Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step Methodology

*Oswaldo A. Arraez-Cancelliere, Nicolás Muñoz-Galeano and Jesús M. López-Lezama*

## **Abstract**

The quality of solar resource data is critical for the economic and technical assessment of solar photovoltaic (PV) installations. Understanding uncertainty and managing weather-related risk are essential for successful planning and operating of solar electricity assets. The input information available for PV designers is usually restricted to 12 monthly mean values of global horizontal irradiation (GHI) and average temperature, which characterize solar climate of locations. However, for calculating the energy production of a photovoltaic system, the global irradiation over the plane of the PV array is necessary. For this reason, this book chapter presents a methodology to appropriately determine the global irradiation over the plane of photovoltaic arrays. The methodology describes step by step the necessary equations for processing the data. Examples with numerical results are included to better show the data processing.

**Keywords:** global horizontal irradiation (GHI), photovoltaic (PV), energy production, solar resource, data processing

## **1. Introduction**

Renewable energy resources have become a promissory alternative to overcome the problems related to high pollution and limited sources of conventional energy. So, the analysis of energy resources and their economic feasibility is a concern topic for researchers around the world [1–4]. In this context, photovoltaic power plants have become one of the most important renewable sources of energy that have rapidly spread in the last decade. However, the assessment of the solar resource is not a topic usually approached by engineers and researchers due to the complexity in the process of computing the data, being extensive when the global horizontal irradiation is processed to obtain the global tilde irradiation. Therefore, this book chapter provides a step-by-step methodology for computing the global irradiation over the plane of photovoltaic arrays.

The quality of solar resource data is critical for economic and technical assessment of solar power installation. Understanding uncertainty and managing

weather-related risk are essential for successful planning and operating of solar electricity assets. High-quality solar resource and meteorological data can be obtained by two approaches: high-accuracy instruments installed at a meteorological station and complex solar meteorological models, which are validated using high-quality ground instruments [5].

*<sup>δ</sup>* <sup>¼</sup> <sup>23</sup>*:*45° � *sin* <sup>360</sup> � ð Þ *dn* <sup>þ</sup> <sup>284</sup>

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step…*

It is the difference between noon and the selected moment of the day in terms of a 360° rotation in 24 h. *ω* is equal to 0 at midday of each day, and it is counted as negative in the morning and positive in the afternoon. The solar hour angle

*Tsolar*ð Þ¼ *<sup>h</sup> Tlocal*ð Þþ *<sup>h</sup>* <sup>4</sup>ð Þþ *Lst* � *Lloc EoT*

where *Tsolar* and *Tlocal* are the solar time and the local clock time, respectively. *Lst* and *Lloc* are the standard meridian for the local time zone and the longitude of the location (east positive and west negative). *ΔTgmt* is the local time zone (e.g.,

Bogotá, �5). *EoT* stands for equation of time, which is the time difference between the apparent solar time for people and the real mean solar time, and takes into

Solar zenith is the angle between the vertical and the incident solar beam, and it can also be described as the angle of incidence of beam radiation on a horizontal surface [6]. The complement of the zenith angle is called the solar altitude, *γs*. These angles can be calculated using Eq. (7) and are function of the declination angle (*δ*), the latitude (*ϕ*) (north positive and south negative), and the true solar time (*ω*).

Eq. (7) can be used to find the sunrise angle (*ωs*Þ since at sunrise *γ<sup>s</sup>* ¼ 0, hence.

In accordance with the sign convention, ω<sup>s</sup> is always negative. The sunset angle

*Td*ð Þ¼ *hour* <sup>2</sup> � *abs*ð Þ *<sup>ω</sup><sup>s</sup>*

It is the angle between the meridians of the locations and the sun. It can also be described as the angular displacement from noon to the projection of beam radia-

*<sup>ω</sup><sup>s</sup>* ¼ � *cos* �<sup>1</sup>

is equal to �ωs, and the length of the day is equal to:

tion on the horizontal plane. The solar azimuth is given by:

**2.4 Solar azimuth (***ψs***)**

**105**

*cos θzs* ¼ *sinδ sinϕ* þ *cosδ cosδ cosω* ¼ *sin γ<sup>s</sup>* (7)

*γ<sup>s</sup>* ¼ 90 � *θzs* (8)

ð Þ � *tan δtanϕ* (9)

15° (10)

*Bn* <sup>¼</sup> <sup>360</sup>

account the perturbation of the earth's rotation [7].

**2.3 Solar zenith (***θzs***) and solar altitude (***γs*Þ

**2.2 Solar hour angle (***ω***)**

*DOI: http://dx.doi.org/10.5772/intechopen.90827*

is given as:

<sup>365</sup> (1)

*ω* ¼ 15 � ð Þ *Tsolar*ð Þ� *h* 12 (2)

<sup>365</sup> ð Þ *dn* � <sup>81</sup> (5)

*Lst* ¼ 15 � *ΔTgmt* (6)

*EoT min* ð Þ¼ 9*:*87 *sin* 2*B* � 7*:*53 *cos B* � 1*:*5 *sin B* (4)

<sup>60</sup> (3)

The input information available for PV designers is usually restricted to the 12-monthly mean values of global horizontal irradiation (GHI) and average temperature, which characterize solar climate of locations. However, the global irradiation over the plane of the PV array is necessary to calculate the energy production of a photovoltaic system.

The assessment of radiation arriving on an inclined surface, using global horizontal data as input, raises two main problems; first, to separate the GHI into their direct and diffuse components (decomposition) and, second, from them, to estimate the radiation components falling on an inclined surface (transposition) [6]. To solve these problems, it is important to describe in detail parameters such as declination angle, solar hour angle, solar zenith, solar altitude, solar azimuth, angle of incidence, solar constant, extraterrestrial irradiance over the horizontal surface, clearness index, and diffuse fraction index [6–8].

As regards decomposition models, in Ref. [9], authors reviewed and compared four decomposition models for monthly average of horizontal daily irradiation: a linear relationship proposed by Page [10], two polynomial equations defined by the authors of Refs. [11, 12], and a local correlation proposed by Macagnan et al. [13]. The authors of Ref. [9] stand out for the Page decomposition model of Ref. [10] in combination with the Perez transposition model [13] as a good performance combination used for passing from global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values. After applying the decomposition models, direct, diffuse, and albedo components of irradiation can be obtained.

