Analysis of the lightning attractive radius of power transmission lines through the use of a physically-oriented model

Models of different degrees of complexity are found in the literature for the estimation of lightning striking distances and attractive radius of objects and structures. However, besides the oversimplifications of the physical nature of the lightning discharge on which most of them are based, till recently the tridimensional structure configuration could not be considered. This is an important limitation, as edges and other details of the object affect the electric field and, consequently, the upward leader initiation. Within this context, the Self-consistent leader initiation and propagation model (SLIM) proposed by Becerra and Cooray is state-of-the-art leader inception and propagation leader model based on the physics of leader discharges which enables the tridimensional geometry of the structure to be taken into account. In this paper, the model is used for estimating the striking distance and attractive radius of power transmission lines. The results are compared with those obtained from the electrogeometric and Eriksson's models. © 2003-2012 IEEE.

On the possible variation of the lightning striking distance as assumed in the IEC lightning protection standard as a function of structure height

The effect of structure height on the lightning striking distance is estimated using a lightning strike model that takes into account the effect of connecting leaders. According to the results, the lightning striking distance may differ significantly from the values assumed in the IEC standard for structure heights beyond 30m. However, for structure heights smaller than about 30m, the results show that the values assumed by IEC do not differ significantly from the predictions based on a lightning attachment model taking into account the effect of connecting leaders. However, since IEC assumes a smaller striking distance than the ones predicted by the adopted model one can conclude that the safety is not compromised in adhering to the IEC standard. Results obtained from the model are also compared with Collection Volume Method (CVM) and other commonly used lightning attachment models available in the literature. The results show that in the case of CVM the calculated attractive distances are much larger than the ones obtained using the physically based lightning attachment models. This indicates the possibility of compromising the lightning protection procedures when using CVM. (C) 2014 Elsevier B.V. All rights reserved.

Investigations on voltages and currents in the lightning protection system of the Indian satellite launch pad-I during a stroke interception

A reliable protection against direct lightning hit is very essential for satellite launch pads. In view of this, suitable protection systems are generally employed. The evaluation of efficacy of the lightning protection schemes among others requires an accurate knowledge of the consequential potential rise at the struck point and the current injected into soil at the earth termination. The present work has made a detailed effort to deduce these quantities for the lightning protection scheme of the Indian satellite launch pad-I. A reduced scale model of the system with a frequency domain approach is employed for the experimental study. For further validation of the experimental approach, numerical simulations using numerical electromagnetic code-2 are also carried out on schemes involving single tower. The study results on the protection system show that the present design is quite safe with regard to top potential rise. It is shown that by connecting ground wires to the tower, its base current and, hence, the soil potential rise can be reduced. An evaluation of an alternate design philosophy involving insulated mast scheme is also made. The potential rise in that design is quantified and the possibility of a flashover to supporting tower is briefly looked into. The supporting tower is shown to have significant induced currents.

Towards a model of spray-canopy interactions : interception, shatter, bounce and retention of droplets on horizontal leaves

Pesticides used in agricultural systems must be applied in economically viable and environmentally sensitive ways, and this often requires expensive field trials on spray deposition and retention by plant foliage. Computational models to describe whether a spray droplet sticks (adheres), bounces or shatters on impact, and if any rebounding parent or shatter daughter droplets are recaptured, would provide an estimate of spray retention and thereby act as a useful guide prior to any field trials. Parameter-driven interactive software has been implemented to enable the end-user to study and visualise droplet interception and impaction on a single, horizontal leaf. Living chenopodium, wheat and cotton leaves have been scanned to capture the surface topography and realistic virtual leaf surface models have been generated. Individual leaf models have then been subjected to virtual spray droplets and predictions made of droplet interception with the virtual plant leaf. Thereafter, the impaction behaviour of the droplets and the subsequent behaviour of any daughter droplets, up until re-capture, are simulated to give the predicted total spray retention by the leaf. A series of critical thresholds for the stick, bounce, and shatter elements in the impaction process have been developed for different combinations of formulation, droplet size and velocity, and leaf surface characteristics to provide this output. The results show that droplet properties, spray formulations and leaf surface characteristics all influence the predicted amount of spray retained on a horizontal leaf surface. Overall the predicted spray retention increases as formulation surface tension, static contact angle, droplet size and velocity decreases. Predicted retention on cotton is much higher than on chenopodium. The average predicted retention on a single horizontal leaf across all droplet size, velocity and formulations scenarios tested, is 18, 30 and 85% for chenopodium, wheat and cotton, respectively.

