A quantitative calculation method for harmonic liability when system-side harmonics dominate

Abstract

The present invention discloses a method for quantitatively calculating harmonic responsibility when harmonics on the system side are dominant, specifically, a method for quantitatively evaluating harmonic responsibility based on a dynamic weighted impedance model, specifically including: first, constructing a static part and a dynamic part of the dynamic weighted impedance model; then, optimizing the parameters of the dynamic weighted impedance model; then, calculating the equivalent impedance value on the user side at the hth harmonic frequency through the impedance values ​​of the static part and the dynamic part; finally, calculating the harmonic voltage responsibility. The present invention calculates the harmonic responsibility of the harmonic source to the concerned busbar based on the dynamic weighted impedance model by calculating the equivalent impedance, solves the problem of harmonic responsibility calculation when harmonics on the system side are dominant, expands the scope of harmonic responsibility calculation, and can efficiently divide the harmonic responsibility of both the power supply and the power user.

Description

Technical Field

[0001] The invention belongs to the field of electric power systems, and relates to a method for quantitatively calculating harmonic responsibility of power quality, and in particular to a method for quantitatively calculating harmonic responsibility when system-side harmonics are dominant. Background Art

[0002] At present, the mainstream method for quantitative calculation of harmonic responsibility is based on equivalent impedance, that is, on the basis of calculating equivalent impedance, the harmonic responsibility of the load of interest is quantified by combining the superposition theorem and the inner product theory. The relevant methods can be mainly divided into two categories: one is the calculation of harmonic responsibility when the user side harmonics are dominant, and the other is the calculation of harmonic responsibility when the system side harmonics are dominant. When the user side harmonics are dominant, it is necessary to calculate the equivalent harmonic impedance on the system side. When the system side harmonics are dominant, it is necessary to solve the equivalent harmonic impedance on the user side. The equivalent harmonic impedance on the system side is relatively constant and relatively easy to calculate. The equivalent harmonic impedance on the user side fluctuates over time and is difficult to track. Traditional harmonic responsibility calculation methods are all for harmonic responsibility calculation when the user side harmonics are dominant, mainly including the fluctuation quantity method and its improved method, the linear regression method and its improved method, the probability statistics method, the independent component analysis method, etc. Up to now, there are few methods for calculating harmonic responsibility when the system side harmonics are dominant.

[0003] Purpose of the Invention

[0004] The purpose of the present invention is to address the difficulties in the prior art and provide a method for calculating harmonic responsibility when the system side harmonics are dominant. According to the variable characteristics of the user side load, the present invention constructs a dynamic weighted impedance model to solve the time-varying equivalent harmonic impedance of the user side, and combines the superposition theorem and inner product theory to quantify the harmonic responsibility of the load of interest. Summary of the invention

[0005] The present invention provides a method for quantitatively calculating harmonic responsibility when system-side harmonics are dominant, based on a dynamic weighted impedance model, and specifically includes the following steps:

[0006] Step 1: Construct the static impedance part and the dynamic impedance part of the dynamic weighted impedance model;

[0007] Step 2: Optimize the dynamic and static weights of the dynamic weighted impedance model;

[0008] Step 3: Calculate the hth harmonic equivalent impedance value at the user side through the static part and dynamic part impedance values;

[0009] Step 4: Calculate the harmonic voltage responsibility using the hth-order equivalent harmonic impedance on the user side obtained in step 3.

[0010] Preferably, in step 1, a dynamic weighted impedance model is constructed for the user-side load, wherein the dynamic weighted impedance model is formed by weighted series connection of a static impedance part and a dynamic impedance part, wherein the static impedance part is a constant impedance model and the dynamic impedance part is an induction motor model; assuming that X s is the stator reactance, R r is the rotor resistance, X r is the rotor reactance, X m is the magnetizing reactance, s is the rotor slip; j represents an imaginary unit, C represents the static model part, and M represents the dynamic model part, that is, the induction motor model; the calculation of the static impedance in the dynamic weighted impedance model adopts a constant impedance model, which is expressed as shown in formula (1):

[0011]

[0012] Among them, U represents the fundamental voltage measurement value of the load of interest, P represents the fundamental active power measurement value of the load of interest, and Q represents the fundamental reactive power measurement value of the load of interest. Indicates the fundamental phase angle value of the load;

[0013] The dynamic impedance in the dynamic weighted impedance model is expressed as shown in formula (2):

[0014] Z M =jX s +(jX m ) / / (jX r +R r / s) (2).

