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In the nominal pi method, the total capacitance of the line is divided into two equal parts centered at the receiver and transmitter ends of the line, and the resistance and inductance are assumed to be distributed midway along the length of the line. which is called the nominal pi ‘π’ method. The figure below shows an equivalent circuit of the nominal pi method.

equivalent circuit of nominal pi method

According to the above circuit in nominal pi method, assume;

V_R = Load voltage per phase,

I_R = Load current per phase,

R = Load resistance per phase,

X_L = Load inductive reactance per phase,

C = Load capacitance per phase,

cos ϕ_R = Receiving end power factor, (lagging)

V_S = Voltage at the sending end,

The following vector diagram is drawn based on the above circuit. where the receiving end voltage \overrightarrow{V_R} is denoted as the reference vector.

Also Read: Nominal T Method of Medium Transmission Line

Nominal-pi-method-vactor diagram

From the above vector in nominal pi method we get,

\overrightarrow{V_R}=V_R\ +j0

Load current, \overrightarrow{I_R}=I_R\ \left(\cos\phi_R-j\sin\phi_R\right)

The charging current at the end connected to the load,

\overrightarrow{I_{C_1}}=j\omega\left(\frac{C}{2}\right)\ \overrightarrow{V_R}\ \ \ =j\pi fC\overrightarrow{V_R}

line current, \begin{array}{l}\overrightarrow{I_L}=\ \overrightarrow{I_R}\ +\overrightarrow{I_{C_1}}\end{array}

The sending end voltage,

\begin{array}{l}\overrightarrow{V_S}=\ \overrightarrow{V_R}\ +\overrightarrow{I_L}\ \overrightarrow{Z}\ \ =\overrightarrow{I_L}\end{array}\left(R+jX_L\right)

The sending end charging current, \begin{array}{l}\overrightarrow{I_{C_2}}=j\omega\left(\frac{C}{2}\right)\ \overrightarrow{V_S}\ \ \ =j\pi fC\overrightarrow{V_S}\end{array}

The sending edge current, \begin{array}{l}\overrightarrow{I_L}=\ \overrightarrow{I_R}\ +\overrightarrow{I_{C_2}}\end{array} 

Nominal pi Method for Medium Transmission Line: Above is shown an equivalent three-phase line circuit and a vector diagram of the nominal ‘π’ method. The above vector diagram is drawn by taking the receiving end voltage V_S as the reference vector.

In the above vector diagram, V_S and V_R are the voltages at the sending end and receiving end. In this method, the total resistance and inductance of each line are divided into two equal parts in the middle of the line and the total capacitance is connected in parallel with the neutral at the sender and receiver ends respectively.

The above figure also shows that I_L R and I_L X_L , is the resistive drop and inductive drop respectively, ϕ_S and ϕ_R is the power factor angle at the transmitting end and receiving end respectively.

Now from the figure it can be seen that, I_s = I_R + I_C . It is divided into two parts viz.- line current, \begin{array}{l}\overrightarrow{I_L}=\ \overrightarrow{I_R}\ +\overrightarrow{I_{C_1}}\end{array} and customer end current, \begin{array}{l}\overrightarrow{I_S}=\ \overrightarrow{I_L}\ +\overrightarrow{I_{C_2}}\end{array} which is below V_R . Adding I_L R and I_L X_L vectorially to V_R gives V_S.

Voltage regulation in nominal pi method

While calculating the voltage regulation the no-load voltage V_R^{\prime} at the receiving end must be calculated keeping the voltage V_S at the transmitting end constant and in that case, the nominal pai “π” method circuit will be of the following form.

no-load circuit of nominal pi method

Now, for the nominal “π” method-

% Regulation = \frac{V_{R^{\prime}}-V_R}{V_R}\times100


% (Efficiency) η = \frac{receiving\ edge\ power}{send\ end\ power}\times100

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