Prediction of domestic appliances usage based on electrical consumption

Forecasting or modeling the expected on-off times of domestic appliances is motivated from two directions: (i) generation of electrical load profiles and (ii) learning and predicting user behavior. Artificial load profile generation (Pflugradt 2016) can be helpful if large numbers of profiles spanning extended durations are required because their collection typically involves arduous measurement campaigns. While the precise prediction of the switch-on/off times is in this case not the main concern, it is an essential part in applications targeting demand response systems: Learning the usage pattern of appliances and therefore, knowledge of the user behavior is a vital input to optimally plan energy usage (Chrysopoulos et al. 2014; Holub and Sikora 2013). While different prediction approaches have been published (Chrysopoulos et al. 2014; Holub and Sikora 2013; Truong et al. 2013; Barbato et al. 2011), an outstanding matter in adequately addressing the forecast of domestic appliance usage is a comparison of the available approaches: Published results are difficult to compare because of diverse performance metrics, different predicted appliances and the large variety of employed datasets, either measured at different geographic locations or even simulated. It is therefore unclear how well a method generalizes (i) over extended time periods and (ii) to other datasets with different attributes such as appliances, number of inhabitants, user habits and behavior.

In this work, we compare published the approaches we are aware of (Chrysopoulos et al. 2014; Truong et al. 2013; Barbato et al. 2011) and extensions from these on three datasets measured over 2 years in households located in Switzerland, Canada and the UK. We implemented these approaches into a common framework and compare their fitness in predicting the usage patterns of the appliances. In doing so, we focused on appliances, whose usage is mainly driven by user behavior and whose switch-on time is flexible. In the relevant literature such appliances are commonly referred to as “shiftable loads”. Examples for such loads are washing machine, dish washer or tumble dryer. The Python source code for the experiments can be obtained from the authors upon request.

The following subsections shortly discuss the main characteristics of the three implemented algorithms. All algorithms have been used to predict the on-off times of appliances with a resolution of 1 h.

Where not otherwise mentioned, results stem from an average over 90 samples, where each individual sample predicted on-off behavior of an appliance during 1 week based on the eight preceding weeks, hence covering in total roughly 2 years of data.

Histogram algorithm

The basic histogram method was tested on all three datasets with the model parameter σ (variance) varying between 0 and 2. Overall best performance with respect to AUC was achieved with σ = 1.3 which was used for all further experiments. The average performance improves by increasing the training window, i.e. increasing the individual train-sets, but saturates for lengths above about 3 months. As a trade-off between prediction quality and a quickly increasing computational effort for the more elaborate algorithms, a training window of 8 weeks was chosen to ensure comparability of the results. Table 1 summarizes the results. The algorithm generally performs in a medium quality range with AUC-values around 0.7. Differences in the AUC of different appliances and datasets are large but are not significant due to the large uncertainty as illustrated in Fig. 1.

	Histogram		Pattern Search		Bayesian Inference
GH9
Dish-Washer	0.64	±0.15	0.72	±0.10	0.72	±0.10
Tumble Dryer	0.74	±0.21	0.78	±0.14	0.71	±0.08
Washing Machine	0.84	±0.10	0.75	±0.09	0.73	±0.08
AMPds2
Dish-Washer	0.68	±0.12	0.66	±0.10	0.74	±0.08
Tumble Dryer	0.72	±0.11	0.73	±0.08	0.77	±0.09
Washing Machine	0.63	±0.17	0.81	±0.08	0.73	±0.10
REFIT
Dish-Washer	0.79	±0.14	0.72	±0.15	0.72	±0.06
Tumble Dryer	0.76	±0.14	0.66	±0.13	0.69	±0.07
Washing Machine	0.74	±0.09	0.68	±0.10	0.77	±0.08

The results summarized in Table 1 lead to the following observations: i) The overall performance of the three algorithms is essentially the same: averaging all appliances in all houses leads to the following values: 0.72 for Histogram and 0.73 for both Pattern Search and Bayesian Inference algorithms. ii) With increasing complexity of the algorithm not only the variances over 2 years decrease, but also the prediction quality across appliances and data-sets becomes more similar. iii) An algorithm’s (relative) performance for a given appliance and data-set does not necessarily relate to another algorithm’s performance on the same data-set. That is, an algorithm performing particularly well on a given appliance of a given data-set does not necessarily imply other algorithms to perform similarly, i.e. the governing reason for the large differences does not seem to be the underlying data. iv) Similarly, no statement is possible about certain appliances performing markedly worse or better across all datasets for a specific algorithm, i.e. no particular algorithm is especially good at predicting a certain appliance. As discussed above the results imply that the mean predictive performance is not affected by the choice of the employed model. Because of the complexity of the implementation and computational considerations this would favor the Histogram algorithm over the two others. It performs at least 2–3 orders of magnitude faster than the algorithm based on Bayesian inference. For most real-world applications, it is, however, not the mean performance that counts most but a reliable performance on any given data. Here the reduced variance of the Bayesian algorithm with respect to the Histogram and Pattern Search approach speaks in favor of the former.

From our viewpoint, a limitation of the Bayesian algorithm in its current form is the fact that it strongly relies on weekly patterns despite its introduction of the latent day-types. This could be addressed by making minor changes to include more data such as weather or schedules (Truong et al. 2013). An alternative could be to combine the Bayesian and the Pattern Search algorithms so that day n would also be predicted based upon the inferred day-types of the immediately preceding days.

One aim of this study was to investigate if the on-off times of domestic appliances can be predicted solely based on electrical usage data. From our results, we tend to negate this hypothesis: On a coarse-grained timescale of 1 h, we achieved on average a mediocre prediction performance with a large variance. However, we believe that for domestic load optimization an improved performance and, in particular, a smaller variance of the prediction would be desirable if not necessary. Our choice of algorithms is far from exhaustive and one can think of various improvements of the examined algorithms. Nevertheless, from our point of view, the presented results based on 2 years of data from three different households reflect a general limit for the hourly predictability of an individual household’s electrical appliances. We conclude that taking solely electrical data of a single family into account, every stochastic approach must suffer from a lack of information, independently of its complexity.