The Value of Starting-Up The Power Plant
Avoiding perfect foresight with Least-Squares Monte Carlo: In this article we demonstrate the impact of various start-stop constraints and costs. This impact analysis is possible by applying advanced techniques for generating realistic Monte Carlo price simulations in combination with techniques for optimising the production pattern.
By Cyriel de Jong, Dirk van Abbema, Henk Sjoerd Los & Hans van Dijken
gas plants is paramount to retrieving the maximum value from the asset. With the increasing penetration of wind power, this flexibility will become essential to balance the system. While starts and stops allow the owner to choose the production hours with the largest margin, they are also associated with various explicit and implicit costs. An important insight that we gain is that different ways to
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limit starts lead to subtle differences in the actual use of the power plant and the corresponding value. We also find that the common modelling assumption of having perfect foresight about the future spark spreads may lead to a significant overstatement of plant value. This latter result contrasts our previous belief [Los et al, 2009], and statements of some other researchers [see Clewlow et al, 2009] who claim that perfect foresight is a reasonable assumption. In particular, when there is a fixed limit to the number of allowed starts, as is common in many Virtual Power Plant (VPP) contracts, uncertainty about future margins is definitely reducing plant value. We are able to show this result using the concept of Least-Squares Monte Carlo as applied to energy assets in e.g. Deng (2006, power plants) and De Jong and Boogert (2008; gas storage).
Building Blocks For Plant Valuation The simplest way to assess the value of a power plant or
a VPP deal is to discount the forward spark spread back to today, assuming production is shut down when forward spark spreads are negative. This means the plant is treated as a strip of European-style call options on the spark spread. This approach ignores the operational costs and constraints that tie production hours together, so overestimates true plant value. On the other hand, it also underestimates true plant value, because the variability in commodity prices generally leads to considerable real option value for flexible assets. In fact, accurate valuation of thermal plants assets requires
three fundamental elements: 1. A realistic model to describe how prices evolve over time; the model should be able to generate realistic Monte Carlo simulations.
2. A powerful methodology to find the optimal production pattern for the different price scenarios, incorporating all relevant costs and constraints.
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as-fired power plants provide the primary source of production flexibility in many power markets. An economically optimal use of the start-stop flexibility of
3. A framework to analyse different trading and hedging strategies.
In a previous article in WorldPower (Los et al, 2009), we
provided a description of all three building blocks. In particular, we highlighted the concept of cointegration: It links power prices to the fundamentals of the market (merit order) and thereby keeps spark spreads within reasonable bounds, while maintaining the stochastic nature of prices. In a case study for a 3-year VPP deal we found that the flexibility (extrinsic) value equaled 40% of intrinsic value if we included a realistic degree of cointegration. Without cointegration, the extrinsic value became far too large though.
Start Limitations Last year’s article1
also showed the impact of various
operational costs and constraints, ranging from minimum runtimes and start costs to maintenance and plant degradation. In this article, we introduce a new constraint, namely a hard limit to the number of times a plant operator may start in a year. We show how this compares to other start constraints and demonstrate that perfect foresight about future prices leads to over-optimistic assessments.
... we introduce a new constraint, namely a hard limit to the number of times a plant operator may start in a year
Some start costs are very clearly defined, such as the purchase
of start fuel, which is the fuel consumed while firing-up to the minimum stable generation level. Other start costs are included to account for the detrimental effect on the condition of a unit caused by stopping and restarting the unit. A challenging aspect of start costs is that they may depend on the temperature of the unit, e.g. cold, warm, or hot. The temperature in turn depends on how long the unit has been offline. A plant operator will need to know for how long they have been offline, in order to make the correct cost calculation. In the solution framework of dynamic programming this creates additional states that the model needs to keep track of. For example, when a hot start is possible after 4 hours, a warm start after 8 hours and a cold start after 24 hours, we have 3 different start cost structures associated with 24 states.
worldPower 2010
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