[0015] Preferably, in step 2, optimizing the dynamic and static weights in the dynamic weighted impedance model specifically includes:

[0016] In the dynamic weighted impedance model, the parameter to be identified is represented as {X s ,Xm,X r ,T d0}, where T d0 For electromagnetic parameters, the dynamic and static weights are optimized by least squares-genetic algorithm;

[0017] N adjacent samples are optimized as a group. The specific optimization model is as follows:

[0018] For the i-th sample, the fitness function f(i) represents the inverse of the sum of squared power errors of the sample, as shown in formula (3):

[0019] f(i)=-((P p (i)-P(i)) 2 +(Q p (i)-Q(i)) 2 ) (3),

[0020] Where P and Q are the measured values ​​of active power and reactive power respectively; P p , Q p are the predicted values ​​of active power and reactive power, P p The calculation formula is shown in formula (4):

[0021]

[0022] In the formula, Z C , X1, U d , U q 、E dp 、E qp is the parameter to be calculated; C is the static impedance value, calculated by the constant impedance model (1); X1 is the electromagnetic parameter, which is determined by the parameter to be identified X m , X r , X s It is expressed as shown in formula (5):

[0023]

[0024] Where U d ,U q Respectively represent the components of the A-phase fundamental phasor voltage of the sample on the p and q axes, through the voltage amplitude U and phase angle To calculate, it is expressed as shown in formula (6):

[0025]

[0026] Where E dp ,E qp is the predicted value of the components of the electromotive force phasor on the d-axis and q-axis, calculated using equations (7) and (8):

[0027]

[0028]

[0029] The variable E in formulas (7) and (8) is d 、E q are the components of the electromotive force phasor on the d-axis and q-axis, which are solved based on electromagnetic dynamics and explicit integration method and are expressed by equations (9) and (10) respectively:

[0030]

[0031]

[0032] X in formulas (7) and (8) is expressed as shown in formula (11):

[0033] X=X s +X m (11)

[0034] I in formulas (7) and (8) d ,I q Respectively represent the components of the A-phase fundamental phasor current value of the sample on the p and q axes, through the current amplitude I and phase angle To calculate, it is expressed as shown in formula (12):

[0035]

[0036] The slip s in formulas (7) and (8) is expressed as shown in formula (13):

[0037]

[0038] Where T is the identification period, that is, the sampling time of N adjacent sample points; w0 is the synchronous angular velocity, which is determined by the rotor resistance R r and the parameter to be identified X r ,X m ,T d0 Calculation is shown in formula (14):

[0039]

[0040] Calculate P based on formulas (4) to (14) p The value of the other predicted value Q in formula (3) p , and its calculation formula is shown in formula (15):

[0041]

[0042] In the formula, the parameters to be calculated are U d ,U q ,E dp ,E qp ,X1,X2; where X1 is represented by formula (5); U d ,U q Calculate according to formula (6); E dp ,E qp Based on equations (7) and (8), X2 is the static partial reactance, which is determined by the line voltage rating U NL and power factor rating cosj N It is expressed as shown in formula (16):

[0043]

[0044] P is calculated from (4)-(16) p ,Qp The value of P p ,O p The value of is substituted into formula (4) to obtain the fitness value; the optimal fitness function value is selected by iterative calculation of sample data multiple times, and the corresponding optimal dynamic and static weights are saved.

[0045] Preferably, the weight corresponding to the minimum power error between the calculated model data and the measured data is the optimal dynamic and static weight; in order to make the equivalent impedance value more accurate, the weights in different situations need to optimize the weight values ​​a1, a2 according to the measured data.

