A stability analysis method for inverter grid-connected system under unbalanced conditions

Abstract

A stability analysis method for an inverter grid-connected system under unbalanced working conditions includes step S1, considering the inverter frequency coupling effect and the three-phase unbalance factor of the power grid, using the harmonic linearization method to model the inverter main circuit and the control circuit respectively, and determining the inverter impedance expression; step S2, converting the inverter impedance and the total impedance of the power grid side into a single-input single-output impedance form respectively; step S3, using the impedance analysis method to analyze the stability of the inverter grid-connected system. The present invention not only fills the gap in the accurate modeling method of the inverter impedance under unbalanced working conditions, effectively improves the reliability of the stability analysis of the inverter grid-connected system, but also reduces the complex matrix operations in the stability analysis process and simplifies the calculation amount.

Description

Technical Field

[0001] The present invention relates to the technical field of novel power electronic grid control, and in particular to a stability analysis method for an inverter grid-connected system under unbalanced working conditions. Background Art

[0002] With a high proportion of new energy sources connected to the grid through power electronic inverters, the grid-connected operation of a large number of inverters has profoundly changed the dynamic characteristics of the system. The interactive oscillation problem between the inverter and the grid has become increasingly prominent, posing a severe challenge to the safety and stability of the system. In order to effectively reduce the potential risk of oscillation instability and improve the stability of the new energy inverter access system, it is urgent to conduct comprehensive and reliable modeling and stability analysis of the inverter grid-connected system. However, existing research mainly focuses on the modeling and stability analysis of inverters under three-phase balanced conditions, and the modeling of inverters under unbalanced conditions is still in its infancy. In actual power grids, due to random load fluctuations, asymmetry often occurs, resulting in grid-connected inverters being in a three-phase unbalanced operating state, and the impedance / admittance model established under three-phase balanced conditions is no longer applicable. In addition, existing studies often ignore the frequency coupling effect inside the inverter during the modeling process, resulting in low accuracy and reliability of the established model, which in turn affects the accuracy of subsequent stability analysis results. Summary of the invention

[0003] The purpose of the present invention is to provide a stability analysis method for an inverter grid-connected system under unbalanced conditions. By considering the inverter frequency coupling effect and the three-phase unbalance factor of the power grid, a harmonic linearization method is used to accurately model the inverter impedance to improve the reliability of the stability analysis of the inverter grid-connected system.

[0004] In order to solve the above technical problems, the present invention adopts the following technical method: a stability analysis method of an inverter grid-connected system under unbalanced working conditions, comprising:

[0005] Step S1, considering the inverter frequency coupling effect and the three-phase imbalance factor of the power grid, the main circuit and the control circuit of the inverter are modeled respectively by using the harmonic linearization method to determine the inverter impedance expression;

[0006] Step S2, converting the inverter impedance and the total grid-side impedance into single-input single-output impedance forms respectively;

[0007] Step S3, analyzing the stability of the inverter grid-connected system by using impedance analysis method.

[0008] Furthermore, the inverter is a grid-connected inverter with droop control.

[0009] Furthermore, in step S1, considering the inverter frequency coupling effect and the three-phase imbalance factor of the power grid, the main circuit, power loop, droop control link, voltage and current dual loop and modulation link of the grid-connected inverter with grid-connected droop control are modeled respectively by using the harmonic linearization method, as follows:

[0010] 1) Main circuit modeling: Determine the frequency domain expression of the inverter main circuit equation; when the inverter works in an unbalanced condition, add a positive sequence voltage disturbance at the PCC point, determine the time domain expression of the voltage and current at the PCC point at this time, and transform the expression from the time domain to the frequency domain;

[0011] 2) Power loop modeling: Ignore the small signal quadratic terms, combine the PCC point voltage and current in the frequency domain, and determine the frequency domain expressions of the inverter output active power and reactive power;

