CN107017762B - A kind of direct current capacitors method for inhibiting harmonic current - Google Patents
A kind of direct current capacitors method for inhibiting harmonic current Download PDFInfo
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- CN107017762B CN107017762B CN201710093778.5A CN201710093778A CN107017762B CN 107017762 B CN107017762 B CN 107017762B CN 201710093778 A CN201710093778 A CN 201710093778A CN 107017762 B CN107017762 B CN 107017762B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/12—Arrangements for reducing harmonics from ac input or output
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M5/00—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases
- H02M5/40—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc
- H02M5/42—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters
- H02M5/44—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac
- H02M5/453—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal
- H02M5/458—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
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Abstract
A kind of direct current capacitors method for inhibiting harmonic current establishes back-to-back converter, and active DC link capacitors electric current is from rectifier i in back-to-back converterdcrWith inverter idciDC current superposition, two electric current idcrAnd idciIn the phase of harmonic component determined by the relative phase PWM carrier wave of rectifier and inverter, the frequency and phase of active control adjusting rectifier and the PWM carrier wave in inverter, so that the same phase of DC link harmonic current from two converter stages, so that capacitor harmonic current minimizes.A kind of direct current capacitors method for inhibiting harmonic current of the present invention, can significantly reduce the harmonic content and current amplitude in the first and second carrier frequency bands of DC link capacitors electric current.Mentioned method can be met power quality specification by the DC link capacitors without using large capacity and can effectively reduce condenser current harmonic wave.
Description
Technical field
The present invention relates to power electronic equipment and harmonics restraint field, specifically a kind of direct current capacitors current harmonics elimination
Method.
Background technique
Two level, three-phase alternating current-DC-AC current transformer be referred to as " back-to-back " current transformer, especially with High Power Factor with
The advantages that ability of high efficiency and bi-directional electric power trend, is famous, and is applied in many fields, such as industrial drives, wind
Power power generation and electric power transport.
Current impulse is injected into DC link by switching power converter from rectifier and inverter side.These electric current arteries and veins
Punching causes DC link capacitors to generate loss, increases the requirement to rated capacitor value, and therefore increase weight, body
Long-pending and cost, and the problems such as cause low power density and reliability.Therefore, the inhibition of DC link capacitors harmonic current
It has received widespread attention.At present to the control for improving electric current or flow of power to inhibit low-frequency harmonics electric current, have a large amount of
Research, but referred to the suppressing method of DC link capacitors harmonic current is rare.
Summary of the invention
The present invention provides a kind of direct current capacitors method for inhibiting harmonic current, can significantly reduce DC link capacitors electricity
The first carrier frequency band of stream and harmonic content and current amplitude in the second carrier frequency band.This method can be by without using big
The DC link capacitors of capacity meet power quality specification；And condenser current harmonic wave can be effectively reduced.
The technical scheme adopted by the invention is as follows:
A kind of direct current capacitors method for inhibiting harmonic current, establishes back-to-back converter, active straight in back-to-back converter
Stream link capacitor electric current is from rectifier idcrWith inverter idciDC current superposition, two electric current idcrAnd idciIn
The phase of harmonic component determine that active control adjusts rectifier and inverse by the relative phase PWM carrier wave of rectifier and inverter
Become the frequency and phase of the PWM carrier wave in device, so that the same phase of DC link harmonic current from two converter stages, so that electric
Container harmonic current minimizes.
A kind of direct current capacitors method for inhibiting harmonic current can be substantially reduced the first load by controlling PWM carrier phase
The frequency and phase of the harmonic wave in direct current harmonic current in wave frequency band, this method are realized in three steps:
Step (1): the quantity of effective harmonic wave in first carrier frequency band is reduced；
Step (2): the frequency of the remaining harmonic wave of rectifier and inverter of the adjustment in first carrier frequency band, so that it
Become identical；
Step (3): making in first band the Phase synchronization of remaining harmonic wave, to realize their final counteracting.
