power swing out-of-step app guide_.docx

7/21/2019 Power Swing Out-of-Step App Guide_.docx

http://slidepdf.com/reader/full/power-swing-out-of-step-app-guidedocx 1/11

Description of MethodPast methods of testing power swing and out of step conditions have often

involved brute force methods of applying voltages and currents to simulate impedances

seen by the relay. By manually ramping the impedance trajectory, or playing severalvector states where a specific impedance was applied, it was possible to trick the relayinto seeing that an impedance was tracking across the measurement zones. However,with more advanced algorithms, trying to trick the relay no longer works. The relay islooking for a smooth transition between the measurement zones, and if it does not seeit, then it will not block the power swing or trip on the outofstep.

!n order to satisfy the conditions for the power swing and outofstep algorithmscurrently in use, a new method is proposed. By superimposing two waveforms ofsimilar fre"uencies, a smooth impedance ramp can be achieved. This method is similar to a two source model in that both sources have similar fre"uencies and amplitudes.The rate of change of impedance can be controlled as well as the minimum and

ma#imum impedances, the number of pole slips, as well as the starting phase anglerelationships. The characteristic e"uation of the output waveform for the voltage andcurrent is as follows$

%". & f I , V (t )=( A1sin ( ω1 t +φ1) )+ A2 sin (ω2 t +φ2 )

'here$ (& ) *agnitude of the first current+voltage source in *- valuesω& ) π/0re"uency-ource&, 10re"uency is in Hz, ω&is in rad+s2φ& ) !nitial phase angle of current+voltage source & in degrees

( ) *agnitude of the second current+voltage source in *- values

ω ) π/0re"uency-ource, 10re"uency is in Hz, ωis in rad+s2φ ) !nitial phase angle of current+voltage source in degreest ) the time of the event in seconds

3sing arbitrary values for %"uation &, 0igure 4 shows the plot of a voltage and currentwaveform with the following parameters$5&) 67.4 5, 5)&7.4 5, !&)&8.94(, !)&:.94(, 0&)8; Hz, 0 ) 47 Hz, φ&<urrent ) ;°,φ<urrent ) ;°, φ&5oltage ) ;°, φ5oltage ) ;°

0igure 4. -uperimposed voltage and current waveforms



Both the voltage and current waveforms decrease and increase at the same timeand remain in phase for the duration of the waveform plot. This is not the behavior of apower swing or outofstep condition. To change this, the phase current needs to beoffset by &=;°. The option is to either change either φ&<urrent or φ<urrent. By changingφ&<urrent, the phase angle will initially start &=;° out of phase and then slowly come back

into phase, then go back out, and repeat indefinitely. -ince it is desirable to control thephase angle from the start, φ<urrent will be set to &=;°. This will allow the two waveformsto start in phase and then slowly go out of phase and come back into phase, andrepeat. ( plot of the waveforms with the appropriate phase shift is shown in 0igure 8.

0igure 8. Plot of voltage and current waveforms with current offset by &=;°

!n 0igure 8, the voltage and current start in phase, then about a "uarter of theway through the swing, it goes out of phase by 7;°, then comes back into phase, thengoes out of phase by 7;° at > of the swing, and back into phase at the end of theswing. This is the general form of the power swing waveform. The ne#t section willdiscuss how to implement a controlled power swing and outofstep condition using anyof the *egger Test -ets.

Applying the Method

Power SwingTo apply a power swing, the following parameters need to be defined first.

&. The *a#imum !mpedance, ?ma#, of the Power -wing+@utof-tep needs to bedefined. This will be based on the outer most characteristic that is tracking theimpedance. !t is recommended that the ma#imum impedance be greater thanthe largest blinder+characteristic impedance, but not so large that the trajectory of the swing e#its the characteristic prematurely.

. The *inimum !mpedance, ?min, of the Power -wing+@utof-tep also needs to bedefined. This will be the stopping point of the swing+step.

:. The -ource 0re"uencies will determine how long of a duration a single powerswing or outofstep condition will be. The source fre"uencies will also factor indetermining the rate of change of the trajectory of the impedance. The larger thedifference in fre"uency between the two sources, the faster the swing+step, andthe smaller the difference, the slower the swing+step.



6. The -tarting Phase (ngle needs to be defined so that proper loading conditionscan be simulated properly.

Here is how to create a power swing with a ma#imum impedance of &4 A, aminimum impedance of & A, a -ource & 0re"uency of 8; Hz, a -ource 0re"uency of

47 Hz, and a starting Phase (ngle of ;.

The first parameter that we can determine is how long a complete power swingcycle will take, t-wing. This is giving by %". .

