CN105099200B - The double active bridge DC converter exchange phasor analysis of phase shifting control and modeling method - Google Patents

The double active bridge DC converter exchange phasor analysis of phase shifting control and modeling method Download PDF

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CN105099200B
CN105099200B CN201510406666.1A CN201510406666A CN105099200B CN 105099200 B CN105099200 B CN 105099200B CN 201510406666 A CN201510406666 A CN 201510406666A CN 105099200 B CN105099200 B CN 105099200B
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phasor
bridge
active
phase shifting
expression formula
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CN201510406666.1A
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CN105099200A (en
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王聪
沙广林
王健宇
胡小菊
马志鹏
程红
王俊
庄园
王浩
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中国矿业大学(北京)
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Abstract

The invention provides a kind of exchange phasor analysis suitable for lower pair of active bridge DC converter of all phase shifting controls and small-signal model modeling method, double active bridges include:Double active H bridges, dual three-level half-bridge, side tri-level half-bridge, the active H bridges of opposite side.Concretely comprise the following steps:1st, each active bridge AC is equivalent to two square-wave voltage sources by equivalent, the superposition that square-wave voltage is decomposed into sinusoidal voltage is decomposed by Fourier space, the phasor expression formula of (2n+1) component of degree n n voltage and inductive current is drawn2nd, the control characteristic of different phase shifting controls and the phasor diagram of control range are drawn according to phasor expression formula in step 1;3rd, the complex power of (2n+1) component of degree n n is obtained according to phasor representation formula in step 1Analyze the active and reactive power characteristic of lower pair of active bridge DC converter of different phase shifting controls;4th, the time domain Fourier space and expression formula of its voltage and electric current are drawn according to step 1 phasor expression formula, the unified small-signal model suitable for all phase-shifting control methods is obtained.

Description

The double active bridge DC converter exchange phasor analysis of phase shifting control and modeling method

Technical field

The invention belongs to Power Electronic Technique and intelligent grid research field, more particularly to a kind of phase shift based on phasor approach The double active bridge circuit power analysis methods of control and modeling.

Background technology

With the development of intelligent grid, no industrial frequency transformer high-power power electronic converter with its high efficiency, intellectuality, The features such as low stain, increasingly causes the concern of people.No industrial frequency transformer high-power power electronic converter common at present is adopted With Cascade Topology Structure, by cascade multi-level AC-DC rectification modules, bidirectional DC-DC converter module and many level DC-AC inversion moulds Block is constituted.

Double active bridge DC-DC converter structures are due to electrical isolation, buck conversion, bidirectional energy transmission, Gao Gong The features such as rate density, is used by bidirectional DC-DC converter module.

The traditional analysis of the double active bridges of phase shifting control is to power characteristic analysis mainly in analysis phase shifting control principle On the basis of waveform, power mathematical modeling is obtained by Definite Integral Calculation, and then the characteristic of transimission power and reactive power is entered Row analysis.Although this method can draw more accurately result, there is also substantially not enough.Its major defect is to count Calculate complicated, physical significance is indefinite, the relation that the result of analysis can not intuitively reflect between transimission power and reactive power, and And can not set up versatility model for a variety of phase shift system traditional analysis.

[1]M.N.Kheraluwala,R.W.Gascoigne,D.M.Divan,and E.D.Baumann, “Performance characterization of a high-power dual active bridge DC-to-DC converter,”IEEE Trans.Ind.Appl.,vol.28,no.6,pp.1294–1301,Nov./Dec.1992.

[2]R.W.DeDoncker,M.H.Kheraluwala,and D.M.Divan,“Power conversion apparatus for DC/DC conversion using dual active bridges,”U.S.Patent 5027264, Jun.25,1991.

