Frequency-constrained multi-source power system scheduling against N-1 contingency and renewable uncertainty

Abstract Security continues to be the most critical concern in power system operation, which is exceptionally important under low inertia and high uncertainty situations induced by an increasing penetration of renewable sources. This paper presents a transient frequency-constrained two-stage stochastic scheduling model to study the day-ahead operation of thermal-hydro-wind-demand response systems. Specifically, (i) limits on rate-of-change-of-frequency and maximum frequency derivation are introduced to provide sufficient governor reserve from multiple sources for guaranteeing dynamic frequency performance against N-1 contingency; (ii) The de-loaded mode of variable speed wind turbines is proposed for leveraging economics of system operation and security of dynamic frequency response; (iii) Virtual inertial constant of power systems with variable speed wind turbines is calculated to simulate performance of the virtual inertial control; (iv) Demand response is considered in the stochastic framework to mitigate the time delay of delivering virtual inertia. Multiple scenarios are generated via Monte Carlo method to simulate wind generation uncertainties. The proposed two-stage stochastic mixed-integer nonlinear programming model with binaries in both stages is solved via an improved generalized Benders decomposition, which takes about 40% less time than the standard generalized Benders decomposition. Several enhanced strategies are discussed to improve computational performance of the generalized Benders decomposition. Numerical simulations illustrate effectiveness of the proposed approach in coordinating multi-resource scheduling of power systems against N-1 contingencies and uncertainties with guaranteed frequency performance. Specifically, numerical results on the 6-bus system illustrate that: (i) The optimal wind generation penetration level of 40% could well balance the wind curtailments and the benefits of variable speed wind turbines for regulation provision; (ii) With 50% penetration of wind generation, doubling the capacity of demand response can reduce the amount of wind curtailment 50.42%, and decrease the transient frequency deviation to 0.25Hz.