A low harmonic 12-pulse rectifier based on zigzag autotransformer by current injection at DC side

LIU Jiongde，CHEN Xiaoqiang,2，WANG Ying，CHEN Tao

(1. School of Automation and Electrical Engineering,Lanzhou Jiaotong University，Lanzhou 730070，China； 2. Key Laboratory of Opto-Electronic Technology and Intelligent Control，Ministry of Education， Lanzhou Jiaotong University，Lanzhou 730070，China)

Abstract：To improve the harmonic suppression ability of multi-pulse rectifier,a 12-pulse rectifier based on zigzag autotransformer by DC side active compensation strategy is proposed.By controlling the small capacity current inverter to generate compensating currents and injecting the currents directly into the DC side of the system,the grid-side currents of the rectifier can be approximated to sine wave.Using zigzag autotransformer as phase-shifting transformer can block the zero sequence current components and reduce the equivalent capacity of the rectifying system.The study on harmonic distortion rate of grid-side currents with the variation of the load shows that the harmonic content of the compensated rectifier decreases significantly under various load conditions.The harmonic content of the grid-side currents of the proposed active injection rectifier is only 1.17%,and the equivalent capacity of the rectifier is calculated.The results show that the rectifier can not only suppress the harmonic currents,but also have a lower equivalent capacity.

Key words：multi-pulse rectifier;active compensation;zigzag autotransformer;equivalent capacity

0 Introduction

In recent years,multi-pulse rectifier technology has been widely used in high-power rectifier[1].Among many multi-pulse rectifiers,the 12-pulse rectifier is the most widely used,which can eliminate the 5th and 7th harmonics.The total harmonic distortion (THD)value of the grid-side current is about 15%[2],but it cannot meet the harmonic requirements when the high-power rectifier is connected to the power grid.

Increasing the number of pulses[3]or installing active or passive circuits on the DC or AC sides of the rectifying system can reduce the harmonic content of the grid-side currents[4].However,simply increasing the number of pulses will increase the difficulty of winding design and debase the accuracy of equipment manufacturing,which leads to the deterioration of system symmetry.The passive harmonic suppression method on the DC side can only suppress the lower harmonics of the grid-side currents,but helpless to the higher harmonics suppression and will double the amplitude of the higher harmonics[5].

An active auxiliary circuit is installed on the DC side of the 12-pulse rectifier,which can effectively eliminate (12k0±1)th harmonics ask0is any positive integer and make the distorted grid-side current into standard sine wave approximately[6-8].In Ref.[9],an active harmonic suppression method is adopted on the DC side to reduce the number of switching devices and make the structure more compact.When the matching condition of the system is satisfied,the harmonics can be suppressed effectively.A current forming method for 12-pulse rectifier is proposed in Ref.[10],in which the rectifier has a inter-phase reactor (IPR)on the AC side and two single-phase boost switch converters in parallel on the DC side.By adding boost harmonic suppression circuits on the DC side of the multi-pulse rectifier,theδTHDi,which represents the currents of THD rate,on the grid-side can be reduced to 1.44% and the power factor of the circuit can be improved[11].A compensation strategy based on isolated transformer multi-pulse rectifier is proposed in Refs.[12] and [13].Compared with the deployment of multiple active power filters on AC side in Ref.[13],the control strategy of three-phase inverter used in Ref.[12] is relatively simple.A high-power rectifier based on star phase-shifting autotransformer is proposed in Ref.[14],which uses an active IPR to eliminate the harmonic of the grid-side current,and requires three IPRs with secondary windings and a current-controlled inverter.

Zigzag transformer can not only be used as grounding transformer in high voltage system[15],but also be used as phase-shifting transformer in multi-pulse rectifying system with the advantages of simple structure and small equivalent capacity[16].Due to the unique characteristic of the zigzag phase-shifting transformer,it can block zero-sequence currents inside the transformer,so the zero sequence blocking transformer (ZSBT)can be omitted in the rectifier based on zigzag autotransformer[17],thus the equivalent capacity of the system is reduced further.

In our work,a zigzag 12-pulse rectifier using active injection method on the DC side is studied.The equivalent capacity of the rectifier can be reduced by using zigzag autotransformer as a phase-shifting transformer.The injected current is realized by a single-phase inverter whose equivalent capacity is only 2.2% of the rated output power,which can effectively reduce theδTHDiof the grid-side and the equivalent capacity of the system without changing the system parts of original 12-pulse rectifier.

