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The study of lightning predates electric power systems by many centuries. Observations of thunder were maintained in some areas for more than a millennium. Franklin and others established the electrical nature of lightning, and introduced the concepts of shielding and grounding to protect structures. Early power transmission lines used as many as six overhead shield wires, strung above the phase conductors and grounded at the towers for effective lightning protection. Later in the twentieth century, repeated strikes to tall towers, buildings, and power lines, contradicting the adage that "it never strikes twice," allowed systematic study of stroke current parameters. Improvements in electronics, computers, telecommunications, rocketry, and satellite technologies have all extended our knowledge about lightning, while at the same time exposing us to ever-increasing risks of economic damage from its consequences.
1 Ground Flash Density
The first return stroke from the direct termination of a negative, downward cloud-to-ground lightning flash is the dominant risk to power system components. Positive first strokes, negative subsequent strokes, and continuing currents can also cause specific problems. A traditional indicator of cloud-to-ground lightning activity is given by thunder observations, collected to World Meteorological Organization standards and converted to Ground Flash Density:
TD is the number of days with thunder per year
TH is the number of hours with thunder per year
GFD is the number of first cloud-to-ground strokes per square kilometer per year
Long-term thunder data suggest that GFD has a relative standard deviation of 30%.
Observations of optical transient density have been performed using satellites starting in 1995. These data have some of the same defects as thunder observations: cloud flash and ground flash activity is equally weighted and the observations are sporadic. However, statistical considerations as well as richly detailed observations of orographic terrain features now favor the use of optical transient density, reported by (Christian et al., 2003; NASA, 2006) over thunder observations to estimate ground flash density.
A good estimate of ground flash density can be obtained by dividing the optical transient density values in FIG. 1 by a factor of 3.0. This average factor is valid in four different continents but may vary across regions, calling for a lower factor in some limited areas where storms have a higher ratio of positive to negative flashes.
TABLE 1 Typical Design Approaches for Overhead Transmission Lines Optical Transient Density from FIG. 1 (Transients per km^2 per Year) Ground Flash Density Range (Flashes per km^2 per Year)
Typical Design Approaches
0.3-1 0.1-0.3 Unshielded, one or three-pole reclosing 1-3 0.3-1
Single overhead shield wire or unshielded with line arresters, upper phases, all towers 3-10 1-3
Two overhead shield wires 10-30 3-10
Two overhead shield wires with good grounding or line surge arresters 30-100 10-30
- - -
Three or more overhead and underbuilt shield wires with good grounding; line surge arresters; underground transmission cables
Electromagnetic signals from individual lightning strokes are unique and have high signal-to-noise ratio at large distances. Many single-station lightning flash counters have been developed and calibrated, each with good discrimination between cloud flash and ground flash activity using simple electronic circuits. It has also been feasible for more than 30 years to observe these signals with two or more stations, and to triangulate lightning stroke locations on a continent-wide basis. Lightning location networks have improved continuously to the point where multiple ground strikes from a single flash can be resolved with high spatial and temporal accuracy and high probability of detection (CIGRE, 2009). A GFD value from these data should be based on approximately 400 counts in each cell to reduce relative standard deviation of the observation process below 5%. In areas with moderate flash density, a minimum cell size of 20 × 20 km is appropriate.
2 Mitigation Methods
Lightning mitigation methods for transmission lines need to be appropriate for the expected long-term ground flash density and power system reliability requirements. Table 1 summarizes typical practices at five different levels of lightning activity to achieve a reliability of 1 outage per 100 km of line per year on an HV line.
Power system insulation is designed to withstand overvoltages that are generated within the power system, under steady state and also when components are switched. Unfortunately, even the weakest direct lightning stroke from a shielding failure to a phase conductor will cause an overvoltage that will flash over across an insulator that is not protected by a surge arrester nearby. Once an arc appears across an insulator, the power system fault current keeps this arc alive until voltage is removed by protective relay action. If the flash incidence is low, Table 1 shows that some utilities can simply accept a high tripout rate, up to 6 interruptions per 100 km per year, and can protect against the consequences using automatic reclosing and redundant paths.
