A Second-Order Cone Programming Model for Planning PEV Fast-Charging Stations

Abstract

Abstract-This paper studies siting and sizing of plug-in electric vehicle (PEV) fast-charging stations on coupled transportation and power networks. We develop a closed-form model for PEV fast-charging stations' service abilities, which considers heterogeneous PEV driving ranges and charging demands. We utilize a modified capacitated flow refueling location model based on sub-paths (CFRLM SP) to explicitly capture timevarying PEV charging demands on the transportation network under driving range constraints. We explore extra constraints of the CFRLM SP to enhance model accuracy and computational efficiency. We then propose a stochastic mixed-integer second order cone programming (SOCP) model for PEV fast-charging station planning. The model considers the transportation network constraints of CFRLM SP and the power network constraints with AC power flow. Numerical experiments are conducted to illustrate the effectiveness of the proposed method.Keywords-Plug-in electric vehicle, charging station, planning, heterogeneous driving ranges, transportation, power system, second order cone programming. NOMENCLATURE Indices/SetsIndex of (type k) plug-in electric vehicles (PEVs). i/I (o/q) Index/set of transportation nodes (on sub-path o/path q), i ∈ I (o/q) . I m Set of transportation nodes connected to distribution bus m. k/K Index/set of PEV types, k ∈ K. m/n/h Index of buses of the distribution network. m/n/h ∈ M. For the reference bus, m/n/h = 0. (m, n)/L Index/set of lines of the distribution network.(m, n) is in the order of bus m to bus n, i.e., m → n, and bus n lies between bus m and bus 0.This work was supported in part by the National Key Research and Development Program (2016YFB0900103) and the National Natural Science Foundation of China (51477082).H. Zhang, Z. Hu and Y. Song are with the Department of Electrical Engineering, Tsinghua University, Beijing, 100084, P. R. China (email: zhang-hc13@mails.tsinghua.edu.cn; zechhu@tsinghua.edu.cn; yhsong@tsinghua.edu.cn).S. J. Moura is with the Department of Civil and Environmental Engineering, University of California, Berkeley, California, 94720, USA, and also with the Smart Grid and Renewable Energy Laboratory, Tsinghua-Berkeley Shenzhen Institute, Shenzhen, 518055, P. R. China (email: smoura@berkeley.edu).W. Qi is with the Desautels Faculty of Management, McGill University, Montreal, Quebec, Canada H3A 1G5 (email: qiwei.0216@gmail.com).M (→m) Set of buses of the distribution network (that are connected to bus m and bus m lies between them and bus 0).Index/set of paths (travel by node i), q ∈ Q (i) . Each path corresponds to one OD pair.Probability density function (PDF) of a normal distribution.Cumulative distribution function (CDF) of a normal distribution. Φ(·)CDF of the standard normal distribution. Parameters of the PEVs R kDriving range of a type k PEV, in km. Required charging time for a (type k) PEV, in h. yThe arrival number of (type k) PEVs in a charging station. Parameters of the transportation network d i,jDistance between node i and j, in km.Volume of ...

Joint PEV Charging Network and Distributed PV Generation Planning Based on Accelerated Generalized Benders Decomposition

“…We adopt the service rate model developed in [16] to describe a PEV charging station's service ability and model PEV load as a function of the traffic flow visiting a station.…”

“…e k is the departure time and t a e k is the arrival time of the PEV e k . Criterion 1 is equivalent to the following Criterion 2 [16]:…”

“…Properly modeling this constraint of PEVs on transportation networks enhances the forecasting accuracy of future PEV charging demands. We utilize the modified CFRLM SP proposed in our previous work [16] to explicitly consider the driving range constraints of PEVs and adopt time-varying traffic flows to define the locations of the charging stations.…”

“…We consider a 25-node transportation network coupled with a 14-node 110 kV high voltage distribution network to illustrate the proposed planning method. Due to limited space, the detailed parameters of the distribution and the transportation networks are omitted in this paper, but can be found in [16].…”

“…This assumption is mild and will not significantly affect the quality of the planning results. Interested readers can refer to[16] for detailed discussion.…”