Observability Analysis for Large-Scale Power Systems Using Factor Graphs

The state estimation algorithm estimates the values of the state variables based on the measurement model described as the system of equations. Prior to applying the state estimation algorithm, the existence and uniqueness of the solution of the underlying system of equations is determined through the observability analysis. If a unique solution does not exist, the observability analysis defines observable islands and further defines an additional set of equations (measurements) needed to determine a unique solution. For the first time, we utilise factor graphs and Gaussian belief propagation algorithm to define a novel observability analysis approach. The observable islands and placement of measurements to restore observability are identified by following the evolution of variances across the iterations of the Gaussian belief propagation algorithm over the factor graph. Due to sparsity of the underlying power network, the resulting method has the linear computational complexity (assuming a constant number of iterations) making it particularly suitable for solving large-scale systems. The method can be flexibly matched to distributed computational resources, allowing for determination of observable islands and observability restoration in a distributed fashion. Finally, we discuss performances of the proposed observability analysis using power systems whose size ranges between 1354 and 70000 buses.Comment: 9 pages, 9 figure, version of the journal paper submitted for publicatio

Fast Real-Time DC State Estimation in Electric Power Systems Using Belief Propagation

We propose a fast real-time state estimator based on the belief propagation algorithm for the power system state estimation. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrix-based state estimation methods, the belief propagation approach is robust to ill-conditioned scenarios caused by significant differences between measurement variances, thus resulting in a solution that eliminates observability analysis. Using the DC model, we numerically demonstrate the performance of the state estimator in a realistic real-time system model with asynchronous measurements. We note that the extension to the AC state estimation is possible within the same framework.Comment: 6 pages; 7 figures; submitted in the IEEE International Conference on Smart Grid Communications (SmartGridComm 2017

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Forecasting Time Series with VARMA Recursions on Graphs

Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task. This work provides contributions in this direction by considering the forecasting of a process evolving over a graph. We make use of the (approximate) time-vertex stationarity assumption, i.e., timevarying graph signals whose first and second order statistical moments are invariant over time and correlated to a known graph topology. The latter is combined with VAR and VARMA models to tackle the dimensionality issues present in predicting the temporal evolution of multivariate time series. We find out that by projecting the data to the graph spectral domain: (i) the multivariate model estimation reduces to that of fitting a number of uncorrelated univariate ARMA models and (ii) an optimal low-rank data representation can be exploited so as to further reduce the estimation costs. In the case that the multivariate process can be observed at a subset of nodes, the proposed models extend naturally to Kalman filtering on graphs allowing for optimal tracking. Numerical experiments with both synthetic and real data validate the proposed approach and highlight its benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin