基于海森矩阵的仿射谐波潮流保守性优化

Conservation optimization of affine harmonic power flow based on Hessian matrix

针对传统仿射谐波潮流的计算结果存在较大保守性的问题,提出一种仿射谐波潮流的保守性优化方法。首先建立电网潮流方程,并采用牛顿-拉夫逊算法进行求解,在求解过程中采用纽曼级数将仿射矩阵的求逆运算转换为乘法运算;然后定义保守度作为保守性的量化指标,以完备性为约束条件、保守度最小为优化目标,基于海森矩阵求解仿射乘法的最优近似;最后将仿射乘法的最优近似用于仿射谐波潮流计算。IEEE 30节点系统仿真结果表明,相较于传统算法,所提方法的计算结果具有更小的保守性。

Aiming at the problem that large conservation exists in the calculation results of traditional affine harmonic power flow,a conservation optimization method for affine harmonic power flow is proposed.Firstly,the power flow equation of power grid is established and solved by Newton-Raphson algorithm,and Newman series is adopted to convert the inverse operation of affine matrix into multiplication operation in the calculation process.Secondly,the conservative degree is defined as a quantitative index of conservation.With the completeness as the constraint condition and the minimum conservative degree as the optimization target,the optimal approximation of affine multiplication is solved based on Hessian matrix.Finally,the optimal approximation of affine multiplication is used for affine harmonic power flow calculation.The simulative results of IEEE 30-bus system show that,compared with the traditional algorithm,the calculation results of the proposed method are less conservative.