Energy and Power Engineering, 2013, 5, 769-773
doi:10.4236/epe.2013.54B148 Published Online July 2013 (
A Full Dynamic Voltage Stability Research Based on
Time-domain Simulation*
Yuyao Chen1, Yanping Zhang1, Jian Zhang1, Yanjun Zhang2, Lixin Song1
1China Electric Power Research Institute, Haidian District, Beijing, China
2Liaoning Electric Power Company Limited, Heping District, Shenyang, China
Received April, 2013
The voltage stability is substantially a dynamic stability, bu t the primary method which is more mature and engineering
practical to analyze the stability of voltage is still static analysis. The time-domain simulation is an important measure
in research of complex power grid. With the development of full dynamic simulation technology, the research of dy-
namic voltage stability by using full dynamic simulation program which is based on time-domain simulation can be
carried out. This paper uses full dynamic simulation program in dynamic voltage stability research, lays special stress
on research in how generator over-excitation limiter functioned and influence in dynamic voltage stability research, and
raise 2 methods and steps to figure out dynamic stable voltage in both over-excitation counted and not counted. The
simulation results of examples indicate the correctness and effectiveness of these methods, and also fully verify the
function and influence of generator over-excitation limiter in full dynamic voltage stability research.
Keywords: Dynamic Voltage Stability; Generator Over-excitation Limiter; Time-domain Simulation
1. Introduction
The voltage stab ility refers to the abili ty that all the bus es’
voltage was sustained in an acceptable range by power
system when it runs in normal or disturbance circum-
stances. Voltage instability stems from the unbalance
between power requirements of load and supply of the
system[1,2]. The voltage stability analysis falls into two
major categories: static and dynamic voltage stability
analysis. Static voltage stability analysis is more mature
than dynamic one. But with deeper research in voltage
instability, it’s gradually becomes more recognized that
the voltage stability is substantially a dynamic stability
and, the results of static analysis need to be verified by
dynamic methods. The main dynamic voltage stability
analysis methods are: small signal stability analysis, dy-
namic power flow analysis, time-domain simulation,
direct method analysis and bifurcation theory analy-
sis[3-8]. The time-domain simulation is one of the best
tools in system planning, management, running and re-
search of electric power system, also in dynamic voltage
stability study. Full dynamic simulation of the power
system that based on time-domain simulation is such a
method in which the electro-mechanical transient,mid-te
rm and long-term dynamic phenomena are unified[9-11].
But voltage instability is a slow process, which means
the simulation would frequently last a few minutes,
sometimes even tens of minutes. It is a typical rigid
nonlinear system that the time constant in simulation
model vary a lot and also combine with fast and slow
dynamic process. And considering of stab ility of integra-
tion by parts and convergence of iteration, a long time
step should not be used. Hence, a large amount of calcu-
lation is needed in time-domain simulation. Furthermore,
the simulation may result unreliable because of the cu-
mulative error of integration by parts with an improper
time step length.
By analyzing the features of solving rigid nonlinear
system and the key problem in existing numerical inte-
gration algorithm of power system dynamic simulation,
Literature [12] raise a new composite numerical integra-
tion algorithm applying to full dynamic simulation which
can overcome the shortages of existing algorithm that
inefficient calculation and complicated intermitten t proc-
essing in electro-mechanical transient process.
By using full dynamic simulation program with the
new algorithm in dynamic voltage stability research, this
paper lays special stress on how generator over-excita-
tion limiter functioned and influence in dynamic voltage
stability research, and raise methods and steps to figure
out dynamic stable voltage in both over-excitation
*This work is supported by the Science Technology Project of State
Grid Corporation of China (Contract N o . XT17201100032).
Copyright © 2013 SciRes. EPE
counted and not counted.
2. Dynamic Voltage Stability and Its
Influencing Factors
Dynamic voltage stability research refers to the distance
between current operating point and voltage collapse
point when the load of power system rises gradually by
certain rate. Influences of those dynamic components
such as dynamic load model, ULTC, generator over-
excitation limiter and others have been considered, which
means the distance can be reported more precisely even
in complicated system. Therefore, the margin informa-
tion can be more valuable to operating crew.
Take many factors in consideration, load characteristic
is the most critical and direct factor in voltage stability. It
determines, to a large extent, the process of voltage in-
stability and collapse. Hence, load modeling occupies a
vital important place in voltage stability research. Load
model is the key factor to the veracity and reliability of
research results of voltage stability[13,14].
