Improved recursive least square based impedance identification method for inverters

Abstract

The application discloses an inverter impedance identification method based on an improved least square method and belongs to the field of electrical systems. The steps of the method comprise sampling 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, using an improved recursive least square method, and identifying filter inductance and circuit equivalent impedance. The identification method improves the robustness and accuracy of the recursive least square algorithm and improves the stability of the inverter system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electrical systems, in particular to an improved recursive least square based impedance identification method for inverters. BACKGROUND

[0002] At present, large-scale development of power systems using renewable energy sources such as wind energy, water energy and solar energy has become the main means to solve energy problems, and has promoted the development of energy towards clean, sustainable and low-carbon.

[0003] Among a series of renewable energy systems, inverters are common bridges to input power grids, and most distributed power generation systems need to be built through inverters to provide renewable clean energy for human society. The common output filter in grid-connected inverters is L-type and LCL-type. Although the LCL-type filter can better suppress high-frequency harmonics in the circuit, it has better suppression effect than the L-type filter at the same cost, but the overall structure is more complex. The construction of the LCL-type filter is prone to system transformation due to different processes or partial aging, which reduces the filtering effect, so that the inverter system of the LCL-type filter cannot work normally, and the normal operation of the system is damaged.

[0004] Although the L-type filter has a simple structure, it is easy to control and easy to implement, so in large power systems, L-type filters are usually used for better stability and longer life. However, in system control, the filter inductance value and equivalent resistance value are used as control parameters, and during system operation, the resistance and inductance values will change due to temperature and other reasons, causing large deviations in control, so that the inverter cannot work normally, affecting the normal operation of the system.

[0005] Existing grid impedance identification can be mainly divided into active detection and passive detection.

[0006] Active detection is to inject non-characteristic harmonic, wide frequency signal, excite filter resonance and other methods into the system through hardware or software, and calculate the grid impedance through voltage and current response. Active detection can effectively identify impedance, but it is difficult to select the disturbance artificially, and improper selection may reduce the identification accuracy, and even affect the stability of the inverter.

[0007] Passive detection is mainly through the system inherent information, mainly through recursive least squares, maximum likelihood estimation and other mathematical methods to identify the size of the grid impedance. Such as the article entitled "Online Inductance Identification of a PWM Rectifier Under Unbalanced and Distorted Grid Voltages", Zhang, Yongchang, Bingyu Li, and Jie Liu, IEEE Transactions on Industry Applications, 2020: 3879-3888 ("PWM rectifier inductance online identification under unbalanced and distorted grid voltage", IEEE Transactions on Industry Applications, 2020, No. 4, 3879-3888), first through the acquisition module to collect voltage and current parameters, establish an equivalent model of the inverter circuit, and then discretize the equivalent model, and then calculate and identify the parameters by recursive least squares method. However, this impedance identification method has the following shortcomings:

[0008] 1) In the identification process, the recursive least squares method cannot forget the old information, and cannot well track the change of new data when the new data changes greatly, resulting in a large deviation between the final result and the actual value, and reducing the robustness of the algorithm.

[0009] 2) The accuracy of the recursive least squares method is low, and it is easy to be disturbed by noise, so that the algorithm cannot effectively track the changing signal. SUMMARY

[0010] The technical problem to be solved by the present application is to compensate for the large deviation, low robustness, low accuracy, easy noise disturbance and inability to effectively track changing signals of the recursive least squares method in the identification process.

[0011] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0012] An inverter impedance identification method based on improved recursive least squares, the inverter topology structure applied by the method includes a DC side voltage source, a three-phase full-bridge inverter circuit, a three-phase circuit impedance and a three-phase power grid, the DC side voltage source and the three-phase full-bridge inverter circuit are connected, the three-phase full-bridge inverter circuit is connected to the three-phase power grid through the three-phase circuit impedance, wherein the three-phase circuit impedance includes a filter inductance and a circuit equivalent impedance;

[0013] The identification method uses improved recursive least squares to identify the filter inductance and the circuit equivalent impedance, and the specific steps are as follows:

[0014] Step 1, sample the voltage of the output point of the three-phase full-bridge inverter circuit, which is denoted as bridge arm side voltage U xc, sampling grid voltage U x , sampling current flowing through filter inductance and recorded as filter current i x , where x is phase sequence, x = a, b, c;

[0015] The mathematical model of the inverter is established as follows:

[0016] U gc -U g = L g i′ g +i g R g

[0017] , where g is any one of the three phases a, b, and c, U gc is the voltage on the g-phase bridge arm, U g is the g-phase grid voltage, i g is the g-phase filter current, i′ g is the derivative of the g-phase filter current i g , L g is the inductance value of the filter inductance, and R g is the impedance value of the equivalent circuit impedance;

