CN1382995A - Digital measuring method of frequency and phase - Google Patents

Abstract

The invention relates to a digital measurement method for frequency and phase, belonging to the technical field of circuit parameter measurement. The method of the present invention samples the AC input signal, obtains two signals with a phase difference of 90° by means of two sets of preprocessing, and then calculates the phase-locked data based on the magnitude of the two signals, and further realizes the frequency and phase based on the phase-locked structure. Measurement. In this way, the phase information contained in the signal waveform itself can be fully utilized, and the phase-locked data can be updated according to the sampling speed, which improves the analysis accuracy of phase discrimination, improves the speed of phase-locked tracking, and reduces the measurement time. In addition, the phase identification link of the method of the present invention is obtained by taking the difference between the locked phase and the locked phase. Therefore, when the phase-locking is basically stable, the phase-locking phase can approach the locked phase with zero mean deviation, which fundamentally overcomes the problem that the phase is only calculated based on the zero-crossing point and is seriously disturbed by noise, and the phase measurement accuracy is greatly improved.

Description

A Digital Measurement Method of Frequency and Phase

technical field

The invention relates to a digital measurement method of frequency and phase. The method measures the frequency and phase data of an AC input signal of a certain frequency based on a phase-locking principle, and belongs to the technical field of circuit parameter measurement.

Background technique

In the fields of communications, home appliances, instrumentation, and automatic control, it is often necessary to measure the frequency of an AC signal and its phase at a certain moment. A traditional method of measuring frequency and phase is based on a phase-locked loop design. Referring to the digital phase-locking technology for AC signals introduced in the book "Phase-Locked Loop: Principles, Design and Application" with the international standard number 0070050503, the method for measuring signal frequency and phase as shown in Figure 1 can be obtained. The input AC signal u first undergoes shaping processing based on the zero-crossing comparison principle to obtain a square wave signal u' in the form of a digital pulse; the signal u' is processed by digital phase detection and loop filtering to obtain the frequency division number N; the frequency division number N control The controllable oscillation signal generation part realized by frequency division generates a counting pulse signal; the counting pulse is then divided by M times to obtain a phase-locking signal; the phase-locking signal is fed back to the digital phase-detection part, thus forming a phase-locking system feedback loop. When the phase lock is stable, the frequency f of the locked signal is inversely proportional to the frequency division number N obtained by loop filtering. Let this inverse coefficient be G, then the frequency f of the AC signal to be measured can be obtained according to the formula f=G/N. On the other hand, if the counting pulse signal generated by the oscillating signal generation part is counted, and the counting process is cleared according to the rising edge or falling edge of the signal u', a counting value can be obtained, and the counting value is converted And phase compensation can get the phase data of the AC signal.

There are some deficiencies in the above-mentioned frequency and phase measurement method based on the phase-locked loop. First of all, the method of phase-locking the signal after shaping can only measure the frequency and phase according to the zero-crossing point of the AC signal, but does not use the phase angle information contained in the amplitude change of the AC signal itself, so the time for the phase-locked loop to stabilize It is often several times the period of the locked signal, and the measurement speed of frequency and phase is relatively slow. Second, the pulse count before obtaining the phase data needs to be cleared by the rising or falling edge of the signal u′, that is, the measurement of the phase depends on the detection of the zero-crossing point of the input AC signal u, but due to the noise on the zero-crossing point Offset, the accuracy of zero-crossing detection will seriously affect the measurement accuracy of phase data. Third, the frequency of counting pulses generated by the oscillation signal generation part after the phase-locking is stable is M times the frequency of the locked signal, and the number of phase data changes in one cycle also depends on the size of M. The larger M is, the shorter the span of phase changes will be. The smaller the value, the finer the phase measurement. However, if M is too large, the stability of the phase-locked system will also be deteriorated. Fourth, the effective number of digits of the controllable frequency division data N of the input oscillating signal generating part will affect the measurement accuracy of the measured frequency data f, and to increase N, it is necessary to increase the fixed frequency signal required by the oscillating signal generating part source frequency, or complex frequency division techniques with fractional control bits are required. Finally, the above frequency and phase measurement methods are difficult to implement in a microprocessor, which is not conducive to design and popularization.

