Power Electronic Systems & Chips Lab., NCTU, Taiwanpemclab.cn.nctu.edu.tw/W3news/實驗室課程網頁/電力電子/講義/2018/【PE-08... · Power Electronic Systems & Chips Lab.,

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PWM DC-AC Inverters

Power Electronic Systems & Chips Lab., NCTU, Taiwan

電力電子系統與晶片實驗室Power Electronic Systems & Chips Lab.交通大學 • 電機控制工程研究所

台灣新竹‧交通大學‧電機與控制工程研究所‧電力電子實驗室~鄒應嶼教授

鄒應嶼教授

國立交通大學電機控制工程研究所

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PWM DC-AC Inverters

Introduction Inverter Topologies

PWM Techniques for Single-Phase Inverters PWM Techniques for Three-Phase Inverters Dead-Time Protection and Distortion Filter Design Modeling in dq-Frame Closed-Loop Control Techniques

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Introduction


台灣新竹‧交通大學‧電機控制工程研究所‧電力電子實驗室~鄒應嶼教授

Chapter 8 Switch-Mode DC-AC Inverters: DC Sinusoidal ACPower Electronics: Converters, Applications and Design, N. Mohan, T. M. Undeland, and W. P. Robbins, John Wiley & Sons, 3rd Ed., 2002.

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Introduction

What is an Inverter? AC/DC: Rectifier DC/DC: Chopper DC/AC: Inverter AC/AC: Cycloconverter

InverterAC OUTPUTDC INPUT

ReferenceCommands

Applications Topologies Characteristics & Dynamics Pulse-width Modulation (PWM) Control Techniques Implementation Issues

An inherent bi-directional DC/AC converter!

5/140

Applications of DC/AC Inverters

PWM Inverters for AC Motor Drives PWM Inverters for AC Power Source Ballast Fluorescent Lamps UPS & AVR Induction Heating Atmospheric Pressure Plasma PV Inverters, Grid Converters Distributed Generators

Single-Channel 150W, PhilipsIEEE Spectrum 2003.

Applications of Inverters

1S 3S 5S

2S 4S 6SdcV

ab

c

3Q

4Q

R

1Q

2QS

VDC = 300~380~420 VDC

P

N

DC/AC Filter Grid

batV

sin(2 )

220 2 1 10% sin(2 60 )g g gv V f t

t

oL

Battery

Grid Inverter: Battery-Based Energy Storage System

Regenerative Motor Drive

7/140

Application in a Grid-Connected PV System

Full-Bridge Inverter

Microcontroller

InverterGate Drive

Meter

DC Side isolation switch

To high efficiency AC

appliances

inverter

PV Array(usually building mounted)

AC mains supply

Main fuse box

PV Panel

DC ACACDC

PV Inverter

ElectricalDistribution

System

FeedbackSensing Circuit

RelayGate Drive

8/140

Applications of Inverters in AC Motor Drives

Single-Phase (One Winding)

Three-Phase (Three Windings)

N

S

SN

(a) Single-phase bipolar

(b) Three-phase bipolar

T4T2

T3T1

T4T2

T3T1

T6

T5


dcV

dcV

a

a

b c

abvai

9/140

Single-Phase Half-Bridge Inverter

Sinusoidal modulation to produce ac output:

For the linear RLC load, the resulting inductor current variation is also sinusoidal.

Hence, current-bidirectional two-quadrant switches are required.

1D1Q

2Q

LAv

Li

Ai

Bi0vC R2D

12 dc

V

12 dc

V Bv

0v12 dc

V

12 dc

V

D15.00

01( ) 2 12 dc

v t D V

( ) 0.5 sin( )mD t D t

( ) 1( ) (2 1)2

o dcL

v t Vi t DR R

gv

When the converter is connected with grid and the current is controlled to be linear proportional to the grid voltage, the load is equivalent to a resistor R and the inductor current is:

10/140

Single-Phase Half-Bridge Inverter

Gat

e D

river

Q1

Q2

Amp

Carrier

refv

D

D

ov 0.15.0

oV

12 dc

V

12 dc

V

12 dc

V

12 dc

V

01( ) 2 12 dc

v t D V

The simplest single-phase inverter topology. The half-bridge inverter is a buck-derived bidirectional converter with a

differential output relative to the neutral point of the source. Output voltage is limited with 0.5Vdc. Unbalance issues of the upper and lower voltage sources under fast and large

external disturbances.

( ) 0.5 sin( )mD t D t

11/140

Single-Phase Half-Bridge Inverter: Current Paths

1dcV1S

2S

a

2dcV

odcV Load

1dcV 1Q

2Q

a

2dcV

oLoad

1D

2D

1dcV 1Q

2Q

a

2dcV

oLoad

1D

2D

1dcV 1Q

2Q

a

2dcV

oLoad

1D

2D

Q1 ON, Q2 OFF Q1 OFF, Q2 OFF, D2 ON Q1 OFF, Q2 ON

MOSFET is a bi-directional switch

v

i1

0

C

N-channel MOSFET

Instantaneous i-v characteristicSymbol

i

v

on

off

on(reverse conduction)

12/140

Single-Phase Half-Bridge Inverter: Load Characteristics

1dcV 1Q

2Q

a

2dcV

o

1D

2D

(a) Grid Inverter

1dcV 1Q

2Q

a

2dcV

o

1D

2D

(c) motor

1dcV 1Q

2Q

a

2dcV

o

1D

2D

(b) AC power supply

Grid inverter: an inductor is used as a current filter and is connected with the utility. AC power supply: An LC filter is used as a voltage filter to generate a regulated ac

voltage source. The motor load can be a PM dc motor or a single-phase ac motor. c

motor

13/140

Characteristics & Dynamics of a Buck Converter

LTVI sdL 4(max)

D0 0.5 1.0

LI

12

3 4

Output voltage and current waveformsOne-quadrant operation.

0

M=0.50 M=0.75

t

L

Rov

oi

dcV

ovoi

dcV

ov

oi

C

14/140

Characteristics & Dynamics

12

3 4

One-quadrant operation.

ov

oi

CCM

ov

oi

L

Rov

oi

dcV C

1.0D

0.9

0.7

0.5

0.3

0.1

AC Source Voltage Regulation Problems

Nonlinearity due to switchingDead-time of the gate drive circuitNon-ideal switching characteristicsNonlinearity due to DCM/CCM

CurrentController

PWMController

L

Li

ov

1S

2S

3S

4S

A

BdcC

invidci

ci

Li

*ov

ov

dcvdcV

Load

Variations in dc-linkRegenerative loadsVoltage drop of batteryUtility RMS variations

C

0 2 4 6 8 10 12 14 16-200

-150

-100

-50

0

50

100

150

200Rectifier load

Vo(

V)

t,(ms)-50

-40

-30

-20

-10

0

10

20

30

40

50

Io(A

), IL

(A)

(b) Output voltage and current

(a) Testing Load

Load uncertainties Parameter variationsLoad variationsNonlinear load Permissible load power factorRegenerative load

16/140

Techniques in Closed-Loop Control of DC/AC Power Converter

~=Inverter

Control

ProcessorSignal

Conditioning

Filter

Sensors

Loadcommand

Controller

feedback

output

Topology Power Devices and Gate Drives Protection and Compensation Power Devices and Gate Drives Snubber Circuit Design Grounding and Noise Reduction

Filter Design Harmonic Analysis HF Magnetic Components

Nonlinear Power Load Regenerative Motor Load Load Characteristics Load Dynamics

Current Sensor Voltage Sensors Placement of Sensors

Control Loop Design Simulation Implementation Issues Controller Implementation

Sampling Techniques Signal Filtering Signal ConditioningA/D & D/A Converters Analog Circuit Design

dcV

GateDriver

PWMModulator

PWM Modulation Strategy Harmonic and THD Analysis Dead-Time Protection Dead-Time Compensation Over-modulation Control Loss Analysis Implementation of PWM modulator

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Inverter Topologies



02【硬體設計】02：Power Converters for Motor Drives.ppt

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Basic Inverter Topologies

1dcV1S

2S

a

2dcV

o

(a) Half-bridge (b) Full-bridge (c) Three-phase

dcV

1S

2S

3S

4S

a

b

ab

cdcV

5S

6S

3S

4S

1S

2S

The DC source can be a voltage source or a current source. Most inverters are voltage source inverters (VSI). Inverters are inherent bi-directional DC-AC converters. Half-bridge inverter compared with the full-bridge inverter with a same dc-link

voltage will produce only one-half output voltage.

dcV

19/140

Classifications of Inverters

Voltage Source Inverter (VCI)

Current Source Inverter (CCI)Square Wave CSI

PWM CSI

PWM Inverter (VVVF Inverter)Single-Phase/Three-Phase

Current-Controlled PWM Inverter

Variable Voltage Inverter

Processed Energy Source and Load (Voltage Source, Current Source) Topology (Single-Phase, Three-Phase, etc.) PWM Strategy (Square, PWM, Sine PWM, Regular PWM, Space Vector PWM, etc.) Switching Devices (SCR, Power Transistor, Power MOSFET, IGBT, etc.) Switching Schemes (PWM, Resonant, Quasi-Resonant, Soft PWM, etc) Control Schemes (Hysteresis, PID, Dead-beat, Variable Structure, Fuzzy, etc.) Controller Implementation (Analog, Microprocessor, DSP, etc.)

