Vehicle Propulsion Systems

Lecture 7

Electric & Hybrid Electric Propulsion Systems Part II

1

Planning of Lectures and Exercises:Week Lecture, Friday, 8:15-10:00, ML F34 Book

chp.Exercise , Friday, 12:00-13:30, CHN E46

38, 20.09.2019 Introduction, goals, overview propulsion systems and options

1 Introduction

39, 27.09.2019 Fuel consumption prediction I 2 Exercise I, Milestone 1

40, 04.10.2019 Fuel consumption prediction II 2 Exercise I, Presentation

41, 11.10.2019 IC engine propulsion systems I 3 Exercise II, Milestone 1

42, 18.10.2019 IC engine propulsion systems II 3 Exercise II, Milestone 2

43, 25.10.2019 Hybrid electric propulsion systems I 4 Exercise II, Presentation

44, 01.11.2019 Hybrid electric propulsion systems II 4 Exercise III, Milestone 1

45, 08.11.2019 Hybrid electric propulsion systems III 4 Exercise III, Milestone 2

46, 15.11.2019 Non-electric hybrid propulsion systems 5 Exercise III, Presentation

47, 22.11.2019 Supervisory Control Algorithms I 7 Exercise IV, Milestone 1

48, 29.11.2019 Supervisory Control Algorithms II 7 Exercise IV, Milestone 2

49, 06.12.2019 Supervisory Control Algorithms III 7 Exercise IV, Milestone 3

50, 13.12.2019 Case Study Exercise IV, Presentation

51, 20.12.2019 Tutorial Lecture, Q & A

Today

• Electric Motors

– Types and Working principles

– Modeling

– DC-Converter / Power-Inverter

• Range Extenders

3

Operating Range

𝜔

𝑇

1st Q.Mot.

2nd Q.Gen.

4th Q.Gen.

3rd QMot.

Speed Limits

Torque/Current Limits

Power Limits

Base speed

4

Usually: tabulated black box model

𝑃𝑒𝑙 = 𝑓(𝜔, 𝑇)

-250

-250

-250

-200

-200-200

-150

-150-150

-100

-100-100

-50

-50-50 -50

0

0 0 0 0

50

5050 50

100

100

100100

150

150150

200

200200

250

250

250

300

300

300

Speed in rpm

Torq

ue in N

m

0 1000 2000 3000 4000 5000 6000

-2000

-1500

-1000

-500

0

500

1000

1500

2000El. Power in kW

Min/Max Torque

80 80 80

80

80

80 80 80

90

90

90 9090

90

90

90 9090

93

93

93

93 93

9393

93

93 93

94

94

94

94

94

94

Speed in rpm

Torq

ue in N

m

0 1000 2000 3000 4000 5000 6000

-2000

-1500

-1000

-500

0

500

1000

1500

2000Efficiency in %

Min/Max Torque

5

-400 -300 -200 -100 0 100 200 300 400-400

-300

-200

-100

0

100

200

300

400

Electric Power in kW

Mechanic

al P

ow

er

in k

W

-400 -300 -200 -100 0 100 200 300 400-400

-300

-200

-100

0

100

200

300

400

Electric Power in kW

Mechanic

al P

ow

er

in k

W

-400 -300 -200 -100 0 100 200 300 400-400

-300

-200

-100

0

100

200

300

400

Electric Power in kW

Mechanic

al P

ow

er

in k

W

Willans Approach

Case 𝑃𝑒𝑙 ≥ 0𝜔𝑇 = 𝑃𝑒𝑙 ⋅ 𝑒 − 𝑃0𝑒 = 92.7%𝑃0 = 2.57kW

Extrapolate to 𝑃𝑒𝑙 < 0

𝜔𝑇 =𝑃𝑒𝑙

𝑒− 𝑃0

Low torque High speed

0 50 1000

20

40

60

80

100

Electric Power in kW

Mechanic

al P

ow

er

in k

W

Speed-dependent Willans-Models work analogously!

6

Normalized Willans Model

• Normalization

– Work balance during one «engine cycle»: 𝑇𝑚𝑁𝜋 = 𝑝𝑚𝑎 ⋅ 𝑆 ⋅ 𝐴𝑟𝑒𝑎

– Mean effective pressure: 𝑝𝑚𝑎 =𝑇𝑚

2𝑉𝑟,

where 𝑉𝑟 is the one characteristic scaling param.

– Mean Speed: 𝑐𝑚 = 𝜔𝑚 ∗ 𝑟 in m/s, where 𝑟 is a characteristic radius

7

Higher Order Models

• Parameters may be speed dependent:

– 𝜔𝑇 = 𝑃𝑒𝑙 ⋅ 𝑒 𝜔𝑚 − 𝑃0 𝜔𝑚

– 𝑝𝑚𝑒 = 𝑝𝑚𝑎 ⋅ 𝑒 𝜔𝑚 − 𝑝𝑚𝑟 𝜔𝑚

• Higher-order terms may be added

– 𝜔𝑇 = 𝑃𝑒𝑙2 ⋅ 𝑒2 𝜔𝑚 + 𝑃𝑒𝑙 ⋅ 𝑒1 𝜔𝑚 − 𝑃0 𝜔𝑚

– 𝑝𝑚𝑒 = 𝑝𝑚𝑎2 ⋅ 𝑒2 𝜔𝑚 + 𝑝𝑚𝑎 ⋅ 𝑒1 𝜔𝑚 − 𝑝𝑚𝑟 𝜔𝑚

8

Model inversion

• Map-based model𝑃𝑒𝑙 = 𝑓 𝜔, 𝑇𝑇 = 𝑓−1(𝜔, 𝑃𝑒𝑙)

