Commitment of Electric Power Generators Under Stochastic Market Prices

Abstract

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.

Electric Power Industry: Operational and Public Policy Challenges and Opportunities

“…The incredibly challenging task of perfectly balancing the supply and demand of electricity at all times Takriti and Krasenbrink (1999), Nowak and R € omisch (2000), , Takriti and Birge (2000), Doorman and Nygreen (2003), Viana et al (2003), Valenzuela and Mazumdar (2003), Thompson et al (2004), Sen et al (2006), Dahal et al (2007), Troncoso et al (2008), Cerisola et al (2009), Toczy lowski and Zoltowska (2009), Corchero and Heredia (2011), Kjeldsen and Chiarandini (2012), Murillo-S anchez et al (2013), Papavasiliou and Oren (2013), Zugno and Conejo (2015), Lorca et al (2016), van Ackooij and Malick (2016), Zugno et al (2016), and Morales and Pineda (2017) Valuation and/or optimal investment level for generation, storage, or transmission assets: single-firm level decision making, includes real options-based papers opens up many research questions that can be addressed with the tools and techniques of OR/MS. Indeed, the electric power industry research has long been an important stream in OR/MS scholarship.…”

Electricity spot price dynamics: Beyond financial models

“…Industry participants need to understand the behavior of deregulated prices in order to price the growing array of electricity derivatives being traded and in order to implement the real option models that are increasingly being advocated for investment and generation decisions in the electricity sector. See, for example, Bhanot (2002) and Deng (2000) on derivative pricing and Deng (2005), Swinand et al (2005), Tseng and Barz (2002), and Valenzuela and Mazumdar (2003) on real option valuation. Modeling prices has therefore become an active area of research, and the use of statistical models commonly applied to financial time series is popular.…”

Large-scale unit commitment under uncertainty: an updated literature survey

“…In [511] the use of UC tools in a deregulated market is discussed. In particular, under the assumptions that prices are stochastic and there is no market power or transmission constraints, a GENCO can solve a self-scheduling UC for each of its units independently, which however, should be a SO model due to uncertainty on prices.…”