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.
Highlights
In recent years, the world has witnessed a dramatic increase in wind power integration into the power grid, as it diminishes fossil fuel consumption and environmental pollution
The parameters in the Dirichlet process Gaussian mixture model (DPGMM) are estimated by the variational inference algorithm. Based on these estimated DPGMM parameters, we developed a data driven polyhedral uncertainty set for the wind power forecast error
As the of the wind power forecast error conditional to the level of forecast the more likely thedistribution historical forecast error distribution is tois follow the future forecast error values, we proved that the closer the historical forecast value is to the future forecast, the more likely distribution
Summary
The world has witnessed a dramatic increase in wind power integration into the power grid, as it diminishes fossil fuel consumption and environmental pollution. The U.S Department of Energy forecasts that wind power will supply 20% of electricity generation by 2030 [1]. In Germany, system operators should see renewable energy, including wind power, as a priority [2]. The large integration of wind power poses enormous challenges in power system operations due to the variable and uncertain nature of wind power. In this cases, it is important to co-optimize the energy and reserve to ensure adequacy of the electricity supply
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