New Perspective of Cost of Wind Energy: MCOE & ACOE

 

New Perspective of Cost of Wind Energy: MCOE & ACOE

 

 

 

Abstract:

 

In the literature, The Levelized Cost of Electricity estimates the value of the kilowatt-hour cost of electricity production. One of the reasons it took this indicator to be perceived as an average cost. This research activity looks at the question of the monthly electricity cost of wind farm operation. Such a prospect will, in fact, allow the national electricity company to benefit from a judicious and applicable cost. A second component puts into perspective the positive impact of depreciation on the annual cost of wind power generation, while considering the rise in operating costs due mainly to the aging of the plant. The particularity of the new LCOE equation is its flexibility in calculating the monthly cost and future annual costs of a wind farm. By economic aspect, it solicits the most profitable wind turbine brand for production in kilowatt hours. Depending on the wind availability rate, in relation to the load factor, the wind speed varies depending on the 10 minutes, months and years. A Granger correlation and causality study showed the strong dependence and cause-and-effect between speed, height, pressure, and temperature. According to Belz's law, the maximum velocity per exploitable surface displays the same behavior as the Weibull and Rayleigh estimates. Their judging qualities deviate from Rayleigh in favor of Weibull.

 

Keys Word:

Energy, LCOE, MCOE, ACOE

 

1. Introduction 

From pollution to the scarcity that results from the high cost and therefore the living conditions of households. A healthy incentive for public decision makers to turn to clean energy at lower cost among which wind then becomes an initiative. Transformed the kinetic power of wind into electricity by means of an aerogenerator. New facilities in 2018 reached 51.3 GW, down 4% from 2017; this decline mainly affected onshore wind: 46.8 GW (-4.5%), while offshore wind rose 0.5% to 4.5 GW, bringing its share to 8%. In the onshore wind, China, leader market since 2008, installed 21.2 GW, far ahead of the United States (7.6 GW), Germany (2.4 GW), India (2, 2 GW) and Brazil (1.9 GW). China's market share in 2018 was 45% onshore and 40% offshore, the United States 16% onshore, Germany 5% onshore and 22% offshore the United Kingdom, 1% onshore and 29% offshore. Global installed capacity reached 591 GW, up 9.4%, including 23 GW at sea (+ 20%). China's share is 36% on land (US: 17%, Germany: 9%, India: 6%) and 20% offshore (UK: 34%, Germany: 28%). (Global Wind Energy Council - World Wind Energy Council).

 

The production of electricity, following the path of renewable energies, particularly the wind power sector, gives considerable importance to cost control. The Levelized Cost Of Electricity / Energy, widely used in the literature, determines the cost price to support the production of electricity. But more than a simple tool of appreciation, it intervenes among other things in the study of comparison of technologies of various electricity productions. By its expression, it extends on the one hand for the part of the cost and on the other hand the quantity of energy produced. The figure opposite shows the decomposition of the LCOE equation.

LCOE

Cost Of  Energy

Energy Production

Project feasibility; Wind cost; Various constructions .....

Capacity Factor; puissance Nominal cumulée…..

Fixe Charge

Variable Charge

Cost of operation, Cost of ownership ...

Speed Wind

 

Various formulas are known in the literature for all forms of production technologies, including hybrid production systems. We will ask in our works the cost of production more specifically that of the wind production. As a first aggregate, the initial investment represents, by component, the pioneer in the calculation. It is from which the costs of exploitation, maintenance including operation, and insurance ... etc. are also deducted from the total life cycle cost. In 2013, the acquisition cost of wind turbines was set at € 989,000 / MW with destination and assembly. [1] In this concept, feasibility studies on the qualification of the best wind area since 2008 are evaluate between $ 50,000 and $ 200,000 (Toby Couture, Yves Gagnon and Tina Poirier) [2]. The knowledge of the unit price suggests to decide the total amount for the acquisition. By its nature, the investment cost takes into account several other working capital, this is the case of civil engineering; network connection; development with the acquisition, totaling 1,282,000 € / MW. The financing of such a project may be of various kinds in the form of bank loans, equity, state subsidies ... etc. The internal components of the investment and operating costs are exposed according to the Energy Regulatory Commission in the following form:

 

The weighted average cost of capital (WACC) intrigues the return on investment to assess the breakeven point of the project within the agreed deadline. Keeping the wind farm in service for profitable electricity production requires a part of the financing integrated into the total cost in the form of operating, maintenance and replacement costs for defective equipment. Generally, this annual hedging cost is between 15% and 30% of the total investment cost, ie approximately € 45,000 / MW / year, half of which is used to finance maintenance (2014 Report, CRE). At the end of the life of a wind farm, the value of unamortized equipment (residual value) and the cost of dismantling may not be included in the investment cost. Regarding the investment of a wind project, we can retain the distribution of costs as modeled NREL [3].

