CN104678170A - Power harmonic analysis method based on harmonic analyzer and harmonic analyzer - Google Patents

Abstract

The invention discloses a power harmonic analysis method based on a harmonic analyzer and the harmonic analyzer. The power harmonic analysis method comprises the following steps: determining a preset base frequency, and designing a first FIR (Finite Impulse Response) comb filter for an input signal according to the preset base frequency; filtering the input signal by the first FIR comb filter and determining the frequency of the filtered signal; when the difference between the frequency of the filtered signal and the preset base frequency is smaller than a preset threshold, taking the frequency of the filtered signal as a base frequency of the input signal; determining the frequency of harmonic according to the base frequency, and designing a second FIR comb filter for the harmonic; filtering the input signal by the second FIR comb filter, determining signal parameters of the harmonic and sending the signal parameters to a processing unit of the harmonic analyzer. The power harmonic analysis method is easily realized, can be used for calculating the harmonic parameters conveniently at high precision and is not affected by frequency drift.

Description

Power harmonic analysis method based on harmonic analyzer and harmonic analyzer

Technical Field

The invention relates to the technical field of signal processing, in particular to a power harmonic analysis method based on a harmonic analyzer and the harmonic analyzer.

Background

With the rapid development of power electronic technology, harmonic pollution of a power system is increasingly serious, harmonic problems brought by a power electronic device form potential threats to the safety, stability and economic operation of the power system, great influences are brought to the surrounding electrical environment, the power quality problem is highly emphasized, the harmonic analysis technology is widely applied to the fields of power quality monitoring, electronic product production inspection, electrical equipment monitoring and the like, and the harmonic analysis technology is an important technical means for power grid monitoring, quality inspection and equipment monitoring. Currently, the commonly used analysis methods mainly include Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), FIR (Finite Impulse Response) based digital filtering algorithm, wavelet transform method, Prony algorithm, and the like.

In engineering application, harmonic analysis always performs finite point sampling, and is difficult to achieve strict synchronous sampling. Thus, when the FFT and DFT are applied to harmonic analysis, there will be long-range leakage due to truncation effect and short-range leakage due to barrier effect, so that the accuracy of the analysis result is not high, even unreliable.

The power system each harmonic analysis based on the FIR digital filter is an algorithm with simple and effective principle in the methods. FIR digital filters can filter out the desired frequency components from the signal, but this method has some side effects that change the amplitude and phase of the remaining frequency components in the signal.

Disclosure of Invention

The invention provides a power harmonic analysis method based on a harmonic analyzer, aiming at overcoming the defect of barrier effect in harmonic analysis in the prior art.

According to the embodiment of the invention, the power harmonic analysis method based on the harmonic analyzer comprises the following steps:

determining a preset fundamental frequency, and designing a first FIR comb filter for an input signal according to the preset fundamental frequency; filtering the input signal through a first FIR comb filter, and determining the frequency of the filtered signal; when the difference value between the frequency of the filtered signal and the preset fundamental frequency is smaller than a preset threshold value, taking the frequency of the filtered signal as the fundamental frequency of the input signal; determining the frequency of the harmonic wave according to the fundamental frequency, and designing a second FIR comb filter for the harmonic wave; filtering the input signal through a second FIR comb filter, determining signal parameters of harmonic waves, and sending the signal parameters to a processing unit of a harmonic wave analyzer, wherein the signal parameters comprise: signal amplitude and signal phase angle.

Preferably, the power harmonic analysis method based on the harmonic analyzer further includes: and when the difference value between the frequency of the filtered signal and the preset fundamental frequency is not less than the preset threshold value, continuing to filter the filtered signal through the first FIR comb filter until the difference value between the frequency of the re-filtered signal and the preset fundamental frequency is less than the preset threshold value, and taking the frequency of the re-filtered signal as the fundamental frequency of the input signal.

Preferably, determining the frequency of the filtered signal comprises:

acquiring three sampling values x (k), x (k +1) and x (k +2) of the filtered signal;

determining the frequency of the filtered signal as:whereinΔ t is the sampling time interval.

Preferably, the signal parameters for determining harmonics comprise:

obtaining two consecutive sampling values x of harmonic_i(k) And x_i(k+1)；

The signal amplitude of the harmonic is determined as: x_i＝2|A_i|；

The signal phase angle of the harmonic is determined as: phi is a_i＝angle(A_i)；

Wherein, f_iat the frequency of the harmonic, Δ t is the sampling time interval.

