Triple Bidirectional Inner Phase Shift Control Method for Optimizing Current Stress of Dual Active Bridge Converter

Abstract

The present invention relates to a triple bidirectional inner phase shift control method for optimizing the current stress of a dual active bridge converter, including: establishing a mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of the triple bidirectional inner phase shift as a function of the inner and outer phase shift ratios; establishing a Lagrange multiplier equation to solve the phase shift ratio combination when the current stress is minimized in the two working modes of the triple bidirectional inner phase shift; determining the working range of the two working modes to obtain the size of the minimized current stress and return power, and modulating the converter by generating PWM pulses through the optimal phase shift ratio. The present invention obtains a triple bidirectional inner phase shift control method by changing the inner phase shift moving direction in the traditional triple phase shift, takes the minimization of current stress as the goal, and solves the optimal phase shift ratio combination in combination with the Lagrange multiplier method, and uses the optimal phase shift ratio combination to control the converter, thereby further optimizing the current stress and return power of the converter and effectively improving the conversion efficiency of the converter.

Description

Technical Field

[0001] The invention relates to the technical field of power electronic conversion, in particular to a triple bidirectional inner phase shift control method for optimizing current stress of a dual active bridge converter. Background Art

[0002] Energy storage systems are an effective way to solve the random volatility of renewable energy generation. Bidirectional DC-DC converters are important equipment in energy storage systems. Dual active bridge converters are one of the most suitable devices for energy storage systems due to their high power density, electrical isolation, and bidirectional energy flow. The reliability and conversion efficiency of dual active bridge converters directly affect the safe and reliable operation of energy storage systems. The optimization control of dual active bridge converters is a hot topic of research at home and abroad and has great engineering significance.

[0003] The current stress of the dual active bridge converter is determined by the peak value of the inductor current. The return power occurs in the stage where the full-bridge output voltage is opposite to the polarity of the inductor current. The converter has problems of large current stress and return power under single phase-shift modulation. Larger current stress will cause additional switching losses and increase the requirements for the performance of switching devices, which is not conducive to the efficient and stable operation of the converter. Larger return power will also cause additional losses. To address this problem, a dual phase-shift modulation method with two control variables has been studied. The current stress and return power can be reduced by optimizing the combination of the two control variables. However, dual phase-shift modulation is a special form of triple phase-shift modulation. The optimization result of dual phase-shift can be further optimized. Traditional triple phase-shift modulation has multiple working modes, which is complex to analyze and has poor universal applicability. Summary of the invention

[0004] The purpose of the present invention is to provide a triple bidirectional inner phase shift control method for current stress optimization of a dual active bridge converter, which can reduce the current stress of the converter, achieve global optimization of the current stress, reduce the reflux power, improve the working performance of the converter and simplify the analysis process.

[0005] To achieve the above object, the present invention adopts the following technical solution: a triple bidirectional inner phase shift control method for optimizing current stress of a dual active bridge converter, the method comprising the following steps in order:

[0006] (1) According to the working state of the triple bidirectional internal phase shift modulation down converter, a mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of triple bidirectional internal phase shift and the change of the internal and external phase shift ratio is established;

[0007] (2) Based on the mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of triple bidirectional internal phase shift and the internal and external phase shift ratios, the Lagrange multiplier equation is established with the minimization of current stress as the control target, and the phase shift ratio combination with the minimum current stress in the two working modes of triple bidirectional internal phase shift control is solved, that is, the optimal phase shift ratio;

[0008] (3) Based on the optimal phase shift ratio and the constraints of the internal and external phase shift ratios of the two working modes, the working ranges of the two working modes are determined. The transmission power, current stress and return power of the two working modes with triple bidirectional internal phase shift are combined with the mathematical model of the relationship between the changes in the internal and external phase shift ratios to obtain the size of the minimized current stress and return power. The PWM pulses are generated by the optimal phase shift ratio to modulate the converter.

