Virtual Admittance Feedforward Compensation and Phase Correction for Average-Current-Mode-Controlled Totem-Pole PFC Converters

Featured Application: This paper proposes virtual admittance feedforward compensation and phase correction for average-current-mode-controlled totem-pole PFC converters. It can effectively reduce total harmonic distortion (THD) and improve the power factor (PF) of the converter. The proposed control strategy can be directly used in on-board chargers (OBCs) for electric vehicles, power supplies for server clusters, communication equipment, industrial equipment, etc. Abstract: This paper explores a current distortion problem in totem-pole bridgeless power factor correction (PFC) converters with average current mode (ACM) control. With in-depth modeling for the current and voltage loops, it was found that the current distortion is caused by the limited current loop bandwidth and input ﬁlter capacitor. These factors lead to the presence of a susceptance component in the input admittance, which degrades the power factor (PF) and total harmonic distortion (THD) of the PFC converter. To solve this problem, this paper proposes virtual admittance feedforward compensation (VAFC) and phase correction methods to adjust the input admittance to pure conductance. The VAFC can generate virtual admittance that compensates for susceptance components in the input admittance, while phase correction can generate an equivalent current source that offsets the current in input capacitors. Furthermore, a phase lock loop (PLL) is introduced to realize the VAFC, which reduces the feedforward interference caused by input voltage sampling noise. Finally, an experimental prototype was built to verify the effectiveness of the proposed strategies. According to the test results, the proposed compensation strategy improves the PF by 1.23%, while reducing the THD by 2.52% and achieving a peak efﬁciency of 98.69%.


Introduction
AC-DC power converters are widely used in industry, communication, medical treatment, and consumer electronics. When their power exceeds 75 W, power factor correction (PFC) is necessary in power electronic equipment; otherwise, the equipment will inject harmonic current into the power grid and degrade the power quality [1]. Boost PFC is the most widely used converter because of its small current pulsation and simple control [2][3][4]. However, the large conduction loss of the rectifier bridge in boosting PFC severely degrades power efficiency and induces serious electromagnetic interference (EMI) [5][6][7]. To solve these issues, extensive research has been carried out to explore PFC converter topologies [8][9][10]. Among various topologies, totem-pole bridgeless PFC is attractive owing to its advantages of high device utilization and low conduction loss [11][12][13]. To further improve power efficiency, SiC MOSFET currently tends to replace Si MOSFET in power converters [14][15][16]. However, these improvements bring new challenges to PFC converters and their control strategy.
Traditional average current mode (ACM) control is widely used in high-power applications owing to its advantages of fixed switching frequency and insensitivity to the inductor current sampling noise [17,18]. However, due to the limited current loop bandwidths under continuous conduction mode (CCM) and the influence of input filter capacitors, the input current and voltage have a non-neglectable phase difference, resulting in current distortion and efficiency degradation [19,20]. Additionally, with the phase difference, the PFC converter will operate in discontinuous conduction mode (DCM) near the input voltage zero-crossing point [21]. In this situation, the transfer function of the PFC converter would be different from that of the CCM, which further degrades the current-tracking ability. Moreover, the sampled input voltage is directly used to generate reference current. Thus, input voltage sampling noise and delay directly affect the performance of the current loop [22]. As the load decreases, the PFC converter current decreases and the current distortion becomes more serious [23].
To improve the current loop performance of power converters, feedforward compensation was used [24]. The sampled input voltage is directly used to generate the feedforward term, which induces the sampling noise to input current and degrades the power factor of the PFC converter. To reduce the feedforward interference caused by input voltage sampling noise, the input voltage is reconstructed by detecting its zero-crossing point and storing sinusoidal table in a DSP controller [25]. However, the output of the zero-crossing detection circuit contains multiple high-frequency pulses due to sampling noise, which is even worse under high output power. A voltage-senseless feedforward method is proposed, which calculates the feedforward duty cycle based on the input current [26]. But, it requires a voltage estimator to calculate the input voltage phase, which induces error in the estimation result during mode change and causes incorrect gate driving signals. Conventional feedforward methods cannot solve the problem caused by input voltage sampling noise and do not provide an in-depth theoretical analysis. Moreover, there are few studies in the literature examining the current distortion caused by input filter capacitors.
To solve the above issues, this paper proposes virtual admittance feedforward compensation (VAFC) and reference current phase correction for totem-pole PFC converters. With in-depth modeling for current and voltage loops, it was found that the limited current loop bandwidth and input filter capacitor cause a phase difference between input current and voltage. It leads to the presence of a susceptance component in the input admittance. Furthermore, VAFC and reference current phase correction are proposed to adjust the input admittance to pure conductance. The VAFC generates virtual admittance that compensates susceptance components in the input admittance, while phase correction generates an equivalent current source that offsets the current in input capacitors. A phase lock loop (PLL) is applied to realize the VAFC, to reduce the influence of input voltage sampling noise and delay. Experimental results demonstrated that the proposed method can further improve PF and reduce THD compared to conventional methods. The output voltage was processed using a notch filter to reduce the sampled voltage ripple, to improve the voltage loop bandwidth.
The rest of this paper is organized as follows. Section 2 presents the current-distortion problem in totem-pole bridgeless PFC converters. In Section 3, the virtual admittance feedforward compensation and reference current phase correction are proposed to adjust the input admittance to pure conductance. Section 4 presents the experimental results. Section 5 concludes this paper.

