基于分岔理论的交直流电力系统电压稳定性分析方法研究
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摘要
当前电力系统向大电网、高电压和远距离输电发展,高压直流输电技术为这种发展趋势提供了较好的解决方案,但也对电力系统稳定性提出了新的挑战,尤其是与直流端相联的弱交流系统的电压稳定性问题变得日益严重。因此,提出一种适应于交直流电力系统电压稳定性分析的理论模式,指导电力系统规划和安全生产,防患于未然,无疑具有重大的理论意义和实际意义。
电力系统是一个大型的、复杂的非线性动态系统,分岔理论是研究非线性动态系统结构稳定性的有力工具。近年来,分岔理论在工程中已经得到广泛应用,在许多研究领域已取得了大量的成果,但它在交直流电力系统电压稳定性分析中的应用仍有待于进一步深入。本文在研究交直流系统潮流算法和分岔点检测的基础上,利用分岔理论,结合小扰动稳定性的特征值分析法,提出了较为系统的交直流电力系统电压稳定性静、动态分岔分析方法,并将其成功地应用于3个典型的交直流互联电力系统中。具体内容如下：
首先,本文在给出发电机系统、负荷以及HVDC的数学模型后,基于HVDC的两类数学模型,得出了相应的交直流系统电压稳定性分析所需的微分代数(DAE)模型。
其次,在分析当前交直流系统潮流算法的基础上,提出了一种新的潮流计算方法一部分直流变量消除法。该方法不仅兼顾了统一迭代法的优点—收敛性较好,而且克服了直流变量消除法(改进的交替迭代法)在处理各种控制模式切换时程序较复杂的不足。
然后,研究了分岔点的检测方法(重点是Hopf分岔)。在比较了常用方法的优缺点、讨论了它们各自适用范围的此基础上,针对传统直接法所解方程维数高的问题,应用分解迭代技术,提出了一种计算Hopf分岔点的简化直接法,提高了计算效率。同时,在应用连续法检测Hopf分岔点时,利用电力系统的分岔特性,提出了以SNB点为起点,逆着平衡解流形鉴别Hopf分岔点的方法。算例表明：在实际工程应用中,该方法可在一定程度上减少计算量。此外,还详细阐述了求解交直流电力系统分岔点的具体步骤。
在获得系统潮流和分岔点的基础上,充分利用分岔点计算过程中得到的附加信息,结合小扰动稳定性的特征值分析法,得出了交直流系统静、动态电压稳定性分析方法。为阐明该方法的具体应用过程及验证其有效性,利用本文的方法分析了3个有代表性的交直流电力系统的电压稳定性,并通过追踪特征根轨迹和仿真验证了分析结果的正确性。
最后,应用本文的方法分析了直流系统对换流母线电压稳定性的影响。分析表明：为确保交直流系统稳定,必须选择恰当的直流系统控制参数、采用合理的控制模式。
As a result of its technical and economical advantages, HVDC technology has been playing an important role in the development toward great power grid, high voltage and long distance transmission of power systems. Although AC/DC combined transmission system has been the inevitable trend, it has also brought new challenge. Especially, the voltage stability problem of weak AC system connected to HVDC system becomes an increasingly serious one. It is necessary to put out a kind of theoretical model to analyze voltage stability of AC/DC power systems, which can serve for the design and security operation of power systems.
Power system is a large, complicated nonlinear dynamic system. It has been proved that bifurcation theory is one of effective tools for studying the structure stability of nonlinear dynamic system. In recent years, bifurcation theory has been widely applied in many engineering fields, and a great deal of results have been obtained, but it is only in the initial stage for the application of voltage stability in power systems. Based on the bifurcation theory and the eigenvalue analysis approach for small disturbance stability, a static and dynamic bifurcation analysis method for voltage stability of AC/DC power systems is introduced in this thesis after the study of on the algorithm of power flow and bifurcation points. Main research works and contributions are summarized as follows.
Firstly, according to two kinds of HVDC models, the corresponding differential algebra equation (DAE) models of AC/DC power systems are modeled for voltage stability analysis, following the mathematic models of generators, loads and HVDC given in this paper.
Secondly, a new power flow algorithm of AC/DC -"partial DC variables elimination method"is proposed in this thesis on the basis of assesment about the existing algorithms. The new algorithm not only keeps the advantage of classical unified approach-good convergence, but also overcomes the disadvantage of "DC variables elimination method" -complicated programme design for dealing with control model convertion of HVDC system.
Thirdly, the identification method of Hopf bifurcation point is studied in this thesis. After review on normal methods to calculate SNB point and Hopf bifurcation point, a new matrix reduction method is presented to directly calculate the Hopf bifurcation point with the resolution-iterative-technique, which is verified to be more efficient than the classic direct method in the samples. Meanwhile, when the continuation method is adapted to locate Hopf bifurcation, equilibrium points are detected inverse the direct of equilibrium manifold beginning from the SNB point, which uses the bifurcation characteristic of power systems. Sample power systems show its effecience. In addition, the procedure of bifurcation point identification in AC/DC power systems is stated in detail.
After power flow and bifurcation points of AC/DC power systems are obtained, the static and dynamic bifurcation analysis method for voltage stability is proposed by the use of byproducts from biburcation point calculation, combining the eigenvalue approach for small disturbance stability. Three classic examples are given in order to verity this method and to illustrate the procedure of voltage stability analysis in this way.
