Single-phase OBC double-frequency ripple suppression method based on series-parallel cooperative virtual impedance

Abstract

The present application relates to single-phase OBC system technical field, especially in kind of based on series-parallel collaborative virtual impedance's single-phase OBC double frequency ripple suppression method, including: S1, the small signal model of establishing bidirectional CLLC converter;S2, based on the small signal model of S1 establishment, constructs double closed loop control system;S3, in the input end of the voltage outer loop of the double closed loop control system of S2 construction, introduce series virtual impedance;S4, in the double closed loop control system after enhancement by S3, introduce parallel virtual admittance;S5, run the double closed loop control system after enhancement by S4, generate switching frequency modulation signal, control the power switch tube of bidirectional CLLC converter, to suppress the double frequency ripple current of battery side.This method can realize high impedance ripple suppression while maintaining good dynamic performance and stability margin of system without increasing additional hardware cost.

Description

Technical Field

[0001] This invention relates to the field of single-phase OBC system technology, and in particular to a method for suppressing second harmonic ripple in single-phase OBC based on series-parallel cooperative virtual impedance. Background Technology

[0002] In the field of electric vehicle charging technology, the single-phase on-board charger (OBC) is a key device connecting the power grid and the battery, and its performance directly affects charging efficiency and battery life. In a typical two-stage single-phase OBC architecture, the front-end power factor correction (PFC) circuit generates second-harmonic instantaneous power fluctuations, resulting in significant second-harmonic ripple in the DC bus voltage. This ripple component is coupled to the battery side via the subsequent bidirectional CLLC converter, causing a large second-harmonic ripple current component in the battery charging or discharging current. This not only exacerbates battery heating and accelerates aging but also interferes with the state assessment accuracy of the battery management system, seriously affecting the charging safety and battery life of electric vehicles.

[0003] To address the aforementioned second-harmonic ripple problem, existing technologies primarily employ the following suppression strategies: First, by adding an active power decoupling circuit on the DC bus side to absorb second-harmonic power fluctuations; second, by implementing compensation control from the pre-stage PFC terminal, adjusting the pre-stage output to suppress ripple generation. However, these methods often require additional hardware circuitry or complex control algorithms, increasing not only system cost but also control complexity and fault risk. Furthermore, traditional single-voltage-loop or dual-closed-loop control strategies have limited impedance gain at the second harmonic, making it difficult to effectively block the ripple propagation path without adding hardware, resulting in unsatisfactory ripple suppression performance.

[0004] Although recent studies have proposed using bandpass filters (BPFs) to construct series virtual impedances and suppress ripple propagation by increasing the system impedance at the second harmonic, the inherent bandwidth limitation of BPFs inevitably extends their high impedance characteristics into adjacent frequency bands. This weakens the damping characteristics of the system near the resonant frequency, degrades dynamic response performance, and reduces system stability margin. This technical contradiction makes it difficult to maintain the system's dynamic performance and stability while ensuring ripple suppression simply by relying on series virtual impedances.

[0005] Therefore, how to achieve high impedance ripple suppression while maintaining good dynamic performance and stability margin of the system without increasing additional hardware costs has become an urgent problem to be solved. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance, which can achieve high impedance ripple suppression while maintaining good dynamic performance and stability margin of the system without increasing additional hardware costs.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance includes the following steps:

[0009] S1. Establish a small-signal model of the bidirectional CLLC converter to characterize the modulation relationship between the switching frequency and the output voltage and the secondary resonant current.

[0010] S2. Based on the small-signal model established in S1, a dual-closed-loop control system is constructed as the basic control framework for ripple suppression control.

[0011] The dual closed-loop control system includes an inner current loop and an outer voltage loop. The inner current loop uses a proportional-integral controller connected in series with a first notch filter. The first notch filter is used to suppress the gain peak near the resonant frequency and enhance the system damping. The outer voltage loop uses a low-bandwidth proportional-integral controller to achieve time-scale separation from the inner current loop.

[0012] S3. Introduce a series virtual impedance at the input terminal of the voltage outer loop of the dual closed-loop control system constructed in S2.

[0013] The series virtual impedance is obtained by multiplying the secondary resonant current signal of the bidirectional CLLC converter with the virtual impedance transfer function constructed based on the second-order bandpass filter, and is used to improve the closed-loop output impedance of the system at the second harmonic.

[0014] S4. In the dual closed-loop control system enhanced by S3, a parallel virtual admittance is introduced;

[0015] The parallel virtual admittance consists of a second notch filter and a zero-pole compensation circuit. The center frequency of the second notch filter is set at the second harmonic to avoid the second harmonic and retain the ripple suppression capability of the series virtual impedance at the second harmonic. The zero-pole compensation circuit includes the zero-point angular frequency and the pole angular frequency, which are used to improve the phase characteristics of the system and enhance the phase margin of the system near the cutoff frequency, so as to improve the dynamic performance of the system.

[0016] S5. The dual closed-loop control system enhanced by S4 is run to generate a switching frequency modulation signal to control the power switching transistors of the bidirectional CLLC converter in order to suppress the double-frequency ripple current on the battery side.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] 1. By establishing a small-signal model of a bidirectional CLLC converter, the modulation relationship between the switching frequency and the output voltage and secondary resonant current is accurately characterized, providing a solid theoretical foundation for subsequent ripple suppression control. Compared with existing technologies that lack accurate modeling or only use simplified models, this scheme can more accurately predict system behavior and provide a reliable basis for control strategy design.

[0019] 2. The constructed dual-loop control system achieves a significant improvement in control performance through the coordinated operation of the inner current loop and the outer voltage loop. The inner current loop employs a proportional-integral controller connected in series with a first notch filter, effectively suppressing gain peaks near the resonant frequency and enhancing system damping. The outer voltage loop uses a low-bandwidth proportional-integral controller, achieving time-scale separation from the inner current loop. Compared to traditional single-voltage loop or simple dual-loop control strategies, this scheme provides a more flexible control framework for subsequent ripple suppression while ensuring system stability.

[0020] 3. The series virtual impedance introduced at the input of the outer voltage loop significantly improves the closed-loop output impedance of the system at the second harmonic by multiplying the secondary resonant current signal with the virtual impedance transfer function constructed by the second-order bandpass filter. Compared with existing technologies that rely solely on hardware filtering or pre-stage compensation, this solution can form a high impedance barrier at the second harmonic without adding additional hardware, effectively blocking the ripple propagation path.

