# Efficiency | Voltage Regulation of Transmission Line

When a transmission line supplies a load current, there is a voltage drop in the line due to resistance and inductance (inductive reactance) of line. Therefore, receiving end voltage VR is generally less than the sending end voltage VS.

This voltage drop in the line is expressed as a percentage of receiving end voltage VR and is called voltage regulation.

# Voltage Regulation of Transmission Line

The rise in voltage at receiving end voltage when the full load is thrown off; the sending end voltage remaining the same, is called voltage regulation of transmission line.

Percentage regulation, % Reg. = [(VS –VR)/VR] 100

The expression for voltage regulation of a short transmission line is given as:

% Reg. = [(IRcos φR+ IXLsin φR)/VR] 100 ………. for lagging p.f.

% Reg. = [(IRcos φRIXLsin φR)/VR] 100 ………. for leading p.f.

It is desirable that the voltage regulation of transmission line should be low.

## Effect of Power Factor on Voltage Regulation of Transmission Line

The voltage regulation in transmission line depends upon the load power factor very much. The expression for regulation of a short transmission line is given as:

% Reg. = [(IRcos φR+ IXLsin φR)/VR] 100 ………. for lagging p.f.

% Reg. = [(IRcos φRIXLsin φR)/VR] 100 ………. for leading p.f.

Hence the voltage regulation of transmission line depends upon the value of IRcos φR and IXLsin φR. The following conclusions can be drawn from the above expression:

• In the case of inductive loads, for a fixed value of VR and I, the voltage regulation of the line increases with the decrease in p.f.
• In the case of capacitive loads, for a fixed value of VR and I, the voltage regulation of the line decreases with the decrease in p.f.
• When the load p.f. is lagging or unity or such a leading that IRcos φR > IXLsin φR, then voltage regulation is positive i.e. the sending end voltage VS is more than the receiving end voltage VR.
• When the load p.f. is such a leading that IRcos φR < IXLsin φR, then voltage regulation is negative i.e. the sending end voltage VS is less than the receiving end voltage VR.

# Efficiency of a Transmission Line

When the load is supplied there are line losses due to the resistance of the line conductors. Therefore, the power received at receiving end is always less than the sending end voltage.

The ratio of receiving end power to the sending end power of a transmission line is called the transmission efficiency of the line. The efficiency of a 3-phase transmission line can be calculated by using the expression below:

Transmission efficiency of a 3-phase transmission line, % ἠ = (Receiving end power/Sending end power)/100

% ἠ = [(Receiving end power/ (Receiving end power + losses)]/100

% ἠ = [(3VR IcosφR) / (3VR IcosφR + 3I2R)]/100

Where,
VR = Receiving end voltage (phase value).
cos φR = Receiving end power factor.
R = Transmission line resistance per phase.

## Effect of Load Power Factor on Efficiency

The efficiency of a transmission line depend to a considerable extent upon the load power factor.

The power delivered to the load is given by the expression:

P = 3VR Icos φR ………….three phase.
Or I = P ÷ 3VRcos φR.

Thus, for a constant amount of power and voltage at the receiving end, the line current is proportional to the load power factor. Consequently, with the decrease in load power factor, line current and hence line losses are increased.

Thus, the efficiency of the transmission line decreases with the decrease in load power factor.

# Classification of Transmission lines

The transmission line performance depends upon the three parameters R, L, and C. These three parameters are distributed uniformly along the whole length of the line. The resistance and inductance form the series impedance and the capacitance exists between the line conductor and earth conductor. To know the transmission line performance, it is required to know the manner in which capacitance is taken into account and accordingly the overhead transmission lines are classified as:

• Short transmission lines.
• Medium transmission lines.
• Long transmission lines.

## Short Transmission Line

When the length of an overhead transmission line is below 60 km and the line voltage is low (below 20 kV), it is usually considered as a short transmission line.

Due to the smaller length and lower voltage of the line, the capacitance effects of the line are extremely small and hence can be neglected. Therefore, while studying the short transmission line performance, only resistance and inductance of the line are taken into account.

Therefore, regulation of short transmission lines depends upon its resistance and inductive reactance.

## Medium Transmission Line

When the length of an overhead transmission line is about 60 to 150 km and the line voltage is high (20 to 100 kV), it is usually considered as a medium transmission line.

Due to sufficient length and voltage of line, the capacitance effects are also taken into account while studying the medium transmission line performance. Though capacitance is uniformly distributed over the entire length of the line yet reasonable accuracy is obtained by considering the capacitance of such a line lumped at one or more places.

## Long Transmission Line

When the length of an overhead transmission line is more than 150 km and the line voltage is very high (more than 100 kV), it is usually considered as long transmission line. To study the performance of such a line, the line constants are considered uniformly distributed over the whole length of the line and rigorous methods are employed for the solution.

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