Motor Runtime

This calculation 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 for the supply and return fans in the Fan Motor.

The calculator uses the following methodology to compute annual energy consumption of a constant speed fan:

1. Convert the fan runtime from seconds per hour to a percentage of the hour the fan is operating (Worksheet: “Step 2. Percent Runtime Calc”) for both supply and return fans.

\begin{equation} \%FanOn_{f}(t_{f}) = \frac{On_{f}(t_{f})}{3600} \end{equation}

Where,

$\hspace{5mm} \%FanOn_{f}(t_{f}) =$ Percent of an hour that the motor is on for either supply or return fan, f, %

$\hspace{5mm} On_{f}(t_{f}) =$ Measured time that motor is on for either supply or return fan, f, in seconds

$\hspace{5mm} t_{f} =$ Index for each measured data point for either supply or return fan, f

2. Average % hour motor is on for each hour, h, of each day of the week, d (Worksheet: “Step 3. Daily Avg Runtime Calcs”).

\begin{equation} \overline{\%FanOn}_{d,h,f} = \frac{\sum_{n_{f}}^{N_{f}(d,h)} \%FanOn_{f}(N_{f})}{N_{f}(d,h)} \end{equation}

Where,

$\overline{\%FanOn}_{d,h,f} =$ Average % time motor is on per hour for given day of week, d, and hour of day, h, for either supply of return fan, f, %

$N_{f}(d,h) =$ Total number of measured data points that fall on day of week, d, and hour of day, h, for either supply or return fan, f

$n_{f} \in t_{f}(d,h) =$ Index for the subset of measured data points that fall on day of week, d, and hour of the day, h, for either supply or return fan

3. Find average hours per day fan is on (Worksheet: “Step 4. Results”).

\begin{equation} \overline{HrsOn}_{d,f} = \sum_{h=0}^{23} \overline{\%FanOn}_{d,h,f} \end{equation}

Where,

$\overline{HrsOn}_{d,f} =$ Average hours per day for given day of week, d, for either supply or return fan, f, hours

4. Calculate energy used for the simulation period that users input for each fan (Worksheet: “Step 4. Results”).

\begin{equation} E_{f} = \sum_{d=1}^{7} \overline{HrsOn}_{d,f} * operating \hspace{2mm} weeks \hspace{2mm} per \hspace{2mm} year * P_{f} \end{equation}

Where,

$E_{f} =$ Annual energy for either supply or return fan, f, kWh

$P_{f} =$ Measured power for either supply or return fan, f, kW

5. Total energy used by Fan Motor (Worksheet: “Step 4. Results”).

\begin{equation} E = E_{supply} + E_{return} \end{equation}

Where,

$E =$ Total energy usage for the Fan Motor, kWh

This calculation is for a cooling tower with constant-speed fans. Measured input data include spot measurements for true power and motor operational time per hour, as measured by motor on/off loggers on each fan in the tower.

The calculator uses the following methodology to compute annual energy consumption of a constant speed cooling tower fan:

1. Convert seconds on per hour to average energy per hour (Worksheet: “Step 2. Energy Calcs”). Repeat for all fans and then sum to get a total for the cooling tower. Note that since the data loggers cannot be perfectly synced, the time stamp for the dataset for each fan will be different. The workbook time-aligns the datasets.

\begin{equation} \overline{E}_{f}(t) = \frac{On_f(t)*P_f}{3600} \end{equation}

\begin{equation} \overline{E}(t) = \sum_{f=1}^{F} \overline{E}_{f}(t) \end{equation}

Where,

$\overline{E}_{f}(t) =$ Average hourly fan motor energy on for each fan, f, kWh

$t =$ Time index

$On_{f}(t) =$ Measured time that motor is on for each fan, f, seconds

$P_{f} =$ One-time power measurement for each fan, f, kW

$\overline{E}(t) =$ Total average energy of all fan motors, kWh

$F =$ Total number of fans

2. Wet-bulb temperature is calculated from the measured dry-bulb temperature and measured relative humidity with the following empirical equation (Worksheet: “Step 3 Wetbulb Calcs”)[1].

\begin{equation} T_{wb} = T_{db}tan^{-1}[0.151977(RH+8.313659)^{1/2}] \end{equation}

\begin{equation*} +tan^{-1}(T_{db}+RH) \end{equation*}

\begin{equation*} -tan^{-1}(RH-1.676331)+0.00391838(RH)^{3/2} \end{equation*}

\begin{equation*} *tan^{-1}(0.023101*RH) - 4.686035 \end{equation*}

Where,

$T_{wb} =$ Wet-bulb temperature, C

$T_{db} =$ Dry-bulb temperature, C

$RH =$ Relative Humidity, %

3. To model the total fan energy at different wet-bulb temperatures, a second-order polynomial regression model is fitted, with total fan energy as a function of wet-bulb temperature (Worksheet: “Step 4 Regression”).

\begin{equation} E(T_{wb}) = a*T_{wb}^{2} + b*T_{wb} + c \end{equation}

Where,

$E(T_{wb}) =$ Average hourly fan energy, kWh

$a,b,c =$ Regression Coefficients

4. Calculate operating hours (Worksheet: “Step 5 Daily Op Hrs”).

\begin{equation} On(t) = \begin{cases} 1 & \text{if } \overline{E}(t) > 0\\ 0 & \text{if } \overline{E}(t) = 0 \end{cases} \end{equation}

\begin{equation} \overline{On}_{d,h} = \begin{cases} 1 & \text{if } \overline{E}(n) > 0 \text{ for any } n \in N(d,h) \\ 0 & 0 \end{cases} \end{equation}

Where,

$On(t) =$ Cooling tower fans are on, binary

$\overline{On}_{d,h} =$ Cooling tower is on for a given day of the week, d, and hour of the day, h, binary

$N(d,h) =$ Total number of measured data points that fall on day of week, d, and hour of the day, h

$n \in N(d,h) =$ Index for the subset of measured data points that fall on day of week, d, and hour of the day, h

5. Calculate energy used for full year for each fan (Worksheet: “Step 6 Results”).

\begin{equation} E = \sum_{t=1}^{8760} \overline{On}_{d,h}(t) * CoolingSeason(t) * E(T_{wb}(t)) \end{equation}

Where,

$E =$ Annual energy, kWh

$CoolingSeason(t) =$ Does the given hour, t, fall within the cooling season, binary

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.

The calculator uses the following methodology to compute annual energy consumption of a constant speed pump:

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