*4.2. Results*

Computer simulations under different operating conditions were carried out using *Matlab-Simulink* environment to evaluate the suitability of both additional control actions counteracting frequency deviations: (i) Two different step load disturbances were considered for Control Area 1

(CA-1), Δ*PL*1 = 0.05 and 0.075 pu; both imbalances remained for 10 min and they were scheduled to disappear after these 10 min of simulation. Control Area 2 remained under balance conditions and non-additional frequency excursions from CA-2 were included in the simulation scenarios. According to the Spanish TSO, different severe situations were collected during the last decade that are in line with the proposed scenarios. Some imbalances were due to wind power curtailments and wind speed oscillations, such as −1.547 MW/min for a 10 min time interval (28 February 2014). Other imbalances were due to special situations, for example a decreasing of 2000 MW for 15 min (3 December 2007) accounting for more than 10% of the power demand. (ii) Different values of the virtual inertia *k*WFs-factor were also applied: *k*WFs = 0, 5 and 10. The analysis thus focused on responses under relevant imbalances in one control area, being frequency response under normal operation conditions out of the scope of this paper. A recent discussion including normal operation analysis can be found in [63].

Figure 8 shows the additional wind power contribution to the power system submitted to an under-frequency excursion. The virtual frequency controller made the WTs behave similarly to a conventional synchronous generator during the event, injecting a temporary extra power into the grid. As can be seen, larger *k*WFs-factor values implied higher amounts of additional power provided by the WTs. Nevertheless, *k*WFs-factor values had to be within a range of active power temporarily achievable by the WTs according to different constraints. Indeed, excessive *k*WFs-factor values might lead to additional power values not allowed to be provided by the WTs. Therefore, the *k*WFs-factor selection process can be considered as a trade-off between an additional inertia provided by the wind resource, i.e., an additional power injected into the power system, and the WT rotational speed deceleration. Contributions focused on low inertia system operation and the relevance of wind turbines to mitigate frequency deviations can be found in [64,65] and in [66] for isolated power systems.

**Figure 8.** VSWT responses under frequency excursion for different values of the virtual inertia factor (*k*WFs) and Δ*PL*1 = 0.05.

Figure 9 shows the CA-1 frequency response when demand-side contribution to frequency control was applied (or not), i.e., Δ*PDS* = 0 and Δ*PDS* = 0, for a series of virtual inertia factor values (*k*WFs). Results with Δ*PDS* = 0 correspond to simulations where the proposed demand-response frequency control was implemented under different inertia factor values, being *k*WFs = 0 a scenario where only demand-response was included. According to these results, the maximum value for under-frequency deviation was significantly reduced by 16.6% when only demand-response was considered (Δ*PDS* = 0, *kWFs* = 0). With regard to virtual inertia factors, larger *kWFs*-factors implied smaller RoCoF values, as a consequence of the additional inertia provided by the WTs to the power system. In this way, decreases of 22.5% and 23.2% were obtained for *kWFs* = 5 and 10, respectively, in comparison to other scenarios without demand-side and WT contribution (Δ*PDS* = 0, *kWFs* = 0). These aforementioned reduction percentages, i.e., 16.6%, 22.5% and 23.2%, corresponded to a participation share of the controlled load from 40.5% to 44.6%, based on the total available controllable loads. As introduced in Section 3.2, this percentage of controllable loads varied gradually depending on the severity of the frequency excursion to avoid over-frequency values. In terms of the supply-side frequency response, Figure 10 compares the extra power provided by the CA-1 conventional generating units during the frequency excursion for the different scenarios. This additional active power delivered by conventional generation was significantly reduced when demand and WT frequency response were considered, i.e., maximum peak value was reduced from 0.092 to 0.076 pu. Therefore, this reduction in active power was significant for the presence of demand-side response Δ*PDS* = 0. Additional benefits from virtual inertia factor values (*kWFs* = 0) could be achieved by including WT frequency control. This last benefit depended on the wind power capacity considered in the proposed power system. Nevertheless, larger *kWFs*-factor also reduced the power reserves from the conventional generation units.

**Figure 9.** Grid frequency variation for CA-1 (Δ*f*1) and Δ*PL*1 = 0.05. Comparison of conventional power plant frequency response (Δ*PDS* = 0, *k*WFs = 0.) vs. demand-side (Δ*PDS* = 0) and VSWT contribution (*k*WFs = 0).

**Figure 10.** Conventional generation response for CA-1 (Δ*PG*1) and Δ*PL*1 = 0.05.

With regard to the response of the demand-side frequency control, the participation of the controlled load was linearly distributed from the beginning of the frequency excursion to 10 min. The load controller actions were then spread out along the time of simulation, i.e., 10 min after the disturbance, secondary control response of the controlled load was fully activated. Figure 11

summarizes the contribution to PFC from the controllable loads, Δ*P PFC DS* , for the different simulated scenarios. In line with the proposed load controller described in Section 2.3 (see Figure 4), the demand response was proportional to the frequency excursion, emulating the natural response of conventional generation units. It is worth pointing out that the demand-side contribution to PFC proportionally disappeared with the frequency deviation, as primary response was progressively replaced by the contribution of demand-side to SFC. Figure 12 shows the controlled load responses for the different frequency excursions as regards demand-side contribution to SFC, Δ*P SFC DS* according to Section 3. Consequently, SFC of controllable loads was implemented by introducing modifications in their thermostat set-point values through Equation (5). Controlled load thermostats were then readjusted, recovering progressively their initial temperature set point values. Figure 13 shows a box-plot of the temperature refrigerator set points, i.e., *Load Group I*, aiming to demonstrate that the temperature variation remained within acceptable limits during the secondary frequency control load participation.

**Figure 11.** PFC response of controlled loads (Δ*P PFC DS* ) when applied to CA-1 and for Δ*PL*1 = 0.05.

**Figure 12.** SFC response of controlled loads (Δ*P SFC DS* ) when applied to CA-1 and for Δ*PL*1 = 0.05.

**Figure 13.** Temperature set point variation for *Load Group I*.
