CN103269211B - The digital filtering method of three-phase alternating current system measurement data - Google Patents

Abstract

A digital filtering method for measuring data in a three-phase AC system, comprising the steps of: converting three-phase voltage signals V _A , V _B , V _C into voltage signals V _α , V _β in a two-phase α β coordinate system; The transfer function performs low-pass filtering on the voltage signals V _α and V _β respectively to obtain the voltage signals V' _α and V'_β; calculate the fundamental frequency phase δ of the voltage signals V' _α and V'_β; calculate the low-pass Filtered fundamental frequency phase delay angle δ ₀ ; convert voltage signals V' _α , V' _β into DC voltages V _d , V _q in the rotating dq two-phase coordinate system according to the fundamental frequency phase δ; use δ‑δ ₀ as the transformation Convert the DC voltage V _d , V _q into voltage signals V' _A , V' _B , V' _C in three-phase coordinates. The above-mentioned digital filtering method for the measurement data of the three-phase AC system can effectively solve the fundamental frequency phase delay problem of the traditional filtering method, and improve the phase control accuracy of the power system.

Description

Digital Filtering Method of Measured Data in Three-phase AC System

technical field

The invention relates to the technical field of digital filtering, in particular to a digital filtering method for measurement data of a three-phase AC system.

Background technique

With the application of high-power switching devices in wind power generation, photovoltaic power generation, flexible AC transmission and other fields, the power system presents more and more significant nonlinearity, especially in voltage source converters based on pulse width modulation (PWM) technology ( In VSC) applications, the amplitude of the high-order characteristic harmonics is close to or even exceeds the amplitude of the fundamental frequency. In order to solve the above problems, a filter can be installed on the primary side of the system. , uncertainty, and the high cost of filtering equipment, the effect obtained by this technology is extremely unsatisfactory.

Due to the waveform distortion caused by high-order harmonics, the system cannot be normally controlled and accurately measured. Therefore, the existing power system generally performs first-order or high-order low-pass digital filtering on the sampled data in the measurement link on the secondary side of the system. The current main research is on the parameter design of the transfer function H(s). However, any physically realizable system will have a delay in practice. No matter how the coefficients in the transfer function H(s) are designed, after the three-phase AC system measurement data is filtered, it is difficult to avoid the fundamental frequency phase delay before and after filtering. The harmonic distortion rate (THD) of the measured data of the three-phase AC system is still high, which makes the phase control of the power system have serious deviations.

Contents of the invention

Based on this, it is necessary to provide a digital filtering method for the measurement data of the three-phase AC system to solve the above problems.

A digital filtering method for measurement data of a three-phase AC system, comprising the steps of:

Convert the three-phase voltage signals V _A , V _B , V _C into voltage signals V _α , V _β in the two-phase αβ coordinate system;

Perform low-pass filtering on the voltage signals V _α and V _β respectively according to the set transfer function to obtain voltage signals V' _α and V'_β;

calculating the fundamental frequency phase δ of the voltage signals V' _α and V'_β;

calculating the fundamental frequency phase delay angle δ ₀ of the low-pass filter according to the transfer function;

Converting the voltage signals V' _α and V' _β into DC voltages V _d and V _q in the rotating dq two-phase coordinate system according to the fundamental frequency phase δ;

The DC voltages V _d , V _q are converted into voltage signals V' _A , V' _B , V' _C in three-phase coordinates by taking δ-δ ₀ as a transformation angle.

The above-mentioned digital filtering method for the measurement data of the three-phase AC system first transforms the three-phase voltage signal from the ABC three-phase coordinates to the αβ two-phase coordinates, and then performs low-pass filtering in the αβ coordinate system, and the filtered fundamental frequency value is determined by the αβ coordinates It is transformed into the DC quantity under the dq rotating coordinate system, and the fundamental frequency phase delay δ ₀ generated by the low-pass filter is compensated when the dq coordinates are transformed back to the ABC coordinates, thereby effectively solving the fundamental frequency phase delay problem of the traditional filtering method, Improve the phase control accuracy of the power system.

Description of drawings

Fig. 1 is the flow chart of the digital filtering method of the three-phase AC system measurement data of an embodiment;

Fig. 2 is a schematic diagram of the structure of the simulation example experimental model;

Figure 3 is a schematic diagram of the simulation experiment results.

detailed description

The specific implementation manner of the digital filtering method for the measurement data of the three-phase AC system of the present invention will be described in detail below in conjunction with the accompanying drawings.

