Post on 21-Jan-2021
Research ArticleDigital Noninterleaved High-Power Totem Pole PFC Based onInternal Model Design
Fei Gao,1,2 Rongfei Xia,1 Yifei Chen,1 and Yongjian Feng 1
1School of Aerospace Engineering, Xiamen University, Xiamen 361005, China2School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, China
Correspondence should be addressed to Yongjian Feng; yjfeng@xmu.edu.cn
Received 4 January 2019; Accepted 11 March 2019; Published 15 April 2019
Academic Editor: Denizar Cruz Martins
Copyright Β© 2019 Fei Gao et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
When the control signal u(t) of totem pole PFC with GaN HEMTs is a function of measurable state variables, the state feedbackgain matrix can be determined by applying state variable feedback control with Ackerman formula, so that the poles of closed-loopsystem can be allocated to the desired position.This correction method is especially beneficial to optimal system control accordingto performance requirements. By introducing the internal model of reference input, a state space function including the first-orderand second-order differential of error is constructed; this novel controller makes controlled system track the reference input signalprogressively with zero steady-state error. A 4 kW PFC prototype is designed to verify this design method.
1. Introduction
Generally, PFC control algorithm adopts PI control, whichrequires a lot of repeated debugging and depends on expe-rience rather than mathematical tools. Applying the statevariable feedback control, as long as the state variables usedfor feedback are measurable and the system control matrixof the state variable model is controllable, the position ofthe poles can be determined according to the performancerequirements, and then the state feedback gain matrix can bedetermined according to the Ackerman formula, so that thepoles can be allocated to the expected position. Comparedwith PI control, state variable feedback control can quicklydetermine control parameters and reduce debugging work-load.
Increasing the control order can effectively improve thesteady-state error of PFC. Usually PFC requires double inte-gral control [1]. Internalmodel control adds internalmodel ofreference input to the state variable feedback control, whichenables the control system to track all kinds of reference inputsignals with zero steady-state error, including step signal,slope signal, and other persistent signals [2, 3]. A PFC controlsystem requires both the magnitude of output voltage andthe waveform of input current, so the internal model should
include an integral cycle of voltage error and two integralcycles of current error. The PFC control model includinginternal model of second-order integral cycles and statevariable feedback control matrix is a fourth-order controlsystem, so it has four poles. Because the analysis method ofsecond-order control system is abundant and mature, twopoles πΌ1 Β± ππ½1 of high-order control system such as fourth-order control system can be set as dominant poles. As longas the other two poles πΌ2 Β± ππ½2 satisfy the condition |πΌ2| >10|πΌ1|, the performance of fourth-order control system can beestimated by second-order control system; that is to say, whenthe absolute value of real part of dominant roots is only 1/10 orless than the nondominant, the response of the second-ordersystem determined by the dominant roots can be used toreplace the response of the higher-order system [4, 5]. In thisway, the empirical formula of the second-order system can beused to determine the damping ratio and natural frequencyaccording to the requirements of overshoot and adjustingtime, so as to determine the dominant poles.
The key problem in the design of state variable feedbackcontroller is whether the poles of the closed-loop systemcan be arbitrarily allocated on the s-plane. These polesof the closed-loop system are actually the eigenvalues ofthe system matrix of the state variable control model. If
HindawiMathematical Problems in EngineeringVolume 2019, Article ID 4368324, 10 pageshttps://doi.org/10.1155/2019/4368324
2 Mathematical Problems in Engineering
L
Vi
Q1
Q2
IL
T1
T2
C R
Vo
(a) Topology of digital high-power totem pole PFC
Vref
Iref+e_v
+ +
β
β
β
βe_vIL
e 1/s 1/sK1
K2
++
d PFCPFC
(K3, K4)
Vout
state variablesfeedback of
K+1
(b) Algorithm of digital high-power totem pole PFC
d β βUo/L
βD/L
β
u+
+ X1 X2 X2X11/s 1/s
1/RC
D/C+
+
+
Vout
IL /C
K3
K4
(c) The detailed diagram of state variables feedback of PFC
Figure 1: Topology and algorithm of digital high-power totem pole PFC.
