CN106771579A - A kind of frequency measuring method of the cross algorithms based on linear interpolation principle - Google Patents

Abstract

The invention discloses a kind of cross algorithm frequency measuring methods based on linear interpolation principle, in being mainly used in power system monitoring and controlling.It is smaller for power system frequency excursion but require the characteristics of frequency-measurement accuracy is high, it is proposed that a kind of cross algorithm frequency measuring methods based on linear interpolation principle.It is a feature of the present invention that its process step is included：Equal interval sampling is carried out to input signal, obtain discrete equally spaced sampled point, the cycle of input signal to be asked and the average deviation of its standard primitive period are calculated according to linear interpolation principle, ask for the weight of each sampled point deviation, and the weighted average of deviation is sought, finally the weighted average according to signal actual cycle and the deviation of normal period asks for frequency.The present invention simplifies signal frequency measuring principle using the cross algorithms based on linear interpolation, average weighted method is used on this basis, it is suppressed that irrational frequency departure, improves the accuracy and adaptability of frequency measurement.

Description

A kind of frequency measuring method of the cross algorithms based on linear interpolation principle

Technical field

The invention discloses a kind of frequency measuring method based on linear interpolation principle cross algorithms, belong to power system monitoring With control field.

Background technology

At present, the electrical power system wide-area measuring system (WAMS) based on synchronous phasor measurement unit (PMU) generally should With power-management centre above the provincial level, WAMS can not only replace traditional data acquisition and supervisor control system (SCADA) power system mesomeric state monitoring task is completed, and can apply to dynamic behaviour monitoring, the stability monitoring of power system With the field such as accident analysis.Access on a large scale with photovoltaic, the blower fan distributed energy, socio-economic development is to power supply reliability It is required that increasingly improving, power distribution network safe and reliable operation is further important, has started to be attempted with control in the monitoring of power distribution network both at home and abroad Using PMU.

Although PMU can real-time monitoring mains frequency, international and national standard regulation PMU effective ranges are 45Hz~55Hz.When microgrid starts independent operating, frequency can occur very big fluctuation, or even the extreme feelings less than 45Hz occur Condition, it is impossible to which application PMU is monitored and control.Frequency measurement link is mainly software algorithm in PMU.Digital filtering, Wavelet Transform, ox Pausing, class algorithm is excessively complicated, and hardware requirement is high, and zero passage method, analytical function realize that but simple frequency measurement is not accurate enough.Original Cross Measuring Frequency Methods are simply easily achieved, but error is big.Error using BP network amendment cross innovatory algorithms is complex, needs Wanting offline network to train cannot realize online real-time, and frequency deviation it is larger when cannot correct.

The content of the invention

It is not enough it is an object of the invention to the existing frequency measuring method of customer service, propose a kind of based on linear interpolation principle cross calculations The frequency measuring method of method, the algorithm simply easily realizes that effectively reduce amount of calculation, real-time is greatly improved, while being also improved Frequency-measurement accuracy.

Technical scheme：For achieving the above object, cross algorithm frequency measurement side of the present invention based on linear interpolation principle Method, comprises the following steps：

Step 1：Equal interval sampling is carried out to input signal, discrete equally spaced sampled point is obtained；

Step 2：The cycle of input signal to be asked and the average deviation of standard primitive period are calculated according to linear interpolation principle；

Step 3：The weight of each sampled point deviation is asked for, and seeks the weighted average of deviation；

Step 4：The final weighted average according to signal actual cycle and the deviation of standard primitive period obtains frequency.

Further, the step 1 carries out equal interval sampling to input voltage signal, obtains discrete equally spaced sampling Point is specially：

If it is f that the standard fundamental frequency of input voltage signal is power frequency_N, sample rate is f_s, then the standard primitive period beSampling number in the standard primitive period isSampling periodIt is derived from discrete equally spaced Sampled point.

Further, the use in the step 2 calculates cycle and the standard base of voltage signal to be asked based on linear interpolation The deviation of period of wave is specially：

If alternating voltage is mathematically represented as：

In formula, u (t) is t alternating voltage instantaneous value, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency, It is voltage initial angle.