[0009] In step (1), the mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of triple bidirectional inner phase shift and the inner and outer phase shift ratio is:

[0010] Mode 1: P N =2(2d-2d 2 +2dd 1 +2dd 2 -d 1 2 -d 1 -d 1 d 2 -d 2 -d 2 2 ) (1)

[0012] Mode 2: P N =2(2d-d 2 +d 1 d 2 -d 1 -d 2 ) (2)

[0013] i N =2(k+2d-kd 1 -d 2 -1) (3)

[0014] Mode 1: Q N =(k+2d-2d 1 -kd 1 -d 2 -1) 2 / 2k+1) (4)

[0015] Mode 2: Q N =(k-kd 1 +d 2 -1)2 / 2k (5)

[0016] Formulas (1) and (2) are the transmission power P N Per-unit expression, the per-unit basis is the maximum transmission power nU 1 U 2 / 8fL, n is the high frequency transformer ratio, U 1 is the input voltage, U 2 is the output voltage, f is the switching frequency, L is the inductance value in the main circuit; Formula (3) is the current stress i N Per-unit expression, the per-unit reference is the current value nU corresponding to the maximum transmission power 2 / 8fL; Formulas (4) and (5) are the return power Q N Per-unit expression, the per-unit basis is the maximum transmission power nU 1 U 2 / 8fL,k=U 1 / nU 2 is the voltage transfer ratio, d is the full bridge H 1 With full bridge H 2 The bridge displacement ratio is called the external displacement ratio, d 1 ,d 2 H 1 , H 2 The bridge moves inwards compared to the original bridge, which is called the inward displacement ratio;

[0017] The constraints for the two working modes of internal and external shifting are:

[0018] Mode 1: d 1 +d 2 <d;

[0019] Mode 2: d 1 +d 2 >d.

[0020] In step (2), the Lagrange multiplier equation is:

[0021] L(d,d 1 ,d 2 ,μ)=i N -μ(P N -P 0 )

[0022] i N =2(k+2d-kd 1 -d 2 -1)

[0023] Where μ is the Lagrange multiplier factor, P 0 is the actual output power per unit value, P N is the transmission power, d is the full bridge H1 With full bridge H 2 The bridge displacement ratio is called the external displacement ratio, d 1 ,d 2 H 1 , H 2 The bridge moves inwards compared to the original bridge, called the inward movement ratio. N is the current stress.

[0024] In step (2), the optimal shift ratio is:

[0025] Mode 1:

[0026] Mode 2:

[0027] Where P 0 is the actual output power per unit value, d is the full bridge H 1 With full bridge H 2 The bridge displacement ratio is called the external displacement ratio, d 1 d 2 H 1 , H 2 The ratio of the inward movement of the bridge is called the inward movement ratio; k = U 1 / nU 2 is the voltage transfer ratio, n is the high-frequency transformer ratio, U 1 is the input voltage, U 2 is the output voltage.

[0028] In step (3), the working ranges of the two working modes are:

[0029] Mode 1: 2(k-1) / k 2 <P 0 ≤1;

[0030] Mode 2: 0 ≤ P 0 <2(k-1) / k 2 ;

[0031] Among them, P 0 is the actual output power per unit value, k = U 1 / nU 2 is the voltage transfer ratio, n is the high-frequency transformer ratio, U 1 is the input voltage, U 2 is the output voltage;

[0032] The minimized current stress is:

[0033] Mode 1:

[0034] Mode 2:

[0035] The reflux power is the full bridge H 1 The output AC voltage is positive and the inductor current is negative. The return power is:

[0036] Mode 1:

[0037] Mode 2: Q N =0.

[0038] It can be seen from the above technical scheme that the beneficial effects of the present invention are: First, the present invention obtains a triple bidirectional inner phase-shift control method by changing the inner phase movement direction in the traditional triple phase-shift. Based on this method, with current stress minimization as the goal, the Lagrange multiplier method is combined to solve the optimal phase shift ratio combination, and the optimal phase shift ratio combination is used to control the converter. Compared with single-phase and double-phase shift control, the converter current stress and return power can be further optimized, and the conversion efficiency of the converter can be effectively improved; Second, the triple bidirectional inner phase-shift control method proposed in the present invention has the advantages of fewer working modes, simple analysis process, simple control process, easy implementation, etc. compared with the traditional triple phase-shift control method. It is more suitable for application in actual engineering and has stronger practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the main topology diagram of the dual active bridge converter;

[0040] Figure 2 It is the timing diagram of the traditional triple phase shift and triple bidirectional inner phase shift switch;

[0041] Figure 3 This is the main voltage and current waveform diagram of the six working modes of the traditional triple phase shift;

