Guided Machine Learning for power grid segmentation

The segmentation of large scale power grids into zones is crucial for control room operators when managing the grid complexity near real time. In this paper we propose a new method in two steps which is able to automatically do this segmentation, while taking into account the real time context, in order to help them handle shifting dynamics. Our method relies on a "guided" machine learning approach. As a first step, we define and compute a task specific "Influence Graph" in a guided manner. We indeed simulate on a grid state chosen interventions, representative of our task of interest (managing active power flows in our case). For visualization and interpretation, we then build a higher representation of the grid relevant to this task by applying the graph community detection algorithm \textit{Infomap} on this Influence Graph. To illustrate our method and demonstrate its practical interest, we apply it on commonly used systems, the IEEE-14 and IEEE-118. We show promising and original interpretable results, especially on the previously well studied RTS-96 system for grid segmentation. We eventually share initial investigation and results on a large-scale system, the French power grid, whose segmentation had a surprising resemblance with RTE's historical partitioning

Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on Decision and Control (CDC), 15-18 December 201

Coordinated Supervisory Control of Multi-Terminal HVDC Grids: a Model Predictive Control Approach

A coordinated supervisory control scheme for future multi-terminal High-Voltage Direct-Current (HVDC) grids is proposed. The purpose is to supervise the grid and take appropriate actions to ensure power balance and prevent or remove voltage or current limit violations. First, using DC current and voltage measurements, the power references of the various Voltage Sources Converters (VSC) are updated according to participation factors. Next, the setpoints of the converters are smoothly adjusted to track those power references, while avoiding or correcting limit violations. The latter function resorts to Model Predictive Control and a sensitivity model of the system. The efficiency of the proposed scheme has been tested through dynamic simulations of a five-terminal HVDC grid interconnecting two asynchronous AC areas and a wind farm

Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions

peer reviewedThis paper deals with day-ahead security management with respect to a postulated set of contingencies, while taking into account uncertainties about the next day generation/load scenario. In order to help the system operator in decision making under uncertainty, we aim at ranking these contingencies into four clusters according to the type of control actions needed to cover the worst uncertainty pattern of each contingency with respect to branch overload. To this end we use a fixed point algorithm that loops over two main modules: a discrete bi-level program (BLV) that computes the worst-case scenario, and a special kind of security constrained optimal power flow (SCOPF) which computes optimal preventive/corrective actions to cover the worst-case. We rely on a DC grid model, as the large number of binary variables, the large size of the problem, and the stringent computational requirements preclude the use of existing mixed integer nonlinear programming (MINLP) solvers. Consequently we solve the SCOPF using a mixed integer linear programming (MILP) solver while the BLV is decomposed into a series of MILPs. We provide numerical results with our approach on a very large European system model with 9241 buses and 5126 contingencies

Minimal Sparsity for Second-Order Moment-SOS Relaxations of the AC-OPF Problem

AC-OPF (Alternative Current Optimal Power Flow)aims at minimizing the operating costs of a power gridunder physical constraints on voltages and power injections.Its mathematical formulation results in a nonconvex polynomial optimizationproblem which is hard to solve in general,but that can be tackled by a sequence of SDP(Semidefinite Programming) relaxationscorresponding to the steps of the moment-SOS (Sums-Of-Squares) hierarchy.Unfortunately, the size of these SDPs grows drastically in the hierarchy,so that even second-order relaxationsexploiting the correlative sparsity pattern of AC-OPFare hardly numerically tractable for largeinstances -- with thousands of power buses.Our contribution lies in a new sparsityframework, termed minimal sparsity, inspiredfrom the specific structure of power flowequations.Despite its heuristic nature, numerical examples show that minimal sparsity allows the computation ofhighly accurate second-order moment-SOS relaxationsof AC-OPF, while requiring far less computing time and memory resources than the standard correlative sparsity pattern. Thus, we manage to compute second-order relaxations on test caseswith about 6000 power buses, which we believe to be unprecedented