A method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model

Abstract

A method for improving the stability of grid-connected inverters across the entire frequency band based on a sequence impedance model, relating to the field of power system technology, is disclosed. The method includes: Step 1, obtaining the grid-connected inverter impedance matrix considering the frequency coupling effect of the inverter through sequence impedance modeling; Step 2, establishing a positive and negative sequence impedance model of the power grid, constructing a single-input single-output impedance expression for the grid-connected inverter, performing stability discrimination, and obtaining the impact of reactive power magnitude on the stability of the grid-connected inverter across the entire frequency band; Step 3, optimizing the reactive current command value of the grid-connected inverter based on the impact of reactive power magnitude on the stability of the grid-connected inverter across the entire frequency band. This invention systematically solves the oscillation problem of grid-connected inverters over a wide frequency range, improves their operational stability under extremely weak power grids, and requires no additional hardware costs, making it easy to implement in engineering.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular, to a method for improving the stability of grid-connected inverters across the entire frequency band based on a sequence impedance model. Background Technology

[0002] The penetration rate of new energy sources, represented by photovoltaics and wind power, in the power grid is continuously increasing. As the interface between new energy power plants and the power grid, the stability of grid-connected inverters is crucial. However, a high proportion of renewable energy integration can lead to a decrease in the grid's short-circuit ratio, potentially causing inverters to operate under harsh conditions such as weak or even extremely weak grids. Under extremely weak grid conditions, grid-connected inverters need to output a certain amount of reactive power, increasing the inverter's static active power output limit. Furthermore, inverters under extremely weak grid conditions also face the risk of broadband oscillations, seriously threatening the safe operation of the power grid.

[0003] In existing technologies, methods to improve the stability of grid-connected inverters mainly include optimizing inverter control parameters, improving inverter control structure, and increasing inverter output reactive current. Optimizing inverter control parameters can enhance system stability by increasing system damping; however, under extremely weak grid conditions, the coupling and interaction of various control links are complex, making it difficult to determine optimal parameters. Furthermore, optimizing inverter control parameters cannot increase the inverter's static output active power limit, thus failing to guarantee stable operation of the inverter under extremely weak grid conditions. Improving the inverter control structure can effectively improve inverter stability, but the implementation process is complex, and its effectiveness heavily depends on specific system parameters. Increasing the inverter output reactive current can increase the inverter's static output active power limit and effectively suppress low-frequency oscillations of the inverter under extremely weak grid conditions; however, this method does not consider the mid-to-high frequency oscillation problem of grid-connected inverters, which may increase the risk of mid-to-high frequency oscillations. Summary of the Invention

[0004] The purpose of this invention is to provide a method for improving the stability of grid-connected inverters across the entire frequency band based on a sequence impedance model, in order to solve the oscillation problem of grid-connected inverters over a wide frequency range.

[0005] To achieve the above objectives, this invention provides a method for improving the stability of a grid-connected inverter across the entire frequency band based on a sequence impedance model. The method includes: Step 1, obtaining the grid-connected inverter impedance matrix considering the frequency coupling effect of the grid-connected inverter through sequence impedance modeling; Step 2, establishing a positive and negative sequence impedance model of the power grid, constructing a single-input single-output impedance expression for the grid-connected inverter based on the positive and negative sequence impedances of the power grid and the aforementioned grid-connected inverter impedance matrix. This single-input single-output impedance expression is the equivalent positive and negative sequence impedance expression of the grid-connected inverter. The Nyquist criterion is used to determine the stability of the ratio of the power grid impedance to the equivalent positive and negative sequence impedance of the grid-connected inverter, thereby obtaining the impact of reactive power magnitude on the stability of the grid-connected inverter across the entire frequency band; Step 3, optimizing the reactive current command value of the grid-connected inverter based on the impact of reactive power magnitude on the stability of the grid-connected inverter across the entire frequency band.

[0006] The beneficial effects of this invention are as follows:

[0007] (1) This invention constructs a precise sequence impedance model for grid-connected inverters that considers frequency coupling, which can comprehensively and accurately evaluate the stability of inverters across the entire frequency band from low frequency to medium and high frequency, providing a solid theoretical basis for reactive power optimization.

