Article
A MajorizationMinimization Approach to Design of Power Transmission Networks
Proceedings of the IEEE Conference on Decision and Control 04/2010; DOI: 10.1109/CDC.2010.5717226
Source: arXiv
ABSTRACT
We propose an optimization approach to design costeffective 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 tradeoff 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 overcomplete network, posed as minimizing the (convex) network power dissipation plus a nonconvex cost on line conductances that encourages sparse networks where many line conductances are set to zero. We develop a heuristic approach to solve this nonconvex optimization problem using: (1) a continuation method to interpolate from the smooth, convex problem to the (nonsmooth, nonconvex) combinatorial problem, (2) the majorizationminimization algorithm to perform the necessary intermediate smooth but nonconvex 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 nonconvex 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)
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 "This paper adopts a dynamic programming algorithm to compute the optimal charging control for each vehicle. An optimization method developed to design power transmission networks with the aim of balancing network efficiency versus the cost of building the network [8]. The above papers are mainly related to the V2G technology, which is focused on some technology to feed energy stored in EVs back to the power grid. "
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 "cluding work on distribution networks [19], hierarchical networks [6] and other methods for assessing load and points of potential failure [33]. There are many such applications for these techniques including transport systems [14] and other utility distribution networks [36] but in this present paper we focus on electrical power distribution networks [1] [7] and associated graph issues [20] [24]. Many of the issues unique to electrical distribution networks arise because of their particular spatial structure and the topological constraints [17] with which they are built [28]. "
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 "It can be shown that in a DCmodel approximation of a power grid, the average power dissipation of the grid is proportional to T r(AL + ), where A is a positive semidefinite matrix [8]. It is easy to verify that the power dissipation can be expressed as a linear combination of pointtopoint resistance distances (similar to the case of network utilization). "
Conference Paper: Krobust network design using resistance distance: Case of RocketFuel and power grids
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ABSTRACT: This paper reconsiders the problem of robust network design form a different point of view using the concept of resistance distance from network science. It has been shown that some important network performance metrics, such as average utilization in a communication network or total power dissipation in an electrical grid, can be expressed in terms of linear combination of pointtopoint resistance distances of a graph. In this paper we choose to have a weighted linear combination of resistance distances, referred to as weighted network criticality (WNC), as the objective and we investigate the vulnerability of different network types. In particular, We formulate a minmax convex optimization problem to design krobust networks and we provide extension to account for joint optimization of resources and flows. We study the solution of the optimization problem in two different networks. First we consider RocketFuel topologies and Abilene as representatives for service provider networks, and we show gains that can be achieved by optimizing link capacities and flows in RocketFuel topologies and Abilene. In the second experience, we show the application of the proposed optimization problem in designing robust electrical grids.