CN114519313A - 12-phase rectification circuit conducted electromagnetic interference modeling method based on state transition - Google Patents
12-phase rectification circuit conducted electromagnetic interference modeling method based on state transition Download PDFInfo
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Abstract
The invention discloses a 12-phase rectification circuit conducted electromagnetic interference modeling method based on state transition, which comprises the following steps of: 1) dividing power supplies of the 12-phase rectifying circuit into four groups, and determining the operation mode of the 12-phase rectifying circuit; 2) determining the working mode of the 12-phase rectifying circuit according to the running mode of the 12-phase rectifying circuit; 3) according to the working modes of the 12-phase rectifying circuit, 12-phase rectifying circuit conducted electromagnetic interference models in different working modes are established, and therefore differential mode voltage and common mode voltage of the 12-phase rectifying circuit in different working modes are determined. The invention provides a differential mode and common mode electromagnetic interference source modeling method aiming at a 12-phase rectification circuit with unbalanced input power supply, which is more in line with the actual circuit condition, and can more accurately predict the electromagnetic interference characteristic of the actual 12-phase rectification circuit.
Description
Technical Field
The invention relates to the field of prediction of electromagnetic compatibility, in particular to a 12-phase rectification circuit conducted electromagnetic interference modeling method based on state conversion.
Background
The rectifier circuit is a power electronic energy conversion device which is most widely applied, has the largest quantity and the largest installed capacity. Because of the advantages of simple structure, convenient control and the like, a rectifying system using a diode or a thyristor as a rectifying device is widely applied to the fields of high-voltage direct-current transmission, electrochemical treatment process, high-power propulsion and the like. However, due to the strong non-linearity and time variability of the rectifying devices, such rectifying systems generate a large amount of harmonics, reduce the power factor of the system, cause voltage distortion, and may adversely affect other electrical devices.
In order to reduce the conducted electromagnetic interference generated by the rectification system, the technologies such as the PWM rectification system and the multiphase rectification system are widely adopted to modify so as to prevent the generation of harmonic waves or to generate harmonic waves as little as possible. The PWM rectification system enables input current and input voltage to have the same phase by controlling the on and off of the full-control device, and the input current has no harmonic wave. The multiphase rectifier system increases the number of load voltage pulses by increasing the number of output phases of the rectifier transformer or the generator, thereby achieving the purposes of suppressing input current harmonics and reducing the ripple factor of the load voltage. Compared with a PWM (pulse-width modulation) rectification system, the multiphase rectification system has a simple structure and higher reliability, and is more suitable for high-current, high-voltage and high-power occasions such as naval vessels and the like.
Meanwhile, compared with a single-phase rectification system and a three-phase rectification system, when the same power is transmitted, the reverse voltage borne by the rectification device of the multi-phase rectification system is lower, and the requirement on the insulation grade of the rectification device is low. Most importantly, when no filter device is used, the total harmonic coefficient of the output voltage and current of the multi-phase rectifying system is much smaller than that of a single-phase rectifying system and a three-phase rectifying system, so that the power grade of the filter device or the power factor correction device is smaller. A series of excellent characteristics of a multiphase rectifying system, in particular a 12-phase rectifying circuit enable the multiphase rectifying system to be widely applied to high-current, high-voltage and high-power occasions such as naval vessels and the like. However, with the gradual and wide application of switching devices such as high-frequency and high-temperature SiC and the like, dv/dt and di/dt are greatly increased compared with the prior generation Si-based semiconductor switching devices, and the more serious electromagnetic interference problem is brought.
Therefore, an accurate calculation method for electromagnetic interference needs to be established for a 12-phase rectification circuit in a naval vessel platform, the electromagnetic environment of equipment in a battle platform is predicted, the interference response of sensitive equipment is further analyzed, and a foundation is laid for inhibiting electromagnetic interference and solving the problem of electromagnetic compatibility. At present, two methods are used for predicting the EMI of a 12-phase rectifier circuit, one method is to build a time domain model in software such as Saber or Simplorer, and the other method is to fit the waveform of a power semiconductor device. However, there are the following problems: 1) although the time domain EMI prediction can accurately fit the transient switching process of the power semiconductor device, particularly has a good prediction effect on the 'ringing' response under high frequency, the calculation time is long, more memories need to be occupied, particularly, when the Simplorer is used for field-path collaborative analysis, a large amount of time is needed for calculation, and the time domain numerical value is unstable in calculation, which may cause divergence; 2) although the precision of the fitting of the switching waveform in the frequency domain is relatively low, the fitting does not cause divergence, although the EMI generated by the 12-phase rectifier circuit can be accurately predicted in a certain precision range, and the EMI can be used for subsequent targeted EMI suppression design, the mechanism of the generation of the electromagnetic interference of the 12-phase rectifier cannot be revealed.
Disclosure of Invention
The invention aims to provide a 12-phase rectification circuit conducted electromagnetic interference modeling method based on state transition, which comprises the following steps:
1) dividing power supplies of the 12-phase rectifying circuit into four groups, and determining the operation mode of the 12-phase rectifying circuit;
the power supply voltages of the 12-phase rectifier circuit are as follows:
in the formula, omega is power angular frequency;
is the phase; u. ua1、ua2、ua3、ua4、ub1、ub2、ub3、ub4、uc1、uc2、uc3、uc4Is the supply voltage; eA1、EA2、EA3、EA4、EB1、EB2、EB3、EB4、EC1、EC2、EC3、EC4Is the peak value of each phase power supply. t is time.
The operation modes of the 12-phase rectifier circuit include the following types:
the first type: a group of power supplies in the 12-phase rectifying circuit is conducted by 2 diodes;
the second type: two groups of power supplies in the 12-phase rectifying circuit are respectively provided with 2 diodes for conduction;
in the third category: three groups of power supplies in the 12-phase rectifying circuit are respectively provided with 2 diodes for conduction;
the fourth type: four groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes;
the fifth type: three groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other group of power supplies is conducted by 3 diodes;
the sixth type: two groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other two groups of power supplies are respectively conducted by 3 diodes;
the seventh type: one group of power supplies in the 12-phase rectifying circuit is conducted by 2 diodes, and the other three groups of power supplies are conducted by 3 diodes;
Eighth type: four groups of power supplies in the 12-phase rectifying circuit are respectively provided with 3 diodes for conduction.
The determining factor of the operation mode of the 12-phase rectification circuit comprises a commutation overlap angle;
the equation for the commutation overlap angle is as follows:
in the formula IdIs a steady-state current value at the output side of the 12-phase rectifying circuit; xBIs the reactance of each phase; e0For each phase of the power supply amplitude; m is the number of pulses in a period; mu is an electrical angle; alpha is the triggered delay angle.