1 Structure of multi-pulse rectifier

Fig.1 shows the schematic diagram of the zigzag 12-pulse rectifier with current injection at DC Side.The proposed rectifier consists of the three-phase voltage sources,a zigzag phase-shifting autotransformer,two groups of diode bridge rectifier (DBR)Ⅰ and DBR Ⅱ,the IPRs and a single-phase inverter.

Fig.1 Main circuit of zigzag 12-pulse rectifier with current injection at DC Side

The IPRs can absorb the instantaneous voltage difference between the two groups of DBRs,so that the two groups of DBRs can work independently.In addition,in Fig.1,Za,ZbandZcrepresent the source impedances;ia,ib,andicrepresent the grid-side currents,the currentsia1,ib1,ic1andia2,ib2,ic2are the three-phase input currents of the DBR Ⅰ and DBR Ⅱ,respectively.The rectifier uses the current hysteresis-band to control the inverter to output a specific current waveform,so that the input current on the grid side is close to the sine wave.In Fig.1,ix1andix2are the specific currents generated by the single-phase inverter in the active auxiliary circuit.

2 Winding design of zigzag autotransformer

Fig.2 Voltage phasor-diagram

The input phase voltages of the rectifier are given as

(1)

whereVsis the root-mean-square (RMS)value of phase voltages.

Therefore,the input line voltages are

(2)

The phase-shifting transformer of the 12-pulse rectifier shall provide two sets of voltages with a phase difference of 30°[3],soαis 15° and here come the formulas

(3)

(4)

whereVis the RMS value of output phase voltages of the phase-shifting transformer.

The transformation ratioK1andK2of phase-shifting autotransformer are set in Fig.3.By Fig.2,we can get

Fig.3 Zigzag autotransformer winding configuration

Vs=Vcosα,

(5)

(6)

(7)

According to Eqs.(1)-(7),we can obtain thatK1=0.333 3 andK2=0.154 7.

3 Theory of active injection

Fig.3 shows the winding configuration of zigzag autotransformer.In Fig.3,currentsi1,i2andi3represent the currents in the windings of the phase-shifting transformer.By applying Kirchhoff's Current Law,currentsia,ibandiccan be expressed as

(8)

The balance relationship of magneto motive force (MMF)of zigzag autotransformer is

(9)

By Eqs.(8)and (9),the relationship between the grid-side currentsia,ib,icand the output currentsia1,ib1,ic1,ia2,ib2,ic2of autotransformer can be calculated as

(10)

The relationship between the input and output sides of the DBRs can be expressed by introducing the switch function.Therefore,the grid-side currents can be presented by the mapping function and the output currents of the DBRs.

(11)

whereSa1(t),Sb1(t),Sc1(t),Sa2(t),Sb2(t),Sc2(t)are the mapping functions of phasea1,phasea2,phaseb1,phaseb2,phasec1,phasec2.

The input currents of the DBRs can be expressed as

(12)

(13)

Meanwhile,by applying Kirchhoff's Current Law in Fig.1,output currents of DBRs can be expressed as

(14)

Combining Eqs.(12),(13)and (14),we can get

(15)

By substituting Eq.(15)into Eq.(10),the grid-side currents expressed by DC load currentIdand injected compensating currentsix1,ix2can be written as

(16)

where

In order to ensure the full compensation of the rectifying system,the three-phase grid-side currents are set as

(17)

From Eqs.(16)and (17),the compensating currentsix1,ix2can be expressed as

(18)

(19)

The expression of compensating currentix1is complex and not easy to implement in practice.Therefore,calculating Eqs.(18)by Matlab,we can approximately obtain the waveform of the ratio of compensating currentix1to DC side load currentId,as shown in Fig.4.The waveform of compensating currentix2is the same as that ofix1,but the phase difference is 30°.Under the condition of power frequency,the waveform shown in Fig.4 can be injected into the DC side of the rectifying system to make the currents on the grid side closer to the sine wave.

Fig.4 Theoretical compensating waveform of ix1/Id

4 Construction of active auxiliary circuit

The single-phase inverter and the IPRs in Fig.5 constitute an active auxiliary circuit.Combining this kind of auxiliary circuit with zigzag phase-shifting12-pulse rectifier can not only reduce the manufacturing difficulty and winding configuration of phase-shifting transformer,but also reduce the harmonic content of rectifying system observably.

