Analysis Of Small Signal Stability Of Power Systems With Time Delays And Parameter Uncertainties

The expansion of the power system in China is creating one of the world's largest interconnected systems, far too large to be controlled by local signals alone. The fast development of wide-area measurement systems (WAMS) technology and communication network in power systems has enabled the use of measured signals from remote locations for the purpose of centralized control. Because of the nature of wide-area interconnections, communication delay cannot be ignored. As a result, the power system controlled by global signals is characterized by inevitable communication delays. If not taken into account, time delays can weaken the system performance or even cause instability. Therefore, it is critical to determine the stability margin of time-delay systems. However, it is complicated to compute the delay margins and there are still many important computation issues to be solved.Furthermore, with the ongoing deregulation of the power system, the growth of distributed generation and the aggrandizement of environmental-economy power dispatch, considering the effects of uncertainties in large-scale interconnected power systems has emerged as an area of increasing attention. Until now, although much focus has been paid to the issue of mitigating possible dynamic performance caused by uncertainty, there still lacks a practical approach for stability estimation of uncertain time-delay systems.In the first part of this dissertation, the modeling of power systems with delay signals and efficient methods to compute delay margins for commensurate and incommensurate delay systems are investigated. Details are as follows,1. The automatic generation control (AGC) system with communication delays is modeled by a linear time-invariant (LTI) delay equation given in the state-space description. Two constant matrices are then obtained from the Kronecker sum and Kronecker product of system matrices. Based on the computation of generalized eigenvalues and eigenvalues of frequency-independent constant matrices, a sufficient and necessary condition of asymptotic stability of delay-independent/delay-dependent systems is proposed and the delay margin of AGC systems with global FFC configurations derived from the East China Power Grid is obtained. The computation is to be performed on constant matrices, and thus few calculations and a high computational precision can be ensured. This method is largely effective for systems of a low order and with a few delays.2. A state-space description is provided for two-level power system stabilizer (PSS) design and the system with additional inter-area damping control. The stability estimation is determined by computing the eigenvalues and generalized eigenvalues of frequency-dependent matrices. A frequency-sweeping test is proposed to find the critical frequencies where the characteristic roots intersect the imaginary axis, and to calculate the corresponding delays. The advantage of this method lies in its computational efficiency, reliability, and its usefulness for analyzing high order systems with many delays.3. The stability analysis of time-delay systems is interpreted as a robust stability problem, using a structured uncertainty matrix with repeated complex scalars to describe the linear time-invariant systems with incommensurate delays. By the use of the D-scaled upper bound, linear fractional transformation (LFT) and frequency-sweeping test, stability regions in delay space are found. Based on theμtheorem, necessary and sufficient conditions for the single delay system and less conservative sufficient conditions for systems with multiple incommensurate delays are provided. There is no call for finding the zeros of the multivariate characteristic quasi-polynomial of high order in this approach, and thus it has the virtue of implementational ease and less conservatism.The other purpose of this paper is to propose a systematic method that can model and analyze the stability of power systems with communication time delays and parameter uncertainties taken into account. Both of them are synthesized in theμanalysis framework, by constructing a block-diagonal matrix with repeated real scalars and complex scalars to describe the delays and uncertainties. There are different convenient methods of modeling the M-Δloop to accommodate different problems. Details are as follows,1. When parameter uncertainty is considered in the LTI AGC system, the varying elements of the system matrices in state-space equations are expressed as the LFTs of their corresponding perturbation elements. A M-Δfeedback interconnection is presented to model the multi-area AGC system with both real parameter uncertainties and communication delays. Based on theμtheorem and frequency-sweeping test, the stability performance of the M-Δloop including mixed structured uncertainties is analyzed. Simulation results of a three-area AGC interconnected system in the case of a single and multi varying parameters, as well as adaptive controllers are reported to validate the methodology.2. The method of modeling uncertain time-delay problems in power system is further discussed. Based on the LFT technique and first order partial derivatives of the Jacobian matrix with respect to parameter variation, the M-Δmodel of PSS systems considering parameter uncertainties and communication delays is proposed. The method underμanalysis framework of estimating the stability region of a mixedμproblem with both repeated complex scalars and real scalars is presented. Simulations results on a three-generator system are reported to validate the methodology.