Preferably, the first FIR comb filter and the second FIR comb filter are FIR window filters;

for a sampling sequence x (k) ═ Xcos (2 pi fk Δ t + phi), after filtering processing is performed by an FIR window filter:

<math> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <msup> <mi>a</mi> <mi>k</mi> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&phi;</mi> </mrow> </msup> <msup> <mi>a</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> wherein a ═ e^j2πfΔt， <math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> </mrow> </math> Is a window correction factor.

Preferably, when the second FIR comb filter is a FIR window filter, determining the signal parameters of the harmonics comprises:

obtaining two consecutive sampling values of a harmonicAnd

the signal amplitude of the harmonic is determined as: x_i＝2|A_i|；

The signal phase angle of the harmonic is determined as: phi is a_i＝angle(A_i)；

Wherein, <math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>WCF</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> f_iat the frequency of the harmonic, Δ t is the sampling time interval.

The method for analyzing the power harmonic wave based on the harmonic wave analyzer is easy to implement, can conveniently calculate harmonic wave parameters, is high in precision, is not influenced by frequency drift, is not required to be 2n times of fundamental wave frequency at the same time, and effectively overcomes the defect that the harmonic wave analysis precision is seriously influenced by leakage, barrier effect, aliasing effect and the like.

The invention provides a harmonic analyzer for overcoming the defect of barrier effect in harmonic analysis in the prior art.

A harmonic analyzer according to an embodiment of the present invention includes:

the first filtering design module is used for determining a preset fundamental frequency and designing a first FIR comb filter for the input signal according to the preset fundamental frequency;

the first filtering module is used for filtering the input signal through a first FIR comb filter and determining the frequency of the filtered signal;

the base frequency determining module is used for taking the frequency of the filtered signal as the base frequency of the input signal when the difference value between the frequency of the filtered signal and the preset base frequency is smaller than a preset threshold value;

the second filtering design module is used for determining the frequency of the harmonic wave according to the fundamental frequency and designing a second FIR comb filter for the harmonic wave;

the second filtering module is used for filtering the input signal through a second FIR comb filter, determining signal parameters of harmonic waves and sending the signal parameters to a processing unit of the harmonic wave analyzer, wherein the signal parameters comprise: signal amplitude and signal phase angle.

Preferably, the first filtering module is further configured to: when the difference value between the frequency of the filtered signal and the preset fundamental frequency is not smaller than the preset threshold value, the filtered signal is continuously filtered through the first FIR comb filter until the difference value between the frequency of the filtered signal and the preset fundamental frequency is smaller than the preset threshold value;

the fundamental frequency determination module is further configured to: and taking the frequency of the re-filtered signal as the fundamental frequency of the input signal.

Preferably, the first filtering module includes:

the first acquisition unit is used for acquiring three continuous sampling values x (k), x (k +1) and x (k +2) of the filtered signal;

a first calculating unit, configured to determine a frequency of the filtered signal as:whereinΔ t is the sampling time interval.

Preferably, the second filtering module includes:

a second acquisition unit for acquiring two consecutive sampling values x of the harmonic_i(k) And x_i(k+1)；

A second calculation unit for determining the signal amplitude of the harmonic as: x_i＝2|A_iL, |; the signal phase angle of the harmonic is determined as: phi is a_i＝angle(A_i)；

Wherein, f_iat the frequency of the harmonic, Δ t is the sampling time interval.

Preferably, the first FIR comb filter determined by the first filter design module and the second FIR comb filter determined by the second filter design module are FIR window filters;

for a sampling sequence x (k) ═ Xcos (2 pi fk Δ t + phi), after filtering processing is performed by an FIR window filter:

<math> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <msup> <mi>a</mi> <mi>k</mi> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&phi;</mi> </mrow> </msup> <msup> <mi>a</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> wherein a ═ e^j2πfΔt， <math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> </mrow> </math> Is a window correction factor.

Preferably, when the second FIR comb filter is a FIR window filter, the second filtering module includes:

a third acquisition unit for acquiring two consecutive sampling values of the harmonicAnd x

A third calculation unit for determining the signal amplitude of the harmonic as: x_i＝2|A_iL, |; the signal phase angle of the harmonic is determined as: phi is a_i＝angle(A_i)；

Wherein, <math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>WCF</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> f_iat the frequency of the harmonic, Δ t is the sampling time interval.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

FIG. 1 is a flow chart of a harmonic analysis method in an embodiment of the invention;

FIG. 2 is a flow chart of a harmonic analysis method according to an embodiment;

fig. 3 is a structural diagram of a harmonic analyzer in an embodiment of the present invention.

