine power system for Stability study

3. The bisector defuzzification method, the oscillation in the steady state is removed and the simulation is fast. From Fig. 5 we note that, the surfaces of the bisector and centroid methods is soft compared to the (mom, lom, som) methods, for that we have fixed oscillation in the steady state when we used (mom, lom, som) methods. Fig. 6, 7 show Vs signal for (bisector defuzzification method) and Vs signal for (mom defuzzification method).There is an oscillation in the Vs signal when use mom method, the oscillation is removed when bisector method is used. 0.08

V. CHOOSING THE DEFUZZIFICATION ALGORITHM

TFPSS

0.06 0.04 vs signal PU

The test system present in MATLAB 7 consists of two fully symmetrical areas linked together by two tie 230 KV lines of 220 Km length. It was specifically designed in [8] to study low frequency electromechanical oscillations in large interconnected power systems. Despite its small size, it mimics very closely the behavior of typical system in actual operation. Each area is equipped with two identical round rotor generators rated 20 KV/900 MVA. The synchronous machines have identical parameters [8] except for the inertias which are H = 6.5s in area 1 and H is = 6.175s in area 2. Thermal plants having identical speed regulators are further assumed at all locations, in addition to fast static exciter with a 200 gain. The load is represented as constant impedance and spilt between the areas.

0.02 0 -0.02 CPSS

-0.04

-3

x 10

0.01

-0.06

0.005 outpu t1

outpu t1

5

0

0

-0.08

-0.005

-5

0

1

-0.01 0.01

0.01 0.005

0.01

0.005

0.005

0

bisector defuzzification

3 t(sec)

4

5

6

-0.005 -0.01

input2

input1

2

Fig. 6: Vs signal (bisector method)

0

-0.005

-0.005 -0.01 -0.01

0.005

0

0

-0.005 input2

0.01

-0.01

input1

0.08

mom defuzzification

CPSS

0.06

0.005

0

0

-0.005

-0.005

-0.01 0.01

-0.01 0.01 0.005

0.01

0.01

-0.01

0

-0.005

-0.005 -0.01

input2

input1

0.02 0 -0.02

0.005

0

0

-0.005 input2

0.005

0.005

0

Vs signal PU

0.005 ou tput1

0.01

-0.005 -0.01

-0.01

-0.04

input1

-0.06

low defuzzification

x 10

som defuzzification

-0.08

TFPSS 0

1

2

3 t(sec)

4

5

6

Fig. 7: Vs signal (mom method)

-3

5 output1

ou tput1

0.04 0.01

VI. SIMULATION STUDIES

0

-5

0.01 0.005

0.01 0.005

0 0

-0.005 input2

-0.005 -0.01

-0.01

input1

Centroid defuzzification

Fig. 5: Surfaces of defuzzification Methods

The performance of the TFPSS was evaluated by applying a large disturbance caused by three-phase fault applied at the middle of one tie line at 0.2 sec. and cleared after 0.133 sec by opening the breakers, with one tie-line the system can reach a stable operating point in

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steady state. A schematic diagram representation of one generator is shown in Fig. 8 For comparison purpose, the system is configured to switch between different controls techniques, In order to show the improvement of the proposed TFPSS over fixed parameter FPSS and CPSS. The optimality is checked by the performance index:

36 34 32

kp2

30 28 26

J p =∑ ∆ω 2

24 22 20

∆ω ref

Governor

0

1

2

3 t(sec)

4

5

6

Fig. 9: TFPSS scaling factor setting (Kp) Machine 2

∆ω T.L

Generat or

35

To other Machines

30

G kd2

25

∆ω

20

CPSS

15

Turbine Exciter

U pss

AVR

10

FPSS

0

1

d/dt

3 t(sec)

4

5

6

Fig. 10: TFPSS scaling factor setting (Kd) Machine 2

TFPSS

Vref

2

d/dt 1.004

Fig 8: Schematic diagram of power system model

It consists of a lag-lead controller with a high pass filter that prevents steady change in speed from modifying the field voltage. The value of the washout time constant Tw should be high enough to allow signals associated with oscillations in rotor speed to pass unchanged. A high value of K STAB is desirable from the viewpoint of transient stability. For the plant with three types, i.e CPSS, fixed parameter FPSS and TFPSS, the system response for various operating conditions have been investigated, for brevity only two cases are shown here. A. Operating condition 1

Real Power Reactive Power

2

3

4

0.96 PU

0.59 PU

0.8 PU

0.78 PU

0.17 PU

0.15 PU

0.09 PU

0.1 PU

1.002

1.001

1

0.999

0

2

4

6

8

10

t(sec)

Fig. 11: Response for GEN # 1 for operating condition 1 1.005 FPSS TFPSS CPSS

1.004 actual speed PU

 sTw   1 + sT 1  1 + sT 3  G PSS (S) = (K STAB ) 1 + sTw  1 + sT 2  1 + sT 4 

actual speed PU

1.003

A CPSS that is used for comparison with this transfer function is:

Table 2: operating condition 1 Generator 1

FPSS TFPSS CPSS

1.003 1.002 1.001 1 0.999

0

2

4

6

8

t(sec)

Fig. 12: Response for GEN #2 for operating condition 1

10

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1.005

1.005 FPSS TFPSS CPSS

1.004

actual speed PU

actual speed PU

FPSS TFPSS CPSS

1

1.003 1.002 1.001 1 0.999

0.995

0

2

4

6

8

10

0.998

t(sec)

