Lighting Plant and Systems Energy ConsumptionCalculation

Introduction

These calculation tools developed by CUNY BPL are used to calculate annual energy consumption, but do not estimate savings. All calculation tools start by using input data (lighting runtime, AC current, etc.) to calculate hourly energy (kWh). Then data is averaged by hour of day and day of the week to get an approximation of how light fixtures operate during any hour of the week. Weekends and weekdays are extrapolated and summed to obtain a full-year estimate. To calculate savings, use the calculation tools with pre- and post-retrofit data and compare the energy consumption results.

The calculation tools will extrapolate data to a full year regardless of how much input data is used, but a minimum of six (6) weeks of data at one-hour intervals is required to adhere to Measurement and Verification standards. If the total fixture inventory for the project is known, data can be used by the calculation tools to determine how much of the lighting load was directly measured, but this data is not necessary for the calculation tools to work. This is useful for someone who only measured a sample of fixtures as part of a sampling plan and wants to compare the annual estimates to the total lighting load.

All lighting calculation tools generate an average hourly energy schedule using the input data. The schedule can be used to determine the interactive heating and cooling effects associated with the lighting retrofit, but it requires separate analysis.

The first three methodologies are used when measuring electricity with data loggers and power meters to determine the annual energy consumption estimate of an electrical distribution system. The last methodology is used when measuring lighting runtime (operating schedule) to determine the annual energy consumption estimate of a lighting fixture system.

Lighting Energy Consumption Calculations

Lighting Electrical Current Output from Electric Panelboard

Lighting fixtures generally require single-phase power to operate, but electrical distribution systems are commonly three-phase. This methodology only applies to a three-phase, four-wire system (wye configuration). Additionally, the panelboard load must be balanced (all three electrical lines, or phases, must have the same current and line-to-neutral voltage). For an unbalanced load where voltage and current are not equal across the three lines, energy should be measured directly with a data-logging power logger capable of measuring a three-phase system. See section A.1.

Calculator

Measurements

The calculator relies on the measured data from the following measurement techniques:

Methodology

The calculator uses the following methodology to compute annual energy consumption of a lighting fixture system via the panelboard.

To estimate the energy consumption of the panelboard, including all fixtures served by it, current should be measured for all three electrical lines of the three-phase system. Current data should be at one-hour intervals and data should consist of an average sample of measurements¹ for each one-hour interval. Power factor, line-to-line voltage, and true RMS power can be obtained from spot measurements with a handheld power meter. CUNY BPL recommends taking multiple spot measurements of those variables and averaging them (measure power factor at least three times at five-minute intervals and calculate the average–see Equation (9)). The average of the spot measurements helps reduce measurement uncertainty and should be used as inputs to the calculation tools. Equation (9) should be applied to power factor, voltage, and true RMS power.

$$\begin{array}{}\text{(1)}& \overline{PF}=\frac{P{F}_{t1}+P{F}_{t2}+P{F}_{t3}+P{F}_{tx}}{x}\end{array}$$

Where,

$\overline{PF}=$ Average of measured power factor

$PF=$ Spot measurement of power factor at the panelboard

$t1=$ First measurement

$t2=$ Second measurement, at least five minutes after the first measurement

$t3=$ Third measurement, at least five minutes after the second measurement

$x=$ Number of spot measurements taken, at least five minutes apart

$$\begin{array}{}\text{(2)}& V_{avg,LL}=\frac{V_{t1}+V_{t2}+V_{t3}+V_{tx}}{x}\end{array}$$

Where,

$V_{avg,LL}=$ Average line-to-line voltage

$V_{t1}=$ First measurement of voltage

$V_{t2}=$ Second measurement of voltage, at least five minutes after the first measurement

$V_{t3}=$ Third measurement of voltage, at least five minutes after the second measurement

$x=$ Number of spot measurements taken, at least five minutes apart

1. Find the average current of the electrical distribution system for each hour interval. Current of all three phases is measured every hour. In this step, the average current of the panelboard is calculated for each hour interval.

$$\begin{array}{}\text{(3)}& I_{h,avg}=\frac{I_1+I_2+I_3}{3}\end{array}$$

Where,

$I_{h,avg}=$ Average current for each hour interval (in Amps)

$I_1=$ Hourly average current of line 1 (in Amps)

$I_2=$ Hourly average current of line 1 (in Amps)

$I_3=$ Hourly average current of line 3 (in Amps)

Equation 11 calculates the three-phase power of the panelboard if line-to-line voltage is measured. If line-to-neutral voltage is measured (from hot wire to ground) the square root of 3 should be replaced with 3 and the line-to-neutral voltage should be used.

2. Calculate three-phase power for each hour interval using the results from Equations (8), (9), and (10) (average current for each hour interval, average voltage, and average power factor). (Worksheet: “Step 2. Power Calcs,” column E, G, I.)

$$\begin{array}{}\text{(4)}& {\overline{kW}}_{h,3P}=\frac{\sqrt{3}\ast I_{h,avg}\ast V_{LL,avg}\ast PF}{1000}\end{array}$$

Where,

${\overline{kW}}_{h,3P}=$ Hourly three-phase power draw of the panelboard (in kW)

$I_{h,avg}=$ Average current for each hour interval (in Amps)

$V_{LL,avg}=$ Measured average line-to-line voltage (in V)

$PF=$ Measured average power factor

3. Calculate average energy consumption for each hour of the week (Worksheet: “Step 3. Avg Energy Calcs,” column C.) This equation helps to reduce the amount of data points to a week by taking the average of each hour for a given day of the week. In this step, the hourly power draw (kW) gets converted to hourly energy consumption (kWh) because data is in one-hour intervals. kWh = kW ∗ h, where h = 1.

$$\begin{array}{}\text{(5)}& {\overline{kWh}}_{d,h}=\frac{\sum _1^{N_f(d,h)}k{W}_{h,3P}}{N_f(d,h)}\end{array}$$

Where,

${\overline{kWh}}_{d,h}=$ Average energy consumption for each hour of each day of the week (in kW)

${\overline{kW}}_{h,3P}=$ Hourly three-phase power draw of the panelboard (in kW)

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

4. Calculate total hourly energy consumption for a given day of the week (Worksheet: “Step 4. Results,” column C.)

$$\begin{array}{}\text{(6)}& {\overline{kWh}}_{d,w}=\frac{\sum _{h=0}^{23}{\overline{kWh}}_{d,h}}{h}\end{array}$$

Where,

${\overline{kWh}}_{d,w}=$ Average hourly energy consumption for a given day of the week of the three-phase panelboard (in kWh)

${\overline{kWh}}_{d,h}=$ Average energy consumption for each hour of each day of the week (in kWh)

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

5. Calculate the average energy consumption for weekdays (Worksheet: “Step 4. Results,” cell D3.)

$$\begin{array}{}\text{(7)}& {\overline{kWh}}_{Wd}=\frac{\sum _{d=2}^6{\overline{kWh}}_{w,d}}{5}\end{array}$$

Where,

${\overline{kWh}}_{Wd}=$ Average energy consumption for weekdays (in kWh)

${\overline{kWh}}_{wd,n}=$ Average hourly energy consumption of each n weekday (in kWh)

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

$24=$ Constant, hours per day

$5=$ Constant, weekdays per week

6. Calculate the average energy consumption for weekend days (Worksheet: “Step 4. Results,” cell D6.)

$$\begin{array}{}\text{(8)}& {\overline{kWh}}_{WEd}=\frac{{\overline{kWh}}_{we,1}+{\overline{kWh}}_{we,7}}{2}\end{array}$$

Where,

${\overline{kWh}}_{WEd}=$ Average energy consumption for a weekend day (in kWh)

${\overline{kWh}}_{we,n}=$ Average energy consumption of each n weekend day (in kWh)

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

$2=$ Constant, weekends per week

7. Calculate the total annual weekday energy consumption (Worksheet: “Step 4. Results,” cell E3.)

$$\begin{array}{}\text{(9)}& {\overline{kWh}}_{WdYr}={\overline{kWh}}_{Wd}\ast (261-X)\end{array}$$

Where,

${\overline{kWh}}_{WdYr}=$ Estimated annual weekday energy consumption (in kWh)

${\overline{kWh}}_{Wd}=$ Average energy consumption for weekdays (in kWh)

$X=$ Number of weekdays that are considered holidays and adjusted to weekend day average energy consumption

$261=$ Constant, number of weekdays per year

8. Calculate the total annual weekend day energy consumption (Worksheet: “Step 4. Results,” cell E6.)

$$\begin{array}{}\text{(10)}& {\overline{kWh}}_{WEdYr}=\overline{kWh}\ast (104+X)\end{array}$$

Where,

${\overline{kWh}}_{WEdYr}=$ Annual weekend day energy consumption (in kWh)

${\overline{kWh}}_{WEd}=$ Average weekend day energy consumption (in kWh)

$X=$ Number of weekdays that are considered holidays and adjusted to weekend day average energy consumption

$104=$ Constant, number of weekend days per year

9. Calculate total annual energy consumption of the panelboard

$$\begin{array}{}\text{(11)}& {\overline{kWh}}_{ann}={\overline{kWh}}_{WdYr}+{\overline{kWh}}_{WEdYr}\end{array}$$

