Modal Computation and Analysis Based on Phase Sequence of …downloads.hindawi.com/journals/mpe/2019/1571609.pdf · predictive control of PV sources in a smart DC distribution system:

Research ArticleModal Computation and Analysis Based on Phase Sequence ofLLC Resonant DC-DC Converter

Lei Sun 1 Xuesong Suo 1 Jianjun Hao1 Jun Zhang1 Yuejin Ma1 and XiaomingWang2

1Hebei Agricultural University College of Mechanical and Electrical Engineering Baoding 071001 China2Universal Energy Electric Co Ltd Baoding 071051 China

Correspondence should be addressed to Xuesong Suo 13903120861163com

Received 11 December 2018 Revised 12 February 2019 Accepted 24 March 2019 Published 8 April 2019

Academic Editor Anna Vila

Copyright copy 2019 Lei Sun 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

LLC resonant DC-DC converter has wide working range good voltage gains and soft switching performance So it is widely used inpower transformation systems of new energy equipment such as UPS electric vehicle and photovoltaics (PV)The conduction lossin the main circuit constitutes the main loss occurred in the LLC resonant converter It may greatly improve the power conversionefficiency of the converter by reducing the conduction loss To solve the above problems a method is proposed to calculate anddesign the parameters of the resonant element in this paper This method abandons the traditional time sequence mathematicalmodel and in order to reduce the effective value of themain loop current of resonant converter the phase sequencemodal analysisis appliedWith ZVS as the constraint condition the design parameters of resonance element that canminimize the conduction losscan be obtained In the final part an experimental prototype (300W) is designed and the effectiveness of the mentioned method isverified

1 Introduction

With the global climate deterioration and the increase ofenergy demand distributed generation (DG) which is uti-lized by the users was used to converse the clean energyto electricity such as wind power and solar power systemsDG has gradually become the key equipment in solvingthe problems of environment and energy In the typicallow voltage DC distributed system such as electric vehiclecharging system and small photovoltaic power generationthe DC-DC converter is not only the physical interface ofpower interaction but also the key equipment which canstabilize the DC generatrix voltage Given that the outputvoltage and current of ESS have a wider range it is necessarythat DC-DC converter has a broad gain and load range andit is supposed to be more efficient stable and reliable asintroduced in literature [1ndash3]

At present the requirements of high conversion efficiencyand high power density have become critical factors whenwe design the DCDC converter Although it can effectivelyreduce the volume of the device by improving the switchoperating efficiency of the converter great switching losses

that followed could result in the decrease in the conversionefficiency of the converter and then it will be difficult toimprove the overall power density of the converter With theadvancement of soft switch technology in recent decadesa lot of auxiliary networks for soft switch are developed toreduce the switching losses in the converter and to improvethe conversion efficiency and the power density Howeversome of these soft switch auxiliary networks have complexstructure while others are difficult to control Besides someof them will cause losses For this reason all of them are notthe best solution to this problem

Three-elements LLC resonant converter is one of thehottest DC-DC converters This converter is controlledby variable frequency conversion Through the reasonabledesign the switches of the primary side and the synchronousrectifier of the secondary side can work under the conditionof soft switching without any auxiliary network Therefore ithas great advantages in conversion efficiency

The half-bridge LLC resonant converter is shown inFigure 1 There are two MOSFETs in the primary sideincluding 1198781 and 1198782 which is composed of crystal diodeDoss1 DOSS2 and shunt capacitor Coss1 Coss2 In the secondary

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 1571609 9 pageshttpsdoiorg10115520191571609

2 Mathematical Problems in Engineering

inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV+

-

Figure 1 LLC resonant DC-DC converter

side half-wave rectification is used including two diodes11986311198632 and two capacitances The resonant tank of the primaryloop consists of resonant inductor 119871119903 magnetic inductance119871119898 and resonant capacitance 119862119903 The operating mode ofthe resonant tank not only depends on the working stage ofconverter but also depends on the working frequency andthe load of converter Therefore it is difficult to calculate andanalyze the resonant characteristics of the LLC converter

The elements involved in resonance include resonantcapacitance 119862119903 resonant inductor 119871119903 and magnetic induc-tance Lm The values of these elements are quite importantin calculating the loss of the main loop Thus the methodof calculating and designing of it has become a hot topicstudied by many experts in this field In literature [4ndash8] a detailed analysis of the basic working principle ofthe LLC resonant converter is conducted and the basiccalculation and design methods of resonance parametersare proposed However all of these methods mentionedabove are based on timing sequence while they lack enoughaccuracy in calculating the energy loss as introduced inliterature [9ndash13] Therefore it is impossible to obtain theoptimized parameters that can improve the power conversionefficiency by using timingmodels It is also difficult to providean intuitive interpretation so inconvenience is caused forthe application of the project as introduced in literature[14ndash22] However through the modal analysis based onthe mode of the phase sequence more accurate relationcurves which can show the maximum load voltage gainvarying over frequency can be obtained and the accuratemodeling and calculation can be realized for the opera-tional model of converter and the optimized parameterswhich minimize the power loss of the converter can beobtained

