Oct-18-2016 PEV charging network planning on coupled ... - Google

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

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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


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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


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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


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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


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Will our old experiences still work?

Gas stations are everywhere! ©Hongcai Zhang


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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


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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


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



Where will PEVs need to get recharged? ©Hongcai Zhang


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



How are transportation and power systems coupled? ©Hongcai Zhang


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Content


©Hongcai Zhang


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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


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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


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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


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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


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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


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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"


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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:" )


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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


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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:@"


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Content


©Hongcai Zhang


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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


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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


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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


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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


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Content


©Hongcai Zhang


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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


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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


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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


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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


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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


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Content


©Hongcai Zhang


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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


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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)


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


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


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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


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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


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


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

46

60 6

48

6

32


Without extra constraints 19 stations with 1017 spots, 81 minutes


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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


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


40000 PEVs/day 49 stations with 2301 spots


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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


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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


©Hongcai Zhang

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113 3

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

31

51


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


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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


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Thank You！

©Hongcai Zhang


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