Electrical Power 3
Lecture No.1
By:
Dr. Naema Mansour
11/2/2023
Power system stability
Power system structure
Structure of the power system
1. Generation:- (in the range of 11 to 35 kV)
2. Transmission system:-
1) Transmission (230 kV and above)
2) Sub-transmission system (69 kV to 138kV)
3) Distribution system.
a) The primary distribution voltage is typically between 4.0 kV and
34.5 kV. Small industrial customers are supplied by primary feeders
at this voltage level.
b) The secondary distribution feeders supply residential and
commercial customers at 120/240 V.
3. Electrical Loads:-
Electrical load refers to the electrical circuit that converts current into
something practical—for instance, a lightbulb, a resistor, and a motor. A load
transforms electricity into heat, light or motion.
The electrical load can be resistive, inductive or capacitive, or a combination of
these. Three fundamental loads are present within circuits: (capacitive-
inductive- resistive) loads. They differ in how they use power in an alternating-
current (AC) configuration.
Voltage level classification Distribution voltage level
Power system control
The function of an electric power system is to convert energy from one of
the naturally available forms to the electrical form and to transport it to the
points of consumption.
An accurate designed operated power system should meet the following
fundamental requirements:
1) The system must be able to meet the continually changing load demand for
active and reactive power. Unlike other types of energy, electricity cannot
be conveniently stored in sufficient quantities. Therefore, adequate
"spinning“ reserve of active and reactive power should be maintained and
appropriately controlled at all times.
2) The system should supply energy at minimum cost and with minimum
environmental impact.
3) The "quality" of power supply must meet certain minimum standards with
regard to the following factors:-
a) Constant frequency.
b) Constant voltage. Power system reliability:-
Addresses the issues of service
c) Level of reliability.
interruption and power supply
loss.
Subsystems of a power system and associated controls
1) Generating unit control:-
a) Prime mover controls:
Are concerned with speed regulation and
control of the energy supply and system
variables such as boiler pressures,
temperatures, and flows.
b) Excitation controls:-
Are concerned with regulation of
generator voltage and reactive power
output.
The desired MW outputs of the individual
generating units are determined by the system
generation control.
The primary purpose of the system-generation
control is to balance the total system
generation against system load and losses so
that the desired frequency and power
interchange with neighboring systems (tie
flows) is maintained.
2) The transmission controls: include
power and voltage control devices,
such as:-
a) Static VAR compensators.
b) Synchronous condensers.
c) Switched capacitors and reactors.
d) Tap-changing transformers.
e) Phase-shifting transformers.
f) HVDC transmission controls.
The various subsystem controls in a synchronous generator that are used to
meet the requirements of stability.
The controls described above contribute to the satisfactory operation of the power
system by:-
1) Maintaining system voltages.
2) Maintaining system frequency and other system variables within their
acceptable limits.
3) They also have a deep effect on the dynamic performance of the power system
and on its ability to deal with disturbances. (It assists the power system to
restore its normal state).
Power system controls assist the operator in returning the system to a
normal state.
If the disturbance is small, power system controls by themselves may be able to
achieve this task.
However, if the disturbance is large, it is possible that operator action such as
generation rescheduling or element switching may be required for a return to the
normal state.
The control objectives are dependent on the operating state of the power system.
Under normal conditions, the control objective is to operate as efficiently as
possible with voltages and frequency close to nominal values. When an abnormal
condition develops, new objectives must be met to restore the system to normal
operation.
Introduction to the Power System Stability Problem
Basic concepts and definitions
Power system 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 disturbances.
Disturbance classification:-
1) Small disturbances:
Such disturbances occur continually on the system because of small
variations in loads and generation. The system must be able to operate
satisfactorily under these conditions and successfully supply the
maximum amount of load.
Small disturbance stability is the ability of the power system to
maintain synchronism under small disturbances.
2) Large disturbances (Transient stability)
Is the ability of the power system to maintain synchronism when subjected to
a severe transient disturbance such as a short-circuit on a transmission line,
loss of a large generator or load, or loss of a tie between two subsystems. The
resulting system response involves large deviation of generator rotor angles
and is influenced by the nonlinear power-angle relationship.
