Approximating a Power Swing and Out-of-Step Condition for Field Testing By Jason Buneo and Dhanabal Mani Megger, Ltd Jason.Buneo@megger.com Dhanabal.Mani@megger.com Abstract Testing a power swing or out-of-step scenario on modern protective relays can be a tricky task. Past methods of testing power swing and out of step conditions have often involved imprecise methods of applying voltages and currents to simulate impedances seen by the relay. By manually ramping the impedance trajectory, or playing several vector states where a specific impedance was applied, it was possible to initiate a power swing block or out-of-step trip in a protective device. However, with more advanced algorithms implemented into modern protective relays, previous methods of testing might not work. One method that has proven to work is applying a simulation of the power system, complete with all of the necessary sources and impedances of the elements under study. The output of the simulation can then be stored in a format suitable for field testing such as COMTRADE. This format can be played to the protective relays and the response measured. Although this method is effective, it can be daunting to personnel who may be required to test these schemes, but who may not have a background in power system protection or simulation. It is for this reason that a simplified method of testing power swing and out of step conditions without the use of complex simulations is desired. This paper will talk about a non-traditional method of that utilizes the superposition of two waveforms of dissimilar frequencies to achieve a power swing and out-of-step condition. The rate of change of impedance can be controlled as well as the minimum and maximum impedances, the number of pole slips, as well as the starting phase angle relationships. These parameters can be manipulated via basic formulas suitable for beginning field personnel. Background and Theory Power swing or out-of-step conditions are generally caused by unexpected changes in a power transmission system such as faults, load shedding, power plant trip outs, etc. In some cases, the power swing may be stable and return to normal operating conditions after a set period of time. In other cases, the swing may be unstable, and can cause serious damage to the generator sources on the system. In order to properly protect the generator and transmission system, protective relays employ various methods to determine if a swing is stable or unstable. [1] For engineers and technicians who need to test protective relays, either for commissioning, or maintenance purposes, the out-of-step and power swing functions can prove to be intimidating. Generally, testing these functions involves setting up a model of the power system and varying the parameters to yield a power swing or out-of-step condition seen by a protective relay. While desirable, this sort of testing might not always be available to personnel out in the field. In many cases, the person testing this function may need to improvise methods that are less than ideal to verify its operation. Some of these methods involved manually ramping the impedance trajectory, or playing several vector states where a specific impedance was applied at each state to simulate an impedance locus travelling across the R-X plane of the measurement zones. However, as protective relays have adopted more advanced algorithms, these on the fly methods will no longer work. The relay is looking for a smooth transition between the measurement zones, and if it does not see it, then it will not block the power swing or trip on the out-of-step. For most protective relays that contain power swing and out-of-step protection elements, their functions are governed by either resistive blinders or mho/quad characteristics in the R-X plane. The method of the actual detection may vary from manufacturer to manufacturer, but some form of characteristic is usually present. Examples of these characteristics are shown in Figures1 and.
Figure 1. Single Blinder Scheme with Impedance Characteristic [] Figure. Multiple Characteristic Scheme [3]
In order to satisfy the conditions for the power swing and out-of-step algorithms currently in use, a new method is proposed. By superimposing two waveforms of similar frequencies, a smooth impedance ramp can be achieved. This method is similar to a two source model in that both sources have similar frequencies and amplitudes. The rate of change of impedance can be controlled as well as the minimum and maximum impedances, the number of pole slips, as well as the starting phase angle relationships. The characteristic equation of the output waveform for the voltage and current is as follows: Eq. 1 ff II,VV (tt) = (AA 1 sin(ωω 1 tt + φφ 1 )) + AA sin(ωω tt + φφ ) Where: A 1 = Magnitude of the first current/voltage source in RMS values ω 1 = π*frequency Source1, (Frequency is in Hz, ω 1 is in rad/s) φ 1 = Initial phase angle of current/voltage source 1 in degrees A = Magnitude of the second current/voltage source in RMS values ω = π*frequency Source, (Frequency is in Hz, ω is in rad/s) φ = Initial phase angle of current/voltage source in degrees t = the time of the event in seconds Using arbitrary values for Equation 1, Figure 3 shows the plot of a voltage and current waveform with the following parameters: V 1 = 49.5 V, V =19.5 V, I 1 =16.75A, I =13.75A, F 1 =60 Hz, F = 59 Hz, φ 1Current = 0, φ Current = 0, φ 1Voltage = 0, φ Voltage = 0 Figure 3. Superimposed voltage and current waveforms Both the voltage and current waveforms decrease and increase at the same time and remain in phase for the duration of the waveform plot. This is not the behavior of a power swing or out-of-step condition. To change this, the phase current needs to be offset by 180. The option is to either change either φ 1Current or φ Current. By changing φ 1Current, the phase angle will initially start 180 out of phase and then slowly come back into phase, then go back out, and repeat indefinitely. Since it is desirable to control the phase angle from the start, φ Current will be set to 180. This will allow the two waveforms to start in phase and then slowly go out of phase and come back into phase, and repeat. A plot of the waveforms with the appropriate phase shift is shown in Figure 4. Figure 4. Plot of voltage and current waveforms with current offset by 180 In Figure 4, the voltage and current start in phase, then about a quarter of the way through the swing, it goes out of phase by 90, then comes back into phase, then goes out of phase by -90 at ¾ of the swing, and back into phase at the end of the swing. This is the general form of the power swing waveform.
