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Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function
Mendoza Osorio, D.; Rosero Garcia, J. Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function. Energies2023, 16, 5566.
Mendoza Osorio, D.; Rosero Garcia, J. Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function. Energies 2023, 16, 5566.
Mendoza Osorio, D.; Rosero Garcia, J. Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function. Energies2023, 16, 5566.
Mendoza Osorio, D.; Rosero Garcia, J. Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function. Energies 2023, 16, 5566.
Abstract
This paper addresses the optimal stochastic allocation of Distributed Energy Resources in distribution Networks. Typically, uncertain problems are analyzed in multi-stage formulations including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed resulting in a single-stage, convex, stochastic optimal power flow problem: The Range-Probability Optimization (RPO) and Value-Probability Optimization (VPO). The RPO maximizes probabilities within a range of uncertainty, whilst the VPO optimizes the values of the random variables and maximizes their probabilities. Random variables are modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. Results indicate that assuming deterministic conditions ends in highly underestimated losses. The RPO showed that by including a ±10 % uncertainty, the losses can be increased up to 40 % with up to −72 % photovoltaic capacity, depending on the system, whereas the VPO resulted in up to 85 % increases in power losses despite PV installations, with 20 % greater probabilities in average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods.
Keywords
Stochastic Programming; DER Allocation; AC-OPF; Convex Optimization; Continuous Distribution; Distributed Energy Resources; Photovoltaic Energy
Subject
Engineering, Electrical and Electronic Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
