2010 Cost of Wind Energy Review (Tegen Et Al 2012)

Abstruse

The statistic of air current energy in the US is presently based on annual average capacity factors, and construction cost (CAPEX). This approach suffers from i major downfall, every bit it does not include any parameter describing the variability of the wind energy generation. Equally a grid wind and solar only requires significant storage in terms of both power and energy to compensate for the variability of the resource, there is a need to account also for a parameter describing the variability of the ability generation. While college frequency data every infinitesimal or less is needed to design the storage, depression-frequency monthly values are considered for dissimilar air current energy facilities. The annual capacity factors have an average of 0.34. They vary significantly from facility to facility, from a minimum of 0.xv to a maximum of 0.5. They as well change year-past-year and are subjected to large month-by-calendar month variability. It is concluded that a better estimation of operation and price of wind free energy facilities should include a parameter describing the variability, and an assart for storage should be added to the cost. When high-frequency data will be eventually made available over a full year for all the wind and solar facilities connected to the same grid of given demand, then it will exist possible to compute growth factors for current of air and solar capacity, full power and energy of the storage, cost of the storage, and finally, aspect this cost to every facility inversely proportional to the annual mean capacity factor and directly proportional to the standard difference about this value. The novelty of the present work is the recognition of the variability of current of air power generation equally a performance and price parameter, and the proposal of a practical way to progress the blueprint of the storage and its cost attribution to the generating facilities.

Introduction

Wind free energy facilities^1,2 uses the variable wind energy resource to generate electricity. Current of air energy is soon the nearly widespread and economical renewable energy^three. While wind electricity supply is certainly less variable than solar photovoltaics, never bachelor during nighttime and strongly affected by clouds and pelting, but it still suffers from meaning variations, over curt as well equally long time scales, because of the fluctuation of the wind free energy resource^4,5. The further uptake of the wind and solar photovoltaic components in a filigree depends on the variability of the 2 sources, and the way to compensate for this variability, for example, trough energy storage⁶.

A proper written report of air current energy supply needs high-frequency data of every current of air energy facility connected to the aforementioned filigree, as well as their sum. To lucifer a given demand, supply from other resources must and then compensate for the still intermittent and unpredictable total air current energy supply. In case of the further expanded capacity of air current energy as well in excess of the grid demand, free energy storage will have to take the extra air current free energy or supply the wind energy in defect of the demand. The costs of intermittency and unpredictability will have then to be shared between the individual wind free energy facilities proportional to the variability of their supply. The availability of loftier-frequency data is therefore of paramount importance to study air current free energy. Unfortunately, high-frequency generation data is very hard to be sourced worldwide for renewable energy facilities such as wind or solar. In the specific, high-frequency data is non available in the United states of america, where the EIA merely provide monthly average values.

A wind and solar only electricity filigree requires a meaning increment of the installed capacity of current of air and solar, as well equally the build-upwardly of big storage, for both power and energy. There is a need to promote higher annual average chapters factors of wind free energy facilities, and smaller fluctuations about these boilerplate values. The aim of this study is thus to appraise real-earth costs, annual average capacity factors, and parameters of the low-frequency fluctuations about these values, for the largest wind energy facilities of the continental Usa, excluding Alaska.

The Present Assessment of the Cost and Performance of Air current Energy Facilities in the United states of america

In the Us⁷ reports the CAPEX (capital expenditure) plus the weighted boilerplate annual capacity factors of different Techno-Resource Grouping (TRG)^8,nine,x,11 areas, characterized by dissimilar average current of air speed and wind speed range. There is no information about the variability of the chapters factors inside the same TRG area.

Statistics for renewable free energy including wind are often based on installed chapters (nominal power), rather than the actual power of generating energy across a year, encounter for instance^7,12 is nether this aspect more authentic, providing the annual capacity cistron, that coupled to the installed capacity, provides a measure of the actual electricity production over the year.

The United states of america is one of the few countries where statistics are fix-up in terms of energy rather than nominal power¹³ and¹⁴. Information on actual energy product is supplied for conventional and renewable free energy plants in¹⁵, at low (upward to monthly) frequency. High-frequency statistics would exist necessary for proper assessments.

During 2017, within the U.s.a., air current turbines contributed half dozen.three% of the total utility-scale electricity generation, with remarkable growth from 6 to 254 billion kWh from 2000 to 2017^13,xiv. While wind energy capacity (installed ability) has increased dramatically over the last few years, wind energy electricity production has increased less. The average capacity factor has non increased, but reduced, with many wind energy facilities performing below expectations.

An introduction to current of air energy in the The states with the location of plants, completion date and number and size of turbines installed is provided in¹⁶. This assessment is not upwards to date.

