Model assumptions

First and most importantly, in order to guarantee the existence of a unique solution, the objective function (eq. 2.2) and constraints conditions (eq. 2.3~2.7) should be strictly quasi-concave and convex respectively. The former is ensured by setting a decreasing demand function of the price and increasing cost functions and the latter is guaranteed by using linear equations in this model.

Secondly, while power plants are discrete units¹¹ in the real world, it is assumed that each firm‟s capacity (of each technology type) is a continuous variable, for the sake of simplicity. In addition, the model considers electricity demands over the course of a year at a

11 A typical power station has units with capacities of 500 to1200MW.

time. The data are grouped as peak, plateau, and off-peak hours according to the load levels with a total of 14 blocks. The total demand for electricity at each load level is given by a linear function of the price. Besides this, the operating cost of firms is modelled as a quadratic fuel consumption function in which all fuel prices such as coal, gas, and heavy oil are assumed to be fixed over whole years. On the other hand, start-up costs and ramp rate constraints in the cost function are excluded, since those conditions have little effect on investment decisions in the long term.

Thirdly, the equilibrium electricity price and investment decisions are determined in a Cournot manner. A linear demand function is employed. Each firm chooses its output given its competitors‟ strategy to maximize its own profit. Then, the equilibrium electricity price is derived from substituting the summed firms‟ output into the inverse demand function (see eq.

8). However, before applying the oligopoly theory to the Korean electricity market, it should be noted that the market has been operating as a Cost-Based Pool (CBP) in which generators had to bid at variable cost and this set the price since 2001. Attempts to create Two Way Bidding Pool (TWBP)¹² competition, which allows distributors to submit price responsive demand bids and generators offer power at prices above variable cost, ceased in 2003 due to the change in the political environment. But the current administration continues to attempt the policy of competition. Therefore, the model assumes that the TWBP is introduced in the electricity market where distribution firms are allowed to bid in order to represent the trend of industry policy and justify application of the oligopoly theory. The assumptions of the Cournot model fit well into the properties of the deregulated electricity market: homogeneous goods, non-storable, and few firms in the electricity market. In addition, the theory assures a

12 Under the CBP system which is a preliminary stage for TWBP, the marginal price is determined by the merit order system in which each unit is ranked according to generators‟ bid based on its variable cost. On the other hand, the electricity price is determined by a market mechanism in the TWBP where both the generation and distribution firms submit supply and demand bids, respectively.

unique equilibrium and avoids complex computational processes. But it often gives very high equilibrium prices compared to real data in the electricity market, because equilibrium prices are sensitive to the price elasticity of demand and firms are assumed not to react to competitors‟ output and price changes¹³. Therefore, this model indicates the price level in a potential market where the price is formed because of the substantial market power by dominant firms under the emission trading scheme rather than forecasting the actual future electricity prices.

Regarding investment decisions, firms are able to choose technology and capacities among nuclear, two types of coal (bituminous and anthracite), CCGT, and oil power plants in order to maximize their profit. Note that renewable investments require subsidy and are therefore exogenous, while the problems in modelling their intermittent output mean that they are best modelled by changing the residual demand curve¹⁴. The Cournot investment equilibrium is accomplished when no firm wishes to change its investment decision given its competitors‟ capacities. It is important to note that each technology has a specific time to build constraint in the real world. For example, while nuclear power plants have the longest lead time, almost 5 years, CCGT plants have the lowest time, 2 years. Although the model does not impose the time to build constraint explicitly, firms are assumed to have perfect foresight so that they are able to choose the optimal time to commence construction of new plants. In addition, they have perfect information about the government scheme for the distribution of emission allowances; when the initial allocation method is implemented by

13 Wolfram (1999) confirms that the price predicted by the Cournot model tends to be higher than the real spot price in the British electricity market from her empirical study, and suggests that the level of the real price can be explained as the effect of threats of other companies entering the market and of regulatory action.

14 Thus the residual demand curve shows the demand facing the traditional sources of power generation.

Renewable energy sources supported from the government‟s policy are often given special treatment in models, because they could not be compared with the traditional technology due to their low economic efficiency and renewable energy‟s intermittent output. Their outputs are usually modelled by using a residual demand curve (see section 2.4.2.). Ventosa et al. (2002) and Linares (2006) have similar short lists of candidate technologies.

each scenario and an auction is introduced in the final stage (see the allocation plans in section 2.4.3.). Lastly, we assume that firms have access to enough capital through efficient capital markets to finance their desired investment programme.

Fourthly, the endogenous emission price modelling is based on Linares et al.‟s work (2008). It is assumed that there are many players in a perfectly competitive emission allowances market. Players in the emission allowances market are classified into two main groups, the electricity sector and non-electricity sector. Further disaggregation would need each sector‟s Marginal Abatement Cost (MAC) to construct its emission allowance demand function. The electricity sector‟s allowances demand function is derived in this model, since firms choose buying or selling the allowances in response to output decisions. As for the non-electricity sector, it is assumed that this sector will play as a price taker (i.e. a competitive fringe) in the emission market. This assumption allows the clearing emission price to be independent of different allocation methods for the non-electricity sectors. Therefore, the residual supply curve is built up by subtracting the non-electricity sector‟s demand from the total supply curve, subject to the emission cap by government (see equations 2.10~12).

Fifthly, we do not model early closures of power plants, for the sake of simplicity. To my best knowledge, there have been no attempts to model decisions for investment and possible closure at the same time in the electricity market studies due to technical difficulties.

Thus, this study simply reflects the plan for closing old power plants by exogenous modelling.

Note that the allocation rules could also affect firms‟ behaviour over closures, as studies such as Neuhoff el al., 2006a and Å hman et al., 2007 point out.

Lastly, the model assumes that relative fuel prices in 2013 will be maintained during the planning horizons in this study. This assumption can be justified by the following two

reasons; firstly, the prices of uranium for nuclear and coal have been stable compared to the prices of LNG and heavy-oil mainly due to relatively abundant reserves. However, LNG and heavy oil prices have been volatile, it is possible, given tight oil and shale gas, that they could be lower over the next decades than they are now, or higher because of rising energy demand.

Assuming a constant level is a compromise between these. Secondly, there is already a big gap between the marginal costs of each technology (Nuclear<Coal<CCGT) in Korea because of their fuel prices and relatively similar efficiencies of power plant (CCGT has the highest one). In particular, Korea imports natural gas as liquefied natural gas, so that the marginal cost of a CCGT is approximately 3.4 times higher than the coal fired plant, which means that reasonable fuel price scenarios without extreme cases do not change the merit order system (output of each technology) in the Korean electricity market and hence the main simulation results. In other words, while the absolute level of electricity prices will depend on these fuel prices, the overall merit order will be insensitive to plausible assumption.