For obtaining radiation components falling on an inclined surface, geometric considerations can be taken into account [9]. In Ref. [9], eight transposition models were reviewed, obtaining the best results using the Perez model [13]. Similar results were obtained in Ref. [14], where four transposition models were compared and validated with two-year data measured at site, and Liu and Jordan isotropic sky model is used in this book chapter due to its simplicity of implementation and good results reported in Ref. [15].

This book chapter describes in detail a methodology to determine the global irradiation over the plane of photovoltaic arrays. The chapter is organized as follows: Section 2 contains the proposed methodology, Section 3 includes experimental results that include data processing, and Section 4 presents the conclusions.

### **2. Proposed methodology**

The proposed methodology includes the data processing and also the definitions to understand it. Therefore, some basic definitions are presented below:

#### **2.1 Declination angle (***δ***)**

It is the angle between the equatorial plane and a straight line drawn between the center of the Earth and the center of the sun. It may be considered as approximately constant over the course of any day. It can be calculated using Eq. (1), where *dn* is the day number counted from the beginning of the year [7].

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step… DOI: http://dx.doi.org/10.5772/intechopen.90827*

$$\delta = 23.45^\circ \times \sin\left[\frac{360 \times (d\_n + 284)}{365}\right] \tag{1}$$

## **2.2 Solar hour angle (***ω***)**

weather-related risk are essential for successful planning and operating of solar electricity assets. High-quality solar resource and meteorological data can be

station and complex solar meteorological models, which are validated using

high-quality ground instruments [5].

*Renewable Energy - Technologies and Applications*

production of a photovoltaic system.

irradiation can be obtained.

results reported in Ref. [15].

**2. Proposed methodology**

**2.1 Declination angle (***δ***)**

**104**

clearness index, and diffuse fraction index [6–8].

obtained by two approaches: high-accuracy instruments installed at a meteorological

The input information available for PV designers is usually restricted to the 12-monthly mean values of global horizontal irradiation (GHI) and average temperature, which characterize solar climate of locations. However, the global irradiation over the plane of the PV array is necessary to calculate the energy

The assessment of radiation arriving on an inclined surface, using global horizontal data as input, raises two main problems; first, to separate the GHI into their direct and diffuse components (decomposition) and, second, from them, to estimate the radiation components falling on an inclined surface (transposition) [6]. To solve these problems, it is important to describe in detail parameters such as declination angle, solar hour angle, solar zenith, solar altitude, solar azimuth, angle of incidence, solar constant, extraterrestrial irradiance over the horizontal surface,

As regards decomposition models, in Ref. [9], authors reviewed and compared four decomposition models for monthly average of horizontal daily irradiation: a linear relationship proposed by Page [10], two polynomial equations defined by the authors of Refs. [11, 12], and a local correlation proposed by Macagnan et al. [13]. The authors of Ref. [9] stand out for the Page decomposition model of Ref. [10] in combination with the Perez transposition model [13] as a good performance combination used for passing from global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values. After applying the decomposition models, direct, diffuse, and albedo components of

For obtaining radiation components falling on an inclined surface, geometric considerations can be taken into account [9]. In Ref. [9], eight transposition models were reviewed, obtaining the best results using the Perez model [13]. Similar results were obtained in Ref. [14], where four transposition models were compared and validated with two-year data measured at site, and Liu and Jordan isotropic sky model is used in this book chapter due to its simplicity of implementation and good

This book chapter describes in detail a methodology to determine the global irradiation over the plane of photovoltaic arrays. The chapter is organized as follows: Section 2 contains the proposed methodology, Section 3 includes experimental

The proposed methodology includes the data processing and also the definitions

It is the angle between the equatorial plane and a straight line drawn between the center of the Earth and the center of the sun. It may be considered as approximately constant over the course of any day. It can be calculated using Eq. (1), where

results that include data processing, and Section 4 presents the conclusions.

to understand it. Therefore, some basic definitions are presented below:

*dn* is the day number counted from the beginning of the year [7].

It is the difference between noon and the selected moment of the day in terms of a 360° rotation in 24 h. *ω* is equal to 0 at midday of each day, and it is counted as negative in the morning and positive in the afternoon. The solar hour angle is given as:

$$w = \mathbf{15} \times (T\_{solar}(h) - \mathbf{12}) \tag{2}$$

$$T\_{solar}(h) = T\_{local}(h) + \frac{4(L\_{\rm tl} - L\_{\rm loc}) + E\sigma T}{60} \tag{3}$$

$$EoT\ (min) = 9.87\sin 2B - 7.53\cos B - 1.5\sin B\tag{4}$$

$$B\_n = \frac{\mathfrak{Z}\mathfrak{G}0}{\mathfrak{Z}\mathfrak{G}} (d\_n - \mathfrak{K}\mathfrak{1})\tag{5}$$

$$L\_{st} = \mathbf{15} \times \Delta T\_{\rm gmt} \tag{6}$$

where *Tsolar* and *Tlocal* are the solar time and the local clock time, respectively. *Lst* and *Lloc* are the standard meridian for the local time zone and the longitude of the location (east positive and west negative). *ΔTgmt* is the local time zone (e.g., Bogotá, �5). *EoT* stands for equation of time, which is the time difference between the apparent solar time for people and the real mean solar time, and takes into account the perturbation of the earth's rotation [7].

## **2.3 Solar zenith (***θzs***) and solar altitude (***γs*Þ

Solar zenith is the angle between the vertical and the incident solar beam, and it can also be described as the angle of incidence of beam radiation on a horizontal surface [6]. The complement of the zenith angle is called the solar altitude, *γs*. These angles can be calculated using Eq. (7) and are function of the declination angle (*δ*), the latitude (*ϕ*) (north positive and south negative), and the true solar time (*ω*).

$$
\cos \theta\_{\text{xs}} = \sin \delta \sin \phi + \cos \delta \cos \delta \cos \alpha = \sin \chi\_s \tag{7}
$$

$$
\gamma\_s = \Re \mathbf{0} - \theta\_\mathbf{x} \tag{8}
$$

Eq. (7) can be used to find the sunrise angle (*ωs*Þ since at sunrise *γ<sup>s</sup>* ¼ 0, hence.

$$
\alpha\_t = -\cos^{-1}(-\tan\delta \tan\phi) \tag{9}
$$

In accordance with the sign convention, ω<sup>s</sup> is always negative. The sunset angle is equal to �ωs, and the length of the day is equal to:

$$T\_d(hour) = \frac{2 \times abs(a\_t)}{15^\circ} \tag{10}$$

## **2.4 Solar azimuth (***ψs***)**

It is the angle between the meridians of the locations and the sun. It can also be described as the angular displacement from noon to the projection of beam radiation on the horizontal plane. The solar azimuth is given by:

*Renewable Energy - Technologies and Applications*

$$\cos\psi\_s = \left(\frac{\sin\chi\_s \times \sin\phi - \sin\delta}{\cos\chi\_s \cos\phi}\right) \tag{11}$$

In the Northern Hemisphere, true solar is the reference of the system, and it is defined as positive toward the west, that is, in the evening, and negative toward the east, that is, in the morning [6]. In **Figure 1**, the solar zenith, solar altitude, and solar azimuth are described.