2) Determining the working mode of the 12-phase rectifying circuit according to the running mode of the 12-phase rectifying circuit;
the working modes of the 12-phase rectifying circuit comprise a 2-4-2 mode, a 4-6-4 mode and a 6-8-6 mode;
when the working mode of the 12-phase rectifying circuit is a 2-4-2 mode, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 2 and 4 in a circulating way;
wherein, if the alpha + mu-pi/12 is more than or equal to the omega t is less than or equal to the alpha, the C of the power supply4Phase B and4phase power supply, a 12-phase rectifying circuit is in a conducting stage, the operation mode is a first type operation mode, and the output voltage of the 12-phase rectifying circuit is recorded as U1；
If alpha is more than ω t and less than or equal to alpha + mu, C of the power supply4Phase, B4Phase, A1Phase B and1phase power supply, a 12-phase rectifying circuit in a phase change stage, a second type of operation mode, and a 12-phase rectifying circuit output voltage marked as U 2；
If alpha + mu is more than ω t and less than or equal to alpha + π/12, power supply A1Phase B and B1Phase power supply, a 12-phase rectifying circuit is in a conduction stage, the operation mode is a first type operation mode, and the output voltage of the 12-phase rectifying circuit is marked as U3；
Output voltage U1Output voltage U2Output voltage U3Respectively as follows:
when the working mode of the 12-phase rectifying circuit is a 4-6-4 mode, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 4 and 6 in a circulating way;
wherein, if ω t is α + μ -pi/12, the power supply of the 12-phase rectifier circuit is driven by the power supply of the 12-phase rectifier circuit
Become into
The operation mode is converted from the third operation mode to the second operation mode;
if ω t is α + pi/12, the power supply of the 12-phase rectifier circuit is driven by the motor
Become into
The operation mode is converted from the second type operation mode to a third type operation mode;
when the working mode of the 12-phase rectifying circuit is 6-8-6, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 6 and 8 in a circulating way;
wherein, if ω t is α + μ -pi/6, the power supply of the 12-phase rectifier circuit is driven by the power supply source
Become into
If ω t is α + pi/12, the power supply of the 12-phase rectifier circuit is driven by the motor
Become into
The operation mode is converted from the third operation mode to the fourth operation mode.
3) According to the working mode of the 12-phase rectifying circuit, a 12-phase rectifying circuit conducted electromagnetic interference model under different working modes is established, and therefore differential mode voltage and common mode voltage of the 12-phase rectifying circuit under different working modes are determined.
The 12-phase rectification circuit conducted electromagnetic interference models in different working modes comprise a 12-phase rectification circuit conducted electromagnetic interference model in a 2-4-2 mode, a 12-phase rectification circuit conducted electromagnetic interference model in a 4-6-4 mode and a 12-phase rectification circuit conducted electromagnetic interference model in a 6-8-6 mode.
The step of establishing the 12-phase rectification circuit conducted electromagnetic interference model under the 2-4-2 mode comprises the following steps:
1) establishing a differential mode voltage expression under a 2-4-2 mode, wherein the steps comprise:
1.1) calculating the differential mode voltage jump value delta U of the DC output side under the condition of alpha moment and no load1Namely:
in the formula of U1(ωt＝α)、U2(ω t ═ α) is the voltage before and after the transition, respectively; e is the peak value of the power supply;
1.2) calculating the differential mode voltage jump value U of the output side of the 12-phase rectification circuit at the alpha momentdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; c filterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculating the differential mode voltage jump value delta U of the direct current output side under the condition of no load at the moment of alpha + mu2Namely:
in the formula of U2(ωt＝α+μ)、U3(ω t ═ α + μ) is a voltage before and after the transition, respectively;
1.4) calculating the differential mode voltage jump value U at the output side of the rectifying circuit at the moment of alpha + mudm2Namely:
1.5) writing the differential mode voltage of the direct current output side into an s-domain form in one period T to obtain:
in the formula, time t1α/ω, time t2＝(α+μ)/ω；Ucm(s) is a differential mode voltage on the direct current output side in the form of s domain;
1.6) converting the differential mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a differential mode voltage expression in a 2-4-2 mode, namely:
in the formula, n and k are integers; u shapedm(jn ω) is the differential mode voltage in the frequency domain; u shapedm1(jnω)、Udm2(jn ω) is a differential mode voltage jump value in the frequency domain;
2) establishing a common-mode voltage expression in a 2-4-2 mode, comprising the following steps of:
2.1) calculating the common-mode voltage of the 12-phase rectifying circuit, namely:
2.2) calculating the voltage jump value delta U of the conduction time alpha respectively1Voltage jump value Δ U at conduction time α + μ2Voltage jump value delta U of conduction time alpha + pi/123And a voltage jump value delta U of alpha + mu + pi/12 at the conduction time 4Voltage jump value delta U of alpha + pi/6 at conduction time5And a voltage jump value delta U of alpha + mu + pi/6 at the conduction time6Voltage jump value delta U of alpha + pi/4 at conduction time7And a voltage jump value delta U of alpha + mu + pi/4 at the conduction time8Namely:
2.3) writing the common mode voltage of the direct current output side in one sixth period into an s-domain form to obtain:
in the formula, time t1α/ω, time t2(α + μ)/ω, time t3(α + π/12)/ω, time t4When is (α + μ + π/12)/ω, andcarving t5(α + π/6)/ω, time t6(α + μ + pi/6)/ω, time t7(α + pi/4)/ω, time t8＝(α+μ+π/4)/ω；
According to the formula (14), establishing a common-mode voltage s-domain expression in one period, namely:
2.4) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 2-4-2 mode, namely:
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain. U shapecm1(jn ω) is the common mode voltage in the frequency domain over one sixth of a period.
The step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model under a 4-6-4 mode comprises the following steps:
1.1) calculation at t1At time α/ω, differential mode voltage jump Δ U at the dc output side in the no-load condition1Namely:
1.2) calculation at t1At time α/ω, the differential mode voltage jump value U at the output side of the 12-phase rectifier circuit dm1Namely:
in the formula, parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculation at t2Time (alpha + mu-pi/12)/omega, differential mode voltage jump value delta U of DC output side under no-load condition2Namely:
1.4) calculation at t2At time (alpha + mu-pi/12)/omega, the differential mode voltage jump value U at the output side of the rectifier circuitdm2Namely:
1.5) establishing a differential mode voltage expression in a 4-6-4 mode, namely:
2) establishing a common-mode voltage expression in a 4-6-4 mode, comprising the following steps of:
2.1) calculating the conduction time t respectively1Voltage jump value delta U of alpha/omega1And conduction time t2Voltage jump value of (alpha + mu-pi/12)/omega2And conduction time t3Voltage jump value delta U of (alpha + pi/12)/omega3And conduction time t4Voltage jump value Δ U of (α + μ)/ω4And conduction time t5Voltage jump value delta U of (alpha + pi/6)/omega5And conduction time t6Voltage jump value of (alpha + mu + pi/12)/omega6And conduction time t7Voltage jump value delta U of (alpha + pi/4)/omega7And conduction time t8Voltage jump value of (alpha + mu + pi/6)/omega 8Namely:
2.2) establishing a common-mode voltage s-domain expression in one sixth of a period, namely:
2.3) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 4-6-4 mode in one period, namely:
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…) (29)
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain.
