Aggregate modeling of distribution systems for multi-period OPF

Distribution systems with active components, such as responsive load, distributed storage and renewables, supplemented with thermostatically controlled loads have the capability to support the transmission grid and provide part of the required capacity reserve. Including distribution system resources in transmission level multi-period economic dispatch is challenging due to the large number of devices. In this paper, a two-level scheme is proposed for optimally dispatching the distribution system's active & reactive support to the grid, over a look-ahead horizon using an aggregate model. Initially, a semidefinite programming problem is solved in order to obtain a maximal dynamic ellipsoidal model of the feasible region for the power consumption of the distribution system. Subsequently, a look-ahead AC-OPF problem is solved for the optimal look-ahead dispatch of the transmission grid, using the aggregate distribution model. The distribution dispatch is then disaggregated to individual devices. The procedure is repeated in a receding horizon basis. Results on the accuracy and benefits of the approach are demonstrated on standard IEEE systems.