1.8.5 An external characteristic in per unit values

Let’s divide the right and left parts of the equation of an external characteristic by E_d0:

Let I_dR – a rated load current. In view of it we could note

If to take into account, that

then

Let's take into account, that an impedance voltage of transformer

From here, we should set up an equation of external characteristic of a single-phase circuit with a centre tap

If this equation to note as

there is suited for any circuit of rectifying with the proper value of A.

1 .9 A single-phase bridge rectifier

Figure 1.18

From cathode group thyristors current is flowing through that the right one witch have anode voltage greater than other one.

From anode group thyristors current is flowing through that the right one witch have cathode voltage less than other one.

1.9.1 Conditions: α>0, L_d=0, L_a=0; r_a=0

For α=0

Figure 1.19

1.9.2 Conditions: α>0, L_d=∞, L_a=0; r_a=0

При α=0

Figure 1.20

1.10 The three-phase rectifier with a centre tap

A three-phase source of energy is applied to mean- and high-power consumers. The transformer primary winding of the three-phase rectifier with a centre tap is connected either in star, or in triangle. Such circuit differs in high operating ratio of the transformer. The filter dimensions could be reduced, or generally do without it.

1.10.1 Conditions: α=0, L_a=0, L_d=0

Figure 1.2 1

Figure 1.21

Constant component the rectified voltage is

The voltage of a transformer secondary winding is

U2=E2=0.853Ud

Let's discover I_TM at L_d=0

At L_d=∞  I_TM=I_d

The constant component of a rectified current is

;

The peak-inverse voltage is

The active value of a secondary winding current at L_d=0 is

The full power of a secondary winding is

Let define the waveforms of primary currents at various transformer connections. A field current is neglected.

I. Δ/Y

iAB iBC iCA iA iB iC

Figure 1.22, 1.23

Let consider that thyristor VS1 is on-state.

At connection of a primary winding in a triangle, the phase current irrespectively of other currents flows through the primary winding. Thus, the phase current of the primary winding i_AB is determined by a alternating component of the current i_2a, i.e.

Similarly for B and C phases:

Line currents:

Let's discover summarized MMF of the transformer limbs:

There are formed unidirectional uncompensated MMF in the transformer limbs, calling a flux of the forced magnetization. As results should be a saturation of the core and a considerable growth of the field current. To avoid these phenomena it is necessary to increase core section

I I. Υ / Υ

Figure 1.24

Let consider that thyristor VS1 is on state.

When a primary winding is in star-connection the primary current flows through three transformer windings at the same time and in an origin the condition is satisfied

( first Kirchhoff’s law)

In view of it and equilibrium of a magnetic system by an alternating component of a windings current is formed by the system of equations with 3 unknowns:

The line currents, which satisfy this system, are

Similarly for intervals of working VS2 and VS3.

i_AB

i_BC

i_CA

i_1A

i_1B

i_1C

Figure 1.25

Summarized MMF of the transformer limbs is

It is obvious that

Similarly for intervals of working VS2 and VS3.

Thus there are formed unidirectional uncompensated MMF in the transformer limbs, but as against the connection of a primary winding by a triangle where F₀ has only a direct component N₂i_2a/3, F₀ has also alternating component for the primary winding by star, i.e. F₀ creates the pulsing magnetic flux, which frequency 3f_C.

3. Υ/ Z

Figure 1.26

It is possible to apply a connection of the secondary windings by zigzag for liquidation of the forced magnetization flux.

The secondary current simultaneously flows through two half-winding located on the next transformer limbs, but in opposite directions, therefore unidirectional no compensated MMF F₀ do not arise.

Through VS1 flows a current, when voltage U₂₁ is greatest.

Figure 1.27

Through VS2 – when voltage U₂₂ is greatest.

Through VS3 - when voltage U₂₃ is greatest.

σ= 30^о

Let's discover summarized MMF on the transformer limbs.

Figure 1.2 8

Similar expressions describe currents and MMF for intervals of conductivity VS2 and VS3.

Thus, the forced magnetic fluxes are absent.

1.10.2. Rated parameters of the transformer at Ld =

1. ∆/Υ

Figure 1.29

II. Υ/Υ - for this windings connection rated parameters of the transformer are the same as for ∆/Υ. As there is no an alternating component of the load current waveform the primary currents are same for ∆/Υ and Υ/Υ at L_d = ∞.

Then

III. Υ/Z

U_d waveform shapes from a phase-to-phase voltage

U_2L=0.853U_d

Phase voltage of a secondary winding is

Loading of thyristors is identical to all three circuits, since the currents waveforms of thyristors i_Т are same:

Comparing S_T it is seen that for the transformer which secondary winding is connected in Z, S_T is greater in 1.09 times than for the transformer which secondary winding is connected in star. However, weight increasing of a magnetic system of the transformer with a secondary star due to the forced magnetic flux is not taken into account in this case.

Weight of a magnetic system of the transformer with a secondary star raises less, than 1.09 times while the rectified current is less than 50-100 A. In the case of the high currents weight of a magnetic system raises more, than 1.09 times comparing with weight of a magnetic system of the transformer with a secondary zigzag.

Therefore at low powers (up to 20-25 KW) is more favorable to apply the circuit with a secondary star, at the high powers - with secondary Z.