Exploratory analysis of the national load

The load can be linked with weather conditions and economic or demographic circumstances. These circumstances are indeed responsible for general trends and cycles of the loads as well as irregularities and abrupt changes. Pierrot and Goude [2011] classified these relationships into 3 groups : social, natural and economic. In this section, we review these relationships and illustrate them with the database, in order to justify our choices of inputs for the models in Chapters 3 and 4. We also highlight the non-stationarity of the load time series.

Note that the variables that we present in this chapter are not independent. In particular, the hour of the day and the position in the year are strongly correlated with the temperatures. Therefore, all the marginal distributions estimated in this section should be interpreted with caution.

2.3.1 Impacts of natural events

While a high diversity is suspected among the ways the meteorological conditions can impact the electricity demand, the pieces of information related to the weather that provably improve the quality of forecasting models are relatively restricted.

They are mainly the temperatures and the cloud covers.

Effectively, the distribution of the loads illustrated in Figure 2.4 is highly corre-lated with the distribution of the temperatures presented in Figure 2.3. In Novem-ber, December and January, the loads were larger in 2013 and 2017, which is consis-tent with the low temperatures plottted in Figure2.3 and the fact that the weather is one of the main driver of the electricity demand. Note also that the distributions of the loads over different years appear much more heterogeneous in winter than in summer.

Additionally, while the wind speed at low altitudes and the humidity are some-times included in load forecasting models, their effect are relatively small and we have chosen not to include them. This is discussed in more details in Section3.7.3.

Instantaneous temperatures The effect of the temperature on the electricity demand is relatively well understood. Heating is roughly responsible for half of the electricity consumption in France every year.

In winter, the national load increase after a 1°C decrease has been stable over the last few years and was estimated by RTE around 2,4 GW [RTE,2016a, 2019c].

All things equal otherwise, the demand is minimal when the outside temperature is close to19°C. Finally above 25°C, the electricity demand slightly increases anew, about +500 MW/°C [RTE,2019d], due to the use of cooling appliances, thus giving the shape of a hockey cross to the marginal load curves in Figure2.5.

Depending on the region and its usual exposure to low and high temperatures, the number of heating and cooling appliances as well as their efficiency may vary.

As a result, temperature variations impact the electricity demand differently. This is illustrated in Figure2.6.

Past temperatures The past temperatures may also impact the present loads.

First, the thermal masses of the buildings make the past temperatures responsible for

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FIGURE 2.4: Distribution of the aggregated load

Box plots of the aggregated load for each month in the dataset. Note the increased variability in winter and in particular the correspondence between the largest demands and the coldest temperatures in Figure 2.3.

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FIGURE 2.5: Average load at a given temperature value

Empirical mean of the national load conditioned on the average tempera-ture. The corresponding density is given in Figure F.5.

the present heating demand. Secondly, people may not react instantaneously to the temperature variations. It is therefore relevant to include the past temperatures in the load forecasting models. Plus, it seems reasonable to always use the observations and never the past forecasts, even in operational conditions.

Cloud cover By impacting the need for artificial light and the heating of the buildings with solar radiations, the sunlight and indirectly the cloud cover also drive the electricity demand. To account for this effect, we have included in the modelings the cloud cover indices provided by Météo-France. We also use a nation-wide indicator of the presence of the sun above the skyline in Paris but we do not have information about the intensity of the sunlight. The interactions between the cloud cover and the indicator of the daylight is of particular interest, if we consider that the cloud cover has no influence on the demand at night. The average load conditioned on the value of the cloud cover index is illustrated in Figure2.7.

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FIGURE 2.6: Load for different temperatures in the North/South Empirical mean of the load conditioned on the average temperature in two different areas : North and South of France. The substations and the weather stations were split into two balanced groups, depending on their latitudes being above or below 46.5°N. For each group, we compute the average loads per substation per quantiles of temperature. Each of these conditional means is then centered, as a function of the temperature, to illustrate that the slope of the average load is globally larger in the South : more positive for warmest temperatures and less negative for cold tempera-tures. These differences may be due to the different appliances installed in each region but a definite causal interpretation is difficult.

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FIGURE 2.7: Load conditioned on the cloud cover index

Empirical mean of the load conditioned on the average cloud cover. The corresponding density is plotted in Figure F.6. The value 0 corresponds to an absence of clouds and the value8to a very cloudy observation. Note that the variations of the load should not be attributed entirely to the cloud cover since the latter is highly correlated with the temperatures, among others.

2.3.2 Impacts of the economic activity

In addition to the weather conditions, the economic activity is another important driver of the electricity demand. While it is not possible to measure people’s oc-cupations, their relationships with the calendar variables such as the hour and the positions in a week or in a year can be leveraged to estimate it.

Daily cycles The hour of the day is an obvious indicator of the level of economic activity and this is reflected immediately by the electricity demand. A similar pat-tern of consumption, illustrated in Figure 2.8, is roughly repeated every day.

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FIGURE 2.8: Daily cycles

Empirical mean of the nationally-aggregated load conditioned on the hour of the day (UTC). The corresponding density is plotted in Figure F.2. The second peak in the evening around 10 pm corresponds to the switch to the off-peak rates of electricity.

The amplitudes and the precise hour of the peaks in the morning and in the evening may depend on the period of the year, as illustrated in Figure2.9. This is due among others, to the switch between Standard Time (ST) and Daylight Saving Time (DST) and to the variations of the sunrise and the sunset times.

Weekly cycles Similarly, the day of the week roughly determines people’s agenda.

Based on preliminary experiments, we believe that it is actually more relevant to consider in the modeling directly the hour of the week which is the combination of the hour of the day with the day of the week and has24×7 = 168 possible values.

The weekly cycles are illustrated in Figure2.10.

Yearly cycles Figure 2.5 illustrates the relationship between the temperatures and the load. Since the temperatures is strongly correlated with the day of the year, we observe yearly cycles in Figure 2.11. Contrary to the temperature that is minimal during winter and maximal during summer, the electricity demand is on average maximal during January-February and minimal during July-August.

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