Sensor-Reduced Active Power Decoupling Method for Single-Phase Rectifiers

Abstract

Active power decoupling (APD) technology demonstrates significant advantages in addressing the mismatched second-order ripple power issue in single-phase rectifiers. However, conventional methods typically require additional voltage or current sensors to achieve precise decoupling control, thereby increasing the cost of the decoupling circuit. To reduce costs and simplify the control system, a sensor-reduced decoupling control method is proposed, with its key advantages highlighted in three aspects: First, the proposed method operates by replacing actual sampled variables with designed reference values, reducing the number of sensors—only the DC bus voltage information is required for operation. Second, the sensor-reduced control scheme is designed based on Lyapunov stability conditions and ensures system stability. Third, virtual impedance produces the reference current of the decoupling circuit, which eliminates grid signal interaction and simplifies control. Simulation and experimental results validate the effectiveness and feasibility of the proposed method.

1. Introduction

The single-phase rectifier is one of the most commonly used power electronic devices, with extensive applications in industrial, commercial, and residential fields [1,2,3]. However, there is an inherent second-order ripple power mismatch between the AC and DC sides of the single-phase rectifier. This ripple power leads to many adverse effects. For example, in applications such as LED lighting drivers and photovoltaic inverters, the ripple power may lead to fluctuations in the DC-side voltage/current, resulting in low-frequency flickering in LEDs [4] or reducing the Maximum Power Point Tracking (MPPT) efficiency of photovoltaic panels [5]. To address the ripple power issue, large electrolytic capacitors are typically used to absorb pulsating power (passive power decoupling), but they increase the system volume and reduce reliability [6,7]. As an alternative solution, Active Power Decoupling (APD) has gained widespread attention from researchers and engineers in recent years [8,9]. APD circuits use small capacitors with large voltage fluctuations to buffer second-order ripple power, greatly reducing electrolytic capacitor requirements.

Although APD technology demonstrates significant advantages in addressing the mismatched second-order pulsating power in single-phase rectifiers, it also introduces new challenges. For instance, the implementation of APD typically requires additional voltage/current sensors. This is because the decoupling circuit increases the system order, requiring additional state variable measurements for control. For example, Reference [10] employed a total of six sensors to realize its designed feedback linearization-based decoupling control method. However, the excessive use of sensors conflicts with key technical metrics such as power density, cost efficiency, and system reliability [8,9]. An increased number of sensors raises the system volume and economic costs, making their extensive use impractical for applications with stringent cost and space constraints, such as LED lighting [11]. Moreover, under non-ideal operating conditions and harsh environments (e.g., high temperature, humidity, and mechanical vibration), the reliability of sensing devices may degrade.

Recently, research on APD control with a reduced sensor count has attracted scholars’ attention. Current sensor reduction decoupling control methods are primarily divided into two categories: observer-based approaches and nonlinear controller design methods. The observer-based method employs observers to estimate variables requiring sampling and utilizes the results for feedback control. The literature [12,13,14,15] analyzes voltage sensor-reduced control methods based on algebraic observers, which transform the state-space average model into a series of observers to estimate the decoupling capacitor voltage. In addition to algebraic observers, the literature [16] proposes a voltage sensor-reduced Multiple Model Predictive Control (MMPC) method for Buck-type decoupling circuits. This method achieves the sensor-reduced prediction of decoupling voltage by reconstructing the dynamic model based on Euler approximation. However, these observer algorithms suffer from noise sensitivity and computational complexity, and they do not fundamentally eliminate the control strategy’s dependence on decoupling capacitor voltage information. Unlike observer-based methods, the nonlinear controller design approach for sensor reduction does not require decoupling capacitor voltage feedback in the control process. The literature [17,18] proposes an optimized modulation strategy that eliminates the need for prior decoupling capacitor voltage information, using ideal voltage reference values as modulation signals to achieve sensor reductions. However, this method requires Linear Matrix Inequality (LMI) to calculate the relevant control parameters when generating voltage reference signals and relies on complex H∞ theory to prove system stability, thereby increasing the system’s computation and application complexity. The literature [19,20] predicts the decoupling capacitor energy and voltage based on energy relationships to realize sensor-reduced control, but it requires two error correctors to compensate for both control accuracy and parameter robustness.

