Artículo Académico / Academic Paper

Recibido: 29-10-2021, Aprobado tras revisión: 18-01-2022

Forma sugerida de citación: Fiallos, D.; Tipán, L.; Jaramillo, M. (2022) “Determinación del punto óptimo de potencia en paneles

fotovoltaicos mediante el modelo de Liu & Jordan”. Revista Técnica “energía”. No. 18, Issue II, Pp. 48-60

ISSN On-line: 2602-8492 - ISSN Impreso: 1390-5074

Determination of the optimum power point in photovoltaic panels using the

Liu &Jordan model considering fuzzy variables

Determinación del punto óptimo de potencia en paneles fotovoltaicos

mediante el modelo de Liu & Jordan considerando variables difusas

D. Fiallos

L. Tipán

M. Jaramillo

Universidad Politécnica Salesiana, Quito, Ecuador

E-mail: mjaramillo@ups.edu.ec; ltipan@ups.edu.ec; mjaramillo@ups.edu.ec

Abstract

This document focuses on solar energy generation,

specifically on the optimum point of power delivered

by the photovoltaic panel. To reach the end of the

study, it is necessary to develop a mathematical

model, which must be followed sequentially; it is

based initially on the solar model of Liu & Jordan,

which allows a study of the amount of incident

irradiance on an inclined surface. Followed by dirt

as a diffuse variable, how it affects the panel. In

addition, climatic variables such as temperature and

humidity are considered, variables necessary to

obtain the optimum power point. The proposed

mathematical model aims to determine the

inclination and orientation of the highest solar

radiation capture on an inclined surface.

Additionally, how to minimize losses due to dirt and

climatic variables as they affect their impact on the

efficiency of the panel. Finally, based on the

aforementioned parameters, results are shown

under three considerations: for the data obtained by

the UPS meters, inclination and orientation obtained

with a compass and inclinometer, the result

calculated under the current conditions of the site

and finally the calculation under optimum

conditions, this determines the optimum power

point..

Resumen

En el presente documento se centra en generación

solar, específicamente en el punto óptimo de

potencia entregada por el panel fotovoltaico. Para

llegar al fin de estudio, es necesario desarrollar un

modelo matemático el cual debe seguirse de manera

secuencial basado inicialmente en el modelo solar de

Liu & Jordan, el cual permite un estudio de la

cantidad de irradiancia incidente sobre una

superficie inclinada. Seguido por la suciedad como

variable difusa, como afecta al panel. Además, se

consideran variables climáticas como temperatura y

humedad, variables necesarias para la obtención del

punto óptimo de potencia. El modelo matemático

propuesto tiene como objetivo determinar la

inclinación y orientación de mayor captación de

radiación solar en una superficie inclinada.

Adicionalmente, como minimizar las pérdidas por

suciedad y las variables climáticas como afectan su

impacto en la eficiencia del panel. Finalmente, en

base a los parámetros ya mencionados se muestran

resultados bajo tres consideraciones: para los datos

obtenidos por los medidores de la UPS inclinación y

orientación ob

tenidos con brújula e inclinómetro,

resultado calculado bajo las condiciones actuales del

emplazamiento y por último el cálculo bajo

condiciones óptimas, con esto se determina el punto

óptimo de potencia.

Index terms



Photovoltaic effects, Solar energy,

Photovoltaic cells, Solar radiation, Solar panels,

Solar power generation

Palabras clave



Efectos fotovoltaicos, Energía

Solar, Celdas fotovoltaicas, Radiación solar, Paneles

solares, generación de energía solar.

Edición No. 18, Issue II, Enero 2022

1. INTRODUCTION

Ecuador has great solar energy potential [1] [2],

which is why the need arises to obtain the greatest

amount of irradiance on an inclined surface, for this

purpose, it is necessary to determine the optimal

inclination and orientation of the photovoltaic panel. To

obtain the inclination parameters as orientation, it is

necessary to consider a solar model, for the document the

Liu & Jordan solar model is presented, from which values

very close to real ones are obtained.

There are authors who have seen the need to

determine the highest irradiance uptake on the solar

panel, mainly using the Liu & Jordan model, for this, it is

of great importance to carry out the study of a certain

place or region in order to determine the optimal

conditions of inclination, for each geographic location of

study [3].