[0008] (2) The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model proposed in this invention can simultaneously ensure the stability of multiple frequency bands of grid-connected inverters, including low frequency, medium frequency and high frequency. It has a wider range of applications, enables the inverter to operate stably under extremely weak power grids, and does not require additional hardware circuits. It is low in cost, simple to implement, and has good economic efficiency and feasibility. Attached Figure Description

[0009] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0010] Figure 1 This is a diagram of the inverter control framework provided in an embodiment of the present invention;

[0011] Figure 2 A flowchart illustrating the method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model provided by this invention;

[0012] Figure 3 This is a schematic diagram illustrating the influence of reactive current command values ​​on the stability of each frequency band, provided in an embodiment of the present invention.

[0013] Figure 4 A schematic diagram of the d-axis voltage waveform and Fourier analysis results at the grid connection point before optimization, provided in an embodiment of the present invention;

[0014] Figure 5This is a schematic diagram of the d-axis voltage waveform at the grid connection point and the Fourier analysis results after optimizing the reactive current command value provided in this embodiment of the invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0016] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0017] Figure 1 The inverter main circuit and control framework diagram provided in the embodiments of the present invention are as follows: Figure 1 As shown, the inverter main circuit is connected to the grid through an L-type filter and the grid impedance. The control circuit includes a phase-locked loop, a DC voltage loop, and a current loop. The abc / dq link is a Park transformation from the three-phase abc coordinate system to the two-phase rotating dq coordinate system, and the dq / abc link is the inverse Park transformation from the two-phase rotating dq coordinate system to the three-phase abc coordinate system. This is the DC-side input power. DC side voltage This refers to the inverter's output power. For DC side capacitors, This refers to the three-phase output voltage of the inverter. For the three-phase current at the grid connection point, Let d be the grid-connected current and q be the grid-connected current, where d is the direct axis in the rotating coordinate system and q is the quadrature axis in the rotating coordinate system. For filter inductance, The phase angle is output by the phase-locked loop. The voltage amplitude at the grid connection point. The phase angle of the voltage at the grid connection point. For grid impedance, For the mains inductance, The voltage at the grid connection point is the voltage on the d-axis and q-axis. The voltage amplitude of the power grid. The phase angle of the grid voltage. This is the DC voltage reference value. This is the equivalent transfer function of the DC voltage loop. This is the proportional coefficient of the DC voltage loop. The integral coefficient of the DC voltage loop. This is the reference value for the d-axis current. The current at the grid connection point along the d-axis is... The current at the grid connection point is the q-axis. This is the reference value for the q-axis current. Let be the equivalent transfer function of the current loop. This is the proportionality coefficient of the current loop. The integral coefficient of the current loop is... The fundamental angular frequency, The voltage at the grid connection point along the d-axis. The voltage at the grid connection point on the q-axis. This refers to the output voltage of the d-axis inverter. This is the output voltage of the q-axis inverter. The equivalent transfer function of a phase-locked loop (PLL) This is the proportional gain of the phase-locked loop. The integral coefficients of the phase-locked loop are... This is the output angular frequency of the phase-locked loop. DC-side input power. For 50kW, the grid voltage amplitude 310V, mains inductance The value is 4.84mH, corresponding to a short-circuit ratio of 1.9.

[0018] Figure 2 The flowchart of the method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model provided by this invention is as follows: Figure 2 As shown below, Figure 2 The method shown will be explained in detail.

[0019] Step 1 involves obtaining the grid-connected inverter impedance matrix considering the frequency coupling effect of the grid-connected inverter through sequence impedance modeling. Specifically, Step 1 includes:

[0020] Step 1-1: In the stationary coordinate system of the sampling stage, establish the frequency domain expression of the three-phase voltage and current at the grid connection point, including the fundamental component, the positive-sequence disturbance component, and the negative-sequence coupling component.

[0021] Wherein, the frequency of the fundamental component is The frequency of the positive-sequence perturbation component is The frequency of the negative-order coupling component is The specific process is as follows:

[0022] Assume the system is three-phase balanced, and the voltage at the grid connection point has a frequency of... The positive-sequence perturbation components and frequencies are The negative-sequence coupling component, then the time-domain expression of the grid connection point voltage is:

[0023] (1)

[0024] In formula (1), The time-domain expression for the phase voltage at grid connection point a, Here is the time-domain expression for the phase b voltage at the grid connection point. Here is the time-domain expression for the c-phase voltage at the grid connection point. The amplitude of the fundamental voltage. This represents the amplitude of the positive-sequence disturbance voltage. The magnitude of the negative sequence coupling voltage. The initial phase angle of the positive-sequence disturbance voltage. t represents the initial phase angle of the negative sequence coupling voltage, and t represents time.