  

These allocations indicate the influence of miscellaneous expenses including operating cost (CapEx) and operating expenses (OpEx), net capacity factor, nominal discount rate and the theoretical life of the project on the project. LCOE. At the end of the service life, the decommissioning process of the plant includes the dismantling of wind turbines; ancillary equipment; the dismantling of the delivery station; the leveling of foundations; the dismantling of the access roads to wind turbines and the future of the local grid connection network, which requires an expenditure of 50 000 € / MW [4]. The rate at which the cash flow (cash flow or value) of a project in a given year is defined by the discount rate. This requires the state of knowledge of financial market rates. In this sense, its calculation calls into question the rate of inflation (generalized price increase), indexation (variation of the consumer price index) and the nominal interest rate on which the loan was granted between the two groups. stakeholders.

 

2. Economic Analysis of Wind Energy: Multiple LCOE Approaches in Literature

 

2.1. LCOE-Diaf, Notton and Broomfield

Studies by Diaf, Notton and Broomfield [5] highlight a new expression of the discounted average cost for the production of electricity from the wind farm. The equation selected is defined as follows: Where Ci: Installation cost ($); Co: Operation cost ($); Tcf: Fixed charge rate (%) and Ea: Annual energy production (KW).

 

 

2.2. LCOE-SAM

In the SAM model, the LCOE is calculated on the basis of expected cash flows for operating and maintenance expenses and capital expenditures. While cash flows are important in determining the actual costs and costs associated with a wind farm project, SAM does not recognize the implementation of penalties or tax credits in its wind energy LCOE model. The SAM model calculates a PPP price in its financial model that does not include tax credits, but the PPP price is only a discounted value of the calculated LCOE and does not take into account the impact of the penalties [6].

 

Where CPEi is the energy production cost for year i and each parameter is given for the nth year.

 

 

 

 

 

Equation (3) explicitly includes the following costs: fuel cost (F), production tax credit (PTC), depreciation (D), tax levy (T) and royalties (R) .This includes the gasoline costs and royalties that are irrelevant (equal to zero) for the wind, however, they are included in the proposed model for generality.

 

2.3. LCOE- Present Value Cost

The Present Value Cost (PVC) method estimates the dynamic development of the relevant economic factors and the different cost and revenue variables, which are taken into account in the formula: The present value of costs (PVC) [7] is determined by the help of the relationship below:

 

 

Where, r, represents the interest rate, i the rate of inflation, t the life of the wind turbine, Fs the Additional Costs and includes the costs of operation, maintenance and repair. To estimate PVC, the following economic quantities are used: The interest rate or discount rate (r) and the rate of inflation (i); the lifetime (t) of the machine estimated between 15 to 20 years. OM Costs: A significant portion of the total annual operating costs of a wind turbine, but their value is not fixed. Operating costs vary each year with changes in inflation and interest rates. However, it is admitted that they (Comr) vary from 15 to 30% of the total investment cost. The factor (Fs) is an additional cost for most wind farms, located near rural areas of the country therefore the costs related to the installation including the cost of civil works, the transport of the turbine and the construction of roads are always high, compared to the costs that would be incurred if wind turbines were installed in an urban area. To compare as an influence in the international journal, let us show a table showing this distinction.

 

2.4. Cost Of Electricity: COE Cost of Energy (COE) Model The study [8] has shown the design objective of maximizing annual energy production or using sequential aerodynamics and structural optimization to be significantly suboptimal compared to the aero-structural integrated methods. For variable rotor diameter and hub height, the optimal rotor diameter can be misleading because of the tower mass dominates the total mass of turbine. Thus, minimizing COE is a much better metric for the full-scale wind turbine optimization objective than minimizing the ratio of turbine mass to annual energy production. The main objective is to minimize the COE of a wind turbine in low wind speed areas. Following the study [9], COE is calculated as:

 

 

Where FCR is the fixed charge rate, ICC is the initial capital cost, AOE is the annual operating expenses, and AEP is annual energy production.

