A Simplified Modeling Method for Inverter Sequence Admittance Considering the Frequency Coupling Effect between AC and DC and the Frequency Coupling Effect on the AC Side

Abstract

The present invention discloses a simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side, belonging to the technical field of distributed new energy grid-connected power generation. First, determine the main circuit filter type and control structure of a three-phase inverter grid-connected system. Based on the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side, obtain the time-domain expressions and frequency-domain expressions of the AC and DC side voltages and currents; establish a DC voltage outer-loop control model according to the DC side dynamic control strategy; establish an AC current inner-loop control model considering the small disturbance of the phase-locked loop, and obtain the sequence admittance model of the inverter with various frequency coupling effects. The present invention can accurately establish a sequence admittance model considering various frequency coupling effects, simplify the derivation process, reduce the computational complexity, and comprehensively analyze the impact of inverter access on the stability of the AC power grid.

Description

Technical Field

[0001] The present invention belongs to the technical field of distributed new energy grid-connected power generation, and particularly relates to a simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side. Background Art

[0002] In order to solve the fossil energy crisis and promote energy transformation, distributed generation technology has developed rapidly. During the process of renewable energy access and the re-electrification of the load side, a large number of equipment with different characteristics such as photovoltaic power sources, loads, and energy storage are connected to the grid through inverters. The connection of these equipment has changed the grid structure from the traditional unidirectional flow of source-grid-load to a bidirectional flow. The wide-band characteristics of its control system are more likely to inject negative damping in different frequency bands into the system, thus bringing a series of stability problems. Therefore, it is necessary to accurately model the impedance characteristics of the inverter system for subsequent stability analysis.

[0003] Generally speaking, most of the current impedance modeling of inverters regards the voltage-stabilizing capacitor on the DC side as infinite, believing that there are no small disturbances on the DC side, and only considering the frequency coupling characteristics of the AC side port. However, with the continuous development of power electronics technology, the number of grid-connected micro-source inverters such as photovoltaic and energy storage has increased, resulting in an increasing dynamic complexity on the DC side of the grid-connected system. At the same time, the multi-port characteristics of the inverter itself make the frequency coupling effect between the AC and DC sides impossible to be ignored. Existing literature has considered the frequency coupling effect between the AC and DC sides by performing an order-raising process on the traditional second-order admittance matrix, but this model cannot be applied to the stability analysis of a multi-inverter grid-connected system.

[0004] Existing research rarely considers the dynamic control characteristics of the micro-source on the DC side and the accurate propagation path of DC side disturbances. And with the refinement of modeling, when considering the frequency coupling characteristics and complex control strategies of the inverter, the modeling process becomes more and more complex, specifically manifested in that the parameters need to be subjected to multiple coordinate transformations during modeling and the expressions of each parameter are lengthy, which is not conducive to operation and popularization. Therefore, in the case of considering multiple frequency coupling effects, there is a lack of a simple method for establishing an accurate model of the inverter. Summary of the Invention

[0005] The present invention aims to provide a simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side.

[0006] To achieve the above object, the technical solution of the present invention is:

[0007] A simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side, comprising the following steps:

[0008] Step S1, determine the main circuit filter type and control structure of the three-phase inverter grid-connected system;

[0009] Step S2, based on the AC-DC frequency coupling effect and the AC-side frequency coupling effect, obtain the time-domain expressions and frequency-domain expressions of the AC-DC side voltages and currents;

[0010] Step S3, establish a DC voltage outer-loop control model according to the DC-side dynamic control strategy;

[0011] Step S4, considering the small disturbance of the phase-locked loop, establish an AC current inner-loop control model to obtain the frequency-domain expressions of the grid-connected voltage and grid-connected current;

[0012] Step S5, according to the convolution characteristics of each component, use the simplified modeling method based on the superposition theorem to obtain the inverter sequence admittance models of various frequency coupling effects;

[0013] Step S6, based on the inverter sequence admittance models of the various frequency coupling effects, derive the positive and negative sequence admittance models after equivalent decoupling of the single-inverter system;

[0014] Step S7, based on the positive and negative sequence admittance models after equivalent decoupling of the single-inverter system, derive the positive and negative sequence admittance models of the multi-inverter, and establish the stability criterion of the multi-inverter grid-connected system.

[0015] Furthermore, in step S1, the outer loop of the inverter grid-connected system adopts DC voltage control, and the inner loop of the inverter grid-connected system adopts grid current and capacitor current control; the inverter is connected to the grid connection point through an LCL filter and then connected to the grid through the grid impedance.