Detailed Description

The following detailed description of the present invention is provided in conjunction with the accompanying drawings, but it should be understood that the scope of the present invention is not limited to the specific embodiments.

According to an embodiment of the present invention, there is provided a power harmonic analysis method based on a harmonic analyzer, as shown in fig. 1, in the embodiment of the present invention, a flow of the harmonic analysis method is as follows:

step 101: and determining a preset fundamental frequency, and designing a first FIR comb filter for the input signal according to the preset fundamental frequency.

The preset fundamental frequency is a theoretical fundamental frequency of the input signal, for example, if the theoretical value of the fundamental frequency of the power signal is 50Hz, the preset fundamental frequency is set to be 50 Hz. The predetermined fundamental frequency is mainly used for designing the first FIR comb filter and comparing the frequency with the frequency of the signal filtered by the first FIR comb filter.

Step 102: the input signal is filtered by a first FIR comb filter and the frequency of the filtered signal is determined.

The first FIR comb filter can filter out the harmonics leaving only the fundamental of the input signal, so that the filtered signal consists mainly of the fundamental.

Step 103: and when the difference value between the frequency of the filtered signal and the preset fundamental frequency is smaller than a preset threshold value, taking the frequency of the filtered signal as the fundamental frequency of the input signal.

Because there is an error between the fundamental frequency of the actual signal and the theoretical preset fundamental frequency, the frequency of the filtered signal is used as the fundamental frequency of the input signal only when the difference between the frequency of the filtered signal and the preset fundamental frequency is smaller than a preset threshold. The preset threshold is preset, and specifically may be 0.1Hz or 0.01Hz, and the like, according to the actual situation.

And when the difference value between the frequency of the filtered signal and the preset fundamental frequency is not less than the preset threshold value, continuing to filter the filtered signal through the first FIR comb filter until the difference value between the frequency of the re-filtered signal and the preset fundamental frequency is less than the preset threshold value, and taking the frequency of the re-filtered signal as the fundamental frequency of the input signal. When the difference between the frequency of the filtered signal and the preset fundamental frequency is not smaller than the preset threshold, the filtered signal is filtered again, and then whether the difference between the frequency of the filtered signal and the preset fundamental frequency is smaller than the preset threshold is judged, if the difference between the two frequencies is still not smaller than the preset threshold, the filtered signal is continuously filtered until the difference between the two frequencies is smaller than the preset threshold.

Step 104: and determining the frequency of the ith harmonic according to the fundamental frequency, and designing a second FIR comb filter for the ith harmonic.

When the fundamental frequency of the input signal is determined, the frequency of the i-th harmonic in the input signal can be determined, which is i times the fundamental frequency, i.e. the frequency f of the i-th harmonic_i＝if₁Wherein f is₁Is the fundamental frequency. The second FIR comb filter is used for filtering out other subharmonics except the ith harmonic in the input signal, namely the ith harmonic is output by the second FIR comb filter.

Step 105: filtering the input signal through a second FIR comb filter, determining signal parameters of ith harmonic and sending the signal parameters to a processing unit of a harmonic analyzer, wherein the signal parameters comprise: signal amplitude and signal phase angle.

The frequency of the ith harmonic can be determined in step 104, the signal amplitude and the signal phase angle of the ith harmonic can be determined in step 105, and the frequency, the amplitude and the phase of the ith harmonic can be determined by combining the two steps, i.e. all signal parameters of the ith harmonic are determined. After the harmonic analyzer receives the signal parameters of the ith harmonic, the harmonic analyzer can analyze and process the harmonic and output the harmonic in a chart or curve mode for relevant technicians to analyze and utilize; the harmonic analyzer can also upload signal parameters of harmonic waves to an upper computer through RS232 and RS485 standard communication ports or a network port (RJ45) communication interface, the upper computer can convert the acquired harmonic signal parameters into various reports, curves and bar charts based on WINDOWS and other operation platforms, and meanwhile, the reports can be converted into WORD or EXCEL formats as required.

