On the interaction between Autonomous Mobility-on-Demand systems and the power network: models and coordination algorithms

We study the interaction between a fleet of electric, self-driving vehicles servicing on-demand transportation requests (referred to as Autonomous Mobility-on-Demand, or AMoD, system) and the electric power network. We propose a model that captures the coupling between the two systems stemming from the vehicles' charging requirements and captures time-varying customer demand and power generation costs, road congestion, battery depreciation, and power transmission and distribution constraints. We then leverage the model to jointly optimize the operation of both systems. We devise an algorithmic procedure to losslessly reduce the problem size by bundling customer requests, allowing it to be efficiently solved by off-the-shelf linear programming solvers. Next, we show that the socially optimal solution to the joint problem can be enforced as a general equilibrium, and we provide a dual decomposition algorithm that allows self-interested agents to compute the market clearing prices without sharing private information. We assess the performance of the mode by studying a hypothetical AMoD system in Dallas-Fort Worth and its impact on the Texas power network. Lack of coordination between the AMoD system and the power network can cause a 4.4% increase in the price of electricity in Dallas-Fort Worth; conversely, coordination between the AMoD system and the power network could reduce electricity expenditure compared to the case where no cars are present (despite the increased demand for electricity) and yield savings of up $147M/year. Finally, we provide a receding-horizon implementation and assess its performance with agent-based simulations. Collectively, the results of this paper provide a first-of-a-kind characterization of the interaction between electric-powered AMoD systems and the power network, and shed additional light on the economic and societal value of AMoD.Comment: Extended version of the paper presented at Robotics: Science and Systems XIV, in prep. for journal submission. In V3, we add a proof that the socially-optimal solution can be enforced as a general equilibrium, a privacy-preserving distributed optimization algorithm, a description of the receding-horizon implementation and additional numerical results, and proofs of all theorem

Map of the area around Barro Colorado Island before flooding (adapted from [38]).

<p>This map depicts the natural course of the Chagres River (flowing southeast to northwest) and positions of former settlements. Land areas remaining after the filling of artificial Lake Gatún in 1914 are shaded in gray. The remaining white background represents the modern lake. Also indicated are the railway to the north (the black dash-dotted line) and the planned course of the Panama Canal (thick solid black line). Topographic contours, from the original map, in meters above sea level.</p

Census data of each census year for <i>Ficus insipida</i> and <i>F</i>. <i>yoponensis</i> found in the Lutz Catchment.

<p>Given are the number of individuals of <i>Ficus insipida</i> and <i>F</i>. <i>yoponensis</i> still alive at each census and the percentage of individuals dead since 1973.</p

Distribution of <i>Ficus insipida</i> and <i>F</i>. <i>yoponensis</i> on Barro Colorado Island.

<p>Depicted is the relative age of the forest from young (white) to old (black) forest as determined from an aerial photo from 1927 (compiled by R. Stallard and D. Kinner 2002). Secondary forest is about 90–150 years old, primary forest at least 400–600 years. The black circle marks the position of the Lutz Catchment, the white rectangle indicates the 50-ha forest-dynamics plot.</p

Mortality of fig trees in the Lutz Catchment.

<p>(a) Annual rainfall on BCI. Rainfall data are provided by the Environmental Studies Program (ESP). (b) Fig tree count per census year (light grey: <i>F</i>. <i>yoponensis</i>, dark grey: <i>F</i>. <i>insipida</i>). (c) Number of dead fig trees and (d) fig mortality in percent per year, estimated with relaxed cubic splines.</p

Results of the fig census in the Lutz Catchment.

<p>(a) Trees and saplings of <i>Ficus insipida</i> and <i>F</i>. <i>yoponensis</i> found alive in the Lutz Catchment in 1973 and (b) in 2011.</p

Map of Luquillo Mountains, Puerto Rico, showing elevation, topography, and watersheds discussed in text.

<p>Map of Luquillo Mountains, Puerto Rico, showing elevation, topography, and watersheds discussed in text.</p

Map of rain gages (past and present) in the Luquillo Mountains, Puerto Rico, and table providing elevation and mean annual precipitation (MAP) for each gage (MAP for some gages were adjusted for low or high precipitation during short periods of record; see S1 Table for more details).

<p>Map of rain gages (past and present) in the Luquillo Mountains, Puerto Rico, and table providing elevation and mean annual precipitation (MAP) for each gage (MAP for some gages were adjusted for low or high precipitation during short periods of record; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180987#pone.0180987.s001" target="_blank">S1 Table</a> for more details).</p