Distributed Multi-Period Optimal Power Flow for Demand Response in Microgrids

The scalability and privacy preserving nature of distributed optimisation techniques makes them ideal for coordinating many independently acting agents in a microgrid setting. However, their practical applicability remains an open question in this context, since AC power flows are inherently non-convex and households make discrete decisions about how to schedule their loads. In this paper, we show that one such method, the alternating direction method of multipliers (ADMM), can be adapted to remain practical in this challenging microgrid setting. We formulate and solve a multi-period optimal power flow (OPF) problem featuring independent households with shiftable loads, and study the results obtained with a range of power flow models and approaches to managing discrete decisions. Our experiments on a suburb-sized microgrid show that the AC power flows and a simple two-stage approach to handling discrete decisions do not appear to cause convergence issues, and provide near optimal results in a time that is practical for receding horizon control. This work brings distributed control for microgrids several steps closer to reality.

[1]  A. Farinelli,et al.  Coalitional energy purchasing in the smart grid , 2012, 2012 IEEE International Energy Conference and Exhibition (ENERGYCON).

[2]  Steven H. Low,et al.  Distributed Optimal Power Flow Algorithm for Balanced Radial Distribution Networks , 2014, 1404.0700.

[3]  Zhi Chen,et al.  Real-Time Price-Based Demand Response Management for Residential Appliances via Stochastic Optimization and Robust Optimization , 2012, IEEE Transactions on Smart Grid.

[4]  Sylvie Thiébaux,et al.  Randomized Load Control: A Simple Distributed Approach for Scheduling Smart Appliances , 2013, IJCAI.

[5]  K. Fujisawa,et al.  Semidefinite programming for optimal power flow problems , 2008 .

[6]  Tomaso Erseghe,et al.  Distributed Optimal Power Flow Using ADMM , 2014, IEEE Transactions on Power Systems.

[7]  Pascal Van Hentenryck,et al.  Residential Demand Response under Uncertainty , 2013, CP.

[8]  O. Alsaç,et al.  DC Power Flow Revisited , 2009, IEEE Transactions on Power Systems.

[9]  B. H. Kim,et al.  A comparison of distributed optimal power flow algorithms , 2000 .

[10]  Debapriya Das.  Reconfiguration of distribution system using fuzzy multi-objective approach , 2006 .

[11]  Joel Andersson,et al.  A General-Purpose Software Framework for Dynamic Optimization (Een algemene softwareomgeving voor dynamische optimalisatie) , 2013 .

[12]  Stephen P. Boyd,et al.  Dynamic Network Energy Management via Proximal Message Passing , 2013, Found. Trends Optim..

[13]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[14]  Michael Chertkov,et al.  Optimal Distributed Control of Reactive Power Via the Alternating Direction Method of Multipliers , 2013, IEEE Transactions on Energy Conversion.

[15]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[16]  Amr M. Youssef,et al.  A Water-Filling Based Scheduling Algorithm for the Smart Grid , 2012, IEEE Transactions on Smart Grid.

[17]  Georgios B. Giannakis,et al.  Residential Load Control: Distributed Scheduling and Convergence With Lost AMI Messages , 2012, IEEE Transactions on Smart Grid.

[18]  Gregor Verbic,et al.  Towards a smart home energy management system - A dynamic programming approach , 2011, 2011 IEEE PES Innovative Smart Grid Technologies.

[19]  Pascal Van Hentenryck,et al.  Convex quadratic relaxations for mixed-integer nonlinear programs in power systems , 2016, Mathematical Programming Computation.

[20]  J. Kalagnanam,et al.  Some Efficient Optimization Methods for Solving the Security-Constrained Optimal Power Flow Problem , 2014, IEEE Transactions on Power Systems.

[21]  M. E. Baran,et al.  Optimal sizing of capacitors placed on a radial distribution system , 1989 .

[22]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

[23]  Babak Hassibi,et al.  Equivalent Relaxations of Optimal Power Flow , 2014, IEEE Transactions on Automatic Control.

[24]  Pascal Van Hentenryck,et al.  A Linear-Programming Approximation of AC Power Flows , 2012, INFORMS J. Comput..

[25]  K. Mani Chandy,et al.  Inverter VAR control for distribution systems with renewables , 2011, 2011 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[26]  Carlo Fischione,et al.  A distributed approach for the optimal power flow problem , 2014, 2016 European Control Conference (ECC).

[27]  R. Jabr.  Radial distribution load flow using conic programming , 2006, IEEE Transactions on Power Systems.

[28]  Jean-Yves Le Boudec,et al.  Impact of demand-response on the efficiency and prices in real-time electricity markets , 2014, e-Energy.

[29]  Sarvapali D. Ramchurn,et al.  Agent-based control for decentralised demand side management in the smart grid , 2011, AAMAS.

[30]  Nicholas R. Jennings,et al.  Prediction-of-use games: a cooperative game theoryapproach to sustainable energy tariffs , 2014, AAMAS.

[31]  Vincent W. S. Wong,et al.  Autonomous Demand-Side Management Based on Game-Theoretic Energy Consumption Scheduling for the Future Smart Grid , 2010, IEEE Transactions on Smart Grid.

[32]  Fred C. Schweppe,et al.  Power System Static-State Estimation, Part II: Approximate Model , 1970 .

[33]  Hamed Mohsenian Rad,et al.  Optimal Residential Load Control With Price Prediction in Real-Time Electricity Pricing Environments , 2010, IEEE Transactions on Smart Grid.

[34]  Georgios B. Giannakis,et al.  Distributed Optimal Power Flow for Smart Microgrids , 2012, IEEE Transactions on Smart Grid.

[35]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..