2 Analysis on the Primary Loop ofthe Converter

In AC circuits the phase angle can reflect the condition ofthe circuit at each moment so it can reflect the change ofsignal Compared to the analysis of the time sequence phasesequence is often used a as method for the frequency-domainanalysis and it helps to make the analysis and calculationmore accurate The phase angle is adopted to perform modaldividingThe three fundamental operating modes of the LLCresonant converter can be broken down to three modes asfollows

P mode the voltage of the magnetic inductance 119871119898 isclamped in 2119899119881119900 the primary side transfers energy tothe secondary sideO mode the voltage of the magnetic inductance 119871119898is less than 2119899119881119900 the primary side will not transferenergy to the secondary sideN mode the voltage of the magnetic inductance 119871119898is clamped in -2119899119881119900 the primary side transfers energyto the secondary side

When the primary side of the LLC resonant converter worksunder the ZVS (Zero Voltage Switch) condition the softswitching can be realized with the switch tubes In idealcondition no energy will be consumed and the resonantcircuit is inductive and it works safely Therefore in mostcases the LLC resonant converter works under the ZVScondition and ZVC condition contains eightmodes P O POPON PN NP NOP and OPO The operating frequency is12120587radic119871119903119862119903 le 119891119904 le 12120587radic(119871119898 + 119871119903)119862119903 during PO mode Asthe parameters for each element in themain circuit have beendesigned when the RMS value of the current passing throughthe main circuit becomes minimum the conduction loss willbeminimumThus in this paper theminimumRMS value ofthe resonant current in this mode represents the minimumconduction loss Then the optimization model can be builtusing ZVS condition as the constraint At last if we analyzethem by using the formulas of 119885119903 = radic119871119903119862119903 119898 = (119871119898 +119871119903)119871119903 119891119899 = 119891119904119891119903 the optimum design can be obtainedIn the PO mode ideal waveforms of components at eachstage are shown in Figure 2 The phase angle is used as theboundary a period can be divided into six working modesAs the characteristics of the first half period are similar to thatof the second half period they are exactly the same except thedirection of the current and voltage is reverseTherefore onlythe first half period is calculated and analyzed in the paper

(1) Stage 1 [1205791199010 sim 120579119901]When the phase angle is 120579119901 the terminalvoltage of 1198781 will decrease to zero and1198631199001199041199041 in the body diode1198781 will turn on The phase angle of resonant current will varyuntil it has a certain value 12057911990101015840 and 1198781 will turn on at the zerovoltage The equivalent circuit is shown in Figure 3

The LLC resonant converter works in P mode at thismoment the voltage is normalized to 2119899119881119900 and the currentis normalized to 2119899119881119900119885119903 119871119903 and 119862119903 start resonating voltageof magnetic inductance 119871119898 is clamped on 2119899119881119900 resonantcurrent 119894119871119903 will change in sine wave shape and its equation of

Mathematical Problems in Engineering 3

0

0Vin

0

Vd

0

0Vgs2

Vgs1

Li

Di

θ

Vgs1 Vgs1

Vgs2

iL

iLm

iD1iD2

iD1

P0 P0 O0O1

O2P

Figure 2 The ideal waveforms of each mode

inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-

Figure 3 Working stage 1

state is 119894119871119903(120579) = 119868119871119903 sin(120579) the state equation can be designedas

119881119894119899 minus 2119899119881119900 sdot 119906119862119903 (120579) minus 2119899119881119900 = 119871119903 sdot 119889119894119871119903 (120579) sdot (2119899119881119900119885119903)119889119905= 119871119903 sdot 2120587119891119903 sdot 2119899119881119900119885119903 sdot 119889119868119871119903 sin (120579)119889120579

119862119903 sdot 119889119906119862119903 (119905) sdot 2119899119881119900119889119905 = 119862119903 sdot 2120587119891119903 sdot 2119899119881119900119889119906119862119903 (120579)119889120579= 2119899119881119900119885119903 sdot 119894119871119903 (120579)

119871119898 sdot 119889119894119871119898 (119905) sdot 2119899119881119900119885119903119889119905 = 2119899119881119900(1)

The normalized result is shown in

119906119862119903 (120579) = minus119868119871119903 cos (120579) minus 1 + 1119872119894119871119898 (120579) = 119868119871119898 + 120579 minus 1205791199010119898 minus 1

(2)

