Abstract—We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial netw...

Power flow optimization is generally nonlinear and non-convex, and a second-order cone relaxation has been proposed recently for convexification. We prove several sufficient conditions under which the relaxation is exact. One of these conditions seems particularly realistic and suggests guidelines on integrating distributed generations.

Convexification is a fundamental technique in (mixed-integer) nonlinear optimization and many convex relaxations are parametrized by variable bounds, i.e., the tighter the bounds, the stronger the relaxations. This paper studies how bound tightening can improve convex relaxations for power network optimization. It adapts traditional constraintprogramming concepts (e.g., minimal network and boun...

The first numerical solution of the 3-D travel time tomography problem is presented. globally convergent convexification method applied.

In this article, a novel convexification approach for small-signal stability constraint optimal power flow has been presented that does not rely on eigenvalue analysis. The proposed methodology is based the sufficient condition stability, developed as bilinear matrix inequality (BMI), and uses network structure-preserving differential algebraic equation modeling of system. formulation semidefin...

‎By p-power (or partial p-power) transformation‎, ‎the Lagrangian function in nonconvex optimization problem becomes locally convex‎. ‎In this paper‎, ‎we present a neural network based on an NCP function for solving the nonconvex optimization problem‎. An important feature of this neural network is the one-to-one correspondence between its equilibria and KKT points of the nonconvex optimizatio...

In this paper, we propose a new method that produces new forms of tight convex underestimators for twice continuously differentiable nonconvex functions. The algorithm generalizes the main ideas used in aBB. The key idea is to determine a new convexification function that is able to handle the off-diagonal elements of the Hessian matrix of the original nonconvex function. The new convexificatio...

This letter presents a novel optimization framework of formulating the three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware (UaO) is: 1) deterministic is less complex than existing frameworks involving uncertainty, and 2) convex such it admits polynomial-time algorithms mature distributed methods. To construct this UaO framework, methodology learning-aided mo...