## **2.5 Angle of incidence (***θi***)**

Most practical applications require the position of the sun relative to an inclined plane to be determined. The angle of solar incidence between the sun's rays and the normal to the surface is given by:

$$\begin{array}{l} \cos\left(\theta\_{i}\right) = \sin\left(\delta\right)\sin\left(\mathcal{Q}\right)\cos\left(\beta\right) - \left[\operatorname{sign}(\mathcal{Q})\right]\sin\left(\delta\right)\cos\left(\mathcal{Q}\right)\sin\left(\beta\right)\cos\left(a\right) \\ + \cos\left(\delta\right)\cos\left(\mathcal{Q}\right)\cos\left(\beta\right)\cos\left(a\right) + \left[\operatorname{sign}(\mathcal{Q})\right]\cos\left(\delta\right)\sin\left(\mathcal{Q}\right)\sin\left(\beta\right)\cos\left(a\right)\cos\left(a\right) \\ + \cos\left(\delta\right)\sin\left(a\right)\sin\left(a\right)\sin\left(\beta\right) \end{array}$$

where *β* is the tilt of the inclined plane (the angle formed with the horizontal), and *α* is the surface azimuth angle conventionally measured clockwise from the south (See **Figure 2**) [8]. The *sign*ð Þ ∅ function is 1 when the latitude is greater than 0 and is �1 otherwise.

## **2.6 Solar constant (***B***0**Þ

It is the amount of solar radiation received at the top of the atmosphere on a normal plane at the mean Earth-sun distance [6]. A good approximation of this value is:

$$B\_0 = \mathbf{1367 W/m^2} \tag{13}$$

(12)

If Eq. (14) is integrated over the day, the following expression is obtained:

*Definition of angles used as coordinates for an element of sky radiation to an inclined plane of tilt β and oriented*

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step…*

Hence, average daily extraterrestrial irradiation in a month over a surface is

*dn*<sup>2</sup> � *dn*<sup>1</sup> þ 1

The value calculated in Eq. (16) is used to estimate the clearness index

It is the relation between the solar radiation at the Earth's surface and the extraterrestrial radiation over the horizontal plane. The clearness index *KTm* for

*KTm* <sup>¼</sup> *Gdm*ð Þ <sup>0</sup>

where *Gdm*ð Þ 0 is the average daily horizontal global irradiation of a month,

It is the relation between the diffuse radiation over the horizontal plane and the global radiation over the horizontal plane. This index is widely used on decomposition models to separate the global radiation into its direct and diffuse components.

*Kdm* <sup>¼</sup> *Ddm*ð Þ <sup>0</sup>

X *dn*<sup>2</sup>

*dn*<sup>1</sup>

<sup>180</sup> *<sup>ω</sup><sup>s</sup> sin <sup>ϕ</sup>sin<sup>δ</sup>*

*B*0*<sup>d</sup>*ð Þ 0 (16)

h i (15)

*<sup>B</sup>*0*dm*ð Þ <sup>0</sup> (17)

*Gdm*ð Þ <sup>0</sup> (18)

360 <sup>365</sup> *dn* � � � � *cos<sup>ϕ</sup> cos<sup>δ</sup>* sin*ω<sup>s</sup>* <sup>þ</sup> *<sup>π</sup>*

*<sup>B</sup>*0*dm*ð Þ¼ <sup>0</sup> <sup>1</sup>

*<sup>B</sup>*0*<sup>d</sup>*ð Þ¼ <sup>0</sup> <sup>24</sup>

**Figure 2.**

*to α.*

obtained by:

(*KTm*) [2].

**107**

**2.7 Clearness index (***KTm***)**

each month is given by:

which is usually an input value [6].

**2.8 Diffuse fraction index (***Kd***)**

*<sup>π</sup> <sup>B</sup>*<sup>0</sup> <sup>1</sup> <sup>þ</sup> <sup>0</sup>*:*<sup>033</sup> *cos*

*DOI: http://dx.doi.org/10.5772/intechopen.90827*

Extraterrestrial irradiance over the horizontal surface (*B*0ð Þ 0 ): Extraterrestrial radiation over a horizontal surface varies over the day, and it is given by:

#### **Figure 1.**

*Position of the sun relative to a fixed point on the earth defining the solar azimuth (ψ*s*), the solar zenith (θzs), and the solar altitude (γ*s*).*

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step… DOI: http://dx.doi.org/10.5772/intechopen.90827*

#### **Figure 2.**

*cos <sup>ψ</sup><sup>s</sup>* <sup>¼</sup> *sin <sup>γ</sup><sup>s</sup>* � *sin <sup>ϕ</sup>* � *sin <sup>δ</sup>*

solar azimuth are described.

*Renewable Energy - Technologies and Applications*

**2.5 Angle of incidence (***θi***)**

0 and is �1 otherwise.

