CN107147121A - A Virtual Resistive Active Filter Control Strategy Based on Least Square Method - Google Patents

Abstract

The invention discloses a kind of virtual resistance type active power filtering control strategy based on least square method, detailed process is as follows：Line voltage and grid-connected current first to sampling carry out Fast Fourier Transform (FFT) and obtain each harmonic component, then the equiva lent impedance of network system is obtained using least square method, control the harmonic current of inverter output, each Equivalent Harmonic resistance of inverter is set to be equal to the modulus value of system each harmonic impedance, so as to realize inverter each harmonic power maximum absorption.The control strategy can quick and precisely obtain the size of virtual harmonic wave resistance by least square method, solve traditional harmonic wave resistance based on linear search and automatically adjust the problem of method search speed is slow, avoid producing prolonged harmonic power fluctuation during regulation, influence the assimilation effect of harmonic power.

Description

A Virtual Resistive Active Filter Control Strategy Based on Least Square Method

technical field

The invention relates to the technical field of power filter control, in particular to a virtual resistance active filter control strategy based on the least square method.

Background technique

When the virtual resistance active power filter absorbs various harmonic currents, it not only increases the user cost, but also makes it difficult to quantify its contribution to the harmonic control work of the power grid, and the relevant departments cannot make compensation for it. Therefore, although the system voltage distortion rate can be reduced, it is still difficult to mobilize the enthusiasm of users to control harmonics in the way of virtual resistance APF. To solve this problem, this patent proposes a new harmonic control strategy based on the virtual resistive active power filter. , calculate the harmonic power absorbed by the APF, and use a certain algorithm to adjust the equivalent harmonic resistance in real time, so that the harmonic power absorbed by the APF reaches the maximum, and the emission or absorption of the harmonic power is used to define the user's The role of the polluter or regulator, who punishes or rewards pollution or governance behaviors. Under this strategy, if an effective mechanism is used, users who actively participate in harmonic governance will receive the greatest incentives based on the maximum harmonic power they absorb. In this patent, the resistance value of each harmonic resistance corresponding to the maximum harmonic power absorbed by the APF is defined as the "best resistance value".

Contents of the invention

The purpose of the present invention is to solve the above defects in the prior art, to provide a virtual resistance active filter control strategy based on the least squares method, and to realize an equivalent virtual harmonic current by controlling the harmonic current output by the inverter Wave resistance, whose resistance value is equal to the modulus value of the equivalent impedance of the system, so as to realize the maximum power absorption of harmonics.

The purpose of the present invention can be achieved by taking the following technical solutions:

A virtual resistance type active filter control strategy based on the least squares method, the virtual resistance type active filter control strategy includes the following steps:

Based on the simple power system with the joint action of harmonic voltage source and harmonic current source, the equivalent impedance of the system is observed by the small disturbance method, and the active filter current is controlled to perform m-order harmonic small disturbance, and the k-th harmonic is recorded respectively Under wave small disturbance, the real part U _ih(Re)k and the imaginary part U _ih(Im)k of the hth harmonic voltage vector of the network point of the APF, the real part Iih(Re) _k of the hth harmonic current vector And imaginary part I _{ih (Im) k} , wherein k=1,2,..., m, form overdetermined equation system AX=b,

in:

In the formula, E _h(Re) is the real part of the equivalent electric potential vector of the system h order harmonic, E _h(Im) is the imaginary part of the system h order harmonic equivalent electric potential vector, R _h is the system h order harmonic, etc. The real part of the effective impedance, X _h is the imaginary part of the equivalent impedance of the system h order harmonic;

Solving the least square solution of the overdetermined equation AX=b is the normal equation system: (A ^T A)X= ^AT b solution, and obtain the harmonic impedance of the system: Z _h ＝R _h +jX _h ;

Let the virtual harmonic resistance R _ih of the inverter match the system harmonic impedance modulus |Z _h |, that is Calculate the output harmonic current command of the inverter according to the system harmonic voltage, and control the inverter to output the corresponding harmonic current, so as to realize the maximum absorption of harmonic power.

