CN114325107A - A method for judging the accuracy of harmonic impedance calculation results - Google Patents

Abstract

The invention discloses a method for judging the accuracy of a harmonic impedance calculation result, which divides nonlinear users into two types according to the condition that the nonlinear users stop operating: only cutting off the harmonic source and keeping the user side impedance connected with the power grid (such as a photovoltaic station and the like), and cutting off the harmonic source and the user side impedance (such as an electric arc furnace and the like); determining the difference between the IEC method and the superposition principle method and the respective application range thereof in the process of verifying and solving the accuracy of the harmonic impedance; based on the characteristics of the two methods and the category of the nonlinear user, the method capable of accurately verifying and obtaining the correctness of the harmonic impedance is provided.

Description

A method for judging the accuracy of harmonic impedance calculation results

technical field

The invention relates to the technical field of power quality sharing, in particular to a method for judging the accuracy of a harmonic impedance calculation result.

Background technique

With the development of power electronic equipment and the increase of nonlinear loads, the harmonic pollution in the power system is becoming more and more serious. Accurate calculation of harmonic impedance is one of the keys to study harmonic problems. Based on the harmonic measurement data at the point of common coupling (Point of Common Coupling PCC), existing scholars have proposed several non-intrusive harmonic impedance estimation methods. After calculating the harmonic impedance, it is necessary to verify the correctness of the calculation result. Accurate estimation of harmonic impedance is important for quantifying harmonic liability, filter design, harmonic control, and system resonance prediction. However, there is still no unified method to verify the correctness of the harmonic impedance.

The main idea of the existing method is to compare the calculated background harmonic voltage with the measured voltage of the PCC point after the user quits operation. If the obtained background harmonic voltage is not much different from the measured voltage of the PCC point, it means that the harmonic impedance has been calculated. Accurate; on the contrary, it shows that there is a large error in the obtained harmonic impedance. Background harmonics can be calculated according to IEC61000-3-6 (called IEC method) or superposition principle method. However, the existing research ignores one point when verifying the accuracy of the harmonic impedance, that is, the IEC method and the superposition principle method have different basic principles, so they need to be selected according to the actual working conditions, and cannot be selected arbitrarily, otherwise there may be Risk of misjudgment of harmonic impedance accuracy.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to divide the nonlinear users into two types of models through the IEC method and the superposition principle, and analyze the differences and application scopes of the two types of models in detail, and then propose an accuracy of harmonic impedance calculation results. Judgment method. The technical solution is as follows:

A method for judging the accuracy of a harmonic impedance calculation result, comprising the following steps:

Step 1: Divide the nonlinear users into Class A nonlinear users and Class B nonlinear users, and calculate the harmonic voltage measured at the PCC when each type of nonlinear user exits operation, that is, the reference voltage of the background harmonics;

由下式求得：1) The Class A nonlinear user is the user whose harmonic source and harmonic impedance are disconnected when it stops running. This class of users calculates the background harmonic voltage according to the circuit model of the IEC method; defines the A of the background harmonic. The class reference voltage is

It is obtained by the following formula:

分别为系统侧的谐波阻抗与谐波电流；Among them, _Zu and

are the harmonic impedance and harmonic current on the system side, respectively;

将与A类参考电压

相等；When the harmonic impedance Zu on the system side is accurately obtained, the background harmonic voltage calculated according to the IEC method

will be with the class A reference voltage

equal;

由下式求得：2) The class B nonlinear user is the user whose harmonic source is cut off and the harmonic impedance is still connected to the power grid when it stops running. This type of user calculates the background harmonic voltage according to the superposition principle model; defines the background harmonic The class B reference voltage is

It is obtained by the following formula:

Among them, Z _c is the harmonic impedance of the user side;

与B类参考电压

相等；When the user-side harmonic impedance Zc and the system-side harmonic impedance Zu are accurately obtained, the background harmonic voltage calculated according to the superposition principle

with class B reference voltage

equal;

Step 2: Verify the accuracy of the obtained harmonic impedance according to the magnitude relationship between the user-side harmonic impedance Zc and the system-side harmonic impedance Zu. The detailed process is as follows:

A) Cases where |Zc| is not much larger than |Zu|

对B类非线性用户采用叠加原理计算

据此验证求得系统侧谐波阻抗Zu和用户侧谐波阻抗Zc的准确性；Calculated by IEC method for Class A nonlinear users

Superposition principle calculation for class B nonlinear users

Based on this, the accuracy of obtaining the harmonic impedance Zu on the system side and the harmonic impedance Zc on the user side is verified;

B) Cases where |Zc| is much larger than |Zu|

Since |Z _c |>>|Z _u |, there is Z _u /Z _c ≈0, and the formula for calculating the background harmonic voltage according to the superposition principle is transformed into the following formula:

与

彼此近似相等，无论是A类非线性用户还是B类非线性用户，均能够基于IEC方法或叠加原理验证求得系统侧谐波阻抗Zu的准确性。but

and

They are approximately equal to each other. Whether it is a Class A nonlinear user or a Class B nonlinear user, the accuracy of the harmonic impedance Zu on the system side can be obtained based on the IEC method or the superposition principle verification.

Further, the method for judging the magnitude relationship between |Zc| and |Zu| is:

When |Zc|>>|Zu|, there is Z _u /Z _c ≈0, so there is

为公共线路上测得的谐波电流，

为用户侧的谐波电流；in,

is the harmonic current measured on the public line,

is the harmonic current on the user side;

与

之间的相似性，间接地评估|Z_c|>>|Z_u|是否成立。by quantifying

and

The similarity between , indirectly evaluates whether |Z _c |>>|Z _u | holds.

Further, in the process of evaluating whether |Z _c |>>|Z _u | is true, the harmonic current on the user side of the source signal is reconstructed by the independent component method

According to the Norton equivalent circuit, when the nonlinear user is connected to the system, there is

与公共线路上测得的谐波电流

构成；矩阵I由谐波源信号系统侧谐波电流

与用户侧谐波电流

构成；矩阵Z由PCC点两侧谐波阻抗构成；Among them, the matrix X is the harmonic voltage measured by the observation signal PCC point

and harmonic currents measured on the public line

The matrix I is composed of harmonic currents on the system side of the harmonic source signal system.

and user side harmonic current

composition; matrix Z is composed of harmonic impedances on both sides of the PCC point;

和

再通过ICA算法重构谐波源信号

Firstly, the fast-varying component of the signal is extracted by median filtering technique

and

Then reconstruct the harmonic source signal through the ICA algorithm

与

之间的相似性则通过相关系数量化；while the signal

and

The similarity between them is quantified by the correlation coefficient;

If the correlation coefficient is greater than the set value, then |Zc|>>|Zu|, otherwise |Zc| is not much larger than |Zu|.

The beneficial effects of the present invention are as follows: the present invention divides nonlinear users into two categories according to the situation that they stop running: 1) only cut off the harmonic source and keep its user-side impedance connected to the power grid (such as photovoltaic stations, etc.), 2) ) cut off the harmonic source and user side impedance (such as electric arc furnace, etc.). Then, the present invention studies the difference between the IEC method and the superposition principle method and their respective applicable ranges in the process of verifying the accuracy of obtaining the harmonic impedance. Finally, based on the characteristics of these two methods and the types of nonlinear users, a method that can accurately verify the correctness of harmonic impedance is proposed.

Description of drawings

Figure 1 shows the equivalent circuit corresponding to the IEC method.

Figure 2 shows the equivalent circuit corresponding to the superposition principle method.

Figure 3 is a flowchart of a method for judging the accuracy of harmonic impedance calculation results.

Figure 4 is the 9th harmonic data of photovoltaic field; (a) harmonic current (b) harmonic voltage.

Figure 5 is the measured data of the 5th harmonic of the electric arc furnace; (a) the measured harmonic voltage at the PCC point (b) the measured harmonic current of the public line.

Figure 6 is the 5th harmonic data of the electric arc furnace; (a) harmonic current analysis (b) harmonic voltage analysis.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. In practical engineering, by comparing the obtained background harmonic voltage with the voltage measured at the PCC point when the user is not working, the accuracy of the obtained harmonic impedance can be indirectly verified. Generally speaking, there are two methods for calculating background harmonics: IEC method and superposition principle method. The specific principles of these two methods are as follows.

(1) Calculate the background harmonic voltage according to the IEC method

分别是系统侧与用户侧的谐波阻抗与谐波电流源。

与

分别为PCC点测得的谐波电压以及公共线路上测得的谐波电流。In the Norton equivalent circuit corresponding to the IEC method shown in Figure 1, Zu, Zc,

They are the harmonic impedance and harmonic current source on the system side and the user side, respectively.

and

are the harmonic voltage measured at the PCC point and the harmonic current measured on the public line, respectively.

