The analysis and these calculations were performed in order to increase the level of lightning resistance of the overhead line {{$substation->voltage_class}} kV. To perform the task, it is necessary to estimate the annual number of line shutdowns without protective devices and after the installation of dischargers manufactured by Streamer International AG.

1. Introduction

    Overhead line lightning strikes can occur as a result of lightning strikes in the phase wire, in the support and in the immediate vicinity of the line.

    For overhead lines of class {{$substation->voltage_class}} kV, almost every direct lightning strike (DLS) into a phase wire is accompanied by a direct overlap of the insulation of this phase to the support closest to the impact site. That is why sections of overhead lines without a cable are practically defenseless against lightning strikes. On sections of overhead lines with a cable, this can happen when lightning breaks through the cable, which happens extremely rarely.

    When lightning strikes a support, the probability of reverse overlapping (OP) of the insulation depends mainly on the ground resistance of the support and the impulse strength of the insulator garland. It is this case that makes the main share in the total number of lightning outages of lines {{$substation->voltage_class}} kV.

    When lightning strikes near the line, inducted overvoltages (IP) occur on the wires, which are able to block the garland of insulators when its impulse strength is exceeded. To a greater extent, this is true for lines of 6-35 kV than for overhead lines {{$substation->voltage_class}} kV, so in this case disconnections from the IP were not considered.

2. Algorithm for calculating lightning outages for overhead lines {{$substation->voltage_class}} kV

    Consider the algorithm for calculating the number of lightning outages based on the techniques presented in RD 153-34.3-35.125-99 Manual for the protection of 6-1150 kV electrical networks from lightning and internal overvoltages, as well as using the international standard IEEE Guide for Improving the Lightning Performance of Electric Power Overhead Distribution Lines, IEEE Std. 1410-2010. Since the main purpose of the calculation is to compare the lightning resistance of overhead lines without dischargers and with them for the projected line, the percentage of successful APV of the line was not taken into account in the calculations.

2.1. Number of shutdowns before installing the dischargers

    In general, the number of disconnections consists of disconnections from impacts to the support and from strikes in the middle of the span (in the case of a cable, these are strikes in the cable and lightning breaks through the cable):

n_total = n_op + n_prl     (1.1)

where n_prl = n_tr + n_cougar in the presence of a cable.

    The number of short circuits on one circuit n^I_op and on two chains n^II_op per 100 km of line when lightning hits the support:

n^I_op = N_pum P_op(P^I_{I Iop} – P^II_Ion) P_d,     (1.2a)

n^II_op = N_cougar P_op P^II_Ion P_D,     (1.2b)

where is the total number of direct lightning strikes per 100 km; – the probability of lightning hitting the support (but not higher than 0.5);

    

    P^I_Iop – the probability of occurrence of a dangerous lightning current to overlap the phase insulators of one circuit on one support when hitting the support;

    P^II_Ion – the probability of occurrence of a dangerous lightning current for overlapping insulators in one phase of both circuits on one support when hitting the support;

    P_{d is the} probability of the transition of the impulse overlap into the arc of the network, which depends on the construction height of the garland.

    The number of short circuits on one circuit n^I_tr and on two chains n^II_tr per 100 km of line when lightning hits the cable:

n^I_tr = N_cougars (1 – P_op)•(P^I_Itr – P^II_Itr) P_d     (1.3a)

n^II_tr = N_cougars (1 – P_op) P^II_Itr P_d     (1.3b)

where P^I_Itr is the probability of a dangerous lightning current to overlap the phase insulators of one circuit on one support when the cable is hit in the middle of the span;

    P^II_Itr is the probability of occurrence of a dangerous lightning current for overlapping insulators in one phase of both chains on one support when hitting a cable in the middle of the span.

    The number of short circuits on one circuit n^I_cougars and on two chains n^II_cougars per 100 km of line when lightning hits the phase wire:

n^I_cougars = N_cougars (1 – P_op)•(P^I_Iprl – P^II_Iprl) P_d•P_pr     (1.4a)

n^II_cougars = N_cougars (1 – P_op) P^II_Iprl P_d•P_pr     (1.4b)

    where is the probability of lightning breaking through the cable,

α is the angle of protection of the cable;

    P^I_{Iprl is the} probability of occurrence of a dangerous lightning current for overlapping the phase insulators of one circuit on one support when the phase wire is hit in the middle of the span;

    P^II_{Iprl is the} probability of a dangerous lightning current for overlapping insulators in one phase of both circuits on the same support when hitting the phase wire in the middle of the span.

    Probabilities of hazardous currents P^I_Iop, P^II_Iop, P^I_Itr, P^II_Itr, P^I_Iprl, P^II_Iprl for overlapping insulators (or triggering dischargers) are determined by calculating the electrical scheme for replacing a section of the line, which includes the following elements: supports with ground resistance, blocks of long lines, taking into account the mutual arrangement of wires relative to each other and wave processes, insulators (or dischargers) with their own 50% pulse voltage, a lightning model, etc.

    The total number of short circuits on one circuit n^I and two chains n^II is added from all thunderstorm effects.

n^I = n^I_op + n^I_tr + n^I_cougar     (1.5a)

n^II = n^II_op + n^II_tr + n^II_cougar     (1.5b)

2.2. Number of shutdowns after installing the dischargers

    In the case of installation of LLPD Line Lightning Protection Devices - {{$substation->voltage_class}}, the probability of occurrence of a short circuit arc is replaced by the probability of unsuccessful operation of the discharger P_d = P_HP = 0.05. Impulse strength of dischargers on {{$substation->voltage_class}} kV should be less by 10-15% than the impulse strength of the insulator string for successful coordination. All the same similar calculations are carried out according to th formulas (1.1) - (1.5) using the specified characteristics of the dischargers.

    To calculate the probabilities of overlaps and disconnections, The Groza software developed by Streamer Electric AG was used. The Groza program allows you to simulate a single-circuit or double-circuit line up to 115 kV, divided into sections, in order to determine the lightning resistance of each section of the line without and with protective devices.

    As input parameters for the calculation, the nominal voltage of the line, the geometric locations of all conductors and cables, the configuration and type of support, linear insulation, thunderstorm activity in the region, etc. The results determine the annual number of disconnections of the line from direct lightning strikes and from induced overvoltages for each section of the line.

3. Circuit, section and substation

    The project {{$project_name}} consist of the circuit, sections and substation(s) as below:

Substation {{$substation->name}} details

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Substation Name	{{$substation->name}}
Voltage Class (Un)	{{$substation->voltage_class}} kV
Calculate short-circuit current	{{$power_transformer}}
Power of transformers (P)	{{$power_transformer_number}} MVa
Short-circuit losses (Uk)	{{$losses}} %
Phase-ground short-circuit (Isc)	{{$phase_ground}} kA
Neutral arrangement	{{$neutral}}
Reclosing Probability (Pr)	{{$substation->reclose}}

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