Current-Distortion Problem in Totem-Pole Bridgeless PFC Converter
A totem-pole bridgeless PFC converter is widely used in high-power applications owing to its high-power efficiency. The topology is shown in Figure 1, where L is the inductor, C o is the output capacitor, R is the load resistor, v in is the AC input voltage, and v o is the output voltage. SiC MOSFETs Q 1 and Q 2 are adopted as the main power switch, to reduce the switching losses. S 1 and S 2 are adopted to realize synchronous rectification, which further improves the power efficiency. The PF of the converter is calculated using where P is the active power and S is the apparent power. The total harmonic distortion is calculated using where I 1 represents the root mean square (RMS) value of the fundamental frequency component of the input current. I 2 , I 3 , . . ., I n represent the RMS values of the harmonic frequency components of the input current, from the second harmonic to the n th harmonic. Average current mode control is widely used in totem-pole PFC converters, owing to its advantages of fixed switching frequency and insensitivity to sampling noise. A control diagram of traditional average current control is shown in Figure 2. Due to the limitation of the current loop bandwidth and input filter capacitor, the phase of the inductor current will lead the input voltage, which degrades the PF and THD. The following provides a detailed theoretical analysis from the perspective of input admittance of the PFC converter.

Current Distortion Caused by Limited Current Loop Bandwidth
The response of the inner current loop directly determines the key performance of the PFC converter, including PF and THD. The inner current loop compares sampled average inductor current with a given sinusoidal reference. With the obtained current error, a PI compensator is adopted to calculate the duty ratio of the power switch. Then, the driving signal is generated according to the duty ratio. With the above principles, the inner current loop diagram is shown in Figure 3. where H i (s) is the transfer function of current sampling, G ci (s) is the transfer function of current loop compensator, G m (s) is the PWM modulation transfer function, G id (s) is the transfer function from duty ratio to inductor current, and 2 . Based on Figure 3, input admittance of the PFC converter is calculated as follows, to analyze the causes of the phase difference between input current and voltage. Based on Figure 3, input admittance of the PFC converter Y(s) is given by Note that since G m (s) = 1/v m , G iv (s) = 1/sL, and G id (s) = v o /sL, Equation (3) is simplified as Substituting the experimental parameters into (4)

Current Distortion Caused by Input Capacitor
Another factor that affects PF is the input filter capacitor. In PFC converters, the AC input needs an EMI filter to reduce the high-frequency switching harmonics of the inductor current. However, the input filter capacitor generates capacitive current, which leads the input voltage and degrades PF. As shown in Figure 5, the filter adopts a single-stage structure. In this figure, C 1 and C 2 are X capacitors, while C 3 and C 4 are Y capacitors. L 1 and L 2 are common-mode inductors, which have small leakage inductance. To simplify the analysis, the following assumptions are made. (a) The influence of Y capacitor is neglected since it is typically much smaller than X capacitor. (b) The equivalent input impedance of the PFC converter is R in . The input resistance R in is calculated with the magnitude of input voltage (v in, m ) and the magnitude of the input current (i in, m ), i.e., In this case, the phase difference caused by input capacitance is calculated using The vector of the total input current is shown in Figure 6. It shows that the input filter capacitor induces a phase difference between input current and voltage. As load power decreases, the phase difference would be even more serious, which severely degrades PF.

Virtual Admittance Feedforward Compensation and Phase Correction to Reduce Current Distortion
To reduce the phase difference between input current and voltage, this paper proposes VAFC and reference current phase correction. The basic idea is shown in Figure 7. With VAFC and phase correction, the input admittance is adjusted to pure conductance. As shown in this figure, the VAFC can generate virtual admittance that compensates Y 1 (s). The phase correction can generate an equivalent current source that offsets the current in the input capacitor.

