Fan Motor Energy Consumption

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 constant speed or two-speed, constant-volume system. Measured input data is average hourly power draw (in kW) as measured by a data logging power meter for the supply and return fans in the AHU.

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

1. Average equivalent % hour motor is on full speed for each hour, h, of each day of the week, d, (Worksheet: “Step 3. Avg Day of Week Calcs”).

\begin{equation} \bar{P}_{d,h,f} = \frac{\sum_{n_f = 1}^{N_f(d,h)} P_f(t_f)}{N_f(d,h)} \end{equation}

Where,

$\bar{P}_{d,h,f} =$ average motor power for given day of week, d, and hour of day, h, for either suply or return fan, f, kW

$P_f(t_f) =$ measured motor power for either supply or return fan, f, kW

$t_f =$ index for measured data points for either supply or return fan, f, datasets

$N_f(d,h) =$ 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 subset of measured data points that fall on day of week, d, and hour of day, h, for either supply or return fan, f

2. 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 \sum_{h = 1}^24 \bar{P}_{d,h,f} * [\textit{operating weeks per year}] \end{equation}

Where,

$E_f =$ annual energy for either supply or return fan, f, kWh

$\bar{P}_{d,h,f} =$ average motor power for given day of week, d, and hour of day, h, for either supply or return fan, f, kW

3. Total energy used by the AHU (Worksheet: “Step 4. Results”).

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

Where,

$E =$ total energy usage for AHU, kWh

1. Convert seconds fan is on per hour to percent fan is on per hour (Worksheet: “Step 2. Percent Runtime Calcs”) for supply and return fans.

\begin{equation} \%FanOn_{high,f}(t_{f}) = \begin{cases} 100\% & \text{if } i_{high,f} * (1+\varepsilon) < i_{f}(t_{f}) \\ \frac{i_{f}(t_{f}) - i_{low,f}}{i_{high,f} - i_{low,f}} & \text{if } i_{low,f} * (1+\varepsilon) < i_{f}(t_{f}) < i_{high,f}* (1-\varepsilon) \\ 0\% & \text{if } i_{f}(t_{f}) < i_{low,f} * (1+\varepsilon) \end{cases} \end{equation}

\begin{equation} \%FanOn_{low,f}(t_{f}) = \begin{cases} 100\% & \text{if } i_{f}(t_{f}) < i_{low,f} * (1+\varepsilon) \\ 1 - \frac{i_{f}(t_{f}) - i_{low,f}}{i_{high,f} - i_{low,f}} & \text{if } i_{low,f} * (1+\varepsilon) < i_{f}(t_{f}) < i_{high,f}* (1-\varepsilon) \\ 0\% & \text{if } i_{high,f} * (1-\varepsilon) < i_{f}(i) \end{cases} \end{equation}

Where,

$\%FanOn_{high,f}(i) =$ Percent of an hour that motor is running at high speed for either supply or return fan, f, %

$\%FanOn_{low,f}(i) =$ Percent of an hour that motor is running at low speed for either supply or return fan, f, %

$i_{f}(t_{f}) =$ Measured current for either supply or return fans, f, Amps

$t_{f} =$ Index for each measured data point for either supply or return fans, f, datasets

$i_{high,f} =$ One-time measured current at high speed setpoint for either supply or return fan, f, Amps

$i_{low,f} =$ One-time measured current at the low speed setpoint for either supply or return fan, f, Amps

$\varepsilon =$ Error tolerance to classify current as representing high speed or low speed operation

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

\begin{equation} \overline{\%FanOn}_{s,d,h,f} = \frac{\sum_{n_f=1}^{N_{f}(d,h)} \%FanOn_{s,f}(n)}{N_{f}(d,h)} \end{equation}

Where,

$\overline{\%FanOn}_{s,d,h,f} =$ Average % time motor is at either low speed or high speed setpoint, s, per hour for given day of wekk, d, and hour of the day, h, for either supple of return fan, %

$N_{f}(d,h) =$ 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

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

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

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

Where,

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

4. Calculate energy used for full year for each fan (Worksheet: “Step 4. Results”).

\begin{equation} E_{f} = \sum_{d=1}^{7} (\overline{HrsOn}_{low,d,f} * P_{low,f} + \overline{HrsOn}_{high,d,f} * P_{high,f}) * 52 [weeks \hspace{2mm} per \hspace{2mm} year] \end{equation}

Where,

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

$P_{s,f} =$ Measured power for either the low speed or high speed setpoint, s, and 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

