Open delta transformer - Z calculation

I'm after some help regarding a transformer impedance calculation I need to produce for a design in the near future; basically the transformer will be 75kVA with a 400V open-delta primary and single phase 230V secondary.
I am familiar on how to calculate the effective secondary impedance on delta /star and single phase transformers by reflecting the impedance of the primary circuit when the transformers percentage impedance is known; however I'm unsure how to do this with the open-delta transformer described above (as open-delta is non-linear).
Regards

Um, open delta is a way for power companies to provide 3 phase to a customer with only 2 transformers instead of 3. I don't think an "open delta" transformer exists. I doubt a 3 phase to single phase transformer exists either. Of course you could use one leg of the secondary but your service would be unbalanced
The usual method of operation a single phase load from 3 phase service is by employing a motor generator called a rotary converter or some solid state equivilant.

Thinking of 2 single phase transformers connected to the 3 phase supply with the primary windings connected in open delta configuration - 1 phase connection of each commoned to one phase of the supply; and the other phase connections, connected to the other phases. The secondary windings connected in series, for the single phase supply.
Regards

This is really a single-phase situation, not three phase. You have a single-phase transformer with two windings in series and two equal winding voltages 120 degrees apart. The result is a third equal voltage at 120 degrees to the other two.
Since your load is single phase, the line currents will be equal and 180 degrees out of phase on the two secondary lines and on the corresponding two primary phases, and will be zero on the common phase. There is no advantage to the two transformers connected open delta. You can simply use one transformer with appropriate kVA and voltage ratings across two of the phases instead, and get the same line current.
Each transformer presents its rated impedance, reflected to the primary side, across two of the primary phases. Since the secondaries are in series, the total impedance seen by the load will be the sum of the two transformer impedances reflected to the secondary side.
Ben Miller

Please don't think that way.
First read up on what 3 phase is. Perhaps if you stated what you wanted to accomplish someone here could suggest a practical way to achieve it.
However, at 75,000 V-A most are probably going to say it's time to consult a local master electrician, licensed engineer, and the local power company.

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You haven't given details on the connections- specifically what phases of the secondary are being used for the secondary nor the ratio of the transformer which appears to be 400/230 if the 3rd leg was present. It is not non-linear but it is unbalanced so 3 phase balanced analysis wont work

Transformer connection have never loomed large in my life. Why would someone even consider an open delta primary unless insufficient single phase capacity were unavailable?
What is meant by "impedance calculation" in such a situation? Are we talking about impedance transformation? That is,the load impedance as seen from the primary side? Is it just the V/I at full load?
This whole inquiry smacks of weirdness.
Bill

However open delta has some drawbacks for 3-phase loads, as stated below. ______________
A.C. POWER DISTRIBUTION FOR OPTIMUM TRANSMITTER PERFORMANCE
by J. B. Pickard
For many years, Harris engineers have recommended that the three phase power distribution system should be either a closed delta or WYE configuration to provide better radio and television transmitter performance by helping prevent line unbalance. Operation with substantial voltage unbalance from line to line results in higher than normal signal-to-noise ratio in the transmitter output signal, increased three phase transformer heating, and overly hot three phase motors.
Overheating From Line Unbalance Even a device as simple as a three phase motor should be operated from a power line in which the voltage is balanced within 1%. It takes only a 3.5% line unbalance to produce a 25% increase above normal temperature. A 5% unbalance will cause destructive temperature rises of 50% greater than normal!
Similar characteristics can be expected in the windings of a three phase power transformer down inside the cabinet of your transmitter. Transformers and motors can be designed with extra safety features where thermal rise is limited to acceptable levels; however, in this case, other transmitter parameters cannot be made acceptable at a reasonable cost.
Transmitter Noise Performance The most difficult parameter to meet with power line unbalance is transmitter AM noise performance. Most large transmitters use six-phase or twelve phase high voltage power supplies. The energy storage capacitors are expensive to install and large stored energies make destructive faults inevitable. A good design will have sufficient energy storage capacitors to meet the specified signal-to-noise but not much more. When the equipment is then operated from an unbalanced line, the power supply ripple frequency will be twice the line frequency instead of six to twelve times. It becomes obvious that it would take three times as much energy storage to achieve the original performance goal.
The Causes of Line Unbalance How does a line unbalance occur? It is a rare case in which a large commercial power producer would generate unbalanced voltage, so we must look elsewhere in the system. When you have large single phase power users on a power line this can cause uneven distribution of the line currents in the system. Uneven currents through balanced impedances will result in line-to-line voltage unbalance.
Another likely source of this problem can come from unbalanced impedances in the power distribution system. Unbalanced impedance will always be seen when an "open" delta three phase distribution system is used. Transformer design textbooks clearly show that the voltage regulation of an unbalanced system is poor.
Three Phase Delta Distribution Transformers Figures 1 and 2 show closed and open delta systems. The closed delta impedance looking into each terminal (A, B & C) is exactly the same; but this is not the case in the open delta configuration. Depending on the impedances of the transformers in the open delta circuit, line voltage unbalance sufficient to impair satisfactory operation of the overall transmitter may result.
The only advantage of the open delta is lower cost, and this is partially offset by the fact that two transformers capable of 0.577 the total kVA are required instead of three 0.333 kVA transformers. Harris customers have experienced difficulties with open delta systems -- but when a third transformer was added to close the delta, the problems disappeared.
There is another problem that can occur with an open delta system, and that is caused by lightning and switching transients. When lightning strikes or heavy loads are switched on a power distribution system, high voltage transients are propagated throughout the system. Unbalanced impedances will enhance these transients and can cause transmitter damage, particularly to solid state rectifiers.
Many transmitters are located at the end of a long AC transmission line which is highly susceptible to transient phenomena. Devices such as Metal Oxide Varistors are inexpensive and very effective in reducing overvoltage spikes. These units are limited in the amount of energy that can be dissipated, but will handle, if designed properly, very large currents. You can't take a direct lightning hit and still operate, but not many things will. Several Harris customers, upon installation of a third transformer and transient protection devices, have eliminated power line difficulties.
Three Phase WYE Distribution Transformers The WYE connected system is also considered a symmetrical form of three phase power distribution. All impedances are balanced as seen from each terminal (see Figure 3). It is important when using a WYE connected system that the fourth wire (neutral) is connected to the mid-point of the system as shown in the diagram. When this connection is made it provides a path for the zero sequence currents as well as any harmonic currents that are generated due to rectification of the secondary voltages.
Today, many transformers are supplied with all of the primary terminals available so that either a delta or WYE connection can be made. Table 1 shows the different line-to-line voltages that are available with this configuration.
In summary, both symmetrical power distribution systems are satisfactory because of their balanced impedances. Use either a closed delta or a four wire WYE system for maximum transmitter performance. Never use an open delta system just to cut costs. It could cost you dearly in the long run.
J. B. Pickard was AM Product Development Manager at Harris Broadcast Products Division (retired - 1994).