**2.6 Solar constant (***B***0**Þ

value is:

**Figure 1.**

**106**

*and the solar altitude (γ*s*).*

normal to the surface is given by:

þ *cos*ð Þ*δ sin* ð Þ *α sin* ð Þ *ω sin* ð Þ *β*

In the Northern Hemisphere, true solar is the reference of the system, and it is defined as positive toward the west, that is, in the evening, and negative toward the east, that is, in the morning [6]. In **Figure 1**, the solar zenith, solar altitude, and

Most practical applications require the position of the sun relative to an inclined plane to be determined. The angle of solar incidence between the sun's rays and the

where *β* is the tilt of the inclined plane (the angle formed with the horizontal), and *α* is the surface azimuth angle conventionally measured clockwise from the south (See **Figure 2**) [8]. The *sign*ð Þ ∅ function is 1 when the latitude is greater than

It is the amount of solar radiation received at the top of the atmosphere on a normal plane at the mean Earth-sun distance [6]. A good approximation of this

Extraterrestrial irradiance over the horizontal surface (*B*0ð Þ 0 ): Extraterrestrial

*Position of the sun relative to a fixed point on the earth defining the solar azimuth (ψ*s*), the solar zenith (θzs),*

radiation over a horizontal surface varies over the day, and it is given by:

*B*0ð Þ¼ 0 *B*<sup>0</sup> � 1 þ 0*:*033 *cos*

*<sup>B</sup>*<sup>0</sup> <sup>¼</sup> <sup>1367</sup> *<sup>W</sup>=m*<sup>2</sup> (13)

*cos θzs* (14)

360 <sup>365</sup> *dn*

þ *cos*ð Þ*δ cos*ð Þ ∅ *cos*ð Þ *β cos*ð Þþ *ω* ½ � *sign*ð Þ ∅ *cos*ð Þ*δ sin* ð Þ ∅ *sin* ð Þ *β cos*ð Þ *α cos*ð Þ *ω*

*cos*ð Þ¼ *θ<sup>i</sup> sin* ð Þ*δ sin* ð Þ ∅ *cos*ð Þ� *β* ½ � *sign*ð Þ ∅ *sin* ð Þ*δ cos*ð Þ ∅ *sin* ð Þ *β cos*ð Þ *α*

*cos γ<sup>s</sup> cos ϕ* 

(11)

(12)

*Definition of angles used as coordinates for an element of sky radiation to an inclined plane of tilt β and oriented to α.*

If Eq. (14) is integrated over the day, the following expression is obtained:

$$B\_{0d}(\mathbf{0}) = \frac{24}{\pi} B\_0 \left[ \mathbf{1} + 0.033 \cos \left( \frac{360}{365} d\_\eta \right) \right] \left[ \cos \phi \cos \delta \sin \alpha\_\circ + \frac{\pi}{180} \cos \phi \sin \delta \right] \tag{15}$$

Hence, average daily extraterrestrial irradiation in a month over a surface is obtained by:

$$B\_{0dm}(\mathbf{0}) = \frac{\mathbf{1}}{d\_{n2} - d\_{n1} + \mathbf{1}} \sum\_{d\_{n1}}^{d\_{n2}} B\_{0d}(\mathbf{0}) \tag{16}$$

The value calculated in Eq. (16) is used to estimate the clearness index (*KTm*) [2].

#### **2.7 Clearness index (***KTm***)**

It is the relation between the solar radiation at the Earth's surface and the extraterrestrial radiation over the horizontal plane. The clearness index *KTm* for each month is given by:

$$K\_{Tm} = \frac{G\_{dm}(\mathbf{0})}{B\_{0dm}(\mathbf{0})} \tag{17}$$

where *Gdm*ð Þ 0 is the average daily horizontal global irradiation of a month, which is usually an input value [6].

## **2.8 Diffuse fraction index (***Kd***)**

It is the relation between the diffuse radiation over the horizontal plane and the global radiation over the horizontal plane. This index is widely used on decomposition models to separate the global radiation into its direct and diffuse components.

$$K\_{dm} = \frac{D\_{dm}(\mathbf{0})}{G\_{dm}(\mathbf{0})} \tag{18}$$

The modeling process for calculating the effective in-plane hourly irradiation when starting from monthly average of horizontal daily irradiation and using monthly average daily irradiance profiles is shown in **Figure 3** [9].

The daily irradiance profile can be defined in terms of irradiance divided by daily irradiation and on assuming that the profile of the extraterrestrial horizontal solar radiation translates directly into the profile of the diffuse component while an empirical correction is needed for global radiation [11]. The following equations describe the model to calculate the daily irradiance profile starting from daily average monthly values:

$$G(\mathbf{0}) = r'\_G \times G\_{dm}(\mathbf{0})\tag{19}$$

irradiation: a linear relationship proposed by Page [10], two polynomial equations defined by the authors of Refs. [11, 12], and a local correlation proposed by Macagnan et al. [13]. The authors stand out the Page decomposition model in combination with the Perez transposition model [13] as a good performance combination used for passing from global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values. The decomposition model proposed by Page consists of a linear equation that correlated the diffuse fraction index and the clearness index using data from loca-

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step…*

Once the global horizontal irradiance is separated into direct and diffuse components and the daily irradiance profile is obtained, it is necessary to calculate the effective irradiance on the plane of the array. The irradiance over the plane with a tilt *β*, in degrees, and oriented to angle *α*, conventionally measured clockwise from

where *G*, *B*, *D*, and *AL* represent global, direct, diffuse, and albedo components,

The beam transposition factor is calculated straightforward from simple geo-

*rB* <sup>¼</sup> *max* ð Þ 0, *cos <sup>θ</sup><sup>i</sup> cos θzs*

Assuming isotropic albedo radiation, the corresponding transposition factor is

1 � *cos β*

where *ρ* is the ground reflection factor. The albedo radiation is scarcely relevant and rarely measured. A general reflection value of 0.2 is considered since this is

The diffuse transposition factor depends on the assumption made for the sky

obtaining the best results using the Perez model. Similar results are obtained in Ref. [14], where four transposition models are compared and validated with two-year data measured at site, and the most accurate results were obtained by the Hay and Davies transposition model and the Perez transposition model. In this work, the Liu and Jordan isotropic sky model is used due to its simplicity of implementation and

In the transposition model proposed by Liu and Jordan, the diffuse radiation is given by an isotropic component coming from the entire celestial hemisphere. The

*rAL* ¼ *ρ*

radiance distribution. In Ref. [9], eight transposition models are reviewed,

respectively. The irradiance components over the plane are given by:

*Kdm* ¼ 1 � 1*:*13*KTm* (26)

*B*ð Þ¼ *β*, *α B*ð Þ� 0 *rB* (28) *D*ð Þ¼ *β*, *α D*ð Þ� 0 *rD* (29) *AL*ð Þ¼ *β*, *α G*ð Þ� 0 *rAL* (30)

<sup>2</sup> (32)

(31)