On-shore based wind energy facilities in the US are discussed in⁷ too as¹⁷, based on the works^{xviii,xix,xx,21,22} and²³. These wind plants accept a capacity in the range from 50 MW to 100 MW¹⁹, with an average 2-MW turbine having a rotor diameter of 102 m and hub heights of 82 m. These were the facilities installed up to 2015^twenty.

Ref. ²¹ defines the renewable energy technical potential as the doable free energy generation per specific turbine installation. The technical potential is quantified by capacity factors. The capacity factors estimated were likewise based on five dissimilar wind turbines, optimized for the range of average annual air current speed at the locations. The chosen wind turbine power curves were representative of the range of wind plant installations in the US in 2015^twenty. The capacity gene is referred to as an 80-one thousand, higher up-footing-level, inter-almanac average hourly wind resources data.

About installed US wind plants align with ATB estimates for functioning in Techno-Resource Groups (TRGs) 5–vii. High wind resources sites (associated with TRGs i and 2) and exceptionally depression wind resource sites associated with (TRGs viii–x) are not as common in the historical data. From¹⁹ and²³, it may be expected for TRG1 a Wind Speed Range 8.two–thirteen.5 m/s, average viii.7 yard/southward, and a 47.4% chapters factor, while for a TRG10 the Wind Speed Range is 1.0–5.3 m/s, average four.0 one thousand/s, for an 11.one% capacity factor. In the virtually common atmospheric condition of TRG five to seven, the wind speed range is six.nine–11.i to 5.four–8.3 m/due south, the average speed is vii.5 to 6.2 grand/s, and the capacity factor is 40.7 to xxx.viii%¹⁷ and⁷ also supply time to come projections based on high, medium, and depression-cost estimates based on the results of a survey of 163 of the world's wind energy experts²¹.

Ref. ⁷ summarizes the forecasted Uppercase EXpenditures (CAPEX) in $ per unit chapters (ability, kW), and annual average capacity factor (ratio of energy produced in kWh to the product of capacity in kW by the number of hours in a twelvemonth). In a location such as Los Vientos, TX, of prevailing wind speed about vii.5 m/s, we may consider the CAPEX values of TRG5, current of air speed range 6.9–11.1 m/s, weighted average wind speed seven.5 m/southward The weighted average CAPEX is i,616 $/kW, and the weighted average capacity gene is xl.vii%. The weighted average annual capacity factor of 2014 is 40–44%, and it is growing.

Unfortunately, high-frequency generation information are not available for the Us, and proper energy storage computations are completely missing in the literature.

Materials and Methods

Low frequency monthly average data of electricity production available from the The states EIA is analyzed to show the variability of capacity factors month-by-month, year-by-year, and facility-by-facility, also in locations sharing almost the same wind energy resource. A numerical method will then be used to explain the variability of the capacity factors in locations of nearly the same air current free energy resource.

The method used here is from^vi. The wind free energy facility nameplate capacity (power) is conventionally given as the sum of all turbine rated capacities (see¹⁷ and⁷). The instantaneous ability of a turbine P depends on current of air speed U, turbine swept area A and air density ρ, according to the equation:

$${P}_{i}=\eta \cdot \frac{1}{2}\cdot \rho \cdot A\cdot {U}^{iii}$$

(1)

where η is the total turbine efficiency, including aerodynamic efficiency, the efficiency of ability transmission, and the efficiency of electric generation. Because of the Betz limit^24,25 the aerodynamic efficiency cannot exceed xvi/27 or 59.three%. Utility-calibration wind turbines take peak aerodynamic efficiency of 75% to 80% of the Betz limit. Density ϱ and speed U vary in time and space, across the rotor area, and from i turbine to another. The rated chapters P_r is obtained at a reference, uniform speed U _r that is usually exceeding the virtually probable wind speed of a specific location, with a uniform reference density ϱ _r .

From the net installed capacity P _r , annual and monthly chapters factors ε are computed past dividing the annual and monthly electricity production Eastward, downloaded from¹⁵ by the capacity P _r and the number n of hours in a yr or a month:

$$\varepsilon =\frac{E}{{P}_{r}\cdot due north}$$

(2)

Wind turbine power data are bachelor from manufacturers. The wind turbine database of²⁶ includes data from 1759 different turbines from 424 manufacturers. The data are valid for reference density weather and air current speed at hub superlative, in about optimal menstruation weather, where the short-term average and turbulent values are compatible across the rotor surface area. Figurer-Aided Technology (CAE) tools such as those of²⁷, may too supply an estimation of the performances of a turbine of a given geometry. These tools are the industry standards for the design and analysis of current of air turbines.