Fig.5 Active auxiliary circuit

In Fig.5,the output ends of the rectifier are connected to two dotted terminals of the IPRs.Similarly,as for compensating currentix1andix2,the single-phase inverter generates them and feed them into the IPRs.In Fig.5,Lxrepresents the filter inductance of the inverter,VDCrepresents the DC input voltage of the inverter,andIdrepresents the load current of the rectifying system.To generate the injection current waveform as shown in Fig.4,we can replace this waveform by a standard triangular wave as shown in Fig.6 with a frequency of 300 Hz,that is,a periodT0of 1/300 s and an amplitude of 0.45Id.

The expressions of injected compensation currents in Fig.6 are given by

Fig.6 Injected triangular waveforms

(k=0,1,2,…),

(20)

(k=0,1,2,…).

(21)

The Fourier series expansions of Eqs.(20)and (21)are

(22)

whereT0is 1/300,Ais the amplitude of the 6 times the power frequency triangular wave,which is 0.45 here.

The total harmonic distortion rate of the currents,which represented by δTHDi,can be expressed as

(23)

whereI1represents the RMS value of fundamental current;Ihrepresents the RMS value of total harmonic currents.

With regard to theδTHDiof zigzag 12-pulse transformer rectifier with current injection at DC side,calculating Eqs.(16),(22)and (23)by Matlab program can get that the averageδTHDiof grid-side in proposed rectifier is 1.24% theoretically,which is less than the 9.10%[17]of conventional zigzag 12-pulse rectifier.So theoretically speaking,the active injection strategy can significantly reduce theδTHDion the grid side of the rectifying system.

The current hysteresis-band control method is adopted to generate the triangular waveform.This control method is easy to realize and it is closed-loop control with strong stability.Fig.7 shows the control schematic diagram of the inverter.

Fig.7 Control block diagram of the inverter

The triangular wave generator produces a triangular wave with 6 times power frequency and amplitude of ±0.45.By comparing the reference current of multiplier with the injection current,the difference signal is connected to the hysteresis controller.After the hysteresis controller generates the driving signal to drive the single-phase inverter,the required 6 times power frequency injection currents which can change with the load current can be obtained.

5 Validation and analysis

In MATLAB/Simulink,the simulation model of the proposed low harmonic 12-pulse zigzag rectifying system is established.Fig.8(a)and Fig.8(b)show the simulation model of zigzag 12-pulse autotransformer and the auxiliary circuit,respectively.

(a)Zigzag transformer

Under the condition of the same power supply and same load,the proposed zigzag autotransformer rectifier is compared with the conventional zigzag autotransformer rectifier.The simulation parameters are listed in Table 1.

Table 1 Parameters for simulation

When the active auxiliary circuit is not working,the main simulation results of the rectifier are shown in Fig.9.

(a)Grid-side currents ia,iband ic

Fig.9(a)shows the current waveform on the grid side of the system without compensating currents.It can be seen that the waveform has been obviously distorted.Fig.9(b)shows the waveforms currentia1andia2.It can be verified from the figure that the phase difference of the two waveforms is 30° to achieve the effect of phase-shifting,indicating that the windings design of the zigzag autotransformer is correct.Fig.9(c)shows the currenti1in the winding of zigzag autotransformer.The waveforms of the winding currentsi2andi3are consistent withi1but the phase difference is 120°.In the case of full load,Fig.9(d)is the spectral analysis diagram of the three-phase grid-side currentia,whoseδTHDiis 12.54%.Obviously,conventional zigzag 12-pulse rectifier cannot meet the standards of IEEE-519[18]and IEC 61000-3[19]that the δTHDishall be lower than 5%.

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When the active auxiliary circuit is working,the waveform of the currentix1in Fig.10,which is generated by the auxiliary circuit in Fig.8(b),is directly injected into the DC side of the proposed rectifier.The frequency of the currentix2is the same as that of the currentix1,both of which are triangular waves of 300 Hz with a phase difference of 30°.

Fig.10 Waveform of current ix1 injected into DC side

The injections of these two triangle waves make the waveforms of the output currentid1andid2of the two DBRs triangular,as shown in Fig.11(a).Although the waveforms of the output currents of the DBRs change after the current injection,the output currents' average values of the DC side are the same.

