Liliana Arevalo

Preliminary study on the modelling of negative leader discharges

Nowadays, there is considerable interest in understanding the physics underlying positive and negative discharges because of the importance of improving lightning protection systems and of coordinating the insulation for high voltages. Numerical simulations of positive switching impulses made in long spark gaps in a laboratory are achievable because the physics of the process is reasonably well understood and because of the availability of powerful computational methods. However, the existing work on the simulation of negative switching discharges has been held up by a lack of experimental data and the absence of a full understanding of the physics involved. In the scientific community, it is well known that most of the lightning discharges that occur in nature are of negative polarity, and because of their complexity, the only way to understand them is to generate the discharges in laboratories under controlled conditions.The voltage impulse waveshape used in laboratories is a negative switching impulse. With the aim of applying the available information to a self-consistent physical method, an electrostatic approximation of the negative leader discharge process is presented here. The simulation procedure takes into consideration the physics of positive and negative discharges, considering that the negative leader propagates towards a grounded electrode and the positive leader towards a rod electrode. The simulation considers the leader channel to be thermodynamic, and assumes that the conditions required to generate a thermal channel are the same for positive and negative leaders. However, the magnitude of the electrical charge necessary to reproduce their propagation and thermalization is different, and both values are based on experimental data. The positive and negative streamer development is based on the constant electric field characteristics of these discharges, as found during experimental measurements made by different authors. As a computational tool, a finite element method based software is employed. The simulations are compared with experimental data available in the literature.

Corona charge produced by thundercloud fields in grounded rods

Electrostatic fields below the thundercloud lead to the formation of glow charge from grounded objects. The charge accumulated after certain time can initiate or inhibit the called streamer formation and consequently the inception and development of upward leaders. By means of a two dimensional numerical model that takes into account the particles behavior is observed that glow charge can smooth the electric field on top of the grounded rod and consequently hinder the inception of streamers and upward leaders from the grounded rod. It is concluded that to be able to initiate unstable upward leaders from the shielded grounded rod a sudden change of electric field is necessary. A two dimensional numerical model that solves the continuity equations for positive and negative ions and electrons coupled with Poisson equation was implemented. Comparison for different magnitudes of electric field and characteristics of rod are included as well.

Streamer to leader transition criteria for propagation of long sparks and lightning leaders

Certain models have been dedicated to analyze the breakdown of long spark gaps and the lightning attachment process based on the mechanism of leader propagation. One of the most important processes on the mechanism of leader is the transition between streamers to leader. The streamer to leader transition is characterized by a rapid increase in the electron density and gas temperature, which is a consequence of the onset of thermal-ionization instability. To simplify the complexity of the physical process lightning attachment and long spark gaps models assumed that a minimum charge of 1μC is necessary to thermalize a leader channel, independently of the electric field and atmospheric conditions as temperature, pressure and humidity. In this paper an approach that takes into account the continuity equations and the gas temperature balance equation is used to investigate the minimum charge required to start the streamer to leader transition. The obtained results are compared with the minimum charge criteria used for long spark gaps and lightning attachment modeling. Simulation shows that the required charge to thermalize a leader depends on the vibrational energy relaxation. Results also indicate that only a small part of the energy input, transferred by electrons to gas molecules in the stem, contributes immediately to the temperature rise.

Laboratory long gaps simulation considering a variable corona region

Different simplified models [1 – 11] have been proposed to simulate long gap discharges under switching-like voltage impulses laboratory experiments [6]. Some models fitted experimental data and others applied the physic of electrical discharges. Nevertheless, the physical models approximate the corona zone as a constant geometrical region; the geometrical shape assumed has been either conical [4] or several parallel filaments [1 – 3]. In the reality, due to the increment or reduction of the electric field, the corona zone should change of geometry and cover a larger or smaller area respectively, instead of keeping a constant region as it has been assumed in previous models. Photographical reports [6–7, 12] of laboratory experiments have shown that the corona zone in a rod - plane arrangement is conical at the initial stage and then its shape becomes hyperboloid and finally cylindrical. The model presented here, analyzes the three dimensional region that fulfils the corona condition for each time step and includes the calculated charge on the leader propagation model. The model was derived from the physical analysis used on [5, 8]. The characteristics of the calculated leader development are compared with experimental results [6], photographical reports [12] and other numerical models [1, 5, 8].

Interaction of multiple connecting leaders issued from a grounded structure simulated using a self consistent leader inception and propagation model (slim)

A self consistent lightning connecting leader inception and propagation model is utilized to study the effect of multiple connecting leaders on the attachment of lightning flashes to grounded structures. In the present study the results obtained in the case of a grounded structure equipped with two lightning rods were presented. As the stepped leader approaches the grounded structure, connecting leaders are issued from both lightning conductors but depending on the location of the stepped leader only one of them succeed in completing the attachment process. Results show that the presence of a small advantage for the growth of a connecting leader from one conductor may drastically reduce the ability of other conductors to launch successful connecting leaders. Results also show that the effect of the competition between multiple leaders is to delay the attachment process.