 

 

 

 

 

 

 

 

 

3. New perspective: LCOE, MCOE and ACOE

 

3.1 Levelized Cost Of Electricity

We propose in this paper, a revision of the LCOE for the case of wind energy. Indeed, the idea chosen is to distinguish the required loads according to their evolution during the lifetime of the project. It results in a separation between current and fixed charge. The first is infected by a discount rate and the second the average amount covering the operation of the project. The production of energy during the service life will depend effectively on the wind speed and therefore the load factor assigned to the operating site.

 

 

Ip being the Primary Investment; Is: Secondary investment; Do: Operating Expense, Dr: Replacement Expense, Dd: Decommissioning Expense, Dc: Miscellaneous Construction Expense, Di: Contingency Expense, Dm: Maintenance Expense, FC: Load Factor, PN: Rated Power, I: Discount Rate and N: Project Life.

 

3.2 Mensual Cost Of Electricity : MCOE

By this formula, we model the monthly version of the wind cost to calculate by deduction of equation 10. The only difference, this expression varies with the monthly load factor ΔFC. In fact, the cost is strongly related to the wind potential in the short term:

 

 

 

3.3 Annual Cost Of Electricity : ACOE

The Levelized Cost of Electricity for the economic analysis of wind farms takes into account the depreciation of costs and energies. We propose in this condition, an alternative to remedy this omission:

 

 

Four scenarios in which the transaction cost rises (25%, 50%, 75% and 100%) are calculated and also include a depreciation rate of 5% on the value of the plant (I'p, I's, D'd, D'd, D'm) to represent an annual cautious cost of the plant.

 

 

 

 

 

 

 

 

4. Sensitivity of LCOE

The LCOE metric is sensitive to capital cost, production forecast and discount rate. In the following graph, we see the influence at different levels that LCOE knows:

 

.

Figure 6. Land-based wind power plant assumptions and ranges for key LCOE input parameters

(Source: NREL)

 

Staffell and Green (2014) found that wind farm performance decreased by 1.6% ± 0.2% per year as wind turbines aged. Their dataset was limited to onshore wind farms because they recognized that the depth of the offshore fleet was insufficient to provide a meaningful basis for the analysis. This remains the case. However, it is recognized that the same factors that lead to onshore performance degradation are likely to be equally valid at sea. As a result, a sensitivity analysis was undertaken to assess the impact on LCOE of annual degradation. performance of 1.6% of production. The impact on LCOE of offshore wind farms assessed here is an increase from 1% to 8%, depending on the date of commissioning of the wind farm.

 

 

 

 

 

 

5. Assessment of the potential of wind energy

 

5.1. Power of a wind turbine

The wind turbine derives its energy from the kinetic energy of the wind. The kinetic energy of the wind depends on its mass and its speed according to the following formula:

 

The mass m of the air is called Rho (ρ). Wind turbines recover this kinetic energy by slowing the wind in the space determined by the surface of their rotor. It is therefore necessary to calculate the air flow that passes through the wind turbine (kg per second).

                     

With V, wind speed; the surface S covered by the blades and the mass of the air ρ. By linking these two formulas, the calculation of the power can be expressed by a simplified formula:

 

In which P is the power (in W or kg.m².s-3); S is the area of ​​the circle of radius equal to the length of a blade; V is the wind speed (in m / s, that is, meter per second) and ρ (Rho) is the density (the "weight") of the air.

 

5.2. Beltz's Law

To produce energy the wind must have a minimum speed (often 3 m / s, ie 10 km / h). For safety if the wind is too strong the wind turbine is disconnected (often from 90 km / h). Between the two, the energy produced increases exponentially until reaching a plateau, then the nominal power is reached. This plateau is reached before the maximum speed. Devices then brake the rotor. Betz, Wind Energy (1926). This law applies to all types of wind turbines, Betz calculates that: the theoretical maximum power recoverable by a wind sensor is equal to 16/27 of the incident power of wind that crosses the wind turbine; this limit will be reached when the wind speed will be divided by three between the upstream and downstream of the wind turbine. The incident power of the wind is kinetic and depends on the surface that the wind sensor proposes to the wind, the wind speed and the density of the air. These results can be grouped according to these formulas:

 

With ρ: density of the fluid (1.15 to 1.20 kg / m³ for air at 20 ° C); S: area of ​​the wind sensor in m²; Vupstream: incident velocity (upstream) of the fluid in m / s.

