Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function
This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabili...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/16/14/5566 |
| _version_ | 1827733211194589184 |
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| author | Diego Mendoza Osorio Javier Rosero Garcia |
| author_facet | Diego Mendoza Osorio Javier Rosero Garcia |
| author_sort | Diego Mendoza Osorio |
| collection | DOAJ |
| description | This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were 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. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on 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. |
| first_indexed | 2024-03-11T01:07:16Z |
| format | Article |
| id | doaj.art-fa9477ba6dbb4a08930614050e0e2432 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-11T01:07:16Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-fa9477ba6dbb4a08930614050e0e24322023-11-18T19:12:19ZengMDPI AGEnergies1996-10732023-07-011614556610.3390/en16145566Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution FunctionDiego Mendoza Osorio0Javier Rosero Garcia1Facultad de Ingeniería, Universidad Nacional de Colombia, Bogotá 111321, ColombiaFacultad de Ingeniería, Universidad Nacional de Colombia, Bogotá 111321, ColombiaThis paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were 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. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on 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.https://www.mdpi.com/1996-1073/16/14/5566stochastic programmingDER allocationAC-OPFconvex optimizationcontinuous distributionlogistic distribution |
| spellingShingle | Diego Mendoza Osorio Javier Rosero Garcia 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 stochastic programming DER allocation AC-OPF convex optimization continuous distribution logistic distribution |
| title | Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function |
| title_full | Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function |
| title_fullStr | Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function |
| title_full_unstemmed | Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function |
| title_short | Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function |
| title_sort | convex stochastic approaches for the optimal allocation of distributed energy resources in ac distribution networks with measurements fitted to a continuous probability distribution function |
| topic | stochastic programming DER allocation AC-OPF convex optimization continuous distribution logistic distribution |
| url | https://www.mdpi.com/1996-1073/16/14/5566 |
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