Voltage Regulation of Transmission Lines: Dependencies and Parameters

Key Takeaways

• Line voltage drop, voltage regulation, and transmission efficiency are important factors that govern the performance of the transmission lines.

• The voltage regulation of a transmission line varies with the effect of the line parameters R, L, and C on the line length.

• In a short transmission line, the voltage regulation depends on the line current, load power factor, and line parameters R and  L.

Line parameters such as R, L, and C influence the magnitude of receiving end voltage in the transmission line

In the history of electricity, electric power transmission has been a much-disputed topic. These disputes led to a sequence of events called “ The War of Currents“. The major debate in this “war” centered on the efficiency of Direct Current ❲DC❳ transmission and Alternating Current (AC) transmission systems. Of course, it was not a real battlefield, so no truce between opponents could be announced. Given that, the debate remained alive in the late 19th century. 

In the present day, high voltage AC transmission systems are the widely used approach for transmitting electric power from remotely located generating stations to the sub-stations near densely populated cities. Even though the high voltage AC transmission is economical, the line voltage drop, voltage regulation, and transmission efficiency are serious concerns when designing the transmission line system. 

A voltage drop in a transmission line causes a reduction in the receiving-end voltage ❲ VR❳ compared to the sending-end voltage ❲ VS❳. The voltage difference VS- VRshould be minimal in an economical power transmission system. Voltage regulation is a measure of how much voltage is dropped along the length of the transmission line from the sending end to the receiving end. 

Line Voltage Drop, Voltage Regulation, and Power Transmission Efficiency

The line voltage drop in the transmission line is mainly due to the transmission line parameters— resistance ❲R❳, inductance ❲L❳, capacitance ❲C❳, and shunt conductance ❲G❳. These parameters offer impedance to the flow of current and voltage drops throughout the length of the transmission line.

When the line voltage drop increases, the receiving-end voltage VRdecreases relatively. The voltage regulation is the ratio of the difference in sending-end and receiving-end voltage to the receiving end voltage. Voltage regulation is usually expressed as a percentage:

At no load, the sending-end voltage and receiving-end voltage are equal ❲VS=VR ❳. When the transmission line carries current under loaded condition, the receiving-end voltage VRdecreases from its no-load condition, and the voltage regulation takes a definite positive value. In some cases, the voltage regulation is expressed with the following equation:

whereVNLis the receiving-end voltage at no-load, and VFLis the receiving-end voltage at full-load. No matter how we are describing the voltage regulation, a low value is desired in any transmission line irrespective of the voltage levels and the length of the line.

Among the distributed line parameters, the resistance of the power cables is significant in causing voltage drop and power loss in the line. Since the power losses take up a fair share of the transmitted power, the receiving end power becomes comparatively less.  The ratio of receiving-end power to the sending-end power in an electric power transmission line is called transmission efficiency. Transmission efficiency can be expressed with the following equation:  

where IR and IS represent the receiving-end and sending-end currents respectively. cos Rand cos Sare the receiving-end and sending-end power factors respectively. Generally, the power factor of a circuit is the ratio of the real power used for operations and the apparent power supplied to the circuit. 

From this section, we can conclude that when the line voltage drop increases, the receiving-end voltage decreases and makes voltage regulation a higher value. Similarly, the power dissipation in the line resistance causes a decrease in the efficiency of the power transmission cables. 

Influence of R, L, and C on Transmission Lines

There is a uniform distribution of R, L, and C throughout the length of the transmission line. The series impedance is formed by the resistance and inductance, whereas the capacitance and shunt conductance between the conductors form the shunt impedance. The influence of these line parameters on the voltage regulation varies with the length of the transmission cables. 

The line resistance R is the material property of the power cable conductor. The R values are dependent on physical parameters such as ambient temperature, conductor arrangement in bundled cables, and spiraling of stranded conductors, or the type of metal in the conductor. The frequency of the AC voltage produces a phenomenon known as “skin effect”, which in turn multiplies the line resistance by a factor of 1.02  ❲skin correction factor, k❳ in 60Hz AC transmission system. The presence of current-carrying lines in the vicinity also adds to the resistance of the transmission cable; this applies most in three-phase transmission lines.

The magnetic and electric fields associated with the current-carrying transmission lines govern the line parameters: series inductance L and shunt capacitance C. The geometrical arrangement of the transmission cable also plays an important role in distributing the reactance parameters along the transmission line length.

The shunt conductance G is counted only when there is leakage current flow in the transmission line. The G parameter is responsible for the leakage current flow between the conductors and the ground. As the leakage current is very small compared to the line current in the electric transmission lines, shunt conductance G is normally neglected in transmission line modeling. 

Table.1 Classification of transmission line and the line parameters considered in its modeling

Transmission Line Modeling

Transmission line modeling is an important step towards achieving better voltage regulation and transmission efficiency. These transmission models usually present an equivalent circuit of the actual transmission line. These models give us better insight into the behavior of the transmission lines. The overhead transmission lines are modeled using the line parameters R, L, and C to analyze performance and determine voltage drop, voltage regulation, and transmission efficiency. The effects of line parameters on the transmission system differ with voltage grade and length of the transmission line. Table 1 gives the classification of overhead transmission lines and the line parameters considered in the modeling.

Voltage Regulation of a Single-Phase Short Transmission Line 

As demonstrated in Table 1, the capacitance effect is ignored in the short transmission line. The line resistance and inductance are taken as lumped parameters, instead of being uniformly distributed. Consider a single-phase short transmission line. The sending-end voltage VSis supplying a current of I Ampere, at a power factor ofcos S. R and XLare the transmission line resistance and reactance respectively (of both phase and neutral conductor). The receiving-end voltage VRand current I are at a lagging power factor of cos R. 

From the phasor diagram of an equivalent transmission line model, the sending-end voltage can be written using the method of components as

For the calculation of voltage regulation, the magnitude of VSis given by the real part of the equation (4). The imaginary part of VSis very small and is neglected. If you don't want to approximate the voltage regulation,  you can include the imaginary part while calculating the magnitude of the sending-end voltage VS. The voltage regulation of the single-phase short transmission line is given by the equation:

If we can model the transmission lines with the line parameters distributed along the length, the line voltage drop and voltage regulation will be more accurate. These models help power system engineers re-invent transmission line engineering in such a way that required voltage is received at sub-stations, with minimum loss along the line length. The present-day power system simulation tools save time and money, and establish the pre-feasibility of the transmission line system design.