It is compared with the traditional method, a kind of direct current capacitors method for inhibiting harmonic current of the present invention, advantage is: can be obvious
Reduce the harmonic content and current amplitude in the first and second carrier frequency bands of DC link capacitors electric current.Mentioned method can
Meet power quality specification by the DC link capacitors without using large capacity and condenser current can be effectively reduced
Harmonic wave.
Detailed description of the invention
Fig. 1 is back-to-back converter structure chart.
Fig. 2 is carrier phase figure.
Fig. 3 is the dc link current frequency spectrum in the back-to-back converter under conventional sinusoidal asymmetric normal sample PWM
Figure.
Fig. 4 is the current spectrum figure using DC link capacitors.
Fig. 5 is l-G simulation test figure.
Fig. 6 (a) is the current waveform figure that the DC bus capacitance of the method for the present invention is not used.
Fig. 6 (b) is using the current waveform figure in the DC bus capacitance under the present invention.
Specific embodiment
A kind of direct current capacitors method for inhibiting harmonic current, establishes the structure chart of back-to-back converter, as shown in Figure 1.Back
Active DC link capacitors electric current is from rectifier i in backrest current transformerdcrWith inverter idciDC current superposition,
Two electric current idcrAnd idciIn harmonic component phase, determined by the relative phase PWM carrier wave of rectifier and inverter.Harmonic wave
Electric current has two aspect reasons: first is that flow of power is uneven；Second is that the influence of pulse width modulation (PWM) switch.
To realizing this purpose, there are two aspect factors to need to consider:
(1): since the fundamental frequency and carrier frequency of two current transformers are typically different, generating in DC link
The frequency of harmonic wave is also different.It is generally impossible to using simple phase in-migration harmonic carcellation.
(2): best PWM Shift Angle can be used to obtain the DC link capacitors harmonic current of minimum, due to straight
The phase angle for flowing link capacitor harmonic current is related with carrier phase angle, using carrier wave angular variation between converter appropriate, comes
It can be zero from the phase difference between the DC link capacitors harmonic current of inverter and rectifier side, can then make
Capacitor harmonic current minimize.However best PWM carrier wave Shift Angle with practical operation condition and current transformer hardware design and
Variation.Because PWM carrier wave Shift Angle is limited by many factors, such as fundamental frequency, the angle between fundamental current and supply voltage,
PWM modulation depth, the angle between fundamental current and current transformer.Frequency converter carrier wave angular variation.So control and regulation of taking the initiative
The frequency and phase of PWM carrier wave in rectifier and inverter, so that the DC link harmonic current from two converter stages
Same phase, so that capacitor harmonic current minimizes.
Embodiment:
A kind of direct current capacitors method for inhibiting harmonic current, comprising the following steps:
In order to fully take into account influence of the single PWM carrier phase to harmonic current components.Back-to-back change as shown in Figure 1
Device is flowed, wherein rectifier and inverter all have three-phase.The DC link harmonic current i that each phase generatesdc(t) it can be expressed as
Exchange iac(t) and the product of switch function sf (t).
idc(t)=sf (t) × iac(t) (1)
Wherein idc(t) the DC link harmonic current generated for each phase, iacIt (t) is ac harmonic currents, sf (t) is
Switch function.
Due to the switching characteristic of current transformer, some harmonic currents are also had in exchange side.However, the amplitude of these harmonic waves is logical
Chang Feichang is small, is substantially negligible.Therefore, alternating current can be indicated only by fundamental component.
iac(t)=Iac cos(2πf0t+β) (2)
Wherein IacIt is the amplitude of fundametal compoment, β is the angle between ac fundamental current and ac supply voltage, f0It is fundamental wave frequency
Rate.Ignore direct current biasing, the harmonic component of the switch function of phase arm is available under sinusoidal asymmetry normal sample PWM
Here sf (t) is switch function, f0It is fundamental frequency, θ0For master phase angle, m is carrier frequency band number, and n is sideband
Number, fcFor PWM carrier frequency, θcFor carrier phase angle.
