阅读说明：本技术 基于谐波状态空间的三相电压源型变换器的建模方法 (Modeling method of three-phase voltage source type converter based on harmonic state space ) 是由 张国荣 徐晨林 于 2020-04-07 设计创作，主要内容包括：本发明公开了一种基于谐波状态空间的三相电压源型变换器建模方法,其步骤包括：1根据三相电压源型变换器的拓扑结构,建立三相电压源型变换器时域模型；2对时域方程中各状态变量及输入变量进行傅里叶变换；3根据三相电压源型变换器时域模型建立其谐波状态空间模型；4建立谐波状态空间单相简化模型。本发明能够简化谐波状态空间建模过程,减小谐波状态空间模型尺寸,在不影响建模精度的前提下准确获得三相电压源型变换器各变量的谐波信息及谐波相互作用机理,从而为解决谐波交互问题提供理论基础。(The invention discloses a three-phase voltage source type converter modeling method based on a harmonic state space, which comprises the following steps: 1, establishing a three-phase voltage source type converter time domain model according to a topological structure of the three-phase voltage source type converter; 2, performing Fourier transform on each state variable and input variable in the time domain equation; 3, establishing a harmonic state space model of the three-phase voltage source type converter according to the time domain model; and 4, establishing a single-phase simplified model of a harmonic state space. The method can simplify the modeling process of the harmonic state space, reduce the size of the harmonic state space model, and accurately obtain the harmonic information and the harmonic interaction mechanism of each variable of the three-phase voltage source type converter on the premise of not influencing the modeling precision, thereby providing a theoretical basis for solving the harmonic interaction problem.)

1. A modeling method of a three-phase voltage source type converter based on a harmonic state space is characterized by comprising the following steps:

step one, according to the topological structure of the three-phase voltage source type converter, establishing a time domain model of the three-phase voltage source type converter by using a formula (1):

in formula (1): r_LA load resistor at the direct current side of the three-phase voltage source type converter; c_dcL DC-side voltage-stabilizing capacitor of three-phase voltage source type converter_gThe filter inductor is an alternating current side filter inductor of the three-phase voltage source type converter; r_gThe equivalent resistance is an alternating current side circuit of the three-phase voltage source type converter; i.e. i_gIs a matrix of the output current of the AC side of the three-phase voltage source type converter, and i_g＝[i_gai_gbi_gc]^TWherein i is_ga、i_gb、i_gcThree-phase output currents of alternating current sides a, b and c of the three-phase voltage source type converter; v. of_dcThe voltage is the direct current side capacitor voltage of the three-phase voltage source type converter; v. of_sa、v_sb、v_scThe voltage of a, b and c three-phase power grid; s is a matrix formed by three-phase switching functions, and s ═ s_as_bs_c]^TWherein s is_a、s_b、s_cRepresenting a switch function for controlling the on-off of the three-phase switches a, b and c; g_a、g_b、g_cIs a, b and c three-phase AC-DC conversion function, and w intersects the DC conversion functionw＝a，b，c；s_wIs a w-phase switching function and has:

in formula (2): c (t) is a triangular carrier function, m_w(t) is a w-phase modulated wave function and has:

m_w(t)＝m_asin(ωt+θ)；w＝a，b，c (3)

in formula (3): m is_aFor modulation index, theta is the phase angle of the modulated wave, and omega is the modulated wave function m of the w phase_w(t) angular frequency, t being a time variable;

performing Fourier transform on each state variable and input variable in the time domain equation:

step 2.1, the state variable and the input variable i contained in the formula (1)_ga、i_gb、i_gc、v_sa、v_sb、v_sc、v_dcIs denoted as x (t), and a fourier transform representation of any variable x (t) is obtained using equation (4):

in formula (4): omega₀Is any one ofFundamental angular frequency of variable x (t), and ω₀＝2π/T₀，T₀Fundamental period, X, of any one variable X (t)_kIs the kth Fourier coefficient of any one variable x (t), andj is the imaginary unit;

and 2.2, obtaining a Fourier transform matrix representation of the formula (4) by using the formula (5):

x(t)＝E(t)X (5)

in formula (5): e (t) is an orthogonal basis matrix related to Fourier series, andx is a matrix formed by fourier coefficients of any variable X (t), and X ═ X_-h… X_-1X₀X₁… X_h]^TWherein h is a self-defined finite number, X_hThe h-th Fourier coefficient of any variable x (t);

step 2.3, obtaining the moment of the nth switching action of the w-phase switch of the three-phase voltage source type converter after the (i + 1) th iteration by using the formula (6)

