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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
- Veröffentlichungsjahr: 2017
Reflecting the changes to the all-important short circuit calculations in three-phase power systems according to IEC 60909-0 standard, this new edition of the practical guide retains its proven and unique concept of explanations, calculations and real-life examples of short circuits in electrical networks. It has also been completely revised and expanded by 20% to include the standard-compliant prevention of short circuits in electrical networks for photovoltaics and wind energy. By understanding the theory any software allows users to perform all the necessary calculations with ease so they can work on the design and application of low- and high-voltage power systems. This book is a practitioner's guide intended for students, electrical engineers, engineers in power technology, the electrotechnical industry, engineering consultants, energy suppliers, chemical engineers and physicists in industry.
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Table of Contents
Cover
Title Page
Copyright
Preface
Acknowledgments
Chapter 1: Definitions: Methods of Calculations
1.1 Time Behavior of the Short-Circuit Current
1.2 Short-Circuit Path in the Positive-Sequence System
1.3 Classification of Short-Circuit Types
1.4 Methods of Short-Circuit Calculation
Chapter 2: Fault Current Analysis
Chapter 3: The Significance of IEC 60909-0
Chapter 4: Supply Networks
4.1 Calculation Variables for Supply Networks
4.2 Lines Supplied from a Single Source
4.3 Radial Networks
4.4 Ring Networks
4.5 Meshed Networks
Chapter 5: Network Types for the Calculation of Short-Circuit Currents
5.1 Low-Voltage Network Types
5.2 Medium-Voltage Network Types
5.3 High-Voltage Network Types
Chapter 6: Systems up to 1 kV
6.1 TN Systems
6.2 Calculation of Fault Currents
6.3 TT systems
6.4 IT Systems
6.5 Transformation of the Network Types Described to Equivalent Circuit Diagrams
6.6 Examples
Chapter 7: Neutral Point Treatment in Three-Phase Networks
7.1 Networks with Isolated Free Neutral Point
7.2 Networks with Grounding Compensation
7.3 Networks with Low-Impedance Neutral Point Treatment
7.4 Examples
Chapter 8: Impedances of Three-Phase Operational Equipment
8.1 Network Feed-Ins, Primary Service Feeder
8.2 Synchronous Machines
8.3 Transformers
8.4 Cables and Overhead Lines
8.5 Short-Circuit Current-Limiting Choke Coils
8.6 Asynchronous Machines
8.7 Consideration of Capacitors and Nonrotating Loads
8.8 Static Converters
8.9 Wind Turbines
8.10 Short-Circuit Calculation on Ship and Offshore Installations
8.11 Examples
Chapter 9: Impedance Corrections
9.1 Correction Factor
K
G
for Generators
9.2 Correction Factor
K
KW
for Power Plant Block
9.3 Correction Factor
K
T
for Transformers with Two and Three Windings
Chapter 10: Power System Analysis
10.1 The Method of Symmetrical Components
10.2 Fundamentals of Symmetrical Components
10.3 General Description of the Calculation Method
10.4 Impedances of Symmetrical Components
Chapter 11: Calculation of Short-Circuit Currents
11.1 Three-Phase Short Circuits
11.2 Two-Phase Short Circuits with Contact to Ground
11.3 Two-Phase Short Circuit Without Contact to Ground
11.4 Single-Phase Short Circuits to Ground
11.5 Peak Short-Circuit Current,
i
p
11.6 Symmetrical Breaking Current,
I
a
11.7 Steady-State Short-Circuit Current,
I
k
Chapter 12: Motors in Electrical Networks
12.1 Short Circuits at the Terminals of Asynchronous Motors
12.2 Motor Groups Supplied from Transformers with Two Windings
12.3 Motor Groups Supplied from Transformers with Different Nominal Voltages
Chapter 13: Mechanical and Thermal Short-Circuit Strength
13.1 Mechanical Short-Circuit Current Strength
13.2 Thermal Short-Circuit Current Strength
13.3 Limitation of Short-Circuit Currents
13.4 Examples for Thermal Stress
Chapter 14: Calculations for Short-Circuit Strength
14.1 Short-Circuit Strength for Medium-Voltage Switchgear
14.2 Short-Circuit Strength for Low-Voltage Switchgear
