ISBN:378-26-138420-0255
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DESIGN OF FUZZY SELF-TUNED LOAD FREQUENCY CONTROLLER FOR POWER SYSTEM T.A.S.JAGADEESH
Dr.R.VIJAYA SHANTI, Asst.Professor, Andhra University
Abstract: In the present paper, Self-Tuning fuzzy Controller is designed for a multi-machine power system. Conventional PID gains are obtained using Ant Colony System (ACS).Basing these gains, Fuzzy Controller gains are designed for solving Load Frequency Control (LFC) problem in a power system. The proposed controller is tested on different loading conditions of a practical thermal, hydel interconnected systems. The proposed controller shows its efficiency when compared with conventional integral controller & ACS-PID controller under different non-linearity’s like Generation Rate Constraint (GRC).
fuzzy logic controllers in the presence of system non-linearity GRC &uncertain parameters are taken from the Egyptian power system load frequency control during summer and winter of 2008[12] and the gains of K p K I K D of the system can be self-tuned on-line using output of the system and the simulated results are designed in the MATLAB/SIMULINK are observed on comparison of proposed fuzzy self tuned-PID & ACS-PID controller.
2. The Conventional Integral & PID System Modeling. Key words: Load Frequency Control; Self-Tuning fuzzy Controller, Generation Rate Constraints.
1. Introduction: The problem of controlling the power output of a generator of a closely knit electric area so as to maintain the scheduled frequency. All the generators in such an area constitute a coherent group. So that all the generators will speed up and slow down together maintaining their relative power angles. Such an area is identified as a control area. The boundaries of a control area will generally coincide with that of an individual Electric Board Company [1]. These perturbations disturb the normal operation of the power system. A very well known PI/PID controller are used after many investigations and these controllers are used over half a centuries in the industrial control and automation process. The PI/PID controllers are simple for implementation [2, 3], design and low cost for linear systems. Whenever an operating condition change, the PID controller which is based on linearized model parameters will also vary the PID controller gains which are designed at operating conditions gives an optimal response at one operating condition gives a suboptimal response at other operating condition. And another drawback of PID controllers is human control of an experienced operator is essential.So,in order to overcome these drawbacks and to get some optimal response at all operating conditions self tuning of PID controllers using Fuzzy logic controllers come into action. Zeigler Nicolas method the most widely used tuning method and is very simple but it is not guaranteed one which will gives an effective response due to the changes that may happen during the process running time of the operating conditions. So, in recent years, Fuzzy logic controllers and fuzzy sets tools are used for designing of fuzzy self tuning of PID gains. This controller is used to update the PID controller gains K p
K I K D to meet closed loop system performance. Several control techniques based on Fuzzy and Takagi-Sugeno (TS) Fuzzy control system theory have been applied to LFC and Power system as a tool to improve the system performance [8, 9] The different loading conditions which we applied to self tuned
x& (t ) = Ax(t ) + Bu (t )
(1)
Assumptions are considered for Power system installed generation capacity and peak load are estimated as 23400MW and 18970MW, in 2008[12].The Approximated installed capacity of Non-reheat, Reheat, and Hydro electric Power stations are given as. 1. Non-reheat generating units represent by gas turbine Power stations represents approximately 25% of the installed capacity. 2. Reheat generating Units represent by the majority of the thermal stations and combined cycle Power stations which are approximated as 63% of the installed capacity. 3. Hydro electric Power stations are approximated as 15% of installed capacity. Fig (1) shows the block diagram of the Power system LFC model is represented by SIMULINK is given below. The Parameters of this model are divided into two sets. The first set of parameters does not depend on system operating conditions. The other set of parameters varies with the time according to the operating condition. The data required to calculate the changing parameters are concerned with the data of each generator including status (ON or OFF),type of unit (Non-reheat,reheat,hydro),unit rating (MW),unit Output (MW) for the operating condition under study, inertia of the unit, and spinning reserve of the unit in percentage of the unit rating. The simulink model considers the generating rate constraints GRC for different units. The applied values for GRC are 0.1P.UMW/min and 0.2p.uMW/min. for the reheat turbines and non reheat turbines, respectively. The GRC of hydro plants is neglected since its actual value is much greater corresponding to the time durations of practical disturbances [2]. The dynamic equations of this model can be written in the statespace form as:
∆P2(t) = x3(t)
= incremental changes reheat plant output in p.u
MW.
Where
x(t ) = [∆F (t )∆P1 (t )∆P2 (t )∆V2 ∆P3∆G(t )]t
∆V2
=
x4(t)
= incremental opening in steam valve of reheat
plant output in p.u MW
∆F (t ) = x1 (t ) = the incremental frequency deviation Hz ∆P1 (t ) = x2 (t ) = MW.
incremental change in non-reheat plant in p.u
∆P3(t) = x5(t)
= incremental change in hydro plant output in p.u
MW
∆Gt ( ) = x6(t)
= incremental opening in hydro plant inlet vane in
p.u MW
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Fig (2) A fuzzy controller with control system structure
The system model matrices A & B are displayed in the Appendix. The three loading conditions of Power system are considered to design ACS-based PI and PID gains.
