Out-of-Step Detection based on Phasor Measurement Unit

ZAID S. AL-SHAMAAIN1, HUSSEIN. D. AL-MAJALI1, BILAL. H. AL-MAJALI2

1Department of Electrical Engineering, Faculty of Engineering

Mu’tah University,

Al-Karak,

JORDAN

2Electronic and Electrical Engineering, Faculty of Engineering

Brunel University London,

Uxbridge,

UNITED KINGDOM

Abstract: - The electrical power systems operate as a huge, interconnected network that extends across a large

area. In the power system, there is an equilibrium between generated power and a load. Any disturbance in the

system, such as a fault or a change in load, will lead to imbalance and electromechanical oscillations. As a

result, the power flow between two areas varies. This is known as a power swing." Large system disturbances

could lead to large rotor angle deviations between groups of generators, resulting in a loss of synchronism

between generators or between interconnected systems. This is known as an out-of-step condition. To avoid

equipment damage and power outages, the interconnected area must be isolated as soon as possible before the

electrical system loses synchronization. In this paper, PMU data is used to measure the current, voltage, and

phase angle of the three phases at both ends of two interconnected area power systems. The measured data is

then used to distinguish between a power swing or fault condition and predict the future phase angle difference

during the disturbances to evaluate the system stability condition. If a swing is detected, then it will be

ascertained whether the swing is stable or not. The performance of the proposed method has been tested on a

simulated system using MATLAB / Simulink software.

Key-Words: - Phasor Measurement Unit, Current Detection Element, Phase Angle Difference, Phasor Current

Difference, Out of step trip, Stability system.

Received: November 25, 2022. Revised: November 26, 2023. Accepted: December 12, 2023. Published: December 31, 2023.

1 Introduction

Typically, power systems operate near or at their

nominal frequency. Under steady-state operation,

there is a balance between generated and consumed

active and reactive powers. However,

electromechanical oscillation will occur when the

system recovers from disturbances caused by faults,

line switching, generator disconnections, or a

change in a large load. During this time, the rotor

angle varies. If the swing is stable, the fluctuations

will decrease. During severe disturbances, however,

the oscillations do not remain stable, resulting in

even more angle separation between the areas. This

results in large swings in power flow as well as

changes in voltages and currents. Eventually, there

is a loss of synchronization, often known as an out-

of-step condition, [1].

During power swing, the load impedance

may cross the operating zone of the relay, causing

unwanted tripping of transmission lines and

cascading outages and power blackouts, [2], [3]. In

the case of a power swing, the Power Swing Block

(PSB) acts to block distance relay element

operation, allowing the power system to return to a

stable operating condition, [4], [5]. The PSB's

primary function is to distinguish between fault and

power swing.

Out of step trip (OST) distinguishes between

stable and unstable power swings and

initiates system area separation at predetermined

network nodes. When an interconnected area system

loses synchronization, the areas must be separated at

predetermined places to maintain load generation

balance, avoid equipment damage, and power

outages. To maintain the stability of the power

system, [6], [7], [8].

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.36

Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

E-ISSN: 2224-350X

354

Volume 18, 2023

A difference in the rate of change of the positive

sequence impedance vector has traditionally been

applied to the PSB and OST to detect power swings

and out-of-step conditions. The operation of

distance relays starts before the impedance enters

the operating zone of the protective relay. The

traditional method for detecting power swing is to

measure the rate of change of impedance and the

time it takes for the impedance vector to pass

through a particular zone. When the impedance

vector enters the zone, a timer starts and stops when

it leaves. If the time taken for measurement exceeds

the preset value, a power swing is detected.

A current differential protection technique that

can detect faults in a transmission line by comparing

the instantaneous current data collected from PMU

at both ends of the line has been provided in, [9],

[10], [11]. It works effectively when intercircuit and

cross-country faults are evolving. It also works for

faults that occur during power swings.

The load angle measurements of synchronous

generators can be utilized to detect an out-of-step

condition, [12]. The suggested method measures the

phase difference of the positive sequence voltages

using an estimation algorithm, [13] and PMU data,

[14], [15], at both ends. When the estimated phase

angle value exceeds a threshold value, the power

swing is assumed to be unstable, and the system

loses synchronism.

