Fast Probabilistic Optimal Power Flow Based on Modified Multi-Parametric Programming

With the rapid increase of renewables and power demands, probabilistic optimal power flow (POPF) has become an important tool to investigate the stochastic characteristics of power systems. However, the POPF calculation requires repeatedly solving a tremendous number of optimization problems. The computational burden has been the main bottleneck for its practical applications. To overcome this problem, this paper adopts a linear OPF model with reactive power and voltage magnitude to construct the optimization model for samples. Then, a modified multi-parametric programming process is introduced to fast calculate the optimal solutions of samples by avoiding the iterative optimization process. Compared with the traditional multi-programming process, the reduced affine maps between the sample optimization solutions and the stochastic variables are explicitly formulated while keeping the desired accuracy. The IEEE 30-bus and 118-bus systems are used to demonstrate the effectiveness of the proposed method.