CN103199707A - Method for controlling drive pulses of DAB type bidirectional isolation DC-DC converter - Google Patents

Abstract

The invention relates to a method for controlling drive pulses of a DAB type bidirectional isolation DC-DC converter. The method for controlling the drive pulses of the DAB type bidirectional isolation DC-DC converter comprises the steps of firstly, carrying out drive pulse control on the DAB type bidirectional isolation DC-DC converter based on a drive pulse working principle; and then inferring relevant formulas in the mode of control, and carrying out characteristic analysis and verification. The method for controlling the drive pulses of the DAB type bidirectional isolation DC-DC converter only needs to control a single variable, is simple and practical, applicable to the state of light load of a system, simple in algorithm, convenient to achieve, and prone to feedback regulation, reduces stress of devices, and effectively improves system efficiency when the system is in light load.

Description

A DAB type bidirectional isolation DC-DC converter driving pulse control method

technical field

The invention relates to a modulation technology of a switching power tube of a bidirectional isolation DC-DC converter, in particular to a driving pulse control method of a DAB type bidirectional isolation DC-DC converter.

Background technique

DAB type DC-DC converter is widely used in uninterruptible power supply (UPS), clean energy conversion system, energy double-fed system, And electric vehicle lithium battery charging and discharging equipment, etc. Its basic topology is shown in Figure 1. The primary full bridge B ₁ is connected to the secondary full bridge B ₂ through a transformer. Each full bridge is composed of 4 controllable switches and anti-parallel diodes. The transformer T ensures electrical isolation. , the transformation ratio is n:1, L is the leakage inductance of the transformer or an external equivalent leakage inductance, which plays the role of transferring energy in the circuit.

The loss of the DAB converter mainly includes conduction loss and switching loss. Among them, the magnetic loss of the transformer and the switching loss of the switching device are positively correlated with _{the peak} current I peak flowing through the transformer, leakage inductance and switching device, the copper loss of the transformer is positively correlated with the effective value of the conduction loss current I _rms of the switching tube, and the current The greater the reactive power Q _L of the leakage inductance, the greater the fluctuation of the output voltage and current, which will lead to the increase of the ESR loss of the capacitor.

At present, the DAB type bidirectional isolated DC-DC converter generally adopts the traditional single-phase-shift control method (Conventional single-phase-shift Strategy, CSPS), the driving pulse of each switching tube is ideally a 50% square wave pulse, and The driving pulses of the upper and lower switching tubes of the same bridge arm are complementary. By controlling the phase-shift duty ratio D of the drive pulse of the _B1 bridge and _B2 bridge corresponding to the switching tubes (such as _Q1 and _S1 , _Q4 and _S4 ), the magnitude and flow direction of the output power P are controlled, while the same side bridge The driving pulses of the inner diagonal switch tubes are synchronized (such as Q ₁ and Q ₄ of the B ₁ bridge, S ₁ and S ₄ of the B ₂ bridge). Taking the power flow direction as the flow from _U1 to _U2 as an example, the driving waveforms of each switching device and related voltage and current waveforms are shown in Figure 2, where U _P and U _S are both 50% square wave voltages, and the leakage inductance voltage U _L and current I _L alternate periodically. However, under this control mode, when the system is light-loaded and the output voltage differs greatly from the rated output voltage of the system, the converter has the following problems:

1. If the current peak value I _peak and current effective value I _rms flowing through the transformer, leakage inductance and switching devices are too large, the stress on the relevant devices will increase, and the cost of the devices will increase.

2. The voltage at both ends of the leakage inductance is large, the maximum rise rate of the inductor current is large, and the external electromagnetic interference to the system increases, resulting in a decrease in system reliability.

3. The peak value of current I _peak , the effective value of current I _rms and the reactive power Q _L of the system are too large, which causes the system loss to increase and the system efficiency to be low.

The current dual-phase-shift control method solves the above problems under the premise of ensuring power output by controlling two phase-shift angle variables, but the dual-phase-shift control method needs to control two phase-shift angle variables, which requires a large amount of calculation and complicated control methods , it is not easy for feedback regulation and engineering realization.