The phase angle 120579 = 12057911990101015840 119894119871119903(12057911990101015840) = 0 because 1198781 hasreached ZVS before Then 1198781 continues to be conductive


and resonant current 119894119871119903(120579) passes through the circuit in areserved direction but the equation for the operating modeand the equivalent circuit remain unchangedWhen the angleof phase reaches 120579119901 119894119871119903(120579119901) = 119894119871119898(120579119901) the diode will beturned off at the secondary side

(2) Stage 2 [1205791198740 sim 1205791198741] The diodes are turned off at thesecondary side LLC converter enters the O mode and theprimary side will not transfer energy to the secondary sideduring this stage 119871119903 119871119898 and 119862119903 take part in resonance inthis mode and the working condition for each element in thecircuit is shown in Figure 4

During this stage 119894119871119903 = 119894119871119898 all the waveforms belong tosine wave Because in the P mode 119894119871119903(120579) = 119868119871119903 sin(120579) (120579radic119898)then 2120587119891119903119905 = 120579 119891119903 = 12120587radic119871119903 sdot 119862119903 During the O mode21205871198911199030119905 = 1205791015840 1198911199030 = 12120587radic(119871119903 + 119871119898) sdot 119862119903 Thus we have1205791015840 = 120579radic119898 This paper assumes that in the mode O 119894119871119903(120579) =119868119871119903 sin(120579radic119898) we can perform differentiation for 1205791015840 (120579radic119898can be regarded as a whole here) and radic119898 will not take partin differentiationThe equation for the mode is (3) as follows

(119871119903 + 119871119898) sdot 119889119894119871119903 (119905) sdot 2119899119881119900119889119905= (119871119903 + 119871119898) sdot 21205871198911199030 sdot 119889119894119871119903 (1205791015840) sdot 21198991198811199001198891205791015840= 119881119894119899 minus 119906119862119903 (1205791015840) sdot 2119899119881119900

119862119903 sdot 119889119906119862119903 (119905) sdot 2119899119881119900119889119905 = 2119899119881119900119885119903 sdot 119894119871119898 (1205791015840)= 119862119903 sdot 21205871198911199030119889119906119862119903 (1205791015840) sdot 21198991198811199001198891205791015840

(3)

The normalized result can be obtained as

119906119862119903 (1205791015840) = minusradic119898119868119871119903 cos( 120579radic119898) + 1119872119906119862119903 (1205791015840) = 119898 minus 1radic119898 119868119871119903 cos( 120579radic119898) (4)

(3) Stage 3 [1205791198741 sim 1205791198742] When the phase angle is 1205791199001 1198781 willturn off Parasitic capacitance 1198621199001199041199041 is charging while 1198621199001199041199042 isdischarging When phase angle is 1205791199002 the terminal voltage of1198781 will equal119881119894119899 and the terminal voltage of 1198782 will equal zerowhich can prepare for ZVSThe state of the circuit is shown inFigure 5 After that the diode of secondary side 1198632 will stayconductive The next half cycle symmetrical to the first halfof cycle will be initiated

Here 119871119903 119871119898 119862119903 1198621199001199041199041 and 1198621199001199041199042 work at the same time inresonance

The state equation can be designed as

(119871119903 + 119871119898) sdot 2120587119891119904 sdot 119889119894119871119903 sdot 2119899119881119900119885119903119889120579 + 2119899119881119900 sdot 119906119862119903 (120579)= 2119899119881119900 sdot 119906cos 1199042 (120579)

1198621199001199041199041 sdot 2120587119891119904 sdot 119889 [119881119894119899 minus 2119899119881119900 sdot 119906cos 1199042 (120579)]119889120579= 2119899119881119900119885119903 sdot 119894119871119903 (120579) + 1198621199001199041199042 sdot 2120587119891119904 sdot 119889119906cos 1199042 sdot 2119899119881119900119889120579

119862119903 sdot 2120587119891119904 sdot 119889119906119862119903 (120579) sdot 2119899119881119900119889120579 = 2119899119881119900119885119903 sdot 119894119871119903 (120579)119871119898 sdot 2120587119891119904 sdot 119889119894119871119898 (120579) sdot 2119899119881119900119885119903119889120579 = 119906119871119898 (120579)

(5)

Assume 1198621199001199041199041 = 1198621199001199041199042 = 119862119900119904119904 (4) and (5) can be combinedand we have

119906cos 1199042 (120579) = 119871119898 + 119871119903119885119903 sdot 2120587119891119904 sdot 119868119871119903 cos( 120579radic119898) minus radic119898sdot 119868119871119903 cos( 120579radic119898) + 1119872

(6)

According to the condition of ZVS when the phase angle is1205791199002 1198782 will turn on under ZVS and 1199061198621199001199041199042(1205791199002) = 0 (6) can betransformed to