Applying the Method Power Swing To apply a power swing, the following parameters need to be defined first. 1. The Maximum Impedance, Z max, of the Power Swing/Out-of-Step needs to be defined. This will be based on the outer most characteristic that is tracking the impedance. It is recommended that the maximum impedance be greater than the largest blinder/characteristic impedance, but not so large that the trajectory of the swing exits the characteristic prematurely. A secondary maximum impedance, Z max, can also be defined. This would be the maximum impedance that would be just inside the blinders or characteristic defined by the relay.. The Minimum Impedance, Z min, of the Power Swing/Out-of-Step will be the stopping point of the swing/step within the blinders/characteristic. 3. The Source Frequencies will determine how long of a duration a single power swing or out-ofstep condition will be. The source frequencies will also factor in determining the rate of change of the trajectory of the impedance. The larger the difference in frequency between the two sources, the faster the swing/step, and the smaller the difference, the slower the swing/step. 4. The Starting Phase Angle needs to be defined so that proper loading conditions can be simulated properly. Here is how to create a power swing with a maximum impedance of 15 Ω, a minimum impedance of 1 Ω, a Source 1 Frequency of 60 Hz, a Source Frequency of 59 Hz, and a starting Phase Angle of 0. The first parameter that we can determine is how long a complete power swing cycle will take, t Swing. This is giving by Eq.. Eq. tt SSSSSSSSSS = 1 ff 1 ff (ss) Eq. 3 tt SSSSSSSSSS = 1 60 59 = 1 ss When applying this method to any type of test routine, t Swing should be the maximum time set for how long the swing should be applied. If multiple turns are desired, then maximum time would be the number of turns times t Swing. Next will be solving for the currents and voltages that should be applied to the relay. To start, only the A phase voltages and currents will be discussed. B and C phases are identical to A, with only the appropriate phase shifts taking place. A nominal voltage should be defined for the maximum impedance, and a fault voltage should be defined for the minimum impedance. Take care in choosing a fault voltage because some of the impedances could still be quite large, with large being defined as around 15 Ω or greater. If the fault voltage is too small, negative valued currents would end up being calculated to create the correct conditions. If that is the case, increase the fault voltage until the currents are at an acceptable level. As a rule of thumb the nominal voltage, V nom, is 69 V line-toground, and the fault voltage, V fault, is around 30 V line-to-ground. The value of V fault can change depending on the impedance and the current required from the test set. The moniker of V fault can also be a little misleading. A power swing event may not necessarily require the extreme values of traditional fault voltages. The swing of impedance may only go from a large value to a slightly smaller value. Such would be the case if the user wanted to swing from 89Ω to 50 Ω. The required fault voltage would not be much less than what was required for starting impedance. The equations for the two voltages for phase a are shown in the following equations. Eq. 4 Eq. 5 Eq. 6 VV 1 = VV ffffffffff + VV nnnnnn VV ffffffffff VV 1 = 30 + 69 30 = 49.5 VV VV = VV nnnnnn VV ffffffffff
Eq. 7 VV = 69 30 = 19.5 VV Then the two currents for I 1 and I will be solved. Eq. 8 II 1 = VV ffffffffff VV ffffffffff VV nnnnnn ZZ mmmmmm ZZmmmmmm ZZ mmmmmm Eq. 9 II 1 = 69 1 30 1 69 15 = 17.3 AA Eq. 10 II = VV ffffffffff VV nnnnnn ZZ mmmmmm ZZmmmmmm Eq. 11 II = 69 1 69 15 = 1.7 AA Other parameters can now be solved such as the rate of change of impedance. Since the swing goes from a maximum impedance to a minimum and back again, the rate should only be calculated based on the time it takes to go from the maximum to the minimum. This is shown in Eq. 1. Eq. 1 ZZ rrrrrrrr = ZZ mmmmmm ZZ mmmmmm tt SSSSSSSSSS Eq. 13 ZZ rrrrrrrr = 15 1 1 = 7 Ω/ss When starting in the pre-fault mode for testing, it is handy to be at the same current level as the starting current for the swing so that there are no discontinuities when the ramp begins. This is minimum current, which is shown in Eq. 14. Eq. 14 II mmmmmm = II 1 II Eq. 15 II mmmmmm = 17.3 1.7 = 4.6 AA For practical applications, three states can be used to simulate a pre-fault, fault and post-fault state. Additional States can be added as well such as including a fault during a swing or out-of-step condition. Figure 5 shows a captured waveform from a protective relay during a power swing block condition. The impedance locus entered the outer characteristic and oscillated for two turns before exiting and returning to a stable condition.