Contents of the invention

In order to solve the problems raised in the above-mentioned background technology, the present invention proposes a new single-phase-shift control method (Novel single-phase-shift Modulation Strategy, NSPS), DAB type bidirectional isolation DC-DC converter drive pulse control method. The idea is: firstly, a DAB-type bidirectional isolation DC-DC converter working in the drive pulse control method is proposed, and secondly, the relevant formulas under this control mode are derived, and the characteristics are analyzed and verified. This control method is mainly suitable for low and medium power output of the system, and well solves the problems mentioned in the background art.

Technical scheme of the present invention is as follows:

A DAB type bidirectional isolation DC-DC converter drive pulse control method, the control method comprising: input side bridge B1 internal phase shifting, control mode 1 of output side bridge B2 without phase shifting and output side bridge B2 internal phase shifting, Control mode 2 without phase shifting in input side bridge B1,

The control mode of the control mode 1 is: if the power flow direction flows from _U1 to _U2 , control the diagonal switch tube _Q1 of the _B1 bridge to be turned on ahead of the time t of the _Q4 tube, and the switch of the _B2 bridge The driving pulses of tubes S ₁ and S ₄ are synchronized with the Q ₄ tube of B ₁ , and at the same time, the driving pulse of switching tube Q ₂ Q ₃ S ₂ S ₃ is complementary to the driving pulse of the switching tube of the same bridge arm; if the power flow direction is determined by When U ₂ flows to U ₁ , the switching tube Q ₁ of the B ₁ bridge is controlled to be turned on after the time t of the Q ₄ tube, and the driving pulses of the switching tubes S _{1 and} S ₄ of the B ₂ bridge are synchronized with the Q ₄ tube of B ₁ . The driving pulse of the switching tube Q ₂ Q ₃ S ₂ S ₃ is complementary to the driving pulse of the switching tube of the same bridge arm;

The control method of the control mode two is: if the power flow direction flows from _U1 to _U2 , then the switching tube _S1 of the _B2 bridge is controlled to be turned on at a time t lagging behind the _S4 tube, and the switching tube of the _B1 bridge The driving pulses of Q ₁ Q ₄ are all synchronized with the Q ₄ tube of B _1. At the same time, the driving pulses of the switching tubes Q ₂ Q ₃ S ₂ S ₃ are complementary to the driving pulses of the switching tubes under the same bridge arm; if the power is controlled by U ₂ flows in the direction of U ₁ , then the switching tube S ₁ of the secondary bridge B ₂ is controlled to be turned on ahead of the time t of the S ₄ tube, and the driving pulses of the switching tubes Q ₁ Q ₄ of the B ₁ bridge are all consistent with the Q ₄ of B ₁ The tubes are kept synchronous, and at the same time, the driving pulses of the switching tubes Q ₂ Q ₃ S ₂ S ₃ are complementary to the driving pulses of the switching tubes under the same bridge arm.

The advantages of the present invention are:

When applied to small and medium power loads: 1. It greatly reduces the peak value and effective value of current flowing through transformers, inductors and switching devices, reducing device stress. 2. The reactive power of the system is greatly reduced. 3. Significantly reduce system loss. 4. Improved system efficiency.

Description of drawings

Figure 1 is the circuit topology on which the invention is based.

Figure 2 is the traditional pulse control method, that is, the CSPS working mode.

Fig. 3 (a) is the Mode1 mode of the pulse control mode (ie NSPS working mode) proposed by the present invention.

Figure 3(b) is the Mode2 mode of the pulse control mode proposed by the present invention (that is, the NSPS working mode).

Fig. 4(a) is a comparison chart of system output power per unit and CSPS working mode under the control mode provided by the present invention.

Fig. 4(b) is a comparison chart of the system output current per unit value and the CSPS working mode under the control mode provided by the present invention.