If t-T_NMoment alternating voltage instantaneous value is：

In formula, u (t-T_N) it is t-T_NMoment alternating voltage instantaneous value, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency Rate,It is voltage initial angle, T_NIt is the standard primitive period.

If the alternating voltage instantaneous value at t- τ moment is：

In formula, u (t- τ) is t- τ moment alternating voltage instantaneous values, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency Rate, τ is the sampling period,It is voltage initial angle.

Following relationship can be obtained according to linear interpolation principle：

In formula, u (t), u [t- (T_N-T)]、u(t-τ)、u[t-(T_N- T)+τ] it is respectively t, t- (T_N-T)、t-τ、t-(T_N- T)+τ moment alternating voltages instantaneous value, T_NIt it is the standard primitive period of alternating voltage, T is the actual week of ac voltage signal to be asked Phase, τ is the sampling period.

In formula, u [t- (T_N-T)]、u(t-T_N)、u(t-Nτ)、u[t-(T_N-T)+τ]、u(t-T_N+ τ), u (t-N τ+τ) respectively It is t- (T_N-T)、t-T_N、t-Nτ、t-(T_N-T)+τ、t-T_N+ τ, t-N τ+τ moment alternating voltage instantaneous values, T_NIt is alternating voltage Standard primitive period, T is the actual cycle of ac voltage signal to be asked, and τ is the sampling period, and N is a standard primitive period Sampling number.

In formula, u (t), u (t-N τ), u (t- τ), u (t-N τ+τ) are respectively t, t-N τ, t- τ, t-N τ+τ moment alternating voltages Instantaneous value, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is sampling period, N It is the sampling number of standard primitive period.

Standard primitive period and one group of deviation of actual cycle are tried to achieve according to formula below：

In formula, Δ T_a(t)、ΔT_bT () is respectively t according to standard primitive period and reality required by two different sampled points Border periodic deviation, u (t), u (t-N τ), u (t- τ), u (t-N τ+τ) are respectively t, t-N τ, t- τ, t-N τ+τ moment alternating voltage winks Duration, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is the sampling period, and N is One sampling number of standard primitive period.

Further, the weight of each sampled point deviation is asked for, and obtains the weighted average of deviation to be specially：

Calculate t deviation average Δ T (t) be：

In formula, Δ T_a(t) and Δ T_bT () is respectively t according to the standard primitive period required by same sampled point difference interpolation With actual cycle deviation.

Within 0~(m-1) τ time periods, the weight α (t) for making t deviation average Δ T (t) is

In formula, D (t)=u (t)-u (t- τ), wherein u (t), u (t- τ) are respectively t, t- τ moment alternating voltage instantaneous values, τ It it is the sampling period, N is the sampling number of standard primitive period.

The deviation delta T ' that then the m deviation of sampled point is tried to achieve by weighted average, i.e. the weighted average of deviation is：

In formula, Δ T (t) is t deviation average, and τ is the sampling period, and α (t) is t deviation average Δ T (t) Weight.

Formula after abbreviation is

In formula, D (t)=u (t)-u (t- τ), u (t), u (t-N τ), u (t- τ) are respectively t, t-N τ, t- τ moment alternating currents Pressure instantaneous value, τ is the sampling period, and N is the sampling number of standard primitive period.

Further, the weighted average deviation in the step 4 according to signal actual cycle and normal period asks for frequency, Specific formula for calculation is：

In formula, f is frequency input signal to be asked, and T is the cycle of input signal to be asked, T_NFor the standard primitive period isf_NFor standard fundamental frequency is power frequency, Δ T ' is to try to achieve deviation after weighted average.

Brief description of the drawings

Fig. 1 is the linear interpolation schematic diagram in the present invention；

Fig. 2 frequency measuring method flow charts of the present invention based on linear interpolation principle cross algorithms.