3. Design of Fuzzy self-tuning of PID controller.
The below Fig (3) shows Designed Fuzzy self tuned PID controller
The Proposed design procedure includes two steps: 1. Finding the optimal gains of PID which Controls the system. 2. Design of fuzzy logic control (FLC), with self-tuning capabilities.
3. General Expressions for PID controller The of a PI controller is given below: K ( s) = K p +
KI + KDs s
(2)
Where K p K I and K D are proportional, integral and differential gains respectively.
U ( s ) = − K ( s ) * ∆F Where U ( s ) = output and,
(3)
∆F is the incremental frequency
deviation.
The designs steps of fuzzy self tuning can be summarized as follows: 1-Write the PID controller by the following equation: de(t ) (4) U = K p + K I ∫ e(t ) dt + K D dt This equation can also be written as: de(t ) U = K P 2 + K I 2 ∫ e(t ) dt + K D 2 dt (5) Where: = KP * KP1 , KI 2 = KI * KI1 , outputs from fuzzy controller.
K p2
KD2 = KD * KD1 are the gain
4. Design of a Controller
The input member ship functions of e and ∆e as shown in the fig (4, 5, 6) and are represented in the rule base are:
The below Fig(1) shows the Two input and one output variables of conventional fuzzy logic system
{ PB-Positive Big, PM-Positive Medium, PS-Positive Small, ZZero, NB-Negative Big, NM-Negative Medium, NS-Negative Small} and the outputs are represented in rule base as {B-Big, VBVery Big, MB-Medium Big, S-Small, MS-Medium Small};
X1 Y Y Fuzzy Logic System
X2 Fig (1)
Fuzzy Logic system
The output membership functions are: ZE-Zero Error, MS-Medium Small, S-Small, M-Medium, B-Big, MB-Medium Big, VB-Very Big Where: e
: error input normalizing gain. ∆e : Change in error input
normalizing gains. The Fig (2) shows below the Fuzzy logic controller with various control schemes
The rule base for KP1 is shown in the table below. ∆e e NB NM NS ZE PS PM PB
NB VB MB B ZE B MB VB
NM VB MB B ZE B MB VB
NS VB MB B ZE B MB VB
Fig (4) Rule base for determining
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ZE VB MB B MS B MB VB
PS VB B MB S MB B VB
PM VB MB B S B MB VB
PB VB VB VB S VB VB VB
K p1
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∆e e NB NM NS ZE PS PM PB
NB
NM
NS
ZE
PS
PM
PB
M M S MS S M M
M M S MS S M M
M M S MS S M M
M M S ZE S M M
M M S MS S M M
M M S MS S M M
M M S MS S M M
Fig (5) Fuzzy rule base for
∆e e NB NM NS ZE PS PM PB
NB ZE MS S M MB B VB
NM
K I1
NS
MS S M B MB MB VB
Results and Discussions: The results show that system is responding effectively for variation of uncertain parameters in the presence of nonlinearity Generation Rate Constraints. The self tuned fuzzy controller meets the required results of uncertain parameters over ACS –PID & conventional Integral controller.
S M B MB VB VB VB
ZE M B MB MB VB VB VB
PB
PS MB B VB VB VB VB VB
PM B B VB VB VB VB VB
VB VB VB VB VB VB VB
Fig(6) Fuzzy rule base for determining K D 1 3) The universe of discourse is normalized, the physical values is of the normalizing gains is obtained by dividing the boundary values of discourse of the input member ship functions of maximum of original values of e and ∆e.
4) Defuzzification is a mathematical process used to convert a fuzzy sets to real number and is a necessary step because fuzzy sets generated by fuzzy inference in rules must be somehow mathematically combined to come up with one single number as output of a fuzzy controller output. Defuzzification is applied as a final step to convert the fuzzy output to crisp value .Defuzzification is a process which converts the range of values of output variables into corresponding universe of discourse and it yields a non fuzzy control action from an inferred fuzzy control action. One of the Defuzzification methods is centroid method it is also called as centre of gravity or centre of area defuzzification .The widely used COA strategy the centre of gravity of the possibility distribution of a control action. r
∑ u =
µ ( xi ) xi
i =1 r
∑
µ ( xi )
i =1
Where x i a running point in the universe of discourse, and µ ( xi ) is its membership value in the member ship function
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The following conditions are: Case 1: Small disturbance in the system ∆ Pd =1%:In this a Small disturbance of 1% is applied to the power system and can observed that the damping of the system frequency is improved and simulation results shows that proposed FST-PID controller has less overshoot & Quick settling time when compared with Integral Controller and ACS-PID controller as shown in the fig(7)and fig(8) below.
Fig(7)
∆F
∆U Fig (8) System dynamic response for case (1)
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Case 2: Disturbance Variations: Fig (8) and fig(9) , illustrates the dynamic response of frequency deviation ∆F and control input ∆U when a step of ∆ Pd = 1% is applied, during 5 ≤ t ≤ 30 seconds. It is clear that the oscillations are quickly damped with the proposed FST-PID as compared to ACS-PID. Besides, the FST-PID settles faster whereas ACS-PID shows the opposite.