Every bit actual operating conditions differ, the actual ability production for a given prevailing air current speed may be unlike. Different hub heights are as well possible for every turbine, translating into different air current speeds. The detailed information about wind speed and direction and air density, both brusk-term average and turbulent across the rotor area of every private wind turbine of a wind free energy facility installation are usually not bachelor. The experimental data of air current resource is normally available simply about the proposed current of air energy facility installation, and not at hub pinnacle, merely at ground level. This resource assessment is also limited to time windows that are not long enough to include climate variability on a multi-decadal scale^28,29, and³⁰.

The theoretical energy production for every calendar month is obtained by integrating in time the power computed from the given wind speed at hub acme. A correction factor is introduced to account for the monthly average temperature at ground level, which affects the air density at the rotor hub. The ground temperature is obtained by using the air temperature information of³¹.

A uncomplicated model is defined to compute the electricity product of a current of air turbine from the measured power curve. The wind speed at a reference hub acme of 100 m is extrapolated from the speed at 10 yard obtained by using the air current speed data of³¹. In wind free energy assessment, assuming a neutral atmosphere, two models are normally used to represent the vertical profile of current of air speed over regions of homogenous, flat terrain. The first approach is the logarithm law. The second arroyo is the power law. Both approaches are subject to uncertainty. Mixing length theory, eddy viscosity theory, and similarity theory provide a logarithmic wind profile with height^32,33. Alternatively, a current of air contour power law may be used^34,35. The exponent γ is an empirically derived coefficient that varies depending upon the stability of the atmosphere. Here we utilize a modest exponent γ = 0.125 in the power-law returning the same velocity multiplying factor of 1.33 from 10 to 100 meters' summit, of a wind contour logarithm law with terrain roughness of 0.01 m. Data at 10 m, to be transformed in data at 100 m (rotor tiptop) log law i.33 multiplication factor. The density of air is 1.205 kg/thousand^three at 20 °C (293.xv K). Temperature reduces with distance 0.98 °C per 100 meters.

It may be argued that the source and characteristics of the weather data are not representative of the conditions at the turbines, and that but multiplying 10 m current of air speeds by 1.33 is non actually a valid way to notice elevated wind speeds, as the atmospheric structure, and the orography, is much more complex than that the simple parameterization would imply.

The theoretical electricity production E is finally:

$$E=\beta {\int }_{{t}_{2}}^{{t}_{1}}P(\blastoff \,U(t))dt$$

(3)

where U is the reference velocity measured at the fourth dimension t, α is a correction coefficient to compute the velocity at hub height, P is the tabulated power function, and β is a correction factor for the density effect. β is taken as the ratio of reference temperature for the power curve, and average temperature over the time interval.

Experimental capacity factors of wind energy facilities in the US

An upwards-to-date description of the bodily onshore wind energy facilities in the United states of america is provided in Fig. 1. The 64 wind energy facilities considered are numbered 1 to 64, as shown in Table one, that is reporting the proper noun, chapters, capacity factor and type of turbines. Over the years 2013 to 2017, these wind energy facilities take run at capacity factors ranging from 15% to 50%, with an average of 34%. Information is from¹⁵. The about role of the wind energy facilities is in TRGs 5–seven, where the Weighted Average Net capacity factors should range from 30.viii% to xl.7%.

Effigy 1

Capacity factors of wind free energy facilities in the face-to-face continental The states. Data from¹⁵. Credit the U.S. Energy Information Administration (Eia).

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Table 1 Capacity and Capacity Factors of wind free energy facilities in the contiguous continental United states. Data from^xv. Credit the U.South. Free energy Information Administration (Environmental impact assessment).

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Figure i and Table 1 show significant differences vs. the pattern depicted in⁷, which appears optimistic. For example, for 2013⁷, reports weighted averages capacity factors of 35 to 39% and oscillations almost these values from 26 to 49%. The naïve average of Tabular array ane for 2013 is 33%, with a minimum of xix% and a maximum of 44%. For 2014⁷, reports weighted averages chapters factors of 39% to 44% and oscillations well-nigh these values from 29 to 51%. The naïve average of Table 1 for 2014 is 34%, with a minimum of 18% and a maximum of 46%. Hence⁷, generally appears optimistic, overrating the average, minimum and maximum chapters factors.

The previous results accept shown significant differences between the different wind energy facilities. These differences are due to a unlike resource, as well every bit a unlike blueprint of the current of air subcontract. Here we show equally also wind energy facilities sharing about the aforementioned resource take different performances. The selected case study is Los Vientos, TX.

Ref. ³⁶ presents the land-based wind speed at 100 m hub for the contiguous states of the United states excluding Alaska with enlarged the area of south Texas where the Los Vientos current of air energy facility circuitous is located. Los Vientos has 5 wind energy facility units in most the same location for wind resources. This is a good instance to show the variability of the capacity factors from one unit to the other. Texas is ane of the preferred areas for wind free energy in the United states of america, for both wind resources and topography. The area of Los Vientos has a prevailing air current speed approaching 7.5 1000/due south.