Finally, HVDC's influence on the converter bus voltage stability is analyzed in the method presented in this paper. Its results show that it is necessary to select proper control parameters and models of DC system for the security of AC/DC power systems.
电力系统是一个大型的、复杂的非线性动态系统,分岔理论是研究非线性动态系统结构稳定性的有力工具。近年来,分岔理论在工程中已经得到广泛应用,在许多研究领域已取得了大量的成果,但它在交直流电力系统电压稳定性分析中的应用仍有待于进一步深入。本文在研究交直流系统潮流算法和分岔点检测的基础上,利用分岔理论,结合小扰动稳定性的特征值分析法,提出了较为系统的交直流电力系统电压稳定性静、动态分岔分析方法,并将其成功地应用于3个典型的交直流互联电力系统中。具体内容如下：
首先,本文在给出发电机系统、负荷以及HVDC的数学模型后,基于HVDC的两类数学模型,得出了相应的交直流系统电压稳定性分析所需的微分代数(DAE)模型。
其次,在分析当前交直流系统潮流算法的基础上,提出了一种新的潮流计算方法一部分直流变量消除法。该方法不仅兼顾了统一迭代法的优点—收敛性较好,而且克服了直流变量消除法(改进的交替迭代法)在处理各种控制模式切换时程序较复杂的不足。
然后,研究了分岔点的检测方法(重点是Hopf分岔)。在比较了常用方法的优缺点、讨论了它们各自适用范围的此基础上,针对传统直接法所解方程维数高的问题,应用分解迭代技术,提出了一种计算Hopf分岔点的简化直接法,提高了计算效率。同时,在应用连续法检测Hopf分岔点时,利用电力系统的分岔特性,提出了以SNB点为起点,逆着平衡解流形鉴别Hopf分岔点的方法。算例表明：在实际工程应用中,该方法可在一定程度上减少计算量。此外,还详细阐述了求解交直流电力系统分岔点的具体步骤。
在获得系统潮流和分岔点的基础上,充分利用分岔点计算过程中得到的附加信息,结合小扰动稳定性的特征值分析法,得出了交直流系统静、动态电压稳定性分析方法。为阐明该方法的具体应用过程及验证其有效性,利用本文的方法分析了3个有代表性的交直流电力系统的电压稳定性,并通过追踪特征根轨迹和仿真验证了分析结果的正确性。
最后,应用本文的方法分析了直流系统对换流母线电压稳定性的影响。分析表明：为确保交直流系统稳定,必须选择恰当的直流系统控制参数、采用合理的控制模式。
As a result of its technical and economical advantages, HVDC technology has been playing an important role in the development toward great power grid, high voltage and long distance transmission of power systems. Although AC/DC combined transmission system has been the inevitable trend, it has also brought new challenge. Especially, the voltage stability problem of weak AC system connected to HVDC system becomes an increasingly serious one. It is necessary to put out a kind of theoretical model to analyze voltage stability of AC/DC power systems, which can serve for the design and security operation of power systems.
Power system is a large, complicated nonlinear dynamic system. It has been proved that bifurcation theory is one of effective tools for studying the structure stability of nonlinear dynamic system. In recent years, bifurcation theory has been widely applied in many engineering fields, and a great deal of results have been obtained, but it is only in the initial stage for the application of voltage stability in power systems. Based on the bifurcation theory and the eigenvalue analysis approach for small disturbance stability, a static and dynamic bifurcation analysis method for voltage stability of AC/DC power systems is introduced in this thesis after the study of on the algorithm of power flow and bifurcation points. Main research works and contributions are summarized as follows.
Firstly, according to two kinds of HVDC models, the corresponding differential algebra equation (DAE) models of AC/DC power systems are modeled for voltage stability analysis, following the mathematic models of generators, loads and HVDC given in this paper.
Secondly, a new power flow algorithm of AC/DC -"partial DC variables elimination method"is proposed in this thesis on the basis of assesment about the existing algorithms. The new algorithm not only keeps the advantage of classical unified approach-good convergence, but also overcomes the disadvantage of "DC variables elimination method" -complicated programme design for dealing with control model convertion of HVDC system.
Thirdly, the identification method of Hopf bifurcation point is studied in this thesis. After review on normal methods to calculate SNB point and Hopf bifurcation point, a new matrix reduction method is presented to directly calculate the Hopf bifurcation point with the resolution-iterative-technique, which is verified to be more efficient than the classic direct method in the samples. Meanwhile, when the continuation method is adapted to locate Hopf bifurcation, equilibrium points are detected inverse the direct of equilibrium manifold beginning from the SNB point, which uses the bifurcation characteristic of power systems. Sample power systems show its effecience. In addition, the procedure of bifurcation point identification in AC/DC power systems is stated in detail.
After power flow and bifurcation points of AC/DC power systems are obtained, the static and dynamic bifurcation analysis method for voltage stability is proposed by the use of byproducts from biburcation point calculation, combining the eigenvalue approach for small disturbance stability. Three classic examples are given in order to verity this method and to illustrate the procedure of voltage stability analysis in this way.
Finally, HVDC's influence on the converter bus voltage stability is analyzed in the method presented in this paper. Its results show that it is necessary to select proper control parameters and models of DC system for the security of AC/DC power systems.
引文
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