Handbook of Electrical Engineering

HARMONIC VOLTAGES AND CURRENTS 429

The supply voltage becomes,

V 15 =I 15 Z1m2

=−

110. 95

√

2

( 0. 00878 +j 0. 7711 )

=− 0. 6888 −j 60 .496 volts

The voltage across the stator impedance is,

V 1 m 5 =( 0. 0053 +j 0. 2350 )(− 78. 453 −j 0 )

=− 0. 4158 −j 18. 4365

The air-gap voltageVm 5 becomes,

Vm 5 =V 15 −V 1 m 5

=− 0. 6888 −j 60. 496 + 0. 4158 +j 18. 4365

=− 0. 273 −j 42 .059 volts

The magnetising currentIm 5 is,

Im 5 =

Vm 5

jnXm

=

− 0. 273 −j 42. 059

0. 0 +j 14. 655

=− 2. 8699 +j 0 .0186 amps

Hence the rotor currentI 25 becomes,

I 25 =I 15 −Im 5

=− 78. 453 +j 0 + 2. 8699 −j 0. 0186

=− 75. 565 −j 0 .0186 amps

If the above calculations are made for all the active harmonics then their results can be added
and the waveforms synthesised. Table 15.6 summarises the results.

Figure 15.13 shows the synthesised currents and air-gap voltage using the first 91 harmonics.

15.5 Filtering of Power Line Harmonics

In modern oil industry power systems there is a probability that one or more variable speed systems
will be present. When the system engineer designs or modifies a power system he will need to take
full account of the effect of the harmonics that will be injected into the system from the rectifier part
of the variable speed drive, see also sub-section 15.1.

The most frequently used reference document based on European practice that makes recom-
mendations on the levels of harmonics that can be tolerated in LV and HV systems is Reference 14,