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Weekly UpdatesINTRODUCTION
The generation business in many parts of the United States is undergoing a radical change from a regulated monopoly toward market competition. Under this new environment toward competition, the following two factors in decision-making have become significant: financial risks and managerial flexibility. The objective of a utility is to maximize profit and minimize risk for its strategic and tactical decisions.
A utility makes strategic decisions such as to construct a power plant based on long-term observation on market conditions (Wang and Min, 2006). On the other hand, a utility also makes tactical decisions based on short-term observations on market conditions. For example, based on the prices of electricity and natural gas, a utility makes tactical operational decisions such as to turn on or turn off a gas power plant. Furthermore, a utility sells its excess power in a day-ahead or real-time market based on price spread in those two markets and plant operational conditions. Such daily trading decisions also attempt to incorporate financial risks and managerial flexibility based on newly available information.
As restructuring of generation business continues, organized day-ahead and real-time markets operated by independent system operators (ISOs) have been formed (Helman, 2006; Olson et al., 2003: Liu and Wu, 2006). Then, the question for a utility is how to decide trading proportion in each of those short-term markets. Historical data has shown that electricity prices in real-time market are volatile (Li and Flynn, 2005). It is also observed that there exist price differentials between real-time and day-ahead market. Furthermore, selling electricity day-ahead exposes a utility to forced outage risks because a utility is committed to serving real-time. If a utility cannot deliver electricity real-time due to forced outages, it needs to purchase electricity in a highly volatile real-time market.
Moreover, selling electricity real-time may cost a utility more revenue sufficiency guarantees (RSG) charges from ISO (RSG: charges and payments in order to account for the non-economic operation of the generators). The day-ahead market is designed to provide information for advance scheduling decisions. Therefore, any self-scheduled real-time plant commitment may increase startup costs and lower market clearing prices (Hogan, 2006). RSG recovers revenue deficiency for the committed plants. Both financial and operational risks make short-term power portfolio optimization a challenging problem.
Power portfolio optimization has been investigated in the literature (see Denton et al., 2003). However, the literature has not focused on short-term trading decisions such as day-ahead versus real-time trading. Sen et al. (2006) consider a power portfolio optimization that integrates spot market and forward market activities. Their model is designed for trading support on a monthly basis. Xu and Luh (2006) formulate a mid-term power portfolio model to provide decisions for multiple supply instruments. In their paper, it is assumed that day-ahead market is merged with real-time market.
In this article, for short-term trading decisions such as amount of power to sell/buy day-ahead, we formulate a power portfolio model to quantify profit, outage risk, and price spread risks in a single framework. Price spread represents price differential between day-ahead market and real-time market. The model represents day-ahead view for the power portfolio.
From a day-ahead point of view, real-time prices and power plant availability are assumed stochastic and will be simulated. Different strategies such as profit maximization and risk minimization will be applied to the formulation of power portfolio for optimal trading decisions. Numerical examples will be presented to show that our proposed strategy improves the performance of power portfolio over the commonly used strategy by traders.
In practice, when traders make trading decisions, the balance of profits and risks is probably in their mind. The key contribution of this article is that, for short-term trading decisions, we formulate a power portfolio model to quantify profits and risks in a single framework. Since profits and risks are objectively and systematically quantified, we are able to make trading decisions that would achieve an optimal balanced point between profits and risks for the portfolio. The results of this will benefit trading operations and therefore utilities themselves.
This article is organized as follows. In the next section, we formulate a valuation model for power portfolio. This will be followed by simulation for uncertainties on day-ahead basis. Next, we consider different strategies on the formulation of power portfolio for optimal trading decisions. Then, we present numerical examples that demonstrate that our proposed strategy produces better performance than commonly used strategies by traders. Finally, we summarize this article and provide future research.
VALUATION FOR DAY-AHEAD POWER PORTFOLIO
In this section, we will formulate a power portfolio model for on-peak hours the next day. The model reflects today's projections for the value of the portfolio tomorrow. On-peak hours are defined as the hours from 6 a.m. to 10 p.m. Monday through Friday. For the formulation of the model, first, we will present valuations of the components of the portfolio. The components include generators, contract load, trades in day-ahead market, trades in real-time market, RSG charges, and financial forward.
Next, we will define notations for deterministic and stochastic inputs for the model. Looking one day ahead, some inputs are more uncertain than the others and will be modeled stochastically. We will also define notations for decision variables. Looking one day ahead, a utility would like to know how much excess power should be traded today (day-ahead) or tomorrow (real-time) to optimize the portfolio. Finally, we will present the valuation of the portfolio that incorporates profit and risk in a single framework.
The output of generators is to serve contract load first. Any output left from serving contract load is sold to physical markets such as day-ahead and real-time markets. On the other hand, if the output of generators is less than contract load due to forced outages, a utility is obliged to acquire power to serve contract load through power purchases. A forced outage occurs when the failure of plant equipment requires that the plant be taken out of service immediately.
The gross margin from generators is equal to the difference between revenues and dispatch costs. Revenues come from contract load and physical markets. Dispatch costs represent variable costs such as fuel costs and variable operations and maintenance costs required to generate electricity. In a contract market, a utility sells electricity by signing contracts with energy consumers. Contract details such as quantity, prices, duration, and delivery point are negotiated between a utility and energy consumers. The revenue from a contract is equal to the product of the contract load and contract price.
Physical markets considered in this article are day-ahead and real-time markets. On day-ahead basis, a utility makes decisions for whether to buy/sell physical power. If a utility trades day-ahead, then the next question is how many megawatts to trade. If a utility sells day-ahead, then the value of the sale is equal to the product of the quantity of the sale and day-ahead price. We note that a utility is obliged to deliver power if it sells physical power day-ahead. Therefore, if a utility tails to deliver power the next day due to forced outages, then it needs to purchase power from the real-time market. On the other hand, if a utility buys physical power day-ahead, then the cost of the purchase is equal to the product of the quantity of the purchase and day-ahead price.
Any power left after serving the contract load and the selling to day-ahead market is sold to the real-time market. The revenue of such power is equal to the product of the quantity of the power and real-time price. On the other hand, if a utility buys physical power day-ahead, then the quantity of power that can be sold in the real-time market is equal to the difference between the sum of day-ahead purchase and output of generators and contract load. Similarly, the revenue of such power is equal to the product of the quantity of the power sold to the real-time market and real-time price.
The RSG cost is equal to the product of the difference between the day-ahead schedule and real-time delivery and the RSG unit charge. For example, if a utility sells 100 MW physical power day-ahead and the utility can only deliver 50 MW real-time, then 50 MW is subject to RSG charges. Moreover, if a utility purchases 100 MW physical power day-ahead but sells 50 MW real-time, then 150 MW is subject to RSG charges.
In addition to physical markets, there exist financial markets. In a financial market, different products for selling/purchasing power at fixed prices are available several months before an expiration date. For example, a trader can sell a forward contract on April 2 for the entire month of September at a fixed price for a given quantity of power. This means that the same quantity of power is sold every day in September. Forward contracts are usually used for hedging purposes. A forward contract is automatically bought back on the expiration date if no action has been taken before that date. Because financial and physical markets are highly correlated, financial forward contracts are commonly used by traders to hedge against the risk exposure of physical power. The revenue of a financial forward is equal to the product of the quantity of power sold forward and forward price.
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