However, all the aforementioned sensor reduction decoupling control methods require interaction with the rectifier to obtain the grid-side voltage, current, and phase angle information, inevitably necessitating a centralized controller and higher-cost, real-time communication technologies. In this study, a Lyapunov equation-based APD control method is proposed. This method ensures stability while eliminating grid-side information dependence. Consequently, it achieves APD control with minimal sensors.

The structure of this paper is organized as follows: Section 2 proposes a sensor-reduced decoupling control strategy based on the Lyapunov equation; Section 3 designs the current reference signal reduction scheme using a virtual impedance approach; Section 4 validates the effectiveness of the proposed method through simulations and experiments; and Section 5 provides a concluding summary of the entire study.

2. Sensor-Reduced Control Strategy Based on Lyapunov Equation

This section analyses and proposes a Lyapunov equation-based sensor-reduced decoupling control strategy. First, the working principle of the Buck-type decoupling circuit is introduced. Then, the designed reference signals are utilized to replace the original sensor measurements, thereby achieving sensor reductions. Based on Lyapunov stability theory, the required conditions for the designed signals are derived, with system stability being rigorously proven.

2.1. Operating Principle of Buck-Type Decoupling Circuit

Figure 1 illustrates a single-phase voltage-source rectifier with a parallel Buck-type decoupling circuit, where the Buck-based decoupling unit, consisting primarily of the decoupling inductor L_d, decoupling capacitor C_d, and switching devices S₅/S₆, is connected in parallel to the DC bus as an independent decoupling module.

During operation, this single-phase rectifier exhibits an inherent second-order ripple power mismatch between its input and output ports. Assuming a sinusoidal AC-side grid voltage v_ac and in-phase current i_ac, the expressions are as follows:

$$\begin{array}{l}{v}_{ac}(t)=\sqrt{2}{V}_{ac}\sin (\omega t)\\ i_{ac}(t)=\sqrt{2}{I}_{ac}\sin (\omega t)\end{array}$$

(1)

where V_ac and I_ac are the root-mean-square values of the grid voltage v_ac and input current i_ac, respectively, and ω is the grid angular frequency.

According to the instantaneous power calculation method, the AC-side power is the product of the instantaneous voltage and current, given by the following:

$$p_{ac}(t)=V_{ac}{I}_{ac}-V_{ac}{I}_{ac}\cos (2\omega t)$$

(2)

Equation (2) shows that p_ac(t) consists of two components: a constant term P_ac and a term related to cos(2ωt). The cos(2ωt) term represents a second-order grid frequency component, whose amplitude is equal to the average power. This implies that, in addition to the DC power delivered to the load, there exists an AC-side ripple power oscillating at twice the grid frequency. This ripple power cannot be directly utilized in the circuit and is inherently determined by the characteristics of single-phase rectifiers. It will not disappear regardless of the topology or control strategy employed. The expression is given by the following:

$$p_{rip}(t)=-V_{ac}{I}_{ac}\cos (2\omega t)$$

(3)

From the perspective of active filtering, the second-order ripple power induces low-frequency voltage/current components in the main circuit. By controlling the decoupling circuit to generate the corresponding compensating voltage/current, these low-frequency components can be cancelled, thereby maintaining a constant DC voltage/current. Therefore, under steady-state conditions, to prevent harmonic currents from flowing into the load, the decoupling circuit must counteract these harmonics. Accordingly, the reference current for the decoupling port i_href should be as follows:

$$i_{href}=-{\displaystyle \frac{V_{ac}{I}_{ac}}{2v_{dc}}}\cos (2\omega t+\phi )$$

(4)

To generate the port current reference, the Buck-type decoupling circuit operates in two distinct modes: the step-down mode is defined as when ripple power is absorbed (where secondary ripple energy flows from the DC bus to the decoupling capacitor with the bus voltage exceeding the capacitor voltage), during which S₅ operates at high frequency while S₆ remains off; conversely, the step-up mode occurs when releasing ripple power (with second-order ripple energy transferring from the decoupling capacitor to the DC bus while maintaining the bus voltage higher than the capacitor voltage), where S₆ performs high-frequency switching while S₅ stays inactive. Figure 2 shows the switching signals and waveforms of i_d and i_h in both modes.

During step-down operation, the average value of i_d per switching cycle derived from the state-space averaging model is as follows:

$${\overline{i}}_d={\displaystyle \frac{d_5^2{v}_{dc}(v_{dc}-v_d)}{\tau v_d}}$$

(5)

where τ = 2L_d/T_sw.

