LLC Series Resonant Converter with PID Controller

for Battery Charging Application

M. Imran Shahzad, Shahid Iqbal, and Soib Taib

School of Electrical & Electronic Engineering,

Engineering Campus, Universiti Sains Malaysia,

14300 Nibong Tebal, Pulau Penang, Malaysia.

ishzd@yahoo.com

Abstract—In this paper, the output voltage regulation of a half-

bridge LLC series resonant DC-DC converter using a PID

controller in feedback loop for the battery charging application is

presented. The PID controller is used to adjust the frequency of

gate pulses generated by the voltage controlled oscillator (VCO)

for deriving the MOSFETs to regulate the output voltage. The

converter is implemented using MATLAB Simulink environment

for the input range of 380 V to 420 V and output range of 28 V to

72 V DC voltage. Simulation results showed that the controller can

quickly adjust the output voltage level for step variations in both

line and the load. The controller can also set the output voltage

level for both step and linear variations in the reference signal.

Keywords—Resonant converter; battery charger; PID

controller; FHA.

I. INTRODUCTION

Due to increased concern about global warming, environmental issues and the threat of fossil fuel depletion, the interest in plug-in hybrid electrical vehicles (PHEVs) and pure electric vehicles is growing continuously. High conversion efficiency, high power density, smooth and quick charging capabilities are the desired features expected from the on-board charger in electrical vehicles. With the improvement in battery technology and capacity high current, high voltage and sophisticated charging algorithms are needed, making charging of the batteries complicated [1].

The commonly used battery charging architecture is shown in Fig. 1, consisting of power factor correction (PFC) stage with AC to DC converter following the isolated DC-DC stage [2]. The PFC stage could be a conventional continuous conduction mode (CCM) boost topology [1]. The main focus of this paper is the DC-DC converter stage which have the main role of regulating the output current and voltage, and the characteristics of the charger depend on this stage [3], [4]. Among various available choices, LLC resonant converter is the most attractive choice because of its salient features like wide operation range, high efficiency, low electromagnetic interference, high power density and ability to achieve soft switching for less conduction losses at both primary and secondary sides [5]. However this topology have many controlling parameters making its design and analysis complicated [6].

AC/DC

PFC

DC Link

DC-DC Converter

DC/DC

Battery

Battery Charger

Fig. 1. Typical power architecture of a battery charger.

For LLC resonant converter many design methods have been proposed in the literature like exact analysis [7] and first harmonic approximation (FHA) analysis [8], [9]. The exact analysis ensures accuracy but is not handy due to model complexity. However, the FHA is much simpler giving acceptably accurate results at or above resonance and has been widely used in literature for the analysis of constant output voltage applications [10]. Below resonance, FHA is still valid with less accurate results making it not a good choice for optimal design but it is useful for qualitative analysis.

In this paper a half-bridge LLC series resonant converter is designed for output voltage range of 28 V to 72 V for a lead-acid battery with charging profile given in [1]. The circuit is simulated using MATLAB Simulink and the output voltage of the converter is regulated using PID controller in feedback path. The PID controller regulates the output voltage by adjusting frequency of the gate pulses of the MOSFETs. In the following section LLC resonant converter configuration and operation is discussed. In Section III converter is analyzed using FHA and circuit operation is explained in section IV. The design procedure is given in section V and simulation results are presented in section VI.

II. LLC RESONANT CONVERTER

LLC resonant converter has gained a lot of attention and has been widely discussed in literature for having simple structure and several desirable features like high power density, reduced switching losses at high frequencies, high efficiency, zero voltage switching (ZVS), zero current switching (ZCS), low electromagnetic interference (EMI) and elimination of reverse recovery of the output rectification diodes [11]-[15]. These converters have much reduced losses due to their sinusoidal

This work was supported by Research University Grant (RUI) 1001/PELECT/814207 from Universiti Sains Malaysia.

978-1-4799-4848-2/14/$31.00 ©2014 IEEE 84

LCC Resonant Tank LLC Resonant Tank

Fig. 2. LCC and LLC resonant tank.

behavior and can reduce the size of reactive components by high frequency operation and are much suited for high power applications.

High power density is an important trend for today’s power supply market. Topologies with high switching frequency capability and high efficiency are needed to meet this trend. But at high frequency, switching losses also exist specially the secondary diode reverse recovery loss and primary switches turn off loss. There are too many parameters for the LLC resonant converter such as resonant inductor Lr, resonant capacitor Cr and magnetic inductance Lm and, different parameters correspond to different working waveforms as well as different switching losses making the design complex [13].