[0012] 3) Droop control link modeling: Substitute the output active power in the frequency domain into the active loop output phase angle equation to construct the frequency domain expression of the output phase angle and the output phase angle disturbance; at the same time, substitute the output active power in the frequency domain into the expression of the droop control output reference voltage to obtain the frequency domain expression of the droop control output reference voltage, and then perform Park transformation to obtain the frequency domain expression of the voltage outer loop d-axis and q-axis reference voltage; according to the frequency domain expression of the output phase angle disturbance and combined with the small signal expression of the grid-connected voltage and grid-connected current, derive the frequency domain expression of the grid-connected voltage and grid-connected current in the dq coordinate system;

[0013] 4) Voltage-current dual-loop modeling: Determine the frequency domain expressions of the d-axis and q-axis reference currents based on the voltage loop circuit equation; determine the frequency domain expression of the modulation signal in the inverter synchronous rotating coordinate system based on the current loop circuit equation;

[0014] 5) Regulation link modeling: Perform Park inverse transform on the modulation signal of the inverter to obtain the frequency domain expression of the modulation signal of the inverter under the positive sequence disturbance frequency and negative sequence coupling frequency;

[0015] Step S1, when determining the inverter impedance expression: substitute the frequency domain expression of the inverter bridge arm midpoint voltage into the frequency domain expression of the main circuit equation, and then combine the frequency domain expression of the bridge arm midpoint voltage, the frequency domain expression of the inverter main circuit equation, and the frequency domain expressions of the PCC point voltage and current to obtain the expression of the inverter coupling impedance matrix.

[0016] Furthermore, in step S2, when the inverter impedance and the total grid-side impedance are converted into a single-input single-output impedance form:

[0017] First, determine the expressions of the grid impedance matrix and load impedance matrix under unbalanced conditions, as follows:

[0018] (1)

[0019] The total impedance matrix on the grid side is expressed as:

[0020] (2)

[0021] In the formula, ; Subscript for When represents the power grid, for : indicates load; is the grid impedance matrix; is the load impedance matrix; is the total impedance matrix on the grid side; is the corresponding element of the power grid or load impedance matrix; For power grid or load Three-phase impedance; is the total impedance matrix element on the grid side;

[0022] Then determine the expression of single-input single-output impedance of the inverter impedance and the total impedance of the grid side, as follows:

[0023] (3)

[0024] (4)

[0025] (5)

[0026] (6)

[0027] In the formula, are the equivalent positive and negative sequence impedances of the inverter respectively; and are the equivalent positive and negative sequence impedances on the grid side, respectively; and is the corresponding element of the inverter coupling impedance matrix; is the amplitude of the positive sequence disturbance voltage; is the amplitude of the positive sequence disturbance current response; is the grid reference voltage; is the grid reference current.

[0028] Preferably, in step S3, when the stability of the inverter grid-connected system is analyzed by using an impedance analysis method:

[0029] Construct the Nyquist stability criterion and convert the positive sequence impedance ratio and negative sequence impedance ratio As a criterion for judging system stability, the calculation formulas of the positive sequence impedance ratio and the negative sequence impedance ratio are as follows:

[0030] (7)

[0031] (8)

[0032] According to the positive sequence impedance ratio and negative sequence impedance ratio The Nyquist image is used to determine the stability of the system; if , The Nyquist curves of do not surround the point (-1, 0), then the system is stable; if , If one or both of the Nyquist curves surround the (-1, 0) point, the system is unstable.

[0033] The stability analysis method of the inverter grid-connected system under unbalanced working conditions provided by the present invention adopts a harmonic linearization method to model the main circuit and control circuit of the inverter respectively, taking full account of the inverter frequency coupling effect and three-phase unbalance factors, so that the inverter AC variable can be transformed from the time domain to the frequency domain, and the frequency domain expression of the variable product term is solved by the frequency domain convolution theorem, and then other high-order small signal terms are ignored according to the description function method, and the nonlinear variables of the inverter are effectively processed, so as to obtain a high-accuracy inverter impedance expression. The present invention then converts the inverter impedance and the total impedance of the grid side into the form of a single-input single-output impedance, and proposes a Nyquist stability criterion to realize the stability analysis of the inverter grid-connected system. The present invention not only fills the gap in the accurate modeling method of the inverter impedance under unbalanced working conditions, effectively improves the reliability of the stability analysis of the inverter grid-connected system, but also reduces the complex matrix operations in the stability analysis process and simplifies the calculation amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of the topological structure of the grid-connected system of the grid-building type droop control inverter in the present invention;