The content of the invention

For the shortcomings and deficiencies of traditional analysis, it is an object of the present invention to propose a kind of shifting based on phasor approach The double active bridge DC converter power analysis of phase control and modeling method, double active bridges include:Double active H bridges, dual three-level half Bridge, side tri-level half-bridge, the active H bridges of opposite side.Set up and a kind of can be used in the unified analysis model of a variety of phase shifting controls simultaneously Small-signal model is set up on the basis of this unified model.

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

The double active bridge DC converter power analysis of phase shifting control based on phasor approach and modeling method, this method pass through Active bridge both end voltage is equivalent to two square-wave voltage sources by the method for effect, then square-wave voltage is decomposed into by Fourier space The superposition of sinusoidal voltage.The active power and reactive power of fundamental wave and each harmonic are analyzed by phasor approach, with plural number Calculating replace sinusoidal quantity calculating, greatly simplify calculating.And propose a kind of physical significance based on phasor approach it is clear, Analysis result is accurate and the analysis method of the simple double active bridge phase shifting controls of computing, can set up double by this analysis method The unified small-signal model of active bridge.

Phase shifting control double active bridge circuit analysis methods and modeling method based on exchange phasor approach, comprise the following steps:

1) double active bridge DC converter equivalent models are replaced, and draw the voltage and inductive current of (2n+1) component of degree n n Phasor expression formula;

2) according to step 1) in phasor expression formula, obtain under different phase shifting controls correspondence phasor diagram;

3) according to step 1) in phasor expression formula, obtain the complex power expression formula of equivalent voltage source, analyze different phase shift controls The lower active power of system and reactive power characteristic;

4) according to step 1) in phasor expression formula and the converter differential equation, obtain Fu of double active bridge steady-state model time domains In leaf sum of series expression formula, using small-signal perturbation technique, small-signal disturbance is introduced into steady-state model, lower pair of phase shifting control is obtained The unified small-signal model of active bridge DC converter.

The present invention further improvement is that, step 1) in, double active bridge DC converters can be substituted with equivalent model, such as Shown in Fig. 1, each active bridge AC voltage can use square-wave voltage source Vab(t)、Vcd(t) represent, and may be expressed as The unlimited superposition of the sine wave signal of different frequency.

Wherein, Vab(t) it is the active AC square-wave voltage of bridge 1, Vcd(t) it is the active AC square-wave voltage of bridge 2, VinFor Input direct voltage, VoutTo export DC voltage,For the high-frequency isolation transformer turn ratio, ω is to exchange angular frequency, n=1,2, 3..., α1For the interior phase shifting angle of active bridge 1, α2For phase shifting angle, α between active bridge 1 and active bridge Bridge 24For the interior phase shift of active bridge 2 Angle, α3For phase shifting angle α in active bridge 24The phase shifting angle α between bridge2Sum.

The present invention further improvement is that, step 1) carry the mould that two sinusoidal ac potential sources are connected by inductive circuit Type, sets up the state equation of switch function:

1) double active bridge DC converter friendship/cross ring section state differential equations:

Wherein RLFor transformer resistance, LsFor transformer leakage inductance, iL(t) it is transformer current.

2) bringing square-wave voltage source equivalent expression (1) and (2) in formula (3) into can obtain equivalent based on switch function The differential equation:

The present invention further improvement is that, step 1) in (2n+1) component of degree n n voltage and inductive current phasor express Formula can draw equilibrium transport amount expression formula according to the equivalent differential equation of switch function in claim 3:

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

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

The present invention further improvement is that, according to step 1) in draw voltage, inductive current (2n+1) component of degree n n phasor Expression formula can show under three kinds of phase shifting controls that equivalent sinusoidal voltage source is answered in double active bridge DC converter (2n+1) component of degree n ns Power and high frequency transformer leakage inductance LSReactive power:

Wherein,

The present invention further improvement is that, step 3) in complex power active power do not considering that circuit loss situation is inferior In DC output power, then active side output current (2n+1) component of degree n n of bridge 2Phasor expression formula be:

