This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
We address the valuation of an operating wind farm and the finitelived option to invest in it under different reward/support schemes: a constant feedin tariff, a premium on top of the electricity market price (either a fixed premium or a variable subsidy such as a renewable obligation certificate or ROC), and a transitory subsidy, among others. Futures contracts on electricity with ever longer maturities enable marketbased valuations to be undertaken. The model considers up to three sources of uncertainty: the electricity price, the level of wind generation, and the certificate (ROC) price where appropriate. When analytical solutions are lacking, we resort to a trinomial lattice combined with Monte Carlo simulation; we also use a twodimensional binomial lattice when uncertainty in the ROC price is considered. Our data set refers to the UK. The numerical results show the impact of several factors involved in the decision to invest: the subsidy per MWh generated, the initial lumpsum subsidy, the maturity of the investment option, and electricity price volatility. Different combinations of variables can help bring forward investments in wind generation. Oneoff policies, e.g., a transitory initial subsidy, seem to have a stronger effect than a fixed premium per MWh produced.
Smart grids in the EU are defined as “electricity networks that can intelligently integrate the behaviour and actions of all users connected to it—generators, consumers and those that do both—in order to efficiently deliver sustainable, economic and secure electricity supplies” [
Public support in turn is usually justified on three grounds: climate change, security of supply and industrial policy. Some of the positive effects of the development of renewables are global, e.g., the abatement of greenhouse gas emissions and the reduction of investment unit costs (because of the learning effect). The impacts of enhanced energy security and industrial policy are, instead, derived at national level. Government policies are also needed to align the market forces and accelerate the speed of adoption of the most promising cleaner energy technologies, so that they progress down the learning curve toward market competitiveness.
A number of electricity markets (in Europe and beyond) have been (or are being) liberalized. Among other things, the liberalization implies that it is private investors driven by profit maximization who make decisions about investments in power plants. In order to pave the way to broader deployment, a number of public support schemes have been put in place. These schemes can be divided in two major groups: (i) regulatory pricebased mechanisms (a payment for kWh of energy produced); and (ii) regulatory quantitybased mechanisms (the government sets a desired level of RESe and “green” generators receive tradable certificates according to their production). But, as Fagiani
Del Río and Tarancón [
Policy characteristics strongly affect the price risk and the quantity risk faced by an investor. However, their scope in mitigating other sources of technical risk [
Current support programmes typically rely on a combination of different measures such as special tax regimes, cash grants and financial incentives; an overview can be found in Daim
A suitable valuation approach for wind projects must not only account for intermittence and uncertainty: it must also take account of their irreversible character and the flexibility enjoyed by project managers (e.g., the option to delay investment). Under these circumstances, traditional valuation techniques based on discounted cash flows have been found inferior to contingent claims or real options analysis; Dixit and Pindyck [
Here we follow the real options approach (ROA) to address the present value of an investment in a wind farm and the optimal time to invest under a number of different payment settings [
We restrict ourselves to marketable attributes (e.g., the electricity output) and attributes which are nonmarketable
In our paper we take the energy and environmental policy as given. Private businesses assess their potential investments in RES under the prevailing rules of the game. Moreover, our sensitivity analyses enable the impact of both market changes and policy changes to be assessed. In short, the ROAbased value captures a crucial dimension (namely, the option to delay an irreversible investment in RES) in a decentralized, deregulated market setting; as such, it should be embodied in the total value of RES.
Following this approach, Adkins and Paxson [
Reuter
Here we address the present value of an investment in a wind farm and the optimal time to invest under a number of different payment settings. We too consider up to three sources of uncertainty, yet our paper differs from others in several respects. We assume more general stochastic processes for the state variables; in particular, we account for mean reversion in commodity prices. We develop a trinomial lattice that supports this behavior. We also make room for seasonal behavior in the price of electricity and in wind load factor. Indeed, they turn out to be correlated to some degree (according to market data and observed measurements), and we treat them as such; this has been typically overlooked elsewhere despite its impact on project value. The dynamics underlying the price of electricity are estimated from observed futures contracts with the longest maturities available (namely, up to five years into the future); this includes the market price of electricity price risk. The dynamics of the wind load factor are estimated from actual (monthly) time series alongside seasonality. The process governing the time path of the ROC price is determined from observed data. The riskless interest rate is taken from financial markets. Both the project's lifetime and the option's maturity are finite; in our simulations below, the size of the time step is not Δ
Here we assess the decision of whether to invest in a renewable energy project and if so when from the viewpoint of a private developer. Deregulation of power markets has gone hand in hand with increased competition between utilities and greater uncertainty for utilities. Under these circumstances, traditional discounted cash flow methods falter. Consequently, better valuation techniques are needed to deal with how energy investors assess their potential investments. This is true in general, but particularly so for RES projects, because if the option to delay an investment is valuable whenever the investment is irreversible, this value is set to increase for projects with: (i) uncertain output (because of natural variability, over and above market variability); (ii) steep learning curves (since these technologies are far from being mature); (iii) a modular structure (which allows for sequential deployment as the future unfolds); and (iv) short construction times (since this feature allows a quick reaction to new information)
