1.
Machine Response During System Disturbances
(By Sarath Chandrasiri)
1. System Disturbances: A system disturbance can be defined as any event that
causes the frequency and/or voltage of the system to deviate from the normal range of
operation. These are caused by incidents such as occurrence of short circuits,
generator trips, feeder trips, sudden increase of power output of a generator due to a
defect in its control system.
The responses of the healthy machines for such events should be so as to return the
system to the normal status as quickly as possible and with as little manual
intervention as possible. Therefore, the response of machines is of utmost importance
from the point of view of system security and reliability.
Machine response to system disturbances: The response of machines should be
considered from two main aspects.
1. Load- frequency response (Governor response)
2. MVAR – Voltage response (AVR response)
Only the first will be considered below.
2. Load- frequency response (Governor response)
The frequency and load response of a machine that remains connected to the system
during the event is shown below:
fdev_dyn= Dynamic frequency deviation
Δf = Quasi steady state frequency deviation
Machine
Load
t
Page 1
f1
fdev_dyn
0 t1 t2 t3 t4
Δf
t
f
B
A

2.
Fig 1 – Frequency variation of a machine after disturbance
The response can be considered to be in 4 stages.
i. Initial response
ii. Primary response
iii. Secondary response
iv. Final stage due to manual action or automatic action through a power system
controller.
These will now be considered in detail.
3. Initial Response (period from t=0 to t=t1 sec)
The initial response of the machine lasts between 0.5 to a few seconds depending on
the speed of response of the machine governors and the system involved. In the case
of the Bahrain system the initial response time duration is between 0.5 and 1 sec.
This period occurs immediately after the incident and the response comes due to the
kinetic energy of the GT rotor (GT + generator). The governor has not started
responding yet. Since any governor, however fast, has a mechanical device (fuel
control valve) as the final element, the response will be delayed due to the inertia of
the mechanical parts.
If the incident is due to a generation loss then the rest of the machines in the system
make a contribution to compensate for the short fall. As given before, the governor
has no time to respond and the opening of the fuel control valve remains unchanged
during this period. Then from where does the energy required for the increased output
of the generators come? It comes from the kinetic energy stored in the generator
rotors. A contribution also comes from the rotating loads such as induction motors
which is produced as a result a decrease in the KE stored in their rotors.
The frequency of the system falls linearly during the period as the stored kinetic
energy is converted to electrical energy.
Telec
=
Opposing
Torque of
Generator
Mover
Tmech
=
Mechanical
Torque of
Prime
Mover
Mover
SHAFT of
Moment of
Inertia I
Page 2

3.
FIG-2
To analyze the situation consider Fig-2, which gives the torques acting on the
Machine shaft.
Tnett =Tmech – Telec = I dω/dt
where ωis the shaft angular speed in radians/sec.
Under normal system conditions, Tnett = 0 as Tmech = Telec. Therefore, ω
remains constant and consequently, the kinetic energy of the rotor remains constant.
Before analyzing the behavior of the generator after the disturbance, occurs it is useful
to consider some basic ideas.
For ease of analysis, it is useful to consider the process to be consisting of 2 different
periods:
1. Pre fault period (t<0)
2. Post fault period (t>0)
The disturbance is considered to occur at the instant t = 0.
Certain physical quantities remain constant as the pre-fault stage ends and the post
fault stage begins while other quantities undergo an abrupt change (step change) at
t=0.
Physical quantities that do not undergo any step change at t=0: These are
associated with energy. It is a physical principle that the energy of a system cannot be
changed abruptly as this would mean that dE/dt (Power) is infinite.
Thus the following quantities do not undergo step changes at t=0.
a) Kinetic energy of the rotor
b) Speed (and hence system frequency)
c) The nett magnetic flux in the direct axis of the generator
d) Mechanical torque produced by the GT.
Physical quantities that undergo a step change at t=0: Some of these are as
follows:
a) Electrical power output of the generator
b) Reverse torque generated by the generator.
c) Generator terminal voltage and current
Page 3

4.
During this period Tnett < 0 as Tmech < Telec. Thus ω decreases linearly as
shown below.
is negative but constant.
Tnett = I dω/dt
dω/dt = Tnett/I (a constant)
The shaft decelerates from a speed corresponding to the rated frequency of f Hz to
one corresponding to f1 Hz.
Storage of Kinetic Energy in the Rotor
Due to its moment of inertia the rotor stores kinetic energy.
KE energy stored in the rotor (EKE) = ½ I ω2
X 10-6
(MJ)
The power available from the shaft can be obtained by differentiating the above.
Rotor Power (EKE) = I ω . dω/dt X 10-6
MW
As shown in the diagram below this power can flow both ways.
• When the speed is decreasing the KE is converted to Electrical Power.
• When the speed is increasing the Mechanical Power is converted to KE.
When the system is considered as a whole the recovery process depends on the
Kinetic energy of the Generating sets and the Motors connected as loads.
Page 4
FIG-3

