area of automatic generation control for multi area interconnected thermal power system. The resultant hybrid algorithm named as âhPSO-PSâ has been applied ...
IEEE 2nd International Conference on Communication, Control and Intelligent Systems (CCIS)
Optimal LFC System of Interconnected Thermal Power Plants using Hybrid Particle Swarm Optimization-Pattern Search Algorithm (hPSO-PS) Niharika Soni Deptt. of Electronics Engg, Rajasthan Technical University, Kota, Rajasthan, India
Rajesh Bhatt Deptt. of Electronics Engg, Rajasthan Technical University, Kota, Rajasthan, India Girish Parmar Deptt. of Electronics Engg, Rajasthan Technical University, Kota, Rajasthan, India
Abstract—In this paper, the application of pattern search algorithm (PS) in conjunction with the well known algorithm “particle swarm optimization” (PSO) has been explored in the area of automatic generation control for multi area interconnected thermal power system. The resultant hybrid algorithm named as “hPSO-PS” has been applied to optimize the parameters of proportional integral controllers in the two areas of power plant. The control optimization problem has been defined with lower and upper bounds of the controller’s parameters along with the ITAE as an objective function. The simulation results have also been compared with the previously proposed PSO/PI and PSO/PID approach in the literature and the results show that the approach hPSO-PS/PI proposed here provides far better results than PSO/PI and PSO/PID for the same system and same ITAE as an objective function in terms of the less settling times and peak overshoots, better dynamic responses, quick response of returning back to the zero frequency as well as the tie line power deviations with fewer oscillations. The results have been simulated in MATLAB environment. Keywords: Automatic Generation Control, Two Areas Interconnected Power Systems, PI Controllers, Particle Swarm Optimization and Pattern Search
I. INTRODUCTION The production of generation of electric power is dependent on the generation plants. The generators are interconnected by transmission network in order to meet the load demand in geographical areas which in turn make the complicated large power systems. The large power systems fall in to two categories according to the control areas based on the principle of coherency. The tie-lines are used to interconnect the coherent areas, exchange contractual energy between areas and provide inter area support during special operation. If a mismatch is occurred in real power balance, it will affect the system frequency. So, in order to maintain the system frequency at a desired level, the automatic generation control (AGC) also known as load frequency control (LFC) 978-1-5090-3210-5/16/$31.00 © 2016 IEEE
comes in the picture which in turns control the generation in an area by eliminating the mismatch as well as the inadvertent exchange of power with other areas via tie-lines [1-2]. The number of control strategies used for LFC problems have been discussed and implemented in [3] and the relative comparison among the AGC controllers for the LFC problems has already been suggested in literatures [4] which include I, PI, ID, PID and IDD have been implemented for controlling load frequency in an AGC system. Because optimization/tuning of the parameters of the controllers used in multi area inter connected thermal power plants is necessity for AGC, number of the research articles in this direction have been published in the literature and this topic has also become a keen interest of the researchers. In this direction, Soft computing based optimization methods have come in the picture to enhance the performance of the AGC of interconnected power system. The soft computing based optimization methods include BFOA and ICA for PID controllers in multi area power system, DE for PI controller, DE for classical controllers in MAMS-PS, TLBO technique for I and PID controllers for a MUMS-PS, an emotional learning based controller for LFC system, FA for AGC of an interconnected unequal three area power system, ABC for AGC system and GSA for PI/PIDF controller for AGC system [5-14]. Further, AI/Soft Computing Techques like Fuzzy Logic, ANN, GA and PSO have been implemented for AGC/LFC with overcoming the limitations of conventional control techniques [15]-[17]. In [18-19] the hGWO-PS algorithm has been applied for the AGC of the two area interconnected non reheat thermal power plant consisting 2DOF-PID controllers and the application of PSO algorithm has been explored in [20] for tuning the parameters of PI and PID controllers of the same system and the comparative study has also been given in [20]
In this paper, an attempt towards evolving the new hybrid technique named as the “hybrid particle swarm optimization and pattern search (hPSO-PS)” to tune the parameters of proportional integral controllers (PI) in the two area thermal power system has been made. The hybrid technique hPSO-PS is the combination of the global search method named as PSO and the local search method named as PS. A comparative study between PSO/PI [19], PSO/PID [19] and proposed hPSO-PS/PI approach is given. The system with PI controllers optimized by hPSO-PS provides far better performance in terms of settling times, overshoots, ITAE values and system oscillations than PSO optimized PI and PID controllers for the same system under investigation.
