A distributed photovoltaic system impedance modeling and stability analysis method and system

Abstract

This invention discloses a method and system for impedance modeling and stability analysis of distributed photovoltaic (PV) systems. The analysis method includes: establishing a small-signal circuit model considering frequency coupling and interphase coupling effects in a three-phase four-wire system; based on this, establishing a multi-input multi-output impedance model of the inverter subsystem considering frequency coupling and interphase coupling effects; based on this impedance model, determining that the main factors affecting phase coupling effects are the phase-locked loop bandwidth and the neutral point inductance; simultaneously, employing a novel extended loop decomposition method to transform the multi-input multi-output impedance model of the inverter subsystem into three independent positive-sequence, negative-sequence, and zero-sequence single-input single-output impedance models; and analyzing the causes of system instability based on the single-input single-output impedance models. This invention avoids analysis errors caused by neglecting frequency coupling and interphase coupling, and can more accurately analyze the stability of a single-phase PV inverter system in a three-phase four-wire weak grid under complex conditions.

Description

Technical Field

[0001] This invention relates to the field of new energy grid connection technology, and in particular to a method and system for impedance modeling and stability analysis of distributed photovoltaic systems that considers interphase coupling effects. Background Technology

[0002] The integration of rooftop solar photovoltaic (PV) systems is expected to bring about significant changes in the physical and technical characteristics of power distribution systems. Driven by declining prices and improvements in solar technology, the number of rooftop PV installations in distribution networks has increased dramatically in recent years. A common scenario is that single-phase rooftop PV inverters are grouped into three-phase units and connected to a three-phase four-wire distribution network in a star (Y) configuration.

[0003] Studies have shown that the interaction between the inverter and a weak grid can lead to stability problems due to the presence of grid impedance. Impedance-based methods have proven applicable and useful in small-signal stability analysis of grid-connected systems because the impedances of the grid-connected inverter and the grid can be easily obtained through analytical modeling or measurement and have clear physical meaning. Currently, the impedance characteristics of single-phase inverters with various phase-locked loop (PLL) control structures, such as T / 4 time delay-based PLLs and second-order generalized integrator-based PLLs, have been studied in considerable depth. Simultaneously, due to the influence of frequency coupling effects in single-phase inverter systems, it is necessary to establish a single-input single-output impedance modeling framework for single-phase inverters that considers frequency coupling effects, as well as a recursive single-input single-output impedance modeling framework, to more intuitively identify system stability. Q. Qian, in the paper [Output impedance modeling of single-phase grid-tied inverters with capturing the frequency coupling effect of PLL,”IEEE Trans. Power Electron., vol.35, no.5, pp.5479–5495, May 2020], established a 3*3 impedance model to capture the coupling frequency components, thereby improving model accuracy.

[0004] In a three-phase inverter, the output currents and voltages of the a-phase, b-phase, and c-phase converters interact through the neutral line inductance, resulting in a phase coupling effect. This phase coupling effect affects the inverter's dynamic and steady-state characteristics. Y. Tang et al., in their paper [Multi DQ Frame Small-Signal Stability Analysis of Three-Phase Systems with Unbalanced Single-Phase Loads Using the Generalized Nyquist Criterion (GNC), "2021 IEEE 22nd Workshop on Control and Modelling of Power Electronics (COMPEL), 2021, pp. 1-6.], established impedance models for a three-phase four-wire inverter and a three-phase four-wire split-capacitor inverter, and evaluated system stability based on inverter impedance and grid impedance using the generalized Nyquist criterion. The paper also suggests that zero-sequence components may lead to system instability.

[0005] It should be noted that these results are not applicable to the stability analysis of single-phase inverters connected to a three-phase four-wire distribution network. This is because single-phase inverters and three-phase four-wire inverters differ significantly in control strategies and circuit structures. These differences lead to significant differences in the impedances of the two types of inverters. Therefore, to intuitively analyze the stability of a single-phase rooftop photovoltaic inverter connected to a three-phase four-wire system, two key points need to be highlighted. (1) The small-signal stability of a single-phase rooftop photovoltaic inverter connected to a three-phase four-wire system, considering frequency coupling and inter-phase frequency coupling, has not yet been analyzed. It is necessary to establish an inverter impedance model that considers frequency coupling effects and inter-phase coupling effects. (2) It is necessary to intuitively and quantitatively analyze the impact of inter-phase coupling effects on inverter impedance and system stability. Research on the above two issues is still relatively lacking. Therefore, the impedance modeling and stability analysis method of distributed photovoltaic systems considering inter-phase coupling effects is of great significance. Summary of the Invention

[0006] In view of the deficiencies of the existing technology, the present invention provides a method and system for impedance modeling and stability analysis of distributed photovoltaic systems that considers interphase coupling effects. The impedance model of the inverter subsystem adopted in this invention considers frequency coupling characteristics and interphase frequency coupling characteristics, avoiding analysis errors caused by ignoring frequency coupling and interphase coupling, thereby enabling more accurate analysis of the stability of single-phase photovoltaic inverter systems in three-phase four-wire weak grids under complex conditions.

