# VPP Participation in the FCR Cooperation Considering Opportunity Costs
## 2 Methodology
* **Symmetric price-taker bid**--Given that the bids need to be \"symmetric\", meaning that they have the same size of upward and downward capacity, the proposed bid size, which is denoted as \(B_{c,t}\), was determined as the minimum among the upward capacity, downward capacity, and the demand of the TSO (\(D_{c,t}\)), as outlined in Equation (4). The term \"price-taker\" implies that \(B_{c,t}\) is offered at a low price, ensuring its acceptance and payment at the international price \(CBMP_{t}\). * **FCR Cooperation bids**--It was assumed that the existing bids (both demand and supply) from actual market sessions were already known. The value of \(CBMP_{t}\) is the result of these market sessions, and the \"price-taker\" strategy of the VPP does not alter it. This is because, given the balanced state of the country, the international price (CBMP) is already established and known. * **Market outcome**--The VPP potential revenues, i.e., \(VPR_{c,t}\), were computed according to Equation (5). **Part 2--Computing opportunity costs:** These refer to the participation of HE, solar, and wind plants in the FCR. * **FCR downward/upward time series**--The values of energy activated by the downward and upward FCRs in France in the period \(t\), i.e., \(DN\_en_{FR,t}\) and \(UP\_en_{FR,t}\), respectively, were retrieved from [10]. * **Downward/upward energy**--It was assumed that the values of the energy activated by the upward and downward FCR bids, i.e., \(DN\_en_{c,t}\) and \(UP\_en_{c,t}\), respectively, were known and proportional to the ones in France and to the submitted VPP bid capacity \(B_{c,t}\), as per Equations (6) and (7). This means that these values were model inputs, which in reality, would be impossible to forecast, although Figure 6 gives us average and standard deviation values, which would be useful for the VPP bidding strategy. * **Energy market price**--The average energy market price in the period \(t\), i.e., \(EMP_{c,t}\), was assumed to be known and was retrieved from [16]. * **Downward opportunity cost**--\(DN\_OPC_{c,t}\) represents the cost of \(DN\_en_{c,t}\), which is essentially wind and solar energy that is not sold in the energy market due to being reserved for FCR. This potential (\"potential\" because only when the VPP naturally participates in the tender (decided in part 3 of the methodology), does this opportunity cost exist) cost was computed using Equation (8). * **HE power purchase agreement (PPA) price** (\(PP\))--It was assumed that HEs will operate with electricity procured via the PPA instead of the energy market [17]. The levelized cost of energy was assumed to be the low end of values for solar and wind energy found in [18], and thus, the \(PPAP\) was assumed to be 27 EUR/MWh. * **Cost of avoided energy consumption by HE--**The upward energy required by the FCR, i.e., \(UP\_en_{c,t}\), comes from energy not consumed by the HEs. Therefore, the cost of this avoided energy, i.e., \(CAE_{c,t}\), was computed according to Equation (9). * **Amount of non-produced H2--\(NPH\)** was computed according to Equation (10), where the parameter \(Ef\) stands for the efficiency parameter assumed to be 50 kWh/kg [19]. * **Upward opportunity cost--\(UP\_en_{c,t}\)** was computed according to Equation (11). The opportunity cost in this case is the missed opportunity of selling hydrogen that would have otherwise been produced if the HEs would consume \(UP\_en_{c,t}\), discounted by the price that the energy would have cost. \(PH\) here stands for the hydrogen remuneration, which was assumed to be 2.8 EUR/kWh. This value came from the European Commission assessment of the costs of blue hydrogen in 2021 [20]; therefore, here it was assumed that \"green hydrogen\" was remunerated exactly as \"blue hydrogen\" in the hydrogen market instead of somehow being subsidized. * **Sum of opportunity costs--**Upward and downward costs were added, as per Equation (12). **Part 3--Decision:** Here, the decision refers to the VPP participation or not in the FCR Cooperation tender \(t\).