Conference-201410-Shahzad-LLC Series Resonant Converter With PID Controller for Battery Charging...

8/9/2019 Conference-201410-Shahzad-LLC Series Resonant Converter With PID Controller for Battery Charging Application

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a soft commutation of the rectifier diodes. The resonance periodis equal to the switching period and the resonant current is sinewave. The operation at series resonance is only a single pointoperation, to cover both line and load variations, the switchingfrequency will have to be adjusted away from the resonancefrequency [19].

Operation below Resonance: Below resonance operationhandles the undervoltage condition due to abrupt load increaseand provides the converter with specified holdup capability. For

fsw < fr1 the resonant current Ir falls equal to the magnetizingcurrentImbefore the end of switching pulse width, causing the

power transfer to the load to be ceased. This is because theresonance duration being smaller than the pulse width.Operation below fr1 achieves primary ZVS and ZCS of therectifier diodes on the secondary side. The rectifier diodes are indiscontinuous current mode and require more circulating currentin the resonant circuit to deliver the same amount of energy tothe load causing conduction losses in both the primary and thesecondary sides. The primary ZVS may be lost if the switchingfrequency becomes low than fr2 resulting in high switchinglosses and several associated issues [19].

Operation above Resonance: The above resonance operation isused to handle overvoltage condition due to abrupt decrease inload. In this mode fsw > fr1 and there is a smaller circulatingcurrent in the resonant circuit. This reduces conduction loss

because the resonant circuits current is in continuous-currentmode, resulting in less RMS current for the same amount of load.In this mode the resonance period is greater than the switching

period. The reverse recovery losses exist because the rectifierdiodes are not softly commutated. The operation above fr1canstill achieve primary ZVS and causes significant frequencyincrease under light-load conditions [19].

III. ACEQUIVALENT CIRCUIT OF THE LLCRESONANT

CONVERTER AND ITS

VOLTAGE

GAIN

The LLC resonant converters nonlinear circuit is replaced

by a linear and time-invariant circuit, based on the first-harmonic approximation (FHA) approach as shown in Fig. 4 [1].This approximation model simplifies the analysis of the maincomplex circuit and illustrates variations of the output voltage

by changing the load and frequency.

The voltage gain of the converter is given as follows [10]:

(3)

with the parameters:

Quality factor:

where withP0as output power.

Normalized frequency:

Fig. 4. AC equivalent circuit of the LLC resonant converter.

GainG

fr1fr2Normalized frequency fn

Fig. 5. Operating regions of LLC series resonant converter.

An approximate relationship between gain and normalized

frequency is given in [21] as:

(4)

Equation (4) gives the approximated value of fsw at requiredoutput voltage which can be used as initial frequency of VCO,

and it will be further adjusted by PID controller. Using (3) theDC characteristics of LLC resonant converter can be derived,and are divided into ZCS and ZVS regions, as illustrated in Fig.5 [22]. Belowfr2is the ZCS region and is not preferred for powerMOSFET application due to the loss of ZVS operation [21].

IV.CIRCUIT OPERATION

In one switching cycle the operation of the LLC resonantconverter in Fig. 3 can be divided into four modes [23] as shownin Fig. 7. Only first two modes in the half switch cycle areexplained. For the next half cycle, operation is similar and isomitted here. The equivalent circuit for these two modes isshown in Fig. 6.

Mode 1: This mode starts when the voltage across S1becomes zero before it turns on. When S1is turned on, the

resonant current Ir starts flowing through it and increases

sinusoidal-type due to resonance between Lr and Cr The

magnetizing inductanceLmis clamped to the output voltage

nV0 and is charged linearly. The magnetizing current Imincreases linearly andLmdoes not participate in resonance.

The rectifier diodeD1is turned on under ZCS condition and

delivers energy to the load. This mode ends when Ir falls

equal toImand energy transfer to the load is ceased resulting

diode currentID1equal to zero.

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S1

RLCo

NPNS

NS

Lr

Lm

Cr

D1

D2

Vin

S2

S1

RLCo

NPNS

NS

Lr

Lm

Cr

D1

D2

Vin

S2

(a) Mode 1

(b) Mode 2

ID1

Ir

Im

Ir

Im

+

_

+

_

Fig. 6. Equivalent circuits for first two modes of operation.

Mode 2: This mode starts whenIr= Imand continues until

both currents remain equal. During this mode, output is

separated from the input and no power is transferred to the

load from the input side.Lmbecomes in series withLr& Cr

participating in resonance operation and, the current

circulates in the primary side. This mode ends after S 1 is

turned off and voltage across it starts rising.For the next half switching cycle operation is similar as above.

V. DESIGN PROCEDURE

The converter specifications for the design are given as follows:

Input DC Voltage range 380 V ~ 420 V.

Output Voltage range 28 V ~ 72 V

LC Resonant frequencyfr1 = 200 kHz

LLC Resonant frequencyfr2 = 85.28 kHz

Switching frequency range 94.6 kHz ~ 226.6 kHz

The design procedure for the converter is summarized in the

following steps [19].

