CN105099200A - Alternating-current phasor analysis method and modeling method for phase-shifting control dual active bridge direct-current converters - Google Patents

Abstract

The present invention provides a kind of exchange phasor analysis for being suitable for all phase shifting controls lower pair active bridge (double active H bridges, dual three-level half-bridge or side tri-level half-bridge, active H bridge in the other side etc.) DC converter and small-signal model modeling methods. Specific steps are as follows: 1, by equivalent each active bridge is exchanged into side be equivalent to two square-wave voltage sources, the superposition that square-wave voltage is decomposed into sinusoidal voltage is decomposed by Fourier space, obtains the phasor expression formula of (2n+1) component of degree n n voltage and inductive current 2, the control characteristic of different phase shifting controls and the phasor diagram of control range are obtained according to phasor expression formula in step 1; 3, the complex power of (2n+1) component of degree n n is obtained according to phasor representation formula in step 1 With Analyze the active and reactive power characteristic of lower pair of active bridge DC converter of different phase shifting controls; 4, the time domain Fourier space and expression formula that its voltage and electric current are obtained according to step 1 phasor expression formula obtain the unified small-signal model suitable for all phase-shifting control methods.

Description

The two active bridge DC converter of phase shifting control exchanges phasor analysis and modeling method

Technical field

The invention belongs to power electronic technology and intelligent grid research field, particularly relate to a kind of two active bridge circuit power analysis method of phase shifting control based on phasor approach and modeling.

Background technology

Along with the development of intelligent grid, no industrial frequency transformer high-power power electronic converter more and more causes the concern of people with features such as its high efficiency, intellectuality, low stain.No industrial frequency transformer high-power power electronic converter common at present adopts Cascade Topology Structure, is made up of cascade multi-level AC-DC rectification module, bidirectional DC-DC converter module and many level DC-AC inversion module.

Two active bridge DC-DC converter structure due to have the features such as electrical isolation, buck conversion, bidirectional energy transmission, high power density adopt by bidirectional DC-DC converter module.

The traditional analysis of the two active bridge of phase shifting control to power characteristic analysis, obtains power Mathematical Modeling by Definite Integral Calculation, and then analyzes the characteristic of through-put power and reactive power mainly on the basis analyzing phase shifting control principle waveform.Although this method can draw result more accurately, also there is obvious deficiency.Its major defect is calculation of complex, and physical significance is indefinite, and the result of analysis intuitively can not reflect the relation between through-put power and reactive power, and can not set up versatility model for multiple phase shift system traditional analysis.

[1]M.N.Kheraluwala,R.W.Gascoigne,D.M.Divan,andE.D.Baumann,“Performancecharacterizationofahigh-powerdualactivebridgeDC-to-DCconverter,”IEEETrans.Ind.Appl.,vol.28,no.6,pp.1294–1301,Nov./Dec.1992.

[2]R.W.DeDoncker,M.H.Kheraluwala,andD.M.Divan,“PowerconversionapparatusforDC/DCconversionusingdualactivebridges,”U.S.Patent5027264,Jun.25,1991.

Summary of the invention

For the shortcomings and deficiencies of traditional analysis, the object of the invention is to, a kind of phase shifting control based on phasor approach two active bridge (two active H bridge, dual three-level half-bridge or side tri-level half-bridge are proposed, the active H bridge of opposite side etc.) DC converter power analysis and modeling method, set up and a kind ofly can be used in the unified analytical model of multiple phase shifting control and set up small-signal model on the basis of this unified model.

In order to realize above-mentioned task, the present invention takes following technical solution:

The two active bridge DC converter power analysis of phase shifting control based on phasor approach and modeling method, active bridge both end voltage is equivalent to two square-wave voltage source by the method for equivalence by the method, then square-wave voltage is decomposed into the superposition of sinusoidal voltage by Fourier series.By phasor approach, the active power of first-harmonic and each harmonic and reactive power are analyzed, replace the calculating of sinusoidal quantity with the calculating of plural number, greatly simplify calculating.And propose that a kind of physical significance based on phasor approach is clear, analysis result accurately and the analytical method of the simple two active bridge phase shifting control of computing, the unified small-signal model of two active bridge can be set up by this analytical method.

Based on the two active bridge circuit analytical method of the phase shifting control exchanging phasor approach and modeling method, comprise the following steps:

1) two active bridge DC converter equivalent model is replaced, and draws the voltage of (2n+1) component of degree n n and the phasor expression formula of inductive current;

2) according to step 1) middle phasor expression formula, corresponding phasor diagram under obtaining different phase shifting control;

3) according to step 1) in phasor expression formula, obtain the complex power expression formula of equivalent voltage source, analyze active power and reactive power characteristic under different phase shifting control;

4) according to step 1) in phasor expression formula and the converter differential equation, obtain Fourier series and the expression formula of two active bridge steady-state model time domain, adopt small-signal perturbation technique, steady-state model is introduced in small-signal disturbance, obtains the unified small-signal model of phase shifting control lower pair of active bridge DC converter.

The present invention improves further and is, step 1) in, two active bridge DC converter can substitute with equivalent model, and as shown in Figure 1, each active bridge AC voltage can use square-wave voltage source V _ab(t), V _cdt () represents, and can be expressed as the unlimited superposition of the sine wave signal of different frequency.