[0035] Figure 2 Schematic diagram of the positive and negative sequence impedance sweep results of the inverter in an embodiment of the present invention (wherein (a) is a schematic diagram of the positive sequence impedance sweep result of the inverter; (b) is a schematic diagram of the negative sequence impedance sweep result of the inverter);

[0036] Figure 3 Schematic diagram of the positive and negative sequence impedance frequency sweep results on the grid side in an embodiment of the present invention (wherein (a) is a schematic diagram of the positive sequence impedance frequency sweep result on the grid side; (b) is a schematic diagram of the negative sequence impedance frequency sweep result on the grid side);

[0037] Figure 4 In the embodiment of the present invention Under different values, and Nyquist diagram of hour, and Nyquist diagram of hour, and Nyquist plot of

[0038] Figure 5 In the embodiment of the present invention Grid-connected current waveform diagram when ;

[0039] Figure 6 In the embodiment of the present invention Grid-connected current waveform diagram when . DETAILED DESCRIPTION

[0040] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0041] A method for analyzing the stability of an inverter grid-connected system under unbalanced working conditions, comprising:

[0042] Step S1, considering the inverter frequency coupling effect and the three-phase imbalance factor of the power grid, the main circuit and the control circuit of the inverter are modeled respectively by using the harmonic linearization method to determine the inverter impedance expression.

[0043] The modeling method of step S1 is applicable to different converters, such as photovoltaic inverters, energy storage inverters, and grid-forming droop-controlled inverters (GFDCI) ... etc. Next, this embodiment will take GFDCI as an example to illustrate the specific content of the modeling method.

[0044] Construction of GFDCI unbalanced operating impedance model taking into account frequency coupling effect:

[0045] like Figure 1 The basic structure of GFDCI is shown in the figure. is the DC side voltage; and is the bridge arm midpoint voltage; and is the filter inductor current; are the d-axis and q-axis inductor currents; and is the point of common coupling (PCC) voltage; and are the d-axis and q-axis grid-connected voltages; and is the grid-connected point current; and are the d-axis and q-axis grid-connected currents; is the modulation signal in the synchronously rotating coordinate system; is a three-phase modulation signal in a stationary coordinate system; is the filter inductor; is the filter capacitor; For unbalanced load; is the grid inductance; is the grid resistance; is the grid voltage; is the inverter output phase angle; is the output active power; is the output reactive power; is the active power reference value; is the reactive power reference value; and is the d-axis and q-axis reference voltage; is the delay function.

[0046] 1) GFDCI main circuit modeling

[0047] Depend on Figure 1 List the frequency domain expressions of the GFDCI main circuit equations:

[0048] (9)

[0049] In the formula, is the Laplace operator.

[0050] When GFDCI works in unbalanced conditions, the frequency added at the PCC point is After the positive sequence voltage disturbance, the time domain expressions of the voltage and current at the PCC point are:

[0051] (10)

[0052] (11)

[0053] Where: and are the amplitudes of fundamental frequency positive sequence voltage, fundamental frequency negative sequence voltage, positive sequence disturbance voltage and negative sequence coupling voltage respectively; and are the amplitudes of fundamental frequency positive sequence current, fundamental frequency negative sequence current, positive sequence disturbance current response and negative sequence coupling current response respectively; They are the fundamental frequency, positive sequence disturbance frequency and negative sequence coupling frequency respectively; and They are the initial phase angles of the fundamental frequency negative sequence voltage, the positive sequence disturbance voltage and the negative sequence coupling voltage respectively; and They are the initial phase angles of the fundamental frequency positive sequence current, fundamental frequency negative sequence current, positive sequence disturbance current response and negative sequence coupling current response respectively.