%". t Swing= 1

f 1−f

2

(s)

%". : t Swing=1

60−59=1 s

'hen applying this method to any type of test routine, t -wing should be the ma#imumtime set for how long the swing should be applied. !f multiple turns are desired, thenma#imum time would be the number of turns times t -wing.

Ce#t will be solving for the currents and voltages that should be applied to therelay. To start, only the ( phase voltages and currents will be discussed. B and <phases are identical to (, with only the appropriate phase shifts taking place. ( nominalvoltage should be defined for the ma#imum impedance, and a fault voltage should bedefined for the minimum impedance. Take care in choosing a fault voltage becausesome of the impedances could still be "uite large, with large being defined as around &4A or greater. !f the fault voltage is too small, negative valued currents would end up

being calculated to create the correct conditions. !f that is the case, increase the faultvoltage until the currents are at an acceptable level. (s a rule of thumb the nominalvoltage, 5nom, is 87 5 linetoground, and the fault voltage, 5 fault, is around :; 5 linetoground.

The value of 5fault can change depending on the impedance and the currentre"uired from the test set. The moniker of 5fault can also be a little misleading. ( powerswing event may not necessarily re"uire the e#treme values of traditional fault voltages.The swing of impedance may only go from a large value to a slightly smaller value.-uch would be the case if the user wanted to swing from =7Ω to 4;Ω. The re"uiredfault voltage would not be much less than what was re"uired for starting impedance.

The e"uations for the two voltages for phase a are shown in the following

e"uations.

%". 6 V 1=V fault +( V nom−V fault

2 )

%". 4 V 1=30+( 69−30

2 )=49.5V



%". 8 V 2=(V nom−V fault

2 )

%". 9 V 2=(69−30

2 )=19.5V

Then the two currents for !& and ! will be solved.

%". = I

1=[(V fault

Z min )−((

V fault

Z min )−(V nom

Z max )

2 )]

%". 7

I 1=

[(69

1 )−( (301 )−(6915 )

2

)]=17.3 A

%". &; I

2=((

V fault

Z min )−(V nom

Z max )

2 )

%". && I 2=((

69

1 )−( 6915 )2

)=12.7 A

@ther parameters can now be solved such as the rate of change of impedance. -incethe swing goes from a ma#imum impedance to a minimum and back again, the rateshould only be calculated based on the time it takes to go from the ma#imum to theminimum. This is shown in %". &.

%". & Z rate=2∗( Z max−Z min

t Swing)

%". &: Z

r ate

=2∗

(15−1

1

)=28Ω /s

'hen starting in the prefault mode for testing, it is handy to be at the same currentlevel as the starting current for the swing. This is minimum current, which is shown in%". &6.

%". &6 I min= I 1− I

2



%". &4 I min=17.3−12.7=4.6 A

These commands were giving in a Pre0ault, 0ault, Post0ault format. 0or apossible front end, more states can be implemented. 0igure 9 shows a capturedwaveform from (5T-.

0igure 9. 'aveform capture of a power swing in (5T-

The time set for the Pre0ault duration is critical in that it is necessary for thewaveform to end at the precise phase angle and magnitude that is e"ual to the start ofthe power swing event. The Pre0ault phase angle of the current should be e"ual to thestarting phase angle of the power swing. This will also ensure smoothness. This isshown previously in the T- commands to the test set. !n 0igure 9, the duration wasset for & second, and the calculated time of & power swing was also calculated at &second. By setting the Pre0ault to the same time as the calculated time of the powerswing, a smooth transition is guaranteed in the waveforms. The time can also be set toa multiple of the swing duration. !n this case, , :, or 6 seconds would also work. (time of ;.4 seconds would not work. This is shown in 0igure =.



0igure =. Power -wing with Pre0ault Duration changed to ;.4 s

<omparing 0igure 9 to 0igure =, the shift of the power swing characteristic is

apparent when the Pre0ault duration is changed to a value other than a multiple of thetime of the swing event. The Pre0ault duration, or any state before a swing eventshould be set according to %"uation &8.

%". &8 T prefault = N ∗t Swing

'here$C ) whole number multiples of t-wing

!t should be noted that if it is desirable to have fle#ible Pre0ault times, then the initialcurrent and voltage magnitudes can be solved for using %". & for the applied times.

