CN105099200B - The double active bridge DC converter exchange phasor analysis of phase shifting control and modeling method - Google Patents
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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
Technical Field
The invention belongs to the field of power electronic technology and smart grid research, and particularly relates to a phase-shift control double-active-bridge circuit power analysis method and modeling based on a phasor method.
Background
With the development of smart power grids, the high-power electronic converter without the power frequency transformer draws more and more attention by the characteristics of high efficiency, intellectualization, low pollution and the like. At present, a common high-power electronic converter without a power frequency transformer adopts a cascade topology and consists of a cascade multilevel AC-DC rectifying module, a bidirectional DC-DC converting module and a multilevel DC-AC inverting module.
The double-active-bridge DC-DC converter structure is adopted by the bidirectional DC-DC conversion module due to the characteristics of electrical isolation, buck-boost conversion, bidirectional energy transmission, high power density and the like.
The traditional analysis method for the phase-shift control double-active bridge analyzes the power characteristics, mainly obtains a power mathematical model through definite integral calculation on the basis of analyzing the waveform of a phase-shift control principle, and further analyzes the characteristics of transmission power and reactive power. Although this method can produce relatively accurate results, it has obvious disadvantages. The method has the main defects that the calculation is complex, the physical significance is not clear, the analysis result cannot visually reflect the relation between the transmission power and the reactive power, and a universal model cannot be established for the traditional analysis method of various phase-shifting modes.
[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-DCconverter,”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 conversionapparatus for DC/DC conversion using dual active bridges,”U.S.Patent 5027264,Jun.25,1991.
Disclosure of Invention
Aiming at the defects and shortcomings of the traditional analysis method, the invention aims to provide a phase-shift control double-active-bridge direct-current converter power analysis and modeling method based on a phasor method, wherein the double-active bridge comprises the following steps: the double-active H bridge, the double three-level half bridge, the three-level half bridge on one side and the active H bridge on the other side. An analysis model which can be used for various phase shift control unification is established, and a small signal model is established on the basis of the unified model.
In order to realize the task, the invention adopts the following technical solution:
the method is characterized in that voltages at two ends of an active bridge are equivalent to two square wave voltage sources through an equivalent method, and then the square wave voltages are decomposed into superposition of sinusoidal voltages through Fourier series. The active power and the reactive power of fundamental waves and each harmonic are analyzed by a phasor method, and the calculation of a sine quantity is replaced by the calculation of a complex number, so that the calculation is greatly simplified. The analysis method for the double-active-bridge phase-shifting control is clear in physical significance, accurate in analysis result and simple in operation based on the phasor method, and a unified small-signal model of the double-active-bridge can be established through the analysis method.
The phase-shift control double-active-bridge circuit analysis method and the modeling method based on the alternating current phasor method comprise the following steps:
1) replacing the equivalent model of the double-active-bridge direct-current converter to obtain a phasor expression of the voltage of the (2n +1) th sub-component and the inductive current;
2) obtaining corresponding phasor diagrams under different phase-shifting control according to the phasor expression in the step 1);
3) obtaining a complex power expression of an equivalent voltage source according to the phase expression in the step 1), and analyzing the characteristics of active power and reactive power under different phase-shifting control;
4) and (2) obtaining the Fourier series and expression of the time domain of the double-active-bridge steady-state model according to the phase-quantity expression and the converter differential equation in the step 1), introducing small-signal disturbance into the steady-state model by adopting a small-signal disturbance technology, and obtaining a unified small-signal model of the double-active-bridge direct-current converter under phase-shift control.
The invention further improves that in the step 1), the double-active-bridge DC converter can be replaced by an equivalent model, as shown in FIG. 1, the AC side voltage of each active bridge can be replaced by a square wave voltage source Vab(t)、VcdAnd (t) and may all be represented as an infinite superposition of sine wave signals of different frequencies.
Wherein, Vab(t) is the AC side wave voltage, V, of the active bridge 1cd(t) is the AC lateral wave voltage of the active bridge 2, VinFor inputting a DC voltage, VoutIn order to output a direct-current voltage,for high frequency isolation transformer turn ratio, ω is ac angular frequency, n is 1,2,3.., α1Is the phase angle of the active bridge 1, α2Is a phase shift angle between an active bridge 1 and an active bridge 2, α4Is the phase angle of the active bridge 2, α3Is an active bridge 2 phase shift angle α4Phase angle α between bridge and bridge2And (4) summing.
The invention is further improved in that the two sinusoidal alternating-current voltage sources provided in step 1) are connected through an inductive line, and a state equation of a switching function is established:
1) the differential equation of the AC/AC ring states of the double-active-bridge DC converter is as follows:
wherein R isLIs a transformer resistance, LsFor leakage inductance of transformer, iLAnd (t) is the transformer current.
