Spatial and Temporal Model of Electric Vehicle Charging Demand Presented by: Hao Liang 2012.5.31...
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Spatial and Temporal Model of Electric Vehicle Charging Demand Presented by: Hao Liang 2012.5.31 Broadband Communications Research (BBCR) Lab Smart Grid
Spatial and Temporal Model of Electric Vehicle Charging Demand
Presented by: Hao Liang 2012.5.31 Broadband Communications Research
(BBCR) Lab Smart Grid Research Group Reference: S. Bae and A.
Kwasinski, Spatial and temporal model of electric vehicle charging
demand, IEEE Transactions on Smart Grid (SI on Transportation
Electrification and Vehicle-to-Grid Applications), vol. 3, no. 1,
pp. 394-403, Mar. 2012.
Slide 2
Outline 2 Introduction Highway Model Description Model
Formulations Numerical Example and Discussions Conclusions
Broadband Communications Research (BBCR) Lab Smart Grid Research
Group
Slide 3
Introduction 3 Broadband Communications Research (BBCR) Lab
Smart Grid Research Group
Slide 4
4 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Transportation Electrification Plug-in Electric
Vehicle (PEV) Plug-in Hybrid Electric Vehicle (PHEV) BMW Electric
Mini Cooper Nissan Leaf Tesla Model S Toyota Prius Chevrolet
Volt
Slide 5
5 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Reduce gasoline consumption Decrease greenhouse gas
emission Reduce energy bill of vehicle owner ? Increase profit of
vehicle manufacturer ? Benefits of Transportation
Electrification
Slide 6
6 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Challenges in Transportation Electrification peak
time (temporal changing nature) Stress on the power system during
the peak time (temporal changing nature) high-income areas, e.g.,
downtown vs. rural (spatial changing nature) Limitations in
distribution transformers, which are aggravated by the uneven PEV
and PHEV penetration favoring high-income areas, e.g., downtown vs.
rural (spatial changing nature)
Slide 7
7 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Main Contributions of the Paper rapid charging
station both spatially and temporally Present a mathematical model
of rapid charging stations electricity demand which may vary both
spatially and temporally fluid traffic model (modified based on
highway Poisson-arrival-location model (PALM)) The arrival rate of
discharged electric vehicles at a specific charging station is
anticipated by the fluid traffic model (modified based on highway
Poisson-arrival-location model (PALM)) M/M/s queueing theory
(Poisson vehicle arrival, exponential vehicle charging time, s
identical charging pumps) EV charging demand is predicted by the
M/M/s queueing theory (Poisson vehicle arrival, exponential vehicle
charging time, s identical charging pumps)
Slide 8
Highway Model Description 8 Broadband Communications Research
(BBCR) Lab Smart Grid Research Group
Slide 9
9 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Traffic Model for Semi-infinite, One-way,
Single-lane Freeway Distance x Distance along the highway from the
spatial origin which is the beginning point of the highway Velocity
field v(x, t) Velocity field of each vehicle Charging stations are
located on each exit or entrance Poisson Vehicle arrives at each
entrance with the Poisson distribution
Slide 10
10 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Extensions of the Traffic Model Multiple-lane
Highway Model Combine basic highway models in which vehicles have
different velocities Bidirectional Highway Model Eastbound v e (x,
t) 0 Westbound v w (x, t) 0 Elaborate Highway Network Model
Superimpose groups of multiple-lane and bidirectional highways
Slide 11
Model Formulations 11 Broadband Communications Research (BBCR)
Lab Smart Grid Research Group
Slide 12
12 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Assumptions full state-of-charge The battery for an
already charged vehicle entering the highway has a full
state-of-charge (e.g., due to the night-time charging at home) last
for the entire range of the trip Fully charged batteries can last
for the entire range of the trip. Hence, the user of an EV that
enters the highway fully charged may exit the highway not because
the batteries are discharged but rather because he/she may require
to rest => This study focuses on the discharged EVs user who
forgets to charge it at night, thus requiring visiting a charging
station on a highway (consider the highway as a prison or
jail)
Slide 13
13 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Definitions of Variables remaining The number of
discharged EVs remaining in the interval (0, x] at time t passed
The number of discharged EVs that have already passed through
through the position x before time t entered the The number of
discharged EVs that have entered the highway highway along the
interval (0, x] before time t exited the The number of discharged
EVs that have exited the highway highway along the interval (0, x]
before time t
Slide 14
14 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Representations of Variables Discharged EVs leaving
the system (i.e., ) are divided into: Permanently depart 1)
Permanently depart from the highway and recharge at their final
destinations (e.g., arrive home) Temporarily leave will return to
the highway after recharging 2) Temporarily leave the highway in
order to recharge their batteries at the highway exit charging
station, and will return to the highway after recharging their
batteries
Slide 15
