Design and analysis of dynamic compressive sensing in distribution grids



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The transition to a smart distribution grid is powered by enhanced sensing and advanced metering infrastructure that can provide situational awareness. However, aggregating data from spatially dispersed sensors/smart meters can present a significant challenge. Additionally, the lack of reliability in communication network used for aggregating this data, prevents its use for real time operations such as state estimation and control. With these challenges associated with measurement availability and accessibility, current distribution systems are typically unobservable. To cope with the unobservability issue, compressive sensing (CS) theory allows us to recover system state information from a small number of measurements provided the states of the distribution system exhibit sparsity. The spatio-temporal correlation of loads and/or rooftop photovoltaic (PV) generation results in sparsity of distribution system states. In this dissertation, we first validate this system sparsity property and exploit it to develop two (direct/indirect) voltage state estimation strategies for a three-phase unbalanced distribution network. Secondly, we focus on addressing the challenge of sparse signal recovery from limited measurements while incorporating their temporal dependence. Specifically, we implement two recursive dynamic CS approaches namely, streaming modified weighted-L1 CS and Kalman filtered CS that reconstruct a sparse signal using the current underdetermined measurements and the prior information about the sparse signal and its support set. Using practical distribution system power measurements as a case study, we quantify, for the first time, the performance improvement achievable with such recursive techniques relative to batch algorithms.

CS based signal recovery efforts typically assume that a limited number of measurements are available. However, in practice, due to communication network impairments, there is no guarantee that even this limited set of information might be available at the time of processing at the fusion/control center. Therefore, for the first time, we investigate the impact of intermittent measurement availability and random delays on recursive dynamic CS. Specifically, we quantify the error dynamics in both sparse signal estimation and support set estimation for a modified Kalman filter-CS based strategy in the presence of measurement losses. Using input-to-state stability analysis, we provide an upper bound for the expected covariance of the estimation error for a given rate of information loss. Next, we develop a modified CS algorithm that leverages apriori knowledge of signal correlation to project delayed measurements to the current signal recovery instant. We derive a new result quantifying the impact of errors in the apriori correlation model on signal recovery error.

Lastly, we study the robustness of CS based state estimation to uncertainty in distribution network topology knowledge. Topology identification is a challenging problem in distribution systems in general and especially, when there are limited number of available measurements. We tackle this problem by jointly estimating the states and network topology via an integrated mixed integer nonlinear program formulation. By developing convex relaxations of the original formulation as well Markovian models for dynamic topology transitions, we illustrate the superior performance achieved in both state estimation and in topology identification.

In summary, this dissertation offers the first comprehensive treatment of dynamic CS in smart distribution grids and can serve as the foundation of numerous follow-on efforts related to networked state estimation and control.



Dynamic compressive sensing, Distribution grid, State estimation, Topology identification, Lossy measurements, Delayed measurements

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Doctor of Philosophy


Department of Electrical and Computer Engineering

Major Professor

Balasubramaniam Natarajan