$V_{ab}\left(t\right)=V_{in}\left\{\frac{2}{\mathrm{\π}}\underset{n=0}{\overset{N}{\Σ}}\frac{sin(2n+1)\left(\mathrm{\ω}t\right)-in(2n+1)(\mathrm{\ω}t-{\mathrm{\α}}_1-\mathrm{\π})}{2n+1}\right\}---\left(1\right)$

$V_{cd}\left(t\right)=\frac{N_p}{N_s}{V}_{out}\left\{\frac{2}{\mathrm{\π}}\underset{n=0}{\overset{N}{\Σ}}\frac{sin(2n+1)(\mathrm{\ω}t-{\mathrm{\α}}_2)-sin(2n+1)(\mathrm{\ω}t-{\mathrm{\α}}_3-\mathrm{\π})}{2n+1}\right\}---\left(2\right)$

Wherein, V _abt () is active bridge 1 AC square-wave voltage, V _cdt () is active bridge 2 AC square-wave voltage, V _infor input direct voltage, V _outfor output dc voltage, for the high-frequency isolation transformer turn ratio, ω is for exchanging angular frequency, n=1,2,3..., α ₁for phase shifting angle in active bridge 1, α ₂for phase shifting angle between active bridge 1 and active bridge Bridge 2, α ₄for phase shifting angle in active bridge 2, α ₃for phase shifting angle α in active bridge 2 ₄and phase shifting angle α between bridge ₂sum.

The present invention improves further and is, step 1) carry the model that two sinusoidal ac potential sources are connected by inductive circuit, set up the state equation of switch function:

1) two active bridge DC converter friendship/cross ring joint state differential equation:

$V_{ab}\left(t\right)-\frac{N_p}{N_s}{V}_{cd}\left(t\right)-R_L{i}_L\left(t\right)-L_s\frac{d}{dt}{i}_L\left(t\right)=0---\left(3\right)$

Wherein R _lfor transformer resistance, L _sfor transformer leakage inductance, i _lt () is transformer current.

2) square-wave voltage source equivalent expression (1) and (2) are brought in formula (3) into the differential equation that can obtain based on switch function equivalence:

$\begin{array}{c}{R}_L{i}_L\left(t\right)+L_s\frac{d}{dt}{i}_L\left(t\right)=V_{in}\left\{\frac{2}{\mathrm{\π}}\underset{n=0}{\overset{N}{\Σ}}\frac{\sin (2n+1)\left(\mathrm{\ω}t\right)-in(2n+1)(\mathrm{\ω}t-{\mathrm{\α}}_1-\mathrm{\π})}{2n+1}\right\}\\ -\frac{N_p}{N_s}{V}_{out}\left\{\frac{2}{\mathrm{\π}}\underset{n=0}{\overset{N}{\Σ}}\frac{\sin (2n+1)(\mathrm{\ω}t-{\mathrm{\α}}_2)-sin(2n+1)(\mathrm{\ω}t-{\mathrm{\α}}_3-\mathrm{\π})}{2n+1}\right\}\end{array}---\left(4\right)$

The present invention improves further and is, step 1) in the voltage of (2n+1) component of degree n n and the phasor expression formula of inductive current can draw equilibrium transport amount expression formula according to the differential equation of claim 3 breaker in middle function equivalence:

$\begin{array}{c}\mathrm{\π}(2n+1)(R_L+{\mathrm{j\ωL}}_S(2n+1\left)\right){\stackrel{\·}{I}}_{L(2n+1)}{e}^{j0}=\sqrt{2}{V}_{in}\left(e^{j0}+e^{j(2n+1)(-{\mathrm{\α}}_1)}\right)\\ -\sqrt{2}\frac{N_p}{N_s}{V}_{out}\left(e^{j(2n+1)(-{\mathrm{\α}}_2)}+e^{j(2n+1)(-{\mathrm{\α}}_3)}\right)\end{array}---\left(5\right)$

And then determine (2n+1) component of degree n n phasor expression formula of square-wave voltage and inductive current:

${\stackrel{\·}{V}}_{ab(2n+1)}=\frac{\sqrt{2}{V}_{in}}{\mathrm{\π}(2n+1)}(\∠0+\∠(2n+1\left)\right(-{\mathrm{\α}}_1\left)\right)---\left(6\right)$

${\stackrel{\·}{V}}_{cd(2n+1)}=\frac{N_p}{N_s}\frac{\sqrt{2}{V}_{out}}{\mathrm{\π}(2n+1)}(\∠(2n+1\left)\right(-{\mathrm{\α}}_2)+\∠(2n+1\left)\right(-{\mathrm{\α}}_3\left)\right)---\left(7\right)$

${\stackrel{\·}{I}}_{L(2n+1)}=\frac{\left(\begin{array}{c}\sqrt{2}{V}_{in}(\∠0+\∠(2n+1)(-{\mathrm{\α}}_1))\\ -\sqrt{2}\frac{N_p}{N_s}{V}_{out}(\∠(2n+1\left)\right(-{\mathrm{\α}}_2)+\∠(2n+1\left)\right(-{\mathrm{\α}}_3\left)\right)\end{array}\right)}{\mathrm{\π}\left(2n+1\right)\left(R_L+{\mathrm{j\ωL}}_S\left(2n+1\right)\right)}---\left(8\right)$

The present invention improves further and is, according to step 1) in draw the equilibrium transport amount expression formula of voltage, inductive current (2n+1) component of degree n n phasor expression formula and converter, step 2 can be drawn respectively) outer phase shift between jackshaft, outer phase shift between phase shift and bridge in single active bridge, and in doube bridge between phase shift and bridge under outer phase shifting control, the phasor diagram of two active bridge DC converter.