• Willans model𝑝𝑚𝑒 = 𝑝𝑚𝑎 ⋅ 𝑒 − 𝑝𝑚𝑟

𝑝𝑚𝑎 =𝑝𝑚𝑒 + 𝑝𝑚𝑟

𝑒

Motor

Speed

Electric PowerTorque Motor

Speed

TorqueEl Power

Possible since 𝑓 isusually monotonic

9

Today

• Electric Motors

– Types and Working principles

– Modeling

– DC-Converter / Power-Inverter

• Range Extenders

15

How to control a DC motor?

• Connecting a DC-motor to a constant voltage DC source (e.g. a battery) yields a constant torque.

• Need to control current!

DC-Voltage-SourceI=f(Ua)

DC-MotorT=f(I)

Voltage

Current

Torque

16

Speed

How to control a DC motor?

• Use DC-converter

• Converter = timed switch that connects and disconnects circuit at high frequency.

DC-Voltage-Source DC-Motor

T=f(I)

DC-ConverterI = f(U)

Voltage

Current

Mech. LoadT

w

ControlledVoltage

PWM Signal

Current

17

DC-Chopper

This is still DC current,flowing only in one direction.„Inversion“ is achieved bybrushes and collectors.Chopping frequency >> motor speed

𝑇

𝑇𝑜𝑛

Duty Cycle = 𝑇𝑜𝑛

𝑇= 𝛼

Voltage out: 𝑈𝑎 = 𝛼𝑈𝑚

DC-MotorDC-Chopper

Switch

18

How to control a DC motor?

𝑈𝑎 𝑡 = 𝐿𝑎dd𝑡𝐼𝑎 𝑡 + 𝑅𝑎𝐼𝑎 𝑡 + 𝑈𝑖 𝑡

dd𝑡𝜔𝑚 𝑡 = 1

Θ𝑚𝑇𝑎 𝑡 − 𝑇𝑚 𝑡

𝑈𝑖 𝑡 = 𝜅𝑖𝜔𝑚 𝑡𝑇𝑎 𝑡 = 𝜅𝑖𝐼𝑎 𝑡

DC-MotorDC-Chopper

19

Electrical Power

𝑃𝑚 𝑡 = 𝑈𝑚 𝑡 𝐼𝑚 𝑡 = 𝐼𝑎 𝑡 𝑈𝑎 𝑡 + 𝑃𝑙,𝑐

=𝑇𝑚𝜅𝑎

𝜔𝑚𝜅𝑖 +𝑅𝑎𝑇𝑚 𝑡

𝜅𝑎+ 𝑃𝑙,𝑐

DC-MotorDC-Chopper

20

Operating Range

𝜔

𝑇 Base speed

𝑇𝑚,𝑚𝑎𝑥 = 𝜅𝑎𝐼𝑎,𝑚𝑎𝑥 𝑇𝑚,𝑚𝑎𝑥 =𝜅𝑎𝑈𝑎,𝑚𝑎𝑥 𝑡

𝑅𝑎−𝜅𝑎𝜅𝑖𝑅𝑎

𝜔𝑚 𝑡

𝜔𝑏𝑎𝑠𝑒 𝑈𝑚 =𝑈𝑚 − 𝑅𝑎𝐼𝑎,𝑚𝑎𝑥

𝜅𝑖21

How to control an AC motor?

• Need to „invert“ DC to AC power

• Need variable frequency AC power

• Often times motors use 3 or 4 phase power.

Source: http://www.homofaciens.com/technics-electric-motors-synchronous-motor_ge_navion.htm22

• Basic principle: timed switching emulates sinusoidal waveform

+−

𝑉𝐷𝐶

𝑆1

𝑆2

𝑆3

𝑆4𝑉𝑥

S1 S2 S3 S4 𝑉𝑥

1 0 0 1 +𝑉𝐷𝐶

0 1 1 0 −𝑉𝐷𝐶

1 0 1 0 0

0 1 0 1 0

23

• More than three voltage levels allow for a more precise emulation of sinusoidal waveform

24

Power Electronics

• Terminology

Input current Output Current

DC DC DC/DC Converter

DC AC Inverter

AC DC Rectifier

AC AC Transformer, …

25

Today

• Electric Motors

• Range Extenders

30

Range Extender

• 2 Degrees of freedom: – Rotational speed

– Electric power

• Control:– control speed and power to setpoints

• Optimization:– For each value of desired power, find best possible

operating point

31

Engine Generator Unit

32

Engine Generator Unit

• Efficiency: 𝜂𝑔 =𝑃𝑔

𝐻𝑙ℎ𝑣 ሶ𝑚𝑓

33