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AbstractThe paper presents the results of magnetic induc-

tion and electrodynamic force calculations acting on arc column during short-circuits in medium voltage air-insu-lated busbars. The gap between the bars was 120 mm and the anticipated short-circuit currents ranged from 4kA to 8kA. The paper also shows the measurement results of av-erage velocity fault arc depending on currents and distance between bars. The relation between calculated arc diam-eter and arc current was established and described. Based on the calculation results of electrodynamic forces acting

on the arc and the calculated arc diameter, as well as the measurements of arc velocity, the relation of aerodynamic resistance coefficient to arc current was presented. Theconclusions indicate, inter alia, the possibility of changing arc’s traveling direction, as a result of changing the direc-tion of electrodynamic forces Attention is also drawn to deformation of arc columns and increase in arc voltage, which cause increase in arc’s power, resulting in greater impact of tri-phase arcing short-circuits in switchboards.

Dynamics of Fault Arc Traveling along Busbars in High Voltage Switchboards

DYNAMICS OF FAULT ARC TRAVELING ALONG BUSBARS IN HIGH VOLTAGE SWITCHBOARDS

Roman Partyka / Gdańsk University of TechnologyDaniel Kowalak / Gdańsk University of Technology

1. INTRODUCTIONIn arcing short-circuits current electrodynamics cause the arc to move along busbar. The resulting rapid

heating of the air inside the switchboard increases the pressure and may be hazardous for switchboard doors and covers.

In enclosed, air-insulated switchboards the effect of arcing short-circuits depends on power of the arc and duration of the short-circuit. Thus, the thermal and electrodynamic impact of arcing short-circuits can be minimized most effectively by decreasing the short-circuit duration and limiting arc’s movement during its travel along busbars.

2. MAGNETIC INDUCTION AND ELECTRODYNAMIC FORCES BETWEEN BUSBARS

In steady states

(1)

and magnetic induction

(2)

Where:

H – vector of magnetic field intensityJ – vector of current densityA – vector potential.

The total force acting on the conductor element located inside the magnetic field is expressed by the fol-lowing relation:

(3)

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3. RESULTS OF INDUCTION AND FORCE CALCULATIONSThe analysis was conducted on a copper flat busbar arrangement of 40x5 mm and 40x10 mm cross-sec-

tional dimensions and the in-between gap of 120 mm. The calculations took into account arcing short-circuits in the range 4 kA to 8 kA.

Based on past research it was determined that during a tri-phase arcing short-circuit taking place on single plane bars there appear two active arcs – between the middle phase (bar) L2 and the external bars - L1 and L3 [2]. Through applying the relations (1), (2) and (3), calculations of induction (Fig. 1 and Fig. 2) and the forces acting on the arc during the short-circuit were obtained. The calculations were conducted using the software Flex PDE v. 5.1.2 [1]. Course of the resultant force acting on the arc column L1–L2 is presented in Fig. 3 and the relation of the average resultant Fyśr acting on the arc L1-L2 (placed perpendicularly to bar axis) to arc current IL is presented in Fig. 4.

Assuming that at the moment of short-circuit’s occurrence the value of current in the phase L2 is equal to 0, after the time period of approximately 8ms the resultant force acting on the arc column L1-L2 is of minimum value and the arc is traveling towards the power supply side. There are two forces acting on the arc at the same time: from the currents of the bar L1 and the arc (force directed away from the power supply), as well as from the currents of the bar L2 and the arc L1-L2 (force directed towards the power supply). These co-acting forces cause deformation and significant elongation of the arc (Fig. 2). This in turn increases the arc voltage. The arcdeformation and the shifting of the arc footing increases the forces (of opposing directions) acting on the arc near the arc footing (Fig. 5, Curve 2).

Fig. 1. Component consistent with the axis direction from induction Bez [T] (z = 0) during a tri-phase arcing short-circuit – arc L1-L2 perpen-dicular to bar axis; t = app. 8 ms, arc current IL = 4 kA, bars 40x5 mm, resultant force Fy = – 0.82 N (directed towards supply source)

Roman Partyka / Gdańsk University of TechnologyDaniel Kowalak / Gdańsk University of Technology

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Fig. 3. Course of resultant force Fy acting on column L1-L2; arc current IL = 4 kA, bars 40x5 mm

Fig. 2. Component consistent with the axis direction from induction Bez [T] (z = 0) – arc L1-L2 shifted, t = app. 8 ms, resultant force Fy – 2.8 N, conditions as in Fig. 1

Fig. 4. Relationship of average resul-tant force Fyśr acting on arc L1-L2 to arc current IL

Fig. 5. Relation of force per distance unit fy acting on the arc L1-L2 to distance x (from edge of bar L2 towards bar L1), 1 – arc as in Fig. 1, 2 – arc as in Fig.2, con-ditions as in Fig. 1

