TECHNICAL NOTE

Sizing of a Photovoltaic Solar Park for the Center for Agricultural Mechanization (CEMA)

Ing. Javier A. León-Martínez^{I  *} 
http://orcid.org/0000-0002-1606-0193

Dr.C. Yanoy Morejón-Mesa^I 
http://orcid.org/0000-0002-1125-3105

Dra.C Gleiby C. Melchor-Orta^II 
http://orcid.org/0000-0003-1352-3639

Ing. Luis M. Rosabal-Padrón^I 
http://orcid.org/0000-0001-6796-9156

MSc. Rolando Quintana-Aput^I 
http://orcid.org/0000-0003-1017-6512

MSc. Geisy Hernández-Cuello^III 
http://orcid.org/0000-0002-9049-3341

^IUniversidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba.

^IIUniversidad Agraria de La Habana, Centro Universitario Municipal de Jaruco, Mayabeque, Cuba.

^IIIUniversidad Agraria de La Habana, Centro de Mecanización Agropecuaria, San José de las Lajas, Mayabeque, Cuba.

ABSTRACT

This work deals with the foundation and proposal for the dimensioning of a photovoltaic solar park destined to satisfy the demand for electrical energy in the facilities of the Center for Agricultural Mechanization (CEMA) of the Agrarian University of Havana. For this, a study of the behavior of electricity consumption was carried out in CEMA, as it is considered a high consumer. It was determined that, to satisfy the energy demand, the photovoltaic solar park must have 323 solar panels of the BS18055 model, an accumulation system composed of 47 Trojan monoblock batteries, two Victron Energy model current regulators (input current of 2054.28 A and 1135.09 A output), as well as a 1000 kWh inverter. An analysis of the economic and environmental impact of the proposed installation was carried out, which showed that it will allow an electrical energy saving of not less than 29,421.72 kWh per year. Likewise, it was determined that, due to this unconsumed energy, at least 33.24 t of CO₂ per year would cease to be emitted into the atmosphere. Then, at least 7.7 t of fossil fuel would stop being consumed in the same period, thus representing a total saving of at least 57,368.23 CUP, for energy not consumed annually. To undertake the proposed installation, the preliminary cost estimate of the investment was calculated, which is around 244,583,376 CUP, if the energy storage system is included, and 935,376 CUP, not including the energy storage system.

Keywords: renewable energy; photovoltaic generation; energy efficiency; dynamic electrical loads

INTRODUCTION

The evolution of man, throughout the millions of years that it took him to arrive from primitive forms to his present form, is intimately linked to the different classes and quantities of each of the energies that he was able to have at each time. At some point, some human groups began to use the energy of certain animals that they were able to domesticate, mainly to carry loads. This was a great advance at that time, because it allowed him to multiply his power and his ability to move (^{Azcón & Talón, 2000}). Later, the peoples who lived near water surfaces learned to navigate over them by means of paddling canoes, again using their physical energy for this purpose. Later, man learned to apply the force of the wind to push sails mounted on his primitive boats and thus he could navigate greater distances, faster and with less effort (^{Derek, 1990}). After millennia without notable technical developments, a great change in the lives of the peoples of Western Europe occurred in the late 18th and early 19th centuries, when they began to use the thermal energy of fuels for more than just warm up in the cold, cooking and obtaining and processing metals. It was about producing mechanical power. On the basis of the combustion of mineral coal fundamentally (very abundant in Europe) water vapor began to be produced in primitive boilers, to power an alternative type power plant. With these machines, the workforce of many people and / or animals together could be replaced in workshops and factories avoiding physical exhaustion, at a much lower cost and with fewer conflicts (^{Derek, 1990}).

The irreversible depletion of world oil reserves, which is currently used as a direct source of energy, or to generate other energies (electricity, for example) through it, has been called "Energy Crisis". The reasons for this phenomenon are diverse:

• Increase in electricity consumption due to constant growth in the residential, industrial and service sectors;

• Increase in the automotive fleet;

• Depletion of other natural resources such as fresh water;

• Among other.

Out of this crisis has arisen the need for a better use of available energy resources. Ways have been devised to use different types of renewable energy resources for the purpose of converting them into electrical energy. Among these are: solar, wind, tidal, geothermal energy, among others (^{Gasquet, 2004}).

