CN116305883A - Inverter impedance identification method based on improved recursive least square method - Google Patents
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Abstract
The invention discloses an inverter impedance identification method based on an improved least square method, and belongs to the field of electrical systems. The method comprises the steps of sampling power grid voltage, filtering current and bridge arm side voltage, constructing an inverter mathematical model, discretizing the inverter mathematical model to obtain a discretized inverter mathematical model, and identifying filter inductance and circuit equivalent impedance by using an improved recursive least square method. The identification method of the invention improves the robustness and accuracy of the recursive least square algorithm and improves the stability of the inverter system.
Description
Technical Field
The invention relates to the field of electrical systems, in particular to an inverter impedance identification method based on improved recursive least square.
Background
At present, the large-scale development of a power system using renewable energy sources such as wind energy, water energy and solar energy becomes a main means for solving the energy problem, and the energy source is promoted to develop towards the directions of cleanliness, sustainability and low carbonization.
In a series of renewable energy systems, an inverter is a common bridge for inputting power grids, and most of distributed power generation systems are required to be constructed through the inverter so as to provide renewable clean energy for human society. The common output filters in the grid-connected inverter are of an L type and an LCL type, the LCL type filter can well inhibit high-frequency harmonic waves in a circuit, and has a good inhibiting effect relative to the L type filter under the same cost, but the integral structure is more complex, and the filtering effect is reduced due to the fact that the LCL type filter is easily built due to different processes or partial aging, system transformation can occur, so that an inverter system of the LCL type filter cannot work normally, and the normal operation of the system is damaged.
The L-type filter is simple in structure, but is easy to control and implement, so that in a large-scale power system, the L-type filter is generally used for better stability and longer service life. However, in the system control, a filter inductance value and an equivalent resistance value are required to be used as control parameters, and the resistance and the inductance value are changed due to temperature and other reasons during the system operation, so that a larger deviation occurs in the control, the inverter cannot work normally, and the normal operation of the system is affected.
The existing power grid impedance identification can be mainly divided into active detection and passive detection.
The active detection is to inject non-characteristic subharmonic, wide frequency signal, excitation filter resonance and other methods into the system in a hardware or software mode, and calculate the power grid impedance through voltage and current response. The active detection can effectively identify the impedance, but the disturbance is difficult to select by artificial addition, and the improper selection can reduce the identification accuracy and even affect the stability of the inverter.
The passive detection mainly uses the inherent information of the system and mainly uses the mathematical methods of recursive least square, maximum likelihood estimation and the like to identify the impedance of the power grid. Such as titled "Online InductanceIdentification of a PWM Rectifier Under Unbalanced and Distorted GridVoltages", zhang, yongchang, bingyu Li, and Jie Liu, IEEE Transactionson Industry Applications,2020:3879-3888 (PWM rectifier inductance on-line identification of unbalanced and disturbed grid voltage, "IEEE Industrial application, no. 4 in 2020, 3879-3888), firstly, voltage and current parameters are collected by a collection module, an inverter circuit equivalent model is built, then the equivalent model is discretized, and then identification parameters are calculated by a recursive least square method. However, this impedance identification method has the following disadvantages:
1) In the identification process of the recursive least square method, old information cannot be forgotten, new data are changed greatly, the change of the new data cannot be tracked well, the final result is greatly deviated from the actual result, and the robustness of the algorithm is reduced.
2) The accuracy of the recursive least squares method is low and is subject to noise interference, so that the algorithm cannot effectively track the changing signal.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the problems that the recursive least square method has larger deviation, lower robustness, lower accuracy, is easy to be interfered by noise, can not effectively track the change signal and the like in the identification process are solved.
