阅读说明：本技术 极坐标系下单相并网逆变器siso幅相阻抗计算方法及系统 (Single-phase grid-connected inverter SISO amplitude-phase impedance calculation method and system under polar coordinate system ) 是由 徐元璨 陈燕东 伍文华 罗安 谢志为 王自力 曹世骧 郭小龙 王衡 于 2021-04-07 设计创作，主要内容包括：本发明公开了一种极坐标系下单相并网逆变器SISO幅相阻抗计算方法及系统,考虑单相并网逆变器电流内环、锁相环、延时以及电网阻抗的影响,首先在旋转极坐标系下建立单相并网逆变器的幅相导纳模型,然后通过矩阵变换推导出SISO形式的幅相阻抗模型,并通过仿真与实验验证了所建模型的准确性。(The invention discloses a method and a system for calculating SISO amplitude-phase impedance of a single-phase grid-connected inverter under a polar coordinate system, wherein the influence of a current inner ring, a phase-locked loop, time delay and power grid impedance of the single-phase grid-connected inverter is considered, an amplitude-phase admittance model of the single-phase grid-connected inverter is firstly established under a rotary polar coordinate system, then an amplitude-phase impedance model in a SISO form is deduced through matrix transformation, and the accuracy of the established model is verified through simulation and experiments.)

1. A SISO amplitude-phase impedance calculation method of a single-phase grid-connected inverter under a polar coordinate system is characterized in that,

SISO power grid side amplitude phase impedance Z is calculated by using the following formula_{T_grid}(s)：

Z_{T_grid}(s)＝(Y_{T_grid_1}+Y_MM+jY'_φM)^-1+(Y_{T_grid_2}+Y_MM+jY'_Mφ)^-1；

Calculating the SISO inverter amplitude-phase impedance Z by using the following formula_{T_VSC}(s)：

Z_{T_VSC}(s)＝(Y_φφ-Y_MM)^-1；

Wherein the content of the first and second substances,

Y_MMis amplitude admittance, Y'_MφIs the corrected amplitude phase angle admittance, Y'_φMFor corrected phase angle amplitude admittance, Y_φφIs the phase angle admittance; l is_gFor equivalent inductance of the network, R_gAs equivalent resistance of the grid, C_fFor filter capacitors, ω is the grid-connected angular frequency, R_cS is the laplace operator, which is the equivalent series resistance of the filter capacitor.

2. The method for calculating the amplitude-phase impedance of the single-phase grid-connected inverter under the polar coordinate system according to claim 1, wherein the method comprises the following steps:

H_pllfor transfer of phase-locked loopsA function;

in order to consider the dq impedance model of the second-order generalized integrator, the dq impedance model is obtained by simultaneous calculation according to the following formula:

andrespectively considering the d-axis current small disturbance component and the q-axis current small disturbance component of the common coupling point after the influence of the generalized second-order integrator is considered;andrespectively considering the d-axis voltage small disturbance component and the q-axis voltage small disturbance component of the common coupling point after the influence of the generalized second-order integrator is considered; delta theta is a phase-locked loop control angle; of, T_{SOGI_dq1}(s)＝0.5t_SOGI(s+jω₁)+0.5t_SOGI(s-jω₁)，T_{SOGI_dq2}(s)＝0.5jt_SOGI(s+jω₁)-0.5jt_SOGI(s-jω₁)，t_SOGIIs a model of a generalized second-order integrator in a natural coordinate system and has the expression ofk_SOGIIs a second-order generalized integrator constant, j is an imaginary unit in the complex number, ω₁The expression of the fundamental component in the frequency domain.

3. The method as claimed in claim 2, wherein the amplitude phase impedance of the single-phase grid-connected inverter is calculated by using the following formula_MφSum phase angle amplitude admittance Y_φM：

Y′_MφAnd Y'_φMThe amplitude phase angle admittance and the phase angle amplitude admittance after correction are respectively.