Effective overhead shielding, with wires placed above the phase conductors to intercept flashes and divert them to ground, is the most common form of lightning protection on transmission lines in areas with moderate to high ground flash density.
When the overhead shield wire is struck, the potential difference on insulators is the sum of the resistive and inductive voltage rises on the tower, minus the coupled voltage on the phase conductors. The potential difference can lead to a "back-flashover" from the tower to the phase conductor.
Back-flashover is probable when peak stroke current is large, when footing resistance is high and when insulation strength is low. Simplified models (CIGRE, 1991; IEEE, 1997; EPRI, 2005) are available to carry out the lightning overvoltage calculations and coordinate the results with insulator strength, giving lightning outage rates. A schematic of this process is given as follows.
3 Stroke Incidence to Power Lines
The lightning leader, a thin column of electrically-charged plasma, develops from cloud down to the ground in a series of step breakdowns. Near the ground, electric fields are high enough to satisfy the conditions for continuous positive leader inception upward from tall objects or conductors. Analysis of a single overhead conductor with this approach leads to…
…where NS is the number of strikes to the conductor per 100 km of line length per year h is the average height of the conductor above ground in meters…
In areas of moderate to high ground flash density, one or more overhead shield wires are usually installed above the phase conductors. This shielding usually has a success rate of greater than 95%, but adds nearly 10% to the cost of line construction and also wastes energy from induced currents. The leader inspection model has been developed to analyze shielding failures more accurately.
The goal was to reduce the failure rate below the IEEE set reliability target of 0.05 per 100 km per year (IEEE, 1997).
4 Stroke Current Parameters
Once the downward leader contacts a power system component through an upward-connecting leader, the stored charge will be swept from the channel into a grounded object through a plasma channel with high internal impedance of 600-4000 Ohm. With this high source impedance relative to the impedance of grounded structures, an impulse current source model is suitable.
Berger (1977) made the most reliable direct measurements of current and charge flow from negative downward cloud-to-ground lightning parameters on an instrumented tower from 1947 to 1977.
Additional observations have been provided by many researchers and then summarized (Anderson and Eriksson, 1980; CIGRE, 1991; Takami and Okabe, 2007). The overall stroke current distribution can be approximated as lognormal with a mean of 31 kA and a log standard deviation of sln(I) = 0.48. The probability of exceeding a first return stroke peak current magnitude I can also be estimated from (CIGRE, 1991; IEEE, 1997; EPRI, 2005; IEEE, 2010):
The peak stroke current associated with a given probability level P can be obtained by inverting Equation 4 to obtain...
This leads to the following probability table.
TABLE 2 Probability of Exceeding First Return Stroke Current in Lightning Flash
Table 2 suggests that there will be a 15% chance that the first negative return stroke peak current will exceed 60 kA, and an 85% chance that it will exceed 16 kA.
The waveshape of the first return stroke current rises with a concave front, giving the maximum steepness near the crest of the wave, then decays with a time to half value of 50 µs or more. The median value of maximum steepness (CIGRE, 1991) is 24 kA/µs, with a log standard deviation of 0.60. Steepness has a strong correlation to the peak amplitude (CIGRE, 1991; Takami and Okabe, 2007) that allows simplified modeling using a single equivalent front time (peak current divided by peak rate of rise).
The mean equivalent front is 1.4 µs for the median 31 kA current, and increases to 2.7 µs as peak stroke current increases to the 5% level of 100 kA. An equivalent front time of 2 µs is recommended for simplified analysis of lightning performance (CIGRE, 1991; IEEE, 1997) with peak currents in the range of 50-150 kA.
5 Calculation of Lightning Overvoltage on Grounded Object
The peak voltage resulting from a lightning flash can be estimated from the sum of two components, the resistive voltage rise of the nearest ground electrode VR and the inductive voltage rise VL. The voltage rise VL associated with conductor and tower series inductance L and the equivalent front time (?t = 2 µs) ...