In [4] the optimal search for the inclination and

orientation of the photovoltaic panel is carried out using

mathematical models and software such as ArcMap, IBM

SPSS Statistics and Matlab. Additionally, once the angles

have been defined, the validation of the Liu & Jordan

solar model is performed by comparing it with other solar

models, showing that this model and the compared

models give very similar irradiance values.

In [5] the optimal orientation and inclination for

Luján are presented by comparing three models: the

diffuse isotropic of Liu & Jordan and the anisotropic of

Klucher and Reindl, where the inclination of the panel

was set at 45 ° towards the four cardinal points. After this,

obtaining a comparison is made with the values measured

at the University of Luján.

In [6], the research focuses on the study for the

location of Salto, Uruguay. Where they are compared

with several solar models to determine the incident

irradiance values on an inclined surface, determining that

the optimal orientation should be towards the equator to

allow the greatest capture of incident irradiance on the

panel.

As it can be seen in the documents analyzed, these

works focus on the irradiance obtained specifically with

the Liu & Jordan model, in this model, dirt is not taken

into account, this being another factor that affects power.

The amount of dirt depends on the climatic conditions of

the site where it is located, that is if the place is desert,

humid, cold, etc. [7] - [9] As there is variation in climatic

conditions it can increase or decrease the level of dirt.

The transmittance of the glass is determined with the

relationship between the dirtier the usable irradiance will

decrease in the photovoltaic panel, therefore the usable

power to feed a certain load will decrease [10], [11].

This analysis of dirt [12] - [14] is carried out in desert

conditions and how they affect the impact on the

efficiency of the panel based on trial and error, showing

that for desert situations such as Pakistan, Qatar and

Rabat the losses become very high. Large dirt impacts on

the panel occur in large urban areas [15].

Additionally, a natural effect of great importance

based on the climatology of the place to be studied is

dew, which is nothing more than the humidity of the

atmosphere that condenses at night and early morning,

causing small drops of water to be generated that settle

on the panel. This climatic phenomenon can be

unfavourable in desert conditions where when it joins the

dust, it turns it into the mud, dirtying the panel even more

[16], this does not happen in the urban environment (case

study) where when it condenses, it will serve to clean the

dirt deposited on the panel [15] [17].

Based on the foregoing, this document is based on the

Liu & Jordan model and the variables previously

described with the mathematical formulation to

determine the optimal solar generation conditions [1]

[18].

The study location is in Ecuador, Quito city,

specifically in the Salesian Polytechnic University

(South Campus), where it is necessary to determine all

the aforementioned variables for greater use of the

photovoltaic panels of the Simax brand (Suzhou) model

SM572-190 with a power of 190 Wp since in the

datasheet it can only be observed under standard

conditions, which differs greatly from reality because the

amount of radiation and temperature varies with the

location, time and weather station. [19]

This analysis will be expanded by first calculating the

inclination and orientation with Liu & Jordan, then the

dirt, temperature and humidity factor is added. Finally,

the results obtained are shown in comparison with the

data measured in the Salesian Polytechnic University

2. PHOTOVOLTAIC ENERGY

The sun is the main source of generation of all types

of energy [20] whose central axis lies in the use for

conversion of electrical energy through the photoelectric

effect which bases its operation on converting solar

radiation into electrical energy by means of devices

semiconductors (photovoltaic cells). These cells are built

on the basis of silicon that must add impurities of

chemical compounds such as phosphorus and boron [21].

The cells constitute the photovoltaic panel. The

output current in the panel is given by the incident global

radiation as already mentioned [20].

2.1. Solar Geometry

In our solar system, the earth describes the

translational motion (it revolves around the sun) and the

rotational motion that rotates on the axis of the sun. In the

first movement the earth moves around the sun forming

an ellipse, this movement lasts 365 days (one year), it is

Fiallos et al. / Determinación del punto óptimo de potencia en paneles fotovoltaicos mediante el modelo de Liu Jordan

important to take this movement into account since the

geometric shape formed between the sun and the earth is

the same, having a variable distance [2] [10].

Figure 1: Movement of the Earth relative to the sun

2.1.1 Declination angle (δ)

It is related to the rotational movement, it is the one

that rotates on its polar axis, and is perpendicular to the

equatorial plane. In this way, the deviation of the axis of

rotation can be determined and it is given at an angle that

can take values from -23.45º to 23.45º at what is known

as the angle of declination at this angle, it is necessary to

mention that it does not depend on the place of study if

not the day of the year and hence its variation is given by

the following equation [4] [22].

