PVS Requirements

One we defined the PVS, these recommendations must be followed:


$$E = \frac{E\_T}{R} \tag{1}$$

$$NP = \frac{E}{0.9 \text{ } \text{Wp } SPH} \tag{2}$$

where *E* is the real energy consumption in kWh, *ET* is the theoretical energetic consumption in kW, *R* is a proportional constant that includes losses related in the batteries use, inverters and electrical wiring, commonly its value is 0.8, *NP* is the number of PV, *SPH* are sun peak hours, and *Wp* is the PVS peak power.

5. Inverter selection: the inverter will be in the function of the charge and operation.

To determine the correct position of the PVS, some variables need to be considered, such as the solar declination angle (δ) that can be defined as the angle formed by the plane that contains the axis of terrestrial rotation and the plane perpendicular to the elliptic [45]. The solar declination angle is positive in the North and varies between −23.45◦ ≤ δ ≤ 23.45◦. Its highest value is on June 21, and its lowest on December 22 [46]. The expression of the solar declination angle in Equation (3) includes Julian days, *n*.

$$\mathcal{S} = 23.45^\circ \sin\left(360(n + 284)/365\right) \tag{3}$$

The angle formed with respect to the equator is called the latitude angle (φ) and is considered positive in the North and negative in the South, its value being between –90◦ ≤ φ ≤90◦.

The hour angle (ω) is formed by solar rays and the meridional plane at the site. The measure is from the meridional plane, in which the position of the Sun at 12:00 h has a ω = 0◦. In the East is positive and in the West is negative, the position of the Sun at 6:00 h, ω = 90◦, at 18:00 h, ω = –90◦. The hour angle is given by Equation (4).

$$
\omega = \frac{360 \text{ (12 -- t)}}{24} \tag{4}
$$

where *t* is time in hours in decimal.

The angle between the horizontal plane and PVS is known as the optimum angle (β), and this angle needs to be oriented at the South in the North hemisphere. This angle has values from 0◦ ≤ β ≤ 180◦ and can be expressed by Equation (5).

$$\beta = |\phi - \delta|\tag{5}$$

The PVS power output components such as module operating temperature and its nominal efficiency (η*ref*) depend on the environmental conditions, as well as the optimum output (η*PV*). The Mexican solar abridgment [47] establishes that the PV module η*PV* is a function of η*ref*, the temperature of the cell *TC*, the module power temperature coefficient β*ref* (which is considered between −0.3% to

−06% per ◦C) [48], and the standard temperature *Tstc;* this last one is provided by the manufacturer. With these conditions, the PVS efficiency can be calculated by Equation (6).

$$
\eta\_{PV} = \eta\_{ref} \left[ 1 - \beta\_{ref} (T\_C - T\_{\rm stc}) \right] \tag{6}
$$

To calculate *TC*, in Equation (7), is necessary to have the air temperature of the site *Ta* and the solar radiation *Irad*, as well as the nominal operating cell temperature (NOCT) provided by the manufacturer.

$$T\_{\mathbb{C}} = T\_{\mathbb{A}} + \frac{\text{NOCT} - 20^{\circ}\mathbb{C}}{800 \text{ W}/m^2} I\_{\text{rad}} \tag{7}$$

The PV power output module is expressed by Equation (8).

$$P\_{\rm out} = P\_{\rm max, stc} \left(\frac{I\_{\rm rad}}{G\_{\rm stc}}\right) \left[1 - \beta\_{ref} (T\_C - T\_{\rm stc})\right] \tag{8}$$

where *Gstc* is the irradiance at standard conditions whose value is 1 kW/m2, and *Pmax,sct* is the cell maximum power at standard test conditions.
