# VPP Participation in the FCR Cooperation Considering Opportunity Costs
## 2 Methodology  
The methodology is represented Figure 7. The main aim was to compute the VPP revenues obtained by participating in the FCR Cooperation and taking into account the opportunity costs of solar, wind, and HEs. This was done by changing a set of user-defined variables. As earlier mentioned, the present study represents an expansion of a previous study [14], where only part 1 of the methodology was applied and opportunity costs were not included. The model presented in this section uses a set of parameters and user-defined variables outlined in Table 1. The model's implementation is available in a downloadable spreadsheet on the Zenodo platform [15]. The set \(t\) represents the tender (or market session) number, ranging from 1 to 5460, while set \(c\) refers to the country (Portugal, Spain). Although this study only focused on two countries, it could be readily extended to explore additional countries, offering a platform for investigating further integration within the FCR Cooperation. Each tender (\(t\)) in the FCR Cooperation spanned a duration of four hours, serving as the time-step for the model. The approach can be outlined through the following parts and steps:  
**Part 1--Without opportunity costs:** VPP potential revenues were computed in this first part. In [14], this part of the methodology was addressed in detail. The VPP _potential_ revenues were computed by considering that the VPP operated at zero opportunity costs in order to assess what revenue the VPP would have in the tender, disregarding the costs it needs to pay in order to attract HE, wind, and solar plants in the FCR market participation. * **Wind and solar generation time series--**The wind and solar production taking place in period \(t\) in country \(c\), denoted as \(G_{c,t}\), was presumed to be known and is provided here as a parameter. * **HE demand--**The demand of HEs (\(DH_{c,t}\)) was likewise treated as a parameter that was dependent on the parameter \(G_{c,t}\). Specifically, it is zero when \(G_{c,t}\) is below the user-defined variable \(HMin\). Subsequently, it increases linearly until it reaches the installed HE installed capacity (\(PN_{c}\)) when \(G_{c,t}\) surpasses the user-defined variable \(HMax\), as outlined in Equation (1). The intuition for \(HMin\) and \(HMax\) is the following:  
Figure 7: Methodology. if in a given hour, the renewable energy generation is small, no hydrogen is generated, and if there is a high renewable energy generation, the hydrogen electrolyzers work at full capacity. This is in line with the strategic objectives of the European Commission in ensuring that the hydrogen generated with grid connected electrolyzers work more during hours with more renewable generation. As for the values of \(Hmin\) and \(Hmax\), they were found after analyzing the time series for renewable energy generation in each country and adjusting Hmin and Hmax such that the capacity factors of HEs (Tables A1 and A2) would be at least 50%. * **VPP downward capacity**--The share of downward reserve that can be supplied by solar and wind power under the VPP, which is denoted as \(DN_{c,t}\), was determined by the product of \(G_{c,t}\) and two coefficients. The first coefficient, i.e., \(VGS_{c}\), signifies the proportion of solar and wind units contracted by the VPP (e.g., 1% of the total solar and wind units). The second coefficient, i.e., \(RGS_{c}\), represents the reserve margin for which these units are available for FCR provision (e.g., 5%, ensuring that a minimum of 95% of the generated power at any given moment is reserved for the energy market). This relationship is expressed in Equation (2). * **VPP upward capacity**--The share of upward reserve that can be supplied by the HEs under contract with the VPP, which is denoted as \(UP_{c,t}\), was determined by the product of \(DH_{c,t}\) and \(RDS_{c}\). Similar to \(RGS_{c}\), \(RDS_{c}\) signifies the reserve margin, representing the availability of these units for FCR provision. This relationship is expressed in Equation (3).