Further, described normal system of equations (A ^T A) X=A ^T b solves with the triangular decomposition method of symmetric matrix, and its process is as follows:

Note G=A ^T A, then G is a symmetric matrix, by triangular decomposition G=LDL ^T , wherein L is a lower triangular matrix, D is a diagonal matrix, the normal equation can be reduced to: LDL ^T X= ^AT b, the normal equation The solution of can be divided into the following three steps:

1) Solve the lower triangular equations: LZ＝A ^T b

2) Solving diagonal equations: DY=Z

3) Solve upper triangular equations: L ^T X = Y

where Z = DL ^T X, Y = L ^T X,

After the above steps, we can solve the

Compared with the prior art, the present invention has the following advantages and effects:

The invention can quickly determine the optimal resistance value of each virtual harmonic resistance, thereby reducing the harmonic power fluctuation caused in the process of adjusting the virtual harmonic resistance. The traditional admittance adjustment method is an automatic adjustment method based on one-dimensional search, but the search speed of this method is slow, and long-term harmonic power fluctuations are generated during the adjustment process, which affects the absorption effect of harmonic power. The above problem can be solved by using the least square method proposed in this patent to calculate the equivalent impedance of the system. The least squares method to find the equivalent impedance of the system refers to superimposing several small disturbances of different amplitude phases on the basis of the original harmonic reference current of the inverter when determining the virtual harmonic conductance _Gh , and then using different small The frequency spectrum under the disturbance forms an overdetermined equation, so that the system equivalent impedance Z _h under the least square solution is obtained, and G _h is the reciprocal of the system equivalent impedance modulus |Z _h |. In this way, the optimal resistance value of each virtual harmonic resistor can be quickly determined through several small disturbances.

Description of drawings

Figure 1 is a simple power system in which the harmonic voltage source and the harmonic current source act together;

Figure 2 is the working principle of the virtual resistance active power filter;

Fig. 3 is a schematic diagram of virtual resistance current generation;

Fig. 4 is the least squares method to find the flow chart of virtual resistance current;

Figure 5 is the simulation waveform when the equivalent load resistance suddenly becomes larger.

detailed description

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Example

This embodiment proposes a new harmonic control strategy based on the virtual resistive active power filter. The virtual resistive active power filter calculates the APF according to the harmonic voltage of the grid-connected point and the harmonic current output by the APF The absorbed harmonic power, and adopt a certain algorithm to adjust the equivalent harmonic resistance in real time, so that the harmonic power absorbed by the APF reaches the maximum, and the user's polluter or user is defined by the emission or absorption of harmonic power The role of the governor, punishing or rewarding pollution or governance behavior. Under this strategy, if an effective mechanism is used, users who actively participate in harmonic governance will receive the greatest incentives based on the maximum harmonic power they absorb. In the embodiment of the present invention, the resistance value of each harmonic resistance corresponding to the maximum value of the harmonic power absorbed by the APF is defined as "optimum resistance value".

The virtual resistance type APF collects the grid-connected point voltage and output current at the same time, and performs harmonic detection on it, and then calculates the harmonic power absorbed by each phase separately, and averages the harmonic power of the three phases, as APF absorption The hth harmonic power Ph _h . Adjust each conductance value G _h according to _Ph . During the operation of the virtual resistance type APF, it does not require a quick response to the load current like the general compensation current type APF, and the power system needs a certain response time for each change of G _h . Therefore, the calculation of each harmonic power The link and each admittance adjustment link can be carried out according to the set time interval. Before each harmonic power is updated, the original value of G _h remains unchanged.

The traditional admittance adjustment method is an automatic adjustment method based on one-dimensional search, but the search speed of this method is slow, and long-term harmonic power fluctuations are generated during the adjustment process, which affects the absorption effect of harmonic power. The above problem can be solved by using the least square method proposed in this patent to calculate the equivalent impedance of the system. The least squares method to find the equivalent impedance of the system refers to superimposing several small disturbances of different amplitude phases on the basis of the original harmonic reference current of the inverter when determining the virtual harmonic conductance _Gh , and then using different small The frequency spectrum under the disturbance forms an overdetermined equation, so that the system equivalent impedance Z _h under the least square solution is obtained, and G _h is the reciprocal of the system equivalent impedance modulus |Z _h |. In this way, the optimal resistance value of each harmonic resistor can be quickly determined through several small disturbances.