Fig. 5(a) is a comparison chart of the three-dimensional characteristic curve of the leakage inductance current peak per unit value under the control mode Mode1 mode provided by the present invention and the CSPS working mode.

Figure 5(b) is a comparison diagram of the two-dimensional characteristic curve of the leakage inductance current peak per unit value in Mode1 mode based on the control method provided by the present invention and the CSPS working mode with the output voltage per unit value as a parameter.

Fig. 5(c) is a comparison chart of the three-dimensional characteristic curve of the leakage inductance current peak per unit value in Mode2 mode based on the control method provided by the present invention and the CSPS working mode.

Figure 5(d) is a comparison diagram of the two-dimensional characteristic curve of the leakage inductance current peak per unit value in Mode2 mode based on the control method provided by the present invention and the CSPS working mode with the output voltage per unit value as a parameter.

Fig. 6(a) is a comparison diagram of the three-dimensional characteristic curve of reactive power per unit value in Mode1 mode based on the control method provided by the present invention and the CSPS working mode.

Fig. 6(b) is a comparison diagram of the two-dimensional characteristic curve of the reactive power per unit value in Mode1 mode based on the control method provided by the present invention and the CSPS working mode with the output voltage per unit value as a parameter.

Fig. 6(c) is a comparison chart of the three-dimensional characteristic curve of reactive power per unit value in Mode2 mode based on the control method provided by the present invention and the CSPS working mode.

Fig. 6(d) is a comparison chart of the two-dimensional characteristic curve of the reactive power per unit value in Mode2 mode based on the control method provided by the present invention and the CSPS working mode with the output voltage per unit value as a parameter.

Detailed ways

First, introduce the working principle of this control method, as shown in Figure 3, the working principle of the driving pulse. The NSPS control method causes the phase shift of the diagonal switch tubes of the full bridge on one side by driving pulses, thereby outputting a three-level voltage waveform, while the full bridge on the other side does not need any phase shift control. Therefore, the NSPS control method includes two control modes, namely Mode 1 (Mode 1): phase shifting in the B1 bridge and no phase shifting in the B2 bridge; Mode 2 (Mode 2): phase shifting in the B2 bridge and no phase shifting in the B1 bridge.

In the control mode of Mode1, if the power flow direction is from _U1 to _U2 , taking the driving pulse of _Q4 tube in Figure 1 as a reference, the time to control the diagonal switch tube _Q1 of the _B1 bridge is ahead of _Q4 tube t is turned on, and the driving pulses _{of the} switch tubes _S1 and _S4 of the _B2 bridge _are synchronized with the _Q4 tube of _{B1 .} The driving pulses are complementary. Similarly, if the power flow direction is from U ₂ to U ₁ , it is enough to control the switching tube Q ₁ of the B ₁ bridge lagging behind the Q ₄ tube time t to turn on, and the driving pulse of the switching tube S ₁ S ₄ of the B ₂ bridge Both are synchronized _with the _Q4 tube _{of B1, and the driving pulse of the switching tube Q2Q3S2S3 is complementary} to the driving pulse of the switching tube of the _same bridge arm.

In Mode1 control mode, taking power flowing from U ₁ to U ₂ as an example, the driving waveforms of each switch tube, the corresponding voltage and current waveforms, and the conduction devices at each stage are shown in Figure 3 (a), and U _P is a three-level Voltage, define the U _P high-level duty cycle as D, 0≤D≤1, then the high-level duration is D*π, t=TD*T, T is half the system duty cycle and T=1/ 2f, f is the operating frequency of the system. And U _S is a voltage square wave with positive and negative symmetry, U _S = _nUN , the rising edge of the high level of _UP is synchronized with the rising edge of the high level of U _S. The voltage U _L and the current _IL at both ends of the inductor are symmetrical and periodic.