The present invention improves further and is, according to step 1) under the voltage that draws, inductive current (2n+1) component of degree n n phasor expression formula can draw three kinds of phase shifting control, equivalent sinusoidal voltage source complex power and high frequency transformer leakage inductance L in two active bridge DC converter (2n+1) component of degree n n _sreactive power:

$\begin{array}{c}{\stackrel{\‾}{S}}_{ab(2n+1)}={\stackrel{\·}{V}}_{ab(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{\left\{\begin{array}{c}4V_{in}^2(1+\cos (2n+1){\mathrm{\α}}_1){\mathrm{cos\φ}}_z\\ -2\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\begin{array}{c}\cos \left(\right(2n+1){\mathrm{\α}}_2+{\mathrm{\φ}}_z)+\cos \left(\right(2n+1)({\mathrm{\α}}_2-{\mathrm{\α}}_1)+{\mathrm{\φ}}_z)\\ +\cos \left(\right(2n+1){\mathrm{\α}}_3+{\mathrm{\φ}}_z)+\cos \left(\right(2n+1)({\mathrm{\α}}_3-{\mathrm{\α}}_1)+{\mathrm{\φ}}_z)\end{array}\right)\end{array}\right\}}{{\mathrm{\π}}^2{(2n+1)}^2\left|Z_{(2n+1)}\right|}\\ +j\frac{\left\{\begin{array}{c}-2\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\begin{array}{c}\sin \left(\right(2n+1){\mathrm{\α}}_2+{\mathrm{\φ}}_z)+\sin \left(\right(2n+1)({\mathrm{\α}}_2-{\mathrm{\α}}_1)+{\mathrm{\φ}}_z)\\ +\sin \left(\right(2n+1){\mathrm{\α}}_3+{\mathrm{\φ}}_z)+\sin \left(\right(2n+1)({\mathrm{\α}}_3-{\mathrm{\α}}_1)+{\mathrm{\φ}}_z)\end{array}\right)\\ -4V_{in}^2(1+\cos (2n+1){\mathrm{\α}}_1){\mathrm{sin\φ}}_z\end{array}\right\}}{{\mathrm{\π}}^2{(2n+1)}^2\left|Z_{(2n+1)}\right|}\\ =P_{ab(2n+1)}+{\mathrm{jQ}}_{ab(2n+1)}\end{array}---\left(9\right)$

$\begin{array}{c}{\stackrel{\‾}{S}}_{cd(2n+1)}={\stackrel{\·}{V}}_{cd(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{\left\{\begin{array}{c}2\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\begin{array}{c}\cos \left(\left(2n+1\right){\mathrm{\α}}_2+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_2-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\\ +\cos \left(\left(2n+1\right){\mathrm{\α}}_2+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_2-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\end{array}\right)\\ -4{\left(\frac{N_p}{N_s}\right)}^2{V}_{out}^2\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right){\mathrm{cos\φ}}_z\end{array}\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^2\left|Z_{2n+1}\right|}\\ +j\frac{\left\{\begin{array}{c}2\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\begin{array}{c}\sin \left(\left(2n+1\right){\mathrm{\α}}_2+{\mathrm{\φ}}_z\right)+\sin \left(\left(2n+1\right)\left({\mathrm{\α}}_2-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\\ +\sin \left(\left(2n+1\right){\mathrm{\α}}_3+{\mathrm{\φ}}_z\right)+\sin \left(\left(2n+1\right)\left({\mathrm{\α}}_3-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\end{array}\right)\\ +4{\left(\frac{N_p}{N_s}\right)}^2{V}_{out}^2\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right){\mathrm{sin\φ}}_z\end{array}\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^2\left|Z_{2n+1}\right|}\\ =P_{cd\left(2n+1\right)}+{\mathrm{jQ}}_{cd\left(2n+1\right)}\end{array}---\left(10\right)$

$Q_{L(2n+1)}=j\left(\frac{-4V_{in}^2(1+cos(2n+1\left){\mathrm{\α}}_1\right){\mathrm{sin\φ}}_z-{\left(\frac{N_p}{N_s}\right)}^2{V}_{out}^2(1+cos(2n+1\left){\mathrm{\α}}_1\right){\mathrm{sin\φ}}_z}{{\mathrm{\π}}^2{(2n+1)}^2\left|Z_{(2n+1)}\right|}\right)---\left(11\right)$

Wherein, $\left|Z_{2n+1}\right|=\sqrt{R_L^2+{\left(\right(2n+1\left){\mathrm{\ωL}}_S\right)}^2},{\mathrm{\φ}}_z={\tan }^{-1}\left(\frac{(2n+1){\mathrm{\ωL}}_S}{R_L}\right).$

The present invention improves further and is, step 3) in complex power active power do not considering to equal DC output power in circuit loss situation, then active bridge 2 side output current (2n+1) component of degree n n phasor expression formula be:

${\stackrel{\·}{I}}_{DC(2n+1)}=j\frac{\left(\begin{array}{c}2\frac{N_p}{N_s}{V}_{in}\left(\begin{array}{c}\cos \left(\left(2n+1\right){\mathrm{\α}}_2+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_2-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\\ +\cos \left(\left(2n+1\right){\mathrm{\α}}_3+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_3-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\end{array}\right)\\ -4{\left(\frac{N_p}{N_s}\right)}^2{V}_{out}\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right){\mathrm{cos\φ}}_z\end{array}\right)}{{\mathrm{\π}}^2{\left(2n+1\right)}^2\left|Z_{2n+1}\right|}---\left(12\right)$

Under not considering to export DC bus capacitor impedance conditions, draw the equilibrium transport amount expression formula of DC side output voltage, DC bus capacitor electric current and load current:

