VPPC 2014, Comparison of Bi-level Optimization Frameworks for Sizing and Control of a Hybrid Electric Vehicle

IEEE Vehicle Power and Propulsion Conference
“Spreading E-Mobility Everywhere”
October 27-30, 2014 — Coimbra, Portugal http://www.vppc2014.org
Comparison of Bi-level Optimization Frameworks for Sizing and Control of a Hybrid Electric Vehicle
Emilia Silvas, Erik Bergshoeff, Theo Hofman, Maarten Steinbuch Control Technology Group, Mechanical Engineering, Eindhoven University of Technology, The Netherlands

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Motivation
E. Silvas (e.silvas@tue.nl)
Multi-level design for HEVs, 28 October 2014
Hybrid propulsion challenges:
 Which topology, size of components or control should be used?
 Which optimization methods can achieve an optimum design?
Drawbacks:
High emissions (CO2, PM, NOx)
Bad fuel efficiency

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Motivation
Challenging multi-level optimization problem:
Static sizing optimization
Dynamic optimal control
Design layers are coupled: nested optimization needed for optimal system level design.
Ex: gear shift, power split
Ex: min. CO2
Ex: motor power,
battery capacity
Ex: costs

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Outline
Powertrain modeling
Performance models
Cost models
Optimization Problem
Available Optimization Frameworks
Results
Hybridization and engine downsizing potential
 Algorithms comparison
Conclusions

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Powertrain Modeling
Performance models
Full loaded 40 ton parallel HEV, used in long haul applications.

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Powertrain Modeling
Cost models
The proposed cost models, based on literature and current market trends, are:
Ψ푒 €=250+25∙푃푒[푘푊]
Ψ푏 €=1000+250∙퐶[푘푊ℎ]
Ψ푚 €=1000+20∙푃푚[푘푊]
Ψ푖 €=500+10∙푃푚[푘푊]

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Optimization Problem
Design of HEVs, for optimal sizing and control, is a constraint multi-objective (fuel, cost, performance..) optimization problem:
typically
Hybridization Costs
The HEV control problem requires fixed sizing of components which makes this, inherently, a bi-level optimization problem:
min 풙 퐽풙=[퐽1풙,퐽2풙,..,퐽푘풙]푇
푠.푡.푔푗풙≤0, ℎ푙풙=0
퐽1풙= 푃푓(푖) 푡푓 푖=1
퐽2풙= Ψ푚+Ψ푖+Ψ푏+Ψ푒

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typically
Hybridization Costs
Sizing Optimization
Optimal Control
min 푃푒,푃푚,퐶∈픇 푱푝(푃푒,푃푚,퐶)
min 푢푝푠푡,훾푡∈픘 푱푐(휉푡,푢푝푠푡,훾(푡)|풘)
푠.푡.푔푗푃푒,푃푚,퐶≤0,
ℎ푙푃푒,푃푚,퐶=0
푠.푡.푔푗휉푡,푢푝푠푡,훾(푡)≤0,
ℎ푙휉푡,푢푝푠푡,훾(푡)=0 휉 푡=푓(휉푡,푢푝푠푡,훾(푡)|풘)

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typically
Hybridization Costs
Sizing Optimization
Optimal Control
min 푃푒,푃푚,퐶∈픇 푱푝(푃푒,푃푚,퐶)
min 푢푝푠푡,훾푡∈픘 푱푐(휉푡,푢푝푠푡,훾(푡)|풘)
푠.푡.푔푗푃푒,푃푚,퐶≤0,
ℎ푙푃푒,푃푚,퐶=0
푠.푡.푔푗휉푡,푢푝푠푡,훾(푡)≤0, ℎ푙휉푡,푢푝푠푡,훾(푡)=0 휉 푡=푓(휉푡,푢푝푠푡,훾(푡)|풘)
푱푝= (푤1퐽1+푤2퐽2)
푱푐=퐽1

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Available Optimization Frameworks
Problem key characteristics:
Large design space
Non-convex cost function and models
Mix-integer manner
A wide variety of derivative free algorithms were used for the outer loop, combined, typically with Dynamic Programming in the inner loop.
More widely used strategies:
Dynamic Programming
Sequential Quadratic Programing (SQP)
Dividing Rectangles (DIRECT)
Particle Swarm Optimization (PSO)
Genetic Algorithms (GA)
Exhaustive search/Brute force

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Results
Design Variable
풙표
풙푚푖푛
풙푚푎푥
풙p
Max. motor Power, 푃푚 [푘푊]
65
10
120
Battery capacity, 퐶 [푘푊ℎ]
6.5
1
12
풙푐
Normalized power-split signal, 푢푝푠 [−]
n/a
−1
1
Gear number, γ [−]
n/a
1
12
Initial design variable and boundary constraints
Hybridization and downsizing potential

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Results
Design Variable
풙표
풙푚푖푛
풙푚푎푥
풙p
Max. motor Power, 푃푚 [푘푊]
65
10
120
6.5
1
12
풙푐
n/a
−1
1
n/a
1
12
 Frameworks comparison
More insights (convergence, computation time..) are given in the paper…

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Results
Design Variable
풙표
풙푚푖푛
풙푚푎푥
풙p
Max. motor power, 푃푚 [푘푊]
65
10
120
6.5
1
12
Max. engine power, 푃푒 [푘푊]
n/a
250
350
풙푐
n/a
−1
1
n/a
1
12

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Results
Design Variable
풙표
풙푚푖푛
풙푚푎푥
풙p
Max. motor power, 푃푚 [푘푊]
65
10
120
6.5
1
12
Max. engine power, 푃푒 [푘푊]
n/a
250
350
풙푐
n/a
−1
1
n/a
1
12

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Conclusions
Hybridization and engine downsizing prove potential of HEVs over conventional vehicles.
Nested optimization frameworks enable fast simulation, with better design space exploration and close-to-gobal optimality solutions.
Besides fuel consumption, hybridization costs are crucial for determining future HEVs.
Address this design problem with more variables (gearbox sizing) and for more topologies.
Analyze design’s sensitivity to more driving cycles and/or usage conditions.
Future work

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VPPC 2014, Comparison of Bi-level Optimization Frameworks for Sizing and Control of a Hybrid Electric Vehicle

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