There are two types of constraints which limit the capability of a power system: If the overloading exceeds limits, the equipment is tripped out by protection systems. b) Stability Constraints: A power system may not be able to cater to power flows beyond a certain point due to stability constraints.

1. Equipment and Stability Constraints
in System Operation

2. Power System Operating Constraints
• A power system is designed to handle several
load demand scenarios. It is done much in
advance (planning stages) based on the expected
demand, while keeping some reserve "margins"
for situations in which one or more equipment is
out of service.
• A planner will not over-design (i.e., have
unreasonably large margins).
• However during operation, it is not possible to
requisition or install equipment at short notice.
Therefore, an operator is forced to ensure that
the system is operated within the existing design
constraints.

3. Equipment Constraints
• An equipment must be operated within the specified
ratings otherwise it may result in damage: the
maximum current handling capability of a conductor,
the maximum voltage across an insulator before it
breaks down etc. Equipment like generators may have a
relatively large number of constraints.
• An equipment which is designed to have a larger
capability is also costlier (e.g. a higher current ability
will require one to use thicker conductors). Therefore,
system and equipment designers do not over-design an
equipment.
• Under abnormal or unforeseen situations, an
equipment may get overloaded. If the overloading
exceeds limits, the equipment is tripped out by
protection systems.

4. Stability Constraints
• A power system may not support power flows beyond a certain
point due to stability constraints. An unstable system is a one
which cannot withstand disturbances, i.e., it may not settle to an
equilibrium although a post-disturbance equilibrium condition
may exist. This is due to the basic physical characteristics which
define the behavior under transient conditions.
• Improvement of stability may require system reinforcement :
adding new transmission lines, and/or improving/augmenting
existing automatic controllers. Inability to come to an equilibrium
may eventually lead to equipment constraints being violated too.
This will cause operation of protection systems.
• Loss of equipment due to stability or equipment constraints may
take the system into an emergency or in-extremis state making
interconnected operation unviable.
• Therefore, it is important to characterize the capability of the
system to handle load power demands and power flows in a
transmission network without violation of the above constraints.

5. Major equipment constraints
• Thermal: Excessive heat produced by
current carrying conductors results in
unacceptable sags in transmission lines
and degradation of insulation in other
equipment. Depending on the thermal
time constants (temperature does not
jump instantaneously), an equipment
may have larger short time thermal
ratings.

6. Major equipment constraints
• Dielectric: Over-voltages result in large
electric fields causing dielectric
breakdown. Dielectric breakdown may
also occur due to aging or degradation of
insulation due to thermal limit violations.
Typically +/- 10% variation in the rated
voltage is often permissible.

7. Major equipment constraints
• For mechanical equipment, parameters such
as steam pressure and temperature (which
may restrict for instance, the rate of ramping
the mechanical power in steam plants) have
to be monitored to prevent overheating.
• Vibration of turbine blades needs to be
monitored especially during off-nominal
frequency operation.
• Consider equipment constraints of 2 major
power system components: (a) Generators
(b) Transmission lines

8. Generator Constraints
• Capability curve defines the safe operating
region.
• MVA loading cannot exceed generator heating
(armature winding current limit)
• MW loading cannot exceed the turbine rating
given as the product of MVA and rated pf.
• Must operate a safe margin away from the
stability limit.
• Maximum field current cannot exceed a specified
valued imposed by rotor heating.

9. Limits
• Voltage limits: The terminal voltage of a
generator is limited due to 2 reasons : i) Dielectric
ii) Heating in core due to excess magnetic flux.
However, the maximum continuous limit due to
excess flux is lower than that due to dielectric
breakdown considerations. Therefore the limit
due to excess flux is the "determining" limit. The
flux in the core is also affected by the frequency (
core flux is proportional to voltage/frequency).

11. Limits
• Armature Winding (heating) Limit: Armature
winding heating results due to the resistive loss in
armature windings.
• The heating limits are dependent on the efficacy
of cooling. A higher pressure of the cooling
medium (hydrogen) results in higher heating
limits. Armature winding current limit is
essentially an MVA limit since terminal voltage
magnitude is maintained near the rated value.
Therefore armature winding limit locus is a circle
on the P-Q plane with origin as the center

12. Limits
• Field Winding (heating) Limit: Ohmic loss and
consequent heating in the field winding,
imposes a restriction on the maximum field
current. Since field winding current is
proportional to the field voltage, after
electrical transients, this limit is equivalent to
a field voltage limit. Field current is higher
when the generator supplies reactive power
and is over-excited.

13. Limits
• Core-end heating limit: Core-end heating results
when field current is low (under-excitation).
During under excitation conditions, the axial
flux in the end region is enhanced. This results in
heating which may limit the capability of a
generator. This is basically an Eddy current loss.
• The end-turn leakage flux enters and leaves in a
direction perpendicular to the stator lamination.
Eddy currents will flow in the lamination, causing
localized heating in the end region.

14. • In overexcited mode, the field current is high and
thus, the retaining ring is saturated so that the end
flux leakage will be small.
• When the generator is operating at a leading power
factor, the flux produced by the rotor is weaker and
more flux is able to leak out from the ends of the
stator core. When this flux leaks out from the ends
of the stator core, it passes through the face of
each lamination and causes large eddy currents to
flow in these laminations. These eddy currents can
cause excessive heating.
• The end-core limit depends upon the turbine
construction and geometry. The limitation can be
severe for gas turbines, while is nonexistent for
hydro units; steam units have a limiting
characteristic in the middle.

15. When generator is over excited, the retaining ring of Rotor is saturated, giving reluctance path to
the leakage flux. Therefore the leakage flux to the stator reduces and hence end part heating.
But when generator is under-excited, the retaining ring of Rotor is not saturated. Hence
retaining ring offers low reluctance path to the leakage flux. Also during under-excited
condition, the flux produced by armature current adds to the flux produced by the field current;
therefore, the end turn flux enhances the flux axial in the end region. This causes more heating
in end part of generator and can severely limit the generator output.