You get a bonus - 1 coin for daily activity. Now you have 1 coin

Peak Short-Circuit Current in AC Circuits

Lecture



The short-circuit surge current is the term for the maximum instantaneous value of the total current under the most unfavorable conditions.

For electrical circuits in which inductance predominates, this occurs if the pre-fault regime was no-load and the short circuit occurs at the instant when the voltage passes through zero (Fig. 2.4).

In this case the periodic component of the short-circuit current starts from its amplitude value. According to the laws of commutation, at the first instant of the short circuit the initial value of the aperiodic component turns out to be the maximum possible and equal to the amplitude of the periodic component of the short-circuit current

Ia(0) = Inm

Peak Short-Circuit Current in AC Circuits

Fig. 2.4. Short-circuit surge current

The largest instantaneous value of the total short-circuit current – the surge current – occurs at the first largest value of the aperiodic component that coincides in sign with the periodic component of the short-circuit current. This instant occurs approximately half a period after the short circuit appears. Under this condition the surge current is

Isc = Ip m + Ip m e –0,01/Ta = Ip m ( 1 + e—0,01/Ta ) = Ip m ksc.(2.9)

The quantityPeak Short-Circuit Current in AC Circuitsis called the surge-current coefficient, characterizing the excess of the surge current over the amplitude of the periodic component of the short-circuit current

Peak Short-Circuit Current in AC Circuits.(2.10)

The surge-current coefficient depends on the decay time constant of the aperiodic component Ta = xk / (314rk).

At Peak Short-Circuit Current in AC Circuits,

and at Peak Short-Circuit Current in AC Circuits, i.e. the values of the surge-current coefficient vary within the range

1<ksc<2.

The dependence of the surge-current coefficient on the ratio xk./rk (the time constant Ta) is shown in Fig. 2.5. Over the interval 3Ta the aperiodic component of the short-circuit current practically decays.

In practical calculations the surge current is determined by the formula

Peak Short-Circuit Current in AC Circuits(2.11)

where I" - the subtransient short-circuit current (the rms value of the periodic component at the first instant of the short circuit).

Peak Short-Circuit Current in AC Circuits

Fig. 2.5. Dependence of the surge-current coefficient on the ratio xk./rk and the time constant of the short-circuited path

Comments

To leave a comment

If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Lectures and tutorial on "Theoretical Foundations of Electrical Engineering"

Terms: Theoretical Foundations of Electrical Engineering

General Information on Transient Processes: Concepts, Definitions, and Types of Short Circuits
Equivalent Circuits of Power Supply Systems
Exact and Approximate Reduction of Element Parameters
Using Per-Unit Values in Solving Transient Process Problems
Standard Formulas for Reducing Element Parameters to Base Conditions in Per-Unit Values
Electromagnetic Transient Processes in Simple Three-Phase Circuits
Peak Short-Circuit Current in AC Circuits
General Equations of the Electromagnetic Transient Process of a Synchronous Machine
Sudden Short Circuit of a Synchronous Machine
Electrical and Mechanical Transient Processes in Electric Motors
1. Three-Phase Short Circuit at Generator Terminals Without Automatic Excitation Control, Finite-Power Source
Initial Instant of a Sudden Disturbance (Transient and Subtransient)
Steady-State Short-Circuit Current
Short-Circuit Current at an Arbitrary Instant
Practical Methods for Calculating Short-Circuit Currents
Practical Calculation of the Initial Three-Phase Short-Circuit Current and Peak Current
Approximate Accounting for the System in Transient Process Analysis
Calculating Short-Circuit Currents Using the Typical Curves Method
1. Symmetrical Components Method for Transient Analysis and Unbalanced Conditions
Element Impedance to Positive- and Negative-Sequence Currents
Element Impedance to Zero-Sequence Currents
Zero-Sequence Impedance of Overhead and Cable Lines
Equivalent Circuits of Individual Sequence Networks
Resultant EMF and Impedances in Calculating Unbalanced Conditions
Transformation of Currents and Voltages of Different Sequences
Single Transverse Asymmetry at an Arbitrary Point of a Three-Phase System
Single-Phase Ground Fault in a System with an Isolated Neutral
Single Longitudinal Asymmetry in AC Systems
Semi-Infinite and Finite-Length Lines, Reflections, and Traveling-Wave Operating Modes
Transposition of Overhead Transmission Line Conductors, with Worked Examples
1. Elements of Electric Circuits and Their Parameters Used in Calculations
2. Topology of an Electric Circuit
3. Representation of Sinusoidal Quantities Using Vectors and Complex Numbers
4. Elements and Devices of a Sinusoidal Current Circuit: Vector Diagrams and Complex Relationships
5. Ohm's Law for a Circuit Section with an EMF Source (Generalized Ohm's Law)
6. Fundamentals of Matrix Methods for Electric Circuit Calculation
7. Energy Conversion in an Electric Circuit: Instantaneous, Active, Reactive, and Apparent Power
8. Resonance in Sinusoidal Current Circuits
9. Phasor and Topographic Diagrams
10. Analysis of Circuits with Inductively Coupled Elements
Матрицы сопротивлений и проводимостей для цепей со взаимной индукцией
12. Calculation Methods Based on the Properties of Linear Circuits
13. Equivalent Generator Method
14. Passive Two-Port Networks
15. Electrical Filters: Types, Operating Principle, Applications, and Tests
16. Three-Phase Electrical Circuits
17. Calculating Balanced and Unbalanced Three-Phase Circuit Modes
18. Using Phasor Diagrams to Analyze Unbalanced Modes
19. Method of Symmetrical Components
20. Active Two-Terminal Network Theorem for Symmetrical Components
21. Rotating Magnetic Field
22. Linear Electrical Circuits under Non-Sinusoidal Periodic Currents
23. Resonance Phenomena in Non-Sinusoidal Current Circuits
24. Transient Processes in Linear Circuits with Lumped Parameters
25. Methods for Deriving the Characteristic Equation
26. Determining the Time Constant: Transient Processes in R-L-C Circuits
27. Operator Method for Transient Process Calculation, with an Example
28. Some Important Notes on the Expansion Formula
29. Duhamel's Integral and the State-Variable Method
30. Nonlinear DC Circuits: Graphical Calculation Methods
31. Nonlinear Circuit Calculation by the Equivalent Generator Method: Analytical and Iterative Techniques
32. Nonlinear Magnetic Circuits under Constant Flux: Basic Concepts and Laws
33. General Characteristics of Problems and Methods for Calculating Magnetic Circuits
34. Nonlinear AC Circuits in Steady-State Modes
36. Piecewise-Linear Approximation Method
37. Equivalent Sinusoid Method (Calculation by RMS Values)
38. Transient Processes in Nonlinear Circuits
39. Graphical Methods for Analyzing Transients in Nonlinear Circuits
40. Circuits with Distributed Parameters (Long Transmission Lines)
41. Distortion-Free Signal Transmission along a Line
42. Input Impedance of a Long Transmission Line
210 Tests on Electronics and Electrical Engineering with Answers and Diagrams
Electrical Safety: Theory and Tests
Permanent Magnets: Calculation of Permanent Magnets and Electromagnets
The Essence of Electric Power Distribution