Characteristic and Surge Impedance Variation Impact on Transmission Line Performance

Modeling of power systems is essential to perform various network analyses. Voltage regulation, line losses and transmission line efficiency are greatly affected by transmission line parameters. Hence, accurate modeling of transmission line is required. The aim of this paper is to study the impact of characteristic and surge impedances on voltage profile, voltage regulation and transmission line efficiency.


INTRODUCTION
Modeling of power systems is essential in order to perform various power system analyses such as load flow studies, short circuit calculations, contingency analyses and transient analyses. Electric power generation, transmission and distribution networks need to be modeled carefully for accurate results. This paper aims to study the effect of characteristic and surge impedance on transmission line performance; therefore, accurate modeling of transmission lines are considered.
In general, a "per-phase" model is used to represent equivalent circuits of transmission lines with appropriate circuit parameters. Depending on the length of the line, three different models are considered. Short transmission line model for length less than 80 km (50 mile) long, medium transmission line model for length between 80 km (50 mile) and 240 km (150 mile) long and long transmission line model for transmission lines longer than 240 km (150 mi) [1]- [5].
All lines are made up of distributed series resistance and inductance as well as shunt capacitance and conductance. They are called line parameters and denoted as R, L, C, and G. The most important parameters are R, L and C as they impact voltage drop, line losses and overall transmission line efficiency [6]- [9].
The paper is organized as follows. Short introduction regarding transmission line is given in Section 1. Modeling of transmission lines is discussed in Section 2. Section 3 describes transmission line voltage regulation and efficiency. The effects of characteristic impedance on transmission line performance are discussed in Section 4. The impacts of surge impedance on transmission line performance are introduced in Section 5. Summary and conclusion are discussed in Section 6.

MODELLING OF TRANSMISSION LINES
The generalized circuit constants commonly known as ABCD constant are used to draw the relationships between sending-and receiving-end voltages and currents as follows [2]- [6], [10]- [14]. (1) It can be written in a matrix form as follows. (3) The total series impedance of the line per phase is given by multiplying the series line impedance per unit length by the total length of the line.

(4)
Where z is the series line impedance per unit length. r is the per-phase resistance per unit length. L is the per-phase inductance per unit length.
 is the angular frequency.
 is the line length.
For short transmission lines, the impact of the line capacitance is negligible. Notwithstanding, for medium and long lines, the capacitance of the transmission lines should be considered.
Where g is the shunt conductance per unit length. C is the line to neutral capacitance per unit length. Y is the total shunt admittance per phase to neutral.
The ABCD constant for long transmission lines are given by: The characteristic impedance Zc is given by: (11) Therefore, By rearranging the two equations and using the identity: (14) One can obtain the equivalent π model for long transmission lines as: Where (17) (18) Figure 1 shows the equivalent π model for long transmission line [2].

TRANSMISSION LINE VOLTAGE REGULATION AND EFFICIENCY
Transmission-line voltages vary depending on load condition. During light load conditions, the voltage is high while it is low during heavy load conditions. Voltage regulation refers to the change in line At no-load, IR=0; therefore, from (12). (20) The sending-end and receiving-end powers are: Transmission line efficiency (η) is given by [2], [3]. (23)

RESULTS AND DISCUSSION
In order to study the effects of the characteristic impedance on the transmission line performance a 380 kV, 60 Hz, 300 km long transmission line is considered. The line transmits a 1000 MVA at 0.8 power factor. The line parameters are r=0.016Ω/km, L=0.97 mH/km, C=0.0115 μF/km and g=0. Z c increases as r and L increase in steps of 5%.

Effects of characteristic impedance on transmission line performance
The relationship between the characteristic impedance and receiving-end voltage is shown in Figure 2. It can be shown that increasing the characteristic impedance from about 285.4 to 346.3 Ω increases the receiving-end voltage from 278.5 to 330.6 kV.
Which is commonly known as the surge impedance. Figure 5 illustrates that increasing the surge impedance from 290.4 to 355.7 Ω also increases the receiving-end voltage from 291.1 to 346. Figure 6 proves that increasing the surge impedance from 290.4 to 355.7 Ω decreases the percentage voltage regulation by about 43.8%. As r=0 and g=0, there is no power losses in the transmission line. Hence, P r =P s and the transmission line efficiency in this case is always 100%.

CONCLUSION
Transmission lines constitute an integral part of power systems and the accuracy of many analyses such as load flow studies, short circuit calculations, contingency and transient analyses depend on the accurate modeling of the transmission lines. It has been proved in this paper that increasing the characteristic impedance or the surge impedance increases the receiving-end voltage. Furthermore, increasing the characteristic impedance or the surge impedance decreases the percentage voltage regulation. Moreover, increasing the characteristic impedance reduces the transmission line efficiency linearly.