## 1 Introduction
### Inertial Response  
#### 3.2.1 Proposed Definition and Its Justification  
Inertia is an inherent characteristic of SGs due to their rotating masses, which prevents fast frequency variations in the first few cycles after a power imbalance occurs. Inertial response means that a SG is able to inject instantly an additional power to the grid which is proportional to the rate of change of the frequency (ROCOF) sensed at its terminals. This power is extracted, in cases of underfrequency events, by the kinetic energy stored in the rotating masses causing their deceleration. In cases of overfrequency events the reverse is true, i.e., additional kinetic energy is stored causing the rotor acceleration. In the case of single SG, it is more meaningful to express the inertia in terms of the inertia time constant, as follows:  
\[H=\frac{E_{kin}}{S_{N}}=\frac{\frac{1}{2}I\cdot\omega^{2}}{S_{N}} \tag{6}\]  
where, \(H\) (in seconds) is the inertia time constant, \(E_{kin}\) is the stored kinetic energy in the rotating masses with equivalent inertia, \(J\) (in kg\(\cdot\)m\({}^{2}\)) and \(S_{N}\) is the nominal apparent power of the SG. In the same way, the equivalent \(H\) of a large power system can be defined. Using the motion equation of the SG the following expression can be derived in pu:  
\[2H\frac{d\omega}{dt}=p_{m}-p_{e} \tag{7}\]  
where, \(p_{m}\) and \(p_{e}\) are respectively the mechanical and electrical power expressed in pu using \(S_{N}\) as basis. It is evident from (7) that the ROCOF depends on the power imbalance and the inertial constant. Realizing that the displacement of conventional SGs by inertialess DRES will result in increased ROCOF, ENTSO-E [46] suggests that the DRES should provide synthetic inertia and that the various TSOs should evaluate the minimum levels of equivalent \(H\) of their areas that are required to maintain the frequency stability of their system. It is also mentioned in [46] that \"_traditional system inertia for a synchronous generator dominated system is of the order of \(H\)_ = 5-6 \(s\)\", although deviations from these values may exist among the various power system control areas. The provision of synthetic inertia by a converter-interfaced DRES requires an ESS, where the equivalent \"kinetic energy\" will be stored. This ESS is associated with an additional installation, operational and maintenance cost that needs to be compensated. Therefore, synthetic inertia should be treated as a new AS and be remunerated, contrary to the current practice, where it is considered an inherent system support function. However there exist no methods for the measurement and quantification of the inertial response provided artificially, despite the fact that there are various methods to make a converter-interfaced DRES exhibit controllable inertial response [47; 48; 49]. In most of these methods, the converters are controlled as voltage rather than current sources, emulating in this way the behaviour of the conventional SGs. It should be mentioned that methodologies have also been proposed [50; 51; 52] in order to make WECS exhibit virtual inertia exploiting their kinetic energy. In fact, some of them have already been implemented in commercially available WECS [53; 54; 55; 56; 57]. However, this approach is energy-neutral, meaning that the energy provided during the inertial response period is then retrieved back from the grid, a phenomenon that may cause adverse effects to the overall frequency response of the system [58] (e.g., a postponed, but equally deep frequency nadir or the appearance of a second nadir). This approach also provides inertial response that depends on the operating point of the WECS, i.e., the provided inertia is rather stochastic, and it is not fully adjustable [59; 60] and causes additional stress on the mechanical parts of the WECS [59]. For these reasons, we focus on inertial response that is based on voltage-controlled converters and on the incorporation of an additional FSS to provide the required energy.