$\begin{array}{c}j\left(2n+1\right)\mathrm{\ω}C{\stackrel{\·}{V}}_{out\left(2n+1\right)}={\stackrel{\·}{I}}_{C\left(2n+1\right)}\\ ={\stackrel{\·}{I}}_{DC\left(2n+1\right)}-{\stackrel{\·}{I}}_{load\left(2n+1\right)}\\ =j\frac{2\frac{N_p}{N_s}{V}_{in}\left(\begin{array}{c}\cos \left(\left(2n+1\right){\mathrm{\α}}_2+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_2-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\\ +\cos \left(\left(2n+1\right){\mathrm{\α}}_3+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_3-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\end{array}\right)}{{\mathrm{\π}}^2{\left(2n+1\right)}^2\left|Z_{2n+1}\right|}\\ -j\frac{4{\left(\frac{N_p}{N_s}\right)}^2{V}_{out}\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right){\mathrm{cos\φ}}_z}{{\mathrm{\π}}^2{\left(2n+1\right)}^2\left|Z_{2n+1}\right|}-{\stackrel{\·}{I}}_{load\left(2n+1\right)}\end{array}---\left(13\right)$

Wherein output voltage (2n+1) component of degree n n, for active bridge 2 side output current (2n+1) component of degree n n, C is output capacitor, for output capacitor electric current (2n+1) component of degree n n, for load current (2n+1) component of degree n n.

Obtain Fourier series and the expression formula of two active bridge steady-state model time domain:

$\begin{array}{c}\frac{{\mathrm{dV}}_{out}\left(t\right)}{dt}=\frac{1}{C}{i}_{DC}\left(t\right)-\frac{1}{C}{i}_{load}\left(t\right)\\ =\frac{2}{{\mathrm{\π}}^{2}C}\frac{N_p}{N_s}\underset{n=0}{\overset{N}{\Σ}}\frac{1}{{\left(2n+1\right)}^2}\left\{\begin{array}{c}\frac{V_{in}}{\left|Z_{2n+1}\right|}\left(\begin{array}{c}\cos \left(\left(2n+1\right){\mathrm{\α}}_2+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_2-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\\ +\cos \left(\left(2n+1\right){\mathrm{\α}}_3+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_3-{\mathrm{\α}}_1\right)+{\mathrm{\φ}}_z\right)\end{array}\right)\\ -2\frac{N_p}{N_s}\frac{V_{out}}{\left|Z_{2n+1}\right|}\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right){\mathrm{cos\φ}}_z\end{array}\right\}\\ -\frac{1}{C}{i}_{load}\left(t\right)\end{array}---\left(14\right)$

Near steady operation point, apply microvariations and substitute in steady-state model, setting up partial differential equation, show that phase shifting control lower pair of active bridge DC converter unifies small-signal model:

$\begin{array}{c}\frac{d\left({\mathrm{\ΔV}}_{out}\left(t\right)\right)}{dt}\\ =\frac{\∂f}{\∂V_{in}\left(t\right)}{|}_0{\mathrm{\ΔV}}_{in}\left(t\right)+\frac{\∂f}{\∂V_{out}\left(t\right)}{|}_0{\mathrm{\ΔV}}_{out}\left(t\right)+\frac{\∂f}{\∂i_{load}}{|}_0{\mathrm{\Δi}}_{load}\left(t\right)+\frac{\∂f}{\∂{\mathrm{\α}}_1}{|}_0{\mathrm{\Δ\α}}_1+\frac{\∂f}{\∂{\mathrm{\α}}_2}{|}_0{\mathrm{\Δ\α}}_2+\frac{\∂f}{\∂{\mathrm{\α}}_3}{|}_0{\mathrm{\Δ\α}}_3\\ =A_{in}{\mathrm{\ΔV}}_{in}\left(t\right)+A_{out}{\mathrm{\ΔV}}_{out}\left(t\right)+B_I{\mathrm{\Δi}}_{load}\left(t\right)+C_{{\mathrm{\α}}_1}{\mathrm{\Δ\α}}_1+C_{{\mathrm{\α}}_2}{\mathrm{\Δ\α}}_2+C_{{\mathrm{\α}}_3}{\mathrm{\Δ\α}}_3\end{array}---\left(15\right)$