4. A single-phase and grid-connected inverter SISO amplitude and phase impedance calculation system under a polar coordinate system is characterized by comprising computer equipment; the computer apparatus is configured to calculate SISO amplitude-phase impedance using the method of any of claims 1 to 3.

Technical Field

The invention relates to the field of renewable energy power generation systems, in particular to a single-phase grid-connected inverter SISO amplitude-phase impedance modeling method under a polar coordinate system.

Background

With the increasing of the power generation permeability of renewable energy sources, the trend of power electronics of a power system becomes more obvious. The power electronic converter is used as an interface for the renewable energy power generation and the power grid, and the operation characteristics of the power electronic converter influence the grid-connected consumption capability of the renewable energy. Therefore, establishing an accurate small-signal model of the power electronic converter is particularly important for analyzing the stability of the power electronic power system.

The existing power electronic converter impedance modeling mainly aims at a three-phase system, and a single-phase system is more complex in impedance characteristic compared with the three-phase system due to special asymmetry of the single-phase system. In the prior art, a single-phase system impedance model is established under a dq coordinate system, but the dq impedance model is not intuitive enough when used for designing system parameters, and the physical meaning is ambiguous. At present, a single-phase system sequence impedance model is established in a static coordinate system in literature, and the frequency coupling phenomenon is further considered, so that the accuracy of the low-and-medium-frequency-band model is improved. However, the sequential impedance model considering the frequency coupling phenomenon is a MIMO system, and the complexity of the model increases. Therefore, a schuler matrix transformation-based order reduction method is proposed in the literature, which reduces the MIMO frequency coupling order impedance model into a single-input single-output (SISO) frequency coupling order impedance model, but an asymmetric nonlinear structure in a single-phase system leads to modeling under consideration of a frequency coupling phenomenon to be carried out to an infinite order, and when a phase-locked loop bandwidth is too wide or control is extremely asymmetric, the order reduction model loses a lot of important frequency response information. Therefore, the difficulty of SISO small-signal impedance modeling of the single-phase grid-connected inverter needs to be broken through urgently.

Disclosure of Invention

The invention aims to solve the technical problem that the SISO amplitude-phase impedance calculation method and the SISO amplitude-phase impedance calculation system of the single-phase grid-connected inverter under a polar coordinate system are provided aiming at the defects of the prior art, and the problem that the SISO form small-signal impedance modeling of the single-phase grid-connected inverter is difficult when the influences of a current inner loop, a voltage feedforward, a phase-locked loop, a time delay and an SOGI module are considered is solved.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a single-phase grid-connected inverter SISO amplitude-phase impedance calculation method under a polar coordinate system utilizes the following formula to calculate SISO power grid side amplitude-phase impedance Z_{T_grid}(s)：

Z_{T_grid}(s)＝(Y_{T_grid_1}+Y_MM+jY'_φM)^-1+(Y_{T_grid_2}+Y_MM+jY'_Mφ)^-1；

Calculating the SISO inverter amplitude-phase impedance Z by using the following formula_{T_VSC}(s)：

Z_{T_VSC}(s)＝(Y_φφ-Y_MM)^-1；

Wherein the content of the first and second substances, Y_MMfor amplitude admittance, Y_M′_φFor corrected amplitude phase angle admittance, Y_φ′_MFor corrected phase angle amplitude admittance, Y_φφIs the phase angle admittance; l is_gFor equivalent inductance of the network, R_gAs equivalent resistance of the grid, C_fFor filter capacitors, ω is the grid-connected angular frequency, R_cS is the laplace operator, which is the equivalent series resistance of the filter capacitor.

WhereinIs an amplitude-phase admittance theoretical model H_pllIs the transfer function of the phase locked loop.

T_{SOGI_dq1}(s)＝0.5t_SOGI(s+jω₁)+0.5t_SOGI(s-jω₁)， T_{SOGI_dq2}(s)＝0.5jt_SOGI(s+jω₁)-0.5jt_SOGI(s-jω₁) Where j is the unit of the imaginary number in the complex number, ω₁Is an expression of the fundamental component in the frequency domain.

