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Comparative Evaluation of Single-phase Unity Power Factorac-dc Boost Converter Topologies
A Pandey, Non-memberProf B Singh, FellowProf D P Kothari, Fellow
This paper presents a comparative evaluation of five topologies of single-phase ac-dc boost converters having powerfactor correction (PFC). These converter topologies are evaluated on the basis of performance and their salient featuresare discussed to analyze their applicability. Operation of these converters and their control schemes are described andmodeled using first-order differential equations. Performance of these converters is simulated and conformity of theseconverters is shown to relevant international standards. This work aims to provide an exposure of PFC converters toresearchers and application engineers dealing with power quality issues.
Keywords: ac-dc power converter; PFC; Power quality improvement; Comparative study
A Pandey and Prof D P Kothari are with Centre for Energy Studies andProf B Singh is with Department of Electrical Engineering, IIT Delhi,Haus Khus, New Delhi 110 016.
This paper (redrafted) was received on July 4, 2003. Written discussion on thispaper will be received until November 30, 2004.
INTRODUCTIONSingle-phase switch mode ac-dc converters are being used asfront-end rectifiers for a variety of applications due to theadvantages of high efficiency and power density. Theseclassical converters, however, draw-non-sinusoidal input accurrents leading to low input power factors and injection ofharmonics into the utility lines1. Research in improved powerquality utility interface has gained importance due to stringentpower quality regulation and strict limits on total harmonicdistortion (THD) of input current placed by standards such asIEC 61000-3-2 and IEEE 519-19922. This has led to consistentresearch in the various techniques for power qualityimprovement. Research into passive and active techniques forinput current wave shaping has highlighted their inherentdrawbacks. Passive filters have the demerits of fixedcompensation, large size and resonance whereas the use ofactive filters is limited due to added cost and controlcomplexity3.
Research into switch mode power factor corrected ac-dcconverters has been in two directions namely buck and boosttype topologies1. The advantage of Buck type topology is thatthe converter can provide variable output voltage, which islower than the input voltage. However, when theinstantaneous input voltage is below the output voltage thecurrent drops to zero and the results in significant increase ininput current THD4.
Design of input filters for power factor improvement in buckconverters is therefore complex and provides only limited im-provement in input current quality. On the other hand theboost type converter generate dc voltage, which is higher than
the input ac voltage. However, the input current in theseconverters flows through the inductor and therefore can easilybe actively wave-shaped with appropriate current modecontrol. Moreover, boost converters provide regulated dcoutput voltage at unity input power factor and reduced THDof input ac current. These converters have found widespreaduse in various applications due to the advantages of highefficiency, high power density and inherent power qualityimprovement at ac input and dc output.
The preferred power circuit configuration of single-phaseboost converter5-18 is the most popular and economical PFCconverter consisting of diode bridge rectifier with step-upchopper. Problems like low efficiency and reduced reliabilityare addressed in subsequent work19-22. Where the semi-boostconverter topologies offers several advantages over basic boosttopology in terms of reduced input current THD, higherefficiency and reliability. Half-bridge converter topology23-28
further enhances the efficiency and performance in sometypical applications. Whereas, the single-phase voltage sourceconverter (VSC) topology with bi-directional power flowcapability29-37 finds application in drives with regenerativebreaking, line interactive uninterruptible power supply (UPS),static VAR compensator and battery energy storage system.This paper provides a comparative study of single-phase PFCtopologies for applications where isolation is not required.Complete mathematical modelling of PFC converters iscarried out. Simulation results are provided for evaluation ofconverter performance under steady state and dynamicconditions and performance of single-phase boost converter isthen experimentally verified. Finally, the converters arecompared on the basis of performance, efficiency, design andcontrol complexity.
CIRCUIT CONFIGRATIONSPFC converter topologies considered in this work aredescribed in this section. The single-phase boost converter
102 IE (I) Journal�EL
with uni-directional power flow shown in Figure 1(a), isrealized by cascading single-phase diode bridge rectifier withboost chopper topology. Another topology with uni-directional power flow, semi-boost converter topology isshown in Figures 1(b) and 1(c). These configurations areimplemented with two semi-conductor switches and twodiodes. The inductor L is on the input side. Figures 1(d) and1(e) show half-bridge boost converter and voltage sourceconverter based on half-bridge and full bridge topologies, re-spectively. These two topologies allow bi-directional powerflow.
CONTROL SCHEMEThe objective of the control scheme of the boost converters isto regulate the power flow ensuring tight output voltageregulation as well as unity input power factor. Cascadedcontrol structure shown in Figure 1(f) is the most extensivelyused control scheme for these converters and essentiallysimilar control philosophy is applied to all the othertopologies of boost converter. In this scheme, the output ofvoltage regulator, limited to a safe value, forms the amplitudeof input reference current. This reference amplitude is thenmultiplied to a template of input voltage to synchronize thereference with input voltage, as required for unity powerfactor operation. The inductor current is forced to track itsreference current using current controller, which generatesappropriate gating signals for the active device(s).