the system matrix can be controlled, the closed-loop polescan be allocated to the desired position according to theperformance requirements. The design of state feedbackcontrol law usually depends on poles assignment methodknown as state feedback gain matrix [6, 7]. The concept ofcontrollability was proposed by Rudolph Kalman in 1960s[8β10]. Modern control technology can deal with systemswhose state vectors are not completely controllable, but thelinear combination of those state vectors or state vectorsthat cannot be controlled should be stable in nature. Suchsystems are called stabilizable systems. When the system isfully controllable, the systemmust be stabilizable.Othermorecomplex state variable design methods can be applied todeal with stabilizable systems, such as Kalman state spacedecomposition. By using thismethod, the linear combinationof state vectors or state vectors can be decomposed intotwo kinds of variables [3, 11], which are controllable anduncontrollable, so that the uncontrollable subspaces can beseparated. For the uncontrollable subspace, the design of thecontrol system can also be carried out theoretically. Moderncontrol technology can also deal with systems whose statevectors are not completely observable, as long as the linearcombination of those state vectors or state vectors that cannotbe observed should be essentially stable; such systems arecalled detectable systems. When the system is fully observ-able, the system must have the detection ability. Observablecontroller can be designed to estimate the state variables.Similarly, the Kalman state space decomposition method can
be applied to deal with the incomplete observable detectionsystem. The state variables of the detection system can bedecomposed into observable and nonobservable variables, sothat the nonobservable subspace can be separated. For thenonobservable subspace, the control system design can alsobe theoretically done. For digital high-power totem pole PFCwith GaN HEMTs, the control system model is controllableand all state variables are measurable, so it is not necessary toconsider the design of observers.
When the power of PFC with Si MOSFETs is higher than2 kW, interleaved structure is recommended [12β14] for thesake of reducing component stress and EMI [15, 16], whileapplying GaN HEMTs, high-power PFC without interleavedstructure could achieve better performance [1]. It should benoted that the control method applied to a noninterleavedPFC is the same as the one applied to an interleavedPFC, as long as the boost converter cells of an interleavedsystem operate in phase-shift mode. Therefore, the controlmethod of internal mode could be applied not only in anoninterleaved system but also in a system consisting of agroup of interleaved converter cells.
2. Algorithm Design
The topology of digital high-power totem pole PFC is shownin Figure 1(a). Q1, Q2 are GaN HEMTs; T1, T2 are SiMOSFETs. Figure 1(b) is the algorithm schematic diagram ofinternal model design, πΌπΏ is the inductance current, ππ is the
Mathematical Problems in Engineering 3
input voltage, Vπππ is the reference voltage, πππ’π‘ is the outputvoltage, βPFCβ is the state equation model of digital high-power totem pole PFC, illustrated in detail in Figure 1(c), e vis the error between output voltageπππ’π‘ and reference voltageVπππ, πΎ = |Vπ|/πππ ππ, |Vπ| and πππ ππ are the absolute valueof instantaneous value and RMS values of input voltage ππ,respectively, Kβe v is the reference current, e is the sum ofcurrent error and voltage error, andK1, K2, K3, andK4 are thecoefficients of the state variable feedback controller. The keyproblem in designing the state variable feedback controller isto determine these coefficients.When designing the feedbackcontrol signals, e is regarded as the error to establish theinternal model.
This paper only discusses the modeling and analysis ofpositive period of input voltage ππ. When ππ is negative, themethod of modeling and analysis is similar to that of positiveperiod of input voltage ππ.
When ππ is positive, Q1 is off, Q2 is on, and k=0, the statespace equation of PFC control system is as follows.πππΏππ‘ = π’ππΏππ’πππ‘ = β π’π
RC
(1)
WhenQ1 is on, Q2 is off, and k=1, the state space equationof PFC control system is as follows.πππΏππ‘ = π’ππΏ β π’ππΏππ’πππ‘ = ππΏπΆ β π’π
RC
(2)
According to (1), (2), and k, the unified state spaceequation of PFC control system can be obtained as follows.πππΏππ‘ = π’ππΏ β ππ’ππΏππ’πππ‘ = π ππΏπΆ β π’π
RC
(3)
The expression of duty ratio d can be deduced byaveraging k in a switching cycle.1π β«π‘0+ππ‘0 π ππ‘ = π (4)
According to (3) and (4), the state space equation withinput signal d can be written as follows.πππΏππ‘ = π’ππΏ β ππ’ππΏππ’πππ‘ = πππΏπΆ β π’π
RC
(5)
According to [1], when πππΏ/ππ‘ = ππ’π/ππ‘ = 0, the systemworks at a stable point. Stability state space equation (6) couldbe derived as follows. πΌπΏ = π2ππππ πΏ (6)
According to the perturbation theory, the control systemcan be linearized near the stable point, and the state variablescan be decomposed into AC signals and DC signals (capitalletters denote DC, small letters with superscript ββΌβ denoteAC). The linearization state space equation can be expressedas follows.