To detect a power swing as well as current fault

with high accuracy and evaluate the system

performance, in this paper an out of step detection

method is proposed simultaneously using positive

phase angle difference and positive sequence current

from the PMU measurements placed at both end of

the interconnected area.

This paper is organized in five sections: section

1 presents a brief overview of power swing

phenomena and distance relay element operation;

section 2 presents conventional power swing

detection methods; and section 3 presents the

proposed detection method, the proposed detection

algorithms, and their performance. The simulation

results and discussion are presented in Section 4, and

finally, the conclusion is organized in Section 5.

2 Conventional Power Swing

Detection Methods

There are several methods that are proposed to detect

out-of-step condition in a power system based on

local-measurements. These methods are briefly

summarized next.

2.1 Conventional Rate of Change of

Impedance

During normal system operation, the measured

impedance is the load impedance, and its locus is far

from the relay operating zone, [16]. When a fault

occurs, the impedance point moves instantaneously

into the relay operating zone; however, during a

power swing, the impedance point moves slowly on

the impedance plane. The elapsed time required by

the impedance vector to pass through a zone is

limited by two additional concentric impedance

characteristics that are used to calculate the rate of

change of impedance. The inner concentric zone

setting should be larger than the largest tripping

characteristic, [17], [18], [19].

Power swing can be detected before the

impedance locus enters the operational

characteristic, which is advantageous. The important

parameters in this method are the delta impedance

and the timer. To find the optimal settings, extensive

stability studies are required. The drawback is that

the maximum load of the transmission line is limited

by the outer zone. This is referred to as load

encroachment.

2.2 Continuous Impedance Calculation

The power swing is determined using a continuous

impedance calculation in this method. For instance,

an impedance calculation is performed for each 4ms

time step and compared to the previous step's

impedance. If there is a deviation, the system is

considered to be out of synchronization. The next

step's impedance is predicted based on the previous

two values. If the prediction is correct, a ten-power

swing is detected. This technique doesn't require the

use of delta time or delta impedance settings. The

detection might fail if the changing impedance

vector is faster than the relay processing speed, [16].

2.3 Blinder Schemes

A. Single blinder scheme

A single blinder method uses only one set of blinder

characteristics. It can also be utilized with auxiliary

logic for out-of-step trip functions. However, it can't

differentiate between a fault and an OOS condition

until the fault has passed through the second blinder

within the given time limit. When an unstable power

swing is detected, this approach can be utilized to

prevent automatic reclosing. The primary advantage

of this method is that it may be used to prevent load

encroachment, [20].

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.36

Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

E-ISSN: 2224-350X

355

Volume 18, 2023

B. Dual blinder scheme

The two-blinder scheme and the concentric

characteristics scheme both operate on the same

basis. When the impedance vector passes through

the outer blinder, the timer starts and stops when it

passes through the inner blinder. If the measured

time exceeds the delta time settings, a power swing

is detected. All elements of distance will be blocked.

If an unstable power swing is detected, the mho

element may trip immediately or after the swing has

passed through, [21], [22]. The advantage of this

technique is that the distance protection settings

have no effect on the power swing detection

settings. However, determining the optimal settings

requires extensive stability studies.

2.4 R-Rdot Scheme

The R-dot scheme is the apparent resistance rate of

change that is supplemented by the OST relay. The

control output of an R-dot relay is described as Y2 =

(R2-R1) + T1 dR/dT, where Y2 is the control output

and R is the apparent resistance measured by the

relay. R1 and T1 are relay setting parameters. When

the power swing trajectory crosses a switching line,

an output in the R-dot plane is generated. For

traditional OST relays, the apparent resistance rate

is enhanced by a vertical line in the R-dot plane

offset by R1, which is the relay setting parameter.

System separation occurs when output Y2 becomes

negative. For small dR/dT and low separation rates,

the R-dot method operates similarly to a

conventional relay scheme. However, for large

dR/dT, a larger negative value of Y2 is produced,

causing tripping to occur earlier due to the high

separation rates. The technique has the same

problems as the blinder scheme in that it requires

extensive simulation studies under various

contingency conditions to set the relay

characteristics. However, determining optimal

settings requires extensive stability analysis, [23].

2.5 Swing Center Voltage Method

The swing center voltage (SCV) technique is a

voltage-based method discussed in, [24]. When the

angular separation between two source-equivalent

systems approaches 180 degrees, the SCV is a point

of zero voltage between them. The electrical center

is the location of zero voltage.

