PEV fast-charging station siting and sizing on coupled transportation and power networks --eCAL Seminar Report

Hongcai Zhang, PhD Candidate With: Scott Moura, Zechun Hu, Wei Qi, Yonghua Song SGOOL, Tsinghua University eCAL, University of California, Berkeley [email protected] Oct 18, 2016 ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

1

Content

Background Service ability modeling of one single charging station PEV drive range logic and transportation network modeling Planning model considering both transportation and electrical constraints Simulation results and conclusion

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

2

Project background: fast-charging network planning in Qinghai Lake Area o Biggest inland lake, most famous tourist resort o Strong demand for public transportation (pollution!) o Abundant Photovoltaic power generation

Qinghai Lake, China (Surface > 4500 km2) ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

3

PEV market in China is booming o 447,200 sold since 2011 through 2015 o Goal: 5 million by 2020

331092

350000 300000 250000 200000 150000 78499

100000 50000

8159

12791

17642

2011

2012

2013

0 2014

2015

EV sales volume China* EV sales volume ininChina*

Best EV sellers in China

*Data source: China Association of Automobile Manufacturers ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

4

Heavy investment on charging infrastructure is underway o 49,000 public spots, 3,600 charging/swapping stations deployed o 4.8 million distributed charging spots and 12 thousand fast charging/swapping stations by 2020 Market scale (Billion US $) 90.0

78.8

80.0 70.0 60.0 50.0 36.6

40.0 30.0 20.0 10.0

13.1 3.3

0.0 2015 Spots

2020 Fast-charging stations

*Data source: China Association of Automobile Manufacturers and www.evpartner.com/ ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

5

Will our old experiences still work?

Gas stations are everywhere! ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

6

PEV charging infrastructure is different o Long service time o Limited drive range o Coupling points of both the transportation & the power networks

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

7

Site and size PEV charging stations on coupled transportation and power networks o Evaluate one single charging station’s service ability n

Serving PEVs with heterogeneous drive ranges and demands

o Model transportation networks with drive range constraints o Describe coupled relationship of transportation & power networks

? = How many charging spots are needed for such amount of demands? ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

8

Site and size PEV charging stations on coupled transportation and power networks o Evaluate one single charging station’s service ability o

Serving PEVs with heterogeneous drive ranges and demands

o Model transportation networks with drive range constraints o Describe coupled relationship of transportation & power networks

Where will PEVs need to get recharged? ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

9

Site and size PEV charging stations on coupled transportation and power networks o Evaluate one single charging station’s service ability n

Serving PEVs with heterogeneous drive ranges and demands

o Model transportation networks with drive range constraints o Describe coupled relationship of transportation & power networks

How are transportation and power systems coupled? ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

10

Content

Background Service ability modeling of one single charging station PEV drive range logic and transportation network modeling Planning model considering both transportation and electrical constraints Simulation results and conclusion

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

11

Literature review: Linear models* o Empirically assume the the demand that one facility can satisfy is a constant: 𝜆" = 𝐴y" o Limitations n

Can not consider heterogeneous charge demands

n

Ignore ‘scale effect’ because of randomness of demand

Demand

Demand

Facility no.

Linear model

Facility no.

Practical performance

* C. Upchurch, M. Kuby, and S. Lim,“A model for location of capacitated alternative-fuel stations,” Geogr. Anal., vol. 41, no. 1, pp. 127–148, 2009.

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

12

Literature review: Queuing models* o Utilizing queuing theory to estimate waiting time, length etc. o Limitations n

Can not consider heterogeneous charging demands

n

No closed-form formulation

250

Actual Piecewise Linear

Average charging demand

200

150

100

110 100 90

50

80 70 50 0

0

50

55 100

60 150

Optimal spot number

* P. Fan, B. Sainbayar, and S. Ren, “Operation Analysis of Fast Charging Stations with Energy Demand Control of Electric Vehicles,” IEEE Trans. Smart Grid, vol. 6, no. 4, pp. 1819–1826, 2015.

