A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control

Abstract

Thermostatically controlled loads (TCLs) are a flexible demand resource with the potential to play a significant role in supporting electricity grid operation. We model a large number of identical TCLs acting autonomously according to a deterministic control scheme to provide frequency response as a population of coupled oscillators. We perform stability analysis to explore the danger of the TCL temperature cycles synchronising: an emergent phenomenon often found in populations of coupled oscillators and predicted in this type of demand response scheme. We take identical TCLs as it can be assumed to be the worst case. We find that the uniform equilibrium is stable and the fully synchronised periodic cycle is unstable, suggesting that synchronisation might not be as serious a danger as feared. Then detailed simulations are performed to study the effects of a population of frequency-sensitive TCLs acting under real system conditions using historic system data. The potential reduction in frequency response services required from other providers is determined, for both homogeneous and heterogeneous populations. For homogeneous populations, we find significant synchronisation, but very minimal diversity removes the synchronisation effects. In summary, we combine dynamical systems stability analysis with large-scale simulations to offer new insights into TCL switching behaviour.

Natural Heterogeneity Prevents Synchronization of Fridges With Deterministic Frequency Control

“…100 per group unless stated otherwise 3 ). There are an estimated 10.1M households in GB with a fridge, and 18.6M with a fridge-freezer [5]. Each combination of parameter values is explored with 36 simulations spanning 12 months during 2015-16, and each simulation runs for 10 days with 1s resolution.…”

“…The associate editor coordinating the review of this manuscript and approving it for publication was Siqi Bu. 1 See, for example, [4], [5] for a description of the different types of frequency response and balancing services more widely. During 2017-18 (and similarly in previous years) the SO in Great Britain (GB) paid approximately £140M for response [6] below the nominal value (50Hz in GB) frequency response providers increase generation (or decrease demand), and vice versa when the frequency rises above nominal.…”

“…Various control schemes have been proposed, generally classed as either (predominantly) centralized or decentralized. Their relative advantages and disadvantages are discussed in [22]. Our choice of decentralized control is largely due to the financial burden and security risks associated with the very large secure communications infrastructure required for centralized control.…”

“…Our work proposes that stochastic control is not necessary to prevent herding behavior, so long as the population of TCLs is sufficiently heterogeneous. There are examples of simulations of heterogeneous TCLs with deterministic control that do not exhibit herding behavior, such as in [13], [22]. Until now, no one has asked how much heterogeneity is required to prevent synchronization problems.…”

Energy Recovery Strategy Numerical Simulation for Dual Axle Drive Pure Electric Vehicle Based on Motor Loss Model and Big Data Calculation

“…By analyzing a large number of drivers' long driving mode, road conditions, weather conditions, and so on, the influence of the electric vehicle at different driving speed, acceleration, and temperature on the energy consumption rate is calculated. However, in the estimation of electric vehicle mileage, it does not consider the influence of motor control strategy [16,17]. Therefore, it is necessary to study the regenerative braking strategy of a dual-axis drive electric vehicle [18].…”