I. INTRODUCTION
Phase-shifted full-bridge (PSFB) converter is extensively used in medium-power and high-power applications because of its advantages of high efficiency and low electric stress on power devices at the same power level [1]-[4]. Operating in the first and third quadrants of the B–H curve is an outstanding characteristic of PSFB converters, but easily leads to transformer core imbalance. Transformer core imbalance is normally observed as the unilateral saturation of transformers or excessive electric stress on power devices [5]-[7].
Transformer core imbalance in the PSFB converter is a result of static current offset on the primary side. Current offset is caused by unavoidable unequal on-state resistance of different diagonal power switches, delay of driver circuits, and nonideal PCB parameters [8]. The effect of this imbalance can be reduced by simply adding a DC blocking capacitor to the primary winding of the transformer in engineering applications. However, the blocking capacitor method cannot completely eliminate transformer core imbalance. Moreover, this method has several disadvantages, such as grievous ratio loss, high cost, and low efficiency. In recent years, several new methods are proposed to eliminate the imbalance issue.
A compensation circuit is proposed to reduce transformer core imbalance in an asymmetrically regulated PSFB converter [9]. However, the method is difficult to apply because many external devices are introduced. Moreover, an uncommon asymmetric full-bridge controller that separately controls the phases of diagonal power switches is necessary.
An accurate model and a digital compensator are proposed in [10]. The model is built to analyze the relationship between nonideal parameters and offset current on the primary side. However, the current sensor in the proposed solution leads to extra cost and power loss, which limit the application range.
Given the disadvantages of low efficiency and high material cost in common transformer core imbalance solutions, a high efficiency and simple method is proposed in this study.
In this study, a transient model is built to analyze the relationship between the imbalance of the magnetic core and cathode voltage of output rectifiers on the secondary side. An approximate control algorithm that eliminates the effect of transformer core imbalance is achieved by a low-cost microcontroller. This paper is organized as follows: In Section II, a conventional PSFB converter is analyzed and simulated to investigate the relationship among the cathode voltage of output rectifiers on the secondary side, primary side current, and magnetic core imbalance. A digital compensator is proposed in Section III, including an external sample circuit and an internal control algorithm. In Section IV, a 60 V/15 A prototype is built and tested to verify the effect of the proposed method compared with conventional PSFB converters.
II. THEORETICAL ANALYSIS OF TRANSFORMER CORE IMBALANCE
A. Transformer Core Imbalance in PSFB Converters
A conventional PSFB converter regulated based on a microcontroller is shown in Figure 1. The primary side includes input capacitor CIN and power MOSFETs M1–M4. LR represents the sum of the resonant inductor and leakage inductance of the transformer; NP represents the primary winding of the transformer; and N1 and N2 represent the secondary windings of the transformer. The secondary side consists of output rectifiers D1–D2, filter inductor LOUT, and filter capacitor COUT. R represents the load. Feedback and control components are composed of sample resistors RVS1–RVS2 and a microcontroller. The internal ADC module samples the feedback voltage, which is divided by RVS1–RVS2 from output voltage VOUT. The function of the logic module is calculating the phase of diagonal transistors. The internal timers output four pulse signals, Driver1–Driver4, based on the logic module. Driver1–Driver4 control VGS of power MOSFETs when amplified by the isolated circuits DriverA–DriverD.
Fig. 1.Basic PSFB converter.
RDS(on) of M1–M4, related parasitic parameters of PCB, and delay time caused by isolated drivers cannot be completely equal because of design and manufacturing limitations. The inequality causes a deviation between positive and negative peak currents on the primary side, which leads to inevitable imbalance of the transformer core in the PSFB converter.
Transformer core imbalance is directly decided by the DC offset of the primary current and is affected by several other phenomena. For example, unequal peak values of the primary current also illustrate the imbalance condition of the transformer core, which has been utilized by peak current mode (PCM) control. A current sensor is required to sample the primary current, which increases the material cost and power loss of the PSFB converter.