... is VL = LI/?t. The VL term will add to, and sometimes dominate, VR.
7 Calculation of Inductive Voltage Rise VL
Lumped inductance of a structure can be approximated from the expression…
L is the inductance in Henries
Z is the element antenna impedance in ohms
h is the wire height above conducting ground (m)
r is the wire or overall structure radius (m)
l is the length of the wire or structure (m)
c is the speed of light (3 × 10^8 m/s)
In numerical analyses, series and shunt impedance elements can be populated using the same procedure. Tall transmission towers have longer travel times t and thus higher inductance, which further exacerbates the increase of stroke incidence with line height. Thin steel pole structures, and wooden poles with bond wires of small radius r, will also have higher inductance than lattice towers with multiple paths to ground, giving a larger overall radius. The inductance of structures with guy wires is given by the parallel combination of the inductance of the central structure and the inductances of the individual guy wires, ignoring mutual coupling (CIGRE, 1991).
8 Calculation of Voltage Rise on Phase Conductor
The high electromagnetic fields surrounding any lighting flash illuminate nearby conductors and cause the flow of current, leading to induced voltages across insulators.
Fields from vertical lightning strokes to ground near overhead lines can induce overvoltages with 100-300 kV peak magnitude in nearby overhead lines without a direct flash termination. This is a particular concern only for MV and LV systems (IEEE, 2010).
In the case of a lightning flash directly to an overhead groundwire (OHGW), a small fraction of the overall current flows in horizontal directions, away from the flash location into every interconnected ground wire, shield wire beneath the phases and any phase conductor protected by a parallel line surge arrester. The voltage rise on each participant in this current flow increases common-mode voltage and reduces differential voltage across insulators through transverse electromagnetic (TEM) or surge impedance coupling to insulated phases. Bundle configurations and corona can improve this desirable surge-impedance coupling to mitigate half of the total tower potential rise (VR + VL), but increasing separation between the phases and ground wires will reduce the effect.
Calculation of the coupling coefficients Cn on the undriven, unprotected phase conductors calls for registering the self and mutual surge impedances of each phase and groundwire, setting the voltage on the stricken conductors to unity and calculating the potential rise on undriven phases from the inverse of the resulting surge impedance matrix. Simplified methods for systems with one or two overhead groundwires (CIGRE, 1991; IEEE, 1997) consider voltage dependent corona effects as well as bundle conductor impedance.
The combined peak stress on an insulator under lightning surge conditions, VPk (kV), with a linear front time ?t of 2 µs, can be approximated by…
IPk is the peak first return stroke current (kA)
Cn is the surge impedance coupling coefficient from n groundwires, modified for corona effects
n is the number of groundwires, including OHGWs, underbuilt OPGW, and neutral wires and phases protected with line surge arresters
ZGW is an average value of surge impedance of the groundwires (Ohm)
Rf is the resistance of the stricken tower to ground from Equation 6 (Ohm)
L is the inductance of the stricken tower from insulator location to ground (H) from Equation 7
9 Joint Distribution of Peak Voltage on Insulators
Since the peak stroke current and the resistivity at the base of a tower are statistically independent, the joint distribution of their voltage stress levels can be obtained by summing over the probability of all possible events.
Table 4 shows that the voltage stress on a transmission line insulator varies by a 50:1 range as a result of statistical variations in lightning peak current magnitude and tower-to-tower changes in soil resistivity.
Electrical utilities will often install additional buried grounding electrodes, such as vertical rods or radial counterpoise wires a meter below grade, at towers that have high soil resistivity. Construction specifications may call for achieving "20 Ohm resistance where practical." Thus, the distribution of footing resistance Rf in Table 4 is modified by a "treatment rule" that follows this general model:
• If Rf < 20 Ohm, do nothing.
