Fuzzy Logic based AGC Regulators for Power System with Asynchronous Tie-lines Incorporating Parametric Uncertainties

Ibraheem, Naimul Hasan and Omveer Singh Deptt. Of Electrical Engg., Faculty of Engg. & Tech.

Jamia Millia Islamia University New Delhi-110025, India

email: omveers@gmail.com

Abstract— A fuzzy logic based approach for the design of optimal automatic generation controllers of three area interconnected power system is proposed in this paper. A three area interconnected power system model consisting of identical power plants with reheat thermal turbines is considered as a test system. The HVDC link in parallel with EHV AC transmission line is incorporated as an area interconnection also. The studies are performed with implementing designed optimal AGC regulators on the system in the wake of 1% load perturbation in the area-1. The effect of variation in system parameters like; B and R is also studied. Simulation results indicate that the proposed optimal AGC regulators designs based on fuzzy logic concept offer appreciably better dynamic system performance and can guarantee the overall system stability even in the presence of system parameter variations.

Keywords- Automatic Generation Control (AGC), Fuzzy Logic Regulator (FLR), Area Control Error (ACE), Integral Regulator (IR), Parameter Variations

I. INTRODUCTION

The objective of overall control in power systems is to minimize the cost of generated power while maintaining its quality and satisfying the system security constraints. In the event of availability of an appropriate control scheme, selection of proper approach for its effective implementation on a particular system has a vital role. The basic concept of the control problem of a system is to achieve the specific objectives for which the system is meant while operating the system within limitations imposed by physical and technical system constraints. Despite the fact that today’s interconnected electric power grids are explosively growing, the automatic generation controls in use today are based on methods developed more than three decades ago. Even present control technologies may no longer be adequate to meet the increased complexity of interconnected system operation. The operational and control aspects of power systems must be modified or replaced by the more advanced control strategies to provide better overall control on the system. With the recent technological innovations, intelligent regulators have been replacing traditional regulators in order to have fast and good dynamic response for power system control problem. It is fast emerging as a tool to help

computer-based intelligent systems mimic the ability of the human mind to employ modes of reasoning that are approximate rather than exact. The basic theme of soft computing is that precision and certainty carry a cost and that intelligent systems should exploit, wherever possible, the tolerance for imprecision and uncertainty. Many soft computing techniques such as fuzzy logic, ANN, PSO, GA etc. are being used extensively in isolated as well as interconnected power system [1-8].

The integral regulators are fine for application in which the environment is known and predictable [9]. But they can lead to the disaster when the assumptions upon which they are built are violated. Unlike the integral regulators, the fuzzy regulators are adaptive and adjust to time or process-phase conditions. Y. H Moon and H.S. Ryu [10] used fuzzy logic to determine the optimal parameters for the extended integral control scheme. This study builds a fuzzy rule base with change of frequency and its rate as inputs. A set of decision rules is established to relate input signals to the decaying factor. As far as the application of fuzzy logic concept in the design of AGC regulators for isolated or interconnected power system is concerned, a large volume of research papers have appeared in literature over the last fifteen years.

One of the main advantages behind the popularity of fuzzy logic based regulator (FLR) is that it is a model-free approach with high capability of reasoning under non linearity and uncertainty. However, the design process of fuzzy regulators at some point becomes a trial-and-error technique which requires a large number of repetitions, and hence it is time consuming and tedious. It is a simplest possible logic regulator, using error and/or rate of change of error as input(s). A FLR using rate of change of error and error is used as the inputs to the FLR. The regulator behaves like an integral regulator. When both error and rate of error are employed as inputs to the FLR the regulator exhibits the characteristics of the integral regulator. If nonlinear defuzzification algorithm is used [11] the regulator becomes equivalent to nonlinear integral regulators.

Keeping in view, this paper is dedicated to present the AGC regulators design based on fuzzy logic concept. The AGC regulators are designed for a three area interconnected power system consisting of identical plants with reheat thermal turbines considering 0.01 p.u.MW perturbation in the area-1. To demonstrate the salient features of a HVDC

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transmission line, an area interconnection consisting of a parallel combination of HVDC and EHV AC transmission links is considered in this study. The simulation study has been performed using MATLAB-7.8 version. The SIMULINK TOOLBOX is also used to achieve the results and their investigations. System dynamic performance has been studied by investigating the response plots of various system states with nominal system parameter values and with the variation of system parameters like B and R.