16/27

Figure 7. Le maximum du rendement

 

 

It is reached for x = 1/3, of which r = 16/27. Hence the Betz limit:

6. Capacity Factor

 

The performance of a turbine can be examined by the turbine or the turbine. The mean power output can be calculated using the following expression based on Weibull distribution function:

 

 

Where vc, vr, vf are the starting wind speed, the nominal wind speed and the breaking wind speed, respectively

.

7. Weibull & Rayleigh

 

7.1 Distribution Indicator

The average wind speed is a first-order indicator and then calculates the wind distributions by which the reservoir potential existing in a site must be evaluated. The average is defined by the following expression:

 

Where v and are the average value of the data and the data sequence, respectively, while n is the number of the wind speed data.

 

 

7.2. Distribution model

The wind velocity data distribution model can be studied using two statistical estimators, asymmetry and kurtosis. These statistical expressions are defined as follows:

 (18)

 

Where v and s are given by the equations. (2.1) and (2.2), respectively, and vi is the nth datatype of the data sequence. Skewness describes the symmetrical characteristic of the data sequence, where Skew= 0 indicates that the distribution scheme of the wind speed data sequence is symmetric and Skews0 that it is not. In addition, as the absolute value of Skew increases, the asymmetry of the wind speed data also increases. Kurtosis is also used to describe the increased degree of the wind speed data sequence. When Kurt = 0, this corresponds to the standard normal distribution. When Kurt> 0, the distribution of the wind speed data sequence is steeper than this distribution, whereas for Kurt <0, the stiffness is not as high as for this distribution.

 

 

The two-parameter Weibull probability density function was used to analyze the wind data. The probability density function of Weibull is given [10-14] as follows:

 

 

 

Where f (v) is the probability of observing the wind speed (v), k is the dimensionless Weibull form parameter and c is the Weibull scale parameter (m / s). The corresponding cumulative distribution F (V) is the integral of the probability density function and is expressed as follows:

 

The Weibull parameters were calculated using the non-parametric quantile and median method. This method is useful and relevant because it does not depend on the variation of winds. Better results are obtained than the graphical method, moment method ... etc. When the value of k is set to two, the above expressions become a Rayleigh distribution function at a parameter and are expressed mathematically, respectively, by [10]:

 

 

Whose distribution function:

 

8. Quality of adjustment

 

8.1. Root Mean Square Error

To illustrate the adequacy of the distributions mentioned in this study, the wind speed data measured in the three sites studied are: relative. The parameters associated with these statistical distribution models were determined using MATLAB. In addition, the results obtained were compared as a function of the square root-mean error, and its equation is given below:

 

Where does he live; w and vi; m are respectively the n th value calculated via the distribution function and the n th measured value, and n the number of measured data.

 

8.2. Goodness of fit (R2)

This test makes it possible to evaluate the coherence of the observations with theoretical observations calculated from a model. A large value of R2 indicates a better fit of the theoretically expected results to the actual observations. Correspondingly, R2 is calculated using:

 

 

 

 

8.3. Index of Agreement (IA)

IA generally presents the degree of precision of the values calculated with respect to the measured values. The concordance criterion goes from 0 to 1, with the highest values showing better agreement between distribution and observations. The AI is calculated by:

 

 

 

 

8.4. Root Relative Mean Square Error (RRMSE)

The RRMSE is obtained by dividing the root-mean error by the average value obtained on the basis of the measured values, in accordance with:

 

 

 

Different ranges of this criterion are:

1) Ideal for RRMSE <0.1

2) Good for 0.1 <RRMSE <0.2

3) Correct for 0.2 <RRMSE <0.3

4) poor for the RRMSE> 0.3.

 

8.5 Coefficient of Efficiency (COE)

The coefficient of efficiency (COE) is another measure of the accuracy of the forecasting model. Its values ​​will generally be used in 1. The value of COE indicates a better deal.