*G*ð Þ¼ *β*, *α B*ð Þþ *β*, *α D*ð Þþ *β*, *α AL*ð Þ *β*, *α* (27)

tions situated between 40°N and 40°S, and it is given by:

*DOI: http://dx.doi.org/10.5772/intechopen.90827*

the south, can be obtained by:

metric considerations [9]:

extendedly used on practice [9].

good results as reported in Ref. [15].

diffuse transposition factor is given by:

given by:

**109**

$$D(\mathbf{0}) = r\_D^\prime \times D\_{dm}(\mathbf{0})\tag{20}$$

$$B(\mathbf{0}) = G(\mathbf{0}) - D(\mathbf{0}) \tag{21}$$

with

$$r'\_D = \frac{B\_0(\mathbf{0})}{B\_{0d}(\mathbf{0})} = \frac{\pi}{T} \times \left(\frac{\cos\alpha - \cos\alpha\_\circ}{\frac{\pi}{180} \times \alpha\_\circ \times \cos\alpha\_\circ - \sin\alpha\_\circ}\right) \tag{22}$$

$$r'\_G = r'\_D \times (a + b \times \cos \alpha) \tag{23}$$

$$a = 0.409 - 0.5016 \times \sin\left(a\_t + 60\right) \tag{24}$$

$$b = 0.6609 + 0.4767 \times \sin\left(a\_t + 60\right) \tag{25}$$

where *ω* and *ω<sup>s</sup>* are expressed in degrees, and *T* is the day length, usually expressed in hours (24 h). The unit of indexes *rD* and *rG* is *T*�<sup>1</sup> , and they can be used to calculate irradiation during short periods centered on the considered instant *ω*. Subscripts "*d*" and "*m*" refer to the daily and monthly average of daily values, respectively.

The diffuse component of the average daily irradiation, *Ddm*ð Þ 0 , is derived from a decomposition model consisting of an empirical relationship between the clearness index, *KTm*, and the diffuse fraction, *Kdm*. In Ref. [9], the authors review and compare four decomposition models for monthly average of horizontal daily

**Figure 3.**

*Calculation of daily irradiation on an inclined surface.*

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step… DOI: http://dx.doi.org/10.5772/intechopen.90827*

irradiation: a linear relationship proposed by Page [10], two polynomial equations defined by the authors of Refs. [11, 12], and a local correlation proposed by Macagnan et al. [13]. The authors stand out the Page decomposition model in combination with the Perez transposition model [13] as a good performance combination used for passing from global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values.

The decomposition model proposed by Page consists of a linear equation that correlated the diffuse fraction index and the clearness index using data from locations situated between 40°N and 40°S, and it is given by:

$$K\_{dm} = \mathbf{1} - \mathbf{1}.\mathbf{1}\mathbf{3}K\_{Tm} \tag{26}$$

Once the global horizontal irradiance is separated into direct and diffuse components and the daily irradiance profile is obtained, it is necessary to calculate the effective irradiance on the plane of the array. The irradiance over the plane with a tilt *β*, in degrees, and oriented to angle *α*, conventionally measured clockwise from the south, can be obtained by:

$$G(\beta, a) = B(\beta, a) + D(\beta, a) + AL(\beta, a) \tag{27}$$

where *G*, *B*, *D*, and *AL* represent global, direct, diffuse, and albedo components, respectively. The irradiance components over the plane are given by:

$$B(\beta, a) = B(\mathbf{0}) \times r\_{\mathbf{B}} \tag{28}$$

$$D(\beta, a) = D(\mathbf{0}) \times r\_{\mathbf{D}} \tag{29}$$

$$AL(\beta, a) = G(\mathbf{0}) \times r\_{AL} \tag{30}$$

The beam transposition factor is calculated straightforward from simple geometric considerations [9]:

$$r\_{\theta} = \frac{\max\left(0, \cos\theta\_i\right)}{\cos\theta\_{\mathfrak{x}}} \tag{31}$$

Assuming isotropic albedo radiation, the corresponding transposition factor is given by:

$$r\_{AL} = \rho \frac{\mathbf{1} - \cos \beta}{2} \tag{32}$$

where *ρ* is the ground reflection factor. The albedo radiation is scarcely relevant and rarely measured. A general reflection value of 0.2 is considered since this is extendedly used on practice [9].

The diffuse transposition factor depends on the assumption made for the sky radiance distribution. In Ref. [9], eight transposition models are reviewed, obtaining the best results using the Perez model. Similar results are obtained in Ref. [14], where four transposition models are compared and validated with two-year data measured at site, and the most accurate results were obtained by the Hay and Davies transposition model and the Perez transposition model. In this work, the Liu and Jordan isotropic sky model is used due to its simplicity of implementation and good results as reported in Ref. [15].

In the transposition model proposed by Liu and Jordan, the diffuse radiation is given by an isotropic component coming from the entire celestial hemisphere. The diffuse transposition factor is given by:

The modeling process for calculating the effective in-plane hourly irradiation when starting from monthly average of horizontal daily irradiation and using

The daily irradiance profile can be defined in terms of irradiance divided by daily irradiation and on assuming that the profile of the extraterrestrial horizontal solar radiation translates directly into the profile of the diffuse component while an empirical correction is needed for global radiation [11]. The following equations describe the model to calculate the daily irradiance profile starting from daily

0

0

*π*

where *ω* and *ω<sup>s</sup>* are expressed in degrees, and *T* is the day length, usually

to calculate irradiation during short periods centered on the considered instant *ω*. Subscripts "*d*" and "*m*" refer to the daily and monthly average of daily values,

The diffuse component of the average daily irradiation, *Ddm*ð Þ 0 , is derived from a decomposition model consisting of an empirical relationship between the clearness index, *KTm*, and the diffuse fraction, *Kdm*. In Ref. [9], the authors review and compare four decomposition models for monthly average of horizontal daily

*<sup>G</sup>* � *Gdm*ð Þ 0 (19)

*<sup>D</sup>* � *Ddm*ð Þ 0 (20)

(22)

, and they can be used

*B*ð Þ¼ 0 *G*ð Þ� 0 *D*ð Þ 0 (21)

*<sup>D</sup>* � ð Þ *a* þ *b* � *cos ω* (23)

*cos ω* � *cos ω<sup>s</sup>*

<sup>180</sup> � *ω<sup>s</sup>* � *cosω<sup>s</sup>* � *sin ω<sup>s</sup>* 

*a* ¼ 0*:*409 � 0*:*5016 � *sin* ð Þ *ω<sup>s</sup>* þ 60 (24) *b* ¼ 0*:*6609 þ 0*:*4767 � *sin* ð Þ *ω<sup>s</sup>* þ 60 (25)

monthly average daily irradiance profiles is shown in **Figure 3** [9].

