# VPP Participation in the FCR Cooperation Considering Opportunity Costs
## 2 Methodology
### Assumptions and Limitations  
An assumption was made that Portugal and Spain were in balance, with no imports or exports. Note that the remaining countries had imports and exports based on the available data, and the local marginal prices (LMPs) may differ from CBMP in these cases; however, such variations did not impact the calculations in this study.  
Following the market rules outlined in Section 1.1, under these circumstances, either of these countries hit the _core_ and _export_ constraints, and their local marginal prices aligned with \(CBMP_{t}\).  
Naturally, if it was the case that Portugal and Spain were exporting and hitting the \"export limit\" constraint in a given period, LMPs would be lower than the assumed CBMPs and the TSO costs would also be lower. But since there are no FCR market data in the past for Portugal and Spain, making a different assumption from the one that was made is intrinsically difficult. Note that this also impacts BSPs: Equation (5) stated that BSPs profits are also proportional to the LMP; therefore, if the tendency would be that BSPs from Portugal and Spain to have consistent scarcity of bids, the VPP would have higher revenues than analyzed in the remainder of this study; conversely, if abundance was the rule, lower profits would be achieved. Another important limitation was the assumption that the CBMP is known in advance; naturally, the VPP would have to forecast it, compute opportunity costs based on forecasts, and decide to participate or not in the market sessions.  
Further limitations existed relative to the VPP, as follows. The first one was related to the the assumption that in the day ahead, the energy that will be demanded by the HEs is known in advance. Note that this value is proportional to the generation from solar and wind at the national level, which nowadays can be predicted with somewhat good accuracy in the day ahead. The lowest value of the four hours (duration of FCR product) of renewable generation is chosen in the proposed methodology (see \(VGS_{c,t}\) in the methodology); therefore, it could be said that the HE demand, and hence, the bid size, is conservative. Another limitation was that there was a single VPP operating in each country. It is well known that increasing market competition drives down profit margins, but the investigation of multiple VPPs lay outside the scope of this study.  
It was also assumed that the FCR upward and downward energy activations (\(UP\_en_{c,t}\) and \(DN\_en_{c,t}\)) were known in advance; this directly influenced the computation of opportunity costs. Although, as stated, it is known that these values are, on average, 10% (Figure 6), the VPP would probably incur higher opportunity costs in some periods and less in others than what was computed, but this value cannot be accurately forecasted in the day ahead in any sense since this depends on imbalances occurring in real time. Also, the market price for hydrogen was assumed to be known and static.  
All the presented limitations in this section would contribute, most likely, to the VPP bids being submitted more cautiously than anticipated in the remainder of the study.