[0021] 4. The introduced parallel virtual admittance achieves comprehensive system performance optimization through the synergistic effect of the second notch filter and the zero-pole compensation stage. The center frequency of the second notch filter is set at the second harmonic, cleverly avoiding the second harmonic point and preserving the ripple suppression capability of the series virtual impedance at that frequency; the zero-pole compensation stage effectively improves the system phase characteristics and enhances the system's phase margin near the cutoff frequency. Compared with the methods of using a single virtual impedance or a simple filter in existing technologies, this scheme solves the problem of system damping reduction caused by the extension of high impedance characteristics to adjacent frequency bands through a series-parallel synergistic design.

[0022] 5. Through the synergistic effect of the above-mentioned technologies, this solution maintains good dynamic performance and stability margin of the system while suppressing the second harmonic ripple current on the battery side. Compared with existing technologies that require a trade-off between ripple suppression effect and system performance, this solution achieves an organic unity of the two, providing a brand-new solution for second harmonic ripple suppression in single-phase OBCs.

[0023] In summary, this method can achieve high impedance ripple suppression while maintaining good dynamic performance and stability margin of the system without increasing additional hardware costs. Through the innovative design of series-parallel coordinated virtual impedance, it effectively resolves the contradiction between ripple suppression and system performance in existing technologies, providing an efficient and reliable control strategy for second harmonic ripple suppression in single-phase OBCs.

[0024] Preferably, in S1, the small-signal model is established based on the extended describing function method; when establishing the small-signal model, state variables are selected, state equations and output equations are written, and a linearized state-space model is obtained by adding small-signal perturbations:

[0025] ;

[0026] in, It is a state vector; The input vector; This refers to the small-signal disturbance of the output voltage. This refers to the small-signal disturbance of the output current. This is a small-signal disturbance to the amplitude of the secondary resonant current. , , , , , , , The coefficient matrix of the state-space model is determined by the linearization process of the small-signal model;

[0027] State vector ;

[0028] in, This refers to the primary harmonic current; This is the primary excitation current; This is the secondary harmonic current; This is the secondary resonant current; This is the primary harmonic voltage; This is the primary resonant voltage; This is the secondary harmonic voltage; This is the secondary resonant voltage; This refers to the output voltage.

[0029] Input vector ;

[0030] in, This refers to the grid voltage. For switching frequency disturbance; For duty cycle perturbation; This is due to load current disturbance.

[0031] Preferably, based on the linearized state-space model, the transfer function from the switching frequency to the output voltage is derived. Transfer function from switching frequency to secondary resonant current :

[0032] ;

[0033] ;

[0034] in, For the Laplace operator; It is the identity matrix; This represents the small-signal disturbance at the switching frequency.

[0035] This setup, by introducing small-signal perturbations and employing the extended describing function method to linearize the nonlinear time-varying system, constructs a high-precision state-space model that includes key variables such as primary / secondary resonant current, voltage, and switching frequency perturbations. This allows for the accurate derivation of the transfer function from the switching frequency modulation to the output voltage and secondary resonant current. Compared to traditional average models or simplified modeling methods that ignore resonant dynamics, this scheme fully preserves the resonant dynamic coupling characteristics of the CLLC converter under switching frequency disturbances. This provides a clear physical basis and frequency selectivity for the virtual impedance strategy designed based on this model, significantly improving the targeting and effectiveness of ripple suppression control.

[0036] Preferably, each coefficient matrix , , , , , , , They are respectively:

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] Where Ω is the steady-state switching angular frequency; ω s f is the switching angular frequency; s L is the switching frequency; r1 For the primary resonant inductance, C r1 L is the primary resonant capacitor. m For the magnetizing inductor, L r2 For secondary resonant inductance, C r2Where C is the secondary resonant capacitor, n is the equivalent turns ratio of the primary and secondary sides of the high-frequency transformer, and C is the secondary resonant capacitor. o R is the output-side filter capacitor, r is the equivalent series resistance of the output-side filter capacitor, and R L R is the equivalent resistance on the battery side or load side. eq For the reason of r and R L The calculated equivalent resistance on the output side, and R eq =rR L / (r+R L );I 1s and I 1c These are the sinusoidal and cosine components of the primary-side resonant current at the steady-state operating point, respectively; I 2s and I 2c These are the sine and cosine components of the secondary resonant current at the steady-state operating point, respectively; V 1s and V 1c These are the sine and cosine components of the primary-side resonant voltage at the steady-state operating point, respectively; V 2s and V 2c These are the sine and cosine components of the secondary resonant voltage at the steady-state operating point, respectively; V Co V is the steady-state value of the output capacitor voltage. o V is the steady-state value of the output voltage. g E represents the steady-state value of the grid voltage. d k is the linearized gain of the primary-side full-bridge fundamental voltage relative to the duty cycle or phase shift control quantity. v The equivalent modulation gain of the fundamental component of the grid voltage;

[0042] I p K represents the fundamental amplitude of the secondary resonant current. 2s and K 2c The amplitude of the secondary resonant current is respectively related to I. 2s and I 2c linearization coefficients, K 2s =I 2s / I p K 2c =I 2c / I p K1, K2, K3, and K4 are equivalent coefficients obtained from the parameters of the bidirectional CLLC resonant network and the turns ratio of the high-frequency transformer, used to characterize the dynamic coupling relationship between the primary resonant branch, the secondary resonant branch, and the excitation branch.

[0043] Let Δ=(L) r1 +L m (L) r2 +L m / n²)−(L m / n)², then K1=Δ / (L m / n), K2=Δ / (Lr2 +L m / n²), K3=(L r1 +L m ) / (L m / n), K4=(L m / n) / (L r2 +L m / n²); q3, q5, q6, q7, and q8 are equivalent coefficients obtained by linearizing the nonlinear terms of the secondary-side rectifier and the output side using the extended describing function method. They are used to characterize the coupling relationship between the sinusoidal and cosine components of the secondary-side resonant current and the output voltage and battery-side current; q3=4I 2s / (πI p ), q5=4I 2c / (πI p ), q6=4V o I 2c ² / (πI p ³), q7 = −4V o I 2s I 2c / (πI p ³), q8=4V o I 2s ² / (πI p ³); C v and D v These are the state-output matrix and input-feedforward matrix in the small-signal equation of the output voltage, respectively; C i and D i These are the state-output matrix and input-feedforward matrix in the small-signal equation for the output current, respectively; C i2 and D i2 These are the state output matrix and input feedforward matrix in the small-signal equation for the amplitude of the secondary resonant current, respectively.