In formula (6): when i is 0, leta_(n)For the triangular carrier function c (t) at the nth time equal to zero, k_mIs the slope and modulation index m of the triangular carrier function c (t)_aA ratio of (A) to (B), andwherein m is_fIs a frequency modulation index;

step 2.4, when the frequency modulation index m_fWhen the number is odd, the w-phase switching function s is obtained by using the formula (7)_wK-th Fourier coefficient S of_wk：

In formula (7): 2_mfCalculating the number of switching moments as required;

step 2.5, the formula (7) is brought into the formula (5) to obtain a w-phase switching function s shown as a formula (8)_wThe fourier transform matrix of (a):

s_w＝E(t)S_w，w＝a，b，c (8)

in formula (8): s_wAs a function of the w-phase switching_wAnd a matrix of Fourier coefficients of, and s_w＝[S_-wh… S_-w1S_w0S_w1…S_wh]^TWherein S is_whAs a function of the w-phase switching_wThe h-th Fourier coefficient of (1);

step three, establishing a harmonic state space model according to the time domain model of the three-phase voltage source type converter:

equations (9) to (11) are derived from equation (5):

a(t)x(t)＝E(t)AX (10)

cx(t)＝E(x)cIX (11)

in formulae (9) to (11): a (t) is a periodic function, c is a constant,is the derivative of X, N is the derivative matrix of the harmonic state space, and N ═ diag ([ -jh ω₀... -jω₀0 jω₀... jhω₀]) A is a Topritz matrix formed by Fourier coefficients of a periodic function a (t), andwherein A is_hIs the h-th Fourier coefficient of the periodic function a (t), and I is an identity matrix of 2h +1 order;

formula (5) and formula (8) are taken together in formula (1) according to formulas (9) to (11), so that a harmonic state space model of the three-phase voltage source type converter shown in formula (12) is obtained:

in formula (12): i is_ga、I_gb、I_gcFor a, b and c three-phase output current i_ga、i_gb、i_gcRespectively, I_gIs three matrixes I_ga、I_gb、I_gcA matrix formed, and I_g＝[I_gaI_gbI_gc]，V_dcIs a DC side capacitor voltage v_dcOf Fourier coefficients, V_sa、V_sb、V_scIs a, b, c three-phase network voltage v_sa、v_sb、v_scAre formed by three matrices S_a、S_b、S_cA matrix formed, and S ═ S_aS_bS_c]^TIn which S is_a、S_b、S_cAs a three-phase switching function S of a, b and c_a、S_b、S_cRespectively, G, of the Fourier coefficients_a、G_b、G_cIs a, b, c three-phase AC-DC conversion function g_a、g_b、b_cThe Fourier coefficients of (A) are respectively formed into a matrix;

step four, establishing a single-phase simplified model of a harmonic state space:

according to the three-phase symmetric characteristic of the three-phase voltage source type converter during balanced operation, obtaining a single-phase simplified model of a harmonic state space of the three-phase voltage source type converter by using a formula (13):

l in the formula (13)_aMatrix S formed by Fourier coefficients of a-phase switching function_aA simplified matrix of, andwherein q is the maximum value of m, and h-6 is more than or equal to q and is less than or equal to h, L_a，h+m+1、S_a，h+m+Respectively, represent a reduced matrix L_aSum matrix S_aRow h + m + 1.

Technical Field

The invention relates to the field of modeling of power electronic devices, in particular to a three-phase voltage source type converter modeling method based on a harmonic state space.

Background

Under the trend of renewable energy sources such as distributed energy power generation and microgrid and the trend of new load grid connection such as energy storage and electric vehicles, the technology based on the power electronic converter, in particular the voltage source converter, is widely applied. The voltage source type converter is used as a nonlinear device, resonance can be generated when the voltage source type converter is connected to a power grid, and a large amount of harmonic waves can be injected into the power grid during operation, so that the quality of electric energy is deteriorated. Meanwhile, with the continuous increase of the number of converters, the harmonic interaction problem is increasingly complex, and a new challenge is provided for the stable operation of the system. To solve these problems, a detailed mathematical model of steady-state and transient analysis must be established to analyze the system harmonic conditions.

