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arXiv 1503.06911eess.SYcs.SYmath.DS
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面向响应负载的统一随机混合系统方法

A Unified Stochastic Hybrid System Approach to Aggregate Modeling of Responsive Loads

The Ohio State University(俄亥俄州立大学)

Lin Zhao, Wei Zhang

AI总结:

本文提出统一的聚合建模方法,用于描述响应负载的群体动态,结合确定性混合系统和随机混合系统模型,推导出描述概率密度演化的偏微分方程,扩展了现有研究的应用范围。

摘要:

聚合负载建模对于系统分析和设计各种需求响应策略具有根本重要性。不同于跟踪单个负载轨迹,聚合建模关注负载群体密度演化的描述。现有模型仅适用于具有一阶线性动态的热控负载(TCL)。本文开发了一种统一的聚合建模方法,适用于通用TCL和可延迟负载。我们提出了一种确定性混合系统模型来描述在需求响应规则下的个体负载动态,并开发了一种通用随机混合系统(SHS)模型来捕捉群体动态。我们还推导出一组偏微分方程(PDE),这些方程描述了SHS的概率密度演化。我们的结果无法通过现有文献中的SHS工具获得,因为所提出的SHS模型涉及随机和确定性切换,具有多维域中的通用切换面。推导出的PDE模型包含许多现有聚合负载建模结果作为特殊情况,并可用于许多其他现实建模场景,这些场景在文献中尚未被研究。

英文摘要:

Aggregate load modeling is of fundamental importance for systematic analysis and design of various demand response strategies. Instead of keeping track of the trajectories of individual loads, the aggregate modeling problem focuses on characterizing the density evolution of the load population. Most existing models are only applicable to Thermostatically Controlled Loads (TCL) with first-order linear dynamics. This paper develops a unified aggregate modeling approach that can be used for general TCLs as well as deferrable loads. We propose a deterministic hybrid system model to describe individual load dynamics under demand response rules, and develop a general stochastic hybrid system (SHS) model to capture the population dynamics. We also derive a set of partial differential equations (PDE) that governs the probability density evolution of the SHS. Our results cannot be obtained using the exiting SHS tools in the literature as the proposed SHS model involves both random and deterministic switchings with general switching surfaces in multi-dimensional domains. The derived PDE model includes many existing aggregate load modeling results as special cases and can be used in many other realistic modeling scenarios that have not been studied in the literature.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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