Generator excitation system’s condition and its limiter
are important factors that influence system voltage sta-
bility. Excitation regulator is the main method of voltage
control in power system, but its regulating range is re-
stricted by excitation winding thermal capacity. When
excitation capacity of the engine set reaches its maxi-
mum limit, the over-excitation limiter will restrict the
exciting current to rated value. This process may cause
active power drop suddenly and then the system voltage
drop correspondingly. Additionally, when the system get
close to its limit state, a sudden excitation reduction of a
single generator may results in chain reaction among
other generators. This situation would leads to system
voltage instability or accelerates the instability. In 2
blackouts in USA in 1996 and 2003, excitation protection
functioned in the last moment when the grid black-out.
Therefore, the influence of generator over-exciting lim-
iter should be fully considered when trying to figure out
the extreme value of system voltage stability [2,15,16].
3. Full Dynamic Simulation
3.1. Load Model
This paper takes fully advantages of time-domain simu-
lation, and uses “static load model + introduction motor
model” which is frequently used by engineering in full
dynamic simulation.
Static load modeling:
012 3
012 3
In this model, 0 is Active Load, 1, 2, 3 are
Constant Impedance Active Load Ratio, Constant Cur-
rent Active Load Ratio and Constan t Power Active Load
Ratio respectively, is System Actual Voltage, 0 is
System Reference Voltage,
is Frequency Variation,
P is percentage change of active power with every
1% of frequency change, and reactive power load model
follow the same naming rule. In the upper formula,
, 123
Introduction motor load modeling:
Based on known motor stator resistance , motor
stator reactance S
, initiation reactance
, rotor
R, rotor reactance
and motor slip fre-
quency , the mechanical torque ratio
, and
can be figure d out . BC
3.2. Generator Over-exciting Limitation
The limitation of excitation system including two func-
tions: transien t limitatio n of ceiling curren t and limitation
of inverse time over-excitation[17]. The primary courses
of over-excitation are including long-term low system
voltage, AVR acting on excitation, or AVR malfunc-
tioning. The system dynamic voltag e stability research is
focus on the over-excitation limit action during system
voltage instability process. In other words, it’s a restrict-
tion function of inverse time over-excitation in excitatio n
Over-excitation process could be nearly constant, or
could be a slow process that takes place and increases
over-excitation value grad ually. Hence, it’s not in general
to use over-excitation duration to define whether over-
excitation limiter activate or not, but to limit the regula-
tor output by calculate the heating value which generated
by excitation set when excitation current exceed long-
term operating permissible value. And the generator rotor
can be protected by restrict the value of generator rotor
current consequently.
Generator over-excitation limitation model, which
aims to avoid generator overheated by excitation over
current, is determined by its own overheat load capacity.
And rotor over current time is connected with excitation
current peak value. See Figure 1 as below.
 
 
 
 
 
 
 
Figure 1. Generator exciting winding current overload ca-
Copyright © 2013 SciRes. EPE
Y. Y. CHEN ET AL. 771
3.3. Calculation of Dynamic Voltage Stability
Figure 2 shows the steps of full simulation calculation of
dynamic voltage stability research. Data preparations
include modeling of network parameter, generator, load
and other dynamic components. Load increase pattern
includes definition of increase range and rate.
In full simulation calculation, the process of system
running from stable into instable when it close to critical
point may caused by load increase and over-excitation
limitation or other automatics like ULTC simultaneously
or individually. Therefore, without consideration of other
automatics, taking over-excitatio n limitation into accoun t
or not would influence the calculation of dynamic voltage
stability margin significantly, its computation steps
differs obviousl y .
With load increase continue, the system is getting
close to its critical point. When over-excitation limitation
is not taking into account, the key factor that cause system
instability is load increase. It’s a single causal relation-
ship, its compu tation steps is conven ience. But when taking
over-excitation into account, the slow dynamic process
before instable is a superimposed effect by load increase
and over-excitation limitation. To figure out dynamic
voltage stability margin precisely in this situation, the
dynamic process of over-excitation limitation caused by
load increase continuously should be sufficiently con-
Figure 2. Computation steps of dynamic voltage stability
margin full simulation.
In Figure 2, is load increase duration, 0 is
initial value of load increase duration, is changing
step of load increase duration, is the maximum
length of load increase duration.