[0016] Furthermore, in step S2, a The grid-connected voltage of the phase , grid-connected current and capacitor current The time-domain expressions are:

[0017]

[0018]

[0019]

[0020] Among them, U g1 , U p , U po respectively represent the amplitudes of the fundamental frequency component, disturbance component and coupling component of the grid-connected voltage; φ p ,φ po respectively represent the phases of the disturbance component and the coupling component of the grid-connected voltage; I g1 and I p and I po respectively represent the amplitudes of the fundamental frequency component, the disturbance component, and the coupling component of the grid-connected current; φ i1 , φ ip , φ ipo respectively represent the phases of the fundamental frequency component, the disturbance component, and the coupling component of the grid-connected current; I c1 and I cp and I cpo respectively represent the amplitudes of the fundamental frequency component, the disturbance component, and the coupling component of the capacitor current, φ ic1 , φ icp , φ icpo respectively represent the phases of the fundamental frequency component, the disturbance component, and the coupling component of the capacitor current; f p and f po respectively represent the frequencies of the disturbance component and the coupling component of the grid connection point, which satisfy f po = f p - 2 f 1, f 1 is the fundamental frequency;

[0021] the grid-connected voltage u ga , the grid-connected current i ga and the capacitor current i ca after Fourier transform, the corresponding frequency-domain expressions are , and :

[0022]

[0023]

[0024]

[0025] where ;

[0026] , ;

[0027] ;

[0028] The DC side includes a DC steady-state component and a coupling component with a frequency of f p - f 1. The DC voltage and DC current in the time domain are expressed as:

[0029]

[0030]

[0031] where U dc , U dcpo are respectively the fundamental frequency component and the disturbance component of the capacitor voltage on the DC side; φ dcpo is the phase of the disturbance component of the capacitor voltage on the DC side; I pvdc , I pvdcpo are respectively the amplitudes of the fundamental frequency component and the coupling component of the input current on the DC side; φ dcipo is the phase of the input coupling component on the DC side; is the frequency of the disturbance component on the DC side, satisfying f dcpo = f p - f 1;

[0032] The DC voltage and the DC current are Fourier-transformed to obtain the corresponding frequency-domain expressions , as:

[0033]

[0034]

[0035] where .

[0036] Furthermore, in step S3, the dynamic control strategy of the DC side is the MPPT dynamic control of the micro-source, and there is a bus voltage disturbance component on the DC side ; If the input power of the micro-source is fixed, there is an input current disturbance component on the DC side ; The bus voltage disturbance component and the input current disturbance component have the following relationship:

[0037]

[0038] Among them, K is the ratio of the output voltage to the output current at the operating power point under a specific time section;

[0039] According to the grid-connected voltage and the grid-connected current the AC-side output voltage and output current of the inverter can be obtained as:

[0040]

[0041] Among them, L f = L 1 + L 2, L 1, L 2 are respectively the inductor on the inverter side and the inductor on the grid side of the LCL filter; According to the law of conservation of energy, the bus voltage disturbance component on the DC side is obtained as:

[0042]

[0043] Among them,

[0044]

[0045] Among them, s p1 =± ( j 2 πf p -j 2 πf 1 ) s p =±j 2 πf p , s p2 =± ( j 2 πf p -j 4 πf 1), s 1 =± 2 πf 1 ; The arm voltage of the inverter U ina at a frequency ±f 1 has a steady-state value of V il , and its conjugate value is V * il ; The arm current of the inverter I ina at a frequency ±f 1 has a steady-state value of I il , and its conjugate value is I * il .

[0046] Furthermore, in step S4, a synchronous reference frame phase-locked loop is selected to obtain the phase angle required for the Park coordinate transformation . When small disturbances are not considered, the phase angle corresponding to the fundamental frequency f 1 is , satisfying ; When the small disturbance of the output phase angle of the phase-locked loop is , the output phase angle of the phase-locked loop satisfies ;

[0047] In the steady state, through the phase angle component transformation of the phase-locked loop, the frequency-domain expressions of the grid-connected voltage, the grid-connected current, and the capacitor current , , are:

[0048]

[0049]

[0050]

[0051] Then, the frequency components dq on the , axis of the grid-connected voltage after the phase angle component transformation are expressed as:

[0052]

[0053]

[0054] The voltage disturbance signal on the DC side will be transmitted to the AC side through the DC voltage outer loop and PWM. H v ( s ) is the transfer function of the PI control of the DC voltage outer loop, that is H v ( s ) = K pdc + K idc / s ; H i ( s ) is the transfer function of the PI control of the grid current inner loop, that is H i ( s ) = K p + K i / s , then the frequency-domain expression of the voltage modulation component on the dq axis , is:

