optimal load scheduling of electric ... - fabian neumann

Project Outline Modelling Optimisation Results Summary

Optimal Load Scheduling of Electric Vehicles inDistribution Networks

Fabian Neumann

Dissertation ProjectMSc Sustainable Energy Systems

School of EngineeringThe University of Edinburgh

August 22, 2017

https://github.com/fneum/ev_chargingcoordination2017

https://github.com/fneum/ev_chargingcoordination2017


Agenda

1 Project Outline

2 Modelling

3 Optimisation

4 Results

5 Summary


Motivation

Electric vehicles will add strain on distribution grids.

Targeted electrification of the transport sector entails

unprecedented loads in distribution networks

voltage drops and overloading of network equipment

Sustainability coupled to decarbonisation of electricity sector

variable generation calls for active network management

use EVs for demand side management as flexible loads

Consensus

Existing networks can accommodate substantial penetration levelsof electric vehicles if charging is coordinated without reinforcement.


Motivation

Joint market- and network-based scheduling is rare.

Much research has already been conducted. However,

1 market- and network-based optimisation is often disjunct;

cost-minimising algorithm disregards network constraints orpeak-shaving algorithm neglects potential economic benefits.

2 consideration of uncertainties about scenarios is moreprevalent than recognition of individual uncertainties inmobility patterns, residential demand and market prices.


Motivation

There are multiple sources of uncertainty in scheduling.

Aggregator

Residences

Power Market

Electric

Vehicle

Electric LoadLocal

Generation

Arrival and

Departure

Times

Battery

Charge Level

upon Arrival

Wholesale

Electricity

Prices

DSO


Research Objectives

Research Objectives

Develop a robust deterministic cost-minimising day-aheadscheduling routine that observes network and demandconstraints in a stochastic environment.

Model the uncertainties involved.

Exploit knowledge about their distributions to hedge risks:

cost of chargingcharging reliability

line overloadingvoltage violations


Research Objectives

Research Questions

1 How can the major uncertainties involved in day-aheadscheduling of electric vehicles be modelled generically

2 How do they limit the reliability of unaware schedulingapproaches in terms of meeting user requirements andobserving network constraints?

3 What is the relative cost and benefit of increasing therobustness towards forecast deviations in day-aheadscheduling by applying more conservative forecast estimates?


Setting and Scope

Setting, Scope and Limitations of Analysis

focus is on suburban low-voltage (400 V) distribution networks

penetration of electric vehicles is 100% for the 55 households

charging occurs exclusively overnight at home, not at work

charging control is devised to one central aggregator withaccess to some abstract wholesale electricity market

optimisation horizon is 24 h an is triggered daily at 1 pm(offline day-ahead scheduling)

time resolution is 15 min

uncertainty modelled via continuous distribution functions, inreality would use empirical distributions

linear power flow


Setting and Scope

European low-voltage test feeder

Substation

11/0.4 kV

33 [619.3]

10 [248.2]

1 [34.1]

2 [47.2]

3 [70.1]

4 [73.1]5 [74.1]

6 [83.2]

7 [178.2]

8 [208.3]

12 [264.3]

9 [225.1]

11 [249.2]

17 [327.3]

16 [320.3]

15 [314.2]

13 [276.2]

14 [289.1]

35 [639.2]

36 [676.2]

37 [682.2]

29 [562.1]

31 [611.1]

25 [502.2]

30 [563.1]

34 [629.1]

24 [458.3]

28 [556.3]

27 [539.3]

26 [522.2]

44 [785.2]

32 [614.3]

38 [688.2]

46 [817.1]49 [861.1]

39 [701.3]

42 [778.3]

40 [702.2]

54 [900.1]

51 [896.1]

41 [755.2]

45 [813.2]

43 [780.3]

47 [835.3]

52 [898.1]

55 [906.1]

50 [886.2]

53 [899.2]

21 [387.1]

19 [342.3]

22 [388.1]

20 [349.1]

18 [337.3]

23 [406.2]

48 [860.1]

Transformer

Load (Phase 1)

Load (Phase 2)

Load (Phase 3)


Data and Parameters

Data and Parameters

Network topology

European LV test feeder

Uncertainty:none

Price time series

UKPX Reference Price Data

Uncertainty:red-noise sequence

Demand time series

CREST demand model

Uncertainty:shifting peaks within 1 h

Mobility data

UK National Travel Survey

Uncertainty: normal distributions,parameters individually assigned

Vehicle specification

EV consumption: 0.17 kWh/km

Battery capacity: 30 kWh

Charging mode: 3.7 kW

Charging efficiency: 93%

Uncertainty:None


Data and Parameters

How do people use their (electric) vehicles?