When over-excitation limitation is not taking into
account, the maximum length of load increase duration
max under current status and load increase pattern can
be figured out by compute one system instability process
under load increase continuously, its computation steps
are as follows:
1) Complete data preparation, confirm load increase
pattern, set t value, order Tt
0 0
2) Execute full dynamic simulation. With load increase
continues, if system runs into instable, execute step 3); if
system maintains stable after load increase for T
seconds, execute step 4)
3) By monitoring system frequency changing, the time
point that corresponding to lowest reading frequency is
T, computation ends.
4) Set 2Tt
, repeat step 2).
When over-excitation limitation is taken into account,
whether generator over-excitation limitation would cause
system instability when load increase for a certain dura-
tion should be considered. Hence, load continue increase
process should be compute repeatedly, generator over-
excitation limit action and system stability situation
should be monitored, and searching constantly for value
of load increase maximum duration max
T using bisec-
tion method. The computation steps are as follows:
1) Complete data preparation, confirm load increase
pattern, set value, order ,
2) Execute full dynamic simulation. With load increase
continues, if system runs into instable, execute step 3); if
system maintains stable after load increase for T seconds,
execute step 4)
3) Set TT t
 , 1
, execute step 5)
4) Set TT t
 , 1
, execute step 6)
5) If 0.5t
, execute step 6), otherwise repeat step
2) 6) Set TT
, computation ends.
Another caveat here is, full simulation calculation du-
ration must be longer than load continue increase dura-
tion T, especially when over-excitation is taking into ac-
count. Simulation duration should be long enough to
monitor the dynamic process of generator over-excitation
limitation and system instability o r recovery process after
load increase no more.
4. Sample Simulation Analysis
Take certain grid with 280 generators and 2030 nodes to
Copyright © 2013 SciRes. EPE
apply simulation analysis. Use ZM (50% constant im-
pedance + 50% introduction motor) model in load model.
And take load frequency factor into account in static
Choose certain receiving grid as load increase sector,
set increasing rate to 1%/s, set initial value of load in-
crease duration to s.
4.1. Without Consideration of Over-excitation
Without consideration of over-excitation limitation, the
result of full dynamic simulation shows: in 60s duration
of receiving grid load continuous increase, system gets
instable, and load sustainable increase time that corre-
sponding to lowest point of system frequency max 52T
s. See Figure 3 as below.
In order to verify the result, set load increase duration
to 52s and 53s, and execute simulation respectively.
The result of simulation shows when , system
runs stably; when , system runs into instability.
See Figure 4 as be low.
4.2. With Consideration of Over-excitation
Taking over-excitation limitation into account, start and
repeatedly compute 7 times from 0s, receiv-
ing grid load sustainable increase duration can be figured
out: max s. The result means when , system
runs stably; when , system runs into instability.
See Figure 5 as be low.
Figure 5 shows:
1) The certain point in time that corresponding to low-
est system frequency point is no longer the value of lo ad
sustainable increase duration T.
2) A longer dynamic adjusting process takes place af-
ter load stop increase. Once the generator over-excitation
limitation activated and causing system voltage fall sud-
denly, then system would led to instability. Figure 6
Figure 3. System frequency changing curve without consid-
eration of over-excitation limitation.
Figure 4. System critical instability frequency changing
curve without consideration of over - e xcitation limitation.
Figure 5. System frequency changing curve with considera-
tion of over-excitation limitation.
Figure 6. Certain generator excitation current changing
curve with consideration of over-excitation limitation
shows certain generator excitation current changing
curve in receiving sector.
3) The longer the load increases duration last, the fast-
er the system runs into instability. Shown by system fre-
quency changing curve when 30Ts in Figure 6.
A final note needs to be mentioned is, load sustainable
Copyright © 2013 SciRes. EPE
Copyright © 2013 SciRes. EPE
increase duration max refers to system instability speed
under current system situation and load increase pattern.
It’s not belongs to system dynamic voltage stability mar-
gin parameter.
5. Conclusions
This paper uses full dynamic simulation program based
on time-domain simulation in dynamic voltage stability
research, raise methods and steps to figure out dynamic
voltage stability in both with and without consideration
of over-excitation limitation, and verifies correctness and
effectiveness of methods by sample simulation. The si-
mulation result also fully verifies the effect and influ-
ence of generator over-excitation limitation in full dy-
namic voltage stability research.
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