[0054] Convert equations (10) and (11) into frequency domain expressions as follows:

[0055] (12)

[0056] In the formula, Represents the frequency component of the corresponding variable, such as: "express The frequency is ; , , , , ; , , .

[0057] 2) GFDCI power loop modeling

[0058] The expressions of GFDCI output active power and reactive power are:

[0059] (13)

[0060] In the formula, and is the line voltage between the two phases.

[0061] Substituting equation (12) into equation (13) and ignoring the small signal quadratic term, we obtain and The frequency domain expression of is:

[0062] (14)

[0063] (15)

[0064] In the formula, the variables are superscripted with “ " represents the conjugate operation of the variable," " represents an imaginary unit, Indicates that the corresponding variable is a DC quantity.

[0065] 3) GFDCI droop control link modeling

[0066] GFDCI active loop output phase angle The equation is:

[0067] (16)

[0068] In the formula, is the active power-frequency droop coefficient; is the grid reference angular frequency.

[0069] Substituting equation (14) into equation (16), we get the output phase angle The frequency domain expression of is:

[0070] (17)

[0071] Where:

[0072] (18)

[0073] (19)

[0074] (20)

[0075] (twenty one)

[0076] After adding the positive sequence disturbance, the droop control output phase angle has a phase angle disturbance According to formula (17), we can get The expression is:

[0077] (twenty two)

[0078] According to the droop relationship between reactive power and voltage, the droop control output reference voltage is obtained. The expression is:

[0079] (twenty three)

[0080] In the formula, is the reactive power-voltage droop coefficient; is the grid reference voltage.

[0081] Substituting equation (15) into equation (23), we get the droop control output reference voltage The frequency domain expression of is:

[0082] (twenty four)

[0083] Where:

[0084] (25)

[0085] (26)

[0086] (27)

[0087] According to formula (24), the frequency domain expressions of the d-axis and q-axis reference voltages of the voltage outer ring are obtained as follows:

[0088] (28)

[0089] (29)

[0090] According to formula (22), combined and Small signal expressions, deriving their expressions in the frequency domain are:

[0091] (30)

[0092] (31)

[0093] (32)

[0094] (33)

[0095] In the formula, and The specific expression is as follows:

[0096] (34)

[0097] (35)

[0098] (36)

[0099] (37)

[0100] (38)

[0101] (39)

[0102] (40)

[0103] 4) GFDCI voltage and current dual loop modeling

[0104] The voltage loop circuit equation is:

[0105] (41)

[0106] In the formula, , is the voltage loop transfer function, is the voltage loop proportional coefficient, is the voltage loop integration coefficient, is the grid fundamental frequency angular frequency, is the d-axis reference current, is the q-axis reference current.

[0107] According to formula (41), we can deduce and The frequency domain expression of is:

[0108] (42)

[0109] (43)

[0110] In the formula, and The specific expression is as follows:

[0111] (44)

[0112] (45)

[0113] (46)

[0114] (47)

[0115] (48)

[0116] (49)

[0117] The current loop circuit equation is:

[0118] (50)

[0119] In the formula, and is the modulation signal in the synchronous rotating coordinate system of the inverter; , is the current loop transfer function, is the current loop proportionality coefficient, is the current loop integration coefficient.

[0120] According to equation (50), the modulation signal of the synchronous rotating coordinate system is derived: and The frequency domain expression of is:

[0121] (51)

[0122] (52)

[0123] In the formula, is the amplitude of the inductor current; is the initial phase angle of the inductor current; is the DC value of the modulating signal.