The control method of Mode2 is similar to that of Mode1. The diagonal switch tubes in the B2 bridge generate a phase shift, while the diagonal switch tubes in the B1 bridge have no phase shift. Under the control mode of Mode2, if the power flows from _U1 to _U2 , the switching tube _S1 of the _B2 bridge is controlled to be turned on after the time t of the _S4 tube, and the switching tube _Q1 of the _B1 bridge is driven by _Q4 The pulses are all synchronized with the _Q4 tube _{of B1} , and at the same time, the driving pulses of the switching tubes _Q2Q3S2S3 are complementary to the _driving pulses of the switching tubes under the _same bridge arm. Similarly, if the power flows from U ₂ to U ₁ , the switch tube S ₁ of the secondary bridge B ₂ is controlled to be turned on ahead of the time t of the S ₄ tube, and the drive pulse of the switch tube Q ₁ Q ₄ of the B ₁ bridge They are all synchronized with the _Q4 tube _{of B1, and at the same time, the driving pulses of the switching tubes Q2Q3S2S3 are complementary to} the driving pulses of the switching tubes under the _same bridge arm.

Under the control mode of Mode2, taking the power flow direction from U ₁ to U ₂ as an example, the driving waveforms of each switch tube, the corresponding voltage and current waveforms, and the conduction devices at each stage are shown in Figure 3(b), and U _S is three Level voltage, U _S =nU _N , and U _S high-level duty cycle is D, 0≤D≤1, high-level duration is D*π, t=TD*T, _UP is positive and negative Symmetrical voltage square wave. The voltage U _L and the current _IL at both ends of the inductor are symmetrical and periodic. It can be known from the above that both Mode1 and Mode2 can realize buck-boost control and bidirectional power flow. For the sake of convenience, the present invention analyzes Mode1 and Mode2 control modes by taking power flowing from _U1 to _U2 as an example.

Under the two control modes of Mode1 and Mode2, the output power P, output current _Io and output voltage _U2 of the entire DAB converter are:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, n is the transformation ratio of the transformer, L is the leakage inductance of the transformer, f is the system frequency, D is the high-level duty cycle of _UP in Mode1 or the high-level duty cycle of U _S in Mode2, R is the load, etc. effective resistance.

Under the two modes, the leakage inductance current values at different moments shown in Fig. 3(a) and Fig. 3(b) are shown in Table 1.

Table 1 Leakage current values at different times in two modes

Under different conditions, the peak value of the leakage inductance current is shown in Table 2

Table 2 Leakage current peak values in two modes

The reactive power flowing through the system is the reactive power of the leakage inductance:

Q=U _rms *I _rms (5)

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; rms</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\sqrt{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}}& \mathrm{<span\; class="notranslate">\; mode</span>}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}}& \mathrm{<span\; class="notranslate">\; mode</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; rms</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 18</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 9</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="mode"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">mode</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="12"\; label="f"\; filenames="2013100874701100003DEST\_PATH\_IMAGE003.png"\; state="\{\{state\}\}">f</figure-callout></span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 18</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 9</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \mathrm{<span\; class="notranslate">\; mode</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="12"\; label="f"\; filenames="2013100874701100003DEST\_PATH\_IMAGE003.png"\; state="\{\{state\}\}">f</figure-callout></span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 18</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 9</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; *</span>\sqrt{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="D.\; mode"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">D.</figure-callout></span><figure-callout\; id="1"\; label="D.\; mode"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">\; </figure-callout>}}& \mathrm{<span\; class="notranslate">\; </span>}\mathrm{<span\; class="notranslate">mode</span>}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="12"\; label="f"\; filenames="2013100874701100003DEST\_PATH\_IMAGE003.png"\; state="\{\{state\}\}">f</figure-callout></span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 18</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 9</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; *</span>\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}}& \mathrm{<span\; class="notranslate">\; mode</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

For the convenience of analysis and comparison, the relevant formulas in the CSPS mode are given, D ₁ is the phase shift duty cycle between bridges, 0≤D ₁ ≤1:

$\mathrm{<span\; class="notranslate">\; CSPS</span>}\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; rms</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; 36</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; rms</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; rms</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; rms</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\end{array}\right.$

In order to make the conclusion more general and to facilitate comparative analysis, all the formulas of the NSPS and CSPS above are converted to the primary side of the transformer and processed as follows.