When the switch is closed and the user is connected to the grid, the harmonic voltage at the PCC is

When the switch is turned off, the user side stops running, and the harmonic voltage at the PCC is

According to the definition of harmonic emission level in the IEC61000-3-6 standard, the harmonic voltage emission level of a nonlinear user is the difference between the harmonic voltage at the PCC point before the user side is connected to the network and after the user is out of operation. Referring to this standard, the harmonic emission levels on the user side and the system side can be expressed as

(2) Calculate the background harmonic voltage according to the superposition principle

Figure 2 is the Norton circuit corresponding to the superposition principle method. When the system side harmonic source and the nonlinear user harmonic source work alone, the harmonic voltage at the PCC point is the respective harmonic voltage emission levels of the system side and the user side, which are expressed as

(3) Verify the method for obtaining the accuracy of harmonic impedance

When the nonlinear user is connected to the power grid, if Zu and Zc can be accurately estimated, the obtained background harmonic voltage is also accurate. Using this principle can indirectly verify the accuracy of the obtained harmonic impedance. When the nonlinear user is out of operation, the harmonic voltages measured at the PCC can be considered as reference voltages for the background harmonics. Therefore, the correctness of the obtained Zu and Zc can be verified by comparing the obtained background harmonic voltage with the reference voltage.

In practice, nonlinear users are diverse and complex. The present invention divides nonlinear users into the following two categories according to the way they exit from operation.

1) Model A:

通过将式(4)中的

替换为

即可计算

因此，当准确求得Zu之后，

将与

相等。值得注意的是，由于式(4)中不含有Zc，因此该方法不能验证求得Zc的正确性。For nonlinear users such as electric arc furnaces, when the user is not working, both the harmonic source and the harmonic impedance are disconnected. For such users, the background harmonic voltage should be calculated according to the circuit model of the IEC method. The reference voltage is defined as

By putting in formula (4)

replace with

can be calculated

Therefore, when Zu is accurately obtained,

Will

equal. It is worth noting that since formula (4) does not contain Zc, this method cannot verify the correctness of Zc.

2) Model B:

通过将式(5)中的

替换为

即可计算

当准确求得Zc与Zu后，则有

与

相等。值得注意的是，由于式(5)中同时含有Zc与Zu，因此该方法可同时验证求得Zc与Zu的正确性。For nonlinear users such as wind farms and photovoltaic power plants, when the user stops running, the harmonic source is cut off, while the harmonic impedance is still connected to the grid. For such users, the background harmonic voltage should be calculated according to the superposition principle model. The reference voltage is defined as

By putting in formula (5)

replace with

can be calculated

When Zc and Zu are accurately obtained, then we have

and

equal. It is worth noting that since formula (5) contains both Zc and Zu, this method can verify the correctness of Zc and Zu at the same time.

After the user category is determined, the accuracy of the harmonic impedance can be verified based on the magnitude relationship between Zc and Zu. The detailed process is as follows.

A) Cases where |Zc| is not much larger than |Zu|

与

彼此不相等。因此，

将不等于

并且

也不等于

理论上，对于模型A，由叠加原理计算出的背景谐波电压与用户切断后测得的谐波电压不匹配。同样，对于模型B，IEC方法计算的背景谐波电压与测得电压不匹配。因此，如果计算背景谐波电压的方法(即IEC方法或叠加原理)选择错误，即使计算结果准确，也会误认为求得谐波阻抗是错误的。When |Zc| is not much larger than |Zu|, according to equations (4) and (5), the obtained background harmonic voltage

and

are not equal to each other. therefore,

will not be equal to

and

does not mean

Theoretically, for model A, the background harmonic voltage calculated by the superposition principle does not match the harmonic voltage measured after the user cuts it off. Likewise, for Model B, the background harmonic voltages calculated by the IEC method do not match the measured voltages. Therefore, if the method for calculating the background harmonic voltage (ie the IEC method or the superposition principle) is selected incorrectly, even if the calculation result is accurate, it will be mistaken for the obtained harmonic impedance to be wrong.

In order to avoid the above misjudgments, it is necessary to use the correct method (IEC method or superposition principle method) to match the user model.

B) Cases where |Zc| is much larger than |Zu|

Under this working condition, the error of obtaining Zc is usually large, so it is only necessary to verify the accuracy of obtaining Zu. Since |Z _c |>>|Z _u |, there is Z _u /Z _c ≈0, equation (5) can be transformed into equation (7). Therefore, the background harmonic voltage can be calculated by the superposition principle with Zc unknown.