[0018] Step 2: Assume that there is one initial period and n identification periods in the identification process, where one sampling is performed in the initial period, recorded as the first sampling, and one sampling and one identification are performed in each of the n identification periods. Any one of the n identification periods is recorded as the current identification period k, k = 1, 2,..., n, and the sampling of the current identification period k is recorded as the (k+1)th sampling;

[0019] Discretize the mathematical model of the inverter obtained in step 1 to obtain the mathematical model of the discretized inverter, expressed as follows:

[0020]

[0021] , where i g (k+1) is the g-phase filter current obtained by the (k+1)th sampling, i g (k) is the g-phase filter current obtained by the kth sampling, U gc (k) is the g-phase bridge arm voltage obtained by the kth sampling, U g (k) is the g-phase grid voltage obtained by the kth sampling, L gk is the filter inductance value calculated after the kth identification period, R gk is the equivalent circuit impedance value calculated after the kth identification period, and T is the sampling period;

[0022] Step 3, according to the least square method, the discrete mathematical model obtained in step 2 is converted into a matrix form of the discrete model, and the expression is as follows:

[0023]

[0024] Wherein,

[0025] y k is the filtered current information obtained at the k+1 sampling, y k = i g (k+1);

[0026] Φ k is the known information obtained at the k sampling, Φ k = [U gc (k) U g (k) i g (k)] T ;

[0027] θ k is the to-be-identified parameter calculation matrix of the k identification period, θ k = [θ 1k θ 2k θ 3k ] T , θ 1k is the to-be-identified parameter calculation matrix parameter 1, θ 2k is the to-be-identified parameter calculation matrix parameter 2, θ 3k is the to-be-identified parameter calculation matrix parameter 3, and the calculation formulas are as follows:

[0028]

[0029]

[0030]

[0031] Step 4, the matrix form of the discrete model obtained in step 3 is substituted into the iteration equation of the improved recursive least square method, and the filter inductance L connected to the inverter circuit and the circuit load impedance R are identified for n times, to obtain the to-be-identified parameter calculation matrix θ n = [θ 1n θ 2n θ 3n ] T of the n identification period.

[0032] Step 5, identify the filter inductance value L g and the circuit equivalent resistance value R g , and the calculation formulas are as follows:

[0033]

[0034] Preferably, the implementation process of the iterative equation of the improved recursive least square method in step 4 is as follows:

[0035] Step 4.1, parameter setting;

[0036] The parameters to be set include the lower limit of the forgetting factor u L , the dead zone coefficient based on the noise level ε, the sensitivity coefficient η, the user-defined parameter m y , and the 1-norm penalty term weight λ;

[0037] Initialize the information matrix R0and the matrix θ0for calculating the to-be-identified parameters;

[0038] Step 4.2, calculate the prediction error e k of the kth identification period:

[0039]

[0040] Where e k is the prediction error between the predicted value and the actual measured value of the kth identification period, and θ k-1 represents the to-be-identified parameters calculated in the k-1th identification period;

[0041] Step 4.3, calculate the forgetting factor u k of the kth identification period, which is expressed as follows:

[0042]

[0043] Where tr(*) is the trace of a matrix, u k is the forgetting factor calculated in the kth identification period, P k-1 is the covariance matrix calculated in the k-1th identification period, and max{} is the maximum value function;

[0044] Step 4.4, calculate and update the information matrix R k calculated in the kth identification period:

[0045]

[0046] Where R k-1 is the information matrix in the k-1th identification period, is the forgetting part of the information matrix in the k-1th identification period;

[0047] The information matrix R k in the kth identification period is expressed as follows:

[0048]

[0049] Where the reserved part of the information matrix of the kth identification period, the forgotten part of the information matrix of the kth identification period, the expression of which is as follows:

[0050]

[0051] wherein ||*|| is the norm of the matrix, (*) -1 is the inverse of the matrix;

[0052] Step 4.5, calculating and updating the covariance matrix P k , the updated information matrix R k is calculated, and the expression is as follows:

[0053]

[0054] Step 4.6, calculating and updating the to-be-identified parameter calculation matrix θ k , the to-be-identified parameter update expression is as follows:

[0055]

[0056] wherein P k-1 is the covariance matrix calculated in the k-1th identification period, θ k-1 represents the to-be-identified parameter calculated in the k-1th identification period, and sgn(*) is the sign function;

[0057] Step 4.7, according to steps 4.1-4.6, the iterative equation of the improved recursive least square method is as follows:

[0058]