[0046] Preferably, in step 3, the equivalent impedance value of the user side at the hth harmonic frequency is obtained when the system side harmonic is dominant, and the static and dynamic equivalent impedance values ​​are respectively recorded as shown in formulas (17) and (18):

[0047] Z C =a1+b1·j (17),

[0048] Z M =a2+b2·j (18),

[0049] Among them, a1, a2, b1, b2, are all real numbers, and j is an imaginary unit;

[0050] The equivalent impedance value of the user side at the fundamental frequency is expressed as shown in formula (19):

[0051]

[0052] Among them, a1, a2, Z 1r ,Z 1i They are all real numbers and a1+a2=1;

[0053] The equivalent impedance value of the user side at the hth harmonic frequency is expressed as shown in formula (20):

[0054] Z h =Z 1r +h·Z 1i ·j (20),

[0055] In step 4, the harmonic voltage responsibility is expressed as shown in formula (21):

[0056]

[0057] From formula (21), we can see that the parameter required to calculate the harmonic voltage responsibility is U h , Z h1 ,I h1 , U h0 , where U h ,I h1is the measurable data, Z h1 is the unknown quantity, U h0 Calculated by formula (22):

[0058]

[0059] The harmonic voltage responsibility can be obtained by substituting the user-side equivalent impedance value at the hth harmonic frequency obtained in step 3 into formula (21). BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a principle diagram based on a dynamic weighted impedance model provided by the present invention.

[0061] Figure 2 The present invention provides an equivalent impedance amplitude result diagram of a certain company and a certain steel plant calculated based on a dynamic weighted impedance model.

[0062] Figure 3 The invention provides a normalized harmonic voltage responsibility diagram of a certain company and a certain steel plant based on a dynamic weighted impedance model.

[0063] Figure 4 1 is a normalized harmonic voltage result diagram of the 5th harmonic voltage responsibility at the PCC point on the system side of a steel plant in an embodiment of the present invention.

[0064] Figure 5 1 is a normalized harmonic voltage result diagram of the third harmonic voltage responsibility at the PCC point on the system side of a steel plant in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The preferred embodiments are described in detail below in conjunction with the accompanying drawings. It should be emphasized that the following description is only exemplary and is not intended to limit the scope and application of the present invention.

[0066] Figure 1 It is a schematic diagram based on a dynamic weighted impedance model provided by the present invention, which is used to optimize weight values ​​a1 and a2.

[0067] The present invention provides a method for quantitatively calculating harmonic responsibility when system-side harmonics are dominant, based on a dynamic weighted impedance model, and specifically includes the following steps:

[0068] Step 1: Construct the static impedance part and the dynamic impedance part of the dynamic weighted impedance model;

[0069] Step 2: Optimize the dynamic and static weights of the dynamic weighted impedance model;

[0070] Step 3: Calculate the hth harmonic equivalent impedance value at the user side through the static part and dynamic part impedance values;

[0071] Step 4: Calculate the harmonic voltage responsibility using the hth-order equivalent harmonic impedance on the user side obtained in step 3.

[0072] In step 1, a dynamic weighted impedance model is constructed for the user side load, wherein the dynamic weighted impedance model is composed of a static impedance part and a dynamic impedance part connected in series, wherein the static impedance part is a constant impedance model and the dynamic impedance part is an induction motor model; assuming that X s is the stator reactance, R r is the rotor resistance, X r is the rotor reactance, X m is the magnetizing reactance, s is the rotor slip; j represents an imaginary unit, C represents the static model part, and M represents the dynamic model part, that is, the induction motor model; the calculation of the static impedance in the dynamic weighted impedance model adopts a constant impedance model, which is expressed as shown in formula (1):

[0073]

[0074] Among them, U represents the fundamental voltage measurement value of the load of interest, P represents the fundamental active power measurement value of the load of interest, and Q represents the fundamental reactive power measurement value of the load of interest. Indicates the fundamental phase angle value of the load;

[0075] The dynamic impedance in the dynamic weighted impedance model is expressed as shown in formula (2):

[0076] Z M =jX s +(jX m ) / / (jX r +R r / s) (2).

