Notes on the Dimension of the Solution Space in Typical Electrical Engineering Optimization Problems

Montoya, Oscar Danilo

doi:10.14483/23448393.19310

Cited by 8 publications

(2 citation statements)

References 11 publications

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“…To solve the MINLP model in Equations ( 1)- (11) in the current literature, the predominant alternative corresponds to the usage of embedded combinatorial optimization methods due to the large dimensions of the solution spaces in these MINLP models [26,27]. These methods allow dealing with the nonlinearities and non-convexities of the model via sequential programming [14].…”

Section: Mathematical Optimization Modelmentioning

confidence: 99%

Efficient Integration of PV Sources in Distribution Networks to Reduce Annual Investment and Operating Costs Using the Modified Arithmetic Optimization Algorithm

2022

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The optimal integration of photovoltaic generation systems is a challenge for distribution utilities since these devices have a direct impact on company finances due to the large amount of investment required at the beginning of the planning project. In this investigation, the problem regarding the optimal siting and sizing of photovoltaic resources in medium-voltage levels is addressed from an economical point of view, where the optimization model that represents said problem corresponds to a mixed-integer nonlinear programming model. The maximum allowed size for single photovoltaic units in the distribution network is set at 2400 kW. The investment costs, energy purchase costs and maintenance costs for photovoltaic units, are considered in the objective function. Typical constraints such as power balance, generation capacities, voltage regulation, among others, are considered in the mathematical formulation. The solution of the optimization model is addressed by implementing a modified version of the Arithmetic Optimization Algorithm, which includes a new exploration and exploitation characteristic based on the best current solution in iteration t, i.e., xbestt. This improvement is based on a Gaussian distribution operator that generates new candidate solutions with the center at xbestt, which are uniformly distributed. The main contribution of this research is the proposal of a new hybrid optimization algorithm to solve the exact optimization model, which is based on a combination of the Arithmetic Optimization algorithm with the Vortex Search algorithm and showed excellent numerical results in the IEEE 34-bus grid. The analysis of quantitative results allows us to conclude that the strategy proposed in this work has a greater effectiveness with respect to the General Algebraic Modeling System software solvers, as well as with metaheuristic optimizers such as Genetic Algorithms, the Newton–Metaheuristic Algorithm, and the original Arithmetic Optimization Algorithm. MATLAB was used as a simulation tool.

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Section: Mathematical Optimization Modelmentioning

confidence: 99%

Efficient Integration of PV Sources in Distribution Networks to Reduce Annual Investment and Operating Costs Using the Modified Arithmetic Optimization Algorithm

2022

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“…Owing to its nature, several metaheuristic techniques have been applied to solve the ORPD problem. The main advantage of these approaches is that they are able to deal with nonconvex optimization problems involving discrete and continuous variables [11,12]. Furthermore, they do not require differentiability of the objective function or constraints, overcoming the disadvantages of classic optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface

et al. 2022

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The Optimal Reactive Power Dispatch (ORPD) problem consists of finding the optimal settings of reactive power resources within a network, usually with the aim of minimizing active power losses. The ORPD is a nonlinear and nonconvex optimization problem that involves both discrete and continuous variables; the former include transformer tap positions and settings of reactor banks, while the latter include voltage magnitude settings in generation buses. In this paper, the ORPD problem is modeled as a mixed integer nonlinear programming problem and solved through two different metaheuristic techniques, namely the Mean Variance Mapping Optimization and the genetic algorithm. As a novelty, the solution of the ORPD problem is implemented through a Python-DIgSILENT interface that combines the strengths of both software. Several tests were performed on the IEEE 6-, 14-, and 39-bus test systems evidencing the applicability of the proposed approach. The results were contrasted with those previously reported in the specialized literature, matching, and in some cases improving, the reported solutions with lower computational times.

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Practical Solution for the Reconfiguration Problem in Electrical Distribution Networks: A Constructive Heuristic Approach

2023

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The problem regarding the reconfiguration of electrical distribution grids is addressed in this research through the implementation of a practical solution using a constructive heuristic algorithm. The most important characteristic of the proposed heuristic approach is its low-computation effort, given that few power flow solutions are required in order to solve the reconfiguration problem. The constructive algorithm starts its exploration of the solution space by closing all the tie lines form a fully meshed distribution network. The distribution line with the minimum current is permanently opened. A new power flow evaluation is made for the new distribution system, and the distribution line with the minimum current is opened if and only if this action does not generate isolated nodes. This procedure is repeated until the number of closed lines is equal to the number of nodes minus one, which is a condition required to maintain a radial configuration. Numerical validations in test feeders composed of 16, 33, 69, 84, 136, and 415 nodes demonstrate that the proposed constructive algorithm finds adequate solutions with minimum processing times. The proposed approach is practical for distribution companies since its implementation only requires a power flow tool for distribution networks that can deal with radial and meshed configurations.

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Notes on the Dimension of the Solution Space in Typical Electrical Engineering Optimization Problems

Cited by 8 publications

References 11 publications

Efficient Integration of PV Sources in Distribution Networks to Reduce Annual Investment and Operating Costs Using the Modified Arithmetic Optimization Algorithm

Efficient Integration of PV Sources in Distribution Networks to Reduce Annual Investment and Operating Costs Using the Modified Arithmetic Optimization Algorithm

Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface

Practical Solution for the Reconfiguration Problem in Electrical Distribution Networks: A Constructive Heuristic Approach

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