[0059] Compared with the prior art, the beneficial technical effects of the present application are:

[0060] The present application identifies the filter inductance value L g and the circuit equivalent impedance value R g by using the improved recursive least square method through the constructed inverter discretization mathematical model by sampling the grid voltage filter, the current flowing through the inductance and the voltage on the inverter side, and improves the robustness and accuracy of the recursive least square algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 is the inverter circuit topology in the specific embodiment of the present application;

[0062] Figure 2 is the identification period schematic diagram;

[0063] Figure 3 is the flow chart of step 4 of the identification method of the present application;

[0064] Figure 4 Filter inductance parameter identification effect diagram of the embodiment of the present application;

[0065] Figure 5 Circuit equivalent impedance parameter identification block diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0066] The present application will be further described in conjunction with the drawings and specific embodiments.

[0067] Figure 1 Inverter circuit topology in the embodiment of the present application, wherein Figure 1 It can be seen that the inverter impedance identification method based on improved recursive least square method of the present application, the inverter topology structure applying the method includes a DC side voltage source, a three-phase full-bridge inverter circuit, a three-phase circuit impedance and a three-phase power grid, the DC side voltage source and the three-phase full-bridge inverter circuit are connected, the three-phase full-bridge inverter circuit is connected to the three-phase power grid through the three-phase circuit impedance, wherein the three-phase circuit impedance includes a filter inductance and a circuit equivalent impedance. Figure 1 In the above, 1 is the DC side voltage source, 2 is the three-phase full-bridge inverter circuit, 3 is the three-phase circuit impedance, 4 is the three-phase power grid, L is the filter inductance, and R is the circuit equivalent resistance.

[0068] Figure 3 The flow chart of the identification method of the present application, from the chart, the identification method uses the improved recursive least square method to identify the filter inductance and the circuit equivalent impedance, and the specific steps are as follows:

[0069] Step 1, sampling the voltage at the output point of the three-phase full-bridge inverter circuit, denoted as bridge arm side voltage U xc , sampling the grid voltage U x , sampling the current flowing through the filter inductance and denoted as filter current i x , wherein x is the phase sequence, x=a, b, c;

[0070] The mathematical model of the inverter is established as follows:

[0071] U gc -U g =L g i′ g +i g R g

[0072] Wherein, g is any one of a, b and c, U gc is the bridge arm side voltage of phase g, U g is the grid voltage of phase g, i g is the filter current of phase g, and i′ g is the filter current i of phase g.g The derivative of L g R is the inductance value of the filter inductor. g This is the impedance value of the circuit's equivalent impedance.

[0073] Step 2: Assume that the identification process includes one initial period and n identification periods. In the initial period, a sampling is performed and recorded as the first sampling. In each of the n identification periods, a sampling and an identification are performed. Any one of the n identification periods is recorded as the current identification period k, k = 1, 2, ... n. The sampling in the current identification period k is recorded as the (k+1)th sampling.

[0074] Discretize the inverter mathematical model obtained in step 1 to obtain the discretized inverter mathematical model, as shown in the following expression:

[0075]

[0076] Among them, i g (k+1) represents the g-phase filter current obtained from the (k+1)th sampling, i g (k) represents the g-phase filter current obtained from the k-th sampling, U gc (k) represents the g-phase bridge arm voltage obtained from the k-th sampling, U g (k) represents the g-phase grid voltage obtained from the k-th sampling, L gk R is the filter inductance value calculated after the kth identification cycle. gk The equivalent impedance value of the circuit is calculated after the kth identification cycle, and T is the sampling period.

[0077] Figure 2 The diagram illustrates the identification cycle, showing the relationship between the identification cycle, the number of samplings, and the number of identifications.

[0078] Step 3: Using the least squares method, transform the discretized mathematical model obtained in Step 2 into the matrix form of the discretized model, as shown in the following expression:

[0079]

[0080] in,

[0081] y k The filtered current information obtained from the (k+1)th sampling is y. k =i g (k+1);

[0082] Φ k For the known information obtained from the k-th sample, Φ k =[U gc (k) U g (k) i g (k)]T ;

[0083] θ k is the calculation matrix of the to-be-identified parameters in the kth identification period, θ k = [θ 1k θ 2k θ 3k ] T , θ 1k is the calculation matrix parameter 1 of the to-be-identified parameters, θ 2k is the calculation matrix parameter 2 of the to-be-identified parameters, θ 3k is the calculation matrix parameter 3 of the to-be-identified parameters, and the calculation formulas are as follows:

[0084]

[0085]

[0086]

[0087] Step 4, the matrix form of the discretization model obtained in step 3 is substituted into the iterative equation of the improved recursive least square method, and the filter inductance L connected to the inversion circuit and the circuit load impedance R are identified for n times to obtain the calculation matrix θ n of the to-be-identified parameters in the nth identification period 1n = [θ 2n θ 3n ] T .

