Efficient Reduction in the Annual Investment Costs in AC Distribution Networks via Optimal Integration of Solar PV Sources Using the Newton Metaheuristic Algorithm

Abstract

This research addresses the problem of the optimal placement and sizing of (PV) sources in medium voltage distribution grids through the application of the recently developed Newton metaheuristic optimization algorithm (NMA). The studied problem is formulated through a mixed-integer nonlinear programming model where the binary variables regard the installation of a PV source in a particular node, and the continuous variables are associated with power generations as well as the voltage magnitudes and angles, among others. To improve the performance of the NMA, we propose the implementation of a discrete–continuous codification where the discrete component deals with the location problem and the continuous component works with the sizing problem of the PV sources. The main advantage of the NMA is that it works based on the first and second derivatives of the fitness function considering an evolution formula that contains its current solution (xit) and the best current solution (xbest), where the former one allows location exploitation and the latter allows the global exploration of the solution space. To evaluate the fitness function and its derivatives, the successive approximation power flow method was implemented, which became the proposed solution strategy in a master–slave optimizer, where the master stage is governed by the NMA and the slave stage corresponds to the power flow method. Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of 26.89% and 27.60% for each test feeder with respect to the benchmark cases.

Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm

“…It is worth clarifying that the maximum and minimum limits of the PV generation units’ complex power generation are always followed by the coding proposed by the DCVSA [ 14 ]. Conversely, the complex power upper limit on node slack is not taken into account as it is assumed to have enough capacity to support all demands, even if no PV sources are installed.…”

“…Note that one main complication of the MINLP model defined from ( 1 ) to ( 12 ) corresponds to the combination of binary and continuous variables with nonlinear non-convex constraints, specifically in the case of the complex balances at each node of the network for each period of time [ 14 ]. To solve this type of model, the specialized literature recommends the use of the master–slave optimization methods that simplify the problem presented by separating the location and dimension of the PV generation units from the power balance in the distribution network [ 35 ].…”

“…Based on the aforementioned opportunity of promoting renewable generation solutions in tropical countries, efficient optimization techniques are required to identify the location and sizing of these systems in distribution networks [ 13 ]. To address this problem, this research document proposes an objective function that simultaneously minimizes generation costs and investment, operation, and maintenance costs of PV sources for a planning horizon of 20 years [ 14 ]. To confront the aforementioned concern, a master–slave optimization methodology is suggested to solve the mixed-integer nonlinear programming model (MINLP) that represents this problem.…”

“…In the specialized literature, it is possible to find different optimization options that rectify the problem of the location and dimension of the distributed generation in distribution networks. Some of these include Genetic Algorithms [ 15 , 16 ], Particle Swarm Optimization [ 17 ], Teaching Learning Based Optimization [ 18 ], Population-Based Incremental Learning [ 19 ], Vortex Search Algorithm [ 13 ], Discrete Sine Cosine Algorithm [ 20 ], Technique of Smalling Area [ 21 ], Improved Harris Hawks Optimizer [ 22 ], mathematical based-approaches in GAMS (i.e., General Algebraic Modeling System) [ 23 , 24 ], and Newton-Based metaheuristic optimizers [ 14 ], among others. The main characteristic of the optimization methodologies described above is that they use the master–slave optimization scheme to solve the problem of both location and optimal sizing of the distributed generation through the minimization of power losses for a given demand condition, which does not replicate what happens in reality given that the system loads and generation of renewable energy exhibit dynamic behavior throughout a day of operation [ 14 ].…”

“…The optimal placement and sizing of PV sources take into consideration the uncertainties and stochastic nature of the PV generation [ 30 , 31 ]. Authors in [ 14 ] presented the application of the recently developed Newton Metaheuristic Algorithm to solve the problem of the optimal placement of PV sources allowing for their investment and operative costs; and authors of [ 16 ] proposed the application of the discrete-continuous version of the Chu and Beasley genetic algorithm to solve the same problem. Both of these have been taken as references as they are the only two approaches analyzing the mentioned aspects for the distribution networks in the last few years.…”