LA ANGUSTIA TERMINA CUANDO LA LEY SIMBÓLICA EMPIEZA

It is broadly agreed upon that the outside air temperature has a large effect on the electricity demand (Kumru & Kumru, 2015; Berm´udez, 2013; Garc´ıa-D´ıaz & Trull, 2016; Bessec & Fouquau, 2008). Currently, ORTEC uses the degree days method (among others) to include temperature in the LPG forecast. This section explains this method and gives its advantages and shortcomings.

Heating- and Cooling degree days

This method makes a distinction between heating degree days (HDDs) and cooling degree days (CDDs). HDDs come with a base temperature (that should be found by optimising theR2 _{when correlating demand with the corresponding HDDs, varying the base tempera-} ture) and provide a measure of how many degrees and for how long the outside temperature was below that base temperature (using the average of the minimum- and maximum tem- perature of a specific day). For example, when the outside air temperature was 3 degrees below the base temperature for 2 days, there would be a total of heating degree days of 6. The advantage of using HDDs over temperature in forecasting is that these HDDs can be aggregated over the time buckets that the user wants to forecast on. CDDs are calculated in a similar fashion, but then the degree days are calculated by taking the number of days and number of degrees that the outside temperature was above that base temperature. This base temperature could be another base temperature than that of HDDs. Moral-Carcedo & Vic´ens-Otero (2005) state that it is not trivial whether to use one or two thresholds. Hav- ing one threshold indicates that when the threshold temperature is passed, there is a sharp change in behaviour whereas when having two thresholds, it is assumed that in between these two thresholds, there is no appreciable change in demand. In other words, there is a neutral zone for mild temperatures where demand is inelastic to the temperature (Bessec & Fouquau, 2008; Psiloglou, Giannakopoulos, Majithia, & Petrakis, 2009).

In formula form the number of degree days is calculated by:

HDDs=Pnd

j=1max(0;T∗−tj) andCDDs=Pndj=1max(0;tj−T∗) where ndis the number

of days in the period over which the user wants to calculate the number of HDDs,T∗ is the threshold temperature of cold or heat, and tj the observed temperature on day j (Moral-

Carcedo & Vic´ens-Otero, 2005). With the help of historical data on the energy consumption and number of degree days, a regression analysis can be used to determine the expected energy consumption given the number of degree days.

Base temperature(s)

Several studies indicate that the relationship between demand and temperature is non-linear. This non-linearity refers to the fact that both increases and decreases of temperature, linked to the passing of certain ‘threshold’ temperatures which we call the base temperature, in- crease demand. This is caused by the difference between the outdoor- and indoor tempera- ture. When this difference increases, the starting-up of the corresponding heating or cooling equipment immediately raises demand for electricity (Moral-Carcedo & Vic´ens-Otero, 2005). The base temperature is the temperature at which electricity demand shows no sensitivity to air temperature (Psiloglou, Giannakopoulos, Majithia, & Petrakis, 2009). The difference be- tween LPG and electricity on this matter is that LPG is primarily used for heating purposes so only one base temperature is required and only HDDs should be considered (Sarak & Sat- man, 2003). In order to determine this base temperature, the temperature should be plotted against the consumption. This is done in Figure 2.7 for three countries that are categorised as ‘warm’ (Greece), ‘cold’ (Sweden), and ‘intermediate’ (Germany) (Bessec & Fouquau, 2008). The y-axis gives the filtered consumption that isolates the influence of climate on electricity use. We will not go into details because it is of no importance here, the shape of the scatter plot is.

Figure 2.7: Demand versus temperature (Bessec & Fouquau, 2008)

Figure 2.8: Demand versus temperature Australia (Hyndman & Fan, 2010)

A clear U-shape can be seen in the ‘warm’ country plot which is often seen, also for other warm countries (Moral-Carcedo & Vic´ens-Otero, 2005; Pardo, Meneu, & Valor, 2002). How- ever, demand of colder countries is more influenced by the heating effect (Bessec & Fouquau, 2008). Australia, that is even warmer than the countries categorised as ‘warm’ by Bessec & Fouquau (2008), has a different shape than those in Figure 2.7. Its shape is similar to that of the right part of Greece (see Figure 2.8) which indicates that demand of hot countries is more influenced by the cooling effect.

The zone where demand is inelastic to temperature is around the base temperature. As mentioned before, a decision must be made between one threshold value or two. Having two indicates a temperature interval within demand is unresponsive to temperature variations whereas one indicates a more instant transition between a regime characterised by cold tem- peratures to a regime corresponding to hot temperatures. Since natural gas (LPG) is used primarily for space heating, using only HDDs is satisfactory which means that only one base temperature is required (Sailor & Mu˜noz, 1997; Sarak & Satman, 2003).

Shortcomings

A problem of the degree-days method is the determination of an accurate base temperature. In the UK for example, a base temperature of 15.5◦C is used since most buildings are heated to 19◦C and some heat comes from other sources such as people and equipment in buildings which account for around 3.5◦C (Energy Lens, 2016). However, the problem with this is that not all buildings are heated to 19◦C, not every building is isolated to the same extent, and average internal heat gain varies from building to building (crowded buildings will have a higher average than a sparsely-filled office with bad isolation and a high ceiling). Energy Lens (2016) states that the base temperature is an important aspect since degree-days-based calculations can be greatly affected by the base temperature used. When the base tempera- ture is chosen wrongly by the forecaster, this can easily lead to misleading results. However, it is difficult to accurately determine whether this base temperature is chosen wrongly since the base temperature can vary over the year depending on the amount of sun, the wind, and patterns of occupancy. Besides, when outside temperature is close to the base temperature, often little or no heating is required. Therefore, degree-days-based calculations are rather inaccurate under such circumstances.

Another important problem is that most buildings are only heated intermittently, for example from 9 to 17 on Monday to Friday for office buildings whereas degree-days cover a continuous time period of 24 hours a day. This means that degree-days often do not give a perfect representation of the outside temperature that is relevant for heating energy consump- tion. The cold night-time temperatures are fully represented by degree-days whereas they only have a partial effect (when the heating system is off at night), namely on the day-time heating consumption since it takes more energy in the morning to heat the building com- pared to a less cold night. When the difference between the outside- and inside temperature becomes bigger, as mentioned in Subsection 2.6, the starting-up of the corresponding heating or cooling equipment raises demand for energy (Moral-Carcedo & Vic´ens-Otero, 2005). Not only nights are an example but also public holidays and weekends. Moral-Carcedo & Vic´ens- Otero (2005) made an adjustment to overcome this problem. They introduce a variable called ‘working day effect’ which represents the effect of calendar in demand of a particular day as a percentage of electricity demand on a representative day.

There are a couple of suggestions on how to overcome these shortcomings of the degree- days method. The most important one is that an appropriate time scale should be used. In the ORTEC case, the energy consumption is given once every two weeks, degree days should be gained accordingly. For example if only weekly degree days are available, those should be summed in order to make them appropriate. Besides, a good base temperature should be used.

results but the combination of the problems stated leads to the overall accuracy of the results being quite low. The results from this method can be used as an approximation of the electricity demand but do not give accurate results.