Variable Frequency Drives  Heat Loss and Required Air Cooling
Avoid overheated variable frequency drives with adequate ventilation.
Variable frequency drives are common for controlling the electric motor speed in applications with fans, pumps, compressors, elevators, extruders etc.
Heat Loss from a Variable Frequency Drive
An amount of the power transferred through a variable frequency drive to the motor is lost as heat. The heat loss from a drive can be expressed as
H_{loss} = P_{t} (1 η_{d}) (1)
where
H_{loss} = heat loss to the variablefrequency drive surroundings (kW)
P_{t} = electrical power through the variablefrequency drive (kW)
η_{d} = variablefrequency drive efficiency
The heat loss expressed in imperial units
H_{loss} = P_{t} 3412 (1 η_{d}) (1b)
where
H_{loss} = heat loss to the variablefrequency drive surroundings (btu/h)
P_{t} = power in to the frequency drive (kW)
η_{d} = variablefrequency drive efficiency
To calculate maximum heat loss  the maximum power transmission through the variablefrequency drive must be used.
It is common that the heat loss from a frequency drive is in the range 2  6% of the KVA rating.
Necessary Ventilation for Cooling a VariableFrequency Drive
Maximum ambient temperature for a frequencydrive is approximately 40^{o}C (104^{o}F). Since frequencydrives often are physical protected in small cabinets or small rooms, ventilation  or even cooling  may be needed to avoid overheating.
The mass flow of air needed for transporting heat from the variablefrequency drive can be expressed as
m_{air} = H_{loss} / c_{p} (t_{out}  t_{in}) (2)
where
m_{air} = mass flow of air (kg/s)
H_{loss} = heat loss to the frequencydrive surroundings (W)
c_{p} = specific heat of air (kJ/kg^{ o}C) (1.005 kJ/kg^{ o}C standard air)
t_{out} = temperature of air out (^{o}C)
t_{in} = temperature of air in (^{o}C)
Combined with (1), the mass flow (2) can be expressed as:
m_{air} =P_{t} (1 η_{d}) / c_{p} (t_{out}  t_{in}) (2b)
The volume flow can be calculated by multiplying (2b) with the specific volume or inverted density:
q_{air} = (1 / ρ_{air}) P_{t} (1  η_{d}) / c_{p} (t_{out}  t_{in}) (2c)
where
ρ_{air} = density of air at the actual temperature (1.205 kg/m^{3} standard air)
Variable Frequency Drive  Heat Loss Air Cooling Chart
Download and print Variable Frequency Drive Heat Loss Air Cooling Chart
Example  Ventilation and Cooling of a VariableFrequency Drive
The heat generation by the variable frequency drive with maximum power of 100 kW and efficiency of 0.95,can be calculate with eq. 1 as
H_{loss} = (50 kW) (1 95 / 100)
= 2.5 kW
The mass of cooling cooling air through the cabinet when the maximum ambient operating temperature for the frequency drive is 40^{ o}C and outside temperature of the cabinet is 20^{ o}C can be calculated with eq. 2 as
m_{air} = (2.5 kW) / (1.005 kJ/kg^{ o}C) ((40^{ o}C)  (20^{ o}C))
= 0.125 kg/s
The volume and density of air depends on the temperature of the air. The density of air at 20^{o}C is 1.205 kg/m^{3} and 1.127 kg/m^{3} at 40^{ o}C.
The volume flow at the inlet (20^{ o}C):
q_{air} = (1 / (1.205 kg/m^{3})) (0.125 kg/s)
= 0.104 m^{3}/s
= 375 m^{3}/h
The volume flow at the outlet (40^{ o}C):
q_{air} = (1 / (1.127 kg/m^{3})) (0.125 kg/s)
= 0.111 m^{3}/s
= 400 m^{3}/h
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