Studies on characteristics of lightning generated currents in an interconnected lightning protection system

An in-depth knowledge about the characteristics of lightning generated currents will facilitate evaluation of the interception efficacy of lightning protection systems. In addition, it would aid in extraction of valuable statistics (from measured current data) on local lightning parameters. Incidentally, present day knowledge on characteristics of lightning induced current in typical lightning protection systems is rather limited. This is particularly true with closely interconnected protection systems, like the one employed in Indian Satellite Launch Pad-II. This system is taken as a specific example in the present study. Various aspects suggest that theoretical modelling would be the best possible approach for the intended work. From the survey of pertinent literature, it is concluded that electromagnetic modelling of lightning return-stroke with current source at the channel base is best suited for this study. Numerical electromagnetic code was used for the required electromagnetic field solution and Fourier transform techniques were employed for computing time-domain results. A validation for the numerical modelling is provided by laborator experiments on a reduced scale model of the system. Apart from ascertaining the influence of various parameters, salient characteristics of tower base currents for different kinds of events are deduced. This knowledge can be used in identifying the type of event, as well as its approximate location. A method for estimation of injected stroke current has also been proposed.

A Macroscopic Model for First Return Stroke of Lightning

A lightning return stroke model for a downward flash is proposed. The model includes underlying physical phenomena governing return stroke evolution, namely, electric field due to charge distributed along the leader and cloud, transient enhancement of series channel conductance at the bridging regime, and the nonlinear variation of channel conductance, which supports the return stroke current evolution. Thermal effects of free burning arc at the stroke wave front and its impact on channel conductance are studied. A first-order arc model for determining the dynamic channel conductance along with a field-dependent conductivity for corona sheath is used in the model. The model predicts consistent current propagation along the channel with regard to current amplitude and return stroke velocity. The model is also capable of predicting the remote electromagnetic fields that are consistent with the experimental observations.

A Physical Model for Inception and Propagation of Upward Lightning Leader from a 1200 kV AC Power Transmission Line

UHV power transmission lines have high probability of shielding failure due to their higher height, larger exposure area and high operating voltage. Lightning upward leader inception and propagation is an integral part of lightning shielding failure analysis and need to be studied in detail. In this paper a model for lightning attachment has been proposed based on the present knowledge of lightning physics. Leader inception is modeled based on the corona charge present near the conductor region and the propagation model is based on the correlation between the lightning induced voltage on the conductor and the drop along the upward leader channel. The inception model developed is compared with previous inception models and the results obtained using the present and previous models are comparable. Lightning striking distances (final jump) for various return stroke current were computed for different conductor heights. The computed striking distance values showed good correlation with the values calculated using the equation proposed by the IEEE working group for the applicable conductor heights of up to 8 m. The model is applied to a 1200 kV AC power transmission line and inception of the upward leader is analyzed for this configuration.

Sensitivity of a coupled climate model to canopy interception capacity

The canopy interception capacity is a small but key part of the surface hydrology, which affects the amount of water intercepted by vegetation and therefore the partitioning of evaporation and transpiration. However, little research with climate models has been done to understand the effects of a range of possible canopy interception capacity parameter values. This is in part due to the assumption that it does not significantly affect climate. Near global evapotranspiration products now make evaluation of canopy interception capacity parameterisations possible. We use a range of canopy water interception capacity values from the literature to investigate the effect on climate within the climate model HadCM3. We find that the global mean temperature is affected by up to -0.64 K globally and -1.9 K regionally. These temperature impacts are predominantly due to changes in the evaporative fraction and top of atmosphere albedo. In the tropics, the variations in evapotranspiration affect precipitation, significantly enhancing rainfall. Comparing the model output to measurements, we find that the default canopy interception capacity parameterisation overestimates canopy interception loss (i.e. canopy evaporation) and underestimates transpiration. Overall, decreasing canopy interception capacity improves the evapotranspiration partitioning in HadCM3, though the measurement literature more strongly supports an increase. The high sensitivity of climate to the parameterisation of canopy interception capacity is partially due to the high number of light rain-days in the climate model that means that interception is overestimated. This work highlights the hitherto underestimated importance of canopy interception capacity in climate model hydroclimatology and the need to acknowledge the role of precipitation representation limitations in determining parameterisations.

