# VPP Participation in the FCR Cooperation Considering Opportunity Costs
## 2 Methodology
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Symbol** & **Type** & **Meaning** \\ \hline \(CBMP_{c}\) & Input & Cross-border marginal price \\ \(D_{c,t}\) & Input & Inelastic demand bid of \(TSO_{c}\) \\ \(G_{c,t}\) & Input & Generation from VRESs \\ \(DH_{c,t}\) & Input & Demand from HEs \\ \(DN\_en_{c,t}\) & Input & Energy activated by the downward FCR \\ \(UP\_en_{c,t}\) & Input & Energy activated by the upward FCR \\ \(EMF_{c,t}\) & Input & Average day-ahead energy market price during the hours of the tender \(t\) \\ \hline \(HMin\) & \(udv\) & Value below which \(DH_{c,t}\) is null \\ \(HMax\) & \(udv\) & Value above which HE demands its nominal power \\ \(VGS_{c}\) & \(udv\) & Percentage of the \(G_{c,t}\) contracted by the VPP \\ \(RGS_{c}\) & \(udv\) & Percentage of the \(VGS_{c}\) that can be offered as reserve \\ \(PN_{c}\) & \(udv\) & Aggregated nominal power of _on-grid_ HEs \\ \(RDS_{c}\) & \(udv\) & Percentage of the \(DH_{c,t}\) that can be offered as reserve \\ \(PPAP\) & \(udv\) & Power purchase agreement price (for HEs) \\ \(Ef\) & \(udv\) & Efficiency of HE conversion (energy to hydrogen) \\ \hline \(DN_{c,t}\) & Output & Downward reserve bid capacity \\ \(UP_{c,t}\) & Output & Upward reserve bid capacity \\ \(B_{c,t}\) & Output & Submitted VPP bid in the market session \\ \(VPR_{c,t}\) & Output & VPP potential revenue in the market session \\ \(DN\_OPC_{c,t}\) & Output & Downward opportunity cost \\ \(CAE_{c,t}\) & Output & Cost of avoided energy (not consumed by HEs due to \\  & & energy activated by the upward FCR) \\ \(NPH_{c,t}\) & Output & Non-produced hydrogen due to \\  & & energy activated by the upward FCR \\ \(UP\_OPC_{c,t}\) & Output & Upward opportunity cost \\ \(Dec_{c,t}\) & Output & VPP’s decision to participate in tender \(t\) \\ \(VR_{c,t}\) & Output & VPP revenue in the market session \\ \(UPRS_{c,t}\) & Output & Upward VPP participants’ revenue share \\ \(DNRS_{c,t}\) & Output & Downward VPP participants’ revenue share \\ \(VRS_{c,t}\) & Output & VPP’s revenue share after discounting opportunity costs \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model inputs, user-defined variables (\(udvs\)), and outputs. \(D_{c,t}\) was 380 MW in Spain and 50 MW in Portugal as in 2021 [21]. \(DH_{c,t}\) was obtained from Equation (1) and depended on the inputs and user-defined variables. The information related to FCR Cooperation (\(CBMP\)) spanning the period from 1 July 2020 to 31 December 2022 was acquired from [22]. Data preceding this date, which involved a single daily tender, was excluded, as it was deemed less suitable for a VPP. VPPs require greater granularity in bids due to the substantial variability in renewable energy generation throughout the day. The initial data cleansing step involved eliminating the second tender. The decision to remove these 121 data points was based on the consideration that only certain TSOs participate in such tenders. Furthermore, data from certain instances where a TSO did not submit demand bids were excluded. Specifically, during the period from 27 June 2022 to 30 June 2022, discrepancies were observed in the data, as most countries seemed to be importing their entire demand without other countries compensating for this. Following the data-cleansing process, there remained 5455 data points. The information pertaining to wind and solar generation (\(G_{c,t}\)) was acquired from [16]. The acquired values were provided at an hourly resolution. In order to align with the market data, it was imperative to resample the data to a 4 h time-step while preserving the lowest value in the series to ensure the activation of the bid in the worst-case scenario. The progression of the monthly average CBMP is depicted in Figure 8. Notably, in the year 2021, the CBMP experienced a nearly tenfold increase. As the TSO demand is inelastic, this implies that the aggregated BSP revenues inevitably escalated in tandem with this proportion.