CN115912489A - LMS-SOGI three-phase-locked loop design method and system suitable for non-ideal power grid - Google Patents
LMS-SOGI three-phase-locked loop design method and system suitable for non-ideal power grid Download PDFInfo
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Abstract
The invention provides a method and a system for designing an LMS-SOGI three-phase-locked loop suitable for a non-ideal power grid, wherein the method comprises the following steps: sampling to obtain three-phase grid-connected voltage of the grid-connected inverter, and obtaining voltage components through Clark conversion; respectively sending the voltage signals into two SOGI structures, and extracting the positive sequence component of the power grid voltage; constructing a least mean square LMS filtering link mathematical model, and designing a step length parameter of the least mean square LMS filtering link; and performing LMS filtering on the grid voltage positive sequence component to obtain fundamental frequency grid-connected voltage d and q-axis positive sequence components, subtracting the fundamental frequency grid-connected voltage q-axis component from 0 to obtain a q-axis voltage phase-locked error signal, obtaining an output signal angular frequency regulating quantity omega through a PI controller, and obtaining a phase theta through integration. And finally, building a three-phase power grid voltage LMS-SOGI phase-locked model in MATLAB/Simulink simulation software, and selecting different power grid voltage conditions to compare and analyze the filtering effect. The invention solves the technical problem that the voltage frequency and the phase are difficult to be accurately locked in a specific scene by the phase locking technology of the grid-connected inverter.
Description
Technical Field
The invention relates to the field of phase-locked loop control of a grid-connected inverter, in particular to a method and a system for designing an LMS-SOGI three-phase-locked loop suitable for a non-ideal power grid.
Background
Currently, the demand of social economic development on energy resources is continuously increased, and in order to reduce the dependence on traditional fossil energy, the grid-connected scale of new energy power generation in China is continuously expanded. With the large-scale access of the new energy inverter, the equivalent impedance of the power grid at the view angle of the inverter is increased, so that the voltage harmonic content of the power grid is increased, the frequency is changed, the operation stability of the power grid is influenced, and the power quality is reduced.
Most power electronic devices are connected with a three-phase power grid, and three-phase locking must be carried out on the power grid to synchronize with the power grid. The traditional phase-locked loop adopts a hardware phase-locked mode to realize the tracking of the voltage phase by detecting a zero crossing point. The method can not be applied to the occasions with serious harmonic pollution, and can only realize single-phase locking and can not track the positive sequence component of the system. The current three-phase software phase locking method is mainly applied as follows: (1) A single/double synchronous coordinate system software phase-locked loop, for example, a related invention patent application document "a method for controlling a second-order decoupling double synchronous coordinate system phase-locked loop of a distribution network loop closing device" with publication number CN115000945A includes: representing the three-phase power grid voltage based on that the three-phase power grid voltage only contains positive and negative sequence fundamental wave components; transforming the power grid voltage from a three-phase natural coordinate system into a two-phase alpha beta coordinate system; the positive and negative sequence Park converter is used for performing mathematical conversion from a two-phase static coordinate system to a two-phase rotating coordinate system; obtaining a second-order low pass filter SOLPF transfer function; deducing a transfer function expression corresponding to the decoupling network DN by combining the second-order low-pass filter SOLPF in the step 3; positive and negative sequence d and q axis voltages output by the decoupling network DN; the loop filter LF is used as a PI regulator and obtains the transfer function. The aforementioned prior art can accurately detect the phase, frequency and amplitude of the grid voltage only when the grid voltage is balanced; (2) A single synchronous coordinate system software phase-locked loop system based on a symmetric component method, for example, a prior invention patent application document with publication number CN102081114A, "a dstacom current detection method based on an instantaneous symmetric component method", includes: firstly, determining a symmetrical component method and a representation method of an instantaneous value in a phasor time domain, secondly, determining an instantaneous value, and thirdly, improving the realization of the instantaneous symmetrical component method; fourthly, a MATLAB simulation tool is adopted to establish a model to carry out simulation analysis on the conclusion, and fifth, filtering, converting and processing are carried out on data; and sixthly, subtracting the three-phase fundamental positive sequence active current iafp +, ibfp + and icfp + from the load current to obtain the required comprehensive compensation command currents iac, ibc and icc containing harmonic waves, negative sequences and reactive power. . The aforementioned prior art can only suppress the 2 nd order harmonic effect caused by the negative sequence component in the grid voltage; (3) The decoupling software phase-locked loop based on the double synchronous coordinate system can effectively overcome the influence of frequency change on the phase-locked loop, but the harmonic suppression mainly depends on a first-order low-pass filter consisting of PI control, and the filtering effect is general; (4) A software phase-locked loop (SOGI) based on biquad generalized integral utilizes the characteristics of a trigonometric function, harmonic influence in the SOGI is filtered out through an orthogonal signal generator, orthogonal signals with a phase difference of 90 degrees are generated at the same time, separation of positive and negative sequence components in the SOGI is realized, the phase-locked loop can meet phase locking under common conditions, but when the quality of a power grid is reduced, the power grid is unbalanced, the amplitude of a large amount of harmonics and other non-ideal power grid occasions exist, the traditional phase-locked loop is difficult to meet requirements, and even the SOGI phase-locked loop is difficult to meet the filtering effect. At present, regarding to the improved scheme of software phase-locked loop control of biquad generalized integral, there are a plurality of academic papers for analysis and reports, for example: 1. an integration link is added on an original framework unit to form a third-order generalized integrator for inhibiting harmonic waves and high-frequency signals; 2. a low-pass filter is arranged in front of the SOGI architecture unit, and the filtering function is added. For example, in the prior invention patent document CN107623522A, "a bi-quad generalized integral phase-locked loop control method based on d-q transformation" step a: obtaining voltages Ualpha and Ubeta by Clark conversion of a three-phase voltage sampling value Ua, a three-phase voltage sampling value Ub and a three-phase voltage sampling value Uc; step B, respectively sending u alpha and u beta to two SOGI structures, extracting the positive sequence component of the power grid voltage and step C: then filtering the positive sequence component of the power grid voltage; step D: and finally, the filtered positive sequence component of the power grid voltage is sent to a phase-locked loop based on a d-q coordinate system to be used as a reference standard of the phase-locked loop. From the foregoing detailed implementation of the prior art, it can be seen that the improvement in the foregoing prior art scheme is that in order to reduce the influence of the negative sequence component and achieve better steady-state accuracy, the cut-off frequency of the loop filter therein must be very low, which greatly affects the speed of the dynamic response.