'hile testing the power swing element, other parameters should be displayed aswell. The user will be interested to see the impedance trajectory of the power swing.This should be plotted in the E plane so the user can trace the circular path. Theinstantaneous impedance, ?, is calculated, followed by the phase angle, θ. Theinstantaneous impedance, ?, is defined in %"uation &9.



%". &9 Z =V

I

The phase angle, θ, is defined in %"uation &=.

%". &= θ= (t Vzero−t Izero)

1

f ∗360

'here$t5zero ) time of the voltage magnitude zero crossing in secondst!zero ) time of the current magnitude zero crossing in secondsf ) fre"uency of the waveform in Hz

The phase angle of power swing is shown in 0igure 7.

0igure 7. Phase angle of the power swing in degrees vs time in seconds

The fre"uency of two superimposed waveforms will not be constant. -ignalprocessing techni"ues should be used to take and accurate measurement of thefre"uency as well as the phase angle. %"uation &= is given as a reference and will notprovide a very accurate phase angle unless a very large sampling rate is used todetermine the zero crossing of the waveform.

@nce the impedance and phase angle are known, then the resistance, , andreactance, E, of the impedance can be determined as shown in %"uations &7 and ;respectively.



%". &7 R=Z ∗cosθ

%". ; X =Z ∗sinθ

@nce the resistance and reactance are determined, they can be plotted. This is shownin 0igure 7.

0igure 7. Trajectory of impedance during a power swing

The trajectory starts out at the ma#imum impedance of &4 A and travels in an arctowards the minimum impedance of & A, and then circles back towards &4 A. Theprocess will repeat if the swing is unstable. To simulate an unstable swing, simplyincrease the duration of the swing in even multiples.

Out-of-Step (pplying an outofstep condition is very similar to applying a power swing

condition. The only difference is that instead of the impedance turning around when theminimum impedance trajectory is reached, the trajectory will continue through the originand e#it out of the other side of the characteristic. !n order to achieve this a few thingsneed to be done first.

The total time of the out of step condition will be the same as the total time for apower swing, t-wing. However, the changes need to be made at the halfway point of thetotal time in order to create an outofstep. This time is important, so it will be called,tevent, and is e"ual to F the time of t-wing as shown in %". &.



%". & t eent =t Swing

2

(t time tevent, the fre"uency and phase angles of currents !& and ! need to be

swapped. This will create a waveform that will continue to a phase angle differencebetween the voltage and current of &=;°. (ll other calculations are the same. Here arethe T- commands to command an out of step condition with the same parameters asthe power swing in the previous e#ample. The swapped phase angles and fre"uenciesare highlighted. %ach part of the outofstep has a duration of tevent.

*PT*@D%@0,t;&hd,t;&cal,t;&ad,t;&sta,t;hd,t;cal,t;ad,t;sto,t;:hd,t;:cau,t;:ad,t;:m,t;6hd,t;6cau,t;6ad,t;6m,t;4hd,t;4cau,t;4ad,t;4m,t;8hd,t;8cau,t;8ad,t;8m,t;9hd,t;9cau,t;9ad,t;9m,t;=hd,t;=cau,t;=ad,t;=m,t;7hd,t;7cau,t;7ad,t;7m,t&;hd,t&;cau,t&;ad,t&;mGtrG@<GT;&*,T;*G

