16th International Conference on Electrical Engineering, July 11-14, 2010 Busan Korea

1

Application of Phasor Measurement Unit (PMU)

Data for Out-of-Step Detection

Dikpride Despa*,**

, Yasunori Mitani *, Masayuki Watanabe* ,

Changson Li,* Bessie Monchusi*

Abstract The algorithm based on equal area criterion is developed and the stability of generators after a fault is assessed. The power swing equation is integrated to calculate the accelerating and decelerating area under the power

delta curve. Phasor Measurement Unit (PMU) data from a four generators power system is utilized in detecting

out-of-step condition. A three phase to ground fault on the power system is simulated by MATLAB and Dymola with

ObjectStab. The algorithm developed is tested by simulations on the four generator power system.

Keywords: Phasor Measurement Unit (PMU), Out of Step Detection, Equal Area Criterion, Transient Stability.

1. Introduction

The stability of an interconnected power system is its

ability to return to normal or stable operation after having

been subjected to some form of disturbance [1]. Certain

disturbances may cause the interconnected power systems

to lose synchronism, which may lead to cascading

blackouts and equipment damage. In order to avoid these

severe results, controlled separation of the system using out-of-step protection is an effective way to preserve stability in several smaller islands. Traditional out-of-step

protection uses distance relays and timers to detect the out-

of-step condition by assessing that the voltage and current

during a power swing is gradual instead of a step change.

Faults and out-of-step condition lead to a change of measured apparent impedance, but the change is much

slower during out-of-step conditions. After the out-of-step

condition is detected, out-of-step protection must block

other fault relays prone to malfunction during out of-step

conditions. Meanwhile, the controlled separation at the pre-

selected points provides load-generation balance in each

separated area with the help of a load-shedding program.

However, the disadvantage of the traditional out of step

protection scheme is that it only uses local measurements to

estimate the condition of the entire power system network,

which inevitably affects its ability to detect the out-of-step

conditions in certain circumstances. Phasor Measurement

Unit (PMU) is widely applied for detecting out of step

condition. A PMU is a device that can measure voltage and

current phasors, i.e. as complex quantities, with a common time reference for all the PMUs in the system. Line parameters such as; resistance, inductance and

capacitance can be calculated, even corona and zero sequence parameters can be determined with the PMU.

PMU provides more precise data at a much faster rate. It is

possible to receive accuracy of synchronization of 1

microsecond or 0.021 for 60 Hz signal [2]. This offers new

opportunities in power system control. The research

focused on a method to detect out of step condition using

phasor measurement, voltage phase angle difference

between different buses and simulate the out of step

scenarios on a four generators power system.

The rest of the paper discusses; 2. Equal Area Criterion, 3.

Phasor Measurements Units, 4. Out-of-step algorithm, 5.

Simulations and 6. Conclusion.

2. Equal Area Criterion

The power-angle relationship and the swing equation are

essential in understanding transient stability and can be

* Dept. of Electrical and Electronic Engineering, Kyushu Institute of

Technology, Japan (i589502d@tobata.isc.kyutech.ac.jp)

** Dept. of Electrical Engineering, Lampung University, Indonesia

2

utilized to describe the Equal-Area Criterion (EAC).The

swing equation describes the swings of the rotor angle () during a disturbance. EAC on the other hand, describes the

movement of the rotor angle using three graphs

representing the pre-fault, fault and post-fault conditions.

Based on the accelerating and decelerating areas of the

rotor angle, under these graphs, EAC assesses transient

stability. The swing equation is given by [3]:

aei PPPdt

dM ==

2

2 (1)

dt

d = (2)

where M = the inertia constant, = the rotor angle of the synchronous machine, Pm = mechanical power, Pe =

electrical power and = rotor speed. The inter-area oscillation component in the voltage variables resulting

from disturbances is utilized for extrapolating system

impedances beyond the measured buses by:

( )P

SinVVxT

21= (3)

where |V1|, |V2|are phasor voltages, is the phase rotor angle and P is the output power. The maximum power transferred between the generators and the mechanical power are estimated using these formulas:

TX

VVP

21

max = (4)

)( 0max SinPPm = (5)

where XT= the total impedance, |V1|and |V2|= the synchronized phasor voltages, maxP = the maximum power,

mP = the mechanical power and 0 = the initial power

angle.