Researchers at home and abroad have studied on the modeling of the converter, and modeling methods can be divided into a numerical simulation method and an analytical modeling method. The numerical simulation method adopts different algorithms to carry out numerical calculation on the converter, thereby obtaining a numerical solution of certain characteristics of the converter, and the physical significance of the numerical solution is ambiguous; the analytical modeling method adopts analytical expressions to describe the characteristics of the converter, and has clear physical significance, so that most of the existing documents adopt the analytical modeling method, wherein a state space average method is the most commonly adopted method. The harmonic state space is used as a new modeling method in an analytic modeling method, can contain each harmonic of system variables for modeling, and provides great potential for solving the harmonic interaction problems such as harmonic interaction among multiple converters and the influence of switching transient voltage distortion on the converters. However, the derivation and processing of the harmonic state space model considering the switching harmonics are very complicated, and the size of the model is also very large, so that the application of the harmonic state space modeling in the power electronic system is limited.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, and provides a modeling method of a three-phase voltage source type converter based on a harmonic state space, so that the modeling process of the harmonic state space can be simplified, the size of a harmonic state space model is reduced, and the harmonic information and the harmonic interaction mechanism of each variable of the three-phase voltage source type converter can be accurately obtained on the premise of not influencing the modeling precision, thereby providing a theoretical basis for solving the harmonic interaction problem.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

the invention relates to a modeling method of a three-phase voltage source type converter based on a harmonic state space, which is characterized by comprising the following steps of:

step one, according to the topological structure of the three-phase voltage source type converter, establishing a time domain model of the three-phase voltage source type converter by using a formula (1):

in formula (1): r_LA load resistor at the direct current side of the three-phase voltage source type converter; c_dcL DC-side voltage-stabilizing capacitor of three-phase voltage source type converter_gThe filter inductor is an alternating current side filter inductor of the three-phase voltage source type converter; r_gThe equivalent resistance is an alternating current side circuit of the three-phase voltage source type converter; i.e. i_gIs a matrix of the output current of the AC side of the three-phase voltage source type converter, and i_g＝[i_gai_gbi_gc]^TWherein i is_ga、i_gb、i_gcThree-phase output currents of alternating current sides a, b and c of the three-phase voltage source type converter; v. of_dcThe voltage is the direct current side capacitor voltage of the three-phase voltage source type converter; v. of_sa、v_sb、v_scThe voltage of a, b and c three-phase power grid; s is a matrix formed by three-phase switching functions, and s ═ s_as_bs_c]^TWherein s is_a、s_b、s_cRepresenting a switch function for controlling the on-off of the three-phase switches a, b and c; g_a、g_b、g_cIs a, b and c three-phase AC-DC conversion function, and w intersects the DC conversion functionw＝a，b，c；s_wIs a w-phase switching function and has:

in formula (2): c (t) is a triangular carrier function, m_w(t) is a w-phase modulated wave function and has:

m_w(t)＝m_asin(ωt+θ)；w＝a，b，c (3)

in formula (3): m is_aFor modulation index, theta is the phase angle of the modulated wave, and omega is the modulated wave function m of the w phase_w(t) angular frequency, t being a time variable;

performing Fourier transform on each state variable and input variable in the time domain equation:

step 2.1, the state variable and the input variable i contained in the formula (1)_ga、i_gb、i_gc、v_sa、v_sb、v_sc、v_dcIs denoted as x (t), and a fourier transform representation of any variable x (t) is obtained using equation (4):

in formula (4): omega₀Is the fundamental angular frequency of any one variable x (t), and ω₀＝2π/T₀，T₀Fundamental period, X, of any one variable X (t)_kIs the kth Fourier coefficient of any one variable x (t), andj is the imaginary unit;

and 2.2, obtaining a Fourier transform matrix representation of the formula (4) by using the formula (5):

x(t)＝E(t)X (5)

in formula (5): e (t) is an orthogonal basis matrix related to Fourier series, andx is a matrix formed by fourier coefficients of any variable X (t), and X ═ X_-h… X_-1X₀X₁… X_h]^TWherein h is a self-defined finite number, X_hThe h-th Fourier coefficient of any variable x (t);

step 2.3, obtaining the moment of the nth switching action of the w-phase switch of the three-phase voltage source type converter after the (i + 1) th iteration by using the formula (6)

