In large energy systems, peak demand might cause severe issues such as service disruption and high cost of energy production and distribution. Under the widely adopted peak-demand pricing policy, electricity customers are charged a very high price for their maximum demand to discourage their energy usage in peak load conditions. In buildings, peak demand is often the result of temporally correlated energy demand surges caused by uncoordinated operation of sub-systems such as heating, ventilating, air conditioning and refrigeration (HVAC&R) systems and lighting systems. We have previously presented green scheduling as an approach to schedule the building control systems within a constrained peak demand envelope while ensuring that custom climate conditions are facilitated. This paper provides a sufficient schedulability condition for the peak constraint to be realizable for a large and practical class of system dynamics that can capture certain nonlinear dynamics, inter-dependencies, and constrained disturbances. We also present a method for synthesizing periodic schedules for the system. The proposed method is demonstrated in a simulation example to be scalable and effective for a large-scale system.