*G*ð Þ¼ 0 *r*

*D*ð Þ¼ 0 *r*

average monthly values:

*r* 0 *<sup>D</sup>* <sup>¼</sup> *<sup>B</sup>*0ð Þ <sup>0</sup>

*Renewable Energy - Technologies and Applications*

*<sup>B</sup>*0*<sup>d</sup>*ð Þ <sup>0</sup> <sup>¼</sup> *<sup>π</sup>*

*r* 0 *<sup>G</sup>* ¼ *r* 0

expressed in hours (24 h). The unit of indexes *rD* and *rG* is *T*�<sup>1</sup>

*T* �

with

respectively.

**Figure 3.**

**108**

*Calculation of daily irradiation on an inclined surface.*

$$r\_D = \frac{1 + \cos \beta}{2} \tag{33}$$

In summary, the global irradiation over the tilted plane is calculated by:

$$G(\beta, a) = B(\mathbf{0}) \times r\_B + D(\mathbf{0}) \times r\_D + G(\mathbf{0}) \times r\_{AL} \tag{34}$$

## **3. Experimental results: Data processing**

*Santa Cruz del Islote* in Colombia was used as a location for the case study. Data that consist on the monthly average daily global horizontal irradiance (*Gdm*) and the monthly average ambient temperature (*Tamb*,*m*) were provided by Solargis through its pvPlanner platform, see **Table 1**.

A MATLAB routine was used to compute the monthly global irradiance over the horizontal and over the plane. Results were also compared with the data that can be processed from Solargis, and **Table 2** shows the results obtained. Comparison shows that the results are good enough for the purpose of this work.


In **Figure 4**, it is shown the daily global profile on the horizontal and on the tilted plane for the first 4 days of the year calculated for the selected location. As expected, global tilde irradiation is higher than the global horizontal irradiation.

This book chapter presented a methodology that describes in detail the data processing to obtain the global irradiation over the plane of photovoltaic arrays. The

methodology includes definitions and equations necessary to perform the processing of the data. The following parameters were described and along with their equations: declination angle, solar hour angle, solar zenith, solar altitude, solar azimuth, angle of incidence, solar constant, extraterrestrial irradiance over the

horizontal surface, clearness index, and diffuse fraction index.

**4. Conclusions**

**Table 2.**

**Figure 4.**

**111**

*Global horizontal and tilted irradiations.*

*Daily global irradiation calculated for "Islote de Santa Cruz."*

**Global horizontal irradiation (kWh/m<sup>2</sup> ) Solargis**

*DOI: http://dx.doi.org/10.5772/intechopen.90827*

**Global horizontal irradiation (kWh/m<sup>2</sup> ) calculated**

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step…*

**Dev (%)**

January 183.6 182.0 0.88% 201.9 198.6 1.65% February 175.6 174.2 0.81% 186.9 184.3 1.41% March 194.3 193.0 0.68% 198.5 196.2 1.14% April 177.2 176.1 0.65% 175 172.9 1.17% May 166.4 165.2 0.70% 160.1 158.8 0.83% June 161.9 160.8 0.71% 153.6 152.6 0.65% July 173.2 172.0 0.69% 165.3 163.9 0.84% August 171.7 170.6 0.65% 167.8 166.1 1.03% September 160.9 159.8 0.70% 162 160.1 1.17% October 155.8 154.4 0.91% 162.4 159.5 1.79% November 149.1 147.7 0.96% 160.5 157.1 2.13% December 161.2 159.7 0.93% 177.8 174.1 2.09% Year 2030.9 2015.3 0.77% 2071.8 2044.1 1.34%

**Global tilted irradiation (kWh/m<sup>2</sup> ) Solargis**

**Global tilted irradiation (kWh/m2 ) calculated**

**Dev (%)**

#### **Table 1.**

*Meteorological input parameters [16].*


*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step… DOI: http://dx.doi.org/10.5772/intechopen.90827*

#### **Table 2.**

*rD* <sup>¼</sup> <sup>1</sup> <sup>þ</sup> *cos <sup>β</sup>*

*Santa Cruz del Islote* in Colombia was used as a location for the case study. Data that consist on the monthly average daily global horizontal irradiance (*Gdm*) and the monthly average ambient temperature (*Tamb*,*m*) were provided by Solargis

A MATLAB routine was used to compute the monthly global irradiance over the horizontal and over the plane. Results were also compared with the data that can be processed from Solargis, and **Table 2** shows the results obtained. Comparison

�5

shows that the results are good enough for the purpose of this work.

**Location Islote de Santa Cruz, Colombia**

[Wh/m<sup>2</sup> ]

January 5922.6 27.8 February 6271.4 27.6 March 6267.7 27.6 April 5906.7 27.7 May 5367.7 27.9 June 5396.7 28.5 July 5587.1 28.7 August 5538.7 28.5 September 5363.3 28.2 October 5025.8 27.9 November 4970.0 27.8 December 5200.0 28.0 Average 5568.1 28.0

Tilt 10 Plane inclination

Azimuth 0 Plane orientation (South = 0°; West 90°) GRF 0.2 Ground reflection factor (0–1)

Latitude 9.79 Longitude �75.859167

Month Daily sum of global irradiation

Time zone (GTM)

**Table 1.**

**110**

*Meteorological input parameters [16].*

*G*ð Þ¼ *β*, *α B*ð Þ� 0 *rB* þ *D*ð Þ� 0 *rD* þ *G*ð Þ� 0 *rAL* (34)

In summary, the global irradiation over the tilted plane is calculated by:

**3. Experimental results: Data processing**

*Renewable Energy - Technologies and Applications*

through its pvPlanner platform, see **Table 1**.

<sup>2</sup> (33)

Default = 0.2

Average diurnal (24-h) air temperature [°C]

*Global horizontal and tilted irradiations.*

**Figure 4.**

*Daily global irradiation calculated for "Islote de Santa Cruz."*

In **Figure 4**, it is shown the daily global profile on the horizontal and on the tilted plane for the first 4 days of the year calculated for the selected location. As expected, global tilde irradiation is higher than the global horizontal irradiation.