15 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Deterministic Fluid Dynamic Model Conservation
Equation (Foundation) Density of Discharged Vehicles, veh/km (Will
show: this is the only unknown variable) Traffic Flow of Discharged
Vehicles, veh/min Densities of Discharged Vehicles Entering or
Leaving the Highway
Slide 16
16 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Deterministic Fluid Dynamic Model (Contd) traffic
theorytraffic flow traffic density vehicles velocity In traffic
theory, traffic flow can be defined as the multiplication of a
traffic density by a vehicles velocity Known (or Measurable)
Slide 17
17 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group All discharged EVs actually arriving at the highway
in Equivalent to the interval (0, x] before time t. Equivalent to
permanently departing All discharged EVs permanently departing from
the highway in the interval (0, x] before time t temporarily
leaving All discharged EVs temporarily leaving the highway in order
to recharge their batteries in the interval (0, x] before time t
Deterministic Fluid Dynamic Model (Contd)
Slide 18
18 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Deterministic Fluid Dynamic Model (Contd) These rate
densities can be identified with the actual arrival rate (i.e., i
(t) ) and the permanent departure rate (i.e., i (t) ) of discharged
EVs at the i th highway entrance/exit and at time t typically
measured in the number of vehicles per minute The condition which
discharged vehicles can only arrive at and depart from the highway
through entrances/exits: Dirac Delta Function Distance from the
Spatial Origin to the i th highway entrance/exit Known (or
Measurable)
Slide 19
19 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Deterministic Fluid Dynamic Model (Contd) Assume
that discharged EVs will return to the highway immediately after
finishing to recharge their batteries Temporarily Departing Rate
per Minute Charging Completion Rate per Minute Average Charging
Power per Vehicle Average Recharged SOC per Vehicle 1/60
Slide 20
20 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Deterministic Fluid Dynamic Model (Contd)
conservation equation By substituting the equations into the
conservation equation, we have An ordinary differential equation
(ODE) which can be solved with numerical methods without many
difficulties, given certain boundary condition arrival rate The
arrival rate of discharged EVs at the i th highway charging
station
Slide 21
21 EVs Charging Demand by the M/M/s Queueing Theory stable The
queueing system is stable if and only if the occupation rate ( ) of
charging pumps is less than 1 minimum number of charging pumps The
minimum number of charging pumps Broadband Communications Research
(BBCR) Lab Smart Grid Research Group
Slide 22
22 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group EVs Charging Demand by the M/M/s Queueing Theory
(Contd) busy charging pumps The expected number of busy charging
pumps power demand of charging station The power demand of charging
station
Slide 23
23 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Stochastic Model expected value The purpose of the
stochastic model presented here is to identify the expected value
of the stochastic EV charging demand Analogous to the deterministic
model
Slide 24
Numerical Example and Discussions 24 Broadband Communications
Research (BBCR) Lab Smart Grid Research Group
Slide 25
25 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Basic Highway Model for a Numerical Example (1/2)
Charging power: 70 kW (level 3 charging station ) Battery capacity:
8.6 kWh 3.4 min to recharge Average charge per vehicle at the
highway charging station is 4 kWh which is about 50% of the battery
capacity (3.4 min to recharge)
Slide 26
26 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Basic Highway Model for a Numerical Example (2/2)
Velocity fields rush hour Velocity fields of vehicles on the
highway is 1 km/min for all x 0 when t 40 or t > 55 min. During
the time interval (40, 55] min corresponding to rush hour, given
by
Slide 27
27 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Simulated Mean Density of Discharged Vehicles
Non-Rush Hour Rush Hour
Slide 28
28 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Simulated Mean Traffic Flow of Discharged Vehicles
Non-Rush Hour Rush Hour
Slide 29
29 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Expected Number of Charging Pumps in Service and
Expected Charging Demand Non-Rush Hour Rush Hour
Slide 30
30 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group Application: Sizing the Energy Storage System
Off-Peak TimePeak Time
Slide 31
Conclusions 31 Broadband Communications Research (BBCR) Lab
Smart Grid Research Group
Slide 32
32 Broadband Communications Research (BBCR) Lab Smart Grid
Research Group fluid traffic model Highway EV model is based on the
fluid traffic model M/M/s queueing theory EV charging demand is
calculated with the arrival rate of discharged EVs by the M/M/s
queueing theory Application I Application I: Sizing the energy
storage system Application II Application II: Distribution system
planning - Traditionally, the planning focuses on local demand move
coordination among neighboring utilities is necessary - With EVs,
demand may move from another utility into the area of the utility
under consideration => coordination among neighboring utilities
is necessary
Slide 33
Thank you! 33 Broadband Communications Research (BBCR) Lab
Smart Grid Research Group
