Ray D. Zimmerman

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

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 MATPOWERs ability to solve large-scale AC and DC OPF problems.

Stability-constrained optimal power flow

Stability is an important constraint in power system operation. Often trial and error heuristics are used that can be costly and imprecise. A new methodology that eliminates the need for repeated simulation to determine a transiently secure operating point is presented. The theoretical development is straight-forward: dynamic equations are converted to numerically equivalent algebraic equations and then integrated into the standard OPF formulation. Implementation issues and simulation results are discussed in the context of a 162-bus system.

On Computational Issues of Market-Based Optimal Power Flow

The deregulated electricity market calls for robust optimal power flow (OPF) tools that can provide a) deterministic convergence; b) accurate computation of nodal prices; c) support of both smooth and nonsmooth costing of a variety of resources and services, such as real energy, reactive energy, voltages support, etc.; d) full active and reactive power flow modeling of large-scale systems; and e) satisfactory worst-case performance that meets the real-time dispatching requirement. Most prior research on OPF has focused on performance issues in the context of regulated systems, without giving much emphasis to requirements a)-c). This paper discusses the computational challenges brought up by the deregulation and attempts to address them through the introduction of new OPF formulations and algorithms. Trust-region- based augmented Lagrangian method (TRALM), step-controlled primal-dual interior point method (SCIPM), and constrained cost variable (CCV) OPF formulation are proposed. The new formulations and algorithms, along with several existing ones, are tested and compared using large-scale power system models.

MATPOWER's extensible optimal power flow architecture

This paper describes the optimal power flow (OPF) architecture implemented in MATPOWER, an open-source Mat-lab power system simulation package. It utilizes an extensible architecture that allows the user to easily add new variables, constraints and costs to the standard OPF problem formulation while preserving the structure needed to use pre-compiled solvers. A software object is used to encapsulate the definition of the problem formulation, manage the corresponding named sets of variables, constraints and costs, and handle all of the tedious index maintenance tasks. The software design has the advantage of minimizing the coupling between variables, constraints and costs, making it possible, for example, to add variables to an existing model without having to explicitly modify existing constraints or costs to accommodate them. The example of adding joint co-optimization of reserves to the OPF, based on fixed zonal reserve requirements, is used to illustrate the capabilities of MATPOWERs extensible OPF architecture.

Fast decoupled power flow for unbalanced radial distribution systems

This paper presents a novel power flow formulation and an effective solution method for general unbalanced radial distribution systems. Comprehensive models are considered including lines, switches, transformers, shunt capacitors, cogenerators, and several types of loads. A new problem formulation of three-phase distribution power flow equations taking into account the radial structure of the distribution network is presented. A distinguishing feature of the new problem formulation is that it significantly reduces the number of power flow equations, as compared with the conventional formulation. The numerical properties as well as the structural properties of distribution systems are exploited resulting in a fast decoupled solution algorithm. The proposed solution algorithm is evaluated on three-phase unbalanced 292-bus and 394-bus test systems with very promising results.

Secure Planning and Operations of Systems With Stochastic Sources, Energy Storage, and Active Demand

This work presents a stochastic optimization framework for operations and planning of an electricity network as managed by an Independent System Operator. The objective is to maximize the total expected net benefits over the planning horizon, incorporating the costs and benefits of electricity consumption, generation, ancillary services, load-shedding, storage and load-shifting. The overall framework could be characterized as a secure, stochastic, combined unit commitment and AC optimal power flow problem, solving for an optimal state-dependent schedule over a pre-specified time horizon. Uncertainty is modeled to expose the scenarios that are critical for maintaining system security, while properly representing the stochastic cost. The optimal amount of locational reserves needed to cover a credible set of contingencies in each time period is determined, as well as load-following reserves required for ramping between time periods. The models for centrally-dispatched storage and time-flexible demands allow for optimal tradeoffs between arbitraging across time, mitigating uncertainty and covering contingencies. This paper details the proposed problem formulation and outlines potential approaches to solving it. An implementation based on a DC power flow model solves systems of modest size and can be used to demonstrate the value of the proposed stochastic framework.

A uniform price auction with locational price adjustments for competitive electricity markets

Competitive electricity markets which rely on centralized dispatch require a mechanism to solicit offers from competing generators. Ideally, such an auction mechanism provides incentives to submit offers equal to the marginal cost of generation for each generator. Economic theory suggests that the Uniform Price auction is an appropriate institution. However, an efficient implementation of this auction in an electricity context requires that the offers used in the auction reflect the appropriate locational price adjustments for transmission losses and congestion. This paper describes a uniform price auction that incorporates locational price adjustments on a Web-based platform suitable for experimentation. Preliminary results show dramatically different price and revenue results when compared with a simple continuous Discriminative auction.

Innovative developments in load as a reliability resource

This paper reports on work the Consortium for Electric Reliability Technology Solutions (CERTS) has been pursuing to hasten the arrival of meaningful load participation in competitive electricity markets. The activities include: experimental economic analysis of the effect of price responsive load in reducing market prices and price volatility; assessments of emerging demand response programs and technologies for enabling customer participation in electricity markets, and demonstrations of load in providing ancillary services (notably, spinning reserve).

Energy auctions and market power: an experimental examination

Testing auction mechanisms experimentally in a controlled environment provides an inexpensive means for evaluating their relative merits. The first part of this paper focuses on the comparison of three different auctions with regard to market efficiency and pricing, given scenarios with two, four, and six competitors. Though the uniform price last accepted offer auction was superior overall, the number of competitors proved to be a more significant factor in determining auction performance. Significant exploitation of market power was observed in the duopoly case. The second part of the paper focuses on a transmission network with six sellers in which network constraints give rise to market power opportunities. Experimental evidence based on tests with student and expert subjects show exploitation of this strategic advantage. Several other scenarios are described in which the transmission network creates market power.

An advanced security constrained OPF that produces correct market-based pricing

Security constrained optimal power flow programs are important tools for ensuring correct dispatch of supply while respecting the many constraints imposed by the delivery system. In addition to getting the dispatch right, locational prices must be calculated with equal precision in order to infuse market participants with the proper incentives for operation and investment. In this paper we discuss a co-optimization framework in which contingencies, ancillary services, and network constraints are correctly accounted for in determining both dispatch and price.