The complex has a full capacity of 910 MW. Unit of measurement I (or 1 A) and II (or 1B), of power 200 and 202 MW, began performance in Dec 2012. Unit III, of power 200 MW, started operations in May 2015. Unit IV, likewise of ability 200 MW, came online in August 2016. Unit V, of power 110 MW, became operational in December 2015. Data is proposed past³⁷.

Los Vientos I has 87 turbines Siemens SWT-two.3–101 of ability 2,300 kW, diameter 101 thousand, and hub height 100 m. Latitude is 26°20′7.viii″. Longitude is −97°38′51.iv″. Los Vientos Ii has 87 turbines Mitsubishi MWT-102-2.4 of power 2,400 kW, diameter 102 yard, and hub peak 80 m. Latitude is 26°twenty′25.5″. Longitude is −97°41′nineteen.6″. Los Vientos Three has 100 turbines Vestas V110/2000, of ability 2,000 kW, and bore 110 chiliad. The hub height is non known. Breadth is 26° 20′ 47.ii″. Longitude is −97°36′58.half dozen″. Los Vientos IV has 100 of the same turbines Vestas V110/2000, of unknown hub height. The precise localization is not given. Los Vientos 5 has 55 of the same turbines Vestas V110/2000, of unknown hub height Latitude is 26°37′17.4″. Longitude is −98°44′53.2″.

The experimental capacity factors for the Los Vientos units 1A, 1B, III and IV (there is no production data yet for unit V) are presented in³⁸. The measured seasonal variability of capacity factors partially agrees with the reference seasonal variability for the lower plains region that is shown in³⁹. This reference seasonal variability was based on data of facilities with a internet chapters >1 MW and above within the specific area over the period 2001–2013. The seasonal and inter-annual variability of the capacity factors for this and other air current energy facilities are discussed in³⁸.

During the year 2017, ε _max , ε _min, and ε _ave were 48.58%, 20.84%, and 37.85%. This is slightly less than the 40.7% weighted average net capacity factor of a TRG5 location (wind speed range six.9–11.1 chiliad/s, weighted average air current speed vii.5 1000/s)⁷.

Over the 5 years of data from 2013 to 2017, unit 1A had an average, maximum and minimum ε of 35.31%, 39.xvi%, and 32.49%, while unit 1B had an boilerplate, maximum and minimum ε of xxx.93%, 33.76% and 28.02%. Unfortunately, there is not enough data for the other wind energy facilities to compute the inter-almanac variability.

The difference vs. the reference seasonal variability for the lower plains of³⁹ is significant over every year.

Los Vientos i A outperformed Los Vientos 1B in terms of free energy of 1.99% in 2013, 6.75% in 2014, 6.01% in 2015, 2.91% in 2016 and 4.07% in 2017³⁸. Los Vientos 1A and Los Vientos III had near the same performances in 2017. Los Vientos Four outperformed both Los Vientos 1A and Los Vientos Iii in 2017. Orography and different relative locations of the turbines affect the result, same as turbine type and hub height.

Figure 2 highlights the capacity factors of 2017 to better testify the seasonal variation of this specific yr. The Los Vientos III and IV wind energy facilities seem to piece of work meliorate during the middle months, while at the outset of the yr, the performance of Los Vientos III was far from optimal and at the end of the year, the advantages are lost. The Los Vientos 1A and 1B current of air free energy facilities have remarkably close performances despite the dissimilar turbines, with better performances of 1A the probable result of a higher hub top. Los Vientos IV had a 2017 capacity factor of 42.ten%. Los Vientos III, of the same turbines, had a 2017 capacity gene of 37.56%. Los Vientos 1B, featuring unlike turbines, likely at a lower hub height than those of Los Vientos IV and Iii, had a 2017 capacity factor of 33.72%. Finally, Los Vientos 1A featuring other turbines had a 2017 capacity cistron of 37.79%. Los Vientos 1B has capacity factors always smaller than Los Vientos 1A.

Effigy two

Monthly capacity factors during the year 2017 in Los Vientos. Image reproduced modified after^6,38.

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The monthly capacity factors of the Los Vientos current of air energy facilities over the full length of their operation accept been ten.61% to 55.32%, an average 33.91%. During 2017, the monthly chapters factors vary between 19% and 55%, with an boilerplate of 38%.

Computational study of air current energy in Los Vientos, TX

Later having shown that also current of air energy facilities sharing the virtually the same resource have different performances, the upshot of one of the blueprint parameters, the power curve of the turbines, is hither analyzed. It is common practice to take every bit the total installed capacity of a wind energy facility the sum of the rated powers of all the turbines. Other design parameters such as hub elevation, and relative position of every turbine in arrays, and influence of the orography, are typically neglected in computing the total installed capacity.

