TIM IMING IS IS EVERYTHING: OPTIMAL ELECTRIC VEHICLE CHARGING TO - - PowerPoint PPT Presentation

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Mar 20, 2023 323 likes β€’440 views

TIM IMING IS IS EVERYTHING: OPTIMAL ELECTRIC VEHICLE CHARGING TO MAXIMIZE WELFARE Miguel Castro Inter-American Development Bank Hourly private and external costs/Current charging profiles 34 45 Current EV charging 40 33 patterns

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SLIDE 1

TIM IMING IS IS EVERYTHING: OPTIMAL ELECTRIC VEHICLE CHARGING TO MAXIMIZE WELFARE

Miguel Castro Inter-American Development Bank

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SLIDE 2

5 10 15 20 25 30 35 40 45 26 27 28 29 30 31 32 33 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Marginal damages Prices

USD/MWh USD Damages/MWh

Hourly private and external costs/Current charging profiles

Current EV charging patterns (Houston & Dallas) withdraw most power after owners return to their home (7-9 PM) Excessive generation cost and environmental damages

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SLIDE 3

5 10 15 20 25 30 35 40 45 26 27 28 29 30 31 32 33 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Marginal damages Prices

USD/MWh USD Damages/MWh

Hourly private and external costs/Current charging profiles

Current EV charging patterns (Houston & Dallas) withdraw most power after owners return to their home (7-9 PM) Excessive generation cost and environmental damages

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SLIDE 4

Introduction

Empirical model

  • Partial equilibrium models of ERCOT wholesale electricity market

(Decentralized market with invariant tariff and Social planner hourly tariff)

  • Simulate how EV charging should be spread among hours to maximize

welfare (charging emissions damages) and surplus (no damages)

  • Simulate second best private and full social costs day-night tariffs

Main findings

  • EV charging in Texas can be met efficiently during the first hours of the

day (0-4 H). First best hourly social tariff.

  • Even day-night and hourly tariff based on private costs (no damages) can

guide users to charge EVs efficiently (overlap of low prices and low marginal carbon emissions during first hours of the day).

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SLIDE 5

Empirical Model (Social Planner)

  • Estimate fossil supply curve with hourly fossil generation, heat input data (EPA), and monthly

fuel costs (EIA Form 860) for ERCOT generators in 2017

  • Data on actual EV mileage (EV and plug-in hybrids) by auto model in TX (2017 National

Household Travel Survey) and current charging patterns (EV Project in Houston and Dallas, DOE, 2013) π‘π‘π‘¦π’ˆ,𝑭𝑾

𝑒=0 23 π‘Ÿπ‘’

𝑄𝑒(π‘Ÿπ‘’)π‘’π‘Ÿπ‘’ βˆ’ 𝐷 𝑔

𝑒 βˆ’ πœπ‘’πΉπ‘Š 𝑒

𝑑. 𝑒.

𝑒=0 23

πΉπ‘Š

𝑒 = πΉπ‘Š

π‘Ÿπ‘’ + πΉπ‘Š

𝑒 = π‘₯𝑒 + 𝑔 𝑒 + π‘œπ‘£π‘™π‘“π‘’

and charging constraints

Where: π‘Ÿπ‘’ Electricity demand π‘₯𝑒 Wind power 𝑔𝑒 Fossil generation πΉπ‘Šπ‘’ charging demand 𝐷𝑒 𝑔𝑒 private fossil generation costs πœπ‘’ Marginal damages (carbon, sulfur, nitrogen

  • xide, and PM 2.5 emissions)
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SLIDE 6

Empirical Model (Decentralized market)

Where: 𝑂𝑑 Number plug-in hybrid (gasoline) electric vehicles and full electric vehicles by model s 𝑓𝑀𝑑 daily individual charging demand based

  • n total annual miles estimated in the NHTS;

and using EPA fuel economy (kWh/mi) 𝑓𝑀𝑑𝑒 hourly EV charging 𝑀 π‘‘β„Žπ‘π‘ π‘•π‘—π‘œπ‘• 𝑒𝑗𝑛𝑓𝑑 for L1 and L2 types

  • Demand is calibrated with a linear functional form and hourly (short run)

elasticity from literature (Deryugina, 2017; Wolak, 2011) 2) π·π‘π‘œπ‘‘π‘£π‘›π‘“π‘  π‘π‘žπ‘’π‘—π‘›π‘π‘šπ‘—π‘’π‘§ π‘‘π‘π‘œπ‘’: 𝑄𝑒 π‘₯𝑒 + 𝑔