In formula (6): when i is 0, leta_(n)For the triangular carrier function c (t) at the nth time equal to zero, k_mIs the slope and modulation index m of the triangular carrier function c (t)_aA ratio of (A) to (B), andwherein m is_fIs a frequency modulation index;

step 2.4, when the frequency modulation index m_fWhen the number is odd, the w-phase switching function s is obtained by using the formula (7)_wK-th Fourier coefficient S of_wk：

In formula (7): 2m_fCalculating the number of switching moments as required;

step 2.5, the formula (7) is brought into the formula (5) to obtain a w-phase switching function s shown as a formula (8)_wThe fourier transform matrix of (a):

s_w＝E(t)S_w，w＝a，b，c (8)

in formula (8): s_wAs a function of the w-phase switching_wAnd a matrix of Fourier coefficients of, and S_w＝[S_-wh… S_-w1S_w0S_w1… S_wh]^TWherein，S_whAs a function of the w-phase switching_wThe h-th Fourier coefficient of (1);

step three, establishing a harmonic state space model according to the time domain model of the three-phase voltage source type converter:

equations (9) to (11) are derived from equation (5):

a(t)x(t)＝E(t)AX (10)

cx(t)＝E(t)cLX (11)

in formulae (9) to (11): a (t) is a periodic function, c is a constant,is the derivative of X, N is the derivative matrix of the harmonic state space, and N ═ diag ([ -jh ω₀... -jω₀0 jω₀... jhω₀]) A is a Topritz matrix formed by Fourier coefficients of a periodic function a (t), andwherein A is_hIs the h-th Fourier coefficient of the periodic function a (t), and I is an identity matrix of 2h +1 order;

formula (5) and formula (8) are taken together in formula (1) according to formulas (9) to (11), so that a harmonic state space model of the three-phase voltage source type converter shown in formula (12) is obtained:

in formula (12): i is_ga、I_gb、I_gcFor a, b and c three-phase output current i_ga、i_gb、i_gcRespectively, I_gIs three matrixes I_ga、I_gb、I_gcA matrix formed, and I_g＝[I_gaI_gbI_gb]，V_dcIs a DC side capacitor voltage v_dcFourier ofMatrix of coefficients, V_sa、V_sb、V_scIs a, b, c three-phase network voltage v_sa、v_sb、v_scAre formed by three matrices S_a、S_b、S_cA matrix formed, and S ═ S_aS_bS_c]^TIn which S is_a、S_b、S_cAs a, b, c three-phase switching function s_a、s_b、s_cRespectively, G, of the Fourier coefficients_a、G_b、G_cIs a, b, c three-phase AC-DC conversion function g_a、g_b、g_cThe Fourier coefficients of (A) are respectively formed into a matrix;

step four, establishing a single-phase simplified model of a harmonic state space:

according to the three-phase symmetric characteristic of the three-phase voltage source type converter during balanced operation, obtaining a single-phase simplified model of a harmonic state space of the three-phase voltage source type converter by using a formula (13):

l in the formula (13)_aMatrix S formed by Fourier coefficients of a-phase switching function_aA simplified matrix of, andwherein q is the maximum value of m, and h-6 is more than or equal to q and is less than or equal to h, L_a，h+m+1、S_a，h+m+Respectively, represent a reduced matrix L_aSum matrix S_aRow h + m + 1.

Compared with the prior art, the invention has the beneficial effects that:

the method is based on the calculation of the switching time, the harmonic content of the switching function is included for modeling, the harmonic influence of the modulation process of the three-phase voltage source converter is definitely considered, and the problem that the system modeling including the switching behavior is extremely difficult due to the nonlinearity and discontinuity of a power switch is solved, so that a universal and easily-realized method is provided for obtaining the harmonic state space model of the voltage source converter;

2, each harmonic of the time domain variable is considered as an independent state variable, so that a detailed harmonic dynamic evolution process and a harmonic interaction mechanism can be obtained, the steady-state and dynamic conditions of the system can be accurately described, and a theoretical basis is provided for solving the harmonic interaction problem;

based on the three-phase symmetric characteristic of the balance system, the three-phase voltage source type converter harmonic state space model is simplified into the three-phase voltage source type converter harmonic state space single-phase model, the model size is reduced on the premise of not influencing the model precision, the problem of huge modeling size of the harmonic state space is solved, and therefore the model calculation speed is increased.

