CN105099200B - AC Phasor Analysis Method and Modeling Method for Dual Active Bridge DC Converter with Phase Shift Control - Google Patents

Abstract

The invention provides an AC phasor analysis method and a small signal model modeling method applicable to all dual active bridge DC converters under phase shift control. The dual active bridges include: dual active H bridges, dual three-level Half-bridge, three-level half-bridge on one side, and active H-bridge on the other side. The specific steps are: 1. By equivalently, the AC side of each active bridge is equivalent to two square wave voltage sources, and the square wave voltage is decomposed into the superposition of sinusoidal voltage by Fourier series decomposition, and (2n+ 1) Phasor expression of secondary component voltage and inductor current 2. According to the phasor expression in step 1, obtain the phasor diagram of the control characteristics and control range of different phase-shift controls; 3. According to the phasor expression in step 1, obtain the complex power of the (2n+1) order component Analyze the active and reactive power characteristics of the dual active bridge DC converter under different phase shift controls; 4. According to the phasor expression in step 1, get the time-domain Fourier series and expression of its voltage and current, and get the applicable A unified small-signal model for all phase-shift control methods.

Description

AC Phasor Analysis Method and Modeling Method for Dual Active Bridge DC Converter with Phase Shift Control

technical field

The invention belongs to the field of power electronics technology and smart grid research, and in particular relates to a phase shift control dual active bridge circuit power analysis method and modeling based on a phasor method.

Background technique

With the development of smart grids, high-power power electronic converters without power frequency transformers have attracted more and more attention due to their high efficiency, intelligence, and low pollution. At present, the common high-power power electronic converter without industrial frequency transformer adopts cascaded topology, which is composed of cascaded multi-level AC-DC rectification module, bidirectional DC-DC conversion module and multi-level DC-AC inverter module.

The dual active bridge DC-DC converter structure is adopted by the bidirectional DC-DC conversion module due to its characteristics of electrical isolation, buck-boost conversion, bidirectional energy transmission, and high power density.

The traditional analysis method of phase-shift control dual active bridge analyzes the power characteristics mainly based on the analysis of the phase-shift control principle waveform, and obtains the power mathematical model through definite integral calculation, and then analyzes the characteristics of transmission power and reactive power. Although this method can obtain more accurate results, it also has obvious deficiencies. Its main disadvantages are that the calculation is complicated, the physical meaning is not clear, and the analysis results cannot directly reflect the relationship between transmission power and reactive power, and the traditional analysis method cannot establish a general model for various phase shifting methods.

[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 conversion apparatus for DC/DC conversion using dual active bridges," U.S. Patent 5027264, Jun.25, 1991.

Contents of the invention

For the defects and deficiencies of traditional analysis methods, the object of the present invention is to propose a phase shift control dual active bridge DC converter power analysis and modeling method based on the phasor method. The dual active bridges include: dual active H bridge, dual three-level half-bridge, three-level half-bridge on one side, and active H-bridge on the other side. A unified analysis model that can be used for multiple phase-shift controls is established, and a small-signal model is established on the basis of this unified model.

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

Phase shift control dual active bridge DC converter power analysis and modeling method based on phasor method. This method uses an equivalent method to equate the voltage at both ends of the active bridge to two square wave voltage sources, and then the square wave The voltage is decomposed into a superposition of sinusoidal voltages by Fourier series. The active power and reactive power of the fundamental wave and each harmonic are analyzed by the phasor method, and the calculation of the sine quantity is replaced by the calculation of the complex number, which greatly simplifies the calculation. And an analysis method based on phasor method with clear physical meaning, accurate analysis results and simple operation of phase-shift control of dual active bridge is proposed. Through this analysis method, a unified small-signal model of dual active bridge can be established.

An analysis method and a modeling method for a phase-shifting control dual active bridge circuit based on an AC phasor method, including the following steps:

1) The equivalent model of the dual active bridge DC converter is replaced, and the phasor expression of the voltage of the (2n+1)th component and the inductor current is obtained;

2) According to the phasor expression in step 1), the corresponding phasor diagrams under different phase shifting controls are obtained;

3) According to the phasor expression in step 1), the complex power expression of the equivalent voltage source is obtained, and the characteristics of active power and reactive power under different phase-shift controls are analyzed;

4) According to the phasor expression and the differential equation of the converter in step 1), the Fourier series and expression of the time domain of the steady-state model of the double active bridge are obtained, and the small-signal disturbance technology is used to introduce the small-signal disturbance into the steady state A unified small-signal model of the dual active bridge DC converter under phase-shift control is obtained.

A further improvement of the present invention is that, in step 1), the double active bridge DC converter can be replaced by an equivalent model, as shown in Figure 1, each active bridge AC side voltage can be a square wave voltage source V _ab (t) , V _cd (t), and can be expressed as an infinite superposition of sine wave signals of different frequencies.