MATHEMATICAL MODELLING OF PFCCONVERTERSThe proposed PFC converter system comprises single-phaseac supply, power converter circuit, and control scheme. In thissection modelling equations of various components of theconverter system are formulated separately to develop acomprehensive model for their performance simulation.
Supply SystemUnder normal operating conditions the supply system can bemodeled as a sinusoidal voltage source of amplitude Vm andfrequency fs . The instantaneous voltage is given as:
vs (t) = V tm sin ω (1)
where ω π= 2 f ts electrical rad/s and t is instantaneous time.
From sensed supply voltage, a template u(t) is estimated forconverter topologies with ac side inductor.
u t v t Vs m( )= ( ) / (2)
Figure 1(a) Boost converter
Figure 1(b) Symmetrical semi-boost converter
vs
is L
s
Cd
vdc
idc
Load
Figure 1(c) Asymmetrical semi-boost converter
Figure 1(d) Half bridge converter
vs
is L
s
Cd
vdc
idc
Load
Figure 1(e) VSC converter
vs
is L
s
Cd
vdc
idc
Load
vs
is L
s
Cd v
dc
idc
Load
vs
is
Ls
Cd
vdc
idc
Load
Figure 1(f) Control scheme of PFC converter
C1
C2
Vol 85, September 2004 103
Ü
u(t)
vs
is L
Cd
Idc
vdc LOAD
Vdc
Vdc
*PI
A
BC
AB/C2
LP Filter
is
ien
LP Filter
is*
u(t) for converter topologies with dc side inductor is obtainedfrom:
u t v t Vs m( ) ( ) /= (3)
DC Voltage ControllerThe objective of dc voltage controller is described earlier. Aproportional integral (PI) voltage controller is selected forvoltage loop for tight regulation of the output voltage. The dcvoltage vdc is sensed and compared with set reference voltagev dc
* . The resulting voltage error ve(n) at nth sampling instant is:
ve(n) = −v vdc dc n*
( ) (4)Output of PI voltage regulator v0(n) at nth sampling instant is:
v0(n) = + − +− −v K v v K vn p e n e n i e n0 1 1( ) ( ) ( ) ( )( ) (5)
where K p and Ki are the proportional and integral gainconstants. ve (n � 1) is the error at the (n � 1)th sampling instant.The output of the controller v0(n) after limiting to a safepermissible value is taken as amplitude of reference supplycurrent A.
PWM Current RegulatorCurrent regulation loop is required for active wave shaping ofinput current to achieve unity input power factor and reducedharmonics.
Reference Supply Current GenerationThe input voltage template B obtained from sensed supplyvoltage is multiplied with the amplitude of reference sourcecurrent A in the multiplier-divider circuit. Moreover, acomponent of input voltage feedforward C is also added toimprove the dynamic response of the converter system to linedisturbances (Figure 1(f)). The resulting signal forms thereference for input current. The instantaneous value of thereference current is given as:
i AB Cs* /= 2 (6)
Active Wave-shaping of Input Current
The inductor current error is the difference of reference
supply current and inductor current ( )*i i ien s s= − . This errorsignal is amplified and compared to fixed frequency carrierwave to generate gating signals for power devices of theconverter. PWM switching algorithm is selected depending onthe converter topology.
Modelling of PFC ConvertersThe converters are modelled using first order non-lineardifferential equations. The number of equations is equal to thenumber of energy storage components in the system.Single-phase Boost PFC ConverterThe boost converter is modelled using two differentialequations for inductor current iL and dc link capacitor voltagevdc .
p i v v L r i LL d p L= − −( ) / ( / ) (7)
p v i v R Cdc p dc d= −( / )/ (8)
where p is the differential operator (d/dt); r, the resistance ofthe inductor L; vd , the rectified line voltage at diode rectifieroutput; R, the resistance of the load and vp is the PWM voltageacross the switch and is defined as
vp = vdc (1 � S) (9)
ip is the current through the boost diode and is defined as
ip = iL (1 � S) (10)
where S is the switching signal obtained from current regula-tion loop. Its value is 1 (ON) or 0 (OFF) depending upon thestate of the switch.
Single-phase Semi-boost ConverterTwo variants of semi-boost converter topologies areconsidered, ie, symmetrical and asymmetrical. Both typeshave identical characteristics. The variations lead to simplifiedcurrent regulation in the symmetrical variant. The converteris described by two differential equations for inductor currentiL and dc link voltage across capacitor vdc .
p i v v r i LL s p L= − −( ) / (11)
p v i v R Cdc p dc d= −( / )/ (12)
where PWM voltage and current are as:
vp = −v S Sdc ( )1 2 (13)
i i S Sp L= −( )1 2 (14)
respectively;
where S1 and S2 are switching states of switches S1 and S2,respectively.