The step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model under a 6-8-6 mode comprises the following steps:
1.1) calculation at t1At time α/ω, differential mode voltage jump Δ U at the dc output side in the no-load condition1Namely:
1.2) calculation at t1At time α/ω, the differential mode voltage jump value U at the output side of the 12-phase rectifier circuitdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculation at t2Time (alpha + mu-pi/6)/omega, differential mode voltage jump value delta U of DC output side under no-load condition2Namely:
1.4) calculation at t2At time (alpha + mu-pi/6)/omega, the differential mode voltage jump value U at the output side of the rectifier circuit dm2Namely:
1.5) establishing a differential mode voltage expression in a 6-8-6 mode, namely:
2) establishing a common-mode voltage expression in a 6-8-6 mode, wherein the common-mode voltage expression comprises the following steps:
2.1) calculating the conduction time t respectively1Voltage jump value delta U of alpha/omega1And conduction time t2Voltage jump value of (alpha + mu-pi/6)/omega2And conduction time t3Voltage jump value delta U of (alpha + pi/12)/omega3And conduction time t4Voltage jump value of (alpha + mu-pi/12)/omega4And conduction time t5Voltage jump value delta U of (alpha + pi/6)/omega5And conduction time t6Voltage jump value Δ U of (α + μ)/ω6And conduction time t7Voltage jump value delta U of (alpha + pi/4)/omega7And conduction time t8Voltage jump value of (alpha + mu + pi/8)/omega8Namely:
2.2) establishing a common-mode voltage s-domain expression in one sixth of a period, namely:
2.3) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 6-8-6 mode in one period, namely:
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…) (44)
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain.
It is worth to be noted that the working mode of the 12-phase rectifying circuit is analyzed firstly, then the instantly finished voltage jump is represented in the form of step signals according to the conducting condition of the switching device in each conducting and phase-changing process, and meanwhile, the time domain delay between each device and the phase is fully considered, and a calculation model of a conduction interference source s domain is deduced. Meanwhile, the widely existing input power source unbalance factors of the actual circuit are fully considered, a conducted interference source calculation model of the 12-phase rectification circuit in the unbalanced state is provided, and a 12-phase rectification circuit conducted electromagnetic interference modeling method based on state conversion is formed.
The technical effects of the invention are undoubted, and the modeling method for the conducted electromagnetic interference of the 12-phase rectification circuit based on state transition, which is provided by the invention, can be used for predicting the conducted electromagnetic interference characteristic of the 12-phase rectification circuit, revealing the generation mechanism of the electromagnetic interference of the 12-phase rectification circuit, further being used for predicting the electromagnetic interference of an independent or non-independent power system level, and providing a prediction model and data support for developing targeted electromagnetic interference suppression. The method can accurately give the electromagnetic interference strength of a ship platform and other scenes using the 12-phase rectification circuit as a conducted interference source, can be further used for conducted interference prediction in equipment or an independent power system, can be used for predicting the conducted electromagnetic interference characteristics of sensitive parts in the equipment or the independent power system, and lays a foundation for taking targeted electromagnetic interference suppression measures. The modeling method of the 12-phase rectifying circuit based on state conversion has clear physical concept and simple calculation method, can accurately model and characterize the electromagnetic interference source of the 12-phase rectifying circuit, and lays a foundation for subsequently adopting targeted electromagnetic interference suppression measures. The invention can provide an analytic solution of differential mode and common mode electromagnetic interference frequency points of the 12-phase rectifying circuit under the balanced state of input phases based on the state conversion of the 12-phase rectifying circuit. The invention provides a differential mode and common mode electromagnetic interference source modeling method aiming at a 12-phase rectification circuit with unbalanced input power supply, which is more in line with the actual circuit condition, and can more accurately predict the electromagnetic interference characteristic of the actual 12-phase rectification circuit. The invention provides a modeling method and a calculation model of electromagnetic interference based on a 12-phase rectification circuit, and can also be directly popularized and applied to the conducted electromagnetic interference modeling of a 24-phase or even more-phase rectification circuit.
Drawings
FIG. 1 is a time domain waveform of 12 phase voltage;
FIG. 2 is a schematic diagram of line voltage for a 12-phase rectifier circuit;
FIG. 3 is an equivalent circuit of the interval [ α + μ - π/12, α ];
FIG. 4 is an equivalent circuit of the interval [ α + μ - π/12, α ];
FIG. 5 shows comparison results of differential mode voltage EMI predictions of FIG. 5;
fig. 6 shows the comparison results of common mode voltage EMI predictions.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 6, a 12-phase rectifier circuit conducted electromagnetic interference modeling method based on state transition includes the following steps:
1) dividing power supplies of the 12-phase rectifying circuit into four groups, and determining the operation mode of the 12-phase rectifying circuit;
the power supply voltages of the 12-phase rectifier circuit are respectively as follows:
in the formula, omega is power angular frequency;
is the phase; u. ofa1、ua2、ua3、ua4、ub1、ub2、ub3、ub4、uc1、uc2、uc3、uc4Is the supply voltage; eA1、EA2、EA3、EA4、EB1、EB2、EB3、EB4、EC1、EC2、EC3、EC4The peak value of each phase power supply.
The operation modes of the 12-phase rectifier circuit include the following types:
The first type is: a group of power supplies in the 12-phase rectifying circuit is conducted by 2 diodes;
the second type: two groups of power supplies in the 12-phase rectifying circuit are respectively provided with 2 diodes for conduction;
in the third category: three groups of power supplies in the 12-phase rectifying circuit are respectively provided with 2 diodes for conduction;
the fourth type: four groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes;
the fifth type: three groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other group of power supplies is conducted by 3 diodes;
the sixth type: two groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other two groups of power supplies are respectively conducted by 3 diodes;
the seventh type: one group of power supplies in the 12-phase rectifying circuit is conducted by 2 diodes, and the other three groups of power supplies are conducted by 3 diodes;
eighth type: four groups of power supplies in the 12-phase rectifying circuit are respectively provided with 3 diodes for conduction.
The determining factor of the operation mode of the 12-phase rectification circuit comprises a commutation overlap angle;
the equation for the commutation overlap angle is as follows:
in the formula IdIs a steady-state current value at the output side of the 12-phase rectifying circuit; xBIs the reactance of each phase; e0For each phase of the power supply amplitude; m is the number of pulses in a period; mu is an electrical angle; alpha is the triggered delay angle.