Among them, V _ab (t) is the square wave voltage on the AC side of the active bridge 1, V _cd (t) is the square wave voltage on the AC side of the active bridge 2, V _in is the input DC voltage, V _out is the output DC voltage, is the turn ratio of the high-frequency isolation transformer, ω is the AC angular frequency, n=1,2,3..., α ₁ is the internal phase shift angle of the active bridge 1, α ₂ is the active bridge 1 and the active bridge 2 The phase shift angle between bridges, α4 is the internal phase shift angle of the active bridge ₂ , and α3 is the sum of the internal phase shift angle α4 _of the active bridge ₂ and the inter _- bridge phase shift angle α2.

The further improvement of the present invention is, the model that two sinusoidal AC voltage sources mentioned in step 1) are connected by inductance line, establishes the state equation of switching function:

1) The state differential equation of the AC/AC link of the dual active bridge DC converter:

Where R _L is the transformer resistance, L _s is the transformer leakage inductance, and i _L (t) is the transformer current.

2) Putting the equivalent expressions (1) and (2) of the square wave voltage source into the equation (3) can obtain the equivalent differential equation based on the switching function:

The further improvement of the present invention is that the phasor expression of the voltage and the inductor current of the (2n+1)th component in step 1) can obtain the steady-state phasor expression according to the differential equation equivalent to the switching function in claim 3:

Then determine the square wave voltage and the (2n+1) component phasor expression of the inductor current:

The further improvement of the present invention lies in that, according to the voltage, inductor current (2n+1) sub-component phasor expressions obtained in step 1) and the steady-state phasor expression of the converter, the outer bridge between the bridges in step 2) can be obtained respectively Phasor diagrams of a dual active bridge DC converter under phase shifting, single active bridge internal phase shifting and inter-bridge external phase shifting, and dual-bridge internal phase shifting and inter-bridge external phase shifting control.

The further improvement of the present invention is that, according to the voltage and inductor current (2n+1) sub-component phasor expressions obtained in step 1), it can be obtained that under three kinds of phase-shift control, the (2n+1)th sub-component of the dual active bridge DC converter ) in the secondary component of the equivalent sinusoidal voltage source complex power and the high-frequency transformer leakage inductance L _S reactive power:

in,

The further improvement of the present invention is that the active power in the complex power in step 3) is equal to the DC output power without considering the circuit loss, then the (2n+1)th component of the output current of the active bridge 2 side The phasor expression of is:

Without considering the capacitance impedance of the output DC side, the steady-state phasor expressions of the DC side output voltage, the DC side capacitor current and the load current are obtained:

in The (2n+1)th component of the output voltage, is the (2n+1)th component of the output current on the 2 side of the active bridge, C is the capacitance of the output terminal, is the (2n+1)th component of the capacitive current at the output terminal, It is the (2n+1)th component of the load current.

Obtain the Fourier series sum expression in the time domain of the dual active bridge steady-state model:

A small disturbance is applied near the steady-state operating point and substituted into the steady-state model, and a partial differential equation is established to obtain a unified small-signal model of the dual active bridge DC converter under phase-shift control:

In the formula:

The method of the present invention analyzes the dual active bridge circuit through the phasor method, the calculation method is simple, an analysis model with clear physical meaning is obtained, and the relationship between the power transmission characteristics of the dual active bridge and the phase shift angle is clearly obtained relationship, and on this basis, a method for establishing a small-signal model for a dual active bridge circuit is proposed.

Description of drawings

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

Figure 1 is a dual active H-bridge DC converter topology;

Figure 2(a) is the equivalent circuit of the dual active bridge DC converter;

Figure 2(b) is the equivalent circuit of the synchronous motor of the dual active bridge DC converter;

Figure 3 is an ideal waveform diagram of phase shift control;

Figure 4 is a phasor diagram of a dual active bridge in a single phase-shift control strategy;

Fig. 5 is the phasor diagram of the extended phase shifting control strategy in mode A;

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

Fig. 6(b) is the phasor diagram when α ₂ =0 for the control strategy of mode B of extended phase shift;

Figure 6(c) is the extended phase-shift B mode control strategy, when phasor diagram when

Figure 7(a) is the phasor diagram of the dual phase shift control strategy;

Figure 7(b) is the phasor diagram when α ₂ =0 and α ₃ =α ₁ in the dual phase shift control strategy;

Figure 7(c) shows the dual phase shift control strategy, when phasor diagram for .

detailed description

In the following, the present invention will be further described by taking the dual active H-bridge DC converter topology shown in FIG. 1 as an example in conjunction with the accompanying drawings and specific implementation methods.

Figure 3 shows the ideal waveforms of three phase shift control strategies: single phase shift, extended phase shift, and double phase shift control; among them, V _ab (t) and V _cd (t) are two single-phase H-bridges The square wave voltage on the AC side takes the phase of the driving signal S1 as the reference phase, the phase delay between the driving signals S4 and S1 is called the inner phase angle α ₁ of H1; the phase delay between the driving signals Q1 and S1 is called the outer phase angle Phase shift angle α ₂ ; the phase delay between the drive signal Q4 and S1, that is, the sum of the inner phase shift angle α ₄ and the outer phase shift angle α ₂ of H2 is called α ₃ (α ₃ =α ₂ +α ₄ ).