2) The differential equation based on the switching function equivalence can be obtained by taking the equivalent expressions (1) and (2) of the square wave voltage source into the expression (3):
the invention is further improved in that the phasor expression of the voltage and the inductance current of the (2n +1) th sub-component in the step 1) can obtain a steady-state phasor expression according to a differential equation equivalent to the switching function in claim 3:
and further determining a (2n +1) secondary component phasor expression of the square wave voltage and the inductive current:
the invention is further improved in that a phasor diagram of the double-active-bridge direct-current converter in the step 2) can be respectively obtained according to the voltage, the inductance current (2n +1) sub-component phasor expression and the steady-state phasor expression of the converter obtained in the step 1), the inter-bridge external phase shift, the single-active-bridge internal phase shift and the inter-bridge external phase shift, and under the control of the double-bridge internal phase shift and the inter-bridge external phase shift.
The invention is further improved in that the equivalent sinusoidal voltage source complex power in the (2n +1) th sub-component of the double-active bridge direct current converter and the leakage inductance L of the high-frequency transformer under three kinds of phase-shift control can be obtained according to the voltage and inductance current (2n +1) sub-component phasor expressions obtained in the step 1)SReactive power:
wherein,
the invention is further improved in that in the step 3), the active power in the complex power is equal to the direct current output power without considering the circuit loss, and the (2n +1) th sub-component of the output current of the active bridge 2 sideThe phasor expression of (a) is:
and obtaining a steady-state phasor expression of the output voltage at the direct current side, the capacitance current at the direct current side and the load current without considering the condition of the capacitance impedance at the output direct current side:
whereinThe (2n +1) th sub-component of the output voltage,the (2n +1) th sub-component of the output current of the side of the active bridge 2, C the output end capacitance,is the (2n +1) th sub-component of the output terminal capacitance current,is the (2n +1) th sub-component of the load current.
Obtaining Fourier series and expression of a double-active-bridge steady-state model time domain:
applying a small disturbance near a steady-state working point and substituting the small disturbance into a steady-state model to establish a partial differential equation to obtain a unified small-signal model of the double-active-bridge direct-current converter under phase-shift control:
in the formula:
the method analyzes the double-active-bridge circuit by a phasor method, has simple calculation method, obtains an analysis model with clear physical significance, clearly obtains the relation between the power transmission characteristic and the phase-shifting angle of the double-active-bridge circuit, and provides a method for establishing a small-signal model for the double-active-bridge circuit on the basis.
Drawings
The invention is further described below with reference to the accompanying drawings.
FIG. 1 is a dual active H-bridge DC converter topology;
FIG. 2(a) is an equivalent circuit of a dual active bridge DC converter;
FIG. 2(b) is an equivalent circuit of a synchronous motor with a double active bridge DC converter;
FIG. 3 is an idealized waveform diagram for phase shifting control;
FIG. 4 is a phasor diagram of a dual active bridge in a single phase shift control strategy;
FIG. 5 is a phasor diagram of an extended phase shift in mode A control strategy;
FIG. 6(a) is a phasor diagram for an extended phase shift B-mode control strategy;
FIG. 6(B) shows the control strategy of the extended phase shift B mode when α2Phasor diagram when 0;
FIG. 6(c) shows the control strategy of the extended phase shift B mode whenPhasor diagrams in time;
FIG. 7(a) is a phasor diagram for a dual phase-shifting control strategy;
FIG. 7(b) shows a dual phase shift control strategy when α2＝0，α3＝α1Phasor diagrams in time;
FIG. 7(c) shows a dual phase shift control strategy whenPhasor diagrams in time.
Detailed Description
The present invention will be further described with reference to the drawings and the detailed description by taking the topology of the dual active H-bridge dc converter shown in fig. 1 as an example.
FIG. 3 shows three phase-shift control strategies: the ideal oscillogram is controlled by single phase shift, extended phase shift and double phase shift; wherein, Vab(t)、Vcd(t) is the AC side wave voltage of two single-phase H-bridges with the phase of the driving signal S1 as the reference phaseThe phase delay between the drive signals S4 and S1 is referred to as the phase shift angle α of H11The phase delay between the drive signals Q1 and S1 is referred to as the out-shifted phase angle α2The phase delay between the drive signals Q4 and S1, i.e., the phase shift angle α of H24And phase shift angle α2The sum is called α3(α3＝α2+α4)。
Taking H1 leading H2 as an example, three phase-shift control strategies are respectively exemplified and analyzed by an alternating current phasor analysis method:
since the inductor resistance is small enough to be negligible, the apparent power of the inductor is derived as follows:
from equation (1), it can be seen that in the phase-shift control strategy, the active power P of the front bridge H1 is exceededab(2n+1)Is fully transferred to the hysteresis bridge H2 as output DC side output power, i.e. Pab(2n+1)＝Pcd(2n+1). The inductive reactive power is provided by the leading bridge H1 and the lagging bridge H2 together.