Quantification of the effects of architectural traits on dry mass production and light interception of tomato canopy under different temperature regimes using a dynamic functional-structural plant model

There is increasing interest in evaluating the environmental effects on crop architectural traits and yield improvement. However, crop models describing the dynamic changes in canopy structure with environmental conditions and the complex interactions between canopy structure, light interception, and dry mass production are only gradually emerging. Using tomato (Solanum lycopersicum L.) as a model crop, a dynamic functional-structural plant model (FSPM) was constructed, parameterized, and evaluated to analyse the effects of temperature on architectural traits, which strongly influence canopy light interception and shoot dry mass. The FSPM predicted the organ growth, organ size, and shoot dry mass over time with high accuracy (>85%). Analyses of this FSPM showed that, in comparison with the reference canopy, shoot dry mass may be affected by leaf angle by as much as 20%, leaf curvature by up to 7%, the leaf length: width ratio by up to 5%, internode length by up to 9%, and curvature ratios and leaf arrangement by up to 6%. Tomato canopies at low temperature had higher canopy density and were more clumped due to higher leaf area and shorter internodes. Interestingly, dry mass production and light interception of the clumped canopy were more sensitive to changes in architectural traits. The complex interactions between architectural traits, canopy light interception, dry mass production, and environmental conditions can be studied by the dynamic FSPM, which may serve as a tool for designing a canopy structure which is 'ideal' in a given environment.

Estimation of light interception in research environments: A joint approach using directional light sensors and 3D virtual plants applied to sunflower (Helianthus annuus) and Arabidopsis thaliana in natural and artificial conditions

Light interception is a major factor influencing plant development and biomass production. Several methods have been proposed to determine this variable, but its calculation remains difficult in artificial environments with heterogeneous light. We propose a method that uses 3D virtual plant modelling and directional light characterisation to estimate light interception in highly heterogeneous light environments such as growth chambers and glasshouses. Intercepted light was estimated by coupling an architectural model and a light model for different genotypes of the rosette species Arabidopsis thaliana (L.) Heynh and a sunflower crop. The model was applied to plants of contrasting architectures, cultivated in isolation or in canopy, in natural or artificial environments, and under contrasting light conditions. The model gave satisfactory results when compared with observed data and enabled calculation of light interception in situations where direct measurements or classical methods were inefficient, such as young crops, isolated plants or artificial conditions. Furthermore, the model revealed that A. thaliana increased its light interception efficiency when shaded. To conclude, the method can be used to calculate intercepted light at organ, plant and plot levels, in natural and artificial environments, and should be useful in the investigation of genotype-environment interactions for plant architecture and light interception efficiency. This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Relative contributions of light interception and radiation use efficiency to the reduction of maize productivity under cold temperatures

Maize (Zea mays L.) is a chill-susceptible crop cultivated in northern latitude environments. The detrimental effects of cold on growth and photosynthetic activity have long been established. However, a general overview of how important these processes are with respect to the reduction of productivity reported in the field is still lacking. In this study, a model-assisted approach was used to dissect variations in productivity under suboptimal temperatures and quantify the relative contributions of light interception (PARc) and radiation use efficiency (RUE) from emergence to flowering. A combination of architectural and light transfer models was used to calculate light interception in three field experiments with two cold-tolerant lines and at two sowing dates. Model assessment confirmed that the approach was suitable to infer light interception. Biomass production was strongly affected by early sowings. RUE was identified as the main cause of biomass reduction during cold events. Furthermore, PARc explained most of the variability observed at flowering, its relative contributions being more or less important according to the climate experienced. Cold temperatures resulted in lower PARc, mainly because final leaf length and width were significantly reduced for all leaves emerging after the first cold occurrence. These results confirm that virtual plants can be useful as fine phenotyping tools. A scheme of action of cold on leaf expansion, light interception and radiation use efficiency is discussed with a view towards helping breeders define relevant selection criteria. This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Radiative transfer, interception and scattering in coniferous forests : models and applications for production ecology and remote sensing

