LLC Series Resonant Converter with PID Controller for Battery Charging Application

Transcription

1 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, 143 Nibong Tebal, Pulau Penang, Malaysia. Abstract In this paper, the output voltage regulation of a halfbridge 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 38 V to 42 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]. This work was supported by Research University Grant (RUI) 11/PELECT/81427 from Universiti Sains Malaysia. PFC AC/DC DC-DC Converter DC Link Battery Charger DC/DC Fig. 1. Typical power architecture of a battery charger. Battery 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 [1]. 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 /14/$ IEEE 84

2 Switching Network LCC Resonant Tank Fig. 2. LCC and LLC resonant tank. 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 L r, resonant capacitor C r and magnetic inductance L m 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 (~%) for both power switches S 1 and S 2 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 V in into a square-wave, with a fixed duty cycle having amplitude equal to V in and a DC offset of V in 2, 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 D 1 and D 2 on the secondary side of the transformer constitute a full-wave rectifier which DC Vin S1 S2 Cr Resonant Tank Lr Lm Transformer NP Fig. 3. Half-bridge LLC series resonant converter. NS NS Rectifier D1 D2 Filter 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 L r and C r and the second involves L m also and are given by 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 f r1. For the above two resonance frequencies f r2 < f r1 and, the separation between f r1 and f r2 depends upon the inductance ratio k = L m / L r and increases with increase in k. The switching frequency f sw controls the power flow from input to the load which increases with the decrease in f sw and vice versa. The range of switching frequency is f min f sw f max where, f min is the frequency at required maximum gain with f min > f r2 to maintain soft switching and, f max is the frequency at required minimum gain with f min f r1. The LLC series resonant converter has the following three region of operations [2]: Below resonance f min f sw f r1 where 2n(V + V f) > V in At resonance f sw = f r1 where 2n(V + V f) = V in Above resonance f r1 f sw f max where 2n(V + V f) < V in Where n is the transformer s turn ratio, V is the output voltage, V in is the input voltage and V f is the secondary diode voltage. Operation at Resonance: In this mode the switching frequency f sw is equal to the series resonant frequency f r1. At f r1, the operation is at load independent point. When switch S 1 is turned off, the resonant current I r falls equal to the magnetizing current I m resulting no further power transfer the secondary side. Due to dead time between switches S 1 and S 2, circuit achieves ZVS and CO RL (1) (2) 85

3 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 f sw < f r1 the resonant current I r falls equal to the magnetizing current I m 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 f r1 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 f r2 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 f sw > f r1 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 f r1 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 firstharmonic 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 [1]: (3) Fig. 4. AC equivalent circuit of the LLC resonant converter. Gain G f r2 f r1 Normalized frequency f n Fig. 5. Operating regions of LLC series resonant converter. An approximate relationship between gain and normalized frequency is given in [21] as: Equation (4) gives the approximated value of f sw 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 f r2 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. (4) with the parameters: Quality factor: where Normalized frequency: with P as output power. Mode 1: This mode starts when the voltage across S 1 becomes zero before it turns on. When S 1 is turned on, the resonant current I r starts flowing through it and increases sinusoidal-type due to resonance between L r and C r The magnetizing inductance L m is clamped to the output voltage nv and is charged linearly. The magnetizing current I m increases linearly and L m does not participate in resonance. The rectifier diode D 1 is turned on under ZCS condition and delivers energy to the load. This mode ends when I r falls equal to I m and energy transfer to the load is ceased resulting diode current I D1 equal to zero. 86

4 S 1 V gs1 V gs2 I r D 1 V in + _ C r L r I m N P I D1 C o R L V ds1 S 2 L m V cr D 2 (a) Mode 1 I L S 1 V in + _ C r I r L r I m N P D 1 C o R L I m S 2 L m D 2 I D1 I D2 (b) Mode 2 Fig. 6. Equivalent circuits for first two modes of operation. Mode 2: This mode starts when I r = I m 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. L m becomes in series with L r & C r 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 ltage range 38 V ~ 42 V. Output ltage range 28 V ~ 72 V LC Resonant frequency f r1 = 2 khz LLC Resonant frequency f r2 = khz Switching frequency range 94.6 khz ~ 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 [2] using the following equations: Mode 1 Mode 2 Mode 3 Mode 4 Fig. 7. Simulation waveforms for modes of operation. Step 3. Choose the resonance frequency f r1 and find equivalent AC resistance R ac, input impedance Z and the load resistance values as; R ac = n 2 R where, Using values of Z 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 =.15, and k = 4.5 the tank parameters are calculated as: C r = 34.2 µf, L r = µf, and L m = µh. where for diodes V f =.6 V and for synchronous rectifier switches V f =.2 V. Step 2. Select the suitable values of inductance ratio k and quality factor Q from the gain versus normalized frequency f n plot of equation (3) satisfying G min and G max. Fig. 8. ltage gain using design steps. 87

5 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 f r1 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. ltage ltage Line Variation 38 Vin/ Line Variation 52 Vin/ Line Variation Vin/11 ltage Fig. 11. Line variation at output voltages 28 V, 48 V and 72 V. Output ltage Regulation with Step and Linear Variations 7 Fig. 9. MATLAB Simulation circuit Load Variation ltage ltage ltage ltage Io x 1-3 Load Variation Io Load Variation Io Fig. 1. Load variation at output voltages 28 V, 48 V and 72 V Fig. 12. ltage regulation with linear and step variations in reference signal at different output voltage levels. Fig. 1 shows the performance of controller for 2% 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 42V and then dropped down to 38V and then adjusted back to the nominal value of V. 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 ltage 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 88

6 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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