Specific embodiment

As Figure 1-Figure 2, a kind of frequency measuring method based on linear interpolation principle cross algorithms of the present invention, based on linear In the frequency measuring method of Interpolation Principle cross algorithms, deviation factor value is calculated using linear interpolation method, frequency is asked for further according to deviation Rate, cross algorithm frequency measuring methods are methods that is a kind of simple and being easily achieved.In practical power systems, the stabilization of frequency is For based on electric voltage frequency, therefore input signal uses voltage signal.Circuit interpolation method is accurate for linear waveform, and For the actual non-linear relation of the voltage signal from power network, represented with their average value cycle of signal with The deviation of normal period, is all inaccurate, is that the presenter of the method employs and takes average weighted method so that algorithm Result of calculation tends to reasonable.

The method mainly comprises the following steps：

Step 1：Equal interval sampling is carried out to input signal, discrete equally spaced sampled point is obtained, specially：

If it is f that the standard fundamental frequency of input voltage signal is power frequency_N, sample rate is f_s, then the standard primitive period beSampling number in the standard primitive period isSampling periodIt is derived from discrete equally spaced Sampled point

Step 2：Using the cycle for calculating based on linear interpolation voltage signal to be asked and the average deviation of standard primitive period Specially：

If alternating voltage is mathematically represented as：

In formula, u (t) is t alternating voltage instantaneous value, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency, It is voltage initial angle；

If t-T_NMoment alternating voltage instantaneous value is：

In formula, u (t-T_N) it is t-T_NMoment alternating voltage instantaneous value, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency Rate,It is voltage initial angle, T_NIt is the standard primitive period.

If the alternating voltage instantaneous value at t- τ moment is：

In formula, u (t- τ) is t- τ moment alternating voltage instantaneous values, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency Rate, τ is the sampling period,It is voltage initial angle；

Such as Fig. 1, formula (4), (5), (6) can be obtained according to linear interpolation principle；

In formula, u (t), u [t- (T_N-T)]、u(t-τ)、u[t-(T_N- T)+τ] it is respectively t, t- (T_N-T)、t-τ、t-(T_N- T)+τ moment alternating voltages instantaneous value, T_NIt it is the standard primitive period of alternating voltage, T is the actual week of ac voltage signal to be asked Phase, τ is the sampling period；

In formula, u [t- (T_N-T)]、u(t-T_N)、u(t-Nτ)、u[t-(T_N-T)+τ]、u(t-T_N+ τ), u (t-N τ+τ) respectively It is t- (T_N-T)、t-T_N、t-Nτ、t-(T_N-T)+τ、t-T_N+ τ, t-N τ+τ moment alternating voltage instantaneous values, T_NIt is alternating voltage Standard primitive period, T is the actual cycle of ac voltage signal to be asked, and τ is the sampling period, and N is a standard primitive period Sampling number；

In formula, u (t), u (t-N τ), u (t- τ), u (t-N τ+τ) are respectively t, t-N τ, t- τ, t-N τ+τ moment alternating voltages Instantaneous value, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is sampling period, N It is the sampling number of standard primitive period；

Standard primitive period and one group of deviation of actual cycle are tried to achieve according to formula (7)：

In formula, Δ T_a(t)、ΔT_bT () is respectively t according to standard fundamental wave required by two different interpolation of same sampled point Cycle and actual cycle deviation, u (t), u (t-N τ), u (t- τ), u (t-N τ+τ) are respectively t, t-N τ, t- τ, t-N τ+τ moment and hand over Stream instantaneous voltage, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is sampling Cycle, N is the sampling number of standard primitive period；

Calculate t deviation average Δ T (t) be：

In formula, Δ T_a(t) and Δ T_bT () is respectively t according to same sampled point difference interpolation (i.e. 2 points of a, b in Fig. 1) Required standard primitive period and actual cycle deviation.