Fig (9) ∆F
∆U Fig (10) System dynamic response for case (2)
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Case 3: Tracking Disturbance Variations Operating conditions: Fig (9) and (10) show the dynamic response of ∆F and ∆U following a variation of as seen in Fig (12) and Fig (13). This variation covers both tracking represented by the ramp and regulation which represented by a step change. It is obvious from Fig (12) and (13) that the system driven by FST-PID controller, shows better performance and clearly improved than ACS- PID fast response with relatively small overshoots).
Condition1
Condition2
Condition3
H
4.9598
6.0168
5.8552
Pn1
0.2730
0.3112
0.2433
Pn2
0.7007
0.5200
Pn3
0.1364
0.1798
0.6179 0.1389
Where H:
Equivalent Inertia constant of the system. & Pn1, Pn2, and Pn3: Nominal rated regulating power output for non-reheat, reheat and Hydro Plants (p.u MW)
List of symbols:
a) Fig(12) ∆F
1) 2) 3) 4) 5) 6) 7)
R1, R2 - 2.5(Hz/p.u MW) R3 - (Hz/p.u MW) D - 0.029(p.u MW/hz) T1 & T2 –0.4Sec T3 - 90sec Tb -6sec Td -5sec
8) 9)
Tw M
10)
-1.0sec - 0.5
TL
- 2.5 sec/Hz
∆U Fig(13) shows the system dynamic response
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In this paper Self tuned FST-PID controller is designed and its performances are compared with conventional Integral controller &ACS-PID controller under different loading conditions. Simulation results prove that the proposed controller shows the robust performance with different non-linearity like GRC under dynamic operating conditions. The simulation results shows that FST-PID controllers is powerful in reducing the frequency deviations under a variety of load perturbations of LFC for proposed power system.
Conclusion:
The dynamic equations are: a=
A=
D − 2H − Pn1 R1T1 − mPn 2 R 2 T2 − Pn 2 R 2 T2 T D − 2 a d − 1 2H a Td D − 1 2 H
1 2H −1 T1
1 2H
0
1 2H
0
0
0
0
−1 Th
0
0
1 m − Th T2 −1 T2
2 aTd 2H
2 aTd 2H
0
− aTd 2H
− aTd 2H
0
0 0 2 aTd 2 − Tw 2H − aTd 2H
0 0 0 2 2 + T3 Tw −1 T3
Pn3 R3T3
0
B= 0
− Pn1 T1
− mPn2 T2
− Pn2 T2
2 * Pn3 T3
− Pn3 T3
Fig (14) The Simulink representation of a power system Load Frequency model
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References: 1) Modern Power system analysis by D.P.Kotari, I.J.Nagarath ‘Third edition’. 2) Design of a Fuzzy Self-Tuning Optimal PID Load Frequency Controller for the Egyptian Power System.
3) C. E. Fosha, O. I. Elgerd, “The megawatt-frequency control problem: a new approach via optimal control theory”, IEEE Trans. PAS, vol. 89, pp. 563–567, April 1970. 4) A. Khodabakhshian, N. Golbon, “Unified PID design for load frequency control”, In Proc. 2004 IEEE Int. Conf. on Control Applications (CCA), Taipei, Taiwan, pp. 1627– 1632, September 2004.
5) G.J. Silva, A. Datta, et al., “New results on the synthesis of PID controllers”, IEEE, Transactions on Automatic Control, 47(2), pp. 241-252, 2002. 6) Keven M. Passino and Stephen Yurkovich, "Fuzzy Control", Addison Wesley longnan, Inc., 1998.
7) G.R. Chen and T.T. Pham, "Introduction to fuzzy sets, fuzzy logic, fuzzy control system", RC. Press,Boac Raton, FL, USA, 2000. 8) Michall Petrov, Ivan Ganchev and Ivan dragotinov, “Design Aspects of Fuzzy PID Control”, International conference on soft computing, Mendel “99”, Brno, Czech Republic, 9-12 June, pp. 277-282, 1999.
9) H. A. Shayanfar and H. Shayeghi A. Jalili, " Takagi-Sugeno Fuzzy Parallel Distribution Compensation Based Three-Area LFC Design", International Journal on Technical and Physical Problems of Engineering, Issue 8, Volume 3, Number 3, pp. 55-64, Sept 20. 10) R. Dhanalakshmi and S. Palaniswami, "Application of SelfTuning Fuzzy Logic PI Controller in Load Frequency Control of Wind-Micro Hydro-Diesel Hybrid Power System", European Journal of Scientific Research ISSN 1450-216X Vol. 79 No. 3, pp. 317-327, 2012.
11) Zareiegovar G., Sakhavati A. , Nabaei V. and Gharehpetian G. B., " A New Approach for Tuning PID Controller Parameters of Load Frequency Control Considering System Uncertainties”, 9th International Conference on Digital Object, pp. 333 – 336, 2008. 12) Egyptian Electricity Holding Company, 2007/2008 Annual Report. http://www.egelec.com/annual%20report/2007.html.
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