[0124] 5) Modeling of GFDCI regulatory links

[0125] right and Implement Park inverse transformation to obtain the inverter ABC three-phase modulation signal. Due to the frequency coupling effect, the modulation signal of each phase contains a frequency of In addition to the modulation signal of Taking phase A as an example, the modulation signal of phase A is and The expression is as follows:

[0126] (53)

[0127] (54)

[0128] In the formula, and The expression is as follows:

[0129] (55)

[0130] (56)

[0131] (57)

[0132] (58)

[0133] (59)

[0134] (60)

[0135] (61)

[0136] (62)

[0137] (63)

[0138] (64)

[0139] Where:

[0140] (65)

[0141] (66)

[0142] 6) Determine the GFDCI impedance expression

[0143] Let the midpoint voltage of the inverter A phase bridge arm be expressed in the frequency domain as:

[0144] (67)

[0145] In the formula, and The expression is as follows:

[0146] (68)

[0147] (69)

[0148] (70)

[0149] (71)

[0150] (72)

[0151] (73)

[0152] (74)

[0153] (75)

[0154] In the formula, , represents the transfer function of the current loop decoupling link, and the expressions of other variables are as follows:

[0155] (76)

[0156] (77)

[0157] (78)

[0158] (79)

[0159] (80)

[0160] (81)

[0161] (82)

[0162] (83)

[0163] (84)

[0164] (85)

[0165] (86)

[0166] (87)

[0167] (88)

[0168] (89)

[0169] (90)

[0170] (91)

[0171] Substituting formula (67) into formula (9) yields:

[0172] (92)

[0173] In the formula, .

[0174] By combining equations (9), (12), (67) and (92), we can obtain the expression of the inverter coupling impedance matrix as follows:

[0175] (93)

[0176] (94)

[0177] In the formula, and are the corresponding elements of the inverter coupling impedance matrix.

[0178] It is worth pointing out that if the inverter frequency coupling effect and the three-phase imbalance of the power grid are considered, when the harmonic linearization method is used to model other types of inverters, the above-mentioned GFDCI modeling ideas can be referred to for analogical derivation and modeling, that is, according to the specific converter, the corresponding time domain expressions are listed, and then the time domain equations are transformed into the frequency domain according to the harmonic linearization method.

[0179] Step S2: Single-input single-output impedance model construction

[0180] In order to simplify the calculation amount of the subsequent stability analysis, the single-input single-output impedance model of GFDCI and the total impedance of the grid side will be determined respectively in this step S2.

[0181] Under unbalanced conditions, the expressions of the grid impedance matrix and load impedance matrix are as follows:

[0182] (1)

[0183] The total impedance matrix on the grid side is expressed as:

[0184] (2)

[0185] In the formula, ; Subscript for When represents the power grid, When it is L, it indicates load; is the grid impedance matrix; is the load impedance matrix; is the total impedance matrix on the grid side; is the corresponding element of the power grid or load impedance matrix; For power grid or load Three-phase impedance; is the total impedance matrix element on the grid side.

[0186] Taking the input disturbance voltage as a single input and the output corresponding current as a single output, the single-input single-output impedance expression of the inverter impedance and the total impedance of the grid side is constructed as follows:

[0187] (3)

[0188] (4)

[0189] (5)

[0190] (6)

[0191] In the formula, are the equivalent positive and negative sequence impedances of the inverter respectively; and are the equivalent positive and negative sequence impedances on the grid side, respectively; and is the corresponding element of the inverter coupling impedance matrix; is the amplitude of the positive sequence disturbance voltage; is the amplitude of the positive sequence disturbance current response; is the grid reference voltage; is the grid reference current.

[0192] Step S3, analyzing the stability of the inverter grid-connected system by using impedance analysis method.

[0193] Before analyzing the stability of the system, let's first verify the accuracy of the GFDCI and grid-side total impedance single-input single-output impedance model constructed by the present invention. Figure 1The GFDCI grid-connected system simulation model shown in the figure adds positive and negative sequence voltage disturbances at the PCC point, and obtains the measured values ​​of positive and negative sequence impedances through frequency sweep simulation. The simulation parameters are shown in Table 1 below, and the simulation results are shown in Figure 2 , Figure 3 As shown. Figure 2 , Figure 3 It can be seen that the positive and negative sequence impedance measurement values ​​obtained by the simulation experiment are highly consistent with the positive and negative sequence impedance theoretical values ​​calculated by using the single-input single-output impedance model involved in the present invention, which can prove the accuracy of the single-input single-output impedance model constructed by the present invention.