1119872 = radic119898 sdot 119868119871119903 cos( 1205791199002radic119898) minus 119871119898 + 119871119903119885119903 sdot 2120587119891119904sdot 119868119871119903 cos( 1205791199002radic119898)

(7)

119868119871119903 is the normalized value of the sinusoidal current in themodeO that equals normalized value of the current at the endof P modeThe first state and the last state of the resonant aresymmetrical Based on (2) (8) can be obtained

119894119871119898 (120579) = 119868119871119898 + 120579 minus 1205791199010119898 minus 1119894119871119898 (1205791199010) = minus119894119871119898 (1205791199010 + 120587) (8)

Uniting these equations (9) can be obtained

119868119871119898 = minus 1205872 (119898 minus 1)119868119871119903119901 = 1205872radic (119875119900 sdot 119885119903)2(2119899119881119900)119868119871119903 = 119868119871119903119901 sdot sin (120579119901)

(9)


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-


inV

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oR

1S

oV

+

-


Uniting (1) (7) (9) (10) can be obtained

1119872 = radic119898 sdot 1205872radic 11987511990021198851199032(2119899119881119900)4 +1(119898 minus 1)2 sdot sin (120579119901)

sdot cos( 1205791199002radic119898) minus 119871119898 + 119871119903119885119903 sdot 2120587119891119904 sdot 1198811199008119899119871119898119891119903sdot 1sin 120579119901119900 cos(

1205791199002radic119898)(10)

Setting M⩾1 in order to get a high voltage gain (11) can beobtained

radic119898 sdot 1205872radic 11987511990021198851199032(2119899119881119900)4 +1(119898 minus 1)2 minus (1 + 1119898 minus 1) sdot 1205871198811199004119899119885119903

sdot 119891119899 le 1(11)

3 Optimization Model

According to Figure 6 the x-axis stands for the normalizedworking frequency 119891119899 = 119891119904119891119903 and the y-axis stands for thevoltage gain 119872 = 119881119900119881119894119899 When 119891119899 varies max gain point(inflection point) to 1 the voltage gain should be greaterthan 1(M⩾1) in order to make sure we obtain the requiredoutput voltage and high power conversion efficiency Asshown in Figure 6 there are many working points which canmeet requirements of gain under the value of same m and

different 119885119903 Therefore the sweep frequency is performedwith different m ((119871119898 +119871119903)119871119903) value as shown in Figure 7 toanalyze the optimization model According to Figure 7 thereare also many working points which can meet requirementsof gain under the value of same 119885119903 and different m With thesame value of m the loss of resonant tank and the gain ofvoltage have same inflection point in terms of their curvesIn order to improve conversion efficiency a higher voltagegain and a lower loss of resonant tank are needed consideringthat we should reduce m value to increase voltage gain andincrease m value to reduce power loss With the optimizedmodel proposed in this paper the balance point for the mvalue can be obtained

In the LLC resonant converter the conductive loss con-stitutes most of losses in the total loss The RMS value ofthe resonant current can reflect the conductive loss If theRMS value of the resonant current can be minimized thenthe conductive loss can be minimized Thus the extremevalues can be worked out with the RMS value of the resonantcurrent as the objective function Based on the analysis of theabove section and (2) and (9) the actual effective value of theresonant current flowing through 119871119903 and 119871119898 can be obtainedthrough

119868119871119903119877119872119878 = 1205872radic2radic 1198751199002(2119899119881119900)2 +(2119899119881119900)2(119898 minus 1)2 sdot 1198851199032

119868119871119898119877119872119878 = 1205872radic3 (119898 minus 1) sdot 2119899119881119900119885119903(12)


M=

VoV

in

fn

20

10

0003 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000

Figure 6 The characteristics of voltage gain under the same m value

0200 0400 0600 0800 1000 1200 1400 1600 180000020W

50KW

100KW

150KW

SELgtgt

0

25

50 m = 1

m = 2m = 3

m = 1

m = 2m = 3

1

Pow

er L

oss

fn

M=

VoV

in

Figure 7 The characteristics of voltage gain under the different m value

Uniting (11) and (12) and considering the characteristics of theresonant converter (13) can be obtained


sdot 119891119899 le 1119868119871119903119877119872119878 = 1205872radic2radic 1198751199002(2119899119881119900)2 +

(2119899119881119900)2(119898 minus 1)2 sdot 1198851199032119868119871119898119877119872119878 = 1205872radic3 (119898 minus 1) sdot 2119899119881119900119885119903

119898 gt 0119885119903 gt 0119891119899 gt 0

(13)

In (11) the value of voltage gain can be set as the minimumvalue 1 (119872 = 1) Then it can be treated as the problem ofthe maximum value of 119868119871119903119877119872119878 119868119871119898119877119872 119881119900 119875119900 n in (13) areall the known quantities thus the values of design requiredparameters such asm Zr fn can be obtained

