# Resetting Temperature Setpoints Based On Outside Air Requires… Linear Interpolation?

I always seem to forget that magical calculation that will reset a Supply Air Temperature Setpoint based on the Outside Air Temperature. I figure… Eh, I’ll Google it. Then realize, “WTH do you call that kind of calculation?” Is it a Slope Calculation? with an interception… er Intercept? No… It’s a:

### Linear Interpolation Calculation Type of Automation Situation

Yeah, sure… whatever. Believe it or not I failed 3 YEARS of High School Mathematics!

Maybe if I had more HS teachers like this Brazilian Beauty,
I might have paid more attention.

I still ended up loving Math because it’s either RIGHT or it’s WRONG. I also love Excel and figuring out all kinds of spreadsheet formulas as well as trying to incorporate mathematic calculations when writing programming code. Learn that math stuff, it helps…ALOT.

### Why Reset the Supply Temperature Setpoint Based on Outside Air

The main reason you want to do this is for Energy Savings by not having to utilize as much mechanical cooling vs. allowing the Ambient Temperature to cool the space.

Ambient – The surrounding area or environment. In HVAC, typically relating to outside or atmospheric conditions.

So if it is pretty cool outside we don’t need to have super cool 52°F supply air shooting down the ductwork. We can allow the supply air to increase up to say 58°F knowing that should be enough cool

air to satisfy the warm areas, but accomplish two energy saving measures:

1. Not use as much mechanical cooling (Chilled Water or DX Cooling) to make supply air temperature setpoint.
2. Not require the heating or reheating of spaces to overcome the cold supply air. Keeping electric heat stages in terminal boxes from coming on is a huge energy saver.

### Now gimme the Calculation or Formula, Einstein!

Alright here it is…

Y2 = Y1 + [(X2-X1)(Y3-Y1)] / (X3-X1)

OAT

• X1 = Lowest OAT Value
• X2 = Current OAT
• X3 = Highest OAT Value

SAT

• Y1 = SAT Setpoint @ X1 OAT
• Y2 = Actual SAT Setpoint
• Y3 = SAT Setpoint @ X3 OAT

Ohhhhh THAT one… yeah I got that already. Easy Cheezy.

### Let’s Try an Example Temperature Reset Calculation

I want to have cold 52°F SAT when the OAT is @ 80°F.

………….and I want 58°F SAT when the OAT is @ 60°F.

OAT

• X1 = 60°F
• X2 = Current OAT is 77°
• X3 = 80°F

SAT

• Y1 = 58°F
• Y3 = 52°F

??? = 58 + [(77-60)(52-58)] / (80-60)

STOP scrolling back up to the teacher pic and

### Delta Controls GCL and Some Other DDC Controls Make It Easier

I have been using Delta Controls for awhile and they long since came up with a function in GCL programming called ‘SCALE’ and it makes using the Linear Interpolation calculation even easier by typing in the following syntax:

SCALE(<the OAT input>, <bias offset>, <OAT@highest SAT>, <highest SAT setpoint>, <OAT@lowest SAT>, <lowest SAT setpoint>)

or

SCALE(AI1, 0, 60, 58, 80, 52)

where AI1 = the physical location of the Outside Air Temperature Input.

Most other Controls Systems have similar functions or programming blocks that you can use.

Temperature Setpoint Reset Based on Outside Air Calculator

If you like this Excel Spreadsheet let me know and I will try to make some more stuff like this in future.

### 20 Responses to Resetting Temperature Setpoints Based On Outside Air Requires… Linear Interpolation?

1. Michael Reed March 4, 2012 at 07:51

53.1. Although, I have not seen a controls company in the last 10 years that didn’t have that block worked into their programming language already. Really hope there aren’t any out there that still haven’t caught up to this industry standard…

2. Michael G. Koch March 4, 2012 at 08:46

Nice thanks for the refresher. and keep it coming

3. Michael Halkiadakis March 5, 2012 at 02:17

Alerton has a function that does all this, so it’s cool!!

4. ben March 7, 2012 at 16:28

Yes good stuff. Great info for newbies like me looking to learn. Wonderful blog Able thank you.

5. Peter Hanlon March 13, 2012 at 07:37

I think I have found your deliberate mistake?

The ans to the first question is 52.9F.

The ans on the spreadsheet should be 61F as the Y3 and Y1 values are reversed. The correct ans is 55F when the Y3 and Y1 values are corrected.

• The Controls Freak March 13, 2012 at 12:52

Peter, I don’t see the error nor where the Y1 and Y3 is reversed. When the OAT (X2) is at 80°(X3), I want the SAT(Y2) to be 52°(Y3). When the OAT(X2) is 60°(X1), I want the SAT(Y2) to be 58°(Y1).