INot to mention the fact that he posted this twice, so our responses are getting disconnected.
I agree, the open delta is really a waste in this case.
When I respopnded to him, I read his mention of transformer impedance percent to mean that he was asking about that. However, now that you mention it I re-read his post, and he might be asking about the load impedance reflected across the windings. He has not been very clear about what he wants to know.
Ben Miller

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-------------- Open Delta connections have been used for some cases where loads (3 phase) are small but expected to grow- then get by with two transformers giving 57% of the capacity of a 3 phase bank until the load justifies adding the third transformer. Single phase loads can be taken between any pair of the 3 terminals. As someone else has pointed out- regulation is poor. This was once done commonly in rural areas and the transformers were mainly low KVA pole pigs that were available. I don't know whether this practice is still common but it was quite common at one time. The only reason is to save a buck or two.
The impedance of concern is the source impedance which, in this case will be unbalanced. The main component of this is generally the transformer bank. This impedance limits fault currents and affects voltage regulation. In this case the impedances are not balanced.

It should be possible to take an ordinary two leg core such as can be made from L shaped laminations to make an open delta primary to a single phase secondary.
Although variations are possible, put two primary windings on one leg to be connected in open delta. If both windings are wound in the same direction, connect the delta's apex (V corner) to one end of one winding and to the far end of the other winding. Then connect the two phases to the remaining ends of the windings. Doing this will provide a 60 degree phase shift between the mmf's generated buy the two windings. This will provide about 86.6% or cos(30°), of the voltage capability you could get with the two windings in series as a single phase winding.
Now just put a secondary winding on the other leg.
Again, I have no idea why someone would want to do that.
Bill

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---------------- Neither would power engineers- that's why they don't bother. Much easier to put a standard single phase transformer between two legs of the supply or between line and neutral of a Y connected system-- as most single phase transformers are connected. For some very large single phase loads the rotary converter can be used but this is something I have not seen and is uncommon. What you suggest is not considered open delta which is a 3 phase configuration with two transformers -essentially a delta connection with one transformer removed.

I am just trying to describe the kind of thing mentioned by the OP. You c oould use separate single phase transformers with the secondaries connected in series to give a zig-zag connection with a 60° shift between the secondary windings' outputs.
I feel somewhat stupid belaboring a stupid transformer design. It would take an amazingly provocative reply for me to respond.
Bill

The rotary converters I have seen have been at remote locations that only have single phase service and are used to operate 3 phase equipment.

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That makes much more sense than going the other way with a rotary converter.
Actually a nice scheme involves use of a 3 phase induction motor which is energised on one phase and started by whatever means is available (rope on a pulley or a small single phase motor) and, as a result, rotor mmf induces voltage in the other phases giving a nearly balanced 3 phase supply to drive smaller motors. I first heard of this from a farmer who did this with a scrounged or surplus machine, and, because of some problems after a move, asked for advice. My first reaction was "huh!" but after some analysis- I sure was impressed with him because this was the first that I had heard of this, and, fortunately, was able to help him. I don't think this hit the textbooks- it should have. A true rotary converter would be more efficient and better all round but in his case as well as many others, this gives a better bang for the buck. I did find that a local utility also applied this in a rural area where the only supply was single phase and this was the cheapest way to provide for a small 3 phase load.

I suspect that the cost + efficiency loss of the rotary converters would be made up over time in less maintenance costs due to a certain amount of surge immunity such a system provides to the load. The converters should laugh off fast transients. That is of course assuming the load is not just more motors.... what equipment doesn't have associated electronics these days?

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But, unless there is a need to go from single to 3 phase (which usually implies motor loads-with or without electronic control), maintenance and capital costs probably be lower be lower with proper solid state surge protection and filtering. Admittedly- getting a DC power supply from a polyphase source does cut down on smoothing filter costs.

I converted a transmitter from three phase to single phase one time. I ran into a "gotcha". It turns out you should not neglect to increase the resistance of the step start resistors if you wish to avoid the main circuit breaker intermittently opening on turn on. The new power transformer was so heavy that the moving company I hired to deliver it broke the loading ramp in half.

I cannot think of any advantage for such a conversion unless three-phase power is unavailable.
Bill