According to the invention, the transfer function model of the second-order generalized integrator is obtained by mapping convolution operation to a rotating coordinate system, the influence of the generalized integrator on the system stability is further considered, the amplitude-phase admittance model considering the influence of the generalized second-order integrator is obtained, and the problem of modeling analysis of the second-order generalized integrator in the amplitude-phase admittance is solved. Admittance due to amplitude phase angle Y_MφSum phase angle amplitude admittance Y_φMAre close in amplitude and 180 deg. out of phase (see fig. 5, 6), and to minimize the error, the amplitude phase angle admittance Y is corrected using the equation_MφSum phase angle amplitude admittance Y_φM：

Y'_MφAnd Y'_φMThe amplitude phase admittance model and the amplitude phase admittance model are respectively corrected, and through correction, the amplitude phase admittance model can be subjected to next matrix transformation, so that an amplitude phase impedance model in a SISO form can be obtained. Therefore, a more intuitive amplitude-phase admittance model in a polar coordinate system is established, and the amplitude-phase admittance model is further reduced to obtain an amplitude-phase impedance model in a SISO form (see fig. 4 for a specific circuit schematic diagram).

Andrespectively considering d-axis current small disturbance component and q-axis current small disturbance component of PCC (namely common coupling point) after the influence of the generalized second-order integrator is considered;andthe method comprises the steps of respectively considering d-axis voltage small disturbance components and q-axis voltage small disturbance components of a PCC point after the influence of a generalized second-order integrator.

The invention also provides a single-phase grid-connected inverter SISO amplitude-phase impedance calculation system under a polar coordinate system, which comprises computer equipment; the computer apparatus is configured to calculate SISO amplitude-phase impedances using the method described above.

Compared with the prior art, the invention has the beneficial effects that: the invention solves the problems of no physical significance and non-intuitive model of the traditional dq impedance and sequence impedance model by establishing the single-phase grid-connected inverter amplitude-phase admittance model under a rotary polar coordinate system, deduces and establishes the amplitude and phase angle change impedance model which can directly reflect the physical quantity of the actual voltage and current, and then obtains the amplitude-phase impedance equivalent circuit in the SISO form after algebraic transformation and matrix transformation of the model. The invention provides a model and a method for analyzing the stability of small disturbance when the single-phase inverter is connected into a weak alternating-current power grid.

Drawings

Fig. 1 is a main circuit topology diagram of a single-phase grid-connected inverter system according to an embodiment of the invention;

FIG. 2 is a control block diagram of a single-phase grid-connected inverter system according to an embodiment of the present invention;

FIG. 3 is a SISO amplitude-phase impedance modeling flowchart of a single-phase grid-connected inverter system according to an embodiment of the present invention;

FIG. 4 is an equivalent circuit diagram of SISO amplitude-phase impedance model of a single-phase grid-connected inverter system according to an embodiment of the present invention;

fig. 5 is an amplitude-phase admittance simulation verification result of the single-phase grid-connected inverter system in a polar coordinate system according to an embodiment of the present invention;

fig. 6 is an amplitude-phase admittance experiment verification result of the single-phase grid-connected inverter system in the polar coordinate system according to the embodiment of the invention.

Detailed Description

FIG. 1 shows a main circuit topology of a single-phase grid-connected inverter system, in which a switching tube Q₁～Q₄Forming a single-phase full-bridge inverter; u shape_dcIs a constant direct current voltage; c_dcA direct current side capacitor; l is_fIs a filter inductor and a parasitic resistor R at the side of the inverter_f；C_fIs a filter capacitor and a series resistor R_cf；L_gEquivalent inductance and R for power grid_gAn equivalent resistance; u. of_gridIs the grid voltage; u. of_pccIs the grid-connected point voltage; i.e. i_pccIs the dot-on-screen current.