B. Transformer Core Imbalance Reflexed by a Voltage Signal
Aside from the peak values of the primary current, another phenomenon also causes transformer core imbalance, that is, voltage oscillation ring of the anode and cathode of rectifiers D1 and D2 on the secondary side, as shown in Figure 1. Even if RC snubbers are paralleled to D1–D2, voltage peaks can be detected on the anode and cathode voltages of D1 during overlapping of M1 and M3 or on the anode and cathode voltages of D2 during overlapping of M2 and M4, as illustrated in Figure 2. Given that the cathode of rectifiers is directly connected, VK is simulated with primary current IP instead of voltage of anodes in Figure 2.
Fig. 2.Simulated waveform of VK and IP.
In Figure 2, the peak values of IP and VK are measured; the range of VK is adjusted to show inequality. Unequal peak values of IP and VK in a switching cycle are illustrated, which indicate that the voltage signal includes information of the imbalance condition of the magnetic core. Moreover, the relationship between oscillation ring VK(D2) (VD2) and primary current ip(t) in the PSFB converter without RC snubbers is verified, which proves that VK is infected by IP.
Confirming whether the relationship remains correct when RC snubbers are added is necessary. RC snubbers are extensively used to prevent overvoltage stress on D1 and D2. The relationship between VK and IP in PSFB converter with RC snubbers should be investigated, such that analysis based on VK can be proven effective.
We let t1 denote the finish time of the ratio loss procedure, which transfers no energy from the primary side to the secondary side. Figure 3 illustrates the schematic and equivalent circuit of the PSFB converter with RC snubbers during the energy transfer procedure from the primary side to the secondary side (defined as t1–t2). During t1– t2, M1 and M3 are on, and the on-state resistances are RDS1 and RDS3. Inductors LR and LP are charged, and the primary side current iP(t) can be expressed as follows:
Fig. 3.Equivalent circuit to reflex anode/cathode voltage of secondary side rectifier.
Secondary current has two parts (Figure 3(a)). The green line denotes that current flows through LOUT to provide output power. LOUT is sufficiently large that LOUT, COUT, and R can be replaced by constant current source ILO during t1–t2. Meanwhile, the red line denotes that current flows through junction capacitance Cj of D1 and RC snubber, which causes resonance of vK(t) when iP(t) increases to its peak value. If LR is converted from primary side to secondary side, then the circuit can be simplified based on the operation principle of the transformer (Figure 3(b)).
By converting inductance LR and voltage across LP to the secondary side, the turns ratio can be expressed as K = (LP/LS1)0.5 = (LP/LS2)0.5, LR becomes LRS = K2LR/4, and voltage across the secondary windings is VS = 2VIN/K. By transferring the circuit from the time domain to the complex frequency domain, as shown in Figures 3(b) and 3(c), the voltage across Cj can be calculated as follows:
In Equation (2), IP(0) represents the primary current at t1. Moreover, if the forward drop of the rectifier is neglected, then vK(s) in the complex frequency domain can be expressed as follows:
vK(s) is a three-order function of variable s according to Equation (3). The initial value of the primary current infects the voltage, which is simulated in the time domain by Matlab (Figure 4). Two values of IP(0) are compared in the same coordinate system, which shows that a higher IP(0) is equivalent to a higher VK. A comparison between the simulation results and tested results proves that the shape of the simulated waveform is similar to the tested waveform when the DC value is neglected. This comparison proves that vK(t) reflexes iP(t), particularly with the difference between the two directions during one cycle.
Fig. 4.Simulated time domain waveform of VK compared with the tested waveform.
According to Figure 4, the theory that VK is related to IP is proven, which indicates that the difference in the peak values of VK in one cycle reflexes the balance condition of the transformer core in the PSFB converter. Magnetization processes in the first and third quadrants of the B–H curve are asymmetric; thus, the offset value of the primary side current can be observed, which should be zero in a balanced condition.
Given that the peak value of VK is directly affected by the primary side current, VK can be used to acquire imbalance state information of the transformer core. If the transformer core is balanced, then the peak value VK-PEAK(D1) should be equal to peak value VK-PEAK(D2) and D1 and D2 represent different rectifiers in different phases. According to the simulations, tests, and theoretical analysis described in this section, the difference between VK-PEAK(D1) and VK-PEAK(D2) affects the imbalance of the transformer core. The conclusion represents the theoretical foundation of the proposed suppression method.
