Introduction
This methodology applies to pump motors that operate at constant or variable speed. Pump motors are used to move water throughout the building for heating or cooling. The calculators provided in this section use equations that estimate the annual energy consumption of a pump motor, regardless of the system of which it is part.
The type of data that is measured from the pump motor will determine the calculator to use. For more information on the type of data to collect, refer to table 1 in the next section.
Pump Motor Calculations
Constant Speed Pump Energy Using Motor Runtime Data
This calculation tool is for a constant speed, constant volume system. Measured input data include spot measurements for true power and motor operational time per hour, as measured by motor on/off loggers.
Calculator
Measurements
The calculator relies on the measured data from the following measurement techniques:
Methodology
The calculator uses the following methodology to compute annual energy consumption of a constant speed pump:
- Convert seconds on per hour to percent on per hour (Worksheet: “Step 2. Percent Runtime Calcs”).
\begin{equation} \%On(t) = \frac{On(t)}{3600} \end{equation}
Where,
$\%On(t) =$ Percent of an hour that the pump motor is on, %
$On(t) =$ Measured time that pump motor is on, seconds
$t =$ Index for each measured data point
- Average % hour motor is on for each hour of each day of the week (Worksheet: “Step 3. Daily Avg Runtime Calcs”).
\begin{equation} \overline{\%On}_{d,h} = \frac{\sum_{n=1}^{N(d,h)} \%On(n)}{N(d,h)} \end{equation}
Where,
$\overline{\%On}_{d,h} =$ Average % time motor is on per hour for given day of week, d, and hour of the day, h, %
$N(d,h) =$ Total number of measured data points that fall on day of week, d, and hour of the day, h
$n \in t(d,h) =$ Index for the subset of measured data points that fall on day of week, d, and hour of the day, h
- Find the average hours per day pump is on (Worksheet: “Step 4. Results”).
\begin{equation} \overline{HrsOn}_{d} = \sum_{h=1}^{24} \overline{\%On}_{d,h} \end{equation}
Where,
$\overline{HrsOn}_{d} =$ Average hours per day for given day of week, d, hours
- Calculate energy used for full year (Worksheet: “Step 4. Results”).
\begin{equation} WeeksPumpOn = (DayOfYear(PumpOperationEndDate) \end{equation}
\begin{equation*} - DayOfYear(PumpOperationStartDate)) * \frac{WeeksPerDay}{DaysPer Year}\end{equation*}
\begin{equation} E = WeeksPumpOn * P\sum_{d=1}^{7} \overline{HrsOn}_{d} \end{equation}
Where,
$E =$ Annual pump energy, kWh
$DayOfYear =$ Function to convert a date to the n^{th} day of the year
$PumpOperationEndDate =$ Cooling season end date, mm/dd/yyyy
$PumpOperationStartDate =$ Cooling season start date, mm/dd/yyyy
$WeeksPumpOn =$ Pump operating time, weeks
$WeeksPerYear =$ 52
$DaysPerYear =$ 365.24
$P =$ Measured pump power, kW
Constant One- or Two-Speed Pump Energy Using kW Data
This calculation tool is for a constant speed, constant volume pump. Measured input data is average hourly power draw (in kW) as measured by a DENT power logger.
Calculator
Measurements
The calculator relies on the measured data from the following measurement techniques:
Methodology
The calculator uses the following methodology to compute annual energy consumption of a constant one- or two-speed pump:
- Average % hour motor is on for each hour of each day of the week (Worksheet: “Step 3. Avg Day of Week Calcs”).
\begin{equation} \bar{P}_{d,h} = \frac{\sum_{n=1}^{N(d,h)} P(t)}{N(d,h)} \end{equation}
Where,
$\bar{P}_{d,h} =$ average motor power for given day of week, d, and hour of day, h, kW
$P(t) =$ measured motor power, kW
$t =$ index for measured data points
$N(h,d) =$ total number of measured data points that fall on day of week, d, and hour of the day, h
$n \in t(d,h) =$ index for subset of measured data points that fall on day of week, d, and hour of the day, h
- Calculate energy used for full year (Worksheet: “Step 4. Results”). WeeksPumpOn is from Equation 5.
\begin{equation} E = WeeksPumpOn * \sum_{d = 1}^7 \sum_{h = 1}^{24} \bar{P}_{d,h} \end{equation}
Where,
$E =$ annual pump energy, kWh
$WeeksPumpOn =$ Pump operating time, weeks
Variable Speed Pump Energy Using kW Data
This calculation tool is for VFD-controlled pumps that are operated at speeds proportional to the heating/cooling load as represented by proxy with OAT. Measured input data include average hourly power draw (kW) as measured by a DENT data logging power logger, and the average hourly OAT as measured by a temperature/RH logger.
Calculator
Measurements
The calculator relies on the measured data from the following measurement techniques:
Methodology
The calculator uses the following methodology to compute annual energy consumption of a variable speed pump:
- Fit a second-order polynomial regression model of true RMS power as a function OAT. (Worksheet: “Step 3. Regression”).
\begin{equation} P(OAT) = a * OAT^{2} + b * OAT + c \end{equation}
Where,
$P =$ Average hourly true RMS power
$a,b,c =$ Regression coefficients
$OAT =$ Outdoor air temperature, F
- Average % hour motor is on for each hour of each day of the week (Worksheets: “Step 4. Schedule Calcs” and “Step 5. Daily Ave Schedule Calc”).
\begin{equation} On(t) = \begin{cases} 1 & \text{if } P(t) > 0\\ 0 & otherwise \end{cases} \end{equation}
\begin{equation} \overline{\%On}_{d,h} = \frac{\sum_{n=1}^{N(d,h)} On(t)}{N(d,h)} \end{equation}
Where,
$P(t) =$ Measures power, kW
$On(t)=$ Motor is on at time, t, binary
$\overline{\%On}_{d,h} =$ Average % time motor is on per hour for given day of week, d, and hour of the day, h, %
$N(d,h) =$ Total number of measured data points that fall on day of week, d, and hour of the day, h
$n \in t(d,h) =$ Index for subset of measured data points that fall on day of week, d, and hour of the day, h
- Total annual pump energy (Worksheets: “Step 6. Energy Calcs” and “Step 7. Results”).
\begin{equation} E = WeeksPumpOn * \sum_{t=1}^{8760} P(OAT'(t)) * \overline{\%On}_{d,h}(t) \end{equation}
Where,
$E =$ Annual energy usage, kWh
$OAT'(t) =$ Hourly climate normal outside air temperature from National Weather Service at station closest to site, F
$WeeksPumpOn =$ Pump operating times, weeks
Further Reading
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For more information on the different types of fans found in AHU systems, please read “Application of Fans in Commercial HVAC Equipment” from the Carrier Corporation: https://www.utcccs-cdn.com/hvac/docs/1001/Public/0F/04-581070-01.pdf
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For more information of the different types of motors that can be used in an AHU retrofit, please read Chapter 7 (starts on page 91) of the Premium Efficiency Motor Selection and Application Guide from the U.S. Department of Energy: https://www.energy.gov/sites/prod/files/2014/04/f15/amo_motors_handbook_web.pdf#page=91
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For general information on Option A M&V guides, please read section 4.2 (starts on page 23) of “M&V Guidelines: Measurement and Verification for Performance-Based Contracts Version 4.0” from the U.S. Department of Energy: https://www.energy.gov/sites/prod/files/2016/01/f28/mv_guide_4_0.pdf#page=23
