TOOLS FOR THE SIMULATION OF EFFECTS OF THE INTERNAL ARC IN TRANSMISSION AND DISTRIBUTION SWITCHGEAR

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TOOLS FOR THE SIMULATION OF

EFFECTS OF THE INTERNAL ARC IN

TRANSMISSION AND DISTRIBUTION

SWITCHGEAR

WG A3.24, rev 11.1, January 26, 2014

Members

N. Uzelac,

Convenor

(US) M. Glinkowski,

Secretary

(US), L. del Rio (ES), M. Kriegel,

Former Convenor

(CH), J. Douchin (FR), E. Dullni (DE), S. Feitoza Costa (BR), E.

Fjeld (NO), H-K. Kim (KR), J. Lopez-Roldan (AU), R. Pater (CA), G. Pietsch (DE), T.

Reiher (DE), G. Schoonenberg (NL), S. Singh (DE), R. Smeets (NL), T. Uchii (JP), L.

Van der Sluis (NL), P. Vinson (FR), D. Yoshida (JP)

Copyright © 2011

“Ownership of a CIGRE publication, whether in paper form or on electronic support

only infers right of use for personal purposes. Are prohibited, except if explicitly

agreed by CIGRE, total or partial reproduction of the publication for use other than

personal and transfer to a third party; hence circulation on any intranet or other

company network is forbidden”.

Disclaimer notice

“CIGRE gives no warranty or assurance about the contents of this publication, nor

does it accept any responsibility, as to the accuracy or exhaustiveness of the

information. All implied warranties and conditions are excluded to the maximum

extent permitted by law”.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

ISBN : (To be completed by CIGRE)

27 28

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TOOLS FOR THE

1

SIMULATION OF THE

2

EFFECTS OF INTERNAL ARC

3

IN TRANSMISSION AND

4

DISTRIBUTION SWITCHGEAR

5

EXECUTIVE SUMMARY

1 2

Recognizing the increasing role of commercial and “home made” modelling software in the power industry, CIGRE 3

Study Committee A3 established the former WG A3.20 to evaluate existing simulation tools and the extent to which 4

they can be used as verification tools. Using a case study based on dielectric design, WG A3.20 concluded that 5

simulation is a valuable development tool, can accurately predict stresses and can provide good performance 6

extrapolation where test data is available on similar designs (interpolation). The scope for “pure” performance 7

prediction (utilizing extrapolation) remains limited. 8

WG A3.24 has continued the analysis of the use of simulation as verification tools with a specific focus on internal 9

arc testing of Medium and High Voltage SF6 and air-filled equipment.

10

The main goal was to reduce the number of tests and - for environmental reasons - to eliminate testing where SF6

11

is released to the environment. The international standard for MV metal-enclosed switchgear, IEC 62271-200, 12

permits SF6 to be replaced by air, while the standard for HV Gas-Insulated switchgear, IEC 62271-203, allows the

13

extension of test results by calculation methods. IEEE standard C37.20.7 for internal arc testing does not address 14

SF6 at all, as the standard is only dedicated to air insulation. Figure 0-1 shows the test setup for internal arc testing.

15 16

17

Figure 0-1: Arc resistance test per IEC 62271-200.

18 19

WG A3.24 started work by reviewing the existing literature (100+ white papers and applicable IEEE and IEC 20

standards, a number of which are referenced later in this technical brochure), and collecting the test data from 21

numerous Internal Arc Tests. Test data was collected for more than 70 different cases; with tank sizes ranging 22

from small 5 l test tanks to large 1200 lGIS tanks, with fault currents ranging from 12 kA to 63 kA, with fault 23

durations ranging from 10 ms to 1.2 s, including single compartment and multi-compartment equipment and 24

including both SF6 and air-insulated switchgear (Figure 0-2).

25

The WG then reviewed existing software tools for calculating the effects of an internal arc fault, focusing on 3 main 26

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a. Pressure rise 1

b. Mechanical stress on enclosure and buildings 2

c. Burn-through 3

This review included various “home made” software tools, ranging from simple spreadsheets in Excel that most 4

engineers could use with a little effort, to a complex 3-D Computational Fluid Dynamic (CFD) software package 5

whose application remain limited to small number of experts due to the complexity and cost of the software. 6

7

Figure 0-2 : Snapshots of some Internal Arc Tests for which A3.24 WG collected data (current, voltage,

8

pressure) and compared the measured vs calculated pressure rise

9 10

•

Pressure rise:

2

After calculating the pressure rise in a number of cases with simple “home made” tools, the 11

WG realized that the calculated pressure peak was within 10-20% of the measured peak, which indicated 12

that usage of the simpler tool should be explored. Encouraged by that finding, the WG has developed a 13

set of “basic equations” and validated this mathematical model for all 70+ cases. It has been found that 14

calculation of pressure curves inside the arc compartment during an internal arc fault gives good 15

agreement between test and simulation as long as the input arc energy is known. These findings are 16

covered in Chapter , which lists the equations for the basic model and identifies its benefits and 17

limitations. Also, it shows different applications of the basic model for both MV and HV switchgear. Detailed 18

set of equations for the basic model is provided in ANNEX A: this can be used to create one’s own “home 19

made” tool. In addition to the basic model, this Technical Brochure also covers the enhanced model and 20

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CFD in Chapter 2 and Chapter 4. For better understanding of the relations between the parameters and 1

their effects on the pressure rise, refer to Sensitivity Analysis covered in Chapter 3 and ANNEX F. 2

Mechanical Stress:

6

Overpressure generated during the internal arc fault test causes mechanical stress on 3

the switchgear enclosures and on building walls. Chapter provides guidelines for calculating mechanical 4

stress using Finite Element Analysis (FEA) and CFD software tools. 5

•

Burn-through:

6.4 This effect is caused by the arc which can burn on a surface of the metallic enclosure (like 6

a switchgear wall or panel, or GIS bus duct), and it melts and punctures walls. It is covered in Section .

7 8

Lastly, in effort to minimize Internal Arc tests, the working group created guideline for Internal Arc Simulation 9

review. Chapter 7 provides the guideline to replace the internal arc withstand test of the specific switchgear by 10

performing a design analysis based on tests of a similar design 11

12 13 14 15

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1 INTRODUCTION

1

1.1 Overview

2

An internal arc fault is an unintentional discharge of electrical energy within an enclosure. When the internal arc 3

fault occurs, the available short circuit current will flow through the arc between phases (see Figure 1-1) and/or 4

from phase(s) to ground. The energy released from an electrical arc heats the SF6 gas or the air within the

5

enclosure, resulting in a pressure rise. 6

7

Figure 1-1: 13 kA electric arc moving between two conductors, at 5cm distance.