III. DESIGN OF A DIGITAL PHASE COMPENSATOR
A. Control Algorithm and Program Loop Design
Based on the analysis presented in Section II, a new method that samples VK as another feedback variable can be proposed. Transformer core imbalance is currently suppressed accurately cycle-by-cycle using PCM. However, in practical applications, serious consequences, such as unilateral transformer saturation or power device failure, are caused by a continuous single-direction imbalance. A current offset in one single-switching cycle causes no harm. Thus, the main idea of suppression in this study is to limit the imbalance range and swing imbalance direction.
If the static offset value of primary side current IP_OS is controlled to alternate between positive and negative, then the average value of IP_OS would be approximately zero during most periods:
In Equation (4), n represents the amount of switching cycles.
Based on the equation, regulating IP_OS with an approximate method is considered to be effective. When the sign of IP_OS changes, the magnetic offset of the transformer can also be controlled to alternate between positive and negative, and the amplitude of imbalance in one switching cycle can be suppressed as well. Although transformer core imbalance occurs during the entire operation procedure, the imbalance is bidirectional and significantly limited; thus, the average value of magnetic flux is also approximately zero in most switching cycles.
According to the analysis, an asymmetric phase regulation method should be applied to maintain a low IP_OS in each cycle. Moreover, the positive or negative sign of IP cannot be maintained for a long period of time. Thus, the phase difference between M1–M3 and M2–M4 should be regulated based on the imbalance state of the transformer core, which is represented by the numerical relationship between the maximum value of VK-PEAK(D1) and VK-PEAK(D2) in the proposed solution (Figure 5).
Fig. 5.Control diagram of the proposed solution.
Compared with the PSFB converter with a conventional controller, an external voltage sampler that is used to sense cathode voltage VK from output rectifiers is inserted to the control loop (Figure 5). Moreover, a few extra algorithm modules are added to the program cycle of the microcontroller in the proposed solution.
In a normal switching cycle, output voltage VOUT of the power topology is sampled by output sampler RVS1–RVS2 (Figure 1). The sampled voltage VFB turns into the error signal VE after being amplified. VE is the input of the phase modulator, which is used to calculate phase D. In a conventional PSFB converter, the phases of M1–M3 and M2–M4 output by the microcontroller are equal to D. However, the phases of power MOSFETs are not the same as previously mentioned. This issue is one of the main factors of transformer core imbalance; thus, imbalance problems can be solved by deliberate unequal phases of M1–M3 and M2–M4.
Figure 6 shows the procedure of the phase controller. To achieve asymmetric regulation in the proposed solution, the peak values of voltage signal VK are captured by the internal ADC of the microcontroller and then converted to digital variables voltageKnode1 and voltageKnode2 in the sample function. The difference between voltageKnode1 and voltageKnode2 reflects the imbalance state of the transformer core in the current cycle. Extra transformer imbalance modulator outputs time variable tD, which is the other input of the logic unit, except for phase D. The function of the logic unit is to generate phases D13(n) and D24(n) based on the current phases D13(n − 1) and D24(n − 1), calculated phase D, and time variable tD. D13(n) and D24(n) would be assigned to related registers of internal timers to modify the phases of M1–M3 and M2–M4 in the subsequent cycle.
Fig. 6.Procedure of the phase controller.
Compared with the conventional digital phase controller of the PSFB converter, the proposed digital phase controller inserts different phase calculation functions to the main program loop.
The driver signals of M1 and M2 are generated by one of the advanced timers in the microcontroller. These two signals would never be regulated, which indicates that the period, ratio, and dead time of M1 and M2 remain constant. The driver signals of M3 and M4 are generated by another advanced timer in the microcontroller. They are regulated in program interruptions based on the values of voltageFB, voltageKnode1, and voltageKnode2. Phase D of the subsequent cycle is set with an initial value, which is calculated based on the phases and sampled voltageFB in the current cycle. In the current cycle, voltageKnode1 and voltageKnode2 are also sampled and compared with the obtained magnetic offset condition.
