Application of Search Group Algorithm for Automatic Generation Control of Multi-area Multi-source Power Systems

This paper proposes a new Search Group Algorithm based PID controller, to deal with Automatic Generation Control of two-area with six unit power system. The supremacy of SGA tuned PID controller is being shown using the comparative study with Firefly Algorithm (FA) optimization method for the same test system using ITAE as an objective function. It has been demonstrated that SGA tuned PID controller improves the performance in a large compared with FA tuned PID controller. Furthermore variation in nominal values of operating load condition and system parameters with the position of step load perturbation is being carried out to achieve sensitivity analysis. From the result of sensitivity analysis it clearly depicts the robustness of the suggested method (SGA with PID controller) for two-area with six unit power system in AGC. Finally for better investigation, the proposed method is also examined by applying randomization in step load.


Introduction
Power systems arena is thriving day by day which leads to consider a major factor as Automatic Generation Control (AGC) for stable and secure power system operation. AGC plays a vital role to maintain the consistency in frequency with tie-line power. There is a great gap between electrical load demand and power generation which leads to deviation in outcomes. AGC nullifies the Area Control Error (ACE) using calculation with respect to corresponding load change in each area by adjusting automatically the generator set points. ACE is defined as the linear combination of frequency variation to the corresponding distortion in net tie-line power interchange [1][2][3][4][5]. Researchers are proposed number of control schemes in AGC of power systems to achieve optimized result.
The authors were investigated the different AGC based generic controllers in multi-area multi-source power system [6][7][8][9]. Sharma et al. have presented optimal design of AGC regulator controller in frequency regulation of multi-area power system with diverse power generating units [10]. Guha et al. have proposed Grey Wolf Optimization (GWO) based classical controller with PI/PID structure for AGC in multi-area power systems [11]. Saroj et al. have presented the supremacy of Firefly Algorithm tuned PID controller of two-area interconnected power system for AGC [12]. The effectiveness of AGC is not limited to artificial intelligence techniques simultaneously it depends on objective function as well the controller structure chosen which is clearly signifies from past literature.
Recently, metaheuristic based algorithm known as the Search Group Algorithm (SGA) is being proposed by Matheus Silva Goncalves et al. for the application to truss structure [13]. SGA is a population oriented search algorithm which maintains the balance in the design domain between the exploration & exploitation. The novel contributions in this paper are: (i) The demonstration of the superiority of new powerful computational intelligence technique like SGA over FA tuned PID controller for AGC (ii) To show robustness of SGA based PID controller. Here, two area six unit like hydro, gas and thermal units are taken for investigation [14]. The empirical analysis result reflects the supremacy of the suggested method. Lastly, to show the effectiveness of the tuned controller parameters, variation in nominal values of system parameters, operating load condition with the position of SLP is carried out to achieve sensitivity analysis.

Power System modelling:
Firstly,2-area with 6-unit power system is demonstrated in Fig.1. The nominal loading is being contributed based on the decision of the participation factor assigned by each unit. After summing each control participation factor the outcome should be equivalent to unity. Participation factor for hydro, gas and thermal units are evaluated as 32%, 13% and 55% respectively. The system parameters values are represented in Appendix. Regulation parameters R1, R2 and R3 shown in Fig.1 denotes thermal, hydro and gas unit respectively.

Fig. 1. Transfer function model of test system
The control outputs are represented as UT for thermal, UH for hydro and UG for gas units. The participation factors are represented as KT for thermal, KH for hydro and KG gas units. TSG, TT represents time constant of speed governor for thermal units and reheat steam turbine in second respectively.TW represents penstock base starting time of water in sec. TRS represents reset time for speed governor, TRH represents time constant for governor droop, TGH represents time constant for main servo of speed governor of hydro turbine in sec respectively. XC represents lead-time constants and YC represents lag-time constants of speed governor for gas turbine in sec respectively. cg represents gas turbine and bg represents valve positioned based gas turbine constant. TF represents time constant of fuel and TCR represents time delay of combustion reaction in sec of gas turbine. TCD represents time constant of discharge volume for compressor based gas turbine in sec. KPS represents gain of power system in Hz/p.u.MW. TPS represents time constant of power system in sec. ΔF, ΔPD are the variation in frequency and load respectively.

Controller design with objective function
Circuit diagram of PID controller is shown in Fig. 2.
Where KP: Proportional gain, KI: Integral gain and KD: Derivative gains. The general s-domain PID controller transfer function is given by.