The SCV approach calculates the maximum rate

of change of voltage at the electrical center.

Detection is normally accomplished at a voltage

angle separation of close to 180 degrees. When

tripping occurs under these conditions, the circuit

breaker is subjected to twice the rated stress. As a

result, the operation of the circuit breaker is delayed

until the voltage angle separation is

less. Furthermore, estimating the SCV using local

measurements of the voltage phasor is only valid

when the impedance angle is 90 degrees.

3 The Proposed Detection Method

The Kundur two area system, which consists of two

areas connected by two weak tie lines, is the most

suitable test system for the study of out-of-step

condition. The tie line serves as the system's

electrical center. If a fault happens on one of the tie-

lines, the power swing will be created with swing

center on the second tie-line.

The test system consists of four generators

divided into two symmetrical areas linked by two tie

lines. Area 1 has a load of 967MW and a generation

capacity of 1400MW. The load in Area 2 is

1767MW, and the generation is 1463MW. Each tie

line transfer approximately 200MW.

The relay is implemented at bus 1. Phasor

Measurement Units (PMU) are placed on buses 1

and 2. The line is tripped after a fault occurs on Tie

line -2. As a result, there is a power imbalance in the

other Tie line, causing power swing, During the

swing, another fault occurs in the line and is

detected by the current differential method. PMUs

placed at the buses calculate the voltage and current

of the three-phase line at a sampling rate of 64

samples per cycle. The PMU data is then used to

measure the positive sequence voltage and current

phasors using the Discrete Fourier Transform.

Fig. 1: Block diagram of simulated system

3.1 Out-of-step Detection Method

A. Phase difference calculation

The phase difference between the two area (Area1

and area 2) are obtained by calculating the phase

difference between the positive sequence voltage

data of the two ends from PMUs.

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Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

E-ISSN: 2224-350X

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B. Calculation of predicted values of phase

difference

The prediction is obtained by using the phase

difference values for present time and previous time,

the future value can be predicted by the equations

below.

(1)

Where,

(2)

(3)

μ =

(5)

δp: predicted relative phase angle

δα, δβ: phase angles

The phase difference δp is predicted for time

TD using 8 data points as shown in Figure 2. These

are the phase difference at the present time δα and

three values (δα-1, δα-2, and δα-3) at negative

increments of time TD. Also, the phase difference

value δβ at the time TM before the current time and

three values (δβ-1, δβ-2, δβ-3) in the negative

increment TD at that time. Where TM is the time

difference that takes a sample point between δα and

δβ (in our case TM= 10ms and TD= 20ms), TD is

the time difference between each pair of sample

points.

Fig. 2: Method of predicting phase angle

When the predicted phase angle difference value

δp obtained by Eq.1 exceeds a critical threshold

value, then it’s judged that the power swing between

the two generator groups will lose synchronism. The

value δ_critical is predetermined by the system

configuration. The value chosen must be such that it

does not operate during a stable swing. The

predicted and measured values are shown in Figure

3. When the predicted phase angle difference value

exceeds a minimum threshold value, the power

swing is assumed to be unstable, and the system will

lose synchronism, [25]. The value of is determined

by the system conditions and is carefully chosen so

that the system does not malfunction during a stable

swing. Many research used new techniques to convert

DC to AC in order to link with grid, [26], [27] and other

research used to convert AC to DC were used HVDC

system, [28], [29], [30].

A current swing detection element, in addition

to the phase angle difference limit, should be

operated to confirm that the system will lose

synchronism in the near future. Figure 3 shows a

swinging condition with both actual and predicted

phase differences. The predicted value is 20ms

earlier than the actual value.

Fig. 3: Predicted and measured phase difference

In Figure 3, which illustrates the predicted and

measured phase angle difference values that are

almost closed to each other during the test of the

method's performance, that means the accuracy is

very high when applying the proposed prediction

method.

C. Current swing detection element

This element serves as a second check criterion to

determine the detected out of step from the

predicted phase difference value. By using a current

input to detect oscillation, it operates when the

swing is unstable and off when it is stable. Figure

4 shows the logical diagram of the current swing

λ =

(4)

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detection element, Table 1 shows the logical

operation of current swing detection element during

power swing.