8

Two ongoing trends in the power industry are causing the possible damage from internal arc faults to increase. 9

One is the increase in the available fault current levels, resulting in an increase in the available arc energy. The 10

other is the evolution towards more compact switchgear, which results in smaller enclosures. These reduced tank 11

volumes result in a higher rate of pressure rise, higher temperatures and larger electro-magnetic forces on the 12

conductors. On the other hand, minimizing SF6 gas release to the environment is becoming a more and more

13

important issue and IEC 62271-200 actually permits SF6 to be replaced by air in an internal arc test. Pressure rise,

14

temperature rise and arcing behaviour, however, might be quite different between SF6 and air, because the

15

relevant physical properties of these gases, such as specific heat, density, etc. are significantly different. Therefore 16

any reasonable way to achieve an equivalent demonstration of the performance of the test object using air should 17

be explored. 18

The incidence of internal arc faults in MV and HV switchgear is very rare, but when an arc fault occurs in an 19

electrical installation it may seriously damage the electrical equipment and the switchgear buildings (see Figure 20

1-2), and endanger personnel. Failures typically occur due to: 21

• external influences

22

• material or mechanical defects

23

• incorrect operation

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1

Figure 1-2: Internal arc fault test.

2

The physical results of an internal arc fault are significant. An internal arc fault has the following physical impacts: 3

• Pressure inside a small closed enclosure (volume 200 liters) can accelerate to 12 bars in 4 cycles of power

4

frequency during a 25 kA fault. 5

• Arc temperature can exceed 10,000 °C.

6

• The arc energy inside the arc compartment from a 25 kA fault for ¼ second is comparable to the energy

7

released by exploding 2 kg of dynamite. 8

• Sound levels can reach 160 dB. By comparison, shotgun noise is measured to be in the range of 150 – 160

9

dB. 10

• Debris may travel at speeds up to 1000 km/h.

11

• Vapourized copper expands to 67,000 times its solid volume (1 cm3 of copper vaporises into 67 L of

12

vapor). For comparison: the conversion of water into steam has an expansion factor of 1670. 13

• The resultant force of the expelled gases following rupture may reach several tones on the walls of an

14

enclosure or walls of an installation room. 15

• The temperature of the hot gases streaming out of an arcing compartment may exceed 1000 °C.

16 17

If a fault arc occurs in an electrical installation, the electrical energy of the arc plasma is transferred to its 18

surroundings by various different mechanisms. The main pressure rise is due to heat transfer. The energy input 19

into the fault arc by Joule heat is balanced by the interactions of the arc column with the electrodes, the arc length 20

and by several energy exchanges. This includes heat conduction, radiation and gas convection inside the 21

compartment where the arc occurs, and also through relief openings in the enclosure of the compartment. The 22

convective transfer of heat and the mass of the gas cause a change in the internal heat of the surrounding gas, and 23

is therefore part of the overall pressure rise. In addition, evaporated metal from the arc roots together with chemical 24

reactions play an important role in the energy transfer from the fault arc to the surrounding gas. As a result, during 25

internal arcing a rather great amount of energy is released in the cubicle and into the environment within a short 26

period of time. 27

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Although the physical processes of energy transfer from the arc to the surroundings can be described in a general 1

manner, it is difficult to describe them quantitatively. 2

The pressure rise resulting from an internal arc in a compartment can be calculated in a number ways as listed 3

below: 4

1.

The calculation of gas pressure is based on gas temperature according to the general gas equation and 6

on mass flow balance through pressure relief openings. The compartment, where the arc is ignited, and 7

other connected rooms are described by their effective volumes and openings between them. Gas 8

properties are assumed to be independent of temperature and pressure. 9

Basic models: 5

2.

These models are based on the same basic equations, effective volumes and openings. Some of them 11

consider temperature and pressure dependent gas properties. They may be extended by including further 12

effects such as exothermic reactions, ablation of material and mixing of gases. 13

Enhanced models: 10

3.

The calculation of gas pressure and temperature is based on the fluid-dynamic equations describing the 15

conservation of mass, momentum and energy of the gas in each finite volume element. The system of 16

equations is solved three-dimensionally with a computational fluid dynamics (CFD) solver. 17

CFD models: 14

The calculation approach in Chapter 2 describes the basic model in detail and provides a comparison with 18

measured data. Enhanced and CFD models are presented and discussed in the brochure (Section 2.6 and Chapter 19

4). Table 1-1 summarizes the application range and the limitations of the three approaches. 20 21 22 23 24 25 26 27 28 29 30 31

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1

Approach /model Appropriate Application Limitations

1) Basic

(low complexity)

To quickly calculate uniform pressure rise inside an arc compartment and the exhaust volume in typical MV switchgear and HV GIS applications.

• Doesn’t consider spatial

non-uniformity of gas parameters (pressure, temperature, density) in each volume part.

• Not applicable if the relief opening

area is too large in relation to the compartment volume.

• Calculations are not reliable, when

gas temperature exceeds approx.

2000 K for SF6 and 6000 K for air.

• Doesn’t consider gas mixtures in the

exhaust compartment.

2)

Enhanced (medium complexity)

To calculate uniform pressure rise as under 1) adding further

approximations to better match test results and calculation.

• Doesn’t consider spatial

non-uniformity of gas parameters (pressure, temperature, density) in each volume part.

• Limitations and applications depend

on the implemented approximations.

3) CFD

(High complexity)

For calculating spatial pressure

distribution and gas flow in odd shapes geometry and large rooms.

• High effort for the modeling and

meshing of the rooms and switchgear

• Requires large computing power

and time.

Table 1-1: Model selection table.

2

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1.2 Definitions and Abbreviations

1

Ablation: Removal of material from the surface of an object by vaporization, or other erosive processes.

2

Arc: High current electric discharge between electrodes in a fluid (liquid or gas).

3

Arc absorber: Meshes, grids, perforated metal sheets or similar devices placed in one or more layers into the

4

exhaust gas flow in order to absorb some energy of the arc exhaust. 5

Arc blast: Direct pressure wave (gas pressure either of hot plasma gases or cold gases, air or a combination of

6

these) that can cause damage to humans, equipment, and surroundings

7

Arc compartment: Enclosed part of metal-enclosed switchgear, where an arc fault occurs. Relatively small

8

openings necessary for interconnection, control or ventilation may be present.

9

Arc duct: Channel connected to the arc-exhaust intended to lead the arc products to another place.

10

Arc exhaust: The expulsion of hot gases from an arc fault through the relief opening of an arc compartment.

11

Arc fault: A high power discharge of electricity caused by a breakdown of insulation or flashover generating

12

excessive heat. 13

Arc fault – single phase: Arc fault occurring between one conductor and ground.

14

Arc fault – three phase: Arc fault occurring between three conductors or between three conductors and ground.

