Benjamin F. Hobbs

Strategic gaming analysis for electric power systems: an MPEC approach

Transmission constraints and market concentration may prevent power markets from being fully competitive, allowing firms to exercise market power and raise prices above marginal cost. We present a strategic gaming model for analyzing such markets; it represents an oligopolistic market economy consisting of several dominant firms in an electric power network. Each generating firm submits bids to an ISO, choosing its bids to maximize profits subject to anticipated reactions by rival firms. The single-firm model is formulated as a mathematical program with equilibrium constraints (MPEC) with a parameter-dependent spatial price equilibrium problem as the inner problem. Power flows and pricing strategies are constrained by the ISOs linearized DC optimal power flow (OFF) model. A penalty interior point algorithm is used to compute a local optimal solution of the MPEC. Numerical examples based on a 30 bus network are presented, including multi-firm Nash equilibria in which each player solves an MPEC of the single-firm type.

Linear Complementarity Models of Nash-Cournot Competition in Bilateral and POOLCO Power Markets

Two Coumot models of imperfect competition among electricity producers are formulated as mixed linear complementarity problems (LCPs), and a simple example is presented to illustrate their application. The two models simulate bilateral markets. The models include a congestion pricing scheme for transmission, but other transmission pricing approaches can also be represented in this framework. The two models differ from each other in that one has no arbitrage between nodes of the network, while in the other model arbitragers erase any noncost-based differences in price. The latter bilateral model tums out to be equivalent to a Coumot model of a POOLCO. The models differ from other Coumot market models in that they include both of Kirchhoffs laws via a dc approximation, can include arbitragers, possess unique solutions, and are readily solved by efficient LCP algorithms. The key assumption that permits their formulation as LCPs is that each producer naively assumes that its output will not affect transmission prices.

Oligopolistic competition in power networks: a conjectured supply function approach

Conjectured supply function (CSF) models of competition among power generators on a linearized DC network are presented. As a detailed survey of the power market modeling literature shows, CSF models differ from previous approaches in that they represent each generation companys (GenCo) conjectures regarding how rival firms will adjust sales in response to price changes. The CSF approach is a more realistic and flexible framework for modeling imperfect competition than other models for three reasons. First, the models include as a special case the Cournot conjecture that rivals will not change production if prices change; thus, the CSF framework is more general. Second, Cournot models cannot be used when price elasticity of demand is zero, but the proposed models can. Third, unlike supply function equilibrium models, CSF equilibria can be calculated for large transmission networks. Existence and uniqueness properties for prices and profits are reported. An application shows how transmission limits and strategic interactions affect equilibrium prices under forced divestment of generation.

Optimization methods for electric utility resource planning

Abstract Electric utility resource planning is the selection of power generation and energy efficiency (conservation) resources to meet customer demands for electricity over a multi-decade time horizon. Because investments in these resources are large, electric utilities became one of the earliest users of optimization methods. The industry is now an eager consumer of the operations researchers wares, and is a continual source of stimulating problems. The first purpose of this review is to examine how the needs of utility planners for optimization models have changed in response to environmental concerns, increased competition, and growing uncertainty. The second purpose is to survey the range of models that have developed in response to those needs, and to identify gaps requiring further research.

Efficient market-clearing prices in markets with nonconvexities

This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf [Journal of Economic Perspectives 8(4) (1994) 111].

Understanding how market power can arise in network competition: a game theoretic approach

This paper considers competition in electric networks and how the network structure affects the competition. The approach is to examine non-cooperative behavior among producers and calculate a Nash equilibrium under different market specifications. Unlike most other treatments of this problem, which utilize either Cournot or Bertrand models of competition, the model used here examines supply function competition. Two and four node networks are considered. Several results that differ from traditional economic theory are found. In both a two-node and four-node market with imperfect competition among producers, transmission constraints increase their profits (compared to an unconstrained network)—but with little or no change in consumer prices or quantities produced. This is because generators profit primarily at the expense of the owner of transmission rights. The size of the increase in profits depends on the number of firms at each node and the size of the transmission constraint. In the four-node case, an example was found in which decreasing market concentration by breaking up suppliers worsens market efficiency, even if there are no cost diseconomies. In particular, increasing competition at one node increases the consumer price at a second node, and causes an overall decrease in consumer surplus. In general, the cases presented here show that strategic behavior on electric networks may produce results that differ from those predicted by traditional economic theory due to the network structure of the problem.

