A market mechanism for solving multi-period optimal power flow exactly on AC networks with mixed participants

The difficult problem of optimal power flow on AC networks has recently been tackled via reformulation as a semidefinite program. New work in the field suggests that a globally optimal solution is attainable in this way. Here, the problem is extended to multiple time periods in order to accommodate the time-coupled nature of power system entities´ costs and constraints. A market mechanism is then developed for the clearing of nodal prices for both real and reactive power, and it is shown that these prices are optimal under standard convexity assumptions. The mechanism is motivated by the separable structure of the Lagrangian associated with the relaxed SDP formulation, allowing the application of a dual subgradient method. Physical insights into the electrical network are then used to make improvements over the standard method that dramatically speed up convergence. The advantage of considering multiple time periods in parallel is that dynamic costs and constraints, e.g. generator ramping and wear, as well as the important price smoothing role of storage, can be accommodated naturally - something existing multi-period auctions do not allow. The mechanism is demonstrated on a 39 bus network populated with a variety of market participant types.