In summary, the prior art has a technical problem that it is difficult to accurately lock the voltage frequency and the phase in a specific scene in the phase locking technology of the grid-connected inverter.
Disclosure of Invention
The invention aims to solve the technical problem that how to solve the problem that the phase locking technology of the grid-connected inverter in the prior art is difficult to accurately lock the voltage frequency and the phase under a specific scene.
The invention adopts the following technical scheme to solve the technical problems: the LMS-SOGI three-phase-locked loop design method suitable for the non-ideal power grid comprises the following steps:
s1, sampling and obtaining three-phase grid-connected voltage U of grid-connected inverter a (t)、U b (t)、U c (t) performing Clark conversion operation to obtain alpha and beta axis components U of grid-connected voltage α (t)、U β (t)；
S2, grid-connected voltage alpha and beta axis component U α (t)、U β (t) respectively sending the two SOGI structures into the two SOGI structures, and extracting the positive sequence component of the power grid voltage under the alpha beta coordinate system of the two-phase static coordinate system through the transformation operation of the SOGI bi-quadratic generalized integrator
S3, constructing a least mean square LMS filtering link mathematical model, and designing a step length parameter of the least mean square LMS filtering link, wherein the step S3 further comprises the following steps:
s31, processing to obtain a mathematical model relation of a least mean square LMS filtering link by using a preset least mean square LMS adaptive filtering module;
s32, acquiring a time domain continuous mathematical model by using a least mean square LMS adaptive filtering module, wherein the preset least mean square LMS adaptive filtering module comprises: an input matrix X (n), an expected response input matrix d (n), an error vector matrix epsilon (n), a weight vector matrix W (n), a step size mu (n) and an output matrix y (n);
s4, processing the positive sequence component of the power grid voltage by using least mean square LMS filtering link mathematical model according to the step length parameter of the least mean square LMS filtering link
So as to obtain the d-axis positive sequence component of the fundamental frequency grid-connected voltage>
And the fundamental frequency grid-connected voltage q-axis positive sequence component->
S5, grid-connected fundamental frequency voltage q-axis component
Subtracting the phase difference with 0 to obtain a q-axis voltage phase-locked error signal e q (t) obtaining an output signal angular frequency adjustment amount omega by processing with a PI controller, and obtaining a phase theta by integration;
and S6, building a three-phase power grid voltage LMS-SOGI phase-locked model in preset simulation software, and obtaining a difference power grid voltage scene according to the output signal angular frequency regulating quantity omega and the phase theta, and comparing and analyzing the filtering effect.
The invention adds a self-adaptive filtering logic in the SOGI system to improve the voltage filtering effect of a three-phase power grid and the steady-state accuracy of phase locking. The SOGI phase-locked loop based on least mean square LMS adaptive filtering effectively avoids the influence of the poor filtering effect of a loop filter on the output frequency and the phase of the phase-locked loop under the non-ideal power grid condition, improves the stability of an inverter, can be widely applied to various occasions with severe working conditions and high requirements on detection speed, and improves the locking precision aiming at the voltage frequency and the phase.
In a more specific technical scheme, in the step S1, the real-time voltage U is connected to the three-phase grid according to the three-phase grid a (t)、U b (t)、U c (t) representing the abc coordinates in a three-phase stationary coordinate system by the following logicFundamental voltage of series:
in the formula of U a0 (t)、U b0 (t)、U c0 (t) is three-phase grid-connected fundamental wave voltage U under an abc coordinate system of a three-phase static coordinate system N Three-phase balanced voltage amplitude, k, of the mains voltage b 、k c Is the unbalance coefficient of three-phase unbalanced voltage B and C phases, omega 0 The fundamental angular frequency.