[0007] Therefore, the technical solution adopted by the present invention is: a method for impedance modeling and stability analysis of distributed photovoltaic systems, which includes the following steps:

[0008] S1: Based on the harmonic transfer function matrix method, impedance modeling is performed on the single-phase photovoltaic inverter to obtain the voltage and current small-signal model under the ABC three-phase disturbance voltage considering the initial phase of the power grid.

[0009] S2: Based on the impedance model characteristics of a single-phase photovoltaic inverter and the obtained voltage and current small-signal models, establish a small-signal model of a three-phase four-wire grid-connected system that considers inter-phase coupling characteristics and frequency coupling characteristics.

[0010] S3: Establish the multi-input multi-output impedance model of the inverter subsystem based on the small-signal model of the three-phase four-wire grid-connected system, and establish the grid impedance matrix based on the grid parameters.

[0011] S4: Based on the grid impedance matrix, the multi-input multi-output impedance model of the inverter subsystem is decomposed into three independent positive-sequence, negative-sequence, and zero-sequence single-input single-output impedance models using the loop decomposition method, and the stability analysis of the three-phase four-wire grid-connected system is performed.

[0012] Furthermore, in step S1, the single-phase photovoltaic inverter is transformed using the following formula to obtain a virtual inverter that considers the initial phase of the power grid. α - β Voltage vector in coordinate system and :

[0013]

[0014] The initial phases of the three phases a, b, and c of the power grid are respectively... va =0、 vb =-2π / 3、 vc =2π / 3, G osgα and G osgβ Defined as the voltage at the common coupling point arrive and The transfer function is given, where T0 is the grid voltage period, preferably T0 = 0.02 seconds.

[0015] Furthermore, in step S1, without sacrificing versatility, a phase-locked loop based on a T / 4 time delay is also used, where T is the sampling period.

[0016] Furthermore, in step S1, considering the frequency coupling effect, the single-phase photovoltaic inverter system, in addition to the voltage and current components with a disturbance frequency of ω, also has voltage and current components with a frequency of ω±2jω1. The impedance model of the single-phase photovoltaic inverter is expressed as:

[0017]

[0018] Among them, the Laplace operators with superscripts "+" and "-" are " s "represents the positive coupling frequency s+2jω1 and the negative coupling frequency s-2jω1, respectively, Y invo ( s Y represents the impedance model of the main circuit of a single-phase photovoltaic inverter. ref ( s () represents the impedance model of a single-phase photovoltaic inverter under the control structure. , , These represent the grid connection point current signals at the negative coupling frequency, fundamental frequency, and positive coupling frequency, respectively. , , These represent the grid connection point voltage signals at the negative coupling frequency, fundamental frequency, and positive coupling frequency, respectively.

[0019] Furthermore, in step S2, the small-signal model of the three-phase four-wire grid-connected system considering phase-to-phase coupling characteristics and frequency coupling characteristics is defined as three sub-circuits at frequencies ω and ω±2jω1, and the coupling relationship between the three sub-circuits is represented by a controlled current source model.

[0020] Furthermore, in step S2, the small-signal model of the three-phase four-wire grid-connected system is represented as follows:

[0021] ,

[0022] Wherein, matrix Y T This is an inverter subsystem impedance matrix model that considers the three single-phase photovoltaic inverters as a whole. This represents the port voltage matrix of the photovoltaic inverter. This represents the port current matrix of the photovoltaic inverter.

[0023] Furthermore, in step S3, the larger the bandwidth of the phase-locked loop in the three-phase four-wire grid-connected system, the stronger the control capability of the phase-locked loop and the stronger the three-phase coupling relationship; the larger the neutral inductance, the stronger the three-phase coupling relationship.

[0024] Furthermore, in step S4, a stability analysis of the three-phase four-wire grid-connected system is performed based on the Nyquist criterion.