[0025] Therefore, a frequency domain expression for the three-phase voltage at the grid connection point (i.e., the three-phase sampled voltage) in a stationary coordinate system considering the sampling stage can be established:

[0026] (2)

[0027] (3)

[0028] (4)

[0029] In formulas (2), (3), and (4), Here is the frequency domain expression for the sampled voltage of phase a at the grid connection point. Here is the frequency domain expression for the sampled voltage of phase b at the grid connection point. Here is the frequency domain expression for the sampled voltage of phase c at the grid connection point. , and These are the frequency domain forms of the fundamental voltage, positive-sequence perturbation voltage, and negative-sequence coupling voltage, respectively. This represents the corresponding frequency of each frequency component. The voltage sampling stage uniformly uses a transfer function. Equivalent Let be the equivalent transfer function of the voltage sampling stage. This refers to the switching cycle of the inverter's switching devices. For the Laplace operator.

[0030] The time-domain expression for the grid connection point current is:

[0031] (5)

[0032] In formula (5), Here is the time-domain expression for the phase current at the grid connection point a. Here is the time-domain expression for the phase b current at the grid connection point. Here is the time-domain expression for the c-phase current at the grid connection point. The amplitude of the fundamental current, This represents the amplitude of the positive-sequence disturbance current. The magnitude of the negative sequence coupling current. The initial phase angle of the fundamental current. The initial phase angle of the positive-sequence disturbance current. t represents the initial phase angle of the negative sequence coupling current, and t represents time.

[0033] Similarly, the frequency domain expression for the three-phase current at the grid connection point can be established:

[0034] (6)

[0035] (7)

[0036] (8)

[0037] In formulas (6), (7), and (8), Here is the frequency domain expression for the sampled current of phase a at the grid connection point. Here is the frequency domain expression for the sampled current of phase b at the grid connection point. Here is the frequency domain expression for the sampled current of phase c at the grid connection point. , and These are the frequency domain expressions for the fundamental current, positive-sequence disturbance current, and negative-sequence coupling current, respectively. The equivalent transfer function representing the current sampling process. Let be the transfer function of the current sampling circuit in the stationary coordinate system. For the Laplace operator.

[0038] Steps 1-2, based on the influence of disturbance components on the phase angle and coordinate transformation of the phase-locked loop output, yield the frequency domain expressions of the grid connection point voltage and current in the rotating coordinate system. The specific process is as follows:

[0039] Based on the influence of disturbance components on the output phase angle of the phase-locked loop, the output phase angle of the phase-locked loop is... Perform a rotational transformation on the grid connection point current, where , To output the phase angle disturbance, the current frequency domain expression in the rotating coordinate system is obtained:

[0040] (9)

[0041] (10)

[0042] In formulas (9) and (10), and These are the frequency domain expressions for the d-axis and q-axis currents, respectively, where the d-axis is the direct axis in the rotating coordinate system and the q-axis is the quadrature axis in the rotating coordinate system. Let be the transfer function between the voltage disturbance component and the output phase angle disturbance. The equivalent transfer function of a phase-locked loop (PLL) This is the proportional gain of the phase-locked loop. The integral coefficients of the phase-locked loop are... Let be the transfer function of the current sampling circuit in the rotating coordinate system. For the Laplace operator.

[0043] Similarly, we can obtain the voltage frequency domain expression in the rotating coordinate system of the grid connection point voltage after considering the phase angle disturbance of the phase-locked loop output:

[0044] (11)

[0045] (12)

[0046] In formulas (11) and (12), and These are the frequency domain expressions for the d-axis and q-axis voltages at the grid connection point, respectively.

[0047] Steps 1-3 involve substituting the output active power in the frequency domain into the dynamic equations of the DC side of the grid-connected inverter to obtain the change in the input DC voltage of the DC voltage loop. That is, the frequency domain expression of the deviation signal of the DC side voltage relative to its reference value; the frequency domain expression of the active current reference value is determined according to the DC voltage loop circuit equation; and the frequency domain expression of the modulation signal in the rotating coordinate system of the grid-connected inverter is determined according to the current loop circuit equation.

[0048] In steps 1-3, the DC voltage loop circuit equation is:

[0049] (13)

[0050] in, This is the active current reference value. DC side voltage This is the DC voltage reference value. This is the transfer function for the DC voltage loop.

