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

J. Warrington, P. J. Goulart, S. Mariéthoz and M. Morari

@inproceedings{WGMM:2012a,
  author = {J. Warrington and P. J. Goulart and S. Mariéthoz and M. Morari},
  title = {A market mechanism for solving multi-period optimal power flow exactly on AC networks with mixed participants},
  booktitle = {American Control Conference},
  year = {2012},
  pages = {3101-3107},
  url = {http://dx.doi.org/10.1109/ACC.2012.6315477},
  doi = {10.1109/ACC.2012.6315477}
}

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 often attainable in this way. Here, the problem is extended to multiple time periods, and it is shown that under standard convexity assumptions, diverse market participants can be included in a clearing mechanism that respects the privacy of local information and achieves optimal nodal prices for both real and reactive power. The mechanism is motivated by the separable structure of the Lagrangian associated with the relaxed SDP formulation, allowing the application of a standard 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 price smoothing role of storage, can be accommodated elegantly ? something existing multi-period auctions do not allow. The mechanism is demonstrated on a 39 bus network populated with generators, inelastic loads, storage units, and wind farms. The results are of particular significance to receding horizon pricing schemes.