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

13

Assumptions o PEVs arrive at a station following a Poisson process n

Occur with a known average rate (parameter 𝜆" ) and independently of the time since the last event

o PEVs are served based on a ‘first-in-first-out’ rule n

The rule does not allow waiting

n

When the charging spots are all occupied in the station and a new PEV arrives, the PEV on board that has charged the most should leave and spare spot to the new PEV

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

14

Service criterion & its equivalence (homogeneous PEVs) o Service criterion 1: the possibility that ‘the PEVs can be charged for at least 𝑻 units of time’ is no less than 𝛼 o Service criterion 2: The probability that 'the number of Poisson arrivals of PEVs in a duration of 𝑻 units of time is less than the number of spot’ is no less than 𝛼

The Poisson arrivals of PEVs in a station (homogeneous drive range)

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

15

Approximation of Poisson distributions o Poisson arrivals at a station in a certain time intervals, e.g., 𝑇, can be approximated as a normal distribution n

𝑁" ~(µ = 𝑇𝜆" , 𝜎 . = 𝑇𝜆" )

n

Accuracy can be guaranteed when 𝑇𝜆" ≫

𝑇𝜆" (say, if 𝑇𝜆" > 4 𝑇𝜆" )

𝑇 𝑇 𝑇

Probability density function of Poisson distributions ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

16

Service rate model for fast-charging stations serving homogeneous PEVs o Service criterion 2: the probability that 'the number of Poisson arrivals of PEVs in a duration of 𝑻 units of time being less than the number of spot, i.e., 𝒚𝒊 ’, is no less than 𝛼 o “the number of Poisson arrivals of PEVs in a duration of 𝑻 units of time”, i.e., x, follows 𝑁(µ = 𝑇𝜆" , 𝜎 . = 𝑇𝜆" )

o Then, the spot number y" is limited by n

y" ≥ 𝑇𝜆" + 𝜙 89 𝛼

©Hongcai Zhang

𝑇𝜆"

SGOOL, Tsinghua and eCAL, UC Berkeley

17

Service rate model for fast-charging stations serving homogeneous PEVs: SOCP form

Diagram of two paths (origin-destination pairs)

o Traffic flow on each path, 𝜆: , is given, while the charge decision of each path at each location, 𝛾:" , are binary variable n

𝜆" = ∑: 𝜆: 𝛾:"

o Original model: y" ≥ 𝑇𝜆" + 𝜙 89 𝛼

𝑇𝜆"

o SOCP model: y" ≥ 𝑇 ∑ 𝜆: 𝛾:" + 𝜙 89 𝛼

©Hongcai Zhang

. . 𝑇 ∑ 𝜆: 𝛾:" (note 𝛾:" =𝛾:" )

SGOOL, Tsinghua and eCAL, UC Berkeley

18

Service rate model for fast-charging stations serving heterogeneous PEVs o Service criterion 3: the possibility that ‘the PEVs can be charged for at least their expected service time, i.e., 𝑻𝒌 for type 𝒌 PEVs’ is no less than 𝛼 o Service criterion 4: the possibility that ‘the summation of K Poisson arrivals of PEVs, i.e., Poisson arrival of type 𝒌 PEV in 𝑻𝒌 units of time, is less than the number of spot’ is no less than 𝛼

The Poisson arrivals of PEVs in a station (heterogeneous drive range) ©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

19

Service rate model for fast-charging stations serving heterogeneous PEVs o Service criterion 4: the possibility that ‘the summation of K Poisson arrivals of PEVs, i.e., Poisson arrival of type 𝒌 PEV in 𝑻𝒌 units of time, is less than the number of spot’ is no less than 𝛼 o Theorem: the summation of independent normal distribution is still a normal distribution o 𝑥~𝑁(µ = ∑@ 𝑇@ 𝜆@" , 𝜎 . = ∑@ 𝑇@ 𝜆@" ) o Heterogeneous PEV drive range model n

y" = ∑@ 𝑇@ 𝜆@" + 𝜙 89 𝛼

n

y" = ∑@ ∑: 𝑇@ 𝜆:@ 𝛾:@" + 𝜙 89 𝛼

©Hongcai Zhang

∑@ 𝑇@ 𝜆@" . ∑@ ∑: 𝑇@ 𝜆:@ 𝛾:@"

