When a pure sine wave is distorted, harmonics are introduced.  A 60 hz power signal is made up of a fundamental (a sine wave at 60 hz) and any other harmonics that are created as a result of powering a load.  With three phase power, the fundamental sine waves in each line are 120 degrees apart in phase.  This allows the load current to be balanced evenly among the three supplying lines.  But with the introduction of a third harmonic, things get upset.  The third harmonic is 3 times the fundamental frequency.  In the case of line A (where the fundamental is a cosine at 60 hz) the third harmonic will be a cosine at 180 hz with no phase shift.  In the case of line B (where the fundamental is a cosine at 60 hz with a phase shift of 120 degrees lagging) the third harmonic will be a cosine at 180 hz with a phase shift of 3 * 120 degrees or 360 degrees.  In the case of line C, the fundamental is a cosine at 60 hz with a phase shift of 240 degrees lagging, but the 3^rd harmonic will be a cosine at 180 hertz with a phase shift of 3 * 240 degrees or 720 degrees.  What you end up with is a cosine at 180 hz, a cosine at 180 hz with a 360 degree phase shift, and a cosine at 180 hz with a 720 degree phase shift.  A cosine with a 360 degree phase shift is identical to a cosine with no phase shift, and a cosine with a 720 degree phase shift ( 2 * 360 degrees) is also identical to a cosine with no phase shift.  This results in three cosines at 180 hz, all with the same phase.  So a third harmonic introduced into the load will result in a current in all three phases with the same magnitude and direction.  These currents, which are all in phase, occur at odd multiples of the third harmonic (3^rd, 9^th, 15^th…) and are called triplens.

            The following matlab code and plot shows a triplen (the third harmonic) and the fundamental 3-phase power.

step = 2*pi/10000;
t = [0:step:4*pi - step];
a = cos(t);
b = cos(t + 120*pi/180);
c = cos(t + 240*pi/180);
a3 = cos(3*t);
c3 = cos(3*(t + 240*pi/180));
b3 = cos(3*(t + 120*pi/180));
plot(t,a,t,a3,t,b,t,b3,t,c,t,c3)