Step 3：The weight of each sampled point deviation is asked for, and obtains the weighted average of deviation to be specially：

Within 0~(m-1) τ time periods, the weight α (t) for making t deviation average Δ T (t) is

In formula, D (t)=u (t)-u (t- τ), wherein u (t), u (t- τ) are respectively t, t- τ moment alternating voltage instantaneous values, τ It it is the sampling period, N is the sampling number of standard primitive period；

Then the m deviation of sampled point is by the deviation delta T ' that weighted average is tried to achieve

In formula, Δ T (t) is t deviation average, and τ is the sampling period, and α (t) is t deviation average Δ T (t) Weight,

Formula after abbreviation is

In formula, D (t)=u (t)-u (t- τ), u (t), u (t-N τ), u (t- τ) are respectively t, t-N τ, t- τ moment alternating currents Pressure instantaneous value, τ is the sampling period, and N is the sampling number of standard primitive period.

Step 4：The final weighted average according to signal actual cycle and the deviation of standard primitive period obtains frequency, has Body is

According to the weighted average of the deviation obtained in step 3, by formula (12) calculated rate,

In formula, f is frequency input signal to be asked, and T is the cycle of input signal to be asked, T_NFor the standard primitive period isf_NFor standard fundamental frequency is power frequency, Δ T ' is to try to achieve deviation after weighted average.

Frequency measurement process is as shown in Figure 1.The present invention proposes a kind of frequency measuring method based on linear interpolation principle cross algorithms. It is hereafter different with frequency, as a example by the input signal of the identical voltage of amplitude.

1) present invention voltage signal in power network is sampled with 50kS/s sample rates, then the sampling period beObtain discrete equally spaced sampled point u (n).Standard fundamental frequency is f_N=50Hz, then standard fundamental wave is all Phase isThen sampling number is in a standard primitive period

If 2) first frequency measurement, from the discrete data of collection taking out 2N=2000 data is stored in array u, otherwise from In taking out N number of Refresh Data array u in the discrete data of collection, even u (t+1000)=u (t), then again will the new number for extracting According to being added sequentially to u (t), wherein t=0~999.

3) deviation of signal is directly calculated according to formula after abbreviation, specially：

In formula, D (t)=u (t)-u (t-N τ), m=N, τ are the sampling period, and N is the sampled point of standard primitive period Number.

4) measurement frequency of input signal is

In formula, f is input signal measurement frequency, and T is the measure the cycle of input signal, T_NFor the standard primitive period isf_NFor standard fundamental frequency is power frequency 50Hz, Δ T ' is to try to achieve deviation after weighted average.

Measurement error rate is

In formula, f₀It is the actual test frequency of input signal, f is the measured frequency of the present invention, and Δ f is frequency measurement error rate

Different frequency input signal comparing result is shown in Table 1

Table 1 frequency measurement result (N=1000m=N, f_N=50Hz)

After being calculated by specific steps, it is possible to draw accurate measurement frequency.

The content not being described in detail in this manual belongs to the known technology of those skilled in the art.

The above, specific embodiment only of the invention, but protection scope of the present invention is not limited thereto, and it is any The change or replacement expected without creative work, should all be included within the scope of the present invention.Therefore, it is of the invention Protection domain should be determined by the scope of protection defined in the claims.

Claims (5)

1. a kind of cross algorithm frequency measuring methods based on linear interpolation principle, it is characterised in that the frequency measurement method is included such as Lower step：

Step 1：Equal interval sampling is carried out to input signal, discrete equally spaced sampled point is obtained；

Step 2：The cycle of input signal to be asked and the average deviation of standard primitive period are calculated according to linear interpolation principle；

Step 3：The weight of each sampled point deviation is asked for, and seeks the weighted average of deviation；

Step 4：The final weighted average according to signal actual cycle and the deviation of standard primitive period obtains frequency.

2. a kind of cross algorithm frequency measuring methods based on linear interpolation principle according to claim 1, it is characterised in that： The step 1 carries out equal interval sampling to input voltage signal, obtains discrete equally spaced sampled point and is specially：

If it is f that the standard fundamental frequency of input voltage signal is power frequency_N, sample rate is f_s, then the standard primitive period be Sampling number in the standard primitive period isSampling periodIt is derived from discrete equally spaced sampled point.

