A Gauss-Markov load model for application in risk evaluation and production simulation

Breipohl, A.M.; Lee, F.N.; Zhai, Di‐Hua; Adapa, R.

doi:10.1109/59.207373

Cited by 30 publications

(7 citation statements)

References 7 publications

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“…3. After adjusting for the variations in the ambient temperature and periodicity, the demand at time t, u(t), is assumed to follow a Gauss-Markov process [Breipohl et al (1992) and ] with u(t) and u(r) following a bivariate normal distribution for any pair (r,t) with E[u(t)]=θ t and Cov[u(r), u(t)]=σ r,t , where θ t and σ r,t are assumed to be known. (Data analysis given in validates this assumption.)…”

Section: Stochastic Model Of the Marketmentioning

confidence: 99%

“…The information on the mean time to repair, mean time to failure, capacity, and marginal cost of each unit required to characterize these processes is assumed available. The hourly demand is represented by a Gauss-Markov process [Breipohl et al (1992)]. have recently reported on the statistical analysis of hourly load data covering a region of the Eastern United States.…”

Section: Introductionmentioning

confidence: 99%

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Commitment of Electric Power Generators Under Stochastic Market Prices

Valenzuela

Mazumdar

2003

Operations Research

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A formulation for the commitment of electric power generators under a deregulated electricity market is proposed. The problem is expressed as a stochastic optimization problem in which the expected profits are maximized while meeting demand and standard operating constraints. First, we show that when an electric power producer has the option of trading electricity at market prices, an optimal unit commitment schedule can be obtained by considering each unit separately. Therefore, we describe solution procedures for the self-commitment of one generating unit only. This description is given for three certainty-equivalent formulations of the stochastic problem. The procedures involve application of optimization methods, statistical analysis, and asymptotic probability computations. The optimization problem uses Schweppe's definition of hourly spot price to drive self-commitment decisions. Under the assumption of perfect market competition, the volatility of hourly spot price of electricity is represented by a stochastic model, which highlights its dependence on demand, generating unit reliabilities, and temperature fluctuations. The exact computations become very time-consuming for large systems; we therefore use several approximation methods (normal, Edgeworth series expansion, and Monte Carlo simulation) for computing the required probability distributions. Dynamic programming is used to solve the stochastic optimization problem. Numerical examples show that for a market consisting of 150 generating units, the self-commitment problem can be accurately solved in a reasonable time.

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Section: Stochastic Model Of the Marketmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Commitment of Electric Power Generators Under Stochastic Market Prices

Valenzuela

Mazumdar

2003

Operations Research

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“…For example, by analyzing load data over a region in the northeastern United States, we have shown that when the temperature and time-of-day effects are removed, the load follows an AR(1) process with Gaussian errors [17]. Similarly, Breipohl et al [4] have advocated the use of the Gauss-Markov process to represent the stochastic behavior of hourly load. For the supply side of the market, we assume that the generation system can be represented by a production costing model [7].…”

Section: Introductionmentioning

confidence: 96%

A Probability Model for the Electricity Price Duration Curve Under an Oligopoly Market

Valenzuela

Mazumdar

2005

IEEE Trans. Power Syst.

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In this paper, we propose a new formulation for the "price duration curve" (PDC) using probability considerations and provide a procedure for constructing it. This curve is expected to be useful in the long-term prediction of market prices and is similar in spirit to the load duration curve. It shows the proportion of time over a given time horizon during which the real-time market price of electricity is expected to exceed specified dollar amounts. The price over a long term is a stochastic quantity that depends on physical factors such as production cost, load, generation availability, unit commitment, and transmission constraints. It also depends on economic factors such as strategic bidding and load elasticity. We illustrate a procedure for constructing a stochastic system-based model for the PDC, taking into account the randomness associated with load and generator outages. The effects of unit commitment, transmission congestion, and transmission outages are not considered. We use two economic models. One is due to Bertrand and represents perfect competition. The other model is due to Rudkevich et al. who have given a closed-form expression for the marketclearing price in an oligopoly consisting of several identical firms.

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“…The solution process was by Lagrangian relaxation. In [47] In [53] Outhred et al presented the various alternatives being considered by the Australian industry for transmission pricing. Of these, the "benefits method" (which consists of allocating the cost of the high voltage network element according to user benefit generators and loads equally), and the distance based MW-Km (or MW-mile) method were selected as the two most favored options.…”

Section: Generation and Transactions Schedulingmentioning

confidence: 99%

Strategic bidding in an energy brokerage

Rajan

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A Gauss-Markov load model for application in risk evaluation and production simulation

Cited by 30 publications

References 7 publications

Commitment of Electric Power Generators Under Stochastic Market Prices

Commitment of Electric Power Generators Under Stochastic Market Prices

A Probability Model for the Electricity Price Duration Curve Under an Oligopoly Market

Strategic bidding in an energy brokerage

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