Hierarchical reserve allocation with air conditioning loads considering lock time using Benders decomposition

With the integration of more and more renewable energy in the power system, more reserves are needed to cope with the intermittent and stochastic characteristics of the renewable energy. To relieve the stress of the reserve supply by the generation side, air conditioning loads can be considered to participate in reserve allocation in dynamic economic dispatch owing to their high proportion in the demand and thermal energy storage characteristics. The lock time of air conditioners should not be ignored since it can avoid the short cycling of compressor. This paper proposes a hierarchical reserve allocation model with air conditioning loads considering lock time to coordinate the power system dispatch and the control of air conditioning loads. An aggregate model of air conditioning loads considering the lock time is proposed and linear constraints of the air conditioning loads are developed. Among these constraints, lockout constraints are linear slack constraints for convenient in computation and the validity of the slack form has been proved. These constraints are integrated into the reserve allocation in dynamic economic dispatch. In such a state, the problem has multi-time scale characteristics and thus, is difficult to solve; therefore, this problem is reconstructed as a three-level hierarchical problem, and Benders decomposition is applied. The first level (operation level) represents the operation of the power system in normal conditions. Each N-1 contingency is placed in the second level (contingency level). The third level (load control level) considers the constraints of the air conditioning loads. To increase the calculation efficiency, we propose three methods, which are adding necessary conditions, adjusting upper bound and applying parallel computing. The simulation results show that air conditioning loads can realize load reserve, and the proposed hierarchical solving method is effective to solve the reserve allocation problem with air conditioning loads considering the lock time.