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.
Project feasibility; Wind
cost; Various constructions .....
|
Capacity
Factor; puissance Nominal cumulée…..
|
Cost of operation, Cost of ownership ...
|
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.
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.
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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