CN106026737B - A kind of three-level current transformer compound circulation inhibition method in parallel - Google Patents

A kind of three-level current transformer compound circulation inhibition method in parallel Download PDF

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CN106026737B
CN106026737B CN201610495576.9A CN201610495576A CN106026737B CN 106026737 B CN106026737 B CN 106026737B CN 201610495576 A CN201610495576 A CN 201610495576A CN 106026737 B CN106026737 B CN 106026737B
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current transformer
level
current
modulation
power
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CN106026737A (en
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赵剑锋
杨斌
刘梦轩
赵志宏
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Southeast University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS 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
    • H02M7/00Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483Converters with outputs that each can have more than two voltages levels
    • H02M7/49Combination of the output voltage waveforms of a plurality of converters
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS 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
    • H02M1/00Details of apparatus for conversion
    • H02M1/12Arrangements for reducing harmonics from ac input or output
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS 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
    • H02M7/00Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/493Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode the static converters being arranged for operation in parallel
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS 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
    • H02M1/00Details of apparatus for conversion
    • H02M1/0048Circuits or arrangements for reducing losses
    • H02M1/0054Transistor switching losses
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02BCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

Abstract

The invention discloses a kind of three-level current transformer for being controlled based on mean power and optimizing SVPWM modulation compound circulation inhibition method in parallel, can solve the zero sequence circulation problem in three-phase tri-level parallel system.Described compound circulation inhibition method includes the compound circulation inhibition method for the SVPWM modulation for controlling and optimizing based on mean power, and it controls the size of current transformer output voltage in control process by the method for power-sharing;A regulatory factor is introduced in modulated process to adjust small vector action time, so that the zero sequence dutycycle of current transformer is zero, it is combined by the control and modulator approach of optimization, reach the purpose for suppressing three-level current transformer circulation in parallel, so as to reduce system output harmonic wave, power attenuation is reduced, the stability that energy utilization rate and parallel system are incorporated into the power networks is improved, there is good feasibility and practical value.

Description

A kind of three-level current transformer compound circulation inhibition method in parallel
Technical field
The present invention relates to a kind of three-level current transformer parallel connection complex loop for being controlled based on mean power and optimizing SVPWM modulation Flow suppressing method.
Background technology
In recent years, with restriction getting worse of the energy and environment problem to human social development, the exploitation of new energy and The protection of environment has been to be concerned by more and more people.It is rapid with new energy energy storage, power network energy storage, electric automobile and micro-capacitance sensor Development, extensive energy storage technology have stronger application demand in power system Generation Side, grid side, user side.
Due to the limitation of the power switch pipe internal pressure grade of traditional two-level inverter, high-power can not be met Requirement.In high voltage applications occasion, generally requiring power device to connect uses, and this needs extra equalizer circuit, led again Cause system realizes the increase of difficulty.
In this case, the appearance of multilevel converter provides one for the development of high-voltage large-capacity voltage source converter topology The new thinking of bar.And three-level inverter is that number of switches is minimum in multi-level inverter circuit, transported in multi-electrical level inverter With the most extensive.The advantages of three-level topology, has:1. switching loss is small, efficiency high;2. voltage change ratio is small during switch motion, draw The electromagnetic interference risen is small;3. harmonic content is few, required filtering inductance is small, beneficial to reduction system cost.As can be seen here, three electricity Flat topological structure has become the popular selection of converter topologies.
On the other hand, with the continuous development of intelligent grid and new energy power generation technology, large-scale energy storage link is built Have become a urgent demand.Energy storage inverter also receives extensively as the key equipment of connection energy storage device and power network General attention and research.Due to being limited by power semiconductor power, work(that separate unit power electronic current transformer can reach Rate grade is difficult to the application scenario for meeting high power level, thus high-power applications occasion typically by the inverter of multimode simultaneously Connection gets up to use, to improve the capacity of system and redundancy;This parallel way is simple and easy simultaneously, is easy to dilatation, thus by Extensive research and application are arrived.
Although many merits of multiple module paralleling operation become a direction of high-power applications by it, due to more The characteristics of wired in parallel topology self structure so that energy distribution is uneven between each phase, and during steady-state operation between each bridge arm Voltage is also impossible to completely the same, causes circulation be present inside each phase bridge arm of current transformer.And the presence of circulation can cause output wave Deformation is poor, load current distribution is uneven, efficiency reduces, it is also possible to causes output inductor saturation, or even damage system power The a series of serious problems such as switch, so the key that the loop current suppression of multimode parallel running becomes parallel technology is asked Topic.
