Modelling start-up costs of multiple technologies in electricity markets

This paper deals with the dispatch problem in providing electric power with minimal costs using different technologies. Initially, we describe this problem in terms of a linear program. This enables us to take generally neglected start-up costs into account. The main result is the explicit solution of a simplified linear program which provides us with a better understanding of the ‘start-up cost’ effects. Furthermore, we show that dominated technologies should be used in the case of limited availability of efficient technologies.      

Unit commitment in electricity pool markets

We consider an electricity generator making offers of energy into an electricity pool market over a horizon of several trading periods (typically a single trading day). The generator runs a set of generating units with given start-up costs, shut-down costs and operating ranges. At the start of each trading period the generator must submit to the pool system operator a new supply curve defining quantities of offered energy and the prices at which it wants these dispatched. The amount of dispatch depends on the supply curve offered along with the offers of the other generators and market demand, both of which are random, but do not change in response to the actions of the generator we consider. After dispatch the generator determines which units to run in the current trading period to meet the dispatch. The generator seeks a supply function that maximizes its expected profit. We describe an optimization procedure based on dynamic programming that can be used to construct optimal offers in successive time periods over a fixed planning horizon.     

Modelling the effects of interconnection between electricity markets subject to uncertainty

Interconnecting distinct electricity markets by adding a new transmission line affects the outcomes in these markets in a complicated way when there is uncertainty in demand or participant behaviour. We use market distribution functions to examine the effects of interconnection using a single transmission line under the assumption that this line has a differentiable loss function and agents in each of the interconnected markets do not change their behaviour in response to the interconnection. We also show how the case with capacity constraints on flows can be represented with appropriately formulated loss functions. We give analytical formulae for computing market outcomes when the uncertain events in the markets being connected are statistically independent, and show by example how to compute these outcomes when these events are correlated.     

Payment mechanisms for electricity markets with uncertain supply

This paper provides a framework for deriving payment mechanisms for intermittent, flexible and inflexible electricity generators who are dispatched according to the optimal solution of a stochastic program that minimizes the expected cost of generation plus deviation. The first stage corresponds to a pre-commitment decision, and the second stage corresponds to real-time generation that adapts to different realizations of a random variable. By taking the Lagrangian and decoupling in different ways we study two payment mechanisms with different properties.     

Bidding in sequential electricity markets: The Nordic case

For electricity market participants trading in sequential markets with differences in price levels and risk exposure, it is relevant to analyze the potential of coordinated bidding. We consider a Nordic power producer who engages in the day-ahead spot market and the hour-ahead balancing market. In both markets, clearing prices and dispatched volumes are unknown at the time of bidding. However, in the balancing market, the market participant faces an additional risk of not being dispatched. Taking into account the sequential clearing of these markets and the gradual realization of market prices, we formulate the bidding problem as a multi-stage stochastic program. We investigate whether higher risk exposure may cause hesitation to bid into the balancing market. Furthermore, we quantify the gain from coordinated bidding, and by deriving bounds on this gain, assess the performance of alternative bidding strategies used in practice.     

Basics of electricity derivative pricing in competitive markets

This paper studies the application of the available financial theory to the deregulated electricity market. The special characteristics of electricity make the market different from all other commodity markets. The paper introduces a coherent framework for the assets and instruments in the electricity markets in the financial tradition. Properties of the instruments that are available in the Scandinavian electricity market are studied in more detail.     

Two-settlement electricity markets with price caps and Cournot generation firms

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a regulatory intervention. In this paper we explore the implications of these two alternative mechanisms in a two-settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and horizontal market power. As an illustrative test case, we use the 53-bus Belgian electricity network with representative generator costs but hypothetical demand and ownership structure. Compared to a price-uncapped two-settlement system, a forward cap increases firms’ incentives for forward contracting, whereas a spot cap reduces such incentives. Moreover, in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified.     