After obtaining the average current value, the dynamic equations for the capacitor voltage v_d and current i_h flowing into the decoupling unit are derived, establishing the mathematical model of the Buck-type decoupling circuit in step-down mode as follows:

$$\left\{\begin{array}{l}{\dot{v}}_d={\displaystyle \frac{d_5^2{v}_{dc}(v_{dc}-v_d)}{\tau C_d{v}_d}}\\ {\overline{i}}_h={\displaystyle \frac{d_5^2(v_{dc}-v_d)}{\tau }}\end{array}\right.$$

(6)

Similarly, the mathematical model of the Buck-type decoupling circuit operating in step-up mode is derived as follows:

$$\left\{\begin{array}{l}{\dot{v}}_d=-{\displaystyle \frac{d_6^2{v}_{dc}{v}_d}{\tau C_d(v_{dc}-v_d)}}\\ {\overline{i}}_h=-{\displaystyle \frac{d_6^2{v}_d^2}{\tau (v_{dc}-v_d)}}\end{array}\right.$$

(7)

2.2. Stability-Conscious Sensor-Reduced Control Strategy Design

According to the Lyapunov stability theorem [17,18,19], system stability can be determined by analyzing a scalar energy function (commonly referred to as the Lyapunov function V(x)). Lyapunov’s direct method states that the equilibrium point is globally asymptotically stable when V(x) meets the following conditions:

(a)

V(0) = 0;

(b)

V(x) > 0, x ≠ 0;

(c)

V(x) → ∞, ||x|| → ∞;

(d)

$\dot{V}(x)<0$, x ≠ 0.

For the system under study, the following positive definite Lyapunov function is considered:

$$V(e)=0.5C_d{e}^2$$

(8)

where e = v_d – v_dref, with v_dref being a specified target reference whose concrete design form will be derived in the subsequent sections. Clearly, V(e) satisfies conditions (a)–(c). To ensure that condition (d) is satisfied, the derivative of Equation (8) is analyzed:

$$\dot{V}(e)=C_d(v_d-v_{dref})({\dot{v}}_d-{\dot{v}}_{dref})=C_{d}e\dot{e}$$

(9)

If the condition is satisfied $\dot{e}e<0$, then $\dot{V}(e)<0$. To achieve this objective, by substituting the Buck-type decoupling circuit model into the derivative expression, the following expression is obtained for step-down operation:

$$C_d\dot{e}=C_d({\dot{v}}_d-{\dot{v}}_{dref})={\displaystyle \frac{d_5^2{v}_{dc}(v_{dc}-v_d)}{\tau v_d}}-C_d{\dot{v}}_{dref}$$

(10)

Since d₅ serves as the control input with design degrees of freedom, it can be configured as required. In conventional control strategies, based on the system model in Equation (6), the steady-state value of d₅ in step-down operation satisfies the following:

$$d_5^2={\displaystyle \frac{\tau i_{href}}{v_{dc}-v_d}}$$

(11)

To eliminate the voltage sensor for v_d and achieve stable decoupling control under a condition where v_d is unknown, the control law in Equation (11) is referenced, where the expression of v_d is replaced with the given signal v_dref, yielding the following:

$$d_5^2={\displaystyle \frac{\tau i_{href}}{v_{dc}-v_{dref}}}$$

(12)

To analyze system stability under this control law, Equation (12) is substituted into Equation (10) (see Appendix A), yielding the following:

$$C_d\dot{e}=v_{dc}{\displaystyle \frac{i_{href}{v}_{dc}-C_d{\dot{v}}_{dref}{v}_d}{v_d(v_{dc}-v_{dref})}}+{\displaystyle \frac{i_{href}{v}_{dc}-C_d{\dot{v}}_{dref}{v}_{dref}}{v_{dc}-v_{dref}}}$$

(13)

Equation (13) determines the system’s stability at the equilibrium point. If condition d is satisfied in Equation (13), this control law achieves stable decoupling control without requiring v_d measurement. Condition d can be reformulated as $\dot{e}e<0$, where the proper design of the relationship between v_dref and i_href must satisfy this requirement. To facilitate the elimination of the second term in Equation (13), the reference voltage v_dref is designed to fulfil the following:

$$C_d{\dot{v}}_{dref}{v}_{dref}=i_{href}{v}_{dc}$$

(14)

Substituting into (13) yields the following:

$$C_d\dot{e}=v_{dc}{\displaystyle \frac{i_{href}{v}_{dc}-i_{href}{v}_{dc}{v}_d/v_{dref}}{v_d(v_{dc}-v_{dref})}}=-\alpha e$$

(15)

where $\alpha ={\displaystyle \frac{i_{href}{v}_{dc}^2}{v_d{v}_{dref}(v_{dc}-v_{dref})}}>0$.