Average departure time

0 500 1000Time [minutes after midnight]

0

50

100

Fre

quen

cy

Histogram of empirical driving profiles Best continuous distribution fit

Standard deviation of departure time

0 200 400 600 800Standard deviation [minutes from mean]

0

50

100

150

200

Fre

quen

cy

Average arrival time

0 500 1000Time [minutes after midnight]

0

50

100

Fre

quen

cy

Standard deviation of arrival time

0 200 400 600 800Standard deviation [minutes from mean]

0

50

100

150

200

Fre

quen

cy

Average daily mileage

0 20 40 60 80 100Distance [mi]

0

10

20

30

Fre

quen

cy

Standard deviation of daily mileage

0 20 40 60 80 100Standard deviation [mi from mean]

0

20

40

60

Fre

quen

cy

Gammaa = 2.61b = 8.28

Logistic = 1009.13

s = 73.07

Gammaa = 26.59b = 23.49

HalfNorm = 159.39

Logistic = 151.36

s = 49.63

Exponential = 14.92


Data and Parameters

How is the travel pattern model built from the data?

Data extraction fromempirical data

Modelling Scenario Generation Realisation of Uncertainty

Create 6 continuous distributionfits noting the average and standard deviation of

1) end of last trip,2) start of first trip, and3) daily mileage

of households participating in the survey.

Assigning parametersdescribing the behaviour

of EV owners

Sample parameter from all 6 model distributions

Each (μ,σ)-tuple describes an aspect of uncertain user

behaviour via normal distribution

Sample from normal distributions to simulate

observed behaviour

μ

σPreliminary

Analysis

observation forecast

μ

Norm(μ,σ)

OptimalScheduling

3 times3 times

for each vehiclein the network

for each vehiclein the network

for eachparticipating household


Data and Parameters

How do empirical data and simulated model compare?


Data and Parameters

Then availability probabilities look something like this:

0 48 960

0.5

1

0 48 960

0.5

1

0 48 960

0.5

1

0 48 960

0.5

1

0 48 960

0.5

1

0 48 960

0.5

1

0 48 960

0.5

1

0 48 960

0.5

1

8 16 24 32 40 48 56 64 72 80 88 96

Time Slot [15 min]

0

0.25

0.5

0.75

1

Figure: Illustration of availability probabilities on an individual (top) oraggregate level (bottom)


Framework

How were the charging approaches evaluated?

Start

End

Initialise

Scenario

Optimise

Simulate

Assign

load

forecasts

Read Global

Parameters

Assign EV

behaviour

parameter set

Generate

price

forecast

MC iterations

complete?

no

yes

Define

problem

formulation

Calculate PF

in OpenDSSLog outputs

Generate

availability

forecast

Generate

EV demand

forecast

updated parameters

To compare different

algorithms choose

identical random seed.

Perform

Evaluation

Uncertainty

Mitigation?

Apply

chosen

algorithm

Apply selected

mitigation mechanisms

to problem formulation

no

yesLog outputs

- As Fast As Possible

- Price-based Heuristic

- Network-based Heuristic

- Linear Programme

Linear PF

Approximation?