(1)

Where:

dn = number of the day of the year.

δ = angle of solar declination.

360/365 = conversion factor of the day of the year in an

orbit position.

23.45 ° = angle of inclination of the earth about its own

axis of rotation.

10 = Value taken since the winter solstice begins before

the beginning of the year.

Figure 2: Annual decline

2.1.2 Daylight angle (ω)

It is the displacement that the sun makes on the

equatorial plane, it is characterized by being negative in

the morning and positive in the afternoon, and its increase

is 15º for each hour. To calculate this angle, we will use

the equation: [10]



=15. (HS-12) (2)

Where:

HS = Hour of the day

Figure 3: Orientation of the photovoltaic panel

2.1.3 Latitude (ϕ)

It is the angular measurement that originates from the

equatorial line, that is, the measurement from this axis to

any point on planet earth. It varies from 0 to 90 ° towards

the north pole and from 0 to -90 ° towards the south pole

[4] 2.1.4 Ángulo azimutal (γ)

The azimuth angle is the orientation in which the

photovoltaic panel is going to be directed, it is measured

clockwise forming an imaginary circumference on our

axis, this circumference will be represented by the four

cardinal axes (north, east, south, west) taking values of

0º, 90º, 180º, 270º and 360º respectively. Its

representation for this document will be the letter of the

Greek alphabet γ [4]

2.2. Dirt in panels

One of the factors that negatively affect the efficiency

of the panel is the accumulation of dust deposited on

them [10]. There are several studies where it is evidenced

that in desert places the losses caused by dust become too

high, up to 40% of energy production [23] [24] unlike an

urban environment that on average becomes 8% [10].

March 21 spring equinox

December 21 winter

soltice

June 21 summer soltice

September 23 autumn equinox

Photovoltaic

Panel

North

East

west

Perpendicular

to the module

South

Edición No. 18, Issue II, Enero 2022

The accumulation of dust considerably affects the

transmittance causing the irradiance that enters the panel

to be lower, a practical way to calculate its efficiency is

determined with experimental values that are given by

the ratio of the irradiance of the dirty panel on the

irradiance when the panel is clean [10].

(3)

Where:

T = Transmittance.

Gsucio = Irradiance in dirty conditions.

Glimpio = Irradiance under clean conditions.

The quantification of the amount of dirt or dust

deposited on the photovoltaic panel is very difficult to

determine exactly because each geographic location has

different climatic conditions [13]. For this case study, it

is located in an urban area where the efficiency will be

determined dividing it into four groups as detailed in

table 1

Table 1: Dirt levels

DIRT LEVELS OPERATING

EFFICIENCY

No dirt

100%

Low dirt

98%

Medium dirt

97%

High dirt

92%

2.2.1 Dew as a cleaning factor

Dew is the droplets produced by the condensation of

moisture, in urban environments it helps to clean the

panel, however, it is not enough for the cleaning in its

entirety, these droplets that when drying leave a circular

mark leaving the panel somewhat dirty, affecting it as we

can see in Fig. 4.

Figure 4: Drew dried microscopy [15]

In places where there is not abundant dust, the dew

provides the phenomenon of self-cleaning, but in desert

places where the accumulation of dust is abundant is a

detrimental factor since they join with the deposition of

dust on the panel generating a layer of mud that when

drying it solidifies preventing radiation from hitting the

panel [16][25].

2.3. Irradiance

Solar irradiance is the power of radiation from the sun

that hits the plane for each square meter (m2), its units of

measurement in the international system are (W / m2), It

is of utmost importance for photovoltaic systems in the

stage of design since it is possible to estimate the power

that a solar park can deliver [20] [26].

In several documents, irradiance is called by the

letters It, which is the sum of direct irradiance (Iβb) plus

diffuse irradiance (Iβd) and plus reflected irradiance

(Iβρ), as shown in equation (3) [20] [26] [27].

(4)

Figure 5: Types of irradiance on the panel

2.3.1 Direct irradiance (Iβb)

It is the amount of radiation that comes from the sun

in a straight way, that is, it has no deviation or a solid

body that prevents or deviates its path in this path [10].