LLC series resonant converter can regulate the output voltage over a wide range of line and load variations. Compared to LCC, LLC resonant converter can achieve soft switching over the entire operating range. The resonant tanks of LCC and LLC converters, which are dual of each other, are shown in Fig. 2. In LLC configuration, the size of the converter can be reduced by integrating the two inductors into the transformer which reduces the components count [6].

A. Configuration of LLC Series Resonant Converter

A half-bridge LLC series resonant converter shown in Fig. 3, is gaining popularity as a high efficiency DC-DC converter [12]-[15]. The main parts of this configuration are discussed below.

Switching Network: The frequency controlled switching network acts as square-wave generator and is configured in a complementary mode having a fixed duty cycle (~50%) for both power switches S1 and S2 which are usually the MOSFETs. The duty cycle have some dead-time between consecutive transitions to prevent the possibility of cross conduction and allow time for ZVS to be achieved. The switching network converts the DC input Vin into a square-wave, with a fixed duty

cycle having amplitude equal to Vin and a DC offset of Vin2, which is then fed to the resonant tank.

Resonant Tank and Transformer: The resonant tank circulates the electric current and delivers energy to the load through the transformer. The resonant tank introduces a phase shift between the voltage and current due to which soft-switching is achievable [19]. The combination of switching network and resonant tank make a resonant inverter which feeds in the sinusoidal or piecewise sinusoidal current and voltage to the transformer. The transformer decides the gain based on the turns ratio of the primary and secondary windings and provides electrical isolation.

Rectifier and Filter: The two diodes D1 and D2 on the secondary side of the transformer constitute a full-wave rectifier which

Switching Network

S1

RLCO

NP

NS

NS

Lr

Lm

Cr

D1

D2

S2

DC

Vin

Resonant Tank Transformer

Rectifier

Filter

Fig. 3. Half-bridge LLC series resonant converter.

converts the AC input to a regulated DC output voltage with the help of output capacitor filter which smooth the rectifier voltage and current. The rectifier can be implemented as a full-wave center-tapped or in a bridge configuration. It can also be implemented with MOSFETs for synchronous rectification which is especially beneficial in high-current and low-voltage applications [19].

B. Operation of LLC Series Resonant Converter

The resonant tank offers minimum impedance to the sinusoidal current at resonant frequency, regardless of the frequency of the input square-wave voltage. To control the portion of energy delivered to the load, the impedance of the resonant tank varies with the switching frequency. For LLC series resonant converter there are two resonant frequencies, the first involves Lr and Cr and the second involves Lm also and are given by

(1)

(2)

Equation (1) is always true regardless of load but (2) is true

only at no load. Mostly LLC resonant converter is designed to operate in the vicinity of resonant frequency fr1. For the above two resonance frequencies fr2 < fr1 and, the separation between fr1 and fr2 depends upon the inductance ratio k = Lm / Lr and increases with increase in k. The switching frequency fsw controls the power flow from input to the load which increases with the decrease in fsw and vice versa. The range of switching frequency is fmin ≤ fsw ≤ fmax where, fmin is the frequency at required maximum gain with fmin > fr2 to maintain soft switching and, fmax is the frequency at required minimum gain with fmin ≥ fr1. The LLC series resonant converter has the following three region of operations [20]:

Below resonance fmin ≤ fsw ≤ fr1 where 2n(V0+ Vf) > Vin

At resonance fsw = fr1 where 2n(V0+ Vf) = Vin

Above resonance fr1 ≤ fsw ≤ fmax where 2n(V0+ Vf) < Vin

Where n is the transformer’s turn ratio, V0 is the output voltage, Vin is the input voltage and Vf is the secondary diode voltage.

Operation at Resonance: In this mode the switching frequency fsw is equal to the series resonant frequency fr1. At fr1, the operation is at load independent point. When switch S1 is turned off, the resonant current Ir falls equal to the magnetizing current Im resulting no further power transfer the secondary side. Due to dead time between switches S1 and S2, circuit achieves ZVS and

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

Operation below Resonance: Below resonance operation handles the undervoltage condition due to abrupt load increase and provides the converter with specified holdup capability. For fsw < fr1 the resonant current Ir falls equal to the magnetizing current Im before the end of switching pulse width, causing the power transfer to the load to be ceased. This is because the resonance duration being smaller than the pulse width. Operation below fr1 achieves primary ZVS and ZCS of the rectifier diodes on the secondary side. The rectifier diodes are in discontinuous current mode and require more circulating current in the resonant circuit to deliver the same amount of energy to the load causing conduction losses in both the primary and the secondary sides. The primary ZVS may be lost if the switching frequency becomes low than fr2 resulting in high switching losses and several associated issues [19].

