An Electricity Market Model with Intermittent Power

Hannesson, Rögnvaldur

doi:10.3390/en18061435

Open AccessArticle

An Electricity Market Model with Intermittent Power

by

Rögnvaldur Hannesson

Norwegian School of Economics, Helleveien 30, N-5045 Bergen, Norway

Energies 2025, 18(6), 1435; https://doi.org/10.3390/en18061435

Submission received: 28 January 2025 / Revised: 13 February 2025 / Accepted: 6 March 2025 / Published: 14 March 2025

(This article belongs to the Special Issue Energy and Environmental Economics for a Sustainable Future)

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Abstract

:

A competitive electricity market model is used to analyze the effects of replacing conventional base load power with an intermittent power supply. The model is a conceptual one and uses linear demand curves with a triangular probability distribution. In a base reference case, there are two types of providers of electricity, base load providers and peak load providers, each with a constant marginal cost. Prices are determined by the highest marginal cost of the active providers or by what the market can bear. The production capacity of each type of provider is determined by rents being equal to fixed costs. This reference case is compared to a case where base load providers have been replaced by intermittent solar and wind energy, with peak load providers still active. Despite lower costs, intermittent power is likely to result in higher and more volatile prices of electricity. Lower electricity prices could result if conventional baseload power is sufficiently expensive. The implications of changes in the availability of intermittent power are also analyzed.

Keywords:

electricity; green energy; power markets; intermittent power

1. Introduction

The ongoing transition to intermittent renewable energy (solar and wind) poses many challenges. The distribution of power produced by solar and wind installations is more costly than from traditional power plants because they are often located in remote areas and more widely spread in space, particularly wind turbines [1]. Wind farm installations are expensive, and their costs are uncertain, especially offshore ones [2]. Then, there are technical challenges such as grid stabilization to avoid blackouts [3,4,5]. Finally, there is, in some countries at least, considerable opposition to solar and wind power installations because of their impacts on nature, including the habitat of wildlife and plants.

The transition to intermittent energy has not gone unnoticed in the academic literature on energy. Over the last 20 years or so, a deluge of articles has been published on this issue. The main focus has been on the effects on prices in the short term. Most papers have found increased price volatility (e.g., [6]), and some have found a difference between solar and wind power in this regard, with solar power sometimes reducing price volatility rather than the opposite [7,8]. Wholesale prices have been found to fall as a result of solar and wind power production with negligible operating costs (e.g., [8]). That, however, raises the question of how to pay for the fixed costs of these types of energy and, no less, how to pay for the fixed costs of the power providers who must be on hand to replace solar and wind power when those sources do not provide enough because of the weather or lack of sunshine.

The purpose of this paper is to provide a conceptual long-term analysis of a market-based energy system relying on solar and wind power that has replaced the traditional base load (coal and nuclear). In a market-based system, the price will be set either by the marginal cost of the most expensive power supply in use or by matching demand to the available supply. In a long-term equilibrium, different types of supply will have to earn rents that cover their fixed costs. Hence, the question arises as to what capacity will emerge and what the prices that cover the fixed costs of this capacity will be. As will be shown, electricity prices in a system where solar and wind have replaced traditional base load are likely to be higher and more volatile, even if both their operating costs and fixed costs are lower than the costs of traditional base load suppliers. This may sound paradoxical, but the reason is quite simply the need to have a double system, as it were, with traditional peak load supply backing up the intermittent supplies of wind and solar.

To analyze this problem, a simple conceptual model of an electricity market with and without intermittent power is developed. Two scenarios are compared: (i) a market with traditional base load and peak load power supply, and (ii) a market where traditional base load power supply has been abandoned and replaced with intermittent power supply, backed up by traditional peak load power plants. This scenario is not entirely unlike what has happened in some countries, Germany and the UK in particular, where nuclear power (Germany) and coal power plants (UK) that used to supply the base load have been taken out of use and replaced with solar and wind power.

The market is assumed to be competitive, consisting of many enough firms within each type of technology to compete to bring the price down to marginal cost as long as the total capacity of each technology is not fully used. Capacity is modeled as the outcome of competitive investment; as long as te rents collected by each technology are higher than the cost of capacity, it will be expanded. Hence, price and production are outcomes of a perfectly competitive market. This is a well-established modeling framework for traditional power sources (see, for example, [9]). This paper extends this framework to also include intermittent energy.

