电力系统小扰动稳定约束下的平衡解与最优潮流研究
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摘要
如何建立合理的模型和数值方法,实现多机系统的小扰动稳定运行点的直接求解,是电力系统稳定性分析中一个值得深入探讨的内容。本文在回顾电力系统小扰动稳定性研究成果的基础上,利用精确的数学理论,通过建立小扰动稳定约束,提出了稳定平衡解模型,寻求了该模型的有效算法,并对小扰动稳定约束下最优潮流问题进行了初步的探讨。
为实现电力系统小扰动下的稳定运行,通过研究小扰动稳定域理论,提出了稳定函数的概念,建立了小扰动稳定约束的数学模型。针对典型的几种不稳定平衡点类型,构造了不同的小扰动稳定约束表达式。通过调节小扰动稳定约束的参数,设定了运行点与稳定域边界之间的距离。小扰动稳定约束是关于非对称的状态矩阵或潮流雅可比矩阵的代数不等式,为避免计算非对称矩阵特征值的困难,运用Cayley变换和谱函数理论将小扰动稳定约束转换为半光滑不等式。
结合小扰动稳定约束与电力系统传统的平衡方程,建立稳定平衡解模型,该模型由稳定约束将非稳定解排除在稳定域之外。运用光滑化函数将该模型转换为光滑方程,寻求稳定平衡解模型的数值求解方法,从而直接求得稳定平衡解。
利用光滑化转换后的小扰动稳定约束,建立了计及小扰动稳定的固定稳定裕度最优潮流模型,计算该最优潮流模型可直接获得满足一定的稳定裕度且经济性最优的运行点。
通过编制MATLAB程序,实现小扰动稳定约束下的稳定平衡解与最优潮流模型及其算法,其计算结果表明了所提模型和算法的有效性。
How to establish a rational model and the numerical algorithm, and then direct obtain operating points for small signal stability in multi-machine power system, is worthy of in-depth study on power system stability analysis. After reviewing research achievements about small signal stability of the power system, in this paper, using precise mathematical theories, on the basis of establishing small signal stability constraints, the concept and formulation of stable equilibrium solution model are presented, efficient algorithm for the model is designed, and optimal power flow with considering small signal stability constraints is preliminary researched.
To realize stable operation of the power system under small disturbance, based on the small signal stability region theories, concept of stability function is presented, and mathematical model of small signal stability constraint is estabilished. Aiming at several typical unstable equilibrium points, corresponding different stability constraints are expressed. The distance between operating point and boundary of stability region can be set by regulating parameter in stability constraint. Small signal stability constraints are algebra inequalities of stat matrix or Jacobian matrix, in order to avoid the difficulty of calculating eigenvalues of non-symmetric matrix, matrix theories and spectral function properties are applied to convert stability constraints into semi-smooth inequalities.
Combining small signal stability constraint with the classical balance equations of power system, stable equilibrium solution model would be established, in which unstable points are excluded out of stability region by stability constraints. Through transforming the model into being smooth using smoothing functions, numerical algorithm for the model is discussed, so that stable equilibrium solution would be direct solved out.
Making use of the small signal stability constraints, which are converted into smooth inequalities, fixed stability margin optimal power flow model with considering small signal stability constraints is established. After solving the optimal power flow model, an operating point would be direct obtained to satisfy fixed stability margin and maximum economical.
Through compiling program using MATLAB, the stable equilibrium solution and optimal power flow model with small signal stability constraint and the algorithm are achieved, so that the feasibility of proposed model and algorithm are testified by calculated results.
为实现电力系统小扰动下的稳定运行,通过研究小扰动稳定域理论,提出了稳定函数的概念,建立了小扰动稳定约束的数学模型。针对典型的几种不稳定平衡点类型,构造了不同的小扰动稳定约束表达式。通过调节小扰动稳定约束的参数,设定了运行点与稳定域边界之间的距离。小扰动稳定约束是关于非对称的状态矩阵或潮流雅可比矩阵的代数不等式,为避免计算非对称矩阵特征值的困难,运用Cayley变换和谱函数理论将小扰动稳定约束转换为半光滑不等式。
结合小扰动稳定约束与电力系统传统的平衡方程,建立稳定平衡解模型,该模型由稳定约束将非稳定解排除在稳定域之外。运用光滑化函数将该模型转换为光滑方程,寻求稳定平衡解模型的数值求解方法,从而直接求得稳定平衡解。
利用光滑化转换后的小扰动稳定约束,建立了计及小扰动稳定的固定稳定裕度最优潮流模型,计算该最优潮流模型可直接获得满足一定的稳定裕度且经济性最优的运行点。
通过编制MATLAB程序,实现小扰动稳定约束下的稳定平衡解与最优潮流模型及其算法,其计算结果表明了所提模型和算法的有效性。
How to establish a rational model and the numerical algorithm, and then direct obtain operating points for small signal stability in multi-machine power system, is worthy of in-depth study on power system stability analysis. After reviewing research achievements about small signal stability of the power system, in this paper, using precise mathematical theories, on the basis of establishing small signal stability constraints, the concept and formulation of stable equilibrium solution model are presented, efficient algorithm for the model is designed, and optimal power flow with considering small signal stability constraints is preliminary researched.
To realize stable operation of the power system under small disturbance, based on the small signal stability region theories, concept of stability function is presented, and mathematical model of small signal stability constraint is estabilished. Aiming at several typical unstable equilibrium points, corresponding different stability constraints are expressed. The distance between operating point and boundary of stability region can be set by regulating parameter in stability constraint. Small signal stability constraints are algebra inequalities of stat matrix or Jacobian matrix, in order to avoid the difficulty of calculating eigenvalues of non-symmetric matrix, matrix theories and spectral function properties are applied to convert stability constraints into semi-smooth inequalities.
Combining small signal stability constraint with the classical balance equations of power system, stable equilibrium solution model would be established, in which unstable points are excluded out of stability region by stability constraints. Through transforming the model into being smooth using smoothing functions, numerical algorithm for the model is discussed, so that stable equilibrium solution would be direct solved out.
Making use of the small signal stability constraints, which are converted into smooth inequalities, fixed stability margin optimal power flow model with considering small signal stability constraints is established. After solving the optimal power flow model, an operating point would be direct obtained to satisfy fixed stability margin and maximum economical.
Through compiling program using MATLAB, the stable equilibrium solution and optimal power flow model with small signal stability constraint and the algorithm are achieved, so that the feasibility of proposed model and algorithm are testified by calculated results.
引文
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