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Voltage Source Inverter & Current Source Inverter

Most conventional inverters are voltage source inverters (VSI). The output of a VSI must be connected with an inductor! The output of a CSI must be connected with a capacitor! CSI with a quasi-Z network (ZCSI) are getting interest in recnt years.

2005.Comparison of Three Phase CSI and VSI Linked with DC to DC Boost Converters for Fuel Cell Generation Systems (epe).pdf【投影片】Inverter Using Current Source Topology (ape2010).pdf

1S

2S

3S

4S

5S

6S

VSI: Voltage Source Inverter CSI: Current Source Inverter

1S

2S

3S

4S

5S

6S

dcV dcI

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Three-Phase Inverter Motor Drives

3-PhasePowerSupply

Voltage (Line to Neutral)

Current (Line)

VSI: Voltage Source Inverter

Voltage (Line to Neutral)

Current (Line)

CSI: Current Source Inverter

3-PhasePowerSupply

N

S

SN

N

S

SN

1S

2S

3S

4S

5S

6S

1S

2S

3S

4S

5S

6S

A DC-link capacitor provides a voltage source!

A DC-link indutor provides a voltage source!

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Inverter Topologies

Single-Phase Half-Bridge

Single-Phase Full-Bridge

2dcV

2dcV ANv

n

1D

2D

1S

2S

dcVoi a

o

Load

p

ANv

3D

4D

3S

4S

dcVoi BLoad1D

2D

1S

2S

A

ai Load1D

2D

1S

2S

b

1D

2D

1S

2S

c

bi

ci

Three-Phase Half-Bridge

Three-Phase Full-Bridge

dcVai Load1

D

2D

1S

2S

a3D

4D

3S

4S

b

5D

6D

5S

6S

c

bi

ci

2dcV

2dcV

o

a

n

p

n

p

n

p

23/140

Derivation of Full-Bridge Converter

Differential connection of load to obtain bipolar output voltage

Differential load voltage is:

The outputs V1 and V2 may both be positive, but the differential output voltage V can be positive or negative.

DC source

load

D

D’

21 VVV

2 ( ') dcV M D V

converter 2

1 ( ) dcV M D V

converter 1

V

dcV

1V

2V

24/140

Differential Connection Using Two Buck Converters

Converter #1 transistor driven with duty cycle D

Converter #2 transistor driven with duty cycle complement D’

Differential load voltage is

'dc dcV DV DV (2 1) dcV D V

)(DM

1

D10

1

5.0

Buck converter 1

Buck converter 2

1

1

2

2

V

dcV

1V

2V

25/140

Simplification of filter circuit, differentially-connected buck converters

1

1

2

2

Bypass load directly with capacitorBuck converter 1

Buck converter 2

1

1

2

2

Original circuit

V

dcV

1V

2V

V

dcV

26/140

Simplification of filter circuit, differentially-connected buck converters

Combine series-connected inductors

Re-draw for clarity

H-bridge, or bridge inverter

Commonly used in single-phase

Inverter applications and in servo

Amplifier applications

1

2 1

2

1

1

2

2

VdcV

1V

2V

dcVLi

LC

R

Derivation of Full-Bridge DC-DC Converter

2

3 4

0

oi

ov

1

(a) (b)

(c)(d)

2

3 40

oi

ov

1

2

3 40

oi

ov

1 2

3 40

oi

ov

1

28/140

Characteristics of a Full-Bridge Converter

Lr

dcV

1S

2S

3S

4S

LA

Bgv

2

3 4

0

oi

ov

1

An inverter is a differential mode 4-quadrant DC-DC converter.

Power can be transferred back and forth between source and load.

Its output can be DC or AC, depend on the selected PWM strategy.

A buck type converter. Input and output voltage do not have a

common ground. A lot of inverter topologies have been

developed. PWM modulation strategy is required to reduce

harmonic distortion as well as switching loss reduction.

Control is required to maintain stable, robust, and fast response.

4Q Operation!

ov

oi

29/140

Dynamics of a Full-Bridge Inverter with Unipolar PWM

ov

oi

1.0D0.9

0.7

0.5

0.3

0.1

1,ov1,oi

1,ov1,oi

1 3

1 32 4

Small signal perturbation at operating point OPx

xOP

30/140

From Single-Phase Inverter to Three-Phase Inverter

Lr

dcV

1S

2S

3S

4S

La

bgvLi

The basic inverter cell for bi-directional three-phase AC/DC converters! Singe-Phase Three-Phase Two-Level Switching Three-Level Switching

The basis for the understanding of major control issues and performance indices for the grid converters.

The basis for learning and developing more sophisticated control schemes.

1S

2S

3S

4S

a

b

5S

6S

c

aR

cecR cL

nbe

bR bLdcV

aeaL

31/140

From Single-Phase Inverter to Three-Phase Inverter

Lr

dcV

1S

2S

3S

4S

La

bgvLi

ab

c

aR

cecR cL

nbe

bR bL

aeaL

dcV

5S

6S

3S

4S

1S

2S

Lr1dcV1S

2S

La

gvLi

2dcV

o

32/140

Full-Bridge Converter: Load Characteristics

Lr

dcV

1S

2S

3S

4S

La

bgv

Li

dcV

1S

2S

3S

4S

L

ovLi C

av

ai

emfv

aRaL

av

ai

emfv

aRaL

(a) A grid inverter

(b) An ac voltage regulator.

(c) A dc servo motor drive

(d) A single-phase BLDC motor drive

dcV

1S

2S

3S

4S

dcV

1S

2S

3S

4S

a

b

a

b

a

b

Split Phase 6-Switch Inverter with Battery Bank at HV DC-Link

Jin Wang, F.Z. Peng, J. Anderson, A. Joseph, and R. Buffenbarger, “Low cost fuel cell converter system for residential power generation,” IEEE Transactions on Power Electronics, vol. 19, no. 5, pp. 1315-1322, Sept. 2004.

5 kW solid oxide fuel cell (SOFC) Vin: 22~41 VDC DC-link Voltage = 400 VDC 5 kW Battery Bank at HV DC-Link Peak Output Power = 10 kW Load: Two split-phase 60 Hz, 120-VAC

Development of Single-Phase Non-Isolated Grid Inverters

【投影片】Latest in PV Inverter & Trends (2012)T. Hauser et. al, Sunways, EUPVConf Valencia 2008, 4DO.8.2

PV Array Filter Basic FB inverter PV Array Filter FB inverter PV Array Filter HERIC FB inverter Grid PV Array Filter FB inverter

1L

2L

2S

1S3S

4S

1D

2D4D

3D

rvC

rvV

vV

5S

5D

rsV

L

N

1L

2L

2S

1S 3S

4S

1D

2D 4D

3D

rvCrvV vVL

N

D

S

S

D

rsV

DC Bypass

1L

2L

2S

1S 3S

4S

1D

2D4D

3D

1rvCrvV

vV

5S

5D

rsV

L

N2rvC

D

D

A

B

6S

6D

Full-bridge(Bipolar/ Unipolar/ Hybrid)

H5 Topology (SMA) HERIC Topology (Sunway) H6Topology (FBDC Bypass)

1L

2L0ABV

2S

1S 3S

4S

1D

2D 4D

3D

rvC

rvV

vVL

N

rsV

PV Array

Filter NPC inverter Filter Grid

rvV

1rvC

2rvC

/ 2rvV

/ 2rvV

rsV

1S1D

2S 2D

3S3D

4S4D

vV

0ABV

1LA

D

D

B

PV Array Filter HB inverter Filter Gri

dClamping SwitchPV ArrayDC Link L

BoostDC Link H HB GridBoost Bypass

AC Bypass Filter

REFU UltraEta NPC (Danfoss) Conergy Topology

rsV

rvV

1rvC

2rvC

rsV

1LD

D

/ 2rvV

/ 2rvV

/ 2AB rvV V1S 1D

2S 2D

Filter GridFilterGridFilterGridFilter

vV

35/140

Selection of Single-phase Three-wire Transformerless Inverter Topologies

(a) Single DC Bus with Split Capacitor

(b) Single-phase three-wire inverter (c) Dual DC bus with central tap ground

[1] T. A. Nergaard, J. F. Ferrell, L. G. Leslie, and J. S. Lai, “Design considerations for a 48 V fuel cell to split single phase inverter system with ultracapacitor energy storage,” Proc. IEEE Power Electronics Specialist Conference, 2002.

