A real options approach to generation capacity expansion in imperfectly competitive power markets

Abstract

This paper proposes a real options approach to generation capacity expansion in imperfectly competitive power markets. Our framework incorporates firms with different levels of market power; heterogeneous technologies, including renewables, base load and peak load; time-varying short-term demand and renewable supply; and long-term demand uncertainty. A real options model allows us to obtain technology-specific thresholds for demand to trigger investment. We apply our model to the German power market and show that a doubling of current demand triggers renewable investment, whereas base load generation requires over 50 times current demand on average. The availability of peak load generation serves to avoid rationing and reduce fluctuations in the electricity price. In the absence of incentive mechanisms, however, demand does not become sufficiently high to trigger investment in this technology. We investigate at which level capacity payments to peak power plants prevent rationing without reducing investments in renewables. Furthermore, by accounting for market power, we illustrate that strategic firms do not increase their market shares over time but hold back investment until market prices are sufficiently high for price-taking firms to expand capacity. As a result, the intensity of competition increases over time.

Appendices

Appendix A: Welfare gain

The welfare gain equals the expected discounted social welfare from the capacity expansions over an infinite time horizon, i.e.

$$\begin{aligned} {{\,\mathrm{{\mathbb {E}}}\,}}_0\bigg [\int _{0}^{\infty } \psi (Y_{t},K_{t}) \mathrm {e}^{- \rho t} \mathrm {d}t - \sum _{f\in \mathbf{F }} \sum _{k\in \mathbf{K }} \int _{0}^{\infty } I_{k} \mathrm {e}^{- \rho t} \mathrm {d}K_{t,f,k}\bigg ], \end{aligned}$$

(64)

where

$$\begin{aligned} \psi (Y,K)=&\sum _{h\in \mathbf{H }}d_{h}\Big (\int _0^{Q_{h}} P_h(Y_t,Q)\mathrm {d}Q -\sum _{f\in \mathbf{F }}\sum _{k\in \mathbf{K }}c_{k}q_{f,k,h}- c_r q_{r,h}\Big ) \end{aligned}$$

is the instantaneous social welfare, i.e. the sum of producer profits and consumer surplus, and $\{K_{t,f}:t\ge 0\}$ is the (approximate) optimal solution to (35).

Appendix B: Input parameters of the illustrative example

See Table 5.

Table 5 Cost data

See Tables 6, 7, 8.

Table 6 Initial installed capacity

Table 7 Parameters for demand shock process, discount rate and $\alpha _1$

Table 8 $Y_0^{\text {grid}}$ and $\gamma$

Appendix C: Input data case study Germany

All costs are given for the years 2017, 2020, 2030 and 2040. We use linear interpolation to determined costs between these years. After 2040, we assume all costs to be fixed at 2040 levels. Validation of data is outside the scope of this paper. See Table 9

Table 9 Investment costs [€/kW]

See Tables 10, 11, 12, 13, 14, 15, 16, 17, 18.

Table 10 Fixed operation and maintenance costs [€/kW]

Table 11 Marginal costs [€/MWh]

Table 12 $\text {CO}_2$-prices, gas prices, hard coal prices, lignite fuel costs and plant efficiencies

Table 13 Initial installed capacity [MW]

Table 14 Inelastic demand in the different time segments [MWh/h]

Table 15 Energy constrained technologies

Table 16 Technical lifetime and annual phase-out rate of different technologies

Table 17 Simulation parameters

Table 18 $Y_0^{\text {grid}}$ and $\gamma$

Appendix D: Determining the level of capacity payment

In implementing capacity payments, the reliability of supply is a major concern. Thus, we argue that capacity payments should be determined such that the level of installed peak load capacity, i.e. gas-fired power plant capacity, approximates the capacity found in Sect. 5.1. Table 19 presents the installed capacity of gas-fired power plants, the share of renewables in 2040, the aggregated rationing from 2017 to 2040 found in section 5.1 and the first paragraph of Section 5.3, i.e. when no capacity policies are implemented. Table 20 shows the effect of different capacity payment levels. We do not examine capacity payments above 31 000 €/MW, as these make OCGT power plants profitable even with sporadic operation.

See Tables 19, 20.

Table 19 Installed capacity of gas-fired power plants, renewable dispatch in 2040, and aggregated rationing from 2017 to 2040 under different capacity payment levels

Table 20 Installed capacity of gas-fired power plants, renewable dispatch in 2040, and aggregated rationing from 2017 to 2040 under different capacity payment levels

Table 20 shows that capacity payments for all types of gas-fired power plants result in high investments in gas-fired power plants at the expense of renewables. Moreover, we find that a capacity payment of 31 000 €/MW to OCGT power plants results in a small level of rationing and an installed capacity of gas-fired power plants close to that of the base case that includes minimization of rationing. We therefore argue for capacity payments of 31 000 €/MW to OCGT power plants.