与

彼此近似相等。因此，无论是A类还是B类非线性用户，都可以基于IEC方法或叠加原理验证求得Zu的准确性。It is worth noting that at this time, equation (7) is equivalent to equation (5), and the obtained

and

are approximately equal to each other. Therefore, whether it is a class A or class B nonlinear user, the accuracy of Zu can be obtained based on the IEC method or the superposition principle verification.

C) The method of judging the relationship between |Zc| and |Zu|

When |Zc|>>|Zu|, there is Z _u /Z _c ≈0, so there is

与

之间的相似性，可间接地评估|Z_c|>>|Z_u|是否成立。在该评估过程中，可通过独立分量法(ICA Independent Component Analysis)重构源信号

ICA是一种盲源分离技术，它可从观测信号中提取潜在变量和原始信号。Therefore, by quantifying

and

The similarity between , can indirectly evaluate whether |Z _c |>>|Z _u | holds. During this evaluation, the source signal can be reconstructed by ICA Independent Component Analysis

ICA is a blind source separation technique that extracts latent variables and raw signals from observed signals.

According to the Norton equivalent circuit (Figure 1 or Figure 2), when a nonlinear user is connected to the system, there is

与

构成，矩阵I由谐波源信号

与

构成，矩阵Z由PCC点两侧谐波阻抗构成。在使用ICA算法之前，需要通过中值滤波技术提取信号的快变分量，以保证各源信号之间的独立性。通过ICA算法可重构谐波源信号

。而信号

与

之间的相似性则通过相关系数量化。相关系数越大，说明两信号越相似。In the formula: the matrix X is determined by the observed signal

and

constituted, matrix I consists of harmonic source signals

and

The matrix Z consists of harmonic impedances on both sides of the PCC point. Before using the ICA algorithm, it is necessary to extract the fast-changing components of the signal through median filtering technology to ensure the independence of each source signal. Harmonic source signal can be reconstructed by ICA algorithm

. while the signal

and

The similarity between them is quantified by the correlation coefficient. The larger the correlation coefficient, the more similar the two signals are.

The flow chart of the above-mentioned method for judging the accuracy of the obtained harmonic impedance is shown in FIG. 3 .

Example verification:

When the photovoltaic power plant stops running at night, the related electrical components (such as transformers, lines and filters, etc.) are still connected to the grid, therefore, only the harmonic source is disconnected from the circuit, and the harmonic impedance of the photovoltaic plant is still related to connected to the system side. The correctness of the method proposed in the present invention is demonstrated by taking a photovoltaic power plant in my country as a typical nonlinear user of model B.

与测得的

几乎吻合，且

与

之间的相关系数较大，为0.998，从而有|Z_c|>>|Z_u|。此时，理论上可通过对比

与

(或

)之间的相关性来判断求得Zu的准确性。而图4(b)表明，

和

均能与

相匹配，从而说明求得Zu具有很高精度。进而论证了所提方法的正确性。For the 9th harmonic, |Zc|>>|Zu| is satisfied, as shown in Fig. 4(a), due to the harmonic current obtained by ICA

with the measured

almost coincident, and

and

The correlation coefficient between is large, 0.998, so there is |Z _c |>>|Z _u |. At this point, theoretically, by comparing

and

(or

) to judge the accuracy of Zu. While Figure 4(b) shows that,

and

can be combined with

match, which shows that the obtained Zu has very high accuracy. Furthermore, the correctness of the proposed method is demonstrated.

Best Practices for Specific Applications:

The electric arc furnace, as a typical nonlinear user in Model A, can be used to verify the correctness of the proposed method. Harmonic data was measured from the 150kV bus of a 100MW DC electric arc furnace with a sampling frequency of 6400Hz. The minute-by-minute voltage and current sample data are analyzed using the Fast Fourier Transform to obtain the harmonics of each harmonic.

In this case, two single-tuned filters are installed on the user side to mitigate the 5th and 7th harmonics. The installation of the filter will result in |Zc| not much larger than |Zu|. The 5th harmonic voltage and current are shown in Figure 5. After 1000 minutes, the electric arc furnace was stopped for a short period of time (corresponding to the downtime).