A stochastic process displaying mean reversion fits our sample data better than a standard geometric Brownian motion (GBM); details of the formal test of the GBM hypothesis are available from the authors upon request. Thus we specify the longterm price of electricity in a riskneutral world [
The mathematical expectation (under the riskneutral probability measure
For a time arbitrarily far into the future (
The wind resource is highly variable, both geographically and temporally. Moreover, this variability persists over a wide range of scales, both in space and time; Burton
The energy available in the wind resource varies as the cube of the wind speed. A number of statistical distributions have been proposed for modelling observed wind speeds. For one, the Weibull distribution does a good job at representing the variation in hourly average wind speed over a year at many typical sites. The Rayleigh distribution is a special case of the former. These variations may also be subject to a strong underlying seasonal component. On shorter (than a season) timescales wind speed variations are somewhat more random and less predictable.
According to Morgan
The wind does not always blow at a given site; when it does, its quality may be inadequate for exploitation [
Power generation from wind stations shows a seasonal pattern. The deterministic term
This model is equivalent to a meanreverting process with seasonality when
Reuter
The UK government has committed to meeting a legally binding EU target of generating 15% of energy from renewable sources by the year 2020. The main financial mechanism for supporting largescale renewable generation is the Renewables Obligation (RO): this is a marketbased mechanism similar to a renewable portfolio standard. The RO places a mandatory requirement on electricity suppliers to source a proportion of electricity from renewable sources. The RO level increases every year (beginning on April 1 and running to March 30 each year); it started in 2002–2003 at 3% and will reach 15.8% in 2012–2013. Support is granted for 20 years. In April 2010, the RO end date was extended from 2027 to 2037 for new projects.
Renewables Obligation Certificates (ROCs) are issued by the regulator Ofgem to accredited renewable generators. They are issued in the ROC Register along with electronic certificates. ROCs store details of how electricity was generated, who generated it and who eventually used it. Demand for ROCs is created by the above quota obligations for electricity suppliers or generators (which are the same at any given time for all of them). The price of an ROC is thus set by the market.
For each MWh of green electricity that a utility generates it receives one ROC [
As just explained, suppliers that do not present ROCs pay into the buyout fund at the buyout price, but do not receive any portion of the recycled fund. If there is a shortfall of renewable generation (below the supplier obligation), the buyout fund will grow and ROC purchasers will anticipate later payments from it on each ROC. This will drive the ROC price above the buyout price thus raising the reward for green electricity generators [
As a first approximation, we propose the following stochastic model for the ROC price at time
Nonetheless, according to the UK Government ([
Regarding
This implies that
We have 26,057 prices of monthly UK Base Electricity Futures from the Intercontinental Exchange (ICE, London). The sample period goes from 1 December 2009 to 30 March 2012 thus comprising 604 trading days (see
The number of contracts traded on the last day of the sample is 59,
The stochastic model in discrete time is:
Here
The seasonally adjusted spot price is
Using the differential equation describing price behavior in the physical (as opposed to risk neutral) world we get:
Discretizing this formula we derive a regression model whose residuals allow us to compute their volatility:
The (annual) riskfree interest rate considered is
In discrete time we have:
The electricity price and the wind load factor can be correlated well through their seasonal patterns. Our model allows for the possibility of their being correlated beyond seasonality. Based on past (say, monthly) data one can get a numerical estimate of the above parameters {
The sample comprises the monthly ratios between output electricity and installed capacity for the whole of the UK from April 2006 to December 2010,
Empirical time series frequently show left skewness for average wind speeds: see for instance Morgan
As
We develop a model that takes account of the potential correlation between
The behavior of the redistribution per ROC presented (
The numerical estimates of the parameters are: α
First we get deseasonalized monthly series of the three state variables over the period 2010–2011. Next we take the natural logarithms of these figures [
Random samples of correlated variables are generated according to the following discretetime schemes [
Regarding the relations between the stochastic components
Deviates ε
Our data below are for the onshore wind farm draw on EIA [
Next we apply these estimates to the case of an onshore wind farm with an installed capacity of
Here, total cost is computed under the assumption that the fixed annual O&M cost grows at the riskless rate of return. We apply the official exchange rates from the European Central Bank on January 2012: 1 = $1.2905, 1 = £0.8321. Thus, the total cost of our wind farm is £96,667,000.
The average load factor is
Now, if there is a fixed feedin tariff
If, instead, the wind farm owner receives as a payment the electricity market price
Note that our simulations below are based on a riskneutral drift. Consequently future cash flows can be discounted at the riskfree rate
Each simulation run
We undertake
The feedin tariff is generally claimed to be the most effective method for promoting renewable energy. Let
A given month
The variable
For the sake of consistency with the following sections, the numerical estimates of the parameters in wind load factor {