[0044] Preferably, in S2, the proportional-integral controller of the inner current loop is connected in series with the first notch filter, and its transfer function is... for:

[0045] ;

[0046] in, and These are the proportional coefficient and integral coefficient of the current loop, respectively; The transfer function of a second-order notch filter; For the Laplace operator;

[0047] The low-bandwidth proportional-integral controller with voltage outer loop has a transfer function for:

[0048] ;

[0049] in, and These are the proportional and integral coefficients of the voltage loop, respectively.

[0050] System closed-loop output impedance for:

[0051] ;

[0052] in, This refers to the open-loop output impedance of the bidirectional CLLC converter. and These are the current feedback coefficient and the voltage feedback coefficient, respectively.

[0053] Preferably, the second-order notch filter Used to suppress gain peaks near the resonant frequency and enhance system damping.

[0054] This setup, by introducing a second-order notch filter into the inner current loop... This design specifically attenuates the open-loop gain peak at the inherent resonant frequency of the CLLC converter, effectively suppressing phase lag and oscillation tendency caused by resonance. This significantly improves the system's damping characteristics and stability margin without sacrificing the dynamic response speed of the current loop. Compared to the traditional current loop design that only uses a pure PI controller, this structure avoids the risk of closed-loop instability caused by the resonance peak. It provides a robust underlying control platform for subsequent high-frequency ripple suppression strategies such as superimposing series virtual impedance. Without this notch filter, the high-gain virtual impedance is prone to exciting resonant modes, leading to system instability.

[0055] Preferably, in S3, the transfer function of the series virtual impedance for:

[0056] ;

[0057] in, This is the impedance gain coefficient, used to adjust the magnitude of the impedance peak at the second harmonic. This is the resonant angular frequency corresponding to the second harmonic; The quality factor is used to adjust the peak impedance bandwidth. For the Laplace operator.

[0058] Preferably, in S3, after introducing the series virtual impedance, the closed-loop output impedance of the system is... Represented as:

[0059] ;

[0060] in, This refers to the open-loop output impedance of the bidirectional CLLC converter. and These are the current feedback coefficient and the voltage feedback coefficient, respectively. The transfer function from switching frequency to output voltage; The transfer function of the proportional-integral controller in the current inner loop; The transfer function of a low-bandwidth proportional-integral controller in the voltage outer loop.

[0061] This setup, by multiplying the secondary resonant current signal with the second-order bandpass virtual impedance and connecting it in series to the forward channel of the voltage loop, achieves a directional increase in the closed-loop output impedance at the second harmonic, thereby actively blocking the transmission path of the second harmonic ripple current to the battery side. Compared to traditional methods that rely solely on hardware filtering or front-end decoupling, this strategy does not require the addition of power devices or energy storage components. Furthermore, because it uses a bandpass structure rather than a wideband high-gain stage, its high impedance characteristics are precisely constrained within a narrow band near the second harmonic, avoiding interference with the dynamic characteristics of adjacent frequency bands. This leaves design space for the phase compensation of subsequent parallel virtual admittance, ensuring compatibility between ripple suppression capability and system stability.

[0062] Preferably, in S4, the transfer function of the parallel virtual admittance for:

[0063] ;

[0064] in, This is the parallel admittance gain, used to adjust the impedance attenuation level in non-target frequency bands; The center angular frequency of the notch filter; The quality factor is used to adjust the bandwidth of the notch filter. and These are the zero-point angular frequency and pole angular frequency of the zero-pole compensation circuit, respectively, used to improve the phase characteristics of the system;

[0065] After introducing parallel virtual admittance, the closed-loop output impedance of the system for:

[0066] .

[0067] This configuration, through a dual mechanism of notch avoidance and phase compensation using parallel virtual admittance, not only retains the high impedance suppression capability of the series virtual impedance at the second harmonic, but also actively improves the system's phase margin near the cutoff frequency through zero-pole configuration, effectively mitigating the phase lag problem that may be caused by the introduction of series virtual impedance. Compared with existing methods that only use a single virtual impedance or a simple notch filter, this scheme achieves decoupling optimization of ripple suppression capability and system dynamic stability, significantly enhancing the robustness and response quality of the control system.

[0068] Preferably, the series virtual impedance transfer function generates an impedance peak at the second harmonic to force the second harmonic ripple current to be absorbed by the DC bus capacitor; the second notch filter in the parallel virtual admittance transfer function has its center frequency set at the second harmonic to avoid the second harmonic point, in order to retain the ripple suppression capability of the series virtual impedance at the second harmonic; the zero-pole compensation circuit is used to improve the phase margin of the system near the cutoff frequency.

[0069] This setup, through precise parameter matching in the frequency domain, ensures that the system's equivalent output impedance remains high at the target suppression frequency, thereby effectively blocking ripple current from being conducted to the load side. Meanwhile, the zero-pole compensation circuit specifically improves the high-frequency phase loss caused by the introduction of the virtual network, so that the system maintains strong ripple suppression capability while its closed-loop stability and dynamic response remain unaffected. Attached Figure Description

[0070] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0071] Figure 1 This is a flowchart of the method;

[0072] Figure 2 This is a topology diagram of the bidirectional CLLC resonant converter in Example 1;

[0073] Figure 3 This is a schematic diagram of the equivalent circuit model of the bidirectional CLLC converter in Example 1;

[0074] Figure 4 This is a block diagram of the dual closed-loop control of the bidirectional CLLC converter in Example 1;

[0075] Figure 5 This is a schematic diagram of a dual closed-loop design block for a CLLC converter with impedance characteristics in Example 1.

[0076] Figure 6 This is a block diagram showing the addition of a series virtual impedance control to the closed-loop system in Example 1.

[0077] Figure 7 This is a block diagram showing the addition of series and parallel virtual impedance control to the closed-loop system in Example 1.

[0078] Figure 8 This is a comparison chart of the system output impedance amplitude-frequency characteristics before and after adding parallel virtual admittance in Example 1;

[0079] Figure 9 This is a comparison of the startup process waveforms under the traditional dual closed-loop, single series virtual impedance, and series-parallel cooperative virtual impedance strategies in Example 2.