[0025] Another technical solution adopted in this invention is: a distributed photovoltaic system impedance modeling and stability analysis system, comprising:

[0026] Voltage and current small-signal model acquisition unit: Based on the harmonic transfer function matrix method, impedance modeling is performed on the single-phase photovoltaic inverter to obtain the voltage and current small-signal model under the ABC three-phase disturbance voltage considering the initial phase of the grid.

[0027] Small-signal model establishment unit: Based on the impedance model characteristics of a single-phase photovoltaic inverter and the obtained voltage and current small-signal models, establish a small-signal model of a three-phase four-wire grid-connected system that considers inter-phase coupling characteristics and frequency coupling characteristics;

[0028] Impedance model establishment unit: Based on the small-signal model of the three-phase four-wire grid-connected system, establish the multi-input multi-output impedance model of the inverter subsystem, and at the same time establish the grid impedance matrix based on the grid parameters;

[0029] Stability assessment unit: Based on the grid impedance matrix, the multi-input multi-output impedance model of the inverter subsystem is decomposed into three independent positive-sequence, negative-sequence, and zero-sequence single-input single-output impedance models using the loop decomposition method, and the stability analysis of the three-phase four-wire grid-connected system is performed.

[0030] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0031] 1. This invention establishes a small-signal circuit model that considers the frequency coupling effect and phase-to-phase coupling effect of a three-phase four-wire system. Based on this model, a multi-input multi-output impedance model of the inverter subsystem is established. Based on this impedance model, the main factors affecting the phase-locked loop (PLL) coupling model are determined to be the PLL bandwidth and the neutral point inductance. The larger the PLL bandwidth or the neutral point inductance, the stronger the phase coupling effect.

[0032] 2. A novel extended loop decomposition method is adopted to transform the multi-input multi-output impedance model of the inverter subsystem into three independent positive-sequence, negative-sequence, and zero-sequence single-input single-output impedance models. Furthermore, the single-input single-output impedance model can be used to accurately evaluate the stability of a three-phase four-wire grid-connected system.

[0033] This invention avoids analysis errors caused by neglecting frequency coupling and phase coupling by using a multi-input multi-output impedance model of the inverter subsystem, thereby enabling more accurate analysis of the stability of a three-phase four-wire weak grid single-phase photovoltaic inverter system (referred to as a three-phase four-wire grid-connected system) under complex conditions. Attached Figure Description

[0034] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0035] Figure 1 This is a flowchart illustrating the impedance modeling and stability analysis method for distributed photovoltaic systems according to the present invention.

[0036] Figure 2 The diagram shows the topology and control diagram of the single-phase photovoltaic inverter for a three-phase four-wire weak grid according to the present invention; wherein, (a) is the topology diagram of the single-phase photovoltaic inverter connected to a three-phase four-wire weak grid; and (b) is the control diagram of the single-phase photovoltaic inverter for a three-phase four-wire weak grid.

[0037] Figure 3 This is a small-signal path diagram of voltage and current in the single-phase inverter of this invention;

[0038] Figure 4 The following diagrams are for a three-phase four-wire small-signal model considering frequency coupling and phase coupling characteristics in this invention; wherein, (a) is a three-phase four-wire small-signal model with frequency ω; (b) is a three-phase four-wire small-signal model with frequency ω+2jω1; and (c) is a three-phase four-wire small-signal model with frequency ω-2jω1.

[0039] Figure 5 This is a schematic diagram of the inverter subsystem impedance model for the CHIL experimental verification of this invention.

[0040] Figure 6 This is a graph showing the ratio of the off-diagonal element amplitude to the diagonal element amplitude of the present invention, where (a1)-(a3) use different phase-locked loop bandwidth parameters; and (b1)-(b3) use different neutral inductors.

[0041] Figure 7 This is a schematic diagram of the circuit decomposition method of the present invention;

[0042] Figure 8 The following is a Bode plot of the zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance model and grid impedance for a three-phase inverter in Case 1 of the specific implementation of the present invention, where (a1)-(a2) are zero-sequence; (b1)-(b2) are positive-sequence; and (c1)-(c2) are negative-sequence.