[2] S. J. Chiang and C. M. Liaw, “Single-phase three-wire transformerless inverter,” IEE Electric Power Applications, vol. 141, pp. 197-205, July 1994.[3] M. Martino, C. Citro, K.Rouzbehi, P. Rodriguez, “Efficiency analysis of single-phase photovoltaic transformer-less inverters,” International Conference on Renewable

Energies and Power Quality (ICREPQ) Santiago de Compostela (Spain), 28th to 30th March, 2012.

1dcC

2dcC

1S

2S

3S

4S1oL

2oL

2oC

1oC1acV

2acV

120V

120V

dcC

3S

4S

5S

6S

1S

2S

1oL

2oL

2oC

1oC1acV

120V

2acV120V

240acV

1dcC

2dcC

1S

2S

3dcC

4dcC

3S

4S

1oL

2oL

1oC

2oC

1acV

2acV

120V

120V

36/140

Interleaved Bi-Directional DC-DC Charger/Discharger with Single-Phase Three-Wire Inverter

P

N

DC/DC DC/ACDC-LinkBattery Filter Grid

3S

4S

5S

6S

1S

2S

1oL

2oL

2oC

1oC 1acV120V

2acV120V

240acV

37/140

Three-Phase Four-Wire Inverter with a Split DC Bus

Min Dai, Mohammad Nanda Marwali, Jin-Woo Jung, and Ali Keyhani, “A three-phase four-wire inverter control technique for a single distributed generation unit in island mode,” IEEE Trans. on Power Electronics, vol. 23, no. 1, pp. 322-332, Jan. 2008.

38/140

Three-Phase Four-Wire Inverter: Control Block Diagram

39/140

Three-Phase Four-Leg Inverter

Gyeong-Hun Kim, Chulsang Hwang, Jin-Hong Jeon, Jong-Bo Ahn, and Eung-Sang Kim, "A novel three-phase four-leg inverter based load unbalance compensator for stand-alone microgrid," Electrical Power and Energy Systems, vol. 65, pp. 70–75, 2015.

40/140

Topology and Control of a Three-phase Four-wire Grid Inverter

41/140

Pioneer on NPC PWM InverterNeutral-Point-Clamped (NPC) 3-Phase PWM Inverter

A. Nabae, I. Takahashi, and H. Akagi, “A new neutral-point-clamped PWM inverter,” IEEE Trans. Ind. Appl., vol. IA-17, pp. 518-523, 1981.

Neutral Point Clamped PWM Inverter PWM Gating Waveforms for the NPC-PWM Inverter

DCL S11 S21 S31

S12 S22 S32

S13 S23 S33

S14 S24 S34

D11

D12

EdU

V

D21

D22

D31

D32

C2

C1

A. Nabae, T. Takahashi, and H. Akagi, “A new neutral-point-clamped PWM inverter,” IEEE IAS Annu. Meeting, Cincinnati, OH, Sep. 28–Oct. 3 1980, pp. 761–776.

ib(S11)

ib(S13)

ib(S14)

ib(S12)

42/140

The Multilevel Converter Concept

Converter output voltage waveform: a) two level, b) three level, c) nine level.

Vdc

a

vaNN

Vdc

Vdc

Vdc

NvaN

a

Vdc

Vdc

N

Vdc a

vaN

mvaNvaNvaNVdc

-Vdc

Vdc

-Vdc

4Vdc

-4Vdc

0 0 0

0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.005 0.01 0.015 0.02 0.025 0.03Time [s] Time [s] Time [s]

(a) (b) (c)

43/140

Comparison of phase voltage of 2- and 3-level-inverters

S+

S-

S+

S-

t t

Sn/ 2dcV

dcV

/ 2dcV

/ 2dcV

/ 2dcVov ov

ovov/ 2dcV

/ 2dcV

Passive NPC inverter

Neutral-Point-Clamped (NPC) Converter

1dcV 1Q

2Q

a

2dcV

o

1D

2D

1dcV 1Q

2Q

a

2dcV

o

1D

2D

[1] A. Nabae, T. Takahashi, and H. Akagi, “A new neutral-point-clamped PWM inverter,” IEEE IAS Annu. Meeting, Cincinnati, OH, Sep. 28–Oct. 3 1980, pp. 761–776. [A. Nabae, I. Takahashi, and H. Akagi, “A new neutral-point-clamped PWM inverter,” IEEE Trans. Ind. Appl., vol. IA-17, pp. 518-523, 1981.]

[2] J. Rodriguez, S. Bernet, P. K. Steimer, and I. E. Lizama, “A survey on neutral-point-clamped inverters,” IEEE Transactions on Industrial Electronics, vol. 57, no. 7, pp. 2219-2230, July 2010.

Three Ways to Realize a Four-Quadrant Switch

v

i

1

0

1i

v

0

v

1i

0

1i

0

v

Different Types of Switching Devices

Lr

dcV

1S

2S

3S

4S

La

bgv

giFilter

IGBT MOSFET SiC MOSFET GaN

Si FRDSi IGBT Si FRDSiMOSFET

SiC SBDSiIGBT

SiC SBDSiCMOSFET

SBD: Schottky Barrier DiodeFRD: Fast Recovery Diode

GaN HEMT

46/140

Neutral-Point-Clamped (NPC) Grid Inverter

1dcV 1Q

2Q

a

2dcV

o

1D

2D

(a) Half-bridge grid inverter

1dcV 1Q

2Q

a

2dcV

o

1D

2D

(b) Three-level NPC grid inverter

1dcV 1Q

2Q

a

2dcV

o

1D

2D

1dcV 1Q

2Q

a

2dcV

o

1D

2D

NPC inverter module

2-Level vs. 3-Level InvertersC

ircui

tPh

ase

Volta

geLi

neVo

ltage

(b) 3-Level PWM(a) 2-Level PWM

ABv

ANv

0

PNV

PNV

P

NA B C

AOv

ABv

0

PNV

0

PNV

PNV

0

PNV

PNV

12 PN

V

adcV b

c

P

N

dcV

Development of Multi-Level Inverter Topologies

(a) 3-level NPC VSC

(c) T-type 3-level NPC VSC with RB-IGBT (Fuji) (d) 5L-MLC2 Converter

(b) T-type 3-level VSC with BB-IGBT

1dC

2dC

abc

1dC

2dC

a

bc

1T V1T U 1T W

2T V2T U 2T W

3T U

4T U3T V

4T V3T W

4T W

a

o

1dC

2dC

b

c

H5 & H10 Converter

50/140

Power Electronics Systems & Chips Lab., NCTU, Taiwan

PWM Techniques for Single-Phase Inverters



Single-Phase (One-Leg) Switch-Mode Inverter

2dV

2dV

ANv

N

AD

AD

AT

AT

dcVoi

Ao

LOAD

Middle point of the DC-link source

The middle point is important for both definition and thinking!

Aov

P

vAo is the inverter output voltage!

Incandescent light bulb

Filter

Speaker

av

ai

emfv

aRaL

DC Motor

Resistive Load

LCR Load

Regenerative Load

52/140

A Simple First-Quadrant Chopper

12

3 4

Input-Output Relationships:

Output voltage and current waveformsOne-quadrant operation.

dco MVV

dcsw

RMSac VLfMM

I32

)1()(,0

0

M=0.50 M=0.75

t

E

L

R

ov

oi

dcV

ov

oi

dcV

sT

os

o dttvTV

0)(1

M is the modulation index and assume the chopper is operating in CCM.

ov

oi

LRfs

ss T

f 1

53/140

Pulse-Width Modulator

Amp comparator

repetitive waveform

switch control signal

(desired)

(actual)

ton toffTs

on on

off off

switch control signal

stV̂

saw-tooth voltage (amplified error)

(switch frequency fs = 1/Ts)

sts Vv

TtD ˆ

controlon

The carrier signal may be a nonlinear function to produce nonlinear PWM control signal.

Modulating signal

Carrier signal

controlv

controlv

stvv control

stvv control

stv

*ov

ov

Concept of Sinusoidal PWM Modulation

)(tc

)(tmmodulatingsignal

carriersignal

PWMModulator

1S

2S

3S

4S

L

RC

virc

v c

vo

ic

i o

i L

rL

1S

Vdc2S

3S

4S

0 t

carrierv

controlv

controlv

carrierv

Trailing-Edge PWM

Leading-Edge PWM

Double-Edge PWM (Central PWM, usually used in sine-wave inverters )

A sinusoidal reference results a sinusoidal output!

