2
V
OLTAGE STABILITY ANA
LYSIS
T
here is rapid
increase in the
electric
energy demand
worldwide
. In or
der to
fulfil
the energy demand,
it is
necessary to operate energy
systems
in the most
effective way. Therefore the determination of
accurate
transfer limits
of power
will pay an important roll in
maintaining a
secure
, stable
and eco
nomic operation of
power system.
The more efficient use of transmission
network has already led to a situation in which many
power systems are operated
more often and longer close
to voltage stability limits
[1]

[2]
. Voltage stability is a
subset of overall power system stability.
Sujit Lande
,
Prof.
S
.
P.
Ghanegaonkar
,
Dr.
N. Gopal
a
krishnan
, Dr.V.N.Pande
1.
The bus magnitude voltage decrease when
reactive power injection at the same bus
Ab
s
tract
–
Economical system expansion strategies and
reliable system operation, requires comprehensive system
simulation studies. For thi
s various simulation tools are
available, which use static load models. This paper deals
with the impact of load modelling on the validity of power
system studies mainly concentrating on voltage stability.
VST toolbox of MATLAB is a powerful tool and is
c
onvenient to use. This is used for load flow, small signal
stability, transient stability
and voltage stability analysis.
Presently static load model is considered for all these
analysis. However static load models are not accurate
enough for capturing the
dynamics of network. So
inclusion of dynamic load model instead of static load
model in the VST for various analysis is presented in this
paper.
For determining the dynamic load parameters,
measurement based approach is preferred due to its
numerous advan
tages over the component based
approach. Sweden based measurement data with large
disturbance voltage variations
is used for determination of
dynamic load model parameters. In place of static load
model, dynamic load model is included in the VST.
Voltage s
tability analysis is carried out on
standard IEEE
14
Bus system with VST including static load model and
dynamic load model. Voltage collapse points on PV curve
of test system in both the cases are compared under
various conditions with different dynamic l
oad
parameters. The paper presents a methodology of
implementation of dynamic load modelling in voltage
stability
toolbox for large disturbance voltage stability
studies.
Voltage stability is the ability of a power system to
maintain steady acceptable voltage at all buses in the
system under normal
operating conditions and after
bei
ng subje
cted to a
disturbance [
2
]
. Voltage instability
is the absence of voltage stability & results in
progressive voltage decrease/ increase. A system enters
a state of voltage instability due to disturbance, load
deman
d, uncontrolled drop in voltage
. Conditions for
Voltage
instability
are as follows
:
1
I
NTRODUCTION
Department of Electrical Engineering
College Of Engineering Pune
Voltage stability is a wide range of phenomena.
It is
convenient to use a simulation tool to analyse
voltage
stability
problems.
In education and research,
Matlab
based voltage stability toolboxes
provides common
platform to
analyse
the voltage stab
ility with static load
models [
3
]

[
4
]
.
Since dynamic load models are more
accurate in capturing the dynamics of network
compar
ed to static load models. More accurate voltage
stability of power system can be achieved by
incorporation of dynamic load models in place of static
load models.
In operation planning, the use of inaccurate load
model may yield optimistically
stable
oper
ating
scenarios
, whereas actual operation under those
scenarios may result in catastrophic blackouts.
Therefore, dynamic load models are needed to predict
the accurate voltage stability
[
5
]

[
7
]
.
This paper
addresses
one important component in the study of
voltage stability and voltage collapse, namely dynamic
load models. This paper discusses the no
n
linear
dynamic load
model
development as a set of
mathematical equations
and
determination of load
parameters. Methodol
ogy to calculate the dynamic load
model parameters based on measurement based
approach in large disturbance voltage stability studies is
described.
Shivajinagar,
Pune
, INDIA
.
Dynamic load
model
and its
in
corporation in M
ATLAB
based
V
oltage
Stability T
oolbox
The structure of paper is as follows. Section 2
discusses bas
ic concept of voltage stability
. Section 3
re
views the
available
power system
simulation
toolboxes
. Section 4
and 5 gives brief idea about
general load
modelling
and
developing the dynamic
load models
which are to be incorporated in toolboxes
.
Section
6
shows the simulation
results
with IEEE 14
Bus s
ystem.
Section 7 and 8 discusses the conclusion
and Future work in this
research
area.
1
Keywords
—
Voltage Stability,
Power System Simul
ation
Toolbox
,
Measurement based d
ynamic
Load Modelling
approach.
17
th
Power Systems Computation Conference
Stockholm Sweden  August 2226, 2011
The majority of power system loads respond
dynamically to voltage disturbances & such contribute
to the overall system dynamics. Power system load
model can be considered as a set of mathe
matical
equations that describe the relationship between the real
& reactive power, voltage & frequency at a given bus
bar in a system.
increased. In the other words, An V