[0043] Figure 9 The following are examples of the zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance models and grid impedance Bode diagrams of a three-phase inverter in Case 2 of the specific implementation of this invention, where (a) is zero-sequence; (b) is positive-sequence; and (c) is negative-sequence. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0045] like Figure 1As shown, the present invention provides an impedance modeling and stability analysis method for distributed photovoltaic systems considering interphase coupling effects, comprising the following steps:

[0046] (1) According to Figure 2 The diagram shown illustrates the structure and control block diagram of a three-phase four-wire grid-connected single-phase photovoltaic inverter system (hereinafter referred to as a three-phase four-wire grid-connected system). First, small-signal modeling of the single-phase photovoltaic inverter is performed, resulting in its voltage and current small-signal models as follows: Figure 3 As shown. In Figure 3 In the middle, the Laplace operator with superscripts "+" and "-" is " s "" represents the positive coupling frequency s+2jω1 and the negative coupling frequency s-2jω1, respectively. It can be seen that due to frequency coupling effects, in addition to the voltage and current components with a disturbance frequency of ω, the system also has voltage and current components with frequencies of ω±2jω1. Figure 3 It can be seen that the grid current at frequencies ω, ω-2jω1 and ω+2jω1 i g It can be represented as:

[0047]

[0048] Among them, Y invo ( s )=[ Y io ( s - ),0,0;0, Y io ( s ),0;0,0, Y io ( s + )], Y io ( s Y is the impedance matrix without considering control elements; ref ( s The expression for ) is:

[0049]

[0050] in, Y xref- ( s ), Y xref0 ( s ), Y xref+ ( s () indicates the voltage from the point of common coupling. exist ω +2 jω 1. ω and ω-2 jω 1 frequency down to ω Port current at frequency The transfer function. The corresponding mathematical expression can be represented as:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] Among them, subscript ' x ' represents the three-phase variables a, b, and c. vx The initial phase of the power grid. Without loss of generality, this invention defines the initial phases of phases a, b, and c of the power grid as follows: va =0、 vb =-2π / 3、 vc =2π / 3. G osgα and G osgβ Defined as the voltage at the common coupling point arrive and The transfer function is given. Without sacrificing versatility, a phase-locked loop based on a T0 / 4 time delay is also employed. T0 is the grid voltage period, T0 = 0.02 seconds. G c It is the proportional-derivative coefficient of the current regulator. G f It is the voltage feedforward gain at the point of common coupling of the power grid. k c It is the capacitor current feedforward gain. k xpp and k xii These are the proportional and integral coefficients of the phase-locked loop, respectively. Gd It is a digital signal control delay, in which G d = e-1.5Ts, where Ts is the control period. U m It is the phase voltage amplitude. L 1 is the filter inductor on the inverter side. L 2 is the filter inductor on the grid side, and C is the filter capacitor.

[0061] Therefore, the single-phase photovoltaic inverter is transformed using the following formula to obtain a virtual inverter that considers the initial phase of the power grid. α - β Voltage vector in coordinate system :

[0062]

[0063] (2) Based on the single-phase photovoltaic inverter impedance model obtained in step (1), apply it to Figure 2 In each single-phase inverter in (a), the following is obtained: Figure 4 The three-phase four-wire small-signal model is shown. Figure 4 In (a), the variables are defined at the disturbance frequency ω. The three impedance elements of the controlled current source represent the input impedance of the single-phase photovoltaic inverter at ω, defined as follows: Y xref0 ( s )+ Y xio ( s ).same, Figure 4 The variables in (b) and 4(c) are defined at coupling frequencies ω+2jω1 and ω-2jω1, respectively.

[0064] The coupling relationship between the three sub-circuits can be modeled using a controlled current source. Due to voltage difference - This decision indicates that the voltage on a single-phase photovoltaic inverter at frequency ω+2jω1 generates a current component with frequency ω. Correspondingly, the controlled current source... Due to voltage difference - The determination is that it represents the current component of frequency ω generated by the voltage across SIa at frequency ω-2jω1. The definitions of controlled current sources SIb and SIc are similar to those of SIa.

[0065] according to Figure 4 The circuit relationship shown in (a) can be obtained as follows:

[0066]

[0067] in, Zgy (s)= sL gx +R gy ( y =a、b、c、n) represents the grid impedance of phases a, b, c, and n.

[0068] Depend on Figure 4 (a) It can be seen that the grid current can be expressed as:

[0069]

[0070] Figure 4 (a) Controlled current source , and Let SIa, SIb, and SIc represent the current components at frequency ω generated by the voltages at frequencies ω-2jω1, respectively. Therefore, , and They are represented as follows:

[0071]

[0072] Among them, Y C+2 ( s )=diag ( Y aref- ( s ), Y bref- ( s ), Y cref- ( s )) is a 3x3 diagonal matrix. Y aref- ( s ), Y bref- ( s ), Y cref- ( s ) can be represented by the relation in step (1). =[ ( s ), ( s ), ( s )] T , =[ ( s - ), ( s - ), (s - )).

