Effect of phase-shift angle on 12-pulse star connection transformer system

HUANG Pingqi, CHEN Xiaoqiang, WANG Jiarong , FU Juxia

(1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China；2. Rail Transit Electrical Automation Engineering Laboratory of Gansu Province,Lanzhou Jiaotong University, Lanzhou 730070, China；3. School of Electric Engineering, Xinjiang University, Urumqi 830047, China)

Abstract： Based on the study of the harmonic suppression on DC side of the multi-pulse rectification system, a software platform is established in Matlab environment. The phase-shift angle is studied from the aspects of system stability and economy, analyzing the effects of phase-shift angle on the input-side line current, the output-side voltage ripple, the equivalent capacity of autotransformer and other auxiliary devices in 12-pulse rectifier system. The software platform can complete the analysis only by inputting the initial conditions, eliminating the derivation of the intermediate formula and reducing the complexity of the system analysis, and have good scalability. The simulation results show that the system can effectively analyze the influence of phase angle on 12-pulse star-connected transformer.

Key words： phase-shift angle; autotransformer； 12-pulse rectification system； Matlab analysis

0 Introduction

Multi-pulse rectification technology has been widely used in industrial and agricultural production, impacting on the industrial and agricultural production significantly, and has become a research hotspot in recent years[1-2]. In multi-pulse rectification system, the autotransformer is used more and more widely in power system because of its small size, low cost and effective elimination of high-order harmonics than isolation transformer[3-4].

With the policy to reduce the pollution from the electricity network, the selection of the traditional phase-shift transformer’s phase-shift angle is mostly considered from eliminating high-order harmonics[5-7], and few literatures consider the influence of phase-shift angle on other auxiliary devices and parameters of the system. With the increased reliability of the system, it is necessary to consider the operation of various devices all-sidedly and to improve and extend the application of phase-shift transformers[8]. Therefore, the selection of phase-shift angle has practical significance in theory and production practice[9]. In addition, it is essential to analyze the effect of phase-shift angle on the main components of the system qualitatively and quantitatively[10-11].

The influence of phase-shift angle on output voltage ripple, equivalent capacity of autotransformer and other auxiliary devices in the system is studied theoretically. A numerical calculation platform is built in Matlab, reflecting the influence of phase-shift angle of 12-pulse autotransformer with different structure on system parameters under a small initial input condition[12-13].

1 Star-connected phase-shift angle of extended 12-pulse autotransformer

The input three-phase phase voltage can be described by

(1)

whereUmis the amplitude of phase voltage of star-connected transformer.

The Phasor diagram of star-connected transformer is shown in Fig.1. The output three-phase voltage can be expressed as

(2)

whereUm1is the amplitude of the output phase voltage. It can be concluded from the Fig.1 thatαis half of the phase-shift angle. The relationship betweenαandφis

φ=2α,

(3)

Fig.1 Phasor diagram of star-connected transformer

Whenαequals 2π/3, the transformer output phase voltage is infinite, and the range ofαshould be 0≤α≤2π/3. Soφis less than 4π/3.

1.1 Influence of phase-shift angle on line current of the input side

12 pulse star-connected autotransformer bridge rectifier connection diagram is shown in Fig.2. Zero sequence blocking transformer (ZSBT) can generate high impedance to three-frequency current to ensure that each diode of the two rectifier Bridges is turned on 120°. The balance reactor IPR can absorb the instantaneous difference of output voltage between the two rectifier Bridges, enabling the two rectifier Bridges to work independently and in parallel. Under the condition of large inductive load, the transformer output current can be described as

(4)

(5)

Fig.3 shows the 12 pulse star-connected autotransformer winding connection diagram. MMF equation is

(6)

whereNpandNqare the number of turns in the primary and secondary windings.

Fig.2 12 pulse star-connected autotransformer bridge rectifier connection diagram

The current in Fig.3 can be calculated by Eq.(7) based on KCL.

(7)

From Figs.1 and 3, it can be obtained that

(8)

According to Eqs.(7) and (8), the three-phase current can be determined by

(9)

Fig.3 Diagram of 12 pulse star-connected autotransformer winding connection

According to Eqs.(4)-(5) and (9), the relation between input current andαcan be described by

(10)

According to the definition of total distortion rate of current harmonics, theTHDcan be calculated by

(11)

whereInis thenth effective value of the harmonic current, andI1is the effective value of the fundamental current. According to Eqs.(10) and (11), the total distortion rate of current harmonicsTHDcan be determined by

By programming and analyzing in Matlab, the function diagram can be obtained as shown in Fig.4.