In formula: $\left\{\begin{array}{c}{A}_{in}=-\frac{2}{{\mathrm{C\π}}^2}{\left(\frac{N_p}{N_s}\right)}^2\underset{n=0}{\overset{N}{\Σ}}\frac{\begin{array}{c}\cos \left(\left(2n+1\right){\mathrm{\α}}_{20}+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_{20}-{\mathrm{\α}}_{10}\right)+{\mathrm{\φ}}_z\right)\\ +\cos \left(\left(2n+1\right){\mathrm{\α}}_{30}+{\mathrm{\φ}}_z\right)+\cos \left(\left(2n+1\right)\left({\mathrm{\α}}_{30}-{\mathrm{\α}}_{10}\right)+{\mathrm{\φ}}_z\right)\end{array}}{{\left(2n+1\right)}^2\left|Z_{2n+1}\right|}\\ A_{out}=-\frac{4}{{\mathrm{C\π}}^2}{\left(\frac{N_p}{N_s}\right)}^2\underset{n=0}{\overset{N}{\Σ}}\frac{1}{{\left(2n+1\right)}^2}\left(\frac{1+\cos \left(2n+1\right){\mathrm{\α}}_{10}{\mathrm{cos\φ}}_z}{\left|Z_{2n+1}\right|}\right)\\ B_I=-\frac{1}{C}\\ C_{{\mathrm{\α}}_1}=\frac{2}{{\mathrm{C\π}}^2}\frac{N_p}{N_s}\underset{n=0}{\overset{N}{\Σ}}\left(\frac{V_{in}\left(\begin{array}{c}\sin \left(\left(2n+1\right)\left({\mathrm{\α}}_{20}-{\mathrm{\α}}_{10}\right)+{\mathrm{\φ}}_z\right)\\ +\sin \left(2n+1\right)\left({\mathrm{\α}}_{30}-{\mathrm{\α}}_{10}\right)+{\mathrm{\φ}}_z\end{array}\right)}{\left(2n+1\right)\left|Z_{2n+1}\right|}+\frac{2V_{out}\sin \left(2n+1\right){\mathrm{\α}}_{10}{\mathrm{cos\φ}}_z}{\left|Z_{2n+1}\right|}\right)\\ C_{{\mathrm{\α}}_2}=\frac{2V_{in}}{{\mathrm{C\π}}^2}\frac{N_p}{N_s}\underset{n=0}{\overset{N}{\Σ}}\frac{-\sin \left(\left(2n+1\right){\mathrm{\α}}_{20}+{\mathrm{\φ}}_z\right)-\sin \left(\left(2n+1\right)\left({\mathrm{\α}}_{20}-{\mathrm{\α}}_{10}\right)+{\mathrm{\φ}}_z\right)}{\left(2n+1\right)\left|Z_{2n+1}\right|}\\ C_{{\mathrm{\α}}_3}=\frac{2V_{in}}{{\mathrm{C\π}}^2}\frac{N_p}{N_s}\underset{n=0}{\overset{N}{\Σ}}\frac{-\sin \left(\left(2n+1\right){\mathrm{\α}}_{30}+{\mathrm{\φ}}_z\right)-\sin \left(\left(2n+1\right)\left({\mathrm{\α}}_{30}-{\mathrm{\α}}_{10}\right)+{\mathrm{\φ}}_z\right)}{\left(2n+1\right)\left|Z_{2n+1}\right|}\end{array}\right.$

Method of the present invention, by phasor approach, two active bridge circuit is analyzed, computational methods are simple, draw physical significance analytical model clearly, clearly draw two relation between active bridge power transfer characteristic and phase shift angle, and propose the method two active bridge circuit being set up to small-signal model on this basis.

Accompanying drawing explanation

Below in conjunction with accompanying drawing, the present invention is further described.

Fig. 1 is two active H bridge DC converter topologys;

Fig. 2 (a) is two active bridge DC converter equivalent electric circuits;

Fig. 2 (b) is two active bridge DC converter synchronous machine equivalent electric circuits;

Fig. 3 phase shifting control ideal waveform figure;

Fig. 4 is the phasor diagram of two active bridge in single phase shifting control strategy;

Fig. 5 is the phasor diagram of expansion phase shift at A mode control strategy;

Fig. 6 (a) is the phasor diagram of expansion phase shift B mode control strategy;

Fig. 6 (b) is expansion phase shift B mode control strategy, works as α ₂phasor diagram when=0;

Fig. 6 (c) is expansion phase shift B mode control strategy, when time phasor diagram;

Fig. 7 (a) is the phasor diagram of dual phase shifting control strategy;

Fig. 7 (b) is dual phase shifting control strategy, works as α ₂=0, α ₃=α ₁time phasor diagram;

Fig. 7 (c) is dual phase shifting control strategy, when time phasor diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments for the two active H bridge DC converter topology shown in Fig. 1, the present invention will be further described.

Figure 3 shows that and be respectively three kinds of phase shifting control strategy: single phase shift, expansion phase shift, dual phase shifting control ideal waveform figure; Wherein, V _ab(t), V _cdt () is two single-phase H bridge AC square-wave voltages, using the phase place of drive singal S1 as reference phase place, the phase delay between drive singal S4 and S1 is called the interior phase shifting angle α of H1 ₁; Phase delay between drive singal Q1 and S1 is called outer phase shifting angle α ₂; Phase delay between drive singal Q4 and S1, the i.e. interior phase shifting angle α of H2 ₄with outer phase shifting angle α ₂sum is called α ₃(α ₃=α ₂+ α ₄).

For the advanced H2 of H1, respectively analyzing examples is carried out to three kinds of phase shifting control strategy by exchanging phasor analysis method:

Because inductive resistance is enough little, negligible, the derivation of the apparent power of inductance is as follows:

$\begin{array}{c}{Q}_{L\left(2n+1\right)}={\stackrel{\·}{U}}_{L\left(2n+1\right)}^{*}{\stackrel{\·}{I}}_{L\left(2n+1\right)}\\ ={\left({\stackrel{\·}{V}}_{ab\left(2n+1\right)}-{\stackrel{\·}{V}}_{cd\left(2n+1\right)}\right)}^{*}{\stackrel{\·}{I}}_{L\left(2n+1\right)}\\ ={\stackrel{\·}{V}}_{ab\left(2n+1\right)}^{*}{\stackrel{\·}{I}}_{L\left(2n+1\right)}-{\stackrel{\·}{V}}_{cd\left(2n+1\right)}^{*}{\stackrel{\·}{I}}_{L\left(2n+1\right)}\\ =j\left(Q_{ab\left(2n+1\right)}-Q_{cd\left(2n+1\right)}\right)\end{array}---\left(1\right)$

As can be seen from formula (1), in phase shifting control strategy, the active-power P of advanced bridge H1 _{ab (2n+1)}be fully transmitted to delayed bridge H2 as output DC side power output, i.e. P _{ab (2n+1)}=P _{cd (2n+1)}.Inductance reactive power is provided jointly by advanced bridge H1 and delayed bridge H2.