According to ^{Bérriz & Álvarez (2008)}, in Cuba, solar radiation has an energy value equivalent to 0.5 kg of oil per square meter per day, a value that varies very little from one place to another in the territory, due to the elongated shape and the orientation from East to West of the Island. This variation is almost negligible from one month to another, which enables the energy use of this energy source throughout the year.

Solar radiation is used directly in thermal and photovoltaic transformations, that is, in the form of heat and electricity. Thermal conversion is currently the most efficient, economical and advantageous way to use solar energy. The generalization of domestic use of solar hot water for personal hygiene, washing and cooking food, mean considerable savings in the consumption of polluting fuels. The consumption of fuels in heating water and other fluids in industry, commerce, tourism and in social buildings such as schools and hospitals is also very high; it could be satisfied with solar installations, in a sustainable and environmentally sound way ^{Bérriz & Álvarez (2008)}.

Photovoltaic solar energy consists of the direct transformation of solar radiation into electrical energy, taking advantage of the properties of semiconductor materials through photovoltaic cells. The base material for the manufacture of photovoltaic panels is usually silicon. When sunlight hits one of the faces of the solar cell it generates an electric current. This electricity generated can be used as an energy source, despite the fact that in the best of cases only 25% of light energy is transformed into electricity (^{Sawin & Martinot, 2011}; ^{Sánchez et al., 2017}; ^{Perpiñán, 2020}; ^{Kaffman, 2021}). To obtain an acceptable level of current intensity, several of them are connected in series. They are called photovoltaic modules or panels. The cells of the panel are protected by glass and are constructed in such a way that they can be joined with other panels. Photovoltaic installations must be equipped with accumulators, capable of storing unused electrical energy in the form of chemical energy. In some cases, it can also be connected in parallel with the grid, to use its energy when the sun is absent (^{Sánchez et al., 2017}; ^{Perpiñán, 2020}).

In the case of photovoltaic systems permanently connected to the national electricity grid, in the hours of little or no solar irradiation (when the photovoltaic generator does not produce enough energy to cover the demand for electricity), it is the network that provides the necessary energy. Considering the opposite case, if during the hours of solar irradiation, the photovoltaic system produces more electrical energy than what is used, the excess is transferred to the grid (^{Prado, 2008}; ^{Martin, 2020}).

At present there is no methodology for sizing a photovoltaic solar park, which fully adjusts to the case of satisfying the demand of a high consumer of electricity, which is also characterized by having dynamic loads, for which the authors consider that the characterization of a proposal for a photovoltaic solar park may be conceived from the perspective dimensioning of the behavior of electricity consumption in them.

The Agricultural Mechanization Center (CEMA) is located on the highway to Tapaste, on the National Highway, kilometer 23½, San José de las Lajas, Mayabeque. It has a concrete plot with an available area of ​​750 m^2. The average radiation is 5.0 kWh/m² and the relative humidity is 70%. It is also characterized by having a predominance of dynamic electric charges. As a result of the study of the behavior of electricity consumption in CEMA, a consumption equivalent to a monthly average of 818.99 kWh has been found. Therefore, the objective of this work was to carry out a proposal for the dimensioning of a photovoltaic solar park, capable of satisfying the demand for electrical energy in the Center for Agricultural Mechanization (CEMA), in order to contribute to the reduction of conventional electricity consumption, from the use of available energy resources in a sustainable and environmentally sound way.

MATERIALS AND METHODS

Installation Consumption Estimate

For the sizing of the photovoltaic solar installation, initially the critical average daily consumption of the load to which energy has to be supplied was determined. This parameter is associated with the days with the highest energy consumption. Due to the fact that in Cuba the behavior of the incidence of solar radiation does not vary sharply during the twelve months of the year and that the four seasons of the year are not clearly reflected, the average monthly value of the incident radiation for an inclination angle of 18°-25° to the south is 5.0 kWh/m² (^{Bérriz, et al., 2016}).

To determine the energy to be delivered by the photovoltaic installation, the losses involving the batteries, the inverter and the conductors were considered. To calculate the average daily consumption of the installation, the critical real average consumption of the load was taken into account and not the average consumption for constant loads or the number of inventories, due to the fact that the equipment with which it works in the area where the study was developed are subjected to dynamic loads such as lathes, mechanical drills, milling machines, mechanical saw, among other machine tools.