Chinese patent CN201210122767.2《Double combining inverter parallel systems based on the control of voltage zero vector feedforward Circulation inhibition method》The difference of non-zero dutycycle in two inverter SVPWM is introduced on the basis of conventional PI control method Feedforward control, but research object is only two-level inverter parallel system, is not directed to three level parallel systems;Chinese patent CN201210579045.X《The circulation inhibition method of multiple-variable flow device parallel system based on zero-sequence current track with zero error》Introduce It is related to zero vector and non-zero dutycycle in multiple current transformer SVPWM, but control strategy is excessively complicated;Chinese patent CN201510126213.3《T-shaped three-level photovoltaic grid-connected inverter parallel connection circulation suppresses and neutral balance method》It is proposed by changing The service time of change small vector suppresses the control strategy of circulation, and output current wave is made moderate progress, but can not have completely The suppression zero sequence circulation of effect.
The content of the invention
Goal of the invention:In order to overcome the deficiencies in the prior art, the present invention provides a kind of based on mean power control With the three-level current transformer compound circulation inhibition method in parallel of optimization SVPWM modulation, can effectively solve three-phase tri-level taken in conjunction The problem of zero sequence circulation in system be present;The inventive method can reach the effect for preferably controlling three-level current transformer loop current suppression in parallel Fruit, and reduce system output harmonic wave, improve the stability that parallel system is incorporated into the power networks, the final utilization rate and electricity for improving power network Net quality.
Technical scheme:To achieve the above object, the technical solution adopted by the present invention is:
A kind of three-level current transformer compound circulation inhibition method in parallel, the current transformer is inverse-impedance type three-level current transformer, Two current transformers are in parallel by the way of direct current altogether and ac bus;Every current transformer is controlled using mean power, to first Platform current transformer is sweared using the section space vector modulation of optimization three level seven to second current transformer using the segmentation space of three level seven Amount modulation;Voltage output caused by the averaged Power Control of First current transformer is as itself optimization three level seven segmentation space arrow The reference voltage of modulation is measured, voltage output is as itself segmentation of three level seven caused by second averaged Power Control of current transformer The reference voltage of space vector modulation;
The mean power control is based on traditional two close cycles PI Control System Designs, in the electricity of two close cycles PI control systems The respectively link that active power and reactive power are added in ring is flowed, it is real-time by average active power and reactive power and current transformer Active power and reactive power are compared to obtain error current, and error current is superimposed into electric current loop, so as to output voltage It is adjusted, makes the active power of two current transformer outputs consistent with reactive power, reach the effect for suppressing circulation;
The optimization three level seven section space vector modulation, in traditional section space vector modulated process of three level seven One regulatory factor f of middle introducing, regulatory factor f was acted on the modulation time of small vector, by the modulation for optimizing small vector Time, to change the zero sequence dutycycle of current transformer, so as to reduce zero sequence circulation;Consider the symmetrical of parallel converters zero sequence circulation Property, three level only are used using the section space vector modulation of optimization three level seven, another current transformer to a wherein current transformer Seven section space vectors are modulated.
Specifically, the mean power control specifically comprises the following steps:
(a1) first, the line voltage line current of two current transformer output ends is sampled, calculates First current transformer Real-time active power and reactive power be P1And Q1, the real-time active power and reactive power that calculate second current transformer are P2And Q2;Then, the average active power of two current transformers of calculating and reactive power areWith
(a2) by average active power and reactive power, real-time with every current transformer active power and reactive power are entered respectively Row compares, and the active power error and reactive power error for obtaining First current transformer areWith The active power error and reactive power error for obtaining second current transformer beWith
(a3) the value e by active power error divided by voltage on line side in dq coordinate systems on d axlesd, obtain First unsteady flow The d axis error electric currents of device areThe d axis error electric currents for obtaining second current transformer areBy reactive power The value e of error divided by voltage on line side in dq coordinate systems on q axlesq, the q axis error electric currents for obtaining First current transformer areThe q axis error electric currents for obtaining second current transformer are
(a4) by the error current Δ i of First current transformer1dWith Δ i1qBelonging to being added on the d axles and q axles of electric current loop, Reference voltage after PI is controlled as itself optimization three level seven section space vector modulation again;By second current transformer Error current Δ i2dWith Δ i2qBelonging to being added on the d axles and q axles of electric current loop, then itself three level is used as after PI is controlled The reference voltage of seven section space vectors modulation.