Operation above Resonance: The above resonance operation is used to handle overvoltage condition due to abrupt decrease in load. In this mode fsw > fr1 and there is a smaller circulating current in the resonant circuit. This reduces conduction loss because the resonant circuit’s current is in continuous-current mode, 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 rectifier diodes are not softly commutated. The operation above fr1 can still achieve primary ZVS and causes significant frequency increase under light-load conditions [19].

III. AC EQUIVALENT CIRCUIT OF THE LLC RESONANT

CONVERTER AND ITS VOLTAGE GAIN

The LLC resonant converter’s 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 main complex 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 with P0 as output power.

Normalized frequency:

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

Gai

n G

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 required output voltage which can be used as initial frequency of VCO, and it will be further adjusted by PID controller. Using (3) the DC characteristics of LLC resonant converter can be derived, and are divided into ZCS and ZVS regions, as illustrated in Fig. 5 [22]. Below fr2 is the ZCS region and is not preferred for power MOSFET application due to the loss of ZVS operation [21].

IV. CIRCUIT OPERATION

In one switching cycle the operation of the LLC resonant converter in Fig. 3 can be divided into four modes [23] as shown in Fig. 7. Only first two modes in the half switch cycle are explained. For the next half cycle, operation is similar and is omitted here. The equivalent circuit for these two modes is shown in Fig. 6.

Mode 1: This mode starts when the voltage across S1

becomes zero before it turns on. When S1 is turned on, the

resonant current Ir starts flowing through it and increases

sinusoidal-type due to resonance between Lr and Cr The

magnetizing inductance Lm is clamped to the output voltage

nV0 and is charged linearly. The magnetizing current Im

increases linearly and Lm does not participate in resonance.

The rectifier diode D1 is turned on under ZCS condition and

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

equal to Im and energy transfer to the load is ceased resulting

diode current ID1 equal to zero.

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S1

RLCo

NP

NS

NS

Lr

Lm

Cr

D1

D2

Vin

S2

S1

RLCo

NP

NS

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 when Ir = Im and 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. Lm becomes in series with Lr & Cr

participating in resonance operation and, the current

circulates in the primary side. This mode ends after S1 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 frequency fr1 = 200 kHz

LLC Resonant frequency fr2 = 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 transformer’s turns ratio, minimum and

maximum gain values [20] using the following

equations:

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 resistance Rac, input impedance Z0 and

the load resistance values as;

Rac = n2R0

where,

Using values of Z0 and k calculate 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 = 34.2 µF, Lr = 1.855 µF, and Lm = 8.356 µH.

Fig. 8. Voltage gain using design steps.

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VI. SIMULATION RESULTS

Fig. 9 shows the MATLAB Simulink model of the LLC resonant DC-DC converter implemented using PID controller with parameters calculated in design procedure. PID controller is used to generate pulses for driving MOSFETs. The frequency of the pulses is adjusted by the voltage controlled oscillator (VCO) which is driven by the PID controller. The initial value given to the VCO is the resonance frequency fr1 which is then adjusted by the controller for the desired output voltage. The controller adjusts the frequency output of the VCO based on the error signal which is the difference between reference signal and the output voltage. The VCO generates the triangular waves of required frequency which is then used to generate the gate pulses for 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 at different 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 the figure that the controller adjusted the load variations for both increase and decrease in load. The effect of load variation increases with the increase in output voltage level. The output current is scaled by 1/9 in the figure.

Fig. 11 shows the effect of step variations in input voltage and the controller’s response for the adjustment of effect. The input voltage was increase to maximum value of 420V and then dropped down to 380V and then adjusted back to the nominal value of 400V. Figure shows the line variation at 28V, 48V and 72V and it can be seen the controller has adjusted the effect more quickly at higher output voltage than the lower one. The output Voltage was scaled by 1/11 in the figure.

Fig. 12 shows the output voltage regulation with step and linear changes in the reference signal at different voltage levels. From the figure it can be seen that the output voltage follows the reference signal in both step and linear variations. The controller has adjusted the output voltage according to the variations in reference 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 Linear Variations

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

Voltage

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 0.021540

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 0.0224

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

88

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

VII. CONCLUSION

The design of half-bridge LLC series resonant converter is presented together with the simulation results using MATALB Simulink for battery charging application. Simulation results showed the controller performance for adjustment of output voltage for both line and load variations. It is shown that the controller has adjusted the effects of step variations in line and load and also tracked the reference signal for both step and linear variations in the reference value. The converter meets the requirements of DC-DC stage in the lead-acid battery charging application.

ACKNOWLEDGMENT

The authors would like to thank the University for providing all necessary facilities and equipment to make this research possible.

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