A Full Dynamic Voltage Stability Research Based on Time-domain Simulation

doi:10.4236/epe.2013.54B148

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Energy and Power Engineering, 2013, 5, 769-773

doi:10.4236/epe.2013.54B148 Published Online July 2013 (http://www.scirp.org/journal/epe)

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

Email: [email protected]

Received April, 2013

ABSTRACT

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).

Y. Y. CHEN ET AL.

770

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

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,

P PP

 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



, 123

1QQQ



.

Introduction motor load modeling:

Based on known motor stator resistance , motor

stator reactance S

, initiation reactance

, rotor

resistance

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

system.

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.



PPPPP fL

QQQQQ fL



 





 



 

 



 





 



 







Figure 1. Generator exciting winding current overload ca-

pacity.

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-

sidered.

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.

t

max

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 ,

Tt0

tt

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

max



, 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

Y. Y. CHEN ET AL.

772

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

parts.

Choose certain receiving grid as load increase sector,

set increasing rate to 1%/s, set initial value of load in-

crease duration to s.

060t

4.1. Without Consideration of Over-excitation

Limitation

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.

52T

53T

4.2. With Consideration of Over-excitation

Limitation

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.

60Tt

23T23T24T

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.

max

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 30Ts in Figure 6.

A final note needs to be mentioned is, load sustainable

Y. Y. CHEN ET AL.

773

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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