In the end condenser method, the total capacitance of the line is captured at the consolidated state at the end of the line. The response of the other two constants of the line, resistance, and inductive reactance, is reflected with respect to the supplied edge. Which is called the End condenser method.
The medium transmission line is affected by all constants. Therefore, resistance, inductance, and capacitance are considered equally during such line calculations. The middle line or medium transmission line is usually calculated in 3 ways.
For example;
1. End Condenser method.
2. Nominal “T” method and
Today we will discuss voltage and current equations in the End Condenser Method of the transmission line. Let’s get started;
Also, Read:
The Equation of End Condenser Method
The end condenser method is the simplest and most common method. In this case, keep in mind that all the capacitances of the line are concentrated at the receiving end and act as a shunt capacitor (line to neutral). Notice the image below.
The figure above shows one phase of the three-phase transmission line. Because it is more convenient to calculate as one phase instead of line to line value.
Hold, as pictured above;
V_R = load voltage per phase.
I_R = load current per phase.
R = resistance of each phase.
X_L = inductive reactance of each phase.
C = capacitance of each phase.
CosϕR = power factor on the receiving edge. (Lagging)
V_S = Transmission edge voltage.
If we take \overrightarrow{V_R} as the reference vector as shown above,
Then we get, \overrightarrow{V_R}\ =\ V_R\ +\ j0
Load Current, \overrightarrow{I_R\ }=\ I_R\ \left(Cos\phi r\ -\ j\ \sin\phi r\right)
Capacitive Current, \overrightarrow{I_C\ }=\ j\overrightarrow{V_R}\omega c\ =\ j2\pi fC\overrightarrow{V_R}
The vector sum of load current \overrightarrow{I_R\ } and capacitive current \overrightarrow{I_C\ } is the \overrightarrow{I_S\ } of the transmitting edge.
For example;
\begin{array}{l}\overrightarrow{I_S}\ =\ \overrightarrow{I_R}\ +\ \overrightarrow{I_C}\\ \ \ \ \ \ \ =\ I_R\ \left(\cos\phi R\ -\ J\sin\phi _R\right)\ +\ J2\pi FCV_R\\ \ \ \ \ \ \ =\ I_R\ \cos\phi _R\ -\ I_R\ J\sin\phi_ R\ +\ J2\pi FCV_R\\ \ \ \ \ \ \ =I_R\ \cos\phi _R\ +\ J\left(-\ I_R\ \sin\phi_R\ +\ 2\pi FCV_R\right)\end{array}
Voltage drop / phase = \overrightarrow{Is}\overrightarrow{Z}\ =\ \overrightarrow{Is}\ \left(R\ +\ jX_L\right)
Transmission edge voltage = \overrightarrow{Vs}\ =\ \overrightarrow{Vr}\ +\ \overrightarrow{Is}\ \overrightarrow{Z}\ \ =\ \overrightarrow{Vr}\ \ +\ \overrightarrow{Is\ }\left(R\ +\ jX_L\right)
Thus we can determine the voltage V_S of the transmission edge.
Interpretation of vector diagrams in End condenser method
ϕ_R The load current \overrightarrow{I_R} is behind the reference vector \overrightarrow{V_R} . Capacitive current \overrightarrow{I_C} is 90 degrees before the reference voltage \overrightarrow{V_R} . And the sum of the vectors in \overrightarrow{I_S} is the current of the transmission line.
% Voltage regulation = \frac{Vs\ -\ Vr}{Vr}\times\ 100
Transmission efficiency = \frac{Power\ transmission\ each\ phase}{Power\ received\ each\ phase}\times\ 100
Limitations of the medium transmission line in the end condenser method
Although the end condenser method is simple in calculating the transmission line, the following limitations have to be observed in this method.
For example,
1. The calculation error (about 10%) will be caught during the calculation. This is because in this method the capacitance of the whole line is assumed to be concentrated at one end.
2. The effect of line capacitance is taken as excess.
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Frequently Asked Questions
Transmission line that have a lenght of 50 to 150 k.m and tansmission voltage of 20 to 100 kv are colled medium transmission lines.
In this method the total capacitance of the line is captured at the end of the line.
As a result of transposition in the transmission line, the values of inductance and capacitance of each line are equal on voltage regulation and efficiency.
As the load power decreases, the loading current flows in response to the capacitance in the line, So that the voltage at the receiving end is higher then the voltage at the transmission end and the value of voltage regulation is negative.