Fig. 13: Response for GEN# 3 for operating condition 1

0

4

6

8

10

t(sec)

Fig. 16: Response for GEN # 2 for operating condition 2

1.005 FPSS TFPSS CPSS actual speed PU

2

1.003 FPSS TFPSS CPSS

1.002

actual speed PU

1.001 1

1 0.999 0.998 0.997

0.995

0

2

4

6

8

10

0.996

t(sec)

Fig. 14: Response for GEN# 4 for operating condition 1

0.995

0

TFPSS

Real Power

0.56 PU 0.01 PU

Reactive Power

18.5 23.8 91.8 85

1.001 1 0.999 0.998 0.997 0.996

2

3

0.92 PU 0.04 PU

4

0.56 PU -0.04 PU

0.61 PU -0.13 PU

FPSS TFPSS CPSS

1.002

0

2

4

6

8

10

t(sec)

1.003

actual speed PU

10

FPSS TFPSS CPSS

1.002

actual speed PU

72 79.4 175 164

B . Operating condition 2 Table 4: operating condition 2 Generator 1

8

1.003

FPSS

213 218 366 350

6

Fig. 17: Response for GEN # 3 for operating condition 2

Jp CPSS

4 t(sec)

Table 3: comparing the performance index operating condition 1

Operating Condition 1 Gen. 1 Gen. 2 Gen. 3 Gen. 4

2

1.001

Fig. 18: Response for GEN # 4 for operating condition 2 Table 5: comparing the performance index operating condition 2

Operating Condition 2 Gen. 1 Gen. 2 Gen. 3 Gen. 4

Jp CPSS 76.4 66.6 155 135

FPSS 42.7 39.5 121 103

TFPSS 31 28 97.5 80

1 0.999 0.998 0.997

0

2

4

6

8

t(sec)

Fig. 15: Response for GEN # 1 for operating condition 2

10

From this two operating conditions it’s observed that. The proposed TFPSS and fixed parameter FPSS has better response in transient condition and steady state error than CPSS. The steady state error is removed when used the proposed TFPSS.

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VII. CONCLUSION

A comparison between the TFPSS, fixed parameters FPSS and CPSS shows that the fixed parameters FPSS has a better performance over a wide of operating conditions than the CPSS, and is less sensitive to change in operating conditions than CPSS, the fixed parameters FPSS provides good transient and damping response even when the operating conditions changes. A Supervisory fuzzy-logic system has been proposed to tune a fuzzy power system stabilizer on line. It’s shown that by tuning the FPSS (TFPSS), better response of the system can be achieved in a wide range of operating condition compared to fixed parameters FPSS and CPSS. The FPSS has a better performance than the CPSS and the proposed TFPSS has improvement the dynamic response. ACKNOWLEDGMENT

The first author is grateful his to the higher education in Libya to support study at Cairo University in Egypt. REFERENCES [1] Al-Hawary M. E. 1998" Electric Power Applications of Fuzzy Systems" New York: IEEE Press. [2] El-Metwally K., and Malik O., "Fuzzy Logic Power System Stabilizer", IEE Proc. Generation, Transmission, and Distribution, vol. 142, no.3, pp.227-281,1995. [3] Elshafei A. L., El-metwally K., Shaltout A. "Design and Analysis of a Variable Structure Adaptive Fuzzy-Logic Power System Stabilizer" Proceedings of the America Control Conference Chicago, Illinois june, 2000, pp. 3959-3963. [4] Hosseinzadeh N. "A self-tuned fuzzy-logic power system stabilizer". 9th Iranian Conference on Electrical Engineering, Tehran, May 8-102001, Proceeding on power, pp.8.1-8.9. [5] Hosseinzadeh N. Kalam A." A rule-based fuzzy power system stabilizer tuned by neural network" IEEE Transactions on Energy Conversion, vol. 14, no 3, Septmber 1999, pp. 773-779. [6] Joe H. Chow, George E. Boukarim, and Alexander Murdoch" Power System Stabilizer as Undergraduate Control Design Project" IEEE Transactions on power systems, vol.19.1 February 2004, pp.144-151. [7] Klein M., Rogers G. J., Moorty S., Kundur P. "Analytical Investigation of Factors Influencing Power System Stabilizer Performance" IEEE PES winter meeting, New York, January 1992, pp. 382-390. [8] Kunder P. "Power System Stability and Control" McGrawHill,1994. [9] Larson E. V. and Swann D. E., "Applying Power system stabilizer: Part I, II and III," IEEE Transactions on Power Apparatus and System, Vol, PAS-100, No. 6, 1991, pp. 3017-3041. [10] Malik O. P., Armin Eichmann, Allessandro Kohler, "A prototype self- tuning adaptive power system stabilizer for damping of active power swings" Conference Proceedings, vol. 1 IEEE PES 2000 Summer Meeting, 16-20 July, Seattle, vol.pp. 122-127. [11] Ruhua You, Hassan J, Eghbali, and M. Hashem Nehrir, "An Online Adaptive Neuro-Fuzzy Power System Stabilizer for Multimachine Systems" IEEE Transactions on power systems vol. 18. no.1 February 2003, pp.128-135.

[12] Rainkov D., Heelendoorn H. & Reinfrank M. (1993) " An introduction to fuzzy control" Berlin: Springer. [13] Taliyat H., Sadeh J., Ghazi R. "Design of Augmented Fuzzy Logic Power System Stabilizer to Enhance Power Systems Stability" IEEE Transactions on Energy Conversion , vol. 11,no.1 , March 1996, pp. 97103.