The model is conceptual, but nevertheless, numerical results are presented. These numbers are for clearer display of the results only; the model parameters are not based on any particular electricity market. They are nevertheless based on known qualitative differences such as one type of technology having a lower operating cost than another and a higher fixed cost. Low elasticity of demand also constrains some parameters.

2. A Base Case with a Traditional Power Supply

The demand for electricity varies over the day and over the year. Let that variability be represented by demand curves distributed between the lowest and the highest outcomes. Figure 1 shows one such case with linear demand functions, the thick downward-sloping lines showing the limits of possible demand. The intersections with the x-axis show the hypothetical demand at a price of zero, which follows from the simplifying assumption of a linear demand. The demand is specified as

p = a (x - Q)

where p is the price, a is a constant, x is the point of intersection with the x-axis, and Q is the quantity demanded and produced.

The demand units are normalized so that the maximum demand at a price of zero is equal to 1. Minimum demand is set at 20 percent of maximum demand at any given price. The price units are normalized such that the price of 1 is thought of as slightly above the unit operating cost of the most expensive production units.

There are two types of units of production. One type has a low operating cost per unit produced (c₁) and a high fixed cost (K₁) per unit of capacity, and the other has a high operating cost per unit produced (c₂ > c₁) and a low fixed cost (K₂ < K₁) per unit of capacity. The market is assumed to be perfectly competitive so that the price will be equal to c₁ if there is insufficient demand to use all the capacity of the first type, versus c₁ < p ≤ c₂ if the demand is higher but less than the total capacity of both types. This is illustrated in Figure 1 with the two horizontal lines, one with p = c₁ up to the capacity of Type 1, and the other with p = c₂ up to the total capacity of both types. Between lines c₁ and c_2, there is an interval where there is no competition between Type 1 units, and they will charge what the market will bear, with demand still less than would support a price equal to the unit cost of Type 2 units. Once demand exceeds that level, the price will stay at c₂ because of competition between Type 2 units until their capacity is fully used. For details, see Appendix A.

When demand exceeds the total capacity of both types, competition among the Type 2 units ceases, and the price will be bid up to what the market will bear. In Figure 1, that price will be somewhere along the vertical line starting at the end of the c₂-line. Its upper limit will be where the vertical line hits the line of highest possible demand in the market.

Equilibrium in the market will be obtained when both types of production units earn enough rents to pay for the fixed cost of capacity. Type 1 units earn no rent unless demand exceeds their full capacity. There are three different price regimes to consider in which Type 1 units will earn rents: (i) demand exceeds the capacity of Type 1 units but is less than supports a price equal to the unit cost of Type 2 units, with the price being somewhere in the interval between c₁ and c₂, depending on demand; (ii) the price stays at c₂ because of competition among the Type 2 units; and (iii) the price is somewhere along the vertical line where the capacity of Type 2 units is fully used. Thus, the rent per unit earned by Type 1 units will be

E R_{1} = (E p_{1}^{*} - c_{1}) [F (x_{2}) - F (x_{1})] + (c_{2} - c_{1}) [F (x_{3}) - F (x_{2})] + (E p_{2}^{*} - c_{1}) [1 - F (x_{3})]

where Ep₁* is the expected market price when Type 1 units are fully used but demand is insufficient to support a price equal to c₂, Ep₂* is the expected price earned in the market where Type 2 units are used at full capacity, and F(x) is the probability distribution function of the demand functions, measured at their points of intersection with the x-axis. For details, see Appendix A.

Type 2 units earn no rent unless demand outstrips their capacity, which happens at the point where the c₂-line hits a demand line, as shown in Figure 1. The expected rent per unit earned by Type 2 units will be

E R_{2} = (E p_{2}^{*} - c_{2}) [1 - F (x_{3})]

where x₃ is the point of intersection with the x-axis of the demand line at the end of the c₂-line. Ep₂* will lie closer to c₂ than to max p, the latter being the point where the vertical line hits the highest possible demand line and thus the highest price ever occurring in the market. This is so because demand beyond the average is less and less likely the higher it is. The expected price is marked with a short horizontal line (for details, see Appendix A). This price could be many times higher than the “normal” price in the market. Even if infrequent, such outcomes typically cause consternation among the general public and politicians. Capping such high prices will obviously cut into the rents necessary for the production units to pay their fixed costs and is often called the missing money problem.

