# Variable Frequency Drives - Heat Loss and Required Air Cooling

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 variable-frequency drive surroundings (kW)

P_{t}= electrical power through the variable-frequency drive (kW)

η_{d}= variable-frequency 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 variable-frequency drive surroundings (btu/h)

P_{t}= power in to the frequency drive (kW)

η_{d}= variable-frequency drive efficiency

To calculate maximum heat loss - the maximum power transmission through the variable-frequency 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 Variable-Frequency Drive

Maximum ambient temperature for a frequency-drive is approximately *40 ^{o}C (104^{o}F)*. Since frequency-drives 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 variable-frequency 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 frequency-drive 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 Variable-Frequency 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*can be calculated with eq. 2 as

^{ o}C*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*and

^{3}*1.127 kg/m*at

^{3}*40*.

^{ o}CThe 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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