2.3.2 Diffuse irradiance (Iβd)

Also known as indirect radiation, it represents the

irradiance that does not arrive directly since after passing

the atmosphere and clouds it causes the irradiance to

disperse. According to [26] it determines that the indirect

irradiance on days when there is no high amount of

clouds represents 15% of the global irradiance but on

days that are gloomy it increases considerably [27].

2.3.3 Reflected Irradiance (Iβp)

It is the amount of radiation that is reflected on the

ground, this component is small, for some calculations, it

is neglected. The reflection coefficient is called albedo,

which varies depending on the reflective characteristics

of the ground and the materials that surround it, taking a

value of 1 for surfaces that are completely reflective, 0.8

for surfaces where there is snow, 0.1 for surfaces where

the colour is opaque. u dark and 0.2 on surfaces that

contain vegetation or grass, which is the case of study, so

DIRECT

IRRADIANCE

ON THE

PANEL

DIRECT

DIFFUSE

IRRADIANCE

ON THE PANEL

DIRECT

IRRADIANCE ON

THE PANEL

REFLECTED

PANEL

Fiallos et al. / Determinación del punto óptimo de potencia en paneles fotovoltaicos mediante el modelo de Liu Jordan

the photovoltaic panels of study are located in a place

where there is vegetation [26].

Table 2: Reflectance in different environments

TYPE OF SURFACE REFLECTANCE

Snow 0.87

Dry sand 0.18

Wet sand 0.09

Forest 0.05

New concrete 0.33

Old concrete 0.23

2.3.4 Photovoltaic panel inclination (β)

Ecuador has a large uptake of the solar resource,

several documents have been dedicated to research on the

optimal angle, all reaching the same conclusion that it

does not need inclination, but for cleaning purposes, if it

is convenient that it has a slope of fall like what says in

[28]. In Ecuador, in the city of Ibarra, tests were carried

out at 0º, 5º, 10º, and 15º concluding that the optimum

angle of inclination should be the closest to 0º. [29]

The basis of this research is carried out in the city of

Quito at the Salesian Polytechnic University, taking the

recommendations of the studies carried out previously,

avoiding generating unnecessary data, an appropriate

value of the β angle will be taken considering the

geographical location, which is why the following

equation it is based on statistical data of annual radiation

at different sites and different inclination angles. [30]

(5)

Where:

βop = suitable angle of inclination (degrees).

| ϕ | = latitude of the place, unsigned in degrees

Figure 6: PV inclination

3. LIU& JORDAN SOLAR MODEL

Solar energy has shown a considerable increase in

recent years, with which it is a priority to be able to

calculate the solar radiation that affects a photovoltaic

panel and thus be able to determine the resulting power

that the photovoltaic system will deliver, that is why

several models have been studied solar systems in

various documents, but for this case the Liu & Jordán

model was considered the most appropriate because it

allows a real approximation with few variables while

maintaining a very small margin of error compared to the

field measurement [31].

However, the correct angle of inclination must be

known, here the variation necessary to determine it is

presented, it should be noted that Ecuador has a great

possibility of solar generation due to its geographical

location, the panels can be placed with an inclination of

0º but it is unfavourable since Not having an angle of

inclination lends itself so that dirt is deposited on them,

requiring a more frequent maintenance plan, and if not,

efficiency would be lost due to loss of transmittance due

to the deposited dirt [28].

The inclination and orientation should be considered

as one of the main parts since these determine the amount

of radiation that the panel can capture, this solar model

allows by means of correction coefficients to determine

the global irradiance on an inclined surface since all the

bases of Available data provide information on a

horizontal surface [28].

The sum of the three irradiances are for horizontal

incidence surfaces, in this case, it is necessary to study

correction factors for an inclined surface described in

equation (4) based on the Liu & Jordan model. [4] [6]

It=Ib * Rb + Id * Rd + Ip*Rr. (6)

Where:

It = It is the total irradiance on the photovoltaic panel

Ib = It is the horizontal direct irradiance

Id = It is the horizontal diffuse irradiance

Iρ = It is the horizontal reflected irradiance

Rd = Geometric component for diffuse irradiance.

Rb = Conversion component for direct radiation on a

horizontal surface

3.1. Geometric conversion factor of direct

irradiance (Rb)

It is the relationship that exists between the irradiance

on the inclined surface and the horizontal surface [32].