Figure 1 shows the equilibrium solution for the parameterization in the first row in Table 1. The parameter a determines the steepness of the demand lines. The value of 30 implies that demand would change about ten percent if the price is reduced by half, or doubled, from the “normal” level of 1 (note that the elasticity of demand is not constant along a linear demand curve). This may be more than is usually the case; the elasticity of demand is typically estimated to be rather low [10]. The expected price when all capacity is fully used is 2.224, almost three times the operating cost of Type 2 facilities, but needed to pay for the fixed cost of these facilities. The maximum price that satisfies even the highest demand when all capacity is used (max p) is much higher, or 5.171, but lasts only for a very short time. The overall expected price in the first row is 0.6, well below the operating cost of Type 2 facilities, driven to such a low level by the low operating cost and large production of the base load facilities (Type 1).

The expected price in the second and third rows is 0.83. We shall return to these cases in the next section. Both of these cases have the same implication for covering the cost of the base load capacity (Type 1), one because the capacity cost increases by a given amount per unit of capacity (0.23 = 0.53 − 0.3), and the other because the rent per unit of production declines by the same amount. The implications for optimal capacity are different, however. The increase in capacity cost leads to a greater reduction in optimal capacity (from 0.605 to 0.302) than the increase in operating cost (from 0.605 to 0.349). The explanation for this is that any given change in operating cost has an expected value that is less than the same change in the unit cost of capacity. A rise of x in the unit operating cost will affect the ability to earn rents less than a rise of x in the unit cost of capacity will affect the need to earn rents, and hence, the effect on optimal capacity will be different. For a proof of this, see Appendix A.

3. The Effect of Intermittent Energy

Figure 2 shows the equilibrium situation in a market with two types of energy producers, producers of intermittent energy (solar and wind) and traditional peak load producers. The change compared with the case shown in Figure 1 is that the base load energy with a low operating cost has disappeared and been replaced by intermittent energy with zero operating cost. There are two situations to be taken into account and shown in the figure, (i) one where both intermittent energy and conventional energy are produced, and (ii) one where intermittent energy is not available and only traditional peak load producers are active. Figure 2 is based on the assumption that the intermittent energy is available only 30 percent of the time, so for the rest of the time, we are stuck with the traditional technology of high operating cost and low fixed cost. In this particular case, the high-cost plants earn no rent when the intermittent energy is available; they only earn rent when the intermittent energy is down. The intermittent energy earns no rent when they do not produce but must earn enough rent otherwise to pay for their fixed cost.

Table 2 shows the parameters and outcomes in this case. The line labeled “both” refers to the case when the intermittent energy is also active; the line labeled “one” refers to the case where only the traditional peak load producers are active. If the intermittent energy had as high a fixed cost as the base load it replaces, it would not earn enough rent to pay for these costs. In the solution shown in Figure 2, the fixed cost has been reduced to 0.2 to produce a meaningful solution. This accords with the fact that intermittent energy has been and still is supported with subsidies.

When the intermittent energy is not available, all the energy comes from the traditional peak load firms. This implies excess capacity of the peak load energy when the intermittent energy is also available, as shown by the dotted line in Figure 2 and the entry for EC₂ in Table 2. This excess capacity has to be paid for out of the rent earned when intermittent energy is not present and leads to high prices in those periods. The maximum price is 5.729 compared with 5.171 in the base case, the expected price when all capacity is fully utilized is 2.41 compared with 2.224 in the base case, and the overall expected price is 0.825 compared with 0.6 in the base case. The cost advantage of intermittent energy is more than eaten up by the costs of intermittency. This accords with the empirical observation that electricity prices are higher in countries with a high share of intermittent energy [11].

It is nevertheless possible that the transition to intermittent energy will lead to a lower expected price. This happens when the cost of traditional base load energy is sufficiently high, as in the two last rows of Table 1. These results were produced by raising the costs of base load energy sufficiently to produce virtually the same expected price as in the case of intermittent energy (Table 2). Hence, a sufficiently high cost of traditional base load energy being replaced by intermittent energy would lead to a lower expected price but greater volatility of prices. Whether or not intermittent energy would lead to lower expected price depends, of course, also on its reliability, to which we now turn.