[0077] In step 2, the optimization of the dynamic and static weights in the dynamic weighted impedance model specifically includes:

[0078] In the dynamic weighted impedance model, the parameter to be identified is represented as {X s ,X m ,X r ,T d0}, where T d0 For electromagnetic parameters, the dynamic and static weights are optimized by least squares-genetic algorithm;

[0079] N adjacent samples are optimized as a group. The specific optimization model is as follows:

[0080] For the i-th sample, the fitness function f(i) represents the inverse of the sum of squared power errors of the sample, as shown in formula (3):

[0081] f(i)=-((P p(i)-P(i)) 2 +(Q p (i)-Q(i)) 2 ) (3),

[0082] Where P and Q are the measured values ​​of active power and reactive power respectively; P p , Q p are the predicted values ​​of active power and reactive power, P p The calculation formula is shown in formula (4):

[0083]

[0084] In the formula, Z C , X1, U d , U q 、E dp 、E qp is the parameter to be calculated; C is the static impedance value, calculated by the constant impedance model (1); X1 is the electromagnetic parameter, which is determined by the parameter to be identified X m , X r , X s It is expressed as shown in formula (5):

[0085]

[0086] Where U d ,U q Respectively represent the components of the A-phase fundamental phasor voltage of the sample on the p and q axes, through the voltage amplitude U and phase angle To calculate, it is expressed as shown in formula (6):

[0087]

[0088] Where E dp ,E qp is the predicted value of the components of the electromotive force phasor on the d-axis and q-axis, calculated using equations (7) and (8):

[0089]

[0090]

[0091] The variable E in formulas (7) and (8) is d 、E q are the components of the electromotive force phasor on the d-axis and q-axis, which are solved based on electromagnetic dynamics and explicit integration method and are expressed by equations (9) and (10) respectively:

[0092]

[0093]

[0094] X in formulas (7) and (8) is expressed as shown in formula (11):

[0095] X=X s +X m (11)

[0096] I in formulas (7) and (8) d ,I q Respectively represent the components of the A-phase fundamental phasor current value of the sample on the p and q axes, through the current amplitude I and phase angle To calculate, it is expressed as shown in formula (12):

[0097]

[0098] The slip s in formulas (7) and (8) is expressed as shown in formula (13):

[0099]

[0100] Where T is the identification period, that is, the sampling time of N adjacent sample points; w0 is the synchronous angular velocity, which is determined by the rotor resistance R r and the parameter to be identified X r ,X m ,T d0 Calculation is shown in formula (14):

[0101]

[0102] Calculate P based on formulas (4) to (14) p The value of the other predicted value Q in formula (3) p , and its calculation formula is shown in formula (15):

[0103]

[0104] In the formula, the parameters to be calculated are U d ,U q ,E dp ,E qp ,X1,X2; where X1 is represented by formula (5); U d ,U q Calculate according to formula (6); E dp ,E qp Based on equations (7) and (8), X2 is the static partial reactance, which is determined by the line voltage rating U NL and power factor rating cosj N It is expressed as shown in formula (16):

[0105]

[0106] P is calculated from (4)-(16) p ,Q p The value of P p ,Q p The value of is substituted into formula (4) to obtain the fitness value; the optimal fitness function value is selected by iterative calculation of sample data multiple times, and the corresponding optimal dynamic and static weights are saved.

[0107] The weight corresponding to the minimum power error between the calculated model data and the measured data is taken as the optimal dynamic and static weight; in order to make the equivalent impedance value more accurate, the weights in different situations need to optimize the weight values ​​a1 and a2 according to the measured data.

[0108] In step 3, the equivalent impedance value of the user side at the hth harmonic frequency is obtained when the system side harmonic is dominant, and the static and dynamic equivalent impedance values ​​are recorded as shown in equations (17) and (18), respectively:

[0109] Z C =a1+b1·j (17),

[0110] Z M =a2+b2·j (18),

[0111] Among them, a1, a2, b1, b2, are all real numbers, and j is an imaginary unit;

[0112] The equivalent impedance value of the user side at the fundamental frequency is expressed as shown in formula (19):

[0113]

[0114] Among them, a1, a2, Z 1r ,Z 1i They are all real numbers and a1+a2=1;

[0115] The equivalent impedance value of the user side at the hth harmonic frequency is expressed as shown in formula (20):

[0116] Z h =Z 1r +h·Z 1i ·j (20),

[0117] In step 4, the harmonic voltage responsibility is expressed as shown in formula (21):

[0118]

[0119] From formula (21), we can see that the parameter required to calculate the harmonic voltage responsibility is U h , Z h1 ,Ih1 , U h0 , where U h ,I h1 is the measurable data, Z h1 is the unknown quantity, U h0 Calculated by formula (22):

[0120]

[0121] The harmonic voltage responsibility can be obtained by substituting the user-side equivalent impedance value at the hth harmonic frequency obtained in step 3 into formula (21).

