  This paper studies a crucial problem in power system balancing control, i.e.,
the multi-time slot economic dispatch (MTSED) problem, for power grids with
substantial renewables, synchronous generators (SGs), and energy storage
devices (ESDs). The target of MTSED is to optimally coordinate active/reactive
power outputs of all controllable units to meet a forecast net demand profile
over multiple time slots within a receding finite time horizon. Firstly, the
MTSED is formulated as an optimization problem with operational constraints,
including the limits on the output of each controllable unit, ramping rates of
SGss, energy levels of ESDs, and bus voltages. Then, a novel projection-based
algorithm is developed to solve the problem in a distributed way. In
particular, the distributed algorithm is not limited to solving the MTSED
problem but also applies to more general optimization problems with both
generic convex objective functions and hard feasibility constraints. Finally,
case studies verify the effectiveness of the proposed method.