The output of PI controller is defined as: PI-Controller:
=
( )+
∫ ( )
(4)
The signal (u) goes to the plant which yields the new output (Y). This new output (Y) goes back to summer through the sensor again to find the new error signal (e). After receiving this new error signal, the controller computes derivative and integral of this error signal e again. This process remains continuous till the error is minimized to optimum value or ideally zero.
The rest of this paper is as follows: In Section II, the two areas interconnected power system of thermal plants and PI controllers have been discussed. The ITAE as objective function is defined in Section III. Section IV provides the brief introduction of PSO and Section VI discusses Pattern Search technique. The simulation results are elaborated in Section V. The conclusion of paper is given in Section VI along with the references at the end. II. TWO AREA INCONNECTED THERMAL POWER SYSTEM WITH PI AND PID CONTROLLER The two area interconnected power system of thermal power plants [6] is considered in the proposed work and it is shown in Fig. 1. The ratings of each area and nominal load are 2000 MW and 1000 MW. From Fig. 1, the ACE for area-1 and area-2 are defined as: Fig. 1: Two Area Interconnected Thermal Power Plants
ACE 1 = B1Δf1 + ΔPTie
(1)
ACE 2 = B2 Δf 2 − ΔPTie
R
e
(2)
u
PI/PID Controller
Y
Plant
A. PI Controller The transfer function of PI controller is given as follows: PI-Controller: ( ) =
+
(3) Fig. 2: Closed Loop System with PID Controller
The block diagram of closed loop control system with PI controller is shown in Fig. 2. The variables for the closed loop system are defined in TABLE I [19] as follows:
III. OBJECTIVE FUNCTION An Integral of time multiplied absolute error (ITAE) is used as an objective function in the present work. and it is defined by (7) instead of other integral based objective functions [18, 20].
TABLE 1: VARIABLES IN C LOSED LOOP CONTROL WITH PI AND PID C ONTROLLERS Abbreviations Nomenclature R Reference input or set-point Y Controlled variable or Actual output e Error signal
Definition/Description What is expected from the system is defined as the set point The variable to be controlled and measured, is defined as the controlled variable or actual out put Error signal is the difference between R and Y and it goes to the PI/PID controller which determines both the derivative and the integral of this error signal.
J = ITAE =
t simulation ∫ 0
(
)
w1 ⋅ Δf1 + Δf 2 + ΔPtie ⋅ t ⋅ dt
(5)
where, Δf1 , Δf 2 represent system frequency deviations;
Δ Ptie is incremental change in tie-line power and; t simulation denotes time range of simulation; 226
uses a series of polls. To get trial points at each poll, a number of trial steps are added to the polls. The objective function value is calculated at these trial points through a sequence of exploratory steps and compared with its previous value. The trial step corresponds to least value of and it is then selected to produce the subsequent estimation of the patterns polls. The trial steps are produced by a step length parameter. The Δ k value is updated in subsequent polls as per value. The improvement of Δ k helps the algorithm to converge [18, 2021]. This method has been introduced in [18, 20-21] in conjunction with the GWO and the resultant hybrid technique has been applied for the same system with 2DOF-PID controllers with better results.
IV. PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHM A population based random optimization technique named as Particle Swarm Optimization (PSO) is inspired by social behavior of bird flocking or fish schooling. The system is initialized with followings: •
A population of random solutions
•
Searches for optima by updating generations.
The followings are in PSO: •
Particles fly through the problem space and the current optimum particles follow them.
•
Each individual manages its flying according to the experience of its own flying and the experience of its companion’s flying.
•
VI. APPLICATION OF HPSO-PS TO POWER SYSTEM AND SIMULATION RESULTS
In the problem space, each particle has track of its coordinates which are associated with the best solution and this value is known as ‘pbest’. Another "best" value is tracked by the particle swarm optimizer and it is known as global best value abbreviated as ‘gbest’.
A. ITAE Value In this paper, two PI controllers have been applied to the two area interconnected non reheat thermal power plant and the SIMULINK environment of MATLAB is used for the simulation. The PSO algorithm run for 40 times and PS for 10 times. The simulation results show that the hPSO-PS optimized PI controllers gives smooth and better system dynamic responsesin terms of peak overshoots, settling times and ITAE value for same system under study as compared to PSO optimized PI and PID controllers [19]for the same system under study.
