Probabilistic Optimal Power Flow Considering Correlation of Wind Farms via Markov Chain Quasi-Monte Carlo Sampling
For power system operators, it provides a more accurate and efficient method for probabilistic optimal power flow under correlated wind uncertainty, though the improvement is incremental.
The paper develops a probabilistic optimal power flow scheme using Markov Chain Quasi-Monte Carlo sampling to handle complex wind speed distributions and correlations among wind farms, achieving faster convergence than standard methods on IEEE 14- and 118-bus systems.
The probabilistic characteristics of daily wind speed are not well captured by simple density functions such as Normal or Weibull distribuions as suggested by the existing literature. The unmodeled uncertainties can cause unknown influences on the power system operation. In this paper, we develop a new stochastic scheme for the probabilistic optimal power flow (POPF) problem, which can cope with arbitrarily complex wind speed distributions and also take into account the correlation of different wind farms. A multivariate Gaussian mixture model (GMM) is employed to approximate actual wind speed distributions from multiple wind farms. Furthermore, we propose to adopt the Markov Chain Monte Carlo (MCMC) sampling technique to deliver wind speed samples as the input of POPF. We also novelly integrate a Sobol-based quasi-Monte Carlo (QMC) technique into the MCMC sampling process to obtain a faster convergence rate. The IEEE 14- and 118-bus benchmark systems with additional wind farms are used to examine the effectiveness of the proposed POPF scheme.