[0051] In steps 1-3, the current loop circuit equation is:

[0052] (14)

[0053] in, This is the active current reference value. Active current, The current loop transfer function, The fundamental angular frequency, For filtering inductors, It is reactive current. For the Laplace operator, This is the output angular frequency of the phase-locked loop. This is the reference value for reactive current.

[0054] By following steps 1-3, the frequency domain expression of the output voltage of the grid-connected inverter after passing through the DC voltage loop and DC current loop in the rotating coordinate system is derived. The specific process is as follows:

[0055] The dynamic equations for the DC side of the grid-connected inverter are as follows:

[0056] (15)

[0057] in, and These are the time-domain expressions for the d-axis and q-axis voltages at the grid connection point, respectively. and These are the time-domain expressions for the d-axis and q-axis currents at the grid connection point, respectively. This is the DC-side input power. DC side voltage This refers to the inverter's output power. For DC side capacitors, For filtering inductors, The imaginary unit, and These are the frequency domain expressions for the d-axis and q-axis voltages at the grid connection point, respectively. and These are the frequency domain expressions for the d-axis and q-axis currents, respectively.

[0058] Therefore, the frequency domain expression for the DC-side disturbance voltage can be obtained as follows:

[0059] (16)

[0060] in, This is the frequency domain expression for the change in DC-side voltage.

[0061] The frequency domain expression of the active current reference value is determined by the inverter control framework based on the DC voltage loop circuit equation, i.e., formula (13). Based on the current loop circuit equation, i.e., formula (14), the frequency domain expression of the inverter output voltage in the rotating coordinate system can be obtained as follows:

[0062] (17)

[0063] (18)

[0064] in, and These are the frequency domain expressions for the d-axis and q-axis voltages of the inverter output, respectively. This is the equivalent transfer function of the DC voltage loop. This is the proportional coefficient of the DC voltage loop. The integral coefficient of the DC voltage loop. Let be the equivalent transfer function of the current loop. This is the proportionality coefficient of the current loop. is the integral coefficient of the current loop.

[0065] Steps 1-4: By performing an inverse Park transform on the frequency domain expression of the modulation signal in the rotating coordinate system of the grid-connected inverter, the frequency domain expression of the grid-connected inverter output voltage, including the fundamental component, positive-sequence disturbance component, and negative-sequence coupling component, is obtained in the stationary coordinate system.

[0066] In steps 1-4, the inverse Park transformation can be used to obtain the fundamental component with a frequency of 50Hz and the component with a frequency of [missing information] in the stationary coordinate system, considering the frequency coupling effect of the grid-connected inverter. The positive-sequence perturbation components and frequencies are The frequency domain expression for the inverter output voltage of the negative-sequence coupled component is as follows:

[0067] Since the system is three-phase symmetrical, the inverter output impedance can be obtained from the single-phase voltage and current at the grid connection point. The inverter's phase a output voltage in the time domain is:

[0068] (19)

[0069] in, Let be the time-domain expression for the output voltage of phase a of the inverter. Let be the time-domain expression for the d-axis output voltage in the inverter's rotating coordinate system. This is the time-domain expression for the q-axis output voltage in the inverter's rotating coordinate system.

[0070] Therefore, the output voltage of phase a in the inverter frequency domain is:

[0071] (20)

[0072] in, Let be the frequency domain expression for the output voltage of phase a of the grid-connected inverter. Indicates the signal The result of performing the Fourier transform, Indicates the signal The result of performing the Fourier transform, express The frequency domain expression is The Fourier transform result, express The frequency domain expression is The Fourier transform result, Representing the frequency difference, it describes the frequency shift relationship in frequency domain convolution, derived from the Fourier transform property that multiplication in the frequency domain corresponds to convolution in the time domain. This represents the frequency variable used for integration in convolution operations.

[0073] Steps 1-5: Based on the main circuit equations, the relationship between the grid-connected point voltage and current in the stationary coordinate system is obtained, thus deriving the positive and negative sequence impedance matrix of the grid-connected inverter. The specific process is as follows:

[0074] Depend on Figure 1 From the main circuit diagram, we know that the inverter output voltage is equal to the sum of the grid connection point voltage and the voltage drop across the L-type filter. Therefore, in steps 1-5, the relationship between the inverter output voltage and the grid connection point voltage, i.e., the main circuit equation, is:

[0075] (twenty one)

[0076] in, Let be the frequency domain expression for the output voltage of phase a of the grid-connected inverter. For the Laplace operator, for Figure 1 The filter inductor of the L-type filter in the diagram. Here is the frequency domain expression for the phase current at grid connection point a. Let be the frequency domain expression of the phase voltage at grid connection point a.

