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Sensitivity analysis of the economic-financial

feasibility study of the Punta de Maisí Wind Farm

project.

Análisis de sensibilidad del estudios de factibilidad

económico - financiera del proyecto ¨del Parque Eólico

Punta de Maisí

Luis Garcia-Faure

Gustavo Fernández-Salva

Lorenzo Enriquez-Garcia

Monserrath Padilla Muñoz

ABSTRACT

In Maisí municipality, the easternmost municipality of Cuba,

belonging to Guantánamo province, at coordinates 20,270

N and 74,220 W approximately, pre-feasibility studies are

being carried out for a wind farm project in two sites

known as Punta Fraile and Punta Quemado. Two variants

are proposed. The objective of this work was to perform

sensitivity analyses on the profitability of the parameters

susceptible to change, in order to determine the limits

within which they can move without the project becoming

unprofitable. For the studies, a program was designed for

pure and hybrid renewable sources; it has a module for the

estimation of the capital cost based on the relevant

parameters of the project, which guarantees equal

conditions in the analysis of variants. The economic-

financial evaluation is carried out using four fundamental

criteria that complement each other. The results are given

in the form of a comparative table of variants and influential

sensitivity parameters.

* Mechanical Engineer. PhD in Technical Sciences.

Professor-Researcher of the Universidad de Oriente in Santiago de Cuba.

lgarcia@uo.edu.cu, https://orcid.org/0000-0003-1237-3915

* Mechanical Engineer. Teacher-Researcher of the Universidad de Oriente in

Santiago de Cuba. Republic of Cuba. gfsalva@elecgtm.une.cu

https://orcid.org/0000-0001-7425-8571

* PhD. In electronics and electrical and control systems. PhD, in energy

efficiency systems. lenriquez@espoch.edu.ec

https://orcid.org/0000-0001-7300-8204

* MSc in Physics and Mathematics. Teacher and researcher at the School

Superior Politécnica de Chimborazo (ESPOCH),

monserrath.padilla@espoch.edu.ec, https://orcid.org/0000-0003-0493-7709

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Keywords: Feasibility studies, Sensitivity analysis,

Parametric cost estimation, Relevant parameters of the

project

RESUMEN

En el municipio Maisí, el más oriental de Cuba,

perteneciente a la provincia Guantánamo, en las

coordenadas 20,270 N y-74,220 O aproximados, se

realizan los estudios de pre factibilidad del proyecto de un

parque eólico en dos emplazamientos conocidos por Punta

Fraile y Punta Quemado. Se proponen dos variantes. El

objetivo de este trabajo fue realizar los análisis de

sensibilidad sobre la rentabilidad de los parámetros

susceptibles de variar, con la finalidad de determinar los

límites dentro de los cuales se pueden mover sin que el

proyecto deje de ser rentable. Para los estudios fue

diseñado un programa para fuentes renovables puras e

híbridas; dispone de un módulo para la estimación del

costo capital a partir de los parámetros relevantes del

proyecto que garantiza igualdad de condiciones en el

análisis de variantes. La evaluación económico - financiera

se realiza mediante cuatro criterios fundamentales que se

complementan. Los resultados se dan en forma de tabla

comparativa de las variantes y parámetros influyentes de la

sensibilidad.

Palabras clave: Estudios de factibilidad, Análisis de

sensibilidad, Estimación paramétrica del costo, Parámetros

relevantes del proyecto

INTRODUCTION

Since 1984, the Universidad de Oriente and the Centro de Investigaciones Solar (CIES)

have been carrying out wind speed measurements in the municipality of Maisí, which

together with the data base accumulated by the meteorological station at the lighthouse

of that strategic point for navigation, made it possible to analyze the seasonal and

monthly behavior of the region.(Burton et al., 2011; García et al., 2016a, 2016b).The

wind map subsequently developed by the Institute of Meteorology of Cuba (Roque-

Rodríguez et al. (Roque-Rodríguez et al., 2019)allowed corroborating the hypothesis

that there was a good wind potential in the area. The mean annual velocity calculated

with the monthly average values and extrapolated to 50 m altitude, as well as the

e-ISSN: 2576-0971. January - March Vol. 7 - 1 - 2023 . http://journalbusinesses.com/index.php/revista

calculation of the wind potential of the sites planned for the turbine emplacement, are

in correspondence with those provided by the wind map of Cuba, Figure 1.