Wherein,
M is PWM modulation depth, q=(m+nf in formula (4)0/fc) pi/2, m is carrier frequency band number, and n is sideband number.In formula (5)
L is line inductance, VacIt is the amplitude for exchanging side voltage source, VdcIt is DC link voltage, IacIt is the amplitude of fundametal compoment, f0It is
Fundamental frequency, β are the angles between ac fundamental current and ac supply voltage, use (1)-(5) formula, can obtain and be generated by a phase
DC link harmonic current.
idc(t) the DC link harmonic current generated for each phase, IacIt is the amplitude of fundametal compoment, f0It is fundamental frequency,
θ0For master phase angle, m is carrier frequency band number, and n is sideband number, fcFor PWM carrier frequency, θcFor carrier phase angle, β is ac base
Angle between wave electric current and ac supply voltage.By analysis (6) formula, it is known that the frequency distribution of dc link current harmonic wave
It is that there is (n+1) f0(n-1) f0Frequency displacement switch function superposition.It can also be seen that alternating current and DC link harmonic wave
Phase variance between electric current is coupled by PWM modulation.Even if direct current harmonic wave is different with the frequency of PWM carrier wave, DC current is humorous
The relative phase of wave can pass through mobile carrier phase θcTo change.
For the rectifier and inverter stage of back-to-back converter, DC link harmonic current is the harmonic wave from each phase
The superposition of electric current.Difference between rectifier and inverter DC current will determine harmonic content, in standard PWM scheme, own
Current transformer branch uses identical carrier signal.Assuming that each branch has individual carrier waveform, it is instantaneous in each branch
Carrier phase angle θcIt may be considered that including the reference carrier phase theta relative to fixed phase angleccWith each alternate phase angle θcp。
As shown in Figure 2.Wherein reference value θccIt is the carrier wave angle of phase A, reference of the phase A as angle between the conductor in two current transformers
Amount, and the carrier phase angle θ of inverterciIt is set as 0.
By using (3)-(6) formula, can derive for the DC link capacitors electric current in back-to-back converter
Formula.
Wherein icapIt (t) is the DC link capacitors electric current in back-to-back converter, idciIt (t) is direct current in inverter
Stream, idcrIt (t) is DC current in rectifier, IacrFor fundametal compoment amplitude, I in rectifieraciFor fundametal compoment width in inverter
Degree, f0rFor rectifier fundamental frequency, fcrFor rectifier carrier frequency, θcpFor each alternate phase angle, θccFor reference carrier phase
Position, f0iFor inverter fundamental frequency, fciFor inverter carrier frequency, m is carrier frequency band number, and n is sideband number, and α is ac fundamental wave electricity
Angle between stream and the side ac current transformer voltage, β is the angle between ac fundamental current and ac supply voltage, and k is number of phases: right
In phase A, B or C, phase is respectively k=0,1 or 2.It can be seen that the frequency and phase of DC link harmonic current components from (7) formula
Position can be regulated and controled by changing the carrier phase of rectifier and inverter.Based on this as a result, can propose a kind of for straight
Flow the Active Control Method that link capacitor harmonic current reduces.
Dc link current spectrogram in the back-to-back converter under conventional sinusoidal asymmetric normal sample PWM is as schemed
Shown in 3, it is known that rectifier and inverter are all in first carrier frequency band (in frequency fc-3f0And fc+3f0) and a harmonic wave second
Carrier frequency band is (in frequency 2fc) there are two significant current harmonics for tool.DC link capacitors harmonic current is the two unsteady flows
The superposition of the harmonic wave of device.
By controlling PWM carrier phase, the harmonic wave that can be substantially reduced in the direct current harmonic current in first carrier frequency band
Frequency and phase, this method realizes in three steps:
Step (1): the quantity of effective harmonic wave in first carrier frequency band is reduced；
Step (2): the frequency of the remaining harmonic wave of rectifier and inverter of the adjustment in first carrier frequency band, so that it
Become identical；
Step (3): making in first band the Phase synchronization of remaining harmonic wave, to realize their final counteracting.
Detailed analysis will be carried out to these three steps below:
Step 1: reduce the quantity of effective harmonic wave in first carrier frequency band:
In the step, carrier wave difference 2 π/3 of phase shift of phase B and C and -2 π/3；Apply the carrier wave phase of (0,2 π/3, -2 π/3)
It moves, the current harmonics in the first carrier frequency band under this phase shift can be exported from (6) formula.