Fig. 1 shows a flow chart of a digital filtering method for three-phase AC system measurement data of an embodiment, including the following steps:

Step S101: Transform the three-phase voltage signals V _A , V _B , V _C into voltage signals V _α , V _β in the two-phase αβ coordinate system.

In one embodiment, before step S101, it further includes: sampling the measurement data of the three-phase AC system to obtain voltage signals V _A , V _B , and V _C in three-phase coordinates.

Specifically, in step S101, the voltage data V _A , V _B , and V _C obtained by measurement and sampling are transformed from the static ABC three-phase coordinates to the static αβ two-phase coordinates. The conversion formula is as follows:

Among them, the ABC→αβ coordinate transformation is an orthogonal transformation, and the α phase is set to have the same axis as A.

Step S102: performing low-pass filtering on the voltage signals V _α and V _β respectively according to the set transfer function to obtain voltage signals V' _α and V' _β .

Specifically, the calculation process includes the following formulas:

In the formula, H(s) is the set transfer function,

Step S103: Calculate the fundamental frequency phase δ of the voltage signals V' _α and V' _β .

Specifically, the calculation process includes the following formulas:

δ=arctg(V' _β /V' _α );

In the formula, δ is the fundamental frequency phase, and V' _α and V' _β are the voltage signals of αβ coordinates after filtering.

Step S104: Calculate the fundamental frequency phase delay angle δ ₀ of the low-pass filter according to the transfer function.

Specifically, the angle of the transfer function H(jω) is the phase delay angle δ ₀ of the low-pass filter link, that is, after the low-pass filter, the fundamental frequency phase δ of the voltage signal in the two-phase αβ coordinate system is relative to A in the three-phase coordinate system , B, C three-phase voltage signal delay δ ₀ , the calculation process of δ ₀ includes the following formula:

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctg</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; H</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The transfer function of the low-pass filter is H (jω), and its general formula can be expressed as:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$

Wherein, a ₀ , a ₁ , b ₀ , b ₁ , and b ₂ are preset constants, the modulus value |H(jω)| of H(jω) is equal to 1, and ω is the fundamental angular frequency.

Step S105: Transform the voltage signals V' _α , V' _β into DC voltages V _d , V _q in the rotating dq two-phase coordinate system according to the fundamental frequency phase δ.

Specifically, the calculation process includes the following formulas:

V _d +jV _q =(V _α +jV _β )e ^-jδ ;

In the formula, V' _α and V' _β are the voltage signals of the αβ coordinates after filtering, δ is the fundamental frequency phase, and V _d and V _q are the voltage signals of the dq rotating coordinate system respectively.

Step S106: Transform the DC voltages V _d and V _q into AC voltage signals V' _A , V' _B and V' _C in three-phase coordinates with δ-δ ₀ as the conversion angle.

Specifically, transform the variables from the rotating dq two-phase coordinates back to the static ABC three-phase coordinates, set the q-axis ahead of the d-axis, and the transformation angle is δ-δ ₀ , the calculation process includes the following:

In the formula, θ=δ-δ ₀ , through the above process, the fundamental frequency phase delay δ ₀ generated in the low-pass filtering process is compensated in the dq→ABC coordinate transformation link.

The digital filtering method of the measurement data of the three-phase AC system of the present invention is aimed at the measurement data processing of the three-phase AC system, and first transforms the sampled three-phase voltage signal (including higher harmonics) from the ABC three-phase coordinates to the αβ two-phase coordinates , and then perform low-pass filtering in the αβ coordinate system, and the filtered fundamental frequency value is transformed from the αβ coordinate to the DC quantity in the dq rotating coordinate system, and the fundamental frequency phase delay δ ₀ generated by the low-pass filter is transformed by the dq coordinate Compensation is performed when returning to the ABC coordinates, thus effectively solving the fundamental frequency phase delay problem of the traditional filtering method.

In order to clarify the technical solution of the present invention, a simulation example will be described below in conjunction with the accompanying drawings.

See Figure 2, which is a schematic diagram of the structure of the simulation example experimental model, in which the transfer function of the low-pass filter adopts the simplest first-order filter H(jω)=G/(1+Ts), and the parameters G=1.606, T= 0.004 seconds.

