Introduction toIntroduction to Power Electronics

i PV S tin PV Systems

ECEN 2060

References:• ECEN4797/5797 Intro to Power Electronics

ece.colorado.edu/~ecen5797• Textbook: R.W.Erickson, D.Maksimovic, Fundamentals of Power

Electronics, 2nd ed., Springer 2000, http://ece.colorado.edu/~pwrelect/book/SecEd.html

Example: Grid-Connected PV System O ibl id t d PV t hit t

AC

iac

++

IPV

PVPower

DC input

IV

One possible grid-connected PV system architecture

AC output tVtv RMSac sin2)( AC

utilitygrid

vac

VPVPV

arrayelectronicsconverter

PVPVPV IVP

PVPV IV , RMSac )( tIti RMSac sin2)(

RMSRMSac IVP

tIVivtp RMSRMS 2cos1)(

Functions of the power electronics converter• Operate PV array at the maximum power point (MPP) under all conditions

tIVivtp RMSRMSacacac 2cos1)(

• Generate AC output current in phase with the AC utility grid voltage• Achieve power conversion efficiency close to 100%

RMSRMSac IVP

PVPVPVconverter IVP

• Provide energy storage to balance the difference between PPV and pac(t)Desirable features

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Desirable features• Minimum weight, size, cost • High reliability

Power electronics converter

ACutilitygrid

iac

+

vac

+

VPV

IPV

PVarray

Powerelectronicsconverter

grid

“Inverter”

One possible realization:

AC

iac

++

IPV

DC DC Single-phase+

One possible realization:

ACutilitygrid

vac

VPVPV

arrayDC-DC

converterSingle-phase

DC-ACinverter

Energy-storage

VDC

gy gcapacitor

Class objectives: introduction to circuits and control of a DC-DC converter and a single phase DC AC inverter

3ECEN2060

and a single-phase DC-AC inverter

Introduction to electronic power conversion

Four types of powerFour types of power electronics converters

• Control is invariably required• In the PV system, for example:

• Control input voltage of the DC-DCControl input voltage of the DC DC input voltage to operate PV at MPP

• Control shape of the DC-AC output current to follow a sinusoidal reference

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reference• Control current amplitude to balance

the input and output power

High efficiency is essential

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Circuit components for efficient electronic power conversion ?efficient electronic power conversion ?

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Ideal switch

Power semiconductor devices (e.g. MOSFETs, diodes) operate as near-ideal power switches:

• When a power switch is ON, the voltage drop across it is relatively small

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p g p y• When a power switch is OFF, the switch current is very close to zero

Capacitor

dtdv

Ci CC iC+

)()()( titvtp CCC CvC

For periodic vC(t), iC(t):

No losses (average capacitor power = 0)

0)0()(2

)()(1 22)(

)0(0

CC

Tv

CC

T

CC vTvT

CdvtvTCdttp

TP

C

)0(0 vC

1)(

TvT

CC C

Capacitor charge balance (average capacitor current = 0)

8ECEN2060

0)0()()(1

)0(0

CCv

CCC vTvTCdv

TCdtti

TI

C

Inductor

iL+

LdtdiLv L

L

vLL

)()()( titvtp LLL

For periodic vL(t), iL(t):

No losses (average inductor power = 0)

0)0()(2

)()(1 22)(

)0(0

LL

Ti

iLL

T

LL iTiTLditi

TLdttp

TP

L

)0(0 iL

1)(

TiT

LL L

Inductor volt-second balance (average inductor voltage = 0)

9ECEN2060

0)0()()(1

)0(0

LLi

LLL iTiTLdi

TLdttv

TV

L

Circuit components for efficient electronic power conversion

Power electronics converters are circuits consisting of semiconductor devices operated as (near-ideal) switches,

capacitors and magnetic components (inductors, transformers)

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p g p ( , )

Boost (step-up) DC-DC converter

switch control

Position 1 Position 2

Ts

DTs

fs = 1/Ts = switching frequency

Ts = switching period

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fs s g q y

D = switch duty ratio (or duty cycle), 0 D 1

Boost converter circuit

Power MOSFET and diode operate as near-ideal switches

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Power MOSFETs and diodesCharacteristics of several commercial power MOSFETsCharacteristics of several commercial power MOSFETs

