Optimal power flow: an introduction to predictive, distributed and stochastic control challenges

Abstract The Energiewende is a paradigm change that can be witnessed at latest since the political decision to step out of nuclear energy. Moreover, despite common roots in Electrical Engineering, the control community and the power systems community face a lack of common vocabulary. In this context, this paper aims at providing a systems-and-control specific introduction to optimal power flow problems which are pivotal in the operation of energy systems. Based on a concise problem statement, we introduce a common description of optimal power flow variants including multi-stage problems and predictive control, stochastic uncertainties, and issues of distributed optimization. Moreover, we sketch open questions that might be of interest for the systems and control community.

[1]  M. Diehl,et al.  Nominal stability of real-time iteration scheme for nonlinear model predictive control , 2005 .

[2]  Matthias Luther,et al.  Dynamic Study Model for the interconnected power system of Continental Europe in different simulation tools , 2015, 2015 IEEE Eindhoven PowerTech.

[3]  Manfred Morari,et al.  Policy-Based Reserves for Power Systems , 2012, IEEE Transactions on Power Systems.

[4]  Francisco J. Prieto,et al.  A Decomposition Methodology Applied to the Multi-Area Optimal Power Flow Problem , 2003, Ann. Oper. Res..

[5]  Colin Neil Jones,et al.  An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the Optimal Power Flow Problem , 2017, J. Optim. Theory Appl..

[6]  Juan C. Vasquez,et al.  Stabilizing plug-and-play regulators and secondary coordinated control for AC islanded microgrids with bus-connected topology , 2018 .

[7]  T. Sullivan.  Introduction to Uncertainty Quantification , 2015 .

[8]  G. Andersson,et al.  Decentralized Optimal Power Flow Control for Overlapping Areas in Power Systems , 2009, IEEE Transactions on Power Systems.

[9]  Brian B. Johnson,et al.  Achieving a 100% Renewable Grid: Operating Electric Power Systems with Extremely High Levels of Variable Renewable Energy , 2017, IEEE Power and Energy Magazine.

[10]  B. H. Kim,et al.  Evaluation of convergence rate in the auxiliary problem principle for distributed optimal power flow , 2002 .

[11]  John Lygeros,et al.  Probabilistic guarantees for the N-1 security of systems with wind power generation , 2013 .

[12]  Joerg Raisch,et al.  Minimax Model Predictive Operation Control of Microgrids , 2014 .

[13]  István Erlich,et al.  PEGASE pan-European test-beds for testing of algorithms on very large scale power systems , 2012, 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe).

[14]  T. Soubdhan,et al.  Classification of daily solar radiation distributions using a mixture of Dirichlet distributions , 2009 .

[15]  M. Suriyah,et al.  On efficient computation of time constrained optimal power flow in rectangular form , 2015, 2015 IEEE Eindhoven PowerTech.

[16]  Veit Hagenmeyer,et al.  Hierarchical Distributed Mixed-Integer Optimization for Reactive Power Dispatch , 2018 .

[17]  Daniel K. Molzahn,et al.  Recent advances in computational methods for the power flow equations , 2015, 2016 American Control Conference (ACC).

[18]  MORITZ DIEHL,et al.  A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control , 2005, SIAM J. Control. Optim..

[19]  Veit Hagenmeyer,et al.  A Generalized Framework for Chance-constrained Optimal Power Flow , 2018, Sustainable Energy, Grids and Networks.

[20]  Lars Grüne,et al.  Closed-loop performance analysis for economic model predictive control of time-varying systems , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[21]  H. Farhangi,et al.  The path of the smart grid , 2010, IEEE Power and Energy Magazine.

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

[23]  Gabriela Hug,et al.  A Case for Nonconvex Distributed Optimization in Large-Scale Power Systems , 2017, IEEE Transactions on Power Systems.

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

[25]  Jürgen Pannek,et al.  Nonlinear Model Predictive Control : Theory and Algorithms. 2nd Edition , 2017 .

[26]  Ivana Kockar,et al.  Dynamic Optimal Power Flow for Active Distribution Networks , 2014, IEEE Transactions on Power Systems.

[27]  E.F. El-Saadany,et al.  Optimal Renewable Resources Mix for Distribution System Energy Loss Minimization , 2010, IEEE Transactions on Power Systems.

