1. Indian Institute of Technology, Bombay
VOLTAGE STABILITY
Ph.D. Seminar
Indian Institute of Technology, Bombay
Jignesh M. Solanki

2. What is voltage stability ?
maintain steady acceptable voltages at all buses in the system
a system enters a state of voltage instability when a disturbance, increase in load demand
inability of a power system to meet the demand for reactive power
a criterion for voltage stability stability is that,
bus voltage magnitude increase as reactive
power injection at the same
bus increase
a system is voltage unstable if,
V-Q sensitivity

3. voltage instability is essentially a local phenomenon
voltage collapse is more complex than simple voltage instability

4. ILLUSTRATION OF VOLTAGE INSTABILITY
Limit of satisfactory operation
For higher load demand , control of power by varying load would be unstable
if load is supplied by transformers with ULTC, the tap-changer action try to raise the load voltage. This has lower effective ZLD and due to that VR goes low still further and
It may call pure form of voltage instability.
A simple radial system for illustration of voltage stability phenomenon

5. CLASSIFICATION OF VOLTAGE STABILITY
LARGE DISTURBANCE VOLTAGE STABILITY
SMALL DISTURBANCE VOLTAGE STABILITY
TRANSIENT VOLTAGE STABILITY
LONGER TERM VOLTAGE STABILITY

6. LARGE DISTURBANCE VOLTAGE STABILITY (LDVS)
It is concerned with systems ability to control voltages following large disturbances such as system faults, loss of generator or circuit contingency.
Load characteristics and the interaction of both continuous and discrete controls and protections.
Determination of LDVS requires the examination of the non-linear dynamic performance of a system over a period of time (ULTC and generator field current limiter)

7. For analysis long-term dynamic simulations are required.
A criterion of large disturbance voltage stability, is that, following a given disturbance and system control actions, voltage at all buses reach acceptable steady state levels.

8. SMALL DISTURBANCE VOLTAGE STABILITY (SDVS)
control voltages following small perturbations
load characteristics, continuous control and discrete control
Basic process a steady state nature
Stability margin, identifying factors influencing stability, examine wide range of system conditions and large number of post contingency scenarios.
A criterion for SDVS, V-Q sensitivity

9. TRANSIENT VOLTAGE STABILITY
0 to 10 seconds, transient rotor angle stability voltage
voltage collapse is caused by unfavorable fast acting load components (IM and DC converters)
For severe voltage dips the reactive power demand of IM increases, contributing to V.C
Electrical islanding and under frequency load shedding resulting V.C. when imbalance is greater than about 50%.

10. Voltage decays faster than frequency
under frequency relays may not operate
There are incidents where the voltage collapses before frequency decays to the under frequency load shedding set points
Voltage and frequency for South Florida blackout

11. LONGER TERM VOLTAGE STABILITY
2-3 minutes
involves high loads, high power inputs from remote generation and a sudden large disturbance (lass of generator or loss of major transmission line)
the disturbance causes high reactive power losses and voltage sags in load areas
the tap changer sense low voltages and act to restore disturbance voltages thereby restoring load power levels

12. further sags of transmission voltages.
generator farther away must then provide reactive power this is inefficient and ineffective
no longer support by generation and transmission system.
partial and complete voltage collapse.

13. RELATION OF VOLTAGE STABILITY AND ROTOR ANGLE STABILITY
Pure voltage stability
transient voltage stability
reactive power control
concerned with load area and load characteristics
load stability
voltage collapse in load area
without loss of synchronism of any generators
generator current limiting is very detrimental to both form of stability
Pure angle stability
transient RAS
reactive power control
integrating remote power plant to a large
system over a long transmission line
generator stability
voltage collapse in transmission system
remote form loads

14. VOLTAGE INSTABILITY IN MATURE POWER SYSTEM
intensive use of existing generation and transmission.
new generation in load areas and transmission lines from remotely sited generation
increased use of shunt capacitor bank.
How V.I. can become a problem in Mature power system?
series reactive P.L. = I2 x take loading is I = 1000 amp, one line outage.
other lines peak up 25%

15. losses = (5 lines x 3 phase x 10002 x 80 ohms ) = 1200 MVA
25% peak up so losses = 1500 MVA.
after several years load growth assume loading is 1500 Amp.
losses = 2700 MVAr
25% increase MVAr
because of these non linear process, V.S. problem develop only in few years.