Q
sensitivity is negative for at least one bus.
• use of Matlab‘
s visualization capability to create
GUI and visualize output data;
• Voltage stability analysis: identification of local
static and dynamic bifurcation points, such as SN, Hopf,
and SI bifurcations;
2.
Progres
sive drop in bus voltage beyond the
acceptable limit.
• use of stand

alone MEX

files to generate classical
power system model equations;
In recent years, the interest in load
modelling
has
been continuously increasing, and power system load
has become a new area for researching into power
systems stability. Inaccurate load
modelling
could lead
to a power system operati
on towa
rds
actual syst
em
collapse. Several studies [
6
],
[
7
] have shown the critical
effect of load representation in voltage stability studies
and therefore the need of finding more accurate load
models than the traditionally used ones. The load model
is one of t
he most important elements in power system
simulation and control.
• use of symbolic toolbox to generate Jacobian and
second order derivative matrices;
Simulation tools for power system stability analysis
can be divided into two classes
—
commercial
programs
and
customized toolboxes
developed for
education and research. Various commercial programs,
are available i
n the market. These programs provide
detailed component/system models and computationally
efficient algorithms for the analysis.
[
3
]

[
4
]
However,
they are not suitable for e
ducational and research
purposes since they usually do not allow modification
or addition of new component models and algorithms.
For education and research purposes, flexibility and
ability of easy prototyping are often more crucial
aspects than computati
onal efficiency.
The main features and application modules of VST
can be summarized as follows.
3.
2
VST Toolbox:
4
L
OAD MODEL
ING
Several Matlab

based programs are available in
power system simulation,
modelling
and analysis, such
as Power System Toolbox (PST), Electromagnetic
Transients Program in Matlab (MatEMTP), P
ower
Analysis Toolbox (PAT)
, Educat
ional Simulation Tool
(EST)
, Sim
Power Systems (SPS) and Matlab Power
System Simulation P
ackage (MatPower)
. Table 1 gives
a comparison of the currently available Matlab

based
tools for power system analysis and VST.
Voltage stability is conce
r
ned with load areas & load
character
istics. Determination of large
disturbance
voltage stability requires examination of dynamic
performance of the system over a period of time. Study
period
of interest may extend from few seconds to tens
of minute.
• small

signal stability analysis;
The load class data is often grouped in industrial,
residential, commercial and
agricultural load data. The
industrial load is mainly related to industrial processes,
and most of the load corresponds to industrial motors,
up to 95%. Heavy industries may include electric
3
P
OWER
S
YSTEM
T
OOLBOXES
In the area of power systems, a
M
ATLAB
[
8
]
software package has become one of the most popular
scientific programming languages for research and
teaching applications.
2
P

V curves (and Q

V curves) are more general method
of assessing the voltage stability.
The
P

V curve
method is also used for large meshed network where P
is the total load in area and V is the voltage
at a critical
or representative bus.
3.
1
Toolboxes for power system analysis:
VST was designed to analyze bifurcation and
voltage stability problems in
electric power systems.
VST combines symbolic and numeric computations
with a graphical menu

driven interface based on Matlab
and its extended symbolic toolbox.
Table 1
• load flow calculat
ions: standard NR and convergent
NRS methods;
The features illustrated in the table are: load flow (LF),
voltage stability analysis (VSA), small

signal stability
analysis (SSA), time

domain (TD) simulation,
electromagnetic transients (EMT), and graphical

user
interface (GUI). As the table clearly indi
cates, the VSA
function included in VST is a great advantage over
other Matlab

