Technical analysis of photovoltaic energy generation for supplying the electricity demand in Brazilian dairy farms


In many Brazilian dairy farms, the supply of electrical energy does not fully meet the demands of the production systems and/or presents frequent fluctuations and interruptions, making the expansion of production chain unfeasible. These and other barriers have motivating the adoption of renewable and independent energy sources, installed directly in the farms. The present study was conducted to perform a technical analysis of photovoltaic energy generation required for supplying the electricity demand in dairy farms located at Minas Gerais State, Brazil. Daily global radiations on tilted panels were estimated by mathematical models and long-term meteorological database (greater than 33 years). Electrical energy generated by grid-connected photovoltaic systems was predicted considering minimum, average, and maximum daily global radiation conditions. Electrical energy demands were monitored in small (66 cows), medium (106 cows), and large (158 cows) dairy farms. The direct use of electrical energy in operations performed at Brazilian dairy farms were 4, 28, 15, 39, and 15%, on average, for lighting, milking, water heating/pumping, milk cooling/refrigeration, and miscellaneous, respectively. The estimated energy consumptions were 0.96, 0.87, and 0.81 kWh cow−1 day−1 for farms with 66, 106, and 158 cows, respectively. The photovoltaic panel area varied considerably among small, medium, and large dairy farms in order to meet 80% of renewable fraction for the electricity demand.

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Fig. 1
Fig. 2


a :

Coefficient that represents the fraction of diffuse radiation to H0 (dimensionless)

A pv :

Modular area of the photovoltaic panel (m2)

b :

Coefficient that represents the fraction of beam radiation to H0 (dimensionless)

d n :

Day number of the year (dimensionless)

E 0 :

Eccentricity correction factor of the earth’s orbit (dimensionless)

E c :

Consumed energy by the equipment (kWh day−1)

E grid :

Electrical energy injected from the photovoltaic system (kWh day−1)

E pv :

Electrical energy generated by the photovoltaic system (kWh day−1)

F :

Operating frequency of the equipment (h day−1)

H :

Daily global radiation on horizontal panels (MJ m−2 day−1)

H 0 :

Daily extraterrestrial radiation on horizontal panels (MJ m−2 day−1)

H b :

Daily beam radiation on horizontal panels (MJ m−2 day−1)

H bβ :

Daily beam radiation on tilted panels (MJ m−2 day−1)

H d :

Daily diffuse radiation on horizontal panels (MJ m−2 day−1)

H dβ :

Daily diffuse radiation on tilted panels (MJ m−2 day−1)

H r :

Daily ground-reflected radiation on tilted panels (MJ m−2 day−1)

H β :

Daily global radiation on tilted panels (MJ m−2 day−1)

I sc :

Mean solar constant (kJ m−2 h−1)

K T :

Clearness index (dimensionless)

N :

Day length (h)

n :

Sunshine duration (h)

N pv :

Number of photovoltaic panels or modules (dimensionless)

P c :

Power consumption of the equipment (W)

R b :

Conversion factor (dimensionless)


Renewable fraction (%)

β :

Optimal tilt angle (degrees)

δ :

Declination solar angle (degrees)

η cab :

Efficiency from cable electricity losses (%)

η inv :

Inverter DC to AC efficiency (%)

η pv :

Photovoltaic panel efficiency (%)

η sys :

System efficiency (%)

ρ :

Ground albedo (dimensionless)

φ :

Geographic latitude (degrees)

ω s’:

Minimum value of sunrise/sunset hour angle (degrees)

ω s :

Sunrise/sunset hour angle (degrees)

Г :

Day angle (radians)


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The authors would like to thank the National Institute of Meteorology (INMET) of Brazil for providing the long-term weather data and the graduate student in Agronomic Engineering Jennifer Alves Camilo for the technical support in this study.


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Steidle Neto, A.J., Lopes, D.d. Technical analysis of photovoltaic energy generation for supplying the electricity demand in Brazilian dairy farms. Environ Dev Sustain 23, 1355–1370 (2021).

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  • Renewable energy
  • Grid-connected photovoltaic system
  • Photovoltaic panels
  • Solar radiation models
  • Energy consumption
  • Farm building