Chapter 15: Equipment for Overcurrent Protection
Chapter 16: Short-Circuit Currents in DC Systems
16.1 Resistances of Line Sections
16.2 Current Converters
16.3 Batteries
16.4 Capacitors
16.5 Direct Current Motors
Chapter 17: Power Flow Analysis
17.1 Systems of Linear Equations
17.2 Determinants
17.3 Network Matrices
Chapter 18: Examples: Calculation of Short-Circuit Currents
18.1 Example 1: Radial Network
18.2 Example 2: Proof of Protective Measures
18.3 Example 3: Connection Box to Service Panel
18.4 Example 4: Transformers in Parallel
18.5 Example 5: Connection of a Motor
18.6 Example 6: Calculation for a Load Circuit
18.7 Example 7: Calculation for an Industrial System
18.8 Example 8: Calculation of Three-Pole Short-Circuit Current and Peak Short-Circuit Current
18.9 Example 9: Meshed Network
18.10 Example 10: Supply to a Factory
18.11 Example 11: Calculation with Impedance Corrections
18.12 Example 12: Connection of a Transformer Through an External Network and a Generator
18.13 Example 13: Motors in Parallel and their Contributions to the Short-Circuit Current
18.14 Example 14: Proof of the Stability of Low-Voltage Systems
18.15 Example 15: Proof of the Stability of Medium-Voltage and High-Voltage Systems
18.16 Example 16: Calculation for Short-Circuit Currents with Impedance Corrections
Bibliography
Standards
Explanations of Symbols
Symbols and Indices
Indices
Secondary Symbols, Upper Right, Left
American Cable Assembly (AWG)
Index
End User License Agreement
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Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Definitions: Methods of Calculations
Figure 1.1 Time behavior of the short-circuit current (see Ref. [1]). (a) Far-from-generator short circuit and (b) near-to-generator short circuit. : initial symmetrical short-circuit current;
i
p
: peak short-circuit current;
i
d.c.
: decaying d.c. aperiodic component; and
A
: initial value of d.c. aperiodic component.
Figure 1.2 Equivalent circuit of the short-circuit current path in the positive-sequence system.
Figure 1.3 Switching processes of the short circuit.
Figure 1.4 Types of short-circuit currents in three-phase networks [1].
Figure 1.5 Methods for the short-circuit calculation. (a) Single line diagram; (b) voltage source at the fault location; (c) superposition; and (d) equivalent voltage source.
Figure 1.6 Network circuit with equivalent voltage source [2]. (a) System diagram and (b) equivalent circuit diagram of the positive-sequence system.
Figure 1.7 Short-circuit current components – switch on.
Figure 1.8 Switching process.
Figure 1.9 Impact of engines on the current.
Figure 1.10 Supply for an industrial company.
Figure 1.11 Equivalent circuit diagram in positive sequence.
Figure 1.12 Power plant with auxiliary power system.
Figure 1.13 Equivalent circuit diagram in positive sequence.
Figure 1.14 Result with NEPLAN.
Chapter 3: The Significance of IEC 60909-0
Figure 3.1 Range of applicability of short-circuit calculations [1, 2].
Chapter 4: Supply Networks
Figure 4.1 Overview of a power transmission and distribution system.
Figure 4.2 Line supplied from a single source.
Figure 4.3 Radial network.
Figure 4.4 Ring network.
Figure 4.5 Meshed network.
Chapter 5: Network Types for the Calculation of Short-Circuit Currents
Figure 5.1 Simple radial networks with different centers of load distribution.
Figure 5.2 Simple radial networks with individual load circuits.
Figure 5.3 Simple radial networks with redundant inputs.
Figure 5.4 Meshed network with different inputs and network nodes with fuses.
Figure 5.5 Industrial load center network.
Figure 5.6 Industrial ring network.
Figure 5.9 Short circuit with simple inputs.
Figure 5.7 (a) Ring network, (b) network with remote station, and (c) network supporting structure.
Figure 5.8 Network configuration for medium-voltage systems.
Figure 5.9 Short circuit with simple inputs.
Figure 5.10 380/110 kV-substation.
Figure 5.12 Generation, transmission, and distribution system.
Chapter 6: Systems up to 1 kV
Figure 6.1 Circuitry of the TN–C–S system.