Wind turbine information shows significant variability across designs. Figure 3 presents the data of power and power density, of 553 dissimilar turbines having power ranging from 2 to 10 MW as a function of the rotor diameter, the most relevant design parameter of a wind turbine. All the turbines are centric flow, three blades. The rated speed used to compute the power varies from one blueprint to the other. This explains the spreading of the two distributions.

Effigy 3

Ability (a) and power density (b) of 553 turbines with ability range 2 to 10 MW vs. rotor diameter.

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The top efficiency η is not reached at the rated speed, just well below. The nigh common functioning of the turbines occurs at wind speeds below the rated speed. Modeling of current of air turbines' power curves, when not available from manufacturers, is discussed in^40,41. Figure four presents the power and efficiency η curves of a subset 20 turbines of power 1.8 to 3.0 MW (information from²⁶). The current of air speed for η_max ranges from a maximum of nine m/s to a minimum of 7 one thousand/s with an boilerplate of 8.2 thousand/s. The η_max ranges from a maximum of 51% to a minimum of 43% with an boilerplate of 47%. The rated speed drastically changes from 1 pattern to the other. College ability densities are institute at higher rated power current of air speed. Rated speed ranges from 10 to 16 thousand/s, with an boilerplate of 12.8 one thousand/southward. The figure shows the spreading of wind turbine power curves.

Figure four

Ability (a) and efficiency (b) curves of 20 turbines with a range of ability i.8 to three.0 MW vs. wind speed. Images reproduced modified afterward⁶.

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While the data bachelor for the turbines of Los Vientos 1B, III and IV is insufficient to develop a model (the specific power curves are unavailable in²⁶, and the hub peak is similarly unspecified for Three and IV), a simple model tin can exist developed for Los Vientos 1A.

Los Vientos 1A has 87 turbines Siemens SWT-2.three-101 (power 2,300 kW, diameter 101 yard)²⁶. has no power bend for this turbine, having rated power 2,300 kW, cutting-in wind speed 3.v m/s, rated wind speed12.v m/s, cut-out wind speed: 25 m/s. However²⁶, has the ability curve of the turbine SWT-ii.3-113 (power 2,300 kW, diameter 113 m) of about same parameters, rated ability two,300 kW, cut-in wind speed 3 m/s, rated wind speed12.5 m/s and cutting-out current of air speed 25 g/s. As a first approximation, the SWT-2.iii-113 power curve is used in lieu of the SWT-two.3-101 power curve.

Effigy five presents a comparison of measured and computed electricity production for Los Vientos 1A during all the years of functioning, and the measured and computed capacity factors. The images are reproduced modified afterward³⁸. Further data may be constitute in³⁸.

Figure 5

Los Vientos 1A measured and computed monthly capacity factors. Images reproduced modified after³⁸.

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The theoretical values are expected to be larger than the bodily values. Despite the method being quite simple, the current of air resources is approximated similarly to the air current turbine curve, the details of terrain and turbine relative location are unknown, and the predicted values are usually slightly in excess than the measured values, with closely followed fluctuations in the electricity product. This validation supports the opportunity to assess the consequence of the detailed current of air turbine power curve on the capacity factor by using this model.

Effigy 6 presents the computed monthly capacity factors over the twelvemonth 2017 for the turbines of Fig. iv having a rotor axis placed at the same hub peak of 100 yard in the Los Vientos 1A location, plus the computed almanac chapters factors for the same year. The maximum, minimum and average capacity factors for the hypothetical wind energy facilities built in the Los Vientos 1A location, with turbines 1–xx, are 44.6%, 24.i%, and 33.nine%. Thus, the difference between designs is quite considerable. Fifty-fifty turbines having about the aforementioned rated wind speed may indeed produce quite different capacity factors, as the bodily shape of a turbine ability bend having the aforementioned cut-in and rated speed still matters. Turbines have superlative efficiency significantly variable betwixt one design and the other. The net effect of a different turbine is to shift upward and down the electricity product, without significantly affecting the shape of the curve.

Figure vi

Monthly capacity factors of different turbines located in Los Vientos 1A over the year 2017 (a) and annual capacity factors (b).

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The monthly capacity factors of the modeled 20 unlike turbines located in Los Vientos during 2017 have been 12.48% to 56.15%, with an boilerplate of 33.88%.

The proposed new cess of the cost and performance of wind free energy facilities

Not simply the forecasted CAPEX and annual average capacity factors of⁷ are optimistic, but the production of electricity is likewise intermittent and unpredictable, and this must exist accounted for. The variability is only minimally shown by the analysis of low frequency (monthly) data. A much higher frequency, 1 minute of less sampling frequency, is indeed needed to appreciate the variability. A procedure is thus proposed to right cost and functioning assessment including variability.