In a more specific solution, in step S1, the following logical Clark transformation operation is utilized:
in the formula of U α (t)、U β (T) is the power grid voltage alpha and beta components under the alpha beta coordinate system of the two-phase static coordinate system, T αβ Is a Clark transform coefficient matrix.
In a more specific technical solution, in step S2, the following logic is used to perform the SOGI biquad generalized integrator transformation operation:
in the formula (I), the compound is shown in the specification,
is the positive sequence component of the power grid voltage under an alpha beta coordinate system of a two-phase static coordinate system, and is based on the comparison result>
Is a three-phase grid-connected fundamental voltage positive sequence component T under an abc coordinate system of a three-phase static coordinate system + Q is a symmetric component normal coefficient matrix, and refers to a phase shift of 90 ° from the original signal in the time domain.
In a more specific technical solution, in step S2, the transfer function of the SOGI structure is expressed by the following logic:
in the formula, v 'and v are two outputs of the SOGI biquadratic generalized integrator module, ω' is the resonance frequency of the SOGI biquadratic generalized integrator module, and k is the reciprocal of the quality factor.
The invention comprises a three-phase power grid voltage self-adaptive filtering and phase locking technology under a non-ideal power grid, which is characterized in that the internal structure of a biquad generalized integral SOGI is improved, the improvement is different from the improvement of adding a prefilter and increasing the order, an LMS least mean square root self-adaptive filtering module replaces a Park conversion module, the function of Park conversion is equal, a better filtering effect can be obtained, and a subsequent phase locking module can more accurately track the grid-connected voltage.
The module not only carries out 90-degree offset on the input voltage signal to construct a two-phase orthogonal voltage signal so as to obtain a power grid voltage positive sequence component, but also can filter high-frequency interference signals.
In a more specific technical solution, in step S31, according to an input matrix X (n), an expected response input matrix d (n), an error vector matrix epsilon (n), a weight vector matrix W (n), a step size mu (n), and an output matrix y (n), a least mean square LMS filtering link mathematical model relation is obtained by processing using the following logic:
y(n)＝X T (n)*W(n)
ε(n)＝d(n)-y(n)＝d(n)-X T (n)*W(n)。
aiming at the problem that the cut-off frequency value of a loop filter must be low to reduce the influence of a negative sequence component and provide steady-state precision in the traditional technology, so that the dynamic response speed is low, in the invention, mu (n) adopts a step-length-variable mode to overcome the contradiction between the dynamic response speed and the steady-state precision.
In a more specific technical solution, in step S32, the step size is obtained by adopting the following step size variation method:
p(n)＝βp(n-1)+(1-β)ε(n)ε(n-1)
μ(n+1)＝αμ(n)+γp 2 (n)
in the formula, p (n) is a step iteration compensation matrix, and alpha, beta and gamma are step iteration coefficients.
The LMS least mean square following self-adaptive filtering module does not adopt a fixed step length or single output model, but extends to a variable step length and multi-output mode, and the high-speed convergence and low-steady state maladjustment characteristics of the LMS least mean square following self-adaptive filtering module realize the high-speed and high-steady state precision detection of the positive sequence voltage component amplitude and the phase angle of the three-phase power grid, so that the phase-locked system can keep good performance on the occasions with serious harmonic distortion and three-phase imbalance, and can quickly detect the sudden change of the three-phase voltage positive sequence component amplitude and the phase as well as the three-phase power grid positive sequence voltage component amplitude and the phase angle.
In a more specific technical solution, according to the weight vector matrix W (n), the following logic is used to perform weight iterative transformation to obtain iterative weights:
W(n+1)＝W(n)+μ(n)ε(n)X(n)。
in a more specific embodiment, the following logic is utilized in step S32. Acquiring a time domain continuous mathematical model corresponding to phase locking in a current LMS least mean square heel self-adaptive filtering module, wherein the time domain continuous mathematical model comprises:
inputting a matrix:
weight vector matrix:
expected response input matrix:
in the formula, cos ω t and sin ω t are phase angle trigonometric functions output by the phase-locked loop,
the positive sequence and negative sequence components of the grid voltage under a dq coordinate system of a two-phase rotating coordinate system.
