I have a question as I am starting my dive into computational analysis.

I have a large set of data (~2 months) which includes the room temperature, HVAC status (heat/cool/off) and the location of this room (I can find detailed information on outdoor temperature).

I would like to do some analysis to find the following information....

  1. Unit Capability (or efficiency).
  2. Loss of energy through the room.

Preferably for each heat/cool cycle i would be able to calculate the efficiency and be able to see a distribution of the results.

What would be the best set of mathematical tools (type of functions/ approaches)?

I know I can attempt regression over each period, however it seems in-efficient.

Thanks in advance!

  • $\begingroup$ Regarding your goal #2, you can find many articles online about calculating approximate heat loss from a building. Here is one: engineeringtoolbox.com/heat-loss-buildings-d_113.html. For a single room the process is similar: you need to know information about construction of the room including insulation of walls and windows. In addition to outside temperature as a function of time, you would also need to know the temperatures in the adjacent rooms. $\endgroup$ Dec 27 '16 at 19:11
  • $\begingroup$ Consider normalising your efficiency output to the carnot efficiency for a given room temp/outdoor temp. That should provide a more accurate metric for how efficient your AC actually is. $\endgroup$
    – Melvin
    Apr 25 '18 at 6:01

An efficiency metric

You could use,

$$\eta = p_{\text{out}}/p_{\text{in}}$$

where the power out ($p_{\text{out}}$) is defined as the heat per second from the room to the environment, and, power in ($p_{\text{in}}$) is the heat per second entering the room from the heat source.

However, it might be more fundamental to compare the thermal conductivity $k$ to characterise heat loss, where,

$$p_{\text{out}} = -\frac{k A}{d} \left(T_2 - T_1\right)$$

where $A$ is the surface area of the wall, $d$ is the thickness, and $\left(T_2 - T_1\right)$ is the temperature gradient between inside and outside.

Alternatively, you could compare the heat capacity $C$ of the room,

$$C = p_{\text{in}} / (T_2 - T_1)$$

How far you can get depends on how much data you have and exactly what it is. It's not so clear from your question.

Energy loss

I think a useful metric here would be power dissipated per unit area (closely related to the thermal conductivity). This would allow you to compare different sized rooms. So calculate the power out per second and divide by the area of the floor the ceiling and the walls (NB, some walls, ceiling and floors might be externally facing so you will find they loose more heat. You may wish to create subcategories at this point for internal and external surfaces).

Some ideas to get you stated!

  • $\begingroup$ Thank you for the insight! i will be playing with what i have... $\endgroup$
    – Caoder
    Dec 30 '16 at 5:04

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