以及分离所得的用户侧谐波电流

如图6(a)所示。可见，在测得的

与求得

之间存在较大差异。此外，

与

之间的相关系数比较小，仅0.33。从而说明|Z_c|并非远大于|Z_u|。基于本发明所得方法，

应与

匹配，而与

不匹配。图6(b)表明，实测

与求得的

幅值基本相等，从而论证了所求Zu的正确性。相比之下，

与

之间差异较大，说明若采用叠加原理方法来分析求得背景谐波正确性，则会误认为求得的Zu具有较大计算误差。The ICA algorithm is used to calculate the harmonic impedance on both sides of the PCC point, and the obtained background harmonic current

and the separated user-side harmonic currents

As shown in Figure 6(a). It can be seen that the measured

and seek

There is a big difference between them. also,

and

The correlation coefficient between them is relatively small, only 0.33. This shows that |Z _c | is not much larger than |Z _u |. Based on the method obtained by the present invention,

should match

matches, while

Mismatch. Figure 6(b) shows that the measured

with the sought

The amplitudes are basically equal, which proves the correctness of Zu. In contrast,

and

The difference between them is large, indicating that if the superposition principle method is used to analyze and obtain the correctness of the background harmonics, it will be mistaken for the obtained Zu to have a large calculation error.

Claims (3)

1. a method for judging the accuracy of harmonic impedance calculation results, is characterized in that, comprises the following steps: Step 1: Divide the nonlinear users into Class A nonlinear users and Class B nonlinear users, and calculate the harmonic voltage measured at the PCC when each type of nonlinear user exits operation, that is, the reference voltage of the background harmonics; 1) The Class A nonlinear user is the user whose harmonic source and harmonic impedance are disconnected when it stops running. This class of users calculates the background harmonic voltage according to the circuit model of the IEC method; defines the A of the background harmonic. The class reference voltage is

It is obtained by the following formula:

Among them, _Zu and

are the harmonic impedance and harmonic current on the system side, respectively; When the harmonic impedance Zu on the system side is accurately obtained, the background harmonic voltage calculated according to the IEC method

will be with the class A reference voltage

equal; 2) The class B nonlinear user is the user whose harmonic source is cut off and the harmonic impedance is still connected to the power grid when it stops running. This type of user calculates the background harmonic voltage according to the superposition principle model; defines the background harmonic The class B reference voltage is

It is obtained by the following formula:

Among them, Z _c is the harmonic impedance of the user side; When the user-side harmonic impedance Zc and the system-side harmonic impedance Zu are accurately obtained, the background harmonic voltage calculated according to the superposition principle

with class B reference voltage

equal Step 2: Verify the accuracy of the obtained harmonic impedance according to the magnitude relationship between the user-side harmonic impedance Zc and the system-side harmonic impedance Zu. The detailed process is as follows: A) Cases where |Zc| is not much larger than |Zu| Calculated by IEC method for Class A nonlinear users

Superposition principle calculation for class B nonlinear users

Based on this, the accuracy of obtaining the harmonic impedance Zu on the system side and the harmonic impedance Zc on the user side is verified; B) Cases where |Zc| is much larger than |Zu| Since |Z _c |>>|Z _u |, there is Z _u /Z _c ≈0, and the formula for calculating the background harmonic voltage according to the superposition principle is transformed into the following formula:

but

and

They are approximately equal to each other. Whether it is a Class A nonlinear user or a Class B nonlinear user, the accuracy of the harmonic impedance Zu on the system side can be obtained based on the IEC method or the superposition principle verification. 2. The method for judging the accuracy of harmonic impedance calculation results according to claim 1, wherein the method for judging the magnitude relationship between |Zc| and |Zu| is: When |Zc|>>|Zu|, there is Z _u /Z _c ≈0, so there is

in,

is the harmonic current measured on the public line,

is the harmonic current on the user side; by quantifying

and

The similarity between , indirectly evaluates whether |Z _c |>>|Z _u | holds. 3. The method for judging the accuracy of harmonic impedance calculation results according to claim 2, wherein, in the process of evaluating whether |Z _c |>>|Z _u | is true, the source signal user is reconstructed by an independent component method side harmonic current

According to the Norton equivalent circuit, when the nonlinear user is connected to the system, there is

Among them, the matrix X is the harmonic voltage measured by the observation signal PCC point

and harmonic currents measured on the public line

The matrix I is composed of harmonic currents on the system side of the harmonic source signal system.

and user side harmonic current

composition; matrix Z is composed of harmonic impedances on both sides of the PCC point; Firstly, the fast-varying component of the signal is extracted by median filtering technique

and

Then reconstruct the harmonic source signal through the ICA algorithm

while the signal

and

The similarity between them is quantified by the correlation coefficient; If the correlation coefficient is greater than the set value, then |Zc|>>|Zu|, otherwise |Zc| is not much larger than |Zu|.

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