[0194] ,

[0195] Next, the stability of the droop control inverter grid-connected system is analyzed.

[0196] Constructing the Nyquist stability criterion: The positive sequence impedance ratio and negative sequence impedance ratio As a criterion for judging system stability, the calculation formula of the positive sequence impedance ratio and the negative sequence impedance ratio is as follows:

[0197] (7)

[0198] (8)

[0199] Using impedance analysis method, according to the positive sequence impedance ratio and negative sequence impedance ratio The Nyquist image is used to determine the stability of the system; if , The Nyquist curves of do not surround the point (-1, 0), then the system is stable; if , If one or both of the Nyquist curves of the system surround the (-1, 0) point, the system is determined to be unstable. Specifically, in this embodiment, the voltage loop proportional coefficient is used as a variable to further illustrate the stability analysis method of the present invention. Figure 4 Impedance ratio under different voltage loop proportional coefficients , Nyquist image. hour, , The Nyquist curve surrounds the (-1, 0) point, the system is unstable, and the current waveform is as follows Figure 5 As shown; when hour, , The Nyquist curves do not surround the (-1, 0) point, the system is stable, and the current waveform is as follows Figure 6 shown.

[0200] In addition to the above method, the present invention can also use other methods when analyzing system stability, for example: judging according to the Bode diagram of the positive and negative sequence impedances of the inverter and the power grid, wherein the positive sequence impedance of the inverter and the positive sequence impedance of the power grid are placed in one diagram, and the negative sequence impedance of the inverter and the negative sequence impedance of the power grid are placed in one diagram, and the phase angle difference corresponding to the intersection of the positive sequence impedance of the inverter and the positive sequence impedance of the power grid is not greater than 180 degrees, that is, the positive sequence system is stable, otherwise the positive sequence system is unstable, and the negative sequence system is judged in a similar way. The grid-connected system is stable only when the positive sequence system and the negative sequence system are stable at the same time, and the grid-connected system is unstable if one of them is unstable.

[0201] The above embodiments are preferred implementation schemes of the present invention. In addition, the present invention may also be implemented in other ways. Any obvious replacement without departing from the concept of the present technical solution is within the protection scope of the present invention.

[0202] In order to make it easier for ordinary technicians in the field to understand the improvements of the present invention over the prior art, some drawings and descriptions of the present invention have been simplified, and for the sake of clarity, some other elements are omitted in this application document. Ordinary technicians in the field should realize that these omitted elements may also constitute the content of the present invention.