In the embodiment of the present invention, the principle of the method for determining the signal parameter in step 102 and step 105 is specifically as follows:

the ideal signal x (t) can be described as: x (t) Xcos (2 pi ft + phi); where X is the signal amplitude, f is the signal frequency, and φ is the signal phase angle. Discrete sampling of the continuous-time signal x (t) with a fixed time interval Δ t, generating a sequence of samples { x (k) }:

x(k)＝Xcos(2πfkΔt+φ) (2)

because of the fact thatEquation (2) can be expressed as:

let a be e^j2πfΔt，z＝Re(a)，Wherein z is the real part of a complex number a^*Is the complex conjugate of a, the sample sequence { x (k) } is:

x(k)＝Aa^k+A^*a^-k (4)

according to Euler's formula e^ixCosx + isinx andformula (4), where m is 2 pi f Δ t, can give:

x(k)+x(k+2)＝A(a^k+a^k+2)+A^*(a^-k+a^-k-2)

＝A[cos(mk)+jsin(mk)+cos(mk+2m)+jsin(mk+2m)]+

A^*[cos(mk)-jsin(mk)+cos(mk+2m)-jsin(mk+2m)]

＝A[2cos(mk+m)cosm+j2sin(mk+m)cosm]+

A^*[2cos(mk+m)cosm-j2sin(mk+m)cosm]

＝2[Ae^j(mk+m)+A^*e^-j(mk+m)]cosm＝2x(k+1)cosm

meanwhile, since z ═ Re (a) ═ Re (cos2 pi f Δ t + jsin2 pi f Δ t) ═ cos2 pi f Δ t ═ cosm, in combination with the above formula, it can be obtained:

$z=\frac{x\left(k\right)+x(k+2)}{2x(k+1)}---\left(5\right)$

and x (k +1) a-x (k) ═ a [ a^k+1a-a^k]+A^*(a^-k-1a-a^-k)＝Aa^k(a²-1), thus:

$A=\frac{x(k+1)a-x\left(k\right)}{a^k(a^2-1)}---\left(6\right)$

since z is cos2 pi f deltat, <math> <mrow> <mi>A</mi> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mi>cos</mi> <mi>&phi;</mi> <mo>+</mo> <mi>j</mi> <mi>sin</mi> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> thus, for the power signal x (t), the signal frequencyThe signal value X is 2| a |, and the signal phase angle Φ is angle (a).

In summary, for the signal x (t), z and thus the signal frequency f of the signal x (t) can be determined according to three discrete sampling values x (k), x (k +1), and x (k + 2); when the signal frequency f and the sampling interval Δ t are known, a and A can be determined, and thus the signal amplitude X and the signal phase angle φ can be determined. The algorithm is applicable to standard sine or cosine signals and therefore also to power harmonics. Calculated by the algorithmThe parameters of the harmonic wave of the signal are calculated, the method is easy to realize, has high precision and is not influenced by frequency drift, and the sampling frequency is not required to be 2 of the fundamental frequencyⁿAnd (4) doubling.

Applying the above algorithm to the embodiment of the present invention, in step 101, if the filtered signal is x (k), determining the frequency of the filtered signal specifically includes:

acquiring three sampling values x (k), x (k +1) and x (k +2) of the filtered signal;

the frequency of the filtered signal is:whereinΔ t is the sampling time interval.

In step 105, determining the signal parameter of the ith harmonic specifically includes:

obtaining two sampling values x of ith harmonic_i(k) And x_i(k+1)；

The signal amplitude of the harmonics is: x_i＝2|A_iL, |; the signal phase angle of the harmonic is: phi is a_i＝angle(A_i)；

Wherein, $A_i=\frac{x_i(k+1)a_i-x_i\left(k\right)}{{a_i}^k({a_i}^2-1)},$ <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> f_iat the frequency of the ith harmonic, Δ t is the sampling interval.

Preferably, the first FIR comb filter and the second FIR comb filter are both FIR window filters;

for a sampling sequence x (k) ═ Xcos (2 pi fk Δ t + phi), after filtering processing is performed by an FIR window filter:

<math> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <msup> <mi>a</mi> <mi>k</mi> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&phi;</mi> </mrow> </msup> <msup> <mi>a</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> wherein a ═ e^j2πfΔt， <math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> </mrow> </math> Is a window correction factor.

