Comparison of AC Optimal Power Flow Methods in Low-Voltage Distribution Networks

Embedded with producers, consumers, and prosumers, active Low-Voltage Distribution Networks (LVDNs) with bi-directional power flows are rising to over-shadow the investment and operation planning in power systems. The Optimal Power Flow (OPF) has been extensively used in the recent years to solve different investment and operation planning problems in LVDNs. However, OPF is inherently a complex non-linear and non-convex optimization problem. Hence, different linearization and convexification models have been introduced in the literature to enhance the modeling accuracy and computational tractability of the OPF problem in LVDNs. In this paper, five multi-period OPF models (including the basic non-linear and non-convex one) are presented, with different linearizations/convexifications for the power flow equations. The proposed models are implemented on the IEEE 34-bus test system and their modeling accuracy and computational complexity are compared and discussed.

[1]  Felix F. Wu,et al.  Network Reconfiguration in Distribution Systems for Loss Reduction and Load Balancing , 1989, IEEE Power Engineering Review.

[2]  Nate Blair,et al.  System Advisor Model (SAM) General Description (Version 2017.9.5) , 2018 .

[3]  Steven H. Low,et al.  Branch Flow Model: Relaxations and Convexification—Part I , 2012, IEEE Transactions on Power Systems.

[4]  David L. Woodruff,et al.  Pyomo: modeling and solving mathematical programs in Python , 2011, Math. Program. Comput..

[5]  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.

[6]  Ian A. Hiskens,et al.  A Survey of Relaxations and Approximations of the Power Flow Equations , 2019, Foundations and Trends® in Electric Energy Systems.

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

[8]  Daniel K. Molzahn,et al.  Inexact convex relaxations for AC optimal power flow: Towards AC feasibility , 2019, Electric Power Systems Research.

[9]  Chongqing Kang,et al.  A Linearized OPF Model With Reactive Power and Voltage Magnitude: A Pathway to Improve the MW-Only DC OPF , 2018, IEEE Transactions on Power Systems.

[10]  J. Boudec,et al.  AC OPF in radial distribution networks – Part I: On the limits of the branch flow convexification and the alternating direction method of multipliers , 2017 .

[11]  W. H. Kersting,et al.  Radial distribution test feeders , 1991, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[12]  Louis Wehenkel,et al.  Advanced optimization methods for power systems , 2014, 2014 Power Systems Computation Conference.

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

[14]  WächterAndreas,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006 .

[15]  Steven H. Low,et al.  A Note on Branch Flow Models With Line Shunts , 2020, IEEE Transactions on Power Systems.