Contents of the invention

The purpose of the present invention is to propose a digital measurement method of frequency and phase, which will also be designed based on the principle of phase locking, but it is hoped that it can overcome the shortcomings of the above-mentioned traditional phase locking method for measuring frequency and phase, so that the measurement system can fully utilize The information contained in the change of the AC signal waveform itself can quickly lock the measured signal, and no longer rely solely on the zero-crossing point of the signal to calculate the phase, which essentially improves the phase measurement accuracy. In addition, the method will be designed based on a digital signal processing method, resulting in improvements in measurement accuracy and measurement speed and ease of control. Finally, the method will facilitate easy adoption of microprocessor-based software implementations.

The digital measuring method of the frequency and the phase that the present invention proposes comprises the following steps:

1. Simultaneously perform the first set of sampling preprocessing and the second set of sampling preprocessing on the AC input signal u(t) whose frequency and phase need to be measured, to obtain discrete signals u ₁ (n) and u ₂ (n) respectively. If the upper frequency limit of the input AC signal u(t) to be tested is f _max and the lower frequency limit is f _min , the aforementioned two sampling preprocessing processes should select the same sampling frequency. If the sampling frequency is set to F _s , then F _s should be greater than 3f _max ; in addition, the two sets of sampling preprocessing processes should also meet the following conditions:

上式对f_min＜f＜f_max成立，而且在满足测量精度要求的情况下，上述等式可以存在一定的误差。Suppose the input AC signal to be tested is u(t)=U _m sin(2πft+θ), where f is the frequency of the AC signal and satisfies f _min <f<f _max , θ is the initial phase of the AC signal, Then after u(t) is preprocessed by the first group of samples, the obtained signal u ₁ (n) should have the following form: $u_1\left(\mathrm{no}\right)=k_1\left(f\right)u_m\sin (2\mathrm{\&pi;}\frac{f}{f_{\mathrm{the\; s}}}\mathrm{no}+\mathrm{\&theta;}+{\mathrm{\&theta;}}_1\left(f\right))$ After the signal u(t) is preprocessed by the second set of samples, the obtained signal u ₂ (n) should have the following form: $u_2\left(\mathrm{no}\right)=k_2\left(f\right)u_m\sin (2\mathrm{\&pi;}\frac{f}{f_{\mathrm{the\; s}}}\mathrm{no}+\mathrm{\&theta;}+{\mathrm{\&theta;}}_2\left(f\right))$ Among them, the gain function k ₁ (f), gain function k ₂ (f), phase shift function θ ₁ (f), and phase shift function θ ₂ (f) are all functions related to the input signal frequency f, and satisfy the following constraints :

The above formula holds true for f _min < f < f _max , and in the case of meeting the measurement accuracy requirements, the above equation may have certain errors.

2. Combining the discrete digital signals u ₁ (n) and u ₂ (n) obtained in the first step above into the coordinates of point A in the Cartesian coordinate system with the origin O (u ₂ (n), u ₁ ( n)), then the resulting vector The included angle with the positive direction of the horizontal axis will be used as the locked phase data α ₀ (n).

3. Combine the phase-locked data α ₀ (n) obtained in the second step above with the phase-locked phase data fed back from the output frequency f(n) and processed by integration and following step 7 phase jump adjustment α'(n) takes the difference to get the phase error Δα(n).

同时使测量过程的传递函数 稳定，并且使具有低通滤波性能，H′(s)的通带截止频率f_LF小于被锁信号频率的下限f_min。4. Process the phase error Δα(n) obtained in the third step above through loop filtering to obtain the frequency f(n) of the signal under test; during the above loop filtering process, its complex frequency domain transfer function H _LP (s) is of the form:

While making the transfer function of the measurement process stable and make It has low-pass filtering performance, and the cut-off frequency f _LF of H'(s) is smaller than the lower limit f _min of the locked signal frequency.

5. The frequency f(n) of the measured signal obtained in the above step 4 and the phase-locked phase data α'(n) obtained in the following step 7 are integrated and accumulated according to the following formula: ${\mathrm{\&alpha;}}_1\left(\mathrm{no}\right)={\mathrm{\&alpha;}}^{\&prime;}(\mathrm{no}-1)+2\mathrm{\&pi;}\&CenterDot;\frac{f\left(\mathrm{no}\right)}{f_{\mathrm{the\; s}}}$ Intermediate phase data α ₁ (n) is obtained.