[0088] Step 5, the filter inductance value L g and the circuit equivalent resistance value R g are identified, and the calculation formulas are as follows:

[0089]

[0090] In the embodiment, the implementation process of the iterative equation of the improved recursive least square method in step 4 is as follows:

[0091] Step 4.1, parameter setting;

[0092] The parameters to be set include the lower limit of the forgetting factor u L , the dead zone coefficient ε based on the noise level, the sensitivity coefficient η, the user-defined parameter m y , and the 1-norm penalty term weight λ;

[0093] Initialize the information matrix R0and the to-be-identified parameter calculation formula matrix θ0;

[0094] Step 4.2, calculate the prediction error e k in the kth identification period:

[0095]

[0096] where e k is the prediction error between the predicted value and the actual measured value in the kth identification period, θ k-1 represents the to-be-identified parameter calculated in the k-1th identification period;

[0097] Step 4.3, calculating the forgetting factor u k in the kth identification period, whose expression is as follows:

[0098]

[0099] where tr(*) is the trace of a matrix, u k is the forgetting factor calculated in the kth identification period, P k-1 is the covariance matrix calculated in the k-1th identification period, and max{} is the maximum value function;

[0100] Step 4.4, calculating and updating the information matrix R k calculated in the kth identification period:

[0101]

[0102] where R k-1 is the information matrix in the k-1th identification period, is the forgetting part of the information matrix in the k-1th identification period;

[0103] The information matrix R k in the kth identification period is expressed as follows:

[0104]

[0105] where, is the reserved part of the information matrix in the kth identification period, is the forgetting part of the information matrix in the kth identification period, whose expression is as follows:

[0106]

[0107] where ||*|| is the norm of a matrix, (*) -1 is the inverse of the matrix;

[0108] Step 4.5, calculating and updating the covariance matrix P k by using the updated information matrix R k , whose expression is as follows:

[0109]

[0110] Step 4.6, calculate and update the to-be-identified parameter calculation matrix θ k , the to-be-identified parameter update expression is as follows:

[0111]

[0112] wherein, P k-1 is the covariance matrix calculated in the k-1th identification period, θ k-1 represents the to-be-identified parameter calculated in the k-1th identification period, and sgn(*) is a sign function;

[0113] Step 4.7, according to steps 4.1-4.6, the iteration equation of the improved recursive least square method is as follows:

[0114]

[0115] In this embodiment, the grid voltage U g = 415V / 50Hz, the DC input voltage value is U dc = 1100V, the filter inductance value L g = 6mH, the circuit equivalent impedance value R g = 1Ω.

[0116] The initial parameters are set as follows:

[0117] The lower limit of the genetic factor u L = 0.9, the dead zone coefficient ε = 20, the sensitivity coefficient η = 0.1, the self-defined parameter m y = 2, the penalty term weight λ = 2, and the sampling period T = 10 -6 s,

[0118] The initial information matrix

[0119] The initial to-be-identified parameter calculation matrix θ0= [0 0 0].

[0120] In this embodiment, the voltage and current of the bridge arm side of any phase, the grid voltage and the filter current are collected by the voltage sensor and the current sensor as known information, and are combined with the above initial parameters to perform identification by the improved recursive least square method.

[0121] After the identification is completed, the identification result is compared with the recursive least square identification result and the real data, and the final effect diagram is as shown in Figure 4 and Figure 5 The identification effect of the filter inductance of the improved recursive least square method is slightly better than that of the recursive least square method, and the identification effect of the equivalent impedance is closer to the real value, which indicates that the identification accuracy of the improved recursive least square method is better than that of the recursive least square method.

