Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Abstract

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

Multi-Indicator Fused Resilience Assessment of Power Grids Considering Wind-Photovoltaic Output Uncertainty during Typhoon Disasters

“…This paper will leverage the rolling non-parametric DPGMM [54] method to model the uncertainties of wind farm output and PV station output, and employ the measured data to sequentially fit and sample the renewable energy output scenarios at the current calculated time. The wind speed and PV station output data within one hour before and after each time are used as input data for the rolling DPGMM [55] to model the probability density of wind-PV output uncertainty at the current time, as shown in Equation (15). When K t is a positive integer greater than one, Equation ( 15) is a generalized expression for a Gaussian mixture model (GMM), whereas in DPGMM, K t is an output parameter, which is the number of the mixtures of Gaussian distribution that the model automatically infers based on the input data.…”