+–

DTs Ts

Low on-resistance implies low pconduction losses

Fast switching enables high switching frequencies, e.g. 100’s of kHz to MHz g g g q g

13ECEN2060 Characteristics of several commercial switching power diodes

Voltage, current and frequency ratings of power semiconductor devices

(SCR)

Voltage rating

Current rating

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MOSFET: Metal Oxide Semiconductor Field Effect TransistorIGBT: Insulated Gate Bipolar TransistorSCR (or Thyristor): Silicon Controlled RectifierGTO: Gate Turn Off thyristor

Boost converter analysis

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Position 1

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Position 2

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Inductor voltage and capacitor current waveforms

D’ 1 DD’ = 1-D

Periodic steady-state operation• Inductor volt-second balance: average inductor voltage = 0

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• Capacitor charge balance: average capacitor current = 0

Inductor volt-second balance

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Boost DC voltage conversion ratio M = Vout/Vg

Boost DC-DC converter steps-up a DC input voltage by a ratio M

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p p p g ywhich is electronically adjustable by changing the switch duty ratio D

Simulink modelECEN2060ECEN2060

Switched-mode BoostDC-DC converter

200 4

1/100

1/Rload

iout

boost_switching.mdl

200.4

Vout

100

Vin

0.5

Duty cycle

Vg

Iout

D

Vout

IL

switch control

BoostDC-DC

(switching)

Boost DC-DCD

Vg

Vout

Vout

iL

switch control

Scope

Input voltage Vg = 100 VI d t L 200 HInductance L = 200 HCapacitance C = 10 FLoad resistance R = 100 Switch duty cycle D = 0.5Switch duty cycle D 0.5Output voltage Vout = 200 VInput current Ig = IL = 4 APower P = 400 W

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Switching frequency fs = 100 kHzSwitching period Ts = 10 s

Averaged (DC) model

No losses:gout V

DV

11

outg ID

I

1

1D1

outoutgg IVIV

Ideal boost DC-DC converter works as an ideal DC transformer with an electronically adjustable step-up ratio

1+ +

1:nIg Iout

DDMn

11)(Vg Vout

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Modeling of lossesL i i h d d• Losses in switched-mode power converters: Conduction losses, due to voltage drops across inductor

winding resistance and across power semiconductorwinding resistance, and across power semiconductor switches when ON

• Conduction losses depend strongly on the output power

Switching losses, due to energy lost during ON/OFF transitions

• Switching losses are not strongly dependent on output power; aSwitching losses are not strongly dependent on output power; a portion of switching loss remains even at zero output power

• Switching losses are proportional to the switching frequency

Other losses incl dingOther losses, including:• Losses in magnetic cores• Power needed to operate control circuitry

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Switching waveforms and switching losses MOSFET turn on transition

vt

MOSFET turn-on transition

Drain voltage

zoom-in

t

itDrain current

vtDTs Ts

it +

L

+

IoutiL

Ig

id

vd+ _+ _vL

t

it

+–

DTs Ts

+–

_

C R

_

voutvtvgateVg pt = vt it

Switching power loss = Transition energy loss * Switching frequency

24ECEN2060

Switching waveforms and switching losses MOSFET turn off transition

vt

MOSFET turn-off transition

Drain voltage

zoom-in

t

itDrain current

it

DTs Ts

it +

L

+

IoutiL

Ig

id

vd+ _+ _vL

vt

+–

DTs Ts

+–

_

C R

_

voutvtvgateVg

Switching power loss = Transition energy loss * Switching frequency

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Averaged (DC) model with losses

+ +1D : 1Ig Iout

RL

Vg

VoutIsw

• Small RL models conduction losses due to inductor winding resistance and power switch resistancesp

• Small Isw models switching and other load-independent losses• Efficiency with losses, when the load current Iout is known:

swswoutL IIIR

2

2)(1

1

26ECEN2060

outoutout IIVD 2)1(

Example: efficiency for various RL

Assume:• Resistive load

R = Vout/Iout

• Isw = 0

RDRL 1

)1(1

1

2

)(

Note that it is more difficult to achieve high efficiency if a large

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Note that it is more difficult to achieve high efficiency if a large step-up ratio is required (i.e. if duty-ratio D is close to 1)

