CAJ | 학술논문

电力系统中一般采用临界点边界的法向量迭代计算潮流方程的局部最近鞍-结分歧点(closest saddle-node bifurcation point，CSNBP)。对于高维非线性系统来说，计算量将非常大。利用渐近数值方法(asymptotic numerical method，ANM)和确定鞍-结分歧点的扩张系统，给出了一种快速计算潮流方程CSNBP的系统化方法。采用步长自适应计算的 ANM 快速逼近指定发电、负荷变化方向对应的鞍-结分歧点，并利用扩张系统确定临界点边界的法向量。核心计算只需求解潮流雅可比矩阵或其转置作为系数矩阵的线性方程组，线性方程组右端向量中潮流方程的二阶导数项通过双线性函数方便确定。2383节点系统和我国实际电网的计算验证了所提方法的有效性和可行性。
전력계통중일반채용림계점변계적법향량질대계산조류방정적국부최근안-결분기점(closest saddle-node bifurcation point，CSNBP)。대우고유비선성계통래설，계산량장비상대。이용점근수치방법(asymptotic numerical method，ANM)화학정안-결분기점적확장계통，급출료일충쾌속계산조류방정CSNBP적계통화방법。채용보장자괄응계산적 ANM 쾌속핍근지정발전、부하변화방향대응적안-결분기점，병이용확장계통학정림계점변계적법향량。핵심계산지수구해조류아가비구진혹기전치작위계수구진적선성방정조，선성방정조우단향량중조류방정적이계도수항통과쌍선성함수방편학정。2383절점계통화아국실제전망적계산험증료소제방법적유효성화가행성。
In power system analysis, the normal vector of the critical manifold is usually used in the iteration procedure to determine the local closest saddle-node bifurcation point (CSNBP) of power flow equations. It requires high computational costs for high-dimensional nonlinear systems. With the asymptotic numerical method (ANM) and extended systems, a systematic approach, which can rapidly compute the CSNBP of power flow equations, is given. The ANM with adaptive step-lengths is used to fast approximate the saddle-node bifurcation point corresponding to the fixed generation and load change direction, and the normal vector of the critical manifold is obtained by solving the extended systems. Only sequences of linear equations with sparse power flow Jacobian matrix or the transposed matrix of the Jacobian as the coefficient matrix are to be solved in the computational procedure, and the second-order derivative terms of power flow equations can be conveniently computed by the bilinear functions. The effectiveness and feasibility of the proposed approach are validated by calculation results of the Polish 2383-bus power system and a certain actual power grids in China.