A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks

Abstract

This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.

Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization

“…Through the use of Equations (3) and (4) and considering that the compensated reactive power has been added as part of the demand with the corresponding signs, we derive the following:…”

“…Due to their radial topology, in these systems, a large percentage of power is often lost (i.e., when power energy is transformed to heat energy). Around 70% of the energy losses are presented in power distribution systems, and 13% of the energy delivered to these systems is lost during the distribution stage [3,4]. The author of [5] discussed the amount of money invested in these systems and the type of losses presented; besides, they mentioned that 2/3 parts of the investment in power systems is associated with the distribution, for which distribution is known as "invisible giant" of the power system.…”

“…Capacitor banks are only useful when their optimal location and suitable size are chosen; accordingly, the power factor and voltage profile are improved. Misdone siting and/or sizing can generate problems such as an increase in power losses or lead the voltage magnitude to reach unacceptable limits [4,14].…”

“…Therefore, it is important to employ efficient mathematical models to address the problem of capacitor banks' location and guarantee their efficient use in the distribution system, improve the technical features of the network for end-customers, [4,13], and increase the economical benefits of energy trading for the network operator.…”

Optimal Integration of Photovoltaic Sources in Distribution Networks for Daily Energy Losses Minimization Using the Vortex Search Algorithm

“…Due to these differences in electrical energy losses, the transmission levels are between 1.5% and 2% of the energy generated in peak hours, while the energy distribution can vary between 6% and 18%. The above-mentioned implies that, in the worst case, 18% of the distribution level energy is transformed into heat in the resistance lines and transformers in the distribution mainly [3,6]. Given the high levels of losses in the energy distribution, it is necessary to quantify them to determine an optimal solution to this problem [7].…”