Single-phase Half-bridge Converter
There are three modelling equations describing the model ofthe converter as:
p i v v v r i LL s p p L= + − −( ) /1 2 ; (15)
pv i v R CC p dc1 1 1= − +{ ( / )}/ ; (16)
pv i v R CC p dc2 2 2= −{ ( / )}/ ; (17)
dc link voltage is as:
vdc = +( )v vC C1 2 (18)
and the PWM voltages and current are as
i S ip L1 1= (19)
i S ip L2 2= (20)
vp1 = S vC1 1 (21)
vp2 = S vC2 2 (22)
here S1 and S2 are switching states of respective switches.
104 IE (I) Journal�EL
Single-phase Voltage Source Converter
The converter is described by two differential equations forinductor current iL and dc link voltage across capacitor vdc .
p i v v r i LL s p L= − −( ) / (23)
p v i v R Cdc p dc d= −( / )/ (24)
where PWM voltage and current are
vp = −v Sa Sbdc ( ) (25)
i i Sa Sbp L= −( ) (26)
respectively;where
Sa = 1 if switches S1 and S4 are ON, otherwise Sa = 0.Sb = 1 if switches S2 and S3 are ON, otherwise Sb = 0.
PERFORMANCE CHARACTERISTICSPerformance simulation of converters modelled and describedin the previous section is carried out for different loadingconditions at 100-kHz switching frequency. The values ofinductor and capacitor are calculated for desired input currentripple and output voltage ripple. A summery of performanceevaluation and topology features is presented in Tables 1 and2, respectively.
Steady-State and Dynamic PerformanceAll five topologies considered in this work provide smooth dcvoltage at a power factor close to unity and show excellentsteady state and dynamic characteristics (Figures 2-5). Inputcurrent THD is well below the limits stipulated by IEC61000-3-2 and other standards. These converters exhibit satisfactoryvoltage regulation at load variations from 325 W to 1625 W ofnominal. This makes these converters suitable for applicationswith significant load variation. Half-bridge converter andvoltage source converter exhibit best characteristics in termsof dc voltage regulation and input current THD. Input currentdistortion at zero crossovers is also non-existent in theseconverters.
Table 1 Summery of performance evaluation
Rectifier THD, % Power Factor Rise/Dip Settling Heavy Light Heavy Light in Output Time Load Load Load Load Voltage, Load % Applica- tion/ removal, ms
Boost 0.3917 1.0572 1.000 0.999 2.41/3 47/47
Semi-boost 0.4789 1.8680 1.000 0.999 2.41/3 47/47
Half-bridge 0.4394 1.8137 1.000 0.999 2.8/3.4 27/37
VSC 0.4699 1.9093 1.000 0.999 2.41/3 37/27
Table 2 Summery of topology/efficiency evaluation
Rectifier Number of Number of Number of Power FlowPower Diodes Voltage
Switches DropAcrossSemi-
conductorDevices
Boost 1 5 3 unidirectional
Semi-boost 2 4 2 unidirectional
Half Bridge 2 2 1 bi-directional
VSC 4 4 2 bi-directional
Figure 2(a) Dynamic performance of single-phase boost converter
Figure 2(b) Harmonic spectrum of input current for single-phase boostconverter at light load (325 W)
2
1.5
1
0.5
00 10 20 30 40 50 60
Mag
nitu
de, A
Harmonic Order
Vol 85, September 2004 105
Time, s
200
0
� 200 0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
10
0
� 10
450
400
350
5
0
Outp
ut
Curr
ent,
A
Outp
ut
Volta
ge,
VIn
put
Curr
ent,
AIn
put
Volta
ge,
V
Figure 2(c) Harmonic spectrum of input current for single-phase boostconverter at heavy load (1625 W)
0 10 20 30 40 50 60
Harmonic Order
Mag
nitu
de, A
10
9
8
7
6
5
4
3
2
1
0
Figure 3(a) Dynamic performance of single-phase semi-boost converter
2
1.5
1
0.5
00 10 20 30 40 50 60
Mag
nitu
de, A
Harmonic Order
Figure 3(b) Harmonic spectrum of input current for single-phasesemi-boost converter at light load (325 W)
Figure 3(c) Harmonic spectrum of input current for single-phase semi-boost converter at heavy load (1625 W)
0 10 20 30 40 50 60Harmonic Order
Mag
nitu
de, A
10
9
8
7
6
5
4
3
2
1
0
200
0
� 200 0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
10
0
� 10
450
400
350
5
0
Time, s
Outp
ut
Curr
ent,
AO
utp
ut
Volta
ge,
VIn
put
Curr
ent,
AIn
put
Volta
ge,
V
106 IE (I) Journal�EL
Figure 4(a) Dynamic performance of single-phase half-bridge converter
0 0.05 0.1 0.15 0.2 0.25
0 0.05 0.1 0.15 0.2 0.25
2
1.5
1
0.5
00 10 20 30 40 50 60
Mag
nitu
de, A
Harmonic Order
Figure 4(b) Harmonic spectrum of input current for single-phase half-bridge converter at light load (325 W)
200
0
� 200
10
0
� 10
720
700
680
5
0
Time, s
Outp
ut
Curr
ent,
AO
utp
ut
Volta
ge,
VIn
put
Curr
ent,
AIn
put
Volta
ge,
V
0 0.05 0.1 0.15 0.2 0.25
0 0.05 0.1 0.15 0.2 0.25
0 10 20 30 40 50 60Harmonic Order
Mag
nitu
de, A
10
9