Figure 6.2 Circuitry of the TN system. (a) Distribution systems, (b) loop impedance, and (c) fault location.
Figure 6.3 Overview of the power supply.
Figure 6.4 Circuitry of the TT system.
Figure 6.5 Circuitry of the IT system.
Figure 6.6 Network transformations. (a) Series circuit, (b) parallel circuit, (c) delta–star transformation, and (d) star–delta transformation.
Figure 6.7 Automatic disconnection for a TN system.
Chapter 7: Neutral Point Treatment in Three-Phase Networks
Figure 7.1 Neutral point treatment of transformers.
Figure 7.2 Surface potential profile and voltages in case of current-carrying earth electrodes (see also Ref. [2]).
Figure 7.3 Isolated network and equivalent circuit diagram.
Figure 7.4 Network with earth fault compensation.
Figure 7.5 Low-resistance grounded network and equivalent diagram.
Chapter 8: Impedances of Three-Phase Operational Equipment
Figure 8.1 Network feed-in and equivalent circuit. (a) System diagram and equivalent circuit diagram without transformer and (b) system diagram and equivalent circuit diagram with transformer.
Figure 8.2 Synchronous machine.
Figure 8.3 Synchronous machine in different operative conditions.
Figure 8.4 Equivalent circuit and phasor diagram of the synchronous machine in the positive sequence.
Figure 8.5 Generator near the short-circuit current.
Figure 8.6 Synchronous machine and the equivalent circuit diagram.
Figure 8.7 Overview of a transformer.
Figure 8.8 Transformer and equivalent circuit.
Figure 8.9 Equivalent resistances and reactances in the zero-sequence and positive-sequence systems for LV transformers.
Figure 8.10 (a) Circuit diagram for a transformer with three windings and (b) equivalent circuit with side
C
open.
Figure 8.11 Equivalent resistances and reactances of transformers for LV and MV networks [7].
Figure 8.12 Cables and lines in the positive-sequence system.
Figure 8.13 The basis of calculation for overhead lines: (a) equivalent circuit of an overhead line; (b) 4× conductor bundle line; (c) 2× conductor bundle line; and (d) mast diagram.
Figure 8.14 (a) Short-circuit current-limiting choke coil, equivalent circuit; and (b) application.
Figure 8.15 Overview of an asynchronous machine (ABB).
Figure 8.16 Asynchronous machine and equivalent circuit.
Figure 8.17 Connection to the HV power network.
Figure 8.18 Wind power plant with asynchronous generator.
Figure 8.19 Wind power plant with a doubly fed asynchronous generator.
Figure 8.20 Wind power with full converter.
Figure 8.21 Wind power with full converter.
Figure 8.22 Equivalent circuit diagram of a star-to-star (Y–Y) transformer in zero sequence.
Figure 8.23 Diagram to assign failure with maximal current [12].
Figure 8.24 Diagram of a one-phase short circuit in partial network.
Figure 8.25 Symmetrical components of a partial network.
Figure 8.26 Impedances for calculating a three-phase short-circuit.
Figure 8.27 Characteristic diagram of high-voltage fuses.
Figure 8.28 Characterization diagram of high-voltage fuse flow operating to a circuit breaker.
Figure 8.29 Factor
k
.
Figure 8.30 Factor
m
and parameter
k
.
Figure 8.31 Circuit diagram of NPT with Y–Δ winding.
Figure 8.32 Circuit diagram of NPT with Z–Z winding.
Figure 8.33 Diagram of a branch without an NPT.
Figure 8.34 Symmetrical components of branch without an NPT.
Figure 8.35 Diagram of a branch with an NPT.
Figure 8.36 Symmetrical components of branch with an NPT.
Figure 8.37 Diagram of a short circuit divided.
Chapter 9: Impedance Corrections
Figure 9.1 Connection and equivalent circuit of a generator.
Figure 9.2 Impedance correction for power station.
Chapter 10: Power System Analysis
Figure 10.1 Delta and star (wye) connection with neutral point (N).
Figure 10.2 Phasor diagram for the positive-sequence, negative-sequence, and zero-sequence systems.
Figure 10.3 Power transmission, three-phase system.
