King Fahd University of Petroleum and Minerals Electrical Engineering Department

2011-12 (111)

IDENTIFIER C-24

APPLICATION OF EQUAL AREA CRITERION IN THE TIME-DOMAIN

FOR OUT OF STEP PROTECTION

Advisor:

Dr. M. A. ABIDO

Professor, EE Department

Submitted by:

Mohammad Ashraf Ali

Student ID: g201102010

January 31, 2012

Application of Equal Area Criterion in the Time-Domain for

Out-of-Step Protection Mohammad Ashraf Ali, ID: g201102010

Abstract- Power system stability refer to the ability of

synchronous machines to move from steady-state operating

point following a disturbance to another steady-state

operating point, without losing synchronism. An Algorithm

to predict the out-of-step protection by mapping the Equal-

Area-Criterion in the time-domain is proposed in the paper.

The criterion is applied to SMIB system on

MATLAB/SIMULINK environment and the classification

between the stable and out-of-step swings is done using the

accelerating and decelerating energies, which represents

the area under the power-time curve. This algorithm is

based only on the local electrical quantities available at the

relay location and does not depend on the network

configuration and parameters. Simulations have been

carried out extensively to test the effectiveness of the

proposed algorithm.

Index Terms –Power system transient stability, Out-of-

Step Protection, Equal area criterion, Power swings.

I. INTRODUCTION

The electric power system is a highly dynamic and

non-linear system. The dynamics are due to changes

such as the load and generation changes, due to

switching phenomena, due to faults such as short

circuits and may be due to lightning surges. The

tendency of a power system to develop restoring forces

equal to or greater than the disturbing forces to

maintain the state of equilibrium is known as stability.

In other words it is the ability of various machine in the

system to remain in synchronism (stay in step), with

each other following a disturbance. The stability

studies may be classified upon the nature of

disturbance as Steady state stability, Dynamic stability,

and the Transient stability. The representation of

synchronous machine in the stability studies differ

from one kind of study to the other. As stated earlier,

the electric power being a non-linear and dynamic

system is subjected to electromechanical oscillations

whenever a disturbance occurs in the system. The

transient stability may be defined of as the ability of a

synchronous machine to maintain synchronism with

respect to other machines following a sudden large

disturbance. Transient stability studies are needed to

ensure that the system can withstand the transient

condition following a sudden major disturbance.

Typically these major disturbances happen when the

power systems are heavily loaded and a number of

multiple outages occur within a short period of time,

causing power oscillations between neighboring utility

systems. Also due to the power mismatch between

generation and load demands these disturbances occur.

These electromechanical oscillations cause variation in

phase and amplitude of voltage and current signals

throughout the power system and consequently it

causes variation in power flow between two areas

known as power swing. A power swing can be

classified as a stable power swing in which the

oscillations are damped and stable operation of the

system is achieved. The other case which leads to loss

of synchronism between generator groups located in

the different areas of a power system is referred to as

Pole Slip or Out-Of-Step (OOS) conditions or loss of

synchronism conditions. When an Out-of-Step

condition occurs in a power system the healthy section

must be islanded from the faulty section. It necessitates

the use of Out-of-Step relays which sense such

conditions and isolate the section where stability is

restored from the faulty section.

There are several techniques available in literature and

in practice to detect Out-of-Step conditions. The

conventional method uses a distance relay with

blinders in the impedance plane and a timer. The

settings of blinder and timer requires the knowledge of

the fastest power swing, the normal operating region

and the possible swing frequencies and is therefore

system specific. These are used in offline stability

studies for obtaining the settings and their complexity

increases for multi-machines.

Another technique proposed out-of-step detection

based on a neural network and application of fuzzy

logic using an adaptive network-based fuzzy interface

(ANFIS). The mechanical input power, generator

kinetic energy deviation and average kinetic energy

deviation are selected as inputs to the neural network.

