418 HANDBOOK OF ELECTRICAL ENGINEERING
Figure 15.6 Circuit diagram of a 12-pulse thyristor bridge.For example, leti 1 =I sinωtandi 2 =I sin(ωt− 120 ◦)be the fundamental instantaneous
currents, theni 12 becomes,
i 12 =I(sinωt−sin(ωt− 120
◦
))
=I(sinωt−sinωtcos(− 120
◦
)−cosωtsin(− 120
◦
))
=I(sinωt+ 0 .866 cosωt+ 0 .5sinωt)
=I(+ 1 .5sinωt+ 0 .866 cosωt)
=√
3 Isin(ωt+ 30 ◦)In order to obtain the full benefit of harmonic cancellation the two bridges must be controlled
in a common manner. The control system will enable the fundamental current in both supply lines of
the same phase to be in-phase, i.e. the star primary line current must be in-phase with the delta primary
line current. See Reference 12, Chapter 3 which emphasises this aspect. The controlled firing of the
delta-star bridgeTucancels the 30◦degree phase shift of the transformer. From the Fourier analysis
point of view this can be achieved by addinga+ 30 ◦phase shift to the delta primary line current.
In sub-section 15.3.1 the line current of the star-star bridgeTl was the same as the phase
current, both having the shape of the 120◦rectangle wave form. When the phase currents are combined
to produce the delta line current the waveform consists of two parts. The first part is a full, rectangular
wave, which can be called the ‘180◦rectangle waveform’. The second part is a narrow rectangular
wave. The width of this rectangle is 60◦, hence call this the ‘60◦rectangle waveform’. The two parts
have the same magnitude, which is 1.0 per unit for the analysis. In both waveforms the rectangles
are centred atπ/2and3π/2, as described in sub-section 15.3.1. The harmonic coefficients for the