Exploring the competition between variable renewable electricity and a carbon-neutral baseload technology

We assume an ideal electricity market in the sense that neither producers nor consumers make strategic bids to affect the market price. Power plants are dispatched according to the merit order (i.e., according to marginal cost of production) and each hour a price is determined that clears the market. We model demand as iso-elastic, so that the relation between the delivered and consumed power \(q_\tau \) and corresponding price \(p_\tau \) in time slice \(\tau \) iswhere \(\epsilon \) is the short term price elasticity of demand and \(p_0\) is a constant. We use elasticity \(\epsilon =-0.05\) and \(p_0 = 3.25\) cent/kWh. The “demand reference level” \(q_{0,\tau }\) is a parameter that shifts the demand curve in each time slice reflecting the variations of demand over seasons and times of day. In this version of the study we utilize German hourly demand levels from year 2011 as a proxy for \(q_{0,\tau }\). This is a simplification, since a low (high) demand level in a certain hour may have been the result of a high (low) price in that hour, rather than a change in consumer preferences.

In each year the power system is characterized by the installed capacity of the different power technologies together with the age profile of the plants. For each time slice the model finds the price that clears the market, i.e., the price at when demand equals supply. The last dispatched plant may operate at a fraction of its full capacity. In this model, the plants with the highest variable operating cost must rely on hours of scarcity to make sufficient revenues to pay back the investment costs. In reality plant owners may use market power to affect prices even during hours when demand is below total capacity, if the excess capacity is sufficiently small [18]. This option is not allowed here.

The year is divided into time slices where each slice \(\tau \) is characterized by demand reference level \(q_{0,\tau }\), wind power output and solar power output as the shares of installed capacity. Appendix A describes the time slicing further. In this study we let the time slicing representation of the year be constant over the modeling horizon (i.e., no change in demand reference level or solar and wind patterns from one year to another). We ignore any operational considerations such as minimum up and down times, ramp rates and part-load performance, which allows us to disregard any chronology within a year. (Costs associated to start-ups and shutdowns are also ignored.) Finally we disregard must-run requirements of conventional power plants necessary for grid services like voltage stabilization etc.

We assume that plants start to operate the year after the investment decision is made and the investment cost is paid. Each plant produces electricity whenever the electricity price is higher than or equal to the variable operating cost. The model starts at time \(t=0\) with an equilibrium capacity of power plants, given a carbon tax of 0 $/\(\hbox {tCO}_2\), and with a uniform distribution of remaining plant lifetimes.

Investment decisions are made as follows. Each year the agents form expectations about future installed capacity, the future demand and the future carbon tax. Based on these expectations the agents calculate the future electricity price if a new investment were to be made in each type of power plant. The predicted electricity price is then used to assess the net present value (NPV) of each investment option. In this study we let agents use a discount rate of 8%/year. This rate is chosen to represent the long term return on capital corrected for risk that an agent investing in power plants would typically assume. In the power market each plant type has its own risk profile that is also strongly affected by the overall capacity mix of the market [19]. The discount rate used typically also varies with type of investor and country. See e.g. [20, 21] for more details. For simplicity we assume that all actors have the same discount rate for all investment options.

We assume that agents (companies) are profit maximizers and that in order to achieve that goal, they rank projects based on their profitability index (PI),¹ i.e., the NPV of future net revenues divided by the investment cost. In addition, since some types of power plants have significantly longer life times than others, we have corrected for this by looking at the expected annuitized net revenues (per euro invested), i.e., the highestwhereis the capital recovery factor, T is the lifetime of the project and r is the discount rate.²

We assume in this model that agents know how much installed capacity there is of each power plant type, which plants will be decommissioned during the year, and how many new plants that currently are being invested in by other agents. Agents also know the carbon tax and the level of demand for the following year. Agents therefore have relatively detailed information about the conditions of the power system the following year, but no additional knowledge beyond that. For this study, agents assume that the conditions of the following year will hold into the future.

We have implemented the model in the following way. In a given year agents are first randomly selected to make investments in new power plants, which they do if there are plants that they expect to be profitable. Information about the investment is made public to the other agents, which means that subsequent investment decisions take into account previous decisions in the same year. When no more agents want to invest, power plants that have reached the end of their lifetimes are decommissioned one at a time. The agents assume that the plants that have not yet been decommissioned will continue to operate in the following year. After each decommissioning the agents make a new prediction and invest in new power capacity if they want to. Plants start to produce electricity at the beginning of the following year. The chosen implementation guarantees that the agents make a correct estimation of future prices as long as the model remains in a steady state over time.

