Critical inertia can be defined as the minimum kinetic energy stored in generators that should be kept for maintaining the frequency stability of the power system. As the frequency control performance of the power system is maintained according to its control criterion, during the inertia response time frame, the expected energy imbalance can be calculated by accumulating the imbalanced power caused by the credible contingency and calculating the available inertia response by considering the allowable operating limit of the frequency. Since the frequency control criterion can be met when the available inertia response becomes larger than the expected energy imbalance, the critical inertia can be calculated by the kinetic energy of the generators, of which the available inertia response is equal to the expected energy imbalance due to the contingency. With this in mind, this paper derives the energy balance condition for the frequency stability in the inertia response time frame based on the frequency control criterion and calculates the minimum inertia, which should be kept in the generators from the energy balance condition for meeting the criterion. In addition, the effectiveness of the proposed method is verified through various case studies employing Korean power systems.

For power grids with a high penetration level of wind power generation, stochastic wind speed variation adversely affects the frequency stability. A variable-speed wind turbine generator would deloads its output by shifting the power operating point to provide frequency response. Because the wind speed variation directly affects the calculation of the operating point, difficulties arise in securing a reliable amount of the frequency response. This paper proposes a control scheme of a doubly fed induction generator (DFIG)-based wind generation providing the primary frequency reserve (PFR), which can improve its reliability and flexibility even with a continuously varying wind speeds. To achieve these objectives, the proposed scheme employs a de-loaded operation control loop associated with the rotational inertia characteristics of the DFIG. In addition, a static gain-based droop control loop was employed to release the required amount of active power from the system operator. In the proposed scheme, the optimal operating point for de-loaded operation varies more smoothly than it does in a conventional scheme by using the rotor inertia characteristics. The performance of the proposed control scheme is demonstrated using an EMTP-RV simulator under various wind speeds. The simulation results indicate that the proposed scheme significantly improves the frequency support capability of the DFIG in both the process of securing and providing the PFR.