The topology of the Buck-type decoupling circuit inherently ensures that the actual decoupling capacitor voltage v_d cannot exceed the DC bus voltage v_dc. Consequently, the feasible range for v_dref is strictly bound between 0 and v_dc. Furthermore, in step-down operation, i_href remains consistently positive (as dictated by the modulation strategy). This guarantees that α will be a positive quantity, thereby satisfying condition (c). Thus, in the step-down mode, the decoupling capacitor voltage v_d will asymptotically converge to its prescribed reference value v_dref.

Considering the step-up operation mode of the decoupling circuit, which is analogous to the step-down mode, the actual voltage v_d is similarly replaced with its reference signal v_dref and the duty ratio is designed as follows:

$$d_6^2=-{\displaystyle \frac{\tau i_{href}(v_{dc}-v_{dref})}{v_{dref}^2}}$$

(16)

Similar to the step-down analysis, step-up mode meets these conditions under control law (16) and reference (14):

$$C_d\dot{e}=C_d({\dot{v}}_d-{\dot{v}}_{dref})=-{\displaystyle \frac{d_6^2{v}_{dc}{v}_d}{\tau (v_{dc}-v_d)}}-C_d{\dot{v}}_{dref}=-{\alpha }^{\prime }e$$

(17)

where ${\alpha }^{\prime }={\displaystyle \frac{-i_{href}{v}_{dc}^2}{v_{dref}^2(v_{dc}-v_d)}}>0$.

In step-up operation, i_href remains consistently negative (as determined by the modulation strategy). Consequently, α′ is guaranteed to be positive, thereby satisfying condition (d). Thus, the decoupling capacitor voltage v_d asymptotically converges to its prescribed reference v_dref in step-up mode.

At this stage, the design of the decoupling voltage reference signal in (14) ensures system stability under the control laws specified in (12) and (16). This achieves the autonomous convergence of the decoupling capacitor voltage v_d, while reducing the number of internal variable samplings required for decoupling control.

3. Current Reference Design and Control System Implementation

This chapter specifically designs the current references for sensor-reduced control based on Lyapunov equations. First, the decoupling module port current reference i_href is obtained using the virtual impedance method. Building on this, the decoupling voltage reference signal v_dref required for sensor-reduced control is further refined. Ultimately, the implemented control system achieves complete independence from the AC-side information exchange with the rectifier, accomplishing the goal of minimal sensor deployment.

3.1. Virtual Impedance-Based Reference Current Design Methodology

Virtual impedance generates current references by emulating an LC resonant circuit at 2ω_g. This creates a low-impedance path for second-order ripple current, diverting it from the load.

As shown in Figure 3, the equivalent admittance of the passive LC resonant circuit is as follows:

$$G=j\omega C||j\omega L={\displaystyle \frac{j\omega C}{1-{\omega }^{2}LC}}$$

(18)

where L and C represent the inductance and capacitance values of the passive resonant circuit, respectively, and the resonant frequency satisfies ${\omega }_r=2\pi \sqrt{LC}$.

When ω = 0, then G = 0, indicating that the resonant circuit behaves as an open circuit to the DC component in i_r. When ω = 2ω_g, the equivalent admittance G approaches infinity, demonstrating that the circuit acts as a short circuit to the second-order component in i_r, thereby bypassing the second-order ripple current through the resonant path.

The control objective of the decoupling circuit is to ensure that the port output characteristics match those of the resonant circuit, thereby achieving an equivalent effect to the resonant circuit. Initially, based on the differential equation relationship between the port voltage and current of the resonant circuit, the transfer function relationship between the input current of the decoupling circuit port and the bus voltage can be derived:

$$i_h(s)={\displaystyle \frac{s/L}{s^2+1/(LC)}}{v}_{dc}(s)$$

(19)

Based on this, the port characteristics can be emulated. In Figure 3b, the reference current for the decoupling module port should be as follows:

$$i_{href}(s)={\displaystyle \frac{k_{r}s}{s^2+{\omega }_r^2}}{v}_{dc}(s)$$

(20)

where the resonant gain k_r = 1/L and the resonant angular frequency ω_r = 2ω_g. From Equation (20), it can be observed that the decoupling current reference based on the virtual impedance method requires only the DC bus voltage v_dc as external information. The decoupling unit no longer reuses the rectifier’s information and eliminates the need for a centralized controller, which is an advantage of this method.