U _b =U ₁ $I_b=\frac{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}{\mathrm{\&omega;L}}$ $P_b=\frac{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1^2}{\mathrm{\&omega;\; L}}---\left(8\right)$

The per unitized results of output power, output current and voltage are as follows.

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; pu</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; \&pi;<figure-callout\; id="2"\; label="d"\; filenames="2013100874701100003DEST\_PATH\_IMAGE005.png,2013100874701100003DEST\_PATH\_IMAGE006.png"\; state="\{\{state\}\}">d</figure-callout></span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; NSPS</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="mode"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">mode</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; andMode</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; \&pi;d</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; CSPS</span>}\end{array}\right.$

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; pu</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; NSPS</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="mode"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">mode</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; andMode</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; CSPS</span>}\end{array}\right.$

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">u</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; NSPS</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="mode"\; filenames="DEST\_PATH\_IMAGE007.png,HDA00002935491700022.png"\; state="\{\{state\}\}">mode</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; andMode</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; CSPS</span>}\end{array}\right.$

Where d is the per-unit value of the output voltage converted to the input side through the transformer, which can also be called the voltage transformation ratio between the output side and the input side.

In terms of power output characteristics, the output power under NSPS reaches its maximum value when D is 50%. 4(b), the maximum output power and current under NSPS are only 1/2 of those under CSPS.

In order to compare and analyze the effects of the two control modes under NSPS and CSPS, all analyzes should be carried out under the condition that the output power is consistent. Under the same output voltage and output current, the comparison diagram of the current peak value under the two modes is shown in Figure 5(a)-Figure 5(d), where the high-level duty cycle under NSPS is 0≤D≤0.5, The CSPS down-phase shift duty ratio is 0≤D ₁ ≤0.5. Figure 5(a) and Figure 5(b) are the 3-D comparison chart and 2-D comparison of the current peak value i _peak of the system under Mode1 mode and CSPS under the same output power when the voltage ratio is 0≤d≤0.5 picture. Figure 5(c) and 5(d) are the 3-D and 2-D comparison diagrams of the current peak value i _peak of the system under Mode2 mode and CSPS under the same output power when the voltage ratio d≥2. According to the above comparison, within the corresponding range of voltage transformation ratio, the current peak value of the system in Mode1 and Mode2 is greatly reduced compared with the CSPS mode, which greatly reduces the system current stress and reduces the system loss. Correspondingly, the current effective value i _rms in the NSPS mode also achieves similar effects.

Correspondingly, the comparison of system reactive power can also draw conclusions similar to the comparison of current stress. Figure 6(a) and 6(b) are the 3-D comparison diagram and 2-D comparison diagram of the reactive power Q of the system under Mode1 mode and CSPS under the same output power when the voltage transformation ratio is 0≤d≤0.5 . Figure 6(c) and 6(d) are the 3-D comparison diagram and 2-D comparison diagram of the reactive power Q of the system under Mode2 mode and CSPS under the same output power when the voltage transformation ratio d≥2. It can be seen from the figure that within the corresponding range of voltage transformation ratio, the reactive power of the system in Mode1 and Mode2 is always smaller than that in CSPS mode, and is greatly reduced. For example, when d=0.1 and I _O [pu]=0.05 , the reactive power in Mode1 mode is only 4% of that in CSPS mode, thus greatly reducing system loss and improving system efficiency.

The following examples illustrate the present invention in detail. It should be emphasized that the following description is exemplary rather than limiting the scope and application of the present invention, and the power flows from _U1 to _U2 as an example.