SGOOL, Tsinghua and eCAL, UC Berkeley

20

Content

Background Service ability modeling of one single charging station PEV drive range logic and transportation network modeling Planning model considering both transportation and electrical constraints Simulation results and conclusion

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

21

Literature review

Node based model*

Traffic based model**

Simulation based model*** * J. Cavadas, G. Homem de Almeida Correia, and J. Gouveia, “A MIP model for locating slow-charging stations for electric vehicles in urban areas accounting for driver tours,” Transp. Res. Part E Logist. Transp. Rev., vol. 75, pp. 188–201, 2015. **J.-G. Kim and M. Kuby, “The deviation-flow refueling location model for optimizing a network of refueling stations,” Int. J. Hydrogen Energy, vol. 37, no. 6, pp. 5406–5420, 2012. ***N. Shahraki, H. Cai, M. Turkay, and M. Xu, “Optimal locations of electric public charging stations using real world vehicle travel patterns,” Transp. SGOOL, 22 Zhang Res. Part D©Hongcai Transp. Environ., vol. 41, pp. 165–176, 2015 . Tsinghua and eCAL, UC Berkeley

Drive range logic based on expanded network * o Drive range after a charge, 100 km

A single path*

An expanded path (optimal result: {B, C} or {B, D})*

* S. A. MirHassani and R. Ebrazi, “A Flexible Reformulation of the Refueling Station Location Problem,” Transp. Sci., vol. 47, no. 4, pp. 617–628, 2013.

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

23

Drive range logic based on sub-path* o Drive range after a charge, 50 miles

Drive range logic of PEVs (with 50 miles’ drive range)

o Constraints formulation (11-12): PEVs shall get charged at least once in each sub-path (13): PEVs can get charged only there is located with a charging station * H.-Y. Mak, Y. Rong, and Z.-J. M. Shen, “Infrastructure Planning for Electric Vehicles with Battery Swapping,” Manage. Sci., vol. 59, no. 7, pp. 1557–1575, 2013.

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

24

Modified Capacitated flow refueling location model based on sub-path (CFRLM_SP) Objective: minimize the investment costs and penalize unsatisfied charging demand Subject to: (10): Service ability

(11-12): PEVs shall get charged at least once in each sub-path (13): PEVs can get charged only there is located with a charging station (14): Lower/upper limit of spot number (31): PEV charging power

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

25

Extra constraints for CFRLM_SP considering practical operation

o The scale of charge choice variable 𝛾:"@ is large o Extra constraints n

PEVs with the same origins have the same charging choices on the coupled sub-paths

n

Constraints: the charge choice variables, i.e., 𝛾:"@ , of different paths with same origins on same sub-paths are the same

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

26

Content

Background Service ability modeling of one single charging station PEV drive range logic and transportation network modeling Planning model considering both transportation and electrical constraints Simulation results and conclusion

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

27

Literature review

Charging network planning considering the influence of electricity price*

Charging network planning considering coupled power & transportation network**

*F. He, D. Wu, Y. Yin, and Y. Guan, “Optimal deployment of public charging stations for plug-in hybrid electric vehicles,” Transp. Res. Part B Methodol., vol. 47, no. 2013, pp. 87–101, 2013. **G. Wang, Z. Xu, F. Wen, and K. P. Wong, “Traffic-constrained multiobjective planning of electric-vehicle charging stations,” IEEE Trans. Power Deliv., vol. 28, no. 4, pp. 2363–2372, 2013.

