Time/Frequency Approach to Phasor Dynamics in Power Systems Analysis

长期以来，电力系统的动力学研究一直利用将网络中所有电压和电流近似为“缓慢变化”的幅度和相位的正弦波来进行分析简化。基于这一假设，动态分析中的网络行为可以用通过复相量表示时域母线电压的潮流方程来表征。这通常被称为“正弦准稳态”近似（在这里缩写为“SQSS”），并广泛应用于用于研究机电行为和控制系统动力学的现代计算机软件包中。对于更快的时间尺度现象，最广泛使用的技术是时域模拟，其中所有相关的网络电压和电流都表示为三相时域信号，而不需要接近正弦的行为。后一种方法涉及巨大的计算负担和分析复杂性，因为使用瞬时量而不是相量，使用动态电路模型而不是代数阻抗关系。本提案中概述的研究目标是在基于阻抗的SQSS表示中固有的近似与将网络电压和电流表示为三相电路中的时域量相关的分析复杂性和计算负担之间提供一个中间地带。特别是，这项工作将采用一种更接近于信号处理中使用的时间/频率表示的相量观点，但将这些表示扩展到动态公式。结果将被称为“相量动力学”（PD）模型，并将涉及一个精心构建的阻抗和电路表示的混合。这种方法将允许在标准相量表示中不可能实现的重要扩展：包括高阶谐波的动态分析。提出的工作将通过将相关状态表示为窄带信号的加权和来处理这些情况，每个信号位于感兴趣的谐波中心频率附近。权重的时间演化由直接从原始瞬时模型导出的动力学方程控制。＊＊＊

9527570 DeMarco Dynamic studies in power systems have long exploited analytic simplifications gained by approximating all voltages and currents in the network as sinusoids of "slowly varying" magnitude and phase. With this assumption, network behavior in dynamic analyses is characterized by power flow equations that represent time-domain bus voltages via complex phasors. This is typically referred to as the "sinusoidal quasi-steady-state" approximation (abbreviated here by the acronym "SQSS"), and is widely utilized in modern computer packages used to study electromechanical behavior and control system dynamics. For faster time-scale phenomena, the most widely used techniques are time-domain simulations in which all relevant network voltages and currents are represented as three-phase, time-domain signals, without any requirement of nearly sinusoidal behavior. This latter approach involves tremendous computational burden and analytic complexity, because one uses instantaneous quantities rather than phasors, and dynamic circuit models rather than algebraic impedance relations. The goal of the research outlined in this proposal is to provide a middle ground between the approximations inherent in an impedance-based SQSS representation, and the analytic complexity and computational burden associated with representing network voltages and currents as time-domain quantities in a three-phase circuit. In particular, this work will adopt a viewpoint on phasors that is closer to time/frequency representations utilized in signal processing, but extending these representations to a dynamic formulation. The result will be termed "Phasor Dynamics" (PD) models, and will involve a carefully constructed hybrid of the impedance and circuit representations. This approach will allow an important extension that is not possible in standard phasor representations: a dynamic analysis that includes higher order harmonics. The work proposed will treat these cases by representing relevant st ates as weighted sums of narrow-band signals, each located about a harmonic center frequency of interest. The time evolution of the weights are governed by dynamic equations derived directly from the original instantaneous model. ***