Thermal-wind dispatch programming using stochastic optimal power flow with discrete variables


  • Rafael Ramos de Souza Professor Doutor, UNESP, Brasil
  • Marina Schimidt Professora Mestra, UNESP, Brasil
  • Antonio Roberto Balbo Professor Livre-docente, UNESP, Brasil



Stochastic Optimal Power Flow, Clean energy, Primal-dual interior/exterior point method


In this study, results for a discrete and stochastic optimal power flow (DSOPF) model inserting wind generators for electricity generation are presented. The objective function of the DSOPF model aims to minimize the cost of active power generation in the system. This cost is composed of nonlinear and non-differentiable functions representing thermoelectric generators, due to the valve loading point effect (VLPE) and by integral functions representing wind generators. The DSOPF model is solved using a modified logarithmic barrier (MLB) primal-dual interior/exterior point method with a predictor-corrector procedure and inertia correction. This method is deterministic and, unlike metaheuristic methods, guarantees local optimal solutions and calculates the price of the energy generated from the dual variables of the problem. To get the results, a 30-bus IEEE system was used to simulate the grid in a city in northeastern Brazil, which experiences significant variation in average wind speed throughout the four seasons of the year. The results show a reduction in generation costs through the substitution of thermal generators by wind generators. The wind power, which is uncertain due to wind speed, is represented and integrated using the Weibull probability distribution function. The article contributes to the Sustainable Development Goals, particularly Goal 7, by minimizing the total cost of energy generation from renewable sources related to wind energy in electric power systems.


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How to Cite

Souza , R. R. de, Schimidt, M., & Balbo, A. R. (2023). Thermal-wind dispatch programming using stochastic optimal power flow with discrete variables. Periódico Eletrônico Fórum Ambiental Da Alta Paulista, 19(6).