The signal introduced into the window correction factor WCF is obtained from equations (5) and (6)The signal parameters of (a) may be expressed as:

<math> <mrow> <mover> <mi>f</mi> <mo>~</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msup> <mi>cos</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>&pi;&Delta;t</mi> </mrow> </mfrac> <mo>,</mo> <mover> <mi>X</mi> <mo>~</mo> </mover> <mo>=</mo> <mn>2</mn> <mo>|</mo> <mover> <mi>A</mi> <mo>~</mo> </mover> <mo>|</mo> <mo>,</mo> <mover> <mi>&phi;</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>amgle</mi> <mrow> <mo>(</mo> <mover> <mi>A</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

wherein: <math> <mrow> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <mover> <mi>A</mi> <mo>~</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>a</mi> <mo>-</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mi>a</mi> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <mi>WCF</mi> </mrow> </mfrac> <mo>,</mo> <mi>WCF</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>.</mo> </mrow> </math>

while the common FIR comb filter extracts the required frequency components, the amplitude and phase of the remaining frequency components in the signal are changed, so that the FIR comb filter is replaced by a FIR window filter. The method for the window correction factor WCF provided by the embodiment of the invention is suitable for any finite sequence digital filter, such as Hamming, Hanning and Blackman window filters, and even DFT of finite complex sequences are included.

The method for analyzing the power harmonic wave based on the harmonic wave analyzer is easy to implement, can conveniently calculate harmonic wave parameters, is high in precision, is not influenced by frequency drift, is not required to be 2n times of fundamental wave frequency at the same time, and effectively overcomes the defect that the harmonic wave analysis precision is seriously influenced by leakage, barrier effect, aliasing effect and the like.

The flow of the power harmonic analysis method is described in detail by the first embodiment.

Example one

In the first embodiment, the power signal is filtered by using a FIR comb filter, which is subjected to windowing and harmonic analysisThe process is shown in figure 2. In one embodiment, the power signal waveform is described as:sampling the signal x (t) with a fixed time interval Δ t, generating a sampling sequence:

<math> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>X</mi> <mi>i</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>k&Delta;t</mi> <mo>+</mo> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>k</mi> <mo>=</mo> <mn>0,1,2,3</mn> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> </mrow> </math>

definition of <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <msub> <mi>j</mi> <mi>i</mi> </msub> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> </mrow> </msup> <mo>,</mo> </mrow> </math> z_i＝Re(a_i)＝cos2πf_iΔt， <math> <mrow> <msup> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>*</mo> </msup> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>j</mi> <mi>i</mi> </msub> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> </mrow> </msup> <mo>.</mo> </mrow> </math>

From the characteristic properties of FIR comb filters, the following conclusions can be drawn:

<math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </munderover> <mi>C</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>;</mo> </mrow> </math>

C(n)＝{{1,-2z₁,1}*{1,-2z₂,1}*...*{1,-2z_m1} }, wherein z_i＝cos2πf_iΔt，^*Is a convolution operator, and n is the number of the feedback loops of the FIR comb filter. The above equation is a characteristic property of FIR comb filter, and is not detailed here for the prior art.

When an FIR comb filter is used to filter out other subharmonic signals except the i-th harmonic, the corresponding FIR comb filter is expressed as:

$C_i\left(n\right)=\frac{C\left(n\right)}{\{1,-2z_i,1\}}=\left\{\right\{1,-2z_1,1\}*...*\{1,-2z_{i-1},1\}*\{1,-2z_{i+1},1\}*...*\{1,-2z_m,1\left\}\right\}.$

in the first embodiment, the procedure of harmonic analysis is specifically as follows:

presetting fundamental frequency f =60Hz, designing filter C₁(n)。

Wherein, C₁(n)＝{{1,-2z₂,1}*{1,-2z₃,1}*...*{1,-2z_m,1}}。

After the discrete power signal x (k) is filtered by the filter C1(n), the waveform expression of the obtained signal is:

<math> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>2</mn> </mrow> </munderover> <msub> <mi>C</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

obtainingThree consecutive sampling values ofAndit can be determined from equation (5) that the signal passes through the filter C₁(n) the frequency of the filtered signal is:

<math> <mrow> <msub> <mi>f</mi> <mi>new</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mi>cos</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>&pi;&Delta;t</mi> </mrow> </mfrac> <mo>,</mo> </mrow> </math> wherein, $z_1=\frac{{\tilde{x}}_1\left(k\right)+{\tilde{x}}_1(k+2)}{2{\tilde{x}}_1(k+1)}.$

determine | f_newIf-f < 0.001Hz is true. Wherein 0.001Hz is the preset threshold, | f_newThe frequency f of the filtered signal is judged if the f is less than 0.001Hz_newWhether the difference value with the preset fundamental frequency of 60Hz is less than the preset threshold value of 0.001 Hz.

