Chance-Constrained Primary Frequency Reserve Optimization Considering Stochastic Disturbances and Contingencies

Traditional primary frequency reserve (PFR) optimization models have incorporated the frequency stability constraints under worst-case contingencies, while neglecting the impacts of stochastic disturbances, such as fluctuations of renewable power generation (RPG), on post-disturbance frequency dynamics. This paper deals with the PFR optimization problem against stochastic disturbances and contingencies. The S-domain aggregated power system model is established to describe the frequency dynamics under the aggregated disturbance. Then, the two-segment linear approximation counterpart of the proposed S-domain model is derived, whose stochastic differential equation (SDE) form in time-domain is further developed. The analytical expressions of the mean and variance of the state variables in the SDEs are provided. Next, the value-at-frequency-deviation (VaFD) index is proposed to quantify the probalistic frequency nadir, which is the function of its arrival time and the confidence level. A successive approximation procedure is devised to derive the analytical expression of the arrival time of the VaFD. Finally, the chance-constrained PFR optimization model is built, where tractable linear counterpart of the nonlinear VaFD constraint as well as operation constraints considering the impacts of the PFR commitment are included. The effectiveness of the proposed methods are verified by the simulation results of the modified IEEE 39-bus system.