The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables (IBRs)

which makes it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch (ED) programs. However

existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation (e.g.

virtual inertia and droop coefficients) in co-operation with other dispatchable resources to improve the system frequency security and dispatch reliability. This paper proposes a joint chance-constrained economic dispatch model that jointly optimizes the frequency-related inverter control

the system up/down reserves

and base-point power for the minimal total operational cost. In the proposed model

multiple dispatchable resources

including thermal units

dispatchable IBRs

and energy storage

are considered

and the (virtual) inertias

the regulation reserve allocations

and base-point power are coordinated. To ensure the system reliability

the joint chance-constraint formulation is also adopted. Additionally

since the traditional sample average approximation (SAA) method imposes a huge computational burden

a novel mix-SAA (MSAA) method is proposed to transform the original intractable model into a linear model that can be efficiently solved via commercial solvers. The case studies validate the satisfactory efficacy of the proposed ED model and demonstrate that the MSAA can save nearly 90% calculation time compared with the traditional SAA.