Wherein idc1ShiftIt (t) is the current harmonics in first carrier frequency band, IacIt is the amplitude of fundametal compoment, q=(m+nf0/fc) pi/2, m is carrier frequency band number, and n is sideband number, f0It is fundamental frequency, fcIt is PWM carrier frequency, M is PWM modulation depth,
θccFor reference carrier phase, α is the angle between ac fundamental current and the side ac current transformer voltage, and β is ac fundamental current and ac electricity
Angle between the voltage of source.
Harmonic wave in first band is moved into frequency (fc-f0) and (fc+5f0), since Bessel function Jx is x
Decreasing function the, so amplitude (f of harmonic wavec+5f0) than (fc-f0) at component it is much smaller, can usually ignore, therefore, the step
It is rapid the result is that the quantity of effective harmonic wave in first carrier frequency band is reduced to 1.
Similarly, the analytic solutions of the second carrier frequency band under the carrier phase of (0,2 π/3, -2 π/3) can be shown
Are as follows:
idc2ShiftIt (t) is the current harmonics in the second carrier frequency band, IacIt is the amplitude of fundametal compoment, q=(m+nf0/fc)
Pi/2, m are carrier frequency band numbers, and n is sideband number, f0It is fundamental frequency, fcIt is PWM carrier frequency, M is PWM modulation depth, θcIt is to carry
Wave phase angle, α are the angles between ac fundamental current and the side ac current transformer voltage, β be ac fundamental current and ac supply voltage it
Between angle.
If not applying carrier wave to shift, calculating current harmonic wave can be carried out by substituting into phase shift (0,0,0) in (6) formula,
idc2NoShiftIt (t) is the current harmonics in the second carrier frequency band when not using carrier wave to shift, IacIt is fundametal compoment
Amplitude, q=(m+nf0/fc) pi/2, m is carrier frequency band number, and n is sideband number, f0It is fundamental frequency, fcIt is PWM carrier frequency, M is
PWM modulation depth, θcIt is carrier phase angle, α is the angle between ac fundamental current and the side ac current transformer voltage, and β is ac fundamental wave
Angle between electric current and ac supply voltage.
Compare (11) formula and (12) formula, it can be seen that by applying proposed method, also can reduce the second carrier frequency
Current harmonics in band.
Step 2: the frequency of the harmonic wave in adjustment first carrier frequency band:
In the second step, make the frequency of the residual current harmonic wave in the first carrier frequency band of condenser current identical, this
Harmonic frequency f can be passed throughhCurrent transformer carrier frequency is adjusted to realize, due to the first band of each current transformer after step 1
In main harmonic frequency be fc-f0, so using
fc=fh+f0 (13)
The first band current harmonics obtained from inverter and rectifier will be in identical frequency fh, and second band
Downside harmonic wave will also be in identical frequency 2fh。
Step 3: synchronous first carrier frequency band harmonic wave:
In the final step, the harmonic current of the inverter in synchronous first carrier frequency band and rectifier, so that they are same
Phase, in this case, the result of superposition will be zero, and the corresponding current harmonics in DC link capacitors will disappear.
The analysis to the remaining harmonic wave in first carrier frequency band can be found.
I in formulacap1It (t) is the residual current harmonic wave in first carrier frequency band, IacrFor fundametal compoment amplitude in rectifier,
IaciFor fundametal compoment amplitude in inverter, q=(m+nf0/fc) pi/2, m is carrier frequency band number, and n is sideband number, and M is PWM modulation
Depth, fhFor harmonic frequency, θccFor reference carrier phase, α is the angle between ac fundamental current and the side ac current transformer voltage, β
It is the angle between ac fundamental current and ac supply voltage.WhereinWherein Δ fcIt is carrier frequency error,
θc0It is original carrier angle, if the phase of harmonic wave depends on two using different operating environment control rectifiers and inverter
The operating condition of a current transformer: PWM modulation depth, size of current and power factor) and opposite original carrier angle θc0rAnd θc0i；
Carrier frequency error Δ fcIt can also be generated by the discretization of numerical control system and any output variance of oscillator, this two
A factor may be introduced into harmonic phase error.
