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^oC (104^oF). 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 ^oC) (1.005 kJ/kg ^oC standard air)

t_out = temperature of air out (^oC)

t_in = temperature of air in (^oC)

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/m³ 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 ^oC and outside temperature of the cabinet is 20 ^oC can be calculated with eq. 2 as

m_air = (2.5 kW) / (1.005 kJ/kg ^oC) ((40 ^oC) - (20 ^oC)) 

      = 0.125 kg/s   

The volume and density of air depends on the temperature of the air. The density of air at 20^oC is 1.205 kg/m³ and 1.127 kg/m³ at 40 ^oC.

The volume flow at the inlet (20 ^oC):

q_air = (1 / (1.205 kg/m³)) (0.125 kg/s)

    = 0.104 m³/s

    = 375 m³/h

The volume flow at the outlet (40 ^oC):

q_air = (1 / (1.127 kg/m³)) (0.125 kg/s)

    = 0.111 m³/s

    = 400 m³/h