Joined: 25 July 2008
A VT is a constant voltage source that's output is dependent on the turns ratio between the primary and secondary windings, and its input voltage. The primary winding is connected in a 'parallel' configuration and has a large impedance with respect to the power system. With the secondary terminal open circuit, the back EMF of the primary winding is restricting the current through the primary winding to virtually zero (magnetization current only). This impedance (inductance) prevents a phase to phase fault. When a load is applied to the secondary winding a current will flow governed by V=IR. This current in the secondary winding will also produce a back EMF in the core, which will partially counter the primary windings inductance, allowing more primary current to flow, and therefore more power to 'flow' through the transformer.
A CT is a constant current source that's output is dependent on the turns ratio between the primary and secondary windings, and its input current - assuming that the burden on the CT is within acceptable tolerances. The primary winding is connected in series and has negligible impedance with respect to the power system and often has a turns ratio of 1, resulting in zero back EMF inductance.
1. Why is a constant voltage not induced in a single primary winding VT (aka a CT) even though a magnetic flux is produced within the iron core.
2. At what point would a CT become a VT? If you had a 'square' CT with single primary winding connected between two phases, a high current would pass and would be scaled down on the secondary side. If the primary winding was increase to 3, the secondary current would increase by three times, with only minor inductance being produced in the primary (three turns) winding, so only limiting the phase to phase current flow a small amount. At what point will the primary turns become such that the inductance will limit the primary current flow and turn the CT into a VT? Also the what is the fewest amount of turns that a power transformer can have
I have negated any maths in the question, but am happy for maths to be provided within the answer if required.
Joined: 14 September 2010
Regarding how many turns a power transformer has - it depends to a large extent on the voltage across the entire winding.
Say, for example, you had a 132 kV - 33 kV power transformer. Across a single winding on the primary, you have 76 kV. Consider how the conductor in the winding is wound. It is a narrow band of copper, insulated with thin paper, each turn of the winding in close proximity to the previous and next turn. The insualtion-breakdown of this paper is small, so the voltage between each turn has to be small. The more turns you have, the smaller the voltage between each winding - if you have 76,000 turns, the voltage between each turn is just 1V. If the voltage is larger than the insulation strength of the papers, then the windings will short out, and you no longer have any turns! (Joseph Henry (surely a genius exceeding Faraday) when making his electro-magnets, first used his wife's silk nightgowns as winding insulation before moving onto varnish as his coils got larger and larger)
Another important consideration is the effectiveness of the transformer.
The magnitude of the time-varying magnetic field in the winding is:
B(t) = u.N.i(t) / L
B(t) = The magnitude of the time-varying magnetic field.
N = The number of turns
i(t) = The time varying current in the winding
L = Length of winding
the magnetic flux through each turn is
f(t) = AB(t)
f(t) = time varying flux
A = area of winding
So, it makes sense, to maximise the effectiveness of the transformer, to make A and B as large as possible. And to make B as large as possible, N shall be large.
The formula for the (perfect) transformer (assuming no losses) is
V2(t) = (N2/N1) x V1(t)
N1 is the number of turns in the primary
N2 is the number of turns in the secondary
V1(t) is the time varying voltage across the primary
V2(t) is the time varying voltage across the secondary
Consider a voltage transformer - there is a significant voltage difference across the primary winding. You can see from the equation that if V1(t) increases, so does V2(t).
In a current transformer, the voltage across the primary winding (a short section of cable or a busbar for example) is effectively zero. If you put zero into the equation above, you get V2(t) = zero. So, you can see that the point at which a CT becomes a VT is when V1(t) is non-negligible.
Edited: 16 February 2014 at 11:39 AM by Zuiko