The numerical value of tD is set to be constant to simplify the control loop; however, the sign of tD would be positive or negative according to the relationship between voltageKnode1 and voltageKnode2. The phases of M1–M3 and M2–M4 in cycle n are calculated as follows:
As Equation (5) shows, the phases in the subsequent cycle are related to the phases in the last cycle, the calculated phase in the current cycle, and the imbalance state in the current cycle. If the direction of transformer core imbalance is reflected as VK-PEAK(D1) > VK-PEAK(D2) , then IPEAK(M1–M3) > IPEAK(M2–M4) in the current cycle Tn, and tD would be negative to decrease D13 and increase D24 in the subsequent cycle Tn+1. If the direction of transformer core imbalance in Tn+1 retains the state of Tn, then tD would again have a negative value and D13 in Tn+2 becomes smaller than D13 in Tn+1.
Moreover, the sign of tD would not change until condition VK-PEAK(D1) > VK-PEAK(D2) becomes VK-PEAK(D1) < VK-PEAK(D2). When VK-PEAK(D1) < VK-PEAK(D2) is built in one cycle, the phase controller would change the sign of tD to build VK-PEAK(D1) > VK-PEAK(D2). Thus, a limited transformer core imbalance is achieved, which no longer causes unilateral saturation of the transformer and power device failures.
B. Design of the RC Snubber of Output Rectifiers
The RC snubber is used to decrease voltage stress across the rectifier [11]. The purpose of designing the RC snubber is based on power loss and stress margin. Quality factor Q is defined as the reflex oscillation in the RLC circuit:
In PSFB applications, the oscillation ring should be suppressed to an underdamping state to make our method effective while ensuring that voltage stress is safe for the rectifiers. The value of R1 can be determined as follows:
In Equation (7), Cj can be derived from the datasheet and Li can be calculated as follows:
C1 is selected in the range of:
Parameter IP is the initial value of the primary side current, and TS represents the period of the PSFB converter. Based on these design considerations, the RC snubber ensures a single ring while the amplitude of the ring is suppressed.
C. Special design of the voltage sensor to sample transformer core imbalance
Program achievement of asymmetric regulation has been proposed; however, the ADC sampler needs special consideration because of difficulty in sampling the peak value of VK.
To sample a reliable VK, a digital signal process function is designed in the microcontroller to capture voltage at a specified time. Sampler design has two rules, as follows:
1) According to the errors of the sampler, several different points should be sampled to filter spikes.
2) Several points unavoidably lead to error of the desired point; thus, the start and end times of the sampler should be set properly based on the relationship between PWM driver and VK waveform.
Based on the rules, the special design of the sampler should be considered. Period TS of the PSFB converter is set by the designer and executed by the MCU, and phase tP of two diagonal MOSFETs is decided by the MCU. Moreover, duty cycle loss time can be calculated as follows:
Ipeak is the peak value of the primary side current, LR is the resonant inductance, Lleak is the leakage inductance of the transformer, and Vin is the input voltage.
According to these settings and calculations, the specific time of the oscillation ring peak is easy to locate; however, sampling the exact value during software execution is difficult particularly because no external sample/hold circuit is added.
Thus, sample consideration in the software should be based on multiple samples; in this case, average value of sampled points is used to reflex true VK. The proposed mechanism is to sample several values right after tloss and TS/2 + tloss, as shown in Fig. 7. A higher peak value of VK indicates a higher sampled value at the corresponding time during the first oscillation ring, such that the accurate average value can be calculated if the sample time is ensured to be sufficiently accurate. Then, these values are averaged to be VK in the half period, as illustrated in Fig. 8.
Fig. 7.Waveform of VGS and primary side current.
Fig. 8.Digital sample design consideration.
When data VK [1, …, n] are stored as variables in each phase, an extra process is necessary to generate a reliable variable, which is called the calculating function of tD:
The average method is the easiest way to process data if point number x in Equation (11) is set as 2M, such as 4, 8, and 16. The point number should be set according to the cost of the sampler because a large amount of data in the sampling module can easily cause poor loop response. Finally, the number of M is set as 3, such that the average value of VK can be rapidly calculated.
Based on these considerations, an asymmetric phase controller is developed. Two external resistors are connected between the cathode of the output rectifiers and output ground to divide the large voltage. The divided voltage is one of the analog inputs of the microcontroller. The designed program generates four channels of PWM signal with asymmetric phases to control power MOSFETs. The test results are given in the subsequent section to show the effect of the proposed method.
