## 1 Introduction
Therefore, on the one hand, TSOs defined additional requirements specifically for assets with limited energy reservoirs to provide FCR, e.g., in Continental Europe and Nordic Synchronous Area they must be able to fully activate FCR continuously (in both positive and negative directions) for at least 15 min (but not exceeding 30 min) [12]. This 15 min criterion is adopted by TSOs to cope with the greatest frequency perturbation. However, even considering the higher frequency deviation occurred in Continental Europe during the last years [13], frequency was restored in less than 8 min. The time elapsed at a deviation equal to or greater than the one required for full activation of provision is even lower. On the other hand, TSOs identify some degrees of freedom (DoF) allowing for BESSs state-of-charge (SoC) management. In the UK, EFR regulation sets a dead-band in which BESS can be freely operated within a \(\pm\)9% range (the maximum export/import power must not exceed 9% of the BESS's full-scale range) [11], this way EFR allows the development of a dead-band strategy for SoC restoration. In addition to the dead-band, a so-called envelope provides flexibility in provision devoted to supporting SoC maintenance. In this envelope, over or under-regulation is permitted. Thus, operators can manage the battery SoC by increasing or decreasing the control power demand indicated by the power-frequency characteristic by a fraction of regulating power. So, in the case of low SoC and frequency above the nominal value, the battery can over-regulate to charge faster and get back to target SoC. In Germany, several degrees of freedom are allowed by the four German TSOs to keep the SoC within the permitted range [14]: in addition to the dead-band strategy, operators can manage the battery SoC by providing over or under-regulation up to 20% of regulating power, adjusting the gradient of the provided FCR power within certain boundaries or trading energy on the electricity market. In Italy, the UPI pilot project, which allows the use of BESSs integrated with conventional relevant units to provide FCR, is underway. During the provision of FCR, the SoC can be restored only by exchanging energy with the integrated programmable plant and not by exchanging energy with the grid [9]. In case SoC diverges, service provision must be interrupted and SoC restored. Other services foresee minimum and maximum SoC thresholds: SoC restoration must operate when SoC gets above the maximum or below the minimum. These thresholds are established based on the requirement of always guaranteeing minimum available energy to activate the service in both upward and downward directions [10]. There is not yet a homogeneous identification of the best DoF for SoC management. In literature, different SoC controllers, aimed at efficiently providing primary frequency control reserve, have been investigated. In [14], a control algorithm that includes the DoF in place in the German market was implemented. It compares the use of dead-band, the exploitation of over-regulation, the use of thresholds for permissible SoC as criteria to implement a restoration strategy. In [15], the reliability in EFR provision is improved by exploiting dead-band strategies for managing SoC. In [16], the possibility of submitting separate bids for positive and negative PCR in Denmark is studied: SoC restoration is provided by forcing battery charge when SoC is below a certain threshold. All these studies present a dedicated energy flow for SoC restoration. Therefore, these strategies can be defined as \"active\" SoC restoration. In active SoC restoration, the dedicated energy flow is usually paid by the asset operator on the electricity market in several forms (e.g., day-ahead or intraday market, imbalance discipline). As previously mentioned, ancillary services (FCR included) are essential for the safe management of the electric system. For this reason, TSOs can ask the BSP not (or partially) correctly providing the required service to pay a penalty.