Claims

1. A stability analysis method for an inverter grid-connected system under unbalanced working conditions, characterized in that: include: Step S1, considering the inverter frequency coupling effect and the three-phase imbalance factor of the power grid, the main circuit and the control circuit of the inverter are modeled respectively by using the harmonic linearization method to determine the inverter impedance expression; Considering the inverter frequency coupling effect and the three-phase imbalance of the power grid, the harmonic linearization method is used to model the main circuit, power loop, droop control link, voltage and current dual loop and modulation link of the grid-connected inverter with grid-connected droop control, as follows: 1) Main circuit modeling: Determine the frequency domain expression of the inverter main circuit equation; when the inverter works in an unbalanced condition, add a positive sequence voltage disturbance at the PCC point, determine the time domain expression of the voltage and current at the PCC point at this time, and transform the expression from the time domain to the frequency domain; 2) Power loop modeling: Ignore the small signal quadratic terms, combine the PCC point voltage and current in the frequency domain, and determine the frequency domain expressions of the inverter output active power and reactive power; 3) Droop control link modeling: Substitute the output active power in the frequency domain into the active loop output phase angle equation to construct the frequency domain expression of the output phase angle and the output phase angle disturbance; at the same time, substitute the output active power in the frequency domain into the expression of the droop control output reference voltage to obtain the frequency domain expression of the droop control output reference voltage, and then perform Park transformation to obtain the frequency domain expression of the voltage outer loop d-axis and q-axis reference voltage; Based on the frequency domain expression of the output phase angle disturbance and combined with the small signal expression of the grid-connected voltage and grid-connected current, the frequency domain expression of the grid-connected voltage and grid-connected current in the dq coordinate system is derived; 4) Voltage-current dual-loop modeling: Determine the frequency domain expressions of the d-axis and q-axis reference currents based on the voltage loop circuit equation; determine the frequency domain expression of the modulation signal in the inverter synchronous rotating coordinate system based on the current loop circuit equation; 5) Regulation link modeling: Perform Park inverse transform on the modulation signal of the inverter to obtain the frequency domain expression of the modulation signal of the inverter under the positive sequence disturbance frequency and negative sequence coupling frequency; When determining the inverter impedance expression: after substituting the frequency domain expression of the inverter bridge arm midpoint voltage into the frequency domain expression of the main circuit equation, the frequency domain expression of the bridge arm midpoint voltage, the frequency domain expression of the inverter main circuit equation, and the frequency domain expressions of the PCC point voltage and current are combined to obtain the expression of the inverter coupling impedance matrix; Step S2, converting the inverter impedance and the total grid-side impedance into single-input single-output impedance forms respectively; First, determine the expressions of the grid impedance matrix and load impedance matrix under unbalanced conditions; Then the expressions of the grid impedance matrix and the load impedance matrix are combined to determine the expression of the total impedance matrix on the grid side; Then, taking the input disturbance voltage as a single input and the output corresponding current as a single output, the single-input single-output impedance expression of the inverter impedance and the total impedance of the grid side is constructed, that is, the equivalent positive and negative sequence impedance expression of the inverter and the equivalent positive and negative sequence impedance expression of the grid side; Step S3, analyzing the stability of the inverter grid-connected system using an impedance analysis method; The Nyquist stability criterion is constructed based on the positive-sequence impedance ratio and negative-sequence impedance ratio between the inverter and the grid side, and the stability of the system is judged according to the Nyquist images of the positive-sequence impedance ratio and the negative-sequence impedance ratio.

2. The method for analyzing the stability of an inverter grid-connected system under unbalanced conditions according to claim 1, characterized in that: The inverter is a grid-connected droop control inverter.

3. The method for analyzing the stability of an inverter grid-connected system under unbalanced conditions according to claim 2, characterized in that: In step S2, when the inverter impedance and the total grid-side impedance are converted into single-input single-output impedance forms respectively: First, determine the expressions of the grid impedance matrix and load impedance matrix under unbalanced conditions, as follows: （1） The total impedance matrix on the grid side is expressed as: （2） In the formula, ; Subscript for When represents the power grid, When it is L, it indicates load; is the grid impedance matrix; is the load impedance matrix; is the total impedance matrix on the grid side; is the corresponding element of the power grid or load impedance matrix; For power grid or load Three-phase impedance; is the total impedance matrix element on the grid side; Then determine the expression of single-input single-output impedance of the inverter impedance and the total impedance of the grid side, as follows: （3） （4） （5） （6） In the formula, are the equivalent positive and negative sequence impedances of the inverter respectively; and are the equivalent positive and negative sequence impedances on the grid side, respectively; and is the corresponding element of the inverter coupling impedance matrix; is the amplitude of the positive sequence disturbance voltage; is the amplitude of the positive sequence disturbance current response; is the amplitude of the negative sequence disturbance voltage; is the amplitude of the negative sequence disturbance current response.

4. The method for analyzing the stability of an inverter grid-connected system under unbalanced conditions according to claim 3, characterized in that: Step S3, when analyzing the stability of the inverter grid-connected system using impedance analysis method: Construct the Nyquist stability criterion and convert the positive sequence impedance ratio and negative sequence impedance ratio As a criterion for judging system stability, the calculation formulas of the positive sequence impedance ratio and the negative sequence impedance ratio are as follows: （7） （8） According to the positive sequence impedance ratio and negative sequence impedance ratio The Nyquist image is used to determine the stability of the system; if , The Nyquist curves of do not surround the point (-1, 0), then the system is stable; if , If one or both of the Nyquist curves surround the (-1, 0) point, the system is unstable.

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