Fast-Cycle Control in the 4-Wire Wye Connected Load. The zero sum is mostly true if the SCR-controlled load is switched in the fast-cycling (burst-firing) mode and all three SCR drive pulses are in unison.
I say mostly because the three currents do not cease in unison at the end of the control pulse. They cease in turn at their own next zero crossing -- at slightly different times. These left over bits of neutral current become more noticeable at short cycle times, though their heating effect will balance over time due to the random distribution of which phase is first off.
Phase-Angle Control in the 4-Wire Secondary. Here, neutral current is zero only at full and balanced load and at zero load (0o and 180o) firing angle.
All levels of load under phase-angle control fall between 0o and 180o and non-zero neutral current.
One example of a load throttled back to some low power level is shown in figure 1. Here, the shark-fin current pulses do not overlap, so they cannot even partially cancel out in the neutral conductor. Take this into account when sizing the neutral conductor. The worst case is when full load occurs with severely throttled back phase-angle control, as with temperature-dependent loads. In this case, you need a neutral conductor sized twice the cross section of a line conductor. So, don't try to run a wye load in phase-angle mode without a neutral conductor.
The current pulses shown in figure 1 would have no return path. The route back, through their partners' SCRs, is not yet open and even then, opens only partially for firing angles of greater than 60o.
Control of Delta Secondary Loads. Figure 2 shows the SCRs inside the closed delta. This arrangement suits both phase-angle and fast cycle modes.
Load Balancing. Where you have unequal load resistances or line voltages your power delivery will be unbalanced. You can correct the unbalance by adjusting the relative shares of the common control signal received by each SCR. This applies equally to the 4-wire wye arrangement with phase-angle or fast-cycling control.
If you are running a three-zone system from only one control loop you may want the three zone temperatures to stay approximately equal. Adjust-ment of load balance could give you -- within limits, the temperature tracking you need.
Better yet, for temperature tracking, you can use SCRs that deliver true power in proportion to control signal, regardless of different load resistances and unbalanced line voltages.