In a more specific technical solution, an LMS-SOGI three-phase-locked loop design system suitable for a non-ideal power grid includes:
the Clark conversion module is used for sampling and acquiring three-phase grid-connected voltage U of the grid-connected inverter a (t)、U b (t)、U c (t) performing Clark conversion operation to obtain grid-connected voltage alpha and beta axis components U α (t)、U β (t)；
The SOGI bi-quad generalized integrator transformation module is used for transforming alpha and beta axis components U of grid-connected voltage α (t)、U β (t) respectively sending the two SOGI structures to extract the positive sequence component of the power grid voltage under the alpha beta coordinate system of the two-phase static coordinate system through the conversion operation of the SOGI bi-quadratic generalized integrator
The SOGI bi-quad generalized integrator transformation module is connected with the Clark transformation module;
the least mean square LMS filtering model building module is used for building a mathematical model of a least mean square LMS filtering link and designing a step length parameter of the least mean square LMS filtering link, wherein the least mean square LMS filtering module further comprises:
the LMS filtering model relation acquisition module is used for processing a mathematical model relation of a least mean square LMS filtering link by utilizing a preset least mean square LMS adaptive filtering module;
a time domain continuous mathematical model obtaining module, configured to obtain a time domain continuous mathematical model by using a least mean square LMS adaptive filtering module, where the preset least mean square LMS adaptive filtering module includes: an input matrix X (n), an expected response input matrix d (n), an error vector matrix epsilon (n), a weight vector matrix W (n), a step size mu (n) and an output matrix y (n);
a filter operation module for processing the positive sequence component of the power grid voltage by the least mean square LMS filter link according to the step length parameter of the least mean square LMS filter link by using the mathematical model of the least mean square LMS filter link
To obtain a fundamental frequency grid-connected voltage d-axis positive sequence component->
And the fundamental frequency grid-connected voltage q-axis positive sequence component->
The filtering operation module is connected with the least mean square LMS filtering model building module;
a phase processing module for combining the q-axis component of the fundamental frequency grid-connected voltage
Subtracting the phase difference with 0 to obtain a q-axis voltage phase-locked error signal e q (t) obtaining an output signal angular frequency adjustment quantity omega by utilizing the PI controller for processing, obtaining a phase theta by integrating, and connecting the phase processing module with the filtering operation module;
and the filtering effect comparison and analysis module is used for building a three-phase power grid voltage LMS-SOGI phase-locked model in preset simulation software, taking a difference power grid voltage scene according to the output signal angular frequency regulating quantity omega and the phase theta, and comparing and analyzing the filtering effect, wherein the filtering effect comparison and analysis module is connected with the phase processing module.
Compared with the prior art, the invention has the following advantages: the invention adds a self-adaptive filtering logic in the SOGI system to improve the voltage filtering effect of a three-phase power grid and the steady-state accuracy of phase locking. The SOGI phase-locked loop based on least mean square LMS adaptive filtering effectively avoids the influence of the poor filtering effect of a loop filter on the output frequency and the phase of the phase-locked loop under the non-ideal power grid condition, improves the stability of an inverter, can be widely applied to various occasions with severe working conditions and higher requirements on detection speed, and improves the locking precision aiming at the voltage frequency and the phase.
The invention comprises a three-phase power grid voltage self-adaptive filtering and phase locking technology under a non-ideal power grid, which is characterized in that the internal structure of a biquad generalized integral SOGI is improved, the improvement is different from the improvement of adding a pre-filter and increasing the order, and an LMS least mean square and self-adaptive filtering module replaces a Park conversion module, so that the function of Park conversion is equal to that of a Park conversion, a better filtering effect can be obtained, and a subsequent phase locking module can more accurately track the grid-connected voltage.
Aiming at the problem that the cut-off frequency value of a loop filter must be low to reduce the influence of a negative sequence component and provide steady-state precision in the traditional technology, so that the dynamic response speed is low, in the invention, mu (n) adopts a step-length-variable mode to overcome the contradiction between the dynamic response speed and the steady-state precision.
The LMS least mean square heel self-adaptive filtering module does not adopt a fixed step size or single output model, but extends to a variable step size and multi-output mode, and the high-speed convergence and low steady state maladjustment characteristics of the LMS least mean square heel self-adaptive filtering module realize the high-speed and high-steady state precision detection of the positive sequence voltage component amplitude and the phase angle of a three-phase power grid, so that the phase-locked system can keep good performance on the occasions with serious harmonic distortion and three-phase imbalance, and can quickly detect the sudden change of the positive sequence component amplitude and the phase of the three-phase voltage and the positive sequence voltage component amplitude and the phase angle of the three-phase power grid. The invention solves the technical problem that the phase locking technology of the grid-connected inverter in the prior art is difficult to accurately lock the voltage frequency and the phase under a specific scene.
Drawings
Fig. 1 is a flowchart of a three-phase power grid voltage adaptive filtering and phase locking technique in a non-ideal power grid according to embodiment 1 of the present invention;
fig. 2 is a schematic diagram of a phase-locked loop model in the voltage adaptive filtering and phase-locking technology of a three-phase power grid under a non-ideal power grid according to embodiment 1 of the present invention;
fig. 3 is a simulated non-ideal three-phase voltage waveform diagram of a three-phase power grid voltage adaptive filtering and phase locking technology in a non-ideal power grid according to embodiment 1 of the present invention;
fig. 4 is a schematic diagram of an SOGI bi-quad generalized integrator module in the voltage adaptive filtering and phase locking technology of a three-phase power grid under a non-ideal power grid according to embodiment 1 of the present invention;
fig. 5 is a wave characteristic diagram of an SOGI biquad generalized integrator module in the voltage adaptive filtering and phase locking technology of a three-phase power grid under a non-ideal power grid according to embodiment 1 of the present invention;
fig. 6 is a schematic diagram of an LMS least mean square and adaptive filtering module in a three-phase power grid voltage adaptive filtering and phase locking technology in a non-ideal power grid according to embodiment 1 of the present invention;
fig. 7 is a comparison graph of the filtering effects of the modules in the voltage adaptive filtering and phase locking technology of the three-phase power grid under the non-ideal power grid in embodiment 2 of the present invention;
fig. 8 is a diagram of a phase-locked loop output phase-locked steady-state effect in a three-phase power grid voltage adaptive filtering and phase-locking technology in a non-ideal power grid according to embodiment 2 of the present invention;
fig. 9 is a diagram of transient phase-locked loop output phase-locked effect in the three-phase power grid voltage adaptive filtering and phase-locking technology in the non-ideal power grid according to embodiment 2 of the present invention.