Currently, the pre-feasibility studies for the wind farm are being carried out in two

variants: the first variant proposes to install 2.5 MW Gamesa turbines for a total of 175

MW at the Punta Fraile and Punta Quemado sites, with 87.5 MW at each site; the second

variant proposes to install 4.5 MW Gamesa turbines, 46 of them at Punta Fraile and 24

at Punta Quemado, with a total installed capacity of approximately 300 MW (Apgar, n.d.;

Siemens, 2020).(Apgar, n.d.; Siemens, 2020).

For the determination of the annual energy produced in each variant, the characteristic

curves of the G-114-2.5MW and G120-4.5 turbines, which can be installed with tower

heights of 100 and 120 meters, respectively, are used (Siemens, 2020). The capital costs

of both projects are influenced by the power to be installed, but also by the number of

turbines and the height of the towers, the parametric model of cost estimation solves

this problem(Enriquez et al., 2019; RENEWABLE POWER GENERATION COSTS IN

2018, 2019; VGB PowerTech, 2019).

The project foresees the interconnection of the machines of both sites with the national

grid, so for the analysis all the energy produced is absorbed by the system.

To ensure a good margin of reliability of the results, certain considerations must be

made:

The sites are located at altitudes ranging from 20 m to 50 m above sea level, so the

turbine output must be corrected for the decrease in air density. - At each

The site will have a large number of turbines, so that regardless of the arrangement

adopted, the total generation of the wind farm will be affected by the wake effect that

occurs behind the turbines (array efficiency)[3], In this work, an acceptable value (90%)

for array efficiency is adopted because of the influence it has on the profitability of the

wind farm.

Figure 1. Map of wind potential in Cuba.

Source: Institute of Meteorology of Cuba

MATERIALS AND METHODS

Three modules of the FRE-LGV-1 program developed by Professor Luis Jerónimo García

Faure

are used to carry out the work:

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- Study of the site's wind potential, annual energy generation and capacity factor of each

site.

- Economic-financial validation

- Sensitivity analysis

The wind speed distribution is used to estimate the wind potential, which will then serve

as an element for calculating the energy that can be produced and the capacity factor

with which the wind farm must operate. The wind power density is defined as the

average value of the power per unit area of all measurements taken during the year

(Manwell et al., 2010). (Manwell et al., 2010)It is given by:

Generally, hourly wind speed measurements are made, in this case n=8760, which are

the hours of a normal year.

Wind potential is considered poor if the wind power density is less than 160 W/m

acceptable or good up to 400 W/m

and excellent above 400 W/m

It is shown [5]: that the useful power produced by a wind turbine for a wind speed v

given by:

Normally manufacturers provide the characteristic curves of their turbines (P-v

)

evaluated in laboratory conditions in order not to have to use the coefficient C

and the

efficiency η

and take the air density for normal atmospheric conditions ofr =1,225 kg/m

, which must be corrected for local conditions. Thus, the energy produced by the turbine

for each wind speed is given by:

And the total annual energy is determined by:

If hourly wind speed measurements are taken n=8760 hours and the product p(v

).8760

are the hours of the year that the speed v

The capacity factor is given by the ratio between the annual energy produced and the

energy that could hypothetically be produced if the turbine were to operate for all 8,760

hours of the year at rated power:

The values of the Weibull parameters k and c were calculated at the reference height

ref

) of 50 meters to determine if the wind potential at that height is in correspondence

with the one indicated in the wind map of Cuba, then they were extrapolated for the

turbine hub height (Z

buje

) to determine the power(Enriquez Garcia & Garcia Faure, 2018;

)1(

DPV

)2(

kWvACP

itpi

×××××=

)3()(

225,1

kWhtvPE

iii

××=

)4(/)()(

225,1

max

akWhvpvP

)5(

8760min

alnoPotencia

producidaanualEnergía

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National Aeronautic and Space Administration NASA, 2015). It is assumed that although

the air speed increases with height, the frequency with which the velocities pass at the

hub and reference heights is the same, that only the magnitude of the velocity varies.

