An ADMM-based Distributed Optimization Method for Solving Security-Constrained AC Optimal Power Flow

In this paper, we study efficient and robust computational methods for solving the security-constrained alternating current optimal power flow (SC-ACOPF) problem, a two-stage nonlinear optimization problem with disjunctive constraints, that is central to the operation of electric power grids. The first-stage problem in SC-ACOPF determines the operation of the power grid in normal condition, while the second-stage problem responds to various contingencies of losing generators, transmission lines, and transformers. The two stages are coupled through disjunctive constraints, which model generators' active and reactive power output changes responding to system-wide active power imbalance and voltage deviations after contingencies. Real-world SC-ACOPF problems may involve power grids with more than 30k buses and 22k contingencies and need to be solved within 10-45 minutes to get a base case solution with high feasibility and reasonably good generation cost. We develop a comprehensive algorithmic framework to solve SC-ACOPF that meets the challenge of speed, solution quality, and computation robustness. In particular, we develop a smoothing technique to approximate disjunctive constraints into a smooth structure which can be handled by interior-point solvers; we design a distributed optimization algorithm to efficiently generate first-stage solutions; we propose a screening procedure to prioritize contingencies; and finally, we develop a reliable and parallel architecture that integrates all algorithmic components. Extensive tests on industry-scale systems demonstrate the superior performance of the proposed algorithms

Linear Optimal Power Flow Using Cycle Flows

Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms use the voltage angles at the buses as optimization variables, but alternatives can be computationally advantageous. In this article we provide a review of existing methods and describe a new formulation that expresses the loading constraints directly in terms of the flows themselves, using a decomposition of the network graph into a spanning tree and closed cycles. We provide a comprehensive study of the computational performance of the various formulations, in settings that include computationally challenging applications such as multi-period LOPF with storage dispatch and generation capacity expansion. We show that the new formulation of the LOPF solves up to 7 times faster than the angle formulation using a commercial linear programming solver, while another existing cycle-based formulation solves up to 20 times faster, with an average speed-up of factor 3 for the standard networks considered here. If generation capacities are also optimized, the average speed-up rises to a factor of 12, reaching up to factor 213 in a particular instance. The speed-up is largest for networks with many buses and decentral generators throughout the network, which is highly relevant given the rise of distributed renewable generation and the computational challenge of operation and planning in such networks.Comment: 11 pages, 5 figures; version 2 includes results for generation capacity optimization; version 3 is the final accepted journal versio

Proposed shunt rounding technique for large-scale security constrained loss minimization

The official published version can be obtained from the link below - Copyright @ 2010 IEEE.Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer nonlinear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.This work was supported in part by the National Grid and in part by the EPSRC. Paper no. TPWRS-00653-2009

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline