Scalable Optimization Methods for Distribution Networks With High PV Integration

This paper proposes a suite of algorithms to determine the active- and reactive-power setpoints for photovoltaic (PV) inverters in distribution networks. The objective is to optimize the operation of the distribution feeder according to a variety of performance objectives and ensure voltage regulation. In general, these algorithms take a form of the widely studied ac optimal power flow (OPF) problem. For the envisioned application domain, nonlinear power-flow constraints render pertinent OPF problems nonconvex and computationally intensive for large systems. To address these concerns, we formulate a quadratic constrained quadratic program (QCQP) by leveraging a linear approximation of the algebraic power-flow equations. Furthermore, simplification from QCQP to a linearly constrained quadratic program is provided under certain conditions. The merits of the proposed approach are demonstrated with simulation results that utilize realistic PV-generation and load-profile data for illustrative distribution-system test feeders.

[1]  Sairaj V. Dhople,et al.  Linear approximations to AC power flow in rectangular coordinates , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[2]  Arie M. C. A. Koster,et al.  Designing AC Power Grids Using Integer Linear Programming , 2011, INOC.

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

[4]  Stephen P. Boyd,et al.  Disciplined Convex Programming , 2006 .

[5]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[6]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[7]  R Tonkoski,et al.  Coordinated Active Power Curtailment of Grid Connected PV Inverters for Overvoltage Prevention , 2011, IEEE Transactions on Sustainable Energy.

[8]  Michael Chertkov,et al.  Options for Control of Reactive Power by Distributed Photovoltaic Generators , 2010, Proceedings of the IEEE.

[9]  Dionysios Aliprantis,et al.  Distributed Volt/VAr Control by PV Inverters , 2013, IEEE Transactions on Power Systems.

[10]  Philip G. Hill,et al.  Power generation , 1927, Journal of the A.I.E.E..

[11]  Brian B. Johnson,et al.  Decentralized Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems , 2014, IEEE Transactions on Energy Conversion.

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

[13]  Marco Liserre,et al.  Online Optimal Reactive Power Control Strategy of PV Inverters , 2011, IEEE Transactions on Industrial Electronics.

[14]  Sairaj V. Dhople,et al.  Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions , 2014, IEEE Transactions on Power Systems.

[15]  Etienne de Klerk,et al.  Exploiting special structure in semidefinite programming: A survey of theory and applications , 2010, Eur. J. Oper. Res..

[16]  Sairaj V. Dhople,et al.  Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems , 2013, IEEE Transactions on Sustainable Energy.

[17]  T. Stetz,et al.  Cost Optimal Sizing of Photovoltaic Inverters - Influence of New Grid Codes and Cost Reductions , 2010 .

[18]  Vijay Vittal,et al.  A relaxed AC optimal power flow model based on a Taylor series , 2013, 2013 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia).

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

[20]  Sylvie Thiébaux,et al.  Distributed Multi-Period Optimal Power Flow for Demand Response in Microgrids , 2015, e-Energy.

[21]  Sairaj V. Dhople,et al.  Engineering systems in the gable home: A passive, net-zero, solar-powered house for the U. S. Department of Energy's 2009 Solar Decathlon , 2010, 2010 Power and Energy Conference At Illinois (PECI).

[22]  Euhanna Ghadimi,et al.  Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems , 2013, IEEE Transactions on Automatic Control.

[23]  S. T. Cady,et al.  Engineering systems in the Re_home: A net-zero, solar-powered house for the U.S. Department of Energy's 2011 Solar Decathlon , 2012, 2012 IEEE Power and Energy Conference at Illinois.

[24]  A. Raghunathan,et al.  Optimal Step-Size Selection in Alternating Direction Method of Multipliers for Convex Quadratic Programs and Model Predictive Control , 2014 .

[25]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[26]  Robert Eriksson,et al.  Coordinated Active Power-Dependent Voltage Regulation in Distribution Grids With PV Systems , 2014, IEEE Transactions on Power Delivery.

[27]  Steven H. Low,et al.  Convex relaxations and linear approximation for optimal power flow in multiphase radial networks , 2014, 2014 Power Systems Computation Conference.

[28]  Pascal Van Hentenryck,et al.  The QC Relaxation: Theoretical and Computational Results on Optimal Power Flow , 2015, ArXiv.

[29]  Carleton Coffrin,et al.  The QC Relaxation: A Theoretical and Computational Study on Optimal Power Flow , 2017, IEEE Transactions on Power Systems.

[30]  S. Zampieri,et al.  On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks , 2014, IEEE Transactions on Power Systems.

[31]  Javad Lavaei,et al.  Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem , 2014, IEEE Transactions on Power Systems.

[32]  Emiliano Dall'Anese,et al.  Fast Consensus by the Alternating Direction Multipliers Method , 2011, IEEE Transactions on Signal Processing.

[33]  Tansu Alpcan,et al.  Optimal Charging of Electric Vehicles Taking Distribution Network Constraints Into Account , 2015, IEEE Transactions on Power Systems.

[34]  Sigifredo Gonzalez,et al.  Performance Model for Grid-Connected Photovoltaic Inverters , 2007 .

[35]  S. Low,et al.  Zero Duality Gap in Optimal Power Flow Problem , 2012, IEEE Transactions on Power Systems.