[28]  Ralf Mikut,et al.  Storage Scheduling with Stochastic Uncertainties: Feasibility and Cost of Imbalances , 2018, 2018 Power Systems Computation Conference (PSCC).

[29]  Goran Andersson,et al.  Analytical reformulation of security constrained optimal power flow with probabilistic constraints , 2013, 2013 IEEE Grenoble Conference.

[30]  Wolfgang Marquardt,et al.  Fast NMPC schemes for regulatory and economic NMPC – A review ☆ , 2016 .

[31]  Gary W. Chang,et al.  Power System Analysis , 1994 .

[32]  Dinh Quoc Tran,et al.  An Inexact Perturbed Path-Following Method for Lagrangian Decomposition in Large-Scale Separable Convex Optimization , 2011, SIAM J. Optim..

[33]  James B. Rawlings,et al.  Postface to “ Model Predictive Control : Theory and Design ” , 2012 .

[34]  Michael Chertkov,et al.  Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty , 2012, SIAM Rev..

[35]  G. Glanzmann,et al.  Incorporation of N-1 Security into Optimal Power Flow for FACTS Control , 2006, 2006 IEEE PES Power Systems Conference and Exposition.

[36]  Begoña Subiza,et al.  Numerical representation of choice functions , 1998, Ann. Oper. Res..

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

[38]  Yuning Jiang,et al.  Distributed AC Optimal Power Flow using ALADIN , 2017 .

[39]  Lars Grüne,et al.  Economic Nonlinear Model Predictive Control , 2018, Found. Trends Syst. Control..

[40]  Fangxing Li,et al.  Small test systems for power system economic studies , 2010, IEEE PES General Meeting.

[41]  Francisco J. Prieto,et al.  A decomposition procedure based on approximate Newton directions , 2002, Math. Program..

[42]  Jesse T. Holzer,et al.  Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming , 2013, IEEE Transactions on Power Systems.

[43]  Steven H. Low,et al.  Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence , 2014, IEEE Transactions on Control of Network Systems.

[44]  L. Grüne,et al.  Hierarchical Distributed Model Predictive Control of Interconnected Microgrids , 2019, IEEE Transactions on Sustainable Energy.

[45]  Henrik Sandberg,et al.  A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems , 2017, IEEE Transactions on Smart Grid.

[46]  Selina Kn.  Improvement of OPF Decomposition Methods Applied to Multi-Area Power Systems , 2007 .

[47]  Oriol Gomis-Bellmunt,et al.  Trends in Microgrid Control , 2014, IEEE Transactions on Smart Grid.

[48]  Michael Chertkov,et al.  Optimal Power Flow with Weighted chance constraints and general policies for generation control , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[49]  Mario Paolone,et al.  An Exact Convex Formulation of the Optimal Power Flow in Radial Distribution Networks Including Transverse Components , 2016, IEEE Transactions on Automatic Control.

[50]  Johan A. K. Suykens,et al.  Distributed nonlinear optimal control using sequential convex programming and smoothing techniques , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

[52]  Gabriela Hug,et al.  Toward Distributed/Decentralized DC Optimal Power Flow Implementation in Future Electric Power Systems , 2018, IEEE Transactions on Smart Grid.

[53]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[54]  G. Hug,et al.  Online optimization in closed loop on the power flow manifold , 2017, 2017 IEEE Manchester PowerTech.

[55]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches , 1999 .

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

[57]  Moritz Diehl,et al.  An Augmented Lagrangian Based Algorithm for Distributed NonConvex Optimization , 2016, SIAM J. Optim..

[58]  Jizhong Zhu,et al.  Optimization of Power System Operation , 2009 .

[59]  Iain Dunning,et al.  JuMP: A Modeling Language for Mathematical Optimization , 2015, SIAM Rev..

[60]  Goran Andersson,et al.  Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints , 2015 .

[61]  Romeo Ortega,et al.  Modeling of microgrids - from fundamental physics to phasors and voltage sources , 2015, Autom..

[62]  J. C. Das.  Load Flow Optimization and Optimal Power Flow , 2017 .

[63]  J. Ramos,et al.  State-of-the-art, challenges, and future trends in security constrained optimal power flow , 2011 .

[64]  Alberto Bemporad,et al.  Scenario-based model predictive operation control of islanded microgrids , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[65]  Moritz Diehl,et al.  CasADi -- A symbolic package for automatic differentiation and optimal control , 2012 .

