Pump Motor Energy ConsumptionCalculation

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 page use equations that estimate the annual energy consumption of a pump motor regardless of the system it is a part of.

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.

Calculators

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.

1. 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

2. 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

3. 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

4. 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.

1. 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

2. Calculate every 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

Constant One or Two Speed Pump Energy Using Electrical Current Data

This calculation tool is for a constant-speed, constant-volume pump. Measured input data include hourly average current (in Amps) as directly measured by current sensors, and spot measurements for true power.

1. Convert average hourly current to percent on per hour (Worksheet: “Step 2. Percent Runtime Calcs”).

\begin{equation} \%On(t) = \begin{cases} \frac{I(t)}{I_{max}} & \text{if } I(t) < I_{max} \\ 100\% & \text{o.w.} \end{cases} \end{equation}

Where,

$\%On(t) =$ percent of an hour that the pump motor is on, %

$I(t) =$ measured time that pump motor is on, seconds

$t =$ index for each measured data point

$I_{max} =$ current measured at the maximum constnat speed, Amps

2. Equations 3 to 5 are used to calculate the annual pump energy.

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.

1. 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

2. 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

3. 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

Variable Speed Pump Energy Using Motor Speed Data

This calculation tool is for VFD-controlled pumps using hourly average motor speed (in RPM) as downloaded from a BAS or VFD, and spot measurements for true power.

1. Convert the speed data from the BAS or VFD to power (Worksheet: “Step 2. Aggregate Data”)

\begin{equation} P(t) = P_{max}(\frac{\omega(t)}{\omega_{max}})^{2.5} \end{equation}

Where,

$P(t) =$ average hourly true RMS power, kW

$P_{max} =$ full speed true RMS power, kW

$\omega_{max} =$ maximum motor speed, rpm

$\omega(t) =$ motor speed, rpm

This equation represents the pump affinity law, where theoretically the exponent is 3. To represent motor losses, the Consortium for Energy Efficiency recommends using a value of 2.5.¹

2. Equations 9 to 12 are used to calculate the annual pump energy.

Further Reading

• 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

• 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

• 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

Footnotes