As wind energy facilities work not simply with annual average capacity factors nigh 0.34, merely also with high-frequency standard deviations of same guild of magnitude, for about unity coefficients of variability⁴², with no certainty of any given production, at any time, the forecasted CAPEX cannot be compared with the CAPEX of, for example, of a combined bike gas turbine power institute, of annual capacity factor in backlog of 0.9, and high predictability of power output.

An energy storage allowance should be included to brand meaningful the comparing between different energy sources, bookkeeping for the variability.

While the bodily costs are not examined in this manuscript, it has been shown as the annual average capacity factors are nigh 0.xv to 0.v, average 0.34, quite far from the forecasted values. Hence, the forecasted CAPEX should exist besides corrected for their bodily almanac average capacity factors, in improver to the assart for energy storage.

It has been also shown, unfortunately only based on a depression-frequency (monthly) statistic, equally the capacity factors likewise vary from year to year and from month to month additional to facility-by-facility.

Different wind energy facilities, fabricated up of different turbines of same nominal capacity, located at unlike hub height, in places of different air current energy resources, placed on unlike land sizes, more or less packed, and suffering of dissimilar topographies, all have the same nominal full capacity, only then they have much different actual production of electricity.

By looking at grid average values, for what concerns the toll, if CAPEX is the cost per unit of measurement nominal power, P_i is this nominal power, and ε_i is the annual capacity factor of the facility i, and so the average CAPEX over all the north facilities connected to the same filigree should be taken as:

$$Greatcoat{X}^{\ast }=\frac{{\sum }_{i=1}^{n}\frac{Greatcoat{X}_{i}}{{\varepsilon }_{i}}\cdot {\varepsilon }_{i}\cdot {P}_{i}}{{\sum }_{i=i}^{due north}\,{\varepsilon }_{i}\cdot {P}_{i}}=\frac{{\sum }_{i=i}^{due north}\,Cape{X}_{i}\cdot {P}_{i}}{{\sum }_{i=one}^{northward}\,{\varepsilon }_{i}\cdot {P}_{i}}$$

(4)

This number should exist so corrected for the energy storage allowance.

Also looking at the grid average values for what concerns performance, at least 2 parameters should be considered. One parameter is the ratio of the annual boilerplate actual generating power to the nominal power, i.eastward. the annual boilerplate chapters cistron, and one additional parameter is introduced to represent the variability about the annual boilerplate value. This may be the standard deviation of the capacity factor, computed by using a loftier-frequency statistic⁴². Both the annual average and the variability parameter of the capacity factor should be measured for every air current energy facility, preferably with high frequency, ideally every infinitesimal of fifty-fifty less. The standard deviation for every facility is

$${\rm{s}}=\sqrt{\frac{ane}{m-1}\mathop{\sum }\limits_{i=1}^{m}{({\varepsilon }_{i}-\varepsilon )}^{2}}$$

(5)

where [ε_i, i = 1, …., yard] are the observed values at the sampling frequency (preferably every minute) over a year, and

$$\varepsilon =\frac{1}{thou}\mathop{\sum }\limits_{i=ane}^{k}\,{\varepsilon }_{i}$$

(half dozen)

is the hateful value of the observations, with m the number of observations. The capacity factors of the unlike wind energy facilities in the statistical sample are weighted on the electricity generated:

$${{\boldsymbol{\varepsilon }}}^{\ast }=\frac{{\sum }_{{\boldsymbol{i}}=1}^{{\boldsymbol{north}}}\,{{\boldsymbol{\varepsilon }}}_{{\boldsymbol{i}}}\cdot {{\boldsymbol{\varepsilon }}}_{{\boldsymbol{i}}}\cdot {{\boldsymbol{P}}}_{{\boldsymbol{i}}}}{{\sum }_{{\boldsymbol{i}}=1}^{{\boldsymbol{n}}}\,{{\boldsymbol{\varepsilon }}}_{{\boldsymbol{i}}}\cdot {{\boldsymbol{P}}}_{{\boldsymbol{i}}}}$$

(7)

Finally,

$${south}^{\ast }=\frac{{\sum }_{i=one}^{due north}\,{s}_{i}\cdot {\varepsilon }_{i}\cdot {P}_{i}}{{\sum }_{i=1}^{north}\,{\varepsilon }_{i}\cdot {P}_{i}}$$

(viii)

The only reasonable performance evaluation of a wind free energy facility tin be made comparing the annual average capacity cistron and the standard deviation of the loftier-frequency distribution with the averaged values of all the facilities continued to the aforementioned grid.