The coefficient of efficiency is given by:

 

 

 

8.6. Relative Percentage Error (RPE)

The RPE shows the percentage difference between wind energy calculated by Weibull function and those obtained using measured values, and its values ​​between 10% and 10% are generally considered acceptable [67]. RPE is defined as:

 

The correlation coefficient between two real random variables X and Y each having a (finite) variance, denoted by Cor (X, Y) or sometimes ρXY is defined by:

 

Indeed, if one variable caused another variable, then necessarily both variables must be correlated. On the other hand, it is not enough for two variables to be correlated so that it has causality (correlation is not causality) [11]:

 

 

The mean statistic 
 
associated with the null hypothesis of Homogenous non-causality (nch) is defined by the average of the N individual realizations of the usual test statistics used in time series for test the non-causality of x towards y. where WiT corresponds to the individual Wald statistic associated with the hypothesis test H0:? i = 0 for the ith individual of the panel. the individual WiT Wald statistic associated with the test of the null hypothesis of non-causality converges to a Chi-square law [11]:

 

 

 

 

 

 

The higher the approval index, the better the reliability of the estimate. We note that the higher the IA index, the higher the coefficient of efficiency. with a low RRMSRE indicator. In any case, the estimation of the Weibull distribution seems to be more reliable than that of Rayleigh. The percentage of relative error is acceptable when the value is between -10% and 10%.

 

Heterogeneous variation has led us to focus on the question of correlation and causality. The wind speed is conjugated in the same way with other parameters including pressure, temperature, height, direction, ... etc. Moreover, CH10 and CH9 are together. As well as CH8 and CH7. CH3 is isolated compared to CH15, CH13, CH1 and CH2. The correlation does not imply causality, the CH1 equation shows that it affects all the other parameters except CH13 with a probability greater than the risk threshold of 5%. The equations of CH2, CH3, CH8 and CH10 show that their effects are significant on all the other parameters. Their critical probabilities are all below the 5% threshold. As a result, Granger causality between these parameters is significant.

 

 

Prospecting; development through rigorous scientific studies on impact, wind potential inspection and site analysis are fully covered by primary investment. We are estimating this cost at $ 200,000. Indeed, the experience of the Walloon region in Belgium shows that the pre-feasibility of a wind project is between the range of 100,000-200,000 € [15]. The acquisition of turbines, mats and other equipment (blades, transformer ... etc.) are financed with the secondary investment (Is). This cost adjusts to $ 160,000,000 for 40 wind turbines at 100MW. The unit price is $ 4,000,000 to 2,5MW (according to a particular supplier in Belgium). The transport, the assembly and the customs right are fixed at 2% [16] with 75% as part of order of the wind in the total cost. Added to this is the 4% grid connection and insurance. Taxes are assessed together at 20% (CRE, 2014). In short, the secondary investment is $ 208,000,000. The expenditure share for miscellaneous construction (Dc) is fixed at 3%, ie $ 18,000,000. The cost of operation (Do) that offsets payroll is 20% or $ 43,200,000. To keep the park in operation, the replacement of certain defective parts are also considered. We estimate the replacement cost (Dr) at 9% or $ 14,400,000 a year. The financial fraction (Di) can be included in the total cost and is estimated at 2% or $ 170,700 per year. The annual expenditure for maintenance is planned at 2% [17] of the total investment, ie nearly $ 4,300,000 per year. At the end of the project, ie the dismantling or renovation with the re-acquisition of new wind turbines, the decommissioning cost (Dd) is fixed at $ 50,000 per wind turbine [18]. The dismantling of 40 wind turbines after 20 years of use amounts to $ 2,000,000. The expected output of the power plant is 100 MW, each of which supplies a maximum of 2.5 MW. The prevailing wind speed is 9m / s, the associated load factor adjusts to 0.436%. For a period of 20 years. Every year 8760 hours of operation are counted. However, the currency difference for all costs between the euro and the US dollar may be negligible, the difference being adjusted to a few cents on the order of 0.12 (30/04/2019). All of these descriptions are included in the calculation of the new version of LCOE for wind energy. On the one hand, information useful for calculating the other cost equations already maintained in the literature and cited in section 2 should be grouped together. The different approaches used in this paper give an average cost of generating the plant is between 5.7 to 9.2 cents. Indeed, the power cost of the plant is fixed at: COE = $ 9 208 140.815.

