A Gradient-Based Approach for Solving the Stochastic Optimal Power Flow Problem with Wind Power Generation - Souza, Rafael R. [UNESP] (2022)
Although wind power generation improves decarbonization of the electricity sector, its increasing penetration poses new challenges for power systems planning, operation and control. In this paper, we propose a solution approach for Stochastic Optimal Power Flow (SOPF) models under uncertainty in wind power generation. Two complicating issues are handled: i) difficulties imposed by probability density functions used to formulate wind power costs and their derivatives; ii) the non-differentiability of the cost function for thermal units. Due to such issues, SOPF models cannot be solved by gradient-based approaches and have been solved by meta-heuristics only. We obtain exact analytical expressions for the first and second order derivatives of wind power costs and propose a technique for handling non-differentiability in thermal costs. The equivalent SOPF model that results from such recasting is a differentiable NLP problem which can be solved by efficient gradient-based algorithms. Finally, we propose a modified log-barrier primal-dual interior/exterior-point method for solving the equivalent SOPF model which, differently from meta-heuristic approaches, is able to calculate important dual variables such as energy prices. Our approach, which is applied to the IEEE 30-, 57- 118- and 300-bus systems, strongly outperforms a meta-heuristic approach in terms of computation times and optimality.