Do not consider under output DC bus capacitor impedance conditions, draw DC side output voltage, DC bus capacitor electric current with bearing Current-carrying equilibrium transport amount expression formula:

WhereinOutput voltage (2n+1) component of degree n n,It is secondary for the active side output current (2n+1) of bridge 2 Component, 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 the Fourier space and expression formula of double active bridge steady-state model time domains:

A microvariations are applied around in steady operation point and are substituted into steady-state model, are set up partial differential equation, are drawn shifting Lower pair of active bridge DC converter of phase control unifies small-signal model:

In formula:

Double active bridge circuits are analyzed by the method for the present invention by phasor approach, and computational methods are simple, drawn physics Meaning clearly analysis model, clearly draws double relations between active bridge power transfer characteristic and phase shift angle, and herein On the basis of propose the method that small-signal model is set up to double active bridge circuits.

Brief description of the drawings

The present invention is further described below in conjunction with the accompanying drawings.

Fig. 1 is double active H bridges DC converter topologys;

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

Fig. 2 (b) is double active bridge DC converter synchronous motor equivalent circuits;

Fig. 3 phase shifting control ideal waveform figures;

Fig. 4 is phasor diagram of double active bridges in single phase shifting control strategy;

Fig. 5 is phasor diagram of the extension phase shift in A mode control strategies;

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

Fig. 6 (b) is extension phase shift B mode control strategies, works as α2Phasor diagram when=0;

Fig. 6 (c) is extension phase shift B mode control strategies, whenWhen 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 α2=0, α31When phasor diagram;

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

Embodiment

With reference to the accompanying drawings and detailed description by taking double active H bridges DC converter topologys shown in Fig. 1 as an example, to this Invention is described further.

Fig. 3 show respectively three kinds phase shifting control strategies:Single phase shift, extension phase shift, dual phase shifting control ideal waveform Figure;Wherein, Vab(t)、Vcd(t) it is two single-phase H bridges AC square-wave voltages, the phase using drive signal S1 is as referring to phase Position, the phase delay between drive signal S4 and S1 is referred to as H1 interior phase shifting angle α1;Phase between drive signal Q1 and S1 is prolonged It is referred to as outer phase shifting angle α late2;Phase delay between drive signal Q4 and S1, the i.e. interior phase shifting angle α of H24With outer phase shifting angle α2Sum Referred to as α3324)。

By taking the advanced H2 of H1 as an example, citing point is carried out to three kinds of phase shifting control strategies respectively by exchanging phasor analysis method Analysis:

Because inductive resistance is sufficiently small, it can be ignored, the derivation of the apparent energy of inductance is as follows:

It is can be seen that from formula (1) in phase shifting control strategy, advanced bridge H1 active-power Pab(2n+1)It is fully transmitted to stagnant Back axle H2 is used as output DC side power output, i.e. Pab(2n+1)=Pcd(2n+1).Inductance reactive power is by advanced bridge H1 and delayed bridge H2 is provided jointly.

1) single phase shifting control strategy phasor analysis method

Work as α1=0 and α4=0, i.e. there is phase shift between only two H bridges.Now, the phasor expression formula of two voltage sources Abbreviation isPhasorDelayed phasor Angle be (2n+1) α2.Fig. 4 is two phases in double phasor diagrams of the active bridge DC converter under single phase shifting control strategy, figure The mould of amount is identical, i.e.,It can be seen that as voltage VinWhen keeping constant, the power of double active bridges is by moving Phase angle α2To adjust.

