Positive sequence component: It has three vectors of equal magnitude but displaced in phase from each other by 120° and has the same phase sequence as the original vectors. It specifies that the current is flowing through the source to load.

Negative sequence component: It has three vectors of equal magnitude but displaced in phase from each other by 120° and has the phase sequence opposite to the original vectors. It specifies that the current is flowing from load to source.

Zero sequence component: It has three vectors of equal magnitude and also are in phase with each other. It specifies that the current is flowing from source to ground.

• Positive sequence components exist in both balanced and unbalanced conditions.
• Negative sequence components exist in unbalanced conditions only.
• Zero sequence components exist in the unbalanced conditions involving ground.

In double line fault or line to line fault, there is no ground. Therefore, the zero sequence current is zero.

• The positive sequence currents involved in all type of systems
• Negative sequence currents involved in only unbalanced systems
• Zero sequence currents involved in systems involving earth
• Thus, in balanced three phase system both negative and zero sequence currents are zero

Concept:

Power system fault:

• Open circuit fault
• Short circuit fault

Open circuit fault: The open-circuit fault mainly occurs because of the failure of one or two conductors. The open-circuit fault takes place in series with the line, and because of this, it is also called the series fault. Such types of faults affect the reliability of the system.

Short circuit fault: In this type of fault, the conductors of the different phases come into contact with each other with a power line, power transformer or any other circuit element due to which the large current flow in one or two phases of the system. The short-circuit fault is divided into the symmetrical and unsymmetrical fault.

Explanation:

So, an Open circuit electrical fault is also called a series fault.

Symmetrical components:

• In the case of a balanced load, the voltage at the load point will be evaluated by using a per phase reactance network along with PU values. The time taking is less, because only one phase is sufficient to steady the system.
• But when it comes to unbalanced conditions the unbalanced load voltages will be evaluated by having individual representation of phase.
• There will be three equations to solve in order to evaluate the unbalanced load voltage. It is time taking, in order to reduce the time taking for evaluation of unbalanced load voltages, it is proposed to express any unbalanced electrical quantity by a set of 3 balanced electrical quantities called symmetrical components.
• Those are namely positive, negative, and zero sequence components.

Three-phase unbalanced voltages in terms of symmetrical components are guven below,

V_R = V_R1 + V_R2 + V_R0

V_Y = V_Y1 + V_Y2 + V_Y0

V_B = V_B1 + V_B2 + V_B0

Phasor rotation operator (a):

In order to reduce the number of symmetrical components, it is proposed to replace the symmetrical components of Y-phase, B-phase, in terms of R-phase by using a suitable notation which is denoted by 'a' namely called as operator 'a'.

Phasor rotation operator 'a' is defined as unity magnitude with 120⁰ phase displacement in anti-clockwise direction i.e it rotates a phasor vector counterclockwise by 120⁰.

So mathematically it can be represented as 

$\mathbf{a}=e^{\frac{2\pi }{3}i}$

In polar form a = 1∠120⁰

In rectangular form a = -0.5 + j 0.8667

̂

Mathematical properties of the operator 'a'

1. a³ = 1
2. a² = a^-1
3. 1 + a + a² = 0

The relation between new per-unit value & old per unit value impedance

$(Z_{pu}{)}_{new}=(Z_{pu}{)}_{old}\times {\left(\frac{k{V}_{base}}{k{V}_{new}}\right)}^2\times \left(\frac{MV{A}_{new}}{MV{A}_{old}}\right)$

Also $Z_{pu}=\frac{Z_{Actual}}{Z_{base}}$

 $Z_{base}=\frac{k{V}_{base}^2}{MV{A}_{base}}$

Where,

(Zpu)new = New per unit value of impedance

(Zpu)old = Old per unit value of impedance

kVbase = Old base value of voltage

kVnew = New base value of voltage

MVAnew = New base value of power

MVAold = Old base value of power

The power factor can be improved by installing a device in parallel with a load that has ​leading reactive power.