Detailed Description
In order to make the objects, 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 with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, the invention provides a LMS-SOGI three-phase-locked loop design method suitable for a non-ideal power grid, which comprises the following basic steps:
s1, obtaining three-phase grid-connected voltage U of a grid-connected inverter through sampling a (t)、U b (t)、U c (t) obtaining a grid-connected voltage alpha and beta axis component U through Clark conversion α (t)、U β (t)；
S2, then adding U α (t)、U β (t) respectively sending the two SOGI structures to extract the positive sequence component of the power grid voltage under the alpha beta coordinate system of the two-phase static coordinate system
S3, constructing a mathematical model of a least mean square LMS filtering link, and designing a step length parameter of the least mean square LMS filtering link;
s4, correcting the positive sequence component of the grid voltage
Performing LMS filtering, wherein the function of the least mean square LMS filtering link is equal to that of park transformation, and obtaining the fundamental frequency grid-connected voltage d and q axis positive sequence component->
S5, obtaining a q-axis component of the fundamental frequency grid-connected voltage
Subtracting the q-axis voltage phase-locked error signal e from 0 q And (t) obtaining an output signal angular frequency adjustment quantity omega through a PI controller, and obtaining a phase theta through integration.
S6, a three-phase power grid voltage LMS-SOGI phase-locking model is built in MATLAB/Simulink simulation software, and different power grid voltage conditions are selected for comparison and analysis of the filtering effect.
As shown in fig. 2, in this embodiment, constructing a phase-locked loop for adaptive filtering of three-phase grid voltage in a non-ideal grid includes: the system comprises a module (1), a grid-connected three-phase voltage module, a module (2), a Clark conversion module, a module (3), an SOGI second-order generalized integral generator module, a module (4 LMS minimum mean square heel self-adaptive filter module, a module (5), a PI control module and a module (6) simulation result observation module.
As shown in fig. 3, in this embodiment, the grid-connected three-phase voltage simulated by the module (1) grid-connected three-phase voltage module is divided into three stages, 0-2 s and 4-6 s, which are normal grid voltages: the amplitude of ABC three-phase voltage is 380V, and the phase difference is 120 degrees; 2-4 s are harmonic wave added and three-phase unbalanced voltage, the unbalanced voltage is 380V of an A phase, 450 of a B phase and 300V of the A phase, and the harmonic wave added is 2, 3, 5, 7 and 10 th harmonic waves with the amplitude of 38V.
In this embodiment, the three-phase voltage sampling module is specifically configured to sample and obtain a three-phase grid-connected real-time voltage U of the grid-connected inverter in step S1 a (t)、U b (t)、U c (t) a fundamental voltage thereof can be expressed as:
wherein U is a0 (t)、U b0 (t)、U c0 (t) is three-phase grid-connected fundamental voltage under the abc coordinate system of the three-phase static coordinate system, and the three-phase balanced voltage amplitude U of the grid voltage N =380V, imbalance coefficient k of three-phase unbalanced voltage B and C b ＝1.184、k c =0.789, fundamental angular frequency ω 0 And (5) =100 pi, and the initial phase angle of the a-phase voltage is 0.
Wherein the Clark transformation, module (2), in step S1 employs the following formula:
wherein U is α (t)、U β (T) is the power grid voltage alpha and beta components under the alpha beta coordinate system of the two-phase static coordinate system, T αβ For a Clark transform coefficient matrix, i.e.
In this embodiment, the conversion of the SOGI biquad generalized integrator in step S2 is as follows:
wherein
Is the positive sequence component of the power grid voltage under an alpha beta coordinate system of a two-phase static coordinate system, and is based on the comparison result>
Is a three-phase grid-connected fundamental voltage positive sequence component T under an abc coordinate system of a three-phase static coordinate system + Is a symmetric component method coefficient matrix, i.e.
Wherein->
q means a phase shift of 90 DEG, i.e. [ alpha ] -, in the time domain with respect to the original signal>
As shown in fig. 4, in this embodiment, the module (3) of the sogi second-order generalized integral generator not only performs 90 ° offset on the input voltage signal to construct a two-phase orthogonal voltage signal so as to obtain a positive sequence component of the power grid voltage, but also filters out a high-frequency interference signal. The transfer function of the SOGI system is:
as shown in fig. 5, in the present embodiment, v ', v are two outputs of the SOGI biquad generalized integrator module, the resonant frequency ω' =50Hz of the SOGI biquad generalized integrator module, and the inverse k =1..414 of the quality factor.