trGTD;.;;;,<&:,on,<&:,(8,5&:,on,5&:,(,%<-%TG-%<&,%<(T%&,T-@-T(,rp,<&,'(5%C3*&,(6.8;;,P;.;,08;.;;;,D;.;;;,5&,'(5%C3*&,(87.;;;,P;.;,08;.;;;,D;.;;;,<,'(5%C3*&,(6.8;;,P&;.;,08;.;;;,D;.;;;,5,'(5%C3*&,(87.;;;,P&;.;,08;.;;;,D;.;;;,<:,'(5%C3*&,(6.8;;,P6;.;,08;.;;;,D;.;;;,5:,'(5%C3*&,(87.;;;,P6;.;,08;.;;;,D;.;;;,'(!&;;;.;,<&,'(5%C3*&,(&9.:;;,P;.;,08;.;;;,D;.;;;,5&,'(5%C3*&,(67.4;;,P;.;,08;.;;;,D;.;;;,<,'(5%C3*&,(&9.:;;,P&;.;,08;.;;;,D;.;;;,5,'(5%C3*&,(67.4;;,P&;.;,08;.;;;,D;.;;;,<:,'(5%C3*&,(&9.:;;,P6;.;,08;.;;;,D;.;;;,5:,'(5%C3*&,(67.4;;,P6;.;,08;.;;;,D;.;;;,<&,'(5%C3*,(&.9;;,P&=;.;,047.;;;,D;.;;;,5&,'(5%C3*,(&7.4;;,P;.;,047.;;;,D;.;;;,<,'(5%C3*,(&.9;;,P:;;.;,047.;;;,D;.;;;,5,'(5%C3*,(&7.4;;,P&;.;,047.;;;,D;.;;;,<:,'(5%C3*,(&.9;;,P6;.;,047.;;;,D;.;;;,5:,'(5%C3*,(&7.4;;,P6;.;,047.;;;,D;.;;;,'(!4;;.;,<&,'(5%C3*&,(&9.:;;,P&=;.;,047.;;;,D;.;;;,5&,'(5%C3*&,(67.4;;,P;.;,08;.;;;,D;.;;;,<,'(5%C3*&,(&9.:;;,P:;;.;,047.;;;,D;.;;;,5,'(5%C3*&,(67.4;;,P&;.;,08;.;;;,D;.;;;,<:,'(5%C3*&,(&9.:;;,P6;.;,047.;;;,D;.;;;,5:,'(5%C3*&,(67.4;;,P6;.;,08;.;;;,D;.;;;,<&,'(5%C3*,(&.9;;,P;.;,08;.;;;,D;.;;;,5&,'(5%C3*,(&7.4;;,P;.;,047.;;;,D;.;;;,<,'(5%C3*,(&.9;;,P&;.;,08;.;;;,D;.;;;,5,'(5%C3*,(&7.4;;,P&;.;,047.;;;,D;.;;;,<:,'(5%C3*,(&.9;;,P6;.;,08;.;;;,D;.;;;,5:,'(5%C3*,(&7.4;;,P6;.;,047.;;;,D;.;;;,-T(T5T&,'(CIEEEEEEE&EE$4;;$<,-T@P5T&,<&,'(5%C3*&,(6.8;;,P;.;,08;.;;;,D;.;;;,5&,'(5%C3*&,(87.;;;,P;.;,08;.;;;,D;.;;;,<,'(5%C3*&,(6.8;;,P&;.;,08;.;;;,D;.;;;,5,'(5%C3*&,(87.;;;,P&;.;,08;.;;;,D;.;;;,

<:,'(5%C3*&,(6.8;;,P6;.;,08;.;;;,D;.;;;,5:,'(5%C3*&,(87.;;;,P6;.;,08;.;;;,D;.;;;,<&,'(5%C3*,(;.;;;,P&=;.;,047.;;;,D;.;;;,5&,'(5%C3*,(;.;;;,P;.;,047.;;;,D;.;;;,<,'(5%C3*,(;.;;;,P:;;.;,047.;;;,D;.;;;,5,'(5%C3*,(;.;;;,P&;.;,047.;;;,D;.;;;,<:,'(5%C3*,(;.;;;,P6;.;,047.;;;,D;.;;;,5:,'(5%C3*,(;.;;;,P6;.;,047.;;;,D;.;;;,'(!&;;;.;,T-@-T@,-%<;,<&,'(5%C3*&,(;.;;;,P4.;,08;.;;;,D;.;;;,5&,'(5%C3*&,(;.;;;,P;.;,08;.;;;,D;.;;;,<,'(5%C3*&,(;.;;;,P&4.;,08;.;;;,D;.;;;,5,'(5%C3*&,(;.;;;,P&;.;,08;.;;;,D;.;;;,



<:,'(5%C3*&,(;.;;;,P64.;,08;.;;;,D;.;;;,5:,'(5%C3*&,(;.;;;,P6;.;,08;.;;;,D;.;;;,G

These commands yield the waveform in 0igure &;, which at first glance, looksvery similar to the waveform in 0igure 9. The difference is in the phase anglerelationship between the voltage and current. 'here the power swing would have ama#imum phase angle difference of 7;°, the outofstep condition has a ma#imumphase angle difference of &=;°. The phase angle relationship over time is shown in0igure &&.

0igure &;. 'aveform capture of an outofstep condition



0igure &&. Phase angle relationship of the outofstep condition vs time

The impedance trajectory is also split. !nstead of the circular path of the powerswing, the return portion of the trajectory is flipped &=;° so that it continues to the otherside of where the relay characteristics would be located. This is shown in 0igure &.

0igure &. !mpedance trajectory of outofstep condition

power swing out-of-step app guide_.docx

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