6. Perform quadrant jump detection on the phase-locked data α ₀ (n) obtained in the second step above to obtain jump detection data J(n). The judgment threshold constant of this jump detection is set to J _TH , and the data J _TH should satisfy constraints, so the relationship between the jump detection data J(n) and the locked phase α ₀ (n) can be expressed according to the following formula:

7. Add the intermediate phase data α ₁ (n) obtained in the above-mentioned step 5 and the jump detection data J(n) obtained in the above-mentioned step 6, that is, α'(n)=α ₁ (n)+J( n) to obtain the phase-locked phase data α'(n) for inputting to the above-mentioned step 3 to form a phase-locked loop.

8. Perform phase compensation and data adjustment processing on the intermediate phase data α ₁ (n) obtained in the sixth step above, that is, α(n)=α ₁ (n)-θ ₁ (f(n))+K·2π, Among them, the function θ ₁ (f) is the phase shift function generated by the first group of sampling preprocessing on the input signal in the first step above, K is an adjustment coefficient, and its value is such that α(n) satisfies 0≤α(n )<2π, the final data α(n) is the signal phase to be measured.

The digital measurement method of frequency and phase that the present invention proposes still utilizes the working principle of phase-locked loop from basic structure, by the phase tracking characteristic of feedback loop, the 4th step in the above-mentioned inventive step measures the frequency of signal, The current phase of the signal is measured in the last eighth step of the inventive steps described above. However, the method of the present invention no longer adopts the zero-crossing shaping preprocessing method for the input signal, but directly samples the AC signal, and obtains two signals u ₁ (n) and u ₂ ( n), and then calculate the phase-locked data α ₀ (n) based on the two signal magnitudes. In this way, the phase information contained in the signal waveform can be fully utilized, and the phase-locked data can be updated according to the sampling speed, thereby improving the analysis accuracy of phase identification, and at the same time improving the speed of phase-locking tracking and reducing measurement time. In addition, the phase identification link of the method of the present invention is obtained by taking the difference between the locked phase α ₀ (n) and the locked phase α'(n). Therefore, when the phase-locking is basically stable, the phase-locking phase can approach the locked phase with zero mean deviation, which fundamentally overcomes the problem that the phase is only calculated based on the zero-crossing point and is seriously disturbed by noise, and the phase measurement accuracy is greatly improved. Finally, it should be pointed out that, except for the signal sampling processing step in the first step, other processing links can be designed and realized by software. It is relatively easy to control the speed, precision and stability of the entire measurement process by adjusting design parameters and data accuracy, and this measurement process can be conveniently realized based on various micro-processing chips.

Description of drawings

Fig. 1 is a functional block diagram of an existing method for measuring signal frequency and phase based on a phase-locked loop.

Fig. 2 is a functional block diagram of the digital measurement method of frequency and phase of the present invention.

Fig. 3 is a waveform curve obtained after the input signal is respectively subjected to the first group of sampling preprocessing and the second group of sampling preprocessing in the first embodiment of the present invention.

Fig. 4 is a block diagram of realization of loop filtering processing in the first embodiment of the present invention.

Fig. 5 is an amplitude-frequency characteristic curve of the transfer function H'(s) in the first embodiment of the present invention.

Fig. 6 is a phase-locked tracking frequency curve of the measurement process in the first embodiment of the present invention.

Fig. 7 is a phase tracking curve in the interval of 0-0.4 seconds in the first embodiment of the present invention.

Fig. 8 is a phase tracking curve in the interval of 1-1.4 seconds in the first embodiment of the present invention.

Specific implementation method

The first embodiment of the digital frequency and phase measurement method of the present invention is used to measure the frequency and phase of an AC voltage signal around 50 Hz, and its realization principle block diagram is shown in FIG. 2 . The specific processing steps are as follows:

1. For the AC signal u(t) whose frequency and phase need to be measured and whose frequency is in the range of 45-65Hz, first perform analog-to-digital conversion on the signal u(t) at the sampling frequency F _s =1000Hz, and further perform discrete data conversion The first group of phase-shifting filter F1 processing to obtain the signal u ₁ (n), thus completing the first group of sampling preprocessing; with the same sampling frequency F _s = 1000Hz, the analog-to-digital conversion is performed on the signal u(t), and the discrete The data is processed by the second group of phase-shift filtering F2 to obtain the signal u ₂ (n), thereby completing the second group of sampling preprocessing.