The effects of varying the probability (s) that the intermittent energy will be available are shown in Table 3. The production of intermittent energy (q₁) increases with the probability of its availability, as it will earn higher and higher rents the more often it is available. The production capacity (q₂) for the traditional peak load production falls as s increases because it will earn rents less frequently. As a result, both the maximum price and the expected price increase when there is no intermittent energy and peak load capacity is fully utilized. The explanation is straightforward. When intermittent energy is available most of the time, the peak load firms seldom earn any rent on their capacity, which nevertheless is needed when intermittent energy is not available. The peak load prices must therefore be higher when intermittent energy is often available. The overall expected price will nevertheless be lower; more production of low-priced intermittent energy will outweigh less production of high-priced traditional energy. Hence, more reliable intermittent energy will result in lower but more volatile prices, and the maximum expected production (EmaxQ) will be greater. It may be noted that the expected price will be lower than in the base case with traditional base load energy when intermittent energy is available 70 percent of the time.

One can ask the counterfactual question: what would happen if intermittent energy were entirely costless? Table 4 provides an answer. Here, both the operating cost and the fixed cost of intermittent energy have been set to zero. The implication is that intermittent energy will satisfy the entire demand at a price of zero when it is available. Two cases for availability are considered, one with a 30 percent and one with a 70 percent probability of availability. The supply of peak load type energy will be less when the probability of intermittent energy is high because the peak load firms will earn rent less often. The overall expected price will be lower because free intermittent energy will be more often available, but prices will be more volatile, as the expected price when only peak load firms produce will be higher. This is, of course, necessary to compensate for the fact that peak-load firms will earn rent less often. Nevertheless, we end up with less electricity production in the cases where intermittent energy is not available: higher availability of costless intermittent energy leads to the paradoxical result of less energy production and more volatile prices.

Finally, what would be the implications of a still less price-sensitive demand? This primarily affects the expected price (Ep₂*) when all capacity is fully utilized and hence the volatility of prices, especially when intermittent energy is around and often available. The effects on total production and prices are small.

4. Conclusions

It is often argued that solar and wind power is cheap. Their operating costs are negligible, and their fixed costs have undoubtedly come down considerably over the last twenty years or so. Nevertheless, these energy sources are hampered by intermittency, with the consequence that their presumptive low costs do not automatically translate into low market prices at all times. To deal with this intermittency, other power sources that can be turned on and off at will must be in place to avoid unwanted shortfalls of electricity. This means greater capacity of peak load plants to compensate for solar and wind power plants when they are not available. At the same time, this full peak load capacity will be needed less often, which means that it will earn rent less often. To compensate for that, peak load prices must be higher. Hence, even if intermittent power is cheaper than traditional base load power, it is likely to lead to higher prices of electricity overall and more volatile prices in particular, as occasionally higher prices than otherwise are needed to produce the rent needed to finance the peak load power plants. A sufficiently high cost of traditional base load energy being replaced by low-cost intermittent energy could, however, lead to lower expected prices.

So what has happened in countries that have gone far in replacing traditional base load energy with intermittent solar and wind energy? Figure 3 shows a plot of electricity prices for households in OECD countries versus the share of solar and wind in the production of electricity. Clearly, the higher the share of solar and wind, the higher the price (the straight line is a regression line). The data are from 2019–2021; we omit later years because of the turbulence in European energy markets in the wake of the war in Ukraine. Korea and Turkey are the countries with lowest prices, with the US not much higher, with Denmark, Germany, and Belgium on top.

Figure 4 shows how the prices of electricity have developed since 1990 in Germany and the United Kingdom, two countries mentioned specifically in this paper, which in 2019–2021 received about one-third of their electricity from solar and wind. Prices fell until the transition to solar and wind energy took off in the early 2000s but increased steadily after that, becoming stabilized in Germany after 2013. It is still too early to tell what will happen to peak load capacity in the long term; there are still many traditional peak load (mainly gas turbines) facilities remaining that have paid off at least a good part of their fixed costs, but to what extent will they be renewed? Only time will tell.

Funding

This research receveid no external funding.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author(s).