When f_newIf-f < 0.001Hz, f is set_newFundamental frequency f as power signal x (k)₁(ii) a When it is not true, then continue to pass through filter C₁(n) pairsAnd filtering until the difference value between the frequency of the filtered signal and the preset fundamental frequency 60Hz is smaller than a preset threshold value.

When fundamental frequency f₁After determination, the amplitude and phase angle of the fundamental wave can be determined according to equation (6):

X₁＝2|A₁|，φ₁＝angle(A₁) (ii) a Wherein:

<math> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>,</mo> <msub> <mi>WCF</mi> <mn>1</mn> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>2</mn> </mrow> </munderover> <msub> <mi>C</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>n</mi> </msup> <mo>.</mo> </mrow> </math>

according to the fundamental frequency f₁The frequency of the ith harmonic can be determined and then filter C can be designed according to the desired ith harmonic_i(n)，C_i(n)＝{{1,-2z₁,1}*...*{1,-2z_i-1,1}*{1,-2z_i+1,1}*...*{1,-2z_m,1}}。

The discrete power signal x (k) passes through a filter C_i(n) after filtering, the expression of the ith harmonic is:

<math> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>2</mn> </mrow> </munderover> <msub> <mi>C</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>

the amplitude and phase angle of the ith harmonic are:

X_i＝2|A_i|，φ_i＝angle(A_i) (ii) a Wherein:

<math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>2</mn> </mrow> </munderover> <msub> <mi>C</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>n</mi> </msup> <msub> <mrow> <mo>,</mo> <mi>a</mi> </mrow> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>=</mo> <msup> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>i</mi> </msup> <mo>.</mo> </mrow> </math>

thus, the ith harmonic is obtainedTwo consecutive sampling values ofAndthe magnitude and phase angle of the ith harmonic can be determined.

The method for analyzing the power harmonic wave based on the harmonic wave analyzer is easy to implement, can conveniently calculate harmonic wave parameters, is high in precision, is not influenced by frequency drift, is not required to be 2n times of fundamental wave frequency at the same time, and effectively overcomes the defect that the harmonic wave analysis precision is seriously influenced by leakage, barrier effect, aliasing effect and the like. The window correction factor method is applicable to any finite sequence digital filter, and different window algorithms and window sizes can be selected to obtain better performance. The power harmonic analysis method based on the harmonic analyzer is suitable for off-line application with requirements, and is also suitable for on-line application if the harmonic analysis method can be realized by parallel computing.

The implementation process of the power harmonic analysis method based on the harmonic analyzer is described above in detail, the embodiment of the invention also provides the harmonic analyzer, and the structure of the harmonic analyzer is described below.

A harmonic analyzer provided in an embodiment of the present invention is shown in fig. 3, and includes: a first filter design module 301, a first filter module 302, a fundamental frequency determination module 303, a second filter design module 304, and a second filter module 305.

The first filter design module 301 is configured to determine a preset fundamental frequency, and design a first FIR comb filter for an input signal according to the preset fundamental frequency;

the first filtering module 302 is configured to filter the input signal through a first FIR comb filter, and determine a frequency of the filtered signal;

the fundamental frequency determining module 303 is configured to, when a difference between the frequency of the filtered signal and a preset fundamental frequency is smaller than a preset threshold, take the frequency of the filtered signal as the fundamental frequency of the input signal;

the second filter design module 304 is configured to determine frequencies of the harmonics according to the fundamental frequency, and design a second FIR comb filter for the harmonics;

the second filtering module 305 is configured to filter the input signal through the second FIR comb filter, determine signal parameters of the harmonic, and send the signal parameters to a processing unit of the harmonic analyzer, where the signal parameters include: signal amplitude and signal phase angle.

Preferably, the first filtering module 302 is further configured to: when the difference value between the frequency of the filtered signal and the preset fundamental frequency is not smaller than the preset threshold value, the filtered signal is continuously filtered through the first FIR comb filter until the difference value between the frequency of the filtered signal and the preset fundamental frequency is smaller than the preset threshold value;

the fundamental frequency determination module 303 is further configured to: and taking the frequency of the re-filtered signal as the fundamental frequency of the input signal.