π (πΌπΏ + οΏ½οΏ½πΏ)ππ‘ = (ππ + οΏ½οΏ½π)πΏ β (π· + π) (ππ + π’π)πΏπ (ππ + οΏ½οΏ½π)ππ‘ = (π· + π) (πΌπΏ + οΏ½οΏ½πΏ)πΆ β (ππ + π’π)π πΆ (7)
Ignoring the DC signal, the products of AC signal, andοΏ½οΏ½π (when regarding π as input signal, οΏ½οΏ½π = 0), the state spaceequation of PFC micro-variable signal can be derived asfollows.
ποΏ½οΏ½πΏππ‘ = βπ·πΏ π’π β πππΏ πππ’πππ‘ = π·πΆ οΏ½οΏ½πΏ β 1RC
π’π + πΌπΏπΆ π (8)
Assume οΏ½οΏ½πΏ = π₯1, π’π = π₯2, π¦ = π’π. According to (8) andπ’π = (0, 1)β(οΏ½οΏ½πΏ, π’π)π+(0)βπ, the system state space equationcan be deduced as follows.
( π₯1π₯2) = π΄π + π΅π= ( 0 βπ·πΏπ·πΆ β 1
RC
)(π₯1π₯2) +(βπππΏπΌπΏπΆ )π,π¦ = πΆπ + π·π = (0 1) (π₯1π₯2)
(9)
The error π = (πΎ + 1)(π’π β ππππ) β ππΏ can be linearizednear the stable point; the result is as follows.
π = (πΎ + 1) π’π β οΏ½οΏ½πΏ (10)
We get the two derivatives of e as follows.
π = (πΎ + 1) π¦ β π₯1 = (πΎ + 1) (0 1) ( π₯1π₯2) β π₯1= (β1 πΎ + 1)( π₯1π₯2) (11)
4 Mathematical Problems in Engineering
According to (9), (10), and (11), the state equation ofthe state variable control system with internal model can beconstructed as follows.
( ππ...π₯1...π₯2)=((
(0 1 0 00 0 β1 πΎ + 10 0 0 βπ·πΏ0 0 π·πΆ 1
RC
)))
(πππ₯1π₯2)
+(((
00βπππΏπΌπΏπΆ)))
π,
E =(((
0 1 0 00 0 β1 πΎ + 10 0 0 βπ·πΏ0 0 π·πΆ 1RC
)))
,
F =(((
00βπππΏπΌπΏπΆ)))
(12)
It is necessary to judge whether the constructed controlsystem is controllable through the controllability matrix π =(πΉ πΉπΈ πΉπΈ2 πΉπΈ3). It can be verified that ππππ(πβ1) = 4, sothe constructed system is controllable.
Assume that the desired poles are πΌ1 Β± ππ½1 and πΌ2 Β± ππ½2;πΌ1 Β± ππ½1 are set as the dominant poles; in order to reduce theinfluence of nondominant poles πΌ2 Β± ππ½2 on the approximatesecond-order system with the dominant pole πΌ1 Β± ππ½1, |πΌ2| >10|πΌ1| should be satisfied. AssumeπΌ1Β±ππ½1 andπΌ2Β±ππ½2 are theroots of polynomial (π2+2ππ1π1π+ππ12) and (π2+2ππ2π2π+ππ22).
According to the empirical formula of the second-ordersystem, ππ = 4/ππ1π1, and the corresponding relationbetween damping coefficient π1 and the overshoot P.O. shownin Table 1, the π1, ππ1value can be determined. ππ is theadjustment time required by the system.
According to the Ackerman formula, the state feedbackcontrol gain matrix (πΎ1 πΎ2 πΎ3 πΎ4) could be calculated asfollows. (πΎ1 πΎ2 πΎ3 πΎ4)= (0 0 0 1) πβ1 (πΈ2 + 2ππ1π1πΈ + ππ12πΌ)β (πΈ2 + 2ππ2π2πΈ + ππ22πΌ) (13)
I is the unitmatrix, whose order is the same as E.The two-order derivative of the state feedback control law is as follows.π = βπΎ1π β πΎ2 π β πΎ3 π₯1 β πΎ4 π₯2 (14)
Getting the double integral of π, the state feedback controllaw is as follows.π = βπΎ1 β«π‘
0β«π‘0π ππ‘ ππ‘ β πΎ2 β«π‘
0π ππ‘ β πΎ3π₯1 β πΎ4π₯2 (15)
According to (15), the program of calculation of switch-on time can be determined. Among these variables, v ref, i l,Vi, Vo, K, v err, err, K1, K2, K3, and K4 denote Vπππ, ππΏ, π’π, π’π,πΎ, π V, π, πΎ1, πΎ2, πΎ3, and πΎ4, and the variable period is halfof the switch period value of DSP. The program is as follows.
