Mathematical Model of Year-Round Renewable Energy Time Series for Power System Planning Based on Multiple Seasonal-Trend Decomposition Using the LOESS and Ito Stochastic Process

Abstract

Generating year-round renewable energy time series with hourly resolution is important for power system planning. This paper provides the characteristic analysis method and mathematical model of the year-round renewable energy time series. First, the multiple seasonal-trend decomposition using the LOESS (MSTL) method is adopted to decouple the historical renewable energy time series into trend, annual, seasonal, and residual components. The annual and seasonal components are repeating cycles, while the trend and residual components are time-dependent stochastic time series. To build the mathematical model for trend and residual components, the mixed Gaussian distribution model is applied to simulate the probabilistic distribution of trend and residual components. Based on these probabilistic distribution functions, the Ito stochastic process is applied to generate massive time series considering the stochastic and temporal dependent characteristics of the primal time series. A discretization formulation of the Ito stochastic process is provided so that the Ito stochastic process can be applied in renewable energy time series generation. The relationship between the drift and diffusion function used in the Ito stochastic process is depicted. Numerical results illustrate that the proposed method could effectively identify the characteristics of renewable energy time series and generate massive similar renewable energy time series for power system planning.