Petter L. Skantze

Stochastic modeling of electric power prices in a multi-market environment

Over the past few years, a number of competitive electric power markets have emerged in the United States. While market structure differs by region, the common denominator has been the high level of price volatility experienced in these markets. As power suppliers, marketers and consumers seek to manage their positions in this volatile environment, understanding the locational spreads in power prices is becoming increasingly important. The paper develops a dynamic model describing the interplay of electricity prices in a multi-market environment. In contrast to most existing price models, it is based on the fundamental interaction of demand and supply processes. We illustrate how delays in the information flow to market participants causes price differentials to occur between markets with unconstrained transmission interfaces. Furthermore we examine how correlation between load processes translates into a correlation between the price processes in a dual-market environment. These results are illustrated in a simulated example. In the context of the new model we examine current state of the art algorithms for valuing locational spread options. The work presented suggests that a single correlation factor may not be sufficient to describe the interplay of prices in a dual-market environment. The model illustrates how the price correlation shifts between two states based on the state of congestion on the system. Possibilities for extensions of current option valuation schemes are discussed.

Power exchange for frequency control (PXFC)

This paper concerns markets for balancing power supply and demand in real-time. Two qualitatively different market mechanisms are of interest: (1) primary electricity market(s) for supplying anticipated demand, and (2) a frequency control market for ensuring that system frequency remains within prespecified limits as demand deviates in real-time from its anticipated pattern. We suggest that both types of markets are necessary for ensuring that frequency remains within its technically acceptable limits as power is provided competitively. In particular, we develop one possible structure of a power exchange for frequency control (PXFC) that ensures frequency quality in a general primary electricity market comprising both bilateral and spot sub-markets.

Valuation, Hedging and Speculation in Competitive Electricity Markets

Valuation, Hedging and Speculation in competitive electricity markets: a Fundamental Approach, examines the unique properties which separate electricity from other traded commodities, including the lack of economical storage, and the impact of a scarce transmission network. The authors trace the sources of uncertainties in the price of electricity of underlying physical and economic processes, and incorporate these into a bid-based model for electricity spot and forward prices. They also illustrate how insufficient market data can be circumvented by using a combination of price and load data in the marking-to-market process.

Electric power systems operation by decision and control. The case revisited

We have witnessed sweeping changes in the organization of the electric power industry. This has had a profound effect on the industrys system operations and planning rules and has created a need to revisit its modeling, decision-making, and control principles. Historically, the decision and control of large-scale electric power systems has developed as the system interconnection has grown. The article begins by assessing principles of operation by decision and control for todays fully regulated industry. Following this summary, several major ongoing changes are interpreted from a systems point of view. It turns out that major challenges-economic, policy, and technical-are inherently systems problems. To illustrate this claim, new decision-making problems essential to having a successful generation business in a competitive industry are defined. This section is very detailed and describes the challenge created by introducing profit-based and risk management issues in the context of under the highly uncertain, often volatile, market price of electricity. Following that, the modified objectives of and decision making by future power delivery companies are described. The discussion shows how these regulatory issues directly impact the hierarchies and complexity of the related dynamic systems problem. Moreover, the so-called load serving entities or energy service providers will be critical to the technologies potentially useful to specific customers.

Investment Dynamics and Long Term Price Trends in Competitive Electricity Markets

Abstract This paper analyses long term price trends in deregulated electricity markets. A price model using explicit supply and demand states is introduced. A stochastic model for demand growth drives future uncertainty, and investors respond by adding new capacity based on price feedback. The effects on price dynamics of delays in the supply response, through information lag or construction time, are illustrated through simulations. The model is extended to account for the physical reliability problem resulting from a lack of generation capacity. It is shown how inappropriate intervention by regulators, through the use of price caps, can result in a critical decrease in the markets’ reserve margin.

Overview of Valuation and Hedging Theory

This book will address a number of decision problems faced by the participants in competitive power markets. The set of problem formulations can best be summed up as commitment problems, since they involve some form of physical or financial commitment from the firm in question. They include investment in physical assets, agreements to deliver electricity to customers over a specified period, bilateral financial agreements, and numerous exchange traded derivatives based on electricity prices.

Optimal Futures Market Strategies for Energy Service Providers

The previous chapter focused on developing a stochastic model for the dynamics of electricity prices. Here we show how the bid-based model can be applied to help market participants optimize their decision making under uncertainty. This chapter will address the problems facing energy service providers. In Chapter 8 we address the supply side of the market.

Arbitrage Pricing and the Temporal Relationship of Electricity Prices

The key issue in relating electricity spot and forward prices is storability. The lack of economic storage opportunities for electricity makes it impossible to form a cash and carry type arbitrage portfolio. As a result we cannot impose any arbitrage free bounds on the relative levels of spot and forward prices. It does not end there however. There is no limit on how far the prices of two forward contracts with different delivery months can diverge, since no arbitrage portfolio can be created to exploit the price differential. The story gets worse when we address the spot market. For a given year there are 8760 delivery hours, each with a unique price. There is no constraint on the relative price of spot power from one hour to the next. Relying purely on arbitrage theory, the number of random variables needed to define the spot and forward markets for one year would therefore be 8772. To use the forward market with a hedge we would need to estimate the entries into the 8772 by 8772 covariance matrix. Electricity markets suffer from a severe case of the curse of dimensionality. To circumvent this problem we must rely on effective modeling solutions. In the next chapter a detailed model for the spot market will be presented, describing the temporal correlation of prices as a function of fundamental drives. Before going through this process, however, we examine the relationship governing the spot and forward markets in the context of non-storability.

Modeling Locational Price Differences

In this chapter we will address the question of how market participants can quantify and hedge locational price risk. The work draws on results from the finance, economics and engineering community, attempting to find a middle ground that allows us to solve the unique problems facing the electricity industry. This includes developing methods for valuing newly emerging transmission dependent derivative contracts. Furthermore we examine the relationship of these new contracts with existing forward and option contracts on locational spot prices. We extend this analysis to include the valuation of investment opportunities in transmission assets, thus allowing a for-profit transmission provider to arrive at a market based valuation of a potential investment, based on observed forward and derivative prices.

A Bid-based Stochastic Model for Electricity Prices

In this chapter we develop a bid-based stochastic model (BSM) of the evolution of prices on electricity spot markets [19]. We assume that the spot market operates as a double auction, with a single hourly market clearing price (MCP) at the intersection of the aggregate supply and demand bid curves.. The model can be modified to account for variations in the auction procedure. We design the model to be applicable to hedging, speculation or investment decisions in electricity markets. As such, it focuses on quantifying the uncertainty of future price movements. We have used a fundamental modeling approach, where the fundamental drivers are load and supply shifts. The model captures the most critical characteristics of demand (load) and supply, as outlined below, in the electricity market.