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_{high,f}(t_{f}) = \begin{cases} 100\% & \text{if } S_{high,f} * (1+\varepsilon) < S_{f}(t_{f}) \\ \frac{S_{f}(t_{f}) - S_{low,f}}{S_{high,f} - S_{low,f}} & \text{if } S_{low,f} * (1+\varepsilon) < S_{f}(t_{f}) < S_{high,f}* (1-\varepsilon) \\ 0\% & \text{if } S_{f}(t_{f}) < S_{low,f} * (1+\varepsilon) \end{cases} \end{equation}

\begin{equation} \%FanOn_{low,f}(t_{f}) = \begin{cases} 100\% & \text{if } S_{f}(t_{f}) < S_{low,f} * (1+\varepsilon) \\ 1 - \frac{S_{f}(t_{f}) - S_{low,f}}{S_{high,f} - S_{low,f}} & \text{if } S_{low,f} * (1+\varepsilon) < S_{f}(t_{f}) < S_{high,f}* (1-\varepsilon) \\ 0\% & \text{if } S_{high,f} * (1-\varepsilon) < S_{f}(i) \end{cases} \end{equation}

Where,

$\%FanOn_{high,f}(i) =$ percent of an hour that motor is running at high speed for either supply or return fan, f, %

$\%FanOn_{low,f}(i) =$ percent of an hour that motor is running at low speed for either supply or return fan, f, %

$S_f(t_f) =$ measured speed from VFD for either supply or return fan, f, rpm

$t_f =$ index for each measured data point for either supply or return fan, f, datasets

$S_{high,f} =$ high speed setpoint for either supply or return fan, f, rpm

$S_{low,f} =$ low speed setpoint for either supply or return fan, f, rpm

$\varepsilon =$ error tolerance to classify current as representing high-speed or low-speed operation

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

\begin{equation} \overline{\%FanOn}_{s,d,h,f} = \frac{\sum_{n_f=1}^{N_{f}(d,h)} \%FanOn_{s,f}(n)}{N_{f}(d,h)} \end{equation}

Where,

$\overline{\%FanOn}_{s,d,h,f} =$ Average % time motor is at either low speed or high speed setpoint, s, per hour for given day of wekk, d, and hour of the day, h, for either supple of return fan, %

$N_{f}(d,h) =$ 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

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

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

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

Where,

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

4. Calculate energy used for full year for each fan (Worksheet: “Step 4. Results”).

\begin{equation} E_{f} = \sum_{d=1}^{7} (\overline{HrsOn}_{low,d,f} * P_{low,f} + \overline{HrsOn}_{high,d,f} * P_{high,f}) * 52 [weeks \hspace{2mm} per \hspace{2mm} year] \end{equation}

Where,

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

$P_{s,f} =$ Measured power for either the low speed or high speed setpoint, s, and 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 VFD-controlled fans that are operated at different speeds proportional to the heating/cooling load. Because the heating/cooling load of a facility is mainly affected by outdoor air temperature (OAT), this data must be collected as well. Measured input data include average hourly power draw (kW) and average hourly OAT.

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

1. Perform second-order polynomial regression analysis of true RMS power as a function of OAT. (Worksheet: “Step 3. Regression”) for supply and return fans.

\begin{equation} P_{f}(OAT) = a*OAT^{2} + b*OAT + c \end{equation}

Where,

$P_{f} =$ Average hourly true RMS Power for either supply or return fan, f, kW

$a,b,c =$ Regression coefficients

$OAT_{f} =$ Outdoor air temperature for either supply or return fan, f

2. Determine if the supply and return motors are on or off at each measurement interval based on the input true RMS power values (Worksheets: “Step 4. Schedule Calcs”).

\begin{equation} On_{f}(t_{f}) = \begin{cases} 1 & \text{if } P_{f}(t_{f}) > 0\\ 0 & otherwise \end{cases} \end{equation}

Where,

$P_{f}(t_{f}) =$ Measured power

$On_{f}(t_{f}) =$ Motor is on at time, $t_{f}$ for either supply or return fan, f, binary

3. Average hourly % motor is on for each hour of each day of the week, for supply and return fan motors (Worksheet: “Step 5. Daily Avg Schedule Calc”).

\begin{equation} \overline{\%FanOn}_{d,h,f} = \frac{\sum_{n_{f}=1}^{N_{f}(d,h)} On_{f}(t_{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 or return fan, f, %

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

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

4. Calculated energy (kWh) every hour based on normalized annual OAT for the supply and return fan motors (Worksheet: “Step 6. Energy Calcs,” column F & G).

\begin{equation} E_{f} = \sum_{t=1}^{8760} P_{f}(OAT'(t))*\overline{\%FanOn}_{d,h,f}(t) \end{equation}

Where,

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

$OAT'(t) =$ Climate normal outdoor air temperature from National Weather Service at station closest to site, F

5. Total energy used by Fan Motor (Worksheet: “Step 7. Results”).

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

Where,

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