Under these conditions, the coefficient k practically remains constant, but the coefficient

c varies according to the following relationship [6]:

The capital cost, as mentioned before, is estimated by the parametric method (Apgar,

n.d.; National Aeronautic and Space Administration NASA, 2015). The model used was

developed based on the three relevant technical parameters that determine the cost of

wind farms: power, number and heights of turbines, taking into account a representative

number of farms built in recent years in 12 of the Latin American countries that make

the greatest use of wind power (Enriquez García & García Faure, 2018; Enríquez et al.,

2019; García et al., 2016b).. It is given by:

For values of 90<Z<130 m

This equation takes into account all costs associated with the initial investment of the

wind farm including transportation and assembly of the turbines, but not the

transmission lines and other external works of the wind farm. When used with any of

the economic-financial validation criteria, it has the advantage of establishing a

continuous relationship between the technical parameters and the criterion used (NPV,

IRR, COE, etc.), which guarantees equal conditions in the evaluation of the

variants(Enriquez et al., 2019; VGB PowerTech, 2019).

From the annual capital cost and the effective working hours of the turbines, operating

and maintenance costs, turbine replacement costs, if any, and the residual value of the

project are deducted.

The integral rate considers the part corresponding to the normal bank discount, the

insurance rate plus other rates that may arise. The maximum limit that this rate can take

is set by the internal rate of return (IRR) above which the NPV becomes negative.

The electricity sales tariff determines the revenue; as it increases, so does the NPV. It

can decrease until it becomes equal to the levelized cost of energy; below that value, the

NPV becomes negative. The analysis of the behavior of the sensitivity variables is carried

out by means of the spider diagram. (ICEAA, 2019)

RESULTS

The wind power density calculated at 50 meters height at the sites is 302 W/m2 with an

average speed of 6.44 m/s, very close to those obtained with the interactive wind map

of the Instituto de Meteorología shown in Figure 1.

)6(/

ref

buje

refbuje

×=

)7($02,18

55,1924,0675,0

ZNPC ×××=

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Variant 1

With 70 Gamesa G114-2.5 MW turbines for a total of 175 MW at the two sites with 35

turbines each.

By applying the FRE-LG-V1 program, it is determined that each site will be able to

contribute 294,062 MWh/year for a total of 588,124 MWh/year, i.e. 588 GWh/year, as

shown in Figure 2. This generation was obtained for a 90% efficiency of the wind farm,

which should increase or decrease depending on the efficiency achieved.

Figure 2. Energy production results for variant 1.

Source: FRE-LGV1 Program

Table 1 shows the parameters calculated and those to be set for the profitability

calculation. These values define the so-called break-even validation.

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Table 1. Summary of economic-financial parameters

of variant 1

Source: Authors, 2022

Results of validation of variant 1

Sensitivity analysis of variables on NPV

In the spider type graph. (ICEAA, 2019)in Figure 3 shows the value taken by the NPV

($65, 684,127) for the values in Table 1. It can be observed, that there are two

parameters that exert a notable influence on the profitability: the integral discount rate

and the electricity sales tariff. The operation and maintenance cost has practically no

influence on the NPV.

Figure 3. Spider diagram for sensitivity analysis.

Source: FRE-LGV1) program.

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Influence of the cost of capital of variant 1 on NPV sensitivity.

The cost of capital also has a marked influence on the profitability of the project: a 25%

decrease in cost represents an increase in NPV of approximately 50%, while a 25%

increase in cost represents a 50% decrease in NPV. Table 2 shows this behavior.

Table 2. Behavior of NPV with the cost of capital

Capital cost ($)

$/kW

VPN

Parametric estimate

238,294,030

1,362

65,684,127

25% decrease

180,764,508

1,032

98,969,425

25 % increase

297,867,537

1,702

29,985,664

Source: Authors, 2022

Variant 2

With 300 MW installed, 67 Gamesa G124-4.5 MW turbines and 120 meters hub height,

43 at the Punta Fraile site and 24 at the Punta Quemado site. Figure 4 shows the annual

energy production. The Punta Fraile site will be able to produce 608,617 MWh/year

while the Punta Quemado site will be able to produce 317,539 MWh/s, for a total of

926,156 MWh/year.