As shown in fig. 6, in this embodiment, the lms least mean square root adaptive filtering module (4) includes: an input matrix X (n), a desired response input matrix d (n), an error vector matrix epsilon (n), a weight vector matrix W (n), a step size mu (n), and an output matrix y (n). The relation of the basic mathematical model of the module is as follows:
y(n)＝X T (n)*W(n)
ε(n)＝d(n)-y(n)＝d(n)-X T (n)*W(n)
in this embodiment, the weight iterative formula becomes:
W(n+1)＝W(n)+μ(n)ε(n)X(n)
in this embodiment, in order to overcome the contradiction between the dynamic response speed and the steady-state accuracy, μ (n) adopts a step-variable manner, and the formula is as follows:
p(n)＝βp(n-1)+(1-β)ε(n)ε(n-1)
μ(n+1)＝αμ(n)+γp 2 (n)
in this embodiment, p (n) is a step iteration compensation matrix, and step iteration coefficients α =0.9, β =0.988, and γ =0.03.
In the present embodiment, it is preferred that, the time domain continuous mathematical model of the corresponding phase lock in the LMS least mean square and adaptive filtering module is as follows:
input matrix
Matrix of weight vectors
Expected response input matrix
Wherein cos ω t and sin ω t are phase angle trigonometric functions output by the phase-locked loop,
the positive sequence and negative sequence components of the grid voltage under a dq coordinate system of a two-phase rotating coordinate system.
In this embodiment, the mathematical model assigns the module output to the module expected input, so that the LMS least mean square and adaptive filtering module adaptively trains weights in the self-tracking process, and adjusts W (t) to approach the time-varying optimal weight matrix through error feedback to obtain the optimal parameter value required by step S4
In this embodiment, the module (5) and the PI control module enable the q-axis positive sequence component of the fundamental frequency grid-connected voltage obtained in S4 to be used as a power supply
Subtracting U from 0 to obtain q-axis voltage phase-locked error signal e q ，/>
Phase locking the q-axis voltage to an error signal e q As an input signal of the PI controller, an output signal of the PI controller is an angular frequency adjustment amount ω, and a phase θ is obtained by integration.
In this embodiment, step S5 is to set up a three-phase power grid voltage LMS-SOGI phase-locked model in MATLAB/Simulink simulation software, and the module (6) simulation result observation module filters the power grid voltage positive sequence component in the two-phase stationary coordinate system α β coordinate system after SOGI through Clark and park transformation
And the power grid voltage positive sequence component ^ is greater than or equal to the power grid voltage positive sequence component in the two-phase rotating coordinate system dq coordinate system after the LMS adaptive filtering>
And performing THD (total harmonic distortion) comparative analysis on the three-phase static coordinate system abc coordinate system to obtain a filter effect.
As shown in fig. 7, in the present embodiment, the sparse dotted line represents the THD of the grid-connected voltage waveform, and the close dotted line represents the grid voltage positive-sequence component after the SOGI filtering
The THD of the waveform under the three-phase static coordinate system abc coordinate system is converted, and a solid line represents the positive-sequence component (^ 4) of the power grid voltage subjected to LMS adaptive filtering>
And the THD of the waveform under the three-phase stationary coordinate system abc coordinate system is transformed.
Wherein, in the stage of normal ideal grid voltage of 0-2 s and 4-6 s, the steady-state values of the three are close to 0; under the condition of a 2s-4s non-ideal power grid, the three steady-state values are respectively THD =14.14% of grid-connected voltage waveform, THD =4.97% of voltage waveform after SOGI filtering and THD =1.79% of voltage waveform after LMS filtering. Therefore, the filtering effect of the LMS-SOGI phase-locked loop is obviously improved on the basis of the SOGI, and the expected target is achieved.
As shown in fig. 8 and 9, in this embodiment, a phase-locked steady-state effect graph and a transient-state effect graph of the three-phase grid voltage adaptive filtering phase-locked loop output under the non-ideal grid are shown, in which a solid line represents the grid fundamental voltage, and a dotted line represents the phase-locked output angle. Wherein the phase-locked steady-state effect diagram is 2.6997 s-2.7002 s of 2s-4s non-ideal power grid stage, and the phase-locked steady-state error is 0.10ms, about 0.5%; the phase-locked transient effect diagram is 1.95 s-2.35 s, which is the transition of the grid voltage from an ideal state to a non-ideal state, the transition point is a 2s time point, and the dynamic response time of the phase-locked loop is about 0.2s after the variable step length design is adopted.
In summary, the present invention adds a self-adaptive filtering logic inside the SOGI system to improve the voltage filtering effect of the three-phase power grid and the accuracy of the phase-locked steady state. The SOGI phase-locked loop based on least mean square LMS adaptive filtering effectively avoids the influence of the poor filtering effect of a loop filter on the output frequency and the phase of the phase-locked loop under the non-ideal power grid condition, improves the stability of an inverter, can be widely applied to various occasions with severe working conditions and higher requirements on detection speed, and improves the locking precision aiming at the voltage frequency and the phase.
