Module 2 : Equipment and Stability Constraints in System Operation
Lecture 8 : Large disturbance Angle stability
Objectives
In this lecture you will learn the following
Spring Mass analogy of a single machine infinite bus system.
Large disturbance angular instability is demonstrated using an example.
Angular stability in multimachine systems.
Impact of angular stability problems on system operation.
A Simple Analogy of a single machine infinite bus system: A spring mass system
In this lecture we first understand the behaviour of the dynamical system qualitatively using a simple analogy
and then use a numerical technique to simulate the behaviour of the system in an example.
The differential equations of a single machine infinite bus(SMIB) system are similar to that of a "mass
connected to a wall by a nonlinear spring" system.
For a linear spring, the restoring force is directly proportional to the stretch of the spring. If the mass is
displaced from its equilibrium, then oscillatory motion results irrespective of the extent of the disturbance.
If the restoring force of the spring is a nonlinear function of the stretch, then the behavior may be different
and depends on the extent of the disturbance.
For example, if the restoring force of the spring is almost a linear function upto a certain stretch but reduces
to zero beyond that value, then for a large disturbance it is possible that the spring will break (as shown in the
figure below).
, To avoid instability (breaking of the spring), the following can be done:
1) Make the spring more stiff.
2) Reduce the disturbance.
3) Keep the equilibrium stretch of the spring small (so that it has more margin to stretch in case
of disturbances).
The behavior of SMIB system is similar. Under normal operating conditions, there are restoring torques
which tend to keep the synchronous machine in synchronism with the infinite bus. However when disturbances
are large, the torque may not be able to "pull back" the machine to synchronism. We now illustrate this by an
example.
Machine Synchronisation
We have seen how the system behaves when subject to large disturbances in the previous example. In the
example, we had assumed that the machine was already connected and was initially in equilibrium (i.e., was in
synchronism with the infinite bus).
It is natural of you to ask : How was the machine "synchronised" when it was first connected to the grid?
When a synchronous machine is connected to a grid, it is important to follow a particular procedure so that the
transients which occur are minimised and the incoming generator is "pulled into synchronism".
This includes ensuring that the generator voltages and the system voltages are in the same phase sequence
and the voltage magnitude of the generator and the grid at the point of interconnection are nearly equal.
Additionally:
a) The electrical speed of the incoming generator should be almost equal to the grid frequency.
b) The phase angular difference between the generator voltage and the grid voltage at the point of
interconnection at the instant of interconnection should be small.
The situation is analogous to connecting two moving masses by a spring. To avoid excessive stretch in the
spring when the masses are inter-connected (which may cause the spring to break), one would need to have
the two masses to be close to each other and to be moving at nearly the same speed at the time of
interconnection. If the interconnection is done smoothly, without breakage of the spring, then the masses
move together at the same speed after transients die out. Thereafter, the masses are held together by the
spring unless a large disturbance causes the spring to break.
In practice, a plant operator starts rotating the generator by introducing a prime mover torque. He ramps up
the speed to a value which is very close to the grid frequency by adjusting the prime mover torque. He then
switches on the field excitation and brings voltage close to the grid voltage at the point of interconnection by
adjusting the field voltage. Using an instrument called a synchroscope, he monitors the phase angular
difference and switches on the interconnecting circuit breaker at the instant when the phase angular difference
is very small.
You can simulate the process of synchronisaton by downloading all of the following MATLAB/SIMULINK
Lecture 8 : Large disturbance Angle stability
Objectives
In this lecture you will learn the following
Spring Mass analogy of a single machine infinite bus system.
Large disturbance angular instability is demonstrated using an example.
Angular stability in multimachine systems.
Impact of angular stability problems on system operation.
A Simple Analogy of a single machine infinite bus system: A spring mass system
In this lecture we first understand the behaviour of the dynamical system qualitatively using a simple analogy
and then use a numerical technique to simulate the behaviour of the system in an example.
The differential equations of a single machine infinite bus(SMIB) system are similar to that of a "mass
connected to a wall by a nonlinear spring" system.
For a linear spring, the restoring force is directly proportional to the stretch of the spring. If the mass is
displaced from its equilibrium, then oscillatory motion results irrespective of the extent of the disturbance.
If the restoring force of the spring is a nonlinear function of the stretch, then the behavior may be different
and depends on the extent of the disturbance.
For example, if the restoring force of the spring is almost a linear function upto a certain stretch but reduces
to zero beyond that value, then for a large disturbance it is possible that the spring will break (as shown in the
figure below).
, To avoid instability (breaking of the spring), the following can be done:
1) Make the spring more stiff.
2) Reduce the disturbance.
3) Keep the equilibrium stretch of the spring small (so that it has more margin to stretch in case
of disturbances).
The behavior of SMIB system is similar. Under normal operating conditions, there are restoring torques
which tend to keep the synchronous machine in synchronism with the infinite bus. However when disturbances
are large, the torque may not be able to "pull back" the machine to synchronism. We now illustrate this by an
example.
Machine Synchronisation
We have seen how the system behaves when subject to large disturbances in the previous example. In the
example, we had assumed that the machine was already connected and was initially in equilibrium (i.e., was in
synchronism with the infinite bus).
It is natural of you to ask : How was the machine "synchronised" when it was first connected to the grid?
When a synchronous machine is connected to a grid, it is important to follow a particular procedure so that the
transients which occur are minimised and the incoming generator is "pulled into synchronism".
This includes ensuring that the generator voltages and the system voltages are in the same phase sequence
and the voltage magnitude of the generator and the grid at the point of interconnection are nearly equal.
Additionally:
a) The electrical speed of the incoming generator should be almost equal to the grid frequency.
b) The phase angular difference between the generator voltage and the grid voltage at the point of
interconnection at the instant of interconnection should be small.
The situation is analogous to connecting two moving masses by a spring. To avoid excessive stretch in the
spring when the masses are inter-connected (which may cause the spring to break), one would need to have
the two masses to be close to each other and to be moving at nearly the same speed at the time of
interconnection. If the interconnection is done smoothly, without breakage of the spring, then the masses
move together at the same speed after transients die out. Thereafter, the masses are held together by the
spring unless a large disturbance causes the spring to break.
In practice, a plant operator starts rotating the generator by introducing a prime mover torque. He ramps up
the speed to a value which is very close to the grid frequency by adjusting the prime mover torque. He then
switches on the field excitation and brings voltage close to the grid voltage at the point of interconnection by
adjusting the field voltage. Using an instrument called a synchroscope, he monitors the phase angular
difference and switches on the interconnecting circuit breaker at the instant when the phase angular difference
is very small.
You can simulate the process of synchronisaton by downloading all of the following MATLAB/SIMULINK
