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This paper presents a modified and novel form of the conventional short-term hydrothermal scheduling problem by incorporating the effects of adding the photovoltaic energy source to the conventional grid. A photovoltaic energy source is intermittent in nature, therefore, to determine the optimal power contribution of the photovoltaic source towards the economic dispatch problem, a detailed strategy is presented in this paper. The proposed design method includes the forecasting of the photovoltaic system's parameters using the Auto-Regressive Integrated Moving Average (ARIMA) model. The analytical model is developed based on the fractional integral polynomials for studying the characteristics of the single photovoltaic module. The optimization of power allocation in the system consisting of conventional and non-conventional energy sources is highly non-linear and classical deterministic methods can not be guaranteed to determine the optimal solution for economic power dispatch. The global optima of such non-linear and non-convex problems can be determined using swarm-based intelligence techniques. This paper presents accelerated particle swarm optimization and the firefly algorithm to determine a solution for short-term non-linear scheduling problems. The multiple test cases have been presented to demonstrate the effectiveness of the proposed solution over classical methods. The overall generation cost of the selected hybrid system is reduced using the proposed methods while meeting the generation constraints of each energy source. Moreover, due to the stochastic nature of the meta-heuristic techniques, a comprehensive statistical comparison, based on the independent T-test results, is also presented to highlight the algorithm which performs better for selected scheduling problems. It has been demonstrated that accelerated particle swarm optimization gives lower mean generation cost of the system whereas the execution time of the firefly algorithm is better compared to its counterpart.

Performance Analysis of APSO and Firefly Algorithm for Short Term Optimal Scheduling of Multi-Generation Hybrid Energy System