Modeling long-term dynamics of electricity markets
Introduction
Before the liberalization of the electricity industry, investments in power plants were the result of an optimized capacity expansion planning at national or regional level. The aim of this planning was to determine the right level of generating capacity, the optimal mix of generating technologies and the timing of investments and retirements of capacity to ensure that future demand in a certain region would be served at minimum cost with an adequate level of reliability (Ku, 1995). In order to decide when and which power plants should be constructed, the minimization of the discounted, cumulated operating and investment cost over the considered planning horizon was the classical approach. In the centrally planned power industry, generation expansion planning was conducted with vast quantities of reliable data. Consequently, uncertainties were narrowly limited to a few variables. In fact, the future demand and the future fuel prices were the only significant source of uncertainty in the decision-making process. The expected profits were not generally subjected to uncertainty, since utilities were allowed to charge customers in order to recover the total costs and gain a fair rate of return on the incurred investments.
After the liberalization of the electricity generation sector, investments and decommissioning of generation capacity are a consequence of decentralized, commercial decisions made by multiple self-oriented firms and no longer the result of a centrally optimized expansion planning. Thereby, the decision of investing in new power plants faces new uncertainties. Unlike the regulated environment, decision-making of market participants is now guided by price signal feedbacks and by an imperfect foresight of the future market conditions that they will face. Future revenue streams are no longer guarantied through regulated tariffs since generators are rewarded an uncertain price for the energy sold. Furthermore, the ability of generators to sell energy depends now upon their cost competitiveness relative to their competitors.
Because of the lack of enough long experience with liberalized electricity markets, models are needed to infer the possible long-run market evolutions for supporting decision-making and policy design. However, most market simulation models recently developed focus on the short term. The few available models to assess long-term market development are based on the widely accepted paradigm that under competitive rules, markets make the same resource allocation that would result of a centrally made optimization. An example of such an approach is the model presented by Hoster (1999) to assess the influence of a European market on the German electricity industry. In general, these models assume that firms act as inter-temporal optimizers and many of them even assume that firms pose perfect foresight. These models commonly neglect the existence of feedbacks and system time constants. Thus, the resulting timing of the simulated investments and the rate at which they occur are those necessary to maintain the system permanently on the optimal trajectory. Under this modeling approach, the system evolution is hence viewed as a sequence of stable and optimal long-run equilibrium states.
Nevertheless, many real economic systems, and particularly the power generation industry, do not meet the requirements to assume that the system remains on the long-run optimal trajectory at every time. As in other capital-intensive industries, power markets cannot immediately adjust the production capacity after perturbations, such as a rapid increase in the demand growth rate. The reasons that prevent immediate response are that expectations need time to be updated to the new market conditions, investments are delayed under uncertainty, and power plants need usually a long time to be constructed and to be brought online. Under these conditions, it is to be expected that power markets experience business cycles, i.e. periods of high investment rates followed by other periods with no investment activity. This might result in severe fluctuations of the reserve margin, and therefore of power prices. This kind of business cycles has been well identified in many other capital-intensive industries, such as pulp and paper industry, chemical and real estate markets (Berends and Romme, 2001; Sharp, 1982; Kummerow, 1999). Moreover, some electricity markets running under competitive rules have experienced periods of excess of investments, and therefore over-capacity, such is the case of UK with a large entry of private investors relying on gas-fired power plants. Others have already experienced long periods without new capacity additions that have ultimately led the market to under-capacity conditions. Such was the case of California during the electricity crisis in the summers 2000 and 2001.
Classical industry models based on long-run equilibrium assumptions fail to explain these cycles since they are not capable of capturing the dynamic nature of the problem. Indeed, characteristics of power markets not considered in these models, such as delays in adjusting timely the production capacity and the fact that aggregated long-term forecasts often behave like simple extrapolation of recent past trends, cause to alternatively over- and undershoot the long-run market equilibrium (Rostow, 1993; Sterman, 2000).
