Lighting Fixture Runtime

The following equations are used to calculate the annual energy consumption of a lighting fixture system. This methodology does not require electrical measurements; only lighting runtime (operating schedule) of the fixtures. Runtime data is collected with a light logger that detects when a light source turns on and off. If multiple fixture types operate with the same schedule, the same runtime data can be used for calculations.

This calculation tool can be used for different fixture types within a single space (e.g., an office space with five different types of fixtures). The number of fixtures of each type must be known as well as the respective power draw (refer to the manufacturer specifications of the lamps and ballasts).

1. Calculate power draw of the fixture type.

\begin{equation} kW_{fix1} = \frac{N * W_{fix1}}{1000} \end{equation}

Where,

$kW_{fix1} =$ Total power draw of single fixture type 1 (in kW)

$W_{fix1} =$ Wattage of fixture type 1 (in W)

$N =$ Number of fixtures of that type with the same operating schedule

2. Convert fixture runtime measurements from seconds per hour to percent per hour (Worksheet: “Step 2. Percent Runtime Calcs”).

\begin{equation} \%_{int} = \frac{t_{int}}{3600} \end{equation}

Where,

$\%_{int} =$ Percent per hour the fixtures are on

$t_{int} =$ Measured number of seconds the fixtures are on in each hour interval (in seconds)

$3600 =$ Constant, number of seconds in one hour

3. Find the hourly average percentage for each day of the week the fixtures are on (Worksheet: “Step 3. Daily Avg Runtime Calcs”).

\begin{equation} \%_{hourly} = \frac{\sum_{1}^{n} \%_{int,n}}{n} \end{equation}

Where,

$\%_{hourly} =$ Hourly average percentage the fixtures are on

$\%_{int} =$ Percent per hour the fixtures are on

$n =$ Number of data points that have the same hour of day and day of week

4. Sum of runtime percentages for a given day of the week to determing the operating hours for that day (Worksheet: “Step 4. Results”).

\begin{equation} \%_{daily} = \sum_{h=0}^{23} \%_{hourly,h} \end{equation}

Where,

$\%_{daily} =$ Daily average hours the fixtures are on

$\%_{hourly} =$ Hourly average percentage fixtures are on

$h =$ Hour of the day where 0 is 12:00 a.m. and 23 is 11:00 p.m.

5. Convert the percentage to hours in order to determine hours per day fixtures are on in space being measured (Worksheet: “Step 4. Results”).

\begin{equation} T_{daily} = \frac{\%_{daily}}{100} \end{equation}

Where,

$T_{daily} =$ Number of hours the fixtures are on for a given day (in hours)

$\%_{daily} =$ Daily average hours in percent per day the fixtures are on

6. Calculate the average energy use per weekday (Worksheet: “Step 4. Results”).

\begin{equation} \overline{kWh}_{Wd,fix1} = \frac{\sum_{d=2}^{6} T_{Wd,fix1,d}}{5} * kW_{fix1} \end{equation}

Where,

$\overline{kWh}_{Wd,fix1} =$ Average energy consumption during weekdays for fixture type 1 (in kWh)

$kW_{fix1} =$ Total power draw of single fixture type 1 (in kW)

$T_{Wd,fix1,d} =$ Number of hours the fixtures are on for a given d weekday (in hours)

$d =$ Day of week (2 = Monday, 3 = Tuesday, ..., 6 = Friday)

7. Calculate the average energy use per weekend day (Worksheet: “Step 4. Results”).

\begin{equation} \overline{kWh}_{WEd,fix1} = \frac{T_{We,fix1,1} + T_{We,fix1,7}}{2} * kW_{fix1} \end{equation}

Where,

$\overline{kWh}_{WEd,fix1} =$ Average consumption during weekend days for fixture type 1 (in kWh)

$kW_{fix1} =$ Total power draw of single fixture type 1 (in kW)

$T_{We,fix1,d} =$ Number of hours the fixtures are on for a given d weekend days (in hours)

$d =$ Day of week (7 = Saturday, 1 = Sunday)

8. Calculate the annual weekday energy consumption for the fixture type (Worksheet: “Step 4. Results”).

\begin{equation} \overline{kWh}_{WdYr,fix1} = \overline{kWh}_{Wd,fix1} * (261 \hspace{2mm} weekdays \hspace{2mm} per \hspace{2mm} year - X) \end{equation}

Where,

$\overline{kWh}_{WdYr,fix1} =$ Annual weekday energy consumption of fixture type 1 (in kWh)

$\overline{kWh}_{Wd,fix1} =$ Average energy consumption during weekdays for fixture type 1 (in kWh)

$X =$ Number of weekdays that are adjusted to use weekend day average energy consumption

9. Calculate the annual weekend energy consumption for the fixture type (Worksheet: “Step 4. Results”).

\begin{equation} \overline{kWh}_{WEd,Yr,fix1} = \overline{kWh}_{WEd,fix1} * (104 \hspace{2mm} weekend \hspace{2mm} days \hspace{2mm} per \hspace{2mm} year + X) \end{equation}

Where,

$\overline{kWh}_{WEdYr,fix1} =$ Annual weekend day energy consumption of fixture type 1 (in kWh)

$\overline{kWh}_{WEd,fix1} =$ Average energy consumption during weekend days for fixture type 1 (in kWh)

$X =$ Number of weekdays that are adjusted to use weekend average energy consumption

10. Calculate total annual estimated energy consumption for the fixture type (Worksheet: “Step 4. Results”).

\begin{equation} \overline{kWh}_{ann,fix1} = \overline{kWh}_{WdYr,fix1} + \overline{kWh}_{WEdYr,fix1} \end{equation}

Where,

$\overline{kWh}_{ann,fix1} =$ Annual estimated energy consumption of fixture type 1 (in kWh)

$\overline{kWh}_{WdYr,fix1} =$ Annual weekday energy consumption of fixture type 1 (in kWh)

$\overline{kWh}_{WEdYr,fix1} =$ Annual weekend day energy consumption of fixture type 1 (in kWh)

11. If multiple fixture types were measured find the sum of the annual estimated energy consumption for all fixture types (Worksheet: “Step 4. Results”).

\begin{equation} \overline{kWh}_{ann} = \sum_{i=1}^{n} \overline{kWh}_{ann,{fix_{n}}} \end{equation}

Where,

$\overline{kWh}_{ann} =$ Total annual energy of all measured fixture types (in kWh)

$\overline{kWh}_{ann,fix1} =$ Annual estimated energy consumption of each measured fixture type (in kWh)

$n =$ Number of fixture types measured