Continuous Random Process Modeling of AGC Signals Based on Stochastic Differential Equations

Reflecting the uncertainty of renewable energy generations and loads, power system AGC signals are essentially random processes. For the sake of the optimal operation and control of the AGC participant, such as energy storage systems (ESSs) in a performance/mileage-based regulation market, taking the uncertain nature, especially the temporal correlation, of the AGC signals into consideration can be beneficial; hence, random process models of the AGC signals are needed. However, a continuous random process model of the AGC signal that jointly considers the probability distribution and the temporal correlation is still lacking. To fill this gap, this paper first presents a systematic methodology for modeling the continuous random processes of AGC signals based on stochastic differential equations (SDEs). It is shown that AGC signals may have a saturated stationary probability density function and a biexponential temporal correlation, which are very different from the renewable generations. To capture these special characteristics, SDEs are then carefully constructed, which are easy to use in optimization and control. Using the PJM traditional and dynamic regulation (RegD and RegA) signals and the signal received from a battery ESS (BESS) plant in Jiangsu, China for example, simulation shows that the SDE is able to simultaneously capture the probability distribution and temporal correlation accurately.