Taking H1 ahead of H2 as an example, three phase-shift control strategies are analyzed through the AC phasor analysis method:

Since the inductor resistance is small enough to be ignored, the apparent power of the inductor is derived as follows:

It can be seen from formula (1) that in the phase-shift control strategy, the active power P _ab(2n+1) of the leading bridge H1 is completely transferred to the lagging bridge H2 as the output power of the DC side, that is, P _ab(2n+1) =P _cd(2n+1) . Inductive reactive power is jointly provided by leading bridge H1 and lagging bridge H2.

1) Single phase shift control strategy phasor analysis method

When α ₁ =0 and α ₄ =0, that is, there is only a phase shift between the two H-bridges. At this point, the phasor expressions of the two voltage sources simplify to Phasor lag phasor The angle of is (2n+1)α ₂ . Figure 4 is the phasor diagram of the dual active bridge DC converter under the single-phase-shift control strategy. The two phasors in the figure have the same modulus, namely It can be seen that when the voltage V _in , When kept constant, the power of the dual active bridge is adjusted by the phase shift angle _α2 .

Under the single phase-shift control strategy, the sum of each harmonic power is

2) Extended phase shift control strategy phasor analysis method

There are two phase shift modes in the extended phase shift control strategy: ①α ₁ ≠0 and α ₄ =0; ②α ₁ =0 and α ₄ ≠0.

①α ₁ ≠0 and α ₄ =0

The voltage phasor expressions are Phasor The included angle with the coordinate axis is half of the internal phase shift angle of HB1, namely Figure 5 is the phasor diagram of extended phase shifting under the control strategy of extended ① mode, the phasor The trajectory falls in Figure 5 with or on an arc that is one quarter of the radius. The reactive power of the inductor is:

in,

exist That is: under the condition of α ₁ = α ₂ , the reactive power of the inductor under the extended phase-shift control strategy ① achieves the minimum value:

Under the condition of α ₁ =α ₂ , the reactive power Q _ab(2n+1) of the leading bridge =0, the inductor current Equivalent voltage source with leading bridge same phase, that is, advanced Q _{L min} is completely provided by the lagging bridge, and the phasor diagram is shown in Fig. 4. Under this condition, the transmission power of the dual active bridge is

②α ₁ =0 and α ₄ ≠0

Figure 6(a) The phasor diagram of the extended phase shift ② control strategy, the phasor expressions of the two voltage sources are expressed as The complex powers of leading bridge H1 and lagging bridge H2 are respectively

When α ₂ =0, the phasor is a constant, then the phasor The trajectory of is the same as the phasor in Figure 5 The trajectory is the same as is a quarter of the radius; the difference is that the phasor The trajectory changes with α ₃ ; according to the geometrical theorem, in this case, the phasor The phase lag of the leakage inductance voltage phase is 90°, then the leakage inductance current phase and phasor The same, so the reactive power of the lagging bridge is zero at this time, and the corresponding phasor diagram is shown in Figure 6(b). When α ₂ =0, the phasor The trajectory line is one of its extended phase-shifting boundary conditions.

when phasor The variation of the trajectory with α ₂ is the phasor Another boundary condition of the trajectory under extended phase-shift control is shown in Fig. 6(c).

in Figure 6 The boundary trajectory is under single phase shift The trajectory line changes with the phase shift angle. So far, the phasor in the case of extended shift ② is obtained The actual control area of , as shown in the shaded part of phase diagram 6.

3) Phasor analysis method of dual phase shift control strategy

The dual phase-shift control strategy is to control the inner phase-shift angles of HB1 and HB2 to be equal, that is, α ₁ =α ₄ . Figure 7(a) is the phasor diagram of the dual phase-shift control strategy, and the shaded part in the figure is the double phase-shift control In the general control area of the strategy, the complex powers of the leading bridge H1 and the lagging bridge H2 are respectively:

When α ₂ =0, α ₃ =α ₁ , as shown in Figure 7(b) by or is the boundary locus of a quarter-radius arc, the phasor with phasor coincidence, the active power of the two H bridges P _ab =P _cd =0, that is, the voltage and current on the inductor are both 0, the complex power of the leading bridge H1 and the lagging bridge H2 can be expressed as:

when and different phase, The trajectory is shown in Fig. 7(c) and the phasor in Fig. 6 in the extended phase shift The trajectory of is the same, and the complex powers of H1 and H2 are:

The above embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and the protection scope of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent replacements to the present invention within the spirit and protection scope of the present invention, and such modifications or equivalent replacements should also be deemed to fall within the protection 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 V_ab(t)、V_cd(t) and may all be represented as an infinite superposition of sine wave signals of different frequencies;

wherein, V_ab(t) is the AC side wave voltage, V, of the active bridge 1_cd(t) is the AC lateral wave voltage of the active bridge 2, V_inFor inputting a DC voltage, V_outIn 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 is_LIs a transformer resistance, L_sFor leakage inductance of transformer, i_L(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 transformer_SReactive power Q_L(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:。