15

Arc flash: Direct physical phenomenon such as flame due to the hot plasma expansion of an arc fault. This can

16

cause burns and fire, and impacts humans as well as equipment and surroundings.

17

Arc plasma: Thermal plasma generated by an arc.

18

Arc power: Active (electrical) power of an arc given by the product of momentary current and voltage measured at

19

the terminals of the test object.

20

Arc voltage: Voltage which appears between the electrodes of an arc.

21

Arcing time: The time elapsing from the ignition of an arc to the interruption of the current.

22

Available (prospective) current: The current that would flow in a circuit if each pole of the switching device was

23

short-circuited by a link of negligible impedance without any other change in the circuit or the supply.

24

Basic model: Mathematical approach for the calculation of pressure rise due to an internal arc using simplified

25

equations under basic assumptions.

26

Burn-through: A hole burnt through the walls of the equipment enclosure or compartment by an arc.

27

Computational fluid dynamics (CFD): A branch of fluid mechanics that uses numerical methods and algorithms

28

to solve and analyze problems that involve fluid flows.

29

Deflection: The degree to which a structural element is displaced or bent under a mechanical load. It may refer to

30

an angle or a distance.

31

Deflectors: Plates placed in the flow of exhaust gas to deflect the stream of gas.

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Discharge coefficient: Ratio of effective opening area of a pressure relief device to its geometric area.Considers

1

the effect of discharge of gases through real and ideal nozzles.

2

Dynamic pressure: The pressure on a surface at which a flowing fluid is brought to rest in excess of the pressure 3

of the fluid at rest (static pressure). 4

Enclosure: A surrounding case or housing used to protect the enclosed equipment and to prevent personnel from

5

accidental contact with live parts.

6

Enhanced model: Mathematical approach for the calculation of pressure rise due to an internal arc applying a

7

number of extensions to the basic model with respect to equations and assumptions.

8

Exhaust channel: See arc duct.

9

Exhaust compartment: Enclosed volume adjacent to the arc compartment which receives the arc exhaust.

10

Exothermic: In thermodynamics, the term exothermic ("outside heating") describes a process or reaction that

11

releases energy from the system.

12

Fault-shorting switch (arc killers): Eliminates arc faults by creating a metallic short circuit. It generally has a

13

sensor to detect the arc and an earthing device to extinguish it. The sensor can be either sensitive to the light 14

generated by the arc or to the pressure reached in gas sealed tank. 15

Finite element analysis (FEA): A numerical technique for finding approximate solutions of partial differential

16

equations (PDE) as well as integral equations.

17

Finite volume method (FVM): A method for representing and evaluating partial differential equations in the form of 18

algebraic equations. "Finite volume" refers to the small volume surrounding each node point of a mesh. 19

Heat capacity ratio: Ratio of the specific heat of a gas taken at constant pressure to that taken at constant volume

20

also termed “adiabatic index”. 21

Heat conduction: A mode of transfer of energy within and between bodies of matter, due to a temperature

22

gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of tangible matter (as 23

distinct from photons). 24

Heat convection: Heat transfer by the flow of a fluid in regions with different temperatures. Convective heat and

25

mass transfer take place through both diffusion (the random Brownian motion of individual particles in the fluid) and 26

by advection, in which matter or heat is transported by the larger-scale motion of currents in the fluid. 27

Heat flux: Heat flux or thermal flux, sometimes also referred to as heat flux density or heat flow rate intensity is a

28

flow of energy per unit of area per unit of time.

29

Heat flux sensor: A transducer that generates an electrical signal proportional to the total heat rate applied to the

30

surface of the sensor. The measured heat rate is divided by the surface area of the sensor to determine the heat

31

flux.

32

Heat radiation:Emission and propagation of energy in the form of electromagnetic waves.

33

Heat transfer: Transfer of heat e.g. from an arc to its surroundings. Heat transfer is classified into various

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Infrared thermography: Thermal imaging cameras detect radiation in the infrared range of the electromagnetic 1

spectrum (roughly 9000–14,000 nanometres or 9–14 µm) and produce images of that radiation, called 2

thermograms. The amount of radiation emitted by an object increases with temperature; therefore, thermography 3

allows one to see variations in temperature. 4

Joule heating: Heating caused by an electric current through a resistive material. 5

𝒌𝒑-factor: Ratio of that part of the arc power (or energy) responsible for the heating of gases inside the arc

6

compartment to the total arc power (or energy).

7

Longitudinal wave: Also known as "l-waves", are waves that have the same direction of vibration as their direction

8

of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the

9

motion of the wave.

10

Metal-enclosed switchgear: A switchgear assembly completely enclosed by sheet metal (except for ventilation

11

openings and inspection windows) containing primary power circuit switching or interrupting devices, or both, with

12

buses and connections, which may also include control and auxiliary devices. Access to the interior of the

13

enclosure is provided by doors or removable covers.

14

Metal evaporation: Heating a metallic part up to a temperature, at which a considerable amount of metal vapour is

15

released from its surface.

16

Navier-Stokes equation: The Navier–Stokes equations describe the motion of fluid substances. These equations

17

arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the

18

sum of a diffusing viscous term (proportional to the gradient of velocity), plus a pressure term.

19

Net compartment volume: Effective volume of a compartment after subtraction of the volume of all built-in

20

components.

21

Overpressure: Pressure above ambient pressure within a pressurized enclosure.

22

Pad-mounted: A general term describing switchgear equipment positioned on a surface-mounted pad located

23

outdoors. The equipment is usually enclosed with all exposed surfaces at ground potential.

24

Pressure relief device: A device which opens on overpressure, releasing gases from a compartment into the

25

ambient atmosphere. A pressure relief device can be a loose flap or even a constant opening to the outside world.

26

Pressure withstand: Maximum pressure which can be withstood by an enclosure.

27

Relief opening area: Area provided by a pressure relief device to expel hot gases.

28

Response (bursting) pressure: Pressure at which a pressure relief device is ruptured or opens.

29

Rupture (bursting) disc: A non-reclosing pressure relief device that, in most uses, protects a pressure vessel,

30

equipment or system from overpressurisation. A rupture disc is a type of sacrificial part because it has a

one-time-31

use membrane that fails at a predetermined differential pressure, either positive or negative.

32

Short circuit: An abnormal connection (including an arc) of relatively low impedance, whether made accidentally or

33

intentionally, between two points of different potential.

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Static pressure: The pressure exerted by a liquid or gas when the bodies on which the pressure exerted are not in

1

motion.

2

Switchgear: A general term covering switching and interrupting devices and their combination with associated

3

control, metering, protective, and regulating devices; also assemblies of these devices with associated

4

interconnections, accessories, enclosures, and supporting structures, used primarily in connection with the

5

generation, transmission, distribution and conversion of electric power.