[0080] Figure 10 This is a comparison of the steady-state waveforms under the traditional dual closed-loop and series virtual impedance strategies in Example 2;

[0081] Figure 11 This is a comparison diagram of steady-state waveforms under the single series virtual impedance and the series-parallel cooperative virtual impedance strategy in Example 2. Detailed Implementation

[0082] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0084] Example 1

[0085] like Figure 1 As shown, this invention provides a method for suppressing second harmonic ripple in a single-phase OBC based on series-parallel cooperative virtual impedance, comprising the following steps:

[0086] S1. Establish a small-signal model of the bidirectional CLLC converter to characterize the modulation relationship between the switching frequency and the output voltage and the secondary resonant current.

[0087] The topology of a bidirectional CLLC resonant converter is as follows: Figure 2 As shown.

[0088] This converter consists of a primary-side full-bridge circuit, a secondary-side full-bridge circuit, and a symmetrical resonant network in the middle. The primary side contains four power switches (S1~S4), and the secondary side contains four power switches (S5~S8). Each switch is connected in parallel with an anti-parallel diode and a parasitic capacitance. The resonant network consists of a primary-side resonant inductor Lr1, a primary-side resonant capacitor Cr1, a magnetizing inductor Lm, a secondary-side resonant inductor Lr2, and a secondary-side resonant capacitor Cr2. This converter adopts a symmetrical resonant cavity structure to ensure that the system maintains similar resonant characteristics and voltage gain patterns in both forward (G2V) and reverse (V2G) operating modes.

[0089] To address the strong nonlinear characteristics of the CLLC converter under frequency conversion control, a small-signal model of the system is established. The equivalent circuit model of the bidirectional CLLC converter is as follows: Figure 3 As shown.

[0090] The primary resonant current, primary resonant voltage, magnetizing current, secondary resonant current, secondary resonant voltage, and output voltage are selected as state variables. The state equations and output equations are then written:

[0091]

[0092]

[0093] The EDF method is used to approximate the switching network and the rectifier network, transforming the nonlinear time-varying equations into a linearized state-space model without explicit time terms.

[0094]

[0095] To analyze the small-signal dynamic characteristics of the system near its steady-state operating point, small-signal disturbances are introduced into the state variables, input variables, and control variables. These disturbances are substituted into the nonlinear equations, and a Taylor expansion is performed while neglecting second-order and higher-order small quantities. This yields the system's small-signal model, which is further refined into a standard small-signal state-space model.

[0096]

[0097] Wherein, the state vector Input vector and output vector The definition is as follows:

[0098]

[0099] State matrix , , , , , , , The specific parsing expression is:

[0100]

[0101]

[0102]

[0103]

[0104] Where Ω is the steady-state switching angular frequency; ω s f is the switching angular frequency; s L is the switching frequency; r1 For the primary resonant inductance, C r1 L is the primary resonant capacitor. m For the magnetizing inductor, L r2 For secondary resonant inductance, C r2 Where C is the secondary resonant capacitor, n is the equivalent turns ratio of the primary and secondary sides of the high-frequency transformer, and C is the secondary resonant capacitor. o R is the output-side filter capacitor, r is the equivalent series resistance of the output-side filter capacitor, and R L R is the equivalent resistance on the battery side or load side. eq For the reason of r and R L The equivalent resistance on the output side obtained by conversion, and R eq =rR L / (r+R L );I 1s and I 1c These are the sinusoidal and cosine components of the primary-side resonant current at the steady-state operating point, respectively; I 2s and I 2c These are the sine and cosine components of the secondary resonant current at the steady-state operating point, respectively; V 1s and V 1c These are the sine and cosine components of the primary-side resonant voltage at the steady-state operating point, respectively; V 2s and V 2c These are the sine and cosine components of the secondary resonant voltage at the steady-state operating point, respectively; V Co V is the steady-state value of the output capacitor voltage. o V is the steady-state value of the output voltage. g E represents the steady-state value of the grid voltage. d k is the linearized gain of the primary-side full-bridge fundamental voltage relative to the duty cycle or phase shift control quantity. v The equivalent modulation gain of the fundamental component of the grid voltage;

[0105] I p K represents the fundamental amplitude of the secondary resonant current. 2s and K 2c The amplitude of the secondary resonant current is respectively related to I. 2s and I 2c linearization coefficients, K 2s =I 2s / I p K 2c =I 2c / I pK1, K2, K3, and K4 are equivalent coefficients obtained from the parameters of the bidirectional CLLC resonant network and the turns ratio of the high-frequency transformer, used to characterize the dynamic coupling relationship between the primary resonant branch, the secondary resonant branch, and the excitation branch.

[0106] Let Δ=(L) r1 +L m (L) r2 +L m / n²)−(L m / n)², then K1=Δ / (L m / n), K2=Δ / (L r2 +L m / n²), K3=(L r1 +L m ) / (L m / n), K4=(L m / n) / (L r2 +L m / n²); q3, q5, q6, q7, and q8 are equivalent coefficients obtained by linearizing the nonlinear terms of the secondary-side rectifier and the output side using the extended describing function method. They are used to characterize the coupling relationship between the sinusoidal and cosine components of the secondary-side resonant current and the output voltage and battery-side current; q3=4I 2s / (πI p ), q5=4I 2c / (πI p ), q6=4V o I 2c ² / (πI p ³), q7 = −4V o I 2s I 2c / (πI p ³), q8=4V o I 2s ² / (πI p ³); C v and D v These are the state-output matrix and input-feedforward matrix in the small-signal equation of the output voltage, respectively; C i and D i These are the state-output matrix and input-feedforward matrix in the small-signal equation for the output current, respectively; C i2 and D i2 These are the state output matrix and input feedforward matrix in the small-signal equation for the amplitude of the secondary resonant current, respectively.

[0107] Since the derivation of the EDF small-signal model involves multi-order state variables and complex nonlinear coupling relationships, the aforementioned state-space matrix and defined variables are mathematically complex. From a physical perspective, the key intermediate variables in the matrix are the equivalent energy storage and coupling coefficients and the nonlinear dynamic impedance coefficients.

[0108] The equivalent energy storage and coupling coefficient are mainly determined by the transformer magnetizing inductance L. m It is composed of leakage inductance and turns ratio n. Among them, L e1 and L e2 These represent the total equivalent inductance of the system referred to the primary and secondary sides, respectively; K1 to K4 are cross-coupling terms derived based on these equivalent inductances. They reflect the energy transfer ratio between the primary and secondary sides and the electromagnetic inertia within the network under steady-state and dynamic conditions. The expressions for the equivalent energy storage and coupling coefficients are as follows:

[0109]

[0110] The nonlinear dynamic impedance coefficient is a direct manifestation of the nonlinear characteristics of the resonant network during the linearization process. Due to the strong nonlinearity of the commutation behavior of the diodes or switches on the rectifier side, the partial derivatives generated after small-signal Taylor expansion near the steady-state operating point constitute these q coefficients. Physically, these variables contain information such as the steady-state resonant current amplitude and steady-state output voltage, equivalent to dynamic equivalent impedance or transconductance. They map the small perturbations of the secondary-side resonant current to the equivalent voltage and current fluctuations at the rectifier bridge input port, accurately characterizing the damping and gain effects of the nonlinear rectifier network on low-frequency small signals under different load conditions. The expression for the nonlinear dynamic impedance coefficient is as follows:

[0111]

[0112] Finally, the transfer function Gvf(s) from the switching frequency to the output voltage and the small-signal transfer function G|i2|f(s) from the switching frequency to the secondary resonant current are derived as the basis for the control system design.

[0113]

[0114] By introducing small-signal perturbations and employing the extended describing function method to linearize the nonlinear time-varying system, a high-precision state-space model was constructed, incorporating key variables such as primary / secondary resonant current, voltage, and switching frequency perturbations. This model then accurately derives the transfer function from the switching frequency modulation to the output voltage and secondary resonant current. Compared to traditional average models or simplified modeling methods that ignore resonant dynamics, this scheme fully preserves the resonant dynamic coupling characteristics of the CLLC converter under switching frequency disturbances. This provides a clear physical basis and frequency selectivity for the virtual impedance strategy designed based on this model, significantly improving the targeting and effectiveness of ripple suppression control.

[0115] S2. Based on the small-signal model established in S1, a dual-loop control system is constructed as the basic control framework for ripple suppression control. The dual-loop control system includes an inner current loop and an outer voltage loop; the inner current loop uses a proportional-integral controller connected in series with a first notch filter, which is used to suppress gain peaks near the resonant frequency and enhance system damping; the outer voltage loop uses a low-bandwidth proportional-integral controller to achieve time-scale separation from the inner current loop.

[0116] Considering the dynamic characteristics of the DC bus side of the OBC system, the constructed dual-loop control block diagram of the bidirectional CLLC converter is as follows: Figure 4 As shown in the figure, and These are voltage and current compensation networks, respectively; G |i2|f (s) describes the modulation effect of the switching frequency on the secondary rectified current; Z Cbus (s) is the DC bus impedance transfer function.

[0117] The current loop design employs a PI controller connected in series with a second-order notch filter to shape the gain peak near the resonant frequency, effectively suppressing the resonant peak and enhancing system damping. The transfer function expression of the current loop controller is:

[0118] In practical implementation, the proportional-integral controller of the inner current loop is connected in series with the first notch filter, and its transfer function is... for:

[0119]

[0120] in, and These are the proportional coefficient and integral coefficient of the current loop, respectively; The transfer function of a second-order notch filter; For the Laplace operator.

[0121] The second-order notch filter Used to suppress gain peaks near the resonant frequency and enhance system damping.

[0122] The voltage loop is responsible for the steady-state regulation of the DC output voltage, and its low bandwidth is set to achieve time-scale separation from the inner current loop. The outer voltage loop uses a low-bandwidth proportional-integral controller with a transfer function... for:

[0123]

[0124] in, and These are the proportional and integral coefficients of the voltage loop, respectively.

[0125] To perform system output impedance model analysis, the power stage is equivalent to the series equivalent impedance of the controlled source Gvf(s). and Z Cbus (s). A block diagram of a dual-closed-loop design for a CLLC converter with impedance characteristics is shown below. Figure 5 As shown.

[0126] According to the appendix Figure 5 The dual closed-loop control block diagram shown is used to derive the system closed-loop output impedance using the Mason gain formula. expression:

[0127]

[0128] in, This refers to the open-loop output impedance of the bidirectional CLLC converter. and These are the current feedback coefficient and the voltage feedback coefficient, respectively.

[0129] denominator This represents the total loop gain T of the system. s (s). Therefore, the closed-loop output impedance mainly depends on the open-loop impedance. The ratio of the loop gain to the total gain.

[0130] For low-frequency disturbances far below the voltage outer loop bandwidth, the voltage outer loop has a strong regulating capability, resulting in a low output impedance characteristic of the system. However, at the second harmonic, the disturbance frequency is significantly higher than the voltage outer loop bandwidth, and the regulating effect of the voltage outer loop on this frequency component is significantly weakened. Therefore, although traditional dual-loop control can ensure stable system operation and improve dynamic performance, it does not have sufficient targeted impedance shaping capability at the specific disturbance frequency of the second harmonic, making it difficult to effectively suppress the transmission of second harmonic ripple to the battery side.

[0131] By introducing a second-order notch filter into the inner current loop This design specifically attenuates the open-loop gain peak at the inherent resonant frequency of the CLLC converter, effectively suppressing phase lag and oscillation tendency caused by resonance. This significantly improves the system's damping characteristics and stability margin without sacrificing the dynamic response speed of the current loop. Compared to the traditional current loop design that only uses a pure PI controller, this structure avoids the risk of closed-loop instability caused by the resonance peak. It provides a robust underlying control platform for subsequent high-frequency ripple suppression strategies such as superimposing series virtual impedance. Without this notch filter, the high-gain virtual impedance is prone to exciting resonant modes, leading to system instability.

[0132] S3. At the input of the voltage outer loop of the dual closed-loop control system constructed in S2, a series virtual impedance is introduced. The series virtual impedance is obtained by multiplying the secondary resonant current signal of the bidirectional CLLC converter with the virtual impedance transfer function constructed based on the second-order bandpass filter. It is used to improve the closed-loop output impedance of the system at the second harmonic.

[0133] In a dual-loop control framework, the essence of series virtual impedance is to add an additional compensation quantity related to the output current into the control loop, so that the actual object regulated by the controller is expanded from the output voltage to the sum of the output voltage and the virtual impedance voltage drop. Therefore, the secondary current flowing through the converter can be multiplied by the virtual impedance function. It is then added to the outer voltage loop reference channel, thereby making the system output exhibit series impedance characteristics under closed-loop conditions. Its equivalent control block diagram is as follows: Figure 6 As shown.