Calculate network

sensitivity matrices

no

yes

sensitivities

parameters

Benchmark

schedule

Calculate

PF in

OpenDSS

Calculate PF

in OpenDSSLog outputs

Realise deviations

from forecasts

updated

parameters

Apply chosen

algorithm with

perfect information

schedule

adapted

schedule


Problem Formulation

Plain Problem Formulation

min{PEV }

C =T∑t=1

K∑k=1

π̂t ·∆t · PEVk,t

s.t. 0 ≤ PEVk,t ≤ PEV

max(1− α̂EV

k,t

)· PEV

k,t = 0

B̂arrk +

T∑t=1

η · PEVk,t ·∆t = Bmax

PF Vmin ≤ V busk,t ≤ Vmax

I line`,t ≤ Imax`

∀k ∈ {1, . . . ,K} ∀d ∈ {1, . . . ,D} ∀t ∈ {1, . . . ,T} ∀` ∈ {1, . . . , L}

Substation had enough capacity by design.


Linear Power Flow Approximation

How are the voltages and line loadings calculated?

Experimentally determine network sensitivities of householdvoltages and line loadings to additional loads.

series of unbalanced three-phase power flow calculations

static load of 2 kW (max. avrg. demand winter)

alternatingly increase one households load by 1 kW

observe voltage and line loading change everywhere

create sensitivity matrices λ and µ

PF: Vmin ≤ V busk,t,init

(D̂k,t

)+

K∑j=1

µj,k · PEVi,t ≤ Vmax

I line`,t,init

(D̂k,t

)+

K∑j=1

λj,` · PEVi,t ≤ Imax

`

Low error for voltages (≤ 0.5%) and lines (≤ 2%) and ratheroverestimating the effect of additional load (uncontrolled EVs)!


Uncertainty Mitigation

Mitigation of EV availability uncertainty

0 120 240 360 480 600 720 840 960 1080 1200 1320 1440

Time [min]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Ava

ilabi

lity

Pro

babi

lity

0

1

2

3

4

5

6

7

PD

F

10-3



Mitigation of EV battery SOC uncertainty

0 1 2 3 4 5 6 7 8 9

PDF / CDF / 10x Time Slots [-]

0.2

0.4

0.6

0.8

1

Rel

ativ

e B

atte

ry S

OC

[-]

Minimum SOC in 70%Minimum SOC in 50%Minimum SOC in 30%Charging PeriodsReference Line(1-CDF) of Battery SOCPDF of Battery SOCPredicted SOC curveUnderestimated SOC curveOverestimated SOC curve

Trade-off:- risk of not fully charging battery- excessive scheduling for uncertainty mitigation



Mitigation of price uncertainty

8 16 24 32 40 48 56 64 72 80 88 96

Time Slot [15 min]

0

5

10

15

20

25

30

35

40

45

Ele

ctric

ity P

rice

[p/k

Wh]

0.01-Quantile0.05-Quantile0.10-Quantile0.50-Quantile ( )0.90-Quantile0.95-Quantile0.99-Quantile

Price Ranges

exemplary distortion of ranking



Mitigation of demand uncertainty

8 16 24 32 40 48 56 64 72 80 88 96

Time Slot [15 min]

0

0.5

1

1.5

Res

iden

tial D

eman

d [k

W]

Expected Residential Demand (individual)Adapted Residential Demand Input (individual)

1h-window


Evaluation Criteria

Evaluation Criteria

Relative charging costseconomic benefit of coordinated vs. uncontrolled charginginterpretation of costs of introducing network constraints ifcompared to unconstrained price-based charging

Demand satisfactionaverage final battery state of chargeminimum final battery state of charge

Severity of constraint violationsmaximum line loadingsminimum bus voltages


Reference Cases

How do the reference cases compare?

3 reference cases:

no EVs

uncontrolled

price-based

Uncontrolled Charging Price-Based Heuristic0

1

2

3

4

5

6Relative Charging Costs

Average Battery SOC Minimum Battery SOC0

0.2

0.4

0.6

0.8

1EV Demand Satisfaction

Max. Loadings [per rating] Min. Voltages [p.u.]0

0.5

1

1.5

2

2.5Constraint Violation Severity

Overloading [ratio] Voltage violations [ratio]0

0.05

0.1

0.15

0.2

0.25Constraint Violation Frequency

No Electric VehiclesUncontrolled ChargingPrice-Based Heuristic


Comparison

Simulated performance w/wo uncertainty mitigation

0 24 48 72 960

50

100

150

kW

Schedule

0 24 48 72 960

20

40

60

Num

ber

of E

Vs

Availability

0 24 48 72 960.8

0.85

0.9

0.95

1

[-]