6

Von-Mises stress: The stress associated with the deformation of material such that the actual distortion energy is

7

equivalent to uniaxial simple tension case.

8

Yield point (yield strength): is defined in engineering and materials science as the stress at which a material

9

begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original

10

shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be

11

permanent and non-reversible.

12

Young’s modulus: It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in

13

which Hooke's Law holds. It can be experimentally determined from the slope of a stress-strain curve created

14

during tensile tests conducted on a sample of the material.

15

1.3 Referred standards

16

EEMAC G14-1, Procedure For Testing The Resistance Of Metal Clad Switchgear Under Conditions Of Arcing Due 17

To An Internal Fault, EEMAC G14-1, 1987. 18

EN 61482-1-2, IEC Standard 61482-1-2. Live working – Protective clothing against the thermal hazards of an 19

electric arc. Part 1-2: Test methods - Method 2: Determination of arc protection class of material and clothing by 20

using a constrained and directed arc (box test). 21

IEC 60076-5, IEC Standard 60076-5. Third edition 2006. Annex A: Theoretical evaluation of the ability to withstand 22

the dynamic effects of short circuit. 23

IEC 60298, IEC 60298 A.C. metal-enclosed switchgear and controlgear for rated voltages above 1 kV and up to 24

and including 52 kV. 25

IEC 62271-200, High-voltage switchgear and controlgear –Part 200: AC metal-enclosed switchgear and 26

controlgear for rated voltages above 1 kV and up to and including 52 kV. Ed.2.0 , 2011 27

IEC 62271-201, High-voltage switchgear and controlgear - Part 201: AC insulation-enclosed switchgear and 28

controlgear for rated voltages above 1 kV and up to and including 52 kV. 29

IEC 62271-203, High-voltage switchgear and controlgear Part 203: Gas-insulated metal-enclosed switchgear for 30

rated voltages above 52 kV. 31

IEEE 1584-2002, IEEE 1584 Standard. IEEE Guide for Performing Arc-Flash Hazard Calculations. 32

IEEE Standard C37.20.7-2007, IEEE Guide for Testing Medium Voltage Metal-Enclosed Switchgear for Internal 33

Arcing Faults. 34

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NFPA 70E-2012, Standard for Electrical Safety in the Workplace, NFPA, 1 Batterymarch Park, Quincy, MA 02169-1 7471. 2 3 4

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2 CALCULATION OF PRESSURE USING A BASIC MODEL

1

2.1 Introduction

2

The first part of this chapter (Sections 2.2-2.4) focuses on describing of the basic equations, assumptions and 3

limitations of the basic model. The derivation of the equations is given in ANNEX A.2. In Section 2.5 the pressure 4

curves measured in several selected test cases are compared with the results of calculations taking the actual test 5

arrangements and measured arc current and voltage into account. In Section 2.6 and ANNEX A.4, modifications of 6

the basic equations leading to enhanced models, which improve the agreement between simulation and test results 7

for certain aspects are presented. 8

2.2 Equations of the basic model

9

2.2.1 Basic arrangement and quantities

10

Figure 2-1 shows schematically an installation consisting of arc compartment, exhaust compartment, and 11

installation room/environment. The arc represented by the temporal development of energy input 𝑄₁ is ignited in the

12

arc compartment with volume 𝑉₁. A pressure relief opening with cross-section 𝐴₁₂ connects the arc to the exhaust

13

compartment with volume 𝑉₂. When the pressure 𝑝₁in the arc compartment reaches the response pressure, the

14

relief device opens and gas flows into the exhaust compartment 𝑉₂. From there, gas flows through the opening with

15

cross-section A23 into the installation room or environment with volume 𝑉₃. 16

Figure 2-1: Principal arrangement and quantities used for pressure calculation.

17 18

The type of insulating gas in each volume is characterized by the corresponding heat capacity ratio (adiabatic 19

index) and the specific gas constant 𝑅_𝑠. In the basic model, these quantities are assumed to be constant. The initial

20

state of the gas is defined by pressure 𝑝 and temperature 𝑇. While volume 𝑉₁ may be filled with air or SF6, volumes

21

𝑉2 and 𝑉3 are typically always filled with air.

22 1

p

A

12 12

m



1

Q



1 V

1

T

2

p

A

23 23

m



2

V

2

T

3

p

3

V

3

T

t

Compartmen

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𝑚1

=

_{𝑅𝑠1𝑇}

𝑝1𝑉

1 1

𝑚2

=

𝑝2𝑉

2

𝑅𝑠2𝑇

2

(2-1)

𝜌

1

=

𝑚

_𝑉

1 1

𝜌

2

=

𝑚

2

𝑉

2

(2-2)

𝑐𝑣1

=

_𝜅1

𝑅𝑠1

₋

₁

𝑐𝑣2

=

_𝜅2

𝑅𝑠2

₋

₁

(2-3)

𝑐

𝑝1

=

𝜅

1

𝑐

𝑣1

𝑐

𝑝2

=

𝜅

2

𝑐

𝑣2

(2-4)

The thermal energy𝑄₁ as a part of the electrical energy 𝑊_𝑒𝑙 heats up the gas.

1

𝑄

1

=

𝑘

𝑝

𝑊

𝑒𝑙

(2-5)

The thermal transfer coefficient 𝑘_𝑝, which is described in Section 2.3.6, describes the relationship between the

2

thermal and electrical energy. In the basic model, 𝑘_𝑝 is taken as constant. The equations for difference of thermal

3

energy (∆𝑄₁=𝑘_𝑝∆𝑊_𝑒𝑙) are provided in Section 2.3.5.

4

2.2.2 Mass flow

5

In the following, all time-dependent quantities are considered before and after a time step Δ𝑡. The mass flow from

6

the arc compartment into the exhaust compartment is given by: 7

Δ𝑚

12

=

𝛼

12

𝐴

12

𝜌

12

𝑤

12

Δ𝑡

(2-6)

𝛼12 is the discharge coefficient, which considers the contraction of gas flow through an opening. Obstacles in the

8

gas flow such as a metallic mesh or lamellas may be included in this coefficient (𝛼₁₂𝐴₁₂ is the effective opening).

