Approximate Probabilistic Power Flow

Power flow analysis is a necessary tool for operating and planning Power systems. This tool uses a deterministic approach for obtaining the steady state of the system for a specified set of power generation, loads, and network conditions. However this deterministic methodology does not take into account the uncertainty in the power systems, for example variability the in power generation, variation in the demand, changes in network configuration. The probabilistic power flow (PPF) study has been used as an useful tool to consider the system uncertainties in power systems. In this paper, we propose another alternative for solving the PPF problem. This paper shows a formulation of the PPF problem under a Bayesian inference perspective and also presents an approximate Bayesian inference method as a suitable solution of a PPF problem. The proposed method assumes a solution drew from a prior distribution, then it obtains simulated data (active and reactive power injected) using power flow equations and finally compares the observed data and simulated data for accepting the solution or rejecting these variables. This overall procedure is known as Approximate Bayesian Computation (ABC). An experimental comparison between the proposed methodology and traditional Monte Carlo simulation is also shown. The proposed methods have been applied on a 6 bus test system and 39 bus test system modified to include a wind farm. Results show that the proposed methodology based on ABC is another alternative for solving the probabilistic power flow problem; similarly this approximate method take less computation time for obtaining the probabilistic solution with respect to the state-of-the-art methodologies.