Convex Relaxations and Linear Approximation for Optimal Power Flow in Multiphase Radial Networks

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 are proposed. We prove that the first SDP relaxation is exact if and only if the second one is exact. Case studies show that the second SDP relaxation is numerically exact and that the linear approximation obtains voltages within 0.0016 per unit of their true values for the IEEE 13, 34, 37, 123-bus networks and a real-world 2065-bus network.Comment: 9 pages, 2 figures, 3 tables, accepted by Power System Computational Conferenc

Optimal Power Flow with Step-Voltage Regulators in Multi-Phase Distribution Networks

This paper develops a branch-flow based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed-delta, and open-delta step-voltage regulators (SVRs). SVRs are assumed ideal and their taps are represented by continuous decision variables. To tackle the non-linearity, the branch-flow semidefinite programming framework of traditional OPF is expanded to accommodate SVR edges. Three types of non-convexity are addressed: (a) rank-1 constraints on non-SVR edges, (b) nonlinear equality constraints on SVR power flows and taps, and (c) trilinear equalities on SVR voltages and taps. Leveraging a practical phase-separation assumption on the SVR secondary voltage, novel McCormick relaxations are provided for (c) and certain rank-1 constraints of (a), while dropping the rest. A linear relaxation based on conservation of power is used in place of (b). Numerical simulations on standard distribution test feeders corroborate the merits of the proposed convex formulation.Comment: This manuscript has been submitted to IEEE Transactions on Power System

Neural network approach for predicting drum pressure and level in coal-fired subcritical power plant

There is increasing need for tighter controls of coal-fired plants due to more stringent regulations and addition of more renewable sources in the electricity grid. Achieving this will require better process knowledge which can be facilitated through the use of plant models. Drum-boilers, a key component of coal-fired subcritical power plants, have complicated characteristics and require highly complex routines for the dynamic characteristics to be accurately modelled. Development of such routines is laborious and due to computational requirements they are often unfit for control purposes. On the other hand, simpler lumped and semi empirical models may not represent the process well. As a result, data-driven approach based on neural networks is chosen in this study. Models derived with this approach incorporate all the complex underlying physics and performs very well so long as it is used within the range of conditions on which it was developed. The model can be used for studying plant dynamics and design of controllers. Dynamic model of the drum-boiler was developed in this study using NARX neural networks. The model predictions showed good agreement with actual outputs of the drum-boiler (drum pressure and water level)