Stability depends on both the initial operating state of the system and the
severity of the disturbance. Usually, the system is altered so that the post-
disturbance steady-state operation differs from that prior to the disturbance.
The stability problem has been one of maintaining synchronous
operation. Since power systems depends on synchronous machines
for generation of electrical power, a necessary condition for
satisfactory system operation is that all synchronous machines
remain in synchronism. This aspect of stability is influenced by the
dynamics of generator rotor angles and power-angle relationships.
Instability may also be occurred without loss of synchronism. For
example, a system consisting of a synchronous generator feeding an
induction motor load through a transmission line can become
unstable because of the collapse of load voltage. Maintenance of
synchronism is not an issue in this instance; instead, the concern is
stability and control of voltage (voltage stability).
Different forms of power system instability
1) Rotor Angle Stability
Rotor angle stability is the ability of interconnected synchronous
machines of a power system to remain in synchronism.
The stability problem involves the study of the electromechanical
oscillations inherent in power systems. A fundamental factor in this
problem is the manner in which the power outputs of synchronous
machines vary as their rotors oscillate.
2) Voltage Stability and Voltage Collapse
Voltage stability is the ability of a power system to maintain steady
acceptable voltages at all buses in the system under normal operating
conditions and after being subjected to a disturbance..
A system enters a state of voltage instability when a disturbance,
increase in load demand, or change in system condition causes a
progressive and uncontrollable drop in voltage. The main factor causing
instability is the inability of the power system to meet the demand for
reactive power.
Power System Stability
Power system consists some synchronous machines operating in
synchronism. For the continuity of the power system, it is necessary
that they should maintain perfect synchronism under all steady state
conditions. When the disturbance occurs in the system, the system
develops a force due to which it becomes normal or stable.
The ability of the power system to return to its normal or stable
conditions after being disturbed is called stability. Disturbances of
the system may be of various types like sudden changes of load, the
sudden short circuit between line and ground, line-to-line fault, all
three-line faults, switching, etc.
Stability studies are helpful for the determination of critical clearing
time of circuit breakers, voltage levels and a transfer capability of
the systems.
Rotor Angle Stability
Synchronous machine characteristics
A synchronous machine has two essential elements:
The field and the armature. Normally, the field is on the rotor and the
armature is on the stator.
• The field winding is excited by direct current. When the rotor is driven by
a prime mover (turbine), the rotating magnetic field of the field winding
induces alternating voltages in the three phase armature windings of the
stator. The stator and rotor fields react with each other and an
electromagnetic torque results from the tendency of the two fields to align
themselves.
The frequency of the induced alternating voltages and of the resulting
currents that flow in the stator windings when a load is connected, depends
on the speed of the rotor. The frequency of the stator current and voltage
are thus synchronized with the rotor mechanical speed.
When two or more synchronous machines are interconnected, the stator
voltages and currents of all the machines must have the same frequency
and the rotor mechanical speed of each is synchronized to this frequency.
Therefore, the rotors of all interconnected synchronous machines must be
in synchronism.
Power versus angle relationship
An important characteristic that has a bearing on
power system stability is the relationship between
interchange power and angular positions of the
rotors of synchronous machines. This relationship
is highly nonlinear.
Two synchronous machines connected by a
transmission line having an inductive reactance
XL but negligible resistance and capacitance. Let
us assume that machine 1 represents a generator
feeding power to a synchronous motor
represented by machine 2.