[0077] Because the output voltage frequency of the grid-connected inverter is The positive sequence components and frequencies are The negative sequence component can be represented by the positive sequence and negative sequence components of the grid connection point voltage and current. , , and Therefore, the relationship between the positive and negative sequence components of the grid connection point voltage and current can be obtained:

[0078] (twenty two)

[0079] in, This is the inverter output impedance matrix. , , and These are the elements of the inverter output impedance matrix.

[0080] Step 2: Establish the grid positive and negative sequence impedance model. Based on the grid positive and negative sequence impedance and the grid-connected inverter impedance matrix, construct the single-input single-output impedance expression for the grid-connected inverter. This single-input single-output impedance expression is the equivalent positive and negative sequence impedance expression for the grid-connected inverter. The Nyquist criterion (e.g., a generalized Nyquist criterion) is used to determine the stability of the ratio of the grid impedance to the equivalent positive and negative sequence impedance of the grid-connected inverter, thus obtaining the impact of reactive power magnitude on the full-frequency stability of the grid-connected inverter. As the amplitude of the reactive current output by the grid-connected inverter increases, the stability of the grid-connected inverter improves in both the low-frequency and mid-to-high-frequency bands.

[0081] Step 2 includes:

[0082] Step 2-1: Establish the positive and negative sequence impedance model of the power grid based on the impedance from the grid connection point to the power grid. The specific process is as follows:

[0083] The positive and negative sequence impedances of the power grid can be obtained from the impedance from the grid connection point to the power grid. , They are respectively:

[0084] (twenty three)

[0085] in, This is the positive sequence impedance of the power grid. For the negative sequence impedance of the power grid, For the mains inductance, For the Laplace operator.

[0086] Step 2-2 involves equivalently incorporating the coupling terms between the positive and negative sequence components of the grid-connected inverter impedance matrix into the output impedance. This allows the positive and negative sequence impedance matrix of the grid-connected inverter to be represented as a single-input, single-output impedance expression for the inverter during stability analysis, thus yielding the equivalent positive and negative sequence impedance expressions for the grid-connected inverter. For a grid-connected inverter considering frequency coupling characteristics, a voltage excitation not only generates a current response at the same frequency but also a response current at a different frequency, causing the inverter to exhibit single-input, dual-output characteristics. Due to the grid impedance, the two response currents generate two grid-connected point disturbance voltages at different frequencies, further impacting the inverter and causing these two frequency components to couple with each other, making the stability criterion analysis more complex.

[0087] The specific process is as follows:

[0088] The output admittance matrix of a grid-connected inverter can be obtained by inverting the impedance matrix:

[0089] (twenty four)

[0090] in, , , and These are the elements of the inverter output impedance matrix, where , , and It can be obtained by inverting the impedance matrix.

[0091] The positive and negative sequence admittances of the grid-connected inverter after decoupling are:

[0092] (25)

[0093] (26)

[0094] in, This is the equivalent positive-sequence output admittance of the grid-connected inverter. This is the equivalent negative sequence output admittance of the grid-connected inverter.

[0095] Steps 2-3: The positive and negative sequence impedances of the grid-connected inverter change with the reactive power command value. Based on the logarithmic Nyquist curve of the ratio of the grid impedance to the equivalent positive and negative sequence impedances of the grid-connected inverter, the influence of reactive power on the inverter's stability across the entire frequency band can be obtained. As the amplitude of the reactive current output by the grid-connected inverter increases, the stability of the low-frequency and mid-to-high-frequency bands of the grid-connected inverter improves. The specific process is as follows:

[0096] If and only if the ratio of the positive and negative sequence components of the grid impedance to the output impedance of the grid-connected inverter is greater than or equal to the value of the positive and negative sequence components of the grid impedance, then the value of the positive and negative sequence components of the grid impedance is greater than or equal to the value of the negative sequence components of the grid impedance. and When both the Nyquist criterion and the grid-connected inverter's interaction with the grid are satisfied, the system is stable. Furthermore, the stability margin of the grid-connected system can be determined using the logarithmic Nyquist curve of the system's positive and negative sequence impedance ratios. The gain margin is the difference between the amplitude-frequency response curve and 0 dB at the frequency where the phase-frequency response curve intersects with -180°. The phase margin is the difference between the amplitude-frequency response curve and -180° at the frequency where the amplitude-frequency response curve intersects with 0 dB. To obtain satisfactory performance, the phase margin should be between 30° and 60°, and the gain margin should be greater than 6 dB. For systems with these margins, stability can be guaranteed even if parameters vary within a certain range.

