A typical distribution network in Australia will look something like the below.
The "MV" section is a delta-connected "three-wire" system, so you are correct in asserting that there is no neutral wire. However, there is a path for neutral or "zero-sequence" currents to flow to ground, via the earthing 'zig-zag' transformer that is installed for this purpose. (The reasons for installing a earthing transformer deserve a separate question and answer.)
There are a few phenomena that may give rise to neutral current on a MV transmission line, but unbalanced LV loads, which cause a current to flow in the LV star-point/neutral, don't cause MV neutral current.
Why is that?
The picture above shows a delta HV, grounded-star LV system. There is a single-phase load which draws 1 unit (1 p.u.) of current from LV winding 1, with the current returning via the LV neutral.
What happens on the HV?
Each of the transformer's HV and LV windings are magnetically coupled by iron cores, so that the law of "amp-turns balance" must apply. I.e. conservation of energy applies between the pairs of HV and LV windings, HV1-LV1, HV2-LV2, and HV3-LV3.
That means that a 1 p.u. current on winding LV 1 must be balanced out by a 1 p.u. current on winding HV1. And since no current flows in LV2 or LV3, no current may flow in HV2 or HV 3 either.
By Kirchoff's Current Law, the 1 p.u. current in Winding HV1 must be sourced from HV line L1 and HV line L2. That is:
For a delta-HV, grounded-star-LV system, single-phase LV loads appear as phase-to-phase loads on the HV system.
This answers your original question: no matter how unbalanced the load on the LV side, no neutral current will flow on the HV side, so no neutral wire is needed.
This leads to the question of: "If no neutral wire is needed on the delta-connected system, why do we bother putting an earthing transformer on it?"
A couple of reasons I can think of - though I am uncertain on these, so don't quote me here...
- Without a connection to earth, the delta network would float relative to ground and might be at any arbitrary potential relative to ground. I.e. the MV system could rise up to 132,000V above ground voltage. The earthing transformer is needed to tie the MV system to ground and keep it from floating to dangerous voltages.
- 'Neutral' zero-sequence currents do flow on the MV network, i.e. from
capacitive line charging current. (Edit 2015-09-22: The charging current is balanced under normal conditions.) The earthing transformer gives these zero-sequence currents a place to go.
- The earthing transformer will be the most attractive return path for any short-circuit fault current resulting from a line-ground fault. So it's an attractive place to put a earth-fault detection relay.
The zero sequence has no phase shift between voltages. Therefore on the delta side of the transformer, voltages will remain equal at all times between terminals, which means no current can flow through these terminals.
In general; no current can flow into a delta when fed by a zero sequence source.
Best Answer
Start with the equivalent circuit for a single phase transformer: -
Lp is the primary leakage inductance
Rp is the primary copper loss
Rc is the core losses due to eddy currents and hysteresis
Lm is the magnetization inductance
Ls is the secondary leakage inductance
Rs is the secondary copper loss
Picture from here.
Then think about the open circuit test; losses are 430 watts so, divide that by three to get the single phase losses and, recognize that those losses are consumed on the primary AND, the only lossy component that fits the bill is Rc. You know the voltage and you know the power so calculate Rc.
Then think about the short circuit test and where the power is dissipated. Your schooling should inform you that Rp and Rs are the main culprits because Rc will have little effect on power wasted with only 500 volts applied.
You can also modify the equivalent circuit I produced at this point; clearly the question isn't formed in such a way that Lp and Ls are significant so they can be shorted out AND, given that you only know the total power of the short circuit test you can assume all that waste is delivered by Rp so, make Rs a short circuit.
Can you take it from here?