The power transferred from the generator to the
motor is a function of angular separation (𝜹)
between the rotors of the two machines. This
angular separation is due to three components:
1) Generator internal angle 𝜹𝑮 (angle by which the
generator rotor leads the revolving field of the
stator);
2) Angular difference between the terminal
voltages of the generator and motor (angle by
which the stator field of the generator leads that
of the motor 𝜹𝑳 );
𝑬𝑮 𝑬𝑴
3) The internal angle of the motor (angle by which 𝑷= 𝒔𝒊𝒏𝜹
the rotor lags the revolving stator field 𝜹𝑴 ). 𝑿𝑻
𝑿𝑻 = 𝑿𝑮 + 𝑿𝑳 + 𝑿𝑴
The power transferred from the generator to the motor is given by:-
𝑬𝑮 𝑬𝑴
𝑷= 𝒔𝒊𝒏𝜹
𝑿𝑻
Where 𝑿𝑻 = 𝑿𝑮 + 𝑿𝑳 + 𝑿𝑴
The power varies as a sine of the angle (𝜹).
1) When the angle is zero, no power is transferred.
2) As the angle is increased, the power transfer increases up to a maximum.
3) After a certain angle, nominally 90°, a further increase in angle results in a decrease in
power transferred.
There is thus a maximum steady-state power that can be transmitted between the two
machines. The magnitude of the maximum power is directly proportional to the machine
internal voltages and inversely proportional to the reactance between the voltages, which
includes reactance of the transmission line connecting the machines and the reactances of the
machines.(it is impossible to run a machine at the steady-state limit of stability since its
ability to resist small changes is zero unless the machine provided with a special fast-acting
excitation system).
When a synchronous machine loses synchronism or "falls out of step" with the rest of the
system, its rotor runs at a higher or lower speed than that required to generate voltages at
system frequency.
If the rotor angle exceeds a relative angle of 90° between the stator and rotor windings, the
synchronous generator is considered out of sync or unstable .Power protection systems will
trip and handle cases of synchronous generators falling out of sync.
Synchronizing Power and Torque Coefficient
Definition: – Synchronizing Power is defined as
the varying of the synchronous power P on
varying in the load angle δ. It is also called the
Stiffness of Coupling, Stability factor or Rigidity
factor. A synchronous machine, whether a
generator or a motor, when synchronized to
infinite busbars has an inherent tendency to
remain in synchronism.
The stability phenomena
The following mathematical equation, known 𝟐
as the swing equation models
𝒅 𝜹
the generator dynamics. 𝑻𝒎 − 𝑻𝒆 = 𝒋 𝒅𝒕𝟐
As observed from the above equation, an imbalance of 𝑻𝒎 and 𝑻𝒆 (i.e. 𝑷𝒎
and 𝑷𝒆 ) results in a change in velocity (Δω) of the turbine. Alternatively, it
can be stated that this imbalance results in an acceleration of the rotor
angle.
Under steady-state conditions, there is equilibrium between the input
mechanical torque and the output electrical torque of each machine, and the
speed remains constant.
If the system is troubled this equilibrium is upset, resulting in acceleration
or deceleration of the rotors of the machines according to the laws of
motion of a rotating body.
If one generator temporarily runs faster than another, the angular
position of its rotor relative to that of the slower machine will advance. The
resulting angular difference transfers part of the load from the slow
machine to the fast machine, depending on the power-angle relationship.
This tends to reduce the speed difference and hence the angular separation.
Beyond a certain limit, an increase in angular separation is accompanied by
a decrease in power transfer; this increases the angular separation further
and leads to instability.
Electric Torques
Mechanical torque from turbine is converted into electrical torque
The electric torque has two components:
Synchronizing torque (in phase with power angle)
Damping torque (in phase with speed)
The lack of either torque render the system unstable
Power system controllers (stabilizers) are used to enhance these torques.
Power system
stability can be
classified into
different categories
and subcategories as
in the flow chart:-
In electric power systems, the change in electrical torque of a synchronous
machine following a disturbances can be resolved into two components:
∆𝑇𝑒 = 𝑇𝑠 ∆𝛿 + 𝑇𝐷 ∆𝜔
𝑻𝒔 ∆𝜹 is the component of torque change in phase with the rotor angle
disturbance ∆𝜹 and is referred to as the synchronizing torque component;
𝑻𝑺 is the synchronizing torque coefficient.
𝑻𝑫 ∆𝝎 is the component of torque in phase with the speed deviation ∆𝝎 and
is referred to as the damping torque component; 𝑇𝐷 is the damping torque
coefficient.