Different types of power plants generally differ in size. For instance, nuclear power plants typically have higher capacity than wind power parks. At the same time not all power plants of the same type are equally large. A 1000 MW nuclear power plant may have a positive NPV while a 1100 MW plant is assessed to be unprofitable. In this implementation we let agents invest in power plant modules of just 50 MW at a time, in order to not disfavor technologies with large plant sizes and to limit the effect that each investment has on prices. The resulting total investments, after a year of accumulated decisions, typically correspond to plants larger than the module value.

In this first study agents do not take their existing portfolios into account when making an investment. They only consider the new investment opportunity in isolation. They are also homogeneous in their strategies. This means that the exact number of agents is insignificant for our analysis. If any new power plant is expected to be profitable, one of the agents will make the investment. Agents are not allowed to change their minds once an investment decision is taken.

The ABM will be compared with an optimization approach that finds the optimal path of investments assuming full information of all aspects of the system for the full time period. The optimization model is a standard non-linear optimization based on maximization of total surplus of consumers and producers, thus reflecting a market equilibrium solution of the transition without uncertainty. The details of the optimization model implementation is presented in Appendix B. The optimization model represents the same stylized power system, and with the same supply and demand characteristics, as the ABM. If the same discount rate is used the two models find the same steady state.

Five types of power plants are included: coal-fired power plants, natural gas fired plants, solar photovoltaic (PV) systems, wind power plants and a generic carbon-neutral baseload technology (CN-Baseload). Each type of power plant is characterized by an investment cost, a variable operating cost, a CO\(_2\) emission intensity and a fixed plant lifetime (see Table 1). The model is initiated with a fleet of power plants corresponding to the equilibrium capacity in our system without a carbon tax. The model is run with a pre-defined carbon tax trajectory (see Fig. 1) where a carbon tax is introduced after 10 years starting at 0 €/ton CO\(_2\) and increasing linearly up to 100 €/ton CO\(_2\) in year 50. The tax remains at that level until year 70. In the EU there is already a price on CO\(_2\) emissions, but it is low. Given the current high supply of emission rights, it may take a decade before the price of CO\(_2\) emissions increases.

The aim of this paper is to explore how VRE and a carbon-free baseload power technology compete in the transition to a low-carbon power system. Figure 2 shows the installed capacity over time and the annual electricity generation in our model. The first years, when there is no carbon tax, our power system is dominated by coal-fired power plants and complemented with a small amount of gas as peak capacity. When the carbon tax is introduced both VRE and CN-Baseload gain a relative advantage compared to coal fired plants, and compete with each other for room in the energy mix as the tax continuously increases. Wind power is the first carbon-neutral technology that is introduced after the adoption of the carbon tax. As the carbon tax continues to increase CN-Baseload and solar PV eventually start growing while wind declines. This happens despite the fact that CN-Baseload has a higher LCOE than wind. At the end of the model run also the installed capacity of solar PV declines. When the carbon tax stabilizes the installed capacity of the different technologies eventually reach their steady state levels.

The capacity factors of CN-Baseload, coal and gas are shown in Fig. 3. CN-Baseload has a low variable operating cost and appears early in the merit order. Its capacity factor is always high, in the range of 82–95%. In this model we let demand be elastic and we have no curtailment of VREs. The capacity factors of solar PV and wind therefore lie at constant levels over the years, at 32% and 12%, respectively.

For gas and coal the story is different. In year 30 we can see a sudden dramatic increase in the electricity generation of gas. This technology starts out as peak capacity running only a few hundred hours per year but then increases its capacity factor to around 80%. At the same time coal decreases its electricity generation. The reason is that coal and gas switch places in the merit order when the tax is sufficiently large. From year 30 the capacity factors of both coal and gas decrease continuously as the carbon tax grows. The reason is the expansion of VREs and CN-Baseload that appear first in the merit order.

Figure 4 shows the development of the electricity price over time. The average yearly electricity price increases when the carbon tax is introduced (see Fig. 4a). The reason is that the carbon tax increases the variable operating costs of coal and gas, which raises the electricity price during the hours when these power sources set the electricity price. It should be noted that the electricity price does not increase in line with the carbon tax after a few decades. The higher cost for fossil power leads to an increasing share of VRE and CN-Baseload in the electricity system, and the cost of these technologies does not increase with the carbon tax, i.e., the price increase expected from the increase in the carbon tax is mitigated by the increasing use of VRE and CN-Baseload. We also have a shift towards more hours with gas on the margin instead of coal. Since the former technology is less carbon intensive than the latter, the average electricity price becomes less affected by the carbon tax.