Single-phase DC-AC grid-connected inverter

vacLi

iin

1 2+ acLiL

iac

+– VDC

1

1

2

2

• Switches in position 1 during DTs, in position 2 during (1D)Ts

• Switching frequency fs is much greater than the AC line frequency (60 Hz or 50 Hz)• By controlling the switch duty ratio D it is possible to generate a sinusoidal ACBy controlling the switch duty ratio D, it is possible to generate a sinusoidal AC

current iac (+ small switching ripple) in phase with the AC line voltage, as long as the input DC voltage VDC is sufficiently high, i.e. as long as VDC is greater than the peak AC line voltage

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Position 1

vacLi

iin

1 2+ acLiL

iac

+– VDC

1

1

2

2 + vL

acDCL vVv ii acL ii

Li ii

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Lin ii

Position 2

vacLi

iin

1 2+ acLiL

iac

+– VDC

1

1

2

2 + vL

acDCL vVv

ii acL ii

Li ii

30ECEN2060

Lin ii

Inductor volt-second balanceN t th t it hi f f li f• Note that switching frequency fs >> ac line frequency

• Over a switching period, vac(t) const.

ssacDC

sacDCL TtDTvV

DTtvVv

,0 ,

ssacDC

sT

acDCacDCacDCLL vVDvVDvVDdttvT

V 0)12())(1()()(1

sT0

12)( DVv

DMDC

ac

1)(1 DM

V t b t th th k f

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VDC must be greater than the peak of vac

Control of AC line current

vacLi

iin

1 2+ acLiL

iac

+– VDC

1

1

2

2

Control objectives:Control objectives:• iac = IM sin (t), in phase with AC line voltage vac(t)• Amplitude IM (or RMS value) adjustable to control power delivered to the AC line

tVtv RMSac sin2)(

tIti RMSac sin2)(

tIVivtp RMSRMS 2cos1)(

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RMSRMSac IVP

tIVivtp RMSRMSacacac 2cos1)(

A simple current controller

+ vacLiL

+ V

iin

1 2

iac

+– VDC

12

sensediLsin(t)

I +

_+

iref

iref iL

switchcontrol

IMrefiref iL comparator

with hysteresismultiplier

)sin( tIi Mrefref switch controlcomparatorwith hysteresis)sin( tIi Mrefref

iL < iref – i/2: position 1iL > iref + i/2: position 2

position 1

with hysteresis

33ECEN2060

iL is always within i/2 of irefposition 2 iref iL

i/2i/2

current ripple

Simulink modelECEN2060ECEN2060

Switched-Mode DC-AC Inverter

200

Vdc

Vdc

Iref

v ac

iac

iin

DC-ACinverter

(switching)

dcac_switching.mdl

W f (t) i (t) i (t) d it h t lStep

Scope

Irefswitch control

DC-AC

Waveforms vac(t), iac(t), iin(t), and switch control over one AC line period (1/60 s)

Input voltage VDC = 200 V

Inductance L = 2 mHAC: 120Vrms, 60HzIMref = 32 = 4.2 AiL = 1 AiL = 1 APac = 360 WWith this simple controller switching

34ECEN2060

controller, switching frequency is variable

Averaged DC-AC inverter model with losses

+ +1 : D 1Iin iacRL

VDC

vacIsw

ideal transformer

• Small RL models inductor winding resistance and power switch resistancesswitch resistances

• Small Isw models switching and other losses

35ECEN2060

DC-AC inverter efficiency exampleECEN2060

Switched-Mode DC-AC Inverter (averaged model)

200

Vdc

Vdc

v ac

iac

iin

D

DC-AC

inverter

(averaged)

v ac

iac

iin

Duty

Simulink modeldcac averaged.mdl

Input voltage VDC = 200 VAC: 120Vrms, 60HzR = 0 8

60

fac

Scope

566.2

Pin

1s

Integrator

4.5

IRMS

0.9537

Iref pin

pout

DC-AC

pin

pout

dcac_averaged.mdl RL = 0.8

Isw = 50 mAPac = 0 to 600 W

80%

90%

100%60

fac1

540

Pout

1s

Integrator1

0.9537

EfficiencyDivide

• Inverter efficiency of about

40%

50%

60%

70%

80%• Inverter efficiency of about 95% is typical

• At high power levels, conduction losses due to RL

10%

20%

30%

40%conduction losses due to RLdominate

• At low power levels, efficiency drops due to switching and

36ECEN2060

0%0 100 200 300 400 500 600

Pac [W]

other fixed losses