The geometric factor of direct irradiance on an inclined

surface can be established as [5]

(7)

VERTICAL LOCATION OF THE SUN

PHOTOVOLTAIC

PANEL

Edición No. 18, Issue II, Enero 2022

Where:

Rb = Geometric conversion factor of direct irradiance.

cos (θ) = Horizontal angle of incidence.

cos (θ

) = Zenith angle.

The angle of incidence on the surface depends on

several factors as described in equation 8.

cos(θ) = sen (δ)* sen(ϕ)*cos(β) – sen(δ)* cos (ϕ)*

sen(β)*cos(γ) + cos(δ)*cos(ϕ)* cos(β)*cos(ω)+

cos(δ)*sen(ϕ)*sen(β)* cos(γ)* cos(ω)+ cos(δ)*

sen(β)*sen(γ)*sen(ω) (8)

Where their components are as listed: δ the solar

declination, ϕ latitude, β angle of inclination of the panel,

γ angle of orientation or azimuth and ω is the hour angle.

Under this assumption for the zenith angle, we will

consider that the orientation (γ) and the inclination (β) is

0 °. [33]

Cos(θ

) = sen (δ)* sen (ϕ) + cos(δ)* cos (ϕ) *cos(ω)

(9)

Figure 7: Zenith angle

3.2. Diffuse irradiance geometric conversion factor

(Rd)

This factor is a part of the diffuse radiation from the

horizontal surface on the inclined panel [4].

(10)

3.3. Reflected irradiance geometric conversion

factor (Rr)

This factor assumes that direct and diffuse radiation

are reflected in the ground in an isotropic way, that is to

say, that the irradiance reflected in the ground will affect

the photovoltaic panel and it can be determined with the

following equation: [5] [22].

(11)

Once the geometric factors for correction of the

inclined surface have been decomposed, our

mathematical model by Liu & Jordan is as follows:

(12)

4. SOLAR MATH MODELING LIU& JORDAN

Optimization pseudocode

Step 1:

Begin

Variables: lat, long, idirec, idif, iref,alb

Step 2:

Print “Ingrese latitud (lat)”

Read lat

Print “Ingrese longitud (long)”

Read long

Print “Ingrese irradiancia directa (idirec)”

Read idirec

Print “Ingrese irradiancia difusa (idif)”

Read idif

Print “Ingrese irradiancia reflejada (iref)”

Read iref

Print “Ingrese albedo (alb)”

Read alb

Step 3:

Calculate Rb with [ δ=0:365;βop=0:90;γop=0:360;ω=-

180:180 ]

Si βop>10°

Calculate Rd with [β=βop]

Calculate Rr with [β=βop]

Opposite Case

Calculate Rd with [β≥10°]

Calculate Rr with [β≥10°]

Calculate Itop=idirec*Rb+idif*Rd+iref*Rr*alb

Step 4:

Calculate Ee=Itop* T

If β<10°; Teff=92%

Opposite Case

If 10°>β<25°; Teff=97%

Opposite case

If 25°>β≤90°; Teff=98%

Eeop if β≥10°

Step 5:

Isop=Isc,ref*Itop/1000*(1+αIsc(Tc-To))

Impop=Imp,ref*Isop/(Isc,ref)

Step 6:

Vocop=Voc,ref+s*∆Tc*ln(Eeop)+βoc(Tc-To)

Fiallos et al. / Determinación del punto óptimo de potencia en paneles fotovoltaicos mediante el modelo de Liu Jordan

Vmpop=Vmp,ref*Vocop/(Voc,ref)

Step 7:

PDcop=Vmpop*Impop

Step 8:

End

With this algorithm, the optimum power point of the

photovoltaic panels understudy will be determined, a

total of 10 panels as shown in Fig. 8.

Figure 8: Photovoltaic panels UPS south campus.

The methodology starts with the amount of irradiance

that affects the photovoltaic arrangement in which

equations (12) and (3) are joined to obtain an effective

irradiance value in which the accumulation of dust or dirt

is related, leaving the following equation

(13)

Once these irradiance values have been obtained, the

temperature of the site is fundamental for determining the

maximum power of electricity generation, this will vary

in terms of the amount of solar radiation and temperature

of the panel [27] for the above, it is necessary to use the

following equations where, with the help of the panel

technical sheet [19] and site conditions, the maximum

power point is determined according to the climatic

conditions at our study point.

(14)

Where:

Isc = Actual short-circuit current

Isc, ref = Short circuit current in datasheet

It = Irradiance on the inclined plane

αIsc = Short-circuit coefficient

Tc = Cell temperature.

To = Temperature under standard conditions

When the real short-circuit current is obtained, the

maximum power current given by the following equation

is calculated.

(15)

Where:

Imp, ref = Maximum reference power current

Afterwards, it is necessary to calculate the open

circuit voltage value, it must be calculated as:

= V

OC,ref

+ s*∆T

* ln(Ee) +β

-T

) (16)

Where:

Voc, ref = Open circuit voltage for reference

s = Number of PV cells connected in series

∆Tc = Thermal Voltage

For the calculation of Voc it is necessary to calculate

the thermal voltage that is given by the following

equation:

(17)

Where:

n = Diode factor

k = Boltzmann constant 1.38066E-23 (J / K)

q = Elemental charge 1.60218E-19

Like the current, it is necessary to calculate the

maximum power voltage described by equation (18).

(18)

Based on equations 15 and 17, we proceed to

calculate the power that will be delivered to the output of

the photovoltaic cells defined as:

PDc=Vmp*Imp (19)

5. RESULTS

Equation (5) allows us to calculate the appropriate

inclination of the panel according to our geographical

location, however, a more in-depth study has to be

carried out since this equation does not study orientation

parameters, dirt, temperature, etc. Once this is

mentioned, this equation is used to have a fairly good

Edición No. 18, Issue II, Enero 2022

approximation to determine the appropriate angle of

inclination.

βop=3.7+0.69*0.28339=3.89°

Once calculated, it is ratified that, for Ecuador, the

optimal inclination must be as close to 0. But the panel

cannot be placed at 0 degrees, which would facilitate the

deposition of dust, for the case study values of 0 ° are

taken at 15 ° to determine the maximum power point

considering all the variables mentioned above.

The geometric factors of diffuse and reflected

irradiance depend directly on the angle of inclination, the

values to be used are observed in the following table.

Table 3: Geometric factors of diffuse and reflected irradiance

Inclination

angle

Rr Rd

0 0 1

1 0.0001 0.9999

2 0.0003 0.9997

3 0.0007 0.9993

4 0.0012 0.9988

5 0.0019 0.9981

6 0.0027 0.9973

7 0.0037 0.9963

8 0.0049 0.9951

9 0.0062 0.9938

10 0.0076 0.9924

11 0.0092 0.9908

12 0.0109 0.9891

13 0.0128 0.9872

14 0.0149 0.9851

15 0.0170 0.9830

The solar hour angle (ω) reaches a minimum value

hours before and after noon than in Ecuador, at this time

the amount of usable radiation is greater, then the angles

increase with a positive or negative sign as shown in Fig.

9, but for our modelling we are going to take values from

7:00 a.m. to 7:00 p.m., these values are taken by the solar

databases of NASA and PvGis of Europe that indicate an

average of hours that Ecuador receives solar radiation

usable 12 hours.

Figure 9: Solar angle variation in the day

Another necessary parameter for the calculation is the

latitude and longitude, the South Campus Salesiana

Polytechnic University is located at latitude -0.28339 and

longitude -78.54959. Regarding the value of albedo,

NASA provides monthly values, to determine the

maximum power point, the average value of 0.19 is

found.

Based on the mentioned values and data provided, the

third geometric conversion factor necessary to proceed to

estimate the amount of solar irradiation on the study site

is obtained, after obtaining the value of the Rb factor,

equation (12) is applied with the different variations to be

able to estimate the appropriate orientation and

inclination.

For our study site, we begin to notice a decrease in

irradiance at 15 ° as shown in Fig. 10, however, it must

be taken into account that the larger the photovoltaic

park, the more notable the irradiance losses that will be

seen. reflected in the delivered power, for which a 10 °

inclination is considered for the place, this eliminates the

possibility of deposit of particles or water that reduce the

efficiency of the panel.

