4. Homotop´ıa 78
4.3. El grupo fundamental y las funciones
4.3.2. Retracciones y retractos
Optimal DER Capacities
For each permutation of tariff, export, and load input scenarios, a DER-CAM optimization was run to determine the optimal PV and storage capacities subject to all EcoBlock constraints. The optimal capacities from each run are shown in Figure 3-26. Optimal PV capacity (in kilowatts) is shown in orange, and optimal storage capacity (in kilowatt-hours) is shown in blue. Each
column of subplots shows a different tariff scenario, while each row of plots shows a different export scenario.
Figure 3-26: Optimal DER Capacities for Each Tariff, Export, EV, and Equipment Retrofit Scenarios
As determined by DER-CAM optimization Source: UC Berkeley
As these plots show, optimal DER capacities are not highly sensitive to the modeled tariffs (i.e., capacities do no change much column to column), nor to EV fleet size (i.e., plot lines are
generally flat). In nearly every modeled scenario, the optimal number of flywheels is three (480 kWh). Given the discrete adoption constraints of storage, this is not unexpected. Optimal PV capacity, which can vary continuously, is generally between 200 and 300 kWh. Optimal PV capacity increases slightly as EV fleet size grows. It is also slightly higher for retrofit load Scenario 1 than for Scenario 2.
The largest impact on optimal DER capacities appears to come from the export scenario, and mostly affects PV capacity. For the low-price LMP scenario, the value of exported PV generation is reduced, so capacities are smaller. For CCA wholesale scenarios with prices between $50–
$80/MWh, optimal capacities do not vary significantly. However, when the wholesale price exceeds $90/MWh, the optimal PV capacity becomes the maximum allowed (500 kW). For prices below this, DER-CAM selected a capacity that reduces retail purchases and uses storage/export to manage midday over-generation. When prices exceed $90/MWh, revenue from export alone is a strong enough incentive to drive increased investment in PV capacity.
Optimal Dispatch Profiles
Given significant differences in input values, it may be surprising that optimal DER capacities appear to change very little between scenarios. To understand the underlying reasons for this, it is helpful to inspect the hourly dispatch profiles for select days. A small subset of results is presented below to explore variations in each parameter. Hourly time series plots were
generated for either energy supply or consumption within the EcoBlock. An example of these time series plots is given in Figure 3-27, which shows both energy supply (or “provision”) and consumption under the “most likely” reference case for typical weekdays during a month in each season of the year. Energy supply plots show the source of energy at each hour (with the abbreviated label in the legend of Figure 3-27): utility purchases (utilPurch), PV generation (PVpotential), battery discharging (batteryOutput), or EV discharging (EVdischarging). For this analysis, V2G discharging is not permitted. Energy consumption plots show the energy sink at each hour: building load (totalLoad), battery charging (batteryInput), EV charging (EVcharging), PV export to the grid (PVexport), and PV curtailment (PVcurtail). The last of these is PV energy that cannot be used locally nor exported.
Figure 3-27: Energy Provision and Consumption Profiles for the “Most Likely” Input Scenario
Note: utilPurch = utility purchases, Pvpotential = PV generation, batteryOutput = battery discharging, Evdischarging = EV discharging, totalLoad = building load, batteryInput = battery charging, Evcharging = EV charging, Pvexport = PV export to the grid, and Pvcurtail
= PV curtailment.
A-10 tariff, $70/MWh export, 24 EVs, load retrofit Scenario 1.
Source: UC Berkeley
Figure 3-27 also includes a state-of-charge (SOC) profile for the flywheel during each of these days. SOC profiles are generally consistent across each scenario: storage is empty around morning, when it is charged with excess PV generation until it is full or nearly full by mid-afternoon. Storage is then discharged to meet some or all building and EV loads in the evening and overnight, returning to empty by mid-morning. Given the consistency in this pattern across input scenarios, additional SOC profile plots are not included in this section.
Input 1: Tariff
Across each tariff scenario, optimal PV capacity does not change significantly: 227 kW for the flat E-1 tariff, 220 kW for the residential TOU E-6 tariff, and 217 kW for the commercial TOU A-10 tariff. It appears there is some relationship between average energy rates and PV capacity;
however, the time-variable rates of the E-6 and A-10 tariffs complicate this assessment. Optimal storage capacity remains a uniform 480 kWh across tariff scenarios. Figure 3-28 shows energy provision profiles for each tariff. Note that all other inputs remain the same as the “most-likely”
case outlined above.
Figure 3-28: Hourly Energy Provision Profiles for Each Modeled Tariff
Source: UC Berkeley
Examining these profiles shows the key differences in behavior between tariff scenarios, particularly related to when and how the EcoBlock purchases energy from the utility. In all scenarios, PV generation is adequate to meet all local loads during the middle of the day (“on-peak” hours for TOU tariffs). However, the presence of demand charges in the A-10 scenario (subplot c) drives the model to purchase electricity at a consistent, low level. Without this driver in the other scenarios, purchase spikes are observed late in the evening to charge EVs. In the A-10 case, EV charging is better distributed throughout the day. Storage is discharged to meet some off-peak loads during winter and nearly all off-peak loads during summer (when
generation is high and loads are low).
