GRD Journals | Global Research and Development Journal for Engineering | International Conference on Innovations in Engineering and Technology (ICIET) - 2016 | July 2016
e-ISSN: 2455-5703
DE and PSO optimized PID Controller for Automatic Generation Control of Multi-Source Power System 1P.
Nagajothi 2Dr. K. Gnanambal 1 PG Scholar 2Professor 1,2 Department of Electrical and Electronics Engineering 1,2 K.L.N. College of Engineering, Pottapalayam - 630 612, Tamilnadu, India. Abstract There are several methods are available for Load Frequency Control in interconnected power system. This paper proposes an optimized PID controller by DE tuning for AGC of two area power system. The gain parameters of the PID controller are optimized by commissioning DE and PSO technique. In this paper ISE criterion is used as a performance index. The action of this proposed power system with optimal tuned PID controller provides a satisfactory balance between frequency overshoot and transient oscillations with minimum steady state error. A comparative study on tuned values has been presented to verify effectiveness between DE and PSO method. The simulation results reveal the effectiveness of the designed system in terms of reduced settling time and oscillations with tuning of DE. MATLAB/SIMULINK was used as simulation tool. Keyword- AGC, Differential Evolutionary algorithm Hydrothermal Power system, ISE,PID controller, PSO algorithm __________________________________________________________________________________________________
I. INTRODUCTION The power system has the main aim of Continual matching of load demand and power generated. The output power from the power system should provide a certain level of consistency in frequency and magnitude of the voltage. Thus, maintaining power system stability is the main challenging issue in recent decades due to frequent variation in load demand. Power system stability means to remain in a condition of operating stability under normal working conditions and to regain an adequate state of equilibrium after disturbance occurs. A power system operator has to continuously monitor the health of a power system and performs control actions when needed. The successful operation of an interconnected power grid is maintaining the system frequency and interchanged power at their respective scheduled power levels. An interconnected power system basically consists of generating units, the transmission lines and the loads[1]. While operating generators there may be some disturbances such as sustained oscillations in the speed or periodic variations in the torque. This kind of disturbances may result in voltage or frequency fluctuation. This may affect the other parts of the interconnected power system. All these disturbances are called as faults[1]. The generators to lose synchronism while fault occurs. With these factors in mind, the primary condition for a power system with stability is synchronism. Besides this condition, there are other important conditions such as steady-state stability, transient stability, harmonics and disturbance, the collapse of voltage and the loss of reactive power[2]. In a power system, there are two types of control mechanisms available to achieve the acceptable voltage and frequency profile. Automatic Voltage Regulator is a control method used to balance the reactive power (i.e,Voltage) and Automatic Generation Control is used to balance the real power (i.e,Frequency) in an interconnected power system network. The main aim of AGC is to minimize the area transient frequency deviations, tie line power interchange and to ensure that steady state errors maintain with zero level[2]. According to Indian Electricity Grid Code(IEGC) if rated system frequency is 50 Hz and the target range for frequency control is should be 49.0-50 HZ, the statutorily acceptable limits are 48.5-51.5 Hz. However, the users of power system change the loads more frequently. This gives the sudden mismatch between the generation and load. This mismatch power causes a change in generator speed and consequently the frequency variation from its nominal value. So the control mechanism is necessary to cancel the random load changes and to keep the frequency at the nominal value. This article is ordered as follows. Section 2 presents a test power system model with their time constant functions and PID controller general structure. We addressed a review in Section 3 which has tuning method of PSO and DE algorithms. In Section 4, the comparison between PSO tuned PID controller and DE tuned PID controller parameters are given which shows the effectiveness of PSO tuned PID controller parameters of an AGC system.
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DE and PSO optimized PID Controller for Automatic Generation Control of Multi-Source Power System (GRDJE / CONFERENCE / ICIET - 2016 / 001)
II. MATERIALS AND METHODS A. Power System Model The AGC system is explored of an interconnection of two areas. Thermal unit is considered as an area 1 and area 2 is a hydro system. The transfer function of each component is described below. The transfer function block diagram model of the two-area hydrothermal system is shown in Fig.1with SMES unit in the thermal area. In this, the effect of SMES is presented with an optimal tuning of PID controller gain values which shows the effectiveness of optimization algorithms and SMES unit. In Fig.1 R1,R2 is considered as regulation parameters of thermal and hydro respectively.B1 and B2 represents the frequency bias parameters.ACE1 and ACE2 stand for Area Control Errors.TG is speed governor time constant of generating units in sec; Tt is steam turbine time constants in sec; TW is nominal starting time of water in penstock in sec; TR is the hydro turbine speed governor reset time in sec; TG is hydro turbine speed governor main servo time constant in sec; Kp is power system gain constant in HZ/Pu;Tp Power system time constant in sec; T12 is the synchronizing coefficient and ΔF1 and ΔF2 are the system frequency deviations in Hz[3].The relevant parameters are given in Appendix[1].Automatic Generation Control system incorporates the following actions in an interconnected area of the power system. They are parameter variations, Uncertainties in transfer function model, Load characteristics, Excitation control and Parallel AC/DC link.