based packages for power system analysis.
• dynamic (time

domain) simulations.
4.1
.
Load Classes & load composition:
17
th
Power Systems Computation Conference
Stockholm Sweden  August 2226, 2011
Where,
(2
Dynamic Load model:
Equations given below express the power dependence
with the voltage, as an exponential function.
Equations in a polynomial model
represent
the sum of
three categories. It is a static load model that represents
power relationship to voltage magnitude as a
polynomial equation, usually in the following form:
s
α
α
s
s = Steady state reactive load voltage dependence
Constant Power
The composition of the load is strongly dependent on
the time of day, month and season, but also on weather.
Load composition of a particular area is characterized
by the load class data, the co
mposition of each one of
the classes, and the characteristics of each single load
component.
β
t
Qr = Reactive Power recovery
P = Po.(V/Vo)
np
Qd = Qr + Qo.(V/Vo)
(1)
Qo.(V/Vo)
= Steady state active load voltage dependence
Vo
, Po and Qo are the values at the initial conditions of
the system for the study, and the coefficients
a
p
,b
p,
c
p
,a
q,
b
q
,c
q
are the parameters of the load model.
4.2
Different Load Models:
Similarly dynamic Reactive
power model can be given
by
α
s
Constant Current [ Power α V ]
Vo = Prefault / Pre disturbance voltage
Qd =Total Reactive power consumption
t
t

t
β
Load models are traditionally classified in two broad
categories, static load models
and
dynamic load models
[
9
]

[1
0
]
. Common types
of load models are mentioned
below:
When t
he traditional static load models are not
sufficient to represent the
behaviour
of the load, the
alternative dynamic load models are necessary [1
1
].
D.Karlsson & Hill proposed the aggregate load
model
which includes
the aggregate effect of numerous load
de
vices such as lighting, heating and motors plus some
levels
of transformer tap changing
[1
2
].
heating processes such as soldering. The residential
load include
s most of the devices related to housing
habits, but also a big percent of electric heating and air
conditioner units during winter and summer
respectively. The commercial load corresponds to air
conditioner units and a large percent of discharge
lighting,
and agricultural load to induction motors for
driving pumps.
Po & Qo are active & reactive power consumption at
rated voltage Vo.
β

Tp. (dPr/dt) +Pr = Po.(V/Vo)
For
modelling
the induction motor
, most stability
programs include
the
dynamic model based on
equivalent circuit as mentioned below.
Q = Qo [ a
q
.(V/)Vo)
2
+ b
q
(V/Vo) + c
q
]
Po.(V/Vo)
Pd = Pr + Po.(V/Vo)
Fig. 1
Induction motor steady state equivalent circuit
It is a static load model that includes the frequency
dependence
. This is usually represented by multiplying
either exponential or polynomial load model by a factor
of following
form:
(1+ A(f
–
fo))
Constant Impedance [ Power α V
2
]
Where,

Tp =
Active load recovery time constant
fo = Rated frequency of bus voltage
f = Frequency of bus voltage
A = Frequency sensitivity parameter of mod
el
Where,
t = Transient reactive load voltage dependence
Induction Motor Load Model
V = Supply voltage
Polynomial Load Model
t
Pr = Active Power recovery
β
Standard Load Model
:
Standard load model comprises
of constant current, constant power and constant
impedance models.
These models are represented by
relationship of voltage and power.
P = Po [ a
p
.(V/)Vo)
2
+ b
p
(V/Vo) + c
p
]
β
Q = Qo.(V/Vo)
nq
= Transient active load voltage dependence
α
Where,
α
P & Q are Load Active &
reactive power respectively.
Rs, Rr, Xs and Xr are the
stator and rotor resistances
and reactances respectively. Xm is the magnetizing
reactance, and s is the motor slip. The stator flux
dynamics are normally neglected in stability analysis,
and the rotor flux in long

term analysi
s.
Pd =Total active power consumption
For the special case, where
np
or
nq
are equal to 0, 1
and 2, the load model will represent a constant power,
constant current or constant
impedance model
respectively.
Frequency Based
Load Model
Exponential Load Model
)
Tq = Reactive load recovery time constant

Tq. (dQr/dt) +Qr = Qo.(V/Vo)
3
17
th
Power Systems Computation Conference
Stockholm Sweden  August 2226, 2011
Field measurement with
continuous acquisition of
data from
normal operation
α
In [
13
],
[
14
] Navarro, described the measurement
based approach
and steps to include the
dynamic load
model.
Implementing the dynamic load model in the
VST toolbox involves following main steps:
I.
Component based approach:
Field measurement with variation of capacitor
banks and tap changers
The method of determining the dynamic load
parameter involves mathematical simplification
of
eq
uatio
n (1) and
(2)
.
It also involves
calculation of
dynamic load parameters
i.e. Tp,
The parameters of the dynamic load models can be
determined either by using a measurement