Static electrical loads are those that have a fixed consumption of electrical energy over time (^{Prado, 2008}; ^{Martin, 2020}). For example: lighting systems, air conditioning systems, televisions, personal computers, electric cooking systems, among others. This type of charge is common in domestic consumers.

In the case of dynamic loads, consumption was determined by the work they do and the type of material they machine, quite the opposite, to those with constant load such as household appliances (lighting fixtures, televisions, washing machines, among others) whose consumption does not vary significantly.

$L_{mdn}=\frac{L_{md}}{{\eta }_{bat}\bullet {\eta }_{inv}\bullet {\eta }_{cond}}, kWh$ (1)

where:

Lmd:	Critical real average consumption of the load, kWh.
ηbat:	Battery efficiency.
ηinv:	Efficiency of the inverter.
ηcond:	Efficiency of the conductors.

Photovoltaic Generator Sizing

To determine the number of solar panels required, a criterion was used based on the estimation of the Ampere-hour (Ah) consumption of the installation as recommended by ^{Hernández (2007)}, with the average daily current consumption required:

$Q_{Ah}=\frac{L_{mdn}}{V_{bat}}, Ah/día$ (2)

where:

Vbat:

battery voltage, V.

Likewise, according to ^{Alonso (2011)} & ^{Cantos (2016)}, the current that a photovoltaic reception field must generate in the critical month of solar radiation is determined as

$I_{gfv,mpp}=\mathrm{ }\frac{Q_{Ah}}{{HPS}_{crit}},\mathrm{ }\mathrm{A}\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }$ (3)

where:

HPScrit:

peak of sun hours of the critical month, h.

Then, being Igfv, mpp the current generated by the photovoltaic capture field (the total number of solar panels installed) and dividing it by the unit current of each photovoltaic module, the total number of modules necessary to connect in parallel is obtained (^{Alonso, 2011}). So that:

$Np=\frac{I_{gfv,mpp}}{I_{mod}}$ (4)

where:

Imod:

Specific unit current of each photovoltaic module, A.

Accumulation System Sizing

According to ^{Cantos (2016)} & ^{Martin (2020)}, to calculate the number of batteries required for a photovoltaic installation, the following must be considered:

• The desired autonomy time for the photovoltaic installation.

• The maximum seasonal discharge depth of the batteries.

• The maximum daily discharge depth of the batteries.

^{Alonso (2011)} & ^{Cantos (2016)} argue that the nominal capacity of the battery as a function of the maximum seasonal discharge is determined according to:

$C_{ne}=\frac{L_{mdn}\bullet N_{DA}}{P_{Dmax,e}\bullet F_{ct}}, kWh$ (5)

$C_{neAh}=\frac{C_{ne}}{V_{bat}}, Ah$ (6)

where:

NDA:	Number of days of the installation autonomy.
PDmax , e:	Maximum seasonal discharge depth of batteries.
Fct:	Total battery charge factor.
CneAh:	Nominal battery capacity based on the maximum seasonal discharge, Ah.

Likewise, the nominal capacity of the battery based on the maximum daily discharge was determined according to:

$C_{nd}=\frac{L_{mdn}}{P_{Dmax,d}\bullet F_{ct}}, kWh$ (7)

$C_{ndAh}=\frac{C_{nd}}{V_{bat}}, Ah$ (8)

where:

PDmax , d:	Maximum daily discharge depth of the batteris.
CndAh:	Nominal battery capacity based on the maximum daily discharge, Ah.

After determining the nominal capacity of the batteries based on the values of maximum stationary and daily discharge, the one with the highest value must be taken and divided by the nominal current capacity of one of the batteries, to obtain the necessary number of them:

$N_{bat}=\frac{C_{nAh}}{C_{nAh,bat}}$ (9)

Regulator and Inverter Sizing

^{Alonso (2011)} & ^{Cantos (2016)} argue that to find the regulator's capacity, the current at its inlet and outlet must be determined. ^{Prado (2008)} states that:

$I_{ent}=\left(1+F_{seg}\right)\bullet N_P\bullet I_{mod,sc}, A$ (10)

where:

Fseg:	Safety factor to avoid occasional damage to the regulator.
Np:	Number of branches in parallel
Imod ,sc:	Unitary current of the photovoltaic module under short -circuit conditions, A

Likewise:

$I_{sal}=\frac{\left(1+F_{seg}\right)\bullet L_{md,max}}{{\eta }_{inv}{\bullet T_{tpc}\bullet V}_{bat}}, A$ (11)

where:

Lmd,max:	Maximum load consumption, kWh.
Ttpc:	Time of maximum load demand, h.