Aggregate Battery SOC

0 24 48 72 960

0.5

1

[-]

Minimum Battery SOC

0 24 48 72 960.85

0.9

0.95

1

1.05pu

Minimum Voltage

0 24 48 72 960

0.5

1

1.5

2

[-]

Line Loading

0 24 48 72 9610

20

30

40

p/kW

h

Electricity Price

Uncontrolled Price-based LP (with mitigation) LP (no mitigation) LP (full knowledge)

0 24 48 72 960

2

4

6

Brit

ish

Pou

nd

Charging Cost

0 24 48 72 960

20

40

60

kW

Residential Load


Comparison

Household-level view on scheduling and effect of controller

0 16 32 48 64 80 96

Time Slot [15 min]

0.5

0.6

0.7

0.8

0.9

1

Vol

tage

[p.u

.] / A

vaila

bilit

y [b

inar

y]

-5

0

5

10

15

20

25

30

35

40

45

Pric

e [p

/kW

h] /

SO

C [k

Wh]

/ C

h. R

ate

[kW

]17 V17 Vmin Psim17 Popt

17B17

16 32 48 64 80 96

Time Slot [15 min]

0.5

0.6

0.7

0.8

0.9

1

Vol

tage

[p.u

.] / A

vaila

bilit

y [b

inar

y]

-5

0

5

10

15

20

25

30

35

40

45

Pric

e [p

/kW

h] /

SO

C [k

Wh]

/ C

h. R

ate

[kW

]54 V54 Vmin Psim54 Popt

54B54

Figure: Two households close to (left) and far from substation (right)


Comparison

The main results summarised in one slide:

Uncontrolled Charging Price-Based Heuristic0

0.5

1

1.5

2

2.5Relative Charging Costs

Uncontrolled ChargingPrice-Based ChargingLinear Program (LP)LP (with mitigation)Reference Line

Average Battery SOC Minimum Battery SOC0.2

0.4

0.6

0.8


Uncontrolled ChargingPrice-Based ChargingLinear Program (LP)LP (with mitigation)

Maximum Loadings [per rating]0.8

1

1.2

1.4

1.6

1.8

2

2.2

Line Loading Violation Severity


Minimum Voltages [p.u.]0.88

0.9

0.92

0.94

0.96Voltage Violation Severity



Comparison

+: Sensitivities of SOC uncertainty mitigation parameters

Uncontrolled Charging Price-based Heuristic0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Relative Charging Costs

Average Battery SOC Minimum Battery SOC0.2

0.4

0.6

0.8


Max. Loadings [per rating] Min. Voltages [p.u.]0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

Constraint Violation Severity

Overloading Voltage Violations [ratio]0

1

2

3

4

5

6

710-3 Constraint Violation Frequency

LP (without frequent cycles)+ SOC mitigation (

B = 0.6)

+ SOC mitigation (B

= 0.7)

+ SOC mitigation (B

= 0.8)


Comparison

+: Sensitivities of rel. charging costs to diff. price spreads

0.2

0.4

0.6

0.8

1

1.2

Relative Charging Costs(compared to uncontrolled charging)

0.96

1

1.04

1.08

1.12

1.16

Relative Charging Costs(compared to price-based heuristic)

LP (low price spread s = 1) LP (medium price spread s = 3) LP (high price spread s = 5) Reference

average90.43 %

average73.59 %

average59.17 %

average100.88 %

average103.47 %

average109.67 %


Summary

The cost of considering technical feasibility is confined to10% indicating that numerous alternative slots with similarcharging costs and suitable network capacities are available.

Uncertainty could be mitigated; particularly recognisingtotal demand uncertainty of electric vehicles is effective(reserving more slots than actually needed). But obviously,this comes at a cost (plus 20 - 40 %).

Dynamic surcharges and levies incentivise participationin demand-side management by amplifying the effect ofvariable electricity prices on the wholesale market(something I didn’t show today).

optimal load scheduling of electric ... - fabian neumann

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