Overhead Line Lightning Strike Severity and Probability

Lightning Phenomenon:

Lightning Strike is the discharge of electric charge accumulated in the clouds to the ground. Clouds accumulate typically the negative charge, and in response the ground produces the counter charge: the positive charge. Electric discharge happens between the two, i.e. clouds and the ground, under certain electric discharge conducive conditions, effectively creating the shortest electrical path.  These conditions include accumulated charge density, humidity in the air (enabling faster dielectric break down), ground elevation (buildings, mountains, tall living things) etc.

Physics behind this phenomenon is much elaborated in several books and articles found in both libraries and internet, and their perusal is recommended.

Lightning Strike Frequency:

Although the frequency of lightning strikes might vary year to year, long term (usually many years to decades) maintained records give a statistical approximate number of expected strikes each year. This is usually referred as Isokeraunic Level [1]. Reference [2] and [3] give typical Isokeraunic Levels around the world, and gives a geography dependent empirical formulae to calculate Ground-Flash Density (or – Strike Density). The empirical relationship between Isokeraunic Level and Ground-Flash Density for UK is given as:

Where, GFD is the Ground-Flash Density in ,  is a factor that varies between , b is a factor that varies between , and  is the Isokeraunic Level in . Isokeraunic Level for Ireland, north UK, mid-west UK  and southern-west UK is typically between 5-10, while for middle-east UK and southern-east UK is between 10-20.

Overhead Hit Frequency:

Strike radius is the scope of the ground elevated structures or ground itself that will be exposed to lightning. This, usually calculated in meters, is very much dependent of lightning strike peak current magnitude.

Lightning strike distance in meters [3],

Where, is the Lightning Strike peak magnitude in kA.

Now, the scope of Lightning Strike area that will hit the OHL will depend on the tower structure. For a un-shielded wood pole structure (assuming all conductors are same height from the ground level), this is given as following:

Strike Area,

Where,  is the sum of strike radius of left most conductor, distance between the farthest conductors, and strike radius of the right most conductor respectively. $latex L$ is the length of the exposed overhead line.

Total estimated OHL Flashes per Year if every flash was as chosen Strike Current, , is given as,

For a given strike current, Cumulative Lightning Strike Probability is given as [3],

For a given strike current, Estimated Annual OHL Lightning Strikes in (Flashes/Yr) =

Now plot a bar chart between various strike current versus expected annual lightning strike frequency, and you see typical decline of Flashes/Yr with increasing strike current magnitude. And if you invert the Flashes/Yr you get expected number of years before you get see a lightning strike for a given strike current peak.

References:

1. Lightningtech Website. [online], Available: http://www.lightningtech.com/d~ta/faq2.html, Accessed: Oct 2009.
2. Chowddhuri, P., Electromagnetic Transients in Power Systems, Exeter: Research Strudies Press Ltd., 1996.
3. Grigsby, L. L., Power Systems, Boca Raton: CRC Press, 2007.

Per Unit Formulae and Conversions

Even the best of the power systems Geeks sometime stumble at the basics. Here are some per unit formulae to brush up if you are one of them or among those willing to learn like me.

A per unit value is a scaled factor of the measured system parameter to the chosen system base value. In other words, the chosen value becomes by which all other values for consider system parameter will be compared. It’s a ratio and is a unit less quantity.

Most common approach, for most studies, is to choose a system apparent power base (typically 100MVA) and system local network voltage (line to line voltage) base values and base values for all other parameters can be estimated there after.

Base Value Calculation:

         (1)

        (2)

        (3)

Per Unit Calculation:

        (4)

        (5)

         (6)

Per Unit Conversion:

        (7)

References:

1. Wikipedia, Per Unit System, Wikipedia. [online]. Available: http://en.wikipedia.org/wiki/Per-unit_system. [Accessed: Sep. 19, 2009].
2. W. D. Stevenson, Jr., Elements of Power System Analysis, 3rd ed. New York: McGraw-Hill, 1994.

Power Factor Capacitor Discharge Resistor Design

When a Power Factor Capacitor (PFC) step, a single unit in a bank of several capacitors, is disconnected or switched off, the discharging resistor connected across the capacitor will discharge it to designed retained voltage value in discharge time seconds. Typical discharge resistor ratings for a given power factor capacitor  in μF or MVAR include: maximum normal operation system voltage  in kV and required retained discharge voltage  in Volts (around 50V) at discharge time  in seconds (usually <60s). The discharge resistor  in kΩ  is given as,

         (1)

Depending whether the PFC bank step is star or delta connected (usually star connected), for given system frequency  and capacitor step’s rated reactive power output in MVAR, the capacitor step’s capacitance  in μF is given as:

• If star connected,
• If delta connected,

Explanation:

Capacitor voltage decay across the resistor is given as, . Rearrange this for Discharge Resistor ‘R’ and you get (1). Simple!

Power Factor Capacitor Detuning

Power Factor Capacitor (PFC) banks are commonly detuned to specific frequencies to reduce or remove harmonic resonances. This is done by introducing a detuning reactor in series with the capacitor cluster at each three phase leg.

At the detuning frequency, detuning reactor will have the same impedance as the PFC capacitance per phase leg, i.e. .

Detune reactor inductance is then given as: Henry

Where, is the PFC detune frequency and C is the PFC capacitance per phase leg.

R and X Values from given Grid Parameters

Wondering how to calculate R and X values from given X/R ratio, system voltage and fault level (kA or MVA) information at a power system node or bus? Here’s how.

Lets define, X/R ratio as: .

Then the node or bus thevenin equivalent resistance and reactance are given as:

,

Where, ‘R’ is the thevenin equivalent resistance in Ω, ‘X’ is the thevenin equivalent reactance in Ω, ‘V’ is the system voltage is kV, ‘S’ RMS break fault power in MVA, ‘I’ RMS break fault current in kA.

RMS break fault level power and current relation is given as:

Download spreadsheet to do the Math.

Explanation:

Thevenin’s equivalent impedance is given as,

        →          (1)

Substituting in (1) gives,

          →          (2)

Also,        →          (3)

From (1) and (3), 

=>         →          (4)

And          →          (5)