Variable-Frequency Drives (Heat Loss and Required Ventilation)

Variable-frequency drives are common for controlling speed of electric motors in applications with fans, pumps, compressors, elevators, extruders etc.

Heat Loss from a Variable-Frequency Drive

A certain amount of the power transferred through the variable-frequency drive to the motor is lost as heat to the surroundings. 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 (W)
P_t = electrical power through the variable frequency drive (W)
η_d = variable frequency drive efficiency

The heat loss can alternatively be expressed in imperial units

H_loss = P_t 3,412 (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 (W)
η_d = variable frequency drive efficiency

For calculating the maximum heat loss - 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

The maximum surrounding 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 capacity of air (kJ/kg ^oC) (1.005 kJ/kg ^oC standar 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 (kg/m³)

Example - Ventilation and Cooling of a Variable-Frequency Drive

The amount of air for cooling a cabinet mounted variable-frequency drive with maximum power of 100 kW and efficiency of 0.95, a maximum surrounding operating temperature of 40 ^oC and an outside temperature of 20 ^oC, can be expressed as (2b):

m_air = (100 kW) (1 - 0.95) / (1.005 kJ/kg.^oC) ((40 ^oC) - (20 ^oC))
    = 0.25 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 for at at 40 ^oC.
The volume flow at the inlet of (20 ^oC):

q_air =   (1 / (1.205 kg/m³)) (0.25 kg/s)
    = 0.208 m³/s
    = 749 m³/h

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

q_air = (1 / (1.127 kg/m³)) (0.25 kg/s)
    = 0.222 m³/s
    = 799 m³/h