The current swing detection element consists of

two detection blocks: a magnitude of change

detection block to measure the size of the current

fluctuation and a rate of change detection block to

ascertain whether a power swing is present. The

element works with AND of these two blocks.

Fig. 4: Current swing detection element

Table. 1. logic operation of current swing detection

element, 1: operate, 0: not operate

The Imax and Imin are the maximum and

minimum values of the positive sequence current

during the predetermined time period ΔT max. The

magnitude of change detection block is operated if

Iset is greater than a predetermined value, Iset and

ΔT max are determined by simulation. ΔI / Δt

represents the rate of change of the current value

over the small-time interval Δt. The rate of change

detection block acts when ΔI / Δt is greater than a

constant N and continues for a longer period of time

than time T1. If both elements are operated, the

current swing detection element gives a positive

output, that means unstable power swing was

detected. ΔTmax=2 sec, Δt=5ms and T1=20ms.

3.2 Fault Detection Method

The main criterion for fault detection and load

conditions is the difference in positive sequence

current phasor at both ends. A threshold value is

determined by carefully comparing the steady-state

and power-swing condition. If the difference

exceeds a certain threshold, the algorithm detects a

fault.

3.3 Flow Chart of the Proposed Detection

Method

A proposed detection method for out-of-step

conditions based on the phase angle difference of

the positive sequence voltage and phasor current

difference of the positive sequence current from

PMU measurements is illustrated in the flowcharts,

which are shown in Figure 5 and Figure 6

respectively.

Fig. 5: Flow chart for the proposed out-of-step

detection method based on phase angle difference

The voltage phase angle from both PMUs at

both ends works as an input for the proposed flow

chart that is shown in Figure 5 After the phase

difference is calculated, the predicted phase angle

difference is obtained from equation (1), then the

predicted angle δp is compared with δ_critical to

determine the swing type, whether stable or not, to

provide a decision for out of step relays.

The phasor current magnitude from both PMUs

at both ends works as an input for the proposed flow

chart shown in Figure 6 after the phasor current

difference and current rate of change are calculated

at a predetermined time. The obtained values are

compared with the setting current and constant

factor N, then the swing type will be classified as

stable or not to provide a decision for out-of-step

relays, which works as a second check criteria with

the phase angle prediction algorithm that was

discussed before.

Power Swing Type

Output

Stable

0

un-stable

1

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Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

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Fig. 6: Flow chart for the proposed out-of-step

detection method based on phasor current difference

4 Results and Discussion

The performance of the proposed detection scheme

has been tested on the system given in Figure 1.

A three-phase fault is a worst case that has been

created in the system in the case of a transient fault,

which has been created here at about 0.5s and

cleared at 1s and δ_critical = 100°, Iset value=

3.4kA. The predicted angle, actual angle, prediction

accuracy, and current swing element operation are

calculated at different sizes of fault (fault resistance

and ground resistance), and the phase angle

predicted value is very close to the actual value with

very high accuracy (around 99.9%) at stable or

unstable conditions, which is also compatible with

the current swing element operation.

Table 2 shows the simulation results of

predicted phase angle difference with actual phase

angle difference in degree and the prediction

accuracy at different sizes of faults.

When the predicted angle is greater than the

critical angle (in this case, δ_critical=100 °) and the

output of the current swing operation element is

positive (mean=1), then it judges whether the

system will lose synchronism or an unstable

condition will occur. On the other hand, if the

predicted angle is less than the critical angle and the

output of the current swing operation element is

negative (mean =0), then it judges the system to be

stable.

The fault detection technique detects a fault

when the difference in current phasors at both ends

exceeds the threshold value (in this case, 3.4 kA).

This technique can detect current fault magnitude

and current difference rate of change in both steady-

state and power-swing conditions; mutual coupling

and series impedance imbalances have no effect on

its performance. The fault is detected as a current

fluctuation (current rate of change A/ms), and a

current difference starts increasing until reaching the

maximum value (in this case around 10KA) during

the transient fault which is simulated at switching

time start from (0.5sec and clear around 1sec). as

shown in Figure 7.

Table 2. Simulation results for different size of fault

Fig. 7: A fault current magnitude and rate of change

detected

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DOI: 10.37394/232016.2023.18.36

Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

E-ISSN: 2224-350X

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Volume 18, 2023

The difference in positive sequence current at

both ends before and after transient fault is shown in

Figure 8 and Figure 9 respectively.