• If 20 Ohm < Rf < 40 Ohm, install enough grounding to reduce to 20 Ohm.
• If Rf > 40 Ohm, install enough grounding to reduce Rf by factor of 2.
This treatment strategy will improve the line outage rate as shown hereafter.
10 Insulation Strength
The lightning impulse flashover gradient (kV CFO per meter of dry arc distance) of typical transmission line insulator strings is linear over a wide range from 1 to 6 m. The critical flashover level (CFO) is the median voltage at which flashover occurs when tested with a standard lightning impulse voltage wave with 1.2 µs rise time and 50 µs time to half value, and is normally distributed with a relative standard deviation of about 5%. The CFO for full lightning impulse voltage waves scales linearly with insulator string dry arc distance as shown in Table 6.
The probability of flashover with 5% relative standard deviation can be approximated conveniently by Equation 11. For example, with VPk = 1136 kV applied to insulation having CFO = 1080 kV, the probability of flashover is 85%. However, accurate normal distribution functions are readily accessible in spreadsheets such as Excel and should be used where available:
The lightning impulse flashover voltage has a pronounced nonlinear volt-time characteristic, giving an increasing ability to withstand short-duration impulses at times t less than 10 µs compared to the full wave CFO strength of 540 kV/m. The lightning surge itself peaks in an equivalent front time of about 2 µs. A simplified method may evaluate the possibility of flashover at this time t, resulting in a fixed strength of 822 kV per meter of dry arc distance DDry Arc based on a volt-time characteristic as follows:
DDry Arc is the dry arc distance of the insulator (m), in the range of 1-6 m
t is the time of flashover (µs), in the range of 0.3-14 µs
CFO is the peak of the applied standard lightning impulse voltage wave (kV) that causes a flashover 50% of the time;
A volt-time curve approach such as Equation 12 remains valid up to the point in time when the applied voltage wave deviates significantly from the standard test wave. In the case of transmission lines, this point is well defined as the time at which cancelling reflections from the ground electrodes of nearby towers arrive, after a propagation time tSpan associated with 90% of the speed of light, c. Table 7 shows that the span length can thus change the critical flashover voltage by ±10%, leading to about ±30% changes in the predicted line outage rate.
11 Calculation of Transmission Line Outage Rate
The lightning outage rate of a transmission line is given by the number of flashes to the line, Equation 3, multiplied by the probability of flashover of each flash. Tables 4 and 5 have shown how the distribution of peak backflashover voltage stress across insulation varies for the probability distribution of peak first return stroke current Ipk and footing resistance Rf , considering that other factors such as tower inductance Ltwr, number of OHGWs n, and the related coupling coefficient Cn in Equation 10 are all fixed. Tables 6 and 7 give the insulation characteristics as a function of insulator dry arc distance DDry Arc and span length, which can also be calculated with Equation 12 for a particular line design or section. Thus, the calculation of a line outage rate simplifies into a calculation of the probability of flashover for each element in Table 4 or 5, summed over the entire range of probability as illustrated in FIG. 2.
Computer programs and methods for calculating lightning outage rates (CIGRE, 1991; IEEE, 1997; Hileman, 1999) make use of the simplified concepts illustrated in FIG. 2, but adding in calculation details related to…
• Automatic calculation of individual conductor surge impedances ZGW and coupling coefficients Cn at each phase conductor, incorporating nonlinear increase in Cn with increasing tower top voltage;
• Automated analysis of the risk of a shielding failure and consequent flashover from a direct lightning flash to a phase conductor;
• Integration of line voltage bias for every degree of phase (0°-360°) to establish the proportion of back flashover failures among phases;
Advanced computer models are available to compute the possibility of multiple-phase or multi-circuit back flashover, and also to investigate the effects of applying transmission line surge arresters across selected insulators to limit their overvoltage stress and increase coupling coefficients on unprotected phases as suggested in (CIGRE, 2010).
