The frequency of the power system is an important indicator of the power system power quality. Its changes not only affect the users, but also affect the power transmission of the power grid. The power system is a dynamic system. The under-adjustment or over-adjustment of the generator speed control system Changing the frequency of the generator When the generator rotor fails, it is often accompanied by a change in frequency. For example, when a generator loses magnetization, the generator changes from the generator state to the motor state. At this time, the motor rotor frequency Hysteresis synchronous speed In addition, it is one of the important applications of frequency tracking to determine whether the low-frequency oscillation occurs in the power system. Therefore, frequency tracking of the power system is an important measure to ensure the safe and reliable operation of the power system and must be valued.

2 Fourier Transform and Wavelet Transform In the digital signal processing and analysis, Fourier analysis plays an extremely important role. Let s(t) be the time signal, then the frequency characteristics of the Mexicohat wavelet function and the Morlet wavelet function can be seen by comparing the Fourier transform to the time and frequency domain characteristics as shown in (a2) and (b2) respectively. Except for the center frequency (such as the fundamental frequency), other frequencies have different degrees of attenuation. Thus, if the signal is analyzed using the Mexicohat or Morlet wavelet transform, the fundamental frequency component of the signal can be detected or analyzed without distortion. Ideally, the signal is only For the fundamental signal, for example, during normal operation, the current and voltage signals of the power system are such that when the system is disturbed, the system signal no longer maintains a constant frequency, and deviations will always occur more or less. In this case, the signal is subjected to Mexicohook wavelet transform or Morlet wavelet transform, which will produce distortion. Table 1 shows the distortion produced when performing Morlet wavelet transform on the signal. Table 1. Distortion when the signal frequency deviates (based on the Morlet wavelet transform , Frequency domain center 50Hz) Tab.1DistortionofMorlet When the frequency offset is ± 2Hz, the signal is based on the characteristics of trapezoidal wavelet transform. Is the superiority of trapezoidal wavelet transform. Currently, wavelet analysis is applied to different areas of power system with its unique characteristics. This paper applies trapezoidal wavelet transform to three different situations respectively, and divides the power frequency signal with frequency timing change in power system.柝 Case 1 Let the constituent elements of the signal sl(t) to be analyzed be the one in which the selection of / is: from a time t0, this time / is equal to 50Hz; after 4 cycles it arrives at time t, at this time / It is equal to 48Hz, and the frequency is maintained for 4.1 cycles; thereafter, the values ​​of to and tl are repeated in order of time t2t3t4tstf, t7 and subsequent values. It can be seen that S1(t) is a comprehensive frequency function.

(a3) The smooth and detailed parts (a4) and (a5) of the trapezoidal wavelet transform for si(t) are the two different algorithms for frequency change of s1(t) with trapezoidal wavelet transform over time, respectively. The characteristic curve. From (a4) and (a5), it can be seen that the trapezoidal wavelet transform can accurately capture the frequency change 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/change from 50 Hz to 52 Hz.

Case 2 sets the constituent element of signal s2(t) to be analyzed equal to s(t) of case 1 where the selection is: from a time t0, this time is equal to 50H; after 4 cycles have passed At time t, / is equal to 49 Hz, and this frequency is maintained for 4.1 cycles; thereafter, at time t2t3t4 t7 and subsequent/values, the values ​​of time t and t1 are repeated in order.

(a3) The smooth and detailed parts of the trapezoidal wavelet transform for s2(t), respectively. (a4) and (a5) are the characteristic curves obtained by the two different algorithms for the frequency change of trapezoidal wavelet transform for s2(t), which can be seen from (a4) and (a5), based on trapezoidal wavelet transform. The same can capture the frequency shift characteristics of the signal so that real-time frequency tracking of the signal (b) (for example, figure (b5)) is relative to (a), except that the frequency/ is changed from 50 Hz to In the case of 51 Hz when the frequency shift is ± the characteristic based on the trapezoidal wavelet transform. Case 3 Let the constituent element of the signal to be analyzed S3(t) be equal to the case of s(t) where / is selected as follows: From a time t0 Observe that at this time/equal to 50 Hz; after 4 cycles arrive at time t1,/equal to 48. 5 Hz, this frequency is maintained for 4.1 cycles; thereafter at and after time t2, the value of / is the same as t. but the moment The value of t3 is equal to 51.5 Hz, and the frequency is maintained for 4.1 cycles. At times t4t5tfft7t8t9t10 and later, the value of / repeats the time t0t1t2t3 in order and the value (a1) is the waveform of the original signal S2(t), (a2) and ( A3) Trapezoidal wavelet transform for S2(t) And a sliding portion details. (a4) and (a5) are the characteristic curves derived from two different algorithms for the s2(t) incoming frequency change over time. From (a4) and (a5), it can be seen that the trapezoidal wavelet transform can also capture the frequency shift characteristics of the signal, thereby realizing the real-time frequency tracking of the signal. In the power system operation, the generator occupies a very important position in the generator. When the stator winding is faulty, the fault features are obvious, so it is easy to detect and determine U. The following uses the trapezoidal wavelet transform to analyze the power loss signal of the power system. The characteristic of the generator flux loss fault is the generator dynamic model.

(a3) The smooth part and the detail part of the trapezoidal wavelet transform for iA(t), respectively. (a4) and (a5) are the characteristic curves of the frequency of the iA(1) after the trapezoidal wavelet transform and then obtained by two different algorithms. Correspondingly, (b1) is the waveform of the original signal ua(1), and (b2) and (b3) are the smooth part and the detail part of the trapezoidal wavelet transform for UA(t), respectively. (b4) and (b5) are the characteristics of the frequency variation over time obtained by two different algorithms after performing trapezoidal wavelet transform on uA(t). It can be seen that the equivalent of access infinity is due to the failure of the generator. In the system, the frequency of the voltage is constant (50Hz), but the frequency of the current changes significantly, and the frequency components contained in the fault signal iA(t) can be clearly understood.

5 Conclusions The trapezoidal wavelet transform has good time-frequency localization characteristics: its time-domain characteristics decay faster, so it only needs a shorter time window to be able to detect the amount of feature information needed in the fault signal; its frequency domain characteristics have Continuity and equal weight are applicable to the detection and analysis of fault signals whose frequency is constantly changing 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 frequency tracking of the power system, and has important significance for improving the safe and reliable operation of the power system.

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