The above-mentioned first group of phase-shifting filters F1 is an infinite impulse response IIR type low-pass digital filter, and its frequency-domain transmission characteristic H _F1 (e ^jω ) has the following form: $h_{f1}\left(e^{\mathrm{j\&omega;}}\right)=\frac{B1\left(1\right)+B1\left(2\right)e^{-\mathrm{j\&omega;}}+B1\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}+B1\left(4\right)e^{-\mathrm{<figure-callout\; id="3"\; label="j"\; filenames="A0211688500152.png"\; state="\{\{state\}\}">j</figure-callout>}3\mathrm{\&omega;}}}{A1\left(1\right)+A1\left(2\right)e^{-\mathrm{j\&omega;}}+A1\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}+B1\left(4\right)e^{-\mathrm{<figure-callout\; id="3"\; label="j"\; filenames="A0211688500152.png"\; state="\{\{state\}\}">j</figure-callout>}3\mathrm{\&omega;}}}$ The specific coefficients are as follows:

B1=[-0.081603248, -0.6662151, 2.0287446, -1.3020016]

A1=[1.3020016, -2.0287446, 0.6662151, 0.081603248]

According to the theory of digital filter design, digital filter F1 is causal, that is, achievable. And further analysis shows that this filtering process is stable.

The above-mentioned second group of phase-shifting filters F2 is also an infinite impulse response IIR type low-pass digital filter, and its frequency domain transfer characteristic H _F2 (e ^jω ) has the following form: $h_{f2}\left(e^{\mathrm{j\&omega;}}\right)=\frac{B2\left(1\right)+B2\left(2\right)e^{-\mathrm{j\&omega;}}+B2\left(3\right)e^{-,2\mathrm{\&omega;}}}{A2\left(1\right)+A2\left(2\right)e^{-\mathrm{j\&omega;}}+A2\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}}$ The specific coefficients are as follows:

B2 = [-0.37078953, 1.2327431, -0.94007795]

A2 = [0.94007795, -1.2327431, 0.37078953]

According to the digital filter design theory, the digital filter F2 is also causal, that is, it can be realized. And further analysis shows that this filtering process is stable.

The amplitude gain of these two groups of digital filters is 1 within the range of 45-65Hz, and their phase-shift characteristics differ by 90°. If there is a sinusoidal AC signal u(t)=sin(2π×50×t) (volts) with an amplitude of 1 and a frequency of 50Hz, the analog-to-digital conversion of u(t) according to the sampling rate F _s =1000Hz The signal is u(n), the output signal u ₁ (n) is obtained after the first group of sampling preprocessing, and the output signal u ₂ (n) is obtained after the second group of sampling preprocessing, then the 100th to 150th The actual waveform curves of u(n), u ₁ (n) and u ₂ (n) within the range of sampling points are shown in Figure 3, where u(n), u ₁ (n) and u ₂ (n) The curves correspond to u, u1 and u2 in Figure 3, respectively. It can be seen from the figure that the u ₂ (n) signal is just 90° ahead of the u ₁ (n) signal in terms of phase relationship.

与横轴正方向的夹角将用以作为被锁相位数据α₀(n)。实施例中取-π≤α₀(n)＜π，则这个处理过程也可以按照如下公式进行计算： 2. Combining the discrete digital signals u ₁ (n) and u ₂ (n) obtained in the first step above into the coordinates of point A in the Cartesian coordinate system with the origin O (u ₂ (n), u ₁ ( n)), then the resulting vector

The included angle with the positive direction of the horizontal axis will be used as the locked phase data α ₀ (n). In the embodiment, if -π≤α ₀ (n)<π, this process can also be calculated according to the following formula:

3. Combine the phase-locked data α ₀ (n) obtained in the second step above with the phase-locked phase that is fed back from the output frequency f(n) and obtained after integration and phase jump adjustment in the seventh step below Take the difference of the data α′(n) to get the phase error Δα(n), the calculation formula is:

Δα(n)=α ₀ (n)-α′(n)

4. The frequency f(n) of the locked signal is obtained by processing Δα(n) obtained in the third step above through loop filtering. This loop filtering process can be implemented with reference to the principle structure in FIG. 4 . The specific process is: the phase error Δα(n) gets y ₁ (n) after the integral link; at the same time, the phase error Δα(n) also gets y ₂ (n) through the proportional delay link; for y ₁ (n) and y ₂ (n) sum to get y(n), that is, y(n)=y ₁ (n)+y ₂ (n); y(n) gets the signal frequency f(n) to be measured through the first-order inertia link .

