The results of the microgrid optimization for the reference case show a microgrid energy supply system with electricity supply technologies, PV and CHP, as well as the heat supply technologies, boiler and CHP. The TAC of the considered microgrid energy supply system are 126,475 €/a.
In buildings 2, 3, 4, 5 and 6 (bd2–bd6), the technology system design for the heat supply is similar. A natural gas boiler combined with a heat storage unit is chosen. A PV installation can be found in buildings 1, 2, 3 and 6. The reason for the missing PV in building 4 and 5 is the unfavorable roof orientation.
3.3.3. Investigation of the Supply Technologies
The microgrid optimization with full-time series (reference case), time series aggregation and the 2-Level Approach show the same technology structure. To meet the electricity and heating demand, the microgrid optimization opts for boilers, CHPs, heat storages and PV as supply technologies. The investigation of all installed supply technologies in the district is considered in the following paragraphs.
Boiler: The mean deviation of the 2-Level Approach related to the reference case is low, with a maximum of −4.46 kWth in 40 typical days and a minimum of −0.12 kWth in 5 typical days. In the time series aggregation, the mean deviation decreases from −51.8 kWth in 5 typical days to −17.57 kWth in 40 typical days. Thus, the mean results show a significantly lower deviation in the 2-Level Approach than in the time series aggregation.
shows a positive deviation of installed boiler capacities in the case of 5, 10, 20 and 40 typical days for building 1 (bd 1) in the 2-Level Approach. The reason for this pattern is that the CHP in the reference case is installed in building 1, as shown in Figure 3
, but in the 2-Level Approach, the CHP is installed in other buildings. A negative deviation of installed boiler capacities is observed in the buildings with additional CHP installation, as shown in Figure 6
. Hence, there is a boiler capacity shift based on changing the CHP location. For example, in the 5 typical days case, the boiler capacities decrease in building 3, because the CHP is installed there and, on the other hand, the installed capacities increase in building 1 because of the missing CHP installation in comparison to the reference case.
Moreover, we can observe that the time series aggregation shows a similar pattern to that in the 2-Level-Approach with respect to the CHP-based capacity shifting. The installed capacities increase in building 1 and decrease in the building with the new CHP location. Additionally, there is a trend of high underestimation of boiler capacities in the buildings, which are not part of the changing CHP location. The underestimation of installed capacities decreases with an increasing number of typical days because of more detailed time series data.
As discussed in the previous paragraph, the CHP installation location changes between the reference case and the 2-Level Approach, as well as the time series aggregation (see Figure 7
). In the case of 5 typical days, the installed CHP shifts from building 1 to building 4, while in the case of 10 and 20 typical days, from building 1 to building 6, and in the case of 40 typical days, from building 1 to building 3.
The mean deviation of the installed CHP capacities computed with the 2-Level Approach is 0.02 kWth
for all typical days. The optimization with the time series aggregation results in a minimal deviation of −0.02 kWth
for 5 typical days and a maximum of 0.39 kWth
for 40 typical days. A possible reason for the building shifting the CHP installation between the different typical days is that the difference in the TAC is not significant. Hence, its location does not affect the TAC. A further analysis is performed in order to investigate the TAC in relation to the location of the CHP in Section 3.3.5
Heat Storage: Comparing the heat storage deviations to the reference case shows that the mean error of installed heat storage capacities changes with the increasing number of typical days, from 5.59 kWh to 21.44 kWh, on the back of the 2-Level Approach. The time series aggregation results exhibit the maximum mean deviation in 5 typical days of -32.98 kWh and the lowest mean deviation in the case of 10 typical days, with 0.57 kWh.
As described in the analysis of boilers and CHPs, the heat storage results also show a clear pattern of capacity shifting between the buildings on the different typical days, especially in the 2-Level Approach, as shown in Figure 8
. In the case of 5 and 10 typical days, the installed heat storage capacities decrease in building 1 and increase in building 6, while in the case of 10 and 20 typical days, the installed capacities shift from building 1 to building 6. The possible reason for the same pattern of capacity shifting as in the CHP investigation is that the heat storage supports the operation of the CHP. The electricity generation costs with the CHP are, at 0.26 €/kWh, cheaper than purchasing electricity for 0.2985 €/kWh from the energy provider. Thus, the CHP is preferred by the optimizer to generate electricity, but the thermal energy of the CHP must be used to fulfil the heating demand or store heat in the storage, because an external chiller is not available for the CHP. Hence, the heat storage follows the CHP to buffer excess thermal energy.
