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Small and large perturbations

power angle characteristic

Voltage Stability





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  1. The power angle characteristic of a machine-infinite bus system is P= 2 sin d (pu).

The initial operating angle is 60 deg., inertia constant H= 5 sec. System frequency is 50 Hz. The angular frequency of oscillation following small perturbation will be

  1. sqrt(31.4) rad/sec
  2. sqrt(15.7) rad/sec
  3. sqrt(62.8) rad/sec

Ans.: (a)


2.        In an interconnected power system ,the frequency of electro-mechanical modes of oscillation lies in the range

(a) 0.5-2.5 Hz

(b) 1-10 Hz

(c) 30-60 Hz


Ans.: (a) Small and large perturbations


3.        If the sending end and receiving end voltages for a 3-phase transmission line are each 33kV(line), and if the reactance of the line is 13 ohms per phase, the maximum power transmitted per phase will be


a.        60 MW

b.       30 MW

c.        29 MW

d.       28 MW


Ans. d


4.        The torque angle corresponding to the steady-state stability limit of a salient-pole alternator is


a.        Less than 90 deg.

b.       Greater than 90 deg.

c.        Equal to 90 deg.


Ans. a


5.        When the alternator stalls (near the stability limit) the armature current is


a.        Less than the rated value

b.       Greater than the rated value

c.        Equal to the rated value.


Ans. a




Power system stability is a term applied to alternating current electric power systems, denoting a condition in which the various synchronous machines of the system remain in synchronism, or "in step" with each other. Conversely, instability denotes a condition involving loss of synchronism, or falling "out of step".


The AIEE standard definition of stability is as follows" Stability when used with reference to a power system, is that attribute of the system, or apart of the system which enables it to develop restoring forces between the elements thereof, equal to or greater than the disturbing forces so as to restore a state of equilibrium between the elements".


Small and large perturbations


A power system is subjected to a variety of disturbances. These are classified into two categories:

         Small perturbations

         Large perturbations


Small Perturbations


Perturbations are characterized as small if the changes in system states are small due to these perturbations. The magnitude of perturbation is small enough o allow the use of linearized state equations obtained by linearizing the nonlinear differential equations around the operating point for studying he dynamics of the system. Random changes in load which occur in the system continuously is a n example of small perturbation. Stability problem associated with small perturbation is known as dynamic stability.


Large perturbations


A power system may be subjected to large perturbations such as :

         Occurrence of faults on the line

         Loss of large generating units

         Loss of major transmission facilities

         Loss of large loads

The stability problem associated with large perturbations is known as transient stability.


Derive and explain the power angle characteristic of

         Machine infinite-bus system

         Two machine system

Discuss the concepts of stable & unstable equilibrium points.

What is meant by steady state & transient stability of a system?


Voltage Stability-ModuleC(.xls file)

This module introduces the static voltage instability problem. The module uses a simple generator connected to a load through two parallel transmission lines. The student can plot PV, QV, or PQ curves for different values of line reactance, generator terminal voltage, and power factor. Parameters can be changed under the parameter column. Different plots can be obtained from the Plot Command. Clicking the Introduction button provides student with basic material to understand the concept of maximum power transfer. The information button includes the instructions needed to plot various curves. The student is asked to calculate the reactive power required maintaining a certain voltage Vr at the load bus for a given Pr, Vs, and Xl. The student is asked to calculate the reduction in maximum power

at the load bus with one line out.