A control method for a dual active bridge type bidirectional DC-DC converter comprises the following steps:

1) The first switching tube Q ₁ , the second switching tube Q ₂ , the third switching tube Q ₃ , the fourth switching tube Q ₄ , the fifth switching tube S ₁ , the sixth switching tube S ₂ , and the seventh switching tube S ₃ and the driving pulses of the eighth switching tube _S4 are square waves. In the NSPS control mode, regardless of whether the power conversion direction is from U ₁ to U ₂ or from U ₂ to U ₁ , ideally, the driving pulse of the second switching tube Q ₂ is complementary to the driving pulse of the first switching tube Q ₁ , the driving pulse of the third switching transistor _Q3 is complementary to the driving pulse of the fourth switching transistor _Q4 . The driving pulse of the sixth switching tube _S2 is complementary to the driving pulse of the fifth switching tube _S1 , and the driving pulse of the seventh switching tube _S3 is complementary to the driving pulse of the eighth switching tube _S4 . The NSPS control mode includes two control modes, MODE1 and MODE2.

2) If the MODE1 control mode is adopted, when the power conversion direction is from _U1 to _U2 , as shown in Figure 3a, the driving pulse of the first switching tube _Q1 should be generated relative to the driving pulse of the fourth switching tube _Q4 Advance phase-shift duty cycle 1-D (that is, make the driving pulse generation time of the first switching tube _Q1 ahead of the driving pulse time of the first switching tube _Q1 by t, t=T-DT), D is The high-level duty cycle of the three-level voltage U _p ; the driving pulse of the fifth switching tube _S1 and the driving pulse of the eighth switching tube _S4 are always consistent; the driving pulse of the fifth switching tube _S1 and the fourth switching tube The driving pulse of the tube _Q4 remains consistent or generates a very small phase-shifting duty cycle D _d (D _d <=0.1).

Similarly, in MODE1 control mode, when the power conversion direction is from _U2 to _U1 , the driving pulse of the first switching tube _Q1 should produce a lag phase-shift duty cycle relative to the driving pulse of the fourth switching tube _Q4 1-D (that is: make the time of the driving pulse of the first switching tube _Q1 lag behind the time of the driving pulse of the first switching tube _Q1 by t, t=T-DT), D is the three-level voltage U _p High-level duty cycle; the driving pulse of the fifth switching tube _S1 is always consistent with the driving pulse of the eighth switching tube _S4 ; the driving pulse of the fifth switching tube _S1 is consistent with the driving pulse of the fourth switching tube _Q4 Consistent or very small phase shift duty cycle D _d (D _d <=0.1).

2) If the MODE2 control mode is adopted, when the power conversion direction is from _U1 to _U2 , as shown in Figure 3b, the driving pulse of the fifth switching tube _S1 should be generated relative to the driving pulse of the eighth switching tube _S4 The hysteresis phase-shift duty cycle is 1-D (that is, the generation time of the driving pulse of the fifth switching tube _S1 is lagged behind the time of the driving pulse of the eighth switching tube _S4 by t, t=T-DT), and D is three The high-level duty cycle of the level voltage U _s ; the driving pulse of the first switching tube _Q1 is always consistent with the driving pulse of the fourth switching tube _Q4 ; the driving pulse of the first switching tube _Q1 is consistent with the driving pulse of the eighth switching tube The drive pulse of S ₄ remains consistent or produces a very small phase-shift duty cycle D _d (D _d <=0.1).

Similarly, in the MODE2 control mode, when the power conversion direction is from _U2 to _U1 , the driving pulse of the fifth switching tube _S1 should generate an advanced phase shift duty relative to the driving pulse of the eighth switching tube _S4 Ratio 1-D (i.e., the generation time of the driving pulse of the fifth switching tube _S1 is ahead of the time of the driving pulse of the eighth switching tube _S4 by t, t=T-DT), D is the three-level voltage U _s The high-level duty cycle; the driving pulse of the first switching tube _Q1 and the driving pulse of the fourth switching tube _Q4 are always consistent; the driving pulse of the first switching tube _Q1 and the driving pulse of the eighth switching tube _S4 Keep consistent or produce very small phase shift duty cycle D _d (D _d <=0.1).