Among them, the calculation formula of the integral link is:

y ₁ (n)=y ₁ (n-1)+0.0362666·Δα(n) Therefore, the complex frequency domain transfer function form of the integration link can be approximately expressed as: $h_1\left(\mathrm{the\; s}\right)=\frac{36.2666}{\mathrm{the\; s}}$ The formula for calculating the proportional delay link is:

y ₂ (n)=0.804868·y ₂ (n-1)+0.708540·Δα(n) The complex frequency domain transfer function of the proportional delay link is approximated as: $h_2\left(\mathrm{the\; s}\right)=\frac{880.3179}{\mathrm{the\; s}+242.4401}$ The calculation formula of the inertia link is:

f(n)=0.932642f(n-1)+0.067358y(n) The form of the complex frequency domain transfer function of the inertial link is approximated as: $h_3\left(\mathrm{the\; s}\right)=\frac{f\left(\mathrm{the\; s}\right)}{\mathrm{the\; y}\left(\mathrm{the\; s}\right)}=\frac{1}{0.013846\mathrm{the\; s}+1}$

Therefore, the form of the complex frequency domain transfer function H _LP (s) of the entire loop filtering processing part is: $h_{\mathrm{LP}}\left(\mathrm{the\; s}\right)=(h_1\left(\mathrm{the\; s}\right)+h_2\left(\mathrm{the\; s}\right))\&Center\; Dot;h_3\left(\mathrm{the\; s}\right)=\frac{66198.5\&Center\; Dot;\mathrm{the\; s}+635019}{\mathrm{the\; s}({\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+314.668\&Center\; Dot;\mathrm{the\; s}+17509.8)}$ F: $h_0\left(\mathrm{the\; s}\right)=h_{\mathrm{LP}}\left(\mathrm{the\; s}\right)\&CenterDot;\mathrm{the\; s}=\frac{66198.5\&Center\; Dot;\mathrm{the\; s}+635019}{{\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+314.668\&Center\; Dot;\mathrm{the\; s}+17509.8}$

Thus, the calculated transfer characteristics of the phase-locked system are: $h\left(\mathrm{the\; s}\right)=\frac{\mathrm{the\; s}\&Center\; Dot;h_0\left(\mathrm{the\; s}\right)}{{\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2\mathrm{\&pi;}{h}_0\left(\mathrm{the\; s}\right)}=\frac{{66198.5\&CenterDot;\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+635019\&Center\; Dot;\mathrm{the\; s}}{{\mathrm{the\; <figure-callout\; id="4"\; label="s"\; filenames="A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^4+314.668\&Center\; Dot;{\mathrm{the\; <figure-callout\; id="3"\; label="s"\; filenames="A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^3+17509.8\&Center\; Dot;{\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+415937\&CenterDot;\mathrm{the\; s}+3989940}$ The four poles of H(s) are: -251.334, -25.1324 and -19.1008±j·16.3345. According to the control theory, the phase-locked system H(s) is stable. Then, the transfer function H'(s) is: $h^{\&prime;}\left(\mathrm{the\; s}\right)=\frac{h_0\left(\mathrm{the\; s}\right)}{{\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2\mathrm{\&pi;}\&CenterDot;h_0\left(\mathrm{the\; s}\right)}=\frac{66198.5\&Center\; Dot;\mathrm{the\; s}+635019}{{\mathrm{the\; <figure-callout\; id="4"\; label="s"\; filenames="A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^4+314.668\&CenterDot;{\mathrm{the\; <figure-callout\; id="3"\; label="s"\; filenames="A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^3+17509.8\&Center\; Dot;{\mathrm{the\; <figure-callout\; id="2"\; label="s"\; filenames="A0211688500142.png,A0211688500152.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+415937\&CenterDot;\mathrm{the\; s}+3989940}$ The amplitude-frequency characteristic curve of H'(s) is shown in Fig. 5, and its abscissa is a logarithmic coordinate system. From the amplitude-frequency characteristics of H'(s), it can be seen that H'(s) has low-pass filter characteristics, and the amplitude-frequency characteristics of H'(s) have dropped below -35dB after greater than 20Hz.

