Abstract

In an effort to reduce greenhouse gas emissions, experts are looking to substitute fossil fuel energy with renewable energy for environmentally sustainable and emission free societies. This paper presents the hybridization of particle swarm optimization (PSO) with grey wolf optimization (GWO), namely a hybrid PSO-GWO algorithm for the solution of optimal power flow (OPF) problems integrated with stochastic solar photovoltaics (SPV) and wind turbines (WT) to enhance global search capabilities towards an optimal solution. A solution approach is used in which SPV and WT output powers are estimated using lognormal and Weibull probability distribution functions respectively, after simulation of 8000 Monte Carlo scenarios. The control variables include the forecast real power generation of SPV and WT, real power of thermal generators except slack-bus, and voltages of all voltage generation buses. The total generation cost of the system is considered the main objective function to be optimized, including the penalty and reserve cost for underestimation and overestimation of SPV and WT, respectively. The proposed solution approach for OPF problems is verified on the modified IEEE 30 bus test system. The performance and robustness of the proposed hybrid PSO-GWO algorithm in solving the OPF problem is assessed by comparing the results with five other metaheuristic optimization algorithms for the same test system, under the same control variables and system constraints. Simulation results confirm that the hybrid PSO-GWO algorithm performs well compared to other algorithms and shows that it can be an efficient choice for the solution of OPF problems.

Highlights

  • The rapid increase in energy demand and higher prices of conventional thermal generators led the world to a challenging problem of greenhouse gas emissions and an unstable economy

  • The application of the proposed HPSO-grey wolf optimization (GWO) algorithm is tested on the modified IEEE 30-bus system while considering different objective functions such as total generation cost, power losses, emissions, and cumulative voltage deviation in the system

  • The voltage profile of the system has been expressed in terms of voltage deviation (VD), which is a gauge of the voltage quality within the system

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Summary

Introduction

The rapid increase in energy demand and higher prices of conventional thermal generators led the world to a challenging problem of greenhouse gas emissions and an unstable economy. Due to the intermittent nature of RES, such as SPV and WT sources, it is hard to transmit power over a large distance between generation and consumers This hurdle can be overcome by integrating enormous storage systems into the transmission network that will help to reduces fluctuations in the network [4]. For OPF problem formulation and solutions, many optimization algorithms and techniques have been developed and used in the past couple of years. These methods can be classified into classical methods, evolutionary based methods, and advanced metaheuristic algorithm-based methods. The authors in [43] used fuzzy based membership functions to form fuzzy optimal power problem formulations with an artificial bee colony (ABC) algorithm.

Mathematical Formulation of OPF Problem
Cost Function Formulation for Thermal Generators
Cost Function Formulation for Emission and Carbon Tax
Cost Function Formulation for SPV and Wind Turbine
Mathematical Modeling of Uncertainties in RES
Objective Function Formulation
OPF Equality Constraints
Inequality Constraints in OPF
Power Losses and Voltage Deviation
Mathematical Formulation for Stochastic SPV and WT Power
Optimization Algorithm for OPF Solutions
Particle Swarm Optimization
Grey Wolf Optimization
HPSO-GWO Optimizer
Simulation Results and Discussion
Case 2
Case 3
Objective functions
Case 4
Case 5

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