Claims

1. An improved recursive least square based method for inverter impedance identification, the inverter topology to which the method is applied comprises a DC voltage source, a three-phase full-bridge inverter circuit, a three-phase circuit impedance and a three-phase power grid, the DC voltage source is connected to the three-phase full-bridge inverter circuit, the three-phase full-bridge inverter circuit is connected to the three-phase power grid through the three-phase circuit impedance, wherein, The three-phase circuit impedance comprises a filter inductance and a circuit equivalent impedance; The recognition method is characterized by recognizing the filter inductance and the circuit equivalent impedance by using an improved recursive least square method, and the specific steps are as follows: Step 1, sample the voltage of the output point of the three-phase full-bridge inverter circuit, and record it as the bridge arm side voltage U xc , sample the grid voltage U x , sample the current flowing through the filter inductor and record it as the filter current i x , where x is the phase sequence, x = a, b, c; The mathematical model of the inverter is established as follows: U gc -U g = L g i' g + i g R g wherein g is any one of the three phases a, b, c, U gc is the voltage on the g-phase bridge arm side, g is the g-phase grid voltage, i g is the g-phase filter current, i' g is the g-phase filter current i g is the derivative of i g is the inductance value of the filter inductance, R g is the impedance value of the circuit equivalent impedance; Step 2, it is assumed that the identification process comprises one initial period and n identification periods, wherein one sampling is performed in the initial period and is recorded as the first sampling, one sampling and one identification are performed in each of the n identification periods, any one of the n identification periods is recorded as a current identification period k, k = 1, 2,..., n, and the sampling of the current identification period k is recorded as the (k+1)th sampling; The mathematical model of the discrete inverter is obtained by discretizing the mathematical model of the inverter obtained in step 1, and the expression is as follows: wherein, i g (k+1) is the g-phase filter current obtained by the k+1th sampling, i g (k) is the g-phase filter current obtained by the kth sampling, U gc (k) is the g-phase bridge arm side voltage obtained by the kth sampling, U g (k) is the g-phase grid voltage obtained by the kth sampling, L gk is the filter inductance value calculated after the kth identification period, R gk is the circuit equivalent impedance value calculated after the kth identification period, T is the sampling period; Step 3, according to the least square method, the discrete mathematical model obtained in step 2 is converted into a matrix form of the discrete model, and the expression is as follows: wherein, y k For the filtered current information obtained in the k+1 sampling, y k =i g (k+1) Φ k known information for the kth sample, Φ k = [U gc (k) U g (k) i g (k)] T ; θ k The matrix of parameters to be identified for the kth identification cycle, θ k = [θ 1k θ 2k θ 3k ] T , θ 1k The matrix of parameters to be identified for the kth identification cycle, θ 2k The matrix of parameters to be identified for the kth identification cycle, θ 3k The matrix of parameters to be identified for the kth identification cycle, θ Step 4, the matrix form of the discretized model obtained in step 3 is substituted into the iteration equation of the improved recursive least square method, and the filter inductance L connected to the inverse circuit and the circuit load impedance R are identified n times to obtain the parameter calculation matrix θ of the n th identification period to be identified n = [θ 1n θ 2n θ 3n ] T ; Step 5, identify filter inductance value L g and circuit equivalent resistance value R g , the calculation formula is as follows:

2. The improved recursive least square based impedance identification method for inverters according to claim 1, wherein, The implementation process of the iterative equation of the improved recursive least square method in step 4 is as follows: Step 4.1, parameter setting; Parameters to be set include a lower bound u of a forgetting factor L , a dead zone coefficient ε based on a noise level, a sensitivity coefficient η, a user-defined parameter m y , a 1-norm penalty term weight λ An information matrix R0 is initialized, and a to-be-identified parameter calculation matrix θ0 is initialized; Step 4.2, calculate the prediction error e for the kth recognition period k : wherein e k is the prediction error between the predicted value and the actual measured value for the kth identification cycle, θ k-1 denotes the to-be-identified parameter calculated for the k-1th identification cycle; Step 4.3, calculate the kth recognition period forgetting factor u k The expression is as follows: where tr (*) is the trace of a matrix, u k forgetting factor calculated for the kth recognition period, P k-1 covariance matrix calculated for the k-1th recognition period, max{} is a maximum function; Step 4.4, Calculate and update the information matrix R calculated in the kth recognition period k : wherein R k-1 is the information matrix of the k-1th identification cycle, is the forgetting part of the information matrix of the k-1th identification cycle; The information matrix R of the kth recognition period is calculated as follows: k is expressed as follows: wherein Rk is the reserved part of the information matrix for the kth identification period, Fk is the forgotten part of the information matrix for the kth identification period, expressed as follows: where ||*|| is the norm of a matrix, (*) -1 is the inverse of a matrix; Step 4.5, compute and update the covariance matrix P k , by the updated information matrix R k , the computation is performed, the expression is as follows: Step 4.6, calculate and update the parameter-to-be-identified calculation matrix θ k The parameter-to-be-identified update expression is as follows: wherein P k-1 is a covariance matrix calculated for the k-1th recognition period, θ k-1 denotes a parameter to be recognized calculated for the k-1th recognition period, and sgn(*) is a sign function. Step 4.7, according to steps 4.1 to 4.6, the iterative equation of the improved recursive least square method is obtained as follows:

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