[0097] Figure 3 This is a schematic diagram illustrating the influence of reactive current command values ​​on stability across different frequency bands, as provided in an embodiment of the present invention. The reactive current command value shows that as the reactive current command value increases from -10A to -40A, the stability of the power grid interaction system in both the low-frequency and mid-to-high-frequency bands improves.

[0098] Step 3: Optimize the reactive current command value of the grid-connected inverter based on the impact of reactive power on the stability of the grid-connected inverter across the entire frequency band, so as to improve the wideband stability of the grid-connected inverter under extremely weak power grid conditions.

[0099] Step 3-1: Based on the logarithmic Nyquist curve of the ratio of the positive and negative sequence impedances of the grid and the equivalent positive and negative sequence impedances of the grid-connected inverter, determine the frequency band where the grid-connected inverter has an instability risk under the current operating conditions. Specifically, such as... Figure 3 As shown, Figure 3 In the figure, the frequency at the intersection of the phase frequency response curve and -180° is 130.5Hz. At this point, the difference between the amplitude frequency response curve and 0dB is close to 0, indicating that the system is at risk of instability. Figure 3 The amplitude-phase characteristic curve is the impedance ratio. In the upper part of the amplitude-frequency characteristic curve, the horizontal axis is f (frequency) in Hz (Hertz) and the vertical axis is the amplitude in dB (decibels). In the lower part of the phase-frequency characteristic curve, the horizontal axis is f (frequency) in Hz (Hertz) and the vertical axis is the phase in ° (degrees).

[0100] In step 3-1, if the amplitude-frequency characteristic curve of the ratio of the grid positive and negative sequence impedance to the grid-connected inverter's equivalent positive and negative sequence impedance is greater than or equal to zero at the frequency point corresponding to the intersection of the phase frequency characteristic curve and -180°, or the difference from zero is less than a preset first threshold (i.e., close to zero), or if the phase frequency characteristic curve of the ratio of the grid positive and negative sequence impedance to the grid-connected inverter's equivalent positive and negative sequence impedance is less than or equal to -180° at the frequency point corresponding to the intersection of the amplitude-frequency characteristic curve and the horizontal axis, or the difference from -180° is less than a preset second threshold (i.e., close to -180°), then the grid-connected inverter is at risk of instability.

[0101] Step 3-2: Based on the influence of reactive power on the stability of the grid-connected inverter across the entire frequency band and based on the operating point of the grid-connected inverter (the operating point of the inverter changes with the influence of reactive power on the stability of the inverter across the entire frequency band), optimize the reactive current command value of the inverter.

[0102] In step 3-2, under extremely weak power grid conditions, the grid-connected inverter needs to output a certain reactive current to improve the static output active power limit in order to suppress the low-frequency oscillation of the inverter under extremely weak power grid conditions. At the same time, if the grid-connected inverter has the risk of instability in the mid-to-high frequency range, it is necessary to increase the reactive current to improve the stability in the mid-to-high frequency range. However, excessive reactive current will cause the grid connection point voltage to exceed the limit range and increase the system power loss, which is not conducive to the economical grid-connected operation of the inverter. Therefore, the minimum reactive current that satisfies the inverter's low-frequency stability limit, mid-to-high frequency stability margin constraint and grid connection point voltage amplitude constraint is used as the reactive current command value for optimizing the inverter.

[0103] like Figure 3As shown, changes in reactive current alter the system's stability margin. To achieve better performance and ensure stable system operation even when parameters vary within a certain range, the phase margin γ and gain margin h of the optimized reactive current command value should satisfy the following constraints:

[0104] (27)

[0105] (28)

[0106] in, The cutoff frequency of the system. The system's crossover frequency, This is the equivalent positive-sequence admittance of the inverter at the cutoff frequency. Let be the positive-sequence impedance of the power grid at the cutoff frequency. This is the equivalent positive-sequence admittance of the inverter at the cross-frequency. Let be the positive sequence impedance of the power grid at the crossing frequency, and be the phase of the impedance ratio at the crossing frequency.