II. POWER SYSTEM MODEL FOR INVESTIGATION

Power system model is three area interconnected power system consisting of power plants with reheat thermal turbines. The area-1 and area-3 are interconnected via parallel EHV AC/HVDC links while other areas are having EHV AC tie-line as area interconnection. The system operating frequency in India is 50 Hz. As per Indian Electricity Rules, 1956 frequency of the power system will be 50 Hz and controlled within the specified limits. The configuration of power system model under consideration is shown in Fig. 1.

E H V A C T i e – line H V D C link R : r e c t i f i er I : I n v e r t e r

R

I

Power System Area-1

Consisting of Plants with

Reheat Thermal Turbines

Power System Area-3

Consisting of Plants with

Reheat Thermal Turbines

Power System Area-2

Consisting of Plants with

Reheat Thermal Turbines

E H V A C T i e – line E H V A C

T i e – line

Fig.1: A Three Area Interconnected Reheat Power System Model

The transfer function model of the system is presented by Fig. 10. The overall control of power system model is suggested through integral square error (ISE) technique. The integral square error criterion is adopted for developing objective function for optimization of parameters. This can be defined as follows:

2

0

ISE= e (t)dt∞

� (1)

where, ISE refers to integral square error, e corresponds to error. For the present study; the formulation of ISE can be given as:

20

0

2ISE= dtACE� (2)

where, ACE represents area control error of a power system areas and is defined as:

The expressions for area control errors (ACE) for all three areas can be given as;

ACE1 = B1 ∆F1+�Ptie12

ACE2 = B2 ∆F2+�Ptie23

and ACE3 = B3 ∆F3+�Ptie31

The ACEs of respective areas are taken as the input to the

integral regulators which can be expressed as: U = -�Ki (ACEi)dt (3)

The nomenclature of various parameters used and their numerical values corresponding to three area power system model are given in the appendix-A & B respectively.

III. FUZZY LOGIC BASED INTEGRAL REGULATOR

The structure of fuzzy logic based AGC regulators, as described by Fig. 2, consists of a fuzzy logic algorithm and a conventional integral control based regulators. The integral regulators have one input signal, namely, the Area Control Error (ACE) of the system, and then the integral regulators output signal (Y) is the input signal for fuzzy logic regulators. Finally, the output signal from the FLR called the control signal (U = � ACE) is used handle the AGC of interconnected power system.

Fig.2 Structure of the Fuzzy Logic Regulators Gain scheduling of a linear and nonlinear power system is generally done when the system dynamics and operating conditions are available, and for which a single linear time-invariant model is not capable [11]. In this paper, we use the technique to set the parameters of integral regulators according to the new area control error ACE.

Fig.3 (i): Membership Functions for FLR The control variable for the conventional integral regulators can be given as: U = -�Ki (ACE)dt =-�Ki (�Ptie,i + Bi �Fi)dt (4)

�

0.6 -0.6 0.3 -0.3 0.07 -0.07 0

X= ACE (ki)

NS NM NB Z PS PM PB

- -

ACE

FLR IR

Y

Ki 1 s

Control Signal U

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Fig.3 (ii): Surface View of Output Control Signal ‘U’

Fuzzy logic based algorithm needs experience for the selection of number of membership functions to be considered for the design of an adequate AGC regulators. In this paper, the system model has been tested with seven triangular membership functions of the FLR. In the proposed scheme, one input and one output is selected while modeling the system using fuzzy logic concept considering seven fuzzy rules of ACE [11]. Triangular membership function shapes of the derivative error according to output ‘Y’ are chosen to be similar for the FLR. However, its horizontal axis limits are taken different values for optimizing the regulators output. There are three area control errors ACE1, ACE2 and ACE3 which are used and their summation is minimized. As shown in Fig. 3, the regulators have the Negative Big NB, Negative Medium NM, Negative Small NS, Zero Z, Positive Small PS, Positive Medium PM, Positive Big PB for the ACE. Rule base are defined in the range of [-0.6, 0.6]. The fuzzy rules are shown in the Table1.