I believe the X and Y variables are the same from the article as they are in the spreadsheet. Now, by inverting the Y1 and Y3 variables you can then use it as a reverse acting calculation for Hot Water or Boiler reset where you want the setpoint to get hotter as the OAT gets colder.

• Joshua July 8, 2014 at 23:01

Check me on this. I don’t think you have to change anything for boiler reset, as in both cases you are increasing the SAT or SWT as OAT decreases.

6. Alberto Rubalcaba March 14, 2012 at 10:58

Hey Abel,

Very Impressed with your knowledge in DDC. Keep the info coming

7. Harris Bynum March 21, 2012 at 13:57

GENERALLY, I often preferred “load reset” wherein (assuming a VAV AHU with box heating coil) anytime any box damper was at full open, decrement the SAT setpoint one degree every 5-10 minutes, and anytime all box dampers were less than 75% open, increment the SAT setpoint one degree every 4-8 minutes; reset schedule shall be bound to SATs no lower than 54F and no greater than 64F. All numeric parameters shall be easily adjusted to suit the design and for operational field tuning. Load reset was introduced before DDC and often uaed on pneumatically controlled multizone AHUs as well as reheat systems and VAV AHUs. Load reset can create a problem where there are over 25-40 boxes on one AHU (often a room or two is undersized and always full open, or a zone temperature sensor setpoint is set too low). Consider the geographical area, the building use, the zone activities, the building operator/engineer, and if load reset fits, use it. I have put in both simple algorithms with a software switch so either could be selected in the field without costly reprogramming.

We called the OA reset application a “ratio functio” which may be “bounded” (bratio) or unbounded (ratio). Bratio had limits beyond which no reset would occur. The ratio function was useful in many HVAC control applications. Hot water temperature OAT reset is popular, but load reset is usually better here also. If all hot water valves are throttling, lower the HWT 1 degree every 8 minutes, and if any HW valve is over 95% open increment the HWT setpoint 1 degree every 4 minutes. (Low HW flow can cause freezing, but rarely will low HW temperature cause it. So if freezing conditions are posssible, good water flow MUST be maintained during below-freezing conditions. Valve position is very useful in freeze protection. Low flow can save pump energy on properly controlled variable speed pumps, but be careful if freezing conditions are possible.)

8. marty April 15, 2012 at 12:15

I recall that being called a “reset schedule”?

• Harris Bynum April 22, 2012 at 17:26

Yes, “reset schedules” have been put on drawings for over 50 years. Prior to digital control, variable reset functions were available with pneumatic and electronic systems. Way back Honeywell had a boiler reset dual bulb thermostat that fired a simple on-off boiler. You could buy it with any one of three reset ratios; 1:1, 1:1.5, or 1.5:1.

Matching the hot water temperature to varying outdoor air temperatures kept better flow in HW coils, reducing stratification attributable to water that was too hot…

9. Plant Automation April 19, 2012 at 06:38

I AM VERY IMPRESSED WITH YOUR BLOG AND YOUR BLOG HAS GOOD STUFF

10. Geoff Melton May 19, 2012 at 08:24

Abel,
Loved the 2 videos on PI control.
I downloaded your Setpoint reset spreadsheet, but unfortunately in Australia we use those other funny units °C. I hope you noticed I used your Alt char set. If you email the password to unlock the sheet, I will convert to SI units on a second tab.
Keep up the great work,
Geoff (Australia)

• Abel B Ramirez II August 20, 2012 at 09:23

Sorry about that Geoff… I actually knew that my visitors are from all over the world and Australia has actually shown some good numbers, but the version I saved and put on the Blog didn’t have the worksheet with those units the rest of the world uses.

Count me as one of the few Americans who wishes I knew the metric system off the top of my head. That way I could easily go anywhere in the world and know what I was measuring. LOL

11. Jay June 2, 2012 at 19:43

Since I have control of most space temp set points too: I float the space temp set point with the OA temp in much the same manner.
US Gov’t facilities.

12. Chris McArthur July 13, 2012 at 17:34

Fantastic resource, great job all round ! Keep it up, Cheers.

• Abel B Ramirez II August 20, 2012 at 09:25

It has been hard lately but I am looking for a big comeback after I finish a cross-country move that I am in the middle of.

13. Mark Howard September 22, 2012 at 11:19

Thanks for the video it helps me understand a little bit more on how it works

14. Lin Alder July 16, 2013 at 13:19

Two thumbs up on the video and spreadsheet. Thanks Abel!

15. Timothy January 26, 2016 at 10:28

Just wanted to take a moment and say THANK YOU!!!!!!!!!!!!!

Timothy Doherty
Chief Operating Engineer
CBRE | Global Workplace Solutions