Figure 4b shows the average revenues received by CN-Baseload, solar PV and wind. We note that the average revenues differ by technology. This is explained by the fact that different technologies generate electricity at different points in time and that the electricity price varies over time. In particular we note that the average revenues per kWh received by wind power remain at a comparatively low level even as the average electricity price rises. This can be explained in the following way. Agents in the model invest in wind (or any technology) as long as there is profit to be made, i.e., the net present value of all revenues exceed total costs including the investment costs. This means that if the average revenue received per kWh of electricity sold by the wind operators is higher than the LCOE for wind power, agents will invest in more wind since there is profit to be made. When that is done, the average revenue drops since the price of electricity will drop the more wind there is in the market. Investments in wind will stop when the average revenue drops below the LCOE for wind. Thus, for that reason the average price of electricity received by wind operators will hoover close to the LCOE of wind. The reason for the drop in the revenues received (during the years 30–45) has to do with transient non-equilibrium phenomena due to limited foresight of the agents. The same reasoning applies to solar PV and other technologies.

How does limited foresight affect the competition between VRE and a carbon-neutral baseload technology such as nuclear? To answer that question we compare what happens in the ABM with our optimization model of the same electricity system.

In Fig. 5 we show the installed capacities of CN-Baseload, wind power and solar PV in the ABM and the optimization model when both models have the same discount rate of 8%/year. The installed capacity of wind is lower in the ABM than in the optimal solution during the first years after the carbon tax is introduced. Between years 25 and 50 this relationship is reversed. Both of these observations can be explained by the agents’ limited foresight. In the first years the agents are ignorant of the increase in the carbon tax which means that they underinvest in wind power. In the later years they fail to anticipate the subsequent introduction of CN-Baseload in the power system and therefore over-invest in wind.

The installed capacity of CN-Baseload is lower in the ABM than in the optimization model in the transient phase. Due to the over expansion of wind power from year 25 there is less room for CN-Baseload to expand profitably in the ABM (prices become depressed). We also note that the ABM invests more in solar PV in years 35-40 than what is given by the optimal solution. Less installed capacity of CN-Baseload makes it possible for solar PV to expand more. At the end of the model run when the carbon tax has stabilized, the two models eventually find the same steady state.

Figure 6 shows the ex-post profitability index of the ABM as a function of the year the investments are made, calculated with a discount rate of 8%/year. We can see that the profitability index of wind ends up well below zero during most of the model run, except in the final years. We note that even though the installed capacity of wind is lower than the optimal solution in years 15–20, the profitability index is still negative during these years. The reason is the subsequent over-investment in wind power, which reduces the revenues also for the wind power plants that were built earlier. In summary, the over-investment of wind (compared to the optimal solution) reduces the competitiveness of CN-Baseload, but also decreases its own profits by expanding “too much”.

Figure 7 shows the CO\(_2\) emission trajectory for three model runs (an ABM run with a discount rate of 8%/year and two runs with the optimization model, one with a discount rate of 4%/year and one with a discount rate of 8%/year). We can see that the emissions are slightly higher in the ABM than in the optimization model with r = 8%/year (i.e., for the same discount rate). The reason for this is that the carbon-neutral technologies are introduced earlier in the optimization model than in the ABM since there is perfect foresight in the optimization model which means that the ever increasing carbon tax is taken into account in the investment decision in the model. Between years 10 and 35 there is also more gas in the former model than in the latter. It is also interesting to compare with the optimization model with a discount rate of only 4%/year (Opt4). In this case the annual emissions are significantly lower, since the lower discount rate tends to benefit technologies with a higher investment cost (like solar, wind and nuclear). Since optimization models typically use the risk free social rate of discount (which is lower than private discount rates) they likely overestimate the CO\(_2\) reduction that would take place in the real world as a consequence of a carbon tax. Although the mechanism behind this is well understood this (likely) underestimation of the required carbon tax is rarely pointed out when results from optimization models are presented. Two recent exception are Iyer et al. [26] and Hirth and Steckel [27].

Both the ABM and the optimization model describe the development of a power system over time as it undergoes a transition. The models are generally not in steady state in any particular time step, except in the initial and final years when all costs are constant over time. In Appendix C we estimate the steady state capacities for each tax level for comparison.

It is interesting to note that the installed capacity of wind first increases with a carbon tax and then decreases. The basic mechanism behind this can be explained in the following way. In Fig. 13 we display the levelized cost of generating electricity (LCOE) over time for the main technologies in this analysis (with data from Table 1).