Fig. 8: Difference in positive sequence current at

both ends during normal condition.

During the normal condition, as shown in

Figure 8, the current difference at both ends of the

tie lines starts fluctuating during the power system

turn-on until the system reaches a steady-state point

(in this case after 0.1sec). After this point (0.1sec),

the current remains constant (around 34.3 A) as long

as there is no fault in the system.

Fig. 9: Difference in positive sequence current at

both ends during fault condition

As shown in Figure 9, the current difference

starts fluctuating around 9.6 KA and starts

increasing sharply during the transient fault (in this

case, the switching time starts at 0.5sec and clears at

1sec), so the fault current during an abnormal

condition can be detected with high accuracy and a

short detection time by the proposed method.

The phase angle difference of the positive

sequence voltage at both ends during the normal

condition is shown in Figure 10. The phase angle

difference starts fluctuating during the operating

condition, and the angle oscillation begins

decreasing until the system reaches a steady-state

point (in this case, around 0.15 sec). After this point,

the phase angle difference will remain constant

(around 26.6°) as long as the system is in normal

operation.

Fig. 10: Phase angle difference of the positive

sequence voltage at both ends during normal

condition.

When a fault occurs at switching time from 0.5s

to 1sec on a faulted line, the unbalance between load

and generation on the other line causes a power

swing. The relay is prevented from operating if the

oscillations are small and the swing is stable

because the predicted phase angle difference is still

less than the critical value, which in this case is

100°.

On the other hand, if the predicted angle goes

above δ_critical= 100° and the current swing

detection operates, then the unstable power swing is

declared, and the relay must be tripped quickly to

separate the asynchronous area from the overall

system to avoid system collapse.

Figure 11 shows the plot of the phase difference

between the two buses without a proposed

protection scheme during an unstable swing. It is

clear that the phase angle difference begins to

fluctuate and increase during the fault time duration

(from 0.5sec to 1sec) and that after the fault

(1.1sec), the phase angle difference between two

interconnected areas starts to separate above 180°.

The system loses stability around 1.15 sec, and the

system will lose the synchronization.

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DOI: 10.37394/232016.2023.18.36

Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

E-ISSN: 2224-350X

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Volume 18, 2023

Fig. 11: System without protection scheme.

Figure 12 represents the phase angle difference

plot of the same case with the proposed protection

scheme. The predicted angle passes the critical

value at around 0.97s, and the current swing

detection element detects the current size, causing

the system to be declared unstable and the relay to

trip at around 0.98s. As a result of this method, the

swinging condition can be predicted in advance,

increasing the decision time for the OST function.

Fig. 12: System with proposed protection scheme.

5 Conclusions

This paper presents a new out-of-step detection

method for multi-machine systems using wide-area

measurements based on PMUs. Two schemes are

proposed: one based on positive phase angle

difference calculation between two interconnected

areas at different fault sizes, which evaluates system

condition based on predicted angle, and the other

based on phasor current difference calculation

between interconnected areas, which works as a

second check criteria where both algorithms work

simultaneously. The proposed method can detect

stable and unstable power swings and faults with

high speed and accuracy (around 99%) without

being affected by system parameters.

The angle prediction time is relatively short

(around 20ms), making it compatible with current

swing element operation. To validate the proposed

method, a different fault resistance range (1mΩ up

to 100Ω), and fault time durations (at switching

times of 0.5sec and clear at 1sec) were created in the

system to evaluate the accuracy of the phase angle

prediction scheme with current swing detection

elements during stable and unstable power swings

using MATLAB/Simulink software.

Nomenclature:

δp = Predicted relative phase angle difference

δα, δβ = phase angles difference measured values at

different time

, , = difference in the phase angle of

the first samples

, , = difference in the phase angle of

the second samples

λ, μ = ratio of phase angle difference

= maximum value of the positive sequence

current

= minimum value of the positive sequence

current

= time period that is determined by the

simulation

N = constant number that is used as a comparator

with a current rate of change

= setting current that is determined by the

simulation

= current rate of change

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Volume 18, 2023

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Contribution of Individual Authors to the

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problem to the final findings and solution.

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Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

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WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.36

Zaid S. Al-Shamaain, Hussein. D. Al-Majali, Bilal. H. Al-Majali

E-ISSN: 2224-350X

363

Volume 18, 2023