Fig. 2. PID controller structure
Errors inputs to the controllers of the corresponding ACE are mentioned in equations (2-3): , 0100 (201 https://doi.org/10.1051/e3sconf/201 0 0 E3S Web of Conferences SeFet 2019 9) 987 87 10 5 5 The performance criteria suitable for AGC studies are Integral Time multiplied Absolute Error (ITAE) as reported in literature [15]. ITAE is used as objective function which is provided in equation (4): Equation (5-6) represents the optimization problem for the design issue Minimize the value of The minimum parameters values are chosen as -2.0 and maximum value is 2.0 of PID controller.

Search Group Algorithm
A population-based optimization method as Search Group Algorithm was being proposed by M.S. Goncalves et al. [13].The important function of SGA is categorized into five steps is depicted in below.

Phase-1: Initial Population
Randomly initial population P is chosen based on equation (7) ) ( Where j = 1 to n, i = 1 to npop Pij represents as the j th design variable of population P for i th individual. All design variables summation is n. npop signifies the total of population. The range of identical variable U [0, 1] is between 0 to 1 which is arbitrary in nature. The lower limit is X j min and the higher limit is X j max of j th design variable.

Phase-2: Initial search group selection
Initially the population has being formed after that objective function is evaluated, a benchmark tournament selection [13] is applied by selecting ng individuals from the population P to build the search group R. In every cycle If Ri denotes the i th row of R, then R1: denotes the finest design, Rng: denotes the coarse design in R, ng: denotes the members count in search group.

Phase-3: Selection of mutated search group
New offspring's (individuals) are generated by substituting nmut individuals from R to increase the capabilities of global population search which is evolved from equation (8) ] Where X mut j j th design variable of known mutated individual.

→ 
Mean, →  Standard deviation, →  random variable Choosing of worst objective function is being replaced by "inverse tournament" selection.

Phase-4: Family generation of every search group member
Family defines as the generation of set of offspring's (individuals) from search group member using perturbation analysed by equation (9).

Firefly Algorithm
Yang et al. [16] developed a meta-heuristic technique termed as Firefly Algorithm (FA) which is based on bioluminescence that is a biochemical process by the flashing characteristics (flashing light) of fireflies. For mating the flashing light may use as the main courtship signals [17,18].It is based on the following three fire-flies characteristics: Every firefly having unisex property gets attracted among them in spite of their sex. Based on brightness the firefly gets attracted using distance parameters. The optimized objective function decides the brightness of a firefly. The Firefly algorithm is elaborated detail in [12].

Analysis of results with discussion
In this paper MATLAB with SIMULINK is used to design and simulate the model for studying the system. SGA programs are written separately with MATLAB(.m) program file using control parameters and SGA parameter by taking step load perturbation of 2% at t=0.0 sec in area-1. SGA parameter plays a prominent role and it is chosen according to literature [13]. Table 1 includes the control parameter values of SGA which is applied in the algorithm. Table 1. SGA Parameter.  Table 2. At t = 0.0 sec a 2 % Step Load Perturbation (SLP) is applied in area-1, the SGA tuned PID controller and FA tuned PID controller system performance is demonstrated in Table 3. The superiority of SGA tuned PID controller with less ITAE value (ITAE=0.2947) than FA tuned PID controller (ITAE=1.6463) is depicted in Table 3 using the same controller with objective function. Again the settling times in frequency variation and deviations in tie power with SGA optimized PID controller are improved compare to FA tuned PID controller. Hence it is clear that SGA superior than FA. The system dynamic response deviations in frequency & deviations in tie-line power is depicted in Figs. 3-5.

Sensitivity analysis
Sensitivity analysis is perform to test the robustness of the proposed approach with variation in the system parameters and operating conditions.   The nominal values varying from +25% to -25% in the operating load condition and system parameters (given in appendix) mentioned in Table 4. It is clearly depicts the system time constants and variations on operating loading conditions over the system performance are negligible as well as reflect the similarity in performance indexes values. Fig.9 shows ±25% variations in the loading conditions with nominal parameters for the deviation in frequency response of area-1. From Fig. 9 it clearly reveals that the deviation in loading condition over the system performance is evaluated as negligible. To evaluate the supremacy of the proposed approach a random step load change is applied in area-1. Fig.10 depicts the random step load based pattern (magnitude and duration) applied to the test system [9]. Fig.11 shows the transient responses for ΔF1. From which it can be conclude that the proposed SGA tuned PID controller which provides superior damping compare to other.

Conclusions
In the present work, SGA/FA methods are used to tune PID controller parameters in a two-area six-unit power system.   PID controller offers significant improvement in the response than the FA tuned PID controller. After that sensitivity analysis is carried out to demonstrate the robustness of the proposed approach to wide variations of system parameter, operating loading conditions with respect to nominal values as well as random load disturbance. It is evident from simulation results that the proposed SGA optimized PID controller is much more effective, robust and furnish best system performance as comparison to FA tuned PID controller.