The reliability of power system varies with the allocation scheme of spinning reserve (SR). To improve the operational reliability of bulk power systems, the operational constraints of SR are embedded into the conventional optimal load shedding model incorporating unit types, ramp rates, component reliability parameters, network typology configuration and transmission capacity limits. Moreover, a sensitivity formula of the expected demand not supplied (EDNS) with respect to the capacity of SR is deduced based on the actual physical meanings of Lagrange multipliers in the inequality constraints. Therefore utilizing the ranking of the sensitivity indices, a heuristic idea is proposed to determine the optimal allocation of SR. Simultaneously, the optimal capacity and allocation scheme of SR are identified to minimize the total cost (the sum of SR cost and customer interruption cost) by joint optimization. Finally, the RBTS power systems are evaluated and the simulation results verify its validity.