D = (1 β v iv o
) ;v err = v ref β v o;err = (K + 1) β v err β i l;
sigma 1+ = err;sigma 2+ = sigma 1;duty delta = βK1 β sigma 2 β K2 β sigma 1 β K3β i l β K4 β v o;
duty = period β D + duty delta
(16)
3. Simulation with Matlab
By substituting the prototype parameters L = 0.0005H, C =0.0023F, Ui = 230V, Uo = 385V, R = 37Ξ©, and πΌπΏ = 17.4A into(9), the uncorrected system state equation (17) is as follows.( π₯1π₯2) = ( 0 β800173.9 β11.8)(π₯1π₯2) + (β7700007573 )π,
π¦ = (0, 1) (π₯1π₯2) (17)
The Bode diagram, root locus, and step response of theuncorrected system can be obtained via (17); it is shown inFigure 2. From the Bode diagram shown in Figure 2(a), it canbe seen that the amplitude margin is -59.7dB and the phasemargin is 144deg. From the root locus shown in Figure 2(b),it can be observed that the system has a zero point in the righthalf plane, so the system is a nonminimum phase system,whose overshoot will be large. From the local root locusshown in Figure 2(c), it can be discovered that when the gainis greater than 0.001, the characteristic root of the system islocated in the right half plane, and then the system is unstable.Figure 2(d) is the open-loop step response of uncorrectedsystem; although it is stable, the steady-state value is closeto - 1000V, and the overshoot is large. Figure 2(e) is theclosed-loop step response of the uncorrected system, whichis unstable.
Mathematical Problems in Engineering 5
Table 1: Relationship between damping coefficient π1 and overshoot P.O.
damping ratio π1 0.9 0.8 0.7 0.6 0.5 0.4 0.3Overshoot P.O. % 0.2 1.5 4.6 9.5 16.3 25.4 37.2
β50
0
50
100M
agni
tude
(dB)
101 102 103 104 105 106β90
0
90
180
Phas
e (de
g)
Frequency (rad/s)
Bode DiagramGm = -59.7 dB (at 0 rad/s) , Pm = 144 deg (at 1.29e+04 rad/s)
(a) Bode diagram of uncorrected system
β1.5 β1 β0.5 0 0.5 1 1.5 2β2000
β1500
β1000
β500
0
500
1000
1500
2000Root Locus
Γ104
Real Axis (seconds-1)
Imag
inar
y A
xis (
seco
nds-
1 )
(b) Root locus of uncorrected system
β2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000β400
β300
β200
β100
0
100
200
300
400 Root Locus
X: 2.205Y: 7.19
Real Axis (seconds-1)
Imag
inar
y A
xis (
seco
nds-
1 )
(c) Local root locus of uncorrected system
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1β2000β1800β1600β1400β1200β1000
β800β600β400β200
0Step Response
Time (seconds)
Am
plitu
de
open loop
(d) Open-loop step response of uncorrected system
0 1 2 3 4 5 6 7β12
β10
β8
β6
β4
β2
0
2Step Response
Time (seconds)
Am
plitu
de
Γ10β3
Γ1024
close loop
(e) Closed-loop step response of uncorrected system
Figure 2: Bode diagram, root locus, and step response of uncorrected system.
6 Mathematical Problems in Engineering
The value of K varies from 0 to 1.414, taking K asdisturbance and assuming its value is 1. By substitutingthe prototype parameters into (12), the state equation withinternal model can be constructed as follows.
( ππ...π₯1...π₯2)=(0 1 0 00 0 β1 20 0 0 β8000 0 173.9 β11.8)( πππ₯1π₯2)
+( 00β7700007573 ) π
πΈ =(0 1 0 00 0 β1 20 0 0 β8000 0 173.9 β11.8) ,πΉ =( 00β7700007573 )
(18)
P could be calculated as follows.