In order to achieve the above purpose, the invention adopts the technical scheme that:
the inverter topological structure applying the method comprises a direct-current side voltage source, a three-phase full-bridge inverter circuit, three-phase circuit impedance and a three-phase power grid, wherein the direct-current side voltage source is connected with the three-phase full-bridge inverter circuit, the three-phase full-bridge inverter circuit is connected into the three-phase power grid through the three-phase circuit impedance, and the three-phase circuit impedance comprises a filter inductor and a circuit equivalent impedance;
the identification method utilizes an improved recursive least square method to identify the filter inductance and the equivalent impedance of the circuit, and comprises the following specific steps:
the inverter mathematical model is built as follows:
U gc -U g ＝L g i′ g +i g R g
wherein g is any one of a, b and c, U gc For g-phase bridge arm side voltage, U g For g-phase grid voltage, i g Filtering the current for g-phase, i' g Filtering the current i for g-phase g Is the derivative of L g For filtering inductance value, R g An impedance value that is the equivalent impedance of the circuit;
step 2, setting an initial period and n identification periods in the identification process, wherein the initial period is sampled once and marked as 1 st sampling, each identification period in the n identification periods is sampled once and identified once, any one of the n identification periods is marked as a current identification period k, k=1, 2..n, and the current identification period k is marked as k+1st sampling;
discretizing the mathematical model of the inverter obtained in the step 1 to obtain the mathematical model of the discretized inverter, wherein the expression is as follows:
wherein i is g (k+1) is the g-phase filtered current obtained by the (k+1) th sampling, i g (k) The g-phase filtering current obtained for the kth sampling, U gc (k) The g-phase bridge arm side voltage obtained by the kth sampling is U g (k) G-phase grid voltage obtained by kth sampling, L gk For the calculated filter inductance value after the kth identification period, R gk The equivalent impedance value of the circuit calculated after the kth identification period is calculated, and T is the sampling period;
wherein,,
y k filtered current information, y, obtained for the k+1th sample k ＝i g (k+1)；
Φ k For the known information obtained for the kth sample, Φ k ＝[U gc (k) U g (k) i g (k)] T ；
θ k Calculating a matrix, θ, for parameters to be identified for a kth identification period k ＝[θ 1k θ 2k θ 3k ] T ，θ 1k Calculating matrix parameters 1, theta for parameters to be identified 2k Calculating matrix parameters 2, theta for parameters to be identified 3k Matrix parameters 3 are calculated for the parameters to be identified, and the calculation formulas are respectively as follows:
Step 5, identifying the filter inductance value L g Sum circuit equivalent resistance value R g The formula is as follows:
preferably, the implementation process of the iterative equation of the improved recursive least square method in step 4 is as follows:
step 4.1, setting parameters;
the parameters to be set include forgetting factor lower bound u L Dead zone coefficient epsilon, sensitivity coefficient eta and user-defined parameter m based on noise level y 1-norm penalty term weight λ;
initializing an information matrix R 0 Initializing a parameter computing matrix theta to be identified 0 ；
Step 4.2, calculating the prediction error e of the kth recognition period k ：
Wherein e k For the prediction error between the kth recognition cycle predicted value and the actual measured value, θ k-1 Representing parameters to be identified calculated in the k-1 identification period;
step 4.3, calculating a kth recognition period forgetting factor u k The expression is as follows:
where tr is the trace of the matrix, u k Forgetting factor, P, calculated for the kth recognition period k-1 A covariance matrix calculated for the (k-1) th recognition period, max { } being a maximum function;
step 4.4, calculating and updating the information matrix R calculated in the kth identification period k ：
Wherein R is k-1 For the information matrix of the k-1 th recognition period,
the left part of the periodic information matrix is identified for the k-1 th;
information matrix R of kth identification period k The expression is as follows:
wherein,,
reserved part of the information matrix for the kth identification period,/for the k identification period>
The expression of the forgetting part of the information matrix for the kth recognition period is as follows:
wherein,, || is the norm of the matrix, (x) -1 Is the inverse of the matrix;
step 4.5, calculating and updating covariance matrix P k By means of an updated information matrix R k The calculation is performed with the following expression:
step 4.6, calculating and updating the parameter calculation matrix theta to be identified k The parameter update expression to be identified is as follows:
wherein P is k-1 Covariance matrix calculated for the (k-1) th recognition period, θ k-1 Parameter to be identified representing the calculation of the k-1 th identification periodNumber sgn is a sign function;
step 4.7, according to step 4.1 to step 4.6, the iterative equation of the improved recursive least square method is obtained as follows:
compared with the prior art, the invention has the beneficial technical effects that:
the invention uses the improved recursive least square method to identify the inductance value L of the filter through sampling the voltage filtering of the power grid, the current flowing through the inductance and the voltage at the side of the inverter circuit and the constructed discretization mathematical model of the inverter g Sum circuit equivalent impedance value R g And the robustness and the accuracy of the recursive least square algorithm are improved.