The inverter power required for the installation was determined according to ^{Mascarós (2016)} where:

$P_{inv}=\left(1+F_{seg}\right)\bullet P_{AC},W$ (12)

When sizing the inverter, it was convenient to consider the effect of the motor start-up peaks to guarantee a satisfactory operation of the installation. Taking into account what was stated by ^{Alonso (2011)} & ^{Alfonso (2016)}, many devices and equipment that include electric motors of medium and high power, produce current peaks at startup, which means that these devices will have an initial demand for power up to four or five times greater than the nominal.

Methodology for Estimating the Economic Impact of the Facility

When a photovoltaic solar park is used, clean, renewable and safe energy is being used efficiently. It contributes significantly to the reduction of greenhouse gases that cause climate change and air quality is considerably improved, since the use of fossil fuels is significantly reduced. As a result of the above, it is necessary to know how much fossil energy is not consumed (number of kWh of electricity avoided monthly and annually) with the implementation of this photovoltaic solar park (^{CanviClimatic, 2011}; ^{Alvarado, 2017}).

^{Alvarado (2017)} points out that from the use of these photovoltaic solar parks a certain amount of electrical energy is saved in a month, therefore:

$Q_{CM}=L_{md}\bullet D_m, kWh$ (13)

where:

Dm:	Days that a month has.

Being the energy saved in a year:

$Q_{CA}={12\bullet Q}_{CM}{\bullet D}_m, kWh$ (14)

To determine the cost of the energy saved in a year, what was established by ^{Bolaños (2021)} was considered, where the electricity rates in Cuban pesos (CUP) are established for the collection of electricity service. In the specific case referred in this work; as it is a research center, whose social purpose is the training of professionals and the development of machinery and technologies that respond to the needs of the agricultural sector; the high voltage tariff system with continuous activity is considered, specifically the one that responds to the energy consumed during daylight hours. Being the cost of the energy saved in one day:

$C_{día}=\left(a\bullet K+b\right)\bullet Q_{cdía}, CUP/día$ (15)

where:

a, b:	Coefficients to be applied according to the type of tariff (1.5282 and 0.7273, respectively), CUP / kWh;
K:	Fuel price variation adjustment factor;
Qcdía:	Energy consumption in a day, kWh / day.

Similarly, the cost of energy saved in one year can be determined based on:

$C_{año}=\left(a\bullet K+b\right)\bullet Q_{CA}, CUP/año$ (16)

where:

QCA:	Energy consumption in a year, kWh / day.

Methodology for Estimating the Environmental Impact of the Facility

In order to implement these heat machines, it was necessary to know the amount of emissions avoided into the atmosphere. The mass of CO₂ emitted into the atmosphere due to the burning of fossil fuels can be determined according to ^{Ruisánchez (2018)} as:

$M_{{CO}_2}=\iota \bullet Q_{CM},kg/mes$ (17)

where:

ι:	Emission index, kg / kWh.

^{Bérriz, et al. (2016)} as well as ^{Ruisánchez (2018)}, suggest that each kWh produced at the generation plant level emits 1.13 kg of CO₂ into the atmosphere. The mass of fossil fuel required to produce a given amount of energy in a month can be determined by:

$M_{CM}=\gamma \bullet Q_{CM},kg/mes$ (18)

where:

γ:	Fuel consumption index, kg / kWh.

The assumed value for the consumption index is 0.262 kg / kWh (^{ICG, 2012}; ^{Bolaños (2021)}.

RESULTS AND DISCUSSION

Assessment of the Electrical Energy Consumption of CEMA

Both static and dynamic electric charges coexist in CEMA. Static electrical charges are those that have a fixed consumption of electrical energy over time (^{Prado, 2008}; ^{Martin, 2020}), for example: lighting systems, air conditioning systems, televisions, personal computers, electric cooking systems, among others. This type of charge is common in domestic consumers.