1) single phase shifting control strategy phasor analysis method

Work as α ₁=0 and α ₄=0, that is, only have between two H bridges and there is phase shift.Now, the phasor expression formula abbreviation of two voltage sources is ${\stackrel{\·}{V}}_{ab(2n+1)}=\frac{2\sqrt{2}{V}_{in}}{\mathrm{\π}(2n+1)},{\stackrel{\·}{V}}_{cd(2n+1)}=\frac{N_p}{N_s}\frac{2\sqrt{2}{V}_{out}}{\mathrm{\π}(2n+1)}\∠(2n+1)(-{\mathrm{\α}}_2).$ Phasor delayed phasor angle be (2n+1) α ₂.Fig. 4 is the two phasor diagrams of active bridge DC converter under single phase shifting control strategy, and in figure, the mould of two phasors is identical, namely can find out as voltage V _in, when remaining unchanged, the power of two active bridge is by phase shifting angle α ₂regulate.

Under single phase shifting control strategy, each harmonic power sum is

$\left\{\begin{array}{c}{P}_{ab}=P_{cd}=8\frac{N_p}{N_s}\frac{V_{in}{V}_{out}}{{\mathrm{\π}}^2{\mathrm{\ωL}}_S}\underset{n=0}{\overset{N}{\Σ}}\frac{\sin \left(2n+1\right){\mathrm{\α}}_2}{{\left(2n+1\right)}^3}\\ Q_{ab}=8\frac{V_{in}}{{\mathrm{\π}}^2{\mathrm{\ωL}}_S}\underset{n=0}{\overset{N}{\Σ}}\frac{8\frac{N_p}{N_s}{V}_{out}\cos \left(2n+1\right){\mathrm{\α}}_2-8V_{in}}{{\left(2n+1\right)}^3}\\ Q_{cd}=8\frac{N_p}{N_s}\frac{V_{out}}{{\mathrm{\π}}^2{\mathrm{\ωL}}_S}\underset{n=0}{\overset{N}{\Σ}}\frac{8\frac{N_p}{N_s}{V}_{out}-8V_{in}\cos \left(2n+1\right){\mathrm{\α}}_2}{{\left(2n+1\right)}^3}\end{array}\right.---\left(2\right)$

2) phase shifting control strategy phasor analysis method is expanded

There are two kinds of phase shift systems in expansion phase shifting control strategy: 1. α ₁≠ 0 and α ₄=0; 2. α ₁=0 and α ₄≠ 0.

1. α ₁≠ 0 and α ₄=0

Voltage phasor expression formula is respectively ${\stackrel{\·}{V}}_{ab(2n+1)}=\frac{\sqrt{2}{V}_{in}}{\mathrm{\π}(2n+1)}(\∠0+\∠(2n+1\left)\right(-{\mathrm{\α}}_1\left)\right),$ phasor with the half that the angle of reference axis is phase shifting angle in HB1, namely fig. 5 is that expansion phase shift is expanding the phasor diagram under 1. mode control strategy, phasor track fall in Figure 5 with or for in the quarter circular arc of radius.The reactive power of inductance is:

Wherein,

? that is: α ₁=α ₂condition under, expansion phase shifting control strategy 1. under the reactive power of inductance obtain minimum value:

At α ₁=α ₂condition under, the reactive power Q of advanced bridge _{ab (2n+1)}=0, inductive current with advanced bridge equivalent voltage source same-phase, that is, in advance q _lminbe provided by delayed bridge completely, phasor diagram as shown in Figure 4.With this understanding, the through-put power of two active bridge is

2. α ₁=0 and α ₄≠ 0

Fig. 6 (a) expands phase shift 2. control strategy phasor diagram, and the phasor expression formula of two voltage sources is expressed as ${\stackrel{\·}{V}}_{cd(2n+1)}=\frac{N_p}{N_s}\frac{\sqrt{2}{V}_{out}}{\mathrm{\π}(2n+1)}(\∠(2n+1\left)\right(-{\mathrm{\α}}_2)+\∠(2n+1\left)\right(-{\mathrm{\α}}_3\left)\right).$ The complex power of advanced bridge H1, delayed bridge H2 is respectively

$\begin{array}{c}{\stackrel{\‾}{S}}_{ab(2n+1)}={\stackrel{\·}{V}}_{ab(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{\left\{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\sin \left(2n+1\right){\mathrm{\α}}_2+\sin \left(2n+1\right){\mathrm{\α}}_3\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ +j\frac{\left\{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\cos \left(2n+1\right){\mathrm{\α}}_2+\cos \left(2n+1\right){\mathrm{\α}}_3\right)-8V_{in}^2\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ =P_{ab\left(2n+1\right)}+{\mathrm{jQ}}_{ab\left(2n+1\right)}\end{array}---\left(6\right)$

$\begin{array}{c}{\stackrel{\‾}{S}}_{cd(2n+1)}={\stackrel{\·}{V}}_{cd(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{\left\{-4\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\sin \left(2n+1\right){\mathrm{\α}}_2+\sin \left(2n+1\right){\mathrm{\α}}_3\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ +j\frac{\left\{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\left(\cos \left(2n+1\right){\mathrm{\α}}_2+\cos \left(2n+1\right){\mathrm{\α}}_3\right)+8{\left(\frac{N_p}{N_s}\right)}^2{V}_{out}^2\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ =P_{cd\left(2n+1\right)}+{\mathrm{jQ}}_{cd\left(2n+1\right)}\end{array}---\left(7\right)$

Work as α ₂when=0, phasor for constant, at this moment phasor track and Fig. 5 in phasor track identical, for for the quarter circular arc of radius; Unlike, phasor track is with α ₃change; According to geological theorems, in this case, phasor delayed phase leakage inductance voltage-phase 90 °, then leakage inductance current phase place and phasor identical, therefore now delayed bridge reactive power is zero, and corresponding phasor diagram is as shown in Fig. 6 (b).α ₂phasor when=0 trajectory is one of its expansion phase shift boundary condition.