In order to keep the harmonic in-phase of rectifier and inverter, by change current transformer, in invention select rectifier it
The closed-loop control of harmonic phase difference is established at one carrier phase angle, according to:
Wherein θccFor reference carrier phase, wherein γ is the first carrier frequency after having applied direct carrier wave displacement
The phase of effective current harmonic wave in band, γrAnd γiValue above formula formula can be used obtain.M is PWM modulation depth, and α is ac
Angle between fundamental current and the side ac current transformer voltage, β are the angles between ac fundamental current and ac supply voltage.
Fig. 4 show the current spectrum using the DC link capacitors after proposed method.
It is specific to calculate example:
The parameter of test platform is chosen: taking dc-link capacitance is 4.4mF, rectifier line inductance LrWith inverter route
Inductance LiIt is all 2.33mH, DC bus-bar voltage 750V, supply voltage 240V, effective harmonic wave frequency in first carrier frequency band
Rate fhFor 7000HZ, bandpass filtering bandwidth is 6900-7100, the side inverter ac electric current IaciFor 7.8A, β 23.Fig. 5 is emulation examination
Test figure.Carry out smooth DC link voltage using large-sized DC link capacitor, therefore voltage harmonic is to the shadow of switch harmonic current
Sound can be ignored.As previous section is discussed, two infinite impulse response are realized using programmable gate array (FPGA)
(IIR) bandpass filter is to extract the current harmonics of first carrier frequency band.PWM generator can also generate required carrier wave displacement
PWM.Rectifier carrier wave angle θ cc calculating harmonic phase is poor, and the alternating voltage fundamental frequency in two current transformers is surveyed by phaselocked loop (PLL)
Amount.
Fig. 6 (a) is the current waveform that the DC bus capacitance of proposed method is not used, and Fig. 6 (b) is in institute moving party
The current waveform in DC bus capacitance under method, two width figures, which clearly illustrate, uses proposed method that can effectively subtract
Harmonic current is lacked, it is feasible for also demonstrating this method.
Claims (1)
1. a kind of direct current capacitors method for inhibiting harmonic current, it is characterised in that: establish back-to-back converter, back-to-back converter
In active DC link capacitors electric current be from rectifier idcrWith inverter idciDC current superposition, two electric currents
idcrAnd idciIn the phase of harmonic component determine that active control is adjusted by the relative phase PWM carrier wave of rectifier and inverter
The frequency and phase of PWM carrier wave in rectifier and inverter, so that the DC link harmonic current from two converter stages
Same phase, so that capacitor harmonic current minimizes；
By controlling PWM carrier phase, the frequency of the harmonic wave in the direct current harmonic current in first carrier frequency band can be substantially reduced
Rate and phase, this method are realized in three steps:
Step 1: reducing the quantity of effective harmonic wave in first carrier frequency band；
Step 2: the frequency of the remaining harmonic wave of rectifier and inverter of the adjustment in first carrier frequency band, so that they become
It is identical；
Step 3: making in first band the Phase synchronization of remaining harmonic wave, to realize their final counteracting；
In step 1: in the step, carrier wave difference 2 π/3 of phase shift of phase B and C and -2 π/3；Apply the load of (0,2 π/3, -2 π/3)
Wave phase shift, the current harmonics in the first carrier frequency band under this phase shift can be exported from (6) formula,
Wherein: idc1ShiftIt (t) is the current harmonics in first carrier frequency band, IacIt is the amplitude of fundametal compoment, q=(m+nf0/fc)
Pi/2, m are carrier frequency band numbers, and n is sideband number, f0It is fundamental frequency, fcIt is PWM carrier frequency, M is PWM modulation depth, θccFor
Reference carrier phase, α are the angles between ac fundamental current and the side ac current transformer voltage, and β is ac fundamental current and ac power supply electricity
Angle between pressure；
Harmonic wave in first band is moved into frequency (fc-f0) and (fc+5f0), since Bessel function Jx is the letter that successively decreases of x
Number the, so amplitude (f of harmonic wavec+5f0) than (fc-f0) at component it is much smaller, can usually ignore, therefore, the knot of the step