Figure 10.4 Schematic of a three-phase network and relationship between components of positive-sequence, negative-sequence, and zero-sequence systems. (a) Unsymmetrical system, (b) Symmetrical system, (c) equivalent one-line diagram of the components, and (d) graphical addition of three components.
Figure 10.5 Circuit diagram of a one-phase short circuit.
Figure 10.6 Equivalent circuits for positive-sequence, negative-sequence, and zero-sequence systems.
Figure 10.7 Measuring circuits for determining the positive-sequence, negative-sequence, and zero-sequence impedances (see also Ref. [1]).
Figure 10.8 Schematic of the equivalent circuit components.
Figure 10.9 Schematic diagram of three-phase delta, star source, and loads. (a) Source and (b) load.
Chapter 11: Calculation of Short-Circuit Currents
Figure 11.1 Equivalent circuit for a three-phase short circuit with equivalent voltage source at the position of the fault.
Figure 11.2 Equivalent circuit of a two-phase short circuit with contact to ground.
Figure 11.3 Vector diagram of the two-phase short circuit with earth contact.
Figure 11.4 Equivalent circuit of a two-phase short circuit without contact to ground.
Figure 11.5 Vector diagram of the two-phase short circuit without earth contact.
Figure 11.6 Equivalent circuit of single-phase short circuit to ground.
Figure 11.7 Vector diagram of the one-phase short circuit.
Figure 11.8 Largest short-circuit currents for asymmetrical short circuits (see also Ref. [1]).
Figure 11.9 Factor κ for calculating the peak short-circuit current
i
p
(see also Ref. [1]).
Figure 11.10 Factor μ for calculating the symmetrical breaking current
I
a
(see also Ref. [1]).
Figure 11.11 Factor
q
for calculation of the symmetrical breaking current for asynchronous machines (see also Ref. [1]).
Figure 11.12 Factors λ
min
and λ
max
for calculating the steady-state short- circuit current
I
k
(see also Ref. [1]).
Chapter 12: Motors in Electrical Networks
Figure 12.1 Short circuit at the terminals of an asynchronous motor.
Figure 12.2 Motor groups supplied from transformers with two windings.
Figure 12.3 Motor groups supplied from transformers with different nominal voltages.
Chapter 13: Mechanical and Thermal Short-Circuit Strength
Figure 13.1 Effects of forces acting on busbars and parallel conductors (see also Ref. [6]).
Figure 13.2 Correction factor
k
12
for the determination of the effective conductor spacing
a
m
(see also Ref. [1]).
Figure 13.3 The factors
m
and
n
(see also Ref. [1]).
Figure 13.4 Rated short-time current density
S
thr
for
T
kr
= 1 s (a) for copper and steel (solid line curves), (b) aluminum (broken line curves) Aldrey and Al/St (see also Ref. [17]).
Figure 13.5 Current limitation through circuit breaker: (a) high power current limitation through circuit breaker and (b) line protection circuit breaker with neutral point quencher, without definite current limitation.
Figure 13.6 Thermally permissible short-circuit current from paper-insulated cables at 1–10 kV (see also Ref. [10]).
Figure 13.7 Thermally permissible short-circuit current from paper-insulated cables at 12/20 kV (see also Ref. [10]).
Figure 13.8 Thermally permissible short-circuit current from paper-insulated cables at 18/30 kV (see also Ref. [10]).
Figure 13.9 Thermally permissible short-circuit current from PVC-insulated cables at 1–10 kV (see also Ref. [10]).
Figure 13.10 Thermally permissible short-circuit current from XLPE-insulated cables (see also Ref. [10]).
Figure 13.11 Thermally permissible short-circuit current of Cu screening (see also Ref. [10]).
Figure 13.12 Feeder of a transformer.
Figure 13.13 Mechanical short-circuit strength.
Figure 13.14 Busbar configuration.
Chapter 15: Equipment for Overcurrent Protection
Figure 15.1 Overview of overcurrent protective devices.
Figure 15.2 Time–current characteristics of limit switch fuses in accordance with IEC 60269-2 (2–1 000 A). (1) Peak current without d.c. part and (2) peak current with d.c. part.
Figure 15.3 Time–current characteristics of limit switch fuses in accordance with IEC 60269-2. (1) Small test current and (2) large test current.
Figure 15.4 Time–current characteristics of limit switch fuses in accordance with IEC 60269-2 (4–1250 A).