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

It is well known that extremely low and extremely high levels of electricity demand are much less likely than intermediate demand levels. We assume that the probability density (f(x)), measured along the x-axis at zero price demand, is triangular between the lowest

(\underline{x})

and highest

(\bar{x})

levels:

f (x) = b (x - \underline{x}) for \underline{x} \leq x \leq \frac{1}{2} (\underline{x} + \bar{x})

f (x) = b (\bar{x} - x) for \frac{1}{2} (\underline{x} + \bar{x}) \leq x \leq \bar{x}

Integration gives

F (x) = \frac{b}{2} {(x - \underline{x})}^{2} for \underline{x} \leq x \leq \frac{1}{2} (\underline{x} + \bar{x})

F (x) = \frac{b}{2} [\frac{1}{2} {(\bar{x} - \underline{x})}^{2} - {(\bar{x} - x)}^{2}] for \frac{1}{2} (\underline{x} + \bar{x}) \leq x \leq \bar{x}

Sin ce F (\bar{x}) = 1 we get b = \frac{4}{{(\bar{x} - \underline{x})}^{2}}

The expected price (Ep^*) when demand outstrips Type 1 capacity but is insufficient to support p = c₂.

We denote the points of intersection of the demand lines at the right end of the c₁-line versus the left end of the c₂-line by x₁ and x₂ (see Figure 1). We find Ep^* in this interval by summing all prices along the straight line connecting the lines c₁ and c₂ in Figure 1 and weighting each price with its probability:

E p^{*} = \int_{x_{1}}^{x_{2}} p (x) \frac{f (x)}{F (x_{2}) - F (x_{1})} d x = \frac{a}{F (x_{2}) - F (x_{1})} \int_{x_{1}}^{x_{2}} (x - Q) f (x) d x

using the demand function in the text (here, Q = q₁). We divide by F(x₂) − F(x₁) because all the weights must sum to 1.

Using the above results for f(x):

If \frac{1}{2} (\underline{x} + \bar{x}) \leq x_{1} < x_{2} < \bar{x}, E p = \frac{a b}{F (x_{2}) - F (x_{1})} [\frac{1}{3} (x_{1}^{3} - x_{2}^{3}) + \frac{1}{2} (Q + \bar{x}) (x_{2}^{2} - x_{1}^{2}) + Q \bar{x} (x_{1} - x_{2})]

If \underline{x} < x_{1} \leq \frac{1}{2} (\underline{x} + \bar{x}) < x_{2}

E p = \frac{a b}{F (x_{2}) - F (x_{1})} [\begin{array}{l} \frac{1}{3} \{{[\frac{1}{2} (\underline{x} + \bar{x})]}^{3} - x_{1}^{3}\} + \frac{1}{2} (Q + \underline{x}) \{x_{1}^{2} - {[\frac{1}{2} (\underline{x} + \bar{x})]}^{2}\} + Q \underline{x} [\frac{1}{2} (\underline{x} + \bar{x}) - x_{1}] \\ + \frac{1}{3} \{{[\frac{1}{2} (\bar{x} + \underline{x})]}^{3} - x_{2}^{3}\} + \frac{1}{2} (Q + \bar{x}) \{x_{2}^{2} - {[\frac{1}{2} (\underline{x} + \bar{x})]}^{2}\} + Q \bar{x} [\frac{1}{2} (\underline{x} - \bar{x}) - x_{2}] \end{array}]

If \underline{x} < x_{1} < x_{2} \leq \frac{1}{2} (\underline{x} + \bar{x}), E p = \frac{a b}{F (x_{2}) - F (x_{1})} [\frac{1}{3} (x_{2}^{3} - x_{1}^{3}) + \frac{1}{2} (Q + \underline{x}) (x_{1}^{2} - x_{2}^{2}) + Q \underline{x} (x_{2} - x_{1})]

For the expected price when all capacity is fully used, note that in this case, Q = q₁ + q₂,

x_{2} = \bar{x}

, and F(x₂) = 1.