2) Determining the working mode of the 12-phase rectifying circuit according to the running mode of the 12-phase rectifying circuit;
The working modes of the 12-phase rectifying circuit comprise a 2-4-2 mode, a 4-6-4 mode and a 6-8-6 mode;
when the working mode of the 12-phase rectifying circuit is a 2-4-2 mode, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 2 and 4 in a circulating way;
wherein, if the alpha + mu-pi/12 is more than or equal to the omega t is less than or equal to the alpha, the C of the power supply4Phase B and4phase power supply, a 12-phase rectifying circuit is in a conducting stage, the operation mode is a first type operation mode, and the output voltage of the 12-phase rectifying circuit is recorded as U1；
If alpha is more than ω t and less than or equal to alpha + mu, C of the power supply4Phase, B4Phase, A1Phase B and1phase power supply, a 12-phase rectifying circuit in a phase change stage, a second type of operation mode, and a 12-phase rectifying circuit output voltage marked as U2；
If alpha + mu is more than ω t and less than or equal to alpha + π/12, A of the power supply1Phase B and1phase power supply, a 12-phase rectifying circuit is in a conducting stage, the operation mode is a first type operation mode, and the output voltage of the 12-phase rectifying circuit is recorded as U3；
Output voltage U1Output voltage U2Output voltage U3Respectively as follows:
when the working mode of the 12-phase rectifying circuit is a 4-6-4 mode, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 4 and 6 in a circulating way;
wherein, if ω t is α + μ -pi/12, the power supply of the 12-phase rectifier circuit is driven by the power supply of the 12-phase rectifier circuit 
Become into
The operation mode is converted from a third type operation mode to a second type operation mode;
when ω t is α + π/12, the power supply of the 12-phase rectification circuit is set by
Become into
The operation mode is converted from the second type operation mode to a third type operation mode;
when the working mode of the 12-phase rectifying circuit is 6-8-6, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 6 and 8 in a circulating way;
wherein, if ω t is α + μ -pi/6, the power supply of the 12-phase rectifier circuit is driven by the power supply source
Become into
If ω t is α + pi/12, the power supply of the 12-phase rectifier circuit is driven by the motor
Become into
The operation mode is converted from the third operation mode to the fourth operation mode.
3) According to the working modes of the 12-phase rectifying circuit, 12-phase rectifying circuit conducted electromagnetic interference models in different working modes are established, and therefore differential mode voltage and common mode voltage of the 12-phase rectifying circuit in different working modes are determined.
The 12-phase rectification circuit conducted electromagnetic interference models in different working modes comprise a 12-phase rectification circuit conducted electromagnetic interference model in a 2-4-2 mode, a 12-phase rectification circuit conducted electromagnetic interference model in a 4-6-4 mode and a 12-phase rectification circuit conducted electromagnetic interference model in a 6-8-6 mode.
The step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model under a 2-4-2 mode comprises the following steps:
1) establishing a differential mode voltage expression in a 2-4-2 mode, wherein the steps comprise:
1.1) calculating the differential mode voltage jump value delta U of the DC output side under the condition of alpha moment and no load1Namely:
in the formula of U1(ωt＝α)、U2(ω t ═ α) is the voltage before and after the transition, respectively; e is the peak value of the power supply;
1.2) calculating the differential mode voltage jump value U of the output side of the 12-phase rectification circuit at the alpha momentdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculating the differential mode voltage jump value delta U of the direct current output side under the condition of no load at the moment of alpha + mu2Namely:
in the formula of U2(ωt＝α+μ)、U3(ω t ═ α + μ) is a voltage before and after the transition, respectively;
1.4) calculating the differential mode voltage jump value U at the output side of the rectifying circuit at the moment of alpha + mudm2Namely:
1.5) writing the differential mode voltage of the direct current output side into an s-domain form in one period T to obtain:
in the formula, time t 1α/ω, time t2＝(α+μ)/ω；Ucm(s) a differential mode voltage on the direct current output side in the form of an s domain;
1.6) converting the differential mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a differential mode voltage expression in a 2-4-2 mode, namely:
in the formula, n and k are integers; u shapedm(jn ω) is the differential mode voltage in the frequency domain; u shapedm1(jnω)、Udm2(jn ω) is a differential mode voltage jump value in the frequency domain;
2) establishing a common-mode voltage expression in a 2-4-2 mode, comprising the following steps of:
2.1) calculating the common-mode voltage of the 12-phase rectifying circuit, namely:
2.2) calculating the voltage jump value of the conduction time alpha respectivelyΔU1Voltage jump value Δ U at conduction time α + μ2Voltage jump value delta U of conduction time alpha + pi/123And a voltage jump value delta U of alpha + mu + pi/12 at the conduction time4Voltage jump value delta U of alpha + pi/6 at conduction time5And a voltage jump value delta U of alpha + mu + pi/6 at the conduction time6Voltage jump value delta U of alpha + pi/4 at conduction time7And a voltage jump value delta U of alpha + mu + pi/4 at the conduction time8Namely:
2.3) writing the common mode voltage of the direct current output side in one-sixth period into an s-domain form to obtain:
in the formula, time t1α/ω, time t2(α + μ)/ω, time t3(α + π/12)/ω, time t4(α + μ + pi/12)/ω, time t5(α + π/6)/ω, time t 6(α + μ + pi/6)/ω, time t7(α + π/4)/ω, time t8＝(α+μ+π/4)/ω；
According to the formula (14), establishing a common-mode voltage s-domain expression in one period, namely:
2.4) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 2-4-2 mode in one period, namely:
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain. U shapecm1(jn ω) is the common mode voltage in the frequency domain over one sixth of a period.
The step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model under a 4-6-4 mode comprises the following steps:
1.1) calculation at t1At time α/ω, differential mode voltage jump Δ U at the dc output side in the no-load condition1Namely:
1.2) calculation at t1At time α/ω, the differential mode voltage jump value U at the output side of the 12-phase rectifier circuitdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculation at t2Time (alpha + mu-pi/12)/omega, differential mode voltage jump value delta U of DC output side under no-load condition 2Namely:
1.4) calculation at t2At the time of (alpha + mu-pi/12)/omega, the differential mode voltage jump value U at the output side of the rectifier circuitdm2Namely:
1.5) establishing a differential mode voltage expression in a 4-6-4 mode, namely:
2) establishing a common-mode voltage expression in a 4-6-4 mode, comprising the following steps of:
2.1) calculating the conduction time t respectively1Voltage jump value delta U of alpha/omega1And conduction time t2Voltage jump value of (alpha + mu-pi/12)/omega2And conduction time t3Voltage jump value delta U of (alpha + pi/12)/omega3And conduction time t4Voltage jump value Δ U of (α + μ)/ω4And conduction time t5Voltage jump value delta U of (alpha + pi/6)/omega5And conduction time t6Voltage jump value of (alpha + mu + pi/12)/omega6And conduction time t7Voltage jump value delta U of (alpha + pi/4)/omega7And conduction time t8Voltage jump value of (alpha + mu + pi/6)/omega8Namely:
2.2) establishing a common-mode voltage s-domain expression in one sixth of a period, namely:
2.3) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 4-6-4 mode in one period, namely:
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…) (29)
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain.
