This paper deals with hierarchical model
predictive control (MPC) of smart grid systems. The
objective is to accommodate load variations on the grid,
arising from varying consumption and natural variations
in the power production e.g. from wind turbines. This
balancing between supply and demand is performed by
distributing power to consumers in an optimal manner,
subject to the requirement that each consumer receives
the specific amount of energy the consumer is entitled
to within a specific time horizon. However, in order to
do so, the high-level controller requires knowledge of
how much energy the consumers can receive within a
given time horizon. In this paper, we present a method
for computing these bounds as convex constraints that
can be used directly in the optimisation. The method is
illustrated on a simulation example that uses measured
wind data as load variation, and fairly realistic consumer
models. The example illustrates that the exact bounds
computed by the proposed method leads to a better power
distribution than a conventional, conservative approach
in case of fast changes in the load.