ASHRAE Journal - May 2024 - 32

TECHNICAL FEATURE
* Below 40% speed, VFD and motor efficiency
typically decline rapidly, so a different method of
calculating power from speed should be used for higher
accuracy. In general, the energy use is already very low
below 40% speed, and any inaccuracies at lower speeds
should have relatively minimal impact when compared
to the 100% speed power draw. For systems consistently
operating below 40% speed, consider obtaining the
power draw from the VFD readout.
* The 2.7 exponent assumes that the VFD torque
or volts per hertz (V/Hz) setting is set to " variable "
or " squared. " If it's set to " constant " or " linear, " an
exponent of 2.2 is more appropriate. See the " VFD
Torque Settings " section.
Power Draw Calculation Best Practices
When using Equation 2, first determine the VFD
input power at 100% speed, then apply the exponent
to calculate the power draw at reduced speeds.
The 2.7 exponent accounts for reduced motor, VFD
and belt efficiency at reduced loads. There's no
need to reapply motor, VFD or belt efficiency in the
denominator.
Three ways exist to determine VFD input power
at 100% speed: obtain a spot measurement (e.g.,
VFD display, line side power or amp draw spot
measurement), use Equation 3 below, or use an alternate
method (e.g., calculate from flow and head).
For calculating VFD input power from a spot
measurement:
* If power draw is read from the VFD readout,
determine if it's the input (line) or output (load) power
draw. If it's output, divide by VFD efficiency to calculate
the input power draw. If it's not clear whether the
readout is showing input or output power draw, either
look this up in the VFD manual or assume the readout
is output power draw (the case for most VFDs). For VFD
efficiency, either use manufacturer's data or average
data from a resource such as Reference 1.
* Example, if a 30 HP (22 kW) VFD reads 6.7 output
kW at 65% speed, the 100% speed power draw is:
6.7 kW/93% VFD efficiency × (100%/65%)2.7 = 23.1 kW
If a spot measurement of the VFD input power at 100%
speed cannot be obtained as described above, Equation 3
can be used to estimate this value.
32
ASHRAE JOURNAL ashrae.org MAY 2024
Input Power =
% motor load × nameplate motor power draw
be
η llt × ηη
×
motor VFD
Equation 3: VFD Input Power from Nameplate
Motor Power Draw
For inch-pound (I-P) units, Equation 3 becomes
Equation 4:
Input Power (kW) =
% motor load × nameplate HP × 0.746 kW/HPP
×
ηη η
belt
×
motor VFD
Equation 4: VFD Input Power from Nameplate Horsepower
(I-P Units)
* Either assume a motor load (e.g., 80%) or, if an
amp draw reading is available from the input side of the
VFD when at 100% speed, calculate the motor load by
dividing the amp draw reading by the motor nameplate
full load amps (FLA).
* For belt and motor efficiency, see the guidance in
the " Flow-to-Power Exponents " section.
* Example, for a VFD-controlled 20 HP (15 kW) motor
serving a direct-driven fan operating at 75% motor load
at 100% speed, VFD input power at 100% speed is 75% ×
20 HP × 0.746/(100% × 92% × 96%) = 12.7 kW.
When adding a VFD to a motor, the baseline fullload
power draw (constant speed, no VFD) will be
less than the 100% VFD speed power draw, due to the
VFD efficiency and potential adjustments to system
components when adding the VFD (e.g., opening
throttling valves, opening dampers).
Speed-to-Power Exponent Derivation
Our company gathered motor speed and VFD
input power trend data for 63 fans and pumps from
past projects and calculated the effective speed-topower
exponent for each fan and pump. The average
effective exponents are shown in Case 1 through Case
5, which are available online at https://tinyurl.com/
JournalExtras. Overall, the average speed-to-power
exponent from the data is 2.7.
The accuracy of the speed and VFD input power
values was not confirmed, and an uncertainty
analysis was not conducted. However, most of the
data is from facilities that have complex HVAC
systems serving spaces with tight temperature and
humidity requirements, so the data is assumed to
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ASHRAE Journal - May 2024

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