發(fā)布時(shí)間：2018-06-25 17:08

  本文選題：不確定系統(tǒng) + 時(shí)滯系統(tǒng)　； 參考：《華北電力大學(xué)(北京)》2016年碩士論文

【摘要】：在電力系統(tǒng)中,系統(tǒng)參數(shù)的不確定性是客觀存在的,譬如系統(tǒng)測(cè)量和建模的精準(zhǔn)度、時(shí)滯現(xiàn)象、風(fēng)電的波動(dòng)和間歇行為等都具有一定的不確定性。由于經(jīng)濟(jì)增長(zhǎng)、產(chǎn)業(yè)結(jié)構(gòu)和能源消費(fèi)結(jié)構(gòu)調(diào)整等影響,電力市場(chǎng)也存在許多不確定因素,如電能需求量的隨機(jī)特性和供求方需求彈性波動(dòng)。不確定性是隨機(jī)性(或偶然性)和模糊性(非明晰性)的總稱,兩者的產(chǎn)生機(jī)理和物理意義有所區(qū)別。不確定因素直接影響系統(tǒng)的穩(wěn)定性,研究其穩(wěn)定機(jī)理對(duì)電力系統(tǒng)穩(wěn)定運(yùn)行有重要意義。本文研究了幾類不確定系統(tǒng)的穩(wěn)定性,并給出其在電力系統(tǒng)中的應(yīng)用。考慮系統(tǒng)不確定因素,利用電力系統(tǒng)、經(jīng)濟(jì)學(xué)和數(shù)學(xué)等知識(shí),結(jié)合隨機(jī)思想、區(qū)間思想、時(shí)滯分割等方法,分別分析含有區(qū)間隨機(jī)的電力市場(chǎng)動(dòng)態(tài)模型、具有區(qū)間時(shí)變時(shí)滯的線性不確定時(shí)滯系統(tǒng)和不確定隨機(jī)時(shí)滯系統(tǒng)的穩(wěn)定性,得到穩(wěn)定性判定條件,并給出其在電力系統(tǒng)中的應(yīng)用。主要包括以下工作：(1)建立電力市場(chǎng)區(qū)間模型、隨機(jī)模型、區(qū)間隨機(jī)模型,并分析其穩(wěn)定性。結(jié)合Alvarado提出的電力市場(chǎng)動(dòng)態(tài)模型,考慮到電能需求量的隨機(jī)特性、供應(yīng)方和消費(fèi)者需求彈性變化的區(qū)間特征,利用經(jīng)濟(jì)學(xué)、區(qū)間系統(tǒng)理論、隨機(jī)微分方程穩(wěn)定性、隨機(jī)過程理論等知識(shí),分別得到了對(duì)應(yīng)模型的相關(guān)穩(wěn)定性判定定理。結(jié)論表明通過該判據(jù)可以找到系統(tǒng)的穩(wěn)定區(qū)間,即能夠使系統(tǒng)穩(wěn)定的需求彈性取值范圍。最后利用電力市場(chǎng)相關(guān)數(shù)據(jù)進(jìn)行仿真分析,驗(yàn)證了結(jié)論的有效性。(2)研究具有區(qū)間時(shí)變時(shí)滯系統(tǒng)的穩(wěn)定性判定準(zhǔn)則,并分析其在電力系統(tǒng)中的應(yīng)用。利用時(shí)滯分段思想把時(shí)滯區(qū)間分割成任意兩段,構(gòu)造合適的Lyapunov-Krasovskii泛函,運(yùn)用改進(jìn)型的積分不等式和凸組合方法,得到系統(tǒng)時(shí)滯相關(guān)穩(wěn)定準(zhǔn)則。應(yīng)用電力系統(tǒng)中的美國(guó)西部聯(lián)合電網(wǎng)(WSCC)3機(jī)9節(jié)點(diǎn)系統(tǒng)進(jìn)行數(shù)值分析,結(jié)果表明WSCC3機(jī)9節(jié)點(diǎn)系統(tǒng)的最大允許時(shí)滯上界增大,且隨著分割精度的增加而增大,優(yōu)于以往文獻(xiàn),系統(tǒng)的保守性減小。(3)分析含有隨機(jī)項(xiàng)的區(qū)間時(shí)變時(shí)滯系統(tǒng)的魯棒穩(wěn)定性,并應(yīng)用到電力系統(tǒng)中。將時(shí)滯區(qū)間分割成任意N小段,構(gòu)造新的Lyapunov- Krasovskii泛函,充分利用時(shí)滯上下界信息及不同時(shí)滯狀態(tài)的信息。在處理泛函導(dǎo)數(shù)時(shí),引入必要的自由權(quán)矩陣,利用凸組合、積分不等式和LMI (Linear Matrix Inequation)方法,得到了該系統(tǒng)時(shí)滯相關(guān)穩(wěn)定判據(jù)。將所得結(jié)論應(yīng)用到單機(jī)無窮大系統(tǒng)中,計(jì)算系統(tǒng)所允許的最大時(shí)滯上界,與前人結(jié)果相比,保守性降低,驗(yàn)證了本方法的有效性。
[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.
【學(xué)位授予單位】：華北電力大學(xué)(北京)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：TM712;TP13

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