Escritura y lectura de datos

The forthcoming chapters of this thesis are organized as follows. Chapter 2 surveys the existing literatures on electricity price modeling, namely, the par- ticular price modeling problems, the usual approaches, popular mathematical tools, and some special techniques. Chapter 3 applies the Microeconomics Price Theory to electricity markets and develops the basic analytical tools for analyzing electricity spot prices. Making use of the analytical tools that are developed in Chapter 3, Chapter 4 introduces the Multi-granularity Framework for analyzing electricity spot prices in three time-perspectives; in each perspec- tive, it endeavors to understand how the operations of fundamental engineer- ing power systems give rise to the very peculiar behaviors of electricity spot prices. Taking advantage of the understanding on electricity spot prices that has been gained in previous chapters, Chapter 5 proposes an electricity spot price model that is based on the idea of decomposition, and demonstrates the modeling methodology in the New-England electricity market. Upon some mi- nor revisions on the model, Chapter 6 brings the same modeling methodology to the Pennsylvania-New Jersey-Maryland(PJM) electricity market. Chap- ter 7 records an early adventure of us trying to model electricity spot prices by Structural Approach. Chapter 8 summarizes and concludes this thesis work.

A Survey of Electricity Price

Models

2.1

Electricity Price Modeling Approaches

From the point of view of a generation company, modeling and forecasting electricity prices are either for formulating bidding strategies, scheduling gen- eration production, pricing electricity derivatives, or generation investment analysis. For formulating bidding strategies one concerns the day-ahead 24- hour spot prices; for scheduling generation and pricing electricity derivatives one cares the spot prices from as short as the next week to as long as the next year; for generation investment analysis, one concerns the electricity spot prices during the life time of a generator, that is, years or even decades. In order to make these pricing, scheduling, and investment decisions, generation companies need a thorough understanding on electricity spot prices, at best, they want a physically well-grounded, simple, and fast electricity spot price model to assist their making these decisions.

A price model suitable for a particular application has to at least satisfy five requirements: it has to capture properly the movements of electricity spot prices, it must give the expected value of the foreseen spot prices, it must quantify the uncertainty of the spot prices, it has to define the prices of a time unit that is suitable for a particular application, and it has to cover the time horizon that a particular application concerns. There are a few mathematical

tools, modeling approaches, or techniques that have been applied to analyze and model electricity prices, i.e., Time Series Models, Financial/Stochastic Process Models, Structural Models, Decomposition Techniques, etc.

In terms of Time Series Models, they start with the price data and define a model to capture the correlations between the prices at one time period and the prices at the previous periods. Time series models are usually good options for short-term applications, like forecasting next-day 24-hr and next week 168-hr prices. We will, start with the simplest time series model and end with some rather involved ones, step by step, discuss the nature of time series models and their possible applications in electricity price modeling and forecasting.

Financial/Stochastic Process Models have seen their successful applica- tions in modeling the financial, commodity, and energy markets. The financial models are defined by stochastic differential equations. The financial models, though complicated at first glance, give final results that are mathematically simple. These mathematically elegant final results enable financial models to be used in applications that desire the least computation and the fastest speed, such as pricing electricity futures, contracts, and other derivatives. We will introduce, carefully, the development of financial models in modeling electric- ity prices, the problems that have been satisfactorily solved, and the problems that are still remain.

Time series models and financial models belong to Statistical Models. Both of them use the historical data to induce, calibrate, and experiment the mod- els. Structural Approach, on the other hand, models electricity spot prices in- directly. It first models the physical forces that underlie electricity spot prices by a few constituent models, then constructs these constituent sub-models into a complete electricity spot price model. For that Structural Approach utilizes the more fundamental knowledge on electricity markets, it could model elec- tricity spot prices of a longer time-horizon than that the statistical approach could usually do. We will briefly introduce the idea of structural models, their advantages and disadvantages, and the literatures along to this line.

Besides the statistical approach and the structural approach in modeling electricity prices, there is another method for studying electricity markets,

which will be referred as Fundamental Approach. Compared with the struc- tural approach, fundamental approach is of much further detail. It may model each generator unit, behavior of each market player, seasonal generation main- tenance and available generation capacity, the dynamics of electricity load demand, the transmission networks, the rules of the electricity market, the investment cycles of the electric power sector, etc. It then uses these detailed models to construct electricity spot prices. Due to these further details, prob- ably there is no analytical result for a fundamental model. In this survey, we will not give any further discussions on the fundamental approach, inter- ested readers please refer to the literatures, such as, Angelus (2001); Bastian et al. (1999); Baughman & Lee (1992); Bessembinder & Lemmon (Jun. 2002); Olsina et al. (2006); Ruibal & Mazumdar (2008); Wang & Mazumdar (2007). Finally, decomposition techniques probably have huge potential in analyz- ing and modeling electricity prices. Electricity prices has a complex nature: intra-week hourly spot prices has an intra-day pattern and a weekday-weekend pattern; intra-year weekly prices has a seasonal pattern, and in different sea- sons prices behave distinctly; and short-life price spikes prevail in electricity markets all over the world. This complex nature of electricity prices is due to the various physical driving forces that underlie electricity spot prices. If the electricity spot prices could somehow be decomposed into a few price com- ponents that are driven by the different and independent physical underlying forces, the original problem then is divided into several sub-problems that are by nature much simpler and thus much easier to solve. We will introduce briefly the various decomposition techniques, such as Fourier Analysis, Wavelet Analysis, and Principal Component Analysis, and discuss their possible appli- cations in electricity price analysis and modeling.