Title: Conditions for Estimation of Sensitivities of Voltage Magnitudes to Complex Power Injections Show Chinese title

Title: 电压幅值对复功率注入的敏感性的估计条件

Abstract: Voltage phase angle measurements are often unavailable from sensors in distribution networks and transmission network boundaries. Therefore, this paper addresses the conditions for estimating sensitivities of voltage magnitudes with respect to complex (active and reactive) electric power injections based on sensor measurements. These sensitivities represent submatrices of the inverse power flow Jacobian. We extend previous results to show that the sensitivities of a bus voltage magnitude with respect to active power injections are unique and different from those with respect to reactive power. The classical Newton-Raphson power flow model is used to derive a novel representation of bus voltage magnitudes as an underdetermined linear operator of the active and reactive power injections; parameterized by the bus power factors. Two conditions that ensure the existence of unique complex power injections given voltage magnitudes are established for this underdetermined linear system, thereby compressing the solution space. The first is a sufficient condition based on the bus power factors. The second is a necessary and sufficient condition based on the system eigenvalues. We use matrix completion theory to develop estimation methods for recovering sensitivity matrices with varying levels of sensor availability. Simulations verify the results and demonstrate engineering use of the proposed methods. Show Chinese abstract

Abstract: 电压相位角测量在配电网和输电网络边界处的传感器中通常不可用。因此，本文研究了基于传感器测量值估计电压幅值相对于复数（有功和无功）电力注入的灵敏度条件。这些灵敏度是逆功率流雅可比矩阵的子矩阵。我们扩展了先前的结果，以表明相对于有功功率注入的节点电压幅值灵敏度是唯一的，并且不同于相对于无功功率的灵敏度。使用经典的牛顿-拉夫森功率流模型，推导出节点电压幅值作为有功和无功功率注入的欠定线性算子的新表示；该表示由节点功率因数参数化。为了解决这个欠定线性系统，建立了两个确保给定电压幅值时存在唯一复数功率注入的条件，从而压缩了解空间。第一个条件是基于节点功率因数的充分条件。第二个条件是基于系统特征值的必要且充分条件。我们利用矩阵补全理论，开发了用于恢复不同传感器可用性水平下的灵敏度矩阵的估计方法。仿真验证了结果，并展示了所提出方法的工程应用。