Drawings
FIG. 1 is a circuit topology of an inverter in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of an identification period;
FIG. 3 is a flowchart of the identification method step 4 of the present invention;
FIG. 4 is a diagram showing the identification effect of the filter inductance parameter according to an embodiment of the present invention;
fig. 5 is a circuit equivalent impedance parameter identification block diagram according to an embodiment of the invention.
Detailed Description
The invention will now be further described with reference to the drawings and detailed description.
Fig. 1 is a circuit topology diagram of an inverter in a specific embodiment of the present invention, and as can be seen from fig. 1, the inverter topology structure based on the improved recursive least square method of the present invention includes a dc side voltage source, a three-phase full bridge inverter circuit, a three-phase circuit impedance and a three-phase power grid, where the dc side voltage source is connected with the three-phase full bridge inverter circuit, and the three-phase full bridge inverter circuit is connected to the three-phase power grid through the three-phase circuit impedance, and the three-phase circuit impedance includes a filter inductance and a circuit equivalent impedance. In fig. 1, 1 is a direct-current side voltage source, 2 is a three-phase full-bridge inverter circuit, 3 is a three-phase circuit impedance, 4 is a three-phase power grid, L is a filter inductance, and R is a circuit equivalent resistance.
Fig. 3 is a flowchart of the identification method of the present invention, which can be seen from the figure, and the identification method uses an improved recursive least square method to identify the filter inductance and the equivalent impedance of the circuit, and specifically includes the following steps:
the inverter mathematical model is built as follows:
U gc -U g ＝L g i′ g +i g R g
wherein g is any one of a, b and c, U gc For g-phase bridge arm side voltage, U g For g-phase grid voltage, i g Filtering the current for g-phase, i' g Filtering the current i for g-phase g Is the derivative of L g For filtering inductance value, R g Is the impedance value of the equivalent impedance of the circuit.
Step 2, setting an initial period and n identification periods in the identification process, wherein the initial period is sampled once and marked as 1 st sampling, each identification period in the n identification periods is sampled once and identified once, any one of the n identification periods is marked as a current identification period k, k=1, 2..n, and the current identification period k is marked as k+1st sampling;
discretizing the mathematical model of the inverter obtained in the step 1 to obtain the mathematical model of the discretized inverter, wherein the expression is as follows:
wherein i is g (k+1) is the g-phase filtered current obtained by the (k+1) th sampling, i g (k) The g-phase filtering current obtained for the kth sampling, U gc (k) For the kth timeSampling the obtained g-phase bridge arm side voltage, U g (k) G-phase grid voltage obtained by kth sampling, L gk For the calculated filter inductance value after the kth identification period, R gk And (3) calculating the equivalent impedance value of the circuit after the kth identification period, wherein T is the sampling period.
FIG. 2 is a schematic diagram of an identification period, showing the relationship among the identification period, the number of samples, and the number of identifications.