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

2) phase shifting control strategy phasor analysis method is extended

Extend phase shifting control strategy and there are two kinds of phase shift systems:①α1≠ 0 and α4=0;②α1=0 and α4≠0。

①α1≠ 0 and α4=0

Voltage phasor expression formula is respectively PhasorAngle with reference axis is the half of phase shifting angle in HB1, i.e.,1. Fig. 5 is extending for extension phase shift Phasor diagram under mode control strategy, phasorTrack fall in Figure 5 withOrFor radius In quarter circular arc.The reactive power of inductance is:

Wherein,

I.e.:α12Under conditions of, under extending phase shifting control strategy 1. Inductance reactive power obtain minimum value:

In α12Under conditions of, the reactive power Q of advanced bridgeab(2n+1)=0, inductive currentIt is equivalent with advanced bridge Voltage sourceSame-phase, i.e.In advanceQL minIt is entirely to be provided by delayed bridge, phasor diagram such as Fig. 4 It is shown.On this condition, the transimission power of double active bridges is

②α1=0 and α4≠0

Fig. 6 (a) extends phase shift 2. control strategy phasor diagram, and the phasor expression formula of two voltage sources is expressed as Advanced bridge H1, delayed bridge H2 Complex power is respectively

Work as α2When=0, phasorFor constant, at this moment phasorTrack and Fig. 5 in phasorTrack it is identical, be withFor the quarter circular arc of radius;Unlike, phasorTrack is with α3Change Become;It can be seen from geological theorems, in this case, phasor90 ° of delayed phase leakage inductance voltage-phase, then leak electricity electrification Flow phase and phasorIt is identical, therefore now delayed bridge reactive power is zero, shown in corresponding phasor diagram such as Fig. 6 (b).α2 Phasor when=0Trajectory extends one of phase shift boundary condition for it.

WhenWhen, phasorTrack is with α2Change turn to phasorTrajectory is under extension phase shifting control Another boundary condition, shown in such as Fig. 6 (c).

In Fig. 6Boundary locus is under single phase shiftWith phase shifting angle variation track line.So far, draw Phasor in the case of 2. extension movesActual control area, as shown in dash area in phase Fig. 6.

3) dual phase shifting control strategy phasor analysis method

Dual phase shifting control strategy is the i.e. α by controlling HB1 equal with HB2 interior phase shifting angle14, Fig. 7 (a) is dual Dash area is the ordinary circumstance control area of dual phase shifting control strategy, advanced bridge in the phasor diagram of phase shifting control strategy, figure H1 and delayed bridge H2 complex power is respectively:

Work as α2=0, α31, such as in Fig. 7 (b) withOrFor the side of the quarter circular arc of radius Boundary track, phasorWith phasorOverlap, then the active-power P of two H bridgesab=Pcd=0, i.e. the electricity on inductance Pressure and electric current are 0, and advanced bridge H1 and delayed bridge H2 complex power are represented by:

WhenWithPhase is different,With expansion in track such as Fig. 7 (c) Phasor in Fig. 6 in exhibition phase shiftTrack it is identical, H1 and H2 complex power are respectively:

Above example is only the exemplary embodiment of the present invention, is not used in the limitation present invention, protection scope of the present invention It is defined by the claims.Those skilled in the art can make respectively in the essence and protection domain of the present invention to the present invention Modification or equivalent substitution are planted, this modification or equivalent substitution also should be regarded as being within the scope of the present invention.

Claims (7)