The step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model under a 6-8-6 mode comprises the following steps:
1.1) calculation at t1At time α/ω, differential mode voltage jump Δ U at the dc output side in the no-load condition1Namely:
1.2) calculation at t1At time α/ω, the differential mode voltage jump value U at the output side of the 12-phase rectifier circuitdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculation at t2Time (alpha + mu-pi/6)/omega, differential mode voltage jump value delta U of DC output side under no-load condition2Namely:
1.4) calculation at t2At time (alpha + mu-pi/6)/omega, the differential mode voltage jump value U at the output side of the rectifier circuitdm2Namely:
1.5) establishing a differential mode voltage expression in a 6-8-6 mode, namely:
2) establishing a common-mode voltage expression in a 6-8-6 mode, wherein the common-mode voltage expression comprises the following steps:
2.1) calculating the conduction time t respectively1Voltage jump value delta U of alpha/omega1And conduction time t2Voltage jump value of (alpha + mu-pi/6)/omega2And conduction time t3Voltage jump value delta U of (alpha + pi/12)/omega3And conduction time t4Voltage jump value of (alpha + mu-pi/12)/omega 4And conduction time t5Voltage jump value of (alpha + pi/6)/omega5And conduction time t6Voltage jump value Δ U of (α + μ)/ω6And conduction time t7Voltage jump value delta U of (alpha + pi/4)/omega7And conduction time t8Voltage jump value of (alpha + mu + pi/8)/omega8Namely:
2.2) establishing a common-mode voltage s-domain expression in one sixth of a period, namely:
2.3) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 6-8-6 mode in one period, namely:
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…) (44)
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain.
Example 2:
a12-phase rectification circuit conducted electromagnetic interference modeling method based on state transition comprises the following steps:
the working mode of the 12-phase rectifying circuit is analyzed, then the instantly finished voltage jump is represented in the form of step signals according to the conduction condition of a switching device in each conduction and phase change process, and meanwhile, the time domain delay between each device and the phase is fully considered, and a calculation model of a conducted interference source s domain is deduced. Meanwhile, the widely existing input power source unbalance factors of the actual circuit are fully considered, a conducted interference source calculation model of the 12-phase rectification circuit in the unbalanced state is provided, and a 12-phase rectification circuit conducted electromagnetic interference modeling method based on state conversion is formed.
The method specifically comprises the following steps:
1) the operation mode of the 12-phase rectifier circuit is first determined.
Because the 12-phase rectifying circuit is usually connected to a twelve-phase synchronous generator or a twelve-phase traction rectifier transformer, each phase of the two has leakage inductance, and the inductance current cannot change suddenly, the phase change process cannot be completed instantly, but the phase change process lasts for a period of time, and the duration time of the phase change process is represented by an electrical angle mu and is called a phase change overlap angle. Due to the power supply particularity of the twelve-phase synchronous generator and the twelve-phase traction rectifier transformer, the phase difference between the phases of each phase of power supply is 15 degrees, the power supplies can be divided into four groups of power supplies, the phase difference between the three power supplies of each group of power supplies is 120 degrees, and the phase difference of each group of power supplies is 15 degrees later.
Let ω be the power supply angular frequency, the twelve-phase power supply voltage expression is as follows:
in order to obtain the clear electromagnetic interference characteristic of the 12-phase rectifying circuit, firstly, each phase power supply is assumed to be in a balanced state, the amplitude value of each phase power supply is assumed to be equal to E, and the initial phase angle of each phase power supply is assumed to be 0. The time domain signal waveforms of the 4 groups of common 12-phase voltages are shown in FIG. 1
And setting the trigger delay angle as alpha, the 12-phase rectifying circuit has more working modes due to the existence of the commutation overlapping angle. When a 12-phase rectifier circuit is operated, at a certain time, there are 8 types of operation modes according to the difference of the number of diodes to be conducted, that is:
Firstly, 2 diodes are conducted in a group of power supplies in the 12-phase rectifying circuit; two groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes; three groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes; four groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes; three groups of power supplies in the 12-phase rectification circuit are respectively conducted by 2 diodes, and the other group of power supplies is conducted by 3 diodes; sixthly, two groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other two groups of power supplies are conducted by 3 diodes; seventhly, one group of power supplies in the 12-phase rectification circuit is conducted by 2 diodes, and the other three groups of power supplies are conducted by 3 diodes; and four groups of power supplies in the eight 12-phase rectifying circuit are respectively provided with 3 diodes for conduction.
In an ideal case, a vector diagram of 12-phase power supply line voltages of a 12-phase rectifier circuit is shown in fig. 2.
The calculation formula of the commutation overlap angle is
Wherein, IdRepresenting steady-state current value, X, at the output side of a 12-phase rectifier circuitBRepresenting the reactance of each phase, E0Represents the power supply amplitude of each phase, and m represents the number of pulses in one cycle.
According to the difference of the phase change overlap angle, the number of the conducted pipes is also inconsistent at different conduction moments, because the 12-phase rectification circuit rarely works in the phase change state of more than 9 pipes, the patent mainly considers several common working modes and divides the working modes into the following modes:
(ii) 2-4-2 mode
The number of the tubes in the working state of the rectifying circuit is changed between 2 and 4 in a circulating way, corresponding to the first and the second operation modes, the whole circuit is in a 2-tube-4-tube-2 operation mode, and the operation mode is called as a 2-4-2 mode.
If the alpha + mu-pi/12 is not less than the omega t is not less than the alpha, C of the 12-phase rectification circuit4And B4When power is supplied, no power source is in the phase change stage, so that the process is called as the conduction stage, which corresponds to the mode (i) in eight operation modes, the circuit at the stage is shown in fig. 3, and the output voltage of the rectifier is
If alpha is more than ω t and less than or equal to alpha + mu, C4，B4，A1And B1Will be used as the power supply of the 12-phase rectification circuit, corresponding to the mode II in the eight operation modes, part of the power supply is in the phase change stage, so this process will be called the phase change stage, the circuit in this stage is shown in FIG. 4, the output voltage of the rectifier is
If the 12-phase rectification circuit satisfies the natural commutation, the voltages in two states above ω t ═ α should be equal, so that the natural commutation angle of the 12-phase rectification circuit is calculated to be equal to 7 π/24.
If alpha + mu is more than ω t and less than or equal to alpha + π/12, A1And B1The power supply of the 12-phase rectifying circuit corresponds to a mode (i) in eight operation modes, the process is a conduction stage, and the output voltage of the rectifier at the stage is
4-6-4 mode
The analysis method is similar to the above, when ω t is alpha + mu-pi/12, the power supply of the 12-phase rectifying circuit is composed of
Become into
The working state of the 12-phase rectifying circuit is converted from state (c) to state (c) until t is alpha + pi/12, and the power supply is switched from
Become into
The working state of the 12-phase rectifying circuit is converted from the state II to the state III, and the number of power supplies of the 12-phase rectifying circuit can be found to be constantly changed between 4 and 6, so that the working mode of the 12-phase rectifying circuit is called as a 4-6-4 mode.
Mode 6-8-6
When ω t is α + μ -pi/6, the power supply of 12-phase rectification circuit is composed of
Become into
The working state of the 12-phase rectification circuit is converted from a state (r) to a state (r) until ω t is equal to α + pi/12, and a power supply is switched from
Become into
The working state of the 12-phase rectification circuit is converted from state cFor the state (iv), it can be found that the number of power supplies of the 12-phase rectifier circuit varies between 6 and 8, and thus the operation mode of such a 12-phase rectifier circuit is referred to as a 6-8-6 mode.
If mu > pi/4, there will be commutation of one of the windings itself, there will be at least 9 tube conduction conditions, which are more loaded than the three modes of operation above, and in practice there will be less cases where the commutation overlap angle is greater than pi/4, and therefore this is not analyzed.