Drawings

FIG. 1 is a schematic diagram of a three-phase voltage source type grid-connected converter based on SPWM modulation in the prior art;

FIG. 2 is a schematic flow chart of a three-phase voltage source type converter harmonic state space modeling method.

Detailed Description

In this embodiment, as shown in fig. 1, the three-phase voltage source type converter adopts an SPWM modulation method, and as shown in fig. 2, a modeling method of the three-phase voltage source type converter based on a harmonic state space is performed according to the following steps:

step one, establishing a time domain model of the three-phase voltage source type converter by using a formula (1) according to a topological structure of the three-phase voltage source type converter:

in formula (1): r_LA load resistor at the direct current side of the three-phase voltage source type converter; c_dcL DC-side voltage-stabilizing capacitor of three-phase voltage source type converter_gThe filter inductor is an alternating current side filter inductor of the three-phase voltage source type converter; r_gThe equivalent resistance is an alternating current side circuit of the three-phase voltage source type converter; i.e. i_gFor the output current station of the AC side of a three-phase voltage source type converterA matrix of formations, and i_g＝[i_gai_gbi_gc]^TWherein i is_ga、i_gb、i_gcThree-phase output currents of alternating current sides a, b and c of the three-phase voltage source type converter; v. of_dcThe voltage is the direct current side capacitor voltage of the three-phase voltage source type converter; v. of_sa、v_sb、v_scThe voltage of a, b and c three-phase power grid; s is a matrix formed by three-phase switching functions, and s ═ s_as_bs_c]^TWherein s is_a、s_b、s_cRepresenting a switch function for controlling the on-off of the three-phase switches a, b and c; g_a、g_b、g_cIs a, b and c three-phase AC-DC conversion function, and w intersects the DC conversion functionw＝a，b，c；s_wIs a w-phase switching function and has:

in formula (2): c (t) is a triangular carrier function, m_w(t) is a w-phase modulated wave function and has:

m_w(t)＝m_asin(ωt+θ)；w＝a，b，c (3)

in formula (3): m is_aFor modulation index, theta is the phase angle of the modulated wave, and omega is the modulated wave function m of the w phase_w(t) angular frequency, t being a time variable;

performing Fourier transform on each state variable and input variable in the time domain equation:

step 2.1, the state variable and the input variable i contained in the formula (1)_ga、i_gb、i_gc、v_sa、v_sb、v_sc、v_dcIs denoted as x (t), and a fourier transform representation of any variable x (t) is obtained using equation (4):

in formula (4): omega₀Is the fundamental angular frequency of any one variable x (t), and ω₀＝2π/T₀，T₀Fundamental period, X, of any one variable X (t)_kIs the kth Fourier coefficient of any one variable x (t), andj is the imaginary unit;

and 2.2, obtaining a Fourier transform matrix representation of the formula (4) by using the formula (5):

x(t)＝E(t)X (5)

in formula (5): e (t) is an orthogonal basis matrix related to Fourier series, andx is a matrix formed by fourier coefficients of any variable X (t), and X ═ X_-h… X_-1X₀X₁… X_h]^TWherein X is_hThe h-th Fourier coefficient of any variable x (t), h is a self-defined finite number, h determines the number of considered harmonic times, the larger the h value is, the higher the model precision is, but the model size will be increased, the slower the calculation speed is, on the contrary, the smaller the h value is, the lower the model precision is, the modeling is convenient and simple, the calculation speed is high, and in a special case, when h is 1, the harmonic state space model is equivalent to an average model;

step 2.3, obtaining the moment of the nth switching action of the w-phase switch of the three-phase voltage source type converter after the (i + 1) th iteration by using the formula (6)

In formula (6): when i is 0, leta_(n)For the triangular carrier function c (t) at the nth time equal to zero, k_mIs the slope and modulation index m of the triangular carrier function c (t)_aA ratio of (A) to (B), andwherein m is_fIs a frequency modulation index;

step 2.4, when the frequency modulation index m_fWhen the number is odd, the w-phase switching function s is obtained by using the formula (7)_wK-th Fourier coefficient S of_wk：