[0107] The reactive current also needs to meet the static stability limit constraint, and the minimum reactive current value. The following relationship needs to be satisfied:

[0108] (29)

[0109] in, This is the DC-side input power. For grid impedance, For the mains inductance, This represents the voltage amplitude of the power grid.

[0110] According to national standards, the per-unit value of the grid connection point voltage The following constraints need to be met:

[0111] (30)

[0112] The optimized reactive current command value can be obtained by combining the constraints of equations (27), (28), (29) and (30) above. Therefore, the corresponding operating point is calculated by the minimum reactive current that satisfies the low-frequency stability limit and medium-to-high-frequency stability margin constraints of the inverter. If the grid connection point voltage amplitude constraint is satisfied, the minimum reactive current can be used as the optimized reactive current command value.

[0113] Step 3-3: Based on the reactive current command value, control the inverter output reactive power through the reactive current loop to improve the stability of the grid-connected inverter.

[0114] In step 3-3, the optimized reactive current command value is used as the given reference value of the reactive current loop. The actual reactive current output by the grid-connected inverter is obtained by sampling, the error between the two is calculated, and the error signal is input to the reactive current loop controller to obtain the reactive voltage compensation amount. Combined with the feedforward decoupling term, the final reactive voltage command value is generated. The inverter output voltage and output reactive power are controlled by coordinate inverse transformation.

[0115] Figure 4 The diagram illustrates the d-axis voltage waveform at the grid connection point before optimization and the Fourier analysis results provided in this embodiment of the invention. Figure 4 As shown, the voltage waveform before optimization is divergent, the system is unstable, and the oscillation frequency is around 125Hz, which is consistent with the sequence impedance analysis results.

[0116] Figure 5 The diagram illustrates the d-axis voltage waveform and Fourier analysis results at the grid connection point after optimizing the reactive current command value, as provided in this embodiment of the invention. Figure 5 As shown, the voltage waveform converges and the system stabilizes after adopting the optimized reactive current command value. Within the same time period after being disturbed, the 125Hz harmonic content after using the method described in this embodiment is only 0.007%, far less than the 3.8% before optimization, verifying the stability improvement effect and effectiveness of the method described in this embodiment. Unlike existing technologies, the technical solution provided in this embodiment only requires adjusting the inverter's reactive current command value to effectively improve the stability of the inverter in the mid-to-high frequency band under extremely weak power grids.

[0117] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0118] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0119] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. A method for improving the stability of a grid-connected inverter across the entire frequency band based on a sequence impedance model, characterized in that, The method includes: Step 1: Obtain the grid-connected inverter impedance matrix through sequence impedance modeling; Step 2: Establish the positive and negative sequence impedance model of the power grid. Based on the positive and negative sequence impedance of the power grid and the impedance matrix of the grid-connected inverter, construct the single-input single-output impedance expression of the grid-connected inverter. This single-input single-output impedance expression is the equivalent positive and negative sequence impedance expression of the grid-connected inverter. The Nyquist criterion is used to determine the stability of the ratio of the power grid impedance to the equivalent positive and negative sequence impedance of the grid-connected inverter, and the influence of the reactive power on the stability of the grid-connected inverter across the entire frequency band is obtained. Step 3: Optimize the reactive current command value of the grid-connected inverter based on the impact of reactive power magnitude on the stability of the grid-connected inverter across the entire frequency band.

2. The method for improving the stability of a grid-connected inverter across the entire frequency band based on a sequence impedance model according to claim 1, characterized in that, Step 1 includes: Step 1-1: In the stationary coordinate system of the sampling stage, establish the frequency domain expression of the three-phase voltage and current at the grid connection point, including the fundamental component, the positive-sequence disturbance component, and the negative-sequence coupling component. Steps 1-2: Based on the influence of disturbance components on the phase angle and coordinate transformation of the phase-locked loop output, the frequency domain expression of the grid connection point voltage and current in the rotating coordinate system is obtained. Steps 1-3 involve substituting the output active power in the frequency domain into the dynamic equations of the DC side of the grid-connected inverter to obtain the change in the input DC voltage of the DC voltage loop. The frequency domain expression of the active current reference value is determined based on the DC voltage loop circuit equation, and the frequency domain expression of the modulation signal in the rotating coordinate system of the grid-connected inverter is determined based on the current loop circuit equation. Steps 1-4: By performing an inverse Park transform on the frequency domain expression of the modulation signal in the rotating coordinate system of the grid-connected inverter, the frequency domain expression of the grid-connected inverter output voltage, including the fundamental component, positive-sequence disturbance component, and negative-sequence coupling component, considering the frequency coupling effect of the grid-connected inverter, is obtained in the stationary coordinate system. Steps 1-5: Based on the main circuit equations, the relationship between the grid-connected point voltage and current in the stationary coordinate system is obtained, so as to obtain the positive and negative sequence impedance matrix of the grid-connected inverter.

3. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 2, characterized in that, In steps 1-3, the DC voltage loop circuit equation is: ； in, This is the active current reference value. DC side voltage This is the DC voltage reference value. This is the transfer function for the DC voltage loop.

4. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 3, characterized in that, In steps 1-3, the current loop circuit equation is: ； in, This is the active current reference value. Active current, The current loop transfer function, The fundamental angular frequency, For filtering inductors, It is reactive current. For the Laplace operator, This is the output angular frequency of the phase-locked loop. This is the reference value for reactive current.

5. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 4, characterized in that, In steps 1-5, the main circuit equation is: ； in, Let be the frequency domain expression for the output voltage of phase a of the grid-connected inverter. For the Laplace operator, For filter inductance, Here is the frequency domain expression for the phase current at grid connection point a. Let be the frequency domain expression of the phase voltage at grid connection point a.

6. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 2, characterized in that, Step 2 includes: Step 2-1: Establish the positive and negative sequence impedance model of the power grid based on the impedance from the grid connection point to the power grid; Step 2-2: The influence of the coupling terms between the positive and negative sequence components in the impedance matrix of the grid-connected inverter is equivalently converted into the output impedance. In order to make the positive and negative sequence impedance matrix of the grid-connected inverter equivalent to the single-input single-output impedance expression of the grid-connected inverter when performing stability analysis, the equivalent positive and negative sequence impedance expressions of the grid-connected inverter are obtained respectively. Steps 2-3: Based on the logarithmic Nyquist curve of the ratio of the positive and negative sequence impedance of the grid to the equivalent positive and negative sequence impedance of the grid-connected inverter, the influence of reactive power on the stability of the inverter across the entire frequency band is obtained.

7. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 6, characterized in that, Step 3 includes: Step 3-1: Determine the frequency band where the grid-connected inverter has an instability risk under the current operating conditions based on the logarithmic Nyquist curve of the ratio of the positive and negative sequence impedances of the power grid and the equivalent positive and negative sequence impedances of the grid-connected inverter. Step 3-2: Based on the influence of the reactive power magnitude on the stability of the grid-connected inverter across the entire frequency band and based on the operating point of the grid-connected inverter, optimize the reactive current command value of the inverter. Step 3-3: Based on the reactive current command value, control the inverter to output reactive power through the reactive current loop to improve the stability of the grid-connected inverter.

8. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 7, characterized in that, In step 3-1, if the amplitude-frequency characteristic curve of the ratio of the positive and negative sequence impedance of the grid to the equivalent positive and negative sequence impedance of the grid-connected inverter is greater than or equal to zero at the frequency point corresponding to the intersection of the phase-frequency characteristic curve and -180°, or the difference from zero is less than a preset first threshold, or if the phase-frequency characteristic curve of the ratio of the positive and negative sequence impedance of the grid to the equivalent positive and negative sequence impedance of the grid-connected inverter is less than or equal to -180° at the frequency point corresponding to the intersection of the amplitude-frequency characteristic curve and the horizontal axis, or the difference from -180° is less than a preset second threshold, then the grid-connected inverter is at risk of instability.

9. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 8, characterized in that, In step 3-2, the minimum reactive current that satisfies the inverter's low-frequency stability limit, mid-to-high frequency stability margin constraint, and grid connection point voltage amplitude constraint is used as the reactive current command value for optimizing the inverter.

10. The method for improving the stability of grid-connected inverters across the entire frequency band based on the sequence impedance model according to claim 9, characterized in that, In step 3-3, the optimized reactive current command value is used as the given reference value of the reactive current loop. The actual reactive current output by the grid-connected inverter is obtained by sampling, the error between the two is calculated, and the error signal is input to the reactive current loop controller to obtain the reactive voltage compensation amount. Combined with the feedforward decoupling term, the final reactive voltage command value is generated. The inverter output voltage and output reactive power are controlled by coordinate inverse transformation.

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