Line Lightning Performance (LLP) Analysis for Transmission Lines – Complete Technical Guide with Numerical Example

A professional engineering reference covering shielding failure, backflashover, CIGRE/IEEE methods, and full worked calculations using real numerical values.

1. Introduction

Line Lightning Performance (LLP) quantifies how often a transmission line experiences flashovers due to lightning. It is typically expressed in:

Flashovers per 100 km per year

LLP analysis is essential for predicting outage rates, optimizing shielding, grounding, tower geometry, and ensuring compliance with reliability targets such as:

• 69–115 kV lines: 3–6 outages /100 km-year
• 138–230 kV lines: 1–3 outages /100 km-year
• 345–500 kV lines: < 1 outage /100 km-year

This guide provides a full technical explanation of LLP analysis based on CIGRE, IEEE, and Eriksson models, using a 230 kV transmission line with actual numerical values.

2. Types of Lightning Flashovers

2.1 Backflashover (BF)

Occurs when lightning strikes the tower or ground wire, raising the tower potential enough to flash over the insulator string.

Lightning → Tower → High Tower Voltage → Insulator Flashover

2.2 Shielding Failure Flashover (SFF)

Occurs when lightning bypasses the shield wire and strikes the phase conductor directly. This depends on shielding angle, conductor height, and striking distance.

Lightning → Misses Ground Wire → Hits Conductor → Flashover

3. Key Input Parameters for LLP

Parameter	Description	Example Value
Ng	Ground flash density	12 flashes/km²-year
h	Tower height	40 m
hs	Shield wire height	42 m
hc	Conductor height	32 m
ρ	Soil resistivity	400 Ω·m
Rt	Tower footing resistance	15 Ω
θ	Shielding angle	25°
CFO	Critical flashover voltage	1050 kV

4. Lightning Stroke Current Distribution

Lightning current follows the well-known IEEE distribution:

P(I > i) = exp(-i / 31)

Where 31 kA is the median current.

5. Shielding Failure Flashover (SFF) Calculation

5.1 Striking Distance (Eriksson Model)

Rs = 10 * I^0.65

Where Rs = lightning striking distance.

5.2 Critical Current for Shielding Failure

Using Eriksson’s geometry:

I_crit = ((hs - hc) / 10)^(1 / 0.65)

Using example values:

• hs = 42 m
• hc = 32 m

I_crit = ((42 - 32) / 10)^(1/0.65)
       = (1)^1.538 = 1 kA

Meaning any lightning stroke above 1 kA can theoretically hit the conductor unless shielding is adequate.

5.3 SFF Rate

SFF = Ng * P(I > I_crit) * L

Compute P(I > 1):

P = exp(-1 / 31) = 0.968

Assume exposure width L = 0.03 km.

SFF = 12 * 0.968 * 0.03 = 0.35 flashovers/100 km-year

6. Backflashover (BF) Calculation

6.1 Tower Surge Voltage

V_tower = I * Rt

Flashover occurs when:

V_tower > CFO

With Rt = 15 Ω, CFO = 1050 kV:

I_BF = 1050 / 15 = 70 kA

6.2 Probability of Current Exceeding 70 kA

P(I > 70) = exp(-70 / 31) = exp(-2.26) = 0.104

6.3 Number of Tower Strokes (per 100 km)

N_t = Ng * (0.1h + 3) * 100

N_t = 12 * (0.1*40 + 3) * 100
N_t = 12 * 7 * 100 = 8400 strokes/100 km-year

For a 350 m span:

Towers per 100 km = 100,000 / 350 = 285 towers

6.4 Backflashover Rate

BF = (N_t / Towers) * P(I > 70)

BF = (8400 / 285) * 0.104 = 29.47 * 0.104 = 0.0876 flashovers/100 km-year

7. Total Lightning Performance (LLP)

LLP = SFF + BF
LLP = 0.35 + 0.0876 = 0.4376 flashovers/100 km-year

Interpretation

A value of 0.44 flashovers/100 km-year represents excellent lightning performance for a 230 kV line. Most utilities target:

• < 3 for 115 kV
• < 1–2 for 230 kV
• < 1 for 345–500 kV

8. Methods to Improve Lightning Performance

• Reduce tower footing resistance (target <10 Ω)
• Improve shielding angle (from 25° → 15°)
• Raise ground wire height
• Add a second shield wire
• Increase insulator string length (higher CFO)
• Install Line Surge Arresters (LSA) in problematic spans

9. Summary of Example Results

Parameter	Value
Ng	12 flashes/km²-year
Shielding angle	25°
Tower footing resistance	15 Ω
BIL (CFO)	1050 kV
SFF	0.35
BF	0.0876
Total LLP	0.44 flashovers/100 km-year

This design meets strict reliability standards for 230 kV overhead transmission lines.