advanced spectral analysis of out-of-step operation of synchronous machines zbigniew leonowicz bsi...
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ADVANCED SPECTRAL ANALYSIS OF OUT-OF-STEP OPERATIONADVANCED SPECTRAL ANALYSIS OF OUT-OF-STEP OPERATION OF SYNCHRONOUS MACHINES OF SYNCHRONOUS MACHINES
Zbigniew Leonowicz Zbigniew Leonowicz
BSI Riken, ABSP Lab.BSI Riken, ABSP Lab. Wako-shi, Saitama, Japan
IntroductionThe out-of step operation conditions (loss of synchronism) of a synchronous machine may occur as a result of a power system three-phase fault. Fault
The power output of the machine is reduced as it is supplying a mainly inductive circuit. However, the input power to the generator from the turbine has not time to change during the short time of the fault and the rotor begin to gain speed to store the excess energy. If the fault persists long enough, the rotor angle will increase continuously and synchronism will be lost. The current waveforms in the stator winding contain three main components, which frequencies depend on the rotor slip. At the beginning of an asynchronous running, differences between the frequencies are small. Therefore, the identification of the components is difficult.
DetectionThe complex impedance measured at the machine terminals is compared with a proper characteristic on the complex impedance plane, to detect the asynchronous operation. The other methods used for identification of out-of-step operations are based on the rate of change of apparent resistance augmentation.The equal area criterionThe observations of phase differences between sub-stations Applications of neural networks.
At the beginning of an asynchronous running, differences between At the beginning of an asynchronous running, differences between the frequencies are small and the identification of the components the frequencies are small and the identification of the components is difficult.is difficult.
Use of FFT for spectral analysis Several performance limitations of the FFT:
Frequency resolution – ability to distinguish the spectral responses of two or more signals.Windowing of the data – leakage in the frequency domain.
Current Waveforms in the Stator Windings
•If the machine running in parallel with other devices is disturbed from its synchronous-state conditions, the rotor winding and the stator winding fluxes rotate with different velocities. •The angular velocities of the fluxes are equal to the angular frequencies of the alternating components of the rotor winding current.
The angular frequencies of the components are: and .
IFAC Symposium on Power Plants & Power Systems, June 8-12, 2003, SEOUL, KOREA
Fault Operation of Synchronous Generator
Generator data: salient-pole synchronous generator: Nominal power 200MVA, nominal voltage 13800 V, nominal frequency 50 Hz.
Modeled power system: Fault Duration 100 ms
T= 1s T=4s
Fault Duration 250 ms
ConclusionsWhen the synchronous running of a synchronous machine is lost, a current in the stator winding can be resolved into two or three components with different frequencies depending on the rotor slip. At the beginning of an asynchronous running, differences between the frequencies are small. For identification of the asynchronous operation, the frequencies of the current components are estimated. The appearance of additional current frequency components can be used as indicator of out-of-step operation of a synchronous machine. Decrease of the frequency differences of the detected current components over the time indicates that the generator is leaving the out-of-step state. Because of very small differences between the frequencies of the components, high-resolution spectrum estimation methods are needed. Therefore, subspace methods have been applied. Extensive investigations confirm the validity of the proposed method.
Tadeusz LobosTadeusz Lobos
Wroclaw University of TechnologyWroclaw University of Technology Wroclaw, Poland
Subspace Methods
•The subspace frequency estimation methods rely on the property that the noise subspace eigenvectors of a Autocorrelation Matrix are orthogonal to the eigenvectors spanning the signal space. The model of the signal in this case is a sum of random sinusoids in the background of noise of a known covariance function. The eigenvectors spanning the noise space are the ones whose eigenvalues are the smallest and equal to the noise power.
MUSICMUSIC
The correlation matrix of the signal vector
is
N-M smallest eigenvalues of the correlation matrix (matrix dimension N>M+1) correspond to the noise subspace and M largest correspond to the signal subspace. The matrices of eigenvectors are defined:
Enoise can be used to form a projection matrix PX for the noise subspaceThe MUSIC pseudospectrum is defined as:
and it exhibits sharp peaks at the signal frequencies where w=si.
TNjj ii ee 11 is
IssR 20
1
T
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M
ix AAE
Msignal eeeE 21 NMMnoise eeeE 21
1wEEwwPw T
noisenoiseT
noiseTjeP
;f s b ss s 1r ss
.
s 1 2 ss
~G T S
0 1 2 3 4 5 6-4
-3
-2
-1
0
1
t [s]
I
0 10 20 30 40 50 60-4
-2
0
2
4
6
8
10
12
f [Hz]0 10 20 30 40 50 60
-4
-2
0
2
4
6
8
10
12
f [Hz]
0 5 10 15 20-3
-2
-1
0
1
2
3
4
5
time [s]
ampl
itude
[p.u
.]
40 45 50 55 6010
0
102
104
106
108
1010
frequency [Hz]
mag
nitu
de
48.08 Hz
52.00 Hz
50.29 Hz
40 45 50 55 6010
0
102
104
106
108
frequency [Hz]
mag
nitu
de
48.58 Hz
50.29 Hz
48.73 Hz 51.27 Hz 48.83 Hz 50.68 Hz