Seminal works recognizing the possibility of business cycles in the electricity industry by means of dynamic simulation models are presented in Bunn and Larsen (1992) and Ford (1999). The work presented here differentiates from the above mentioned in many respects as it does not aim at simulating any actual power market, but it focuses predominantly on the formulation of the mathematical framework to extend significantly the modeling methodology. In this model, capacity additions are not based on only one generating technology. On the contrary, the addition of base-, middle- and peak-load power plants is allowed depending on their economic attractiveness at each time. Therefore, investment decisions in the various generation technologies are coupled, in the sense that investments in one technology depend upon capacity additions of other technologies. Furthermore, generation capacity is differentiated in vintages for each technology to consider the progress registered in thermal efficiencies of generating units as well as the decommission rate of generation capacity. In this way, the age structure of the generating park can be adequately modeled, since it influences the potential profit for new power plants. Another important feature is the modeling of the market price with its associated annual distribution and not solely as an average price over the year. This allows computing the economic attractiveness of investing in each type of generating technology at a certain time. This price distribution accounts explicitly for price spikes derived from tight supply conditions. Other important aspect is the inclusion of time lags in the feedback loop governing the long-term supply adjustment, particularly the delay concerning the option to defer irreversible investments under uncertainty.
This paper is organized as follows: Section 2 analyzes the microeconomic foundations of investments in liberalized power markets. Additionally, the most relevant characteristics of investments in generation capacity that affect investment behavior are discussed. Section 3 presents the model for the supply and the demand side of the market. A model of the price formation considering price spikes is in this section proposed. The different hypotheses on expectation formations are here discussed jointly with the model of investment responsiveness. In Section 4, market simulations carried out on a test system under different assumptions are presented and analyzed. In Section 5 some conclusions are outlined. In Appendix A at the end of the paper, the dynamical equations governing the system dynamics (SD) are derived and some important implications discussed.
Section snippets
Microeconomic foundations
Under the assumption of a perfectly competitive market, generators are paid at each time a market clearing price equals to the marginal cost of the most expensive dispatched generator. At this price, demand and supply are in balance, and it is called competitive price. Since the load varies over time and generating units are sometimes unavailable, the system marginal cost (SMC) fluctuates as long as more or less expensive generators set the competitive price. If the market design contemplates
Model overview
The industry model presented here can be characterized as a structural model, since the long-run development of the power market is determined by modeling the variables having direct influence on long-term movements of supply and demand. The model is based on SD, which is a branch of control and system theory applied to economical and managerial systems. The beginning of SD can be traced to the seminal works of Forrester (1961) in the late fifties.6
Simulations and analysis
In this section, simulations carried out on the described long-term market model with the input data given in Section 3 are shown, and the results are analyzed. The system's initial conditions are set to the long-run equilibrium. Therefore, the system is, at the beginning of the simulations, in a resting state. To avoid introducing exogenous sources of dynamics and gain insight into the endogenously generated dynamics, fuel prices, investment costs and the load growth rate are maintained
Conclusions
In this work, a complete and self-contained methodology to simulate the long-run development of liberalized power markets has been developed. The method assumes inherently that long-term movements respond to changes in market fundamentals. Since the long-run market evolution is driven mainly by generation capacity investments, the model focuses fundamentally on the supply side. The methodology is flexible enough to consider adequately feedbacks, non-linearities and time delays present in actual
Acknowledgment
The authors would like to expressly thank the National Council for Science and Technology (CONICET, Argentina) and the German Academic Exchange Service (DAAD) for their financial support.
References (35)
- et al.
Mr. Keynes’ theory of investmentsdo forward looking expectations and weight really matters?
Journal of Economic Psychology
(1997) - et al.
Cyclicality of capital-intensive industriesa system dynamics study of the paper industry
Omega
(2001) - et al.
Differential-difference equations in economicson the numerical solution of vintage capital growth models
Journal of Economics Dynamics and Control
(1997) - et al.
Sensitivity of reserve margin to factors influencing investment behaviour in the electricity market of England and Wales
Energy Policy
(1992) - et al.
Rational entry into risky markets with negative expected returns
Journal of Economic Behavior and Organization
(1992) - et al.
The economics of the combined cycle gas turbine—an experience curve analysis
Energy Policy
(2002) Economist's stories, and culpability in deregulation
The Electricity Journal
(2002)Capacity development and profitability of wind turbines
Energy Policy
(1999)- et al.
Solving DDEs in MATLAB
Applied Numerical Mathematics
(2001) The dynamics of the UK chemical plant investment cycle
European Journal of Operational Research
(1982)
On the behavioral and rational foundations of economic dynamics
Journal of Economic Behavior and Organization
Modeling the formation of expectationsthe history of energy demand forecasts
International Journal of Forecasting
Reliability Evaluation of Power Systems
Corporate planning and capital investment
Journal of Economic Behavior and Organization
Why bounded rationality?
Journal of Economic Literature
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