small signal stability of 1- machine infinite bus

8/10/2019 Small Signal Stability of 1- Machine Infinite Bus

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Small Signal Stability of 1- MachineInfinite Bus System


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contents | Seminar

PowerSystemStability

SmallSignal

Stability

1-M/cconnected to bus

SwingCurve

Conclusion,References


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Ability of the system to bring back its operation to steadystate condition within minimum possible time after havingundergone some sort of transience or disturbance in the line

definition | Power System Stability


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A system in steady state has numerous properties which are

not changing with time . For those properties p of the system,the partial derivate with respect to time is zero.

=

concept | Steady State


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Therefore for stable operation itis important for the bus to bewell synchronized with thegenerators over the entireduration of transmission.

importance | Power SystemStability

HFO Generator Set

In the power plants, severalsynchronous generators areconnected to the bus terminalshaving the same frequency

and phase sequence as thegenerators.


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concept | Types of Stability

Power SystemStability

Steady State

Stability

Transient

Stability

Dynamic

Stability


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definition | Small Signal Stability

Ability of the system to be in synchronism when subjected to small disturbances

The disturbances can be switching of small loads, generators ortransmission line tripping


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understanding | Small Signal

Stability

Can linearize the power system around the steady state operatingpoint for small disturbances.


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analysis | 1 M/c connected to

an infinite Bus

The internal rotor angle is .

Single Line Diagram of Single Machine Infinite Bus System


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an infinite Bus

The prime mover gives mechanical energy to the generator rotor andin turn the generator converts the mechanical energy into electricalenergy through magnetic coupling. The dynamics of a rotational

mechanical system can be represented as

2

2 = e

- mechanical angle of the rotor field axis with respect to stator

referenceJ - inertia constant of the rotating machine

- mechanical input torque due to the prime mover

e - electrical torque


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an infinite Bus

The angular displacement at any time t is given by:

=+ ms t

- mechanical angle of the rotor field axis with respect to statorreference

- angular displacement of rotor with reference axis

ms - synchronous speed


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SMIB analysis | continued

We have,

2

2 = e (i)

=+ ms t (ii)

By differentiating (ii),

= + ms (iii)

Differentiating (iii),

2

=2

(iv)


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analysis | continuedThe rate of change of the rotor mechanical angle with respect to time isnothing but the speed of the rotor.

= m

Substituting in = +ms

, we get

= m ms (v)

Substituting2

=2

, in 2

2 = e,

we get,

2

2 = e (vi)


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If we multiply m on both sides of 2

2 = e, we get

m2

2 = e .. (vii)

analysis | continued


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If we multiply12 ms

on both sides of previous equation and divide by the base

MVA SB, we get


(viii)


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The machine inertia constant H is given by

=2

p.u.

Substituting the value of H in the previous equation (viii), we get

2

2 =12 m

( e)


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2

2 =12 m

( m e)

e = Pma x sin

By substituting, we get:

2

2 =12 m

( m P max sin ) (ix)


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analysis | Small SignalStability

In the steady state, that is when the speed of the generator rotor is constant atsynchronous speed, the rate of change of rotor speed will become zero due towhich:

= P max sin

= sin 1Pmax

, sin 1Pmax


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Final step | SwingCurve


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result | StabilityAnalysis

By making small perturbationsat the points A and B, thestability of the system can be

analyzed.

Going back to the notion ofStability:Ability to return to the originalstate after disturbance.


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conclusion

Point A is called stable equilibrium point and operatingpoint B is called as unstable equilibrium point.

Similarly, o is the stable steady state rotor angle and max isan unstable rotor angle.


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References

Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitionsKundur, P; Andersson, G; Paserba, J

Stability Swing Curves, IEEEWB Boast

Linearized Modelling of Single Machine Infinite Bus Power System,International Journal of Advanced Research in ComputerEngineering & TechnologyBalwinder Singh Surjan

small signal stability of 1- machine infinite bus

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