π = (πΉ πΉπΈ πΉπΈ2 πΉπΈ3)=((
0 0 0.000000078514600 β0.0000261568877200 0.000000078514600 β0.000026156887720 β0.011231602427096β0.000000077000000 β0.000000605840000 0.010705091088000 0.2106045356384000.000000000757300 β0.000013381363860 β0.000263255669548 1.858508923302534))
(19)
It can be easily verified that rank (Pβ§(β1)) = 4, so thesystem function is controllable.
Table 1 is the corresponding relationship between thedamping coefficient and the overshoot P.O when the systemhas no zero point in the right half plane. On the contrary, theovershoot is often larger than those shown in Table 1. Aftercorrecting, the step response of closed-loop and Bode dia-gram can be observed when the damping coefficients π1 are0.7, 0.9, 1.2, 1.5, 1.8, and 2, respectively, andππ1 = 10, |ππ2π2| =10|ππ1π1|. The improved effects are shown in Figure 3; as thedamping coefficient increases, the amplitude margin and the
phase margin increase accordingly in Figure 3(a), while theovershoot decreases in Figure 3(b).
When π1 = 2, both the amplitude margin and phasemargin are reasonable, the overshoot of step response is lessthan 20%, and the adjustment time is less than 2s. Whenπ1 = 2, ππ1 = 10, and |ππ2π2| = 10|ππ1π1|, Q can be calculatedas follows.
Q = (Eβ§2 + 40 β E + 100 β I)β (Eβ§2 + 400 β E + 10000 β I) (20)
According to (13), the coefficients of state variables feedbackgain matrix are as follows.
(πΎ1 πΎ2 πΎ3 πΎ4) = (β0.003692304056808 β0.001635317766189 β0.000578675009682 0.000821370994958) (21)
The corrected system is shown in Figure 4(a), the syso andπΎπΊπππ are regarded as an open-loop transfer function and again, respectively. In practical control, when the value of e v isgreater than 30V, its amplitude is limited to 30V, and the valueof K+1 is less than or equal to 2.414, so the value of K+1βπΌπΏis less than 2.414, and the value of πΎπΊπππ is less than 72V. Theroot locus and the local root locus are shown in Figure 4(b).
From the local root locus, it can be seen that when the gainexceeds 75, the corrected system remains stable.
4. Experiment Results
A4kWdigital totempole PFCprototype is shown in Figure 5.Under different input voltage and output power condi-
tions, the waveforms of input voltage and input current are
Mathematical Problems in Engineering 7
β500
0
Mag
nitu
de (d
B)
100 102 104 1060
180
360
Phas
e (de
g)
Bode Diagram
Gm = 30.7 dB (at 122 rad/s) , Pm = 41.9 deg (at 6.62 rad/s)
Frequency (rad/s)
β500
0
500
Mag
nitu
de (d
B)
100 102 104 1060
180
360
Phas
e (de
g)
Bode DiagramGm = 31.8 dB (at 132 rad/s) , Pm = 48.6 deg (at 6.63 rad/s)
Frequency (rad/s)
β500
0
500
Mag
nitu
de (d
B)
100 102 104 1060
180
360
Phas
e (de
g)
Bode Diagram
Gm = 33.4 dB (at 147 rad/s) , Pm = 55.6 deg (at 6.59 rad/s)
Frequency (rad/s)
β500
0
500
500
Mag
nitu
de (d
B)
100 102 104 1060
180
360
Phas
e (de
g)
Bode Diagram
Gm = 35.1 dB (at 162 rad/s) , Pm = 60.4 deg (at 6.47 rad/s)
Frequency (rad/s)
β500
0
500
Mag
nitu
de (d
B)
100 102 104 1060
180
360
Phas
e (de
g)
Bode Diagram
Gm = 36.6 dB (at 179 rad/s) , Pm = 63.8 deg (at 6.29 rad/s)
Frequency (rad/s)
β500
0
500
Mag
nitu
de (d
B)
100 102 104 1060
180
360
Phas
e (de
g)
Bode Diagram
Gm = 37.6 dB (at 190 rad/s) , Pm = 65.5 deg (at 6.14 rad/s)
Frequency (rad/s)
zeta=0.7,omega=10 zeta=0.9,omega=10 zeta=1.2,omega=10
zeta=1.5,omega=10 zeta=1.8,omega=10 zeta=2,omega=10
(a) Bode diagrams of different damping coefficient π1
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
1.4Step response
zeta=0.7,omega=10zeta=0.9,omega=10zeta=1.2,omega=10zeta=1.5,omega=10zeta=1.8,omega=10zeta=2,omega=10
(b) Step responses of different damping coefficient π1
Figure 3: Bode diagrams and step responses of different damping coefficient π1.