Rents

Expected rents per unit capacity of Type 1 and Type 2 units (ER₁ and ER₂):

1. Base case

E R_{1} = [E p^{*} (q_{1}) - c_{1}] [F (x_{2}) - F (x_{1})] + (c_{2} - c_{1}) [F (x_{3}) - F (x_{2})] + [E p^{*} (q_{1} + q_{2}) - c_{1}] [1 - F (x_{3})]

x_{1} = q_{1} + c_{1} / a, x_{2} = q_{1} + c_{2} / a, x_{3} = q_{1} + q_{2} + c_{2} / a

E R_{2} = (E p^{*} (q_{1} + q_{2}) - c_{2}) [1 - F (x_{3})]

2. Case with intermittent energy

Here, Type 1 is intermittent energy.

s = probability of intermittent energy delivering

Superscript r denotes intermittent energy delivery, superscript n denotes the absence of intermittent energy.

E R_{1} = s \{(E p^{*} (q_{1}) - c_{1}) F (x_{1}^{r}) + (c_{2} - c_{1}) [F (x_{2}^{r}) - F (x_{1}^{r})] + [E p^{*} (q_{1} + q_{2}^{r}) - c_{1}] [1 - F (x_{3}^{r})]\}

E R_{2} = s (E p^{*} (q_{1} + q_{2}^{r}) - c_{2}) [1 - F (x_{3}^{r})] + (1 - s) (E p^{*} (q_{2}^{n}) - c_{2}) [1 - F (x_{3}^{n})]

In the cases reported in the main text,

F (x_{3}^{r}) = 1

The equilibrium solution is obtained when ER₁ = K₁ and ER₂ = K₂.

The effect of a change in unit cost of capacity versus unit operating cost.

In equilibrium, the total cost of capacity is equal to the expected value of rents. We denote the probability that rents will be earned by π(q):

K q = π (q) [p - c] q

\frac{d q}{d K} = \frac{1}{(p - c) π^{'} (q)} < 0, π^{'} (q) < 0

\frac{d q}{d c} = \frac{π (q)}{(p - c) π^{'} (q)} < 0

|\frac{d q}{d K}| > |\frac{d q}{d c}|

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Figure 1. Equilibrium in a market with two types of traditional electricity suppliers.

Figure 2. Equilibrium in a market with traditional and intermittent energy. Upper level: Both energy types deliver. Lower level: Only traditional energy is active.

Figure 3. Price of electricity for households 2019–2021 in OECD countries versus the share of wind and solar in electricity production (source: OECD).

Figure 4. Electricity prices for households versus share of solar and wind in electricity production in Germany and the United Kingdom (Source: OECD).

Table 1. Parameters and outcomes for three cases without intermittent energy.

a	c₁	c₂	K₁	K₂	q₁	q₂	Max p	Ep₂*	Ep
30	0.3	0.75	0.3	0.1	0.605	0.222	5.171	2.224	0.6
30	0.3	0.75	0.53	0.1	0.302	0.526	5.171	2.224	0.83
30	0.53	0.75	0.3	0.1	0.349	0.478	5.171	2.224	0.83

Table 2. Parameters and outcomes for a case with intermittent energy available 30 percent of the time.

	c₁	c₂	K₁	K₂	q₁	q₂	Max p	Ep₂*	Ep	EC₂
Both	0	0.75	0.2	0.1	0.376	0.599	0.75	0.75	0.825	0.210
One	0	0.75	0.2	0.1	0	0.809	5.729	2.410	0.825	0.210

Table 3. How outcomes vary as the probability of availability of intermittent energy varies. Note that q₂ refers to the production capacity of Type 2 energy firms. Parameters are the same as in Table 2.

s	q₁	q₂	EC₂	max p	Ep₂*	Ep	EmaxQ
0.3	0.376	0.809	0.210	5.729	2.410	0.825	0.859
0.5	0.574	0.789	0.388	6.320	2.607	0.665	0.882
0.7	0.638	0.755	0.418	7.354	2.951	0.525	0.909

Table 4. How outcomes vary with the availability of costless intermittent energy. Other parameters are the same as in Table 2.

s	q₁	q₂	max p	Ep₂*	Ep
0.3	1	0.809	5.729	2.410	0.625
0.7	1	0.755	7.361	2.954	0.325

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APA Style

Hannesson, R. (2025). An Electricity Market Model with Intermittent Power. Energies, 18(6), 1435. https://doi.org/10.3390/en18061435

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An Electricity Market Model with Intermittent Power

Abstract

1. Introduction

2. A Base Case with a Traditional Power Supply

3. The Effect of Intermittent Energy

4. Conclusions

Funding

Data Availability Statement

Conflicts of Interest

Appendix A

References

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