Table 1: Fuzzy Rule base

Fuzzy Rules for the FLR Rule1 If(ACE is NB) then (U is PB)(1)

Rule2 If(ACE is NM) then (U is PM)(1)

Rule3 If(ACE is NS) then (U is PS)(1)

Rule4 If(ACE is Z) then (U is Z)(1)

Rule5 If(ACE is PS) then (U is NS)(1)

Rule6 If(ACE is PM) then (U is NM)(1)

Rule7 If(ACE is PB) then (U is NB)(1)

IV. IMPLEMENTATION AND SIMULATION RESULTS

The simulation work is carried out using the conventional integral and the FLR for AGC of three area interconnected power system considering 0.01 p.u MW step load disturbance in area-1.

The dynamic responses of �F1, �F2, �F3, �Ptie12, �Ptie23 and �Ptie31 are shown in Figs. 4-9. In all the response

plots FLR shows its effectiveness in both the cases and also exhibit better system dynamic response over conventional IR. The investigations of these response plots reveal that implementation of FLR considering HVDC link in parallel with EHV AC tie-line reduces the overshoots of the first peak of response plots to a great extent and completely removes the oscillations from the dynamic responses as well as compared to that obtained with FLR without HVDC link in area interconnection system. The numerical values of settling time and overshoots for frequency deviation of area-1 with and without HVDC Link as shown in Table 2 also justify the effectiveness of FLR. The proposed technique gives favorable effect on dynamic performance of the power system.

Figs. 10-15 describe the system dynamic responses obtained with FLR for nominal system parameters and with 60% variation in the system parameters ‘B’ and ‘R’. It is also revealed that magnitudes of the oscillations in the system dynamic responses are considerably reduced although the settling time is approximately equal with and without parametric uncertainties. As shown in Table-3, settling time and overshoots for frequency deviation of area-1 considering parametric uncertainties in ‘B’, & ‘R’ are reduced with reduction in these parameters.

0 10 20 30 40 50 60 70 80 90 100-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Time (sec)

∆∆ ∆∆ F

1

IRFLR (Without H VD C Link)FLR (With H VD C Link)

Fig. 4: Dynamic response of �F1

0 10 20 30 40 50 60 70 80 90 100-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time (sec)

∆∆ ∆∆ F

2

IRFLR (Without H VD C Link)FLR (With H VD C Link)

Fig. 5: Dynamic response of �F2

0 10 20 30 40 50 60 70 80 90 100-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

∆∆ ∆∆ F

3

Time (sec)

IRFLR (Without H VD C Link)FLR (With H VD C Link)

Fig. 6: Dynamic response of �F3

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0 10 20 30 40 50 60 70 80 90 100-10

-8

-6

-4

-2

0

2

4 x 10-3

Time (sec)

∆∆ ∆∆ P

tie 12

IRFLR (Without H VD C Link)FLR (With H VD C Link)

Fig. 7: Dynamic response of �Ptie12

0 10 20 30 40 50 60 70 80 90 100-5

0

5

10 x 10-3

Time (sec)

∆∆ ∆∆ P

tie 23

IRFLR (Without H VD C Link)FLR (With H VD C Link)

Fig. 8: Dynamic response of �Ptie23

0 10 20 30 40 50 60 70 80 90 100-6

-4

-2

0

2

4

6

8

10

12 x 10-3

Time (sec)

∆∆ ∆∆ P

tie 31

IRFLR (Without H VD C Link)FLR (With H VD C Link)

Fig. 9: Dynamic response of �Ptie31

0 5 10 15 20 25-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

Time (sec)

∆∆ ∆∆ F

1

N ominal System Parameters60% Reduction in System Parameters B, R

Fig. 10: Dynamic response of �F1

0 5 10 15 20 25-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time (sec)

∆∆ ∆∆ F

2

N ominal System Parameters60% Reduction in System Parameters B, R

Fig. 11: Dynamic response of �F2

0 5 10 15 20 25-0.02

-0.015

-0.01

-0.005

0

Time (sec)

