In this section, the methodology used to calculate the quarter-hourly load at the municipal level is introduced. The modeling is developed in a top-down approach that uses the total load of each TSO. For a more detailed spatial resolution, the gross domestic product and population are used to specify the load at a municipal level. The load factor for each municipality is fitted with statistical data in order to adjust the model.
3.1. Regional Load Via Gross Domestic Product and Population
The available data from the TSOs only has a rough spatial resolution, which is not sufficient for detecting the local effects of the grid load. Therefore, a suitable parameter needs to be found in order to achieve a significant spatial resolution with reasonable computational costs. In this paper, the resolution is increased to the municipal level, leading to a subdivision of Germany into 11,268 zones. Each of these municipalities is referenced by the official municipality key (“Amtlicher Gemeindeschluessel”, AGS), which contains information on the federal state (for example, Baden-Württemberg or Bavaria), administrative region (for example, Kassel) and district (for example, Oberbergischer Kreis or Olpe) in which the municipality is located. The structure of the AGS is shown in
Figure 3.
To correctly distribute the load over the municipalities, national gross domestic product (GDP) is a good indicator that is also commonly used in the literature [
39]. From 1990 to 2012, a linear correlation between GDP and electricity consumption with a correlation coefficient of 0.91 can be discerned [
40].
Due to the fact that GDP is only provided for each administrative district, it must be calculated for each municipality. By simplification, GDP correlates with the population in each municipality, meaning that we can divide the district-level GDP by the number of inhabitants of the district. This simplification leads to a different load compared to the real one in municipalities with a higher GDP compared to the average load on the district level and vice versa.
The population of each district can be generated using the district’s aggregated municipalities: Pop = population, Dis = district, Mun = municipality; x
ij = 1 if municipality j is in district i, otherwise x
ij = 0:
By dividing the GDP of the district by its population:
the GDP for each inhabitant in the district is thereby generated. Now, the GDP per municipality can be calculated as:
When the GDP is known for each municipality, the load of each TSO’s region can be transferred from the TSO- to the municipalities-level. The GDP of all municipalities in the TSO area must be aggregated using y
TSO,j = 1 if municipality j is in the TSO area, otherwise y
TSO,j = 0.
Now, for each municipality, an individual load factor can be calculated. This load factor represents the load share of the municipality in the overall load from the TSO:
3.2. Adjustment of Load Factors
The load factors can be used to visualize the related electrical load in each municipality for each period of time, as shown in
Figure 4 for the highest (a) and lowest (b) loads recorded in 2013. To show this value at an hourly resolution, the four quarterly-hour values in this hour were summarized.
Figure 4 also shows the major load consumption in the large cities of Berlin ((a) 2701 MW, (b) 1402 MW), Hamburg ((a) 2496 MW, (b) 1296 MW), Munich ((a) 2112 MW, (b) 330 MW) and Stuttgart ((a) 1016 MW, (b) 453 MW). Heavy industry, shown as a high load, in the states of North Rhine-Westphalia (NRW) and Saarland can also be seen. The average load in NRW of ((a) 48.6 MW per municipality and (b) 23.3 MW per municipality) is higher than the German average load per municipality in both cases, namely 6.71 MW (a) and 2.62 MW (b).
To validate the model with existing data at the same resolution was not possible due to the non-existing data. Especially at the distribution level, detailed knowledge of the load is missing. Therefore, to validate the model’s results, the loads it depicts are compared with consumption drawn from statistical data. Due to the fact that statistical data on consumption are only available at the state level and only for a period of one year, the load for each municipality was aggregated at the state level.
Table 3 shows the difference between the modeled data and that from the statistics for 2010. In 10 of the 16 states, the maximum consumption difference was about 15%. To reduce errors, the load factors were adjusted.
The borders of the states do not necessarily correspond to the borders of the TSOs. Therefore, each state is assigned one or more TSO and its specific share. The shares of the four TSOs in each state were investigated using master data (“Anlagenstammdaten”) from the TSOs.
These master data contain information on nearly all renewable energy sources (RES) in Germany. In addition to other information, the location, state, municipality and TSO are included in these master data. Hence, each municipality with RES can be associated with the corresponding TSO. Municipalities with no RES are associated with the TSO nearest to the municipality. To calculate the share of the TSO in each state, the population of the municipality was divided by the population falling under the TSO. Thus, the population was used instead of the area. In this way, areas with no population, for example forests, were excluded. The results are shown in
Table 4. Berlin, Brandenburg, Hamburg, Mecklenburg-Western Pomerania, Saxony and Thuringia are in the area of 50 Hertz. In contrast, Amprion, TenneT and TransnetBW hold a share in Baden-Württemberg.
The share of each TSO in the states, as shown in
Table 4, the statistical consumption data in
Table 3 and the load values in
Table 5 can now be used to calculate the share of each TSO and each state from the statistical data:
The load value of the TSO must then be divided by 4, as it is the sum of quarterly-hour values.
Optimally, the sum of the shares of each TSO should be 100% for the quotient of statistical data of consumption and load value. However, the “real” statistical data shares of 50 Hertz, TenneT and TransnetBW (see
Table 6) actually add up to 101.4%, 116.5% and 115.1%, respectively. These values are therefore too high, while the share of Amprion, at 95.94%, is too low. These deviations result from the different values for aggregated load and consumption (see
Table 3 and
Table 5), yet the statistical consumption was 5% higher than the modeled data. To counteract this problem, the statistical data was normalized as follows:
The result is shown in
Table 6, in the column labeled “real normed”. In order to compare the modeled and real normed data, the variance between them is calculated in
Table 6. For example, according to statistical data, the share of 50 Hertz in Berlin is 14.23%. According to the real normalized, this share is 14.03%, which is 6.96% lower than the modeled data, at 20.99%.
The adjustment factor is:
Table 7 shows the factors calculated for each state. To generate the adjusted load factor, the normal load factor was multiplied by the adjustment factors from
Table 7. The computational steps are now explained using the example of 50 Hertz and Berlin. The “Real
TSO,State” was determined by multiplying the share value of 50 Hertz in Berlin, taken from
Table 4, by the quotient of the consumption data for Berlin, taken from
Table 3, “Consumption statistic data”, divided by the aggregated load of “50 Hertz”, taken from
Table 5. In other words:
This calculation was performed for every state and TSO. Then, the values for “Real
TSO,State” were added up for each TSO. The sums for each TSO are given in the last row of
Table 6 in the column, “Real”. The “Real
TSO,State” values can be normalized with these sums:
The adjustment factor for Berlin can then be calculated using the values in
Table 6 in the columns “Real normalized” and “Model”. The adjustment factor is given in
Table 7.
Due to the fact that the load from the TSOs only covers about 91% of the total load (compare
Table 2), an additional steady load will in the end be applied to the model according to the methodology from Agora Energiewende ([
57], p. 5). For the year 2013 this steady load is for example 7.4 GW, which will be divided up by the average of the yearly load to the load at the municipality level.