CAJ | 학술논문

电力系统全过程动态仿真能够将机电暂态、中期和长期动态过程有机地统一起来进行数字仿真,仿真过程中需要多次求解大型稀疏线性方程组。该方程组由电力系统设备模型的微分-代数方程式差分后的代数方程和输电网络模型的代数方程形成,其快速求解算法是电力系统全过程动态仿真的难点之一。文中提出一种利用仿真中矩阵结构特点的分块快速直接求解算法,并开发实现了大型电力系统线性方程组稀疏求解器(ESS)。该算法首先将稀疏矩阵分为4个分块矩阵,然后将其中规模最大的对角块进一步细分为多个更小的对角分块矩阵,并利用部分小分块具有相同结构的特点进行矩阵LU 符号分解和数值分解,最后根据分块矩阵进行前代和回代求解计算。与现有其他求解器进行的算例对比表明,ESS 具有较为明显的整体求解速度优势,特别是在矩阵LU分解方面。
전력계통전과정동태방진능구장궤전잠태、중기화장기동태과정유궤지통일기래진행수자방진,방진과정중수요다차구해대형희소선성방정조。해방정조유전력계통설비모형적미분-대수방정식차분후적대수방정화수전망락모형적대수방정형성,기쾌속구해산법시전력계통전과정동태방진적난점지일。문중제출일충이용방진중구진결구특점적분괴쾌속직접구해산법,병개발실현료대형전력계통선성방정조희소구해기(ESS)。해산법수선장희소구진분위4개분괴구진,연후장기중규모최대적대각괴진일보세분위다개경소적대각분괴구진,병이용부분소분괴구유상동결구적특점진행구진LU 부호분해화수치분해,최후근거분괴구진진행전대화회대구해계산。여현유기타구해기진행적산례대비표명,ESS 구유교위명현적정체구해속도우세,특별시재구진LU분해방면。
Power system whole process dynamic simulation is such a method in which the electro-mechanical transient,medium-and long-term dynamic phenomena are organically unified.During the whole process of dynamic simulation,it is one of the key steps to solve sparse systems of linear equations composed of two kinds of equations:difference equations from dynamic equipment and algebraic equations from power network.Because of its very high order and large numbers of solving,the algorithm for fast solving is very important for this kind of dynamic simulation.This paper proposes a new method based on the block matrix for fast solving this linear equation and has developed an electric sparse solver (ESS).It first divides the sparse matrix into four big blocks.Many decoupled diagonal smaller blocks which are related to the equipment on buses in the power system are further divided from the largest diagonal block.Next,by utilizing the same structure among these small blocks,these diagonal blocks are symbolically and numerically LU factorized one by one.Finally,the equations are solved block by block using conventional forward and backward substitution.This algorithm has been implemented in a new linear system solver called ESS.The results from several linear equations in power system whole process dynamic simulations show that compared with other solvers,ESS can achieve higher computational efficiency,especially in the factorization phase.