∆∆ ∆∆ F

3

N ominal System Parameters60% Reduction in System Parameters B, R

Fig. 12: Dynamic response of �F3

0 5 10 15 20 25-7

-6

-5

-4

-3

-2

-1

0

1 x 10-3

∆∆ ∆∆ P

tie 12

Time (sec)

N ominal System Parameters60% Reduction in System Parameters B, R

Fig. 13: Dynamic response of �Ptie12

0 5 10 15 20 25-3

-2

-1

0

1

2

3 x 10-3

Time (sec)

∆∆ ∆∆ P

tie 23

N ominal System Parameters60% Reduction in System Parameters B, R

Fig. 14: Dynamic response of �Ptie23

0 5 10 15 20 250

0.5

1

1.5

2

2.5

3

3.5

4

4.5 x 10-3

∆∆ ∆∆ P

tie 31

Time (sec)

N ominal System Parameters60% Reduction in System Parameters B, R

Fig. 15: Dynamic response of �Ptie31

Table 2: Comparison of the Regulators

Type of

Regulator Peak Overshoot (�F1), p.u.

Settling Time (�F1),sec

IR 0.001 � 100 FLR without

HVDC Link 0.008 24.8

FLR with HVDC Link

Nil 24.7

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Table 3: Comparison with Parametric Uncertainties

Parametric Uncertainties

Peak Overshoot (�F1), p.u.

Settling Time (�F1), s

Nominal Parameters

0.008 24.8

60% reduction in Parameters

0.003 23.4

V. CONCLUSION

A fuzzy logic algorithm based design of optimal FLR for automatic generation control of interconnected power system with EHV AC-HVDC parallel tie-lines and parametric uncertainties is presented. The proposed regulators design has been successfully applied to a three area interconnected reheat type power system model. Simulation results reveal that the designed Fuzzy Logic Regulators are very effective in suppressing the frequencies oscillations while simultaneously improving the system stability as compared to conventional Integral Regulators. Furthermore, the incorporation of HVDC link in parallel with EHV AC transmission line as an area interconnection between two of three power system areas has an ameliorating effect on system dynamic performance.

APPENDIX (A) Nomenclature:

�Fi : i :

Kgi : Tgi : Kri : Tri : Kti : Tti : Kpi : Tpi : Bi : Ri : �Pdi:

2�Ti,j : Kdc: Tdc:

ACEi:

Incremental change in the frequency subscript referring to area (i = 1, 2, 3) Speed governor gain Speed governor time constant Gain of reheats in thermal unit Reheat time constant, s Reheat thermal turbine gain constant Turbine time constant, s Power system gain constants Power system time constants, s Frequency bias constant, pu MW/Hz Speed regulation parameter, Hz/pu MW Incremental change in load demand, pu MW/Hz Synchronizing coefficient of ac tie-link Gain associated with dc link Time constant of HVDC link, s Area control errors

APPENDIX (B) Numerical Data:

nominal system frequency = 50Hz Kg1 = Kg2 = Kg3 = 1 Tg1 = Tg2 = Tg3 = 0.08 sec Kr1 = Kr2 = Kr3 = 0.5 sec Tr1 = Tr2 = Tr3 = 10 sec Kt1 = Kt2 = Kt3 = 1 Tt1 = Tt2 = Tt3 = 0.3 sec Kp1 = Kp2 = Kp3 = 120 Hz/ p.u. MW Tp1 = Tp2 = Tp3 = 20 sec B1 = B2= B3= 0.425 R1 = R2 = R3 = 2.4 Hz/ p.u. MW �Pd1 = 0.01 p.u.MW 2�Ti,j = 0.545 p.u.MW Kdc = 1.0, Tdc = 0.2s

REFERENCES

[1] O. I. Elgerd, “Electric Energy System Theory: An Introduction”, Tata Mc-Graw Hill, 1982.

[2] J. Nanda and B. L. Kaul, “Automatic Generation Control of an Interconnected Power System,” IEE Proc. Generation, Transmission and Distribution, vol. 125, no. 5, pp. 384-390, May 1978.

[3] M. L. Kothari, J. Nanda and D. Das, “Discrete Mode AGC of a Two Area Reheat Thermal System with New Area Control Error,”IEEE Trans. Power Apparatus and Systems, vol. 4, no. 2, pp. 730-738, May 1989.