Switching Logic modulatingsignal

Sinusoidal modulation

Trapezoidal modulation1 4,S S

2 3,S S

Bipolar PWM

dead-time not shown

ab

carriersignal

Trailing-Edge PWM

Three Types of PWM Modulation Schemes

Leading-Edge PWM

Double-Edge PWM (Central PWM, usually used in sine-wave inverters )

Usually used in DC-DC & PFC Boost Converters

Analog PWM Implementation Trailing-edge modulation is most common in DC–DC converters. Double-edge modulation eliminates certain harmonics when the reference is a sine

wave, and is a preferred method for AC–DC and DC–AC converters where the PWM reference contains a sinusoidal component.

A combination of synchronized leading-edge and trailing-edge modulation has also been used to control a boost single-phase power factor correction (PFC) converter and a buck DC–DC converter to reduce ripple in the intermediate DC bus capacitor [1].

Analog PWM is also called natural-sampling PWM in contrast to the regular-sampling PWM fir its digital implementation.

[1] UCC38501 BiCMOS PFC/PWM Combination Controller datasheet. Texas Instruments, Dallas, Texas, USA (1999)

2dcV

2dcV

1 lfundamenta , )( AoAo vv uAo

controlv carrierv

( )1f s

0t

t0

0 t

carrierv

controlv

controlv

carrierv

comparator

57/140

Operation states of three modulation schemes in the full-bridge topology

Woo-Jun Cha, Kyu-Tae Kim, Yong-Won Cho, Sung-Ho Lee, and Bong-Hwan Kwon, “Evaluation and analysis of transformerless photovoltaic inverter topology for efficiency improvement and reduction of leakage current,” IET Power Electronics, vol. 8, no. 2, pp. 255-267, Feb. 2015.

(a) Bipolar PMW (c) Hybrid PWM (current circulates alternatively)

(b) Unipolar PMW

switching

switchingMode 1

Mode 2

Mode 3

Mode 4

58/140

Pulsewidth Modulator for a Half-Bridge Converter

Switching States

Conduction Modes and PWM Strategies

IGBT + DIODE FQICEI

FQV

Loss LossRDIrI

rVFDV

FQ FQ FD RDLoss=V I +V IC EV

IGBT DIODE

MOSFET + DIODE

FIDSI

FV

Loss LossRDIrI

rVFDV2F ON FD RDLoss=I R +V I

D SV

ONRMOSFET DIODE

2dcV

2dcV ANv

N

1D

2D

1S

2S

dcVoi

Ao

Load

emfv

The inductor current must keep its continuity!

The current path defines its conduction mode.

IGBT is a 1Q switch. MOSFET is a 2Q switch. MOSFET converter can

provide extra conduction paths and its PWM strategy can be more complicated.

The converter is a 4Q bi-directional converter.

DC/DC, DC/AC, AC/DC, AC/AC are all possible!

For a regenerative load, such as a motor, the power flow can flow back to the source.

Current loop area must be kept in minimum for practical implementation to reduce EMI.

FQFQ FQ CE Q FQV I =(V +I r )I

60/140

Conduction Modes

2dcV

2dcV ANv

N

1D

2D

1S

2S

dcVoi

Ao

Load

emfv

2dcV

2dcV ANv

N

1D

2D

1S

2S

dcVoi

Ao

Load

emfv

S1 ON & S2 OFF

S1 OFF & S2 OFF, D2 ON


Current path during these time periods.


61/140

Conduction Modes

2dcV

2dcV ANv

N

1D

2D

1S

2S

dcVoi

Ao

Load

emfv

2dcV

2dcV ANv

N

1D

2D

1S

2S

dcVoi

Ao

Load

emfv

S1 OFF & S2 ON

S1 OFF & S2 OFF, D1 ON




PWM Waveforms and Inductor Current

2kt

sT sT

t

t

( )fU t

3kt

2dcV

2dcV

ANv

N

1D

2D

1S

2S

dcVoi

Ao

Loademfv

Average output voltage

63/140

Double edged PWM strategy with half-bridge converterThe Voltage Reference Command

The modulation signal can be updated in every half-cycle of the switching period, and achieve a double switching effect as compared with the single-edge PWM strategy.

64/140

Single-Phase (One-Leg) Switch-Mode Inverter

)2

(273.12

4)ˆ( 1 dcdcAoVVV

nVV AonAo 1

)ˆ()ˆ(

1.41.21.00.80.60.40.2

00 1 3 5 7 9 11 13 15

)2

/()ˆ( 1 dcAoVV

N-th: harmonics of VAo

2dcV

2dcV

vAo

11f

0

Spectrum of Square-Wave Inverter

2dcV

2dcV ANv

N

AD

AD

AT

AT

dcVoi

Ao

P

t

4 1.273( )2 2dc dcV V

No dc component and even harmonics, if output waveform is symmetric!

65/140

Half-Bridge Singe-Phase PWM Inverter

2dcV

2dcV ANv

N

AD

AD

AT

AT

dcVoi

Ao

P2dcV

2dcV

vAo

11f

0t

sf

1.41.21.00.80.60.40.2

00 1 3 5 7 9 11 13 15

)2

/()ˆ( 1 dcAoVV

N-th: harmonics of VAo

14ˆ( ) 1.273( )

2 2dc dc

AoV VV D

Dn

VV AonAo 1)ˆ()ˆ(

Spectrum of PWM InverterD

sf

1ffs In general,

1ffs

4 1.273( )2 2dc dcV V

66/140

Half-Bridge Singe-Phase Sine Wave PWM Inverter

2dcV

2dcV ANv

N

1D

2D

1S

2S

dcVoi a

o

Load

o: middle point of the DC sourceP: DC source positiveN: DC source negativevao: voltage applied to the load

0 t

1s

2s

controlvcarrierv

controlv

carrierv

P

Natural-Sampling Sinusoidal PWM

Comparator

Half-Bridge Inverter

0 t

vcontrol

vcarriervcontrolvcarrier

0 t

0 t

t = 0

controlV triV

( )1f s

1)( lfundamenta , AovAov uAo

V d2

V d2

off : ,on :tricontrol

AA TTvv

off : ,n :tricontrol

AA ToTvv

Harmonics distribution

同一種電路拓撲，其表現行為主要決定於PWM的控制方式！

This is what we need!

PWM Techniques

Gat

e D

river

Q1

Q2Carrier

12 dc

VrefV

D

ov

( )1f s

( )mv t

1,ABvABv

0

0

t

t

)(tvc

avgLi ,Li

0t

Harmonic Spectrum of Output Voltage

THD of Output Current

x

x

x x

x

x x

x xx x

xx xxx x

x

x

Modulation index

THD (%)

1.0

12 dc

V

12 dc

V

12 dc

V

12 dc

V

12 dc

V

69/140

Natural Sampling Sinusoidal PWM for Half-Bridge Inverter

off : ,on :tricontro

AA

l

TTvv


AA TTvv

2dcV

2dcV

1 lfundamenta , )( AoAo vv uAo

controlV triV

( )1f s

0t

t0

t = 0

tri

controlˆ

ˆ

VVma

1ffm sf

Amplitude Modulation Ratio

Frequency Modulation Ratio

dcAoA VvTvv 21 on, istricontrol

dcAoA VvTvv 21 on, istricontrol

dcAonNAoAN Vvvvv 21

hAohAN VV )ˆ()ˆ(

2dcV

2dcV

ANv

Ai

dcV

N

AD

AD

AT

AT

Ao

70/140

Single-Phase PWM Inverter: Waveform and Spectrum

1.2

1.0

0.8

0.6

0.4

0.2

0.0

x

x

x x

x

x x

x xx x

xx xxx xx

x1

0 t

0 t

t = 0

controlV triV

( )1f s

1, ( ) fundamental aoao vv uAo

2dcV

2dcV


AA TTvv

off n tricontrol

:,: AA ToTvv

( )mf 2mf

ˆ( )/ 2

ao h

dc

VV

( )2 1mf 2mf 3mf

( )3 2mf

m ma f 0 8 15. ,

1 of Harmonics f

Harmonics distribution

One-leg switch-mode PWM inverter

DA+TA+

TA- DA-

2dcV

2dcV

dcVai

aNv

N

ao

71/140

Natural Sampling PWM

Simple Easy to be implemented by analog circuit

Beat effect phenomenon Not easy to be implemented with MCU-based software Asynchronous (modulating and carrier signal) Limited linear voltage control range

Advantages:

Disadvantages:


72/140

Waveforms under Overmodulation

Vd2

Vd2

, 1( ) fundamental ao aov vaov

controlVtriV

( )1f s

0 t

t0

0

1ˆ( ) / ( )

2dc

aoVV

1.0

0 1.0 3.24

Linear modulation range

over-modulation

Square-wave

273.14

am

73/140

Bipolar and Unipolar PWM

Bipolar PWM

Unipolar PWM

1Q

3Q

74/140

Current Ripple Analysis of Bipolar PWM

,1 (2 1)ab dcV D V )(DM

1

D10

1

5.0

0

abv

Bipolar PWM (a) voltage and (b) current.