Figure 5. Event record of a power swing block with multiple turns Figure 6 show a power swing trip condition where the impedance locus has entered the protective characteristics and remains inside the inner characteristic for the duration of the turns. Upon exiting the power swing trip function is triggered in the relay. Figure 6. Power swing trip condition with multiple turns While the bulk of this testing method has been shown, there are other parameters that would be useful to the user in determining what is occurring during the test. One parameter would be the impedance trajectory of the power swing. This should be plotted in the R-X plane so the user can trace the locus path. The instantaneous impedance, Z, is calculated, followed by the phase angle, θ. The instantaneous impedance, Z, is defined in Equation 16.
Eq. 16 ZZ = VV II The phase angle, θ, is defined in Equation 17. Eq. 17 θθ = (tt VVVVVVVVVV tt IIIIIIIIII ) 1 ff 360 Where: t Vzero = time of the voltage magnitude zero crossing in seconds t Izero = time of the current magnitude zero crossing in seconds f = frequency of the waveform in Hz The phase angle of power swing is shown in Figure 7. Figure 7. Phase angle of the power swing in degrees vs time in seconds The frequency of two superimposed waveforms will not be constant. Signal processing techniques should be used to take and accurate measurement of the frequency as well as the phase angle. Equation 18 is given as a reference and will not provide a very accurate phase angle unless a very large sampling rate is used to determine the zero crossing of the waveform. Once the impedance and phase angle are known, then the resistance, R, and reactance, X, of the impedance can be determined as shown in Equations 18 and 19 respectively. Eq. 18 Eq. 19 RR = ZZ ccccccθ XX = ZZ ssssssss Once the resistance and reactance are determined, they can be plotted. This is shown in Figure 8.
Figure 8. Trajectory of impedance during a power swing The trajectory starts out at the maximum impedance of 15 Ω and travels in an arc towards the minimum impedance of 1 Ω, and then circles back towards 15 Ω. The process will repeat if the swing is unstable. To simulate an unstable swing, simply increase the duration of the swing in even multiples. Out-of-Step Applying an out-of-step condition is very similar to applying a power swing condition. The only difference is that instead of the impedance turning around when the minimum impedance trajectory is reached, the trajectory will continue through the origin and exit out of the other side of the characteristic. In order to achieve this a few things need to be done first. The total time of the out of step condition will be the same as the total time for a power swing, t Swing. However, the changes need to be made at the halfway point of the total time in order to create an outof-step. This time is important, so it will be called, t event, and is equal to ½ the time of t Swing as shown in Eq. 0. Eq. 0 tt eeeeeeeeee = tt SSSSSSSSSS At time t event, the frequency and phase angles of currents I 1 and I need to be swapped. This will create a waveform that will continue to a phase angle difference between the voltage and current of 180. All other calculations are the same. The waveform in Figure 9 is very similar to that of Figure 5 and 6, but convey two totally different things. The difference is in the phase angle relationship between the voltage and current. Where the power swing would have a maximum phase angle difference of 90, the out-of-step condition has a maximum phase angle difference of 180. The phase angle relationship over time is shown in Figure 10.
Figure 9. Waveform capture of an out-of-step condition Figure 10. Phase angle relationship of the out-of-step condition vs time The impedance trajectory is also split. Instead of the circular path of the power swing, the return portion of the trajectory is flipped 180 so that it continues to the other side of where the relay characteristics would be located. This is shown in Figure 11.
Figure 11. Impedance trajectory of out-of-step condition The trajectory of the out-of-step impedance is different than what would be normally seen in a more sophisticated simulation scenario. The almost sinusoidal path is a result of the phase angle being tied to the natural slip frequency between the two superimposed waveforms. This, however, does not detract from its ability to successfully test an out-of-step function. Conclusions A non-traditional method of that utilizes the superposition of two waveforms of dissimilar frequencies to achieve a power swing and out-of-step condition has been discussed. This method vastly simplifies the often complex routines of power system simulation to provide a field applicable approach to testing these functions. The parameters needed to control the test were derived from straight forward algebraic equations. The rate of change of impedance can be controlled as well as the minimum and maximum impedances, the number of pole slips, as well as the starting phase angle relationships. References 1. Power Swing and Out-of-Step Considerations on Transmission Lines, A report to the Power System Relaying Committee of the IEEE Power Engineering Society, Working Group D6, 005. SEL-700G Generator and Intertie Protection Relays Instruction Manual, 011 3. D60 Line Distance Protection System Instruction Manual, Revision 5.7X, GEK-113519B, 010