Short Circuit Currents and Symmetrical Components

Short Circuit Currents and Symmetrical Components . Understanding short circuit currents and symmetrical components is essential for ensuring the reliability and safety of electrical power systems. Electrical faults can cause massive disruptions, damage equipment, and even pose safety hazards. This article delves into the concepts, applications, and importance of these critical components in electrical engineering.

Understanding Short Circuit Currents

Definition and Causes

Short circuit currents arise when an unintended connection occurs between two points of different electrical potential, bypassing the normal load. Common causes include insulation failure, equipment faults, or external factors like lightning strikes.

Types of Short Circuits

Line-to-Ground (L-G)
- Most common type, involving one phase and the ground.
Line-to-Line (L-L)
- A fault between two phases without involving the ground.
Three-Phase Faults
- A simultaneous fault across all three phases, often the most severe.

Impact on Electrical Systems

Short circuits can lead to:

Equipment overheating.
Damage to generators, transformers, and cables.
Voltage instability and power outages.

Read More : Infrared Motion Detector Circuit

Short Circuit Faults and Currents

Short-circuits can occur phase-to-phase and phase-to-earth, mainly due to:

Dielectric breakdown of insulating materials (ageing, severe overheating and overvoltages, mechanical stress and chemical corrosion are the main factors for dielectric breakdown)
Decrease of creepage distance (the shortest path between two conductive parts – or between a conductive part and the bounding surface of the equipment – measured along the surface of the insulation)
Decrease of safety distance
Non-controlled partial discharges (corona)

When one or more of these situations occur a “solid” or “incipient” contact between conductors of different phases or between a conductor and a metallic no-live part can be established, causing a short-circuit, which diagrams are shown in Figure 1.

Short Circuit Currents and Symmetrical Components

Phase-to-phase and phase-to-earth short-circuits may evolve towards three-phase short-circuit (the worst situation), due to dielectric breakdown caused by the high magnitude of currents.

Short-circuits cause thermal and electrodynamics stress on equipments and conductors.

Thermal stress is due to overheating of conductors (Joule law) and can cause dielectric breakdown and melting of metallic materials.

Electrodynamics stress is caused by the electromagnetic force, which is one of the four fundamental interactions in nature and it is described by electromagnetic fields that is defined by Lorentz law.

The value of this force is in direct proportion to the electric current value.

The calculation of short-circuit currents is used to design the installation and to define the characteristics of equipment, namely the breaking capacity of circuit breakers and the set-point of protection relays.

According to IEC Standard 60865-1 e 2 the equations to be used for the calculation of short-circuit currents are:

Phase-to-phase:

Three-phase

I”_k3= 1.1xUn / (√3xZ_d) – maximum

I”_k3= 0.95xUn / (√3xZ_d) – minimum

Phase-to-phase

I”_k2= 1.1xUn / (2xZ_d) – maximum

I”_k2= 0.95xUn / (2xZ_d) – minimum

Phase-to- earth:

I”_k1= 1.1xUn / (2xZ_d+Z₀) – maximum

I”_k1= 0.95xUn / (2xZ_d+ Z₀) – minimum

Read More : What is an Oil Circuit Breaker?

Definition of Symmetrical Components

All networks and equipments have internal impedance that can be split into three symmetrical components associated with the rotation of the electromagnetic field.

An unbalance system is divided into three separated symmetrical systems:

Positive or synchronous sequence (Xd / Zd) – where the three fields rotate clockwise, with a phase displacement of 120°
Negative sequence (Xi / Zi) – where the three fields rotate anti-clockwise, with a phase displacement of 120°
Zero sequence (X0 / Z0) – a single fields which does not rotate, with each phase together (0° apart)

Figure 2 – Symmetrical components (currents)

Once the sequence networks are known, determination of the magnitude of the fault is relatively straight forward.

The ac system is broken down into its symmetrical components as shown above.

Each symmetrical system is then individually solved and the final solution obtained by superposition of these.

Positive, negative and zero sequence impedance data are often available from manufacturers.

A common assumption is that for non rotating equipment the negative sequence values are taken to be the same as the positive (X_d= X_i / Z_d= Z_i)

Zero sequence impedance values are closely tied to the type of earthing arrangements and do vary with equipment type.

While it is always better to use actual data, if it is not available (or at preliminary stages), the following approximations shown in Table 1 can be used.