(2) Deducing a conducted electromagnetic interference modeling method of the 12-phase rectification circuit according to the working mode;
1)2-4-2 mode
Differential mode EMI
The differential mode voltage at the output side of the rectifier jumps in the switching process of the conduction stage and the phase conversion stage, and for the whole process, the voltage jump can be regarded as instantaneous completion, and in order to simplify theoretical calculation, modeling description is directly carried out by using a step function.
At time α, the differential mode voltage jump value on the DC output side in the no-load condition is
Combining the voltage jump at this moment with the equivalent circuit shown in fig. 3, the differential mode voltage jump at the output side of the rectifier circuit is obtained:
wherein Z isS＝RS+sLS，Z1＝Rdv/dt+1/sCdv/dt，Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL)。LSAnd RSRespectively, inductance and resistance, L, of the power supply of each phaseinHigh-frequency parasitic inductance, C, on the DC side of the rectifier circuitfilterIs a filter capacitor, Rdv/dtAnd Cdv/dtIs for dv/dt, RLIs a load resistance of the rectifier circuit, CpAnd C0Respectively a ground capacitor at the output side of the rectifying circuit and a ground capacitor at the neutral point of the 12-phase power supply.
At the time of alpha + mu, the differential mode voltage jump value of the DC output side under the no-load condition is
The voltage jump at this time is combined with the equivalent circuit shown in fig. 4 to obtain the differential mode voltage jump value at the output side of the rectifier circuit:
At other commutation moments, the differential mode voltage analysis process on the direct current side is similar to that described above, and is not described again. And through analysis, the differential mode voltage jump of the direct current side is equal to U at all the commutation starting momentsdm1At the end of all commutation moments, the differential mode voltage jump on the DC side is equal to Udm2。
Considering the periodicity and the convenience of an s-domain, in one period, the direct current output side differential mode voltage is written into the form of the s-domain:
wherein, t1＝α/ω，t2＝(α+μ)/ω
When the s domain is changed into the frequency domain, s is changed into jn omega, and a differential mode interference frequency domain expression on the output side of the rectifying circuit is obtained
From the above analysis, it is found that, in the state where the 12-phase rectifier circuit is in equilibrium, the differential mode interference on the output side of the rectifier circuit contains only 24k (k is 1,2,3, …) subharmonics.
Common mode EMI
If the alpha + mu-pi/12 is not less than the omega t is not less than the alpha, C of the 12-phase rectification circuit4And B4Supply a common-mode voltage of the rectifier in this stage of
Uc1＝(uc4+ub4)/2＝E/2cos(ωt+π/4)
If alpha is more than omega t and less than or equal to alpha + mu, C of 12-phase rectification circuit4，B4，A1And B1Supply a common-mode voltage of the rectifier in this stage of
Uc1＝((uc4+ua1)/2+(ub4+ub1)/2)/2
＝-E/2sin(π/24)sin(ωt+5π/24)
Consistent with the differential mode voltage analysis method, it can be found that 48 conduction moments in a cycle can be divided into six groups, the first group is in an interval [ α, α + pi/3 ], and at different conduction moments ω t ═ α, α + μ, α + pi/12, α + μ + pi/12, α + pi/6, α + μ + pi/6, α + pi/4, α + μ + pi/4, voltage jump is respectively as follows:
ΔU1＝E/2cos(π/24)sinα
ΔU2＝E/2cos(π/24)sin(α+μ)
ΔU3＝-E/2sin(π/24)cosα
ΔU4＝E/2sin(π/24)cos(α+μ)
ΔU5＝ΔU7＝ΔU3
ΔU6＝ΔU8＝ΔU4
In consideration of the periodicity and the convenience of an s-domain, in the interval, the common-mode voltage on the direct-current output side is written into the form of the s-domain:
wherein, t1＝α/ω，t2＝(α+μ)/ω，t3＝(α+π/12)/ω，t4＝(α+μ+π/12)/ω，t5＝(α+π/6)/ω，t6＝(α+μ+π/6)/ω，t7＝(α+π/4)/ω，t8＝(α+μ+π/4)/ω
Therefore, the common mode voltage during this sixth period can be expressed as
When the s domain is changed into the frequency domain, s is changed into jn omega, and a common-mode interference frequency domain expression of the output side of the rectifying circuit in one period is obtained
From the above analysis, it is found that the common mode interference on the output side of the rectifier circuit includes only 3m (m is 1,3,5, …) subharmonics.
2)4-6-4 modes
Differential mode EMI
Similar to the analysis method of the 2-4-2 mode, it can be obtained that1α/ω and t2Differential mode voltage jump value at time (α + μ -pi/12)/ω:
and combining the voltage jump at the moment with the equivalent circuit to obtain a differential mode voltage jump value at the output side of the rectifying circuit:
from this, the differential-mode voltage expression in one cycle can be obtained:
common mode EMI
The same analysis method as that in the above 2-4-2 operation mode can be obtained at t1＝α/ω，t2＝(α+μ-π/12)/ω，t3＝(α+π/12)/ω，t4＝(α+μ)/ω，t5＝(α+π/6)/ω，t6＝(α+μ+π/12)/ω，t7＝(α+π/4)/ω，t8Common mode voltage jump value at time (α + μ + pi/6)/ω.
The common mode voltage during these one sixth period can be expressed as:
when the s domain is changed into the frequency domain, s is changed into jn omega, and a common-mode interference frequency domain expression of the output side of the rectifying circuit in one period is obtained
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…)
3)6-8-6 mode
Difference mode EMI
Similar to the analysis method of the 2-4-2 mode, it can be obtained that1α/ω and t2Differential mode voltage jump value at time (α + μ -pi/6)/ω:
and combining the voltage jump at the moment with the equivalent circuit to obtain a differential mode voltage jump value at the output side of the rectifying circuit:
from this, the differential-mode voltage expression in one cycle can be obtained:
common mode EMI: the same analysis method as that in the above 2-4-2 operation mode can be obtained at t1＝α/ω，t2＝(α+μ-π/6)/ω，t3＝(α+π/12)/ω，t4＝(α+μ-π/12)/ω，t5＝(α+π/6)/ω，t6＝(α+μ)/ω，t7＝(α+π/4)/ω，t8Common mode voltage jump value at time (α + μ + pi/8)/ω:
therefore, the common mode voltage during these one sixth period can be expressed as:
when the s domain is changed into the frequency domain, s is changed into jn omega, and a common-mode interference frequency domain expression of the output side of the rectifying circuit in one period is obtained: u shapecm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…)
(3) Considering that each phase power supply of the 12-phase rectifying circuit is not in a strict balance state in practice, the method is combined with the analysis method and applied to conducted electromagnetic interference modeling of the 12-phase rectifying circuit;
1) determining the unbalance degree of the amplitude and the phase angle of each phase power supply: the 12-phase rectifying circuit is usually connected to a diesel generator set or a traction rectifier transformer, and according to ISO 8528-5:2005, the voltage unbalance deviation of the diesel generator set is not more than 1%, and the steady-state frequency band is not more than 0.5%; according to JB/T10693-2007, the unbalance degree of the no-load line voltages of the two groups of valve sides of each traction rectifier transformer is not more than 0.3%; for a 12-phase traction rectifier transformer adopting a phase shifting mode, the deviation of a valve side no-load line voltage phase angle (15 degrees) corresponding to a net side main tap and other taps is +/-1.5 percent. And in the range of the voltage amplitude and the phase angle deviation of the 12-phase rectifying circuit, the voltage amplitude and the phase angle of each phase power supply are obtained in a uniformly distributed mode.