𝑒 + π‘œπ‘£π‘™π‘“π‘’ βˆ’ πΉπ‘Š 𝑒 = π‘žπ‘’ βˆ€π‘’

3) πΊπ‘π‘‘π‘‘π‘—π‘š π‘•π‘“π‘œπ‘“π‘ π‘π‘’π‘π‘  π‘π‘žπ‘’π‘› π‘‘π‘π‘œπ‘’: 𝐷′ 𝑔

𝑒 = π‘žπ‘’π‘₯ βˆ€π‘’

Wholesale cost recovery condition: 5) π‘žπ‘’π‘ 

𝑒=0 23

(π‘Ÿπ‘’ + πΉπ‘Š

𝑒) =

𝑒=0 23

(π‘₯𝑒 + 𝑔

𝑒 + π‘œπ‘£π‘™π‘“π‘’) βˆ— π‘žπ‘’π‘₯

Charging constraints:

6) 𝑑 𝑒=0

23 𝑂𝑑 βˆ— 𝑓𝑀𝑑𝑒 = 𝑑 𝑂𝑑 βˆ— 𝑓𝑀𝑑 = 𝑒=0 23 πΉπ‘Šπ‘’ = πΉπ‘Š

7) 𝑓𝑀𝑑𝑒 ≀

𝑐𝑏𝑒𝑒𝑓𝑠𝑧 𝑑𝑗𝑨𝑓𝑑 𝑀 π‘‘β„Žπ‘π‘ π‘•π‘—π‘œπ‘• 𝑒𝑗𝑛𝑓𝑑 βˆ€π‘‘

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SLIDE 7

Empirical Model (Marginal damages and emissions)

𝑍

𝑒 𝑛 = 𝛾0𝑛 + β„Ž=0 23

π›Ύπ‘šβ„Žπ‘› πΌπ‘ƒπ‘‰π‘†β„Ž βˆ— 𝐸𝑒 +

β„Ž=0 23

𝛾π‘₯β„Žπ‘› πΌπ‘ƒπ‘‰π‘†β„Ž βˆ— 𝑋

𝑒 + πœ€π‘₯ + 𝛿π‘₯𝑓 + πœπ‘’

where: 𝑍

𝑒 𝑛emissions (tCO2, lbs SO2, lbs NOx, and lbs PM2.5) and total air pollution damages (summation of

SO2, NOx, and PM2.5 damages in 2017 USD) at hour t in the entire grid, 𝑋

𝑒, 𝐸𝑒 are ERCOT aggregate wind power and demand (load) in MWh at hour t,

πœ€π‘₯ stands for weekly fixed effects and 𝛿π‘₯𝑓 for weekend FE, 𝜸 are regression coefficients. Average partial effects π›Ύπ‘šβ„Žπ‘› give the estimate of the hourly marginal emissions and damages of increasing load in one MWh Air pollution damages using county level marginal damages (morbidity and mortality) for medium and tall stacks from AP2 Model (Holland et al., 2016)

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SLIDE 8

Baseline calibration

Decentralized market, one invariant daily tariff

USD/MWh

Year-round total generation Year-round prices Average seasonal generation Year-round fossil generation

Band depicts a 95% confidence interval, while the solid lines represent medians. Model reproduces fairly well the median and trends for the entire year and even for different seasons. Static version of startup and ramp up costs, no transmission congestion constraints, but it captures with simplicity the main features and results

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SLIDE 9

Results

Welfare maximizing charging schedule (0-4 H) is the opposite of current patterns (18-23 H). Unconstrained first best charging has welfare gains of ~42% of wholesale prices (10.44 USD per MWh charged) Constraining power withdrawals to L1 and L2 chargers limits using energy from hours with lower prices and marginal carbon emissions reducing welfare gains Overlap of low prices and low marginal carbon emissions from 0-4H. 5-8H rapid increase in carbon emissions and air pollution.

*The bands depict a 95% confidence interval, while the solid lines represent averages.

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SLIDE 10

Results

Second best day-night tariff: based on the

  • ptimal

hours from welfare maximization problem (1-7AM, 12AM) Day-night private tariff (only generation costs) cause EV charging mostly at 4-5 AM. It captures ~93.7% of first best gains. Day-night social tariff (generation costs + emissions damages) EV charging at 3-4 AM, less emissions and larger gains ~98% of FB. Without emissions taxes, both hourly and day-night tariffs increase carbon and air pollution damages compared to current patterns charging

*The bands depict a 95% confidence interval, while the solid lines represent averages.