3) The duty cycle of the drive pulse is 50% (ideally). The first switch tube Q ₁ , the second switch tube Q ₂ , the third switch tube Q ₃ , the fourth switch tube Q ₄ , the fifth switch tube S ₁ , and the sixth switch tube S ₂ are controlled by an analog circuit or a microprocessor. , the driving pulses of the seventh switching tube _S3 and the eighth switching tube _S4 .

4) The closed-loop working mode of the dual active bridge bidirectional DC-DC converter under the NSPS control mode is shown in Figure 6. Compare the sampling voltage V at the output of the dual active bridge bidirectional DC-DC converter with the set reference voltage V_ref in real time, and control the size of D through feedback adjustment, and finally adjust the driving pulse of the switching tube to control the dual active bridge Bidirectional DC-DC converter. The basic feedback adjustment principle is: when the sampling voltage V is lower than the set voltage V_ref, if the working range of D is 0<=D<=0.5, increase the value of D, if the working range of D is 0.5≤D<=1 , reduce the value of D. When the sampling voltage V is higher than the set voltage V_ref, if the working range of D is 0<=D<=0.5, reduce the value of D; if the working range of D is 0.5<=D<=1, increase the value of D value. Since there is only one controlled quantity, the control method is simple and convenient for feedback adjustment. If the power output exceeds the power output range under the NSPS control mode, it can be switched to other control modes, such as the CSPS control mode, to ensure the system output power requirements.

It can be seen from the above that the NSPS control method proposed by the present invention is suitable for small and medium power loads, and greatly reduces the effective value, peak value and system reactive power of the current flowing through the transformer. It is of great significance to reduce device stress, improve system stability, reduce system loss, and improve system efficiency. Experiments have proved that the maximum system efficiency can be increased by 30% under NSPS control mode.

It should be understood that the above detailed description of the technical solution of the present invention with the aid of preferred embodiments is illustrative rather than restrictive. Those skilled in the art can modify the technical solutions recorded in each embodiment on the basis of reading the description of the present invention, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the corresponding technical solutions Essentially deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (1)

1. the two-way isolation DC-DC of DAB type converter driving pulse control method, it is characterized in that this control method comprises: phase shift in the input side bridge B1, phase shift in the control model one of not phase shift and the outlet side bridge B2 in the outlet side bridge B2, the control model two of not phase shift in the input side bridge B1

The control mode of described control model one is: if the flow of power direction is by U ₁To U ₂Flow control B ₁The diagonal switching tube Q of bridge ₁Be ahead of Q ₄The t conducting of pipe time, and B ₂The switching tube S of bridge ₁And S ₄Driving pulse all and B ₁Q ₄Pipe is synchronous, simultaneously, and switching tube Q ₂Q ₃S ₂S ₃Driving pulse and the driving pulse complementation of same brachium pontis switching tube; If the flow of power direction is by U ₂To U ₁Flow, then control B ₁The switching tube Q of bridge ₁Lag behind Q ₄The t conducting of pipe time, B ₂The switching tube S of bridge ₁S ₄Driving pulse all and B ₁Q ₄Pipe is synchronous, switching tube Q ₂Q ₃S ₂S ₃Driving pulse and the driving pulse complementation of same brachium pontis switching tube;

The control mode of described control model two is: if the flow of power direction is by U ₁To U ₂Direction flows, and then controls B ₂The switching tube S of bridge ₁Lag behind S ₄The t conducting of pipe time, and B ₁The switching tube Q of bridge ₁Q ₄Driving pulse all and B ₁Q ₄Pipe keeps synchronously, simultaneously, and switching tube Q ₂Q ₃S ₂S ₃Driving pulse all with same brachium pontis under the driving pulse complementation of switching tube; If power is by U ₂To U ₁Direction flows, and then controls secondary bridge B ₂Switching tube S ₁Be ahead of S ₄The t conducting of pipe time, and B ₁The switching tube Q of bridge ₁Q ₄Driving pulse all and B ₁Q ₄Pipe keeps synchronously, simultaneously, and switching tube Q ₂Q ₃S ₂S ₃Driving pulse all with same brachium pontis under the driving pulse complementation of switching tube.

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