Aggregate modeling and analysis of air conditioning load using coupled Fokker–Planck equations

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.

A Review of Air Conditioning Load Aggregation in Distribution Networks

“…Randomness is also one of the difficulties in modeling the aggregation model. To solve the randomness of the air conditioning load aggregation model, Cheng et al (2018) adopted the electric power change and heat transfer process in the process of the load operation. The load aggregation model was derived by using the Fokker-Planck equation.…”

Technologies and Practical Implementations of Air-conditioner Based Demand Response

“…A novel control approach is explored in [170], namely the evaporation pressure control reading (EPCR) method, which is based upon evaporation pressure and humidity reading. A Fokker-Planck mod-el has also been explored in [171] to control the aggregate AC demand.…”

Pengujian Arus pada Simulator Sistem Kelistrikan Air Conditioner (AC)

“…Setelah dilakukan penyaringan pada refrigerant [5], maka cairan refrigerant akan masuk ke katup ekspansi untuk diturunkan temperature dan tekanannya sehingga refrigerant tersebut akan berubah bentuk menjadi gas dengan temperatur dan tekanan menjadi 3ºC dan 2,1 kg/cm2 [6]. Refrigerant akan ditarik lagi oleh kompresor sehingga proses siklus kerja sistem ac ini akan terjadi secara berulang-ulang.…”