51st North American Power Symposium

Jingyi Yuan

Arizona State University

Oct 15, 2019

Optimizing EV Charging Station Placement with Social Welfare and Economic Parameters

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station

DG

DG

Contents

2

Motivation

Distribution + Transportation

Flexible Architecture? + Econ. Para.+ Social Welfare

Linearize Constraints

The Optimal EV Charging Station

Placement?

Cross-disciplinary Integration

Model Convexification

Mathematical Formulation

EV: Electric Vehicle

Motivation

[1] https://evadoption.com/ev-charging-stations-statistics/ 3

When Needed No Charging Station

Planning Difficulties

• Uncertainty

• Impractical

• Non-convex

How to solve?

EVs

Charging Stations

Fig. 1. The comparison of EVs and EV charging stations [1].

Extremely Bad!

Cross-disciplinary Integration

Transportation Network

Electrical Network

GIS (Geographic Information System)

ZIP Codes (Latitudes & Longitudes)

EV Charging Loads

Traffic Circulations

1 + 1 = 3?

Public Cloud

Private Cloud

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station

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4

Abstraction from Integrated Networks

Abstraction

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station

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Minimizing Levelized Costs

Decision: Placement of EV Charging Stations

Nodes CouplingRealistic Setup

1. Physical System 2. Diagrams 3. Nodal Representation 4. Mathematical Formula

Components

5

Transportation Systems

Transactive Domain Factors

✔ Quantified

[2] California Plug-in Electric Vehicle Driver Survey Results: May 2013 (California Center for Sustainable Energy, 2013). [3] Census Data (United States Census Bureau, accessed 15 October 2016); https://www.census.gov/data.html

Cyber-Physical Systems

Electrical Systems

Human Factor

6

Best Solution?

Social Welfare

Transactive Domain Factors

Inflation RateDiscount Rate

Lon

g-Te

rmP

lan

nin

g

Levelized Costs

Nonconvex!

[2] California Plug-in Electric Vehicle Driver Survey Results: May 2013 (California Center for Sustainable Energy, 2013). [3] Census Data (United States Census Bureau, accessed 15 October 2016); https://www.census.gov/data.html 7

Piecewise Step Functions

Low Approximation Errors

Linear Curve-Fitting

Cost ($)

Current (A)

Cacq

Id1Id0 Id2 Id4

Cinst/Cuninst

Cmain

c=1 c=4c=3c=2

Convexified

Numerical Validation: Convexity Helps?

✔Guarantee Global Optimum

Sioux FallsTransportation Network

IEEE 123-bus Distribution Network

Realistic Networks

WithWithout

19.8% Failed 0% Failed

$8.07 × 107 $7.96 × 107

Saved ~ 100,000

105.6 s (avg.)112 to 2,115 secExhaust all Search once

9

Global Minimum

Convexification

Avg. Minimum Cost

Time

Results

Cut Time

Num. Validation: Flexibility + Indicator

Without Levelized Costs Overestimation𝑆Levelized

Costs𝜶/𝜷

𝚻/yrs

𝑆1 No 0/0 20

𝑆2 Yes 5%/5% 20

𝑆3 Yes 5%/5% 5

𝑆4 Yes 1%/5% 20

𝑆5 Yes 5%/15% 20 Zoom-in

Economic Parameters

Long-term vs. Short-term

10

DiversifiedScenarios

𝜶: Inflation Rate𝜷: Discount Rate

IndicateBounding Constraints

System Planning: Analytical Tools!!

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Conclusion

2

Motivation

Distribution + Transportation

Flexible Architecture? + Econ. Para.+ Social Welfare

Linearize Constraints

Cross-disciplinary Integration

Model Convexification

Mathematical Formulation

EV: Electric Vehicle

Planning Tools

• Global Optimum

• Computational Reduction

• Flexibility + Indicators

Back Up Slides

[4] C. Meneses and J. Mantovani, “Improving the grid operation and reliability cost of distribution systems with dispersed generation,” IEEE Transactions on Power Systems, Aug 2013.

[5] A. Garces, “A linear three-phase load flow for power distribution systems,” IEEE Transactions on Power Systems, Jan 2016. 8

Model Convexification

Convexified!

✔AC Power Flow Linearization

✔ Linear Combination

Piecewise Step Functions

Low Approximation Errors

Linear Curve-FittingCost ($)

Current (A)

Cacq

Id1Id0 Id2 Id4

Cinst/Cuninst

Cmain

c=1 c=4c=3c=2

Similarly, …

[4] C. Meneses and J. Mantovani, “Improving the grid operation and reliability cost of distribution systems with dispersed generation,” IEEE Transactions on Power Systems, Aug 2013.

[5] A. Garces, “A linear three-phase load flow for power distribution systems,” IEEE Transactions on Power Systems, Jan 2016. 8