When the phase-shift angleφis at π/6, π/2, 5π/6 and 7π/6, theTHDminimum value of input line current is about 15.2% (Fig.4).

Fig.4 Influence of phase-shift angle on THD of input line current

1.2 Influence of phase-shift angle on output voltage

According to the modulation principle, the output voltage of the two rectifier bridges in Fig.2 can be expressed as

(13)

where thesa1(t),sa2(t),sb1(t)，sb2(t),sc1(t) andsc2(t) refer the map function of thea1,a2,b1,b2,c1andc2, respectively.

(14)

From Fig.2, the load voltage is

ud=(ud1+ud2)/2.

(15)

The load voltage ripple coefficient can be defined by

(16)

whereudmax，udminandudavare the maximum, minimum and average, respectively. Combination Eqs.(2), (13)-(16), the Fig.5 can be obtained after programming and analyzing in Matlab.

In Fig.5, When the phase-shift angleφis at π/6, π/2, 5π/6 and 7π/6, the minimum value of the ripple coefficient of load voltage can be obtained, and the minimum value is about 0.017.

Fig.5 Influence of phase-shift angle on output voltage ripple

1.3 Influence of phase-shift angle on transformer capacity

It can be obtained from the MMF equation that

(17)

The capacity of star-connected transformer is

(18)

The equivalent capacity of the transformer is shown as

Seq=S/P0,

(19)

whereP0=UdIdis output power. According to Eqs.(17)-(19)， the relation betweenφandSeqis shown in Fig.6.

Fig.6 Influence of phase-shift angle on equivalent capacity of transformer

From Fig.6, it can be seen that with theφincreasing, there is an upward trend ofSeq. Whenφis at π/6, π/2, 5π/6 and 7π/6, the values ofSeqare 21%, 57.8%, 99.7% and 113%, respectively.

1.4 Influence of phase-shift angle on IPR and ZSBT

It can be obtained from Fig.2 that

uIPR=ud1-ud2.

(20)

Under the condition of large inductance load, the current flowing through IPR is half of the load current. Combining with Eq.(20) and program analysis, the Fig.7 can be obtained.

In Fig.7, all the values are 2.034% whenφis at π/6, π/2, 5π/6 or 7π/6.

Assuming two pointsm2andm4in Fig.2, the voltages at the two points arevm2nandvm4n, respectively. It can be obtained from Fig.2 that

(21)

(22)

wherei=a,b,c, the calculation formula ofuZSBTin the Fig.2 is

(23)

According to Eqs.(21)-(23), the Fig.8 can be obtained.

Fig.8 Influence of phase-shift angle on ZSBT equivalent capacity

In Fig.8, all the values are 6.72% whenφis at π/6, π/2, 5π/6 or 7π/6.

2 Simulation experiment

The Fig.9 shows the simulation circuit diagram built in Matlab. In Figs.10 and 11, the curves are obtained from the experimental data of input current THD and transformer capacity varying with phase shift angle, respectively； and the other curves are obtained by theoretical analysis.

Fig.9 System simulation diagram

The correctness of the analysis results can be seen from Figs.10-11.

Fig.10 Experimental data and theoretical data of input line current THD at different phase-shift angle

Fig.11 Experimental data and theoretical data of transformer capacity at different phase-shift angl

3 Conclusions

Whenφis at π/6, π/2, 5π/6 or 7π/6, theTHDof the input current and the ripple coefficient of the output voltage in the system are all the smallest, and the minimum values are about 15.2% and 0.017, respectively. Whenφis at π/6, the transformer equivalent capacity is about 21% smaller than the other three values. While theφis at π/6, π/2, 5π/6 or 7π/6, the equivalent capacity of IPR or ZSBT is equal. The equivalent capacity of the IPR and ZSBT is 2.034% and 6.72%, respectively. It shows that if only considering the effect of phase-shift angle on the input side current, theTHDof input side current is the smallest and can be used as the phase-shift angle of the system whenφis π/6, π/2, 5π/6 or 7π/6. However, if considering the input currentTHD, output voltage ripple coefficient, transformer equivalent capacity, IPR and ZSBT equivalent capacity synthetically, it can be concluded that the whole system is smaller and more economical whenφis π/6 not π/2, 5π/6 or 7π/6.