In formula (7): 2m_fCalculating the number of switching moments as required;

step 2.5, the formula (7) is brought into the formula (5) to obtain a w-phase switching function s shown as a formula (8)_wThe fourier transform matrix of (a):

s_w＝E(t)S_w，w＝a，b，c (8)

in formula (8): s_wAs a switching function s of the w-phase_wAnd a matrix of Fourier coefficients of, and S_w＝[S_-wh… S_-w1S_w0S_w1… S_wh]^TWherein S is_whAs a function of the w-phase switching_wThe h-th Fourier coefficient of (1);

step three, establishing a harmonic state space model according to the time domain model of the three-phase voltage source type converter:

in order to convert the three-phase voltage source type converter time domain model into the harmonic state space model, equations (9) to (11) are obtained by derivation of equation (5):

a(t)x(t)＝E(t)AX (10)

cx(t)＝E(t)cLX (11)

in formulae (9) to (11): a (t) is a periodic function, c is a constant,is the derivative of X, N is the derivative matrix of the harmonic state space, and N ═ diag ([ -jh ω₀... -jω₀0 jω₀... jhω₀]) A is a Topritz matrix formed by Fourier coefficients of a periodic function a (t), andwherein A is_hIs the h-th Fourier coefficient of the periodic function a (t), and I is an identity matrix of 2h +1 order;

formula (5) and formula (8) are taken together in formula (1) according to formulas (9) to (11), so that a harmonic state space model of the three-phase voltage source type converter shown in formula (12) is obtained:

in formula (12): i is_ga、I_gb、I_gcFor a, b and c three-phase output current i_ga、i_gb、i_gcRespectively, I_gIs three matrixes I_ga、I_gb、I_gaA matrix formed, and I_g＝[I_gaI_gbI_gc]，V_dcIs a DC side capacitor voltage v_dcOf Fourier coefficients, V_sa、V_sb、V_scIs a, b, c three-phase network voltage v_sa、v_sb、v_scAre formed by three matrices S_a、S_b、S_cA matrix formed, and S ═ S_aS_bS_c]^TIn which S is_a、S_b、S_cAs a, b, c three-phase switching function s_a、s_b、s_cRespectively, G, of the Fourier coefficients_a、G_b、G_cIs a, b, c three-phase AC-DC conversion function g_a、g_b、g_cRespectively constructed of fourier coefficientsA matrix of the result;

step four, establishing a single-phase simplified model of a harmonic state space:

the three-phase symmetric characteristic of the three-phase voltage source type converter during balanced operation is shown as a formula (13):

l in the formula (13)_gak、I_gbk、I_gckFor a, b and c three-phase output current i_ga、i_gb、i_gcK-th Fourier coefficient of (V)_sak、V_sbk、V_sckIs a, b, c three-phase network voltage v_sa、v_sb、v_scK-th Fourier coefficient of (1), S_ak、S_bk、S_ckAs a function of three-phase switching s_a、s_b、s_cThe kth fourier coefficient of (1);

therefore, the current-voltage conditions of the two phases b and c can be obtained from the equation (13) only by using the current-voltage condition of the phase a. However, the DC-side capacitor voltage v in the formula (12)_dcIs a matrix V formed by fourier coefficients of_dcIn the equation of state of (2), three matrices S_a、S_b、S_cThe formed matrix S and three matrices I_ga、I_gb、I_gcThe formed matrix I_gThe three phases are coupled to each other, so the coupling terms are decoupled by equation (14):

S^TI_g＝S_aI_ga+S_bI_gb+S_cI_gc＝3L_aI_ga(14)

l in the formula (14)_aMatrix S formed by Fourier coefficients of a-phase switching function_aA simplified matrix of, andwherein q is the maximum value of m, and h-6 is more than or equal to q and is less than or equal to h, L_a，h+m+1、S_a，h+m+Respectively, represent a reduced matrix L_aSum matrix S_aRow h + m + 1.

The formula (14) is introduced into the formula (12), so that a harmonic state space single-phase simplified model of the three-phase voltage source type converter shown as the formula (15) is obtained:

the solution formula (15) can obtain the three-phase voltage source type converter AC measured a-phase output current i_gaAnd a DC side capacitor voltage v_dcThe content of each subharmonic can be obtained by using the formula (13) to measure a and b phase output current i of the three-phase voltage source type converter_gb、i_gcThe harmonic content of (1). The three-phase output current i of a, b and c obtained by the solution is then utilized by the formula (5)_ga、i_gb、i_gcRespectively, of Fourier coefficients_ga、I_gb、I_gcAnd a DC side capacitor voltage v_dcIs a matrix V formed by fourier coefficients of_dcConverted into the time domain.