1Q

2Q

3Q

4Q

Vdcabv

a babi

abi

abv

abI

(max)12

dc sab

V TIL

( )dc emf sab

V V DTI

L

If the IR drop is neglected,

dcemf VDV )12( 2(1 )dc s

abV D DTI

L

(1 )2

ab dc sI V T D DL

abi

ABv

dcV

dcV

abi

75/140

Current Ripple Analysis of Unipolar PWM

,1ab dcV DV

)(DM

D10

1

0

Bipolar PWM (a) voltage and (b) current.

1Q

2Q

3Q

4Q

Vdc

(max)14

dc sab

V TIL

( )dc emf sab

V V DTI

L

If the IR drop is neglected,

dcemf DVV (1 )dc s

abV D DTI

L

The negative voltage is controlled by another control signal DIR.

(1 )2 2

ab dc sI V T D DL

abIabi

abv

dcV

dcV

abv

a babi

abv

abi

ABv

abi

76/140

Voltage Ripple Analysis: Bipolar and Unipolar PWM

Vr,rms in a full-bridge converter using PWM: (a) with bipolar voltage switching; (b) with unipolar voltage switching.

-1.0 0 1.0-0.5 0.5

(a) bipolar

(b) unipolar

rm s

13 rr , r

d d M AX

VV IV V I

d

o

VV

0.25

0.50

0.75

1.0

bipolarD0 1.00.5

bipolarD1.00

For a same output voltage, the PWM duty ratios are different using different PWM control schemes. For a 50% VDC output,

5.075.0

unipolar

bipolar

DD

The current ripple ratio is:

162)1(

22 LTVDD

LTVI sdcsdcAB

163)1(

2 LTVDD

LTVI sdcsdcAB

2

3

Bipolar PWM

Unipolar PWM

For DC-DC converter, the current ripple profile can be plotted as a function of the modulation index. While for DC-AC inverter, the current ripple profile can be plotted as a function electrical angle and modulation index.

Hybrid PWM

S11 ON / S12 OFFS11 OFF / S12 ON

PWMcarrier, c

Modulation waveform, m =de

Effective duty ratio de(t)

S11 OFF / S12 ONS11 ON / S12 OFF

S21 OFF / S22 ON S21 ON / S22 OFF

1 / of0

Modulation waveform Carrier waveform

(a)

(b)

0

0

gV

gVABv

1/ of

1/ sf

11S

12S

21S

22S

gV C RL

ov tABv

A

B

Li t oi t

sino m ov t V t

S11 and S12: High Frequency Switching Leg S21 and S22: Line Frequency Switching Leg

[1] R. S. Lai and K. D. T. Ngo, “A PWM method for reduction of switching loss in a full-bridge inverter,” IEEE APEC Conf. Proc., 1994.

Unipolar PWM: Current Ripple Profile

max 8dc sV TIL

0 0.002 0.004 0.006 0.008Time (s)

0

0.2

0.4

0.6

0.8

1

Vr1 Vr2 Vr3 Vr4 Vr5 Vr6

0.7am

0.8am

0.9am

1.0am

/ 2

0.5am

0.6am

1.0

0.8

0.6

0.4

0.2

04

When ma = 0.707, the maximum ripple occurs at max=45º.

( ) (1 sin ) sin2dc s

a aV TI m m

L

Lr

dcV

1S

2S

3S

4S

LA

BgvLi

Calculate the RMS value of ripple current with a specified modulation index?

[1] P.A. Dahono, A. Purwadi, and Qamaruzzaman, “An LC filter design method for single-phase PWM inverters,” International Conference onPower Electronics and Drive Systems (PEDS), pp. 571-576, 21-24 Feb 1995.

[2] Hyosung Kim and Kyoung-Hwan Kim, “Filter design for grid connected PV inverters,” IEEE International Conference on Sustainable EnergyTechnologies (ICSET). pp. 1070-1075, 24-27 Nov. 2008.

79/140


PWM Techniques for Three-Phase Inverters



80/140

PWM Strategies for Motor Drives & Grid Converters

The main purpose of the modulation techniques is to attain the maximum voltage with the lowest Total Harmonic Distortion (THD) in the output voltages.

PWM strategy plays a most important role for the improvement of voltage control range and linearity and reduction of current harmonics, leakage current, and switching loss for a motor drive.

Digital link

Controller Converter

Powersource

PWMModulator

Motor Load

SpeedTorque

Sensor signals

81/140

PWM Strategies for Power Converters

D. G. Holmes and T. A. Lipo, Pulse Width Modulation for Power Converters: Principles and Practice, M. E. El-Hawary, Ed. New Jersey: IEEE Press, Wiley-Interscience, 2003.

82/140

Classification of PWM Techniques

PWM Techniques Two-Level Inverter

Multilevel Inverter

Continuous PWM SPWM Regular-Sampled SPWM SVPWM Trapezoidal PWM Harmonic Injection …

Discontinuous PWM DPWMMIN DPWMMAX ….

Programmed PWM SHE Optimal PWM

83/140

Two-Level Natural Sampling Sine PWM

a

c

bdcV o

asi

bsi

csi

anv

bnv

cnv

1S

2S

3S

4S

5S

6S

dcV21

dcV21

ar

cecr cL

nbe

br bL

aL ae

carrier wave

sinewave Modulation signal

n

upper transistor on

lower diode onper phase output voltage (with respect to dc center tap)

dcV21

dcV21

dcV21

dcV21

Commut int.

Switchingpattern

volt. vector

10000

carrier int.21004

31015

41117

51015

61004

70000

J J + 1

Pole Commutation Sequence Rule

bov

aov

cov

a

c

b

84/140

Three-Phase Inverter for AC Power Source

3-phaseload

3-PhaseMotor

3-PhasePowerSupply

SVPWM Generator

dcV

85/140

Representation of Stator Voltage Vector

2 2, exp( )3s a b c

v v v j v

v V ta m sin ,

v V tb m sin( ) , 120

v V tc m sin( ) , 120

The motor stator voltage vector (or current vector) can be expressed as a combination of theinverter output phase voltage va , vb and vc which can be expressed in the vector form as

where

and Vm is the amplitude of the fundamental component.

86/140

Space Vector Representation of 3-Phase Systems

Space vector based analysis method can also used for the analysis if three-phase inverter.The inverter output voltage vector (or current vector) can be expressed as a combination ofthe inverter output phase voltage va , vb and vc which can be expressed in the vector form as

2 2, exp( )3s a b c

j v v v vsin ,a mV tvsin( 120 ) ,b mV t v

sin( 120 ) ,c mV t v

where

and Vm is the amplitude of the fundamental component. Note: The va is sometimes denoted as vaswith a subscript s meaning to apply to the stator.

(a)t

v tas( ) v tbs( ) v tcs( )

(b)

output voltage vectorbs

cs

asv tas( )

)(tvbs v tcs( )

( )sqs tv

)(tv sds

( )s tv

( )s tv

mV

87/140

Vector Representation of 3-Phase Quantities

22 ( )3

j js as bs cs

s sds qs

v v e v e

v jv

v

stator voltage vector

23

bs

cs

asv tas( )

v tbs( )v tcs( )

v tqss ( )

v ts( )

v tdss ( )

(b)(a)

t

v tas( ) v tbs( ) v tcs( )

88/140

Space Vector Representation of 3-Phase Inverter

70 , vv : zero voltage vector

I

II

III

IV

V

VI

v2

v1

v3 v4

v5

v6

V7 (1 1 1)

(a) (b)

4 6 2 3 1 5S1

S2

S3 S5

S6

o nVdc

A

C

BS4

asi

csi

bsibsv

asv

csv

V4 (1 0 0) V6 (1 1 0) V2 (0 1 0)

V3 (0 1 1) V1 (0 0 1) V5 (1 0 1) V0 (0 0 0)

89/140

Vector Decomposition Using Basic Switching Vectors

Fig. (a) The switching configurations of a 3-phase PWM inverter, (b) the correspondingvectors, and (c) the decomposition of the voltage vector.

(a) (b) (c)

44 v

TT

s

66 v

TT

s

vref

6v

4v

v V j nn d

23

13

exp ( )where n = 1, 2, .., 6, and v0 = v7 = 0.

The 8 basic switching vectors:

: zero voltage vector

III

III

IV

V

VI

v2

v1

v3 v4

v5

v6

70 , vv

V7 (1 1 1) V4 (1 0 0) V6 (1 1 0) V2 (0 1 0)

V3 (0 1 1) V1 (0 0 1) V5 (1 0 1) V0 (0 0 0)

90/140

Representation of 8 Basic PWM Switching Vectors

The stator voltage vector can be decomposed to two orthogonal components in a two-axiscoordinate or as a combination of the two basic vectors of Fig. 2(b). An example of thevoltage vector decomposition is shown in Fig. 2(c). The SVPWM strategy aims tominimize the voltage/current harmonic distortion by proper selection of the switchingvectors and determination of their corresponding dwelling widths.

v V jn

n d

23

13

exp( )

where n = 1, 2, .., 6, and v0 = v7 = 0.