Table 1 Design specifications of the prototype

Parameter ValueVin 300sim350VVo 24VIo 125APo 300Wn 7fmax 100kHzfmin 50kHz

Resonant elements can be calculated by

119862119903 = 12120587119885119903 sdot 119891119899 sdot 119891max

119871119903 = 1(2120587119891119899 sdot 119891max)2 sdot 119862119903119871119898 = (119898 minus 1) sdot 119871119903

(14)

4 Experimental Verification

To verify the effectiveness of the proposed method in thispaper a 300W LLC resonant converter experimental proto-type is designed Design specifications are listed in Table 1


Table 2 Resonant tank parameters of the prototype

Parameter Value119871119898 335120583H119871119903 86120583H119862119903 57nF

Figure 8 LLC resonant converter experimental prototype

Based on the method proposed in this paper the neces-sary variables of the resonant parameters can be obtained as

119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)

Based on (14) the resonant tank parameters can be obtainedwhich are listed in Table 2

The experimental prototype developed in this paper isshown as in Figure 8

As shown in Figure 9 during the heavy load conditionthe resonant current 119894119871119903 of the primary loop the drive voltage119881g1199041 of the switch tube 1198781 the drain-source voltage Vcoss1 isconsistent with the ideal waveform As shown in Figure 10the resonant current 119894119871119903 will change in ways approximate toa triangular wave shape The waveform is same as the idealwaveform and ZVS can be realized Under such workingcondition 119894119871119903 will be close to 119894119871119898 and there is just alittle current flowing through the transformer As shown inFigure 11 the main circuit voltage119881119889 of the converter reacheszero before 119894119871119903 does it proves that the converter realize ZVSand the converter has a good performance

The power conversion efficiency of the converter isanalyzed using the power analyzer as shown in Figure 12The output power of the converter varies within a small rangeclose to the rated power and the max efficiency is 97 Asthe output power which varies within a small range closeto the rated power accounts for 92 and above it is provedthat if the parameters are obtained using the proposed designmethod in this paper higher power conversion efficiency ofconverter can be realized

i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL

Figure 9 The waveforms of the prototype during the heavy loadcondition

i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V

Figure 10 The waveform of the prototype during the light loadcondition

5 Summary

In aviation power supply electric vehicles photovoltaicpower generation and other fields DC-DC converter is thephysical port that achieves energy-interaction between DCbus and distributed power supply and energy storage system(ESS) so its working capability and the power conversionefficiency is of great significance LLC resonant DC-DCconverter has a broader range of work higher voltage gainand a good performance of soft switching thus the converteris widely concerned and applied The main loss of LLCconverter is the conduction loss of the main circuit Theparameter values of the resonant elements have a decisiveeffect on the conduction loss Therefore to optimize calcula-tion and design of the parameters is the main way to improvethe conversion efficiency of the LLC resonant converterThe traditional mathematical model of time sequence isabandoned in this paper while a method based on the modalanalysis of the phase sequence is proposed The optimizationgoal of this method is to reduce the RMS value of current inthe main circuit and ZVS is used as the constraint conditionUsing this method can not only ensure the LLC converterworks smoothly but also improve the power conversionefficiency and realize the optimal design of converter Finally


t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL

Figure 11 The waveforms of the main circuit during the heavy loadcondition

98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()

Figure 12 The power conversion efficiency of the converter

a 300W experimental prototype is designed to verify theeffectiveness of the proposed method

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Jianjun Hao and Yuejin Ma contributed equally to this work

Acknowledgments

This work is supported by Hebei Oil Plants Innovation Teamin Modern Agricultural Industry Technology System theproject of ldquoEnergy Subsystem in Stratospheric Satelliterdquo theproject National High-tech RampD Program (863 Program)

of China (2015AA050603) and Science and TechnologySupport Program of Baoding (18ZG011)

References

[1] F M Shahir E Babaei M Sabahi and S Laali ldquoA new DCndashDCconverter based on voltage-lift techniquerdquo International Trans-actions on Electrical Energy Systems vol 26 no 6 pp 1260ndash1286 2016

[2] E Babaei Z Saadatizadeh and V Ranjbarizad ldquoA new noniso-lated bidirectional DC-DC converter with ripple-free input cur-rent at low-voltage side and high conversion ratiordquo InternationalTransactions on Electrical Energy Systems vol 27 no 1 ArticleID e2494 2017

[3] E Babaei and O Abbasi ldquoA new topology for bidirectionalmulti-input multi-output buck direct currentndashdirect currentconverterrdquo International Transactions on Electrical Energy Sys-tems vol 27 no 2 Article ID e2254 2017