Dynamic pricing of electricity in retail markets

This paper aims at defining a dynamic and flexible tariff structure for a distribution company that protects the retail consumers against the excessive fluctuations of the wholesales market prices. We propose a two-stage pricing scheme that sets in a first-stage a time-of-use tariff that is corrected later by a dynamic component once the real-time demand has been observed. A personalized tariff scheme may be offered by a distribution company to each dynamic customer by allowing him to choose the appropriate robustness level expressed in terms of variability between the first and the second-stage decisions. The arising limited recourse model has been tested on realistic test problems, by using a slight modification of a recently proposed interior point solution framework.      

Mathematical programming and electricity markets

The electric power industry in Europe and all over the world is undertaking major regulatory and operational changes. The underlying rationale behind all these changes is to move from a centralized operation approach to a competitive one. That is, the understanding of power supply as a public service is being replaced by the notion that a competitive market is a more appropriate framework to supply reliable and cheap electric energy to consumers. In some cases, the aforementioned transition process has included the privatization of power utilities. This new framework requires new tools and procedures, and some of these procedures drastically differ from traditional ones. Therefore, new challenging mathematical programming and operations research problems naturally arise in this context. This paper provides a review of some of these problems, particularly operational problems spanning a time horizon from one day to one year. The approach adopted emphasizes mathematical programming issues, describing the structure and characteristics of these problems and suggesting appropriate solution techniques. Relevant comments and suggestions were provided by Alexis Motto from McGill University, Montréal, Québec, Canada.     

Implicit collusion and individual market power in electricity markets

Wholesale electricity markets may not produce competitive outcomes, either as a result of the exercise of market power, or through problems of implicit collusion. In comparison with the great amount of attention paid to issues of market power, the problems of implicit collusion have not been extensively studied. In this paper, we use a coevolutionary approach to explore the effect of the price elasticity of demand, capacity and forward contracts on implicit collusion in a duopoly. We will demonstrate that implicit collusion has the most importance in market conditions under which there is an intermediate amount of market power. Thus markets which are either highly competitive or in which one or both of the two generators can exercise considerable market power, are also markets in which implicitly collusive outcomes are less likely to arise.     

Behavioural simulations in spot electricity markets

We study the consistency of behavioural simulation methods used to model the operations of wholesale electricity markets. We include different supply and demand representations and propose the Experience-Weighted Attractions method (Camerer and Ho, 1999) to encompass several behavioural paradigms. We compare the results across assumptions and to standard economic theory predictions. The match is good under flat and upward-slopping supply bidding, and also for plausible demand elasticity assumptions. Learning is influenced by the number of bids per plant and the initial conditions. The simulations perform best under reinforcement learning, less well under best-response and especially poorly under fictitious play. The overall conclusion is that simulation assumptions are far from innocuous. We link their performance to underlying features, and identify those that are better suited to model liberalised electricity markets.     

Financial transmission rights in convex pool markets

This paper studies financial transmission rights in electricity pool markets with nodal pricing. We prove that simultaneous feasibility entails revenue adequacy in a general framework of convex optimization, and show by counterexample as to how this result might fail in the absence of convexity.     

Equilibrium prices supported by dual price functions in markets with non-convexities

The issue of finding market clearing prices in markets with non-convexities has had a renewed interest due to the deregulation of the electricity sector. In the day-ahead electricity market, equilibrium prices are calculated based on bids from generators and consumers. In most of the existing markets, several generation technologies are present, some of which have considerable non-convexities, such as capacity limitations and large start-up costs. In this paper we present equilibrium prices composed of a commodity price and an uplift charge. The prices are based on the generation of a separating valid inequality that supports the optimal resource allocation. In the case when the sub-problem generated as the integer variables are held fixed to their optimal values possess the integrality property, the generated prices are also supported by non-linear price functions that are the basis for integer programming duality.     

A proposed model for co-optimization of energy and reserve in competitive electricity markets

Operating reserve assessment has become increasingly important in the new utility environment in which ancillary services have been assigned a value. This paper presents a procedure for compulsory provision of spinning reserve using a risk-constrained cost-based mechanism. In this mechanism, the electrical energy and spinning reserve are dealt with simultaneously because the provision of reserve cannot be decoupled from the provision of energy. Generators are paid the opportunity cost associated with their reduced energy because compulsion is financially unattractive among them. The transmission system reliability is considered in a simplified manner when computing composite system risk. In the proposed structure, the Independent System Operator (ISO) is responsible for reliability management and is thus responsible for providing sufficient reserve on behalf of the users of the system. The method is applied to the Roy Billinton Test System (RBTS). The General Algebraic Modeling System (GAMS Rev. 140) is used to solve the mixed integer nonlinear co-optimization problems.     