based
approach, by carrying field measurements and
observing the load response as a result of alterations in
the system, or by using a c
omponent

based approach
D] Static load without synchronous Condenser
s
F] Pmax

Qmin Dynamic load without synchronous
Condenser
Field measurement involves data collection
of real
power (P), reactive power (Q) & voltage (V) at various
buses.
For data
collectio
n measurement
setup is
required with software for data acquisition and
waveform analysis.
the measured data for various seasons
from
80 to 200 sec
0.3 to 1.65
Voltage step variations are of special interest due to
their r
elation with daily normal
and
abnormal
operation
at a substation,
i.e. connection
and disconnection of
capacitors and tap changer operations.
To encounter the
load dynamics different test are carried out.
t)
,
II.
Measurement based approach:
In this the dynamic variat
ion of aggregate load is
recorded during
a disturbance
. The
recording device
installed at the load
bus
& load model is further
determined either on

line or off
–
line. The
measurement

based approach involves placing sensors
at various load buses to determine
model structures and
model parameters. In this prior knowledge of the actual
load composition is not needed.
5
I
MPLEMENTATION OF DYN
AMIC LOAD MODELS
:
Range
β
B] Geometric mean Dynamic load with synchronous
Condenser
t, Tq,
4
Transient active load voltage
dependence (
A] Static load with synchronous Condenser
β
β
Load Parameter identification
5.3
Determination of Dynamic Load Model
Parameters:
[
14
]
Final comparison is made between the static load and
dynamic load values. Table
3
shows the comparison of
the static load
and variation of dynamic load at various
buses on IEEE 14 bus system.
Dynamic load parameter
Dynamic load model parameters proposed from Case
study of Swedish power system are used in the analysi
s.
The details of case study on Swedish power system are
included in [
13
]. The ranges of dynamic load
parameters proposed from the Sweden study are given
in Table
2
as follows:

C] Pmax

Qmin Dynamic load with synchronous
Condenser
Table 2
Comparison of Static and dynamic load model values:
s)
t
The component
based approach builds up the
model
of the composition of loads &
corresponding specific
models of main components. The difficulty of this
approach for a large utility is a collection of statistics
information of load
components.
The
component

based
approach builds up the load model from information on
dynamic
behaviour
s
of all the individual components
and load components (load composition data + load
mixture data) of a particular load bus. For a large utility
the surveys of load components are very difficult tasks.
Steady state active load voltage dependence (
s)
0.3 to 1.2
β
throughout the
5.2
Detection of Voltage Variation:
5.4
Voltage Stability analysis using dynamic load
model
:
Steady state reactive load voltage dependence (
s,
year
t
α
α
Final calculation involves measurement of total
active & reactive power
demand
Pd and Qd
respectively.
Then us
e
these values for
defining the
dynamic
load models in voltage stability toolbox.
For
simulation different cases are prepared with and
without synchronous condenser effects and with
different values of loads. The test system is studied with
VST toolbox for f
ollowing conditions.
Transient reactive load voltage dependence (
Voltage Stability Analysis using dynamic load
model
1.26 to2.23
E] Geometric mean Dynamic load witho
ut synchronous
Condenser
Measurement/Estimation of the Load data
α
Reactive load recovery time constant
(Tq)
0.67 to 1.35
)
Detection of voltage variation
5.1
Measuremen
t/Estimation of the Load data
This approach has the advantage of direct
measurement of actual load
behaviours
. It is simple as
compared to component based approach & possible
to
track seasonal variations in load. However accuracy of
final results depends on measurement kit accuracy. This
approach requires large data handling.
.
Active load recovery time constant
(Tp)
78 to 216 sec
17
th
Power Systems Computation Conference
Stockholm Sweden  August 2226, 2011
Bus
no.6
7.75
19.31
Power (MW)
151.768
0.8471
31.16
Bus
no.13
29.5
0.9898
12.87
5.8
Case
[
E]
11.99
L
oad
95.14
9.46
Case
[
B]
1.68
13.6
5
0
6.44
0
0
0.8206
0.8253
Bus 6
0.8408
9
Study
Cases
9.136
1.653
229.749