Sensitivity analysis of leader channel models used in long air gap positive discharge modelling

Leader models used in electrical discharge simulation have been proposed in theoretical works by different authors. Their application can be found in the study of lightning upward connecting leaders or long air gap laboratory testing, and can be considered engineering or physical according to their detail level. Based on simplifications and assumptions, these models are capable of predicting the 50% breakdown voltage for certain electrode arrangements, time evolution of physical phenomena like particle densities, temperatures, electric fields, leader and streamer progress, among others. An important parameter in a leader model is the potential distribution along the channel as it propagates. In present work, we compare an engineering and a physical leader model against experimental data recorded while testing a rod-to-plane 10 m gap with switching-like voltage impulse. A sensitivity analysis was done with some basic input parameters of two leader models in order to compare the outcome for different cases. The results showed a strong dependence of the leader channel evolution with the assumed constant average potential gradient used in most of the leader models.

‘The mesh method’ in Lightning protection standards - revisited

At present the design of the Lightning protection systems (LPS) for structures as stipulated in standards is based on the electro - geometrical method, which was initially used to protect power lines from lightning. A derivative of the electro-geometrical method is the rolling sphere method. This method together, with the protection angle method and mesh method are used almost in all lightning standards as the measure in installing the lightning protection systems of grounded structures. In the mesh method, the dimension of the cell size in different levels of protection is determined using the rolling sphere method. Since the rolling sphere method does not take into account the physics of the lightning attachment process there is a need to evaluate the validity of the stipulated value in standards of the minimum lightning current that can penetrate through the mesh in different levels of protection. In this paper, meshes of different sizes as stipulated in the lightning protection standards were tested for their ability to intercept lightning flashes using a lightning attachment model that takes into account the physics of connecting leaders on. The results are in reasonable agreement with the specifications given in the lightning protection standards.

Attractive zone of lightning rods evaluated with a leader progression model in a common building in Brazil

Modeling the lightning attachment process is required on any method to design the air-termination elements of a lightning protection system. An attachment model that adopts the leader progression concept is used to evaluate the three-dimensional attractive zone of a lightning rod on a common 54-m tall building in Sao Paulo, Brazil. Electric field and scalar potential distributions are calculated numerically with a finite element method. The result is compared with the interception volume predicted by the electro-geometric model, as applied by the rolling sphere method. The results show that the electro-geometric theory underestimates the striking distance and the attractive radius. Moreover, in the presence of upward connecting leaders, the striking distance varies according to the field enhancement on the geometry of the structure and the lateral displacement of the stepped leader. The simulated propagated distances and speeds of the downward and upward leaders are compared with a recently published high-speed video analysis of a natural lightning attachment case observed on the evaluated lightning rod. A reasonable agreement between the simulated and measured leader characteristics has been found.

Upward leader inception caused by a sudden change of cloud electric field

Discharge processes such as glow, streamer, and leader inception among others take place before an upward leader can be launched from a grounded structure during thunderstorms. Electrostatic fields below the thundercloud could lead to the formation of glow charge from grounded objects. if the electric field is high enough and ionization keeps expanding into the gap, streamers can be incepted. Depending on the available charge and the thermodynamic properties of the gas, there is a possibility to incept or not a positive upward leader towards the cloud. Usually, the inception of positive upward leaders is directly related with the appearance of a downward coming leader from cloud towards the grounded object. Such a downward leader will intensify the electric field in such a way that the streamer discharges could thermalize and produce an unstable upward leader channel. However, experimental observations have indicated the inception of upward leaders from grounded structures without registering connecting downward leaders towards the structure. The present paper intends to explain the inception of positive upward leaders from the top of a rod, whenever the electric field produced by the cloud suddenly changes e.g. due to intra-cloud discharges or distance cloud to ground flash. A two dimensional model based on the gas-dynamic equations, the main processes responsible for gas heating such as vibrational excitation and transfer of energy into electronic, rotational and translational excitation, coupled with Poisson equation is presented in this paper. Rods of different lengths under thundercloud electric field were studied. Simulation results indicate that positive upward leaders can be incepted from long rods under certain conditions of thundercloud electric field without the need of a coming downward leader. However, for rods of tenths of meters the thundercloud electric field is not enough to incept positive upward leaders and an intensification of the electric field is required in order to incept a positive upward leader from the structure, e.g., a coming downward leader.

A reliable numerical method for the calculation of breakdown voltages

When it comes to the design of high voltage equipment, transmission lines and substations there is a general interest on predicting the breakdown characteristics for different gap geometries. Nowadays, the knowledge on this kind of design is based on experimental results of arrangements like rod - rod and rod - plane, conductor - rod, conductor - plane, and the well - known K factor, which is the relation between the breakdown voltage of a specific gap and a rod - plane gap with the same gap distance. Standards and Guidelines [3 – 5] have accepted an approximation of the experimental results and some authors have worked to develop equations based on experiments [6 – 8]. In the present work we present the results obtained while applying a self consistent model to calculate the breakdown voltages for different electrode configurations used by Paris [1]. The well known K factor is calculated and compared with the experimental results.