AC power supply or load typically involve some inductors (e.g. transormers, motors) . DC current in such case may become very high due to low DC resistance of such inductors or at least may cause magnetic saturation of the core possibly resulting in catastrophic failure. If the DC current is not very high it may cause some rise of even harmonics due to saturation and therefore higher neutral current.
If negative terminal in D.C is taken as neutral/ground the A.C wave will shift upward(positive side) for all phase, as we use D.C biasing in amplifier (A.C signal, will superimpose on D.C).For E.H.V AC long transmission line loss due to capacitive charging current can be reduced, and is good topic for further research!!!!!!!!!!.
When you add a DC voltage to an AC signal, as far as the shape of the resulting signal is concerned, the AC signal would be lifted upward on the voltage axis. For example if you add a DC voltage Vdc=Vp to an AC signal Vac=Vp*sin(wt), then the resulting signal would vary from 0 to 2*Vp where as the original AC signal was varying from -Vp to Vp.
On the other hand, as Pavlov pointed out, the effect of DC voltage on the inductive elements available in power network would be destructive..
Adding one more point, If the load is of RL-type and ac and the dc sources are connected in parallel or in series, according to superposition theorem, both AC and DC response of the circuit will be superimposed on each other and the response will be function of the time constant of the circuit.
DC supply can be modulated on three phase supply using ZIG-Zag transformer ,on the transmission line.At the other end of transmission line similarly using zig-Zag transformer, it can be demodulated before using these both supplies for load separately.
@Satnam Why Zigzag transformer supply is necessary? I have already done simulation in PSCAD and I have already mentioned the result I have obtained while doing the simulation......IF you want to modulate a DC it will not remain DC...Doing fourier analysis Modulated DC wave will become sinusoid with harmonics......Hope you know about Biasing BJT for amplifier....
Doing what is drawn will require a bit of care as the output of a regular DC power supply would appear as a small resistance shorted by capacitors across the AC source. Also the transformer windings will be a short circuit to the DC supply. This also represents a very large charged inductance that will very likely become an arc threat to loads.being attached among other safety hazards.
A Y four wire configuration would give a place to ground a DC supply without AC shorting two phases. Placing a cap between the winding and the DC input isolates the transformer windings from being a DC short. You can duplicate the setup for each phase and create dc offsets relative to neutral on each phase by adjusting the dc voltages on each. It also would create DC difference offsets between phases that seem to be the OP's goal.