[0042] Figure 4 It is the main voltage and current waveform diagram of the two working modes of triple bidirectional internal phase shift;

[0043] Figure 5 It is a comparison chart of current stress of single phase shift, double phase shift, traditional triple phase shift and triple bidirectional inner phase shift modulation;

[0044] Figure 6 It is a comparison chart of the return power of single phase shift, double phase shift, traditional triple phase shift and triple bidirectional internal phase shift modulation;

[0045] Figure 7 It is a block diagram of triple bidirectional inward-shifted closed-loop phase control. DETAILED DESCRIPTION

[0046] like Figure 1 As shown, a triple bidirectional inner phase shift control method for optimizing current stress of a dual active bridge converter comprises the following steps in sequence:

[0047] (1) According to the working state of the triple bidirectional internal phase shift modulation down converter, a mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of triple bidirectional internal phase shift and the change of the internal and external phase shift ratio is established;

[0048] (2) Based on the mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of triple bidirectional internal phase shift and the internal and external phase shift ratios, the Lagrange multiplier equation is established with the minimization of current stress as the control target, and the phase shift ratio combination with the minimum current stress in the two working modes of triple bidirectional internal phase shift control is solved, that is, the optimal phase shift ratio;

[0049] (3) Based on the optimal phase shift ratio and the constraints of the internal and external phase shift ratios of the two working modes, the working ranges of the two working modes are determined. The transmission power, current stress and return power of the two working modes with triple bidirectional internal phase shift are combined with the mathematical model of the relationship between the changes in the internal and external phase shift ratios to obtain the size of the minimized current stress and return power. The PWM pulses are generated by the optimal phase shift ratio to modulate the converter.

[0050] In step (1), the mathematical model of the relationship between the transmission power, current stress and return power of the two working modes of triple bidirectional inner phase shift and the inner and outer phase shift ratio is:

[0051] Mode 1: P N =2(2d-2d 2 +2dd 1 +2dd 2 -d 1 2 -d 1 -d 1 d 2 -d 2 -d 2 2 ) (1)

[0053] Mode 2: P N =2(2d-d 2 +d 1 d 2 -d 1 -d 2 ) (2)

[0054] i N =2(k+2d-kd 1 -d 2 -1) (3)

[0055] Mode 1: Q N =(k+2d-2d 1 -kd 1 -d 2-1) 2 / 2k+1) (4)

[0056] Mode 2: Q N =(k-kd 1 +d 2 -1) 2 / 2k (5)

[0057] Formulas (1) and (2) are the transmission power P N Per-unit expression, the per-unit basis is the maximum transmission power nU 1 U 2 / 8fL, n is the high frequency transformer ratio, U 1 is the input voltage, U 2 is the output voltage, f is the switching frequency, L is the inductance value in the main circuit; Formula (3) is the current stress i N Per-unit expression, the per-unit reference is the current value nU corresponding to the maximum transmission power 2 / 8fL; Formulas (4) and (5) are the return power Q N Per-unit expression, the per-unit basis is the maximum transmission power nU 1 U 2 / 8fL,k=U 1 / nU 2 is the voltage transfer ratio, d is the full bridge H 1 With full bridge H 2 The bridge displacement ratio is called the external displacement ratio, d 1 d 2 H 1 , H 2 The bridge moves inwards compared to the original bridge, which is called the inward displacement ratio;

[0058] The constraints for the two working modes of internal and external shifting are:

[0059] Mode 1: d 1 +d 2 <d;

[0060] Mode 2: d 1 +d 2 >d.

[0061] In step (2), the Lagrange multiplier equation is:

[0062] L(d,d 1 ,d 2 ,μ)=i N -μ(P N -P 0 )

[0063] i N =2(k+2d-kd 1-d 2 -1)

[0064] Where μ is the Lagrange multiplier factor, P 0 is the actual output power per unit value, P N is the transmission power, d is the full bridge H 1 With full bridge H 2 The bridge displacement ratio is called the external displacement ratio, d 1 ,d 2 H 1 , H 2 The bridge moves inwards compared to the original bridge, called the inward movement ratio. N is the current stress.