FIG. 2 is a control block diagram of a single-phase grid-connected inverter system, collecting u_pccAnd i_pccConstructing a current virtual orthogonal quantity i through an SOGI module_pccβSum voltage virtual quadrature quantity u_pccβObtaining the current I under dq rotation coordinate system after clark transformation_pccd、I_pccqSum voltage quantity U_pccd、U_pccq；θ_pllFor phase-locked loop output phase, omega is the grid-connected angular frequency, K_ppllIs a phase lockControl of the proportional control parameter, K, by the loop PI_ipllControlling an integral control parameter for a phase-locked loop PI; i is_drefAnd I_qrefRespectively giving reference values for the dq-axis current; h_iIs a current inner loop PI controller, where K_piAnd K_iiProportional control parameters and integral control parameters of the current inner ring; g_delIs a decoupling controller; d_dAnd D_qThe duty ratio is output by the controller under the dq coordinate system, and the duty ratio D under the static coordinate system is obtained after coordinate transformation_αAnd D_β；

Firstly, establishing an amplitude-phase admittance model of the single-phase grid-connected inverter under a rotary polar coordinate system, then obtaining an amplitude-phase impedance model in a SISO form and an equivalent circuit thereof through matrix transformation, and FIG. 3 is a SISO amplitude-phase impedance modeling flow chart of the single-phase grid-connected inverter.

The method for establishing the amplitude-phase admittance model part of the single-phase grid-connected inverter system under the polar coordinate system under the rotary polar coordinate system comprises the following steps:

1) in the time domain, a group of linearly uncorrelated small-signal voltage disturbance signals are injected into the alternating-current side of the single-phase LC type grid-connected inverter, and before injection, omega needs to be injected_pAnd omega₁A comparison is made. When ω is_p<ω₁The frequency of the injected disturbance should be ω₁+ω_pAnd ω₁-ω_pWhen ω is_p>ω₁The frequency of the injected disturbance should be ω₁+ω_p、ω_p-ω₁And ω_p-ω₁- π/2. Acquiring output voltage and current of the AC side of the inverter, and further converting the output voltage and current of the AC side of the inverter in a frequency domain;

2) grid-connected reference angle theta output by phase-locked loop of single-phase grid-connected inverter_pllIs formed by a fundamental wave grid-connected voltage steering angle theta₁And the steering angle delta theta of the disturbance voltage signal. Therefore, in steady state operation, i.e., when Δ θ is 0, T is transformed according to the clark coordinate_αβ/dq(θ₁) And obtaining the frequency domain expression of the output end voltage and the output current of the grid-connected inverter under the rotating coordinate systemAndthe clark change matrix is:

wherein theta is₁The grid-connected voltage steering angle is under the stable working condition.

3) The phase-locked loop control angle delta theta and delta theta generated by the disturbance voltage obtained by the phase-locked loop controlThe frequency domain relation between the two is obtained after linearizationAnd Δ θ:

combined under stable working conditionAndobtaining the output voltage and current of the single-phase grid-connected inverter at the alternating current side under the rotating polar coordinate system after considering the influence of the phase-locked loopAndand under stable working conditionAndthe following equation is a conversion relationship after the small disturbance is linearized, and the disturbance is represented by a symbol Δ:

4) obtaining a frequency domain expression d of a modulation signal under a rotating rectangular coordinate system after considering single-phase grid-connected inverter current inner loop control, current feedforward decoupling control and power grid voltage feedforward control_d(s) and d_q(s)：

5) In addition, an output end voltage and current expression can be obtained according to the topological graph of the main circuit:

6) and simultaneously considering a conversion relation of voltage and current between two coordinate systems after the influence of the phase-locked loop, and considering a modulation signal equation of current inner loop control, current feedforward decoupling control and power grid voltage feedforward control, and finally obtaining a traditional dq impedance model of the single-phase grid-connected inverter under a rotating coordinate system (see: zhouyi, Wai Tao, Yangxiao Wei, who is rightful, electrified railway network coupling system low frequency oscillation analysis [ J ]. China Motor engineering Proc, 2017,37(S1): 72-80.).