Assume that the unit payment to the owner of the wind farm strictly amounts to the market price of electricity; this can be thought of as the case of a generator who is ineligible for renewable energy support (or of the feedin tariff suddenly ceasing to apply). In this case we resort to simulation in order to take account of the situations in which high electricity prices (due to strong demand) coincide with high wind generation (owing to seasonal weather). Random paths for
We use the parameter values in
Under ρ
This (private) NPV of investing in a wind farm under this market scheme is not the only positive outcome that would result from investing immediately in a wind farm. There are other impacts (which are, admittedly, harder to quantify accurately) that could justify the existence of public support schemes to investment: employment, industrial development, tax collection, health,
For a nowornever investment, our simulationbased
Here we assume that the wind farm owner gets a payment that is composed of the electricity price plus an extra premium for each megawatthour generated. For example, onshore wind projects in Spain receive a premium of 29.29 €/MWh in 2007 during their first 20 years of operation (Klessmann
Each amount in the second column consists of two parts. The first one comes from MC simulation, namely
Here we assume that the developer of the wind farm receives a total payment comprising the electricity price plus the ROC price for each megawatthour generated. The payment received for one renewable MWh per year over 20 years is:
Using the above estimates (
If delaying investment is not feasible, this scheme is set to achieve the strongest effects in terms of triggering investment since the ROC price is a sizeable amount. The underlying assumption is that the utility does not meet the mandatory requirement in the Renewables Obligation and is forced to purchase ROCs or, alternatively, that it wants to generate “excess” green electricity so as to sell spare ROCs on the market. This scheme thus allows the developer to receive a sizeable payment as NPV. But this amount grows over time (under the current circumstances), so if postponement is feasible it may be optimal to delay investment.
Here we consider several other support schemes that could be implemented.
A subsidy on capital expenditure. This amounts to reducing the initial cost by the size of the subsidy. If it is available now but not later, it would be effective for encouraging earlier investment: The option to wait is worth the same as before, but the current NPV increases by the amount of the subsidy. The subsidy can be combined with a lower feedin tariff.
Partial or total subsidy on (fixed) interest rates. This results in a lower present value of costs. For instance, assume that the developer borrows £75 M (instead of using its own resources) to be repaid over 10 or 20 years in constant yearly installments. The present value of the subsidy as a function of the interest rate appears in
Impact of credit rating on the cost of borrowing. The interest rate that the developer will ultimately face depends on its rating. Obviously, as the developer moves down the notch scale, a growing surcharge is added to the interest rate (+1%, +2%,
Tax deduction from investments. If the rate is 10% (of the investment cost) and accrues one year later, its impact is:
The developer is required to make enough profit to apply for the deduction. A similar procedure can be adopted to assess the impact of a reduction in the tax rate and of accelerated amortization.
Reduction in the tax rate. Assume that the initial rate is 35% of the utility's profits. The present value of the profits times the tax rate is 0.35 ×
Accelerated amortization over 10 years. Under the 35% tax rate, this results in an NPV of £11.601 M. Thus the utility saves 13.836 − 11.601 = £2.234 M.
When the developer of the wind farm receives as a payment just the electricity price or the market price augmented by a fixed premium the future value of the investment depends only on the realization of a stochastic process (namely
The investment time horizon
Consider an asset whose riskneutral, seasonallyadjusted behavior follows the differential equation:
This can also be written as:
Since it is usually easier to work with the processes for the natural logarithms of asset prices, we carry out the following transformation:
In a trinomial lattice there are three probabilities
Now, at the end of the investment horizon (time
This means that we run 1000 simulations of 1200 steps at each final node. Since the option to invest is akin to a “call” option we denote its value by
At earlier times, however, the option to invest is worth the maximum of two other values: that of investing immediately and that of waiting to invest for one more period (thus keeping the option alive):
When the future value of the investment depends on the realizations of two stochastic processes (electricity price and ROC price) we develop a twodimensional binomial lattice (that again supports mean reversion in
Starting from a given node with certain prices (
All the following cases rest on the same starting values of the underlying variables; see
Let
For low investment costs (
The prices involved in the futures curve play an important role here. According to our estimates, the (deseasonalised) electricity price starts at
At the same time, the expected rise in electricity prices implies that the bigger profits are to be reaped in the last part of the useful lifetime. Thus (leaving volatility aside for the moment), the NPV of investing in, say, one year's time would be higher than that of investing immediately (even after discounting to the present, as long as the futures curve is steeper than the riskfree rate). The incentive to wait is therefore clear. When volatility enters the evaluation, it reinforces this underlying trend.
Sometimes policy makers grant different subsidies to renewable energy developers (e.g., to help pay for the capital costs of offshore wind farms). They are meant to enhance the appeal of investments which in their absence would not seem to pay off. The impact of these measures depends on their specific terms and on the institutional environment in place.
In the case of a feedintariff that is kept constant over time, the argument is straightforward: all the relevant information is available at the very outset. The (gross) present values in
Now we check how the decision to invest reacts to a public subsidy
As a benchmark for comparison, consider
This effect is similar to that of a feedin tariff. The latter is available from the very beginning till the end of the 20year period. Without uncertainty, there is no value in waiting, so investing sooner rather than later makes sense. The same holds for a known subsidy. Nonetheless, as long as it is only available for a limited time, there is a cost to waiting. Therefore, in principle its impact on hastening investment would be stronger.