Fruit is that the quantity of effective harmonic wave in first carrier frequency band is reduced to 1；
Similarly, the analytic solutions of the second carrier frequency band under the carrier phase of (0,2 π/3, -2 π/3) can be shown as:
Wherein: idc2ShiftIt (t) is the current harmonics in the second carrier frequency band, IacIt is the amplitude of fundametal compoment, q=(m+nf0/fc)
Pi/2, m are carrier frequency band numbers, and n is sideband number, f0It is fundamental frequency, fcIt is PWM carrier frequency, M is PWM modulation depth, θcIt is to carry
Wave phase angle, α are the angles between ac fundamental current and the side ac current transformer voltage, β be ac fundamental current and ac supply voltage it
Between angle；
If not applying carrier wave to shift, calculating current harmonic wave can be carried out by substituting into phase shift (0,0,0) in (6) formula,
Wherein: idc2NoShiftIt (t) is the current harmonics in the second carrier frequency band when not using carrier wave to shift, IacIt is fundametal compoment
Amplitude, q=(m+nf0/fc) pi/2, m is carrier frequency band number, and n is sideband number, f0It is fundamental frequency, fcIt is PWM carrier frequency, M is
PWM modulation depth, θcIt is carrier phase angle, α is the angle between ac fundamental current and the side ac current transformer voltage, and β is ac fundamental wave
Angle between electric current and ac supply voltage；
Compare (11) formula and (12) formula, it can be seen that by applying proposed method, also can reduce in the second carrier frequency band
Current harmonics；
Above-mentioned (6) formula is as follows:
Wherein: idc(t) the DC link harmonic current generated for each phase, IacIt is the amplitude of fundametal compoment, f0It is fundamental frequency,
θ0For master phase angle, m is carrier frequency band number, and n is sideband number, fcFor PWM carrier frequency, θcFor carrier phase angle, β is ac base
Angle between wave electric current and ac supply voltage；
In step 2: keeping the frequency of the residual current harmonic wave in the first carrier frequency band of condenser current identical, this can be by humorous
Wave frequency rate fhCurrent transformer carrier frequency is adjusted to realize, due to the main harmonic in the first band of each current transformer after step 1
Frequency be fc-f0, so using
fc=fh+f0 (13)
f0It is fundamental frequency；
The first band current harmonics obtained from inverter and rectifier will be in identical frequency fh, and under second band
Side harmonic wave will also be in identical frequency 2fh；
In step 3: the harmonic current of inverter and rectifier in synchronous first carrier frequency band, so that their same phases, this
In the case of, the result of superposition will be zero, and the corresponding current harmonics in DC link capacitors will disappear, and can find pair
The analysis of remaining harmonic wave in first carrier frequency band:
In formula, icap1It (t) is the residual current harmonic wave in first carrier frequency band, IacrFor fundametal compoment amplitude, I in rectifieraciFor
Fundametal compoment amplitude in inverter, q=(m+nf0/fc) pi/2, m is carrier frequency band number, and n is sideband number, and M is PWM modulation depth,
fhFor harmonic frequency, θccFor reference carrier phase, α is the angle between ac fundamental current and the side ac current transformer voltage, and β is ac base
Angle between wave electric current and ac supply voltage；
Wherein,ΔfcIt is carrier frequency error, θc0It is original carrier angle, if using different operation rings
Border controls rectifier and inverter, then the phase of harmonic wave depends on the operating condition of two current transformers: PWM modulation depth, electric current
Size and power factor and opposite original carrier angle θc0rAnd θc0i；Carrier frequency error Δ fcBy numerical control system from
Any output variance of dispersion and oscillator generates, the two factors may be introduced into harmonic phase error；
In order to keep the harmonic in-phase of rectifier and inverter, by changing current transformer, one of rectifier is selected in invention
The closed-loop control of harmonic phase difference is established at carrier phase angle, according to:
θcc=γi-γr (15)
Wherein, γ is in the phase for having applied the effective current harmonic wave in the first carrier frequency band after direct carrier wave displacement
Position, γrAnd γiValue bandpass filter can be used found from the dc link current of each current transformer.
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