# Multi-Timescale Control of Variable-Speed Wind Turbine for Inertia Provision
## 1 Introduction
This is because the significant mechanical energy stored in the rotor can be temporarily released to respond to a power grid frequency event. The earlier application can be traced back to the wind turbine system in the Hydro-Quebec system, as well as that in Ontario [21]. For the normal stage, the wind turbine operates at the maximum power point (MPP). When a grid-frequency drop is detected, the reference power of the wind turbine is increased by 5-10% to provide active power support. After a certain amount of time, the wind turbine decreases its output power reference by 30% until the rotor speed is gradually recovered. Similar techniques have also been reported in recent publications. In [22], a supplementary electromagnetic torque component proportionally linked with the grid RoCoF was included to achieve the desired inertia emulation. In [23; 24], a high-pass filter was implemented to avoid the high-frequency noise amplification concern. In [25], the dynamics between a type 3 wind turbine and the SG were compared. On this basis, the phase motion of the SG was reconstructed in a wind turbine system to enable the inertia function. In [26], frequency droop control was implemented as an alternative for a synthetic inertia strategy through control parameter optimization. Moreover, in [27], a cascaded control structure was proposed to regulate DC-link energy and subsequently control the rotor kinetic energy to support the grid frequency, which minimizes the impacts on wind energy harvesting. In addition to this, the inertia provision function of a doubly fed induction generator (DFIG) unit was enabled by rotor current control and optimized through status assessment in [28]. In [29], a power management strategy was developed that blends the energy stored in the high-voltage direct current (HVDC) link and the energy of a wind turbine to provide quick frequency responses. Consequently, the power capability requirement of wind turbines can be relieved. The common principle behind these proposals is to link the power grid frequency (or the RoCoF) with the rotor speed (or the electromagnetic torque) of the wind turbine. It should be mentioned that the wind turbine needs to recover after the settling of a frequency event (i.e., post-event operation). However, the speed recovery process can significantly affect the inertia-provision effect if it is not properly designed [30]. It is likely that a subsequent frequency drop, as the second frequency event, will occur due to the interaction between speed recovery control and inertia control [2]. For the worst scenarios, the coupling between inertia provision and the dynamic characteristic of a wind turbine system may even affect the small-signal stability of the entire power system and lead to power oscillations [31; 32]. To address this problem, a multi-timescale control scheme for inertia provision of a DFIG wind conversion system is proposed in this paper. A schematic diagram of the DFIG power conversion system is shown in Figure 1. By properly selecting the rotor-side converter (RSC) control parameters, the dynamics of inertia control and those of speed recovery control can be decoupled in the frequency domain to avoid control conflict. As a benefit, inertia provision, as well as speed recovery objectives, can be simultaneously achieved. Compared to prior-art approaches, the contributions of this paper are summarized as:  
1. Revealing the coupling effect between virtual inertia control and speed recovery control of the wind energy conversion system with an investigation of the corresponding impact on the performance of RoCoF suppression;
2. Decoupling of rotor speed recovery control and inertia control into different timescales; as a result, the inertia provision and speedy post-event recovery objectives can be simultaneously achieved;
3. Designing a noise-free approach to acquire the real-time grid RoCoF, the response time of which is less than 0.1 s;
4. Conducting simulations to verify the theoretical analysis and control performance.