9

Reaching the response pressure in 𝑉₁, the pressure relief device opens. 𝜌₁₂ and 𝑤₁₂are the gas density and gas

10

velocity within the opening 𝐴₁₂, which are different from the values in 𝑉₁ and 𝑉₂ [Schmidt1958]. 11

𝜌12

=

𝜌1

�

𝑝12

_𝑝1

�

1 𝜅1

_(2-7)

𝑤

12

=

�

_𝜅

2 𝜅1

1

−

1 𝑝1

𝜌

1

�

1 − �

𝑝12

𝑝

1

�

𝜅1−1 𝜅1

_�

_(2-8)

If the ratio of pressure in 𝑉₁ and 𝑉₂ i.e. 𝑝₁/𝑝₂ exceeds a value of 1.89 for air and 1.70 for SF6, respectively, 𝑝₁₂ is 12

determined by the critical pressure 𝑝₁∗; for smaller ratios 𝑝₁₂ is equal to the pressure in 𝑉₂. 13

(20)

𝑝

1∗

=

𝑝1

�

_𝜅1

2 _{+ 1}

�

𝜅1

𝜅1−1

_(2-10)

The mass in volume 𝑉₁ is reduced after the time step Δ𝑡 by the mass Δ𝑚₁₂

1

Δ𝑚

1

=

−Δ𝑚

12

(2-11)

The mass from the exhaust compartment flowing into the installation room (𝑉₃) is given by:

2

Δ𝑚23

=

𝛼23𝐴23𝜌23𝑤23Δ𝑡

(2-12)

Density and flow velocity are calculated using the equations provided above with all indices incremented by one. 3

The change of mass in volume 𝑉₂within Δ𝑡is the difference between the incoming mass Δm₁₂and the outgoing

4 mass Δm₂₃ during Δ𝑡. 5

Δ𝑚

2

=

Δ𝑚

12

− Δ𝑚

23

(2-13)

2.2.3 Gas temperature

6

The temperature change in the arc compartment with volume 𝑉₁ after the time step Δ𝑡 is determined by the

7

difference between the thermal energy input by the arc (Δ𝑄₁) and the energy loss due to gas flow out of the

8

compartment (see ANNEX A.2.4 for details): 9

Δ𝑇

1

=

Δ𝑄1

− Δ𝑚12�𝑐𝑝1

_𝑚

− 𝑐𝑣1�𝑇

1

𝑐

𝑣1

(2-14)

The corresponding temperature change in 𝑉₂is:

10

Δ𝑇

2

=

Δ𝑚

12

�𝑐

𝑝1

𝑇

1

− 𝑐

𝑣2

𝑇

_𝑚

2

� − Δ𝑚

23

�𝑐

𝑝2

− 𝑐

𝑣2

�𝑇

2 2

𝑐

𝑣2

(2-15)

The summation of all temperature changes Δ𝑇_𝑖 provides the temperature at time 𝑡.

11

2.2.4 Gas pressure

12

With given gas mass and temperature, the pressure in 𝑉₁ and 𝑉₂ at time 𝑡 is given by the ideal gas law:

13

𝑝

1

=

(

𝜅1

_𝑉

−

1)

1

𝑚

1

𝑐

𝑣1

𝑇

1

𝑝

2

=

(

𝜅2

−

1)

𝑉

2

𝑚

2

𝑐

𝑣2

𝑇

2

(2-16)

Temperature 𝑇₃ and pressure 𝑝₃ in the installation room are calculated correspondingly.

(21)

2.3 Input parameters

1

2.3.1 Gas data

2

The model requires the input of two basic gas quantities, i.e. the heat capacity ratio and the specific gas constant 3

𝑅𝑠. They depend on the specific heats, 𝑐𝑣 and 𝑐𝑝, (see Section 2.2.1). These quantities are assumed to be constant

4

and are given in Table 2-1 taken from publications. The value of 𝜅_{is calculated directly from}𝑐_𝑝 and 𝑅_𝑠 using

5

equations (2-3) and (2-4). The assumption of 𝑐_𝑝 being independent of temperature is acceptable up to

6

temperatures where gases start to dissociate (approximately 2000 K for SF6 and 6000 K for air). For higher

7

temperatures, distinct maxima in the specific heat capacity curves occur which change the values of 𝜅 and 𝑅_𝑠

8

significantly (see Section A.4.8). This limits the applicability of the model. Typically such high gas temperatures are 9

reached in the arc compartment after opening of the relief device. 10

Parameter Air

[Mende1975]

SF6

[Solvay]

𝑐𝑣

specific heat capacity at constant volume 716 608 J kg-1/K

𝑐

𝑝 specific heat capacity at constant pressure 1005 665 J kg-1/K

𝜌

gas density 1.205 6.07 kg/m3

𝜅

heat capacity ratio (kappa) 1.403 1.0936

𝑀

molar mass 29 146 kg/kmole

𝑅

universal (molar) gas constant 8314 8314 J K-1 kmole-1

𝑅𝑠

specific gas constant 287 56.9 J K-1 kg-1

Table 2-1: Basic gas quantities at normal conditions (20 °C and 101.3 kPa).

11

For SF6 insulated switchgear, the flow of SF6 out of the arc compartment leads to an SF6/air mixture in the exhaust

12

compartment. Gas mixing is not considered in this model, i.e. the gas properties in the exhaust compartment are 13

taken to be those of pure air. However the mass and energy exchange is considered correctly. This simplification is 14

reasonable as long as the SF6 concentration is low (e.g. in large exhaust compartments). For high concentrations,

15

gas data from mixtures have to be considered (see Section A.4.4). 16

2.3.2 Volume

17

All volumes in the model are net volumes i.e. volume of compartment minus volume of built-in components. The 18

shape of the compartment is not considered. The volume of the built-in components might reach 10 to 20 % of that 19

of the arc compartment. The energy supplied by the arc is taken as homogeneously distributed inside the arc 20

compartment. That is why the model does not cover pressure waves, which might play a role in long, narrow 21

compartments (channels). 22

(22)

2.3.3 Pressure relief opening

1

Relief openings are represented by effective areas, i.e. the geometric cross-section of the opening diminished by 2

the area of frames, slats, grills etc. (see Section 2.2.2). The discharge coefficient is assumed to be 0.7 for air 3

[Dubbel1997] and 0.8 for SF6 [Anantavanich2008]. The opening of the relief device occurs instantaneously at the

4

response pressure. For heavy relief flaps, the opening process possibly needs some time and might increase the 5

over-pressure in the compartment. 6

If openings are large compared to the volume of the compartment, then the equations of the model are no longer 7

applicable. A critical dimension could be in the order of 10 % of the area of a side surface assuming the net volume 8

is a cube. 9

The response pressure of the relief device is most often given as a static value. If the value is determined from 10

arcing tests, it is a “dynamic” value. Experience shows that the difference between both is of the same order as the 11

scatter from sample to sample. 12

2.3.4 Arc current

13

For pressure calculation the temporal development of the single or three-phase fault current must be known. This 14

current development can be taken from test or from simulation. The asymmetry of the short circuit current might 15

influence the initial pressure build-up, however, has little influence on the later pressure curve. As long as the 16

supply voltage is much higher than the arc voltage, the arc resistance does not influence the current asymmetry 17

(see Section 5.2.4). Knowing the d.c. time constant of the circuit 𝜏_𝑑_._𝑐_., of the source circuit, the temporal

18

development of the current 𝑖(𝑡) in a three-phase system can be calculated using e.g. the formula:

19

𝑖𝑝ℎ𝑎𝑠𝑒

=

√

2 𝐼𝑟𝑚𝑠

�

sin

�𝜔𝑡

+

𝜑 − 𝜃𝑝ℎ𝑎𝑠𝑒� −

sin

�𝜑 − 𝜃𝑝ℎ𝑎𝑠𝑒�𝑒

−𝜏𝑑𝑡.𝑐.