When time, phasor track is with α ₂be changed to phasor trajectory another boundary condition under expansion phase shifting control, as shown in Fig. 6 (c).

In Fig. 6 boundary locus is under single phase shift with phase shifting angle variation track line.So far, shown that expansion moves 2. phasor in situation working control region, as shown in dash area in phase Fig. 6.

3) dual phase shifting control strategy phasor analysis method

Dual phase shifting control strategy is equal by phase shifting angle in control HB1 and HB2, i.e. α ₁=α ₄, Fig. 7 (a) is the phasor diagram of dual phase shifting control strategy, and in figure, dash area is the ordinary circumstance control area of dual phase shifting control strategy, and the complex power of advanced bridge H1 and delayed bridge H2 is respectively:

$\begin{array}{c}{\stackrel{\‾}{S}}_{ab(2n+1)}={\stackrel{\·}{V}}_{ab(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{\left\{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\sin \left(2n+1\right){\mathrm{\α}}_2\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ +j\frac{\left\{4V_{in}\left(\frac{N_p}{N_s}{V}_{out}\cos \left(2n+1\right){\mathrm{\α}}_2-V_{in}\right)\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ =P_{ab\left(2n+1\right)}+{\mathrm{jQ}}_{ab\left(2n+1\right)}\end{array}---\left(8\right)$

$\begin{array}{c}{\stackrel{\‾}{S}}_{cd(2n+1)}={\stackrel{\·}{V}}_{cd(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{\left\{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\sin \left(2n+1\right){\mathrm{\α}}_2\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ +j\frac{\left\{4\frac{N_p}{N_s}{V}_{out}\left(V_{in}\cos \left(2n+1\right){\mathrm{\α}}_2-\frac{N_p}{N_s}{V}_{out}\right)\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ =P_{cd\left(2n+1\right)}+{\mathrm{jQ}}_{cd\left(2n+1\right)}\end{array}---\left(9\right)$

Work as α ₂=0, α ₃=α ₁, as in Fig. 7 (b) with or for the boundary locus of the quarter circular arc of radius, phasor with phasor overlap, then the active-power P of two H bridges _ab=P _cd=0, that is, the voltage and current on inductance is 0, and the complex power of advanced bridge H1 and delayed bridge H2 can be expressed as:

$Q_{ab\left(2n+1\right)}=\frac{\left\{4V_{in}\left(\frac{N_p}{N_s}{V}_{out}-V_{in}\right)\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}---\left(10\right)$

$Q_{cd\left(2n+1\right)}=\frac{\left\{4\frac{N_p}{N_s}{V}_{out}\left(V_{in}-\frac{N_p}{N_s}{V}_{out}\right)\left(1+\cos \left(2n+1\right){\mathrm{\α}}_1\right)\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}---\left(11\right)$

When with phase place is different, track as in Fig. 7 (c) with phasor in Fig. 6 in expansion phase shift track identical, the complex power of H1 and H2 is respectively:

$\begin{array}{c}{\stackrel{\‾}{S}}_{ab(2n+1)}={\stackrel{\·}{V}}_{ab(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\left\{\begin{array}{c}\sin \left(2n+1\right){\mathrm{\α}}_2\left(1+\sin \left(2n+1\right)\frac{\mathrm{\π}}{2}\right)\\ -\sin \left(2n+1\right)\frac{\mathrm{\π}}{2}\left(\cos \left(2n+1\right){\mathrm{\α}}_2-1\right)\end{array}\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ +j\frac{4V_{in}\left(\frac{N_p}{N_s}{V}_{out}\cos \left(2n+1\right){\mathrm{\α}}_2-V_{in}\right)\left(1+\sin \left(2n+1\right){\mathrm{\α}}_2\sin \left(2n+1\right)\frac{\mathrm{\π}}{2}\right)}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ =P_{ab\left(2n+1\right)}+{\mathrm{jQ}}_{ab\left(2n+1\right)}\end{array}---\left(12\right)$

$\begin{array}{c}{\stackrel{\‾}{S}}_{cd(2n+1)}={\stackrel{\·}{V}}_{cd(2n+1)}^{*}{\stackrel{\·}{I}}_{L(2n+1)}\\ =\frac{4\frac{N_p}{N_s}{V}_{in}{V}_{out}\left\{\begin{array}{c}\sin \left(2n+1\right){\mathrm{\α}}_2\left(1+\sin \left(2n+1\right)\frac{\mathrm{\π}}{2}\right)\\ -\sin \left(2n+1\right)\frac{\mathrm{\π}}{2}\left(\cos \left(2n+1\right){\mathrm{\α}}_2-1\right)\end{array}\right\}}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ +j\frac{4\frac{N_p}{N_s}{V}_{out}\left(V_{in}\cos \left(2n+1\right){\mathrm{\α}}_2-\frac{N_p}{N_s}{V}_{out}\right)\left(1+\sin \left(2n+1\right){\mathrm{\α}}_2\sin \left(2n+1\right)\frac{\mathrm{\π}}{2}\right)}{{\mathrm{\π}}^2{\left(2n+1\right)}^3{\mathrm{\ωL}}_S}\\ =P_{cd\left(2n+1\right)}+{\mathrm{jQ}}_{cd\left(2n+1\right)}\end{array}---\left(13\right)$

Above embodiment is only exemplary embodiment of the present invention, and be not used in restriction the present invention, protection scope of the present invention is defined by the claims.Those skilled in the art can in essence of the present invention and protection range, and make various amendment or equivalent replacement to the present invention, this amendment or equivalent replacement also should be considered as dropping in protection scope of the present invention.