Fig. 6. Relation of measured average arc velocity vL along flat arrangement tri-phasebusbar to arc current IL and distance be-tween bars d; 1 – d = 120 mm, 2 – d = 180 mm, 3 – d = 240 mm [2]

2

1,6

1,2

0,8

0,4

Dynamics of Fault Arc Traveling along Busbars in High Voltage Switchboards

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4. ARC VELOCITYIn analyzing the phenomena which accompany arcing short-circuits important role is played by the veloc-

ity of arc movement along bars. The velocity depends mainly on short-circuit currents and distances between bars. Analyzing the velocity is of particular importance in brief times of breaking short-circuits with traveling arc since with the same currents and distances between bars, the power and energy of arcing short-circuit is smaller in comparison with the power and energy of short-circuits with stationary arc. With the same currents and distances between bars, the voltage of a traveling arc is lower than that of a stationary arc [2].

Presented in Fig. 6 are the results of calculations of arc velocity vL, depending on short circuit currents IL with varied distances between bars [2].

Approximately linear relationship of arc vL to current IL was observed. There exist analytical methods allowing for calculating arc velocity. The following relationship may be

used to define arc velocity:

(4)

Where:vL – arc velocitykFL – coefficient depending on short-circuit typecL – coefficient of arc’s aerodynamic resistanceFy – average electrodynamic force acting on arc, e.g., on column of arc L1-L2AL. –cross-sectional area of column arc on a plane perpendicular to bar axis ρ – gas densityThe electrodynamic interaction force FL is proportional to the square of the IL, and the surface area AL

grows with increase of the current IL. Calculations should take into account the aerodynamic resistance of gas inside the switchboard, placed on arc column moving along bars. Calculating the arc velocity vL based on the above relation (4) requires knowing the values of listed coefficients and measurements which are usually ob-tained by experiment. Cross-section area of column arc AL was set based on results of calculated arc diameter dL. According to literature [3] the dL diameter of arc cooled in gas environment is:

(5)

Where:p – gas pressure, MPa; assumed p = 0.1 MPaIL – arc current, Ak = 0.4 × 10-2. m = 0.22÷0.27, n = 0.65

Relation of calculated arc diameter dL to arc current is presented in Figure 7.

Fig. 7. Relation of calculated arc di-ameter dL to arc current IL

Fig. 8. Relation of aerodynamic resis-tance coefficient cL to arc current IL

1,64

1,6

1,56

1,52

1,48

Roman Partyka / Gdańsk University of TechnologyDaniel Kowalak / Gdańsk University of Technology

75

Using the results of average arc velocity measurements and the calculated arc column diameter, the analysis of change in arc’s aerodynamic resistance coefficient cL was carried out with conversion of the relation (4). The relation of coefficient cL to arc current IL is presented in Fig. 8. The calculation assumed kFL = 0.8 and gas density ρ20 = 1.18 kg/m3.

4. CONCLUSIONResults of calculating magnetic induction and electrodynamic forces under the conditions of fault arc oc-

curring in covered, air-insulated busbars allow for quite extensive analysis of velocity of arc movement along bars depending on arc parameters and busbar configurations. By using measurements results of average arcvelocity in a flat busbar arrangement, one can calculate arc diameter, as well as coefficient of its aerodynamicresistance. The analysis presented above allows for forming the following conclusions:

1. During tri-phase arcing short-circuits occurring on bars placed on a single plane the traveling velocity of each of the two arcs (occurring between middle bar and outside ones) may differ due to the activity of electrodynamic forces of a tri-phase system.

2. Electrodynamic forces cause arc deformation and elongation, as well as rising arc voltage. This in-creases arc power and amplifies the effects of short-circuits in medium voltage switchboards.

3. Decreasing value of coefficient cL along with increasing value of current IL may point out to decreasing impact of the reversing arc phenomenon on the resultant arc velocity. The reversing arc phenomenon, i.e. changing direction of arc movement, stems from the activity of electrodynamic forces present in a tri-phase busbar arrangement.

Detailed analysis of arc movement along bars allows for better assessment of the impact of arcing short-circuits in switchboards and may contribute to significant reduction of negative effects, therefore improving thereliability and safety of using these switchboards.

LITERATURE

1. Flex PDE 5.1.2. User Guide. PDE Solution Inc. 2005.2. Partyka R., Badanie skutków zwarć łukowych w rozdzielnicach osłoniętych, Monografie 70, Politechnika Gdańska,

Gdańsk 2006.3. Ciok Z., Procesy łączeniowe w układach elektroenergetycznych, WNT Warszawa 1982.

Dynamics of Fault Arc Traveling along Busbars in High Voltage Switchboards