What is voltage stability ?
maintain steady acceptable voltages at all buses in the
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
a criterion for voltage stability stability is that,
bus voltage magnitude increase as reactive
power injection at the same
a system is voltage unstable if,
voltage instability is essentially a local phenomenon
voltage collapse is more complex than simple voltage
ILLUSTRATION OF VOLTAGE
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
LARGE DISTURBANCE VOLTAGE
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)
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.
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
SMALL DISTURBANCE VOLTAGE
TRANSIENT VOLTAGE STABILITY
0 to 10 seconds, transient rotor angle stability
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%.
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
Voltage and frequency for South Florida blackout
LONGER TERM VOLTAGE STABILITY
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
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.
RELATION OF VOLTAGE STABILITY
AND ROTOR ANGLE STABILITY
Pure voltage stability
transient voltage stability
reactive power control
concerned with load area and load
voltage collapse in load area
without loss of synchronism of any
generator current limiting is very
detrimental to both form of
ROTOR ANGLE STABILITY
Pure angle stability
reactive power control
integrating remote power plant to a large
system over a long transmission line
voltage collapse in transmission system
remote form loads
VOLTAGE INSTABILITY IN MATURE
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
other lines peak up 25%
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
losses = 2700 MVAr
25% increase 3375 MVAr
because of these non linear process, V.S. problem develop
only in few years.
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
reactive power of the generators can be plotted on same
V-Q curve sketches showing effect of voltage sensitive loads and tap changers on limit
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
VOLTAGE STABILITY ANALYSIS
for detailed studies of specific voltage control situations.
co-ordination of protection and controls and testing of
dynamic simulations also examine whether and how the
steady-state equilibrium point will be reached.
allow examination of a wide range of system conditions
nature of the problem and identify the key condition
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.
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
insufficient load reactive compensation.
CAUSES OF VOLTAGE COLLAPSE
PREVENTION OF VOLTAGE
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
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
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
Pt(V) = V, Ps(V) = P0Va; Qt(V) = V, Qs(V) = Q0Vb
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
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
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
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