[0073] Similarly, controlled current source , and The current component with frequency ω generated by the single-phase inverter voltage at frequency ω+2jω1 can be expressed as:

[0074]

[0075] Among them, Y C-2 ( s )=diag ( Y aref+ ( s ), Y bref+ ( s ), Y cref+ ( s )) is a 3x3 diagonal matrix. Y aref+ ( s ), Y bref+ ( s ), Y cref+ ( s ) can be represented by the relation in step (1). =[ ( s ), ( s ), ( s )] T , =[ ( s + ), ( s + ), ( s + )] T .

[0076] Current , and The current component with frequency ω generated by the voltage of a single-phase inverter at frequency ω can be expressed as:

[0077]

[0078] Among them, Y SIO ( s =diag(Y SIOa ( s ), Y SIOb ( s ), Y SIOc ( s )) is a 3x3 diagonal matrix. Y SIOx ( s )= I xref0 ( s )+ Y io ( s x = a, b, c are three-phase variables. =[ ( s ), ( s ), ( s )] T U 1 ( s )=[ ( s ), ( s ), ( s )] T .

[0079] Depend on Figure 4 (b) It can be seen that the controlled current source , and The current component with frequency ω+2jω1 generated by the single-phase inverter voltage at frequency ω can be expressed as:

[0080]

[0081] Where, Y C+2 ( s + )=diag ( Y aref- ( s + ), Y bref- ( s + ), Y cref- ( s + )) is a diagonal matrix. =[ ( s+ ), ( s + ), ( s + )] T U 1 ( s )=[ ( s ), ( s ), ( s )] T .

[0082] Similarly, current , and The current component with frequency ω+2jω generated by the voltage of a single-phase inverter at frequency ω+2jω can be expressed as:

[0083]

[0084] Among them, Y SIO ( s + =diag( Y SIOa ( s + ), Y SIOb ( s + ), Y SIOc ( s + )) is a 3x3 diagonal matrix. Y SIOx ( s + )= I xref0 ( s + )+ Y io ( s + Current matrix and voltage matrix U +2 ( s + This can be represented as: =[ ( s + ), ( s + ), (s + )] T and =[ ( s + ), ( s + ), ( s + )] T .

[0085] Depend on Figure 4 (b) The grid current and terminal voltage of the inverter subsystem at frequency ω+2jω1 can be obtained as follows:

[0086]

[0087] The relationship between the terminal voltages of the inverter subsystem at frequency ω+2jω1 and frequency ω can be expressed as:

[0088]

[0089] Where matrix I is a diagonal identity matrix.

[0090] Similarly, the relationship between the terminal voltages of the inverter subsystem at frequency ω-2jω1 and frequency ω can be expressed as:

[0091]

[0092] (3) Further, the multi-input multi-output impedance model of the inverter subsystem can be obtained, which can be expressed as:

[0093]

[0094] Matrix Y T This is an inverter subsystem impedance model that considers the three single-phase inverters as a whole. Treating the three single-phase inverters as a subsystem takes into account frequency coupling and inter-phase coupling, thus improving the accuracy of system stability analysis. This is caused by the coupling current at ω-2jω1. It is caused by the coupling current at ω+2jω1, which is zero when frequency coupling is ignored.

[0095] (4) Furthermore, considering that the small-signal impedance model is established in the frequency domain, the frequency sweep test is an effective method to obtain impedance measurements by injecting small-signal disturbances. By comparing the measured results with those of the control hardware-in-the-loop (CHIL) experiment, the correctness of the established inverter subsystem impedance model can be verified.

[0096] The comparison results are as follows Figure 5 As shown, where Y Tij The impedance matrix Y T The impedance matrix of the first j th The first in the column i th Each element. For example... Figure 5 As shown, both cases are validated. Case 1 demonstrates that in f ab = f bb = f cb =200Hz, L g The inverter subsystem impedance is 3mH. Case 2 illustrates this. f ab = 200Hz f bb =100Hz f cb Impedance of the inverter subsystem at 80Hz. f ab , f bb and f cb These are the phase-locked loop bandwidths for SIa, SIb, and SIc, respectively. Other parameters are shown in Table 1. Figure 5 It can be seen that the impedance matrix Y T The measurement results were well fitted in the range of 10Hz to 1000Hz.