[0065] In step (2), the optimal shift ratio is:

[0066] Mode 1:

[0067] Mode 2:

[0068] Where P 0 is the actual output power per unit value, d is the full bridge H 1 With full bridge H 2 The bridge displacement ratio is called the external displacement ratio, d 1 ,d 2 H 1 , H 2 The ratio of the inward movement of the bridge is called the inward movement ratio; k = U 1 / nU 2 is the voltage transfer ratio, n is the high-frequency transformer ratio, U 1 is the input voltage, U 2 is the output voltage.

[0069] In step (3), the working ranges of the two working modes are:

[0070] Mode 1: 2(k-1) / k 2 <P 0 ≤1;

[0071] Mode 2: 0 ≤ P 0 <2(k-1) / k 2 ;

[0072] Among them, P 0 is the actual output power per unit value, l = U 1 / nU 2 is the voltage transfer ratio, n is the high-frequency transformer ratio, U 1 is the input voltage, U 2 is the output voltage;

[0073] The minimized current stress is as follows:

[0074] Mode 1:

[0075] Mode 2:

[0076] The reflux power is the power of the positive AC voltage output by the full-bridge H 1 when the inductor current is negative. The magnitude of the reflux power is:

[0077] Mode 1:

[0078] Mode 2: Q N = 0.

[0079] The following is a further description of the present invention in conjunction with Figures 1 to 7 the following.

[0080] The topology of the dual active bridge converter is as Figure 1 shown, including full-bridge H 1 , full-bridge H 2 , auxiliary inductor L, high-frequency transformer with a turns ratio of n:1, input and output support capacitors C 1 , C 2 ; in the figure, S 1 ~S 8 are the switching tubes of the two full-bridges, i L is the current flowing through the inductor, U L is the voltage across the inductor, U 1 , U 2 are the AC voltages output by full-bridge H 1 , full-bridge H 2 respectively, and U 1 , U 2 are the input and output voltages respectively.

[0081] The switching timing diagrams of traditional triple phase-shift and triple bidirectional inner phase-shift modulation are as Figure 2 shown. Triple bidirectional inner phase-shift modulation changes the moving direction of the inner phase-shift ratio d 2 on the basis of traditional triple phase-shift modulation.

[0082] The main voltage and current waveforms of traditional triple phase-shift modulation are as Figure 3 shown. According to the relationship between the inner and outer phase-shift ratios d, d 1 and d 2 , it is divided into 6 working modes. The constraint conditions of each mode are:

[0083] Mode 1: 0 ≤ d 1 ≤ d ≤ 1 && d 1 ≤ d + d 2 ≤ 1

[0084] Mode 2: 0 ≤ d 1 ≤d≤1&&1≤d+d 2 ≤1+d 1

[0085] Mode 3: 0 ≤ d 1 ≤d≤1&&1+d 1 ≤d+d 2 ≤2

[0086] Mode 4: 0≤d≤d 1 ≤1&&0≤d+d 2 ≤d 1

[0087] Mode 5: 0≤d≤d 1 ≤1&&d 1 ≤d+d 2 ≤1

[0088] Mode 6: 0≤d≤d 1 ≤1&&1≤d+d 2 ≤1+d 1

[0089] The main voltage and current waveforms of triple bidirectional internal phase shift modulation are as follows: Figure 3 As shown, according to the comparison of the inner and outer displacements d and d 1 and 2 The relationship is divided into two working modes, and the constraints of the two working modes are:

[0090] Mode 1: d 1 +d 2 <d

[0091] Mode 2: d 1 +d 2 >d

[0092] According to the working state of the converter, the traditional triple phase shift transmission power, current stress and return power expressions are derived by sampling segment analysis method.

[0093] The transmission power expression is:

[0094]

[0095] Where: T is half a switching period, U 1 is the input voltage, i L is the current flowing through the inductor, and dt is the integration time.

[0096] The current stress expression is:

[0097] i Lmax =max(i L (t0 ),i L (t 1 )......i L (t n ))

[0098] Where: i Lmax is the maximum current flowing through the inductor, i L (t 0 ) is t 0 The current flowing through the inductor at any moment, i L (t 1 ) is t 1 The current flowing through the inductor at any moment, i L (t n ) is t n The current flowing through the inductor at any time.

[0099] The expression of return power is:

[0100]

[0101] Where: T is half a switching period, U 1 is the input voltage, i L is the current flowing through the inductor, and dt is the integration time.