3. a kind of cross algorithm frequency measuring methods based on linear interpolation principle according to claim 1, it is characterised in that： The average deviation in cycle and standard primitive period that the use in the step 2 calculates voltage signal to be asked based on linear interpolation has Body is：

If alternating voltage is mathematically represented as：

In formula, u (t) is t alternating voltage instantaneous value, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency,It is electricity Pressure initial phase angle；

If t-T_NMoment alternating voltage instantaneous value is：

In formula, u (t-T_N) it is t-T_NMoment alternating voltage instantaneous value, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency, It is voltage initial angle, T_NIt is the standard primitive period.

If the alternating voltage instantaneous value at t- τ moment is：

In formula, u (t- τ) is t- τ moment alternating voltage instantaneous values, U_mIt is alternating voltage amplitude, ω is alternating voltage angular frequency, and τ is Sampling period,It is voltage initial angle；

Formula (4), (5), (6) can be obtained according to linear interpolation principle；

$\left\{\begin{array}{c}\frac{u\left(t\right)-u\[t-(T_N-T)\]}{T_N-T}=\frac{u\left(t\right)-u(t-\mathrm{\τ})}{\mathrm{\τ}}\\ \frac{u\left(t\right)-u\[t-(T_N-T)\]}{T_N-T}=\frac{u\[t-(T_N-T)+\mathrm{\τ}\]+u(t-T_N)}{\mathrm{\τ}}\end{array}\right.---\left(4\right)$

In formula, u (t), u [t- (T_N-T)]、u(t-τ)、u[t-(T_N- T)+τ] it is respectively t, t- (T_N-T)、t-τ、t-(T_N- T)+τ when Carve alternating voltage instantaneous value, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is Sampling period；

$\left\{\begin{array}{c}u\[t-(t_N-T)\]=u(t-T_N)=u(t-N\mathrm{\τ})\\ u\[t-(T_N-T)+\mathrm{\τ}\]=u(t-T_N+\mathrm{\τ})=u(t-N\mathrm{\τ}+\mathrm{\τ})\end{array}\right.---\left(5\right)$

In formula, u [t- (T_N-T)]、u(t-T_N)、u(t-Nτ)、u[t-(T_N-T)+τ]、u(t-T_N+ τ), u (t-N τ+τ) be respectively t- (T_N-T)、t-T_N、t-Nτ、t-(T_N-T)+τ、t-T_N+ τ, t-N τ+τ moment alternating voltage instantaneous values, T_NIt is the standard of alternating voltage Primitive period, T is the actual cycle of ac voltage signal to be asked, and τ is the sampling period, and N is the sampling of standard primitive period Points；

$\left\{\begin{array}{c}\frac{u\left(t\right)-u(t-N\mathrm{\τ})}{N\mathrm{\τ}-T}=\frac{u\left(t\right)-u(t-\mathrm{\τ})}{\mathrm{\τ}}\\ \frac{u\left(t\right)-u(t-N\mathrm{\τ})}{T_N-T}=\frac{u\[t-N\mathrm{\τ}+\mathrm{\τ}\]-u(t-N\mathrm{\τ})}{\mathrm{\τ}}\end{array}\right.---\left(6\right)$

In formula, it is instantaneous that u (t), u (t-N τ), u (t- τ), u (t-N τ+τ) are respectively t, t-N τ, t- τ, t-N τ+τ moment alternating voltages Value, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is the sampling period, and N is one The sampling number of individual standard primitive period；

Standard primitive period and one group of deviation of actual cycle are tried to achieve according to formula (7)：

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_a\left(t\right)=T_N-T=N\mathrm{\τ}-T=\frac{u\left(t\right)-u(t-N\mathrm{\τ})}{u\left(t\right)-u(t-\mathrm{\τ})}\·\mathrm{\τ}\\ {\mathrm{\ΔT}}_b\left(t\right)=T_N-T=N\mathrm{\τ}-T=\frac{u\left(t\right)-u(t-N\mathrm{\τ})}{u(t-N\mathrm{\τ}+\mathrm{\τ})-u(t-\mathrm{\τ})}\·\mathrm{\τ}\end{array}\right.---\left(7\right)$