5.
4. The H-Constant
It is useful to define a quantity called H which is directly proportional to the Moment
of Inertia I of the rotor.
If the f0 is the rated frequency in Hz (50 Hz)
Pn the Rated Load in MW
KE0 the Kinetic Energy of the rotor in MWs
Then H=( KE0 / Pn)
The advantage of using the H constant is that it is essentially independent of the
generator size. Typical values of H lie in the range 2 to 8 sec.
Initial rate of decrease of frequency = (df/dt)0 = ΔPf0/2H
Thus the rate of drop of frequency will increase with decreasing H and increasing ΔP
(pu).
Therefore, it is advantageous to have a high H.
5. Primary Response (period from t= t1 to t=t3 sec)
At the beginning of this period the fuel control valve starts to move, increasing its
opening in response to the output signal from the governor (PRIMARY
CONTROLLER), which increases in response to the drop in frequency.
With the increased flow of fuel, the Mechanical Torque of the GT (Tmech) starts to
increase and at point B on the graph in Fig -1 it Tmech becomes equal to Telec .
Therefore at this point deceleration of the shaft ceases.
The controller continues to increase its output signal and the shaft accelerates back to
a speed corresponding to a freq of f2 Hz. However, the controller cannot bring the
frequency back to f due to the droop of the control system, which is explained in the
next section.
During this period the primary controllers alter the power delivered by the generators
until a balance is re-established between the load power and the generated power. The
period is characterized by oscillatory phenomena due to the dynamic response of the
controllers and the process.
Dynamic Frequency Deviation (fdev_dyn): The magnitude of this (See Fig-1) depends
on the following:
• The magnitude of the disturbance
Page 5

6.
• KE of rotating machines in the system
• The primary controller reserve of all generators
• Dynamic characteristics of the machines (including controllers)
• Dynamic characteristics of the loads, particularly the self regulating effect
loads.
Quasi Steady State Frequency Deviation (Δf): The magnitude of this (See Fig-1)
depends on the following:
The magnitude of the disturbance
Power – frequency characteristic of the system
6. Secondary Response (period from to t=t3 to t4 sec)
During this period, the generator operates at a steady frequency of f2 Hz, which is less
than the rated frequency Δf = (f-f2) H z. The magnitude of Δf depends on the Speed
Droop of the governor.
Speed Droop: The steady state Load vs. frequency characteristic of the governor
system has a drooping characteristic, which is built in to achieve stable operation of
the generators ting in parallel.
FIG-4
The interpretation of the above speed droops is as follows:
Page 6

7.
If the machine is operating initially at 50% load and a frequency of 50 Hz and a
disturbance occurs, which causes a steady state drop of frequency by 0.5 % (0.25
Hz), then the steady state load rise would be,
• 10% if the droop was 5% and
• 25% if the droop was 2%.
In general the droop SG of a generator is defined as follows:
Under steady state (secondary response) conditions,
Δ PG = The change in load due to Primary Control action
PGn = Rated Load
Δf = The change in frequency that is necessary for the Primary Controller to
produce the above load change
f0= Rated frequency
Then, SG = (-Δf / f0) / (Δ PG / PGn) in %
The – sign takes care of the fact that a negative Δf produces a positive Δ PG and vice
versa, provided the Primary Control Reserve has not been completely used up (see
below).
FIG-5
The contribution of a generator to a system disturbance depends mainly upon
• The Droop
• The Primary Control Reserve
Referring to FIG-5, in case of a minor disturbance (frequency offset < ΔfB ) the
contribution of generator a (which has the controller with a smaller droop) will be
greater than that of generator b which has the controller with the smaller droop.
Page 7
fA
fB
fN
PMAX
fN = Rated Freq

8.
In case of a major disturbance (frequency offset > ΔfB ), the contributions of both
generators to PRIMARY CONTROL under quasi – steady-state conditions will be
equal.
The operation of the system though stable in terms of frequency and voltage is not
acceptable for an extended period as the above parameters would be out of their
normal range.
It is also undesirable from the point of view of power flow in the tie lines (if there are
any) as the actual active and reactive power flows are different from the specified
levels.
Furthermore, since the system frequency and voltage are lower than rated there is a
possibility that those of the system stability will be lost if another disturbance occurs.
Due to these reasons it is necessary to restore the frequency and voltage to rated levels
as soon as possible. This can be done manually or through a power system controller.
In the secondary response period the governor load set points are adjusted by the
operators to bring the system frequency back to normal.
Final Response:
7. Dead Band: Usually there is a provision in the governor control system to
introduce a dead band. The dead band makes the controller insensitive to small band
of frequency changes (Ex 0.1 Hz) around the rated frequency.
The dead band serves the following purposes:
• Immunity to power system noise: If the GT is is only to play a stabilizing
role when large frequency deviations occur, the dead band can be switched on
to obtain some insensitivity to frequency. The governor would not react to
frequency deviations adjustable over a range of ±0.5 Hz from the set point
frequency. The dead band functions only when the machine is on load.
• In interconnected systems, where a stable system frequency with very narrow
tolerances (± 0.05 Hz) and closely defined cross border tie line power between
subsystems are required the dead band merely suppresses the power system
noise.
• Lower thermal loading of the turbine blades: Turbine blades are highly
susceptible to temperature gradients. Therefore, the dead band provides a way
of suppressing constant changes of turbine inlet temperature to some extent.
This prolongs the life of the blades.
• Compressor surges: The dead band also has the effect of keeping the
operating point away from the point at which the compressor surge protection
starts to operate.
Page 8

9.
Prepared by K. A. Chandrasiri
Senior General Engineer
Office of the Director of Electricity Production
Page 9

10.
References:
Electrical Energy Systems Theory by Olle L. Elgerd
Transient Processes in Electrical Systems by V. Venikov
Page 10