This presentation deals with various aspects of voltage stability and various tools to analyze and stabilize voltage.

1. POWER SYSTEM
VOLTAGE STABILITY
Akash Choudhary
I.D. No. 43232
B.Tech 4th year
Electrical Engineering
College of Technology
GBPUAT

2. Voltage collapse is still the biggest single
threat to the transmission system. It’s what
keeps me awake at night
• - Phil Haris, PJM President and CEO, March
2004

3. Introduction
• Present day power systems are being operated
closer to their stability limits due to economic
constraints. Maintaining a stable and secure
operation of a power system is therefore very
important and challenging issue.

4. What is voltage stability?

5. Voltage stability
• The definition of voltage stability as proposed by
IEEE task force is as follows:
Voltage stability refer to the ability of power system
to maintain steady voltages at all buses in the
system after being subjected to a disturbance from a
given initial operating point. The system state enters
the voltage instability region when a disturbance or
an increase in load demand or alteration in system
state results in an uncontrollable and continuous
drop in system voltage.

6. Continued
• A system is said to be in voltage stable state if 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.
• A system is voltage unstable if for at least one bus in
the system, the bus voltage magnitude decreases as
the reactive power injection at the same bus is
increased.
• It implies that if, V-Q sensitivity is positive for every
bus the system is voltage stable and if V-Q
sensitivity is negative for at least one bus, the system
is voltage unstable.

7. Voltage Instability Time frames and
mechanism
• Transient Voltage stability • Longer term voltage stability

8. Transient voltage stability
• Time frame varies from zero to about ten seconds
• Voltage collapse is caused by unfavorable fast acting
load component such as large induction motor and
D.C. converters.
• During under frequency load shedding there is
possibility that system voltage may collapse
whenever imbalance in reactive power is more than
50%.
• HVDC circuits cause transient voltage stability
problem as converters and inverters require large
amount of reactive power.

9. Longer term voltage stability
• The time frame is few minutes typically 2-3 minutes
and hence operator intervention is not possible.
• Involves high loads, high power imports from
remote generation and a sudden large disturbance
which could be in the form of loss of large
generators and loss of transmission lines.
• The disturbance causes high reactive power losses
and voltage sags in load areas.
• Rapid voltage decay starts and partial or complete
voltage collapse follows.

10. Relation of voltage stability to rotor
angle stability

11. Comparision
Rotor angle stability Voltage stability
• synchronous machine
connected to infinite bus or a
large system.
• Normally concerned with
integrating remote power
plant to a large system.
• It is basically generator
stability.
• When asynchronous load
connected to a large system.
• Concerned with load areas and
load characteristics.
• It is basically load stability.

12. Continued.
• If voltage collapses at a point in transmission
system remote from loads, it is an angle
instability situation . However, if voltage
collapses in a load area it is mainly a voltage
instability situation.

13. Why does voltage instability occur
in mature power system?

14. Voltage instability in mature power
system
• Intensive use of existing generation and
transmission.
• Vast use of shunt capacitor banks for reactive
power compensation. It results into voltage
collapse prone fragile network.

15. Series capacitor compensation
• The reactive power generation due to series
capacitance compensates for the reactive power
consumption due to series inductance of the
line.
• Series capacitor reactive power generation
increases with the current squared, thus
generating reactive power when most needed.

16. Voltage stability of simple two bus
system

17. Continued
• Real power transfer from bus 1 to bus 2 is given by
P= {E*V*sin(d)}/X -(1)
• Reactive power transfer from bus 1 to bus 2 is given
by
Q=-(V^2)/X+{E*V*cos(d)}/X -(2)
• Normalizing the terms in equation (1) and (2) with
v=V/E
p=(P*X)/E^2
q=(Q*X)/E^2
• v^4+v^2(2q-1)+(p^2+q^2)=0 -(3)

18. Continued
• Positive real solutions of v from equation (3) are
given by
v={.5 -q±(.25-p^2-q)^.5}^.5 -(4)
• Corresponding to each point (p, q) there are two
solutions for voltage, one is high voltage or stable
solution which is the actual voltage at the bus, and
the other one is the low voltage or unstable solution.
• The equator along which the two solutions of v are
equal, represents maximum power points.
• An increase in p or q beyond maximum power point
makes the voltage unstable.

19. Variation of bus voltage with active
and reactive power loading.

20. Tools for voltage stability analysis
• P-V curve method.
• V-Q curve method and reactive power reserve.

21. P-V curve method
• Widely used method for voltage stability analysis.
• Gives available amount of active power margin
before the point of voltage instability.
• For a simple two bus system as shown in previous
fig. equation (4) gives real solution of v^2 provided
(1-4*q-4*p^2)  0 -(5)
• Assuming contant power factor load such as q/p=k,
the inequality can be expressed as,
p 5{(1+k^2)^.5-k} -(6)

22. Continued
• Equation p 5{(1+k^2)^.5-k} determines
maximum value of p.
• Thus representing the load as a constant power
factor type with a suitably chosen power factor,
the active power margin can be computed from
above equation.

23. Normalized P-V curves for 2 bus
system

24. V-Q curve method and reactive power
reserve.
• Voltage security of a bus is closely related to the available
reactive power reserve, which can be easily found from
the V-Q curve of the bus under consideration.
• The reactive power margin is the MVAR distance
between the operating point and the nose point of the V-
Q curve.
• Stiffness of the bus can be qualitatively evaluated from
the slope of the right portion of the V-Q curve. The
greater the slope is, the less stiff is the bus, and therefore
the more vulnerable to voltage collapse it is.

25. Normalized V-Q curves for two bus
system

26. Methods of improving voltage stability
• Planning of generation system.
• Maintenance of generation system.
• Operation of generation system.
• Reactive power compensation.
• Capacitor bank.
• Tap changing.

27. Continued
• Planning of generation system
The reliability aspect of supply can be improved
by sitting generating plants in the load areas.
• Maintenance of generation system
Over excitation and under excitation limiters,
alarm settings, tap changer settings need to be
verified and maintained.
• Operation of generation system
During peak load period, power import over the
transmission network should be reduced.

28. Continued
• Reactive power compensation
Extra high voltage transmission lines requires shunt
reactors for energization and under lightly loaded
condition. These shunt reactors should be switched off
during voltage emergencies.
• Capacitor bank
Shunt capacitor banks act as constant reactive power
sources.
• Tap changing
The tap changing transformers change the
transformation ratio and thus the voltage in the
secondary circuit is varied and voltage control is
obtained.

29. Conclusion
• There are many aspects of voltage stability and
also has many solutions associated to the voltage
stability in terms of generation, transmission
and distribution .Power system engineer job is to
find low cost solution whenever possible which
require special control and special power system
operation.

30. References
• S Chakrabarti, Dept. of EE, IIT Kanpur, Notes
on power system stability.
• C.L. Wadhwa, Electrical power systems, 2010.
• C Radhakrishna, Voltage stability analysis-1.
• Carson W. Taylor, Voltage stability for
undergraduates.

31. Thank you…