  The undergoing transition from conventional to converter-interfaced renewable
generation leads to significant challenges in maintaining frequency stability
due to declining system inertia. In this paper, a novel control framework for
Synthetic Inertia (SI) provision from Wind Turbines (WTs) is proposed, which
eliminates the secondary frequency dip and allows the dynamics of SI from WTs
to be analytically integrated into the system frequency dynamics. Furthermore,
analytical system frequency constraints with SI provision from WTs are
developed and incorporated into a stochastic system scheduling model, which
enables the provision of SI from WTs to be dynamically optimized on a system
level. Several case studies are carried out on a Great Britain 2030 power
system with different penetration levels of wind generation and inclusion of
frequency response requirements in order to assess the performance of the
proposed model and analyze the influence of the improved SI control scheme on
the potential secondary frequency dip. The results demonstrate that the
inclusion of SI provision from WTs into UC can drastically impact the overall
system costs.
