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The double three-phase rectifier with balancing reactor

Figure 1.37

1.12.1 Conditions: a=0; Ld = ¥; 0 < L_br <¥.

Regime 1. As L_br®¥ so switching from the thyristor of one group to the thyristor another group is impossible so both thyristor groups operate as three-phase rectifiers with centre tap independently one from other.

Let there is the highest phase EMF in the anode circuit of the thyristor VS1 of thegroup 1 and VS2 of the group 2.

Lengthways of contour O1, VS1, VS2, O2, L_br according second Kirchhoff’s low

e_2a + e_2Z = U_{K .}

For intervals of operation of two any thyristors of different groups

e_II + e_I = U_K.

Voltage drop across a half-winding of balancing reactor is .

Then for the contour O1, VS1, Ld, Rd, O:

.

For the contour O2, VS2, Ld, Rd, O:

.

From here

.

Without taking into account losses of the transformer

For intervals of operation of two any thyristors of different groups

As L_br have limited value through the contour O1, VS1, VS2, O2, L_br flows the alternating current i_K limited by inductance L_br. The phase lag of the first harmonic i_K(1) concerning voltage U_K is p¤2. This alternating current i_K is imposed on a direct component of a thyristor current of group 1 and groups 2.

Regime 2 At reduction of a load current to value I_d/2=I_{_к m} the circuit will be operate as an equivalent six-phase rectifier due to field current of balancing reactor is not provided needed value due to L_br is reduced and it is possible to consider L_br asanode inductance. The g angle depends from a load current I_d. Simultaneously from one up to four thyristors are conducted.

The waveform of the rectified voltage is under construction in view of g. For no-load regime e_d(u) is a top envelope of phase EMF of both groups. So average value of e_d(u) is

Thus, the external characteristic will be as

Figure 1.39

1.12.2. Definition of parameters for a choice of thyristors, calculation of the transformer and the balancing reactor

As I_km @ 0.5¸1% I_dM it is possible to not take into account i_k for a choice of thyristors and calculation of the transformer and to consider a current through a thyristor and a secondary winding of the transformer

Hence, calculation of a current through thyristor will be as for the 3-phase rectifier with center tap at L_d = ¥, but under condition of I_TM=Id/2

The waveform of an primary current

 

 

Figure 1.40

From here we shall define RMS currents values of primary and secondary windings of the transformer, and also full power of windings and type power of the transformer

Let's define type power of the current-balancing reactor S_{T br}

The average voltage of the current-balancing reactor for half-wave determines Φ_m

Let's reduce the voltage U_KAV to equivalent sinusoid with frequency 50 Hz

where - a form factor.

For a regime 1

From here result is exceeded

К_с > 1 takes into account operating conditions of the core in the real circuit at f=150 Hz.

Usually К_с=2, from here

For the controlled rectifier

Form U_k would depend from α.

If the angle of regulation varies in a range , that

For

Thus with growth α, U_KAV and S_Tbr are increased hence, S_Tbr depends from α_max.

Further, as well as at α=0, we shall define

It is possible to use functional association

where

It is necessary to take into account, that as I_d would not depend from α, that

where

 

Figure 1.41

 

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