Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
复制标题
恒温控制负载的集合：统计物理方法
作者：
M. Chertkov;V. Chernyak
恒温控制负载，例如，空调和加热器是迄今为止最广泛的电力消耗者。通常，这些器件经过校准，以提供所谓的开关控制-根据温度从开到关，反之亦然。我们认为聚合成一个统计系综，其中的设备按照相同的动力学，随机扰动和随机，泊松开/关切换策略。利用统计物理的理论和计算工具，分析了系综如何弛豫到一个稳定的分布，并建立了弛豫与混合（离散、开关和连续温度）相空间中与器件循环相关的概率通量统计之间的关系。这使我们能够推导出非平衡（详细的平衡打破）统计系统的频谱，并揭示开关政策如何影响振荡趋势和放松的速度。系综的弛豫具有实际意义，因为它描述了系综如何从显著的扰动中恢复，例如，强制临时关断旨在利用集合的灵活性来提供“需求响应”服务，以临时改变消耗，从而平衡较大的电网。我们讨论了如何统计分析可以指导新兴的需求响应技术的进一步发展。
Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control – changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices’ cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide “demand response” services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.