symmetrical components

SYMMETRICAL COMPONENTS

By, Pn. Zetty Nurazlinda Zakaria

PPK Sistem Elektrik UniMAP

End of this chapter, you should be able to:

Explain the important of symmetrical component.

Construct positive sequence networks for a power system.

Construct negative sequence networks for a power system.

Construct zero sequence networks for a power system.

Symmetrical Components??? By C.L. Fortescue (1918)

Allows unbalanced 3 phase phasor quantities to be replaced by the sum of 3 separate but balances symmetrical components:

Applicable to current and voltage

Permits modeling of unbalanced systems and networks

Symmetrical Component Transformation

Representative symmetrical components;

POS-SEQ: 3 phasors with equal magnitudes, ±120° phase displacement and positive sequence

NEG-SEQ: 3 phasors with equal magnitudes, ±120° phase displacement and negative sequence

ZERO-SEQ: 3 phasors with equal magnitudes and zero phase displacement

Fig. 1(a) Fig. 1(b) Fig. 1(c)



Positive sequence phasors (refer Fig.1(a));

Where operator a identities;


Negative sequence phasor (refer Fig.1(b));

Zero sequence phasor (refer Fig.1(c));


Relating unbalanced phasors to symmetrical components:

In matrix notation:


[A] is known as the symmetrical components transformation matrix:

Solving for the symmetrical components leads to :

Symmetrical Component Transformation In component form, the calculation for symmetrical

components are:

From above, the zero-sequence component of current is equal to one-third of the sum of the phase currents.

Therefore, when the phase currents sum to zero, e.g, in the 3 phase system with ungrounded neural, the zero sequence cannot exist.

If the neutral of power system is grounded, zero-sequence currents flows between the neutral and the ground.


Similar expressions exist for voltages:

The apparent power may also be expressed in terms of symmetrical components:

Example 1 Obtain the symmetrical components of a set of

unbalanced currents:

Solution Example 1:

Example 2 The symmetrical components of a set of unbalanced

voltages are:

Obtain the original unbalanced voltages.

Solution Example 2:

Sequence Impedances

The impedance offered to the flow of positive-sequence currents is known as positive-sequence impedance (Z1)

The impedance offered to the flow of negative-sequence currents is known as negative-sequence impedance (Z2)

When zero-sequence currents flow, the impedance is called as zero-sequence impedance (Z0)

Sequence Impedances

Augmented network models:

Generators

3-phase transformers

Y-connected balanced loads

# For this class, we will see the sequence impedance of Y-connected load only!

Sequence impedances of Synchronous Machine

Sequence Circuits of Y-Connected Loads

If impedance Zn is inserted between the neutral and ground of the Y-connected impedances shown in figure below, then the sum of the line currents is equal to the current In in the return path through the neutral:


Expressing the unbalanced line currents in term of their symmetrical components gives:

In = Ia + Ib + Ic

= (Ia0+Ia1+Ia2)+(Ib0+Ib1+Ib2)+(Ic0+Ic1+Ic2)

= (Ia0+Ib0+Ic0) +(Ia1+Ib1+Ic1)+(Ia2+Ib2+Ic2)

= 3Ia0

Since the +ve sequence and –ve sequence currents added separately to zero at neutral point n, there cannot be any +ve sequence and –ve sequence currents in the connections from neutral to ground regardless of the value of Zn.


Moreover, the zero-sequence currents combining together at n become 3Ia0

produces the voltage drop 3Ia0 Zn between neutral and ground.

Van = voltage of phase a with respect to neutral

Va = voltage of phase a with respect to ground

Thus, Va = Van + Vn, where Vn = 3Ia0 Zn


zero-sequence equivalent circuit

positive-sequence equivalent circuit

negative-sequence equivalent circuit

Sequence impedances of Transformer

Construction of Sequence Networks of A Power System

Complete sequence networks of a power system can be constructed by using all the sequence networks discussed before; synchronous machines, transformer and lines.

Start with one-line diagram with respect to impedances;

POS-SEQ – has synchronous machine (generators & motors) in the sequence network.

NEG-SEQ –has same sequence network like POS-SEQ but it has zero voltages.

ZERO-SEQ- combine all the zero sequence networks of SMs, transformers and lines. No voltage sources present in the sequence.

Example 3 For the power system below, sketch the positive

sequence, negative sequence and zero sequence network.

Example 4 A 25 MVA, 11 kV, 3-phase generator has a subtransient

reactance of 20%. The generator supplies two motors over a transmission line with transformers at both ends as shown in figure below. The motors have rated inputs of 15 and 7.5 MVA, both 10 kV with 25% subtransient reactance. The 3-phase transformers are both rated 30 MVA, 10.8/121 kV, connection ∆-Y with leakage reactance of 10% each. The series reactance of the line is 100 ohms. Draw the positive and negative sequence networks of the system

with the reactances marked in per unit.

Example 5 Draw the zero sequence network for the system in

Example 4. Assume zero sequence reactances for the generator and motors are 0.06 per unit. Current limiting reactors of 2.5 ohms each are connected in the neutral of the generator and motor No. 2. The zero sequence reactance of the transmission line is 300 ohms.

symmetrical components

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