The invention comprises a three-phase power grid voltage self-adaptive filtering and phase locking technology under a non-ideal power grid, which is characterized in that the internal structure of a biquad generalized integral SOGI is improved, the improvement is different from the improvement of adding a pre-filter and increasing the order, and an LMS least mean square and self-adaptive filtering module replaces a Park conversion module, so that the function of Park conversion is equal to that of a Park conversion, a better filtering effect can be obtained, and a subsequent phase locking module can more accurately track the grid-connected voltage.
Aiming at the problems that in the prior art, in order to reduce the influence of a negative sequence component and provide steady-state precision, the cut-off frequency value of a loop filter must be low, so that the dynamic response speed is low, in the invention, mu (n) adopts a step length changing mode to overcome the contradiction between the dynamic response speed and the steady-state precision.
The LMS least mean square following self-adaptive filtering module does not adopt a fixed step length or single output model, but extends to a variable step length and multi-output mode, and the high-speed convergence and low-steady state maladjustment characteristics of the LMS least mean square following self-adaptive filtering module realize the high-speed and high-steady state precision detection of the positive sequence voltage component amplitude and the phase angle of the three-phase power grid, so that the phase-locked system can keep good performance on the occasions with serious harmonic distortion and three-phase imbalance, and can quickly detect the sudden change of the three-phase voltage positive sequence component amplitude and the phase as well as the three-phase power grid positive sequence voltage component amplitude and the phase angle. The invention solves the technical problem that the phase locking technology of the grid-connected inverter in the prior art is difficult to accurately lock the voltage frequency and the phase under a specific scene.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A design method of an LMS-SOGI three-phase-locked loop applicable to a non-ideal power grid is characterized by comprising the following steps:
s1, sampling and acquiring three-phase grid-connected voltage U of grid-connected inverter a ()、U b ()、U c () According to the Clark conversion operation, the alpha and beta axis components U of the grid-connected voltage are obtained α ()、U β ()；
S2, enabling the grid-connected voltage alpha and beta axis components U α ()、U β () Respectively sending the two voltage signals into two SOGI structures, and extracting the positive sequence component of the power grid voltage under an alpha beta coordinate system of a two-phase static coordinate system through the conversion operation of an SOGI bi-quad generalized integrator
S3, constructing a least mean square LMS filtering link mathematical model, and designing a step length parameter of the least mean square LMS filtering link, wherein the step S3 further comprises the following steps:
s31, processing to obtain a mathematical model relation of a least mean square LMS filtering link by using a preset least mean square LMS adaptive filtering module;
s32, acquiring a time domain continuous mathematical model by using the least mean square LMS adaptive filtering module, wherein the preset least mean square LMS adaptive filtering module comprises: an input matrix X (n), a desired response input matrix d (n), an error vector matrix epsilon (n), a weight vector matrix W (n), a step size mu (n) and an output matrix y (n);
s4, utilizing the least mean square LMS filtering link mathematical model, and processing the power grid voltage positive sequence component through LMS filtering according to the least mean square LMS filtering link step length parameter
To obtain d-axis positive sequence component of fundamental frequency grid-connected voltage
And the fundamental frequency grid-connected voltage q-axis positive sequence component->
S5, mixing the above groupsFrequency grid-connected voltage q-axis component
Subtracting the q-axis voltage phase-locked error signal e from 0 q () Obtaining an output signal angular frequency regulating quantity omega by utilizing the processing of a PI controller, and obtaining a phase theta by integrating;
and S6, building a three-phase power grid voltage LMS-SOGI phase-locked model in preset simulation software, and taking a difference power grid voltage scene according to the output signal angular frequency regulating quantity omega and the phase theta, and comparing and analyzing the filtering effect.
2. The LMS-SOGI three-phase-locked loop design method suitable for the non-ideal power grid according to claim 1, wherein in the step S1, the real-time voltage U is obtained according to three-phase grid connection a ()、U b ()、U c () The fundamental wave voltage in the three-phase stationary coordinate system abc is expressed by the following logic:
in the formula of U a0 ()、U b0 ()、U c0 () Is three-phase grid-connected fundamental voltage U under an abc coordinate system of a three-phase static coordinate system N Three-phase balanced voltage amplitude, k, of the mains voltage b 、k c Is the unbalance coefficient of three-phase unbalanced voltage B and C phases, omega 0 The fundamental angular frequency.
3. The LMS-SOGI three-phase-locked loop design method for non-ideal power grid according to claim 1, wherein in step S1, the Clark transformation operation is performed by using the following logic:
in the formula of U α ()、U β () Is the power grid voltage alpha, beta components, T, in the alpha beta coordinate system of the two-phase static coordinate system αβ Is a Clark transform coefficient matrix.
