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Synchronous generators are operating for less time than before or being decommissioned in the National Electricity Market (NEM) of Australia, due to the proliferation of asynchronous wind and solar generation. Sub-networks of the NEM will face inertia shortages in the near future. This paper develops a formulation of zonal inertia constrained generator dispatch for power systems with a diversified generator portfolio including synchronous generators, synchronous condensers, inverter-interfaced generators and energy storages. Zonal inertia constraints are formulated in unit commitment and optimal power flow to limit the rate of change of frequency (RoCoF) in the event of network separation. Load frequency relief is also considered to reduce the ramp rate requirement of primary reserve. The proposed formulation can reduce the average cost of primary reserve and maintain zonal inertia adequacy to constrain RoCoF in case of the trip of the interconnector(s). [ABSTRACT FROM AUTHOR]