There are eight basic switching configurations of the 3-phase PWM inverter as shown inFig. 2(a) and their corresponding voltage vectors are shown in Fig. 2(b) which can beexpressed as

91/140

Flux Trajectories

V4T2

V3T1

V3T1

V4T2

R

R

V3T1

V4T2

120 *

: zero voltage vector

I

II

III

IV

V

VI

v3tv4t

v3t

trajector of the flux linkage

v2

v1

v3 v4

v5

v6

v v7 8,

Vector Decomposition

92/140

Synthesis of Flux Trajectory by Integration of Voltage Vectors

The flux produced by the reference voltage vector in a PWM switching period is acombination of each individual flux resulted by its corresponding voltage vector. Theirrelationships can be expressed as

0 0 1 1 2 71 01

0

2

0

7Tref

TTT

TT

TTs v dt v dt v dt v dt v dt.

Because the voltage vector v1 and v2 are constant vector, and v0 and v7 are zero vector,we can obtain

v vTT

vTTref s s

11

22

where Ts is the switching period, T1 and T2 are the dwelling time for v1 and v2 ,respectively.

Note: The voltage vectors v1 and v2 are used for illustration purpose only.

93/140

Decomposition of a Voltage Vector

11

s

T vT

22

s

T vT

refv

2v

1v

The voltage space vector can be described in rectangular coordinates as follows

T V T V T V ad d s d1 223

10

23

6060 2

23

cossin

cossin

where , , and Vd is the dc-link voltage.a v Vref d 2 3 0 60

T T as1 260

60

sin( )sin

T T as2 2 60

sinsin

T T T T Ts7 0 2 12

The equivalent PWM waveforms, which produce same average flux, may havevarious combinations of the basic vectors.

94/140

Possible Voltage Compositions of a Stator Voltage Vector

(a)

1

-11

-11

-1

vVda

0.5

vVdb

0.5

vVdc

0.5

t

t

t

(b)

Ts

1

-1

1

-11

-1

vVda

0.5

vVdb

0.5

vVdc

0.5

T02

Ts2

t

t

t

T12

T22

T72

T0 T7T2 T1

(c) (d)

1

-11

-11

-1

vVda

0.5

vVdb

0.5

vVdc

0.5

t

t

t

1

-11

-11

-1

vVda

0.5

vVdb

0.5

vVdc

0.5

t

t

t

T2T1T02

T02

Ts

T2 T1T02

T02

Ts

95/140

Symmetric vs. Asymmetric SVPWM

1

-11

-11

-1T02

Ts2

T12

T22

T72

(a)

vVda

0.5

vVdb

0.5

vVdc

0.5

t

t

t

1

-11

-11

-1

T0

Ts2

T1 T2T7

(b)

vVda

0.5

vVdb

0.5

vVdc

0.5

t

t

t

T0 T2 T1 T7

96/140

Generation of Optimum PWM Patterns for SVPWM

(a)

1

-11

-11

-1

Ts

T0 T7T2 T1

1

-11

-11

-1T02

Ts2

T12

T22

T72

(b)

1

-11

-11

-1

Ts2

T12

T22

(c)

vVda

0.5t

t

t

vVdb

0.5

vVdc

0.5

vVda

0.5

vVdb

0.5

vVdc

0.5

vVda

0.5

vVdb

0.5

vVdc

0.5

t

t

t

t

t

t

97/140

PWM Gating Signals of SVPWM at Each Operation Section

I II III IV VVISASASBSBSCSC

I II III IV VVISASASBSBSCSC

98/140

Flux TrajectoriesOutput Frequency from 0,094 Hz to 1500 Hz

(b) 5Hz (c) 60Hz(a) 94mHz

(e) 1000Hz(d) 300Hz (f) 1.5kHz

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

General Form of Harmonic Injection Scheme

Switchinglogic

Dead time protection

Dead-time compensation

Protection latch

Gate Driver

*am

*bm

*cm

dcadcnom

adc

aa kvVVv

Vvm

***

11

ZeroSequenceSignalCalculator

0e

bm

cm

am

1999.Simple analytical and graphical methods for carrier-based PWM-VSI drives (pe).pdf

100/140


Dead-Time Protection and Distortion



101/140

Dead-Time Protection & Distortion

Top transistor

Bottom transistor

ONON ON

ONON

Dead-Time

2dcV

2dcV

ANv

ai

dcV

N

Ao

To prevent shoot-through!

AT

AT

AD

AD

The turn off of one transistor trig the delay (dead time) of its complementary turn on.

Example of output current due to dead-time distortion.

Current with Correction Disabled

PWM Dead-Time Distortion Caused by Inductive Loads

12 DC

V

DCV21

Causes poor low-speed motor performance

Torque ripple Distorts current Produces noise in audible

region

103/140

Analysis of Dead-time Effect

Dead-times effect: when a positive current IO flows through the load, the actual on time for switch S1 is shorter than the desired one. Consequently, the average voltage across the load is different from the desired one.

Output voltage error due to the dead-time:

Logi

c ga

te s

igna

lsA

pplie

d ga

te s

igna

lsLo

ad V

olta

ge

( )2DC dead

ao oS

V tv sign iT

DCV21

DCV21

o a

1D

1D

1G

2G

1S

2S

1E

2E

ai

sRsLse

Lv

*1GEv

*2GEv

1GEv

2GEv

aov

1ONt

2ONt

deadt

ST t

DCV21

12 DC

V

Effect of Blanking Time t

t

t

t

t

t

t

t

0

0

0

0

0

0

0

t

t

lossideal

actual

actual

gain

(c)

(d)

(f)

(e)

vcontrolvtri

0Ai

0Ai ideal

aov

(a)

DCV21

DCV21

oa

1D

2D

1G

2G

1S

2S

1E

2E

ai se

sRsL

Lv

aov

0ai 0ai

refvV

V

(b)

1GEv

2GEv

Ideal condition (no dead time)

Ideal condition (no dead time)1GEv

2GEv

sT

105/140

Outputs Distortion Due to Dead-time Effect

aov

0ai 0ai

refvV

V(b)

,1aoV t

,1aI t

t

t

with dead time

0

0

(c)

No dead time

V

(a)

( )2DC dead

aS

V tV sign iT

DCV21

DCV21

o a

1D

2D

1G

2G

1S

2S

1E

2E

ai

sesRsL

Lv

Due to the current sign change

Voltage Drop Vo Induced by the Blanking Time

actualideal )()( ANAN vvv

0

0

dc As

AN

dc As

t V iT

Vt V iT

0

0

dc As

BN

dc As

t V iT

Vt V iT

2 0

2 0

AN BN dc As

o

dc As

tV V V iT

Vt V i

T

0ideal actual

Ts

0

Ts

0

t

t

t

dcVAi

ov

oi

BiA BBD

BD

AD

AD

AT

AT

BT

BT

ANv

BNv

0Ai

107/140

Effect of t on Vo

(a)

0

Vo

Vo

No blanking time(independent of io)

(b)

Effect of t on Vo, where Vo is defined as a voltage drop if positive.

dcVAi

ov

ov

oicontrolv

Bi

0oi

0oi


A BBD

BD

AD

AD

AT

AT

BT

BT

108/140

Effect of ton the Sinusoidal Output

0

0

t

t

ideal

actual

Measured current of a PWM inverter with dead-time distortion.