3.2. Overall Structure of Sensor-Reduced Control

According to the virtual impedance strategy, the reference signal i_href should be selected as follows:

$$i_{href}={\displaystyle \frac{k_{r}s}{s^2+{\omega }_r^2}}{v}_{dc}$$

(21)

To determine v_dref, substitute the known expression from Equation (21) into Equation (14), which gives the following:

$$v_{dref}={\displaystyle \frac{1}{C_d}}\sqrt{V_{d0}+{\displaystyle \int i_{href}{v}_{dc}dt}}$$

(22)

where $V_{d0}$ is an initial voltage integration constant.

In summary, the system control block diagram is shown in Figure 4. The rectifier adopts a classic dual-loop voltage–current control strategy to regulate the input current and maintain the average output voltage. The decoupling control uses open-loop virtual impedance to calculate the port current reference. It calculates the duty cycles using the reference voltage v_dref for stable decoupling. The control diagram reveals that neither the actual decoupling inductor current i_d nor the decoupling capacitor voltage v_d requires sampling. Moreover, the decoupling control operates without information exchange with the AC grid side of the rectifier. The entire decoupling control system only needs the DC bus voltage information, realizing decoupling control with the minimum number of sensors.

4. Qualitative and Quantitative Assessments

To verify the effectiveness of the proposed control strategy, a qualitative comparative analysis table, along with simulation and experimental platforms, was constructed. The overall control block diagram is shown in Figure 4, where the rectifier adopts a classic voltage outer-loop and current inner-loop control scheme, with the voltage outer-loop regulating the average DC bus voltage as the reference to achieve average power control. The decoupling circuit employs the proposed sensor-reduced control strategy, with the following key controller parameters: ω_r = 100, k_r = 50, α = 5 × 10⁻⁷.

4.1. Qualitative Comparative Analysis

The traditional capacitor decoupling and sensor-reduced decoupling control methods are selected for comparison with the proposed method in this paper. A characteristic comparison table is established in

Table 1. The qualitative comparison of different methods.

Comparison Aspect	Capacitor Decoupling [6,7]	APD Method in [12,13,14,15]	APD Method in [16]	Proposed Method
Decoupling Principle	Passive filtering via large capacitors	Algebraic observer-based control	Voltage-sensorless modulated model predictive control	Lyapunov-based and virtual impedance control
Sensors	None	3 Sensors	1 Sensor	1 Sensor
Reliability	Low	Medium	High	High
Complexity	Low	Medium	High	Medium
Volume	Large	Medium	Small	Small
DC Bus Ripple	>5%	<5%	<5%	<5%
Power Factor	0.9~0.95	>0.98	>0.98	>0.98
THD	10%~15%	<3%	<2%	<3%

.

Through qualitative comparisons, it can be seen that the proposed method has advantages in the number of sensors, resulting in fewer fault points and higher reliability. On the other hand, the proposed method is simple to implement, requiring less parameter tuning and lower complexity.

4.2. Simulation Verification and Analysis

First, a simulation model of the single-phase PWM rectifier with a parallel Buck-type decoupling circuit (shown in Figure 1) was built in the MATLAB/Simulink platform. The Buck-type decoupling unit under the control scheme illustrated in Figure 4 was then verified through a simulation, with the circuit parameters specified in

Table 2. Parameters of main circuit and control system.

Parameter	Symbol	Value
Grid voltage	vac	110 VRMS
Grid frequency	fg	50 Hz
Output power	Pdc	600 W
DC bus voltage	Vdc	300 V
DC-link capacitor	Cdc	20 μF
Decoupling capacitor	Cd	90 μF
Decoupling inductor	Ld	0.5 mH
Switching frequency	fsw	20 kHz
Proportional gain of PI1	Kp1	0.8
Integral gain of PI1	Ki1	1.5
Proportional gain of PI2	Kp2	5
Integral gain of PI2	Ki2	8

.