Preferably, the first filtering module 302 includes:

the first acquisition unit is used for acquiring three continuous sampling values x (k), x (k +1) and x (k +2) of the filtered signal;

a first calculating unit, configured to determine a frequency of the filtered signal as:whereinΔ t isSample time intervals.

Preferably, the second filtering module 305 includes:

a second acquisition unit for acquiring two consecutive sampling values x of the harmonic_i(k) And x_i(k+1)；

A second calculation unit for determining the signal amplitude of the harmonic as: x_i＝2|A_iL, |; the signal phase angle of the harmonic is determined as: phi is a_i＝angle(A_i)；

Wherein, f_iat the frequency of the harmonic, Δ t is the sampling time interval.

Preferably, the first FIR comb filter determined by the first filter design module 301 and the second FIR comb filter determined by the second filter design module 304 are FIR window filters;

for a sampling sequence x (k) ═ Xcos (2 pi fk Δ t + phi), after filtering processing is performed by an FIR window filter:

<math> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <msup> <mi>a</mi> <mi>k</mi> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&phi;</mi> </mrow> </msup> <msup> <mi>a</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> wherein a ═ e^j2πfΔt， <math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> </mrow> </math> Is a window correction factor.

Preferably, when the second FIR comb filter is a FIR window filter, the second filtering module 305 includes:

a third acquisition unit for acquiring two consecutive sampling values of the harmonicAnd

a third calculation unit for determining the signal amplitude of the harmonic as: x_i＝2|A_iL, |; the signal phase angle of the harmonic is determined as: phi is a_i＝angle(A_i)；

Wherein, <math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>WCF</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> f_iat the frequency of the harmonic, Δ t is the sampling time interval.

The harmonic analyzer provided by the embodiment of the invention can quickly calculate harmonic parameters according to harmonic sampling values, has high precision, is not influenced by frequency drift, and simultaneously has no need of the sampling frequency being 2 of the fundamental frequencyⁿAnd the defects that leakage, a barrier effect, an aliasing effect and the like seriously influence the harmonic analysis precision are effectively overcome.

While the present invention is susceptible of embodiment in many different forms, there is shown in the drawings, and herein will be described in detail, specific embodiments with reference to the accompanying drawings, which are not intended to limit the invention to the specific forms set forth herein, but rather to limit the invention to the specific forms set forth herein.

Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will understand that various changes, modifications and substitutions can be made without departing from the spirit and scope of the invention as defined by the appended claims. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (12)

1. A power harmonic analysis method based on a harmonic analyzer is characterized by comprising the following steps:

determining a preset fundamental frequency, and designing a first FIR comb filter for an input signal according to the preset fundamental frequency;

filtering the input signal through the first FIR comb filter and determining the frequency of the filtered signal;

when the difference value between the frequency of the filtered signal and the preset fundamental frequency is smaller than a preset threshold value, taking the frequency of the filtered signal as the fundamental frequency of the input signal;

determining the frequency of a harmonic according to the fundamental frequency, and designing a second FIR comb filter for the harmonic;

filtering the input signal through the second FIR comb filter, determining signal parameters of the harmonic waves, and sending the signal parameters to a processing unit of a harmonic wave analyzer, wherein the signal parameters include: signal amplitude and signal phase angle.

2. The method of claim 1, further comprising:

and when the difference value between the frequency of the filtered signal and the preset fundamental frequency is not less than a preset threshold value, continuing to filter the filtered signal through the first FIR comb filter until the difference value between the frequency of the re-filtered signal and the preset fundamental frequency is less than the preset threshold value, and taking the frequency of the re-filtered signal as the fundamental frequency of the input signal.

3. The method of claim 1 or 2, wherein determining the frequency of the filtered signal comprises:

acquiring three sampling values x (k), x (k +1) and x (k +2) of the filtered signal;

determining the frequency of the filtered signal as:whereinΔ t is the sampling time interval.

4. The method of claim 1 or 2, wherein said determining signal parameters of said harmonics comprises:

obtaining two consecutive sample values x of the harmonic_i(k) And x_i(k+1)；

Determining the signal amplitude of the harmonic as: x_i=2|A_i|；

Determining a signal phase angle of the harmonic as: phi is a_i=angle(A_i)；

Wherein, f_iat is the frequency of the harmonic, Δ t is the sampling time interval.

