Value of Coordination inElectric Vehicle Charging

18-777 December 8th 2011

Jon Donadee

Outline

• Background• “Dumb” EV Charging• “Smart” EV Charging• “Smarter” EV Charging• Results and Comparison• Conclusions

Background• EVs are gaining popularity

– Environmental reasons• CO2• Local air quality

– Energy Independence – 840,000 EVs sold per year by 2020

“Dumb” Charging

• Decision to charge EV is independent of price• Inefficiencies

– Increase peak load• Requires more generators

– Overload transformers– Doesn’t minimize line losses– Doesn’t minimize Cost

• Reasoning for this strategy– Charging an EV is cheap

Energy Price

100 400 700 1000 1300 1600 1900 220020.00

40.00

60.00

80.00

100.00

120.00

Average Price($/MWh) vs Time of Day

Average PriceExponential (Average Price)

Time of day

$/M

Wh

Uncoordinated “Smart” Charging

• Individuals plan charging schedule based on predicted prices• Uncoordinated• Issue: Assumes they have no impact on the price

– True for small number of EVs

• Equivalent to aggregator ignoring effect on price

“Smart” Optimization Model

Variables:

= total EV energy for vehicle v in hour h

= Energy Charged to vehicle v in

timestep t

Parameters:

= Assumed Price at hour h

= energy required by EV owner

=maximum charging rate for vehicle v

= timestep size

S = scale factor for # of Evs represented in Agg

C = scale factor for commute time

= Efficiency from generator to battery

Uncoordinated Cost Problem v

S.T.

Simulation Data• Simulation of 1M Evs

– Optimize 1000 over EVs – Scale so each EV represents 1000 Evs – S=1000

• Randomly assigned charging equipment– 30% L1 Charging 3.3kW– 60% L2 Charging 16.8kW– 10% L3 50kW

• Randomly Generated Driving Patterns– Plug-in/Unplug Times– Energy requirements for commute to work

• EnergyReq(kWh)=(2*CommuteTime*30mph)/(3mi/kWh)• Losses

– Assume 90% efficient from generator to battery• Assumptions

– EVs only charging at home– No energy loss while parked at work– Travel time is the same in both directions

EV Driving Pattern Generation

• Hour of Arrival at work– A ~ N( 9, 0.5)

• Time at work– W~N(8.5,0.2)

• Commute time– Lognormal

• Mean 30 min• Variance 80

10 20 30 40 50 60 70 80 900

50

100

150

200

250

300

350

Nu

mb

er

of V

eh

ice

s

Commute Time (min)

Distribution of Commute Times

EV Driving Patterns

0 5 10 15 20 25 306

8

10

12

14

16

18

20

Car #

Tim

e of

Day

Arrive Home

Leave Work

Arrive Work

Leave Home

Expected Energy Price

100 400 700 1000 1300 1600 1900 220020.00

40.00

60.00

80.00

100.00

120.00

Average Price($/MWh) vs Time of Day

Average PriceExponential (Average Price)

Time of day

$/M

Wh

Optimized Charging Schedule

12am 1am 2am 3am 4am 5am 6am0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Energy Usage(MWh) vs Time

Time of Day

Ener

gy P

urch

ased

(MW

h)

Energy Market

50000 60000 70000 80000 90000 100000 110000 120000 13000020

40

60

80

100

120

140

f(x) = 6.25541624531637E-13 x³ − 1.50684823824867E-07 x² + 0.012574895490486 x − 323.491186405765R² = 0.973573255226382

Price($/MWh) vs Quantity(MWh)

Price($/MWh) Polynomial (Price($/MWh))

MWh

Pric

e ($

/MW

h)

Uncoordinated Charging Results

4pm5pm

6pm7pm

8pm9pm

10pm11pm

12am1am

2am3am

4am5am

6am7am

8am9am

10am0

1

2

3

4

5

6

Price Differences($/MWh) vs Time

Time of Day

Pric

e Ch

ange

($/M

Wh)

• Graph of the difference between the Actual Price resulting from “Smart” charging and the Assumed Price used in Optimization

Uncoordinated Charging Results• Results if travel distance and # of vehicles is doubled

4pm5pm

6pm7pm

8pm9pm

10pm11pm

12am1am

2am3am

4am5am

6am7am

8am9am

10am02468

101214161820

Price Differences($/MWh) vs Time

Time of Day

Pric

e D

iffer

ence

($/M

Wh)

Coordinated Charging

Variables:

= total fleet energy purchased in hour h

= Energy Charged to vehicle v in

timestep t

= total fleet energy purchased timestep t

Parameters:

= Predicted Price at hour h

= Predicted Exogenous Demand in hour h

= energy required by EV owner

=maximum charging rate for vehicle v

= timestep size

S = scale factor for # of Evs represented in Agg

C = scale factor for commute time

= Efficiency from generator to battery

Optimization Problem Convexity

0 20 40 60 80 100 120 140 1600

2

4

6

8

10

12x 10

8

Obje

ctive F

unction V

alu

e

Et+Dt (GW)

Results

12am 1am 2am 3am 4am 5am 6am0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Energy Usage(MWh) vs Time

Time of Day

Ener

gy P

urch

ased

(MW

h)

Coordinated Charging Uncoordinated Charging

Results

Error of Uncoordinated

Model($/day)

Error of Uncoordinated

Model(%)

Savings vs Uncoordinated

Model(%)

Savings vs Uncoordinated

Model$/day

1 Million EVs 43,211 10.26 4.32 $17,457 2 Million EVs 167,939 18.18 10.46 $87,445 3 Million EVs 434,445 27.71 21.80 $280,611 2x Distance1Million EVs

110,078

12.48 4.94 $41,550 2x Distance

2 Million EVs519,334

25.169 17.16 $302,221

Conclusions

• EVs may have a significant Effect on Energy Prices in the future

• Coordinated charging can anticipate effect of consumption on price

• Problem may be convex, TBD

Questions?