1. Figure 1 is a simple power system in which the harmonic voltage source and the harmonic current source act together. The equivalent impedance of the system is observed with a small disturbance, and the following equations can be listed:

Z _h =R _h +jX _h (5)

U _ih(Re) ＝I _ih(Re) R _h -I _ih(Im) X _h +E _h(Re) (6)

U _ih(Im) =I _ih(Im) R _h +I _ih(Re) X _h +E _h(Im) (7)

In the above equation, is the network point h harmonic voltage vector of APF, U _{ih (Re)} is the real part of the network point h harmonic voltage vector of APF, U _{ih (Im)} is the imaginary part of the network point h harmonic voltage vector of APF, is the system h-order harmonic equivalent potential vector, E _h(Re) is the real part of the system h-order harmonic equivalent potential vector, E _h(Im) is the imaginary part of the system h-order harmonic equivalent potential vector, I _{ih (Re)} is the real part of the h order harmonic current vector of APF entering the network, I _{ih (Im)} is the imaginary part of the h order harmonic current vector of APF entering the network, Z _h is the system The equivalent impedance of the hth harmonic, R _h is the real part of the hth harmonic equivalent impedance of the system, and X _h is the imaginary part of the hth harmonic equivalent impedance of the system. Among them, E _h(Re) , E _h(Im) , _Rh , X _h are constant parameters to be estimated, U _ih(Re) , U _ih(Im) , I _ih(Re) , I _ih(Im) are observations.

According to the above equation, the matrix equation for m small disturbances can be obtained:

AX=b (8)

in,

In the formula, U _ih(Re)k is the real part of the h-order harmonic current vector of the APF entering the grid obtained by FFT at the kth small disturbance, and _Iih(Im)k is the APF obtained by FFT at the kth small disturbance The imaginary part of the h-th order harmonic current vector of the incoming grid, U _ih(Re)k is the real part of the h-order harmonic voltage vector of the APF network point when the k-th small disturbance occurs, and U _ih(Im)k is the k-th small disturbance The imaginary part of the network point h harmonic voltage vector of APF.

The least square solution of the overdetermined equation AX=b is a normal equation system: (A ^T A)X=A ^T b solution. Solve normal equation system (A ^T A) X=A ^T b with the triangular decomposition method of symmetric matrix, record G=A ^T A, then G is a symmetric matrix, by triangular decomposition G=LDL ^T , wherein L is a lower triangular matrix, D is a diagonal matrix, and the normal equation can be reduced to: LDL ^T X = A ^T b. The solution of the normal equation can be divided into the following three steps:

1) Solve the lower triangular equations: LZ＝A ^T b

2) Solving diagonal equations: DY=Z

3) Solve upper triangular equations: L ^T X = Y

Where Z = DL ^T X, Y = L ^T X.

After the above steps, we can solve the

2. Match the virtual resistance to absorb the maximum harmonic power

It can be seen from the circuit principle that when the load resistance When , the active power absorbed by the resistive load reaches the maximum value. Therefore, by controlling the output harmonic current of the inverter to be equivalent to a virtual resistance, the function of absorbing harmonic active power can be maximized.

3. Active filter control algorithm

Fig. 2 is a schematic diagram of the working principle of a virtual resistive active power filter. In the figure, i ^* _c1 is the virtual resistance reference current, i ^* _c2 is the reference current output by the DC voltage control loop, i ^* _c is the total reference current, _ic is the actual output current; S _a , S _b , S _c are switches Tube drive signal. It can be seen from the figure that the main difference between the virtual resistor type active power filter and the traditional harmonic current source type active power filter is that the generation methods of the respective reference currents are different. The reference current of the traditional active power filter is generally synthesized by the output value of the voltage outer loop regulator on the DC side and the harmonic and reactive current of the load, while the virtual resistor type active power filter is equivalent to a harmonic resistor. The reference current should include the output value of the above-mentioned DC voltage outer loop adjustment and the harmonic currents proportional to the harmonic voltages at the common coupling point, that is, the virtual resistance current in Figure 2. Therefore, the ratio of each harmonic voltage to each harmonic current is the equivalent each harmonic resistance.

Figure 3 is the generation process of the virtual resistance current. In the figure, the harmonic detection link is used to extract the harmonic voltages of the common coupling point, the phase detection link is used to detect the phase information of the voltage in real time, and the phase information is used to convert each harmonic voltage into an instantaneous value, and then each The sub-harmonic voltage is multiplied by each sub-harmonic conductance G _h to obtain each reference current, and the virtual resistance current reference value is obtained by summing each sub-current. The harmonic conductance G _h shown in the figure is the reciprocal of the harmonic resistance. By adjusting the harmonic conductance G _h of each order, the harmonic resistance of each order can be adjusted equivalently. The calculation of G _h is obtained by obtaining the least squares solution by using the real and imaginary parts of the voltage and current harmonics obtained from the harmonic detection under the regular small disturbance of the inverter output harmonic current.