Accordingly,waveforms of input currentsia1,ia2and winding currenti1of the DBRs have been improved,as shown in Fig.11(b)and Fig.11(c).As can be seen from Fig.3,grid-side currentiais synthesized by currentsia1,ia2and winding currenti1,so its waveform should be close to the standard sine wave,as shown in Fig.11(d).

According to the spectral analysis of the grid-side currentiain Fig.11(e),itsδTHDiis 1.17%.Obviously,when the single-phase inverter is working,the grid-sideδTHDiof the 12-pulse rectifying system is very small and can meet the harmonic requirements of IEEE-519 and IEC 61000-3.

(a)Output currents id1,id2 of DBRs

Under the condition of full load,Table 2 shows the harmonic parameters of the grid-side currents of the rectifying system after the injection of compensating currents.When no compensating currents are injected,the average grid-sideδTHDiis 12.537% which is less than the theoretical value due to the influence of leakage inductance of transformer windings,but theδTHDicannot meet the requirements[18-19].

Table 2 Harmonic parameters comparison of grid-side currents with or without compensating currents

After the injection of compensating currents,the average δTHDiof three-phase grid-side currents is 1.162%.Obviously,conclusion can be drawn from Table 2 and Fig.11(e)that the zigzag 12-pulse rectifier with active injection at DC side can not only reduce the average grid-sideδTHDi,but also debase the content of the 11th and the 13th harmonics.

After the compensation circuit is working and the selected load values are between 10% and 100% of the rated load,simulation is carried out to study the influence of various load on the grid-side currents.Fig.12 shows the change trend.It can be clearly seen that the harmonic content of the grid-side currents changes little with the load before and after current injection.Although the grid-sideδTHDiincreases when the rectifying system is under light load,as a whole,the harmonic content of the rectifying system after compensation can still meet the standards[18-19].

Fig.12 Trend chart of grid-side currents harmonic content changing with load

According to Ref.[5],the equivalent capacity of the transformer can be calculated as

Seq=0.5×∑VRMS×IRMS,

(24)

whereSeqrepresents the equivalent capacity of the transformer;VRMSrepresents the RMS value of voltage at both ends of each winding of the transformer;IRMSrepresents the RMS value of the current flowing through each winding of the transformer.

The RMS value of currents fed to the windings of autotransformer,IPRs and single-phase inverter can be obtained by the simulation model.The equivalent capacity of the zigzag autotransformer,IPRs and inverter by computation is 23.35%,2.11% and 2.21% of the output power of the load side respectively,so the total equivalent capacity of the magnetic elements in the whole system is 27.66%.

To demonstrate the correctness and applicability of constructing an active auxiliary circuit through a small capacity inverter,theδTHDiand equivalent capacity of two topologies,topology-A and topology-B,are compared in Table 3 under the condition of rated load,in which topology-A is the zigzag 12-pulse rectifier with boost converter[20],topology-B is the proposed rectifier.By Table 3,the grid-sideδTHDiof topology-B is 1.17%,which is less than 2.64% of that of topology-A.In terms of the equivalent capacity of this two rectifiers,due to the different harmonic suppression methods on the DC side,the winding currents of the autotransformer,IPRs and auxiliary circuit also vary.Table 3 shows that the equivalent capacity of topology-A is 3.54% higher than that of topology-B,indicating that topology-B gets higher power density.Therefore,the topology-B has better performance in the aspect of the effect of the rectifying system on the grid-side currents and the equivalent capacity of whole system.

Table 3 Comparison of parameters for different topologies

6 Conclusions

A zigzag 12-pulse rectifier by active injection at DC side has been proposed.The calculation method of the winding configuration parameters of zigzag phase-shifting autotransformer is given.When the grid-side currents are sinusoidal,the current waveform of active injection compensation is analyzed.At last,the rectifying system model is built and the theoretical analysis is confirmed by simulation.The conclusions can be draw as follows：

1)When the output currents of the auxiliary circuit are triangular and their frequency is 6 times grid frequency,the grid-side δTHDiis about 1.17%.Hence the current harmonics are notably suppressed.

2)When the load is changed,the current hysteresis-band control method used by the multi-pulse rectifier can adjust the output compensating currents,which can restrain the increase of the harmonics content of the grid-side current.

3)After using zigzag autotransformer as phase-shifting transformer and using small capacity inverter to generate compensating currents,the system equivalent capacity is only about 27% of the load power,which can reduce the volume and improve the power density of rectifying system.