Another method based on fuzzy logic uses machine

angular frequency deviation and impedance angle

measured at the machine terminals as inputs. The

above two techniques are able to make decisions

quickly for a new case, which has close resemblance to

a known predefined case for which the algorithm is

trained. It requires enormous training effort to train all

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possible swing cases. This makes the training process

tedious and also the complexity increases as system

interconnections increase.

The other method based on the Liapunov energy

function criterion for loss-of-synchronism detection for

a complex power system. During unstable swings, the

entire power system oscillates in two groups, and series

elements called cutset connect them. It requires

measurements all across series elements to find the

cutset. It is difficult to implement a protection

algorithm by this technique because of wide area

information involved in the protection systems.

Another method monitors the rate of change of swing

center voltage (SCV) and compares it with a threshold

value to differentiate between a stable and unstable

swing. The SCV is obtained locally from the voltage at

the relay location. It is independent of power sysem

parameters but this technique requires offline stability

studies to set the threshold value making it system

specific.

Reference [8] proposed an out-of-step detection

technique based on classical equal area criterion (EAC)

in the power angle (δ) domain. This technique requires

pre-and post- disturbance power angle (Pe-δ) curves of

the system to be known to the relay. Many

measurement devices are required at various locations

to acquire the current system information as the Pe-

delta curves are dependent on system configuration.

In this paper, we modify the concept of equal area

criterion EAC to the time-domain to detect the loss of

synchronism condition. We have devised an algorithm

to detect out-of-step swing using the time-domain

concept of EAC. We have obtained the power-time

(Pe-t) curves for the system instead of the conventional

Pe-δ curves. This algorithm does not require any power

system parameters information and only requires

measurements of local quantities available at the relay

location. The transient energy areas under the Pe-t

curve are calculated and the swing may be identified as

stable or out-of-step swing. This algorithm is

successfully tested on SMIB (single machine infinite

system) using the SIM POWER SYSTEMS toolbox of

SIMULINK.

In the first part of this paper some introduction about

the power system oscillation is presented. In the second

part, equal area criterion for out-of-step protection is

described and modified to the time-domain. In section

IV a brief description about the dynamic model used in

the simulation studies is discussed. In section V

simulation results for Single Machine Infinite Bus

(SMIB) model are presented.

II. POWER SYSTEM OSCILLATION

A simple power system consisting of one generator

connected through a transmission grid to an infinite bus

is shown in Fig.1. This model can be used to describe

the oscillating parts of a power system.

It can be shown that the maximum power, that can

be transmitted through the line, depends on the

difference of the voltages at the two terminals. This

angle may be expressed as .

The power flow from the synchronous machine to the

infinite bus is given by the equations as follow:

Where,

The amplitudes of E‟ and can be different but the

phase difference of voltages is more important. Fig. 2

shows a typical example of current, voltage and active

power flow due to variation of angle difference

between the two EMF‟s during loss of synchronism.

When the phase voltages are maximum and the

currents are at a minimum the two areas are in phase.

Conversely, the two areas are out of phase or 180ο the

voltages are at minimum and the currents are at a

maximum.

3

Fig.2 Typical examples of voltage, current and power

flow during loss of synchronism

The frequencies of oscillation are inherent to the

system and are about few Hz (0.2Hz-3Hz). The sizes of

oscillations depend upon the system inertia and

impedance between different machines in the system.

The Swing Equation corresponding to SMIB system is

as follow:

Where

Pm = mechanical power input p.u.

Pmax= maximum electrical power output p.u.

H = inertia constant in MW-s/MVA

δ = rotor angle in elec. Radians

t = time in s

The curve drawn between Power P and δ is known as

power angle curve and it is shown in fig.3 below.

III. EQUAL AREA CRITERION

Figure 1 shows a SMIB system; we have the sending

end voltage ES leading the receiving end voltage ER by

delta. This angle delta is referred is to as power angle.

The steady state output power of the generator is Pe

and is equal to the mechanical power input Pm to the

generator. This system has two parallel lines with

impedances equal to X1 and X2 respectively.

A three phase fault at the middle of the line TL-II is

applied and this fault is cleared after some delay by

opening the two breakers „A‟ and „B‟. The transient

response following a disturbance in the SMIB

configuration is obtained by solving the swing

equation.