### **4. Conclusions**

This book chapter presented a methodology that describes in detail the data processing to obtain the global irradiation over the plane of photovoltaic arrays. The methodology includes definitions and equations necessary to perform the processing of the data. The following parameters were described and along with their equations: declination angle, solar hour angle, solar zenith, solar altitude, solar azimuth, angle of incidence, solar constant, extraterrestrial irradiance over the horizontal surface, clearness index, and diffuse fraction index.

The obtention of the global irradiance over a tilde plane requires decomposition models, which provide direct, diffuse, and albedo components of irradiation. This book chapter provides global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values.

**References**

10.12691/aees-2-3-2

s12206-018-0241-6

thermal.505498

[1] Taner T, Demirci OK. Energy and economic analysis of the wind turbine plant's draft for the Aksaray City. Applied Ecology and Environmental Sciences. 2014;**2**(3):82-85. DOI:

*DOI: http://dx.doi.org/10.5772/intechopen.90827*

[8] Demain C, Journée M, Bertrand C. Evaluation of different models to estimate the global solar radiation on inclined surfaces. Renewable Energy. 2013;**50**:710-721. DOI: 10.1016/j.

[9] Moretón R, Lorenzo E, Pinto A, Muñoz J, Narvarte L. From broadband

horizontal to effective in-plane irradiation: A review of modelling and derived uncertainty for PV yield prediction. Renewable and Sustainable Energy Reviews. 2017;**78**:886-903. DOI:

10.1016/j.rser.2017.05.020

1976

[10] Page JK. The Estimation of Monthly Mean Values of Daily Short Wave Irradiation on Vertical and Inclined Surfaces from Sunshine Records for Latitudes 60 N to

40 S [Thesis]. University of Sheffield;

[11] Collares-Pereira M, Rabl A. The average distribution of solar radiationcorrelations between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy.

1979;**22**:155-164. DOI: 10.1016/ 0038-092X(79)90100-2

[12] Erbs DG, Klein SA, Duffie JA. Estimation of the diffuse radiation fraction for hourly, daily and monthlyaverage global radiation. Solar Energy. 1982;**28**(4):293-302. DOI: 10.1016/

0038-092X(82)90302-4

01425919408914262

[13] Macagnan MH, Lorenzo E, Jimenez C. Solar radiation in Madrid. International Journal of Solar Energy. 1994;**16**(1):1-14. DOI: 10.1080/

[14] SolarPower Europe. O&M Best Practices Guidelines [Internet]. 2019. Available from: https://www.researchga te.net/publication/304624410\_Sola rPower\_Europe\_OM\_Best\_Practices\_ Guidelines. [Accessed: 15-11-2019]

renene.2012.07.031

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step…*

[2] Taner T. Economic analysis of a wind power plant: A case study for the Cappadocia region. Journal of Mecha nical Science and Technology. 2018; **32**(3):1379-1389. DOI: 10.1007/

[3] Taner T, Dalkilic ASA. Feasibility study of solar energy-techno economic analysis from Aksaray City, Turkey. Journal of Thermal Engineering. 2019;**3**(5):1-1. DOI: 10.18186/

[4] Taner T, Naqvi SAH, Ozkaymak M. Techno-economic analysis of a more efficient hydrogen generation system prototype: A case study of PEM Electrolyzer with Cr-C coated SS304 bipolar plates. Fuel Cells. 2019;**19**:1-8.

DOI: 10.1002/fuce.201700225

zonaws.com/public/doc/d

15-11-2019]

968024

**113**

[5] Solargis. Solargis Solar Resource Database Description and Accuracy [Internet]. 2019. Available from: https:// solargis2-web-assets.s3.eu-west-1.ama

143113beb/Solargis-database-desc ription-and-accuracy-v2.pdf. [Accessed:

[6] Luque A, Hegedus S. Handbook of Photovoltaic Science and Engineering. 2nd ed. Chichester: Wiley; 2011. p. 1132.

[7] Khatib T, Elmenreich W. A model for hourly solar radiation data generation from daily solar radiation data using a generalized regression

International Journal of Photoenergy. 2015;**2015**:1-13. DOI: 10.1155/2015/

DOI: 10.1002/9780470974704

artificial neural network.

This book chapter is extensive in the use of geometric considerations. This is due to the fact that input data are global horizontal irradiation and average temperature, while output data are the global irradiation over a tilde PV plane. Therefore, equations and schemes were provided for facilitating the explanation.

## **Acknowledgements**

The authors gratefully acknowledge the financial support provided by the Colombia Scientific Program within the framework of the call "Ecosistema Científico" (Contract No. FP44842-218-2018). The authors also want to thank the "Programa de Sostenibilidad de la UdeA."

## **Author details**

Oswaldo A. Arraez-Cancelliere, Nicolás Muñoz-Galeano\* and Jesús M. López-Lezama Facultad de Ingeniería, Grupo GIMEL, Universidad de Antioquia, Medellín, Colombia

\*Address all correspondence to: nicolas.munoz@udea.edu.co

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Computing the Global Irradiation over the Plane of Photovoltaic Arrays: A Step-by-Step… DOI: http://dx.doi.org/10.5772/intechopen.90827*

## **References**

The obtention of the global irradiance over a tilde plane requires decomposition models, which provide direct, diffuse, and albedo components of irradiation. This book chapter provides global horizontal irradiation to effective in-plane irradiance

This book chapter is extensive in the use of geometric considerations. This is due to the fact that input data are global horizontal irradiation and average temperature, while output data are the global irradiation over a tilde PV plane. Therefore, equa-

The authors gratefully acknowledge the financial support provided by the Colombia Scientific Program within the framework of the call "Ecosistema Científico" (Contract No. FP44842-218-2018). The authors also want to thank the

when it is started from monthly average of daily irradiation values.

tions and schemes were provided for facilitating the explanation.

Oswaldo A. Arraez-Cancelliere, Nicolás Muñoz-Galeano\* and

\*Address all correspondence to: nicolas.munoz@udea.edu.co

provided the original work is properly cited.

Facultad de Ingeniería, Grupo GIMEL, Universidad de Antioquia, Medellín,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**Acknowledgements**

**Author details**

Colombia

**112**

Jesús M. López-Lezama

"Programa de Sostenibilidad de la UdeA."