[4] Fujita et al, “Automatic Generation Control for DC-link Power System”, Transmission and Distribution Conf. and Exhibition: Asia Pacific, IEEE/PES, vol. 3, pp. 1584-1588, Oct. 2002.

[5] Ibraheem and P. Kumar, “Dynamic Performance Enhancement of Hydropower Systems with Asynchronous Tie-lines,” J. Electric Power Components and Systems, vol. 31, no. 7, pp. 605–626, 2003.

[6] Ibraheem and P. Kumar, “Optimal Control of Interconnected Power System with parallel AC/DC Links and Parameter Uncertainties,” Proc. 19th National Systems Conf., Coimbatore, India, pp. 137-142, Dec. 1995.

[7] D. M. Vinod Kumar, “Intelligent Regulators for Automatic Generation Control,” IEEE-10 Int. Conf. on Global Connectivity in Energy, Computer, Communication and Control, pp. 557-574, 1998.

[8] Ibraheem, P. Kumar and D.P. Kothari, “Recent Philosophies of Automatic Generation Control Strategies in Power Systems,” IEEE Trans. Power System, vol. 11, no. 3, pp. 346-357, February 2005.

[9] P. K. Hota, “Fuzzy-set based Optimization Technique for Economic Load Dispatch,” J. Institution of Engineers (IEI), vol. 80, pp. 99–103, Nov. 1999.

[10] Young-Hyum Moon and Heon-Su Ryu, “Fuzzy Logic based Extended Integral Control for Load Frequency Control,” IEEE Power Engineering Society Winter Meeting, vol. 3, pp. 1289-1293, Feb. 2001.

[11] H. Ying, W. Siler and J. J. Buckley, “Fuzzy Control Theory: a Nonlinear Case,” Automatica, vol. 26, no. 3, pp. 513-520, 1990.

BIOGRAPHIES

Ibraheem: with the Department of Electrical Engineering, Faculty of Engineering and Technology, Jamia Millia Islamia (Central University), New Delhi, India, where he is currently a Professor of electrical engineering and also Head of MBA (Evening) Department. He has published a number of research papers in national/international journals and has been continuously engaged in guiding research activities at graduate/post-graduate and Ph.D. levels. Dr. Ibraheem received a Gold Medal from the Union Ministry of Power and Energy (India) in 1998 for one of his research articles. Naimul Hasan: is presently working as Asst. Prof. in the Electrical Engineering at Faculty of Engineering & Technology, JMI, New Delhi, India. He is also guiding research scholars in the field of artificial intelligence. His research interests include power system operation and control, security analysis, energy management. Omveer Singh: is Research Scholar in Electrical Deptt., Faculty of Engg. And Technology, Jamia Millia Islamia University, New Delhi, India. His major field of interest includes advanced power systems, soft computing techniques.

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B1

1/R1

U1

- -

+

Kg1

1+STg1

Kp1

1+STp1 �

2�T13 S

�Pd1

+

-

ACE1

- -

+

+

2�T12 S

- - �

�

B2

1/R2

U2

- -

+

Kg2

1+STg2

Kp2

1+STp2 �

�Pd2

+

-

ACE2

- -

�

B3

1/R3

U3

- -

+

Kg3

1+STg3 Kt3

1+STt3

Kp3

1+STp3 �

�Pd3

+

-

ACE3

- -

�

�

�

�

�

�

2�T21 S

2�T23 S

�

2�T32 S

2�T31 S

�

�

�

�

�

+ -

+ -

- -

+ -

+ -

- -

- -

+ -

- -

+ -

- -

+ -

+ -

+ -

+ -

+ -

+ -

1+SKr3Tr3 1+STr3

U1

1+SKr3Tr3 1+STr3

1+SKr3Tr3 1+STr3

Kt3 1+STt3

Kt3 1+STt3

+

+

+

+

U3

U2

�Ptie12

�Ptie23

�Ptie31

�F1

�F2

�F3

Area-1

Area-3

Area-2

Kdc

1+STdc

Fig. 10: Three Area Interconnected EHV AC parallel with HVDC Link Power System Model

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