Specifically, the optimization three level seven section space vector modulation specifically comprises the following steps:
(b1) first, in real time in the detection section space vector modulated process of three level seven in small vector during the effect of vector Between, the zero sequence dutycycle for calculating First current transformer isCalculate the zero sequence dutycycle of second current transformer ForWherein, t11And t12The respectively modulation time of the small vector of First current transformer and middle vector, t21And t22 The small vector of respectively second current transformer and the modulation time of middle vector;
(b2) the zero sequence dutycycle of two current transformers is made the difference, draws the zero sequence duty cycle difference of two current transformers
(b3) regulatory factor is added in the modulator of First current transformerSo that the seven of First current transformer The modulation time of each vector of segmentation is respectively:WithThen The zero sequence dutycycle of First current transformer is optimized forThen zero of two current transformers after optimization Sequence duty cycle difference is Δ dz=0;Wherein t13For the modulation time of the big vector of First current transformer.
Beneficial effect:Three-level current transformer provided by the invention compound circulation inhibition method in parallel, compared with prior art, With following advantage:1st, the control method that the present invention uses can effectively solve zero sequence be present in three-phase tri-level parallel system The problem of circulation;2nd, be the advantages of three-level structure inverter output du/dt it is small and equivalent switching frequency is high, can reduce simultaneously The volume of net reactance, be advantageous to modular stack design;Switching loss, the reactor of combining inverter can also be reduced simultaneously Loss, so as to further improve overall transformation efficiency;3rd, the present invention can be substantially reduced system output harmonic wave, improve parallel system The stability and power supply reliability being incorporated into the power networks.
Brief description of the drawings
Fig. 1 is the system principle diagram of the present invention;
Fig. 2 is the control block diagram of mean power control;
Fig. 3 is space vector modulation switching sequence figure in small sector I;
Fig. 4 is the space vector timing diagram after adjustment;
Fig. 5 is the oscillogram of zero sequence dutycycle before and after addition regulatory factor f (after 0.25s);
In Fig. 6:(a) it is the A phase circulation oscillograms before suppression;(b) control and optimize using mean power after being 0.25s and adjust A phase circulation oscillograms after system;
In Fig. 7:(a) it is the zero sequence circulation simulation waveform before suppression;(b) after mean power control is added after being 0.25s Zero sequence circulation simulation waveform;(c) the zero sequence circulation added after being 0.25s after mean power control and optimization modulation emulates ripple Shape figure.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
It is as shown in Figure 1 a kind of three-level current transformer compound circulation inhibition method in parallel, the current transformer is inverse-impedance type three Level current transformer, two current transformers are in parallel by the way of direct current altogether and ac bus;Mean power is used to every current transformer Control, to First current transformer using the section space vector modulation of optimization three level seven, three level are used to second current transformer Seven section space vectors are modulated;Voltage output caused by the averaged Power Control of First current transformer optimizes three level as itself The reference voltage of seven section space vectors modulation, voltage output caused by second averaged Power Control of current transformer are used as itself The reference voltage of the section space vector of three level seven modulation.
The control block diagram of mean power control is illustrated in figure 2, mean power control is controlled based on traditional two close cycles PI System design, the respectively link of active power and reactive power is added in the electric current loop of two close cycles PI control systems, by flat Error current is obtained compared with equal active power and reactive power active power real-time with current transformer and reactive power, by error Electric current is superimposed into electric current loop, so as to which output voltage be adjusted, the active power and reactive power that allow two current transformers to export Unanimously, the effect for suppressing circulation is reached.The mean power control specifically comprises the following steps:
(a1) first, the line voltage line current of two current transformer output ends is sampled, calculates First current transformer Real-time active power and reactive power be P1And Q1, the real-time active power and reactive power that calculate second current transformer are P2And Q2;Then, the average active power of two current transformers of calculating and reactive power areWith
(a2) by average active power and reactive power, real-time with every current transformer active power and reactive power are entered respectively Row compares, and the active power error and reactive power error for obtaining First current transformer areWith The active power error and reactive power error for obtaining second current transformer beWith
(a3) the value e by active power error divided by voltage on line side in dq coordinate systems on d axlesd, obtain First unsteady flow The d axis error electric currents of device areThe d axis error electric currents for obtaining second current transformer areBy reactive power The value e of error divided by voltage on line side in dq coordinate systems on q axlesq, the q axis error electric currents for obtaining First current transformer areThe q axis error electric currents for obtaining second current transformer are
(a4) by the error current Δ i of First current transformer1dWith Δ i1qBelonging to being added on the d axles and q axles of electric current loop, Reference voltage after PI is controlled as itself optimization three level seven section space vector modulation again;By second current transformer Error current Δ i2dWith Δ i2qBelonging to being added on the d axles and q axles of electric current loop, then itself three level is used as after PI is controlled The reference voltage of seven section space vectors modulation.
