Abstract
The mismatch between power generation and load demand causes unwanted fluctuations in frequency and tie-line power, and load frequency control (LFC) is an inevitable mechanism to compensate the mismatch. For this issue, this paper explores the influence of energy storage device (ESD) on ameliorating the LFC performance for an interconnected dual-area thermal and solar photovoltaic (PV) power system. Initially, to alleviate the frequency and tie-line power deviations, a proportional-integral (PI) controller is chosen and utilized in the system due to its effectiveness and simplicity in practice. For achieving the highest performance from this controller, salp swarm algorithm (SSA) is employed to search for optimal controller parameters by using integral of time-multiplied absolute error (ITAE) criterion. To affirm the contribution of SSA optimized PI controller, it is contrasted with a recent approach utilizing PI controller optimized by genetic algorithm (GA) and firefly algorithm (FA). It is observed that the results acquired for SSA are better than for GA and FA. To improve the system performance further, ESD such as redox flow battery (RFB) famous for its excellent disturbance rejection capability is integrated with the thermal power unit for the first time in the literature. It is divulged from the results that the system performance with RFB has boosted considerably with regard to shorter settling time, less undershoot/overshoot and smaller ITAE value of the frequency and tie-line power fluctuations. According to the sensitivity analysis, our proposal is found robust against system parameters variations and different loading conditions.
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Appendices
Appendix 1
The system data and the algorithms’ control parameters used in the compared work [2] are shown below:
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1.
\({T}_{ps}=20\) s, \({K}_{ps}=120\) Hz/puMW, \({T}_{g}=0.08\) s, \({T}_{t}=0.3\) s, \({K}_{r}=0.33\), \({T}_{r}=10\) s, \({T}_{12}=0.545\) puMW/Hz, \(B=0.8\) puMW/Hz, \(R=0.4\) Hz/puMW, \({F}^{0}=60\) Hz
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2.
The parameters of FA: the contrast of the attractiveness = 1.0, the attractiveness = 0.1 at \(r\) = 0, randomization parameter (\(\alpha \)) = 0.1, maximum number of generations = 100, number of fireflies = 50.
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3.
The parameters of GA are as follows: maximum generation number = 100, population size = 50, crossover probability = 0.75, mutation probability = 0.1.
There are only two control parameters in SSA such as number of search agents and maximum iteration. They are set equally for both cases with and without RFB as: maximum iteration number (\({M}_{iter}\)) = 50, number of salps (\(n\)) = 50.
The RFB parameters are set in the current work as follows:
\({T}_{d}=0.025\) s, \({T}_{r1}=0.1\) s, \({K}_{r1}=0.5\), \({K}_{RFB}=1.8\)
Appendix 2: Validation of the superior performance of SSA
For the justification of employing SSA as optimizer, a comparative study is established by applying well-known and recent algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), artificial bee colony (ABC) algorithm, firefly algorithm (FA), flower pollination algorithm (FPA), gray wolf optimizer (GWO) and moth-flame optimization (MFO) to the optimization of PI controller parameters in the studied system without RFB. These are good comparative algorithms in the literature able to challenge the SSA and accordingly to see how competitive SSA is in comparison with the state-of-the-art variants. For the fairness of comparison, number of fitness function evaluations (NFFE) is set to 5000 in all the algorithms.
For eliminating the situation in which best solution is found by chance, each algorithm is run 20 times and the results are averaged over 20 independent runs. The average and standard deviation (std) of the best solutions found in the last iteration are employed to qualify the overall performance of SSA against other set of algorithms. Although these two metrics give us a credible conclusion, the collected results have been also examined from nonparametric statistical point of view to check how competitive the results are. To this end, Wilcoxon rank-sum test is applied at the 5% significance level. According to the test decision, p values less than 0.05 suggest a rejection of the null hypothesis, whereas those greater than 0.05 signify a failure to reject the null hypothesis at the given level of significance.
The numerical results for the minimization of ITAE value are presented in Table
5. For convenience, better results are highlighted by bold numbers and p values greater than 0.05 are made Italic. N/A (not applicable) shown in the table states that the best algorithm cannot be compared with itself in the rank-sum test. Inspecting the results of average and std, SSA provides better results than all other algorithms. As per the relevant p values, the performance of SSA is significant compared with that of the remaining algorithms excepting GWO. SSA cannot outperform GWO remarkably, and they show identical performance for the current problem. However, considering the complexity of coding, computational expense and number of algorithmic parameters, SSA is more advantageous than GWO and thus, SSA is the best choice as optimizer in the present work.
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Çelik, E., Öztürk, N. & Houssein, E.H. Influence of energy storage device on load frequency control of an interconnected dual-area thermal and solar photovoltaic power system. Neural Comput & Applic 34, 20083–20099 (2022). https://doi.org/10.1007/s00521-022-07558-x
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DOI: https://doi.org/10.1007/s00521-022-07558-x