�

(2-17)

inserting the angular frequency 𝜔, the angle of fault initiation 𝜑, and the shift between the phases, 𝜃_{𝑝ℎ𝑎𝑠𝑒}.

20

2.3.5 Arc voltage

21

The arc voltage is one of the most important parameters determining arc energy and hense the pressure rise. In 22

tests the arc energy is determined from measured line currents and phase-to-ground voltages: 23

Δ𝑊

𝑒𝑙

= (

𝑢

𝑅

𝑖

𝑅

+

𝑢

𝑆

𝑖

𝑆

+

𝑢

𝑇

𝑖

𝑇

)

Δ𝑡

(2-18)

The term in brackets is the arc power. The arc voltage is the voltage drop of an arc between its roots. For pressure 24

calculations (and the comparison with measured values) averaged arc voltages 𝑈_𝑎𝑟𝑐 are used. In a three-phase

25

system, the phase-to-ground voltage may not be identical with the arc voltage. If the arc appears between the 26

phases only two arcs appear simultaneously commutating between the phases. In this case the arc energy during 27

Δ𝑡 is given by [Welich1984]:

28

(23)

If an arc burns between phase and ground (enclosure wall), the arc voltage is identical with the phase-to-ground 1

voltage and the arc energy during Δ𝑡 is given by:

2

Δ𝑊

𝑒𝑙

=

𝑈

𝑎𝑟𝑐

(|

𝑖

𝑅

| + |

𝑖

𝑆

| + |

𝑖

𝑇

|)

Δ𝑡

(2-20)

Because of the ambiguity of equations (2-19) or (2-20), it is recommended to always use equation (2-18) and the

3

three measured phase-to-ground voltages for the determination of the arc energy. In principle, the mean arc 4

voltage, 𝑈_𝑎𝑟𝑐, over a certain period can be determined by equating the measured arc energy with equation (2-19).

5

This gives the correct mean arc voltage for a phase-to-phase arc. For simplicity, sometimes equation (2-20) is used

6

as an input for calculation; however, it will give only correct arc energies when the lower (approximately factor of 2) 7

arc voltage for a phase-to-ground arc is inserted. This has to be kept in mind. 8

Arc voltage fluctuates, e.g. due to arc looping, and varies in time, e.g. caused by strong evaporation of electrode 9

material. The arc voltage differs between an arc ignited in an empty or in a fully equipped compartment. Some 10

experiments show that the arc voltage increases with rising pressure in the compartment and decreases later after 11

pressure reduction [Dullni1994]. 12

If arc voltage data is missing, basic formulas, which have been extracted from three phase internal arc tests with 13

MV metal enclosed switchgear separately for air and SF6 and copper electrodes might be used [AiF2011]. These

14

voltages have to be applied together with the energy equation (2-19) for arcs between phases.

15

𝑈

𝑎𝑟𝑐

𝑑

= 30

V

cm +

1

2 𝐼𝑟𝑚𝑠

V

cm kA

≤

40 V

cm (air)

(2-21)

𝑈

𝑎𝑟𝑐

𝑑

= 40

V

cm +

1

2 𝐼𝑟𝑚𝑠

V

cm kA

≤

50 V

cm (SF

6

)

(2-22)

Here 𝑈_𝑎𝑟𝑐 is the arc voltage between phases, 𝑑 is the distance between pole centres, and 𝐼_𝑟𝑚𝑠 is the effective short

16

circuit current. 17

For single phase HV aluminium enclosures filled with 1 to 4 bar of SF6 the following formula has been derived from

18

a survey of available data for certain specific conditions (details see [König1984]). 19

𝑈

0

𝑉

= 250 +

�

𝐷

mm

−

50 �

+ 4

𝐼

𝑟𝑚𝑠

kA

(2-23)

Here 𝑈₀ is the arc voltage including the 𝑘_𝑝 -factor, 𝐷 is the clearance between conductor and wall, and 𝐼_𝑟𝑚𝑠 is the

20

effective short-circuit current. 21

Internal arc faults in electrical switchgear in 3-phase arrangements typically start as a phase to ground or as a 22

phase to phase fault. If this arc fault cannot be eliminated automatically in a short time (in the millisecond range), 23

and no single pole solid insulation is present, it will most likely develop into a three-phase arc fault. A three phase 24

arc fault consists of two parallel arcs with arc roots changing among the three phases. In the case of close 25

proximity of the enclosure, the fault may rapidly develop into three parallel phase-to-ground arcs. 26

Depending on the network voltage, the time constant of the asymmetrical arcing current will decrease to about half 27

of the value for a solid short circuit (12 kV, 20 kA will result in 22 ms time-constant out of the standard 45 ms). This 28

(24)

means that a fully asymmetrical current will sooner become symmetrical due to the arc resistance than the current 1

from a solid short circuit would do. 2

Figure 2-2: Momentary arcing powers. Asymmetrical (

τ

= 45 ms) first 5 periods (100 ms) and symmetrical

3

one period.

4

2.3.6 k

p

- factor

5

The heat transfer coefficient 𝑘_𝑝 determines that fraction of the electrical arc energy, which directly results in a

6

pressure rise in the arc compartment. Theoretical approaches to calculate 𝑘_𝑝 based on a detailed energy balance

7

e.g. [Zhang2002] exist, however, this approach is not really feasible. In practice, 𝑘_𝑝 is determined by fitting the

8

calculated pressure rise to the measured one before the operation of the pressure relief device. If exothermic 9

reactions occur, e.g. between aluminium and SF6, additional energy might heat up the gas resulting in a 𝑘_𝑝-factor

10

possibly larger than 1. 11

It is highly recommended that 𝑘_𝑝-factors are determined from tests under similar conditions. If no experiments are

12

available, 𝑘_𝑝 -factors taken from publications should be used with caution. It has been found that in general 𝑘_𝑝 in air

13

is lower than in SF6 [Dullni1994, Friberg1995]. Based on these experimental investigations, 𝑘_𝑝 for air at standard

14

conditions with copper electrodes ranges from 0.40 to 0.65 and in case of SF6 from 0.50 to 0.70. For aluminium

15

electrodes 𝑘_𝑝 might be higher due to exothermic reactions. The authors have calculated values of 𝑘_𝑝 up to 1.6 with

16

the basic model. It has also been found by experiment that 𝑘_𝑝 depends on gas density. This is important for

17

compartments with relief openings, where gas density is considerably reduced during the exhaust of gas (see 18

Section A.4.1). In general, 𝑘_𝑝 decreases with gas density [Dullni1994, Zhang2002].