Under the control of electric current loop, can by the output voltage undulated control of each current transformer in minimum zone, because This zero sequence circulation can be effectively suppressed.
The optimization three level seven section space vector modulation, in traditional section space vector modulated process of three level seven One regulatory factor f of middle introducing, regulatory factor f was acted on the modulation time of small vector, by the modulation for optimizing small vector Time, to change the zero sequence dutycycle of current transformer, so as to reduce zero sequence circulation;Consider the symmetrical of parallel converters zero sequence circulation Property, three level only are used using the section space vector modulation of optimization three level seven, another current transformer to a wherein current transformer Seven section space vectors are modulated.
In traditional section space vector modulated process of three level seven, the model of n-th (n=1,2) platform current transformer is:
In formula:dnj∈ { 1,0, -1 } represents the switching tube state of n-th current transformer, and j represents phase;ea,eb,ecRepresent power network Voltage;uonFor neutral point of electric network voltage;uc1,uc2For the condenser voltage of DC side;ina,inb,incFor the three of n-th current transformer Phase output current;LnFor the AC filter inductance of n-th current transformer;C1,C2For DC bus capacitor device;inoFor n-th current transformer DC current.
Assuming thatBy taking First current transformer as an example, its averaging model is:
To simplify the analysis, it is transformed to using dq coordinate system transformations, above-mentioned model:
The zero sequence circulation for defining n-th current transformer is inz=ina+inb+inc, and due to i1z=-i2z, therefore zero sequence circulation Model may be defined as:
Wherein:d1z=d1a+d1b+d1cAnd d2z=d2a+d2b+d2cRespectively First current transformer and second current transformer Zero sequence dutycycle.
Because line impedance can be ignored, therefore above formula can be reduced to:
It is illustrated in figure 3 by taking small sector I as an example, traditional three-level current transformer space vector modulation switching sequence figure.
Optimize the modulation of the section space vector of three level seven, draw in traditional section space vector modulated process of three level seven Enter a regulatory factor f, regulatory factor f was acted on the modulation time of small vector, by optimizing the modulation time of small vector, To change the zero sequence dutycycle of current transformer, so as to reduce zero sequence circulation.
After adding regulatory factor f, space vector modulation switching sequence figure is as shown in Figure 4 in small sector I.
Optimize the modulation of the section space vector of three level seven to specifically comprise the following steps:
(b1) first, in real time in the detection section space vector modulated process of three level seven in small vector during the effect of vector Between, the zero sequence dutycycle for calculating First current transformer isCalculate the zero sequence dutycycle of second current transformer ForWherein, t11And t12The respectively modulation time of the small vector of First current transformer and middle vector, t21And t22 The small vector of respectively second current transformer and the modulation time of middle vector;
(b2) the zero sequence dutycycle of two current transformers is made the difference, draws the zero sequence duty cycle difference of two current transformers
(b3) regulatory factor is added in the modulator of First current transformerSo that the seven of First current transformer The modulation time of each vector of segmentation is respectively:WithThen The zero sequence dutycycle of First current transformer is optimized forThen zero of two current transformers after optimization Sequence duty cycle difference is Δ dz=0;Wherein t13For the modulation time of the big vector of First current transformer.
The oscillogram (after 0.25s) for adding current transformer zero sequence duty cycle error before and after regulatory factor f is illustrated in figure 5, Amplitude represents amplitude.