Fig. 1 P- Curve

The EAC integrates the energy gained when the turbine-generator is accelerating, during the fault (area A, in Fig. 1 )

and compares that area with the decelerating area, (area B, in Fig. 1). When the generator exports the energy stored

during the fault. The accelerating and decelerating area at

the different generator conditions are calculated by integration of the power swing equation between the

boundary angles. In Fig. 1 the simplest condition is shown,

i.e. immediately at the occurrence of a fault, the electric

power output drops to zero and as soon as the fault is

cleared the electric power output returns to its initial curve.

Equation (6) and (7) describes area A and area B. Transient stability assessment can be explained using Equal-Area

Criterion by Fig. 1. Area A is the accelerating or positive

area and B is the decelerating or negative area

dPPAcl

faultem )sin(0 , =

(6)

=f

cldPPB m

)sinmax (7)

Where cl stands for clearing time, f is the fault time.

Transient stability of the system is guaranteed if A

16th International Conference on Electrical Engineering, July 11-14, 2010 Busan Korea

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When A and B are equal, the stability limit of the system is

reached and the accelerating power (Pa) is equal to zero.

The unstable case is reached when A>B, the angle keeps

increasing and goes out-of-step, or becomes unstable.

3. Phasor Measurement Units

PMUs are also known as synchronized phasor units for they

allow more finely calibrated observation power flows on

the power system. PMU data from different utilities is time-

synchronized and combined to create a detailed and

comprehensive view of the broader system. Conventional

methods measure voltage, current, real and reactive power

for determining the operating condition of the electric

network. These technologies cannot measure voltage phase

angles while PMU provide the phasors of voltage and

currents measured at a given substation. PMU is able to

measure phase difference at different locations. Instead of

the indirect measurements or estimation used in traditional

out-of-step protection, the voltage frequency and angle

measurement from different buses can provide the ability to

directly monitor system transient stability conditions.

4. Out-of-Step Algorithm

An out-of-step condition in a network occurs when a

generator or a group of generators lose synchronism with

the rest of the network. The event forces generators to

shutdown and sometimes large parts of the network are

forced out of service. Before losing synchronism the

network normally experiences power oscillations between

neighboring generator groups. The oscillations cause

voltage and current variations throughout the power system

and there will be a variation in power flow between two

areas, this phenomenon is called a power swing. The out-

of-step algorithm creates vectors of complex current,

voltage and impedance from phasor measurements. For the

construction the P- curve, the equivalent phase angle for

the system is calculated using the COA algorithm [4].

=

==

N

ii

i

N

ii

COA

1

1

(8)

The total Impedance of the power system is calculated

using the equivalent phase angle.

I

VeVX

i

ref

T

= (9)

And applied to determine the equivalent rotor angle is

calculated by :

=

T

T

jX

X1tan (10)

The total power of the system is calculated by :

( ) ( ) += sinsin2

T

xref

T X

VV

X

VP (11)

Utilizing (11) the total mechanical power can be calculated

using the initial values of voltage, impedance, and delta. The phase angle and power value of generator 3 the steady

state condition are used as a reference and compared to the

phase angle and power of the other generator at different

time step. Using time phase angle and power vector at each

time step the P- curve is constructed. The area under the

curves is calculated using the Riemann Integration. To

estimate the power output for the fault and post fault at

different time steps, a constant is calculated by:

SinP

tCons =tan (12)

The new value of outP for fault and post fault at

different steps are given by:

2sintancos

XtP new = (13)

4

0 20 40 60 80 100 120 140 160 1800

0.5

1

1.5

2

2.5

Angle [degrees]

Power [p.u.]