The reason for the other typical day’s high deviation of heat storage capacities in 40 typical days is a result of the underestimation of boiler capacities in building 3 for 40 typical days, which does not influence the TAC of the energy supply system.
PV: As well as the 2-Level Approach, the time series aggregation meets the installed PV capacities in the reference case for the different investigated typical periods. Thus, both approaches represent the installed PV capacities very well with no deviation from the reference case.
3.3.4. Investigation of Peak Load
The peak load is the maximum electrical load, which flows over the grid assets. In general, a transformer in a microgrid optimization is the connection between a district and a higher grid level (e.g., between a low voltage and a medium voltage grid). The load flow is divided into two directions: The top-down load flow with the electricity from higher grid level flows via the transformer to fulfil the electricity demand in the district, whereas the bottom-up load flow is defined as the flow from the district (lower) to the higher grid level via the transformer. Bottom-up load flow occurs when the locally produced electricity (e.g., from PV, CHP) exceeds the local electricity demand in the district. The peak load is essential to analyzing the stress of the transformer. Furthermore, voltage issues may become relevant in real grids but are out of scope for this investigation. The peak load investigation is only applied to the electricity grid and not to the natural gas network.
The bottom-up peak load and the top-down peak load of the reference case is very well addressed with the 2-Level Approach, as shown in Figure 9
. The time series aggregation underrepresents the peak load for different typical days. Only in the case of 20 typical days in the bottom-up peak load is the result of the time series aggregation close to the reference case. The result is probably based on a coincidence, as it is worse with 40 typical days.
The reason for the underrepresentation of the bottom-up load and top-down load in the time series aggregation is a missing data problem due to the clustering of time series. An increase of the typical days should tend to lead to a more accurate representation of peak periods with the time series aggregation because of the smaller cluster. Also, it is possible to add peak periods to the time series aggregation, which leads to a more accurate solution. On the other hand, adding peak periods leads to an increase in optimization complexity and increasing computing time due to additional time periods. Hence, the investigation shows that the 2-Level Approach is well suited to represent the bottom-up peak load and top-down peak load while the time series aggregation represents it insufficiently.
3.3.5. Impact Analysis of Fixed CHP Position
The investigation of CHPs in Section 3.3.3
showed that only one CHP was installed in one building in the analyzed microgrid energy supply system, but the building location of the CHP installation changes between the different typical days. In the reference case, the CHP was installed in building 1. In the 2-Level Approach, the CHP was installed in building 4 for 5 typical days, in building 6 for 10 and 20 typical days, respectively, and in building 3 for 40 typical days. To investigate the impact of the changing installed CHP location for different typical days, an analysis was performed. In this analysis, the buildings with the installed CHP were fixed one after another to investigate the deviation of TAC related to the reference case. The results of the analysis are shown in Table 4
. Impact of different fix CHP locations on the TAC. On the one hand, the table shows the location of the fixed installed CHP location in columns and, on the other hand, the deviation of the TAC related to the reference case for 5, 10, 20 and 40 typical days.
The analysis shows that the deviation of the TAC for different fixed CHP locations is low compared to the reference case with 0.013% to 0.151%. The lowest deviation of 0.013% can be reached if the CHP is fixed in building 1, which corresponds to the location of the reference case. The highest deviation of TAC is identifiable for a fixed CHP location in building 2, with 0.151% and 10 typical days. However, in general, all results with the fixed location of the CHP show low deviations compared to the reference case. Therefore, the impact of the different placements of CHPs on the TAC is low.
The next pattern of CHP capacity shifting is shown for different fixed CHP locations. The pattern was seen for 5, 10, 20 and 40 typical days. The arrows in Figure 10
represent the trend of installed capacity shifting for the technologies of boilers and heat storage. A dash indicates no changing of installed capacities in comparison to the reference case.
If the CHP is installed in building 1, which is the location of the reference case, there is no changing with respect to the installed capacities for boilers and heat storage. In the other cases of a fixed CHP location, there is a clear pattern that boiler capacities decrease and heat storage capacities increase in the building of the fixed CHP installation. Furthermore, in building 1, the boiler capacities increase, and the heat storage capacities decrease. The reason for increasing boiler capacities in building 1 is that the thermal capacities of the CHP are missing.