Initially, when the carbon tax is zero or very low, coal is the most competitive technology (see Fig. 13) and the electricity system is also dominated by coal. As the carbon tax increases, coal becomes more expensive and by the year 15–20, wind is beating coal (with this measure). In Fig. 2a we see that wind starts to expand rapidly behind this point in time

However, with the carbon tax level that is reached around the year 30, coal also becomes more expensive than CN-Baseload. This means that there will be no more investment in coal, because coal is beaten by both wind and CN-Baseload. We can thus see in Fig. 2a that CN-Baseload increases over the period 30-55.

In an electricity system, there is demand for electricity all the time, but wind is an intermittent technology. Wind without storage (or a lot of trade with other regions) cannot meet demand at all points in time so market incentives will trigger investments in dispatchable technologies. In our model investments will be made in CN-Baseload when the carbon tax is sufficiently high. Once CN-Baseload is expanded, it is cheaper to run those plants than to build wind power plants, i.e., the variable operating cost of CN-Baseload is lower than the LCOE of wind. For that reason, CN-Baseload takes most of the market once the carbon tax makes coal (and gas) too expensive.

Finally, our results and analysis illustrate that LCOE is sometimes a poor measure of comparing the competitiveness of electricity generating technologies. The reason for this is that LCOE only refers to the cost of generating the electricity and disregards from the revenues. For technologies that generate electricity at the same time, this is not a problem since their average revenues will be the same. Under these circumstances LCOE is useful as seen here in our analysis of what happens in our ABM when CN-Baseload starts to compete with coal. But for wind, and in particular solar, the average revenues may differ substantially from the average price of electricity, in particular when large amounts of wind and solar are put in place in the electricity system. Under these conditions, LCOE is not a good measure of the competitiveness of the different technologies. We see here in our model analysis that investments are made in CN-Baseload despite the fact that its LCOE is higher than that of wind (and solar).

So far, we have explained why CN-Baseload expands at the expense of wind despite the fact that it is (according to LCOE) a more costly technology than wind. Now, we also need to explain why wind takes a larger share of the electricity market around the years 25–30 than around the year 50, i.e., when it competes primarily against coal than when its primary competitor is CN-Baseload.

This has to do with the fact that the variable operating cost for coal (with the carbon tax) is much higher than the variable operating cost of CN-Baseload and that the electricity price is set by the variable cost of the marginal power technology in the system. (The exception is when generating capacity is scarce and prices are pushed up even higher.) When there is a lot of coal in the market and the carbon tax is relatively high (e.g., years 25–30), wind is more competitive than when coal has been pushed out by CN-Baseload. For that reason the optimal level of wind drops once CN-Baseload enters the market (becomes competitive over coal and gas). However, if CN-Baseload is replaced by a different carbon-neutral dispatchable technology with a high variable operating cost (i.e., CN-Dispatchable in Sect. 4.4.3) wind may keep its competitiveness.

Thus, we can make the following more general observation. Assume that an intermittent technology like wind, competes in an electricity system with either a dispatchable technology A or a dispatchable technology B. Assume further that technologies A and B have the same ex ante estimated levelized cost of electricity (given a certain load factor) but that A has lower variable cost and higher investment cost than B (i.e., technology A could be nuclear and B could be a biogas fueled combined cycle power plant). Still, the resulting share of wind when allowed to compete against either of these technologies, will be higher or even much higher when competing against B than competing against A.

In Sect. 4.2 we show how the electricity price develops over time in our model. We find that the price rises as the carbon tax increases. It is interesting to compare this result with other empirical and modeling studies of how the expansion of VREs impacts the electricity price, e.g., [31‐39].

In these studies, the price of electricity drops with the expansion of VRE. It drops both on average and, more significantly, during the hours when wind and solar generates most of its electricity. The reason for this is that solar and wind have low (or close to zero) running costs and decrease the price through the merit order effect (see e.g. Hirth [40]). The studies cited here concern markets where wind and solar are introduced through a subsidy scheme. It is important to keep in mind that a lower electricity price does not necessarily imply lower total costs for the consumer since the subsidy is paid via a levy on top of the electricity price or by the government.

In our study we assume that there is no subsidy and that the only policy incentive to reduce emissions is the carbon tax. Under these conditions, there is a relative drop in the electricity price compared to the increase that otherwise would have been expected without VREs. However, there is no absolute drop in the electricity price as a result of the introduction of VRE as is the case in many countries today that introduce VRE through subsidy scheme. This distinction may be important to keep in mind.

In this paper we use our ABM to study the effect of limited foresight during the transition to a low-carbon power system. Limited foresight in energy systems models is not new, see e.g. [41‐44]. The motivation for such an assumption is, as often stated, to better simulate market behavior, in comparison with optimization models, and the decision environment under which decision makers must operate. In future work we intend to study different learning mechanisms and how they affect a transition of the power system.