Then the input ABC three-phase voltage signal is V _A , V _B , V _C , the effective value of the phase voltage of the fundamental frequency (50Hz) is 1.0, the content of the 7th harmonic is 10%, the content of the 19th harmonic is 180%, and the total harmonic The wave distortion rate (THD) is 180.278%, and the output voltage signals after filtering are V' _A , V' _B , V' _C .

As shown in Figure 3, Fig. 3 is the schematic diagram of simulation experiment result, among the figure V _A is the A-phase voltage signal waveform of input, and wherein, V' _A is the A-phase voltage signal waveform of output after filtering through the filtering method of the present invention, The effective value of the fundamental frequency of V' _A is 1.0, and the phase is the same as that of V _A , the 7th harmonic content is 1.812%, the 19th harmonic content is 12.007%, and the total harmonic distortion (THD) is 12.143%.

It can be seen from the experimental results of the above simulation examples that even if the transfer function H(s) adopts the unoptimized and simplest first-order low-pass filter function, the filtering method of the present invention can also reduce the total harmonic distortion (THD) More than 90%, and the amplitude and phase of the fundamental frequency remain unchanged.

The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but should not be construed as limiting the patent scope of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent for the present invention should be based on the appended claims.

Claims (5)

1. the digital filtering method of a three-phase alternating current system measurement data, it is characterised in that comprise the steps:

By three-phase voltage signal V_A、V_B、V_CBe converted to the voltage signal V under biphase α β coordinate system_α、V_β；

According to the transmission function set respectively to described voltage signal V_α、V_βCarry out low-pass filtering and obtain voltage signal V'_α、V'_β；

Calculate described voltage signal V'_α、V'_βBase Ld phase δ；

The base Ld phase delay angle δ of described low-pass filtering is calculated according to described transferometer₀；Including:

${\mathrm{\&delta;}}_0=arctg\left(\frac{\mathrm{Im}H\left(j\mathrm{\&omega;}\right)}{\mathrm{Re}H\left(j\mathrm{\&omega;}\right)}\right);$

Wherein, H (j ω) is transmission function, and its formula can be expressed as:

$H\left(j\mathrm{\&omega;}\right)=\frac{a_0+a_{1}j\mathrm{\&omega;}}{b_0+b_{1}j\mathrm{\&omega;}-b_2{\mathrm{\&omega;}}^2};$

Wherein, a₀、a₁、b₀、b₁、b₂For default constant, equal to 1, ω is fundamental frequency angular frequency to the modulus value of H (j ω) | H (j ω) |, j Imaginary part for plural number；

According to described base Ld phase δ by described voltage signal V'_α、V'_βBe converted to rotate the DC voltage under dq two phase coordinate system V_d、V_q；

With δ-δ₀For angle of transformation by described DC voltage V_d、V_qBe converted to the voltage signal V' under three phase coordinates_A、V'_B、V'_C。

The digital filtering method of three-phase alternating current system measurement data the most according to claim 1, it is characterised in that described By three-phase voltage signal V_A、V_B、V_CBe converted to the voltage signal V under biphase α β coordinate system_α、V_βStep also include:

The measurement data of three-phase alternating current system is carried out the voltage signal V under sampling acquisition three phase coordinates_A、V_B、V_C。

The digital filtering method of three-phase alternating current system measurement data the most according to claim 1, it is characterised in that described meter Calculate described voltage signal V'_α、V'_βThe step of base Ld phase δ include:

δ=arctg (V'_β/V'_α)；

In formula, δ is base Ld phase, V'_α、V'_βIt is respectively the voltage signal under α β coordinate after filtering.

The digital filtering method of three-phase alternating current system measurement data the most according to claim 1, it is characterised in that described According to described base Ld phase δ by described voltage signal V'_α、V'_βBe converted to rotate the DC voltage V under dq two phase coordinate system_d、V_q's Step includes:

V_d+jV_q=(V_α+jV_β)e^-jδ；

In formula, V'_α、V'_βBeing respectively the voltage signal under α β coordinate after filtering, δ is base Ld phase, V_d、V_qIt is respectively the biphase seat of dq Voltage signal under Biao, j is the imaginary part of plural number.

The digital filtering method of three-phase alternating current system measurement data the most according to claim 1, it is characterised in that with δ-δ₀ For angle of transformation by described DC voltage V_d、V_qBe converted to the voltage signal V' under three phase coordinates_A、V'_B、V'_CStep include:

Wherein, θ=δ-δ₀。