3.97
0
Power (MW)
Bus
no.10
Reactive load
demand
0.9969
74.336
0
Bus
12
G. M.
value
(Q
G.M
)
Max.
value
(P
max
)
1.8
Fig. 7
Case
B]
G
.M.
dynam
ic load with S
yn
.
Cond
.
V curves are shown
0
23.88
6
6.1
58.31
0
151.726
12.98
218.27
0.9408
94
.48
Bus
10
1.6
0
0
1.97
0
Bus
14
11.43
5.17
5.297
Bus
13
Nose point
details
Case
[
D]
Bus
no.14
144.45
14.9
5.88
76.109

3.92
Voltage (p.u.)
In Fig.
6
to
8
nose point coordinates are shown on P

V curve for various conditions. Value Y denotes the
voltage at nose point in p.u. and X denotes the alpha
( i.e incremental change in active power loading) at that
bus. Based on values of X and Y obtained from voltage
stability simulation final table is prepared; which shows
voltage in p.u. and active power loading at that bus at
nose point or collapse point. The comparison of
voltage (in p.u.) & maximum power loading (in MW)
for various simulation cases is shown in Ta
ble
4.
15.06
94.598
L
oad
15.44
80.76
73.53
10.03

0
0.8309
Bus 9
Case
[
C]
Min
value
(
P
min
.)
Fig
.
6
Case A]
Static load with synchronous
Condenser:
160.956
12.7
Bus
no.9
0.8622
19.06
5
78.44
5.88
0.8412
Dynamic load
7.935
0.9867
3.55
0
6.29
91.89
7.654
0
0.8609
6.28
11.2
Voltage (p.u.)
5.8
α
Power (MW)
21.7
Bus 5
13.5
Bus
11
0.8614
0.9368
3.5
94.2
160.79
0.9383
18.14
96.26
6
16.6
D
ema
nd
0.9419
Table
3
Comparison of Static
load values with dynamic
load
values on test system
6.2
47.8
16.09
84.277
57.393
48.71
Case
[
A]
76.89
15.01
6
0
Voltage (p.u.)
144.61
0.8207
0
0.8686
6.85
0
Min
value
(Q
min
)
0.9902
80.45
0.8691
Bus 7
202.517
8.375
Case
[
F]
Bus 4
22.68
6.19
0.8456
0.8474
1.6
Power (MW)
8
49.8
Fig. 8
Case C]
Pmax

Qmin dynamic load with Syn.
Cond.
5
0.841
62.115
Active load demand
5.05
0
). The results are shown on sample bus 6 of test
Voltage (p.u.)
7.5
Power (MW)
206.5
0.8288
1.63
1.746
0
0.8686
Voltage (p.u.)
29.98
Max.
value
(Q
max
)
5.095
214.193
55.494
Static load
0
6.08
Voltage (p.u.)
0

4.02
Bus 8
21.98
0.9445
86.77
0.9356
0

3.9
19.18
Reacti
ve
3.7
33.22
13.69
14.18
1.83
0.9975
Bus
No.
79.548
G. M.
value
(P
G.M.
)
system. The P
54.62
48.07
13.25
234.1
Bus 1
0
0.9969
Table
4
Comparison of nose point for six simulation
cases
1.62
with synchro
16.87
Bus 3
3.95
7.6
17.49
Power (MW)
1.61
1.9
19
7.645
condenser.
Active
D
ema
nd
After calculation of the dynamic load model values
for equivalent static load values; the same load model
parameters are entered in the VST toolbox for voltage
stability analysis with six different cases. The P

V
curv
es
are
drawn with details of nose point x and y
coordinates. Here, curves are drawn with Voltage (V) in
p.u. and incremental change in active power demand
alpha(
0
6
SIMULATION
RESULTS:
0
Bus 2
nous
0.8229
17
th
Power Systems Computation Conference
Stockholm Sweden  August 2226, 2011
www.epri.com
T
he measurement data is taken from case study of
Swedish power system. In future work, similar
measurements can be carried out to develop the
dynamic load model suitable for Indian power system
which will consider the different load compositio
n as
well as different operating conditions considering the
seasonal variations in load.
1] Taylor C. W., ―Power System Voltage Sta
bility‖,
McGraw

Hill, New York, USA, 1994.
9
] IEEE Task Force on Load Representation for
Dynamic Performance, ― Load representation for
dynamic performance analysis‖ , IEEE Trans. on Power
sys, Vol.8, no.2, pp472