1. a kind of double active bridges of phase shifting control based on exchange phasor approach, double active bridge DC converter analysis methods and modeling side Method, double active bridges include:Double active H bridges, dual three-level half-bridge, side tri-level half-bridge, the active H bridges of opposite side, its feature exist In comprising the following steps:
1) double active bridge DC converter equivalent models are replaced, and draw the voltage of (2n+1) component of degree n n and the phasor of inductive current Expression formula;
2) according to step 1) in phasor expression formula, obtain under different phase shifting controls correspondence phasor diagram;
3) according to step 1) in phasor expression formula, obtain the complex power expression formula of equivalent voltage source, analyze under different phase shifting controls Active power and reactive power characteristic;
4) according to step 1) in phasor expression formula and the converter differential equation, obtain the Fourier of double active bridge steady-state model time domains Sum of series expression formula, using small-signal perturbation technique, introduces steady-state model by small-signal disturbance, obtains lower pair of phase shifting control active The unified small-signal model of bridge DC converter.
2. the double active bridge DC converter exchange phasor approach analysis methods of phase shifting control according to claim 1 and modeling side Method, it is characterised in that step 1) in, double active bridge DC converters can be substituted with equivalent model, each active bridge AC Voltage can use square-wave voltage source Vab(t)、Vcd(t) represent, and may be expressed as different frequency sine wave signal it is unlimited Superposition;
Wherein, Vab(t) it is the active AC square-wave voltage of bridge 1, Vcd(t) it is the active AC square-wave voltage of bridge 2, VinFor input DC voltage, VoutTo export DC voltage,For the high-frequency isolation transformer turn ratio, ω is to exchange angular frequency, n=0,1, 2..., α1For the interior phase shifting angle of active bridge 1, α2For phase shifting angle, α between active bridge 1 and active bridge Bridge 24For the interior phase shift of active bridge 2 Angle, α3For phase shifting angle α in active bridge 24The phase shifting angle α between bridge2Sum (α324)。
3. the double active bridge DC converter exchange phasor approach analysis methods of phase shifting control according to claim 2 and modeling side Method, it is characterised in that substitute into step 1) model that two sinusoidal ac potential sources are connected by inductive circuit is carried, set up switch The differential equation of function:
1) double active bridge DC converter friendship/cross ring section state differential equations:
Wherein RLFor transformer resistance, LsFor transformer leakage inductance, iL(t) it is transformer current
2) bringing square-wave voltage source equivalent expression (1) and (2) in claim 2 in formula (3) into can obtain based on switch letter The equivalent differential equation of number:
4. the active bridge DC converter exchange phasor approach analysis method of lower pair of phase shifting control according to claim 3 and modeling Method, it is characterised in that step 1) in (2n+1) component of degree n n voltage and the phasor expression formula of inductive current can be according to power Profit requires that the equivalent differential equation of switch function draws equilibrium transport amount expression formula in 3:
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 exchange phasor approach analysis method of lower pair of phase shifting control according to claim 4 and modeling Method, it is characterised in that according to step 1) in draw voltage, inductive current (2n+1) component of degree n n phasor expression formula and stable state Phasor 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 doube bridge Between interior phase shift and bridge under outer phase shifting control, the phasor diagram of double active bridge DC converters.
6. the active bridge DC converter exchange phasor approach analysis method of lower pair of phase shifting control according to claim 5 and modeling Method, it is characterised in that according to step 1) in show that voltage, inductive current (2n+1) component of degree n n phasor expression formula can draw three Plant under phase shifting control, equivalent sinusoidal voltage source complex power in double active bridge DC converter (2n+1) component of degree n nsAnd high frequency transformer leakage inductance LSReactive power QL(2n+1)
Wherein,
7. the active bridge DC converter exchange phasor approach analysis method of lower pair of phase shifting control according to claim 6 and modeling Method, it is characterised in that step 3) in complex power active power be equal to direct current output work(in the case of circuit loss is not considered Rate, then active side output current (2n+1) component of bridge 2Phasor expression formula be:
Do not consider under output DC bus capacitor impedance conditions, draw DC side output voltage, DC bus capacitor electric current and load electricity The equilibrium transport amount expression formula of stream:
Wherein,Output voltage (2n+1) component of degree n n,For active secondary point of the side output current (2n+1) of bridge 2 Amount, C is DC output end shunt capacitance,For output capacitor electric current (2n+1) component of degree n n,For load electricity Secondary point of stream (2n+1), obtains the Fourier space and expression formula of double active bridge steady-state model time domains:
A microvariations are introduced near steady operation point and are substituted into steady-state model, partial differential equation is set up, draws phase shift control Lower pair of active bridge DC converter of system unifies small-signal model:
In formula:
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