Fig. 4 is the flow chart of calculating the virtual resistance current by least square method, and its steps are:

(1) initialization,

(2) Let k=1

(3) In the original reference harmonic current On the basis of superimposing different amplitude and phase small perturbations

(4) Use FFT to calculate the frequency spectrum of the grid point voltage and grid current of the inverter

(5) Make k=k+1; Enter (6) if k is greater than m, otherwise return (3);

(6) Use U _ih(Re)k , U _ih(Im)k , _Iih(Re)k , Iih( _Im)k to form an overdetermined equation system AX=b, and use the triangular decomposition method of a symmetric matrix to solve the normal equation system , to obtain the equivalent harmonic impedance of the system Z _h ＝R _h +jX _h ;

(7) Calculate the voltage spectrum with FFT according to Obtain the harmonic reference current spectrum, and then convert the frequency domain reference current into a time domain value;

(8) Calculate and store the optimal power value;

(9) Calculate the real-time power P _Hrt ;

(10) Calculate Abs(P _h -P _hRT ), if it is greater than the threshold δ, return to (2), otherwise return to (7). 4. In order to verify the optimal resistance automatic adjustment method described above and to be more universal, this patent simulates Figure 2 based on PSCAD/EMTDC, where R _s is 0.00001Ω, system inductance L _s is 0.00637H, That is, for the 5th harmonic, the corresponding X _s is 10Ω, and the equivalent load is respectively set as 20Ω for R1 and 10Ω for R2. Assuming _{three -} phase balance, the 5th harmonic is taken as the object of discussion, and the harmonic current of phase A is The harmonic voltage of phase A system is It can be calculated that when the equivalent load is R ₁ , the theoretical optimal resistance value is R ^* _F01 = 8.945Ω, and the corresponding conductance value is G ^* ₀₁ = 0.112S; when the equivalent load is R ₂ , the theoretical optimal resistance value It is R ^* _F02 = 7.0714Ω, and the corresponding conductance value is G ^* ₀₂ = 0.141S.

Figure ₅ is the harmonic power change _curve when the equivalent load changes suddenly from R2 to R1. In the first stage 0-1s, the value of G _h obtained by the least square method is 0.1426, and P _Fh is stable at around 1.141kW. At 1s, after the equivalent load resistance changes suddenly, the value of G _h obtained by the least square method is 0.1187 S, P _Fh finally stabilized around 1.62kW.

The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (2)

1. A virtual resistance type active filtering control strategy based on a least square method is characterized by comprising the following steps:

a simple power system based on combined action of a harmonic voltage source and a harmonic current source observes equivalent impedance of the system by a small disturbance method, controls current of an active filter to carry out m-order harmonic small disturbance, and respectively records a real part U of a voltage vector of an h-order harmonic of a grid-connected point of an APF (active power filter) under the k-th harmonic small disturbance_ih(Re)kAnd imaginary part U_ih(Im)kCurrent direction of h-th harmonicReal part of quantity I_ih(Re)kAnd imaginary part I_ih(Im)kWhere k is 1,2, … …, m, forming an overdetermined system of equations AX b,

wherein:

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in the formula, E_h(Re)Is the real part of the equivalent potential vector of the h harmonic of the system, E_h(Im)For the imaginary part, R, of the equivalent potential vector of the h harmonic of the system_hIs the real part, X, of the equivalent impedance of the h harmonic of the system_hThe imaginary part of the h harmonic equivalent impedance of the system;

solving a least squares solution, i.e., a normal system of equations, of the overdetermined equation AX ═ b: (A)^TA)X＝A^Tb solution, finding each systemSub-harmonic impedance: z_h＝R_h+jX_h；

Let inverter virtual harmonic resistance R_ihHarmonic impedance modulus | Z of matching system_hI.e. thatAnd solving an output harmonic current instruction of the inverter according to the harmonic voltage of the system, and controlling the inverter to output corresponding harmonic current, thereby realizing maximum harmonic power absorption.

2. The least squares based virtual resistance type active filtering control strategy of claim 1, wherein the normal equation set (A)^TA)X＝A^Tb, solving by using a triangular decomposition method of the symmetric matrix, wherein the process is as follows:

let G be A^TA, G is a symmetric matrix, and G is decomposed into LDL by triangle^TWhere L is a lower triangular matrix and D is a diagonal matrix, the normal equation can be: LDL^TX＝A^Tb, solving the normal equation can be divided into the following three steps:

1) solving the following set of trigonometric equations: LZ ═ A^Tb

2) Solving a system of diagonal equations: DY ═ Z

3) Solving the upper set of trigonometric equations: l is^TX＝Y

Wherein Z is DL^TX，Y＝L^TX，

Through the steps, the solution can be solvedZ_h＝R_h+jX_h。