1) Phasor analysis method of single phase-shift control strategy
When α10 and α40, i.e. there is a phase shift between only two H-bridges. At this time, the phasor expression of the two voltage sources is simplified intoPhasorsLagging phasorIs (2n +1) α2. FIG. 4 is a phasor diagram of a dual active bridge DC converter under a single phase-shift control strategy, where the two phasors have the same modulus, i.e.It can be seen that when the voltage V isin、While remaining unchanged, the power of the dual active bridge passes through phase shift angle α2To adjust.
Under the single phase-shift control strategy, the sum of the power of each harmonic is
2) Phasor analysis method for extended phase-shift control strategy
① α two phase-shifting modes exist in the extended phase-shifting control strategy1Not equal to 0 and α4＝0；②α10 and α4≠0。
①α1Not equal to 0 and α4＝0
The voltage phasor expressions are respectively PhasorsAt an angle to the coordinate axis of half the phase angle of the phase shift HB1, i.e.FIG. 5 is a phasor diagram of extended phase shift under an extended ① mode control strategyFalls in fig. 5 toOrIs on a quarter arc of radius. The reactive power of the inductor is as follows:
wherein,
in thatNamely α1＝α2Under the condition of (3), the reactive power of the inductor under the extended phase-shift control strategy ① obtains the minimum value:
at α1＝α2Under the condition of (1), the reactive power Q of the front axle is exceededab(2n+1)Inductance current of 0Equivalent voltage source with leading bridgeThe phase of the signals, i.e.,advance inQL minIs provided entirely by the hysteresis bridge and the phasor diagram is shown in figure 4. Under this condition, the transmission power of the dual active bridge is
②α10 and α4≠0
FIG. 6(a) is an expanded phase shift ② control strategy phasor diagram, the phasor expression of two voltage sources is shown as The complex powers of the front bridge H1 and the lag bridge H2 are respectively
When α2When equal to 0, phasorIs constant when phasorThe locus of (2) and the phasor of (5)Has the same track asIs a quarter arc of radius; except that the phasorTracing α3(ii) a change; according to the geometric theoremIn this case, phasorsThe phase lag of the leakage inductance voltage is 90 DEG, the phase and phasor of the leakage inductance currentSimilarly, the reactive power of the lag bridge is zero at this time, and the corresponding phasor diagram is shown in FIG. 6 (b). α20 time phase quantityThe trace is one of its extended phase shift boundary conditions.
When in useTime, phasorTracing α2Is a phasorAnother boundary condition of the trace under extended phase shift control is shown in FIG. 6 (c).
In FIG. 6The boundary trace being at a single phase shiftUp to this point, the phasor for the case of the extended shift ② is obtainedAs indicated by the shaded portion in fig. 6.
3) Dual phase-shifting control strategy phasor analysis method
Dual phase-shifting control strategySlightly by controlling HB1 to be equal to HB2, i.e. α1＝α4Fig. 7(a) is a phasor diagram of the dual phase shift control strategy, the shaded area in the diagram is the general control region of the dual phase shift control strategy, and the complex powers of the leading bridge H1 and the lagging bridge H2 are respectively:
when α2＝0，α3＝α1As in FIG. 7(b) toOrBoundary locus, phasor, of a quarter-circle arc of radiusAnd phasorCoincidence, then active power P of two H bridgesab＝PcdAt 0, i.e. both the voltage and the current on the inductor are 0, the complex power of the leading bridge H1 and the lagging bridge H2 can be expressed as:
when in useAndthe phase of the phase-shifted signal is different,traces are as in FIG. 7(c) and the phasors in FIG. 6 in extended phase shiftThe trajectories of H1 and H2 are the same, respectively:
the above embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and the scope of the present invention is defined by the claims. Various modifications and equivalents may be made by those skilled in the art within the spirit and scope of the present invention, and such modifications and equivalents should also be considered as falling within the scope of the present invention.