8 Mathematical Problems in Engineering
β
β ββ β
+ + ++
1/s 1/s Vout
IL
K3K4K2
K1 PFCe_vVref e
Iref+e_vsysoKGain
K+1
(a) Corrected system
β1 β0.5 0 0.5 1β1.5
β1
β0.5
0
0.5
1
1.5Root Locus
β1 0 1 2β250
β200
β150
β100
β50
0
50
100
150
200
250
Gain<75
Root Locus
Real Axis (seconds-1) Real Axis (seconds-1)
Imag
inar
y A
xis (
seco
nds-
1 )
Imag
inar
y A
xis (
seco
nds-
1 )
Γ104
Γ104
Γ105
(b) Root locus and local root locus of corrected system
Figure 4
Figure 5: An 4 kW digital totem pole PFC prototype.
shown in Figure 6. It can be observed that the higher theinput voltage and output power, the better the input current.As shown in Figure 6(a), when the input voltage is 115 V and
the output power is 2 kW, the RMS and peak-to-peak valueof the input current are 17.88 A and 61.2 A, respectively. Asshown in Figure 6(b), when the input voltage is 230V and theoutput power is 4 kW, the RMS and peak-to-peak value of theinput current are 17.47 A and 55.6 A, respectively.
The test results of efficiency and power loss are shownin Figure 7(a). As the input voltage increases, the efficiencyincreases and the power loss decreases. The peak efficiencyis 99.02% (230V) and 98.08% (115V) when the switchingfrequency is 66 kHz. As shown in Figure 7(b), when the loadis more than half, the THD is below 4% regardless of whetherthe input voltage is 115V or 230V.The minimum THD valuesare 2.8% (115 V) and 2.6% (230 V), respectively.
5. Conclusion
Using GaN HEMTs as switching device, a prototype of 4kW digital noninterleaved totem pole PFC based on statevariable feedback controlwith internalmodel is introduced indetail in this paper. Due to the advantages of control method
Mathematical Problems in Engineering 9
RMS(C2) 114.9V
RMS(C2) 17.88V
Pk-Pk(C2)β 61.2V
Ch1 100V Ch2 20.0V
2
1
(a) Vi=115 V, P=2 kW
RMS(C1) 229.7V
RMS(C2) 17.47V
Pk-Pk(C2)β 55.6V
M 10.0ms 500kS/s 2.0s/ptCh1 100V Ch2 20.0V
2
1
(b) Vi=230 V, P=4 kW
Figure 6: The test waveforms of input voltage and input current.
500 1000 1500 2000 2500 3000 3500 4000 450096.0
96.5
97.0
97.5
98.0
98.5
99.0
230V Efficiency115V Efficiency230V Power Loss115V Power Loss
Power (W)
Effici
ency
(%)
0
10
20
30
40
50
60
70
80
90
Pow
er L
oss (
W)
(a) The test results of efficiency and power loss
0 500 1000 1500 2000 2500 3000 3500 4000 4500
2
4
6
8
10
12
14
16
THD
i (%
)
Power (W)
230V115V
(b) The test results of THD
Figure 7: The test results of efficiency and power loss and THD.
10 Mathematical Problems in Engineering
and GaNHEMT, the prototype achieves better performancessuch as efficiency, power loss, THD related to EMI, compactstructure, and higher power density than the PFC basedon traditional PI control with Si MOSFETs. Noninterleavedstructure effectively reduces the number of devices and thecost of filtering. Therefore, the cost of totem pole PFC withGaN HEMT is not higher than the traditional PFC with SiMOSFET. It should be noted that PFC with GaN HEMThas obvious advantages in efficiency only when it works inhard switching mode of CCM, not in DCM and CRMmode.Soft switching can be achieved in DCM and CRM with SiMOSFET, and the switching loss is not large in this case. Butno matter whether in CCM or DCM and CRM, PFC withGaN HEMTs achieves better performances in EMI than theone with Si MOSFETs.
Data Availability
The data used to support the findings of this study areincluded within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper.
Acknowledgments
This work was supported by the Science and Technol-ogy Projects of Guizhou Province of China (Grant No.2014LH7050) and the Science and Technology Projects ofGuizhou Education Department (Grant No. QianJiaoKe2010018).
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