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...short-term production intertemporal, and the conventional 'price vs. marginal cost' rule not sufficient to predict production in thermal power plants. This paper analyzes how the optimal production decision is influenced by climate policies: namely, C[O.sub.2] trading mechanisms, the expansion of renewables and the interaction between these policies.
The main result is that higher power price variation (as a result of increased wind power production) makes the thermal power producer less flexible, but the effect on emissions is ambiguous. A C[O.sub.2] cost (as a result of an emission trading system) increases the flexibility of the producer and the operation decision resembles the conventional 'price vs. marginal cost' rule more. This implies lower emissions. However, when the C[O.sub.2] price is coupled with higher power price variation, the positive effects may be reversed since the two policies have opposing effects.
1. INTRODUCTION
Climate policies directed towards the electricity industry aim to reduce C[O.sub.2] emissions by reducing the use of fossil fuels. Considering the long-term nature of the climate change, long-term trends have been the natural focus of attention for most economic studies (see e.g., Weyant (1999), Springer (2003) and de la Chesnaye and Weyant (2006) for an overview of different numerical models and their results). However, climate policies also influence electricity markets in the short term: by changing market prices and the costs of producers, the policies influence not only long-term (investment and closure) decisions, but also the short-term production decision--whether to produce today (or even in a given hour) or not.
Climate policy measures aimed at the electricity industry in the European Union (EU) follow two distinctly different strands and influence fossil-fuelled plants in different ways. First, the cost of C[O.sub.2] emissions is increased through an emissions trading system (EC, 2003). By increasing the cost of fossil fuels, the C[O.sub.2] cost has a direct impact on traditional thermal power plants. (1) Higher costs are likely to transmit into higher prices and, unless leakages occur, producers with low emissions replace producers with high emissions (Amundsen et al., 1999, Hauch, 2003). Second, fossil fuels are meant to be crowded out through the subsidization of renewables (EC, 2001). Renewables will influence the fossil-fuelled producer only indirectly, through the electricity market and the price mechanism. Boosting renewables' capacity (wind power in many cases) through subsidies implies a lower price level: many renewable technologies have low marginal operating costs and will therefore replace conventional power plants, thus reducing the marginal costs of electricity production and hence the market price (Hindsberger et al., 2003; Unger and Ahlgren, 2005; Morthorst, 2006). However, wind power is a variable energy source: it can only be produced when there is wind and, for any given level of wind power capacity, the actual level of production is uncertain. (2) Since electricity cannot be stored, the variation in wind power production will be transmitted to power prices if production in other plants cannot be adjusted quickly and easily. (3,4)
In economic analyses, it is common to assume that power plants are perfectly flexible: power plants can start production instantly and without incurring any extra cost. Nonetheless, there are costs related to starting and stopping a thermal power plant even in the short-term (i.e., apart from the long-term issues pertaining to investments, mothballing and scrapping a plant), see Wood and Wollenberg (1996). On the one hand, an idle plant will not necessarily start if prices are expected to be higher than the short-term marginal costs for a short period of time. On the other hand, if a plant is already producing, it will not stop during a short period of low prices. The production decision is then an intertemporal decision, and the conventional 'price vs. marginal cost' rule is not sufficient to predict production in thermal power plants.
Moreover, due to the intertemporal decision in the presence of start and stop costs, the impact of climate policies is not clear-cut: the total production and emissions of a thermal power plant may be either lower or higher than predicted by the conventional 'price vs. marginal cost' rule. In addition, the start-up itself contributes to higher emissions (due to higher fuel use) than a smoother mode of production. In a cap-and-trade system, higher emissions imply a higher quota price, if the total cap is to be met.
This paper fills a gap in the literature by incorporating start and stop costs in an analysis of climate policies. Mansur (2003) finds, in an econometric study of potential market power in the Pennsylvania, New Jersey and Maryland electricity market, that the start-up costs, together with other short-term intertemporal constraints, explain a large part of the mark-up (i.e., the portion in excess of marginal costs) in power producers' bids to the market. Mansur's empirical findings suggest that the start-up costs substantially alter the operation decisions of power plants. This has implications for the market and, hence, policy outcomes. Tseng and Barz (2002) use real options theory for valuation of generation assets and find that failure to take into account the short-term constraints may lead to the overvaluation of power plants. Although the remaining economic literature (excluding the aforementioned papers by Mansur and Tseng and Barz) has ignored the issues related to the intertemporal constraints of power plants, these issues have been extensively studied in electrical engineering literature (under the term unit commitment); see e.g., Sen and Kothari (1998) or Sheble and Fahd (1994) for an overview. This strand of literature has, however, focused on the technicalities of modeling, being concerned with finding suitable algorithms for the actual operation of large power systems. Climate policy issues have not been at the center of attention.
This paper analyzes how the optimal production decision of a fossil-fuelled power producer is influenced by higher uncertainty about the power price (as a result of more renewables), higher costs of fossil fuels (as a result of C[O.sub.2] trading mechanisms) and the interaction of these effects (as a result of the simultaneous use of the two policy measures). This is analyzed in a numerical model, using data from Denmark as an illustration. The focus is on a single producer's operation decisions in the very short term, given its costs and exogenous prices.
2. THE MODEL
Dixit's (1989) seminal paper on entry and exit decisions under uncertainty has become a workhorse in investment analyses. Employing the analogy between real and financial options, the entry and exit decisions are regarded as call options. Investment and abandonment costs lead to hysteresis in investments in an uncertain environment. Dixit and Pindyck (1994) present extensions to the model. Here, a similar framework is applied to a short-term production decision. Since prices in the Nordic power pool Nord Pool are cited hourly, a discrete time framework is appropriate for the problem at hand.
Consider a firm that can produce [q.sub.t] units of output in each time period t. Assume that this is an on/off technology, producing either at its maximum capacity level [q.sup.max] or not at all: [q.sub.t] = [q.sup.max] or [q.sub.t] = 0. (5) With an exogenous output price [p.sub.t] and short-term marginal production costs c, the firm can earn ([p.sub.t] - c)[q.sub.t] in each period. The output price is a continuous variable with state space [p.sub.t] [member of] [0, [infinity]). However, in addition to the short-term marginal costs, the producer faces a start-up cost [C.sub.start] if he did not produce in the previous period and starts to produce in this period, and a shut-down cost [C.sub.stop] if he stops production. The start-up and shut-down costs are sunk costs.
Thus, the profit for each period depends on the two state variables price and the operational status of the firm (on/off) that are observed at the beginning of the period. The 'status variable' [d.sub.t] is a binary variable, [d.sub.t] [member of] {0,1} ([d.sub.t] = if the plant is 'off', i.e., not producing; [d.sub.t] =...
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