8
7
6
5
4
3
2
1
0
Figure 4(c) Harmonic spectrum of input current for single-phasehalf-bridge converter at heavy load (1625 W)
0 10 20 30 40 50 60Harmonic Order
Mag
nitu
de, A
10
9
8
7
6
5
4
3
2
1
0
Figure 5(b) Harmonic spectrum of input current for single-phase voltagesource converter at light load (325 W)
Figure 5(c) Harmonic spectrum of input current for single-phase voltagesource converter at heavy load (1625 W)
Vol 85, September 2004 107
Figure 5(a) Dynamic performance of single-phase voltage sourceconverter
2
1.5
1
0.5
00 10 20 30 40 50 60
Mag
nitu
de, A
Harmonic Order
EfficiencyVoltage drops across semi-conductor devices can havesignificant effect on the overall efficiency of the converters.Number of voltage drops across single-phase boost converteris three, whereas it�s reduced to two in semi-boost and voltagesource topologies. In half-bridge topology its further reducedto one thereby improving the efficiency considerably.However, this improvement in efficiency is achieved atincreased cost of additional active switches and fast recoverydiodes. Low efficiency of half-bridge converters inapplications requiring bi-directional power flow cannot beavoided as the capacitors are discharged into supply.
APPLICATION POTENTIAL OF PFC CONVERTERSBoost Converter is most economical and optimal converter interms of performance and efficiency and providesunidirectional power flow. This converter is used as powerfactor pre-regulators for power supplies, electronic ballast andlow power drive applications where bi-directional power flowis not required.Semi-boost topologies are used in applications whereefficiency is critical. These converters provide increasedefficiency at the cost of added design and control complexity.These converters are however, identical to boost converter interms of performance. Half bridge toplogy is used for drives/on-line UPS applications. This converter provides a step up
ratio of 2 2 at very high efficiency and excellent dynamiccharacteristics.Single-phase voltage source converter is used for applicationswhere bi-directional power flow is required. This converterhas found use in traction drives, UPS etc. It has excellentdynamic characteristics and operates at high efficiency.
EXPERIMENTAL TESTING OF SINGLE-PHASEBOOST CONVERTERPerformance of single-phase boost converter is experimentallytested to identify the numerous non-topological factors that
Time, s
200
0
� 200 0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
0 0.05 0.1 0.15 0.2 0.25 0.3
10
0
� 10
450
400
350
5
0
Outp
ut
Curr
ent,
A
Outp
ut
Volta
ge,
VIn
put
Curr
ent,
AIn
put
Volta
ge,
V
Figure 6 Input current and voltage waveforms of diode rectifier
Figure 7(a) Input voltage and current waveforms of single-phase boostconverter
connections. Moreover, incorporating these factors inmathematical model can complicate analysis and simulation.
CONCLUSION
Modelling and simulation of PFC converters are carried outand single phase boost converter is experimentally tested toverify the simulation results and identify the numerousreasons impacting PFC converters in general. Performanceand applicability of these converters are presented on the basisof simulated results under identical line and load conditions. Acomprehensive summery of performance indices andtopological features are provided. From the study it can beinferred that single-phase boost topology is optimal in terms ofperformance, efficiency, cost and power density and istherefore suitable for most applications. Half-bridge toplogy isthe most efficient topology with excellent performance. Itsapplication is however limited due to restriction on minimumstep-up ratio of 2 2 and low efficiency during inverter mode.Semi-boost topologies provide excellent performance and highefficiency for power factor pre-regulator applications forswitched power supplies and drives systems albeit at highercost of implementation and control. Voltage source convertersoffer bi-directional power flow at high efficiency and variablepower factor. The potential applications of VSC can be UPS,static VAR compansator, and battery charging.
ACKNOWLEDGEMENTFirst named author expresses sincere thanks to the Council ofScientific and Industrial Research for the financial assistanceprovided under Award No 9/86(456)/2000-EMR-I to carryout this research.
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108 IE (I) Journal�EL
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