Introduction
One of my favorite physicists stopped by today and wanted to talk about the cost of cooling electronics like fans and air conditioners. The talk was somewhat mathematical and worth discussing here because the basic math is what a homeowner should do when evaluating the cost of different air conditioning options. In fact, my son recently chose an air conditioner based on this same calculation.
Problem Statement
The following problem statement pretty closely mirrors what I was asked today. I have omitted a few details having to do with the particular hardware chosen.
I have a customer who wants to add 200 Watts of electronics to an air-conditioned electronic enclosure. How much more will this customer's cooling costs increase each year when he adds this hardware to his enclosure?
Seems like a simple question and it is. Let's dig in ...
Approach
My approach to solving this problem is as follows.
- Determine the total amount of power you are adding to the electronic enclosure.
Most of the time you need to add up all the power dissipations and also add the cost of power conversion that may be involved. For example, telecommunications gear is often powered by 48 V gear. This means that the total power dissipation will include the power dissipated from the 48 V supply and the power dissipated when converting the building power (AC) to 48 V. The conversion process is ~80% efficient. The exact number depends on the specific power converter you are using.The total power dissipated, including conversion losses, is given by the equation PTotalThermal = PThermal/kEfficiency, where PThermal is the power dissipated within the telecommunications gear, PTotalThermal is PThermal plus conversion losses, and kEfficiency is the conversion efficiency.
- Convert the electrical power from Watts to BTUs.
I live in the US. Unit conversion is a part of life.
- Use the Seasonal Energy Efficiency Ration (SEER) to convert BTUs of cooling to electrical power in kilo-Watts (kW).
SEER is a conversion factor that air conditioner manufacturers are required to state. The Wikipedia has an excellent discussion on SEER and you should go there for more information.
- Compute the yearly energy usage.
Just multiply the Watts dissipated times the total number of hours in a year to get Watt-hours, which can then be converted to kW-hours.
- Convert kW to dollars using the local cost of electricity.
The US Department of Energy (DoE) publishes the average cost of electricity in every state. I have a blog post that presents this data in graphic form.
Analysis
Figure 1 summarizes my analysis in Mathcad.
Figure 1: Analysis of the Yearly Airconditioning Cost Increment
Figure 2 repeats my graph of electrical costs in the US from this blog post.
Figure 2: Electrical Power Costs in the US.
Conclusion
The customer is going to burn more than $67 every year just to power the air conditioner for this hardware. Of course this is assuming they have HVAC repair at regular intervals. The cost will only go up the longer the air conditioner units have gone without cleaning or servicing. Thus, understanding the need of a timely inspection of an HVAC unit by a professional similar to ac services Douglas County (or similar others) is of utmost importance. The cost may only go down if the customer finds a more efficient conditioner than the one they're currently using on the market, but now we're just getting into hypotheticals.
To get the total electrical cost, the customer will need to add the cost of powering the electronics itself. This is all part of the cost of doing business I suppose.