Input 2: Electric Vehicles
Figure 3-29 shows hourly consumption profiles for EV scenarios with fleets of 8 (a), 16 (b), and 24 (c) vehicles. Varying fleet size across these scenarios does not impact optimal storage, and only slightly impacts optimal PV (8 EVs: 197 kW; 16 EVs: 208 kW; 24 EVs: 217 kW). The possible relationship between fleet size and PV capacity makes sense, as a larger fleet introduces larger charging loads. However, under the assumed usage patterns, charging for 24 EVs comprises only 20 percent of total consumption. This is evident in Figure 3-29, where the EV charging portion of the consumption plots changes between scenarios, and the changes are small relative to the building load profiles. Reducing the number of EVs to 8 represents about a 12 percent reduction in total consumption, and achieves a 9 percent reduction in optimal PV capacity.
Given the relative size of the building loads to the EV fleet considered, changes to EV charging appear to have only small impacts on the larger system performance.
Figure 3-29: Hourly Energy Consumption Profiles for Each Modeled EV Fleet
Source: UC Berkeley
Input 3: PV Export
Figure 3-30 shows that the sizing decision within Oakland EcoBlock appears to be most
sensitive to changes in the export scenario. This make sense, as changes to how PV exports are compensated and how much they are compensated will significantly impact the economically optimal PV capacity. Figure 3-26 shows the energy consumption profiles for a subset of the modeled export scenarios: NEM, and CCA models with prices of LMP (i.e., real-time marginal prices) and flat prices of $50, $80, or $90 per MWh.
Again, across each of these scenarios, the optimal storage capacity is 480 kWh. The PV capacities vary substantially across export scenarios. As stated earlier, PV capacity is selected as the maximum allowed when the wholesale price of PV export is sufficiently high, and thus is 500 kW in the $90 and $100 scenarios. PV capacity is also high under the NEM scenario
(266 kW), because exported energy is compensated at retail prices. Effective NEM export prices are relatively high—$110 to $230 per MWh under the modeled tariffs—compared to CCA scenarios. However NEM exports are limited by total imports, and so an upper bound for economically feasible PV capacity exists below the technically maximum PV capacity that could be hosted at the EcoBlock site.
The capacity for $50–$70 scenarios are very similar (215–217 kW) and slightly higher for the
$80 scenario (245 kW). The LMP PV capacities are considerably lower (193 kW) due to the lower export price. As Figure 3-30 illustrates, the behavior for how PV generation is used does not vary much until export prices in the CCA model exceed a certain threshold. At that point optimal PV is sized almost exclusively to pursue revenue from energy exports, which dominate subplot e.
Figure 3-30: Hourly Energy Consumption Profiles for a Subset of Modeled Export Scenarios
Source: UC Berkeley
Input 4: Residential Retrofits
Figure 3-31 shows the consumption profiles for each load scenario. The deeper retrofits of Scenario 2 produce a much lower overall load profile, and therefore result in a lower optimal PV capacity: 178 kW for Scenario 2 versus 217 kW for Scenario 1. In total, consumption (including
20 percent lower. Scenario 2, consequently, exports a higher fraction of its PV generation under these conditions. There are no other major differences in operation strategies between these load scenarios.
Figure 3-31: Hourly Energy Consumption Profiles for Load Scenarios
1 (standard retrofit) and 2 (deep retrofit).
Source: UC Berkeley
One significant difference due to load scenarios occurs under the NEM export scenario. Recall that under NEM, total energy exports cannot exceed total purchases per annum. Because total load (and therefore potential purchases) under load Scenario 2 are 40 percent lower than they are for Scenario 1, the opportunity for export is also 40 percent lower. Examining the NEM row in Figure 3-26, the optimal PV capacities for Scenario 2 are commensurately lower, given this constraint. Additional PV generation in this scenario could not be exported under the NEM rules (as defined in this analysis), and therefore would need to be curtailed. This obviously
suboptimal behavior tightly constrains PV adoption in this case.
EcoBlock DER Capacity Selection
The analysis above is helpful in selecting a final DER portfolio that performs well across all the possible scenarios. Storage selection presents a simple decision: in nearly every scenario the DER-CAM optimization selected a 480 kWh system. Storage appears to be sized to allow for loads to be served by PV generation during off-peak evening and overnight hours. Only in some cases (see Figure 3-26) does the optimal storage system fall below this level, and only for the deep retrofit load Scenario 2.
Selecting the appropriate capacity for PV presents a more complicated decision, as PV sizes vary between 112 kW and 500 kW in the modeled scenarios. This range can be reduced by excluding some of the less realistic export scenarios. To be conservative, CCA export scenarios with very high prices (i.e., >$80 per MWh) are unlikely to accurately represent the long-term
operational landscape for the Oakland EcoBlock. Without such scenarios, the upper bound is now 275 kW. The lower end of the range corresponds to scenarios with both low load
(Scenario 2) and small EV fleets (8 EVs). If these scenarios are put aside, the median optimal PV capacity across remaining scenarios is 215 kW. Examining the range of optimal systems in Figure 3-26, this appears to be a reasonable selection, given the uncertainty in inputs.