Table 1 – Zero sequence impedance approximation

Equivalent Impedance of Equipment And Network Equivalent

The equivalent impedances of equipments and upstream network are:

Generators

Z_G = jX”_d(Ω)xS_n

Upstream network

Z_N= R_N+ jX_N
IZ_NI = 1.1xU_n /√3xI”k₃or IZ_NI = 1.1xS”_k3 /√3xU_n²
R_N = 0.1xX_N (empirical)

Transformers and reactors

Z_T=R_T+ jX_T
IZ_TI = u_k(%)xU_n² /100xS_n
R_T= P_cu/ 3xI_n²

Motors

Z_M= jX_M
X_M= U_n/ ((I_start/I_n)x√3xIn
I”_kM= 1.1xU_n/√3xX_M

Cables

Z_C= ρ_20°Cxl/s + j2πfxL
R_C= ρ_20°Cxl/s
X_C = 2πfxL

Overhead Lines

For calculation purposes an overhead line may be represented by a “π diagram”, as shown in Figure 3.

Figure 3 – π Diagram of an overhead line

In extra-high voltage (EHV) and high voltage (HV) overhead lines resistance of the line is usually negligible compared with the inductive reactance, but in low voltage (LV) and medium voltage (MV) overhead lines that resistance must be taken into account to calculate the impedance of the line.

For the calculation of short-circuit currents that do not involve faults to the ground th capacitive reactance is disregarded.

The equivalent positive (and negative) impedance of the line is calculated as follows:

R_OL= ρ_20°Cxl/s
X_OL = 2πfxl₁x(μ₀/2π)x(ln (d/r_e)+(1/4n)) – single-circuit line
X_OL = 2πfxl₁x(μ₀/2π)x(ln (dxd’/r_exd”)+(1/4n)) – double-circuit line

Total equivalent impedance

Legend

S”_k3: Short circuit power
I”k₃: Short circuit current
Z_d: Synchronous impedance
Z₀: Zero-sequence impedance
S_n: Rated power
U_n: Rated voltage
I_n: Rated current
Z: Impedance
ӀZI: Modulus of Z
X: Inductance
X”: Sub transient reactance
R: Resistance
ρ: Resistivity
s: Conductor cross section
l: Cable length
l₁: Overhead line length
d, d’, d”: Mean geometric distance between the three phase conductors of the line(s).
d_12,d’₁₂: distance between conductors of phases 1 and 2 (line 1 and line 2)
d₂₃, d’₂₃: distance between conductors of phases 2 and 3 (line 1 and line 2)
d₃₁, d’₃₁: distance between conductors of phases 3 and 1 (line 1 and line 2)
d”₁₁, d”₂₂, d”₃₃: distance between conductors of phase 1 (2 and 3) of line 1 and line 2
r_e: Equivalent radius for bundle conductors
n: Number of strands in bundle conductor
μ₀: Space permeability – 4πx10^-4 H/km
ln: natural logarithm
L: Inductance
u_k: Transformer impedance voltage drop
P_cu: Transformer resistive losses
f: Frequency

Read More : Cable and Wire Tester Circuit Diagram

Tips :

A solid fault happens when there is a straight contact between live conductors or between live conductors and earth.

When that contact is not straight the fault is designated as incipient. Incipient faults if not cleared will evolutes towards solid faults.

Benefits of Using Symmetrical Components

Improved Fault Analysis Accuracy

Decomposing faults into balanced components ensures precise calculations, crucial for designing effective protection.

Easier System Balancing and Design

Symmetrical components simplify the process of designing systems that withstand or mitigate unbalanced conditions.

Challenges and Limitations

Practical Challenges

Complex Calculations: Initial learning curve for engineers.
Dependency on Accurate Data: Errors can propagate through analyses.

Common Misconceptions

Some believe symmetrical components are unnecessary for simple systems, but even small networks can benefit from their insights.

FAQs

1. What causes short circuits in electrical systems?

Short circuits occur due to insulation failure, equipment faults, or environmental factors like lightning.

2. How do symmetrical components simplify fault analysis?

They decompose unbalanced faults into balanced components, making calculations more straightforward.

3. What is a three-phase fault?

A fault affecting all three phases simultaneously, typically the most severe type of electrical fault.

4. Why are symmetrical components important in power systems?

They ensure accurate fault analysis, improve system design, and help in stabilizing unbalanced systems.