Give-and-take

In the case report of the 64 largest wind energy facilities in the continental US excluding Alaska, over the years 2013–2017, the annual chapters factors have been betwixt 0.15 to 0.50, with an average of 0.34. The all-time performing wind energy facilities are aligned with the TRG values of⁷, but the other wind energy facilities, the majority, are performing less.

In the 4 units of Los Vientos, TX, the annual capacity factors of 2017 vary from a maximum of 0.4858% to a minimum of 0.2084%, with an average of 0.3785%. In this TRG5 location of wind speed range half-dozen.9–11.i chiliad/due south, and weighted boilerplate wind speed 7.5 grand/due south, from^seven the weighted average capacity gene is expected to be 0.407%. Besides from these data, the chapters factors of^vii appear to be optimistic.

Similarly, optimistic is the CAPEX of^vii, which is referred to the nominal rather than the actual generating capacity, with the first number much larger than the second, almost three times. Wind energy facilities are non nuclear power plants, that work on average at chapters factors about 0.92⁴³, with small differences betwixt one found and the other, nor they are combined cycle gas turbines power plants, that too may work above 0.nine and are highly predictable. From Table one, the chapters factors are 0.32 to 0.38 on average, depending on the year, and strongly variable between different air current farms, from 0.xv to 0.50.

The CaPEX of⁷ given as the cost per unit of measurement nominal ability, should be replaced by the cost per unit actual power. This is only achieved by dividing the CAPEX of a facility by the capacity factor of that facility. But then, this CAPEX should likewise exist corrected to include the grid average assart for free energy storage.

Theoretically, the almanac capacity factors of 2017 of the xx turbines considered, placed at the aforementioned hub acme in Los Vientos vary from a maximum of 0.446 to a minimum of 0.241, with an boilerplate of 0.339. The reduced annual average capacity factor is likely partly because of the shape of the turbines' power curve, plus the influence of hub height, with orography and relative position of the turbines, plus a variation of wind management and air density, and turbulence, playing the remainder.

The further uptake of wind energy calls for a ameliorate statistic, accounting for the actual cost referred to the actual annual average generating power, plus the actual chapters factor, and parameters describing the oscillations nigh the annual value of the capacity factor, computed by using the highest possible sampling frequency. Variability affects the actual cost of electricity. The standard deviation about the hateful value is 1 elementary parameter describing this variability.

The proposed statistic may permit to better assess the performance of the filigree average wind energy facility and to individuate those who perform above, or below average, fostering cost reduction, too equally improving the ratio of actual annual average to nominal generating capacity, and reducing the fluctuations.

The case of the Australian National Electricity Market (NEM) grid, roofing the most function of the population of the southeastern states of Australia, is the only example worldwide where information of ability generation facilities, including current of air and solar, is made bachelor every 5 minutes by the Australian Energy Market place Operator (AEMO). Ref. ⁴⁴ collects the data of the AEMO in daily and monthly graphs. These data are presented equally daily power graphs of 5-infinitesimal data, and monthly power graphs of 3-60 minutes data, since 2018. Function of the information for 2018 is also available in CSV format. While the Australian data, is not as completed as the EIA United states of america data, that is spanning the last xx years, it may serve the purpose to show the effect of the sampling frequency in the wind free energy time serial.

The high-frequency data of the Australian NEM filigree have been recently⁴⁵ used to compute the growth factors for wind and solar installed chapters, and the storage actual power and energy needed, to make this specific grid current of air and solar but. In the case of the Us, now characterized by multiple grids, the practice could be repeated once like loftier-frequency data could exist made available over one full yr, for every grid, too equally for a hypothetical single grid. A single US grid could reduce the grid average variability of wind and solar, even if at the cost of larger transmission losses, and thus the energy storage requirements.

As shown in Ref. ⁴², the average capacity factors of air current are 0.3–0.38, and their standard deviations have about the same values, for coefficients of variations about unity. This indicates the extreme variability, that makes had to provide about constant outputs even over significant space average.

As an example, Fig. 7 presents the performance of all the wind energy facilities during January 2019, a midsummer month, likewise as the operation of the 3 units of Hornsdale, in South Commonwealth of australia, i of the all-time performing wind farms of Australia, directly connected to the Hornsdale ability reserve battery. The tick, black line is the grid-average. The filigree average air current free energy facility works oft above threescore%, simply also below v%, of the nominal power. This produces significant issues to the grid, and pregnant costs compensating for this variability.

Figure vii

(a) Performance of the air current energy facilities connected to the electricity filigree in south-east Australia over Jan 2020 (a mid-summer month). (b) Performance of the Hornsdale wind energy facility in South Australia over the same calendar month. Images reproduced modified from⁴⁴. anero.id/energy/. Credit Andrew Miskelly.

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Energy storage^46,47 is thus essential for renewable free energy. If we want all the free energy of the grid wind and solar photovoltaics only, without any fully dispatchable combustion fuels ability plants, and so we do demand massive energy storage^vi.