)(tvo

oi


109/140


Filter Design for Grid Inverters



110/140

Control Architecture of a Single-Phase NPC Grid Inverter

Sourceor

Load

ModulatorController

ev

1L gL

cv

2L gi

gvfCci

ai

*v

v

GRID

PLL

gv

ai

gicv

1dcv

1dcv

P

N

O

LCL Ripple Filter & EMI Filter of a Grid Inverter

ev

gLgi

gv

GRIDPWM Inverter

dcV

1S

2S

3S

4S

a

b

DC-link Return

DC-link

1L 2L

C

Ripple Filter EMI Filter

xC yC

yC

yT xTxC

F1

L

G

NF2

RV1

Protection

2LC1L

CLL

oC

1L 2L

1st-order L Filter 2nd-order LC Filter 3rd-order LCL Filter 4st-order LLCL Filter

oL

Voltage FedCurrent Fed Current Fed Current Fed

Frequency Response of the LCL Filter

2011.A Single Phase Grid Connected DC-AC Inverter with Reactive Power Control for Residential PV Application (Xiangdong Zong).pdf

2 sf 1 2

1L L 1 2

1( )C L L

60 /dB dec

20 /dB dec

0dB

70dB

gvdcV

1L 2Lcv

ci1Li 2LifC

gi

dcCdR

0

3 21 2 1 2 1 2

( )( )

( )

1( ) ( )

g

gf

ab v

f d

f f d

i sH s

v s

sC Rs L L C s C R L L s L L

a

b

0

1sL

0

1 2

20log L dBL L

Inductance reduction with LCL filter:

60HzdB

( )fH s

100

( ) 1( )( )

g

gf

ab v

i sH s

v s sL

1S

2S

3S

4S

60 Hz

Frequency Response of LCL Ripple-Rejection Filter

60 Hz

1sL

20

0

-20

-40

-60

-80

-100

Gai

n [d

B]

210 410 51010

( )fH s

20 logQ

60HzdB

fsdB

-60dB/dec

1 2

12 ( )L L 0

12 L

1 2

12 ( )r f

fL L C

sfHz

1 2

1( )s L L

-20dB/dec

1 2

12 L L C

310

31 2

1

fs L L C

114/140

Single Inductor Filter Design: Design Guide Lines

單電感濾波器的設計較為簡單，也可提供濾波器與控制迴路設計的參考。

併網電流在額定輸出的總諧波失真(≤5%)是濾波器設計的主要規格。假設其中2%來自電流漣波，另外3%來則其他非線性導致的失真，則來自電流漣波所導致的總諧波失真THD=2%可作為一階單電感濾波器的設計規格。

濾波器與控制器頻率響應所構成的控制迴路，應使其閉路之頻寬介於電網頻率與開關頻率之間，同時維持足夠之相位邊界(phase margin > 60)。

1 2

1L L

1 2

1( )C L L

60 /dB de c

20 /dB de c

0dB

70dB0

1sL

60HzdB

( )fH s

2 sf

60 Hz

115/140

References: LCL Filter Design

[1] Chapter 11: Grid Filter Design, Grid Converters for Photovoltaic and Wind Power Systems, Remus Teodorescu, Marco Liserre, and Pedro Rodriguez, Wiley; 1 Ed., IEEE Press, April 12, 2011.

[2] P.A. Dahono, A. Purwadi, Qamaruzzaman, “An LC filter design method for single-phase PWM inverters,” IEEE Power Electronics and Drive Systems (PEDS) Conf. Proc., pp. 571-576, 21-24 Feb 1995.

[3] Michael Lindgren and Jan Svensson, “Control of a voltage-source converter connected to the grid through an LCL-filter-application to active filtering,” IEEE IAS Annual Meeting, pp. 229-235, 1998.

[4] M. Liserre, F. Blaabjerg, and S. Hansen, “Design and control of an LCL-filter based three-phase active rectifier,” IEEE IAS Annual Meeting, pp. 299-307, 2001. [see also: M. Liserre, F. Blaabjerg, and S. Hansen, “Design and control of an LCL-filter-based three-phase active rectifier,” IEEE Trans. Ind. Appl. vol. 41, no. 5, pp. 1281-1291, October 2005.]

[5] M. Liserre, F. Blaabjerg, and A. Dell’Aquila, “Step-by-step design procedure for a grid-connected three-phase PWM voltage source converter,” International Journal of Electronics, vol. 91, no. 8, pp. 445–460. August 2004.

[5] F.A. Magueed and J. Svensson, “Control of VSC connected to the grid through LCL -filter to achieve balanced currents,” IEEE IAS Annual Meeting, pp. 572-578, 2005.

[6] R. Hamid and Hadi Saghafi, “Basic criteria in designing LCL filter for grid connected converters,” IEEE ISIE Conf. Proc., pp. 1996-2000, July 2006.

[7] Fei Liu, Shanxu Duan, Pengwei Xu, Guoqiang Chen, and Fangrui Liu, “Design and control of three-Phase PV grid connected converter with LCL filter,” IEEE IECON Conf. Proc., pp. 1656-1661, Nov. 2007.

[8] A. Papavasiliou, S.A. Papathanassiou, S.N. Manias, and G. Demetriadis, “Current control of a voltage source inverter connected to the grid via LCL filter,” IEEE PESC Conf. Proc., pp. 2379-2384, June 2007.

[9] S. Saridakis, E. Koutroulis, and F. Blaabjerg, “Filter optimization of Si and SiC semiconductor-based H5 and Conergy-NPC transformerless PV inverters,” 15th European Conference on Power Electronics and Applications (EPE), pp. 1-10, 2-6 Sept. 2013.

[10] A. Reznik, M.G. Simoes, A. Al-Durra, and S.M. Muyeen, “LCL filter design and performance analysis for grid-interconnected systems,”IEEE Transactions on Industry Applications, vol. 50, no. 2, pp. 1225-1232, March-April 2014.

[12] S. Sen, K. Yenduri, and P. Sensarma, “Step-by-step design and control of LCL filter based three phase grid-connected inverter,” IEEEInternational Conference on Industrial Technology (ICIT), pp. 503-508, 2014.

[10] Y. Zhang, M. Xue, M. Li, Y. Kang, and J. M. Guerrero, “Co-design of the LCL filter and control for grid-connected inverters,” Journal of Power Electronics, vol. 14, no. 5, pp. 1047-1056, 2014.

116/140


Modeling of Grid Inverters



117/140

A Hybrid DC & AC Microgrid System

Solar irradiation

PVTemperature

WindSpeed

UtilityGrid

Gear

DFIG

Boost Converter

AC/DC/AC

Breaker

Battery Converter

Main Converter

Battery

AC Load

pvi 1i1L 1R

pvvpvC

STTv dcv dC

1 11i dD

DC

Load

7ST

8ST

D

ci dcibi

7Dbi

8D

3L 3Rbatv

Dv

aci

1ST 3ST 5ST5D3D1D

2L 2R

4ST4D

6ST6D

2ST2D

CB

A2C

CiBiAi

Modeling of a Single-Phase Grid Inverter

REF: Bradford Christopher Trento, Modeling and Control of Single Phase Grid-Tie Converters, Master Thesis, University of Tennessee, Knoxville, 2012.

(a) Full-bridge grid inverter

(b) Hybrid NPC Full-bridge grid inverter

Single-Phase Half-Bridge Grid Inverter

Summary of dq-Transformation

c

b

a

fff

ff

23

230

21

211

32

ff

ff

q

d

cossinsincos

c

b

a

q

d

fff

ff

sinsinsincoscoscos

32

0 cba fff

abc dq

1( )s tv

( )bv t ( )cv t

b

c

a

q

( )av t

1.5

1.0

0.5

23

d

( )bv t ( )cv t

1t

( )av tmV

23 = angle between d-q and reference frames

121/140

Summary of dq-Transformation ..

abcdq

0 cba fff

q

d

ff

ff

cossinsincos

1 0

1 32 21 32 2

a

b

c

ff

ff

f

q

d

c

b

a

ff

fff

sincossincos

sincos

122/140

Modeling of a Full-Bridge Grid Inverter in Natural Reference Frame

Modeling of a Full-Bridge Grid Inverter in dq-Model Synchronous Reference Frame

Simulation Model for a Three-Phase Grid-Connected PV Inverter System

REF: Marcelo G. Molina, and Luis E. Juanico, “Dynamic modelling and control design of advanced photovoltaic solar system for distributed generation applications,” Journal of Electrical Engineering: Theory and Application, vol. 1, pp. 141-150, 2010.

Tbst

PV Solar ArrayBoost DC/DC

ConverterThree-Phase Three-LevelVoltage Source Inverter Line Filter

Step-UpCoupling

Transformer

Electric Utility Grid

PCC

Lb Db

CbDfd

Cd1

Cd2

0 NPa

bc

-Vd /2

+Vpv /2

-Vpv /2

+Vd /2LF1

LF2

LF3

CF1

CF2CF3

PV

PV

PV

PV

PV

PV

Yg):N( :1

Np

Ns

125/140


Control of Grid Inverters



126/140

Intelligent Distributed Power Generation

電力網路

交流柴油發電機

併網型太陽光變頻器

併網型燃料電池變頻器

微型渦輪發電機

電池儲能發電機變頻器

併網型風力發電變頻器

儲能系統

110/220 V, 50/60 Hz

DCAC

DCAC

DCAC

DCAC

DCAC

DCAC

127/140

Generic Control Structure for a PV Inverter with Boost Stage

PVPanelsString

dc-dcboost

dc-acPWM-VSI

LCLfilter

X’form&

Grid

VdcControl

GridSynchronization

CurrentControl

Basic Functions (grid connected converter)

MPPTAnti-IslandingProtections

Grid /PV plantMonitoring

PV specific functions

Active FilterControl

Micro GridControl

Grid Support(V,f,Q)