[0122] Example

[0123] Collect the harmonic voltage (U), harmonic current (I), harmonic active power (P), harmonic reactive power (Q), and harmonic power factor of the PCC point The measured data comes from the continuous data of a company and a steel plant.

[0124] Step 1: Calculate the static impedance Z using equation (1) C Value

[0125] Step 2: Calculate the equivalent harmonic impedance value of the load of interest. Apply the least squares-genetic algorithm to optimize the dynamic and static weights, set the parameter optimization range based on national standards and the latest research, and input the sample's P, Q, U, I, The measured value of Z is output as the optimal parameter. Substituting the optimal parameter into formula (2) yields Z M .

[0126] Step 3: Z M Substitute into equation (21) to obtain the harmonic voltage responsibility.

[0127] Figure 2 , Figure 3 It is the equivalent impedance calculation result of a certain company and a certain steel plant.

[0128] Based on the equivalent impedance values ​​of a company and a steel plant, the 5th harmonic voltage responsibility of the system side of a company at the PCC point and the 3rd harmonic voltage responsibility of the system side of a steel plant at the PCC point are calculated. The normalized results of the harmonic responsibility of the two examples are as follows: Figure 4 , Figure 5 shown.

[0129] The beneficial effect of the present invention is that it calculates equivalent impedance based on a dynamic weighted impedance model, and quantifies the harmonic responsibility of the harmonic source on the busbar of interest based on this. This solves the problem of large error in harmonic responsibility calculation when harmonics dominate the current system side, effectively improves the quantification accuracy of harmonic responsibility, expands the scope of application of the harmonic responsibility calculation method, and lays a good theoretical and technical foundation for the efficient division of harmonic responsibilities between the power supply and the power user.

[0130] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for quantitatively calculating harmonic responsibility when the system side harmonics are dominant is based on a dynamic weighted impedance model, characterized in that: The specific steps include: Step 1: Construct the static impedance part and the dynamic impedance part of the dynamic weighted impedance model; Step 2: Optimize the dynamic and static weights of the dynamic weighted impedance model; Step 3: Calculate the user-side equivalent impedance value at the hth harmonic frequency through the static part and dynamic part impedance values; Step 4: Calculate the harmonic voltage responsibility by using the equivalent impedance value on the user side at the hth harmonic frequency obtained in step 3; In step 1, a dynamic weighted impedance model is constructed for the user side load, wherein the dynamic weighted impedance model is composed of a static impedance part and a dynamic impedance part connected in series, wherein the static impedance part is a constant impedance model and the dynamic impedance part is an induction motor model; assuming that X s is the stator reactance, R r is the rotor resistance, X r is the rotor reactance, X m is the magnetizing reactance, s is the rotor slip; j represents the imaginary unit, C represents the static model part, and M represents the dynamic model part, i.e., the induction motor model; In step 2, the optimization of the dynamic and static weights of the dynamic weighted impedance model specifically includes: In the dynamic weighted impedance model, the parameter to be identified is represented as {X s ,X m ,X r ,T d0 }, where T d0 For electromagnetic parameters, the dynamic and static weights are optimized by least squares-genetic algorithm; N adjacent samples are optimized as a group. The specific optimization model is as follows: For the i-th sample, the fitness function f(i) represents the inverse of the sum of squared power errors of the sample, as shown in formula (3): f(i)=-((P p (i)-P(i)) 2 +(Q p (i)-Q(i)) 2 ) (3), Where P and Q are the measured values ​​of active power and reactive power respectively; P p , Q p are the predicted values ​​of active power and reactive power, P p The calculation formula is shown in formula (4): In the formula, Z C , X1, U d , U q 、E dp 、E qp is the parameter to be calculated; C is the static impedance value, calculated by the constant impedance model (1); X1 is the electromagnetic parameter, which is determined by the parameter to be identified X m , X r , X s It is expressed as shown in formula (5): Where U d ,U q Respectively represent the components of the sample's A-phase fundamental phasor voltage on the p and q axes, through the voltage amplitude U and the load fundamental phase angle value To calculate, it is expressed as shown in formula (6): Where E dp ,E qp is the predicted value of the components of the electromotive force phasor on the d-axis and q-axis, calculated using equations (7) and (8): The variable E in formulas (7) and (8) is d 、E q are the components of the electromotive force phasor on the d-axis and q-axis, which are solved based on electromagnetic dynamics and explicit integration method and are expressed by equations (9) and (10) respectively: X in formulas (7) and (8) is expressed as shown in formula (11): X=X s +X m (11), I in formulas (7) and (8) d ,I q Respectively represent the components of the A-phase fundamental phasor current value of the sample on the p and q axes, through the current amplitude I and the fundamental phase angle value of the load To calculate, it is expressed as shown in formula (12): The slip s in formulas (7) and (8) is expressed as shown in formula (13): Where T is the identification period, that is, the sampling time of N adjacent sample points; ω0 is the synchronous angular velocity, which is determined by the rotor resistance R r and the parameter to be identified X r ,X m ,T d0 Calculation is shown in formula (14): Calculate P based on formulas (4) to (14) p The value of the other predicted value Q in formula (3) p , and its calculation formula is shown in formula (15): In the formula, the parameters to be calculated are U d ,U q ,E dp ,E qp ,X1,X2; where X1 is represented by formula (5); U d ,U q Calculate according to formula (6); E dp ,E qp Based on equations (7) and (8), X2 is the static partial reactance, which is determined by the line voltage rating U NL and power factor ratings It is expressed as shown in formula (16): P is calculated from (4)-(16) p ,Q p The value of P p ,Q p The value of is substituted into formula (4) to obtain the fitness value; the optimal fitness function value is selected by iterative calculation of sample data multiple times, and the corresponding optimal dynamic and static weights are saved.

