  As renewable generation becomes more prevalent, traditional power systems
dominated by synchronous generators are transitioning to systems dominated by
converter-interfaced generation. These devices, with their weaker damping
capabilities and lower inertia, compromise the system's ability to withstand
disturbances, pose a threat to system stability, and lead to oscillations and
poor frequency response performance. While some new converter-interfaced
generations are capable of providing superior damping and fast frequency
control, there is a lack of effective measures to incentivize manufacturers to
adopt them. To address this gap, this paper defines the joint oscillation
damping and inertia provision services at the system level, seeking to
encourage converter-interfaced generation to provide enhanced damping and fast
frequency response capabilities. Our approach is anchored in a novel convex
parametric formulation that combines oscillation mode and frequency stability
constraints. These constraints ensure a sufficient damping ratio for all
oscillation modes and maintain transient frequency trajectories within
acceptable limits. They are designed to integrate smoothly into various
operational and planning optimization frameworks. Using this formulation, we
introduce a joint service for oscillation damping and inertia provision based
on a cost-minimization problem. This facilitates the optimal allocation of
damping and virtual inertia to converters, achieving both small-signal
stability and frequency stability. Furthermore, we investigate the economic
effects of introducing this service into a new ancillary service market,
assessing its impact on system operations and cost-efficiency. Numerical tests
highlight the service's efficacy in ensuring both small-signal stability and
frequency stability, and offer insights into potential economic benefits.