Figure 15.5 Time–current characteristics of limit switch fuses in accordance with IEC 60269-2. (1) Small test current and (2) large test current.
Figure 15.6 Time–current characteristics of high voltage–high power (HH) fuses in accordance with IEC 60282-1.
Figure 15.7 Application of fuses in power systems.
Figure 15.8 Time–current characteristics of miniature circuit breakers in accordance with IEC 60898-1.
Figure 15.9 Tripping curves with thermal relays for different starting classes.
Figure 15.10 Tripping curves with motor protection device.
Figure 15.11 Time–current characteristics of circuit breakers.
Chapter 16: Short-Circuit Currents in DC Systems
Figure 16.1 Typical paths for short-circuit currents.
Figure 16.2 Standardized approximation functions.
Figure 16.3 Equivalent circuit for the calculation of short-circuit currents.
Figure 16.4 Equivalent circuit of a converter arm.
Figure 16.5 Equivalent circuit of a battery.
Figure 16.6 Equivalent circuit of a capacitor.
Figure 16.7 Equivalent circuit of an externally excited DC motor.
Chapter 17: Power Flow Analysis
Figure 17.1 Network section with the nodes
i
and
k
and the reference point 0.
Figure 17.2 Calculation of the line currents between two nodes
i
,
k
from the node voltages , and the branch impedance with (a) a constant current and (b) constant power.
Figure 17.3 Representation of a power system.
Figure 17.4 Circuit diagrams for power flow calculations.
Figure 17.5 One-line diagram and equivalent circuit.
Figure 17.6 Flow diagram.
Figure 17.7 Illustration of the Newton–Raphson algorithm.
Figure 17.8 Equivalent circuits for power flow calculations.
Figure 17.9 Application of Cramer's rule.
Figure 17.10 Power flow calculation with NEPLAN.
Chapter 18: Examples: Calculation of Short-Circuit Currents
Figure 18.1 Example 1: network representation.
Figure 18.2 Example 2: calculation with source impedance.
Figure 18.3 Example 3: power plant network with service panel.
Figure 18.4 Example 4: transformers in parallel.
Figure 18.5 Equivalent circuit.
Figure 18.6 Example 5: connection of a motor.
Figure 18.7 Example 6: Calculation for a load.
Figure 18.8 Equivalent circuit for .
Figure 18.9 Example 7: network diagram.
Figure 18.10 Example 8: network diagram.
Figure 18.11 Meshed network.
Figure 18.12 Delta star transformations.
Figure 18.13 Supply to a factory.
Figure 18.14 Calculation with impedance corrections.
Figure 18.15 Example 12: connection of a transformer through an external network and a generator.
Figure 18.16 Example 13: influence of motors on the current.
Figure 18.17 Network design – single-phase representation with network input and transformers.
Figure 18.18 Operational equipment with equivalent circuit.
Figure 18.19 Equivalent circuit in the positive-sequence system at fault location F1.
Figure 18.20 Equivalent circuit in the positive-sequence system at fault location F2.
Figure 18.21 Equivalent circuit in the positive-sequence system at fault location F3.
Figure 18.22 Dimensioning of the circuit breakers ; (1) input field, (2) load field, and (3) coupling field.
Figure 18.23 Example 16: Calculation of short-circuit currents with impedance corrections.
List of Tables
Chapter 1: Definitions: Methods of Calculations
Table 1.1 Voltage factor
c
, according to IEC 60909-0: 2016-10 [1]
Chapter 3: The Significance of IEC 60909-0
Table 3.1 Selection of short-circuit currents.