Fig. 1: The two area hydrothermal block diagram model with the SMES unit in thermal area
B. Controller Structure and Objective Function To control the frequency deviations, PID controllers are presented in each area, The structure of PID controller is shown below
Fig. 2: General Parallel PID controller
C ( s) K P
K P (1
Ki Kd s s
1 Td s ) Ti s
(1) (2)
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DE and PSO optimized PID Controller for Automatic Generation Control of Multi-Source Power System (GRDJE / CONFERENCE / ICIET - 2016 / 001)
The area control errors are given as the input to the controllers, ACE is given by[2]; e1(t)=ACE=B1ΔF1+ΔPtie (3) e1(t)=ACE=B2ΔF2-ΔPtie (4) The output of PID controller U is given as the control inputs of power system[4].The standard output specifications in the time domain analysis are peak overshooting, rise time, settling time and minimizing steady state error. In this paper, Integral Squared Error is used as error criteria. ISE criterion has the main function of integrating the squared error over time. ISE will penalize large errors because large errors will be much bigger than smaller ones. ISE is specified to eliminate large errors quickly and this control system designed parameter leads to fast response. The power change between control areas will minimize quickly, ISE is a better objective function in AGC studies and hence employed in the present paper. The objective function is expressed as: t
J=
(f
f 22 Ptie2 12 )dt
2 1
(5)
0
From the above equation (5) the optimum PID controller gain settings are obtained.
III. OPTIMIZATION OF THE PID CONTROLLER GAIN SETTINGS (KP,KI,KD) The optimal gain settings of the PID controller are obtained using Integral Squared Error’s criterion is applied for weighs large errors heavily and small errors lightly.ISE performance index is defined as follows, t
J=
(f
f 22 Ptie2 12 )dt
2 1
(9)
0
In This work PID, controller gains are tuned by DE and PSO algorithms [3][4]. The effectiveness of the SMES unit in interconnected area is compared with the area without SMES unit. A. Proposed methodology for tuning of controller using Differential Evolutionary algorithm and Particle Swarm Optimization Differential Evolution is the population based algorithm. This method has real coding of floating point numbers.[3,8].The basic idea behind the DE is generating trial parameter vectors and it adds the weighted difference between two population vectors to the third vector. The general Pseudo code for Differential Evolutionary and Particle Swarm Optimization algorithm is given below[5]. By using this general structure the coding is formed with the objective function as mentioned above equation (9). 1) Pseudo code for DE algorithm Input: P0, Population, NP, F, CR. Output: S. Repeat P1=Random member(Population). Until P1≠P0 Repeat P2 =Random member(Population). Until P2≠P0ѴP2≠P1 Repeat P3=Random member(Population). Until P3≠P0ѴP3≠P1ѴP3≠P2 Cutpoint=Random Position(NP) S=0 For (I to NP) If(i=cutpoint Rand()<CR) Si=P3i+F*(P1i-P2i) Else Si=P0i End End Return(S). From the above pseudo code S represents output of the objective function, F denotes Weighting factor (0,2),Cross Overweight ratio is (0,1).
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DE and PSO optimized PID Controller for Automatic Generation Control of Multi-Source Power System (GRDJE / CONFERENCE / ICIET - 2016 / 001)
2) Pseudo Code for PSO Algorithm 1) For each particle: Initialize particle 2) Do: a) For each particle: 1) Calculate fitness value 2) If the fitness value is better than the best fitness value (pBest) in history 3) Set current value as the new pBest End b) For each particle: 1) Find in the particle neighborhood, the particle with the best fitness[7]. 2) Calculate particle velocity according to the velocity equation (10) Vik+1=wVik+c1rand1(..)x(pbesti-sik)+c2rand2()x(gbest-sik) (10) where, vikvelocity of agent i at iteration k, wWeightingfunction. cjweightingfactor, randuniformly distributed random number between 0 and 1, Sikcurrent position of agent i at iteration k, pbestipbest of agent i, gbestgbest of the group. 3) Apply the velocity constriction. 4) Update particle position according to the position equation.(11) w=wMax-[(wMax-wMin )x iter] / max Iter (11) where wMax initial weight, wMin final weight, maxIter maximum iteration number, iter current iteration number. 5) Apply the position constriction. End. While maximum iterations or minimum error criteria are not attained. In the initialization step, the position in each dimension is initialized randomly. Velocities can be initialized randomly or set to 0.In the original algorithm; particles' velocities on each dimension are clamped to a maximum velocity Vmax. If the sum of accelerations would cause the velocity on that dimension to exceed Vmax, which is a parameter specified by the user, then the velocity on that dimension is limited to Vmax. In practical applications, there is also a position constriction. The search space is bounded, so the particles' positions in each dimension have to be constrained within those bounds.