2. The method for quantitatively calculating harmonic responsibility when the system side harmonics are dominant according to claim 1 is characterized in that: The calculation of static impedance in the dynamic weighted impedance model adopts a constant impedance model, which is expressed as shown in formula (1): Among them, U represents the fundamental voltage measurement value of the load of interest, P represents the fundamental active power measurement value of the load of interest, and Q represents the fundamental reactive power measurement value of the load of interest. Indicates the fundamental phase angle value of the load; The dynamic impedance in the dynamic weighted impedance model is expressed as shown in formula (2): Z M =jX s +(jX m ) / / (jX r +R r / s) (2).

3. The method for quantitatively calculating harmonic responsibility when the system-side harmonics are dominant according to claim 1 is characterized in that: The weight corresponding to the minimum power error between the calculated model data and the measured data is defined as the optimal dynamic and static weight; in order to make the equivalent impedance value more accurate, the weights in different situations need to optimize the weight values ​​α1, α2 according to the measured data.

4. The method for quantitatively calculating harmonic responsibility when the system side harmonics are dominant according to claim 1 is characterized in that: In step 3, the equivalent impedance value of the user side at the hth harmonic frequency is obtained when the system side harmonic is dominant, and the static and dynamic equivalent impedance values ​​are recorded as shown in equations (17) and (18), respectively: From C =a1+b1·j (17), <h2 style=";text-align:left;direction:ltr">Z<h2 style=";text-align:left;direction:ltr"> M <h2 style=";text-align:left;direction:ltr"> (a2+b2·j) (18) Among them, a1, a2, b1, b2, are all real numbers, and j is an imaginary unit; The equivalent impedance value of the user side at the fundamental frequency is expressed as shown in formula (19): Among them, α1, α2, Z 1r ,Z 1i All are real numbers and α1+α2=1; The equivalent impedance value of the user side at the hth harmonic frequency is expressed as shown in formula (20): Z h =Z 1r +h·Z 1i ·j (20)。 5. The method for quantitatively calculating harmonic responsibility when the system side harmonics are dominant according to claim 1 is characterized in that: In step 4, the harmonic voltage responsibility is expressed as shown in formula (21): From formula (21), we can see that the parameter required to calculate the harmonic voltage responsibility is U h , Z h1 ,I h1 , U h0 , where U h ,I h1 is the measurable data, Z h1 is the unknown quantity, U h0 Calculated by formula (22): By substituting the user-side equivalent impedance value at the hth harmonic frequency obtained in step 3 into equation (21), the harmonic voltage responsibility can be obtained.

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