Sparse Recovery from Nonlinear Measurements with Applications in Bad Data Detection for Power Networks
Sparse Recovery from Nonlinear Measurements with Applications in Bad Data Detection for Power Networks
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发表时间：
2011-12
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通讯作者：
Weiyu Xu;Meng Wang;A. Tang
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作者：
Weiyu Xu;Meng Wang;A. Tang
本文研究了非线性测量的稀疏恢复问题，该问题在电网的状态估计和不良数据检测中具有广泛的应用。采用迭代混合l1和l2凸规划，通过局部线性化非线性测量来估计系统的真实状态。当测量值为线性时，利用线性子空间的近似欧几里得性质，导出了稀疏不良数据和加性观测噪声下状态估计误差的性能界。当测量值为非线性时，我们给出了迭代算法的解收敛于真实状态的条件，即使局部线性化的测量值可能不是实际的非线性测量值。我们也在数值上评估了一种迭代凸规划方法在非线性电网问题中执行不良数据检测。作为一个副产品，在本文中，我们利用几何泛函分析中的“逃过网格”定理，给出了线性子空间的几乎欧几里得性质的明确界限。
In this paper, we consider the problem of sparse recovery from nonlinear measurements, which has applications in state estimation and bad data detection for power networks. An iterative mixed l1 and l2 convex programming is used to estimate the true state by locally linearizing the nonlinear measurements. When the measurements are linear, through using the almost Euclidean property for a linear subspace, we derive a new performance bound for the state estimation error under sparse bad data and additive observation noise. When the measurements are nonlinear, we give conditions under which the solution of the iterative algorithm converges to the true state even tho ugh the locally linearized measurements may not be the actual nonlinear measurements. We also numerically evaluate an iterative convex programming approach to perform bad data detections in nonlinear electrical power networks problems. As a byproduct, in this paper we provide sharp bounds on the almost Euclidean property of a linear subspace, using the “escape-through-a-mesh” theorem from geometric functional analysis.