*Renewable Energy - Technologies and Applications*

[1] Taner T, Demirci OK. Energy and economic analysis of the wind turbine plant's draft for the Aksaray City. Applied Ecology and Environmental Sciences. 2014;**2**(3):82-85. DOI: 10.12691/aees-2-3-2

[2] Taner T. Economic analysis of a wind power plant: A case study for the Cappadocia region. Journal of Mecha nical Science and Technology. 2018; **32**(3):1379-1389. DOI: 10.1007/ s12206-018-0241-6

[3] Taner T, Dalkilic ASA. Feasibility study of solar energy-techno economic analysis from Aksaray City, Turkey. Journal of Thermal Engineering. 2019;**3**(5):1-1. DOI: 10.18186/ thermal.505498

[4] Taner T, Naqvi SAH, Ozkaymak M. Techno-economic analysis of a more efficient hydrogen generation system prototype: A case study of PEM Electrolyzer with Cr-C coated SS304 bipolar plates. Fuel Cells. 2019;**19**:1-8. DOI: 10.1002/fuce.201700225

[5] Solargis. Solargis Solar Resource Database Description and Accuracy [Internet]. 2019. Available from: https:// solargis2-web-assets.s3.eu-west-1.ama zonaws.com/public/doc/d 143113beb/Solargis-database-desc ription-and-accuracy-v2.pdf. [Accessed: 15-11-2019]

[6] Luque A, Hegedus S. Handbook of Photovoltaic Science and Engineering. 2nd ed. Chichester: Wiley; 2011. p. 1132. DOI: 10.1002/9780470974704

[7] Khatib T, Elmenreich W. A model for hourly solar radiation data generation from daily solar radiation data using a generalized regression artificial neural network. International Journal of Photoenergy. 2015;**2015**:1-13. DOI: 10.1155/2015/ 968024

[8] Demain C, Journée M, Bertrand C. Evaluation of different models to estimate the global solar radiation on inclined surfaces. Renewable Energy. 2013;**50**:710-721. DOI: 10.1016/j. renene.2012.07.031

[9] Moretón R, Lorenzo E, Pinto A, Muñoz J, Narvarte L. From broadband horizontal to effective in-plane irradiation: A review of modelling and derived uncertainty for PV yield prediction. Renewable and Sustainable Energy Reviews. 2017;**78**:886-903. DOI: 10.1016/j.rser.2017.05.020

[10] Page JK. The Estimation of Monthly Mean Values of Daily Short Wave Irradiation on Vertical and Inclined Surfaces from Sunshine Records for Latitudes 60 N to 40 S [Thesis]. University of Sheffield; 1976

[11] Collares-Pereira M, Rabl A. The average distribution of solar radiationcorrelations between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy. 1979;**22**:155-164. DOI: 10.1016/ 0038-092X(79)90100-2

[12] Erbs DG, Klein SA, Duffie JA. Estimation of the diffuse radiation fraction for hourly, daily and monthlyaverage global radiation. Solar Energy. 1982;**28**(4):293-302. DOI: 10.1016/ 0038-092X(82)90302-4

[13] Macagnan MH, Lorenzo E, Jimenez C. Solar radiation in Madrid. International Journal of Solar Energy. 1994;**16**(1):1-14. DOI: 10.1080/ 01425919408914262

[14] SolarPower Europe. O&M Best Practices Guidelines [Internet]. 2019. Available from: https://www.researchga te.net/publication/304624410\_Sola rPower\_Europe\_OM\_Best\_Practices\_ Guidelines. [Accessed: 15-11-2019]

[15] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes. 4th ed. Hoboken, New Jersey, United States: Wiley; 2013. p. 910. DOI: 10.1002/9781118671603

[16] Solargis. pvPlanner [Internet]. 2019. Available from: https://solargis.info/ pvplanner/#tl=Google:hybrid&bm=sate llite. [Accessed: 15-11-2019]

**115**

**Chapter 8**

**Abstract**

conditions.

**1. Introduction**

rather limited.

technologies [5].

pressing, extraction, biofuel

Pulsed Electrical Discharge and

Pulsed Electric Field Treatment

*Ivan Shorstkii and Evgeny Koshevoi*

during Sunflower Seed Processing

For the successful implementation of emerging electrical technologies in the oil pressing process, optimization of process parameters in combination with parameters from electrical process is crucial. The aim of this study was to evaluate the effect of the following pretreatments: pulsed electrical discharge (PED) and pulsed electric field (PEF) on rheological properties, morphological capillaryporous structure, and oil recovery of sunflower seed. FESEM analysis of the surface microstructure, pressing, and solvent extraction were used to obtain treatment efficiency after novel technologies. The results of this study show that PED and PEF treatments could be used as a pretreatment before sunflower seed processing to modify internal structure, increase the oil yield, or contribute to the mechanical destruction of oil globules and the release of free oil to the surface under gentle

**Keywords:** pulsed electric field, electrical discharge, crop, oil, oilseeds, processing,

Sunflower oil production is rapidly emerging in Russia, Ukraine, Turkey, and other countries, filling an important niche of locally supplied protein and fat sources. Sunflower seeds are becoming of outmost importance to fulfill the requirements for safe products and find efficient ways to reduce potential chemical and technological hazards. Current methods of sunflower seed processing rely on well-developed and established food industry thermal treatment (roasting, drying, heating, and cooling), mechanical treatment (cleaning, flaking, grinding, and pressing), and fractionation methods (extraction, sedimentation, separation, centrifugation, etc.) [1–4]. Application of novel emerging processing technologies, which potentially can improve processing efficiency and quality of the products to the sunflower seeds, is

Development of a novel scientific direction should be based on an active imple-

mentation of green technologies [5]. Green technologies include methods that enhance the efficiency of extraction of target components (oils, fats, phospholipids, polyphenols, pigments, etc.) from plant materials and can improve the traditional processing technology or combine traditional technology with novel emerging

## **Chapter 8**

[15] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes. 4th ed. Hoboken, New Jersey, United States: Wiley; 2013. p. 910. DOI:

*Renewable Energy - Technologies and Applications*

[16] Solargis. pvPlanner [Internet]. 2019. Available from: https://solargis.info/ pvplanner/#tl=Google:hybrid&bm=sate

10.1002/9781118671603

llite. [Accessed: 15-11-2019]

**114**