This work develops methods to account for shoot structure in models of coniferous canopy radiative transfer. Shoot structure, as it varies along the light gradient inside canopy, affects the efficiency of light interception per unit needle area, foliage biomass, or foliage nitrogen. The clumping of needles in the shoot volume also causes a notable amount of multiple scattering of light within coniferous shoots. The effect of shoot structure on light interception is treated in the context of canopy level photosynthesis and resource use models, and the phenomenon of within-shoot multiple scattering in the context of physical canopy reflectance models for remote sensing purposes. Light interception. A method for estimating the amount of PAR (Photosynthetically Active Radiation) intercepted by a conifer shoot is presented. The method combines modelling of the directional distribution of radiation above canopy, fish-eye photographs taken at shoot locations to measure canopy gap fraction, and geometrical measurements of shoot orientation and structure. Data on light availability, shoot and needle structure and nitrogen content has been collected from canopies of Pacific silver fir (Abies amabilis (Dougl.) Forbes) and Norway spruce (Picea abies (L.) Karst.). Shoot structure acclimated to light gradient inside canopy so that more shaded shoots have better light interception efficiency. Light interception efficiency of shoots varied about two-fold per needle area, about four-fold per needle dry mass, and about five-fold per nitrogen content. Comparison of fertilized and control stands of Norway spruce indicated that light interception efficiency is not greatly affected by fertilization. Light scattering. Structure of coniferous shoots gives rise to multiple scattering of light between the needles of the shoot. Using geometric models of shoots, multiple scattering was studied by photon tracing simulations. Based on simulation results, the dependence of the scattering coefficient of shoot from the scattering coefficient of needles is shown to follow a simple one-parameter model. The single parameter, termed the recollision probability, describes the level of clumping of the needles in the shoot, is wavelength independent, and can be connected to previously used clumping indices. By using the recollision probability to correct for the within-shoot multiple scattering, canopy radiative transfer models which have used leaves as basic elements can use shoots as basic elements, and thus be applied for coniferous forests. Preliminary testing of this approach seems to explain, at least partially, why coniferous forests appear darker than broadleaved forests in satellite data.

Numerical Electromagnetic Analysis of Current and Voltage Distribution along Down Conductors and Towers Hit by Direct Lightning

In order to answer the practically important question of whether the down conductors of lightning protection systems to tall towers and buildings can be electrically isolated from the structure itself, this work is conducted. As a first step in this regard, it is presumed that the down conductor placed on metallic tower will be a pessimistic representation of the actual problem. This opinion was based on the fact that the proximity of heavy metallic structure will have a large damping effect. The post-stroke current distributions along the down conductors and towers, which can be quite different from that in the lightning channel, govern the post-stroke near field and the resulting gradient in the soil. Also, for a reliable estimation of the actual stroke current from the measured down conductor currents, it is essential to know the current distribution characteristics along the down conductors. In view of these, the present work attempts to deduce the post-stroke current and voltage distribution along typical down conductors and towers. A solution of the governing field equations on an electromagnetic model of the system is sought for the investigation. Simulation results providing the spatio-temporal distribution of the post-stroke current and voltage has provided very interesting results. It is concluded that it is almost impossible to achieve electrical isolation between the structure and the down conductor. Furthermore, there will be significant induction into the steel matrix of the supporting structure.

Investigation on the Potential Rise and Currents in Insulated Mast Scheme with Single Tower During Stroke Interception

The insulated mast scheme for the lightning protection system can be found in a few practical designs. Many advantages over conventional protection system are some times envisaged. However, the technical literature on the analysis of such schemes and further quantification of their protection efficacy is rather scarce. As a first step to address this problem, the present work is taken up and the potential rise at the top and ground end currents in insulating mast scheme with single tower is investigated for several tower heights and pertinent values of other parameters. The quantities that are investigated are the potential difference across the insulation and ground end currents for both tower and the ground wires. Quantifications are carried out for the relevant range of stroke current front times. The influence of number of ground wires, their earthing location and to a limited extent, the length of the insulating support have been ascertained. Some relevant discussion on insulation strength is made. These findings are quite novel and aid in quantification of the practical efficacy of the insulated mast scheme. The level of induction to the support tower and possible flashover to the same are not in favour of this scheme.

Investigation on the Sources of Reflection at the Junction of Tall Grounded Object and Lightning Channel

During lightning strike to a tall grounded object (TGO), reflections of current waves are known to occur at either ends of the TGO. These reflection modify the channel current and hence, the lightning electromagnetic fields. This study aims to identify the possible contributing factors to reflection at a TGO-channel junction for the current waves ascending on the TGO. Possible sources of reflection identified are corona sheath and discontinuity of resistance and radius. For analyzing the contribution of corona sheath and discontinuity of resistance at the junction, a macroscopic physical model for the return stroke developed in our earlier work is employed. NEC-2D is used for assessing the contribution of abrupt change in radii at a TGO-channel junction. The wire-cage model adopted for the same is validated using laboratory experiments. Detailed investigation revealed the following. The main contributor for reflection at a TGO-channel junction is the difference between TGO and channel core radii. Also, the discontinuity of resistance at a TGO-channel junction can be of some relevance only for the first microsecond regime. Further, corona sheath does not play any significant role in the reflection.