Predict power consumption using linear regression

I want to predict power consumption per hour with this data using linear regression.

How can i do this?

Answer 1

[Star Strider]

There are 89 days in the data, so the data ‘wrap’ to 24 hours.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1172328/data2022.csv', 'VariableNamingRule','preserve')

T1 = 2159×5 table
    time    power_consumption(MW)    temperature(¡ÆC)    humidity(%)    insolation(MJ/m2)
    ____    _____________________    ________________    ___________    _________________

      1            808.08                  3.3               66                  0       
      2            776.95                  3.2               59                  0       
      3            753.25                    3               62                  0       
      4            750.78                  2.5               61                  0       
      5            753.73                  2.2               67                  0       
      6            768.75                  2.2               68                  0       
      7            790.86                  1.5               71                  0       
      8            801.18                  0.9               74               0.01       
      9            760.35                    2               71               0.21       
     10            631.42                  6.3               52               0.91       
     11            562.01                  7.7               42                1.5       
     12            524.11                  8.5               41               1.93       
     13            503.51                  8.2               40                  2       
     14            527.51                  8.7               42               1.83       
     15            554.49                  8.2               40               1.41       
     16            636.05                  7.5               42               0.56       

VN = T1.Properties.VariableNames;
nrDays = nnz(T1.time == 24)

nrDays = 89

mdl = fitlm(T1.time, T1.('power_consumption(MW)'))

mdl = 
Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate      SE       tStat       pValue  
                   ________    _______    ______    __________

    (Intercept)     698.61      5.0312    138.86             0
    x1              5.2509     0.35226    14.906    6.6857e-48


Number of observations: 2159, Error degrees of freedom: 2157
Root Mean Squared Error: 113
R-squared: 0.0934,  Adjusted R-Squared: 0.093
F-statistic vs. constant model: 222, p-value = 6.69e-48

[y,yci] = predict(mdl, T1.time);

figure
plot(T1.time, T1.('power_consumption(MW)'), '.')
hold on
plot(T1.time, y, '-r')
plot(T1.time, yci, '--r')
hold off
grid
xlabel(VN{1})
ylabel(strrep(VN{2},'_','\_'))

.

[Hkl]

Thank you for answer, but how can i use temperature, humidity and insolation to make linear regression model y~1+x1+x2+x3+x4?

[Star Strider]

As always, my pleasure!

Perhaps this —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1172328/data2022.csv', 'VariableNamingRule','preserve')

T1 = 2159×5 table
    time    power_consumption(MW)    temperature(¡ÆC)    humidity(%)    insolation(MJ/m2)
    ____    _____________________    ________________    ___________    _________________

      1            808.08                  3.3               66                  0       
      2            776.95                  3.2               59                  0       
      3            753.25                    3               62                  0       
      4            750.78                  2.5               61                  0       
      5            753.73                  2.2               67                  0       
      6            768.75                  2.2               68                  0       
      7            790.86                  1.5               71                  0       
      8            801.18                  0.9               74               0.01       
      9            760.35                    2               71               0.21       
     10            631.42                  6.3               52               0.91       
     11            562.01                  7.7               42                1.5       
     12            524.11                  8.5               41               1.93       
     13            503.51                  8.2               40                  2       
     14            527.51                  8.7               42               1.83       
     15            554.49                  8.2               40               1.41       
     16            636.05                  7.5               42               0.56       

VN = T1.Properties.VariableNames;
nrDays = nnz(T1.time == 24)

nrDays = 89

mdl = fitlm(T1{:,[1 3:end]}, T1{:,2})

mdl = 
Linear regression model:
    y ~ 1 + x1 + x2 + x3 + x4

Estimated Coefficients:
                   Estimate      SE        tStat       pValue   
                   ________    _______    _______    ___________

    (Intercept)         845     8.1843     103.25              0
    x1               6.6603    0.19058     34.948    2.3131e-212
    x2              -12.007    0.36211     -33.16    3.6738e-195
    x3             -0.50587    0.11485    -4.4045     1.1121e-05
    x4              -92.248     2.3169    -39.815    2.7465e-260


Number of observations: 2159, Error degrees of freedom: 2154
Root Mean Squared Error: 60.3
R-squared: 0.743,  Adjusted R-Squared: 0.743
F-statistic vs. constant model: 1.56e+03, p-value = 0

[y,yci] = predict(mdl, T1{1:24,[1 3:end]});

y = 24×1

778.6527 790.0547 797.5988 810.7686 817.9959 824.1503 837.6980 849.1226 825.6428 725.7094

yci = 24×2

773.2093 784.0961 784.5065 795.6030 792.4571 802.7405 805.6705 815.8667 813.1286 822.8632 819.4295 828.8710 832.6390 842.7571 843.5727 854.6725 820.7574 830.5282 721.6099 729.8089

figure
plot(T1.time, T1.('power_consumption(MW)'), '.')
hold on
plot(T1.time(1:24), y, '-r')
plot(T1.time(1:24), yci, '--r')
hold off
grid
xlabel(VN{1})
ylabel(strrep(VN{2},'_','\_'))

I am not certain what you want to do. This uses columns [1 3 4 5] to predict column 2, and only plots the first 24 hours because the plot looks extremely messy plotting all the data. (This is a linear regression, however it does not appear linear because of the independent predictor variables involved.)

Experiment to get the result you want.

.

[Hkl]

I appreciate it.

[Star Strider]

As always, my pleasure!

Answer 2

[Florian Bidaud]

Hi,

You can use the function polyfit with x being the time and y being the power consumption, you will have to choose n to fit your data as you want. In your data, I guess when the time comes back to 1 it means it's another day ? Then you will need to change 1,2,3,..., 23 to 25,26,27,....47 for the second day and so on