几类不确定系统的稳定性在电力系统中的应用

发布时间：2018-06-25 17:08

本文选题：不确定系统 + 时滞系统　；参考：《华北电力大学(北京)》2016年硕士论文

【摘要】：在电力系统中,系统参数的不确定性是客观存在的,譬如系统测量和建模的精准度、时滞现象、风电的波动和间歇行为等都具有一定的不确定性。由于经济增长、产业结构和能源消费结构调整等影响,电力市场也存在许多不确定因素,如电能需求量的随机特性和供求方需求弹性波动。不确定性是随机性(或偶然性)和模糊性(非明晰性)的总称,两者的产生机理和物理意义有所区别。不确定因素直接影响系统的稳定性,研究其稳定机理对电力系统稳定运行有重要意义。本文研究了几类不确定系统的稳定性,并给出其在电力系统中的应用。考虑系统不确定因素,利用电力系统、经济学和数学等知识,结合随机思想、区间思想、时滞分割等方法,分别分析含有区间随机的电力市场动态模型、具有区间时变时滞的线性不确定时滞系统和不确定随机时滞系统的稳定性,得到稳定性判定条件,并给出其在电力系统中的应用。主要包括以下工作：(1)建立电力市场区间模型、随机模型、区间随机模型,并分析其稳定性。结合Alvarado提出的电力市场动态模型,考虑到电能需求量的随机特性、供应方和消费者需求弹性变化的区间特征,利用经济学、区间系统理论、随机微分方程稳定性、随机过程理论等知识,分别得到了对应模型的相关稳定性判定定理。结论表明通过该判据可以找到系统的稳定区间,即能够使系统稳定的需求弹性取值范围。最后利用电力市场相关数据进行仿真分析,验证了结论的有效性。(2)研究具有区间时变时滞系统的稳定性判定准则,并分析其在电力系统中的应用。利用时滞分段思想把时滞区间分割成任意两段,构造合适的Lyapunov-Krasovskii泛函,运用改进型的积分不等式和凸组合方法,得到系统时滞相关稳定准则。应用电力系统中的美国西部联合电网(WSCC)3机9节点系统进行数值分析,结果表明WSCC3机9节点系统的最大允许时滞上界增大,且随着分割精度的增加而增大,优于以往文献,系统的保守性减小。(3)分析含有随机项的区间时变时滞系统的鲁棒稳定性,并应用到电力系统中。将时滞区间分割成任意N小段,构造新的Lyapunov- Krasovskii泛函,充分利用时滞上下界信息及不同时滞状态的信息。在处理泛函导数时,引入必要的自由权矩阵,利用凸组合、积分不等式和LMI (Linear Matrix Inequation)方法,得到了该系统时滞相关稳定判据。将所得结论应用到单机无穷大系统中,计算系统所允许的最大时滞上界,与前人结果相比,保守性降低,验证了本方法的有效性。
[Abstract]:In power system, the uncertainty of system parameters exists objectively, such as the accuracy of measurement and modeling, time-delay phenomenon, fluctuation of wind power and intermittent behavior. Due to the influence of economic growth, industrial structure and energy consumption structure adjustment, there are many uncertain factors in the electricity market, such as the stochastic characteristics of power demand and the demand elasticity fluctuation on the demand side. Uncertainty is a general term of randomness (or contingency) and fuzziness (non-clarity). The uncertain factors directly affect the stability of the power system. It is very important to study the stability mechanism of the system. In this paper, the stability of some uncertain systems is studied, and its application in power system is given. Considering the uncertain factors of the system, using the knowledge of power system, economics and mathematics, combining the stochastic thought, the interval thought, the time-delay segmentation and so on, the dynamic model of the electricity market with interval random is analyzed, respectively. The stability of linear uncertain time-delay systems and uncertain stochastic time-delay systems with interval time-varying delays is obtained. The stability criteria are obtained and their applications in power systems are given. The main contributions are as follows: (1) establish the interval model, stochastic model and interval stochastic model of electricity market, and analyze its stability. Based on the dynamic model of electricity market proposed by Alvarado, considering the stochastic characteristic of electricity demand and the interval characteristic of elasticity of demand between supplier and consumer, the stability of stochastic differential equation is obtained by using economics, interval system theory and stochastic differential equation. Based on the theory of stochastic process, the relative stability theorems of the corresponding models are obtained. The results show that the stability interval of the system can be found by the criterion, that is, the demand elasticity value range of the system stability can be obtained. Finally, the validity of the conclusion is verified by using the relevant data of the power market. (2) the stability criterion of time-varying time-delay systems with interval is studied, and its application in power system is analyzed. The delay-dependent stability criterion is obtained by using the improved integral inequality and convex combination method. The delay-delay interval is divided into any two segments by using the idea of piecewise delay. The appropriate Lyapunov-Krasovskii Functionals are constructed. The numerical analysis of the 3-machine 9-bus system of the United States Western Power Grid (WSCC) is carried out. The results show that the upper bound of the maximum allowable delay for the 9-bus system of the WSCC3 machine increases and increases with the increase of the division accuracy, which is superior to the previous literatures. The conservatism of the system is reduced. (3) the robust stability of interval time-varying time-delay systems with stochastic terms is analyzed and applied to power systems. A new Lyapunov-Krasovskii functional is constructed by dividing the delay-interval into any N segment, which makes full use of the upper and lower bounds of delay and the information of different delay states. In dealing with functional derivatives, the necessary free form matrix is introduced. By means of convex combination, integral inequality and LMI (Linear Matrix Inequation) method, the delay-dependent stability criterion of the system is obtained. The results obtained are applied to the single-machine infinite bus system, and the maximum delay upper bound of the system is calculated. Compared with the previous results, the proposed method is less conservative and validates the effectiveness of the proposed method.
【学位授予单位】：华北电力大学(北京)
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TM712;TP13

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