Ancillary functions

L

N

IPV

VPV

PWMPWM

gV

gI

dcV

C

128/140

Modeling of a Single-Phase Grid Inverter

ai 1L

dcC

dcv

bati

1S

2S

3S

4S

a Lr

invi

ci

GaN

b

gegL

gi

gv

Grid

MOSFET

IGBT

cvfC

2LPCC

Grid Disturbances

batv

0R2R

2V2C

oE

I

oV

1R

1C1V

Battery Bank

Nonlinear Characteristics of Filter Inductance

Block Diagram of a Single-Phase Grid Inverter

CurrentControl

PLL

MPPT

BatteryDC

AC

DC

DC

ctrlVDC

)sin( tgrid

Grid Islanding Protection

CurrentController

gridi

refi

dcV

*dcv

dcv

dci

gridv

Load Power Control

PLL Controller

Loop Filter VCO*

av

ff

PI

Line VoltageDetector

ˆavav

1sPDdcV

1S

2S

3S

4S

LA

BgvLi

*CHGi

dcC

Control Issues of Grid Inverters

1S

2S

3S

4S

a

bdcC

invici

dcvsv

sR

Large variation of grid voltage (may be shorted due to fault) Variations of grid impedance (inductive, resistive, or

nonlinear rectifier) Disturbances, operation, and protection due to grid faults Filter dynamics and nonlinear characteristics (saturation

effect of filter inductor) Nonlinearities of PWM inverter (dead-time effect, voltage

drop of switching devices, etc.) PWM control due to selected inverter topology Noise corrupted feedback signal sensing (instantaneous

average signal sampling, EMI due to switching, isolation, CM noise rejection, etc.)

Large dc-link voltage variations Sampling effect due to PWM and digital control Parallel operation of multiple inverters

fL

cvfC gvGL

AC Grid220V, 60Hz

R

R

dci

Fault Protection Test Shorted Circuit Test Open Circuit Test L/HHRT L/HVRT

Current Control of Single-Phase VSI Inverters

Fen Li, Yunping Zou, Wei Chen, and Jie Zhang, “Comparison of current control techniques for single-phase voltage-source PWM rectifiers,”IEEE International Conference on Industrial Technology (ICIT), pp.1-4, 21-24 April 2008.

PI Control IP Control Proportional Resonant (PR) Control Feed-Forward PR Control

sKK ip

PWMBridge

2)1 (r

r

K

s

2)1 (r

r

K

s

PKabv

sv

mv

mv

mv

abvsv

sv

si

si

si

1

L sr sL

1

L sr sL

1

L sr sL

*si

*si

*si

PK

PWMBridge

PWMBridge

CurrentController

PWMController

sL

si

sv

1S

2S

3S

4S

A

B

dcC

PVi

ci

si

*si

sv

dcviK

sPWMBridge

mv abvsv

si1

L sr sL*si

PK

invi

132/140

Current Control Architectures

(a) Hysteresis control.

(c) PWM ramp control.

(b) Adaptive hysteresis control.

(d) Predictive control.

AdaptiveController

aS

bS

cS

si

*si

abc

3

aS

bS

cSsi

*si

abc

3

aS

bS

cS

si

*si

3

abc

sv

*sv a

S

bS

cS

3

ki ks ki

1ki

*ki Minimization

of g functionPredictive

model

Current Control Architectures of 3-Phase VSI

(a) Stationary PI in three-axis coordinates

(b) PI in synchronous coordinates(c) PI in stationary coordinates

SA

SBSC

Three-phaseLoad

uAcuBc

uCc

Carrier

Three-phaseLoad

PWMmodulator

isd

isq

isqc

isdcPI

PI

dq

ABC

ABC

dq

ssinscos

Currentregulator

Coordinatetransformation

PWMmodulator

ABC

ABC

ibia

ic

K2

K1

K1

K2

i

ii

ci

c

cii

cu

cu

Three-phaseLoad

dcV

dcV

(b) State feedback controller in three-axis

PWMmodulator

Statefeedback

FeedforwardDisturbance

Integral part

usc

Three-phaseLoad

dKfK

iK

pK

*si

si

dcV

dcV

ai

bi

ci

*ai*bi*ci

ai

bi

ci

134/140

Current Control Techniques

CurrentController

PWMController

sL

si

sv

1S

2S

3S

4S

A

B

dcC

ci

si

*si

sv

dcv

dci invi

dcv

CurrentController

PWMController

sL

si

sv

1S

2S

3S

4S

A

B

dcC

ci

*di

dcv

dci invi

dcv

CoordinateTransform

PLL

*qi

si

sv

di qiqv

CT

(b) Control in synchronous rotating frame with control of signals in dc quantities.

(a) Control in stationary frame with control of signals in ac quantities.

135/140

Control in Stationary Reference Frame

abc

PRcontroller

PRcontroller

HC

HCdq

*i

*i

i

i

*v

*v

GridModulation

AndPWM

InverterQcontroller

DC-linkcontroller

PLL

*di

*qi

ai bi ci av bv cv

*dcV

*Q

Q

dcV

2 20( )

2 20

0( )

0

ip

PRi

p

K sKs

G sK sK

s

General structure for stationary reference frame control strategy using resonant controllers and harmonic compensators.

136/140

Control in Synchronous Reference Frame

PIcontroller

Qcontroller

PIcontroller

Modulationand

PWMInverter

Grid

DC-linkcontroller

L

L

PLL

*di

*qi

di

qi di qi

*dcV

*Q

Q

dcV*dv

*qv

qv

dv

ai bi ciavbvcv

qvdv

General structure for synchronous rotating frame control using cross-coupling and voltage feedforward terms.

( )0

( )0

ip

dqPR

ip

KKsG s

KKs

dqabc

dqabc

Control in the synchronous reference frame transforms the reference signals and the feedback signals to dc quantities from a fixed reference frequency.

In this control scheme, the accuracy of this reference angle () of the reference frame is the key for the elimination of the steady-state error. The design of the PLL plays an important role for both transient and steady-state responses.

Synchronous Reference Frame Current Control for Single-Phase PV Inverters

2008.Synchronous Reference Frame Grid Current Control for Single-Phase Photovoltaic Converters (ias).pdf

Grid Current

Grid Voltage

CurrentController

PLL

PVString

0dV

sksk ip

s1

V

dV̂

ff

V

,qd ,

Delay

*dI dv

qd

0* qI v

dI

qI

i

i

PI

PI

PLL

TV

2

-1

qvto

qd to

qV̂

Â

̂

̂

PWMModulator

̂

*gI

138/140

Control of Three-Phase Three-Level Grid Inverter

vrvm

VpvPg

Kv∆v

iqr min

vm idr max

Ipv vmPr1 idr mix

TtrackDiniC1

D

idr1

vq1 vd1

vq vd idiqid1

iq1

va vb vc ia ib ic

θs

θs

iqr manVCM

MPPT Voltage Control

LC1

APCM

LPF

Mag(v)

LPF LPF

MPPTAlgorithm

dq0abc abc

dq0

Lagcompensator

PIDcontroller

PI1iqr 1 ∆iqr1

Lmax

Lminiq1

id1

idr1 ∆idr1

x1

Lmax

PIDcontroller

PI3

Lmin

PIDcontroller

Lmax

Lmin

LPF

idr* PI2

x2

∆Vd ∆Vdr

Vd max

Vd min

Vd D

Current Control PWM Control

dq0abc

vinv q1

θs

vinv d1

vinva vinv b vinvc

1

-1

4

4

4

1

0

Three-phasedq-PLL

Three-PhaseThree-LevelVSI SPWM

DC-DCConverter

PWM 1

Three-phase

VSIIGBTsControlPulses

DC-DCConverter

IGBTsControlPulses

dV

L‘s

L‘s

av bv cv s

139/140

Evaluations of Current Controllers

A. Timbus, M. Liserre, R. Teodorescu, P. Rodriguez, and F. Blaabjerg, “Evaluation of current controllers for distributed power generation systems,” IEEE Transactions on Power Electronics, vol. 24, no. 3, pp. 654-664, March 2009.

(a) General structure for synchronous rotating frame control using cross-coupling and voltage feedforward terms.

(b) General structure for stationary reference frame control strategy using resonant controllers and harmonic compensators.

Control Algorithms for the Grid Inverters

11

1LrsL

si

dcv

dm

dc

vv

abv sv*si

PWMModulator

Hysteresis Control, Variable Hysteresis Control PI Control, IP Control, Adaptive PI Control Dead-Beat Control, Soft Dead-Beat Control Predictive Control, Adaptive Predictive Control Proportional Resonant (PR) Control Repetitive Control, Adaptive Repetitive Control Repetitive Control with Limited BW Constraint H∞ Repetitive Control Fuzzy Control Phase-Locked Loop Control Control Loop Design with LCL, LCCL, and LLCL Filter

Documents

Power Electronic Systems & Chips Lab., NCTU, Taiwanpemclab.cn.nctu.edu.tw/W3news/實驗室課程網頁/電力電子/講義/2018/【PE-08... · Power Electronic Systems & Chips Lab.,