Emulation is carried out by software Matlab/Simulink to topological sum control method proposed by the invention to test Card, as a result as shown in Figure 6 and Figure 7, Current represent electric current.It can thus be seen that the level of one kind three proposed by the invention becomes Parallel operation compound circulation inhibition method in parallel can effectively suppress zero sequence circulation in three-phase tri-level parallel system be present, and significantly Reduction system output harmonic wave, improve stability and power supply reliability that parallel system is incorporated into the power networks.
Described above is only the preferred embodiment of the present invention, it should be pointed out that:For the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (2)

1. a kind of three-level current transformer compound circulation inhibition method in parallel, the current transformer is inverse-impedance type three-level current transformer, two Platform current transformer is in parallel by the way of direct current altogether and ac bus;It is characterized in that:Mean power control is used to every current transformer System, to First current transformer using the section space vector modulation of optimization three level seven, three level seven are used to second current transformer Section space vector is modulated;Voltage output caused by the averaged Power Control of First current transformer optimizes three level seven as itself Section space vector modulation reference voltage, voltage output caused by second averaged Power Control of current transformer as itself three The reference voltage of the section space vector of level seven modulation;
The mean power control is based on two close cycles PI Control System Designs, is added in the electric current loop of two close cycles PI control systems Active power and reactive power divide equally link, by average active power and reactive power and the real-time active power of current transformer and Reactive power is compared to obtain error current, and error current is superimposed into electric current loop, so as to which output voltage be adjusted, is allowed The active power of two current transformer outputs is consistent with reactive power, reaches the effect for suppressing circulation;The mean power control tool Body comprises the following steps:
(a1) first, the line voltage line current of two current transformer output ends is sampled, calculates the reality of First current transformer When active power and reactive power be P1And Q1, the real-time active power and reactive power that calculate second current transformer are P2With Q2;Then, the average active power of two current transformers of calculating and reactive power areWith(a2) will be flat Equal active power and reactive power compared with real-time with every current transformer active power and reactive power, obtain First respectively The active power error and reactive power error of current transformer beWithObtain second current transformer Active power error and reactive power error areWith
(a3) the value e by active power error divided by voltage on line side in dq coordinate systems on d axlesd, obtain the d of First current transformer Axis error electric current isThe d axis error electric currents for obtaining second current transformer areBy reactive power error Divided by value e of the voltage on line side in dq coordinate systems on q axlesq, the q axis error electric currents for obtaining First current transformer are The q axis error electric currents for obtaining second current transformer are
(a4) by the error current Δ i of First current transformer1dWith Δ i1qBelonging to being added on the d axles and q axles of electric current loop, then pass through Reference voltage after PI controls as itself optimization three level seven section space vector modulation;By the error electricity of second current transformer Flow Δ i2dWith Δ i2qBelonging to being added on the d axles and q axles of electric current loop, then itself segmentation of three level seven is used as after PI is controlled The reference voltage of space vector modulation;
The optimization three level seven section space vector modulation, introduces one in the section space vector modulated process of three level seven Regulatory factor f, regulatory factor f was acted on the modulation time of small vector, by optimizing the modulation time of small vector, to change The zero sequence dutycycle of current transformer, so as to reduce zero sequence circulation;The symmetry of parallel converters zero sequence circulation is considered, only to wherein one Platform current transformer uses the section space vector of three level seven using the section space vector modulation of optimization three level seven, another current transformer Modulation.
2. three-level current transformer according to claim 1 compound circulation inhibition method in parallel, it is characterised in that:The optimization The modulation of the section space vector of three level seven specifically comprises the following steps:
(b1) first, the action time of vector in small vector in the section space vector modulated process of three level seven is detected in real time, The zero sequence dutycycle for calculating First current transformer isThe zero sequence dutycycle for calculating second current transformer isWherein, t11And t12The respectively modulation time of the small vector of First current transformer and middle vector, t21And t22Point Wei not the small vector of second current transformer and the modulation time of middle vector;
(b2) the zero sequence dutycycle of two current transformers is made the difference, draws the zero sequence duty cycle difference of two current transformers
(b3) regulatory factor is added in the modulator of First current transformerSo that seven segmentations of First current transformer Each the modulation time of vector is respectively:WithThen first The zero sequence dutycycle of platform current transformer is optimized forThe then zero sequence duty of two current transformers after optimization It is Δ d than differencez=0;Wherein t13For the modulation time of the big vector of First current transformer.
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