I am trying to model the relationship between Load & variables say X and (T - 1,2,3,4,5,6) according to the following equation:
Load = [ alpha(X) + B1*T1 + B2*T3 + B3*T4 + B4*T4 + B5*T5 + B6*T6] for X = 1 to 672
1) I have Load in the form of 15 minute interval data for a few months
2) X is a variable that is defined like this based on time:
Monday 00.00 am to 00.15 am = 1
Monday 00.15 am to 00.30 am = 2
Sunday 11.45 pm to 00.00 am = 672
This repeats again from 1 to 672 for the next week and is not a running number
T1 T2 T3 T4 T5 T6 are temperatures at each 15 min interval
Additional Info :
I can feed L, X, and T1 to T6. How can i perform regression on my equation to get coefficients alpha and B1 to B6. Observe B1 to B6 do not change with X but alpha does. So my regression output needs to be a vector of coefficients for Alpha, one for each X from 1 to 672 and a single value for B1 B2 B3 B4 B5 & B6 since they dont chage with X. I tries various ways and looked online.. All of them only say how to do this
Load = Alpha*X + B1*T1 + B2*T3 + B3*T4 + B4*T4 + B5*T5 + B6*T6
I have attached a subset of the data - about 8 weeks
- Ok ! Let me go in detail. I have several months of load data for a chiller at 15 minute intervals. The assumption is that chiller load not only depends on temperature but also on time of week.
- For ex, Lets say on a Wednesday at 10.00 - 10.15 am there is generally less occupancy so chiller load might be less than some other day with similar Outside air temperature. So the chiller load dependency is not just purely Outside temperature but also time of week.
- The temperature at each interval is broken down into 6 components to get a piecewise continuous linear equation. (not important). So thats the T1 to T6 you see.
- Then to incorporate time of week, we break a week into 672 15 minute intervals. The first X=1 starting at Monday 00.00 am to 00.15 am and so on till X = 672.
- So the chiller load equation is modelled as:
[ Load = Alpha(function of time of week variable X) + B1*T1 + B2*T3 + B3*T4 + B4*T4 + B5*T5 + B6*T6
X = 1 to 672 ] where Alpha and B1 to B6 are regression coefficients
In a week there are 672, 15 minute intervals = 7 days * 24 * hours * 60 minutes / 15 minutes = 672 intervals
- So I want to feed Load, X, T1 to T6 using several months of data. In the sample file we have 8 weeks of data.
- In 8 weeks we will have 8 instances/datapoints of Monday 00.00 to 00.15 am (X=1) and so on. These are to be used to estimate alpha at X = 1. Similarily for X = 2 till 672. This is just a sample set. If you try to find a regression coefficient Alpha for each X using 8 weeks of data since you have only 8 datapoints for each 15 minute interval or X you will likely overfit alpha. I am not sure of this ..just FYI
- In 8 weeks of data, you will have so many more data points to estimate B1 to B6 since these have no time of week or X dependency.
- The load curve over time will look roughly like the +ve half of a sine curve
Again, Thank you all !