2) Determining the size of the commutation overlap angle and the working mode of the 12-phase rectifying circuit according to the mode in (1); 3) after the working mode of the 12-phase rectifying circuit is determined, differential mode and common mode voltage jump values at the starting time and the ending time of each phase change are analyzed according to the analysis mode, and the differential mode and common mode voltage jump values at the output side are obtained by combining a specific circuit; 4) and (3) fully considering time domain delay of each device and phases to obtain a conducted interference source calculation model of an s domain, and converting s into jn omega to obtain a 12-phase rectification circuit differential mode and common mode conducted electromagnetic interference calculation model in an unbalanced state.
Example 3:
in order to verify the correctness and reliability of the 12-phase rectification circuit conducted electromagnetic interference modeling method based on state conversion, experimental test results are compared with theoretical results. Specific circuit parameters are shown in table 1, and comparison results are shown in fig. 5 and fig. 6, which prove that the modeling method can be used for predicting the EMI of the 12-phase rectifier circuit.
Table 112 phase rectifier circuit specific parameters
Claims (8)
1. A12-phase rectification circuit conducted electromagnetic interference modeling method based on state transition is characterized by comprising the following steps:
1) the power supplies of the 12-phase rectifier circuit are divided into four groups, and the operation mode of the 12-phase rectifier circuit is determined.
2) Determining the working mode of the 12-phase rectifying circuit according to the running mode of the 12-phase rectifying circuit;
3) according to the working modes of the 12-phase rectifying circuit, 12-phase rectifying circuit conducted electromagnetic interference models in different working modes are established, and therefore differential mode voltage and common mode voltage of the 12-phase rectifying circuit in different working modes are determined.
2. The method according to claim 1, wherein the supply voltages of the 12-phase rectifier circuit are as follows:
in the formula, omega is power angular frequency;
is the phase; u. ofa1、ua2、ua3、ua4、ub1、ub2、ub3、ub4、uc1、uc2、uc3、uc4Is the supply voltage; eA1、EA2、EA3、EA4、EB1、EB2、EB3、EB4、EC1、EC2、EC3、EC4The peak value of each phase power supply; t is time.
3. The method according to claim 1, wherein the operating mode of the 12-phase rectifier circuit comprises the following types:
the first type: a group of power supplies in the 12-phase rectifying circuit is conducted by 2 diodes;
the second type: two groups of power supplies in the 12-phase rectifying circuit are respectively provided with 2 diodes for conduction;
in the third category: three groups of power supplies in the 12-phase rectifying circuit are respectively provided with 2 diodes for conduction;
the fourth type: four groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes;
The fifth type: three groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other group of power supplies is conducted by 3 diodes;
the sixth type: two groups of power supplies in the 12-phase rectifying circuit are respectively conducted by 2 diodes, and the other two groups of power supplies are respectively conducted by 3 diodes;
the seventh type: one group of power supplies in the 12-phase rectifying circuit is conducted by 2 diodes, and the other three groups of power supplies are conducted by 3 diodes;
eighth type: four groups of power supplies in the 12-phase rectifying circuit are respectively provided with 3 diodes for conduction.
4. The method according to claim 3, wherein the determining factor of the operation mode of the 12-phase rectification circuit comprises a commutation overlap angle;
the equation for the commutation overlap angle is as follows:
in the formula IdIs a steady-state current value at the output side of the 12-phase rectifying circuit; xBIs the reactance of each phase; e0For each phase of the power supply amplitude; m is the number of pulses in a period; mu is an electrical angle; alpha is the triggered delay angle.
5. The method for modeling conducted electromagnetic interference of a 12-phase rectifier circuit based on state transition as claimed in claim 3, wherein the operating modes of the 12-phase rectifier circuit include a 2-4-2 mode, a 4-6-4 mode, and a 6-8-6 mode;
When the working mode of the 12-phase rectifying circuit is a 2-4-2 mode, the number of diodes in the working state in the 12-phase rectifying circuit is circularly changed between 2 and 4;
wherein if alpha + mu-pi/12 is not less than omega t not more than alpha, the C of the power supply4Phase B and B4Phase power supply, a 12-phase rectifying circuit is in a conduction stage, the operation mode is a first type operation mode, and the output voltage of the 12-phase rectifying circuit is marked as U1(ii) a Omega is the angular frequency of the power supply; t is time;
if alpha is more than ω t and less than or equal to alpha + mu, C of the power supply4Phase, B4Phase, A1Phase B and1phase power supply, a 12-phase rectifying circuit in a phase change stage, a second type of operation mode, and a 12-phase rectifying circuit output voltage marked as U2；
If alpha + mu is more than ω t and less than or equal to alpha + π/12, A of the power supply1Phase B and1phase power supply, a 12-phase rectifying circuit is in a conducting stage, the operation mode is a first type operation mode, and the output voltage of the 12-phase rectifying circuit is recorded as U3；
Output voltage U1Output voltage U2Output voltage U3Respectively as follows:
when the working mode of the 12-phase rectifying circuit is a 4-6-4 mode, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 4 and 6 in a circulating way;
wherein, if ω t is α + μ -pi/12, the power supply of the 12-phase rectifier circuit is driven by the power supply of the 12-phase rectifier circuit 
Become into
The operation mode is converted from a third type operation mode to a second type operation mode;
if ω t is α + pi/12, the power supply of the 12-phase rectifier circuit is driven by the motor
Become into
The operation mode is converted from the second type operation mode to a third type operation mode;
when the working mode of the 12-phase rectifying circuit is 6-8-6, the number of diodes in the working state in the 12-phase rectifying circuit is changed between 6 and 8 in a circulating way;
wherein, if ω t is α + μ -pi/6, the power supply of the 12-phase rectifier circuit is driven by the power supply source
Become into
If ω t is α + pi/12, the power supply of the 12-phase rectifier circuit is driven by the motor
Become into
The operation mode is converted from the third operation mode to the fourth operation mode.