7) According to a transfer function expression T of the generalized second-order integrator under a static coordinate system_SOGI(s), simultaneous clark coordinate transformation T_αβ/dq(θ₁) After convolution operation, obtainGeneralized second-order integrator frequency domain model T mapped to rotating coordinate system_{SOGI_dq}(s)。

T_SOGI(s) and T_{SOGI_dq}(s) are respectively:

in the formula:

T_{SOGI_dq1}(s)＝0.5t_SOGI(s+jω₁)+0.5t_SOGI(s-jω₁)

T_{SOGI_dq2}(s)＝0.5jt_SOGI(s+jω₁)-0.5jt_SOGI(s-jω₁)

8) according to the small signal conversion relation T between the rotating coordinate system and the polar coordinate system_dq/Mφ(phi) combining a generalized second-order integrator frequency domain model T mapped to a rotating coordinate system_{SOGI_dq}(s) obtaining a frequency domain model T of the generalized second-order integrator mapped to the polar coordinate system_{SOGI_ploar_u/i}(s)。

Phi is an included angle between the electric quantity and the d axis, and the small signal conversion relation between the rotating coordinate system and the polar coordinate system is as follows:

delta is the included angle between the current amount and the d axis under the natural coordinate system,is the angle between the voltage magnitude and d in the natural coordinate system, and is thus mapped toThe frequency domain model expressions of the generalized second-order integrator for voltage and current conversion under the polar coordinate system are respectively as follows:

9) then mapping the frequency domain model T of the generalized second-order integrator under a polar coordinate system_{SOGI_ploar_u/i}(s) the amplitude-phase admittance model Y of the single-phase grid-connected inverter under the polar coordinate system can be obtained by connecting the traditional dq impedance model of the single-phase grid-connected inverter under the rotating coordinate system_{Mφ_VSC}(s)。

10) Amplitude-phase admittance model Y of single-phase grid-connected inverter_{Mφ_VSC}(s) is a 2X 2 matrix of amplitude admittance Y_MM(s), amplitude phase Angle admittance Y_Mφ(s), phase angle amplitude admittance Y_φM(s), and phase angle admittance Y_φφ(s). The specific expression is as follows:

in the formula:

in the formula: h_pll(s)＝K_ppll+K_ipllThe/s is a phase-locked loop expression; h_i(s)＝K_pi+K_iiThe/s is a current inner controller expression; g_F(s)＝1/T_Fs+1，T_FIs the time constant of the voltage feedforward control;T_idelay time, omega, of current sampling stage_iCutting off frequency for a current sampling filtering link;T_vdelaying the voltage sampling stageTime, omega_vCutting off frequency for a voltage sampling filtering link;T_sis the PWM switching period. The laplacian(s) is omitted from all the above equations in order to simplify the expression.

The specific implementation process for establishing the SISO amplitude-phase impedance model of the single-phase grid-connected inverter system under the rotary polar coordinate system comprises the following steps:

1) amplitude-phase admittance model Y considering single-phase grid-connected inverter_{Mφ_VSC}(s) medium amplitude angular admittance Y_Mφ(s), phase angle amplitude admittance Y_φM(s) the amplitudes are close, the phase angles differ by 180 °, and in order to establish a SISO-type amplitude-phase impedance model, the amplitude phase admittance and the phase angle amplitude admittance are corrected:

2) considering the impedance characteristic of the weak alternating current power grid, establishing a power grid amplitude-phase admittance model Y under a polar coordinate system_{RLC_grid}(s), then, the model is subjected to unitary matrix transformation to obtain a power grid side amplitude phase admittance equivalent circuit model Y_{T_grid}(s). Obtaining an inverter amplitude-phase admittance equivalent circuit model Y after unitary matrix transformation by the same method_{T_VSC}(s)。