[66]  Veit Hagenmeyer,et al.  The Price of Uncertainty: Chance-Constrained OPF vs. in-Hindsight OPF , 2018, 2018 Power Systems Computation Conference (PSCC).

[67]  John Lygeros,et al.  Probabilistic security-constrained AC optimal power flow , 2013, 2013 IEEE Grenoble Conference.

[68]  Steffen Rebennack,et al.  An introduction to optimal power flow: Theory, formulation, and examples , 2016 .

[69]  Florin Capitanescu,et al.  Critical review of recent advances and further developments needed in AC optimal power flow , 2016 .

[70]  Ioana Popescu,et al.  A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions , 2005, Math. Oper. Res..

[71]  Steven H. Low,et al.  Distributed algorithm for optimal power flow on a radial network , 2014, 53rd IEEE Conference on Decision and Control.

[72]  Ross Baldick,et al.  Coarse-grained distributed optimal power flow , 1997 .

[73]  Gabriela Hug,et al.  Consensus + Innovations Approach for Distributed Multiagent Coordination in a Microgrid , 2015, IEEE Transactions on Smart Grid.

[74]  P. Kundur,et al.  Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions , 2004, IEEE Transactions on Power Systems.

[75]  Frank Allgöwer,et al.  Real time economic dispatch for power networks: A distributed economic model predictive control approach , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[76]  Enrico Carpaneto,et al.  Probabilistic characterisation of the aggregated residential load patterns , 2008 .

[77]  Mingbo Liu,et al.  Fully Decentralized Optimal Power Flow of Multi-Area Interconnected Power Systems Based on Distributed Interior Point Method , 2018, IEEE Transactions on Power Systems.

[78]  Steven H. Low,et al.  Convex Relaxation of Optimal Power Flow—Part II: Exactness , 2014, IEEE Transactions on Control of Network Systems.

[79]  Yuning Jiang,et al.  Distributed Optimal Power Flow using ALADIN , 2018, ArXiv.

[80]  Yuning Jiang,et al.  Distributed Stochastic AC Optimal Power Flow based on Polynomial Chaos Expansion , 2018, 2018 Annual American Control Conference (ACC).

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

[82]  I.A. Hiskens,et al.  MPC-Based Load Shedding for Voltage Stability Enhancement , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[83]  Antonio J. Conejo,et al.  Decomposition Techniques in Mathematical Programming: Engineering and Science Applications , 2006 .

[84]  Veit Hagenmeyer,et al.  Solving stochastic AC power flow via polynomial chaos expansion , 2016, 2016 IEEE Conference on Control Applications (CCA).

[85]  Giuseppe Carlo Calafiore,et al.  Stochastic model predictive control of LPV systems via scenario optimization , 2013, Autom..

[86]  Lars Grne,et al.  Nonlinear Model Predictive Control: Theory and Algorithms , 2011 .

[87]  Veit Hagenmeyer,et al.  Solving optimal power flow with non-Gaussian uncertainties via polynomial chaos expansion , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[88]  P. Aitchison,et al.  Optimal power flow solutions using the gradient projection method. I. Theoretical basis , 1990 .

[89]  OrtegaRomeo,et al.  A survey on modeling of microgrids-From fundamental physics to phasors and voltage sources , 2016 .

[90]  Pu Li,et al.  Application of sparse-grid technique to chance constrained optimal power flow , 2013 .

[91]  Canbing Li,et al.  Chance-Constrained Optimization-Based Unbalanced Optimal Power Flow for Radial Distribution Networks , 2013, IEEE Transactions on Power Delivery.

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

[93]  Hui Zhang,et al.  Chance Constrained Programming for Optimal Power Flow Under Uncertainty , 2011, IEEE Transactions on Power Systems.

[94]  Ralf Mikut,et al.  On the use of probabilistic forecasts in scheduling of renewable energy sources coupled to storages , 2018 .

[95]  Tomaso Erseghe.  A distributed approach to the OPF problem , 2015, EURASIP J. Adv. Signal Process..

[96]  Karl Worthmann,et al.  Hierarchical distributed ADMM for predictive control with applications in power networks , 2018, IFAC J. Syst. Control..

[97]  Thomas J. Overbye,et al.  Data-Driven Power System Operations , 2006, International Conference on Computational Science.