6. The method for modeling 12-phase rectifier circuit conducted electromagnetic interference based on state transition according to claim 1, wherein the step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model in a 2-4-2 mode comprises:
1) establishing a differential mode voltage expression under a 2-4-2 mode, wherein the steps comprise:
1.1) calculating the differential mode voltage jump value delta U of the DC output side under the condition of alpha moment and no load1Namely:
in the formula of U1(ωt＝α)、U2(ω t ═ α) is the voltage before and after the transition, respectively; e is the peak value of the power supply;
1.2) calculating the differential mode voltage jump value U of the output side of the 12-phase rectification circuit at the alpha moment dm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; parameter Z1＝Rdv/dt+1/sCdv/dt；LSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculating the differential mode voltage jump value delta U of the direct current output side under the condition of no load at the moment of alpha + mu2Namely:
in the formula of U2(ωt＝α+μ)、U3(ω t ═ α + μ) is a voltage before and after the transition, respectively;
1.4) calculating the differential mode voltage jump value U at the output side of the rectifying circuit at the moment of alpha + mudm2Namely:
1.5) writing the differential mode voltage of the direct current output side into an s-domain form in one period T to obtain:
in the formula, time t1α/ω, time t2＝(α+μ)/ω；Ucm(s) is a differential mode voltage on the direct current output side in the form of s domain;
1.6) converting the differential mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a differential mode voltage expression in a 2-4-2 mode, namely:
in the formula, n and k are integers; u shapedm(jn ω) is the differential mode voltage in the frequency domain; u shapedm1(jnω)、Udm2(jn ω) is a differential mode voltage jump value in the frequency domain;
2) establishing a common-mode voltage expression in a 2-4-2 mode, comprising the following steps of:
2.1) calculating the common-mode voltage of the 12-phase rectifying circuit, namely:
2.2) calculating the voltage jump value delta U of the conduction time alpha respectively1And a voltage jump value delta U of alpha + mu at the time of conduction2And a voltage jump value delta U of alpha + pi/12 at the conduction time3And a voltage jump value delta U of alpha + mu + pi/12 at the conduction time4Voltage jump value delta U of alpha + pi/6 at conduction time5And a voltage jump value delta U of alpha + mu + pi/6 at the conduction time6Voltage jump value delta U of alpha + pi/4 at conduction time7And a voltage jump value delta U of alpha + mu + pi/4 at the conduction time8Namely:
2.3) writing the common mode voltage of the direct current output side in one sixth period into an s-domain form to obtain:
in the formula, time t1α/ω, time t2(α + μ)/ω, time t3(α + π/12)/ω, time t4(α + μ + pi/12)/ω, time t5(α + π/6)/ω, time t6(α + μ + pi/6)/ω, time t7(α + pi/4)/ω, time t8＝(α+μ+π/4)/ω；
According to the formula (14), establishing a common-mode voltage s-domain expression in one period, namely:
2.4) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 2-4-2 mode, namely:
in the formula of Ucm(jn ω) is a common mode voltage in the frequency domain; u shapecm1(jn ω) is the common mode voltage in the frequency domain over one sixth of a period.
7. The method for modeling 12-phase rectifier circuit conducted electromagnetic interference based on state transition according to claim 1, wherein the step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model in a 4-6-4 mode comprises:
1.1) calculation at t1At time α/ω, differential mode voltage jump Δ U at the dc output side in the no-load condition1Namely:
1.2) calculation at t1At time α/ω, the differential mode voltage jump value U at the output side of the 12-phase rectifier circuitdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l isinA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculation at t2Time (alpha + mu-pi/12)/omega, differential mode voltage jump value delta U of DC output side under no-load condition2Namely:
1.4) calculation at t2At time (alpha + mu-pi/12)/omega, the differential mode voltage jump value U at the output side of the rectifier circuitdm2Namely:
1.5) establishing a differential mode voltage expression in a 4-6-4 mode, namely:
2) establishing a common-mode voltage expression in a 4-6-4 mode, comprising the following steps of:
2.1) calculating the conduction time t respectively1Voltage jump value delta U of alpha/omega1And conduction time t2Voltage jump value of (alpha + mu-pi/12)/omega2And conduction time t3Voltage jump value delta U of (alpha + pi/12)/omega3And conduction time t4Voltage jump value Δ U of (α + μ)/ω 4And conduction time t5Voltage jump value delta U of (alpha + pi/6)/omega5And conduction time t6Voltage jump value of (alpha + mu + pi/12)/omega6And conduction time t7Voltage jump value delta U of (alpha + pi/4)/omega7And conduction time t8Voltage jump value of (alpha + mu + pi/6)/omega8Namely:
2.2) establishing a common-mode voltage s-domain expression in one sixth of a period, namely:
2.3) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 4-6-4 mode in one period, namely:
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…) (29)
in the formula of Ucm(jn ω) is the common mode voltage in the frequency domain.
8. The method for modeling 12-phase rectifier circuit conducted electromagnetic interference based on state transition according to claim 1, wherein the step of establishing a 12-phase rectifier circuit conducted electromagnetic interference model in a 6-8-6 mode comprises:
1.1) calculation at t1At time α/ω, differential mode voltage jump Δ U at the dc output side in the no-load condition1Namely:
1.2) calculation at t1At time α/ω, the differential mode voltage jump value U at the output side of the 12-phase rectifier circuitdm1Namely:
in the formula, the parameter ZS＝RS+sLS(ii) a Parameter Z1＝Rdv/dt+1/sCdv/dt(ii) a Parameter Zparallel＝Z1RL/(Z1+RL+sCfilterZ1RL) (ii) a s represents a complex parameter variable; l isSAnd RSRespectively representing the inductance and the resistance of each phase of power supply; l is inA high-frequency parasitic inductance on the direct current side of the rectifying circuit; cfilterIs a filter capacitor; rdv/dtAnd Cdv/dtRespectively representing a load resistance and a capacitance; rLA load resistor of the rectifying circuit;
1.3) calculation at t2Time (alpha + mu-pi/6)/omega, differential mode voltage jump value delta U of DC output side under no-load condition2Namely:
1.4) calculation at t2At time (alpha + mu-pi/6)/omega, the differential mode voltage jump value U at the output side of the rectifier circuitdm2Namely:
1.5) establishing a differential mode voltage expression in a 6-8-6 mode, namely:
2) establishing a common-mode voltage expression in a 6-8-6 mode, wherein the common-mode voltage expression comprises the following steps:
2.1) calculating the conduction time t respectively1Voltage jump value delta U of alpha/omega1And conduction time t2Voltage jump value of (alpha + mu-pi/6)/omega2And conduction time t3Voltage jump value delta U of (alpha + pi/12)/omega3And conduction time t4Voltage jump value of (alpha + mu-pi/12)/omega4And conduction time t5Voltage jump value delta U of (alpha + pi/6)/omega5And conduction time t6Voltage jump value Δ U of (α + μ)/ω6And conduction time t7Voltage jump value delta U of (alpha + pi/4)/omega7And conduction time t8Voltage jump value of (alpha + mu + pi/8)/omega8Namely:
2.2) establishing a common-mode voltage s-domain expression in one sixth of a period, namely:
2.3) converting the common-mode voltage of the direct current output side in the s-domain form into a frequency domain form to obtain a common-mode voltage expression in a 6-8-6 mode in one period, namely:
Ucm(jnω)＝6Ucm1(jnω),(n＝3m,m＝1,3,5,…) (44)
In the formula of Ucm(jn ω) is the common mode voltage in the frequency domain.
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| WO2022007232A1 (en) * | 2020-07-06 | 2022-01-13 | 北京交通大学 | Method for calculating steady-state fault current of modular multilevel converter |
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| WO2022007232A1 (en) * | 2020-07-06 | 2022-01-13 | 北京交通大学 | Method for calculating steady-state fault current of modular multilevel converter |
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