482, May 1993.
15
] VST toolbox files from Drexel university
website:
6
7
] W. Xu, Y. Mansour. ―Voltage Stability using
generic dynamic load models‖, IEEE Trans. Power sys.,
Vol. 9, no.1, Feb 1994.
1
1
] D.J.Hill, ―Nonlinear dynamic load models with
recovery for voltage stability studies‖,IEEE Trans.
Power Sys.,Vol.8,No.1,Feb.1993.
13
] I.R.Navarro, ―Esti
mation of time

varying
dynamic load parameters during normal operation‖,
Ph.d. Thesis, Lund University, Sweden 2002
Simulation results show that voltage stability have
improved with dynamic load model. This work uses the
methodology of P

V curve for determining the voltage
collapse
in the system. This work can be examined
more thoroughly by a dynamic simulation of a practical
system. For this purpose, necessary programes for
dynamic modeling and simulation needs to be
developed.
6
] K. Morison, H.hamadani, L.Wnag, ― Practical
Issues in load modeling for Voltage stability Studies‖,
IEEE Tran
s. Power Sys.,Feb.2003.
On test system, maximum power that can be
transferred from system to load has been investigated
with different load characteristics under various system
operating conditions. Simulation study employing the
dynamic load model shows that, with
dynamic load
model nose point or collapse point shifts further away
on right hand side direction. Voltage collapse of system
without synchronous condensers occurs earlier even for
lesser load conditions compared to system with
synchronous condensers.
1
0
] IEE
E Task Force on Load Representation for
Dynamic Performance, ― Bibliography on Load models
for power flow and dynamic performance simulation‖,
IEEE Trans. on Power sys, Vol. 10, No.1, pp 523

538,
Feb 1995.
16
] EPRI Websit
e:
I.
Future Work:
5
] M.K.Pal, ―Voltage stability conditions considering
load characteristics‖, IEEE Trans. on Power Sys., Vol.7
no.1, Feb. 1992, pp 243

249.
14
]
I. R. Navarro, O. Samuelsson and S. Lindahl.
‗Automatic Determination of Parameters in Dynamic
Load Models from Normal Operation Data‘.
Submitted
and accepted for Panel session on load modeling at
IEEE Power Engg. Society meeting in July 2003,
Toronto.
R
EFERENCES
3
]
J. H. Chow and K. W. Cheung, .A Toolbox for
Power System Dynamics and Control
Engineering
Education and Research,.
IEEE Tra
ns. Power Syst.
, vol.
7, no. 4, pp. 1559

1564, Nov. 1992.
1
2
] D. Karlsson, D.J.Hill, ―Modelling and
identification of nonlinear dynamic loads in power
systems‖,IEEE Trans. Power sys.,Vol. 9, no.1, Feb
1994.
http://power.ece.drexel.edu
This paper has presented an approach
to improve the
voltage
stability toolbox
by incorporating
dynamic load
models
.
This
will improve the accuracy of predicting
voltage stability analysis and will be useful to
researchers in the power system and allied areas.
Measurement based approach can be used fo
r
dynamic load modeling with powerful and accurate
instrumentation setup
. The
method of determining
dynamic load parameters from measurement of voltage,
current, active and reactive power is described. Matlab
simulink based exponential dynamic load model i
s
developed.
7
CONCLUSION:
4
]
C. D. Vournas, E. G. Potamianakis, C. Moors, and
T. Van Cutsem, .An Educational Simulation Tool for
Power System Control and Stability,.
IEEE Trans.
Power Syst.
, vol. 19, no. 1, pp. 48.55, Feb. 2
004.
Various power system toolboxes available in market
are
classified into commercial and Matlab based
toolboxes. Matlab based toolboxes are compared from
voltage stability point of view. Matlab based VST
toolbox features which is used for simulation is
explained in brief.
8
] Saffet Ayasun,Chika Nwankpa and Harry Kwatny
―Voltage Stability Toolbox for Power system Education
&
Research‖ IEEE Trans. on Power Sys.
Edu.,vol.49,no.4,Nov 2006.
2] Kundur P., ―Power System stability and control‖,
McGraw

Hill, New York, USA, 1994.
The nose point in case [B], Geometric Mean Dynamic
load model
is further than the static load model.
Voltage dependence in GM load model is observed to
be more compared to static model. In case [C], Pmax

Qmin load, stability improves.
17
th
Power Systems Computation Conference
Stockholm Sweden  August 2226, 2011
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