IV. EXPERIMENTAL RESULTS
A 220 VAC input, 60 V/15 A output prototype is built to verify the effect of the proposed method (Fig. 9). The PSFB converter consists of two PCBs vertically connected via plug-in parts. The PSFB topology board includes basic PSFB converter, isolated drivers of four power MOSFETs, and power supply for chips, fan, and driver circuits. The control board is made up of voltage followers, a 48 MHz microcontroller (STM32F051xx from STMicroelectronics), and driver ICs. The main parameters that correspond to the circuit in Figure 1 are shown in Table I.
Fig. 9.Photograph of the 60 V/15 A prototype.
TABLE IPARAMETERS OF THE PSFB CONVERTER
In a regular PSFB converter without asymmetric control under 310 VDC input and 59 V/15 A output condition, waveforms of the primary side current and cathode voltage of output rectifiers are tested, as shown in Fig. 10(a).
Fig. 10.Test waveforms of VK and IP (test condition: 310 V input, 60 V/15 A output): khaki, VK (100 V/div); brown, abs(IP) (10 A/div); green, IP (10 A/div); time, 10 μs/div: (a) Basic PSFB converter without asymmetric control, (b) SFB converter with the proposed control method.
Given that the peak value of the primary side current in waveforms has alternating signs, the green line is difficult to detect. Thus, a square–square root mathematical (absolute value, abs) calculation is executed to shift the negative to positive, shown as the brown line in Fig. 10(a). The difference between two adjacent cycles is measured as 2 A according to the red auxiliary lines, which indicates that magnetic offset is sufficiently significant to affect the reliability of power devices.
Fig. 10(b) shows the experimental results when the proposed method is utilized by a conventional PSFB converter. Waveforms are tested under the condition of 310 V input and 59 V/15 A output. The test results are equal to the prototype under symmetrical control technique and higher than the converter with blocking capacitance.
In Fig. 10(b), the primary side current is also processed to a nonnegative range, shown as a brown line. A red auxiliary line is drawn in Fig. 10(b), where the peak value of abs(IP) is approximately equal to the adjacent cycle, which indicates that the imbalance of the magnetic core is effectively suppressed.
In addition, other indices should be tested to verify the proposed method. Efficiency under different load currents is tested. Fig. 11 shows that efficiency is higher in the proposed method than that in the PCM in the load range of 30–100%. The peak value of efficiency in the proposed method is 93.2%, which is 0.2% higher than that in the PCM solution.
Fig. 11.Efficiency comparison of PCM and the proposed method (test condition: 310 V input, 60 V/1–15 A output).
Moreover, the suppression effect of the two methods is compared to prove the effectiveness of our method. Notably, the proposed method does not reduce the imbalance of the transformer core in a single period. The purpose of the proposed method is to regulate the direction of the imbalance, such that the average peak current on the primary side is zero for a long period of time. Table 2 shows the comparison between PCM and the proposed method. The experimental results prove that the effect of our method is not as good as that in PCM, although the proposed method achieves the objective of imbalance suppression for the entire operation procedure.
TABLE IISUPPRESSION EFFECT COMPARISON BETWEEN PCM AND THE PROPOSED METHOD
According to these experimental results, the proposed method is proven to be effective in suppressing the imbalance of the transformer core, and its efficiency is slightly higher than that in the PCM solution.
Light to heavy load variation is also tested; the waveforms of VK and primary side current are shown in Fig. 12. Transient cost is approximately 30 ms. The time cost is reasonable given the large output capacitance.
Fig. 12.Load variation from 6 A to 15 A (test condition: 310 V input, 60 V/6–15 A output).
According to the low-clock frequency of the selected microcontroller, regulation accuracy is insufficient to reduce the imbalance of the transformer core completely; however, the proposed method can maintain a relatively limited imbalance state. The imbalance direction is controlled to invert every switching cycle in steady state, such that the range of imbalance is limited. The possibility of power device failure is reduced in the PSFB converter because of the limited range. Furthermore, only several external passive devices are introduced compared with the conventional solution, which indicates that the proposed method hardly affects the efficiency of the PSFB converter.