Step 1. Calculate the transformers turns ratio, minimum and

maximum gain values [20] using the followingequations:

where for diodes Vf = 0.6 V and for synchronous

rectifier switches Vf= 0.2 V.

Step 2. Select the suitable values of inductance ratio k and

quality factor Q from the gain versus normalized

frequency fn plot of equation (3) satisfying Gmin and

Gmax.

0

0

Mode 1 Mode 2 Mode 3 Mode 4

ID1 ID2

Im

IL

Vcr

Vds1

Vgs1 Vgs2

0

0

Fig. 7. Simulation waveforms for modes of operation.

Step 3. Choose the resonance frequency fr1 and find

equivalent AC resistanceRac, input impedanceZ0and

the load resistance values as;

Rac= n2R0

where,

Using values of Z0 and kcalculate the tank parameters

as:

Step 4. Find the minimum and maximum switching

frequencies from the gain plot.

The gain plot is shown in Fig. 8. Using above steps with n= 9,

Q = 0.15, and k= 4.5 the tank parameters are calculated as:

Cr= 34.2F, Lr= 1.855F, and Lm= 8.356H.

Fig. 8. Voltage gain using design steps.

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VI. SIMULATION RESULTS

Fig. 9 shows the MATLAB Simulink model of the LLCresonant DC-DC converter implemented using PID controllerwith parameters calculated in design procedure. PID controlleris used to generate pulses for driving MOSFETs. The frequencyof the pulses is adjusted by the voltage controlled oscillator(VCO) which is driven by the PID controller. The initial valuegiven to the VCO is the resonance frequency fr1which is then

adjusted by the controller for the desired output voltage. Thecontroller adjusts the frequency output of the VCO based on theerror signal which is the difference between reference signal andthe output voltage. The VCO generates the triangular waves ofrequired frequency which is then used to generate the gate pulsesfor MOSFETs with required fixed duty cycle.

Fig. 9. MATLAB Simulation circuit.

Fig. 10. Load variation at output voltages 28 V, 48 V and 72 V.

Fig. 11. Line variation at output voltages 28 V, 48 V and 72 V.

Fig. 12. Voltage regulation with linear and step variations in reference signal atdifferent output voltage levels.

Fig. 10 shows the performance of controller for 20%variation in load at 28V, 48V and 72V. It can be seen from thefigure that the controller adjusted the load variations for bothincrease and decrease in load. The effect of load variationincreases with the increase in output voltage level. The outputcurrent is scaled by 1/9 in the figure.

Fig. 11 shows the effect of step variations in input voltageand the controllers response for the adjustment of effect. Theinput voltage was increase to maximum value of 420V and thendropped down to 380V and then adjusted back to the nominal

value of 400V. Figure shows the line variation at 28V, 48V and72V and it can be seen the controller has adjusted the effect morequickly at higher output voltage than the lower one. The outputVoltage was scaled by 1/11 in the figure.

Fig. 12 shows the output voltage regulation with step andlinear changes in the reference signal at different voltage levels.From the figure it can be seen that the output voltage follows thereference signal in both step and linear variations. The controllerhas adjusted the output voltage according to the variations inreference signal. For higher voltage level adjustment is quicker

0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016

40

45

50

55

60

65

70

Output Voltage Regulation with Step and LinearVariations

Simulation Time

Voltage

Vref

Vo

3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6

x 10-3

16

18

20

22

24

26

28

Simulation Time

Volta

ge

Load Variation

Vref

Vo

Io

0.01 0.0105 0.011 0.0115 0.012 0.0125

28

30

32

34

36

38

40

42

44

46

48

Simulation Time

Voltage

Load Variation

Vref

Vo

Io

0.0185 0.019 0.0195 0.02 0.0205 0.021 0.0215

40

45

50

55

60

65

70

75

Simulation Time

Voltage

Load Variation

Vref

Vo

Io

0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.02

24

26

28

30

32

34

36

38

Simulation Time

Voltage

Line Variation

Vref

Vo

Vin/11

0.024 0.0245 0.025 0.0255 0.026 0.0265 0.027 0.0275

34

36

38

40

42

44

46

48

50

52

Simulation Time

Voltage

Line Variation

Vref

Vo

Vin/11

0.0335 0.034 0.0345 0.035 0.0355 0.036 0.0365 0.037

35

40

45

50

55

60

65

70

75

Simulation Time

Voltage

Line Variation

Vref

Vo

Vin/11

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than that of lower voltage level. In linear variation, the outputvoltage has almost followed the reference signal.

VII. CONCLUSION

The design of half-bridge LLC series resonant converter ispresented together with the simulation results using MATALBSimulink for battery charging application. Simulation resultsshowed the controller performance for adjustment of output

voltage for both line and load variations. It is shown that thecontroller has adjusted the effects of step variations in line andload and also tracked the reference signal for both step and linearvariations in the reference value. The converter meets therequirements of DC-DC stage in the lead-acid battery chargingapplication.

ACKNOWLEDGMENT

The authors would like to thank the University for providingall necessary facilities and equipment to make this research

possible.

REFERENCES

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