Virtual Admittance Feedforward Compensation
With the analysis in Section 2, the input admittance shows the resistance-capacitance characteristic due to the limited current loop bandwidth. It makes the input current lead the input voltage, which degrades the power factor. To solve this problem and improve the power factor, this paper proposes VAFC to generate virtual admittance, which neutralizes the susceptance component and adjusts the input admittance as pure conductance. Figure 8 shows the current control loop diagram with VAFC. With the proposed compensation method, the input admittance of the PFC converter Y(s) is calculated as where the virtual admittance Y 3 (s) is given by With the input admittance analysis in Section 2.1, the leading phase of Y(s) is mainly caused by Y 1 (s). Therefore, by setting the susceptance component is neutralized. By solving (9), the transfer function of the feedforward compensator is given by Therefore, the feedforward term is calculated using With the proposed VAFC, the phase difference between input current and voltage is eliminated, and the input admittance of the PFC converter becomes pure conductance. Therefore, the PF and THD of the converter are improved.

Reference Current Phase Correction
With the analysis in Section 2.2, the input filter capacitor generates capacitive current, which degrades the power factor. To eliminate the influence of the input capacitor, the reference current phase should be lagged by ϕ, i.e., where θ is the phase of the input voltage. Therefore, the total input current is calculated using Since ϕ is usually small, the total input current i in,total is simplified as (14), where the input current phase error caused by the input capacitor is eliminated.

Overall Control Diagram
The overall block diagram of the proposed control strategy is shown in Figure 9. By realizing the proposed VAFC, the phase difference between input current and voltage caused by limited bandwidth of the current loop is reduced. The influence of the input capacitor is eliminated with the proposed reference current phase correction. Additionally, a phase lock loop is adopted in the controller, to reduce feedforward interference caused by input voltage sampling noise. A notch filter is adopted to filter line frequency ripple in output voltage sampling. Traditional average current control methods directly use the sampled input voltage to generate reference current, which is sensitive to the delay and disturbance of the sampling circuit. To solve this problem, PLL is adopted to process the sampled input voltage. It generates an ideal sine wave that is in phase with the input voltage. The structure of PLL based on the second-order generalized integral is shown in Figure 10. The principle of the second-order generalized integrator is shown in Figure 11. The second-order generalized integrator generates the signal v' in and the orthogonal signal qv' in , and the d-axis component v d and q-axis component v q are obtained with Park transformation. Then, the q-axis component v q is adjusted to v q * with the PI controller, to realize phase-locking. The output of PLL is an ideal sine wave that is in phase with the input voltage, which is used to generate a current loop reference and solve the problems caused by the delay and disturbance of the sampling circuit. Due to the sampling and calculation delay of the PLL system, the input phase of the Park transformation (θ) lags behind the real system, which induces an error in the Park transformation. However, given that the sampling and calculation frequency (20 kHz) is much higher than the frequency of the input signal (50 Hz), the relative error is small. Specifically, the sampling and calculation delay is 1/20 kHz = 50 µs, and the relative error is calculated as 50 µs/20 ms·100% = 0.25%.  A Saber/Simulink co-simulation model was built to verify the above theory. Figure 12a shows the simulation waveform without feedforward compensation when the input power is 600 W, while Figure 12b shows the simulation waveform with the proposed VAFC. In Figure 12a, the inductor current shows a phase difference where an input voltage and current distortion exists near the input voltage zero-crossing point. With the proposed VAFC, the phase difference and current distortion is almost eliminated and the input current tracking performance is significantly improved. The harmonic analysis results of the input current show that THD is reduced to 6.12%.

Hardware Design of the Totem-Pole Bridgeless PFC Converter
The overall structure of the totem-pole bridgeless PFC converter based on SiC devices is shown in Figure 13, which includes the main power topology, soft-start circuit, current and voltage sampling circuit, gate driving circuit, and controller. The main power topology consists of a PFC inductor, four power switches, and output bus capacitors. To ensure safety, the main power topology is electrically isolated from the control circuit. The main specifications of the totem-pole bridgeless PFC converter designed in this paper are shown in Table 1, where v in = 220 VAC, v o = 400 VDC, P o = 1600 W, and f s = 100 kHz. The SiC MOSFET is C3M0030090K from CREE, while the Si MOSFET is IPW65R045C7 from Infineon. The inductor is 350 µH, and the output capacitor is 7 × 160 µF. The controller is TMS320F280049 from Texas Instruments. A prototype of the totem-pole bridgeless PFC is shown in Figure 14. It contains a main power board and a control board. The size of the main power board is 20 cm × 10 cm, which includes an EMI filter, soft-start circuit, PFC inductor, SiC and Si switches, a gate driving circuit, and the high-voltage side of the sampling circuit. The size of the control board is 7 cm × 4 cm, which mainly includes the peripheral circuit of the digital controller and the low-voltage side of the sampling circuit.