wherein,,
y k filtered current information, y, obtained for the k+1th sample k ＝i g (k+1)；
Φ k For the known information obtained for the kth sample, Φ k ＝[U gc (k) U g (k) i g (k)] T ；
θ k Calculating a matrix, θ, for parameters to be identified for a kth identification period k ＝[θ 1k θ 2k θ 3k ] T ，θ 1k Calculating matrix parameters 1, theta for parameters to be identified 2k Calculating matrix parameters 2, theta for parameters to be identified 3k Matrix parameters 3 are calculated for the parameters to be identified, and the calculation formulas are respectively as follows:
Step 5, identifying the filter inductance value L g Sum circuit equivalent resistance value R g The formula is as follows:
in this embodiment, the implementation procedure of the iterative equation of the improved recursive least square method in step 4 is as follows:
step 4.1, setting parameters;
the parameters to be set include forgetting factor lower bound u L Dead zone coefficient epsilon, sensitivity coefficient eta and user-defined parameter m based on noise level y 1-norm penalty term weight λ;
initializing an information matrix R 0 Initializing a parameter computing matrix theta to be identified 0 ；
Step 4.2, calculating the prediction error e of the kth recognition period k ：
Wherein e k For the prediction error between the kth recognition cycle predicted value and the actual measured value, θ k-1 Representing parameters to be identified calculated in the k-1 identification period;
step 4.3, calculating a kth recognition period forgetting factor u k The expression is as follows:
where tr is the trace of the matrix, u k Forgetting calculated for kth recognition cycleFactor, P k-1 A covariance matrix calculated for the (k-1) th recognition period, max { } being a maximum function;
step 4.4, calculating and updating the information matrix R calculated in the kth identification period k ：
Wherein R is k-1 For the information matrix of the k-1 th recognition period,
the left part of the periodic information matrix is identified for the k-1 th;
information matrix R of kth identification period k The expression is as follows:
wherein,,
reserved part of the information matrix for the kth identification period,/for the k identification period>
The expression of the forgetting part of the information matrix for the kth recognition period is as follows:
wherein,, || is the norm of the matrix, (x) -1 Is the inverse of the matrix;
step 4.5, calculating and updating covariance matrix P k By means of an updated information matrix R k The calculation is performed with the following expression:
step 4.6, calculating and updating the parameters to be identifiedCalculating matrix θ k The parameter update expression to be identified is as follows:
wherein P is k-1 Covariance matrix calculated for the (k-1) th recognition period, θ k-1 Representing parameters to be identified calculated in the k-1 identification period, wherein sgn is a symbol function;
step 4.7, according to step 4.1 to step 4.6, the iterative equation of the improved recursive least square method is obtained as follows:
in the present embodiment, the grid voltage U g =415V/50 Hz, dc input voltage value U dc =1100V, filter inductance value L g =6mh, equivalent impedance value of circuit R g ＝1Ω。
Initial parameters were set, the initial values were as follows:
lower bound of genetic factor u L =0.9, dead zone coefficient ε=20, sensitivity coefficient η=0.1, custom parameter m y =2, penalty weight λ=2, sampling period t=10 -6 s，
Initial information matrix
Initial parameter to be identified calculation matrix theta 0 ＝[0 0 0]。
In this embodiment, the voltage sensor and the current sensor collect the bridge arm side voltage, the grid voltage and the filter current of any phase as known information, and combine with the above initial parameters, and the identification is performed by improving the recursive least square method.
After the identification is finished, the identification result is compared with the identification result of the recursive least square method and the real data, and the final effect diagram is shown in fig. 4 and 5. The filter inductance effect of the improved recursive least square method identification is slightly better than that of the recursive least square method, and in the identification effect of equivalent impedance, the improved recursive least square method is closer to a true value, so that the improved recursive least square method identification precision is better than that of the recursive least square method.
Claims (2)
1. The inverter topological structure applying the method comprises a direct-current side voltage source, a three-phase full-bridge inverter circuit, three-phase circuit impedance and a three-phase power grid, wherein the direct-current side voltage source is connected with the three-phase full-bridge inverter circuit, the three-phase full-bridge inverter circuit is connected into the three-phase power grid through the three-phase circuit impedance, and the three-phase circuit impedance comprises a filter inductor and a circuit equivalent impedance;
the identification method is characterized by identifying the filter inductance and the equivalent impedance of the circuit by using an improved recursive least square method, and comprises the following specific steps:
step 1, the voltage of the output point of the sampling three-phase full-bridge inverter circuit is recorded as bridge arm side voltage U xc Sampling grid voltage U x The current flowing through the filter inductance is sampled and recorded as a filter current i x Wherein x is the phase sequence, x=a, b, c;
