6. Thyristor as logical switch

Figure 1.3

Thyristor is been turning on, i.e. switch is been short-circuiting, when

• u_D()≥0 – voltage applied across thyristor is hit-crossing zero point to positive direction;

• a control pulse is applied;

Thyristor is been turning off, i.e. switch is been disconnecting, when

- i_T()0- anode current is hit-crossing zero point to negative direction.

1.7 A single-phase half-wave rectifier

Figure 1.4

1.7.1 Operation of single-phase half-wave rectifier with active load

Conditions: La = 0, Ld = 0, =0

id e2 UV Rd VS iV ~

e i1 i1(1) Id Открыт Закрыт Ud id U1, i1 Ud 2π π е2 0 0 0 0 id=i2=iV e2m Udm Uобрm

The a peak rectified current of the load and a peak thyristor current are

Direct component of a rectified voltage is

Direct component of rectified current and current of the thyristor are

RMS current of the thyristor is equaled to RMS current of a secondary winding of the transformer

A peak inverse voltage

Let's define 1-th harmonic U_d and i_d

It is an even function.

Then

A RMS rectified voltage

A ripple factor of rectified voltage U_d for 1-th harmonic is

A ripple factor of rectified voltage U_d is

RMS value of EMF of secondary winding is

.

Instantaneous value of i₁ we should define from a magnetic balance condition of the transformer by a variable component. Magnetic voltage drop is not taken into account. The direct component is not transferred into a primary winding.

Then

Let’s define rms value of i₁

Let’s define the total powers of the transformer’s windings.

For a secondary winding

where Pd – the power of direct components of rectified voltage U_d and rectified current I_d.

For a primary winding

Type power or electrical rating is

Active power of a rectified current is

,

i.e. P_ad is approximately 2,5 times greater than P_d. That is the reason of increasing of the transformer. In the core of the transformer is created the additional permanent magnetic flux penetrating the core due to a constant component of a secondary winding current. This phenomenon is named as the permanent magnetization of the transformer. As a result the magnetizing current grows up by a few times. So it is necessary to increase sections of a wire of a primary winding and the dimensions of the transformer at whole. It is also necessary to increase the dimensions of the transformer thanks availability of higher harmonics at primary current.