自适应Levenberg-Marquardt方法提高潮流计算收敛性

Improving the Convergence of Power Flow Calculation by a Self-adaptive Levenberg-marquardt method

Levenberg-Marquardt(LM)方法是一种求解病态非线性方程组的数值算法。LM方法的性能取决于阻尼因子的选取及更新策略。提出一种带自适应阻尼因子的LM方法来提高潮流计算的收敛性。针对电力系统良态潮流、病态潮流和潮流无解等3种情况,详细分析所提方法提高潮流计算收敛性的原因和机理。针对自适应LM迭代步中求逆矩阵的特殊结构,提出一种自适应LM迭代步的稀疏实现方法。对4个实际系统(含国网21 479节点系统)和1个IEEE 300节点标准系统进行仿真计算后结果表明:自适应LM方法能够得到良态或病态潮流的精确解以及潮流无解时的最小二乘解,因此具有很强的适应能力。在病态或无解的情况下,所提方法得到的计算结果可为后续的潮流调整提供有效依据。

Levenberg-Marquardt（LM） method is a numerical algorithm for solving the ill-conditioned nonlinear system of equations. The performance of LM method relies on the determination and update of the damping factor. A self-adaptive LM method was presented to improve the convergence of power flow calculation. The reasons and theories of the improvement made by this method in the convergence of power flow calculation were analyzed in three situations involving the well-conditioned, the ill-conditioned and the unsolvable power flow. In view of the special structure of the inverse matrix, a sparsity-oriented method was proposed to implement each LM step. Simulation results of four real-world power systems（including a state grid 21479-node system） and an IEEE 300-node standard system indicate that the self-adaptive LM method is capable of obtaining the exact solution of a well-conditioned or ill-conditioned power flow as well as the least square solution of an unsolvable power flow, thus, the proposed method has strong adaptability. Furthermore, for ill-conditioned or unsolvable cases, the convergent solution of the proposed method could provide effective instructions for the follow-up data rectifications.