[4] L ZhenyaGlobal Energy Internet Electric Power Press BeijingChina 2015

[5] R Haroun A Cid-Pastor A El Aroudi and L Martinez-Salamero ldquoSynthesis of canonical elements for power process-ing in DC distribution systems using cascaded converters andsliding-mode controlrdquo IEEE Transactions on Power Electronicsvol 29 no 3 pp 1366ndash1381 2014

[6] M B Shadmand R S Balog and H Abu-Rub ldquoModelpredictive control of PV sources in a smart DC distributionsystem maximum power point tracking and droop controlrdquoIEEE Transactions on Energy Conversion vol 29 no 4 pp 913ndash921 2014

[7] F Xueqian C Haoyong L Guote et al ldquoPower qualitycomprehensive evaluation method for distributed generationrdquoProceedings of the CSEE vol 34 no 25 pp 4270ndash4276 2014

[8] W Shouxiang and H Liang ldquoComplex affine arithmetic basedmethod for the analysis of DGrsquos uncertainty influence on dis-tribution networkrdquo CSEE Journal of Power and Energy Systemsvol 34 no 31 pp 5507ndash5515 2014

[9] HMa and FQi ldquoAn improved designmethod for resonant tankparameters of LLC resonant converterrdquo CSEE Journal of Powerand Energy Systems vol 28 no 33 pp 6ndash11 2008

[10] W Feng F C Lee and PMattavelli ldquoOptimal trajectory controlof burst mode for LLC resonant converterrdquo IEEE Transactionson Power Electronics vol 28 no 1 pp 457ndash466 2013

[11] H Hu W Wang W Sun S Ding and Y Xing ldquoOptimalefficiency design of LLC resonant convertersrdquo Zhongguo DianjiGongcheng XuebaoProceedings of the Chinese Society of Electri-cal Engineering vol 33 no 18 pp 48ndash56 2013

[12] J Ke and R Xinbo ldquoHybrid full bridge three-level LLC resonantconverterrdquo CSEE Journal of Power and Energy Systems vol 26no 3 pp 53ndash58 2006

[13] M Noah K Umetani J Imaoka and M YamamotoldquoLagrangian dynamics model and practical implementationof an integrated transformer in multi-phase LLC resonantconverterrdquo IET Power Electronics vol 11 no 2 pp 339ndash3472018

[14] D B Fu Y Liu L C Fred et al ldquoA novel driving schemefor synchronous rectifiers in LLC resonant convertersrdquo IEEETransactions on Power Electronics vol 24 no 5 pp 1321ndash13292009

[15] B Lu W D Liu Y Liang et al ldquoOptimum design methodologyfor LLC resonant converterrdquo in Proceedings of the IEEE AppliedPower Electronics Conference and Exposition pp 533ndash538 2006


[16] B Yang F C Lee M Concannon et al ldquoOver current protec-tion methods for LLC resonant converterrdquo in Proceedings of theEigtheenth Annual IEEE Applied Power Electronics Conferenceand Exposition vol 2 pp 605ndash609 2003

[17] C-C Hua Y-H Fang and C-W Lin ldquoLLC resonant converterfor electric vehicle battery chargersrdquo IET Power Electronics vol9 no 12 pp 2369ndash2376 2016

[18] B-R Lin andC-WChu ldquoHybrid full-bridge andLLC converterwith wide ZVS range and less output inductancerdquo IET PowerElectronics vol 9 no 2 pp 377ndash384 2016

[19] R Severns ldquoTopologies for three element resonant convertersrdquoin Proceedings of the Applied Power Electronics Conference andExposition pp 712ndash722 Los Angeles Calif USA 1990

[20] W LMalan DM Vilathgamuwa andG RWalker ldquoModelingand control of a resonant dual active bridge with a tuned cllcnetworkrdquo IEEE Transactions on Power Electronics vol 31 no10 pp 7297ndash7310 2016

[21] S Zou J Lu A Mallik and A Khaligh ldquoBidirectional CLLCconverter with synchronous rectification for plug-in electricvehiclesrdquo IEEE Transactions on Industry Applications vol 54no 2 pp 998ndash1005 2018

[22] C Liu J Wang K Colombage C Gould and B Sen ldquoACLLC resonant converter based bidirectional EV charger withmaximum efficiency trackingrdquo in Proceedings of the 8th IETInternational Conference on Power Electronics Machines andDrives PEMD rsquo16 London UK 2016

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Submit your manuscripts atwwwhindawicom


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV+

-

Figure 1 LLC resonant DC-DC converter

side half-wave rectification is used including two diodes11986311198632 and two capacitances The resonant tank of the primaryloop consists of resonant inductor 119871119903 magnetic inductance119871119898 and resonant capacitance 119862119903 The operating mode ofthe resonant tank not only depends on the working stage ofconverter but also depends on the working frequency andthe load of converter Therefore it is difficult to calculate andanalyze the resonant characteristics of the LLC converter