 

 

 

 

 

 

 

 

Method PVC
Parameter	Value
Inflation rate	0.024
interest rate	0.12
Buying price	226400000
COMR	60373333.33
FS	15093333.33		PVC	760589416.4
T	20		E	8203200000
E (GWH)	10.254		LCOE ($/kw)	0.092718624

Table 5. Result of LCOE-PVC method

 

Method Diaf, Notton et Broomfield
	Valeur
Purchass Cost (75%)	226400000
Installation Cost (5%)	11320000
Annual Oprating Expenses(20%)	45280000
Fixed Charge Rate	0.8134	LARR+AOE	238650957
Capacity Factor	0.3715	AAEP	3047488800
Energy	10.254	LCOE LCOE ($/kw)	0.07831069

Table 6. Result of LCOE-DNR method

 

Method SAM
Parameter	Value
Inflation Rate	0.024
Intêrest Rate	0.12
It	226400000
OM	40000000
F	0
PTC	10400000
D	16000000
T	8000000		Cost	2117822595
R	0		E	3744164292
E	10254000		LCOE($/kw)                                  0.056846874

Table 7. Result of LCOE-SAM method

NEW Method
IP	200000	DO	32000000
IS	216000000	DR	4000
DM	32000000	DI	1600000
DD	2000000	DI	1600000
DC	4800000	PN	100000
T	8000000	CF	0.3715
	Cost Life	609154452
	E	6508680000
	LCOE($/kw)	0.09359109

Table 8. Result of Next perspective LCOE

From the same observation, the average cost per turbine shows a monthly fluctuation trend than the load capacity. Indeed, the higher the wind potential, the more efficient the profitability of the production. Although the characteristics of the wind turbine we disclose the preferential approach that must be solicited between the turbines economically. Nordex's LCOE is significantly higher than that of EWT over the period 2014 to 2015 5 (in all 24 months). The wind patterns in 2014 and 2015 are heterogeneous, their average costs also follow the same trend. This calculation procedure will allow the company to follow the evolution of its activity in a more judicious dimension from which certain policies can be deployed. Compared to the ACOE, the LCOE does not take into account the depreciation of the value and the increase in cost of operation that can infect the plant. We propose four scenarios of 25, 50, 75 and 100% increase in operating cost, and we relaunch the LCOE calculation simulating ACOE results.

Months (2014-2015)

 

 

 

10. Conclusion

 

Obviously, the average discounted cost expresses nothing more than the ratio of the multiple charges required for the generation of electricity. An estimate, which in no way reflects the selling price. Various authors propose equations whose principles are identical but the components remain distinct. For better judgment of the quality of the equation, the results from different expressions are relatively close between 5.5 to 9.5 cents per kilowatt hour produced. It was set up with the aim of creating an independent and profitable private institution in its production activity. Its composition is due to the fact that the loads are distributed so that they are current and fixed during the life expectancy of the plant. This distinction is important in order to reflect the reality of financial coverage to be maintained, which is reflected in the calculation of costs. For the production of the plant, the load factor according to the monthly speed between 2014 and 2015. The cost is 9.3 cents per kilowatt hour.

The NEW LCEO equation by its various features, it is possible to determine the monthly cost of wind generation. Due to its values, we are questioning the adoption of the EWT wind turbine seems. The annual cost by ACOE method, we stands out with the average cost of 9, 3 cents of LCOE. This cost drops to 4 cents until fully amortized in 2039 to $ 0. We consider 2020 as the first year of production of the wind power plant. Correlation and causality show the dependence of pressure, temperature, wind direction with wind speeds at different heights. Granger causality is in two directions at the risk threshold of 5%.

 

 

 

Abréviation

LCOE : Levelized Cost of Electricity

MCOE : Mensual Cost Of Electricity

ACOE : Annual Cost Of Electri city

CRE : Commision of  Regulation European

MW : Megawatt hour

KW : Kilowatt hour

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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[23] U.S. energy information administration: "leveled cost and leveled cost of new generation in the annual energy outlook 2018".

 

[24] Agence internationale de la francophonie: "wind energy".

 

[25] John Aldersey-Williams, Ian D. Broadbent, Peter A. StrachanBetter estimates of LCOE   from audited accounts, Energy Policy, p1-11.