5. The frequency f(n) of the measured signal obtained in the above step 4 and the phase-locked phase data α'(n) obtained in the following step 7 are integrated and accumulated according to the following formula:

α ₁ (n)=α′(n-1)+0.002π·f(n) to obtain intermediate phase data α ₁ (n).

跳变检测数据J(n)的计算公式是：

6. Perform quadrant jump detection on the phase-locked data α ₀ (n) obtained in the second step above to obtain jump detection data J(n). Set the judgment threshold constant of jump detection as J _TH =4, since f _max =65Hz, so the data J _TH satisfies

The calculation formula of jump detection data J(n) is:

7. Add the intermediate phase data α ₁ (n) obtained in the above-mentioned step 5 and the jump detection data J(n) obtained in the above-mentioned step 6, that is, α'(n)=α ₁ (n)+J( n) to obtain phase-locked phase data α'(n) for inputting to the third step above to form a phase-locked loop.

8. Perform phase compensation and data adjustment processing on the intermediate phase data α ₁ (n) obtained in the sixth step above. In the first step above, the phase shift function generated by the first group of sampling preprocessing on the input signal can be calculated by the following approximate formula (unit: radian)

θ ₁ (f)＝0.822384-0.0574974·f+0.000256414·f ²

(45≤f≤65) So, the output measured phase (unit: radian) is:

α(n)=α ₁ (n)-θ ₁ (f(n))+K·2π Among them, K is an adjustment coefficient whose value makes α(n) satisfy 0 ≤ α(n)<2π integer.

The first embodiment of the present invention is used to measure the frequency and phase of an input signal. The input signal is a sinusoidal AC signal u(t) with a frequency of 50 Hz and a fundamental wave amplitude of 1 volt within 0 to 1 second. After one second, the frequency of the input signal jumps to 55 Hz, and its fundamental wave amplitude Still at 1 volt. In addition, from 0 to 2 seconds, the signal always contains 2 to 20 harmonics and noise, and the amplitude of the second harmonic reaches 0.2 volts. The frequency tracking curve of the embodiment of the present invention for the input signal within 0-2 seconds is shown in FIG. 6 , and the frequency is basically locked after 0.4 seconds. After locking, the output frequency data f(n) still fluctuates to a certain extent, which is caused by harmonics and noise. However, it can be seen from the amplitude of the fluctuation that the measurement system already has a strong suppression effect on harmonics and noise. In addition, FIG. 7 shows the phase tracking curve of the embodiment within the time period of 0-0.4 seconds; FIG. 8 shows the phase tracking curve of the embodiment within the time period of 1-1.4 seconds.

The second embodiment of the frequency and phase digital measurement method of the present invention is aimed at a three-phase power grid, and is used to measure the frequency and phase of the A-phase voltage signal.

Suppose the A-phase voltage of the three-phase power grid is:

u _A (t) = U _m sin (2πft + ) where  is the initial phase of the A-phase voltage. Then the voltages of phase B and phase C are respectively:

u _B (t)＝U _m sin(2πft-120°+)

u _C (t)＝U _m sin (2πft+120°+) CB line voltage is:

u _CB (t)＝u _C (t)-u _B (t) It can be seen that the CB line voltage signal u _CB (t) is ahead of the phase A voltage signal u _A (t) by 90°.

随后的第2～7步与第一个实施例完全相同，不再赘述。第二个实施例的第8步中，所取的移相函数为θ₁(f)＝0，然后按照公式α(n)＝α₁(n)-θ₁(f(n))+K·2π计算出所测的A相电压信号的相位。通过测量出A相电压的频率和相位，也就可以进一步得到电网频率和B、C相的相位。In the first step of processing in the second embodiment of the present invention, the input phase A voltage u _A (t) is first sampled at a frequency F _s =1000 Hz, and the first group of sampling preprocessing outputs are directly obtained: The second group of sampling preprocessing utilizes the phase shift characteristics of the grid itself to the three-phase voltage. The specific steps are: first, the line voltage between phase C and phase B is sampled according to the frequency F _s =1000Hz to obtain the signal u _CB (n), and then calculated according to the following formula:

Subsequent steps 2-7 are exactly the same as those in the first embodiment, and will not be repeated here. In the 8th step of the second embodiment, the phase shift function taken is θ ₁ (f)=0, then according to formula α (n)=α ₁ (n)-θ ₁ (f (n))+K 2π calculates the phase of the measured A-phase voltage signal. By measuring the frequency and phase of the A-phase voltage, the grid frequency and the phases of the B and C phases can be further obtained.