Chapter 7: Neutral Point Treatment in Three-Phase Networks
Table 7.1 Decisive currents for the dimensioning of grounding systems [2]
Table 7.2 Summary of the isolated network
Table 7.3 Summary of the compensated network
Table 7.4 Summary of the low-resistance grounded network
Table 7.5 Arrangement of neutral point
Table 7.6 Application of neutral point arrangements
Chapter 8: Impedances of Three-Phase Operational Equipment
Table 8.1 Reactances of a synchronous machine [6]
Table 8.2 Characteristic values of high-voltage (HV) transformers
Table 8.3 Impedances for polyvinyl chloride (PVC)-insulated three-phase NYY cables [8]
Table 8.4 Resistance values for PVC-insulated four- and five-conductor cables with copper conductors at 55 °C conductor temperature [8]
Table 8.5 Resistance values for PVC-insulated 3.5- and 4.5-conductor three-phase cables with copper conductors at 55 °C conductor temperature [8]
Table 8.6 Resistance values for PVC-insulated single-conductor three-phase cables with PE or PEN next to each other, with copper conductors at 55 °C conductor temperature [8]
Table 8.7 Resistance values for PVC-insulated single-conductor three-phase cables with PE or PEN at a distance
d
from each other, with copper conductors at 55 °C conductor temperature [8]
Table 8.8 Resistance values at 80 °C for copper cables and conductors [9]
Table 8.9 Resistance values at 20 °C for copper cables and conductors [9]
Table 8.10 Resistances per unit length
r
in a positive-sequence system for overland line conductors manufactured in accordance with DIN 48 201 and
f
= 50 Hz at 20 °C [9]
Table 8.11 Inductive reactances per unit length
x
in Ω/km in a positive-sequence system for overland line conductors at
f
= 50 Hz [9]
Table 8.12 Quotients of effective resistances and inductive reactances in the zero-sequence and positive-sequence systems for NAYY and NYY cables as a function of the ground return system at
f
= 50 Hz [9]
Table 8.13 Resistances
r
per unit length of conductors for copper conductors.
Table 8.14 Impedance
z
for main outgoing and return lines of power supply companies
Table 8.15 Resistances of conductors in XLPE-insulated cables (6–30 kV) at 20 °C [10]
Table 8.16 Resistances per unit length of XLPE-insulated copper cables (6–20 kV) for
f
= 50 Hz [10]
Table 8.17 Inductances of XLPE-insulated copper cables (6–30 kV) for
f
= 50 Hz [10]
Table 8.18 Effective capacitances of XLPE-insulated copper cables [10]
Table 8.19 Ground fault currents of XLPE-insulated copper cables [11]
Table 8.20 Rating of the ground short-circuit current
I
″
k2E
Table 8.21 Results of the minimal one-phase short-circuit calculation in NEPLAN with a cable temperature of 80 °C
Table 8.22 Results of the minimal one-phase short-circuit calculation in NEPLAN with a cable temperature of 160 °C
Table 8.23 Maximal one-phase short-circuit currents with and without a connected NPT
Chapter 9: Impedance Corrections
Table 9.1 Impedance corrections
Chapter 12: Motors in Electrical Networks
Table 12.1 Calculation of short circuits at the terminals of motors
Chapter 13: Mechanical and Thermal Short-Circuit Strength
Table 13.2 Factors α and β for different support point arrangements (see also Ref. [6])
Table 13.1 Moments of resistance and moments of inertia
Chapter 18: Examples: Calculation of Short-Circuit Currents
Table 18.1 Summary of results
Table 18.2 Summary of results for at subdistributor
Table 18.5 Summary of results for at load
Table 18.6 Checking the short-circuit strength
Table 18.7 Current carrying capacities for the 110/20-kV level
Table 18.8 Rated voltages for the 110/20-kV level
Table 18.9 Selection values and rated values for load interrupter switches in accordance with IEC 282
Table 18.10 Selection values and rated values for load interrupter switches in accordance with IEC 282
Table 18.11 Selection values and rated values for disconnect switches and grounding switches in accordance with IEC 282
Table 18.12 Dimensioning of the circuit breakers
Table 18.13 Dimensioning the circuit breakers at different connection points on the busbar
Short Circuits in Power Systems
A Practical Guide to IEC 60909-0
Ismail Kasikci
Second Edition
Author
Ismail Kasikci
Biberach University of Applied Sciences
Karlstraße 11
88400 Biberach
Germany
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Cover Design Adam-Design, Weinheim, Germany
Preface
This book is the result of many years of professional activity in the area of power supply, teaching at the VDE, as well as at the Technical Academy in Esslingen. Every planner of electrical systems is obligated today to calculate the single-pole or three-pole short-circuit current before and after the project management phase. IEC 60909-0 is internationally recognized and used. This standard will be discussed in this book on the basis of fundamental principles and technical references, thus permitting a summary of the standard in the simplest and most understandable