[0102] For the convenience of analysis, the transmission power, current stress and return power are normalized to per unit. The normalized transmission power, current stress and return power are:

[0103]

[0104] in:

[0105] Combining the above formula and Figure 4 The triple bidirectional internal phase-shifted transmission power, current stress and return power can be obtained as:

[0106]

[0107] i N =2(k+2d-kd 1 -d 2 -1)

[0108]

[0109] The Lagrange multiplier method is usually used to solve the minimum current stress d and d 1 d 2 The optimal shift phase combination is used to establish the Lagrange multiplier method equation for solving the minimum current stress:

[0110] L(d,d 1 ,d2 ,μ)=i N +μ(P N -P 0 )

[0111] To obtain the optimal shift ratio combination, i N and P N Substitute the expression into the above formula and let:

[0112]

[0113] By solving the above equations, we can get the optimal shift phase combination:

[0114] Mode 1:

[0115] Mode 2:

[0116] According to the constraints of triple bidirectional inner phase shift modulation and inner and outer phase shift phase ratio, the power range of mode 1 and mode 2 can be obtained as follows:

[0117] Mode 1: 2(k-1) / k 2 <P 0 ≤1;

[0118] Mode 2: 0 ≤ P 0 <2(k-1) / k 2 .

[0119] Substitute the obtained optimal shift ratio combination into i N and Q N The minimum current stress and return power are obtained by using the following expressions:

[0120]

[0121]

[0122] According to the above analysis, the relationship curves of current stress and return power with transmission power of triple bidirectional internal phase shift modulation are obtained. At the same time, the relationship curves of current stress and return power with transmission power of single phase shift modulation, double phase shift modulation and traditional triple phase shift modulation are given, as shown in Figure 2. Figure 5 , Figure 6 shown.

[0123] Figure 7 The closed-loop control block diagram of the triple bidirectional inner phase shift control method with current stress optimization is given. First, the input voltage and current and the output voltage and current are sampled, and the sampled output voltage value is subtracted from the command voltage value. The difference is sent to the closed-loop regulator to obtain the outer phase shift ratio d. The output voltage is controlled to be stable through d, and then the inner phase shift ratio d is obtained according to the current stress optimization algorithm. 1 d2 , combined with internal and external phase shift d, d 1 d 2 Generate a PWM drive signal to modulate the converter. Specifically, first calculate the output power, determine the working mode of the converter, and then obtain the internal shift ratio d of the corresponding mode. 1 d 2 , d, d 1 d 2 Sent to the controller to generate PWM drive signal.

[0124] To summarize, the present invention obtains a triple bidirectional inner phase-shift control method by changing the moving direction of the inner phase in the traditional triple phase-shift. Based on this method, with current stress minimization as the goal, the Lagrange multiplier method is combined to solve the optimal phase shift ratio combination, and the converter is controlled using the optimal phase shift ratio combination. Compared with single-phase and double-phase-shift control, the converter current stress and return power can be further optimized, and the conversion efficiency of the converter can be effectively improved. The triple bidirectional inner phase-shift control method proposed in the present invention has the advantages of fewer working modes, simple analysis process, simple control process, and easy implementation compared to the traditional triple phase-shift control method. It is more suitable for application in actual engineering and has stronger practicality.

