Pump Motor Energy Consumption Calculation Methodology and CalculatorCalculation

Introduction

Calculators

Pump Motor Calculations

Constant-speed, constant-volume pump energy calculations

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} WeeksChillerOn = (DayOfYear(CoolingSeasonEndDate) \end{equation}

\begin{equation*} - DayOfYear(CoolingSeasonStartDate)) * \frac{WeeksPerDay}{DaysPer Year}\end{equation*}

\begin{equation} E = WeeksChillerOn * 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

$CoolingSeasonEndDate =$ Cooling season end date, mm/dd/yyyy

$CoolingSeasonStartDate =$ Cooling season start date, mm/dd/yyyy

$WeeksChillerOn =$ Length of cooling season, weeks

$WeeksPerYear =$ 52

$DaysPerYear =$ 365.24

$P =$ Measured pump power, kW

Variable-speed, variable-volume pump energy calculations

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.

9. 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

10. 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

11. Total annual pump energy (Worksheets: “Step 6. Energy Calcs” and “Step 7. Results”).

\begin{equation} E = WeeksChillerOn * \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

$WeeksChillerOn =$ Cooling season (see Equation 5), weeks

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