基于预处理共轭梯度迭代法的电力系统状态估计算法

随着中国电网省地一体化和输配一体化的不断发展,电力系统计算的维度越来越高.状态估计作为电力系统态势感知中的基础环节,需要保证其实时性,而加权最小二乘法是电力系统运用最广泛的状态估计方法.为此,针对加权最小二乘法在牛顿迭代过程中矩阵乘法和线性方程组求解耗时较长的特点,根据Krylov子空间方法中共轭梯度法的思想,设计了一种基于预处理共轭梯度迭代法的电力系统状态估计算法.该方法采用不完全LU分解法对原始线性方程组进行预处理,并采用图形处理器(GPU)并行加速技术对矩阵乘法、线性方程预处理和共轭梯度法迭代进行加速.算例分析表明了文中方法加速效果明显,内存和显存占用较低,经过不完全LU分解法预处理的线性方程组迭代次数少,能够满足大规模电力系统状态估计的实时性要求.

State Estimation Algorithm of Power System Based on Preconditioned Conjugate Gradient Iteration

With the continuous development of provincial-regional power grid integration and transmission-distribution network integration in China, the dimension of power system calculation is getting higher and higher. As a basic component of power system situation awareness, state estimation needs to ensure its real-time performance. Weighted least squares (WLS) method is the most widely used state estimation method in power systems. Therefore, according to the time-consuming characteristic when solving matrix multiplication and linear equations in the Newton iteration by WLS, this paper designs a state estimation algorithm of power system based on preconditioned conjugate gradient iteration with the idea of conjugate gradient method in Krylov subspace method. This method uses incomplete LU decomposition to preprocess the original linear equations, and adopts graphics processing unit (GPU) parallel acceleration technology to accelerate matrix multiplication, linear equation preprocessing, and conjugate gradient method iteration. The case analysis shows that the method in this paper has obvious acceleration effect, low memory and video memory requirement, and less iterations of the linear system of equations preprocessed by the incomplete LU decomposition method, which can meet the real-time requirements of large-scale power system state estimation.