A Majorization-Minimization Approach to Design of Power Transmission Networks

04/2010; DOI: 10.1109/CDC.2010.5717226
Source: arXiv

ABSTRACT We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network efficiency (low power dissipation within the transmission network) and the cost to build the network. We begin with a convex optimization method based on the paper ``Minimizing Effective Resistance of a Graph'' [Ghosh, Boyd \& Saberi]. We show that this (DC) resistive network method can be adapted to the context of AC power flow. However, that does not address the combinatorial aspect of selecting network structure. We approach this problem as selecting a subgraph within an over-complete network, posed as minimizing the (convex) network power dissipation plus a non-convex cost on line conductances that encourages sparse networks where many line conductances are set to zero. We develop a heuristic approach to solve this non-convex optimization problem using: (1) a continuation method to interpolate from the smooth, convex problem to the (non-smooth, non-convex) combinatorial problem, (2) the majorization-minimization algorithm to perform the necessary intermediate smooth but non-convex optimization steps. Ultimately, this involves solving a sequence of convex optimization problems in which we iteratively reweight a linear cost on line conductances to fit the actual non-convex cost. Several examples are presented which suggest that the overall method is a good heuristic for network design. We also consider how to obtain sparse networks that are still robust against failures of lines and/or generators. Comment: 8 pages, 3 figures. To appear in Proc. 49th IEEE Conference on Decision and Control (CDC '10)

  • [Show abstract] [Hide abstract]
    ABSTRACT: We explore optimization methods for planning the placement, sizing and operations of flexible alternating current transmission system (FACTS) devices installed to relieve transmission grid congestion. We limit our selection of FACTS devices to series compensation (SC) devices that can be represented by modification of the inductance of transmission lines. Our master optimization problem minimizes the l1 norm of the inductance modification subject to the usual line thermal-limit constraints. We develop heuristics that reduce this non-convex optimization to a succession of linear programs (LP) that are accelerated further using cutting plane methods. The algorithm solves an instance of the MatPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop—a speed that allows the sizing and placement of a family of SC devices to correct a large set of anticipated congestions. We observe that our algorithm finds feasible solutions that are always sparse, i.e., SC devices are placed on only a few lines. In a companion manuscript, we demonstrate our approach on realistically sized networks that suffer congestion from a range of causes, including generator retirement. In this manuscript, we focus on the development of our approach, investigate its structure on a small test system subject to congestion from uniform load growth, and demonstrate computational efficiency on a realistically sized network.
    New Journal of Physics 10/2014; 16(10):105015. DOI:10.1088/1367-2630/16/10/105015 · 3.67 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Complex socioeconomic networks such as information, finance and even terrorist networks need resilience to cascades--to prevent the failure of a single node from causing a far-reaching domino effect. We show that terrorist and guerrilla networks are uniquely cascade-resilient while maintaining high efficiency, but they become more vulnerable beyond a certain threshold. We also introduce an optimization method for constructing networks with high passive cascade resilience. The optimal networks are found to be based on cells, where each cell has a star topology. Counterintuitively, we find that there are conditions where networks should not be modified to stop cascades because doing so would come at a disproportionate loss of efficiency. Implementation of these findings can lead to more cascade-resilient networks in many diverse areas.
    PLoS ONE 11/2010; 5(11):e13448. DOI:10.1371/journal.pone.0013448 · 3.53 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Vehicle-to-Grid (V2G) is that the energy stored in the batteries of electric vehicles can be utilized to send back to the power grid. And then, the energy in the batteries of electric vehicles can move with electric vehicles (EVs). Based on above characteristics, this paper introduces the concept of a mobile electrical grid and discusses the energy routing problem. It focuses on the optimization problem of how to find routes from the energy sources to charge stations, especially, when some paths are clogged by traffic jam. A bipartite graph model is used to analyze the route problem and two algorithms are presented to compute minimal energy metric route. Both of algorithms are tested by real-world transporting data in Manhattan and the Pioneer Valley Transit Authority(PVTA). Simulations show that the method is efficient.
    Mobile Ad-Hoc and Sensor Systems (MASS), 2013 IEEE 10th International Conference on; 01/2013


1 Download
Available from