Claims (1)

1, a kind of digital measurement method of frequency and phase, it is characterized in that the method comprises the steps: (1) Assuming that the AC input signal that needs to measure the frequency and phase is u(t)=U _m sin(2πft+θ), the first group of sampling preprocessing and the second group of sampling preprocessing are performed on the signal at the same time, and the discrete Signal $u_1\left(\mathrm{no}\right)=k_1\left(f\right)u_m\sin (2\mathrm{\&pi;}\frac{f}{f_{\mathrm{the\; s}}}\mathrm{no}+\mathrm{\&theta;}+{\mathrm{\&theta;}}_1\left(f\right))u_2\left(\mathrm{no}\right)=k_2\left(f\right)u_m\sin (2\mathrm{\&pi;}\frac{f}{f_{\mathrm{the\; s}}}\mathrm{no}+\mathrm{\&theta;}+{\mathrm{\&theta;}}_2\left(f\right));$ Where f is the frequency of the AC signal and satisfies f _min <f<f _max , θ is the initial phase of the AC signal, gain function k ₁ (f), gain function k ₂ (f), phase shift function θ ₁ ( f), the phase shift function θ ₂ (f) is any function related to the input signal frequency f that satisfies the following relationship: (2) Combine the discrete digital signals u ₁ (n) and u ₂ (n) obtained in the above step (1) into the coordinates of point A in the Cartesian coordinate system whose origin is O (u ₂ (n), u ₁ (n)), the resulting vector The included angle with the positive direction of the horizontal axis is taken as the locked phase data α ₀ (n); (3) Feedback the phase-locked data α ₀ (n) obtained in step (2) above from the output frequency f(n), and after integration and phase jump adjustment in step (7) below Take the difference of phase-locked phase data α'(n) to obtain phase error Δα(n); (4) Process the phase error Δα(n) obtained in step (3) above through loop filtering to obtain the frequency f(n) of the signal under test; during the above loop filtering process, its complex frequency domain transfer The function H _LP (s) has the form:

While making the transfer function of the measurement process

stable and make With low-pass filtering performance, the passband cut-off frequency f _LF of H'(s) is less than the lower limit f _min of the frequency of the locked signal; (5) The frequency f(n) of the measured signal obtained in the above step (4) and the phase-locked phase data α'(n) obtained in the following step (7) are integrated and accumulated according to the following formula to obtain the intermediate phase Data α ₁ (n): ${\mathrm{\&alpha;}}_1\left(\mathrm{no}\right)={\mathrm{\&alpha;}}^{\&prime;}(\mathrm{no}-1)+2\mathrm{\&pi;}\&Center\; Dot;\frac{f\left(\mathrm{no}\right)}{f_{\mathrm{the\; s}}}$ (6) Carry out quadrant jump detection on the phase-locked data α ₀ (n) obtained in the above step (2), to obtain jump detection data J(n), the judgment threshold constant of the jump detection is set as J _TH , The constant J _TH satisfies

So the relationship between the jump detection data J(n) and the locked phase α ₀ (n) is expressed as: (7) Add the intermediate phase data α ₁ (n) obtained in the above-mentioned step (5) to the jump detection data J(n) obtained in the above-mentioned step (6), that is, α'(n)=α ₁ ( n)+J(n), which is input to the above-mentioned (3) step process to form the phase-locked phase data α'(n) of the phase-locked loop; (8) Perform phase compensation and data adjustment processing on the intermediate phase data α ₁ (n) obtained in the above step (6), and obtain the required measured signal phase α(n)=α ₁ (n)-θ ₁ (f (n))+K·2π, where the function θ ₁ (f) is the phase shift function generated after the first set of sampling preprocessing of the input signal in the above step (1), K is the adjustment coefficient, and its value An integer satisfying 0≤α(n)<2π for α(n).

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