Notes:-
Lack of sufficient synchronizing torque results in instability through an
aperiodic drift in rotor angle.
On the other hand, lack of sufficient damping torque results in oscillatory
instability.
A single power system stabilizer (PSS) is used to add damping torque
through controlling the field excitation system to change the electrical
torque. When the PSS provides a sufficient amount of compensation to
produce an electrical torque in phase with speed deviation, rotor oscillations
will damp.
Rotor angle stability
Stability depends on the existence of both components of torque for
each of the synchronous machines.
Aperiodic or non-oscillatory instability: lack of sufficient
synchronizing torque cause an increase in rotor angle through a non-
oscillatory or aperiodic mode.
Oscillatory instability:- lack of damping torque causes rotor
oscillations of increasing amplitude.
It is usual to characterize the rotor angle stability
phenomena in terms of the following two categories:
1) Small-disturbance stability
Instability that may result can be of two forms:
a) Steady increase in rotor angle due to lack of
sufficient synchronizing torque.
b) Rotor oscillations of increasing amplitude due to
lack of sufficient damping torque.
The nature of system response to small disturbances
depends on a number of factors including:-
1) The initial operating.
2) The transmission system strength.
3) The type of generator excitation controls used. Natural of small disturbance response.
For a generator connected radially to a large power system, in the absence of automatic
voltage regulators (i.e., with constant field voltage) the instability is due to lack of
sufficient synchronizing torque. This results in instability through a non-oscillatory mode,
as shown in Figure (a).
With continuously acting voltage regulators, the small disturbance stability problem is
one of ensuring sufficient damping of system oscillations. Instability is normally through
oscillations of increasing amplitude. Figure (b) illustrates the nature of generator response
with automatic voltage regulators.
2) Transient stability:-
Is the ability of the power system to maintain synchronism when subjected to a severe
transient disturbance. The resulting system response involves large deviation of generator
rotor angles and is influenced by the nonlinear power-angle relationship.
Stability depends on:-
1) The initial operating state of the system.
2) The severity of the disturbance.
Usually, the system is altered so that the post-disturbance steady-state operation differs
from that prior to the disturbance.
Disturbances of widely varying degrees of severity and probability of occurrence can occur
on the system. The system is, however, designed and operated so as to be stable for a
selected set of contingencies.
The contingencies usually considered are short circuits of different types:
1) Phase-to ground.
2) Phase-to-phase-to-ground.
3) Three-phase.
They are usually assumed to occur on transmission lines, bus or transformer.
The fault is assumed to be cleared by the opening of appropriate breakers to isolate the
faulted element. In some cases, high-speed reclosure may be assumed.
Progressive drop in bus voltages can also be associated with rotor angles going out of step.
The figure shows the behavior of a
synchronous machine for stable and
unstable situations.
1) In the stable case (Case 1 ),
The rotor angle increases to a
maximum, then decreases and
oscillates with decreasing amplitude
until it reaches a steady state.
2) In Case 2, the rotor angle continues to increase steadily until
synchronism is lost. This form of instability is referred to as first
swing instability and is caused by insufficient synchronizing torque.
3) In Case 3: the system is stable in the first swing but becomes
unstable as a result of growing oscillations as the end state is
approached. This form of instability generally occurs when the post
fault steady-state condition itself is unstable, and not necessarily as
a result of the transient disturbance.
Voltage Stability and Voltage Collapse
Voltage stability is:-
The ability of a power system to maintain steady acceptable
voltages at all buses in the system under normal operating
conditions and after being subjected to a disturbance.
A system enters a state of voltage instability when a disturbance,
increase in load demand, or change in system condition causes a
progressive and uncontrollable drop in voltage.
The main factor causing instability is the inability of the power
system to meet the demand for reactive power.
The heart of the problem is usually the voltage drop that occurs when
active power and reactive power flow through inductive reactances
associated with the transmission network.
A criterion for voltage stability is that, at a given operating condition
for every bus in the system, the bus voltage magnitude increases as
the reactive power injection at the same bus is increased.
