In this section, we study the results of the heat load forecast in the three buildings over a period of winter and spring seasons by studying the four cases of the proposed model. The behavioural parameters as shown in Table 2. are added to all the four cases.
For evaluating the proposed classification model, it is necessary to compute the accuracy of clas-sification. The accuracy of classification highlights the ability of the model to correctly predict classes and also to differentiate the classes. To get the complete picture of the performance of the classifier, it is imperative to study the confusion matrix [66]. We consider a classifier which
is trained to distinguish between StatesA,B andC. We assume that there are a total of 70 in-stances including 30 inin-stances inStateA, 20 instances inStateB and 20 instances inStateC. One possible confusion matrix for such a classifier is shown in Table 5. The actual states are represented in the rows while the predicted states are represented in the columns. From the confusion matrix it can be observed that out of 30 instances ofStateA, the classifier predicted 25 instances correctly. 3 instances of StateA were classified as StateB while the remaining two instances were classified asStateC. Similarly, out of 20 instances ofStateB, 18 were pre-dicted correctly by the classifier as belonging to StateB. For StateC, the classifier predicted 15 instances correctly out of the total 20 instances. Therefore the accuracy of classification in simple terms is computed by dividing the total number of correct classifications by total num-ber of instances. The correct numnum-ber of classifications for each state is represented along the diagonal of the confusion matrix.
Accuracy of classif ication= N umber of correct classif ications
T otal number of instances (25)
Accuracy of classif ication= 25 + 18 + 15
70 = 0.8285 (26)
Therefore, the classification accuracy for this example is 82.85%. We compute the accuracy for the states of heat load in our model in a similar fashion. Since we are computing the accuracy of the heat load forecast, we will refer it as forecasting accuracy.
Table 5.Example of a confusion matrix
Actual/P redicted StateA StateB StateC
StateA 25 3 2
StateB 1 18 1
StateC 2 3 15
4.2.1 Case I : Influence of DHS operational parameters on heat load forecast
In this case, we observe the influence of DHS operational parameters (shown in Table 2) on the heat load forecast. The accuracies of the heat load forecast across both winter and spring seasons for all four cases is presented in Figures 26 and 27. The results of forecasting accuracy for Case I indicate that the accuracy of heat load forecast decreases with the forecasting horizon
for a particular building. This can be explained by Eq. 12. The magnitude of the heat load consumption at a substation depends on the current values of DHS operational parameters which are used for forecasting heat load using our trained Bayesian network. With the increase in the forecasting horizon, the dependency of the heat load forecast decreases on the current values of DHS operational parameters, which results in the decrease in accuracy. It can also be observed that Building A achieves the highest accuracy with EWD in both winter and spring seasons for all horizons.
Figure 26.Accuracy of heat load forecast across winter season.
Figure 27.Accuracy of heat load forecast across spring season.
4.2.2 Case II : Influence of outdoor temperature forecast on heat load forecast
In this case, we compute the heat load forecast by training the model with the outdoor tem-perature forecast and behavioural parameters as shown in Table 2. In both winter and spring seasons, the accuracy of the heat load forecast across various horizons almost remains constant for a particular building. This maybe due to the fact that the heat load forecast at different horizons has similar dependency on the outdoor temperature forecast. Building A achieves the highest accuracy with EWD in both winter and spring seasons for all horizons.
4.2.3 Case III : Influence of DHS operational parameters and outdoor temperature fore-cast on heat load forefore-cast
In this case, we study the influence of DHS operational parameters and outdoor temperature forecast on the heat load forecast. Figures 26 and 27 show the variation of the forecasting accuracy across different horizons for both winter and spring seasons respectively for this case.
In the winter season, there was no clear trend in the accuracy of load forecast across various horizons. In the spring season, the accuracy decreases with the increase in forecasting horizon in majority of the cases for all buildings. Building A achieves the highest accuracy with EWD in both winter and spring seasons for all horizons.
4.2.4 Case IV : Influence of current heat load consumption and outdoor temperature forecast on heat load forecast
In this case, we study the impact of the current heat load consumption and outdoor temperature forecast on the heat load forecast. During the winter season, the accuracy of forecastingHL(t+1) is higher than the accuracy of forecasting heat load for other horizons. This indicates that the current heat load consumption has a strong influence on the heat load forecast. However, with increasing forecasting horizon, the dependency of heat load forecast on the current heat load decreases which results in a decrease in the forecasting accuracy. In the spring season, in most of the cases, the forecasting accuracy increases from 6 hour to 24 hour horizon. This is because of the user activity pertaining to a daily routine, which influences the heat load forecast.
4.2.5 Utilizing less training data forHL(t+1)forecast
In this section, we present the best case results for forecasting heat load for the next hour, ob-tained by using EWD and Naive Bayes classifier in Case IV(using outdoor temperature forecast and current heat load consumption). Figure. 28 shows the accuracy of HL(t+1) forecast for different percentages of training data for Buildings A, B and C over the period of both seasons.
We observe that we achieve a good accuracy by just using training data between 10-20% with our Bayesian network. These results indicate that the proposed model would be effective in forecasting the heat load with less training data. There are around 5000 substations in the city of Skellefteå. The smart meter data collected from these substations at a high resolution poses the challenge of analysis of a large amount of data to forecast the heat load demand [37]. Our results indicate that in case of a large number of buildings and large amount of data, our model would be suitable for heat load forecast.
Figure 28.Forecasting accuracy forHL(t+1)with different percentages of training data using EWD and Naive Bayes in Case IV.