Comparison of Mixed-Integer Programming and Genetic Algorithm Methods for Distributed Generation Planning

This paper applies recently developed mixed-integer programming (MIP) tools to the problem of optimal siting and sizing of distributed generators in a distribution network. We investigate the merits of three MIP approaches for finding good installation plans: a full AC power flow approach, a linear DC power flow approximation, and a nonlinear DC power flow approximation with quadratic loss terms, each augmented with integer generator placement variables. A genetic algorithm-based approach serves as a baseline for the comparison. A simple knapsack problem method involving generator selection is presented for determining lower bounds on the optimal design objective. Solution methods are outlined, and computational results show that the MIP methods, while lacking the speed of the genetic algorithm, can find improved solutions within conservative time requirements and provide useful information on optimality.

[1]  Arindam Ghosh,et al.  Optimal allocation and sizing of capacitors to minimize the transmission line loss and to improve the voltage profile , 2009, Comput. Math. Appl..

[2]  Thomas J. Overbye,et al.  A comparison of the AC and DC power flow models for LMP calculations , 2004, 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the.

[3]  Graham Ault,et al.  Multi-objective planning framework for stochastic and controllable distributed energy resources , 2009 .

[4]  Nikolaos V. Sahinidis,et al.  Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs , 2009, Optim. Methods Softw..

[5]  Leo Liberti,et al.  Introduction to Global Optimization , 2006 .

[6]  R. Ramakumar,et al.  An approach to quantify the technical benefits of distributed generation , 2004, IEEE Transactions on Energy Conversion.

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

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

[9]  Ran Quan,et al.  A two-stage method with mixed integer quadratic programming for unit commitment with ramp constraints , 2008, 2008 IEEE International Conference on Industrial Engineering and Engineering Management.

[10]  M.M.A. Salama,et al.  An integrated distributed generation optimization model for distribution system planning , 2005, IEEE Transactions on Power Systems.

[11]  D. Sibley.  Spot Pricing of Electricity , 1990 .

[12]  N. S. Rau,et al.  Optimum location of resources in distributed planning , 1994 .

[13]  Jorge J. Moré,et al.  Benchmarking optimization software with performance profiles , 2001, Math. Program..

[14]  A. C. Rueda-Medina,et al.  A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems , 2013 .

[15]  Nicholas J. Higham,et al.  Matlab guide, Second Edition , 2005 .

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

[17]  L.S. Barreto,et al.  Multistage Model for Distribution Expansion Planning With Distributed Generation—Part I: Problem Formulation , 2008, IEEE Transactions on Power Delivery.

[18]  F. Hover,et al.  Linear Relaxations for Transmission System Planning , 2011, IEEE Transactions on Power Systems.

[19]  Benjamin F. Hobbs,et al.  Leader-Follower Equilibria for Electric Power and NOx Allowances Markets , 2006, Comput. Manag. Sci..

[20]  R. Belmans,et al.  Usefulness of DC power flow for active power flow analysis , 2005, IEEE Power Engineering Society General Meeting, 2005.

[21]  Wenzhong Gao,et al.  Optimal distributed generation location using mixed integer non-linear programming in hybrid electricity markets , 2010 .

[22]  J. A. Domínguez-Navarro,et al.  NSGA and SPEA Applied to Multiobjective Design of Power Distribution Systems , 2006, IEEE Transactions on Power Systems.

[23]  J. Bandler,et al.  A New Method for Computerized Solution of Power Flow Equations , 1982, IEEE Transactions on Power Apparatus and Systems.

[24]  G. Nemhauser,et al.  Integer Programming , 2020 .

[25]  Gérard Cornuéjols,et al.  An algorithmic framework for convex mixed integer nonlinear programs , 2008, Discret. Optim..

[26]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[27]  D. Hill,et al.  On Convexity of Power Flow Feasibility Boundary , 2008, IEEE Transactions on Power Systems.

[28]  Lennart Söder,et al.  Distributed generation : a definition , 2001 .

[29]  S. S. Venkata,et al.  Distribution System Planning through a Quadratic Mixed Integer Programming Approach , 1987, IEEE Transactions on Power Delivery.

[30]  M. Carrion,et al.  A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem , 2006, IEEE Transactions on Power Systems.

[31]  Yasuhiro Hayashi,et al.  Application of tabu search to optimal placement of distributed generators , 2001, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[32]  Sven Leyffer,et al.  Branch-and-Refine for Mixed-Integer Nonconvex Global Optimization , 2008 .

[33]  D.J. Cornforth,et al.  The distributed generator placement and sizing test suite and analysis tool , 2009, 2009 IEEE/PES Power Systems Conference and Exposition.

[34]  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.

[35]  F. Galiana,et al.  Quantitative Analysis of Steady State Stability in Power Networks , 1981, IEEE Transactions on Power Apparatus and Systems.

[36]  G. Platt,et al.  An introduction to multiobjective optimisation methods for decentralised power planning , 2009, 2009 IEEE Power & Energy Society General Meeting.

[37]  Benjamin F. Hobbs,et al.  A Nested Benders Decomposition Approach to Locating Distributed Generation in a Multiarea Power System , 2003 .

[38]  B. Foote,et al.  Distribution-system planning using mixed-integer programming , 1981 .

[39]  F. Wu,et al.  Analysis of linearized decoupled power flow approximations for steady-state security assessment , 1984 .

[40]  Ariovaldo V. Garcia,et al.  A Constructive Heuristic Algorithm for Distribution System Planning , 2010, IEEE Transactions on Power Systems.

[41]  Tuba Gozel,et al.  An analytical method for the sizing and siting of distributed generators in radial systems , 2009 .

[42]  A. Klos,et al.  Physical aspects of the nonuniqueness of load flow solutions , 1991 .

[43]  J. Mitra,et al.  Distributed Generation Placement for Optimal Microgrid Architecture , 2006, 2005/2006 IEEE/PES Transmission and Distribution Conference and Exhibition.

[44]  Susan Mccusker,et al.  Distributed Utility Planning Using Probabilistic Production Costing and Generalized Benders Decomposition , 2002, IEEE Power Engineering Review.

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

[46]  Ruben Romero,et al.  Distribution network planning using a constructive heuristic algorithm , 2009, 2009 IEEE Power & Energy Society General Meeting.

[47]  Timothy C. Green,et al.  Real-World MicroGrids-An Overview , 2007, 2007 IEEE International Conference on System of Systems Engineering.

[48]  J. Driesen,et al.  A Long-Term Multi-objective Planning Tool for Distributed Energy Resources , 2006, 2006 IEEE PES Power Systems Conference and Exposition.

[49]  Andreas Wächter,et al.  A Global-Optimization Algorithm for Mixed-Integer Nonlinear Programs Having Separable Non-convexity , 2009, ESA.

[50]  T. Gozel,et al.  Optimal placement and sizing of distributed generation on radial feeder with different static load models , 2005, 2005 International Conference on Future Power Systems.