EE 369 POWER SYSTEM ANALYSIS. Lecture 5 Development of Transmission Line Models Tom Overbye and Ross Baldick. Reading. For lectures 5 through 7 read Chapter 4 we will not be covering sections 4.7, 4.11, and 4.12 in detail Read Section 1.5,
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Development of Transmission Line Models
Tom Overbye and Ross Baldick
1) all flux is within the coil
2) all flux links each turn
3) Radius of each turn is negligible compared to R
Circular path Γ of radius R within the iron core encloses all N turns of the coil and hence links total enclosed current of Ie = NI.
Since the radius of each turn is negligible compared to R, all circular paths within the iron core have radius approximately equal to R.
1. flux linkages outside of the wire
2. flux linkages within the wire
To determine the
inductance of each
conductor we integrate
as before. However
now we get some
Direction of integration
Key Point: Flux linkage due to currents in each conductor tend
to cancel out. Use superposition to get total flux linkage.
Now assume we now have k conductors, each with
current ik, arranged in some specified geometry.
We’d like to find flux linkages of each conductor.
Each conductor’s flux
linkage, lk, depends upon
its own current and the
current in all the other
To derive the flux linkage for conductor 1, l1, we’ll be integrating from
conductor 1 (at origin) to the right along the x-axis.
Rk is the
We’d like to integrate the flux crossing between b to c. But the flux crossing between a and c is easier to calculate and provides a very good approximation of l1k. Point a is at distance d1kfrom conductor k.
At point b the net
contribution to l1
from ik, l1k, is zero.
Calculate the reactance for a balanced 3f, 60Hz
transmission line with a conductor geometry of an
equilateral triangle with D = 5m, r = 1.24cm (Rookconductor) and a length of 5 miles.
To increase the capacity of high voltage transmission
lines it is very common to use a number of
conductors per phase. This is known as conductor
bundling. Typical values are two conductors for
345 kV lines, three for 500 kV and four for 765 kV.
Typical Transmission Tower
Aerial or side view of conductor positions over the length
of the transmission line.
“a” phase in
“a” phase in
“a” phase in