The elements involved in resonance include resonantcapacitance 119862119903 resonant inductor 119871119903 and magnetic induc-tance Lm The values of these elements are quite importantin calculating the loss of the main loop Thus the methodof calculating and designing of it has become a hot topicstudied by many experts in this field In literature [4ndash8] a detailed analysis of the basic working principle ofthe LLC resonant converter is conducted and the basiccalculation and design methods of resonance parametersare proposed However all of these methods mentionedabove are based on timing sequence while they lack enoughaccuracy in calculating the energy loss as introduced inliterature [9ndash13] Therefore it is impossible to obtain theoptimized parameters that can improve the power conversionefficiency by using timingmodels It is also difficult to providean intuitive interpretation so inconvenience is caused forthe application of the project as introduced in literature[14ndash22] However through the modal analysis based onthe mode of the phase sequence more accurate relationcurves which can show the maximum load voltage gainvarying over frequency can be obtained and the accuratemodeling and calculation can be realized for the opera-tional model of converter and the optimized parameterswhich minimize the power loss of the converter can beobtained

2 Analysis on the Primary Loop ofthe Converter

In AC circuits the phase angle can reflect the condition ofthe circuit at each moment so it can reflect the change ofsignal Compared to the analysis of the time sequence phasesequence is often used a as method for the frequency-domainanalysis and it helps to make the analysis and calculationmore accurate The phase angle is adopted to perform modaldividingThe three fundamental operating modes of the LLCresonant converter can be broken down to three modes asfollows

P mode the voltage of the magnetic inductance 119871119898 isclamped in 2119899119881119900 the primary side transfers energy tothe secondary sideO mode the voltage of the magnetic inductance 119871119898is less than 2119899119881119900 the primary side will not transferenergy to the secondary sideN mode the voltage of the magnetic inductance 119871119898is clamped in -2119899119881119900 the primary side transfers energyto the secondary side

When the primary side of the LLC resonant converter worksunder the ZVS (Zero Voltage Switch) condition the softswitching can be realized with the switch tubes In idealcondition no energy will be consumed and the resonantcircuit is inductive and it works safely Therefore in mostcases the LLC resonant converter works under the ZVScondition and ZVC condition contains eightmodes P O POPON PN NP NOP and OPO The operating frequency is12120587radic119871119903119862119903 le 119891119904 le 12120587radic(119871119898 + 119871119903)119862119903 during PO mode Asthe parameters for each element in themain circuit have beendesigned when the RMS value of the current passing throughthe main circuit becomes minimum the conduction loss willbeminimumThus in this paper theminimumRMS value ofthe resonant current in this mode represents the minimumconduction loss Then the optimization model can be builtusing ZVS condition as the constraint At last if we analyzethem by using the formulas of 119885119903 = radic119871119903119862119903 119898 = (119871119898 +119871119903)119871119903 119891119899 = 119891119904119891119903 the optimum design can be obtainedIn the PO mode ideal waveforms of components at eachstage are shown in Figure 2 The phase angle is used as theboundary a period can be divided into six working modesAs the characteristics of the first half period are similar to thatof the second half period they are exactly the same except thedirection of the current and voltage is reverseTherefore onlythe first half period is calculated and analyzed in the paper

(1) Stage 1 [1205791199010 sim 120579119901]When the phase angle is 120579119901 the terminalvoltage of 1198781 will decrease to zero and1198631199001199041199041 in the body diode1198781 will turn on The phase angle of resonant current will varyuntil it has a certain value 12057911990101015840 and 1198781 will turn on at the zerovoltage The equivalent circuit is shown in Figure 3

The LLC resonant converter works in P mode at thismoment the voltage is normalized to 2119899119881119900 and the currentis normalized to 2119899119881119900119885119903 119871119903 and 119862119903 start resonating voltageof magnetic inductance 119871119898 is clamped on 2119899119881119900 resonantcurrent 119894119871119903 will change in sine wave shape and its equation of


0

0Vin

0

Vd

0

0Vgs2

Vgs1

Li

Di

θ

Vgs1 Vgs1

Vgs2

iL

iLm

iD1iD2

iD1

P0 P0 O0O1

O2P


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-





119871119898 sdot 119889119894119871119898 (119905) sdot 2119899119881119900119885119903119889119905 = 2119899119881119900(1)



(2)








(3)









(5)



(6)



(7)





(9)


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-


inV

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oR

1S

oV

+

-





1205791199002radic119898)(10)



sdot 119891119899 le 1(11)






119868119871119898119877119872119878 = 1205872radic3 (119898 minus 1) sdot 2119899119881119900119885119903(12)


M=

VoV

in

fn

20

10

0003 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000


0200 0400 0600 0800 1000 1200 1400 1600 180000020W

50KW

100KW

150KW

SELgtgt

0

25

50 m = 1

m = 2m = 3

m = 1

m = 2m = 3

1

Pow

er L

oss

fn

M=

VoV

in






119898 gt 0119885119903 gt 0119891119899 gt 0

(13)