Low power factor can be avoided by:

• Using synchronous motors instead of induction motors
• Using high-speed induction motors to low-speed machines
• Not operating induction motors at less than the rated output
• By using the following equipment

1. Static capacitors
2. Synchronous condenser
3. Phase advancer

Causes of low power factor:

• Most of the AC motors are of induction type (1φ and 3φ induction motors) which have a low lagging power factor
• These motors work at a power factor which is extremely small on light load (0.2 to 0.3) and rises to 0.8 or 0.9 at full load
• Arc lamps, electric discharge lamps and industrial heating furnaces operate at a low lagging power factor
• The load on the power system is varying; being high during morning and evening and low at other times
• During low load period, the supply voltage is increased which increases the magnetisation current, this results in the decreased power factor

Per unit (p.u.) quantity:

The per-unit value of any quantity is defined as the ratio of actual value in any unit to the base or reference value in the same unit.

The per-unit value is dimensionless.

​Per unit impedance (Z_pu):

Z_pu is defined as the ratio of actual value to base impedance.

It is also defined as The ratio of full-load volt-amperes to short-circuit volt-amperes.

$Z_{pu}=\frac{Z{}_a}{Z_B}$

$Z_{pu}=\frac{Z_a\times {\left(kVA\right)}_B}{{\left(kV\right)}_B^2\times 1000}$

Z_a = Actual impedance

Z_B = Base impedance

$$\begin{gathered} Z\propto \frac{1}{kVA} \\ \frac{Z_a}{Z_B}=\frac{kV{A}_B}{kV{A}_a}=Z_{pu} \end{gathered}$$

(kVA)a = Rated kVA

(kVA)_B = Base kVA

(kV)_B = Base voltage in kV

Important points:

• Per unit voltage (V_pu) = (kV)_actual / (kV)_B
• Short circuit current in pu = Actual current / Base current

Unsymmetrical Faults:

• Unsymmetrical faults are the faults that lead unequal currents with unequal phase shifts in a three-phase system
• The unsymmetrical fault occurs in a system due to the presence of an open circuit or short circuit of transmission or distribution line
• It can occur either by natural disturbances or by manual errors
• The natural disturbances are heavy wind speed, ice loading on the lines, lightning strikes and other natural disasters

Symmetrical faults:

• A symmetrical fault is a fault where all phases are affected so that the system remains balanced
• A three-phase fault is a symmetrical fault
• As symmetrical faults result in balanced conditions, they may be analyzed using per-phase analysis

Irrespective of the causes, both symmetrical faults, and unsymmetrical faults occur in a 3-phase system.

Sequence Impedance:

The sequence impedance of the network describes the behavior of the system under asymmetrical fault conditions.

Positive Sequence Impedance

1) The impedance offered by the network to the flow of positive sequence current is called the positive sequence impedance.

2) The positive sequence means all the electrical quantities are numerically equal and displaces each other by 120º.

Negative Sequence Impedance

The negative sequence impedance means the impedance offered by the network to the flows of negative sequence current.

Zero Sequence Impedance

The impedance offered to zero sequence current is called the zero sequence impedance.

Generally, resistance offered by the power system is less when compared to reactance.

So, the resistance of the system is neglected and reactance is considered.

Values of sequence reactance of some equipment are as follows:

Where,

X0 is the zero sequence reactance

X1 is the positive sequence reactance

X2 is the negative sequence reactance

Xd” is the direct axis reactance

• Harmonics can be best described as the shape or characteristics of a voltage or current waveform relative to its fundamental frequency
• The ideal power source for all power systems is smooth sinusoidal waves
• These perfect sinewaves do not contain harmonics
• When waveforms deviate from a sinewave shape, they contain harmonics
• These current harmonics distort the voltage waveform and create distortion in the power system which can cause many problems
• In power generation, harmonics leads to low voltage and low power factor generation in the power system