Claims

1. A triple bi-directional internal phase-shift control method for optimizing the current stress of a dual-active-bridge converter, characterized in that: This method includes the following steps in sequence: (1) According to the working states of the converter under triple bi-directional internal phase-shift modulation, establish a mathematical model of the relationship between the transmission power, current stress and reflux power of the two working modes of triple bi-directional internal phase-shift with the change of the internal and external phase-shift ratios; (2) Based on the mathematical model of the relationship between the transmission power, current stress and reflux power of the two working modes of triple bi-directional internal phase-shift with the change of the internal and external phase-shift ratios, taking the minimization of current stress as the control target, establish a Lagrangian multiplier equation, and solve the phase-shift ratio combination when the current stress is minimized in the two working modes of the triple bi-directional internal phase-shift control method, that is, the optimal phase-shift ratio; (3) Based on the optimal phase-shift ratio, combined with the constraint conditions of the internal and external phase-shift ratios of the two working modes, determine the working ranges of the two working modes, and combined with the mathematical model of the relationship between the transmission power, current stress and reflux power of the two working modes of triple bi-directional internal phase-shift with the change of the internal and external phase-shift ratios, obtain the magnitudes of the minimized current stress and reflux power, and generate PWM pulses through the optimal phase-shift ratio to modulate the converter; In step (1), the mathematical model of the relationship between the transmission power, current stress and reflux power of the two working modes of triple bi-directional internal phase-shift with the change of the internal and external phase-shift ratios is: Mode 1: P N = 2(2d - 2d 2 + 2dd 1 + 2dd 2 - d 1 2 - d 1 - d 1 d 2 - d 2 - d 2 2 )(1) Mode 2: P N = 2(2d - d 2 + d 1 d 2 - d 1 - d 2 )(2) i N = 2(k + 2d - kd 1 - d 2 - 1)(3) Mode 1: Q N =(k + 2d - 2d 1 - kd 1 - d 2 - 1) 2 / 2(k + 1)(4) Mode 2: Q N =(k - kd 1 + d 2 - 1) 2 / 2k (5) Equations (1) and (2) are for the transmission power P N per-unit expressions, with the per-unit base being the maximum transmission power nU 1 U 2 / 8fL, where n is the turns ratio of the high-frequency transformer, U 1 is the input voltage, U 2 is the output voltage, f is the switching frequency, and L is the inductance value in the main circuit; Equation (3) is for the current stress i N per-unit expression, with the per-unit base being the current value nU corresponding to the maximum transmission power 2 / 8fL; Equations (4) and (5) are for the reflux power Q N per-unit expressions, with the per-unit base being the maximum transmission power nU 1 U 2 / 8fL, k = U 1 / nU 2 is the voltage transmission ratio, d is the phase shift ratio between the full-bridge H 1 and the full-bridge H 2 bridge, called the external phase shift ratio, d 1 and d 2 are respectively the internal phase shift ratios of the H 1 and H 2 bridges, called the internal phase shift ratios; The constraint conditions of the internal and external phase-shift ratios of the two working modes are: Mode 1: d 1 +d 2 <d; Mode 2: d 1 +d 2 >d.

2. The triple bi-directional internal phase-shift control method for optimizing the current stress of a dual-active-bridge converter according to claim 1, characterized in that: In step (2), the Lagrangian multiplier equation is: L(d,d 1 ,d 2 ,μ)=i N -μ(P N -P 0 ) i N = 2(k + 2d - kd 1 - d 2 - 1) where μ is the Lagrange multiplier factor, P 0 is the per-unit value of the actual output power, P N is the transmission power, d is the phase shift ratio between the full-bridge H 1 and the full-bridge H 2 bridges, which is called the external phase shift ratio, d 1 , d 2 are respectively the internal phase shift ratios of the H 1 , H 2 bridges, which are called the internal phase shift ratios, i N is the current stress.

3. The triple bi-directional internal phase-shift control method for optimizing the current stress of a dual-active-bridge converter according to claim 1, characterized in that: In step (2), the optimal phase-shift ratio is: Mode 1: Mode 2: Where, P 0 is the per-unit value of the actual output power, d is the phase shift ratio between the full-bridge H 1 and the full-bridge H 2 bridges, known as the external phase shift ratio, d 1 , d 2 are respectively the internal phase shift ratios of the H 1 , H 2 bridges, known as the internal phase shift ratios; k = U 1 / nU 2 is the voltage transfer ratio, n is the turns ratio of the high-frequency transformer, U 1 is the input voltage, and U 2 is the output voltage.

4. The triple bi-directional internal phase-shift control method for optimizing the current stress of a dual-active-bridge converter according to claim 1, characterized in that: In step (3), the working ranges of the two working modes are: Mode 1: 2(k - 1) / k 2 <P 0 ≤ 1; Mode 2: 0 ≤ P 0 <2(k - 1) / k 2 ; Among them, P 0 is the per-unit value of the actual output power, k = U 1 / nU 2 is the voltage transmission ratio, n is the turns ratio of the high-frequency transformer, U 1 is the input voltage, U 2 is the output voltage; The minimized current stress is: Mode 1: Mode 2: The reflux power is the power in the stage when the AC voltage output by the full-bridge H 1 is positive and the inductor current is negative. The magnitude of the reflux power is: Mode 1: Mode 2: Q N = 0.

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