119862119903 = 12120587119885119903 sdot 119891119899 sdot 119891max


(14)








119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)





i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL


i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V


5 Summary



t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018









0

0Vin

0

Vd

0

0Vgs2

Vgs1

Li

Di

θ

Vgs1 Vgs1

Vgs2

iL

iLm

iD1iD2

iD1

P0 P0 O0O1

O2P


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-





119871119898 sdot 119889119894119871119898 (119905) sdot 2119899119881119900119885119903119889119905 = 2119899119881119900(1)



(2)








(3)









(5)



(6)



(7)





(9)


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-


inV

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oR

1S

oV

+

-





1205791199002radic119898)(10)



sdot 119891119899 le 1(11)






119868119871119898119877119872119878 = 1205872radic3 (119898 minus 1) sdot 2119899119881119900119885119903(12)


M=

VoV

in

fn

20

10

0003 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000


0200 0400 0600 0800 1000 1200 1400 1600 180000020W

50KW

100KW

150KW

SELgtgt

0

25

50 m = 1

m = 2m = 3

m = 1

m = 2m = 3

1

Pow

er L

oss

fn

M=

VoV

in






119898 gt 0119885119903 gt 0119891119899 gt 0

(13)





119862119903 = 12120587119885119903 sdot 119891119899 sdot 119891max


(14)








119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)





i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL


i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V


5 Summary



t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018














(3)









(5)



(6)



(7)





(9)


inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-


inV

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oR

1S

oV

+

-





1205791199002radic119898)(10)



sdot 119891119899 le 1(11)






119868119871119898119877119872119878 = 1205872radic3 (119898 minus 1) sdot 2119899119881119900119885119903(12)


M=

VoV

in

fn

20

10

0003 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000


0200 0400 0600 0800 1000 1200 1400 1600 180000020W

50KW

100KW

150KW

SELgtgt

0

25

50 m = 1

m = 2m = 3

m = 1

m = 2m = 3

1

Pow

er L

oss

fn

M=

VoV

in






119898 gt 0119885119903 gt 0119891119899 gt 0

(13)





119862119903 = 12120587119885119903 sdot 119891119899 sdot 119891max


(14)








119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)





i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL


i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V


5 Summary



t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018









inV

1S

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oRoV

+

-


inV

2S

oss1D

oss2D

oss1C

oss2C

rC rL

mL

n 11D

2D

1C

2C

oR

1S

oV

+

-





1205791199002radic119898)(10)



sdot 119891119899 le 1(11)






119868119871119898119877119872119878 = 1205872radic3 (119898 minus 1) sdot 2119899119881119900119885119903(12)


M=

VoV

in

fn

20

10

0003 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000


0200 0400 0600 0800 1000 1200 1400 1600 180000020W

50KW

100KW

150KW

SELgtgt

0

25

50 m = 1

m = 2m = 3

m = 1

m = 2m = 3

1

Pow

er L

oss

fn

M=

VoV

in






119898 gt 0119885119903 gt 0119891119899 gt 0

(13)





119862119903 = 12120587119885119903 sdot 119891119899 sdot 119891max


(14)








119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)





i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL


i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V


5 Summary



t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018









M=

VoV

in

fn

20

10

0003 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000


0200 0400 0600 0800 1000 1200 1400 1600 180000020W

50KW

100KW

150KW

SELgtgt

0

25

50 m = 1

m = 2m = 3

m = 1

m = 2m = 3

1

Pow

er L

oss

fn

M=

VoV

in






119898 gt 0119885119903 gt 0119891119899 gt 0

(13)





119862119903 = 12120587119885119903 sdot 119891119899 sdot 119891max


(14)








119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)





i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL


i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V


5 Summary



t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018













119898 = 49119885119903 = 39 (119876 = 042)119891119899 = 072

(15)





i (1

5Ad

iv)

u (1

50V

div

)u

(10V

div

)

coss1V

t (4sdiv)

gS1V

iL


i (50

0mA

div

)u

(20V

div

)u

(20V

div

)

t (8sdiv)

gS1V

iL

gS2V


5 Summary



t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018









t (4sdiv)

i (1

5Ad

iv)

u (1

50V

div

)

dV

0

iL


98

96

94

92

90

88

86

200 220 240 260 280 300 320 340 360

P (W)

Effici

ency

()



Data Availability






Acknowledgments



References































Journal of












Journal of







Volume 2018






Volume 2018























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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Modal Computation and Analysis Based on Phase Sequence of …downloads.hindawi.com/journals/mpe/2019/1571609.pdf · predictive control of PV sources in a smart DC distribution system: