This article explains the calculations done in the Occupancy Sensor Calculator, designed to estimate energy savings, cost benefits, and environmental impact of installing occupancy sensors in commercial lighting systems.
The Occupancy Sensor Calculator estimates energy savings, cost benefits, and environmental impact for commercial lighting systems by combining several mathematical steps.
First, it determines the current annual operating hours:
$$ CHPY = H_{day} \times D_{week} \times W_{year} $$
Depending on the chosen method, the proposed annual hours are computed either as a percentage of the current hours:
$$ PHPY = percent_{occupied} \times CHPY $$
or by reducing the daily operating hours:
$$ PHPY = (H_{day} - H_{reduction}) \times D_{week} \times W_{year} $$
Next, power consumption per fixture is calculated:
$$ PCF = \frac{N_{bulbs} \times W_{bulb} \times BF}{1000} $$
Multiplying by the total number of fixtures gives the total system power:
$$ TPC = PCF \times N_{fixtures} $$
This power is used to find the current and proposed electrical consumption:
$$ CEC = TPC \times CHPY \quad \text{and} \quad PEC = TPC \times PHPY $$
with the energy savings determined as:
$$ ES = CEC - PEC $$
Cost savings come next. Electricity cost savings are given by:
$$ ECS = ES \times EC $$
and, if the system operates at peak demand, the demand cost savings are calculated as:
$$ DCS = DS \times DC \times 12 $$
Carbon emission reductions are estimated by:
$$ CES = \frac{ES \times CI}{2205} $$
Maintenance savings are also factored in by assessing bulb replacement rates and comparing current versus proposed replacement material and labor costs. Finally, implementation costs are summed up as:
$$ TIC = IMC + ILC $$
and the simple payback period is derived by:
$$ SP = \left(\frac{TIC}{TCS}\right) \times 12 $$
where total cost savings, $TCS$, is the sum of electricity, demand, maintenance material, and labor cost savings. For a more in-depth financial review, the internal rate of return (IRR) is calculated by solving:
$$ \sum_{t=0}^{n} \frac{CF_t}{(1 + IRR)^t} = 0 $$