Consider the case in which the owner of the wind farm receives the market price of electricity augmented by a fixed premium.
For
Now, consider that the developer receives the electricity price plus the ROC price. The present value and the continuation value are shown in
According to our estimates, α
Intuitively, if the investment option is available over a shorter time frame there is less to be gained from waiting to invest. As a consequence the continuation value will fall and investment will take place earlier.
As the time for which the option is available shortens, the difference between the continuation value (always positive) and the investment value decreases. Consider, for example,
A combination of short option maturities and transitory public subsidies only available at
Initial subsidies of a certain amount are very effective in that they raise the threshold below which it is optimal to invest. Note, however, that the marginal effect of each additional monetary unit decreases significantly.
Just as the option value changes with
Again we consider
Regarding the numerical results in
Up to now we have assumed that the wind farm entails a constant investment cost. Nonetheless, in reality technological progress shows up in the form of lower costs. Next we consider the case in which it decreases at a constant rate over time (note that this is a deterministic pattern, so the number of risk sources remains the same). Thus, at time
Assume that the developer receives just the electricity price (Section 6.1).
These figures show the results for the same “starting” investment costs. As could be expected, the continuation value is higher than before in all the cases. Further, the gap between the continuation value and the investment value widens, so waiting to invest is even more justified than before.
We have implicitly assumed that the amount of support remains constant indefinitely. But several specific support schemes show declining rates over time [
Consider the case of a feedin tariff (Section 7.2). If
Assume instead that it is the fixed premium (Section 6.4) that declines at an annual rate of 2%. We consider the same two levels as before,
We can also calculate the joint impact of decreasing premium levels and investment costs. See the right hand of
It is also possible to assess the joint impact when support comes from a feedin tariff. If
We have found that wind developers whose only source or revenue is the electricity market have hardly any reason to invest immediately. To some extent this is due to the particular sample period used. Specifically, the sizeable gap between current prices and the (higher) expected future ones pushes toward delaying investment in a finitelived wind farm. In short, under this reward scheme the incentives to wait are clear. By the same token, support schemes are required to persuade potential investors that early investment is in their best interest.
A fixed feedin tariff can well do the trick. As long as it is set at any of the levels considered in our computations (which are in turn close to standard practice), the NPV of investing immediately surpasses the continuation value. So, in terms of encouraging early investment, this support scheme is effective: it is preferable to receive a given NPV sooner rather than later (because of the time value of money). Thus, according to our results a feedin tariff of £70.55/MWh is equivalent (in NPV terms) to receiving the electricity market price [
Alternatively, policy makers can reduce the economic risks faced by developers only partially through a constant premium on top of the electricity price. A fixed premium does certainly increase the NPV of an immediate investment. Yet this measure is not particularly effective: the continuation value also increases with the fixed premium. Our results show that developers find it better to wait (note here the implicit assumption that the fixed premium is available indefinitely, which implies that waiting has little or no cost). From the viewpoint of encouraging earlier deployment of renewable electricity, a feedin tariff of £70.55+premium (per MWh generated) would be more effective than a combined market price+premium scheme.
A oneoff, transitory subsidy, however, can be more effective in bringing forward investments while at the same time putting less pressure on public finances. When there is a subsidy that is only available at the outset, the NPV of investing at that time rises while the continuation value remains the same. The chances for earlier investment in wind farms increase accordingly. Let us first consider its impact relative to the case with revenues only from the electricity market. For investment costs
Another support measure consists in granting tradable ROCs to RESe generators. Under this scheme they earn revenue on the electricity market and the ROC market. According to our results, the ROCs raise both the NPV and the continuation value significantly. Nonetheless, the latter stands above the former, so it is better to delay investment. The effect of the ROCs is thus similar to that of a fixed premium.
The above instruments do not necessarily operate in isolation. For example, a transitory subsidy can be established in combination with a predetermined time frame for investment. Thus, if the option to invest is available only for a short period, the incentives to invest provided by the transitory subsidy are reinforced. Similarly, as long as policy makers are able to lower the volatility of electricity prices they effectively contribute to bridging the gap between the NPV and the continuation value, thus pushing toward earlier deployment of these irreversible investments.
On the other hand, innovations in wind power technology translate into lower investment costs. This clearly pushes for postponing investment, thus delaying further progress down the learning curve. A tool that policy makers can deploy to offset this effect is a timevarying support scheme with declininig rates over time. The support level can well be flat during the operational lifetime of the farm, but if this level falls as the start of operation is postponed then developers will have a strong incentive to invest early.