Where,

${\overline{kWh}}_{ann}=$ Estimated annual energy consumption of the panelboard (in kWh)

${\overline{kWh}}_{WdYr}=$ Estimated annual weekday energy consumption (in kWh)

${\overline{kWh}}_{WEdYr}=$ Estimated annual weekend day energy consumption (in kWh)

10. If more than one panelboard was measured, sum the annual energy consumption of all panels to find the total energy consumption of all measured panelboards.

$$\begin{array}{}\text{(12)}& \overline{kWh}={\overline{kWh}}_{n_1}+{\overline{kWh}}_{n_1}+...\end{array}$$

Where,

$\overline{kWh}=$ Total energy consumption of all measured panelboards (in kWh)

${\overline{kWh}}_n=$ Total energy consumption for each panelboard (in kWh)

$n=$ Number of panelboards measured

Lighting Electrical Current from Circuit Breakers

Lighting fixtures generally require single-phase power to operate, but electrical distribution systems are commonly three-phase. When measuring individual circuits of a panelboard, it is essential to know which phase the circuit is connected to. A proper line-to-neutral connection is required to accurately measure the circuit’s voltage.

Calculator

Measurements

The calculator relies on the measured data from the following measurement techniques:

Methodology

The calculator uses the following methodology to compute annual energy consumption of a lighting fixture system via the panelboard.

This calculation tool requires the phase of the circuit to be specified in order to calculate annual energy consumption. If multiple circuits are measured and are connected to the same phase, then only the voltage of that phase is necessary Additionally, the user should ensure that the panelboard is balanced (i.e., all three electrical lines, or phases, must have the same current and line-to-line voltage). If the panelboard is not balanced, then it must be specified in the calculation tool (see worksheet ‘Step 1.1 Circuit Raw Data’).

The following equations are used to calculate the annual energy consumption of a lighting electrical distribution system where AC current is measured at the output of circuit breakers in an electrical panelboard. AC current should be measured using a data logger with current transformers (e.g., Onset HOBO 4-channel analog logger and the Onset CTV-x current transformer sensors) for one or more circuit breakers; a group of circuits can be measured with a single transformer. Current data should be at one-hour intervals and data should be averaged with a sample of measurements¹ for each one-hour interval. Obtain voltage from spot measurements (i.e., measured one time) with a power meter at the circuit breakers.

It is assumed that multiple spot measurements are taken and averaged (e.g., measure line-to-neutral voltage for a circuit breaker three times at five-minute intervals and calculate the average) see Equation (20). The average value should be used with these equations to reduce measurement uncertainty. In this scenario, the line-to-neutral voltage is measured for a single circuit. If measuring multiple circuits, be sure to take multiple spot measurements of line-to-neutral voltage for all circuits.

$$\begin{array}{}\text{(13)}& V_{LN,avg}=\frac{V_{t1,n}+V_{t2,n}+V_{t3,n}+V_{tx,n}}{x}\end{array}$$

Where,

$n=$ The electrical line that was measured of the three-phase system

$V_{avg,n}=$ Average line-to-neutral voltage of a circuit in electrical line n

$V_{t1,n}=$ First measurement of voltage for electrical line n

$V_{t2,n}=$ Second measurement of voltage for electrical line n, at least five minutes after the first measurement

$V_{t2,n}=$ Third measurement of voltage for electrial line n, at least five minutes after the second measurement

$x=$ Number of spot measurements taken, at least five minutes apart

1. For each circuit or group of circuits measured, calculate average power for each hour interval (Worksheet: “Step 2. Power Calcs.”). Power is calculated using line-to-neutral voltage and current of the circuit.

$$\begin{array}{}\text{(14)}& {\overline{kW}}_{h,n}=\frac{I_n\ast V_{LN,avg}}{1000}\end{array}$$

Where,

${\overline{kW}}_{h,n}=$ Average hourly power for a circuit n (in kW)

$I_n=$ Measured average houry current for a circuit (in Amps)

$V_{I,N,avg}=$ Measured average line-to-neutral voltage for a circuit (in V)

2. Calculate average energy use for each hour of each day of the week (Worksheet: “Step 3. Avg Energy Calcs, column C, D, E, F.”). In this step, the hourly power draw (kW) gets converted to hourly energy consumption (kWh) because data is in one-hour intervals. kWh = kw * h, where h = 1.

$$\begin{array}{}\text{(15)}& {\overline{kWh}}_{d,h,c}=\frac{\sum _1^{N_f(d,h)}k{W}_h}{N_f(d,h)}\end{array}$$

Where,

${\overline{kWh}}_{d,h,c}=$ Average energy of each hour for each day of the week for each circuit (in kWh)

$k{W}_h=$ Total power at each hour of each day of each week (in kW)