19

2.4 Application limits of the basic model

20

Due to the assumptions implemented in the basic model, the user should be aware of how the application range is 21

(25)

• Pressure rise in a closed arc compartment in air and SF6 1

• Pressure rise in an arc compartment with relief opening in air and SF6

2

• Energy transfer from the arc to the exhaust compartment

3

The limitations to be considered are as follows: 4

• The simulation of pressure development is feasible until the dissociation temperature is reached in the arc

5

compartment. The calculation should be stopped at temperatures of about 6000 K in air and about 2000 K 6

in SF6. In fact, here the calculations have been continued up to 20000 K for both gases. The temperature

7

limit is reached faster the smaller the volume of the arc compartment, the higher the arc energy and the 8

larger the relief opening (due to the reduced gas density). 9

• The model does not consider the evaporation of metal or insulation material, which influences gas

10

composition, density and temperature. This influence is negligible as long as the density of the insulating 11

gas (air or SF6) is larger than the density of the vapour. Due to the exhaust of gas from the arc

12

compartment, the density of the insulating gas drops within this compartment, and the proportion of gas 13

resulting from evaporation becomes more and more important. For long arcing times the gas in the arc 14

compartment may practically consist only of evaporated material. Because evaporation is not considered in 15

the model, the simulation results become uncertain when the insulating gas density in the arc compartment 16

drops significantly. 17

• If considerable gas flow occurs in any compartment (e.g. in elongated rooms or channels) the approach

18

with spatially averaged quantities is not applicable. As a consequence, reliable results are only achieved 19

for pressure relief opening areas limited to not more than 10 % of the side surface of the arc compartment 20

(see Section 2.3.3). 21

• The energy transfer out of the arc compartment determines the pressure rise in the exhaust compartment.

22

The model assumes a constant gas type in the exhaust compartment. Typically the exhaust compartment 23

is filled with air. In case of SF6-insulated switchgear the gas in the exhaust compartment will be a mixture

24

of SF6 and air. Therefore the assumption of only air in the exhaust compartment is violated when the SF6

25

portion becomes remarkable. This might be the case for small exhaust volumes. These considerations do 26

not affect air-insulated switchgear. 27

Some of these limitations can be overcome to some extent by additional approaches (e.g. enhanced models, see 28

Section 2.6). These include for example the application of real gas data, the evaporation of metal and insulation 29

material, gas mixtures, the density dependence of the 𝑘_𝑝-factor and exothermic reactions. Such modifications do

30

not really increase the accuracy of the pressure calculation in the arc compartment, but allow the extension of the 31

calculation for longer arcing times and a calculation of the pressure rise in the exhaust compartment or installation 32

room. Spatial resolution, if necessary, can be achieved using CFD tools. Anyhow these are in principle subject to 33

the same limitations as discussed above. 34

(26)

2.5 Application of the basic model to selected test cases

1

2.5.1 General

2

Within the CIGRE A3.24 working group 70 data sets of internal arc tests covering MV and HV tests of air and SF6

3

insulated switchgear have been collected and recalculated with the basic model. All of them have been evaluated 4

concerning typical pressure-related parameters.. The test arrangements of the selected cases are shown in 5

Section 2.5.2. These cases can be used by readers to benchmark their own calculation programs. 6

The following procedure has always been applied: 7

• insulation gas and filling pressure are taken from the test conditions;

8

• geometrical input values are derived from available drawings;

9

• discharge coefficient is chosen between 0.7 to 1 (adapted to the measured pressure decay);

10

• energy input is based on the measured currents and averaged phase-to-ground voltages using equation

11

(2-18) (see Section 2.3.5); 12

• 𝑘𝑝-factor results from adapting the calculated to the measured pressure rise (slope

∆𝑝

/

∆𝑡

up to the

13

response pressure of the relief device); 14

• response pressure pburst of the relief device is taken from measured pressure curves;

15

• the limitations described in Section 2.4 are respected.

16

The input parameters and initial values of the selected cases are listed in Table 2-3, Table 2-4 and Table 2-5 17

respectively. Some details of the test arrangements or switchgear configurations are given in Section 2.5.2. 18

Calculated and measured pressure curves are shown in Figure 2-10 to Figure 2-17. The red curves show the 19

calculated pressure in the arc compartment, the blue curves the pressure in the exhaust compartment, if available. 20

Grey curves present measured data. The simulation stops when the gas temperature in the arc compartment 21

reaches 20000 K. The changes in the gas pressure in the arc and exhaust compartments are characterised by 22

values determined from measured pressure curves. These values are depicted in Figure 2-3 and listed in Table 23

2-2. 24

Peak pressure 𝒑_𝒎𝒂𝒙 Maximum pressure measured after opening of the relief device

Time to peak 𝒕_𝒎𝒂𝒙 Time between start of pressure rise and maximum pressure 𝑝_𝑚𝑎𝑥

Response pressure 𝒑_{𝒃𝒖𝒓𝒔𝒕} Pressure value, at which the relief device opens

Response time 𝒕_{𝒃𝒖𝒓𝒔𝒕} Time, at which the relief device opens

Decay time 𝒕_{𝒅𝒆𝒄𝒂𝒚} Duration of pressure drop starting from peak pressure 𝑝_𝑚𝑎𝑥

Pressure slope 𝒔_{𝒃𝒖𝒓𝒔𝒕} Initial rise of pressure until 𝑡_{𝑏𝑢𝑟𝑠𝑡}

Table 2-2: Characteristic values for the pressure curve.

25

The change of gas pressure in the exhaust volume can be characterised by the two values 𝑝_𝑚𝑎𝑥and 𝑡_𝑚𝑎𝑥. The

26

onset of pressure rise in this volume is identical to 𝑡_{𝑏𝑢𝑟𝑠𝑡} determined from the pressure rise in the first volume.

(27)

When the arc compartment is already filled with gas at e.g. rated pressure, the pressure curve starts above the 1

zero line as shown in Figure 2-3. 2

3

Figure 2-3: Characteristic values determined from calculated or measured pressure curve.

4

2.5.2 Test arrangements

5

Side view of container

• Welded cube-shaped steel container

• Single phase Cu terminals

• Linear electrode arrangement

• Arc ignited between two electrodes

• Circular relief device with bursting disc

•

Exhaust into open air

Figure 2-4: Test cubicle used for cases A and E.

