Abstract
Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can play an active role in ancillary services by regulating their aggregated power consumption. The aggregation of air conditioners is essential to the control of air conditioning loads. In this paper, linear state equations are proposed to aggregate air conditioning loads by solving coupled Fokker–Planck equations (CFPEs) using the finite difference method. By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle. Stationary solutions of the CFPEs are obtained by analytical and numerical methods. Furthermore, a classification method using dimension reduction is proposed to deal with the problem of heterogeneous parameters and interval estimation is applied to describe the stochastic behavior of air conditioning loads. The simulation results verify the effectiveness of the proposed methods.
Highlights
Maintaining the balance between the power generation and the demand is a key issue in power system operation
By considering the probability distribution of a population of air conditioners and making the assumption that the population is homogeneous, Malhameand Chong (M&C) [19] proved that it is possible to construct a system of coupled Fokker–Planck equations (CFPEs) to describe the dynamics of the population
The aggregate modeling of air conditioning loads is shown in (40)–(42), in which linear state equations are developed by solving CFPEs using the finite difference method (FDM)
Summary
Maintaining the balance between the power generation and the demand is a key issue in power system operation. To facilitate the control of air conditioners, the main idea is to establish the aggregate model, which can characterize the temperature probability density evolution of the air conditioner population. In [11] and [12], the statebin-based 1st-order TCL model was proposed and the state space matrix was identified by a Kalman filter. In [7] and [13], state-binbased 1st-order TCL models considering the device lockout time were proposed for different control purposes. Time-domain solutions of CFPEs are essential to the aggregation of air conditioning loads. The main contributions of this paper are as follows: 1) The linear state equations, which characterize the temperature probability density evolution of the air conditioner population considering randomness, are proposed by solving CFPEs using the FDM to aggregate air conditioning loads.
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