Fig 3 Pe-δ a curves illustrating stable case.

Fig 4 Pe-delta curves illustrating unstable case.

The swing equation can be solved graphically using the

equal area criterion. This method is based on the

graphical interpretation of the energy stored in the

rotating mass as aid to predict the condition for

stability. This method is only applicable to SMIB

system or a two-machine system.

4

In Pe-t domain we do not need to solve the swing

equation and prediction of out-of-step condition is

quite easy as the complete data is available through

relays. Hence this method is used in the paper. Fig 3,

Fig 4 shows the Pe- curves for the stable and unstable

swings. The Pe-t curves corresponding to these cases

are shown in figures 5&6. We use these curves to

describe the proposed algorithm.

Fig 5 Pe-t curve illustrating stable case

Fig 6 Pe-t curve illustrating unstable case.

Consider the figure 5, the areas A1 and A2 represents

the accelerating and decelerating areas under the Pe-t

curves. The area A1 is positive as for t= t0 to

t1. Similarly the areaA2 is obtained by integrating the

Pe-t curve from t1. to tmax. The time t0correspond to the

fault initiation time. The time t1correspond to the case

when . The time tmaxis the time at which

.

The areas A1 & A2 are given by the following

equation:

∫ ( ( ))

[ ]

∫ ( ( ))

[ ]

For stable condition,

∫ ( ( ))

For out of step condition or unstable power swing we

have,

∫ ( ( ))

This shows that for a stable condition the rotor

oscillations and the rotor will attain a new stable

operating point and for unstable power swing the rotor

speed increases indefinitely and the machine may go

out-of-step or it may synchronism with the infinite bus.

Thus the areas obtained by the above equations form

the basis of the proposed algorithm to detect out-of-

step condition. As per the proposed algorithm the

system will be stable if the decelerating area is more

than or equal to the accelerating area. And an unstable

condition occurs if the accelerating area is more than

the decelerating area.

IV. SOFTWARE SIMULATIONS

The proposed algorithm is applied to a SMIB (Single

Machine Infinite Bus) system in order to test the

effectiveness of the algorithm in detecting the stable

and unstable power swing.

Figure bellows shows the block diagram of the SMIB

system implemented on SIMULINK.

5

A) PROCEDURE:

A power system shown in Fig 1 is used to test the

proposed algorithm. This system is simulated in

SIMULINK environment of MATLAB R 2010b. The

simulation steps are given below.

1. The mechanical power input is kept at Pm=0.8

p.u keeping simulation time 10 seconds.

2. The initial power angle 0 is determined.

3. The time corresponding to the initial power angle

t0 is computed, the time t1, and tmax corresponding

to = max.

4. The critical clearing time(200 msec)) and critical

angle is calculated.

5. The fault clear time(130msec & 220 msec) is

varied over critical clearing time and the Pe-t

curve is obtained.

6. The accelerating and decelerating areas A1 & A2

under the Pe-t curve are calculated.

7. The areas A1 & A2 are compared to test for out-

of-step condition.

Next the following cases are tested.

1. The mechanical power input is raised to Pm =0.9

p.u keeping simulation time 10 seconds.

2. The initial power angle 0 is determined.

3. The time corresponding to the initial power angle

t0 is computed; the time t1 and tmax are also

calculated.

4. The critical clearing time (170 msec) and critical

angle is calculated.

5. The fault clear time(170 msec & 180 msec) is

varied over critical clearing time and the Pe-t

curve is obtained.

6. The accelerating and decelerating areas A1 & A2

under the Pe-t curve are calculated.

7. The areas A1 & A2 are compared to test for out-

of-step condition.

B) EXCITATION SYSTEM:

In the transient stability studies, the excitation systems

play an important role. AVR (Automatic Voltage

Regulator) improves the first swing stability but

reduces stability in following swings.