Figure 5 presents the steady-state waveforms under the proposed control: DC bus voltage v_dc, decoupling capacitor voltage v_d, grid-side voltage v_ac, and grid-side current i_ac. As can be seen from the figure, the grid-side current i_ac is a sinusoidal wave in phase with the grid voltage, with a power factor (PF) = 0.99 and total harmonic distortion (THD) = 1.6%. Meanwhile, the bus voltage exhibits minimal fluctuations with a ripple ratio of 2.8%, meeting the IEC 61000-3-2 standard [21]. On the other hand, the decoupling capacitor voltage fluctuates at twice the grid frequency (100 Hz), with its average value stabilized at 170 V. These results verify that the proposed sensor-reduced decoupling control scheme achieves equivalent performance to conventional decoupling control methods [22] without requiring decoupling capacitor voltage sensor sampling, demonstrating both efficient and stable operation of the decoupling unit.

FFT spectral analysis was performed on the steady-state DC bus voltage waveform, yielding the voltage spectrum shown in Figure 6. The results indicate that the second-harmonic component in the DC bus voltage is merely 0.01%, demonstrating the proposed control strategy’s excellent steady-state decoupling performance.

4.3. Experimental Verification and Analysis

Building upon the simulation verification, experimental validation was conducted using the test platform shown in Figure 7.

The experimental waveforms are shown in Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12, with Figure 8 displaying the overall operational waveforms of the system, including the decoupling capacitor voltage v_d, DC bus voltage v_dc, input voltage v_ac, and input current i_ac in sequence. The system incorporates a soft-start function to prevent current overshoot during startup, implemented by fixing the duty cycle d₅ at a constant value of 0.05 to achieve a gradual voltage ramp-up. When the control program’s interrupt counter reaches 8000 (equivalent to 40 ms), the decoupling capacitor voltage charges to approximately 150 V, after which the system enters its normal operation mode with the decoupling circuit buffering the second-order ripple power. Subsequently, the decoupling circuit is disconnected, allowing the bus voltage to resume its ripple characteristics.

Figure 9 presents the key waveforms before and after shutdown to visually demonstrate the decoupling control performance. The results show that during normal operation of the decoupling circuit, the capacitor voltage v_d exhibits a 100 V peak-to-peak ripple with a 170 V average value, confirming the decoupling capacitor’s effectiveness in smoothing voltage fluctuations and ensuring a stable DC output. The output voltage is precisely regulated at 300 V with minimal fluctuations (Δv_dc ≈ 3.3%V_dc). The measured input current characteristics reveal the THD of 2.9% and the PF of 0.99, fully complying with the IEC 61000-3-2 Class standards. These results demonstrate that the system meets International Electrotechnical Commission requirements and can operate safely and reliably in various applications.

Figure 10 displays the internal variable waveforms of the decoupling circuit, including the decoupling capacitor voltage v_d and decoupling inductor current i_d. The results clearly show the inductor operating in its discontinuous conduction mode (DCM), with the inductor current exhibiting second-order grid frequency ripple characteristics, which aligns perfectly with the theoretical analysis presented in Figure 2.

Figure 11 and Figure 12 document the output voltage reference tracking test results, designed to evaluate the system’s dynamic response to reference voltage variations. The experiment toggled the output voltage reference between 300 V and 250 V to monitor the behavior of both the decoupling capacitor voltage reference v_dref and its actual value v_d. When increasing the output voltage from 250 V to 300 V, the v_dref calculated through the control strategy in Equation (22) displayed an increased fluctuation range. Conversely, decreasing the output voltage from 300 V to 250 V resulted in opposite variation characteristics for v_dref. Notably, v_d stably tracked v_dref during transitions, showing that the control strategy has good tracking performance.

5. Conclusions

This work proposes a sensor-reduced control strategy based on Lyapunov theory. By replacing actual voltage sampling with designed references, it minimizes sensors while guaranteeing stability. Simultaneously, a virtual impedance-based method is adopted to derive the reference current signal required for the sensor-reduced control at the decoupling port, eliminating the information exchange process between the decoupling control and the AC grid side of the rectifier. Ultimately, the entire control system requires only the DC bus voltage as the sole information input, realizing decoupling control with a minimal sensor configuration.

The experimental results show the following: (1) The decoupling unit effectively suppresses the DC bus voltage ripple to within 3.3% (Δv_dc ≈ 3.3% of V_dc = 300 V) below the 5% threshold; (2) Only the DC bus voltage sensor is required, achieving minimal sensor control; (3) When the output voltage references toggle between 250 V and 300 V, the decoupling capacitor voltage v_d stably tracks the reference v_dref; (4) The rectifier achieves a power factor (PF) of 0.99 and a total harmonic distortion (THD) of 2.9%, complying with IEC performance standards.