[0134] A virtual impedance based on a second-order bandpass filter (BPF) is introduced into the voltage reference channel. Its transfer function is designed to generate an impedance peak at the second harmonic (100Hz), and a software algorithm is used to simulate the physical high impedance, forcing the ripple current to be absorbed by the DC bus capacitor.

[0135] Transfer function of series virtual impedance for:

[0136]

[0137] in, ω is the impedance gain coefficient, used to adjust the peak impedance at the second harmonic; 2r =2π×100rad / s is the resonant angular frequency; Q s It is the quality factor, used to adjust the peak impedance bandwidth.

[0138] After introducing the series virtual impedance, the closed-loop output impedance of the system Represented as:

[0139]

[0140] By multiplying the secondary resonant current signal with the second-order bandpass virtual impedance and connecting it in series to the forward channel of the voltage loop, a directional increase in the closed-loop output impedance at the second harmonic is achieved, thereby actively blocking the transmission path of the second harmonic ripple current to the battery side. Compared with traditional methods that rely solely on hardware filtering or front-end decoupling, this strategy does not require the addition of power devices or energy storage components. Furthermore, because it adopts a bandpass structure rather than a wideband high-gain stage, its high impedance characteristics are precisely constrained within a narrow band near the second harmonic, avoiding interference with the dynamic characteristics of adjacent frequency bands. This leaves design space for the phase compensation of subsequent parallel virtual admittance, ensuring compatibility between ripple suppression capability and system stability.

[0141] S4. In the dual closed-loop control system enhanced by S3, a parallel virtual admittance is introduced. The parallel virtual admittance consists of a second notch filter and a zero-pole compensation circuit. The center frequency of the second notch filter is set at the second harmonic to avoid the second harmonic and retain the ripple suppression capability of the series virtual impedance at the second harmonic. The zero-pole compensation circuit includes the zero-point angular frequency and the pole angular frequency, which are used to improve the phase characteristics of the system and enhance the phase margin of the system near the cutoff frequency, so as to improve the dynamic performance of the system.

[0142] Because the designed virtual impedance uses a bandpass filter structure, its peak impedance has a certain bandwidth near the second harmonic. When the quality factor Q... s In limited cases, this high impedance characteristic not only appears at the second harmonic frequency but also extends to its adjacent frequency bands. This will cause the average output impedance of the system to increase in the low to mid-frequency range. According to the impedance characteristic theory of power supply systems, while increasing the output impedance is beneficial for suppressing ripple current at specific frequencies, it also reduces the system's equivalent damping and may weaken the system's dynamic adjustment capability to load disturbances. Therefore, while achieving ripple suppression, the system's dynamic performance and stability margin may be affected to some extent.

[0143] To compensate for the decrease in stability margin in non-target frequency bands caused by the series branch, a parallel branch consisting of a notch filter and a zero-pole compensation circuit is introduced. The notch filter avoids the second harmonic to retain suppression capability, while the compensation circuit improves the phase margin of the system near the cutoff frequency, thus improving dynamic performance. Its equivalent control block diagram is shown below. Figure 7 As shown.

[0144] Transfer function of parallel virtual admittance for:

[0145]

[0146] In the formula, This is the parallel admittance gain, used to adjust the impedance attenuation level in non-target frequency bands; The center angular frequency of the notch filter; The quality factor is used to adjust the bandwidth of the notch filter. and These are the zero-point angular frequency and pole angular frequency of the zero-pole compensation circuit, respectively, used to improve the phase characteristics of the system;

[0147] After introducing parallel virtual admittance, the closed-loop output impedance of the system for:

[0148]

[0149] By employing a dual mechanism of notch avoidance and phase compensation with parallel virtual admittance, this approach not only retains the high impedance suppression capability of the series virtual impedance at the second harmonic, but also actively improves the system's phase margin near the cutoff frequency through zero-pole configuration. This effectively alleviates the phase lag problem that may be caused by the introduction of the series virtual impedance. Compared with existing methods that only use a single virtual impedance or a simple notch filter, this scheme achieves decoupling optimization of ripple suppression capability and system dynamic stability, significantly enhancing the robustness and response quality of the control system.

[0150] In practice, the series virtual impedance transfer function generates an impedance peak at the second harmonic to force the second harmonic ripple current to be absorbed by the DC bus capacitor; the second notch filter in the parallel virtual admittance transfer function has its center frequency set at the second harmonic to avoid the second harmonic point, in order to retain the ripple suppression capability of the series virtual impedance at the second harmonic; the zero-pole compensation circuit is used to improve the phase margin of the system near the cutoff frequency.

[0151] By precisely matching parameters in the frequency domain, the system's equivalent output impedance is kept high at the target suppression frequency, thus effectively blocking the ripple current from being conducted to the load side. Meanwhile, the zero-pole compensation circuit specifically improves the high-frequency phase loss caused by the introduction of the virtual network, so that the system maintains strong ripple suppression capability while its closed-loop stability and dynamic response remain unaffected.

[0152] Through the coordinated control of the series virtual impedance and the parallel virtual admittance, the system maintains a high output impedance at the second harmonic to suppress the second harmonic ripple current on the battery side, while reducing the output impedance in the non-target frequency band, thereby improving the dynamic response performance and stability margin of the system under load change conditions.

[0153] To facilitate a better understanding of the dual closed-loop control system S2-S4 in this method, the DC bus impedance was compared. Output impedance when only series virtual impedance is used and the output impedance after adding series and parallel coordinated virtual impedance. The impedance amplitude-frequency characteristic diagram, such as Figure 8 As shown.

[0154] Compared to a single series virtual impedance strategy, the series-parallel coordinated virtual impedance control significantly reduces the output impedance level in other frequency bands while maintaining high impedance characteristics at the second harmonic. This not only ensures ripple suppression capability but also improves the system's equivalent DC output impedance and dynamic adjustment capability, effectively alleviating the contradiction between ripple suppression and dynamic response in a single series virtual impedance strategy.

[0155] S5. The dual closed-loop control system enhanced by S4 is run to generate a switching frequency modulation signal to control the power switching transistors of the bidirectional CLLC converter in order to suppress the double-frequency ripple current on the battery side.