The first curious and apparently contradictory fact observed is that despite the increase

in the energy produced by the increase in installed power and the hub height of the

machines, there is a decrease in the capacity factor.

In order to understand this behavior, it is necessary to refer to equations 2, 4 and 6 on

the calculation of power, turbine energy and capacity factor. In equation 2, the power

calculation is a function of the power coefficient and the turbine efficiency, both

parameters depending on the type of turbine and the power at which it is working. In

similar turbines the behaviors of Cp and η follow similar curves, but as the turbine power

increases, their higher values move towards higher powers. In the case of the turbines

analyzed, for the G114-2.5 MW the highest values are obtained at lower wind speed.

When plotting the Weibull probability curves, it can be seen that as the hub height varies

from 100 m to 120 m, the curves maintain their shape, but below 9 m/s the probabilities

of occurrence are higher for the lower power turbine, which is where its power and

efficiency coefficients are higher. Figure 5 shows both probability distributions, and

although they appear very close (at 120 m it shifts to the right), the values of the

ordinates p(vi) differ sufficiently to produce the results obtained. From 9 m/s the

situation is reversed; in this case the higher probabilities of occurrence of the velocities

occur at higher altitudes, so that a relative increase of energy is obtained in the turbine

of higher power, but not enough to achieve the same capacity factor as with the turbine

of lower power. If the wind potential were higher, the turbines would work most of the

time at speeds higher than 9 m/s, the situation would be different.

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Figure 4. Energy production results for variant 2.

Source: FRE-LGV1 program

Figure 5. Weibull velocity distribution curves at 100 m and 120 m altitude.

Source: FRE-LGV1 program

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Table 3. Summary of economic-financial parameters of variant 2

Source: Authors, 2022

Table 3 shows that only those variables involved in cost and profitability are considered;

the remaining parameters remain the same as in variant 1 in order to establish a

comparison between the validation criteria.

Results of the validation of variant 2

Sensitivity analysis

As can be seen in Figure 6, as in variant 1, the two parameters that have the greatest

influence on NPV are the integral discount rate and the electricity tariff. In order to

establish the comparison between the two variants, equal values were taken for both

parameters.

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Figure 6. Sensitivity analysis of variant 2.

Source: FRE-LGV1 program

Table 4. Comparative summary

Item to compare

Variant 1

(175 MW)

Variant 2

(300 MW)

Difference (V2-

V1)

Energy production (GWh/a)

588

926

+57%

Capacity factor

0,38

0,34

-11%

Capital cost ($)

238,294,030

468,398,167

+96,5%

Life cycle cost ($)

137,871,607,

238,175,154

+73%

Net Present Value ($)

65,684,127

82,376,579

+25%

Levelized cost of energy

($/kWh)

0,1016

0,1115

+9%

Internal rate of return (%)

11,78

11,36

-3.5%

Source: Authors, 2022

CONCLUSIONS

The calculations made for both variants were performed for the same conditions and

equal equilibrium values as shown in tables 1 and 3 and whose results are summarized

in table 4. If the same wind potential is maintained, any variation that occurs in the

sensitivity parameters (integral rate of return, electricity sales tariff, capital cost),

produces an alteration (positive or negative) on the NPV and the remaining validation

criteria, but the ratio of the variants given in table 4 must be maintained.

The increase in power from 175 MW and height from 100 m of variant 1 to 300 MW

and 120 m height in variant 2 represents:

1. 57% increase in energy but must increase 96.5% of capital cost and 73% of life cycle

cost

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2. A 25% increase in net present value

3. An increase in the cost of energy production (COE) of 9%.

4. A decrease in the internal rate of return (IRR) of 3.5%.

However, as explained above, if the wind potential of the site were higher, all indices

for variant 2 would be expected to improve.

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from www.iceaaonline.com

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Second Edition. In L. John Wiley & Sons (Ed.), Wind Energy Handbook, Second

Edition. John Wiley and Sons. https://doi.org/10.1002/9781119992714

Enriquez García, L. A., & García Faure, L. J. (2018). Engineering economics / Anthony J.

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