Claims (7)

1., based on two active bridge (two active H bridge, dual three-level half-bridge or a side tri-level half-bridge, the active H bridge of opposite side etc.) the DC converter analytical method of the phase shifting control exchanging phasor approach and modeling method, it is characterized in that, comprise the following steps:

1) two active bridge DC converter equivalent model is replaced, and draws the voltage of (2n+1) component of degree n n and the phasor expression formula of inductive current;

2) according to step 1) middle phasor expression formula, corresponding phasor diagram under obtaining different phase shifting control;

3) according to step 1) in phasor expression formula, obtain the complex power expression formula of equivalent voltage source, analyze active power and reactive power characteristic under different phase shifting control;

4) according to step 1) in phasor expression formula and the converter differential equation, obtain Fourier series and the expression formula of two active bridge steady-state model time domain, adopt small-signal perturbation technique, steady-state model is introduced in small-signal disturbance, obtains the unified small-signal model of phase shifting control lower pair of active bridge DC converter.

2. the two active bridge DC converter of phase shifting control according to claim 1 exchanges phasor approach analytical method and modeling method, it is characterized in that step 1) in, two active bridge DC converter can substitute with equivalent model, and each active bridge AC voltage can use square-wave voltage source V _ab(t), V _cdt () represents, and can be expressed as the unlimited superposition of the sine wave signal of different frequency;

Wherein, V _abt () is active bridge 1 AC square-wave voltage, V _cdt () is active bridge 2 AC square-wave voltage, V _infor input direct voltage, V _outfor output dc voltage, for the high-frequency isolation transformer turn ratio, ω is for exchanging angular frequency, n=0,1,2..., α ₁for phase shifting angle in active bridge 1, α ₂for phase shifting angle between active bridge 1 and active bridge Bridge 2, α ₄for phase shifting angle in active bridge 2, α ₃for phase shifting angle α in active bridge 2 ₄and phase shifting angle α between bridge ₂sum (α ₃=α ₂+ α ₄).

3. the two active bridge DC converter of phase shifting control according to claim 2 exchanges phasor approach analytical method and modeling method, it is characterized in that, substitute into step 1) carry the model that two sinusoidal ac potential sources are connected by inductive circuit, set up the differential equation of switch function:

1) two active bridge DC converter friendship/cross ring joint state differential equation:

Wherein R _lfor transformer resistance, L _sfor transformer leakage inductance, i _lt () is transformer current

2) square-wave voltage source equivalent expression (1) and (2) in claim 2 are brought in formula (3) into the differential equation that can obtain based on switch function equivalence:

。

4. the active bridge DC converter of lower pair of phase shifting control according to claim 3 exchanges phasor approach analytical method and modeling method, it is characterized in that, step 1) in the voltage of (2n+1) component of degree n n and the phasor expression formula of inductive current can draw equilibrium transport amount expression formula according to the differential equation of claim 3 breaker in middle function equivalence:

And then determine (2n+1) component of degree n n phasor expression formula of square-wave voltage and inductive current:

。

5. the active bridge DC converter of lower pair of phase shifting control according to claim 4 exchanges phasor approach analytical method and modeling method, it is characterized in that, according to step 1) the middle voltage that draws, inductive current (2n+1) component of degree n n phasor expression formula and equilibrium transport amount expression formula, step 2 can be drawn respectively) outer phase shift between jackshaft, outer phase shift between phase shift and bridge in single active bridge, and in doube bridge between phase shift and bridge under outer phase shifting control, the phasor diagram of two active bridge DC converter.

6. the active bridge DC converter of lower pair of phase shifting control according to claim 5 exchanges phasor approach analytical method and modeling method, it is characterized in that, according to step 1) under the voltage that draws, inductive current (2n+1) component of degree n n phasor expression formula can draw three kinds of phase shifting control, equivalent sinusoidal voltage source complex power and high frequency transformer leakage inductance L in two active bridge DC converter (2n+1) component of degree n n _sreactive power:

Wherein,

7. the active bridge DC converter of lower pair of phase shifting control according to claim 6 exchanges phasor approach analytical method and modeling method, it is characterized in that, step 3) in complex power active power do not considering to equal DC output power in circuit loss situation, then active bridge 2 side output current (2n+1) component phasor expression formula be:

Under not considering to export DC bus capacitor impedance conditions, draw the equilibrium transport amount expression formula of DC side output voltage, DC bus capacitor electric current and load current:

Wherein, output voltage (2n+1) component of degree n n, for active bridge 2 side output current (2n+1) component of degree n n, C is DC output end shunt capacitance, for output capacitor electric current (2n+1) component of degree n n, for secondary point of load current (2n+1), obtain Fourier series and the expression formula of two active bridge steady-state model time domain:

Near steady operation point, introduce microvariations and substitute in steady-state model, setting up partial differential equation, show that phase shifting control lower pair of active bridge DC converter unifies small-signal model:

In formula: .