In formula, Δ T_a(t)、ΔT_bT () is respectively t according to the standard primitive period required by two different interpolation of same sampled point With actual cycle deviation, u (t), u (t-N τ), u (t- τ), u (t-N τ+τ) are respectively t, t-N τ, t- τ, t-N τ+τ moment alternating currents Pressure instantaneous value, T_NIt it is the standard primitive period of alternating voltage, T is the actual cycle of ac voltage signal to be asked, and τ is sampling week Phase, N is the sampling number of standard primitive period；

Calculate t deviation average Δ T (t) be：

$\mathrm{\Δ}T\left(t\right)=\frac{{\mathrm{\ΔT}}_a\left(t\right)+{\mathrm{\ΔT}}_b\left(t\right)}{2}---\left(8\right)$

In formula, Δ T_a(t) and Δ T_bT () is respectively t according to standard primitive period and reality required by same sampled point difference interpolation Border periodic deviation.

4. a kind of cross algorithm frequency measuring methods based on linear interpolation principle according to claim 1, it is characterised in that： The weight of each sampled point deviation is asked in the step 3, and obtains the weighted average of deviation to be specially：

Within 0~(m-1) τ time periods, the weight α (t) for making t deviation average Δ T (t) is

$\mathrm{\α}\left(t\right)=\frac{D\left(t\right)\·D(t-N\mathrm{\τ}+\mathrm{\τ})}{\underset{t=0}{\overset{(m-1)\·\mathrm{\τ}}{\Σ}}\[D\left(t\right)\·D(t-N\mathrm{\τ}+\mathrm{\τ})\]}---\left(9\right)$

In formula, D (t)=u (t)-u (t- τ), wherein u (t), u (t- τ) are respectively t, t- τ moment alternating voltage instantaneous values, and τ is to adopt Sample cycle, N is the sampling number of standard primitive period；

Then the m deviation of sampled point is by the deviation delta T ' that weighted average is tried to achieve

${\mathrm{\ΔT}}^{\′}=\underset{t=0}{\overset{(m-1)\·\mathrm{\τ}}{\Σ}}\mathrm{\Δ}T\left(t\right)\·\mathrm{\α}\left(t\right)---\left(10\right)$

In formula, Δ T (t) is t deviation average, and τ is the sampling period, and α (t) is the power of t deviation average Δ T (t) Heavy, the formula after abbreviation is

${\mathrm{\ΔT}}^{\′}=\frac{0.5\·\underset{t=0}{\overset{(m-1)\·\mathrm{\τ}}{\Σ}}\[u\left(t\right)-u(t-N\mathrm{\τ})\]\[D\left(t\right)+D(t-N\mathrm{\τ}+\mathrm{\τ})\]}{\underset{t=0}{\overset{(m-1)\·\mathrm{\τ}}{\Σ}}\[D\left(t\right)\·D(t-N\mathrm{\τ}+\mathrm{\τ})\]}\·\mathrm{\τ}---\left(11\right)$

In formula, D (t)=u (t)-u (t- τ), u (t), u (t-N τ), u (t- τ) are respectively t, t-N τ, t- τ moment alternating voltage winks Duration, τ is the sampling period, and N is the sampling number of standard primitive period.

5. a kind of cross algorithm frequency measuring methods based on linear interpolation principle according to claim 1, it is characterised in that： Asking for the specific formula of frequency according to signal actual cycle and the weighted average deviation of normal period in the step 4 is：

According to the weighted average of the deviation obtained in step 3, by formula (12) calculated rate,

$f=\frac{1}{T}=\frac{1}{T_N-{\mathrm{\ΔT}}^{\′}}---\left(12\right)$

In formula, f is frequency input signal to be asked, and T is the cycle of input signal to be asked, T_NFor the standard primitive period is f_NFor standard fundamental frequency is power frequency, Δ T ' is to try to achieve deviation after weighted average.