[0097]

[0098] Figure 6 (a1)-(a3) give the ratio of the off-diagonal element amplitude to the diagonal element amplitude when the phase-locked loop uses different bandwidth parameters (240Hz, 200Hz, 180Hz). Figure 6 The solid lines in (a1)-(a3) are respectively Y T12 / Y T11 、Y T23 / Y T22 、Y T31 / Y T33 The dashed lines are respectively Y T13 / Y T11 、Y T21 / YT22 、Y T32 / Y T33 Comparing the solid and dashed curves, it can be seen that the larger the bandwidth of the phase-locked loop (PLL), the stronger its control capability and the stronger the three-phase coupling relationship.

[0099] Figure 6 (b1)-(b3) are different neutral inductors L gn At (2mH / 3mH / 5mH), the ratio of the amplitude of the off-diagonal element to the amplitude of the diagonal element ( Y T12 / Y T11 、Y T23 / Y T22 、Y T31 / Y T33 and Y T13 / Y T11 、Y T21 / Y T22 、Y T32 / Y T33 As can be seen from the diagram, the neutral inductor... L gn The larger the value, the stronger the three-phase coupling. The degree of interphase coupling is related to the neutral inductance. L gn The values ​​are positively correlated. In extreme cases, if the neutral line inductance... L gn If the value is zero, then there is no coupling relationship between the three phases. This also illustrates that the weaker the power grid, the more attention should be paid to inter-phase coupling effects when conducting stability analysis.

[0100] (4) From the above analysis, the system model of the three-phase current and voltage at the disturbance frequency can be obtained:

[0101]

[0102] Transforming the three-phase system model using symmetrical components and sequence impedance can simplify system stability analysis. Symmetrical component analysis decomposes each phase current or voltage in the three-phase system into a sequence of zero, positive, and negative components.

[0103] definition , ,in,

[0104] The sequence current and sequence voltage vectors can be expressed as:

[0105] ,

[0106]

[0107]

[0108]

[0109] When the system is perfectly symmetric, Y T012 and Z S012 It is a diagonal matrix. The stability of the system can be analyzed independently using positive-sequence, negative-sequence, and zero-sequence single-input single-output impedance models. However, when the system is asymmetric, there is a coupling relationship between the zero-sequence positive-sequence impedance and the negative-sequence impedance, and the stability of the system is then analyzed through the eigenvalue trajectories of the multi-input multi-output impedance model. This numerical analysis provides little insight and is not conducive to drawing general conclusions. To intuitively analyze the system stability, the multi-input multi-output impedance model of the inverter subsystem is decomposed into three independent single-input single-output impedance models through extended loop decomposition, such as... Figure 7 As shown. Figure 7 (a) is a multi-input multi-output impedance model. y T012ij For matrix Y T012 No. j th The first of the columns i th Each element. z S012ij Representation matrix Z S012 ( s ) j th The first in the column i th The system has three elements. Using the extended loop decomposition method, the multi-input multi-output impedance model containing sequence impedance coupling characteristics is transformed into three independent single-input single-output impedance models. The stability of the system can then be analyzed using these three independent single-input single-output impedance models. Figure 7 (b) The equivalent zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance models of the system can be expressed as:

[0110]

[0111] (5) Based on the single-input single-output impedance model of the three-phase inverter and the grid impedance matrix in step (4), the stability of the system can be analyzed. When the three-phase inverter impedance is symmetrical, the zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance models and grid impedance matrices of the inverter subsystem are as follows: Figure 8 As shown. Y e0x , Y e1x , Y e2x These are the zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance models of the inverter subsystem considering phase-to-phase coupling and frequency coupling, respectively. Y ew0x , Y ew1x Y ew2x For the zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance models of the inverter subsystem without considering interphase coupling, we can obtain:

[0112]

[0113] Among them, Y TW ( s =diag( Y SIa , Y SIb , Y SIc ), Y SIa , Y SIb ,and Y SIc These are the impedance models for SIa, SIb, and SIc. Y SIa , Y SIb and Y Sic It is calculated by adding a neutral inductor to each phase inductor and setting the neutral inductor to zero.

[0114] Figure 8 middle, Y ex1 This indicates that when considering interphase coupling, in f ab = f bb =f cb =180Hz, I ref Impedance at 35A. Y ex2 This indicates that when considering interphase coupling, in f ab = f bb =f cb =90Hz, I ref Impedance at 35A.Y ex3 This indicates that when considering interphase coupling, in f ab = f bb =f cb =180Hz, I ref Impedance at 21A. Y ewx1 This indicates that when interphase coupling is not considered, in f ab = f bb =f cb =180Hz, I ref Impedance at 35A.