Performance Test under Different Power Rates
The input voltage is supplied by an AC source IT7326, while the load resistor is realized with electronic load AN23606E-600-420. Waveforms of input voltage, input current, inductor current, and output voltage are measured with an oscilloscope MDO3024. PF, THD, and power efficiency are measured using a power analyzer PA5000H. The input voltage is 220 VAC. The load changes from 266 Ω to 100 Ω, where the output power changes from 600 W to 1600 W. According to the PA5000H data manual, the voltage, current, and power measurement error are shown in Table 2. In the proposed system, the input signal frequency is 50 Hz, and the output signal is direct current (DC). According to Table 2, the measurement error is within 0.05%. Additionally, to ensure the accuracy and credibility of the measurement result, the following steps are carried out. (1) Calibration and verification: regularly calibrate and verify the PA5000H analyzer according to manufacturer guidelines and industry standards. This helps minimize systematic errors and ensures accurate readings. (2) Measurement uncertainty analysis: perform a comprehensive measurement uncertainty analysis for our specific measurement setup. After the analysis, it was found that connecting the input current port to the source ground side can effectively reduce the measurement error. Waveforms and key performance of the PFC converter under different power rates are shown in Figure 15. The power efficiency is above 98.35% over the whole load range and achieves a peak efficiency of 98.69%. As the load power increases from 589 W to 1570 W, PF increases from 99.11% to 99.82% and THD decreases from 7.69% to 3.92%.

Waveform Comparisons with and without Feedforward Compensation
To further verify the effectiveness of the proposed control method, comparative experiments were carried out on the totem-pole bridgeless PFC prototype. The experimental results with direct input voltage feedforward are shown in Figure 16. It shows that the input current is superimposed with high-order harmonics under direct input voltage feed-forward, which is induced by sampling the noise of input voltage, whereas with PLL based feedforward, the sampling noises are almost eliminated as shown in Figures 17 and 18.   Waveforms of the input voltage, input current, inductor current, and output voltage with proposed control at P o = 784 W are shown in Figure 17. With the proposed VAFC, current distortion near the input voltage zero-crossing point is significantly reduced. PF is increased from 98.65% to 99.43%, while THD is reduced from 8.27% to 5.92%. Figure 18 shows the comparative experimental results at P o = 1570 W. Current distortion near the zero-crossing point is reduced, which improves the THD from 5.53% to 3.92% and improves the PF from 99.50% to 99.82%.
Correlations between input admittance and virtual admittance of the PFC converter at 50 Hz under different output power are shown in Figure 19. It shows that the proposed control method can generate virtual admittance to eliminate the imaginary part of the input admittance, achieving a pure conductance input characteristic. Thus, the PF and THD of the PFC converter can be improved. The input current harmonic analysis at P o = 784 W and P o = 1570 W are given in Figures 20a and 20b, respectively. The harmonic distortion of the input current mainly comes from odd harmonic currents. With the proposed VAFC, the odd current harmonic contents, including the third and fifth harmonics of the input current are reduced, which improves PF and reduced THD.  Figure 21 compares the PF and THD of the prototype with the proposed control method, with direct feedforward and without feedforward. In Figure 21a, PF of the prototype is improved via the proposed feedforward over the whole load range. At P o = 589 W, the PF with the proposed feedforward is 99.11%. Compared to direct feedforward, an improvement of 0.41% is obtained. Compared to the control method without feedforward, the PF is improved by 1.23%. At P o = 1570 W, the proposed method improves the PF from 99.50% to 99.82% compared to the control method without feedforward, and an improvement of 0.3% is achieved. In Figure 21b, the proposed method reduces the THD more than 1.61% compared to the method without feedforward. Compared to direct feedforward, the proposed method reduces the THD more than 0.37%. Because of the proposed reference current phase correction, the improvement in the PF is larger than that of THD.  Figure 22 shows an efficiency comparison of the prototype. The efficiency is improved at light load, where an improvement of 0.24% is achieved at P o = 589 W. The peak efficiency is 98.69% at about 1250 W, and the efficiency is 98.62% at rated power.

Conclusions
This paper proposes virtual admittance feedforward compensation (VAFC) and reference current phase correction to adjust the input admittance of the PFC converter to pure conductance. By thoroughly modeling the current loop and calculating input admittance of the PFC converter, it was found that the current distortion is caused by the limited bandwidth and input filter capacitor. With the proposed VAFC and input current phase correction, the input admittance is tuned as pure conductance, which improves PF and reduces THD. The VAFC is realized based on a phase lock loop, which avoids the interference induced by input voltage sampling noise. A SiC-based totem-pole PFC converter is built to verify the effectiveness of the proposed method. The proposed controller can generate a virtual admittance of 0-3.2 mS, which eliminates the imaginary part of the input admittance under various load power. Thus, the proposed control can achieve a pure conductance input characteristic. Under the proposed control, the phase of the input current is near 0, which improves the PF and THD of the converter.