Ambitious goals in energy and environmental issues have been set recently in a number of places. One of the latest cases involves Sweden and Norway; beginning in 2012, both countries have agreed on a common green certificate system for RESe. It is the first European example of a bilateral collaboration between two countries to achieve a common goal with respect to renewable energy. The political signal is that wind power has a reasonable chance to be realized. However, as Blindheim [
We have developed a valuation model for investments in wind energy in deregulated electricity markets when there are futures markets with long maturities. The results are thus focused on developed electricity markets where short and longterm transactions take place regularly and it is possible to reward wind generation through a “pure” scheme (
Looking at the UK futures market we find that contracts for electricity display mean reversion; this in turn has some implications for the valuation model. We estimate the parameters underlying the stochastic behavior of prices (including the seasonal effect) from actual market data. We also estimate another stochastic model (with seasonality) for electricity generation by wind energy at any time as a function of the availability of wind.
The option to invest in a wind farm can be exercised up to a point into the future; thus it is an Americantype option. To maximize its value it must be exercised at the optimal time. To assess this option we have built a trinomial lattice which supports mean reversion in prices. A new feature here (to our knowledge) is that the values involved in the decision to invest at each node are derived from Monte Carlo simulations where stochastic realizations of the electricity price and ROC price (where appropriate) are combined with those of wind availability (and thus generation level) at any time. We derive optimal exercise (investment) rules in terms of threshold investment costs below which it is optimal to invest immediately.
Our numerical results show the impact of a number of factors involved in the decision to invest in a wind farm. Thus, when the only source of revenue for developers is the electricity market price, delaying investment is in their best interest. A fixed feedin tariff, however, certainly brings investment forward. When it comes to a lumpsum subsidy, a onetime or transitory initial subsidy works better for prompting investment than a higher subsidy available for longer. The onetime subsidy can also outperform a constant premium per MWh received over the project's lifetime. Augmenting the electricity price with the ROC price significantly raises the value of the project; nonetheless, it is proven to be similar to a fixed premium in that it does not contribute effectively to early investment.
Both the net present value (of investing immediately) and the option value are affected by the expected electricity price as set on the futures market. Starting from £48.91/MWh, it is expected to reach £85.91/MWh in the long term. Thus, the futures curve displays a positive slope. Because of this rising profile, the higher final prices more than offset the lower initial ones, which results in an
Sensitivity analyses show that different combinations of variables can have an influence in bringing forward investments in wind generation. One example is a short maturity of the option to invest and an initial subsidy available only for limited time. Electricity price volatility is clearly a major driver when developers only receive the electricity price. As volatility falls, the NPV remains the same while the continuation value falls. This pushes for early deployment; the problem is, under this setting the former always falls short of the latter so it is optimal to wait. On the other hand, if the investment cost decreases over time there is a further reason to delay investment. The opposite happens when it is the support level that declines. In this case there is a cost to waiting, so the optimal decision is to invest initially (if at all).
Our analysis is subject to some limitations, so several qualifications are in order. We have assumed that the capital markets available in the economy are complete (
We have considered the variable character of the electricity produced at wind farms. The effect of this variability is sometimes called “profile costs”. But we have set aside the socalled “balancing costs” and the “gridrelated costs” which arise because of forecast errors in RESe generation that need to be balanced at short notice and the locational nature of the RESe generated, respectively. See Hirth [
On the other hand, we have discussed a number of barriers to the deployment of wind technology. We have focused on reducing the uncertainty faced by developers when forecasting their future revenues form wind farms. Several RESe support schemes that address this subject have been considered. However, their success (or the lack thereof) is far from sure. Del Río and Tarancón [
Another area of potential conflicts involves the policy goals. For example, enhanced security of supply does not necessarily go hand in hand with lower dependence on fossil fuels, or the abatement of carbon emissions. At a closer level, analyzing the behavior of power generators operating on both the electricity market and the ROC market (studying their strategic behavior and the impact on ROC prices) should be the subject of future research; Fagiani
We gratefully acknowledge financial support from the Spanish Ministry of Science and Innovation under research project ECO201125064, from the Basque Government GIC12/177IT39913, and from Fundación Repsol under the Low Carbon Programme joint initiative [
The authors declare no conflict of interest.
According to Hirth, the market value of intermittent or variable RES is affected by three intrinsic technological properties: (i) their supply is variable (electricity is a timeheterogeneous good, and variability affects its market value by determining when it is generated); (ii) their output is uncertain
Gross
The ROA is hardly new to corporate decision makers: Graham and Harvey use a sample of several hundred CFOs who report on the practice of corporate finance and the different criteria used to assess investment projects at their businesses. According to their results, the internal rate of return (IRR) and the NPV are the most frequent valuation methods. Moreover, 26.59% of the CFOs surveyed always or almost always used Real Option methods. The ROA is not therefore a marginal valuation technique.
Hence it is possible later to try and make further progress in the quest for the (broader, allencompassing) “true” value. To be sure, the correct financial value is a necessary but not a sufficient component of the latter.