IV. RESULTS AND DISCUSSIONS A two area power system with a diverse source of the generation is considered. The PID controller gains are tuned by using DE and PSO optimization algorithms in the interconnected power system. The simulation outputs are given below and their respective optimal gain and ISE values are mentioned. A. Implementation of optimization Algorithms DE algorithm are controlled by two parameters: Scaling Factor(s) and CrossOver Constant(CR).These parameters are generally chosen in the range 0 to 1.Moreover the number of population and maximum iteration should be properly chosen so that the satisfactory performance algorithm can be achieved with minimum computational effort. The tuned control parameters are: number of population size=50, maximum iteration=100,Scalling Factor(s)=0.5,Cross Over(CR)=0.8[6]. For PSO [7] algorithm the controlled variables are population size(NP),Number of iterations(iter),Cognitive Constant(C1), Social Constant(C2) and inertia weight. Their values respectively 50,100,2,2,0.6. B. Dynamic Responses and Results Discussions The simulation was performed to investigate the performance of two area hydrothermal system with tuning of DE[8] and PSO technique[6].The gains of the PID controller, ISE and settling time of the system is discussed below.By simulating the given two area model the objective function ISE will be obtained. The dynamic responses of the system by commissioning soft computing techniques are shown in fig( 4,5 ). The optimum values of PID controller gains by PSO-PID and DE-PID are given in table 1.The dynamic response of frequency deviation shown in Fig 3 and the corresponding tie line incremental deviation is shown in Fig 4.
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DE and PSO optimized PID Controller for Automatic Generation Control of Multi-Source Power System (GRDJE / CONFERENCE / ICIET - 2016 / 001)
Fig. 4: Dynamic response of frequency deviation (Δf) with 1% step load disturbance.
Fig. 5: Dynamic responses of incremental change in power (ΔPtie12) with 1% step load disturbance. Parameters DE-PID PSO-PID Kp 2.5041 2.6258 Ki 0.0148 0.0014 Kd 0.0751 0.7149 ISE 0.0204 0.0680 MaxΔf 0.0021 -0.0253 ΔPtie12 0.2506 0.2507 Table 1: Optimized PSO and DE tuned PID controller parameters.
The above table the significant improvements in terms of ISE and maximum frequency deviation are obtained in the system response with proposed PSO and DE-tuned PID controller parameters. From statistical analysis of table 1,it is clear that minimum objective function value is obtained with DE tuning (ISE:DE-PID=0.0204, MaxΔf=0.0021). That from the tabe1 the proposed soft computing method DE is better than the PSO tuning in terms of ISE and frequency deviations value obtained.
V. CONCLUSION A comprehensive mathematical model for AGC of two area interconnected hydrothermal power system has been presented in this paper. The system frequency and steady state errors due to small load disturbances were found to persist for a longer duration even with optimal gain settings of PID controller. It has been shown that oscillations can be effectively damped out with DE tuned PID controller. It has also been observed that the PID controller with Evolutionary tuning of ACE for a AGC system substantially reduces the settling time of oscillated frequency deviation.
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DE and PSO optimized PID Controller for Automatic Generation Control of Multi-Source Power System (GRDJE / CONFERENCE / ICIET - 2016 / 001)
APPENDIX P1 = KP2 = 120 Hz/p.u. MW TP1 = TP2 = 20 s R1 = R2 = 2.4 Hz/p.u. MW B1 = B2 = 0.4249 TG = 0.08 s TT = 0.3 s T12 = 0.0866 T1 = 41.6 s T2 = 0.513 s TR = 5 s TW = 1 s D1 = D2 = 8.333 · 10_3 p.u. MW/Hz PR1 = PR2 = 1200 MW
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