Particle Swarm Optimization by Natural Exponent Inertia Weight for Economic load Dispatch

Abstract

ABSTRACT:In this paper ,various inertia weight strategy particle swarm optimization is used to obtain the optimal power dispatch for 6 unit generator system with constraints satisfaction and minimizing the operating cost. The results are compared among classical Particle Swarm Optimization(CPSO),e1PSO, e2PSO methods. The numerical results affirmed the robustness and proficiency of proposed approach over other existing method.KEYWORDS: E1-PSO, E2-PSO,Economic load dispatch, PSO, Inertia weight, Prohibited operating zones. I.INTRODUCTIONThe economic load dispatch (ELD) of power generating units has always occupied an important position in the electric power industry. The primary objective of ELD is to schedule the committed generating units output so as to meet the required load demand at minimum cost satisfying all unit and system operational constraints. The optimal ELD should meet load demand, generation limit, ramp rate, prohibited operating zone, [1,2] [19,20] have been given attention by many researchers due to their ability to find an almost global optimal solution for ELD problems with operation constraints. ELD problem is non linear, non convex type with multiple local optimal point due to the inclusion of valve point loading effect, multiple fuel options with diverse equality and inequality constraints. Dynamic programming method is one of the approaches to solve the non-linear and discontinuous ELD problem, but it suffers from the problem of "curse of dimensionality" or local optimality. Thus the conventional methods have failed to solve such problems as they are sensitive to initial estimates and converge into local optimal solution and computational complexity. Modern heuristic optimization techniques based on operational research and artificial intelligence concepts, such as simulated annealing [14][15], evolutionary programming [13] , genetic algorithm, tabu search [19][20], neural network, particle swarm optimization provides better solution. The PSO originally developed by Eberhart and Kennedy in 1995[25], is a population based stochastic algorithm. The PSO is an evolutionary optimization tool of swarm intelligence field based on a swarm (population), where each member seen as a particle and each particle is a potential solution to the problem under analysis. Each particle in PSO has a randomized velocity associated to it, which moves through the space of the problem, and implements the simulation of social behavior. PSO however, allows each particle to maintain a memory of the best solution that it has found and the best solution found in the particle's neighborhood is swarm. The main advantage of PSO algorithm is summarized as: simple concept, easy implementation, robustness to control parameters, and computational efficiency when compared with mathematical algorithms and other heuristic optimization techniques. PSO can be easily applied to nonlinear and non-continuous optimization problem.

An Improved Particle Swarm Optimization and Adaptive Neuro-Fuzzy Inference System for Predicting the Energy Consumption of University Residence

“…where w start and w end are given as 0.6 and 0.1, respectively. Te modifed LDIWPSO can be considered an extended version of LDIW which incorporates the natural (base e) inertia weight strategy [60].…”

An enhanced flower pollinated algorithm with a modified fluctuation rate for global optimisation and load frequency control system

“…where t is the present iteration, T max is the maximum iterations, w start and w end are given as 0.9 and 0.4, respectively. The proposed inertia weight can be considered an extended version of linear decreasing inertia weight that incorporates the natural (base e) inertia weight strategy [63]. The description of the proposed FPAPFA is shown in Figure 1, while the pseudocode is described in Figure 2.…”

“…() [65]: $$\begin{equation}\omega = \left( {{\omega _{start}}\ - {\omega _{end}}} \right)\left( {\frac{{{T_{max}}\ - \ t}}{{{T_{max}}}}} \right) + {\omega _{end}} \times {e^{ - {{( {\frac{t}{{\frac{{{T_{max}}}}{4}}}} )}^2}}} \end{equation}$$where $$t$$ is the present iteration, $${T_{max}}$$ is the maximum iterations, $${w_{start}}$$ and $$\ {w_{end}}$$ are given as 0.9 and 0.4, respectively. The proposed inertia weight can be considered an extended version of linear decreasing inertia weight that incorporates the natural (base e) inertia weight strategy [63]. The description of the proposed FPAPFA is shown in Figure 1, while the pseudocode is described in Figure 2.…”

“…In this line of thought, a new linearly decreasing inertia weight (LDIW) mechanism which incorporates the natural (base e) inertia weight strategy, as presented in Eq. ( 10), is incorporated to improve the proposed algorithm's global search capability and convergence rate [63]. Given the rapid and decreasing nature of exponential functions, these functions have become a preferable option instead of the conventional decreasing inertia weight (DIW) strategies [64].…”

Optimal Dispatch of Real Power Generation using Particle Swarm Optimization: a Case Study of Egbin Thermal Station

“…In a PSO system, particles fly around in a multi-dimensional search space. During flight, each particle adjusts its position according to its own experience and the experience of the neighboring particles, making use of the best position encountered by itself and its neighbors [8].…”