V. CONCLUSION
A high-efficiency and low-cost solution is proposed to suppress transformer core imbalance in PSFB converters. Compared with the common methods, the proposed solution creates an asymmetric control algorithm, which does not accurately balance the transformer core. An approximate control consideration is achieved by a microcontroller, which generates unequal phases in the subsequent cycle according to the imbalance state in the current cycle. The proposed solution is verified by a 60 V/15 A prototype. Experimental results show that the goal of a balanced transformer core can be achieved. The efficiency of the proposed method is slightly higher than that of the PCM, and the performances of other methods are also tested and compared.
참고문헌
- Y.-C. Hsieh and C.-S. Huang, “Li-ion battery charger based on digitally controlled phase-shifted full-bridge converter,” IET Power Electron., Vol. 4, No. 2, pp. 242-247, Feb. 2011. https://doi.org/10.1049/iet-pel.2009.0206
- H. Bai, Y. Zhang, C. Semanson, C. Luo, and C. C. Mi, “Modelling, design and optimisation of a battery charger for plug-in hybrid electric vehicles,” IET Electrical Systems in Transportation, Vol. 1, No. 1, pp. 3-10, Mar. 2011. https://doi.org/10.1049/iet-est.2010.0038
- T. Mishima, K. Akamatsu, and M. Nakaoka, “A high frequency-link secondary-side phase-shifted full-range soft-switching PWM DC–DC converter with ZCS active rectifier for EV battery chargers,” IEEE Trans. Power Electron., Vol. 28, No. 12, pp. 5758-5773, Dec. 2013. https://doi.org/10.1109/TPEL.2013.2258040
- B. Gu, J.-S. Lai, N. Kees, and C. Zheng, “Hybrid-switching full-bridge DC–DC converter with minimal voltage stress of bridge rectifier, reduced circulating losses, and filter requirement for electric vehicle battery chargers,” IEEE Trans. Power Electron., Vol. 28, No. 3, pp. 1132-1144, Mar. 2013. https://doi.org/10.1109/TPEL.2012.2210565
- X. Zhou, D. Chen, and C. Jamerson, "Leading-edge modulation voltage-mode control with flux unbalance correction for push-pull converter," in 15th Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Vol. 1, pp. 327-333, 2000.
- W. Eberle and Y.-F. Liu, "A zero voltage switching asymmetrical half-bridge DC/DC converter with unbalanced secondary windings for improved bandwidth," in IEEE 33rd Annual Power Electronics Specialists Conference(PESC), Vol. 4, pp. 1829-1834, 2002.
- J. Kim, H.-S. Song, and K. Nam, “Asymmetric duty control of a dual-half-bridge DC/DC converter for single-phase distributed generators,” IEEE Trans. Power Electron., Vol. 26, No. 3, pp. 973-982, Mar. 2011. https://doi.org/10.1109/TPEL.2010.2070877
- B. A. Gusev, V. I. Meleshin, and D. A. Ovchinnikov, "Transformer core unbalancing issue in a full-bridge DC-DC converter with current doubler rectifier," in International Conference on Power Electronics, Drives and Energy Systems, pp. 1-6, Dec. 2006.
- J. A. Claassens and I. W. Hofsajer, "A flux balancer for phase shift ZVS DC-DC converters under transient conditions," in 21st Annual IEEE Applied Power Electronics Conference and Exposition, Mar. 2006.
- J.-H. Cho, K.-B. Park, J.-S. Park, G.-W. Moon, and M.-J. Youn, “Design of a digital offset compensator eliminating transformer magnetizing current offset of a phase-shift full-bridge converter,” IEEE Trans. Power Electron., Vol. 27, No. 1, pp. 331-341, Jan. 2012. https://doi.org/10.1109/TPEL.2011.2158115
- G. R. Zhu, D. H. Zhang, W. Chen, and F. Luo, "Modeling and analysis of a rectifier voltage stress mechanism in PSFB converter," in 27th Annual IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 857-862, Feb. 2012.
피인용 문헌
- Current-Sensorless Power-Decoupling Phase-Shift Dual-Half-Bridge Converter for DC–AC Power Conversion Systems Without Electrolytic Capacitor vol.32, pp.5, 2017, https://doi.org/10.1109/TPEL.2016.2587813