Systems that are said to have dynamic load are those in which their electricity consumption depends significantly on their state of charge (^{Prado, 2008}; ^{Martin, 2020}) institution. For this reason, the great variability of its electrical consumption can be appreciated as shown in the Figure. 1.

FIGURE 1 Behavior of the daily energy consumption of CEMA (September 2016- April 2019). 

From the analysis it was found that the year 2017 was the year with the highest energy consumption with 12,772 kWh and the month of September 2017 the one with the highest consumption of electricity with 81,727 kWh / day, which shows that CEMA is a high consumer of electrical energy.

Proposal for a Photovoltaic Solar Park for CEMA

To carry out the proposal for a photovoltaic solar park in CEMA areas, solar panels from the manufacturer Brisban were used. The corresponding technical data are shown in Table 1.

TABLE 1 Technical data of the solar panels of the manufacturer Brisban model BS18055 

Parameter		Specification
Module power peak under standard conditions	W	180
Module maximum voltaje	V	36,55
Module short-circuit current	A	5,30
Module maximum unitary current	A	4,9
Inverter efficiency		0,9
Conductors efficiency		1
Batteries efficiency		0,95

In addition, Trojan batteries were selected, the technical data of which are shown in Table 2.

TABLE 2 Technical data of the proposed Trojan monoblock batteries 

Parameter		Specification
Voltage	V	12
Current capacity	A	240
Seasonal maximum discharge depth	%	70
Diary maximum discharge depth,	%	15
Efficiency		0.9 - 0.95

For this proposal, the Victron Energy brand inverter was also taken into account (Figure 2) with a power 2 0% greater than that demanded by the equipment. They are also distributed by SunFields.

FIGURE 2 Victron Energy Investors. 

In this case, the use of a regulator for monitoring the maximum power point is not considered, since the photovoltaic systems that include it constitute systems that improve the efficiency of the installation between 10 and 25%. The fundamental problem of these regulators lies in their high cost for small and medium size installations. In the case of this proposal, due to the volume of energy to be generated, it would require a large capacity regulator with the capacity to monitor the maximum power point, which would raise the total cost of the installation by at least 30 and 40% more only for this concept (^{Gasquet, 2004}; ^{Acevedo, 2016}; ^{Alvarado, 2017}).

Sizing of the Parts of the Proposed Photovoltaic Solar Park

For the dimensioning of the parts of the proposed solar photovoltaic park, a series of essential aspects were taken into account as shown in Table 3. It summarizes the parameters calculated for the dimensioning of the photovoltaic solar park in CEMA areas, based on equations (4), (9), (10), (11) and (12).

TABLE 3 Summary of the parameters to be determined for the sizing of the photovoltaic solar park 

Parameter	Symbol	Value
Average daily power consumption	Lmdn, kWh	94,73684
Average daily current consumption	QAh, Ah/day	7 894,73
Current to be generated by the photovoltaic field in the critical month of solar radiation	Igfv,mpp, A	1 578,946
Quantity of solar panels	Np	323
Nominal capacity of the battery in function of the seasonal maximum discharge	Cne, kWh	135 338,5
	CneAh, Ah	11 278,21
Quantity of batteries	Nbat	47
Input current	Ient, A	2 054,28
Output current	Isal, A	1 135,09
Power of the inverter	Pinv, kW	98,0724

These results are consistent when compared to those obtained by other authors like ^{Prado (2008)}; ^{Acevedo (2016)}; ^{Márquez (2017)}; ^{San Juan (2017)}; ^{Martin (2020)}, who have used a similar methodology applied to the sizing of facilities of different kinds.

Preliminary Economic Analysis of the Proposed Facility

With the use of a clean and sustainable energy source such as solar, it is expected to reduce the costs of conventional fuels to produce electricity. Such is the case of the proposed photovoltaic solar park. The cost of the electrical energy not consumed from the use of the energy generated from the proposed installation is 57,368.23 CUP per year. Like ^{Cantos (2016)} & ^{Mascarós (2016)}, the authors consider that energy saving, although it does not represent an energy source itself, it is used to consider it as such since it offers the possibility of satisfying more energy services, which is equivalent to have more energy. For the installation of a photovoltaic solar park it is necessary to carry out a study of its economic feasibility. Table 4 summarizes the preliminary costs of this system.