Claims (7)
1. A phase-shift control double-active bridge based on an alternating current phasor method, a double-active bridge direct current converter analysis method and a modeling method are provided, the double-active bridge comprises: double active H bridge, double three level half bridge, one side three level half bridge, the active H bridge of opposite side, its characterized in that includes the following steps:
1) replacing the equivalent model of the double-active-bridge direct-current converter to obtain a phasor expression of the voltage of the (2n +1) th sub-component and the inductive current;
2) obtaining corresponding phasor diagrams under different phase-shifting control according to the phasor expression in the step 1);
3) obtaining a complex power expression of an equivalent voltage source according to the phase expression in the step 1), and analyzing the characteristics of active power and reactive power under different phase-shifting control;
4) and (2) obtaining the Fourier series and expression of the time domain of the double-active-bridge steady-state model according to the phase-quantity expression and the converter differential equation in the step 1), introducing small-signal disturbance into the steady-state model by adopting a small-signal disturbance technology, and obtaining a unified small-signal model of the double-active-bridge direct-current converter under phase-shift control.
2. The method for analyzing and modeling the phase-shift controlled double-active-bridge DC converter by the AC phasor method according to claim 1, wherein in the step 1), the double-active-bridge DC converter can be replaced by an equivalent model, and each active-bridge AC side voltage can be replaced by a square wave voltage source Vab(t)、Vcd(t) and may all be represented as an infinite superposition of sine wave signals of different frequencies;
wherein, Vab(t) is the AC side wave voltage, V, of the active bridge 1cd(t) is the AC lateral wave voltage of the active bridge 2, VinFor inputting a DC voltage, VoutIn order to output a direct-current voltage,for high frequency isolation transformer turn ratio, ω is ac angular frequency, n is 0,1,2.., α1Is the phase angle of the active bridge 1, α2Is a phase shift angle between an active bridge 1 and an active bridge 2, α4Is the phase angle of the active bridge 2, α3Is an active bridge 2 phase shift angle α4Phase angle α between bridge and bridge2The sum (α)3＝α2+α4)。
3. The phase-shift control double-active-bridge direct-current converter alternating-current phasor method analysis method and modeling method according to claim 2, characterized in that a model that the two sinusoidal alternating-current voltage sources provided in the step 1) are connected through an inductance circuit is substituted to establish a differential equation of a switching function:
1) the differential equation of the AC/AC ring states of the double-active-bridge DC converter is as follows:
wherein R isLIs a transformer resistance, LsFor leakage inductance of transformer, iL(t) is the transformer current
2) The differential equation based on the switching function equivalence can be obtained by taking the square wave voltage source equivalent expressions (1) and (2) in claim 2 into the expression (3):
。
4. the method for analyzing and modeling the alternating-current phasor method of the dual-active-bridge direct-current converter under the phase shift control according to claim 3, wherein the phasor expression of the voltage and the inductive current of the (2n +1) th sub-component in the step 1) can obtain a steady-state phasor expression according to the differential equation equivalent to the switching function in claim 3:
and further determining a (2n +1) secondary component phasor expression of the square wave voltage and the inductive current:
。
5. the method for analyzing and modeling the alternating-current phasor method of the dual-active-bridge direct-current converter under the phase shift control according to claim 4, wherein the inter-bridge external phase shift, the single active-bridge internal phase shift and the inter-bridge external phase shift in the step 2) and the phasor diagram of the dual-active-bridge direct-current converter under the control of the dual-bridge internal phase shift and the inter-bridge external phase shift can be respectively obtained according to the voltage and inductive current (2n +1) sub-component phasor expression and the steady-state phasor expression obtained in the step 1).
6. The method for analyzing and modeling AC phasor method of dual-active-bridge DC converter under phase shift control according to claim 5, wherein three kinds of phase shift control can be obtained according to the phasor expression of the secondary component of voltage and inductive current (2n +1) obtained in step 1), and the complex power of equivalent sinusoidal voltage source in the (2n +1) th secondary component of dual-active-bridge DC converter under phase shift controlAnd leakage inductance L of high-frequency transformerSReactive power QL(2n+1)：
Wherein,
7. the method for analyzing and modeling the AC phasor method of the dual-active-bridge DC converter under the phase shift control according to claim 6, wherein in the step 3), the active power in the complex power is equal to the DC output power without considering the circuit loss, and then the (2n +1) th component of the output current of the active bridge 2 sideThe phasor expression of (a) is:
and obtaining a steady-state phasor expression of the output voltage at the direct current side, the capacitance current at the direct current side and the load current without considering the condition of the capacitance impedance at the output direct current side:
wherein,the (2n +1) th sub-component of the output voltage,the (2n +1) th sub-component of the output current of the side 2 of the active bridge, C is a parallel capacitor of the direct current output end,is the (2n +1) th sub-component of the output terminal capacitance current,obtaining the Fourier series and expression of the double-active-bridge steady-state model time domain for the (2n +1) th time division of the load current:
introducing a small disturbance near a steady-state working point and substituting the small disturbance into a steady-state model to establish a partial differential equation to obtain a unified small-signal model of the double-active-bridge direct-current converter under phase-shift control:
in the formula:。
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