CONSTRAINTS
IN SYSTEM OPERATION
TYPES OF CONSTRAINTS WHICH LIMIT THE
CAPABILITY OF A POWER SYSTEM
 Equipment Constraints
 Stability Constraints
EQUIPMENT CONSTRAINTS
 An equipment must be operated within the specified ratings otherwise it may
result in damage.
 Examples of such ratings are the maximum current handling capability of a
conductor, the maximum voltage across an insulator before it breaks down.
 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.
STABILITY CONSTRAINTS
 A power system may not be able to cater to power flows beyond a certain point
due to stability constraints.
 An unstable system is a one which cannot withstand disturbances. This is due to
the basic physical characteristics which define the behavior under transient
conditions.
 Improvement of stability may require system reinforcement (like 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.
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 (note that the temperature
does not jump instantaneously), an equipment may have larger short time
thermal ratings.
 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.
GENERATOR CONSTRAINTS
GENERATOR CAPABILITY IS CONSTRAINED
MAINLY BY THE FOLLOWING LIMITS
 Voltage limits
 Armature Winding (heating) Limit
 Field Winding (heating) Limit
 Core-end heating limit
VOLTAGE LIMITS
The terminal voltage of a generator is limited due to 2 reasons
1) Dielectric
2) Heating in core due to excess magnetic flux.
ARMATURE WINDING (HEATING) LIMIT
Armature winding heating results due to the resistive
loss in armature windings.
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, this limit is
equivalent to a field voltage limit.
 Field current is higher when the generator supplies reactive power
and is over-excited.
CORE-END HEATING LIMIT
Core-end heating results when field current is low (underexcitation). 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.
TRANSMISSION LINE
CONSTRAINTS
TRANSMISSION LINE THERMAL LIMITS
A large current flow increases the losses in the form of heat. This results in
increased conductor temperatures. Excessive temperature may result in expansion
and resultant sag of conductors causing decreased clearance to ground.
Temperature extremes have an "annealing effect" causing reduced mechanical
strength of aluminum.
THERMAL CAPABILITY IS A FUNCTION OF
 ambient temperature
 Wind conditions
 Condition of conductor
 Conductor type and
 ground clearance.
TYPICAL STEADY STATE THERMAL SPECIFICATIONS
OF CONDUCTORS USED FOR 400 KV OVERHEAD
TRANSMISSION
 ACSR (aluminum conductor steel reinforced) Moose Conductor (520 sq mm):
 For an ambient temperature of 40º C, and a maximum conductor temperature of 75º C,
ampacity is 700 A (approx.).
 If AAAC (all aluminum alloy conductor) of 520 sq mm is used, higher conductor
temperatures as compared to ACSR are possible.
 For an ambient temperature of 40º C, and a maximum conductor temperature of 85º C,
ampacity is 850 A (approx.).
DIELECTRIC LIMITS
 Exceeding dielectric limits (maximum electric field strength) results in failure of
insulation, causing faults.
 Electric fields may be excessive (due to overvoltage) under low loading conditions
on long ac transmission lines (Ferranti Effect) or during abnormal conditions like
lightning strokes.
 Deviation of voltages beyond certain limits can also be considered to be an
unacceptable compromise on the quality of power being supplied to consumers.
Low or high voltages can also damage electrical equipment.
VOLTAGES AND REACTIVE POWER DEMAND OF
TRANSMISSION LINES ARE AFFECTED BY:
 Line parameters
 Length of line
 Power transfer
LINE PARAMETERS
Line parameters are dependent on the conductor dimensions and relative
placement. The surge impedance of most overhead lines is around 250-350 ohms
whereas it is 30-50 ohms for cables.
Typical positive sequence inductance and capacitance parameters for a 400 kV
overhead line:
 L = 1.044mH/km
 C = 12 nF/km
Typical positive sequence parameters For a 400 kV paper-insulated leadcovered(PILC) cable:
 L = 0.78 mH/km
 C = 0.95 uF/km
END