[0115] Depend on Figure 8 It can be seen that, within the 300Hz range, the impedance model considering interphase coupling ( Figure 8 (a1), (b1), (c1)) and the impedance model that does not consider interphase coupling ( Figure 8 Significant differences exist between (a2), (b2), and (c2), leading to significant differences in the evaluation of the system instability frequency by the two impedance models. It is important to note that the difference between the two impedance models is limited to the bandwidth of the phase-locked loop (PLL). Considering interphase coupling, the inverter's zero-sequence impedance amplitude intersects with the grid's zero-sequence impedance amplitude at 101 Hz, with a phase difference of 199°. According to the Nyquist criterion, the system becomes unstable at this frequency. In contrast, the instability frequency determined by the impedance model without considering interphase coupling is 93 Hz.

[0116] contrast Y e01 ( Figure 8 (The solid curve in (b1)) and Y e02 ( Figure 8 As can be seen from the dashed curve in (b1), reducing the bandwidth of the phase-locked loop effectively reduces the inverter impedance amplitude and shrinks the negative resistance region. (Comparison) Y e01 ( Figure 8 (The solid curve in (b1)) and Y e03 ( Figure 8 As can be seen from the solid curve in (b2), reducing transmission power (I) ref This will result in a smaller conductance amplitude and a smaller negative resistance region in the inverter.

[0117] (5) Based on the single-input single-output impedance model of the three-phase inverter and the grid impedance matrix in step (4), the stability of the system can be analyzed. When the three-phase inverter impedance is asymmetrical, Figure 9 The zero-sequence, positive-sequence, and negative-sequence single-input single-output impedance models and grid impedance matrices of the inverter subsystem are given when the three-phase inverter impedance is asymmetrical. Y e04 , Y e14 , Y e24 When considering interphase coupling effects, in f ab = 200Hz, f bb = 100 Hz f cb = 80Hz, I ref = Positive and negative zero sequence impedance at 35A. Y ew02 , Y ew12 , Y ew22 This indicates that when interphase coupling effects are not considered, in f ab = 200Hz, f bb = 100 Hz f cb = 80Hz I ref = Positive and negative zero sequence impedance at 35A.

[0118] Depend on Figure 9 It is evident that within the 300Hz range, there is a significant difference between the impedance considering interphase coupling (solid curve) and the impedance not considering interphase coupling (dashed curve). This difference leads to significant discrepancies in the system stability evaluation conclusions of the two impedance models. When considering interphase coupling, the inverter's zero-sequence impedance amplitude intersects with the grid's zero-sequence impedance amplitude at 112Hz, with a phase difference of 154°. According to the Nyquist criterion, the system will remain stable. In contrast, without considering interphase coupling (dashed curve), the system is unstable at 113Hz when evaluated by impedance. This analysis demonstrates that the stability analysis considering interphase coupling yields completely different results than the stability analysis without considering interphase coupling.

[0119] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for impedance modeling and stability analysis of a distributed photovoltaic system, characterized in that, Includes the following steps: S1: Based on the harmonic transfer function matrix method, impedance modeling is performed on the single-phase photovoltaic inverter to obtain the voltage and current small-signal model under the ABC three-phase disturbance voltage considering the initial phase of the power grid. S2: Based on the impedance model characteristics of a single-phase photovoltaic inverter and the obtained voltage and current small-signal models, establish a small-signal model of a three-phase four-wire grid-connected system that considers inter-phase coupling characteristics and frequency coupling characteristics. S3: Establish the multi-input multi-output impedance model of the inverter subsystem based on the small-signal model of the three-phase four-wire grid-connected system, and establish the grid impedance matrix based on the grid parameters. S4: Based on the grid impedance matrix, the multi-input multi-output impedance model of the inverter subsystem is decomposed into three independent positive-sequence, negative-sequence and zero-sequence single-input single-output impedance models by the loop decomposition method, and the stability analysis of the three-phase four-wire grid-connected system is carried out. In step S2, the small-signal model of the three-phase four-wire grid-connected system considering phase-to-phase coupling characteristics and frequency coupling characteristics is defined as three sub-circuits at frequencies ω and ω±2jω1, and the coupling relationship between the three sub-circuits is represented by a controlled current source model. In step S3, the larger the bandwidth of the phase-locked loop in the three-phase four-wire grid-connected system, the stronger the control capability of the phase-locked loop and the stronger the three-phase coupling relationship. The larger the neutral inductance, the stronger the coupling relationship between the three phases.