Fig. 2 Shows the power-output and the mechanical

power for the power system in steady state

operation.

0 20 40 60 80 100 120 140 160 1800

0.5

1

1.5

2

2.5

Angle [degrees]

Power [p.u.]

Fig. 3 Shows the power output and mechanical

power under fault and post fault conditions

Its applied in calculating the output power and mechanical

power. The new vectors of phase angle and power for all

time steps are calculated from the above complex values.

To detect angle change the difference between the reference

value and a value at a specific time-step is calculated. If the

difference is too much, the algorithm to detect the power

swing will start. The reference value is taken from studying

the graphs of the change of phase angle. If the phase angle

has changed too much and the electric power output has

decreased to a level below the mechanical power input, it is

for sure that the system will experience a power swing. If

the accelerating area is greater than decelerating area, the

system will go out of step.

5. Simulation

The Algorithm developed is tested on the four generators,

two areas power system (shown in Fig. 4) on MATLAB.

The system is designed by Dymola with ObjectStab. The

generators have an exciter and a turbine governor.

Simulations are performed with a three phase to ground

fault on the transmission line as shown in Fig. 4 PMUs are

placed on the generators bus bars (1, 2, 11 and 12)

Fig. 4 Four Generators Two Areas Power System

Fig. 5 P- Curve for Generator 1

In Fig. 5 the power at the state and change of power around

the time of the instant fault are shown for Generator 1 by

the solid graph. Generator 3 is chosen as a reference

generator. The impedance of the equivalent power system is

utilized in the calculation of the maximum power and

mechanical power. The output power for the fault and after

fault condition is shown by graphs with dashes. The

generator is not out of step with the other generators in the

power system.

16th International Conference on Electrical Engineering, July 11-14, 2010 Busan Korea

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Fig. 6 P-Curve for Generator 2

In Fig. 6 the solid curve shows the stable electric power

output before the fault. The dashed curves represent the

electric power output during and after the fault. The

mechanical power input is represented by the dotted line. In

this case, the generator is far from losing synchronism. The

power will oscillate back to its stable equilibrium point.

A fault has occurred but the system remains stable.

Fig. 7 P- Curve for Generator 4 Generator 4 does not loose synchronism even if there is a

fault in the power system. The power at the stable point and

the change of power around the time of the instant fault for

generator 4 are shown in Fig. 7. From the results of the

simulations, it can be concluded that the fault in the system

is not severe enough to cause all the generators to loose

synchronism.

Fig. 8 P-Curve for Generator 1 out-of-step

Fig. 9 P-Curve for Generator 2 out-of-step

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Fig 10. P-Curve for Generator 4 out-of-step Figures 8-10 show the P-curves for out-of-step condition, for generators 2, 3 and 4. The out-of-step message is issued

to warn that the generators 1 and 2 are out- of- step while

generator 3 remains in synchronism with generator 4.

5. Conclusion

Phasor measurements are utilized to calculate the vectors of

complex current, voltage and impedance which are applied

to determine the new vectors with phase angle and power

for all time steps. The angle change is determined by the

difference between the reverence value and a value at a

specific time-step is calculated. The Equal Area Criterion is

utilized to detect if the generators are going out of step or

not. A three phase to ground fault is simulated on the four

generators power system.

Acknowledgements

This work was supported by in part by Grant-in-Aid for

Science Research (A) 18206028 of JSPS.

References [1] I J Nagrath, DP Kothari, Modern Power System

Analisys, McGraw Hill, 1980.

[2] Mark R Gerald T.H. Phasor Measurement Unit

Data in Power System State EstimationJanuary

2005.

[3] Prabha Kundur Power System Stability and

Control,McGraw Hill, 1993.

[4] B. B. Monchusi Optimal Approach Towards Using

Phasor Measurement (PMU) Data in Equal-Area

Criterion Based Systems for Power System Transient

Stability Assessment, PhD Thesis, Graduate School

of Engineering, Kyushu Institute of Technology,

Japan, February 2010.