4. The LMS-SOGI three-phase-locked loop design method as claimed in claim 1, wherein in step S2, the conversion operation of the SOGI biquad generalized integrator is performed by using the following logic:
in the formula (I), the compound is shown in the specification,
is the positive sequence component of the power grid voltage under an alpha beta coordinate system of a two-phase static coordinate system, and is based on the comparison result>
Is a three-phase grid-connected fundamental voltage positive sequence component T under an abc coordinate system of a three-phase static coordinate system + Q is a symmetric component normal coefficient matrix, and refers to a phase shift of 90 ° from the original signal in the time domain.
5. A LMS-SOGI three-phase-locked loop design method suitable for non-ideal power grid according to claim 1, wherein in step S2, the transfer function of the SOGI structure is expressed by the following logic:
in the formula, v 'and v are two outputs of the SOGI biquad generalized integrator module, ω' is the resonant frequency of the SOGI biquad generalized integrator module, and k is the reciprocal of the quality factor.
6. An LMS-SOGI three-phase-locked loop design method suitable for a non-ideal power grid according to claim 1, wherein in step S31, the least mean square LMS filtering element mathematical model relation is obtained by processing according to the input matrix X (n), the expected response input matrix d (n), the error vector matrix e (n), the weight vector matrix W (n), the step size μ (n), and the output matrix y (n) by using the following logic:
y(n)＝X T (n)*W(n)
ε(n)＝d(n)-y(n)＝d(n)-X T (n)*W(n)。
7. the LMS-SOGI three-phase locked loop design method suitable for a non-ideal power grid according to claim 1, wherein in step S32, the step is obtained by adopting the following step-size-variable manner:
p(n)＝βp(n-1)+(1-β)ε(n)ε(n-1)
μ(n+1)＝αμ(n)+γp 2 (n)
in the formula, p (n) is a step iteration compensation matrix, and alpha, beta and gamma are step iteration coefficients.
8. An LMS-SOGI three-phase-locked loop design method suitable for non-ideal power grid according to claim 1, wherein the weight iterative transformation is performed by using the following logic according to the weight vector matrix W (n) to obtain iterative weights:
W(n+1)＝W(n)+μ(n)ε(n)X(n)。
9. the LMS-SOGI three-phase locked loop design method for non-ideal power grid according to claim 1, wherein the following logic is used in step S32. Obtaining the time domain continuous mathematical model corresponding to the phase lock in the current LMS least mean square root adaptive filtering module, wherein the time domain continuous mathematical model includes:
inputting a matrix:
weight vector matrix:
expected response input matrix:
in the formula, cos ω t and sin ω t are phase angle trigonometric functions output by the phase-locked loop,
the positive sequence and negative sequence components of the grid voltage under a dq coordinate system of a two-phase rotating coordinate system.
10. An LMS-SOGI three-phase-locked loop design system for non-ideal power grids, the system comprising:
the Clark conversion module is used for sampling and acquiring three-phase grid-connected voltage U of the grid-connected inverter a ()、U b ()、U c () According to the Clark conversion operation, the alpha and beta axis components U of the grid-connected voltage are obtained α ()、U β ()；
The SOGI bi-quad generalized integrator transformation module is used for transforming the alpha and beta axis components U of the grid-connected voltage α ()、U β () Respectively sending the two signals into two SOGI structures, and extracting the positive sequence component of the power grid voltage under an alpha beta coordinate system of a two-phase static coordinate system through the transformation operation of an SOGI bi-second order generalized integrator
The SOGI bi-quad generalized integrator transformation module is connected with the Clark transformation module;
the least mean square LMS filtering model building module is used for building a mathematical model of a least mean square LMS filtering link and designing a step length parameter of the least mean square LMS filtering link, wherein the least mean square LMS filtering module further comprises:
the LMS filtering model relation acquisition module is used for processing a mathematical model relation of a least mean square LMS filtering link by utilizing a preset least mean square LMS adaptive filtering module;
a time domain continuous mathematical model obtaining module, configured to obtain a time domain continuous mathematical model by using the least mean square LMS adaptive filtering module, where the preset least mean square LMS adaptive filtering module includes: an input matrix X (n), an expected response input matrix d (n), an error vector matrix epsilon (n), a weight vector matrix W (n), a step size mu (n) and an output matrix y (n);
a filtering operation module for processing the positive sequence component of the power grid voltage by using the least mean square LMS filtering link mathematical model according to the step length parameter of the least mean square LMS filtering link
To obtain a fundamental frequency grid-connected voltage d-axis positive sequence component->
And the fundamental frequency grid-connected voltage q-axis positive sequence component->
The filtering operation module is connected with the least mean square LMS filtering model building module;
a phase processing module for combining the q-axis component of the fundamental frequency grid-connected voltage
Subtracting the phase difference with 0 to obtain a q-axis voltage phase-locked error signal e q () Obtaining an angular frequency adjustment amount omega of the output signal by processing with a PI controller, obtaining a phase theta by integration, and the phase processing moduleThe filtering operation module is connected;
and the filtering effect comparison and analysis module is used for building a three-phase power grid voltage LMS-SOGI phase-locked model in preset simulation software, taking a difference power grid voltage scene according to the output signal angular frequency regulating quantity omega and the phase theta, and comparing and analyzing the filtering effect, and is connected with the phase processing module.
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