The frequency of the power system is an important indicator of the power quality of the power system. Its changes not only affect the users, but also affect the power transmission of the power grid. The power system is a dynamic system, and the under- or over-regulation of the generator speed control system will Changing the frequency of the generator When the generator rotor fails, it is often accompanied by a change in frequency. For example, when the generator has a loss of magnetism, the generator changes from the generator state to the motor state. At this time, the frequency of the motor rotor Hysteresis Synchronous Speed ​​In addition, judging whether the power system has low frequency oscillation is one of the important applications of frequency tracking. Therefore, frequency tracking of power systems is an important measure to ensure the safe and reliable operation of power systems, and must be taken seriously.
2 Fourier transform and wavelet transform Fourier analysis plays an extremely important role in digital signal processing and analysis. Let s(t) be the time signal, then the Fourier transform is compared with the time domain and frequency domain characteristics as shown in (a2) and (b2) respectively. It can be seen that the frequency characteristics of the Mexican hatchlet function and the Morlet wavelet function are Except for the center frequency (such as the fundamental frequency), other frequencies have different degrees of attenuation. If the signal is analyzed by the Mexicohat or Morlet wavelet transform, the fundamental component of the signal can be detected or analyzed without distortion. Ideally, the signal is only For the fundamental frequency signal, for example, during normal operation, the current and voltage signals of the power system are the same, but when the system is disturbed, the signal of the system no longer maintains a constant frequency, and the deviation always occurs more or less. In this case, the distortion occurs when the signal is subjected to the Mexico Hat wavelet transform or the Morlet wavelet transform. Table 1 shows the distortion when the signal is subjected to Morlet wavelet transform. Table 1 shows the distortion of the signal frequency (based on Morlet wavelet transform) , frequency domain center 50Hz) Tab.1DistortionofMorlet When the frequency is offset by ±2Hz, the signal is based on the characteristics of the trapezoidal wavelet transform. It is the advantage of trapezoidal wavelet transform. At present, wavelet analysis is applied to different fields of power system with its unique characteristics. In this paper, trapezoidal wavelet transform is applied in three cases to divide the power frequency signal of frequency timing change in power system.æŸ Case 1 The constituent elements of the signal sl(t) to be analyzed are: The selection of / is such that: from a certain time to to observe, at this time / equal to 50 Hz; after 4 cycles, arrive at time t, at this time / It is equal to 48 Hz, and the frequency is kept for 4.1 cycles; thereafter, at time t2t3t4tstf, t7, and later values, the values ​​of times to and t1 are sequentially repeated. It can be seen that S1(t) is an integrated frequency function.
(a3) The smoothing part and the detail parts (a4) and (a5) of the trapezoidal wavelet transform for si(t) are respectively two different algorithms for the frequency change of the trapezoidal wavelet transform of s1(t) with time. The characteristic curve. It can be seen from (a4) and (a5) that the trapezoidal wavelet transform can accurately capture the frequency variation characteristics of the signal, thereby realizing the real-time frequency tracking of the signal (for example, 1) 2), 3), 4) and ( B5)) is relative to (a), except that the frequency/ is changed from 50 Hz to 52 Hz.
Case 2 The constituent elements of the signal s2(t) to be analyzed are equal to the s(t) of case 1 where the selection of / is such that it starts from a certain time to, at this time / equals 50H; after 4 cycles The time t, / is equal to 49 Hz, and the frequency is kept for 4.1 cycles; thereafter, at time t2t3t4 t7 and later/values, the values ​​of the times t and t1 are sequentially repeated.
(a3) is a smooth portion and a detail portion of the trapezoidal wavelet transform for s2(t), respectively. (a4) and (a5) are characteristic curves obtained by two different algorithms for the frequency change of s2(t) with trapezoidal wavelet transform over time, as can be seen from (a4) and (a5), based on trapezoidal wavelet transform The same can capture the frequency recursive characteristics of the signal, so that the real-time frequency tracking of the signal (b) (for example, Figure (b5)) is relative to (a), except that the frequency / is changed from 50Hz to 51 Hz case when the frequency offset ± based on the characteristics of the trapezoidal wavelet transform 3 The constituent elements of the signal S3(t) to be analyzed are equal to the s(t) of case 1 where the selection of / is such that starting at a certain time t0 Observe, at this time / equal to 50Hz; after 4 cycles, arrive at time t1, / equal to 48.5 Hz, this frequency is kept for 4. 1 cycle; thereafter at time t2 and after, the value of / is the same as t. The value of t3 is equal to 51.5 Hz, and the frequency is kept for 4.1 cycles; at time t4t5tfft7t8t9t10 and later, the value of / is repeated at the time t0t1t2t3 / the value (a1) is the waveform of the original signal S2(t), (a2) and ( A3) is a trapezoidal wavelet transform for S2(t) (a4) and (a5) are characteristic curves obtained by two different algorithms for changing the frequency of s2(t) with time. It can be seen from (a4) and (a5) that the trapezoidal wavelet transform can also capture the frequency recursive characteristics of the signal, thereby realizing the real-time frequency tracking of the signal. In the operation of the power system, the generator occupies a very important position. When the stator winding is faulty, the fault characteristics are obvious, so it is easy to detect and judge. U. The following is the application of trapezoidal wavelet transform to analyze the signal characteristics of the power system generator's loss of magnetic fault. The data of the generator's loss of magnetic fault is from the generator dynamic model.
(a3) is a smooth portion and a detail portion of the trapezoidal wavelet transform for iA(t), respectively. (a4) and (a5) are characteristic curves of frequency with time obtained by two different algorithms after trapezoidal wavelet transform on iA(1). Correspondingly, (b1) is the waveform of the original signal ua(1), and (b2) and (b3) are the smoothed and detailed portions of the trapezoidal wavelet transform for UA(t), respectively. (b4) and (b5) are the characteristic curves of the frequency obtained by two different algorithms after the trapezoidal wavelet transform on uA(t), respectively. It can be seen that the fault is equivalent to access infinity due to generator failure. The system, so the frequency of the voltage is constant (50 Hz), but the frequency of the current has changed significantly, and the frequency components contained in the fault signal iA(t) can be clearly understood.
5 Conclusion The trapezoidal wavelet transform has good localization characteristics in time-frequency domain: its time domain characteristic is attenuated faster, so it can detect the amount of feature information required in the fault signal with a short time window; its frequency domain characteristics have Continuity and equal weighting are therefore applicable to the detection and analysis of fault signals with varying frequencies within a certain range. Therefore, the trapezoidal wavelet transform can accurately distinguish the frequency change information contained in the signal, which has strong advantages in realizing the frequency tracking of the power system, and is of great significance for improving the safe and reliable operation of the power system.
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