Interior Point Method applied to a Stochastic Programming Model related to the Optimal Power Flow Problem with Uncertain Demand

The Optimal Power Flow Problem is relevant to the energy sector due to its application in economic dispatch, generation and transmission reliability analysis, safety analysis, and short-term generation scheduling. However, demand is usually predetermined in these applications, meaning uncertainty is often disregarded. Given this, we establish an approximation for the demand probability distribution based on the consumption history, and we propose a Two-Stage Quadratic Stochastic Programming model with Fixed Recourse for the Optimal Power Flow Problem with Uncertain Demand. The active power generation sources considered were hydroelectric and thermoelectric plants. We implemented an Interior Point Method to solve the proposed model based on the Path-Following Method, which converged at all times of each day of the week. The value of the stochastic solution was positive for all tests performed, indicating that it would be advantageous to consider the stochastic solution. Numerical tests were performed on real Brazilian power systems and IEEE test cases.