The methodology adopted here, namely Contingent Claims Analysis, is consistent with financial valuations. It does not require the world around us to be risk neutral. Quoting from Dixit and Pindyck (p.147): “
There is a growing literature that tackles the modelling of electricity prices. Geman (Section 11.6) and Möst and Keles provide an overview of stochastic models dealing with price risks in deregulated electricity markets. Broadly speaking, electricity prices exhibit various characteristics, among them shortterm and longterm dynamics. The short run behavior displays mean reversion, seasonality, stochastic volatility and, in many instances, discrete jumps. Long run behavior, though, is determined by the dynamics of the equilibrium price.
Grid extensions are certainly necessary for the physical integration of variable RES in general. But they also have important financial consequences for all power system participants; see for example Schaber
To meet a given fraction of the load thus requires a comparatively bigger capacity installed. Furthermore, if the fraction to be met by wind is high, the absence of wind at one particular site must be offset by wind generation at other sites (preferably with low correlation between them).
This is the default value. In 2009 the UK government introduced banding to discriminate between technologies depending on their relative maturity, development cost and associated risk. Thus offshore wind facilities receive 2 ROC/MWh, while onshore installations receive just 1. Other renewable technologies get less than 1 ROC/MWh; still others are not eligible for ROCs at all. These banding levels are currently (as of July 2013 under review.
And conversely, if renewable generation surpasses the RO percentage, the ROC price will fall below the buyout price.
From their counterparts' point of view, spare ROCs can be retained. Again, the sum of the buyout price and the recycling payment acts to some extent as a lower bound in their willingness to accept.
Nonetheless, in view of its low volatility σ
It can also be seen that this process is a particular case of the more general process:
The maximum possible output for each month is calculated from the installed capacity of the wind farm: Maximum output (MWh) = Installed capacity (MW) * number of days * 24. The actual output is then expressed as a percentage of the maximum possible output over the same time interval. Source: CLOWD.
Reuter
This is the case, for example, when a constant annual capacity factor is chosen, say 35%.
In countries with a high share of wind power this correlation has become negative.
There are no futures markets for the ROCs and the load factor which would enable the corresponding riskneutral processes to be estimated. Therefore, in both cases we are basically working with the processes in the physical/real world and assuming that their market price of risk is zero (Kalkuhl
For readers specifically interested in offshore wind farms, Sun
This is equivalent to saying that January generation amounts to 24 × 31 × 0.328341 = 244.28 MWh per MW of capacity installed. This figure changes from one month to another.
For the sake of simplicity each cash flow is assumed to be received at the end of the month.
The level of
Nonetheless, the expectation of an upwardsloping price of electricity may not be enough to trigger investment. When there is an option to delay, if the (risk neutral) drift rate of the electricity price is higher than the riskless interest rate then it is optimal to postpone investment; see Section 6. On the other hand, electricity price volatility is a major driver of the value of the option to wait. Consequently, those support schemes that entail a lower volatility of the wind farm profits push toward earlier investment in this technology. Furthermore, assuming a perfect market for electricity in the UK, it might be possible to hedge (at some length) the profit margins of wind farms.
We have daily prices of month futures contracts. From these futures prices we estimate the process for the longterm price of electricity in a riskneutral world. We compute the wind farm's revenues over 20 years at each node of the trinomial lattice through Monte Carlo simulation. This simulation, which accounts for seasonality, comprises 60 time steps per year, and 1,000 runs.
Negative probabilities are avoided by using the expressions in
PérezArriaga expects the volatility of marginal prices to increase in deregulated electricity markets with substantial penetration of renewables. Of course, volatility can also be caused by a number of reasons, many of which fall beyond the realm of policy makers. One such example is the price of natural gas on the international markets, as long as it serves sometimes as a reference for establishing the price of electricity (in conjunction with other factors such as the emission allowance price in those countries where electric utilities are subject to carbon constraints).
Note that we use daily UK Base Electricity Futures prices of month contracts. From these futures prices we estimate the process for the longterm price of electricity in a riskneutral world. We can thus estimate the spot price (as inferred from ICE futures prices) for any time.
The developer faces volumetric risk to some extent, as a function of the instantaneous shocks to the load factor. Nonetheless, since the wind resource is free, the farm will operate whenever it is possible to do so. As long as positive forecast errors are similar to negative ones, the volumetric risk can be expected to be offset over the whole useful lifetime of the wind farm.
To the extent that organized exchanges or OTC markets are liquid enough to allow the hedging operations required at any time.
Arguably there are numerous public benefits of RES that are neither well understood nor properly valued. For instance, public benefits resulting from further RES deployment (e.g., GDP losses avoided) are neither directly appropriated by private businesses nor factored into their decision making processes. This is typically the case unless energy and environmental policy takes such benefits into account and alters the behavior of businesses. This change can be accomplished by means of a subsidy on RES or a tax on more polluting technologies (which pushes electricity prices upward to encourage a positive performance of the overall economy).
UK base electricity futures prices on London ICE, 30 March 2012.
Monthly load factor of UK wind farms 2006–2010.
Distribution of wind load factor.
Time path of buyout price and ROC price (₤).
UK electricity futures (ICE).
 