2. The method for impedance modeling and stability analysis of distributed photovoltaic systems according to claim 1, characterized in that, In step S1, the single-phase photovoltaic inverter is transformed using the following formula to obtain a virtual inverter that considers the initial phase of the power grid. α - β Voltage vector in coordinate system and : The initial phases of the three phases a, b, and c of the power grid are respectively... va =0、 vb =-2π / 3、 vc =2π / 3, G osgα and G osgβ Defined as the voltage at the common coupling point arrive and The transfer function is given by T0, where T0 is the grid voltage period.

3. The method for impedance modeling and stability analysis of distributed photovoltaic systems according to claim 2, characterized in that, In step S1, without losing versatility, a phase-locked loop based on a T / 4 time delay is also used, where T is the sampling period.

4. The method for impedance modeling and stability analysis of distributed photovoltaic systems according to claim 1, characterized in that, In step S1, considering the frequency coupling effect, the single-phase photovoltaic inverter system has voltage and current components with frequencies of ω±2jω1 in addition to the voltage and current components with a disturbance frequency of ω. The impedance model of the single-phase photovoltaic inverter is expressed as: Among them, the Laplace operators with superscripts "+" and "-" are... s "represents the positive coupling frequency s+2jω1 and the negative coupling frequency s-2jω1, respectively, Y invo ( s Y represents the impedance model of the main circuit of a single-phase photovoltaic inverter. ref ( s () represents the impedance model of a single-phase photovoltaic inverter under the control structure. , , These represent the grid connection point current signals at the negative coupling frequency, fundamental frequency, and positive coupling frequency, respectively. , , These represent the grid connection point voltage signals at the negative coupling frequency, fundamental frequency, and positive coupling frequency, respectively.

5. The method for impedance modeling and stability analysis of distributed photovoltaic systems according to claim 1, characterized in that, In step S2, the small-signal model of the three-phase four-wire grid-connected system is represented as follows: ， Wherein, matrix Y T This is an inverter subsystem impedance matrix model that considers the three single-phase photovoltaic inverters as a whole. This represents the port voltage matrix of the photovoltaic inverter. This represents the port current matrix of the photovoltaic inverter.

6. The method for impedance modeling and stability analysis of distributed photovoltaic systems according to claim 1, characterized in that, In step S4, the stability analysis of the three-phase four-wire grid-connected system is performed based on the Nyquist criterion.

7. A system for impedance modeling and stability analysis of distributed photovoltaic systems, characterized in that, include: Voltage and current small-signal model acquisition unit: Based on the harmonic transfer function matrix method, impedance modeling is performed on the single-phase photovoltaic inverter to obtain the voltage and current small-signal model under the ABC three-phase disturbance voltage considering the initial phase of the grid. Small-signal model establishment unit: Based on the impedance model characteristics of a single-phase photovoltaic inverter and the obtained voltage and current small-signal models, establish a small-signal model of a three-phase four-wire grid-connected system that considers inter-phase coupling characteristics and frequency coupling characteristics; Impedance model establishment unit: Based on the small-signal model of the three-phase four-wire grid-connected system, establish the multi-input multi-output impedance model of the inverter subsystem, and at the same time establish the grid impedance matrix based on the grid parameters; Stability assessment unit: Based on the grid impedance matrix, the multi-input multi-output impedance model of the inverter subsystem is decomposed into three independent positive-sequence, negative-sequence, and zero-sequence single-input single-output impedance models using the loop decomposition method, and the stability analysis of the three-phase four-wire grid-connected system is performed. In the small-signal model building unit, the small-signal model of the three-phase four-wire grid-connected system considering phase-to-phase coupling characteristics and frequency coupling characteristics is defined as three sub-circuits at frequencies ω and ω±2jω1. The coupling relationship between the three sub-circuits is represented by a controlled current source model. In the impedance model establishment unit, the larger the bandwidth of the phase-locked loop in the three-phase four-wire grid-connected system, the stronger the control capability of the phase-locked loop and the stronger the three-phase coupling relationship. The larger the neutral inductance, the stronger the coupling relationship between the three phases.

8. The distributed photovoltaic system impedance modeling and stability analysis system according to claim 7, characterized in that, In the voltage and current small-signal model acquisition unit, the single-phase photovoltaic inverter is transformed using the following formula to obtain a virtual model considering the initial phase of the power grid. α - β Voltage vector in coordinate system and : The initial phases of the three phases a, b, and c of the power grid are respectively... va =0、 vb =-2π / 3、 vc =2π / 3, G osgα and G osgβ Defined as the voltage at the common coupling point arrive and The transfer function is given by T0, where T0 is the grid voltage period.

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