the inverter mathematical model is built as follows:
U gc -U g ＝L g i′ g +i g R g
wherein g is any one of a, b and c, U gc For g-phase bridge arm side voltage, U g For g-phase grid voltage, i g Filtering the current for g-phase, i' g Filtering the current i for g-phase g Is the derivative of L g For filtering inductance value, R g An impedance value that is the equivalent impedance of the circuit;
step 2, setting an initial period and n identification periods in the identification process, wherein the initial period is sampled once and marked as 1 st sampling, each identification period in the n identification periods is sampled once and identified once, any one of the n identification periods is marked as a current identification period k, k=1, 2..n, and the current identification period k is marked as k+1st sampling;
discretizing the mathematical model of the inverter obtained in the step 1 to obtain the mathematical model of the discretized inverter, wherein the expression is as follows:
wherein i is g (k+1) is the g-phase filtered current obtained by the (k+1) th sampling, i g (k) The g-phase filtering current obtained for the kth sampling, U gc (k) The g-phase bridge arm side voltage obtained by the kth sampling is U g (k) G-phase grid voltage obtained by kth sampling, L gk For the calculated filter inductance value after the kth identification period, R gk The equivalent impedance value of the circuit calculated after the kth identification period is calculated, and T is the sampling period;
step 3, converting the discretized mathematical model obtained in the step 2 into a matrix form of the discretized model according to a least square method, wherein the expression is as follows:
wherein,,
y k filtered current information, y, obtained for the k+1th sample k ＝i g (k+1)；
Φ k For the known information obtained for the kth sample, Φ k ＝[U gc (k) U g (k) i g (k)] T ；
θ k Calculating a matrix, θ, for parameters to be identified for a kth identification period k ＝[θ 1k θ 2k θ 3k ] T ，θ 1k Calculating matrix parameters 1, theta for parameters to be identified 2k Calculating matrix parameters 2, theta for parameters to be identified 3k Matrix parameters 3 are calculated for the parameters to be identified, and the calculation formulas are respectively as follows:
step 4, substituting the matrix form of the discretization model obtained in the step 3 into an iteration equation of an improved recursion least square method, and identifying the filter inductance L and the circuit load impedance R connected with the inverter circuit n times to obtain a parameter to be identified calculation matrix theta in an nth identification period n ＝[θ 1n θ 2n θ 3n ] T ；
Step 5, identifying the filter inductance value L g Sum circuit equivalent resistance value R g The formula is as follows:
2. the method for identifying the impedance of the inverter based on the improved recursive least square method as set forth in claim 1, wherein the iterative equation of the improved recursive least square method in step 4 is implemented as follows:
step 4.1, setting parameters;
the parameters to be set include forgetting factor lower bound u L Dead zone coefficient epsilon, sensitivity coefficient eta and user-defined parameter m based on noise level y 1-norm penalty term weight λ;
initializing an information matrix R 0 Initializing a parameter computing matrix theta to be identified 0 ；
Step 4.2, calculating the prediction error e of the kth recognition period k ：
Wherein e k For the prediction error between the kth recognition cycle predicted value and the actual measured value, θ k-1 Representing parameters to be identified calculated in the k-1 identification period;
step 4.3, calculating a kth recognition period forgetting factor u k The expression is as follows:
where tr is the trace of the matrix, u k Forgetting factor, P, calculated for the kth recognition period k-1 A covariance matrix calculated for the (k-1) th recognition period, max { } being a maximum function;
step 4.4, calculating and updating the information matrix R calculated in the kth identification period k ：
Wherein R is k-1 For the information matrix of the k-1 th recognition period,
the left part of the periodic information matrix is identified for the k-1 th;
information matrix R of kth identification period k The expression is as follows:
wherein,,
information for the kth identification periodReserved part of matrix, ">
The expression of the forgetting part of the information matrix for the kth recognition period is as follows:
wherein,, || is the norm of the matrix, (x) -1 Is the inverse of the matrix;
step 4.5, calculating and updating covariance matrix P k By means of an updated information matrix R k The calculation is performed with the following expression:
step 4.6, calculating and updating the parameter calculation matrix theta to be identified k The parameter update expression to be identified is as follows:
wherein P is k-1 Covariance matrix calculated for the (k-1) th recognition period, θ k-1 Representing parameters to be identified calculated in the k-1 identification period, wherein sgn is a symbol function;
step 4.7, according to step 4.1 to step 4.6, the iterative equation of the improved recursive least square method is obtained as follows:
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| CN117375471B (en) * | 2023-12-08 | 2024-03-12 | 浙江大学 | Permanent magnet motor moment of inertia and load torque identification method and system |
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