All contracts  26,057  54.88  7.69 
1 Month  604  44.95  6.03 
6 Months  604  47.53  7.31 
12 Months  594  49.68  5.60 
24 Months  422  54.80  3.82 
36 Months  422  58.34  4.21 
48 Months  422  61.83  4.30 
60 Months  25  68.59  0.59 
 
 
March (1 less hour clock change):  35 days × 24 h − 1 = 839 MWh  
February (leap year):  29 days × 24 h = 696 MWh  
January, February, April, May, July, August, November:  28 days × 24 h = 672 MWh  
June, September, December:  35 days × 24 h = 840 MWh  
October (1 extra hour clock change):  28 days × 24 h + 1 = 673 MWh 
Source: ICE Futures Europe: “UK Base Electricity Futures”.
Nonlinear leastsquares estimates of the price process.
0.1134  0.001939  58.47  0.000  

85.9128  0.542854  158.3  0.000 
γ  3.02281  0.020658  146.3  0.000 
φ (years)  0.03139  0.0010417  30.13  0.000 
Seasonal (OLS) estimates in wind load factor.
8.7442  9.1273  
−2.0608  −2.1511  
6.2505  6.5244  
−4.1947  −4.8954  
−4.6595  −5.4378  
−11.3065  −13.1949  
−8.8292  −10.3039  
−3.8895  −4.5392  
1.4574  1.7009  
1.7411  2.0320  
12.4732  14.5565  
4.4757  5.2232 
Expected ROC price (£).
0  36.99  10.65  51.34 
5  42.19  9.43  55.84 
10  48.12  8.35  61.28 
15  54.88  7.39  67.76 
20  62.59  6.55  75.40 
Correlation matrix between state variables.
Electricity price  1.0000  0.1038  0.2008 
Wind load  0.1038  1.0000  −0.0071 
ROC price  0.2008  −0.0071  1.0000 
Wind farm's characteristics.
Onshore  2011  100  2437  0  28.07 
Offshore  2015  400  5974  0  53.33 
Wind farm (50 MW) expenses.
$M  121.85  1.40  149.92 
£M  78.567  0.905  96.667 
Present value of a 50 MW wind farm under a feedin tariff.
50  86,654,277  86,638,266 
60  103,985,132  103,965,920 
70  121,315,988  121,293,573 
80  138,646,843  138,621,226 
90  155,977,698  155,948,880 
Present value under the electricity price.
0  122,196,833  122,745,535  −548,702 
0.1038  122,262,434     
0.2  122,314,986     
Present value under the electricity price plus a premium.
130.9  139.5  148.2  156.9  165.5  174.2  191.5  208.8 
Other incentive schemes: A subsidy to interest rate (£M).