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

28

Coupled transportation and power systems o 110 kV distribution network, connected to one 220 kV substation n

With a large service radius more than several hundred km

o Coupling relationship between both networks n

Some transportation nodes are coupled with distribution buses

n

Others have to invest distribution lines to access to electricity

PEV charging network ©Hongcai Zhang

High voltage distribution network

SGOOL, Tsinghua and eCAL, UC Berkeley

29

Two-stage stochastic programming model o Objective n

Investment costs + weighted average of operation costs

o Variables n

First-stage: station investments, charge decision

n

Second-stage: power purchase, consumption, curtailment, nodal voltage, and branch current during each time interval of each scenario

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

30

Objective formulation o Investment costs Investment for charging stations Investment for grid upgrades

o Operation costs Electricity purchase costs Penalty for unsatisfied demands

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

31

Constraints formulation o Transportation constraints: CFRLM_SP o Electrical constraints: AC power flow (SOCP)

o Coupled constraints n

Each transportation node can be mapped to a distribution bus Power at transportation node Power at distribution bus

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

32

Content

Background Service ability modeling of one single charging station PEV drive range logic and transportation network modeling Planning model considering both transportation and electrical constraints Simulation results and conclusion

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

33

Case overview o 25 node transportation network, with 93 candidate locations o 14 node distribution network, 110 kV, 150 MW capacity o

4 PEV types with drive range {200, 300, 400, 500} km

A 25 nodes transportation network ©Hongcai Zhang

A high voltage distribution network

SGOOL, Tsinghua and eCAL, UC Berkeley

34

Scenario preparations o 24 scenarios (weekday and weekend of 12 months in a year) 0.9

power

0.8 0.7 0.6

1.1

Residential Commercial loadload profiles profiles in weekend in weekday

1

Month Month 1 1 Month Month 2 2 Month Month 3 3 Month Month 4 4 Month Month 5 5 Month Month 6 6 Month Month 7 7 Month Month 8 8 Month Month 9 9 Month Month 10 10 Month Month 11 11 Month Month 12 12

1 0.9 0.9

0.8

0.8 0.7

0.7

0.6

0.65 0.6 0.55

0.6 0.5

0.5

0.4

0.4

0.4 0.4 2

4

6

8

0.3 0.3

10 12 14 16 18 20 22 24

0.35 2

24

46

68

time (h)

power

1 0.8 0.6

AgricultureTime loaddistribution profiles in weekend of arrivals in weekday

1.40.15

2

1

0.15

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12

1.2

power arrival (per-unit)

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12

1.2

0.1

0.8 0.6 0.05 0.4

0.4 0.2 0

0.3

810 10 12 12 14 14 16 16 18 18 20 20 22 22 24 24

timetime (h) (h)

Agriculture load profiles in weekday

1.4

0.5 0.45

0.5

arrival (per-unit)

0.3

Co

0.7

power

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12

power power

Residential load profiles in weekday

1

0.1

0.05

0.2

2

4

6

8

10 12 14 16 18 20 22 24

0

0

2

42

6 48

time (h)

10 6 128 14 10 16 18 12 201422 16 24

time (h)

18

20

22

24

time (h)

* PG&E, “2000 static load profiles.” [Online]. Available: https://www.pge.com/nots/rates/2000 static.shtml, accessed Sep 30, 2016. ** A. Santos, N. McGuckin, H. Y. Nakamoto, D. Gray, and S. Liss, “Summary of travel trends: 2009 national household travel survey,” tech. rep., 2011.

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

35

0

2

Problem scale o Investment binary variables, 𝑥" : 93 n

Relaxed integer spot number variable to be continuous

o Charge choice binary variables 𝛾:@" : n

5668 (with extra constraints on charging choices)

n

16096 (without extra constraints on charging choices)

o Second order cone constraints n

Service rate model: 93*24*24=93,568

n

AC power flow: 13*24*24=7,488

o Solution time n

Several minutes (with extra constraints on charging choices)

n

1 ~ 10 hours (without extra constraints on charging choices)

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

36

Simulation results: heterogeneous drive range o Consider homogeneous DR leads to very conservative results 5

