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The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use…
This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…
We propose a hidden convexity-based method to address distributed optimal energy flow (OEF) problems for transmission-level integrated electricity-gas systems. First, we develop a node-wise decoupling method to de-compose an OEF problem…
Large horsepower induction motors play a critical role as industrial drives in production facilities. The operational safety of distribution networks during the starting transients of these motor loads is a critical concern for the…
Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is…
Increasing integration of distributed energy resources (DERs) within distribution feeders provides unprecedented flexibility at the distribution-transmission interconnection. To exploit this flexibility and to use the capacity potential of…
Optimal power flow (OPF) is the fundamental mathematical model in power system operations. Improving the solution quality of OPF provide huge economic and engineering benefits. The convex reformulation of the original nonconvex alternating…
We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance…
Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow…
The ever increasing penetration of Renewable Energy Resources (RESs) in power distribution networks has brought, among others, the challenge of maintaining the grid voltages within the secure region. Employing droop voltage regulators on…
The concept of dispatchable region plays a pivotal role in quantifying the capacity of power systems to accommodate renewable generation. In this paper, we extend the previous approximations of the dispatchable regions on direct current…
Large-scale power system planning mostly uses linearized, active power only approximations of the power flow equations, ignores many operational constraints, and tests the operational feasibility of the resulting systems only under strongly…
High penetration of renewable generation poses great challenge to power system operation due to its uncertain nature. In droop-controlled microgrids, the voltage volatility induced by renewable uncertainties is aggravated by the high droop…
AC optimal power flow (AC OPF) is a fundamental problem in power system operations. Accurately modeling the network physics via the AC power flow equations makes AC OPF a challenging nonconvex problem. To search for global optima, recent…
We consider the problem of learning local Volt/Var controllers in distribution grids (DGs). Our approach starts from learning separable surrogates that take both local voltages and reactive powers as arguments and predict the reactive power…
As power systems become more complex and uncertain, low-voltage distribution networks face numerous challenges, including three-phase imbalances caused by asymmetrical loads and distributed energy resources. We propose a robust stochastic…
Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the…
Typical formulations of the optimal power flow (OPF) problem rely on what is termed the "bus-branch" model, with network electrical behavior summarized in the Ybus admittance matrix. From a circuit perspective, this admittance…
This paper proposes a simple and flexible storage model for use in a variety of multi-period optimal power flow problems. The proposed model is designed for research use in a broad assortment of contexts enabled by the following key…
The growing penetration of distributed energy resources (DERs) is leading to continually changing operating conditions, which need to be managed efficiently by distribution grid operators. The intermittent nature of DERs such as solar…