PRESENTED BYSAMEER KUMAR SINGH (10M206)TARESH KUMAR MITTAL (10M207)NIKHIL KUSHWAHA (10M212)

First Swing Stabilty

Stability

The stability of an interconnected power system is its ability to return to normal or stable operation after having been subjected to some form of disturbance.

Machine Connected to Infinite Bus

Fault makes generator electric Power zero

Generator accelerates. Can generator get back to constant --synchronous speed?

Only if it can get rid of excess KE

Excess KE needs to go into the infinite bus through the line? Will it? What happens if it can’t?

Stability means returning to synchronous speed

KEBuilds up Excess KE

Needs to be removed

SPEED

Line Real Power P

PP

∞ ∞

Instability

Instability means a condition denoting loss of synchronism or falling out of steps.

Types of Power System Stability

Pe = (EV/X) sinδPe = (VsVr/X)sinδ

Power-angle curve of the system

jXL+

E’/δ

Pe

jXd’

V/0

Fixed (Infinite Bus)

Pm

P

δ0°

180°

Pmax

SWING EQUATION

Definition: The electromechanical equation describing the relative motion of the rotor load angle (δ) with respect to the stator field as a function of time is known as Swing equation.

M(d²δ/dt²) = Pm – PeM = Angular MomentumPm = Mechanical or shaft power inputPe = Electrical power outputδ = rotor angle with respect to a synchronously rotating reference

For Stable Condition

Pmax

180°0°

Pm=PeP

δ

d2δ/dt2 =0 Pm = Pe

dδ /dt =0 ω = ωsyn

Equal Area Criteria

Equal Area Criteria

First Swing Stability

Following a large disturbance, a power system can be considered as first swing stable if the angle of all machines in center of angle (COA) reference frame initially increases (decreases) until a peak (valley) is reached where the angle starts retuning to the stable equilibrium point

First Swing Stability

First Swing Stability

Applications

1. Establish initial conditions2. Define sequence of events and network for

each event3. Develop Power angle curves4. Apply EAC

Applications Of FACTS Controller

1. Power transfer capability

2. Power oscillation Damping

3. Transient Stability

4. Prevent blackouts

Fundamental of improving FSS

Pe = (EV/X) sinδPe = (VsVr/X)sinδPower systems

are normally designed to be transiently stable, with defined pre-fault contingency scenarios and post-fault system degradation when subjected to a major disturbance .

Improvement of FSS using Shunt Devices

Pe = (V2/X)sinδ (for Uncompensated system)

Pe = 2(V2/X)sinδ/2 (for compensated system)

P- δ curves for various operating conditions of SVC

areas when the angle increases areas when the angle decreases.

System with a STATCOM

Equivalent circuitP- δ curve.

Improvement of FSS using series Devices

P= V2sinδ (1-k)X

Q= 2V2. k . (1-cosδ) X (1-k)2

K= Xc ,o<k<1 X

Improvement of FSS using Series compensator

Without compensation With compensation

Using Phase Angle Regulator

P= V2sin(δ- ) X

Q= V2. {1-cos(δ - )} X

Conclusion

When the fault is cleared (after roughly 0.1 s) the power system has to be restored to sufficiently small angle deviations between the generator rotors again. After the first swing we require damping of the oscillations.

In the first phase, the electrical properties are very quickly adjusting to the new situation.

In the second phase the unbalance between mechanical input and electrical output of each generator are causing a change of generator mechanical speed.

In the third phase protection and control are coming into play.

References

[1] PAVELLA M., ERNST D., RUIZ-VEGA D.: ‘Transient stability of power systems: a unified approach to assessment and control’ (Klumer Academic Publishing, Boston, 2000)

[2] KUNDUR P., PASERBA J., AJJARAPU V., ET AL.: ‘Definition and classification of power system stability’, IEEE Trans. Power Syst., 2004, 19, (2), pp. 1381–1401 2003, 142, (2), pp. 59–67

[3] HAQUE M.H.: ‘Improvement of first swing stability limit by utilising full benefits of shunt FACTS devices’, IEEE Trans. Power Syst., 2004, 19, (4), pp. 1894–1902

[4] CHANG J., CHOW J.H.: ‘Time-optimal control of power systems requiring multiple switchings of series capacitors’, IEEE Trans. Power Syst. 1998, 13, (2), pp. 367–373.

[5]Narain G. Hingorani , Understanding FACTS

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