16. V-Q CURVES
voltage security is closely related to reactive power and a v-q curves gives reactive power margin at the test bus.
the slope of the V-Q curves indicated the stiffness of the test bus
reactive power of the generators can be plotted on same graph
V-Q curve sketches showing effect of voltage sensitive loads and tap changers on limit

17. the effect of voltage sensitivity loads ( i. e
the effect of voltage sensitivity loads ( i.e. prior to tap changing ) will have much greater reactive power margins and much lower critical voltages
when tap changer hit limits, the curves tend to flatten out rather then turn up on the left side

18. VOLTAGE STABILITY ANALYSIS
DYNAMIC ANALYSIS
for detailed studies of specific voltage control situations.
co-ordination of protection and controls and testing of remedial measures.
dynamic simulations also examine whether and how the steady-state equilibrium point will be reached.

19. STATIC ANALYSIS
allow examination of a wide range of system conditions
nature of the problem and identify the key condition factors

20. DETERMINATION OF SHORTEST DISTANCE TO INSTABILITY
increase load from Po,Qo in some direction until an eigen value of a Jacobian is practically zero.
surface S represents the locus of all combinations of P and Q which results in a zero eigen value of Jacobian.
P1,Q1 corrosponding to this point is the stability limit which lies on or extremely near to S.

21. CAUSES OF VOLTAGE COLLAPSE
the load on the transmission lines is too high.
the voltage sources are too far from the load centres.
the source voltages are too low.
large distances between generation and load.
ULTC action during low voltage conditions.
poor co-ordination between various control and protective systems.
insufficient load reactive compensation.

22. PREVENTION OF VOLTAGE COLLEPSE
application of reactive power compensating devices
control of network voltage and generator reactive o/p
co-ordination of protection / controls
control of transformer tap changers
undervoltage load shedding
stability margin
spinning reserve
operators' action

23. GENERIC DYNAMIC LOAD MODEL
Pt = V or Pv = c2V2 + c1V + c0
Ps = P0V or Ps = P0(d2V2 + d1V + d0)
where V is the per-unit magnitude of the voltage imposed on the load
It can be seen that, at steady-state, state variable x of the model is constant
A generic dynamic model

24. e = Ps – P, must be zero
The transient output is then determined by the transient characteristics P = xPt
The mismatch between the model output and the steady-state load demand is the error signal e
This signal is fed back to the integration block that gradually changes the state variable x
This process is continues until a new steady-state (e=0) is reached
Pt(V) = V, Ps(V) = P0Va; Qt(V) = V, Qs(V) = Q0Vb

25. LOAD MODELLING ix3 = ixE = ixM + ixC ; iy3 = iyE + iyN + iyC
Exponential load Polynomial load
P(V3) = Po (V3/V3o) P =  Po [aP(V/Vo)2 + bP(V/Vo) + CP]
Q(V3) = Qo (V3/V3o) Q =  Qo [aQ(V/Vo)2 + bQ(V/Vo) + CQ]
, depends on load ; aP + bP + cP = aQ = bQ = cQ = 1
Po,Qo is consumed power at reference voltage
complex current injected in to the network
IE = - (S/V3) = -[ P(V3) – jQ(V3)/Vx3 – j Vy3 ] = ixE + j VyE

26. CONCLUSION Three key concepts of voltage stability are
the load characteristics as seen from the bulk power network
the available means for voltage control at generators and in the network
the ability of network to transfer power particularly reactive power from the point of production to the point of consumption
The network steady state loadability limit is not necessarily the voltage instability limit
Static power flow based analyses of the post disturbance steady state is the useful method of analyzing longer term voltage stability
The fundamental cause of voltage instability is identified as incapability of combined transmission and generation system to meet excessive load demand in either real power or reactive power form

27. Thank You