- •Introduction
- •1. Rectifiers
- •1.1 Employment, basic constituents
- •1.2. Technical and economic indexes of rectifier
- •1.3. Classification of rectifiers
- •1.4 Calculated basic parameters of designing
- •1.5 Some definitions
- •Thyristor as logical switch
- •1.7 A single-phase half-wave rectifier
- •1.7.1 Operation of single-phase half-wave rectifier with active load
- •For a secondary winding
- •For a primary winding
- •1.7.2. Operation of the half-wave rectifier with active - inductive load and limited inductance
- •1.7.3. Operation of the half-wave rectifier with resistive-capacitive load
- •1.8. A single-phase full-wave rectifier with a centre tap
- •1.8.1. Operation of a full-wave rectifier with a centre tap with an active load
- •1.7.2. Operation of a full-wave rectifier with centre tap and active - inductive load and limitеd inductance
- •1.8.3. Operation of a full-wave rectifier with centre tap and active - inductive load with infinite inductance
- •1.8.4. Consideration of a stage of switching of thyristors for a full-wave rectifier with centre tap and active - inductive load with infinite inductance
- •1.8.5 An external characteristic in per unit values
- •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.
- •1.10 The three-phase rectifier with a centre tap
- •1.10.3 The controlled three-phase circuit with a centre tap
- •1.10.4 The account of a stage of switching for three phase rectifier with centre tap
- •1.10.5 External characteristic
- •1.11 Three-phase bridge rectifier
- •The external characteristic
- •1.12 The double three-phase rectifier with balancing reactor
- •1.12.2. Definition of parameters for a choice of thyristors, calculation of the transformer and the balancing reactor
- •1.12.3 Merits and demerits, conditions of application
- •1.13 Equivalent polyphase circuits
- •1.13.2. Parallel connection of double three-phase bridge rectifiers
- •Average value of the rectified voltage is
- •1.14 Operation of the rectifier with opposite- emf
- •1.14.1. Operation of the half-wave rectifier with center tap with opposite- emf and active load
- •1.14.2. Operation of the half-wave rectifier with center tap and opposite-emf and active-inductive load
- •2. Dependent inverters
- •2.1 Transition from a rectifying conditions to an inverting conditions
- •External characteristics
- •3. Equipment and characteristics
- •3.1 Transformers for converting sets
- •3.2 The higher harmonics of a current and a voltage
- •The higher harmonics in a curve of the rectified voltage
- •3.2.3 The higher harmonics in a curve of a prime current
- •3.3. Power characteristics of the converter
- •3.3.1. Efficiency
- •3.3.2 Power factor
The external characteristic
Figure 1.36
1.12 The double three-phase rectifier with balancing reactor
Figure 1.37
1.12.1 Conditions: =0; Ld = ; 0 < Lbr <.
At this scheme there are 2 secondary windings located on the same core of a transformer and differentially connected. The rectifier has two commutating groups of thyristors: VS1, VS3, VS5 and VS4, VS6, VS2 which are separated by reactor Lbr. Load is arranged between centre tap of balancing reactor and common cathodes of thyristors. There are 2 types of these rectifier regimes:
1) Independent operation of two three-phase rectifiers with center taps;
2) A six-phase regime.
Figure 1.38
Regime 1. As Lbr 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 the group 1 and VS2 of the group 2.
Lengthways of contour O1, VS1, VS2, O2, Lbr according second Kirchhoff’s low
e2a + e2Z = UK.
For intervals of operation of two any thyristors of different groups
eII + eI = UK.
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 Lbr have limited value through the contour O1, VS1, VS2, O2, Lbr flows the alternating current iK limited by inductance Lbr. The phase lag of the first harmonic iK(1) concerning voltage UK is 2. This alternating current iK 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 Id/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 Lbr is reduced and it is possible to consider Lbr as anode inductance. The angle depends from a load current Id. Simultaneously from one up to four thyristors are conducted.
The waveform of the rectified voltage is under construction in view of . For no-load regime ed() is a top envelope of phase EMF of both groups. So average value of ed() 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
Asm dM it is possible to not take into account ik 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 Ld = , but under condition of ITM=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 ST br
The average voltage of the current-balancing reactor for half-wave determines Φm
Let's reduce the voltage UKAV to equivalent sinusoid with frequency 50 Hz
where - a form factor.
For a regime 1
From here result is exceeded
Кс > 1 takes into account operating conditions of the core in the real circuit at f=150 Hz.
Usually Кс=2, from here
For the controlled rectifier
Form Uk would depend from α.
If the angle of regulation varies in a range , that
For
Thus with growth α, UKAV and STbr are increased hence, STbr depends from αmax.
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 Id would not depend from α, that
where
4
3
2
1
30о 60о
90о α
Figure 1.41