TABLE 4 Preliminary investment costs 

Component	Capacity	Reference rate	Costs,	CUP
Panels	58140 W	14,4 CUP/W	83 7216,00
Batteries	135,360 kWh	1800 CUP/kWh	243 648 000,00
Regulator	4800 VA	19,2 CUP/VA	92 160,00
Inverter	1000 kWh	6 CUP/kWh	6 000,00
Preliminary costs of the investment (with the accumulation system)			244 583 376,00
Preliminary costs of the investment (without the accumulation system)			935 376,00
Time for the investment recovery (with the accumulation system), years			4 263,39
Time for the investment recovery (without the accumulation system), years			16,3

As it can be seen in Table 4, the preliminary cost of the investment considering the proposed accumulation system is considerably higher than in the case in which it was dispensed with. As this is a preliminary study, the authors have used market reference rates for cost estimation. However, it is up to the decision makers with the capacity to act, orient a market study for the selection of offers and suppliers, which allows a definitive cost study to be carried out in order to undertake the investment process of the proposed facility.

The economic pre-feasibility analysis carried out, although it is limited and preliminary, provides an approximate idea about the cost of an installation of these characteristics, considering both, the saving of energy carriers in the form of fossil fuels, as well as the environmental impact due to the non-emission of polluting gases and the greenhouse effect. It can be affirmed that the construction of a large-scale photovoltaic solar park is viable to satisfy the consumer demand of the Agrarian University of Havana, where CEMA is located.

Analysis of the Environmental Impact of the Proposed Facility

Solar panels, by using a clean energy source to produce electrical energy, do not consume any type of fossil fuel. Thus, with equation (13) the electrical energy that would cease to be consumed with the use of these voltaic systems was determined. Furthermore, with these results it is possible through expression (17) to know the mass of CO₂ that is not emitted into the atmosphere. As a result of the foregoing, the mass of fossil fuel necessary to produce this amount of electricity was determined by equation (18) and it is shown in Table 5.

TABLE 5 Results of the environmental impact as a consequence of the proposed installation 

Parameter	Estimated value
Not-consumed electric power, kWh/day	81,72
Saved electric power, kWh/year	29 421,72
Mass of CO2 not emitted to the atmosphere, t/year	33,24
Not-consumed mass of fossil fuel, t/year	7,70

Increasing energy efficiency has an immediate and direct environmental benefit, since it implies a reduction in the use of natural resources and in the emission of pollutants, including CO₂. Without a doubt, the cleanest energy is the energy saved.

CONCLUSIONS

• The selected site meets the construction characteristics required to undertake the installation of the photovoltaic solar park.

• It was determined that, with the assembly of 323 solar panels, 47 batteries, two current regulators and an inverter, the demand for electrical energy in the area where the study was carried out could be covered.

• The proposed installation would have a positive impact on the environment, since 29,421.72 kWh / year would be saved, in addition, 33.24 t / year of CO₂ would cease to be emitted into the atmosphere, saving a mass of 7.70 fossil fuel t / year.

• It was concluded that the installation of the photovoltaic solar park is economically feasible since 57 368.23 CUP would be saved in one year from unconsumed energy.

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La mención de marcas comerciales de equipos, instrumentos o materiales específicos obedece a propósitos de identificación, no existiendo ningún compromiso promocional con relación a los mismos, ni por los autores ni por el editor.

Received: February 16, 2021; Accepted: September 20, 2021

^*Author for correspondence: Javier A. León-Martínez, e-mail: [e-mail], [e-mail]

Javier A. León-Martínez, Profesor Asistente, Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail], [e-mail].

Yanoy Morejón-Mesa, Profesor Titular, Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail]

Gleiby C. Melchor-Orta, Profesora Asistente, Universidad Agraria de La Habana, Centro Universitario Municipal de Jaruco, Mayabeque, Cuba, e-mail: [e-mail]

Luis M. Rosabal-Padrón, Profesor en adiestramiento, Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail].

Rolando Quintana-Aput, Profesor Auxiliar, Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail].

Geisy Hernández-Cuello, Investigadora Auxiliar, Universidad Agraria de La Habana, Centro de Mecanización Agropecuaria, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail].

Los autores de este trabajo declaran no presentar conflicto de intereses.