Polar coordinate system electric network amplitude-phase admittance model Y_{RLC_grid}(s) is:

the unitary matrix is:

power grid side amplitude phase admittance equivalent circuit model Y after unitary matrix transformation_{T_grid}(s) is:

wherein:

inverter amplitude-phase admittance equivalent circuit model Y_{T_VSC}(s) is:

3) meanwhile, unitary matrix transformation is carried out on the voltage and the current at the AC side, and the relation between the voltage and the current at the inverter side and the power grid side after the simultaneous matrix transformation is carried out, so that a characteristic equation of the system and a SISO amplitude-phase impedance model of the single-phase LC grid-connected inverter can be obtained, wherein the amplitude-phase impedance of the SISO inverter is defined as Z_{T_VSC}(s) SISO grid side amplitude phase impedance is Z_{T_grid}(s), the specific expression is as follows:

Z_{T_VSC}(s)＝(Y_φφ-Y_MM)^-1

Z_{T_grid}(s)＝Z_{T_grid_1}+Z_{T_grid_2}＝(Y_{T_grid_1}+Y_MM+jY'_φM)^-1+(Y_{T_grid_2}+Y_MM+jY'_Mφ)^-1

fig. 4 is an equivalent circuit diagram of a SISO amplitude-phase impedance model of the single-phase grid-connected inverter system. Voltage current amplitude disturbance variable quantityAnd the amount of phase angle disturbance changeObtaining voltage response delta u after matrix transformation_resp1,Δu_resp2And current response Δ i_resp1,Δi_resp2。

Fig. 5 is a measurement result of the amplitude-phase admittance of the single-phase grid-connected inverter in a polar coordinate system. Y is_MM(s) is amplitude admittance, Y_Mφ(s) is amplitude phase angle admittance, Y_φM(s) is the phase angle amplitude admittance, Y_φφAnd(s) is a phase angle admittance, wherein a solid line is an inverter amplitude-phase admittance model derived theoretically, a circle is an amplitude-phase admittance value measured by simulated sweep frequency, the simulation measured amplitude-phase admittance value has very high goodness of fit with the theoretical model as can be seen from fig. 5, and fig. 6 is an experimental measurement result of the amplitude-phase admittance of the single-phase grid-connected inverter, and the experimental measured amplitude-phase admittance value has very high goodness of fit with the theoretical model as can be seen. Simulation and experimental results verify the amplitude-phase admittance accuracy of the single-phase grid-connected inverter under the established rotary polar coordinate system.

As can be seen from FIGS. 5 and 6, the phase angle admittance Y_φφ(s) has an amplitude which is overall greater than the amplitude admittance Y_MM(s) and thus the phase angle admittance Y can be predicted_φφ(s) is a main factor influencing the amplitude-phase admittance of the inverter, namely, under the condition that the inverter is disturbed, the difference between the phase angles of the voltage and the current quantities is a main factor influencing the output impedance characteristics of the inverter, so that when the inverter is subsequently designed, a more appropriate control strategy and parameters can be selected by detecting the robustness of the phase angles of the output voltage and the output current of the inverter under the condition of small disturbance. And phase angle amplitude admittance Y_φM(s) and amplitude phase Angle admittance Y_Mφ(s) the phase angle amplitude admittance Y is obtained from FIG. 5 and FIG. 6 by correcting and matrix transforming the input signal to the grid side amplitude impedance_φM(s) and amplitude phase Angle admittance Y_MφThe amplitude of(s) is higher in the middle-low frequency band, the high frequency band is smaller, namely the interactive coupling effect of the amplitude phase angle of the middle-low frequency band is obvious, the coupling effect of the high frequency band is weak, compared with the traditional dq impedance and sequence impedance model, based on the amplitude-phase impedance model under the polar coordinate system provided by the invention, the design can be carried out by specifically analyzing the amplitude and the phase angle coupling effect of the voltage and the current through the frequency division band when the full-frequency band impedance characteristic of the inverter is designed, and the design and the calculation are reducedOf the system.