Renewable energy on need from hydropower, which in Australia is presently 8%, but it is projected to reduce beneath three% by 2030⁴⁸, can help, but this is not enough. Additionally, to the hydro gravity facility being retrofitted with pumping capabilities to work equally pumped hydro energy storage (PHES) facilities, other saltwater coastline PHES facilities, besides as battery facilities, are needed.

Presently⁴⁹, bombardment energy storage in Australia is limited to about 200 MW power and almost 200 MWh energy, also including the world's largest bombardment, the 100 MW/129 MWh facility in Southward Commonwealth of australia.

Battery storage is indeed in its infantry. The batteries cannot be fully discharged, the world'south largest bombardment only lasts less than 1 hour and i half if discharged at a very optimistic acme power of 100 MW.

As shown in⁴⁵, current of air and solar capacities must be increased to 53.2 and ninety.5 GW (growth gene 7.94) to fully cover the present NEM filigree need with additionally a minimum bodily storage power of more than 45 GW net, and bodily storable energy in backlog of 3,500 GW·h. The nominal power and energy of the storage are much larger as information technology depends on the specific technology adopted, as for example battery storage only works at a fraction of the nominal power during charge and discharge, and only a fraction of the nominal chapters can exist used, with round-trip efficiencies everything but unity. Worth to notation, is also the length of the storage. Equally both wind and solar are strongly affected past seasonality, and the full production of wind and solar vary with the season, a wind and solar but grid as well necessitate long term storage, that is an boosted challenge non considered before.

When loftier-frequency data volition be eventually made available for the US over a total twelvemonth for all the air current and solar facilities connected to the same grid of given demand, then it will be possible to compute growth factors for air current and solar chapters, total power, and energy of the storage, cost of the storage, and finally attribute this cost to every facility, inversely proportional to the annual hateful capacity gene, and straight proportional to the standard deviation about this value.

Conclusions

The CAPEX and annual average chapters factors forecasted in technology assessments for current of air are optimistic. The production of electricity from wind energy facilities is intermittent and unpredictable, and this must be accounted for, the aforementioned as the actual annual average generating power.

The CAPEX of a wind energy facilities that are working not only with almanac average chapters factors about 0.34, but also with high-frequency standard deviations of same guild of magnitude of the hateful capacity factors, for about unity coefficients of variability, and no certainty of any given production at any time, cannot exist compared with the CAPEX of ability plants of annual capacity factor in excess of 0.9 and high predictability. An energy storage allowance should be included to make the comparing meaningful, bookkeeping for the variability.

While the bodily costs are not examined, information technology is also shown equally the almanac average capacity factors are virtually 0.15 to 0.5, average 0.34, quite far from the forecasted values. Information technology is besides shown based on a low-frequency (monthly) statistic equally the capacity factors also vary from year-by-year and from month-by-month.

Dissimilar wind energy facilities, of different turbines albeit of same nominal capacity, located at different hub superlative, in places of different wind energy resource, and sited on unlike terrains, more or less packed together, may all have the same nominal capacity, but then they have much unlike actual product of electricity. To take the sum of the nominal power of all the turbines as the reference power of a wind energy facility is an oversimplification not recognizing the value of ameliorate pattern, thus not rewarding the developers that are building ameliorate air current energy facilities.

The energy storage issue should be acknowledged the sooner the better, as without, air current and solar free energy are unable to supply the energy needed by a balanced grid without combustion fuels.

The novelty of the present work is the recognition of the variability of wind ability generation as a performance and toll parameter, and the proposal of a practical way to progress the design of the storage and its cost attribution to the generating facilities.

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Acknowledgements

The authors want to thank Andrew Miskelly for permission to reuse the images of his web site in the manuscript.

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Affiliations

1. Department of Mechanical Engineering, College of Engineering science, Prince Mohammad Bin Fahd University, Al Khobar, Saudi Arabia

   Alberto Boretti

2. Schoolhouse of Applied science, Regal Melbourne Institute of Technology (RMIT) University, Bundoora, Victoria, Australia

   Stefania Castelletto

Contributions

A.B. defined the method. A.B. and S.C. both downloaded and analyzed data, and discussed the results. A.B. wrote the first typhoon of the manuscript. Both authors participated in the further revisions of the manuscript.

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Correspondence to Alberto Boretti.

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Boretti, A., Castelletto, S. Cost of wind free energy generation should include energy storage allowance. Sci Rep 10, 2978 (2020). https://doi.org/10.1038/s41598-020-59936-x

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• Received: 12 November 2019

• Accepted: 05 February 2020

• Published: nineteen Feb 2020

• DOI : https://doi.org/ten.1038/s41598-020-59936-10

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