## 1 Introduction
[39] propose a fuzzy controller for the allocation of the fast-varying power reference to individual units in a group of BESS stations, based on techno-economic criteria. Although effective, these methods do not facilitate storage participation in aFRR economic scheduling on equal terms with conventional units. In [40], the proposed AGC scheme allocates BESS capacity to secondary frequency regulation, also considering their minute-level charge/discharge capability. [PERSON] et al. [40] note that distributing the AGC regulation signal to participating units based on pre-defined fixed allocation percentages is ineffective when BESSs are participating in secondary frequency regulation due to SOC management limitations. [PERSON] et al. [41] propose a BESS control strategy reducing the rate of non-compliance to AGC signals in a regulation area. A similar SOC regulation method is also used in [38; 42]. In all three papers, BESS charge/discharge is restricted, once energy reserves in the batteries reach their minimum/maximum limits. A \"conditional neutrality controller\" is applied by PJM, to restore the energy reserves of storage units, estimating SOC based on the timeseries of commands dispatched to the units and applying proportional SOC control, whose gain is adjusted depending on the SOC level [10]. The resulting SOC regulation term modulates the reference point of conventional resources [10]. In [43; 44], an LFC scheme is presented where battery systems compensate for the low ramping capabilities of conventional units through a continuously active battery SOC controller, regulating battery output in parallel to the AGC. References [45; 46] study the participation of storage in standard LFC schemes, with the latter proposing an adjustment of the ESS setpoint every 15-60 min, according to the energy injected/absorbed. However, such a SOC regulation method does not consider the effect that ESS setpoint variations may have on system reserves; this factor is taken into account to a certain extent in [47], where the BESS active power reference is given by the superposition of a frequency containment reserve (FCR) term and an appropriately capped charging/discharging reference (e.g., at 20% of rated capacity). The negative impact on frequency regulation when an ESS participating in LFC reaches its SOC limits is noted in [35], indicating the need to consider SOC regulation under such circumstances, which needs to be incorporated in the central AGC system to avoid a detrimental effect on frequency stability. [PERSON] et al. [48] propose a hierarchical control for isolated systems dominated by ESSs, where multiple battery systems participate in isochronous frequency control, while diesel units do not participate in LFC, but regulate the SOC of the storage units. A similar approach is described in [49], where a BESS operates in grid-forming mode, thus completely taking up system power equilibrium maintenance, with its SOC regulation being performed by a diesel generator. Both [50] and [51] deal with the support that an ESS system can provide to RESs participating in reserve provision. [PERSON] et al. [50] propose a fuzzy control method for a BESS to support participation of photovoltaics (PVs) in LFC, without, however, addressing SOC regulation, whereas the support of a wind farm in the provision of frequency-related reserves is addressed in [51], also applying an adaptive state-of-charge regulation scheme. In [52], BESSs provide solely secondary frequency regulation, via a fuzzy logic controller regulating energy reserves when frequency is near its nominal value. However, the SOC restoration consumes secondary reserves provided by other units. [PERSON] et al. [53] propose a control scheme for an isolated AC-DC microgrid, in which a fuzzy-logic controller is regulating BESS power output, taking account of their SOC and the power deficit/surplus of each microgrid.