MATPOWER is an open-source Matlab-based power system simulation package that provides a high-level set of power flow, optimal power flow (OPF), and other tools targeted toward researchers, educators, and students. The OPF architecture is designed to be extensible, making it easy to add user-defined variables, costs, and constraints to the standard OPF problem. This paper presents the details of the network modeling and problem formulations used by MATPOWER, including its extensible OPF architecture. This structure is used internally to implement several extensions to the standard OPF problem, including piece-wise linear cost functions, dispatchable loads, generator capability curves, and branch angle difference limits. Simulation results are presented for a number of test cases comparing the performance of several available OPF solvers and demonstrating MATPOWER's ability to solve large-scale AC and DC OPF problems.

/pdf/matpower-steady-state-operations-planning-and-analysis-tools-1v40ihity5.pdf

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education

A practical method is given for solving the power flow problem with control variables such as real and reactive power and transformer ratios automatically adjusted to minimize instantaneous costs or losses. The solution is feasible with respect to constraints on control variables and dependent variables such as load voltages, reactive sources, and tie line power angles. The method is based on power flow solution by Newton's method, a gradient adjustment algorithm for obtaining the minimum and penalty functions to account for dependent constraints. A test program solves problems of 500 nodes. Only a small extension of the power flow program is required to implement the method.

Optimal Power Flow Solutions

The Dommel-Tinney approach to the calculation of optimal power-system load flows has proved to be very powerful and general. This paper extends the problem formulation and solution scheme by incorporating exact outage-contingency constraints into the method, to give an optimal steady-state-secure system operating point. The controllable system quantities in the base-case problem (e.g. generated MW, controlled voltage magnitudes, transformer taps) are optimised within their limits according to some defined objective, so that no limit-violations on other quantities (e. g. generator MVAR and current loadings, transmission-circuit loadings, load-bus voltage magnitudes, angular displacements) occur in either the base-case or contingency-case system operating conditions.

/pdf/optimal-load-flow-with-steady-state-security-3m8ff3du29.pdf

Optimal Load Flow with Steady-State Security

This paper describes a simple, very reliable and extremely fast load-flow solution method with a wide range of practical application. It is attractive for accurate or approximate off-and on-line routine and contingency calculations for networks of any size, and can be implemented efficiently on computers with restrictive core-store capacities. The method is a development on other recent work employing the MW-?/ MVAR-V decoupling principle, and its precise algorithmic form has been determined by extensive numerical studies. The paper gives details of the method's performance on a series of practical problems of up to 1080 buses. A solution to within 0.01 MW/MVAR maximum bus mismatches is normally obtained in 4 to 7 iterations, each iteration being equal in speed to 1? Gauss-Seidel iterations or 1/5th of a Newton iteration. Correlations of general interest between the power-mismatch convergence criterion and actual solution accuracy are obtained.

Fast Decoupled Load Flow

It is often appealing to assume that existing solutions can be directly applied to emerging engineering domains. Unfortunately, careful investigation of the unique challenges presented by new domains exposes its idiosyncrasies, thus often requiring new approaches and solutions. In this paper, we argue that the “smart” grid, replacing its incredibly successful and reliable predecessor, poses a series of new security challenges, among others, that require novel approaches to the field of cyber security. We will call this new field cyber-physical security. The tight coupling between information and communication technologies and physical systems introduces new security concerns, requiring a rethinking of the commonly used objectives and methods. Existing security approaches are either inapplicable, not viable, insufficiently scalable, incompatible, or simply inadequate to address the challenges posed by highly complex environments such as the smart grid. A concerted effort by the entire industry, the research community, and the policy makers is required to achieve the vision of a secure smart grid infrastructure.

/pdf/cyber-physical-security-of-a-smart-grid-infrastructure-k72rknn16y.pdf

Cyber–Physical Security of a Smart Grid Infrastructure

The ac power flow problem can be solved efficiently by Newton's method. Only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method, are required for an exact solution. Problem dependent memory and time requirements vary approximately in direct proportion to problem size. Problems of 500 to 1000 nodes can be solved on computers with 32K core memory. The method, introduced in 1961, has been made practical by optimally ordered Gaussian elimination and special programming techniques. Equations, programming details, and examples of solutions of large problems are given.

Power Flow Solution by Newton's Method

Sensitivity is defined as the ratio ?x/?y relating small changes ?x of some dependent variable to small changes ?y of some independent or controllable variable y. In power systems, two dominant types of sensitivity relations are defined, namely 1) sensitivity of one electrical variable, such as the voltage Vi at node i, with respect to another electrical variable, such as reactive production Qj at node j, and 2) sensitivity of the operating cost F with respect to such electrical variables as the consumption Ci at node i and the production Pj at node j.

Sensitivity in Power Systems

The now classical problem of optimlum dispatching miimizes the cost of production and transmission of electrical power to meet a specified demand under normal operating conditions. It appears logical and desirable to utilize and extend the methodology of optimum dispatching to problems encountered during abnormal operating conditions. This paper, as a first step in that direction, discusses a systematic approach toward minimizing the curtailment of service in a power system after a severe fault. The problem of minimizing load curtailment under a given set of emergency conditions is formulated as a problem of static optimization, subject to operational and equipment constraints. First, a feasible steady-state solution is obtained for the postfault network configuration. Starting from this initial feasible solution, the optinum (minimum curtailment) is approached by a gradient technique. An efficient computational procedure is based on the Newton-Raphson technique for solving the power flow equations, and the Kuhn-Tucker theorem for the optimization. The analytical results are verified on a 26-node example problem. Two typical emergency situations are considered: the loss of generation and the loss of an interconnection tie line. The same optimization procedure and the computed dual (Lagrangian) variables can be utilized for computer programs involving optimum service restoration, generation reserve scheduling, and system expansion studies.

William F. Tinney

Papers

Power Flow Solution by Newton's Method

Sensitivity in Power Systems

Optimum Load-Shedding Policy for Power Systems