TRANSMISSION LINE
Classification: On the basis of length of transmission line, the transmission lines are divided into three categories:
1. SHORT TRANSMISSION LINE
A transmission is defined as a short transmission if its length is less than 80 km.
Assumptions :
Equivalent Circuit:
Sending end parameters Is = Ir, Vs = Vr + IrZ
Where Is, Vs are sending end current and voltage and Ir, Vr are the receiving end current and voltage respectively and Z is the impedance of transmission line.
In matrix from
VOLTAGE REGULATION:
% voltage regulation =
Where Vs is the sending voltage or no load receiving end voltage and Vr is full load rated receiving end voltage.
Where fr is the phase angle at receiving end.
Voltage regulation =
Note:
Remember:
or tan r = (R/x)
EFFICIENCY:
The ratio of power at the receiving end to the power at the sending end is known as efficiency of the transmission line.
% efficiency = (Power delivered at he receiving end / Power sent from the sending end) x 100
ABCD PARAMETERS:
The sending end quantities Vs, Is can be represented in terms of receiving end quantities Vr, Ir by the following equations.
Vs = AVr + BIr
Is = CVr + DIr
This is known as transfer admittance.
where P is the power received at the receiving end and R is the resistance per phase of the line.
2. MEDIUM TRANSMISSION LINE
A transmission line is defined as medium transmission line if it has length between 80 km and 240 km and its single phase equivalent circuit can be represented as nominal p or nominal T circuit configuration.
Assumption:
Nominal Circuit
∴
Nominal π Circuit:
VS = A Vr + Z*Ir
3. LONG TRANSMISSION LINE
A transmission line is defined as long transmission line if it has length greater than 240 km.
Assumptions:
Here a line of length l > 250km is supplied with a sending end voltage and current of VS and IS respectively, whereas the VR and IR are the values of voltage and current obtained from the receiving end. Lets us now consider an element of infinitely small length Δx at a distance x from the receiving end as shown in the figure where.
Where, Z = z l and Y = y l are the values of total impedance and admittance of the long transmission line.
Therefore, the voltage drop across the infinitely small element Δx is given by
Now to determine the current ΔI, we apply KCL to node A.
Since the term ΔV yΔx is the product of 2 infinitely small values, we can ignore it for the sake of easier calculation.Therefore, we can write
Now derivating both sides of eq (1) w.r.t x,
Now substitutingfrom equation (2)
The solution of the above second order differential equation is given by.
Derivating equation (4) w.r.to x.
Now comparing equation (1) with equation (5)
Now to go further let us define the characteristic impedance Zc and propagation constant δ of a long transmission line as
Then the voltage and current equation can be expressed in terms of characteristic impedance and propagation constant as
Now at x=0, V= VR and I= Ir. Substituting these conditions to equation (7) and (8) respectively.
Solving equation (9) and (10),We get values of A1 and A2 as,
Now applying another extreme condition at x = l, we have V = VS and I = IS.
Now to determine VS and IS we substitute x by l and put the values of A1 and
A2 in equation (7) and (8) we get
By trigonometric and exponential operators we know
Therefore, equation (11) and (12) can be re-written as
Thus compared with the general circuit parameters equation, we get the ABCD parameters of a long transmission line as,
FERRANTI-EFFECT
When a long line is operating under no load or light load condition, the receiving end voltage is greater than the sending end voltage. This is known as Ferranti-effect.
Remember:
Remember:
Remember:
POWER FLOW
Important Observations:
The total power is three times the power per phase.
Real and Reactive Power
At receiving end
At sending end
For short transmission line
the transmission line has very small resistance as compared to inductive reactance.
Important Conclusion:
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