Nash-Cournot Equilibria in Power Markets on a Linearized DC Network with Arbitrage: Formulations and Properties

Extending a prior arbitrage-free model of Hobbs (2001), this article presents two models of an electric power market with arbitrage on a linearized DC network with a affine price functions. The two models represent a decentralized system involving bilateral contracts between producers and consumers in which the system operators role is limited to providing transmission services. The two models differ in how arbitrage is handled. In the first model, the producers anticipate the effect of arbitrage upon prices at different locations (Stackelberg assumption), and therefore treat the arbitrage amounts as decision variables in their profit maximization problems. In the second model, the firms take the arbitrage quantities as inputs in their problems (Cournot assumption), and the arbitrager solves a separate profit maximization problem that takes the electricity prices and the transmission costs as inputs. In each model, we adopt a Nash-Cournot equilibrium as the solution concept for the game among producers. We show that the resulting equilibrium problems can be formulated as monotone mixed linear complementarity problems. Based on such a formulation, we obtain existence,uniqueness,and various quantitative properties of the equilibrium solutions to the models. It is also demonstrated that these two models of a bilateral market yield the same prices, producer outputs, and profits as a model of Cournot competition in a “Poolco” system,in which a system operator runs a centralized auction and buys all production, and then resells it to consumers. This result implies that Cournot competition among producers yields the same outcomes for two distinct market designs. Finally, we present a numerical example to illustrate the theoretical results.

Optimal Generation Mix With Short-Term Demand Response and Wind Penetration

Demand response, defined as the ability of load to respond to short-term variations in electricity prices, plays an increasingly important role in balancing short-term supply and demand, especially during peak periods and in dealing with fluctuations in renewable energy supplies. However, demand response has not been included in standard models for defining the optimal generation technology mix. Three different methodologies are proposed to integrate short-term responsiveness into a generation technology mix optimization model considering operational constraints. Elasticities are included to adjust the demand profile in response to price changes, including cross-price elasticities that account for load shifts among hours. As energy efficiency programs also influence the load profile, interactions of efficiency investments and demand response are also modeled. Comparison of model results for a single year optimization with and without demand response shows peak reduction and valley filling effects, impacting the optimal amounts and mix of generation capacity. Increasing demand elasticity also increases the installed amount of wind capacity, suggesting that demand response yields environmental benefits by facilitating integration of renewable energy.

Building public confidence in energy planning: a multimethod MCDM approach to demand-side planning at BC gas

Abstract Multicriteria decision-making (MCDM) methods are one means of quantifying stakeholder values, but the way such methods are usually applied can cause people to feel manipulated by a ‘black-box’ methodology. An approach is proposed to mitigate this problem. It asks each person to apply two or more methods and to then resolve disagreements in the results in order to build understanding. The approach recognizes that no single method is best for every person. We describe a successful application by a diverse stakeholder group. The results confirm that decisions yielded by alternative MCDM methods can disagree and that a multimethod approach builds insight and confidence.

Multicriteria methods for resource planning: an experimental comparison

Multicriteria decision making (MCDM) methods are widely used for comparing alternatives when there are multiple objectives. For instance, utilities use them for resource bidding, externality quantification, facility siting, and resource planning. There are many alternative methods, differing in their ease of use, validity, results, and appropriateness to resource planning. Several MCDM methods are compared in an experiment involving the choice of resource portfolio for Seattle City Light. Planners and interest group representatives applied direct weight assessment, tradeoff weight assessment, additive value functions, and goal programming. Most of the participants concluded that MCDM methods could promote insight and confidence in decision making. However, the authors also confirmed the existence of method biases previously identified by psychologists. No single method emerged as best. Thus, application of two or more methods as consistency checks is recommended to guard against bias, and to stimulate insight. >