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

3. Calculate the sum of average hourly energy of all circuits (Worksheet: “Step 3. Avg Energy Calc” column G.)

$$\begin{array}{}\text{(16)}& {\overline{kWh}}_{d,h,n}=\sum _{c=1}^4{\overline{kWh}}_{d,h,c}\end{array}$$

Where,

${\overline{kWh}}_{d,h}=$ Total average energy for all circuits of each hour for each day of the week (in kWh)

${\overline{kWh}}_{d,h,c}=$ Total average energy for each hour for each day of the week for each circuit (in kWh)

$c=$ Circuit that was measured

4. Calculate total daily energy consumption for a given day of the wekk (Worksheet: “Step 4. Results,” column C.)

$$\begin{array}{}\text{(17)}& {\overline{kWh}}_{d,w}=\sum _{n=0}^{23}{\overline{kWh}}_{d,h}\end{array}$$

Where,

${\overline{kWh}}_{d,w}=$ Total average energy for each day of the week (in kWh)

${\overline{kWh}}_{d,h}=$ Total average energy of each h hour for each day of the week (in kWh)

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

5. Calculate the average energy consumption for weekdays in a week for all circuits (Worksheet: “Step 4. Results,” cell D3.)

$$\begin{array}{}\text{(18)}& {\overline{kWh}}_{WdCT}=\frac{\sum _{n=2}^6{\overline{kWh}}_{d,w}}{5}\end{array}$$

Where,

${\overline{kWh}}_{WdCt}=$ Average energy on a weekday (in kWh)

${\overline{kWh}}_{d,w}=$ Average hourly energy for each n weekday of the week (in kWh)

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

$24=$ Hours per day

6. Calculate the average energy consumption for weekend days in a week for all circuits (Worksheet: “Step 4. Results,” cell D6.)

$$\begin{array}{}\text{(19)}& {\overline{kWh}}_{WEdCT}=\frac{{\overline{kWh}}_{1,w}+{\overline{kWh}}_{7,w}}{2}\end{array}$$

Where,

${\overline{kWh}}_{WEdCT}=$ Average energy on a weekend day (in kWh)

${\overline{kWh}}_{d,w}=$ Average hourly energy of each circuit for each n weekend day (in kWh)

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

$24=$ Hours per day

7. Calculate the total annual weekday energy consumption (Worksheet: “Step 4. Results,” cell E3.)

$$\begin{array}{}\text{(20)}& {\overline{kWh}}_{WdYr}={\overline{kWh}}_{Wd}\ast (261weekdaysperyear-X)\end{array}$$

Where,

${\overline{kWh}}_{WdYr}=$ Annual weekday energy consumption (in kWh)

${\overline{kWh}}_{Wd}=$ Average weekly weekday energy consumption (in kWh)

$X=$ Number of weekdays that are considered holidays and adjusted to weekend day average energy consumption

8. Calculate the total annual weekend day energy consumption (Worksheet: “Step 4. Results,” cell E6.)

$$\begin{array}{}\text{(21)}& {\overline{kWh}}_{WEdYr}={\overline{hWh}}_{WEd}\ast (104weekenddaysperyear+X)\end{array}$$

Where,

${\overline{kWh}}_{WEdYr}=$ Annual weekend day energy consumption (in kWh)

${\overline{kWh}}_{WEd}=$ Average weekly weekend day energy consumption

$X=$ Number of weekdays that are considered holidays and adjusted to weekend day average energy consumption

9. Calculate total annual estimated energy consumption.

$$\begin{array}{}\text{(22)}& {\overline{kWh}}_{ann}={\overline{kWh}}_{WdYr}+{\overline{kWh}}_{WEDYr}\end{array}$$

Where,

${\overline{kWh}}_{ann}=$ Annual energy consumption (in kWh)

${\overline{kWh}}_{WdYr}=$ Annual weekday energy consumption (in kWh)

${\overline{kWh}}_{WEdYr}=$ Annual weekend day energy consumption (in kWh)

Equation (26) is the annual energy consumption of the measured circuits for a panelboard. If additional circuits were measured for the same panelboard with a different data logger, be sure to consolidate the results (annual energy consumption) to obtain the total panelboard annual energy consumption. Additionally, if multiple panelboards were measured, be sure to sum up the annual consumption of all panelboards to obtain the total system energy consumption.

Further Reading

• 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

• Richman, EE. (October 2012) “Standard Measurement and Verification Plan for Lighting Retrofit Projects for Buildings and Building Sites.” Richland, WA: Pacific Northwest National Laboratory.

• Richman, EE. (February 2016) “Measurement and Verification of Energy Savings and Performance from Advanced Lighting Controls.” Richland, WA: Pacific Northwest National Laboratory.

Footnotes