Bilevel optimization applied to strategic pricing in competitive electricity markets

In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures is illustrated in case studies with configurations derived from the Brazilian power system.     

Impact of some parameters on investments in oligopolistic electricity markets

It is seldom the case that one has the opportunity to compare investments as projected by a long-term multi-period model to what is eventually realized in practice. Further, although sensitivity analysis is of common use in any optimization setting, the impact of some parameters on strategic investments is not yet fully assessed in the context of the deregulated electricity industry. Starting with a benchmark model of the Finnish industry, we precisely explore the impact on equilibrium investments of varying such parameters as direct- and cross-price elasticities, length of the planning horizon and the depreciation rate of capacity. We run the model with different parameter values and compare the predicted equilibrium with what companies have actually done. The model is a stochastic dynamic game involving three players and played over a ten-year period.Our results show the depreciation rate and the planning horizon have a notable effect on investment levels, whereas price elasticities seem to play a lesser role. Although the model’s results are rather well aligned to total industry investments, it diverges from individual levels. This may be due to the cost parameter used and/or to the open-loop information structure adopted in the computations. In any event, these results should be of methodological and practical interest to scholars and practitioners involved in strategic investment in the electricity industry.     

Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we apply two approximations: we aggregate the decision stages and solve the resulting problem in linear decision rules (LDR). The LDR approach consists of restricting the set of recourse decisions to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.     

Validation and verification of social processes within agent-based computational organization models

The use of simulation modeling in computational analysis of organizations is becoming a prominent approach in social science research. However, relying on simulations to gain intuition about social phenomena has significant implications. While simulations may give rise to interesting macro-level phenomena, and sometimes even mimic empirical data, the underlying micro and macro level processes may be far from realistic. Yet, this realism may be important to infer results that are relevant to existing theories of social systems and to policy making. Therefore, it is important to assess not only predictive capability but also explanation accuracy of formal models in terms of the degree of realism reflected by the embedded processes. This paper presents a process-centric perspective for the validation and verification (V&V) of agent-based computational organization models. Following an overview of the role of V&V within the life cycle of a simulation study, emergent issues in agent-based organization model V&V are outlined. The notion of social contract that facilitates capturing micro level processes among agents is introduced to enable reasoning about the integrity and consistency of agent-based organization designs. Social contracts are shown to enable modular compositional verification of interaction dynamics among peer agents. Two types of consistency are introduced: horizontal and vertical consistency. It is argued that such local consistency analysis is necessary, but insufficient to validate emergent macro processes within multi-agent organizations. As such, new formal validation metrics are introduced to substantiate the operational validity of emergent macro-level behavior. Levent Yilmaz is Assistant Professor of Computer Science and Engineering in the College of Engineering at Auburn University and co-founder of the Auburn Modeling and Simulation Laboratory of the M&SNet. Dr. Yilmaz received his Ph.D. and M.S. degrees from Virginia Polytechnic Institute and State University (Virginia Tech). His research interests are on advancing the theory and methodology of simulation modeling, agent-directed simulation (to explore dynamics of socio-technical systems, organizations, and human/team behavior), and education in simulation modeling. Dr. Yilmaz is a member of ACM, IEEE Computer Society, Society for Computer Simulation International, and Upsilon Pi Epsilon. URL: http://www.eng.auburn.edu/~yilmaz     

Risk management in power markets: The Hedging value of production flexibility

Since the 1990s power markets are being restructured worldwide and nowadays electrical power is traded as a commodity. The liberalization and with it the uncertainty in gas, fuel and electrical power prices requires an effective management of production facilities and financial contracts. Thereby derivatives build essential instruments to exchange volume as well as price risks. The challenge for participants in the newly competitive market environment is how to design, price and hedge derivative contracts in particular combination with the flexibility embedded in dispatch strategies of production assets. Accordingly, an adequate basis for management and investment decisions is needed which responds to the highly complex market situation.