5. The method of claim 1 or 2, wherein the first FIR comb filter and the second FIR comb filter are FIR window filters;

for the sampling sequence x (k) = Xcos (2 pi fk Δ t + phi), after filtering processing is performed by an FIR window filter:

<math> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <msup> <mi>a</mi> <mi>k</mi> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&phi;</mi> </mrow> </msup> <msup> <mi>a</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> wherein a = e^j2πfΔt， <math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> </mrow> </math> Is a window correction factor.

6. The method of claim 5, wherein said determining signal parameters of said harmonics comprises:

obtaining two consecutive sample values of the harmonicAnd

determining the signal amplitude of the harmonic as: x_i=2|A_i|；

Determining a signal phase angle of the harmonic as: phi is a_i=angle(A_i)；

Wherein, <math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>WCF</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> f_iat is the frequency of the harmonic, Δ t is the sampling time interval.

7. A harmonic analyzer, comprising:

the first filtering design module is used for determining a preset fundamental frequency and designing a first FIR comb filter for an input signal according to the preset fundamental frequency;

a first filtering module, configured to filter the input signal through the first FIR comb filter, and determine a frequency of the filtered signal;

a fundamental frequency determining module, configured to, when a difference between the frequency of the filtered signal and the preset fundamental frequency is smaller than a preset threshold, take the frequency of the filtered signal as the fundamental frequency of the input signal;

the second filtering design module is used for determining the frequency of the harmonic wave according to the fundamental frequency and designing a second FIR comb filter for the harmonic wave;

a second filtering module, configured to filter the input signal through the second FIR comb filter, determine a signal parameter of the harmonic, and send the signal parameter to a processing unit of a harmonic analyzer, where the signal parameter includes: signal amplitude and signal phase angle.

8. The harmonic analyzer of claim 7, wherein the first filtering module is further configured to: when the difference value between the frequency of the filtered signal and the preset fundamental frequency is not less than a preset threshold value, continuing to filter the filtered signal through the first FIR comb filter until the difference value between the frequency of the re-filtered signal and the preset fundamental frequency is less than the preset threshold value;

the fundamental frequency determination module is further configured to: and taking the frequency of the re-filtered signal as the fundamental frequency of the input signal.

9. The harmonic analyzer of claim 7 or 8, wherein the first filtering module comprises:

the first acquisition unit is used for acquiring sampling values x (k), x (k +1) and x (k +2) of the filtered signal in three consecutive times;

a first calculating unit, configured to determine that a frequency of the filtered signal is:whereinΔ t is the sampling time interval.

10. The harmonic analyzer of claim 7 or 8, wherein the second filtering module comprises:

a second acquisition unit for acquiring two consecutive sampling values x of the harmonic_i(k) And x_i(k+1)；

A second calculation unit for determining the signal amplitude of the harmonic as: x_i=2|A_iL, |; determining a signal phase angle of the harmonic as: phi is a_i=angle(A_i)；

Wherein, f_iat is the frequency of the harmonic, Δ t is the sampling time interval.

11. The harmonic analyzer of claim 7 or 8, wherein the first FIR comb filter determined by the first filter design module and the second FIR comb filter determined by the second filter design module are FIR window filters;

for the sampling sequence x (k) = Xcos (2 pi fk Δ t + phi), after filtering processing is performed by an FIR window filter:

<math> <mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mi>j&phi;</mi> </msup> <msup> <mi>a</mi> <mi>k</mi> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>+</mo> <mfrac> <mi>X</mi> <mn>2</mn> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&phi;</mi> </mrow> </msup> <msup> <mi>a</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msup> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> wherein a = e^j2πfΔt， <math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> </mrow> </math> Is a window correction factor.

12. The harmonic analyzer of claim 11, wherein the second filtering module comprises:

a third acquisition unit for acquiring two consecutive sampling values of the harmonicAnd x

A third calculation unit for determining the signal amplitude of the harmonic as: x_i=2|A_iL, |; determining a signal phase angle of the harmonic as: phi is a_i=angle(A_i)；

Wherein, <math> <mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>k</mi> </msup> <mrow> <mo>(</mo> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>WCF</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&pi;</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> <mi>&Delta;t</mi> </mrow> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>WCF</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>n</mi> </msup> <mo>,</mo> </mrow> </math> f_iat is the frequency of the harmonic, Δ t is the sampling time interval.