 

0.0205  75.0  0.0  75.0  0.0 
0.01  70.9  4.0  67.7  7.2 
0.00  67.1  7.8  60.8  14.1 
Other incentive schemes: Impact on market funding (£M).

 

0.0205  75.0  0.0  75.0  0.0 
0.03  78.7  3.7  81.6  6.6 
0.04  82.6  7.6  88.6  13.6 
0.05  86.6  11.6  95.8  20.8 
0.06  90.6  15.6  102.9  27.9 
Formulae for the probabilities in the trinomial lattice.
Normal 



High X ( 



Low X ( 



Option value (£M) under the electricity market price.
47.2  59.0  59.0  
25.6  40.4  40.4  
22.2  37.5  37.5  
−2.8  18.3  18.3  
−27.8  7.7  7.7 
Trigger cost
£19.3 M  £61.9M  £98.1 M  £122.4 M 
Option value (£M) under electricity price plus a premium.


 

81.9  64.6  89.1  74.0  89.1  74.0  
60.2  42.9  70.1  55.2  70.1  55.2  
56.9  39.6  67.2  52.4  67.2  52.4  
31.9  14.6  45.6  31.1  45.6  31.1  
6.9  −10.4  24.6  14.0  24.6  14.0 
Option value (£M) under electricity price plus ROC price.
153.2  163.1  163.1  
131.5  143.3  143.3  
128.2  140.3  140.3  
103.2  117.5  117.5  
78.2  94.9  94.9 
Option value (£M) as a function of the option's maturity


 

47.2  47.2  47.2  54.7  51.6  49.2  54.7  51.6  49.2  
25.6  25.6  25.6  34.9  30.9  28  34.9  30.9  28  
22.2  22.2  22.2  31.8  27.7  24.7  31.8  27.7  24.7  
−2.8  −2.8  −2.8  11.8  7.4  3.7  11.8  7.4  3.7  
−27.8  −27.8  −27.8  3.3  1  0.1  3.3  1  0.1 
Trigger cost
£26.0 M  £77.7 M  £115.0 M  £119.1 M  £122.6 M  £130.7 M  £136.4 M  £142.0 M 
Option value (£M) as a function of electricity price volatility σ


 

£47.2 M  £47.2 M  £57.7 M  £55.5 M  £57.7 M  £55.5 M  
£25.6 M  £25.6 M  £39.1 M  £37.0 M  £39.1 M  £37.0 M  
£22.3 M  £22.3 M  £36.3 M  £34.2 M  £36.3 M  £34.2 M  
−£2.8 M  −£2.8 M  £16.2 M  £13.4 M  £16.2 M  £13.4 M  
−£27.8 M  −£27.8 M  £5.1 M  £1.2 M  £5.1 M  £1.2 M 
Option value (£M) under the electricity price with decreasing cost.
Continuation value  63.9  47.2  44.6  25.8  12.0 
Option value  63.9  47.2  44.6  25.8  12.0 
Option value (£M) under the electricity price enhanced by a premium.

 

Investment value  60.2  60.2  60.2  60.2  
Continuation value  70.1  66.6  76.5  72.4  
Option value  70.1  66.6  76.5  72.4  
 
Investment value  42.9  42.9  42.9  42.9  
Continuation value  55.2  53.3  61.8  59.6  
Option value  55.2  53.3  61.8  59.6 