Figure 10: Irradiance according to the inclination of the

photovoltaic panel

IRRADIANCE

HOURS

Fiallos et al. / Determinación del punto óptimo de potencia en paneles fotovoltaicos mediante el modelo de Liu Jordan

Another study factor for maximum irradiance uptake

is the orientation of the panel, the four cardinal points

north, south, east and west are taken as a case study,

showing that in Quito-Ecuador, specifically in the study

place, losses are negligible. caused by the variation of the

orientation (azimuth), as can be seen in Fig. 11. In this

comparison, the variation of the inclination from 0 to 15

degrees in the 4 cardinal points was taken into account.

Figure 11: Irradiance depending on the orientation of the panel

The angle and orientation for the case study have been

determined at 10 ° and an orientation towards a north

azimuth of 0 ° being the most optimal for our site, with

these data we proceed to calculate the short-circuit

current, shown in Fig. 12 that the greater the irradiance,

the greater the short-circuit current and this, in turn, is

reflected in the maximum power current (Imp), since in

the datasheet voltage values, coefficients are tested under

standard circumstances of 1000w / m2 and at a

temperature of 25 ° Celsius, which varies for each

geographic location and weather station.

Figure 12: Short circuit current in real conditions

Figure 13: Current at maximum power in real conditions

The short-circuit current (Isc) and the current of the

maximum power point (Imp) are similar as seen in Figs.

12 and 13, but for the calculation of the optimum

powerpoint, the Imp is taken. It is necessary to calculate

the maximum power voltage, for which the real open

circuit voltage is calculated, which depends on variables

such as temperature and dirt (Fig. 14), for Quito the

average temperature is maintained in a range of standard

conditions which is favourable Due to the higher

temperature its voltage decreases and due to the proposed

inclination of 10 °, natural gravity allows any dust or dirt

particle to fall to the floor, in addition to this, the spray

factor that occurs in the early morning helps cleaning

while they fall. water droplets due to inclination, the

location under these considerations has a low dirt

efficiency of 98%.

Figure 14: Open circuit voltage

In Fig. 14 the variation of the voltage in open circuit

in real conditions is observed, equation 16 is used which

depends on temperature, irradiance and dirt deposited on

the panel.

VOLTAGE [V]

AMPERES [A]

HOURS

CURRENT AT MAXIMUM POWER POINT

AMPERES [A]

HOURS

SHORT CIRCUIT CURRENT

VOLTAGE [V]

OURS

OPEN VOLTAGE CIRCUIT

IRRADIANCE

HOURS

Edición No. 18, Issue II, Enero 2022

Figure 15: Voltage at maximum power point

Once the Imp and Vmp have been obtained, the

maximum power point can be obtained, which is nothing

more than the multiplication of the two factors mentioned

as indicated in equation 19.

Figure 16: Highest efficiency maximum power point of the panel

Once all the required values have been obtained for

both the Liu & Jordan model and the calculation of power

with all the variables that considerably influence the

efficiency of the panel, the comparison of energy

supplied with the panels installed at the Salesian

Polytechnic University is carried out. The irradiance data

are taken from the aforementioned solar databases which

are for horizontal surfaces, hence the importance of the

Liu & Jordan model with the geometric correction factors

for different orientation and inclination angles,

additionally energy data is taken supplied from the

energy meter located on campus, orientation and

inclination data using a compass and inclinometer,

temperature values provided by the university from its

meteorological base. Once the simulation and data

collection has been carried out, the current installation is

compared with the optimal requirements.

Figure 17: Energy comparison between solar model and measured

data

In Fig. 17, it can be seen the comparison of energy

supplied by the photovoltaic panels currently installed in

the Universidad Politécnica Salesiana and the energy

after the calculation of optimal conditions based on the

proposed solar model, that is, the amount of energy

capable of delivering the photovoltaic panel would

increase after making the necessary adjustments in the

study photovoltaic park.

Table 4: Power delivered from UPS vs Power after optimizing

TIME

ENERGY

at UPS

(Wh)

23°

ENERGY

LIU &

JORDAN

(Wh) 23°

ENERGY LIU &

JORDAN

(Wh) OPTIMAL 10°

7:00 0.83 1.23 50.00

8:00 217.47 225.27 311.52

9:00 498.97 510.71 520.15

10:00 750 768.13 811.25

11:00 920.12 931.84 1003.15

12:00 830.51 838.68 991.75

13:00 816.25 824.91 900.14

14:00 648.50 659.10 728.50

15:00 312.25 383.04 467.62

16:00 246.15 266.10 315.01

17:00 108.28 124.69 176.19

18:00 27.03 31.23 33.10

19:00 0.08 0.07 0.08

POWER [Wh]

