- What is Surge Impedance?
- Surge Impedance Formula (SIL Formula)
- Important Information on Surge Impedance
- What is Surge Impedance Loading (SIL)?
- Factors affecting SIL
- Different Techniques to reduce L
- What is Characteristic Impedance (Zc)?
- Surge Impedance of a Transmission Line
- Application of Surge Impedance Loading (SIL)

**What is Surge Impedance?**

Surge impedance, also referred to as characteristic impedance, is a term utilized in the analysis of the electrical transmission lines.

It is defined as the voltage/current ratio of a moving wave on a line. Surge impedance is especially relevant in the presence of high-frequency signals (or) transient phenomena like as lightning strikes or switching surges.

**Surge Impedance Formula (SIL Formula)**

The formula for surge impedance (Z_{0})

**(Z**_{0}**) = âˆš(L/C)**

Where,

L – Inductance/Length &

C â€“ Capacitance/Length

of transmission line.

Thus, from the given formula, we clearly observe two key conclusions.

- The surge impedance of a transmission line is determined by its inductance and capacitance.
- The surge impedance is independent of transmission line’s length.

In this post, we will explore the concept of surge impedance loading.

**Important Information on Surge Impedance**

- The surge impedance for transmission line (overhead) is 400Î© (Z
_{0}=400Î©). - The surge impedance for underground cables is 40Î© (Z
_{0}=40Î©). - Pure inductors have infinite surge impedance (Z
_{0}=âˆž) since their capacitance is zero. - A pure capacitor has no surge impedance (Z
_{0}=0) since its inductance is zero. - Transformers typically have a surge impedance of around (Z
_{0}=5000Î©).

**What is Surge Impedance Loading (SIL)?**

Surge impedance loading (SIL) can be described as the amount of power delivered when the load connected to transmission line equals the surge impedance.

**Surge Impedance Loading (SIL) = V**_{s}^{2}**/Z**_{0}** (W)**

Where,

V_{s} = source voltage (or) operating voltage, and

Z_{0} = surge impedance.

In other terms, SIL is the megawatt power delivered by a load with an impedance equal to the transmission line’s surge impedance (Z_{0}).

So we can express it as,

**SIL = 3 V**_{ph}** I**_{ph}**cosÏ†**

The load is resistive, therefore cosÏ†=1

**I**_{Ph}** = V**_{ph}**/R = V**_{ph}**/Z**_{0}** = V**_{L}**/âˆš3 Z**_{0}

**SIL = 3Ã—V**_{L}**/âˆš3Ã—V**_{L}**//âˆš3Z**_{0}** = V**_{L}^{2}**/Z**_{0}

**SIL = V**_{R}^{2}**/Z**_{0}**= V**_{S}^{2}**/Z**_{0}**=V**_{S}^{2}**âˆšC/L**

Where

V_{S} and V_{R} represent line voltage

C & L represent phase value

**Factors affecting SIL**

Surge impedance loading (SIL) is proportional to the square of source (or) line voltage.

**SIL âˆž V**_{S}^{2}

SIL is proportional to square root of capacitance.

**SIL âˆž âˆšC**

SIL is inversely proportional to square root of inductance.

**SIL âˆž 1/âˆšC**

**Different Techniques to reduce L**

The different methods to reduce L include:

- By utilizing parallel lines,
- Utilizing series capacitance,
- Using bundled conductor.

**What is Characteristic Impedance (Z**_{c}**)?**

_{c}

It is square root of the ratio of the series impedance to the shunt admittance. It indicates that characteristic is the transmission line’s impedance at any given point.

**Z**_{c}** = âˆšZ/Y**

Where

Z_{c} – Characteristic Impedance

Z – Series Impedance

Y – Shunt Admittance

**Surge Impedance of a Transmission Line**

The surge impedance of a transmission line is an important element in determining wave propagation over the line.

It controls how voltage & current waves react as they move along the transmission line.

Transmission line surge impedance ranges from 200-400Î© based on voltage class, with a phase angle of 0-15 degrees. The table below provides typical HV & EHV overhead transmission line surge impedance values.

Overhead Transmission Lines | Average of Surge Impedance (Z_{0}) | |||

Rated Voltage (kV) | Z_{0} | Surge Impedance Load (MW) | ||

EHV | 69 | 360-393 | 14-13 | ~400Î© |

115 | 370-404 | 35-32 | ||

138 | 371-404 | 51-47 | ||

161 | 379-406 | 68-64 | ||

230 | 365-394 | 145-134 | ||

HV | 345 | 280-366 | 425-325 | ~300Î© |

500 | 233-294 | 1075-850 | ||

765 | 254-266 | 2300-2200 |

For overhead lines, apply the following rule of thumb to calculate series inductance & shunt capacitance.

Overhead Transmission Lines | |||

Average Inductance | Average Capacitance | Average of Surge Impedance (Z_{0}) | |

HV (69kV-230kV) | ~2.1mH/Mile | ~14nF/Mile | ~400Î© |

~1.3mH/KM | ~8.75nF/KM |

**Application of Surge Impedance Loading (SIL) **

- SIL is essential for establishing transmission lines that maintain voltage stability and provide efficient power delivery.