6 7

(28)

Use of graphical symbols:

• Red arrow: Current in-feed

• Brown cones: current bushings

• Yellow symbol: arc ignition point

• Blue area: relief device

•

Light green: SF6 or air-filled volume

Top view of switchgear housing.

• Welded switchgear housing (steel)

• Three phase Cu terminals

• Side-by-side electrode arrangement

• Arc ignited between Cu electrodes

• Rectangular relief device with bursting

disc

• Exhaust into open air

Figure 2-5: Switchgear used for case F.

1

Front view of bus bar compartment

• Three phase Cu bars

• Side-by-side electrode arrangement

• Arc ignited in fully equipped bus bar

compartment

• Exhaust into Channel 𝑉₂

Figure 2-6: Switchgear used for cases D and G.

2 3

(29)

Front view of switchgear (RMU)

• Double phase terminals (cable plugs)

• Side-by side electrode arrangement´

• Arc ignited in cable compartment

• Rectangular relief device with flap

• Combination of all volumes into one

•

Exhaust into open air

Figure 2-7: Switchgear used for case C.

1 2

Top view arc and exhaust volumes

• Two welded steel housings

• Single phase Cu terminals

• Linear electrode arrangement

• Arc ignited in volume

𝑉

₁

• Exhaust into volume

𝑉

₂

Figure 2-8: Experimental arrangement used for case B.

(30)

Cross-section of encapsulation

• Cast aluminum housings

• Single phase circular Al bar

• Coaxial electrode arrangement

• Arc ignited at spacer

• Exhaust into open air

Figure 2-9: Arrangement of single-phase HV components used for case H.

1

2.5.3 MV switchgear with air insulation

2

Case No. A B C D

Volume of arc comp. (𝑉₁) 0.509 0.509 0.648 0.27 m³

Volume of exhaust comp. (𝑉₂) >1000 1.275 >1000 0.58 m³

Volume of installation room (𝑉₃) n/a >1000 n/a >1000 m³

Initial filling pressure in 𝑉₁ 150 160 100 120 kPa abs air

Initial filling pressure in 𝑉₂ 100 100 100 100 kPa abs air

Area of the relief opening 𝐴₁₂ 0.00456 0.00456 0.0763 0.049 m²

Discharge coefficient of 𝐴₁₂ 0.7 1.0 0.7 1.0

Response pressure of relief device 276 285 35,3 220 kPa rel

Area of the opening 𝐴₂₃ 0 0.010 0 0.195 m²

Short-circuit current 14.5 14.5 14.5 38.8 kA rms

Number of phases 1 1 2 3

Averaged phase-to-ground voltage 314 424 400 250 V

𝑘𝑝

-

factor 0.4 0.55 0.7 0.6

Table 2-3: Input parameters and initial values for MV switchgear cases with air insulation.

3

4 5 6

(31)

1

Figure 2-10: Case A – Measured and calculated pressure development in

_V

1

in air.

2

3

4

Figure 2-11: Case B – Calculated pressure developments in

_V

1

and

V

2

in air and comparison with test.

5 Case A 22 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 time [s] pr es s ur e [ M P a] P1 calculated P1 measured Case B 27 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 time [s] pr es s ur e [ M P a] P1 calculated P2 calculated P1 measured P2 measured

(32)

1

2

Figure 2-12: Case C – Calculated pressure development in

_V

1

in air and comparison with test.

3

4

5

Figure 2-13: Case D – Calculated pressure developments in

_V

1

and

V

2

with air as filling gas and

6

comparison with test.

7 8 9 Case C 70 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 time [s] pr es s ur e [ M P a] P1 calculated P1 measured Case D 14 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 time [s] pr es s ur e [ M P a] P1 calculated P2 calculated P1 measured P2 measured

(33)

For air as the filling gas in the compartment, calculation with the basic model and measured results show good 1

agreement. Peak pressure and drop of pressure in the arc compartment show good coincidence. The 𝑘_𝑝-factor is

2

taken between 0.4 and 0.7, which is in accordance with published data. The calculation of the pressure 3

development in the exhaust compartment shows less satisfying agreement with the test results. This could be a 4

matter of the position of the pressure sensor during the particular test when the exhaust compartment is much 5

longer than wide (like a channel). In this case, the pressure measured at the end of the channel will show a delay 6

depending on the length of the channel and the gas speed. This effect could explain the discrepancy in case D 7

(Figure 2-13). For case C (Figure 2-12), all 14 volumes between the arc ignition point at the cable terminals and the 8

pressure relief device in the vertical exhaust channel at the side of the switchgear arrangement were combined into 9

one volume in order to achieve the best agreement. This measure is recommended if there are small (intermediate) 10

volumes with large openings between volumes. 11

Overall, the agreement between experiment and calculation is better than 10% considering that the arc voltage has 12

been provided from the tests and the 𝑘_𝑝-factor as well as the discharge factor have been adapted to give the best

13

results. This result is supported by the range of deviations of the peak pressure shown in Section 2.5.6 for all test 14

cases. 15

2.5.4 MV switchgear filled with SF

6

gas

16

Case No. E F G

Volume of arc comp. (𝑉₁) 0.509 1.217 0.27 m³

Volume of exhaust comp. (𝑉₂) >1000 >1000 0.58 m³

Volume of installation room (𝑉₃) NA NA >1000 m³

Initial filling pressure in 𝑉₁ 150 166 120 kPa abs SF6

Initial filling pressure in 𝑉₂ 100 100 100 kPa abs air

Area of the relief opening 𝐴₁₂ 0.00456 0.062 0.049 m²

Discharge coefficient of 𝐴₁₂ 1.0 1.0 1.0

Response pressure of relief device 310 1400 220 kPa rel

Area of the opening 𝐴₂₃ NA NA 0.195 m²

Short-circuit current 14.2 25 38 kA rms

Number of phases 1 3 3

Averaged phase-to-ground voltage 350 1700 400 V

𝑘𝑝-factor 0.75 0.7 0.76

Table 2-4: Input parameters and initial values for MV switchgear cases with SF

6

insulation.

17 18

(34)

1

Figure 2-14: Case E – Measured and calculated pressure developments in

_V

1

with SF

6

as filling gas.

2

3

Figure 2-15: Case F – Measured and calculated pressure developments in

_V

1

with SF

6

as filling gas.

4 Case E 24 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 time [s] pr es s ur e [ M P a] P1 calculated P1 measured Case F 03 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.1 0.2 0.3 0.4 0.5 0.6 time [s] pr es s ur e [ M P a] P1 calculated P1 measured

TOOLS FOR THE SIMULATION OF EFFECTS OF THE INTERNAL ARC IN TRANSMISSION AND DISTRIBUTION SWITCHGEAR