18

2

13

65

50

34

22

23

42

66

20

13

35

3

6 10 25

21

30

47

37

11

59

86

60

64

106 31 2

Coupled Node Charging Station

With heterogeneous drive range 29 stations with 1168 spots ©Hongcai Zhang

11

137

9

4 17

3

149 190 30

26

79

5 106

103

63 56

7 10

8

64

76

82

11

32

53

28

4

23 185

5

74 21

87

48

17

2

103 64

156 118

123 148

200 38

3

Coupled Node Charging Station 3

Without heterogeneous drive range 47 stations with 2693 spots

SGOOL, Tsinghua and eCAL, UC Berkeley

37

Simulation results: extra constraints on coupled paths o Consider extra constraints leads to slightly conservative results 5

18

34

2

13 50

34

22

30

23

37

11

59

86

45

56

17

3 81

87

5

23

60

109 91

183

7 26

10

66 155

106

79

4

82

11

185

26

9

4

31 2

Coupled Node Charging Station

With extra constraints 29 stations with 1168 spots, 9 minutes ©Hongcai Zhang

46

60 6

48

6

32

Coupled Node Charging Station

Without extra constraints 19 stations with 1017 spots, 81 minutes

SGOOL, Tsinghua and eCAL, UC Berkeley

38

Simulation results: PEV population (1) o Investment increases with PEV population 5

18

20 18

2

13

45

50

34

22

23

35

11

59

86

17

57 80

87

48 23 185 60

42

82

11 26

10

49

31 2

22 76 12 79

44 159

Coupled Node Charging Station

20000 PEVs/day 29 stations with 1168 spots ©Hongcai Zhang

13

61

151

106

79

16

164

7

194 147

7

10 16

46

4

19

6

105

57

31

49

3

42 4

13

32

4

3

36

37

5

36 21

12

30

3

8

152 43

15

4

Coupled Node Charging Station

40000 PEVs/day 49 stations with 2301 spots

SGOOL, Tsinghua and eCAL, UC Berkeley

39

Simulation results: PEV population (2) o Investment increases with PEV population

node 10 9 8 node 9 node 8 node 4 7 11 node 12 10 2 node 1 node 11 3 node 3 12 1 5 node 13 node 6 node 2 13 4 node 5 node 14 node 7 6

1 0.8 0.6 0.4 0.2

node 10 9 8 node 9 node 8 node 4 7 11 node 12 10 2 node 1 node 11 3 node 3 12 1 5 node 13 node 6 node 2 13 4 node 5 node 14 node 7 6

0

20000 PEVs/day 0.00% unsatisfied demands

©Hongcai Zhang

1 0.8 0.6 0.4 0.2 0

40000 PEVs/day 4.83% unsatisfied demands

SGOOL, Tsinghua and eCAL, UC Berkeley

40

Simulation results: power grid o Ignore power grid influence leads to higher investment costs 5

18

2

17

17

2

13 50

34

22

23

50

36

18

24 30

42

37

11

59

86

17

40

56

16

52 87

48

4

23

60

92

82

11

185

26

10

89

110 95

7

52 38

49

106

79 31 2

Coupled Node Charging Station

©Hongcai Zhang

53

113 3

20000 PEVs/day 29 stations with 1168 spots (10.1M$)

31

51

Coupled Node Charging Station

20000 PEVs/day 24 stations with 1146 spots (11.1M$)

SGOOL, Tsinghua and eCAL, UC Berkeley

41

Conclusion o Service rate model of PEV charging station service abilities n

Closed-form second order cone constraint

n

Heterogeneous PEV drive range

o Capacitated flow refueling location model based on sub-paths n

Time-varying OD traffic flow

n

Techniques to enhance model accuracy & computational efficiency

o Transportation constraints & AC power flow constraints o Limitations n

Computational efficiency for large-scale systems

n

Two stage stochastic programming’s accuracy (scenario numbers)

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

42

Thank You！

©Hongcai Zhang

SGOOL, Tsinghua and eCAL, UC Berkeley

43