The flowchart given in Fig. 3 describes the process in brief. Start
Specify the parameters for PSO
At t=0 second, a 10% step load increase in area-1 is introduced and the parameters, oscillations and ITAE value obtained for hPSO-PS optimized PIcontrollersare listed in TABLE II and PSO optimized PI/PID controllers [19] are also tabulated in TABLE II for showing the superiority of proposed approach hPSO-PS over [19] for the same system under consideration and for the same objective function in terms of less ITAE value and better smoothness.
Generate initial population Gen.=1 Objective function evaluation Find the fittness of each particle in the current population
TABLE 2: COMPARISON TABLE OF TIME DOMAIN PARAMETERS FOR D IFFERENT APPROACHES (HPSO-PS/PI, PSO/PI AND PSO/PID) FOR C ONSIDERED SYSTEM
Gen.=Gen.+1 Gen. > Max. Gen.?
Stop Yes
No Update the particle position and velocity
Techniques/ Controllers PSO/PI[19]
ITAE
KP
KI
KD
3.8669
0.4076
0.4054
-
PSO/PID [19]
1.5149
0.4029
0.4929
0.4730
hPSO-PS/PI [proposed]
0.3848
0.2045
0.3195
-
Fig. 3: Flow Chart of PSO Algorithm
Oscillations More oscillations Very less oscillations Less oscillations than [19]
B. Comparison of System Dynamic Responses
V. PATTERN SEARCH ALGORITHM
A step increase in demand of 10% is applied in the area-1 at time t=0 second:
The complex problem which cannot be solved by conventional optimization techniques, are easily solved by pattern search algorithm which is effective and simple in nature [18, 20-21]. A flexible operator is used in PS algorithm to optimize the local explore capability finely. The PS method
To show the superiority of the introduced approach hPSOPS/PI over PSO/PI and PSO/PID [19], the relative comparisons are given in Figs. 4-7. The simulation results 227
show that the hPSO-PS/PI for AGC of considered system provides the better dynamic responses as compared to PSO/PI and PSO/PID approaches in terms of settling times, peak overshoots and oscillations or smoothness. The ITAE values, settling times and overshoots in frequency and tie-line power deviations for the aforementioned disturbance are also given in Table 3 for better illustration of the proposed approach. Table 3 shows that the hPSO-PS/PI approach gives improved time domain specifications as compared to PSO?PI and PSO/PID approaches in literature [19] for the same system Fig. 7: ∆
with hPSO-PS/PI, PSO/PI and PSO/PID Approaches
TABLE 3: TIME DOMAIN PARAMETERS OBTAINED BY D IFFERENT APPROACHES ITAE 1.5149 ITAE 3.8669 ITAE Fig. 4: ACE with hPSO-PS/PI, PSO/PI and PSO/PID Approaches 0.3848
Settling Times (2% band) PSO/PID [19] ∆ ∆ ∆ 8.38 9.51 9.98 Peak Overshoots 0.1203 0.078 0.0259 Settling Times (2% band) PSO/PI [19] ∆ ∆ ∆ 25.68 24.16 22.21 Peak Overshoots 0.1894 0.396 0.04678 Settling Times (2% band) hPSO-PS/PI (Proposed) ∆ ∆ ∆ 7.32 11.98 10.32 Peak Overshoots 0.022 0.027 0.0077
VII. CONCLUSION
Fig. 5: ∆
A Load frequency control system (LFC) of two area interconnected thermal power plants with two proportional Integral controllers has been considered for the sake of analysis. The parameters of the PI controllers have been optimized by the new hybrid algorithm called as hPSO-PS along with the ITAE as an objective function. The hPSO-PS is the combination of the global search algorithm PSO and local search algorithm PS. The results have been simulated using MATLAB/SIMULINK software. The dynamic responses of the system under investigation have been studied for 10% step load change at area1 and the relative comparison between hPSO-PS/PI, PSO/PID and PSO/PI approaches for the same system has been given. The simulation results show that hPSO-PS/PI approach for AGC provides better dynamic performances and smooth response in terms of lower ITAE, less settling times and less overshoot over PSO/PI and PSO/PID approach for the same system.
with hPSO-PS/PI, PSO/PI and PSO/PID Approaches
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with hPSO-PS/PI, PSO/PI and PSO/PID Approaches 228
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