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In electrical power system, economic load dispatch is a generic operation for optimal sharing of generation units to meet the system load. With the rapid development of the renewable infrastructure and wide encouragement for green energy have emerged hybrid generating systems in power systems. However, there continuous ever-increasing production is creating challenges as well as implicating economic factor also in operation. A collective cost function is considered with the conventional thermal generators along with the consideration of renewable energy sources to envisage the economic factor. For these renewable sources, like wind and solar, the proportional cost, their uncertainty and variability by overestimation and underestimation cost are considered. To achieve this economic day-ahead scheduling, dynamic operation in time scale of 1 h interval is performed. The stochastic nature of wind and solar is modelled by Weibull and Beta distributions, respectively. Moreover, economic optimisation is obtained by a newly developed algorithm called improved fireworks algorithm with nonuniform operator (IFWA-NMO). This introduces adaptive dimension strategy, limiting mapping operator and non-uniform operator. The effectiveness of proposed IFWA-NMO is investigated on standard dynamic economic load dispatch (DELD) system and also employed to solve conventional DELD with wind-solar system.

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This paper proposes a dynamically controlled particle swarm optimization method to solve nonconvex economic dispatch problem of large dimensions. It essentially aims to improve the performance of the conventional particle swarm optimization by suggesting improved cognitive and social components of the particle's velocity through preceding and aggregate experience of the swarm, respectively. The control parameters of the governing equation are controlled dynamically by introducing new exponential functions. The overall methodology effectively regulates the velocity of the particles during their whole course of flight and results in substantial improvement. The effectiveness of the proposed method has been investigated on 40 generators and 140 generators test generating systems by considering general operational constraints. The application results show that the proposed method is very promising to solve large-dimensional economic dispatch problems.greatly depends on its parameters tuning [7], and it often suffers from the problems such as being trapped in local optima because of premature convergence [8], lack of efficient mechanism to treat the constraints [9], loss of diversity and performance in optimization process [1], and so on. PSO is a population-based optimization technique in which the movement of the particles is governed by the two stochastic acceleration coefficients, that is, cognitive and social components and the inertia component [1,6,7].Several modified versions of PSO have been reported in the recent past to enhance the performance of the conventional PSO by modulating inertia weight, improvising cognitive and social behavior, using constriction factor approach, or modifying the control equation of the PSO, and some of them can be discussed here.Some experiments with the inertia weight have been reported in Refs [6,7,[10][11][12][13]. Chaotic PSO in Ref. [11] proposed adapted inertia weight that varies dynamically with fitness value for exploration, and a chaotic local search was used to determine the particle position for better exploitation. The improved PSO in Ref.[12] suggested chaotic inertia weight that decreases and oscillates simultaneously under the decreasing line in a chaotic manner. In this way, additional diversity is introduced, but it requires tuning of chaotic control parameters. In Ref.[13], the inertia coefficient is controlled with respect to the objective function to provide unique velocity in the convergent direction of the best particle. In this approach, the velocity of the best particle stagnates, whereas the rest of the particles increase. This enhances the chances of local trapping, and to avoid it, an empirical formula is used to limit particles' velocities. Many researchers [10,[14][15][16] have attempted to vary the cognitive and social behavior of the swarm during the search process by dynamically controlling the acceleration coefficients within maximum and minimum bounds. Again, the determination of limiting values of the acceleration coefficients is a difficult ta...