Figure below depicts the general structure of a detailed

excitation system model having a one-to-one

correspondence with the physical equipment. While

this model structure has the advantage of retaining a

direct relationship between the model parameters and

physical parameters, such detail is considered too great

for general system studies.

IEEE Type I DC excitation system is used in the

stability studies.

V. ANALYSIS OF RESULTS

Table below shows some of the simulation results for

the SMIB system. In each case, calculated accelerating

(A1) and decelerating (A2) areas from the Power-time

(Pe-t) curve are presented in the Table.

In the case 1, the mechanical power input Pm = 0.8 p.u.

is fixed constant. The fault time is kept at 130 msec

well above the Critical clearing time (200msec) thereby

calculating the areas A1 = 0.0592 & A2 = 0.0973. And

by keeping fault operation time at 220 msec, above the

critical clearing time and calculated areas A1 = 0.1297

& A2 = 0.1155.

Case 1 2 3 4

Pm(p.u.) 0.8 0.8 0.9 0.9

Critical time(ms)

200 200 170 170

Fault clear time(ms)

130 220 140 180

Area A1 (pu-s)

0.0592 0.1297 0.074 0.1572

Area A2 (pu-s)

0.0973 0.1155 0.3902 0.1100

Decision Stable Out-of-step

Stable Out-of-step

6

Pm=0.8 p.u. and t(op) =130msec

Pm=0.8 p.u. and t(op) =220 msec

Pm=0.9 p.u. and t(op) =140 msec

Pm=0.9 p.u. and t(op) =180 msec

VII. COMPARISON WITH THE REFERENCE PAPER

Case 1 2 3 4

Pm(p.u.) 0.8 0.8 0.8 0.8

Critical time(ms)

200 200 200 200

Fault clear time(ms)

167 200 233 267

Area A1 (pu-s)

0.0993 0.1144 0.1270 0.1451

Area A2 (pu-s)

0.4530 0.1406 0.0717 0.0367

Decision Stable Stable Out-of-step

Out-of-step

Pm=0.8 p.u. and t(op) =167msec

Pm=0.8 p.u. and t(op) =200msec

7

Pm=0.8 p.u. and t(op) =233msec

Pm=0.8 p.u. and t(op) =267msec

VII. CONCLUSION

An algorithm for out-of-step detection in the time-domain has

been proposed by modifying the classical equal area criterion

condition. The effectiveness of this technique has been tested

for SMIB system. The proposed algorithm perfectly

discriminated between stable and out-of-step swings based on

the local voltage and current information available at the relay

location. This algorithm does not require the line parameter

information and also do not require any off-line system

studies. The proposed technique also does not need the inertia

constant „M‟ and is therefore more accurate than the classical

equal area criterion.

VIII. REFERENCES

[1] D. Tziouvaras and D. Hou, “Out-of-Step Protection

Fundamentals and Advancements,” Proc.30th Annual

Western Protective Relay Conference, Spokane, WA,

October 21–23, 2003.

[2] E. W. Kimbark, Power System Stability, vol. 2, John

Wiley and Sons, Inc., New York, 1950.

[3] IEEE Recommended Practice for Excitation System

Models for Power System Stability Studies, IEEE Std.

421.5, 1992.

[4] IEEE Guide for Synchronous Generator Modeling

Practices and Applications in Power System Stability

Analyses, IEEE Std. 1110, 2002.

[5] “Out of step relaying using phasor measurement unit

and equal area criterion”, M chehreghani Bozchalui and

M Sanaye Pasand.

[6] P. Kundur, Power System Stability Control. New York:

McGraw-Hill1994.

[7] V.Centeno, A.G.Phadke and A.Edris, “Adaptive Out-of-

step relaywith phasor measurements”, IEEE Conf Pub

No.434 1997, pp. 210-213.

[8] “Out of Step Protection using Equal Area Criterion”,

Shengli Cheng, Mohindar S. Sachdev.

[9] “Application of Equal Area Criterion Condition in Time

Domain for Out of Step Protection”, Sumit Paudyal,

Gokaraju Ramakrishna, Mohindar S. Sachdev.