12 Improving the Transmission Line Lightning Outage Rate
There are a number of options that affect the transmission line outage rate. A design with adequate shielding performance will use OHGWs to provide an estimated 0.05 shielding failures per 100 km year on new designs. It is difficult to reposition existing OHGWs on existing lines. If a study shows that time-correlated lightning outages on a line are the result of surges with low peak amplitudes (<20 kA), estimated from a lightning location system, then the application of transmission line surge arresters of suitable energy rating should be considered.
12.1 Increasing the Insulator Dry Arc Distance
Insulator dry arc distance, or the number of disks selected for insulator strings, has a remarkable effect on the lightning performance of transmission lines. At the 115 and 138 kV levels, it is common to use 7 or 8 standard (146 × 254 mm) disks or the equivalent polymer insulator length, giving DDry Arc = 1-1.2 m. At 230 kV, 14 disks are common and EHV lines may use 23-26 disks at the 500 kV level for DDry Arc = 3.4-3.8 m.
This range of dry arc dimensions can change the lightning performance of a typical transmission line by a factor of 10 or more, as shown in Tables 8 through 10.
12.2 Modifying the Distribution of Footing Resistance
The simplified spreadsheet example of FIG. 2 shows the relative outage rate in Tables.8 and.9 obtained when a utility makes an effort during construction to reduce most footing resistance values to less than 20 Ohm "where feasible" using the modification schedule in Table 5. If no effort is made to improve grounding, leading to the untreated resistance and voltage stress values in Table 4, the efficiency of double OHGW protection decreases from 78.7% to 73.0%, meaning that the lightning fault rate would be 27% higher without treatment for a dry arc distance of 1 m with other line characteristics fixed. As dry arc distance increases, improved grounding makes a larger fractional reduction in a decreasing outage rate.
12.3 Increasing the Effective Number of Groundwires Using UBGW
The number of shield wires in parallel, n, has a direct role in Equation 10 as well as an indirect influence on the value of Cn, the electromagnetic coupling coefficient from all n driven shield wires (those carrying a small fraction of lightning current) and the insulated phase. The ground wires consist of the traditional overhead groundwires (OHGWs) as well as underbuilt groundwires (UBGWs) and any phases protected with line surge arresters, including circuits at lower distribution voltages. UBGWs have been used on transmission lines to provide convenient access to optical fibers, giving a protected location of the metal-sheathed OPGW that is not exposed to direct f lashes, as well as to manage ac fault currents and to reduce electric and magnetic fields in urban areas. UBGWs are preferred to buried continuous counterpoise for the safety and lightning protection functions as they have reduced installation cost, less environmental impact, easier inspection, and greater physical security. The improved coupling coefficient Cn associated with a single UBGW is seen in Tables 8 and 9 to be roughly as effective as grounding improvements to maintain 20 ohm resistance "where feasible."
12.4 Increasing the Effective Number of Groundwires Using Line Surge Arresters
When selected properly, line surge arresters clip the transient overvoltages across insulators in lightning surge conditions to prevent flashovers across nearby insulators. The limit distance related to lightning equivalent front time typically means that arresters on one transmission tower are typically too far away to provide protection of insulators on the same phase of adjacent towers. Tables 8 through 10 suggest that, in addition to eliminating flashovers on the protected phases, the flow of current through the arresters and the resulting rise in potential on the protected phases make important improvements in the lightning performance of unprotected phases on the same tower. More detailed examples, including the use of arresters on a lower voltage circuit to protect a higher voltage circuit, are found in (CIGRE, 2010).
Direct lightning strokes to any overhead transmission line are likely to cause impulse flashover of sup porting insulation, leading to a circuit interruption. The use of overhead shield wires, located above the phase conductors and grounded adequately at each tower, can reduce the risk of flashover by 70%-99.8% depending on insulation dry arc distance and soil conditions. Underbuilt groundwires and phases protected with line surge arresters both improve electromagnetic coupling and can further reduce the risk of backflashover to achieve protection efficiency that exceeds 90%, even for systems with 1 m dry arc distance.
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