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Register a new userExact Topology Reconstruction of Radial Dynamical Systems with Applications to Distribution System of the Power Grid
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Added by
Saurav Talukdar
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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In this article we present a method to reconstruct the interconnectedness of dynamically related stochastic processes, where the interactions are bi-directional and the underlying topology is a tree. Our approach is based on multivariate Wiener filtering which recovers spurious edges apart from the true edges in the topology reconstruction. The main contribution of this work is to show that all spurious links obtained using Wiener filtering can be eliminated if the underlying topology is a tree based on which we present a three stage network reconstruction procedure for trees. We illustrate the effectiveness of the method developed by applying it on a typical distribution system of the electric grid.
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Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a comprehensive framework based on spectral graph theory that fully and rigorously captures how multiple simultaneous line failures propagate, distinguishing between non-cut and cut set outages. Using this spectral representation of power systems, we identify the crucial graph sub-structure that ensures line failure localization -- the network bridge-block decomposition. Leveraging this theory, we propose an adaptive network topology reconfiguration paradigm that uses a two-stage algorithm where the first stage aims to identify optimal clusters using the notion of network modularity and the second stage refines the clusters by means of optimal line switching actions. Our proposed methodology is illustrated using extensive numerical examples on standard IEEE networks and we discussed several extensions and variants of the proposed algorithm.
Coordinating multiple local power sources can restore critical loads after the major outages caused by extreme events. A radial topology is needed for distribution system restoration, while determining a good topology in real-time for online use is a challenge. In this paper, a graph theory-based heuristic considering power flow state is proposed to fast determine the radial topology. The loops of distribution network are eliminated by iteration. The proposed method is validated by one snapshot and multi-period critical load restoration models on different cases. The case studies indicate that the proposed method can determine radial topology in a few seconds and ensure the restoration capacity.
Recently, there has been a surge of interest in adopting deep neural networks (DNNs) for solving the optimal power flow (OPF) problem in power systems. Computing optimal generation dispatch decisions using a trained DNN takes significantly less time when compared to using conventional optimization solvers. However, a major drawback of existing work is that the machine learning models are trained for a specific system topology. Hence, the DNN predictions are only useful as long as the system topology remains unchanged. Changes to the system topology (initiated by the system operator) would require retraining the DNN, which incurs significant training overhead and requires an extensive amount of training data (corresponding to the new system topology). To overcome this drawback, we propose a DNN-based OPF predictor that is trained using a meta-learning (MTL) approach. The key idea behind this approach is to find a common initialization vector that enables fast training for any system topology. The developed OPF-predictor is validated through simulations using benchmark IEEE bus systems. The results show that the MTL approach achieves significant training speeds-ups and requires only a few gradient steps with a few data samples to achieve high OPF prediction accuracy.
The modern power grid features the high penetration of power converters, which widely employ a phase-locked loop (PLL) for grid synchronization. However, it has been pointed out that PLL can give rise to small-signal instabilities under weak grid conditions. This problem can be potentially resolved by operating the converters in grid-forming mode, namely, without using a PLL. Nonetheless, it has not been theoretically revealed how the placement of grid-forming converters enhances the small-signal stability of power systems integrated with large-scale PLL-based converters. This paper aims at filling this gap. Based on matrix perturbation theory, we explicitly demonstrate that the placement of grid-forming converters is equivalent to increasing the power grid strength and thus improving the small-signal stability of PLL-based converters. Furthermore, we investigate the optimal locations to place grid-forming converters by increasing the smallest eigenvalue of the weighted and Kron-reduced Laplacian matrix of the power network. The analysis in this paper is validated through high-fidelity simulation studies on a modified two-area test system and a modified 39-bus test system. This paper potentially lays the foundation for understanding the interaction between PLL-based (i.e., grid-following) converters and grid-forming converters, and coordinating their placements in future converter-dominated power systems.
We explore optimization methods for planning the placement, sizing and operations of Flexible Alternating Current Transmission System (FACTS) devices installed into the grid to relieve congestion created by load growth or fluctuations of intermittent renewable generation. We limit our selection of FACTS devices to those that can be represented by modification of the inductance of the transmission lines. Our master optimization problem minimizes the $l_1$ norm of the FACTS-associated inductance correction subject to constraints enforcing that no line of the system exceeds its thermal limit. We develop off-line heuristics that reduce this non-convex optimization to a succession of Linear Programs (LP) where at each step the constraints are linearized analytically around the current operating point. The algorithm is accelerated further with a version of the cutting plane method greatly reducing the number of active constraints during the optimization, while checking feasibility of the non-active constraints post-factum. This hybrid algorithm solves a typical single-contingency problem over the MathPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop---a speed up that allows the sizing and placement of a family of FACTS devices to correct a large set of anticipated contingencies. From testing of multiple examples, we observe that our algorithm finds feasible solutions that are always sparse, i.e., FACTS devices are placed on only a few lines. The optimal FACTS are not always placed on the originally congested lines, however typically the correction(s) is made at line(s) positioned in a relative proximity of the overload line(s).
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