[0156] This invention establishes a small-signal model of a bidirectional CLLC converter, accurately characterizing the modulation relationship between the switching frequency and the output voltage and secondary resonant current, providing a solid theoretical foundation for subsequent ripple suppression control. Compared to existing technologies that lack precise modeling or only use simplified models, this scheme can more accurately predict system behavior, providing a reliable basis for control strategy design. Furthermore, the dual-loop control system constructed by this method achieves a significant improvement in control performance through the coordinated operation of the inner current loop and the outer voltage loop. The inner current loop uses a proportional-integral controller connected in series with a first notch filter, effectively suppressing the gain peak near the resonant frequency and enhancing system damping; the outer voltage loop uses a low-bandwidth proportional-integral controller, achieving time-scale separation from the inner current loop. Compared to traditional single-voltage loop or simple dual-loop control strategies, this scheme provides a more flexible control framework for subsequent ripple suppression while ensuring system stability.

[0157] The series virtual impedance introduced at the input of the outer voltage loop significantly improves the closed-loop output impedance of the system at the second harmonic by multiplying the secondary resonant current signal with the virtual impedance transfer function constructed by the second-order bandpass filter. Compared with existing methods that rely solely on hardware filtering or pre-stage compensation, this scheme can form a high impedance barrier at the second harmonic without adding additional hardware, effectively blocking the ripple propagation path. In addition, the parallel virtual admittance introduced in this method achieves comprehensive optimization of system performance through the synergistic effect of the second notch filter and the zero-pole compensation stage. The center frequency of the second notch filter is set at the second harmonic, cleverly avoiding the second harmonic point and preserving the ripple suppression capability of the series virtual impedance at that frequency; the zero-pole compensation stage effectively improves the system phase characteristics and enhances the phase margin of the system near the cutoff frequency. Compared with existing methods that use a single virtual impedance or a simple filter, this scheme solves the problem of system damping reduction caused by the extension of high impedance characteristics to adjacent frequency bands through series-parallel synergistic design.

[0158] Through the synergistic effect of the aforementioned technologies, this solution suppresses the second harmonic ripple current on the battery side while maintaining good dynamic performance and stability margin of the system. Compared to existing technologies that require a trade-off between ripple suppression effect and system performance, this solution achieves an organic unity of the two, providing a completely new solution for second harmonic ripple suppression in single-phase OBCs. This method can achieve high-impedance ripple suppression while maintaining good dynamic performance and stability margin of the system without increasing additional hardware costs. Through the innovative design of series-parallel coordinated virtual impedance, the contradictory relationship between ripple suppression and system performance in existing technologies is effectively resolved, providing an efficient and reliable control strategy for second harmonic ripple suppression in single-phase OBCs.

[0159] Example 2

[0160] To facilitate better understanding, the following verification explanation is provided for this method.

[0161] To verify the effectiveness of the proposed series-parallel virtual impedance strategy in improving system output impedance and suppressing the transmission of second-harmonic ripple current to the battery side at the second harmonic, while also improving system dynamic performance, a simulation model was built consisting of a front-end single-phase grid-connected bidirectional AC / DC converter, a DC bus, a rear-end bidirectional CLLC converter, and an equivalent battery model. A series virtual impedance Zs(s) and a parallel virtual admittance Yp(s) were added to the model, and the steady-state output waveform of the system after the control strategy was added was analyzed.

[0162] Under rated operating conditions, the startup waveforms of three strategies—traditional dual-closed-loop control, single series virtual impedance control, and series-parallel coordinated virtual impedance control—are compared, such as... Figure 9 As shown.

[0163] The steady-state waveforms of the system after traditional dual closed-loop control and after adding series virtual impedance control are compared, such as... Figure 10 As shown.

[0164] The steady-state waveforms under a single series virtual impedance strategy and a series-parallel cooperative strategy will be compared, such as... Figure 11 As shown.

[0165] analyze Figures 9 to 11 It is known that the single series virtual impedance strategy proposed in this invention can effectively improve the output impedance of the system at the second harmonic and suppress the transmission of second harmonic ripple to the battery side. However, it also weakens the system damping and reduces the closed-loop stability margin, leading to increased system startup shock and oscillation. However, after adding parallel virtual admittance, while maintaining the second harmonic ripple suppression capability basically unchanged, the overshoot, oscillation and settling time during startup are significantly improved, achieving coordinated optimization of ripple suppression capability and system dynamic performance.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for suppressing second harmonic ripple in a single-phase OBC based on series-parallel cooperative virtual impedance, characterized in that, Includes the following steps: S1. Establish a small-signal model of the bidirectional CLLC converter to characterize the modulation relationship between the switching frequency and the output voltage and the secondary resonant current. S2. Based on the small-signal model established in S1, a dual-closed-loop control system is constructed as the basic control framework for ripple suppression control. The dual closed-loop control system includes an inner current loop and an outer voltage loop. The inner current loop uses a proportional-integral controller connected in series with a first notch filter. The first notch filter is used to suppress the gain peak near the resonant frequency and enhance the system damping. The outer voltage loop uses a low-bandwidth proportional-integral controller to achieve time-scale separation from the inner current loop. S3. Introduce a series virtual impedance at the input terminal of the voltage outer loop of the dual closed-loop control system constructed in S2. The series virtual impedance is obtained by multiplying the secondary resonant current signal of the bidirectional CLLC converter with the virtual impedance transfer function constructed based on the second-order bandpass filter, and is used to improve the closed-loop output impedance of the system at the second harmonic. S4. In the dual closed-loop control system enhanced by S3, a parallel virtual admittance is introduced; The parallel virtual admittance consists of a second notch filter and a zero-pole compensation circuit; the center frequency of the second notch filter is set at the second harmonic to avoid the second harmonic point in order to retain the ripple suppression capability of the series virtual impedance at the second harmonic. The zero-pole compensation circuit includes zero-angular frequency and pole-angular frequency, which are used to improve the phase characteristics of the system and increase the phase margin of the system near the cutoff frequency, so as to improve the dynamic performance of the system. S5. The dual closed-loop control system enhanced by S4 is run to generate a switching frequency modulation signal to control the power switching transistors of the bidirectional CLLC converter in order to suppress the double-frequency ripple current on the battery side.

2. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 1, characterized in that, In S1, the small-signal model is established based on the extended describing function method. When establishing the small-signal model, state variables are selected, state equations and output equations are written, and a linearized state-space model is obtained by adding small-signal perturbations. ； in, It is a state vector; The input vector; This refers to the small-signal disturbance of the output voltage. This refers to the small-signal disturbance of the output current. This is a small-signal disturbance to the amplitude of the secondary resonant current. , , , , , , , The coefficient matrix of the state-space model is determined by the linearization process of the small-signal model; State vector ; in, This refers to the primary harmonic current; This is the primary excitation current; This is the secondary harmonic current; This is the secondary resonant current; This is the primary harmonic voltage; This is the primary resonant voltage; This is the secondary harmonic voltage; This is the secondary resonant voltage; This refers to the output voltage. Input vector ; in, This refers to the grid voltage. For switching frequency disturbance; For duty cycle perturbation; This is due to load current disturbance.

3. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 2, characterized in that, Coefficient matrices , , , , , , , They are respectively: ； ； ； ； Where Ω is the steady-state switching angular frequency; ω s f is the switching angular frequency; s L is the switching frequency; r1 For the primary resonant inductance, C r1 L is the primary resonant capacitor. m For the magnetizing inductor, L r2 For secondary resonant inductance, C r2 Where C is the secondary resonant capacitor, n is the equivalent turns ratio of the primary and secondary sides of the high-frequency transformer, and C is the secondary resonant capacitor. o R is the output-side filter capacitor, r is the equivalent series resistance of the output-side filter capacitor, and R L R is the equivalent resistance on the battery side or load side. eq For the reason of r and R L The equivalent resistance on the output side obtained by conversion, and R eq =rR L / (r+R L );I 1s and I 1c These are the sinusoidal and cosine components of the primary-side resonant current at the steady-state operating point, respectively; I 2s and I 2c These are the sine and cosine components of the secondary resonant current at the steady-state operating point, respectively; V 1s and V 1c These are the sine and cosine components of the primary-side resonant voltage at the steady-state operating point, respectively; V 2s and V 2c These are the sine and cosine components of the secondary resonant voltage at the steady-state operating point, respectively; V Co V is the steady-state value of the output capacitor voltage. o V is the steady-state value of the output voltage. g E represents the steady-state value of the grid voltage. d k is the linearized gain of the primary-side full-bridge fundamental voltage relative to the duty cycle or phase shift control quantity. v The equivalent modulation gain of the fundamental component of the grid voltage; I p K represents the fundamental amplitude of the secondary resonant current. 2s and K 2c The amplitude of the secondary resonant current is respectively related to I. 2s and I 2c linearization coefficients, K 2s =I 2s / I p K 2c =I 2c / I p K1, K2, K3, and K4 are equivalent coefficients obtained from the parameters of the bidirectional CLLC resonant network and the turns ratio of the high-frequency transformer, used to characterize the dynamic coupling relationship between the primary resonant branch, the secondary resonant branch, and the excitation branch; let Δ=(L r1 +L m (L) r2 +L m / n²)−(L m / n)², then K1=Δ / (L m / n), K2=Δ / (L r2 +L m / n²), K3=(L r1 +L m ) / (L m / n), K4=(L m / n) / (L r2 +L m / n²); q3, q5, q6, q7, and q8 are equivalent coefficients obtained by linearizing the nonlinear terms of the secondary-side rectifier and the output side using the extended describing function method. They are used to characterize the coupling relationship between the sinusoidal and cosine components of the secondary-side resonant current and the output voltage and battery-side current; q3=4I 2s / (πI p ), q5=4I 2c / (πI p ), q6=4V o I 2c ² / (πI p ³), q7 = −4V o I 2s I 2c / (πI p ³), q8=4V o I 2s ² / (πI p ³); C v and D v These are the state-output matrix and input-feedforward matrix in the small-signal equation of the output voltage, respectively; C i and D i These are the state-output matrix and input-feedforward matrix in the small-signal equation for the output current, respectively; C i2 and D i2 These are the state output matrix and input feedforward matrix in the small-signal equation for the amplitude of the secondary resonant current, respectively.

4. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 2, characterized in that, Based on the linearized state-space model, the transfer function from switching frequency to output voltage is derived. Transfer function from switching frequency to secondary resonant current : ； ； in, For the Laplace operator; It is the identity matrix; This represents the small-signal disturbance at the switching frequency.

5. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 4, characterized in that, In S2, the proportional-integral controller of the inner current loop is connected in series with the first notch filter, and its transfer function is... for: ； in, and These are the proportional coefficient and integral coefficient of the current loop, respectively; The transfer function of a second-order notch filter; For the Laplace operator; The low-bandwidth proportional-integral controller with voltage outer loop has a transfer function for: ； in, and These are the proportional and integral coefficients of the voltage loop, respectively. System closed-loop output impedance for: ； in, This refers to the open-loop output impedance of the bidirectional CLLC converter. and These are the current feedback coefficient and the voltage feedback coefficient, respectively.

6. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 5, characterized in that, The second-order notch filter Used to suppress gain peaks near the resonant frequency and enhance system damping.

7. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 1, characterized in that, In S3, the transfer function of the series virtual impedance for: ； in, This is the impedance gain coefficient, used to adjust the magnitude of the impedance peak at the second harmonic. This is the resonant angular frequency corresponding to the second harmonic; The quality factor is used to adjust the peak impedance bandwidth. For the Laplace operator.

8. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 7, characterized in that, In S3, after introducing the series virtual impedance, the closed-loop output impedance of the system... Represented as: ； in, This refers to the open-loop output impedance of the bidirectional CLLC converter. and These are the current feedback coefficient and the voltage feedback coefficient, respectively. The transfer function from switching frequency to output voltage; The transfer function of the proportional-integral controller in the current inner loop; The transfer function of a low-bandwidth proportional-integral controller in the voltage outer loop.

9. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 8, characterized in that, In S4, the transfer function of the parallel virtual admittance for: ； in, This is the parallel admittance gain, used to adjust the impedance attenuation level in non-target frequency bands; The center angular frequency of the notch filter; The quality factor is used to adjust the bandwidth of the notch filter. and These are the zero-point angular frequency and pole angular frequency of the zero-pole compensation circuit, respectively, used to improve the phase characteristics of the system; After introducing parallel virtual admittance, the closed-loop output impedance of the system for: 。 10. The single-phase OBC second harmonic ripple suppression method based on series-parallel cooperative virtual impedance according to claim 1, characterized in that, The series virtual impedance transfer function generates an impedance peak at the second harmonic to force the second harmonic ripple current to be absorbed by the DC bus capacitor; the second notch filter in the parallel virtual admittance transfer function has its center frequency set at the second harmonic to avoid the second harmonic point, in order to preserve the ripple suppression capability of the series virtual impedance at the second harmonic; the zero-pole compensation circuit is used to improve the phase margin of the system near the cutoff frequency.

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