HOUR

WATTS

HOURS

MAXIMUN POINT OF POWER

HOURS

MAXIMUM POWER VOLTAGE

Fiallos et al. / Determinación del punto óptimo de potencia en paneles fotovoltaicos mediante el modelo de Liu Jordan

Finally, based on Fig. 17, the importance of carrying

out an investigation with an appropriate solar model can

be determined, it is considered that Liu & Jordan is a

model that is quite approximate to real values as shown

in table 4, where the values obtained are detailed. with

mathematical modelling and physical installation, being

quite similar. Finally, the installation is then compared in

optimal conditions, allowing us to observe that a greater

amount of power can be used. For optimal conditions,

several degrees of inclination were taken as indicated in

Fig. 10, additionally, all these degrees of inclination in

different orientations are considered as indicated in Fig.

11.

6. CONCLUSIONS

Based on the results, an adequate study of the

inclination and orientation of the panel is necessary to

capture the maximum possible irradiance, for which in

the case of study an optimal orientation value is obtained

as close to 0 °, in [29] and [4] also suggest it this way, but

it is also necessary to take into account the dirt and

accumulation of dust, for this reason, it is concluded that

the appropriate inclination should not be less than 10 °.

Based on the irradiance calculations it is shown that

for the geographical location of Ecuador the most usable

hour of solar irradiation is at noon, this is because the

solar rays fall perpendicularly on the solar collector

allowing it to receive the greatest amount of radiation

solar and does not spread around the site.

The solar hour angle (ω) for our model goes from 7:00

a.m. to 7:00 p.m., which is the approximate time that it

receives usable solar radiation, so it could be observed

that at noon this angle tends to zero, but it is the moment

in which the global irradiance on the panel is greater,

determining that the smaller the angle of the solar hour,

the greater the incident irradiance will be.

In works such as [16] and [13] they are desert places

with great solar potential, however, the dew is an

unfavourable aspect for desert places in which said

condensation generates that with the high amount of dust

it mixes and ends up making mud. which dirties the panel

reducing the output power capacity, in the study [15] it is

an urban location similar to the one studied in this it can

be observed that, like Ecuador, they generate a self-

cleaning effect when they are at an optimal inclination

that allows by gravity the drops of waterfall with the dust

particles, however, it is necessary to have a maintenance

plan for cleaning them.

7. FUTURE WORK

Based on the research developed, it is suggested that

the investigation can be expanded by geometrically

determining the effective hours of the site, for our case

study we take it from NASA, but calculating it

mathematically will be able to obtain a more realistic

approximation. It is also suggested to expand the

investigation with the amount of pollution produced by

vehicles that run on fossil fuels.

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David Darío Fiallos Chamorro.-

Nació en Quito, Ecuador en 1991.

Recibió su título de Ingeniero

Eléctrico de la Universidad

Politécnica Salesiana en 2020 . Sus

campos de investigación están

relacionados con el Desarrollo de

generación distribuida, y Gestión

de Energías Renovables.

Luis Fernando Tipán Vergara.-

Recibió su título de Ingeniera

Electrónica en control de la Escuela

Politécnica Nacional,sus estudios de

postgrado los hizo en la Escuela

Politécnica Nacional Facultad de

Ingeniería Mecánica, obteniendo el

grado de Magister en Eficiencia

Energética. La mayor parte de su vida profesional la

dedico al sector industrial y petrolero. Actualmente está

involucrado en las áreas de Energías Alternativas y

Eficiencia Energética en la Universidad Politécnica

Salesiana. Sus intereses de investigación incluyen los

métodos de GD con Energías alternativas, el iOT

basándose en controladores de bajo consumo.

Electrónica de Potencia, entre otros.

Manuel Dario Jaramillo Monge.-

Realizó sus estudios superiores en

la Universidad de las Fuerzas

Armadas ESPE de Quito, donde

se graduó de Ingeniero Electrónico

en Automatización y Control en

el 2014. Además, cursó estudios

de posgrado en la Universidad de

Newcastle, Reino Unido, donde

obtuvo el título en Máster en Electrical Power.

Actualmente es profesor ocasional a tiempo completo

de la Universidad Politécnica Salesiana.