[0055]

[0056]

[0057] where D 0 and Q 0 are the steady-state values of the dq axis components of the leg voltage, and there is:

[0058]

[0059] Further, in step S5, in the frequency domain, the voltage modulation component on the dq axis includes a steady-state component without small disturbances and , dq axis grid-connected current and capacitor current disturbance components and , small-signal components introduced into the AC side after considering the DC side dynamics and ; the steady-state component without small disturbances and the small-signal components introduced into the AC side after considering the DC side dynamics contain fewer disturbance vectors; the dq axis grid-connected current and capacitor current disturbance components contain many disturbance vectors, and the dq axis component signs have incomplete symmetry;

[0060] Thedq The voltage modulation component of the shaft can be expressed as:

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] Wherein,

[0068]

[0069] The corresponding abc Components in the coordinate system are:

[0070]

[0071]

[0072]

[0073] According to the superposition theorem, the expression of the main circuit of the inverter is:

[0074]

[0075]

[0076] The expression of the second-order admittance matrix of the inverter can be obtained as:

[0077]

[0078] Wherein, Y 11 , Y 12 , Y 21 , Y 22 Are the admittance elements of the second-order admittance matrix.

[0079] Furthermore, in the step S6, the equivalent positive-sequence impedance Of the single inverter is:

[0080]

[0081] The equivalent negative-sequence impedance of the single inverter is:

[0082] .

[0083] Connect m in parallel several inverters with the same model parameters to the grid. Then, for the j th inverter, the expressions of the equivalent controlled sources and satisfy the following relationship:

[0084]

[0085] It can be deduced that m the positive and negative sequence aggregated impedances , of the parallel power generation system of several inverters are expressed as:

[0086]

[0087]

[0088] Then, the system admittance Y re seen from a grid-connected inverter satisfies the following relationship:

[0089]

[0090] where Z cline is the line impedance from each inverter to the grid connection point, and Z load is the load impedance.

[0091] Furthermore, in step S7, when multiple inverters form a multi-inverter grid-connected system, the stability criterion for the multi-inverter grid-connected system considering various frequency coupling effects is that the ratios of the equivalent grid impedance to the positive and negative sequence impedances of the inverter ( Z cline / m + Z load ) / Z scp and ( Z cline / m + Z load ) / Z scn both satisfy the Nyquist criterion, and the multi-inverter grid-connected system is stable.

[0092] Beneficial effects: The proposed simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side can accurately establish a sequence admittance model considering various frequency coupling effects, greatly simplify the derivation process and reduce the computational complexity, comprehensively analyze the impact of inverter connection on the stability of the AC power grid, and has strong applicability.

[0093] To make the above features and advantages of the invention more obvious and understandable, specific embodiments are hereinafter given and described in detail in conjunction with the accompanying drawings. Brief Description of the Drawings

[0094] Figure 1 is the main circuit diagram of a three-phase LCL inverter grid-connected system.

[0095] Figure 2 is the inner and outer loop control block diagram of a three-phase LCL inverter.

[0096] Figure 3 is a schematic diagram of the measurement method of the grid-connected inverter admittance.

[0097] Figure 4 is the flow chart of the simplified modeling method for the inverter sequence admittance.

[0098] Figure 5 is the simulation verification diagram of each element of the inverter second-order admittance matrix. Detailed Embodiments

[0099] To make the objectives and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0100] The present invention proposes a simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side, including the following steps:

[0101] Step S1, determine the main circuit filter type and control structure of the three-phase inverter grid-connected system.

[0102] As Figure 1 shown is the main circuit diagram of a three-phase LCL inverter grid-connected system. In the three-phase LCL inverter grid-connected system, the inverter is connected to the point of common coupling (PCC) through an LCL filter and then connected to the AC distribution network through the grid impedance. As Figure 2As shown, the inverter is controlled by an inner AC current loop and an outer DC voltage loop; the grid current and the capacitor current form a dual-current inner loop, and the dual-current inner loop and the grid voltage constitute a full feed-forward structure; the weighted average of the output current and the grid-connected current of the inverter is used as the feedback value, which can effectively suppress resonance.

[0103] Step S2: Based on the AC-DC frequency coupling effect and the AC-side frequency coupling effect, obtain the time-domain and frequency-domain expressions of the AC-DC side voltage and current.

[0104] Considering the AC-side frequency coupling effect of the inverter, when injecting a perturbation component with frequency f p at the grid connection point, the grid-connected voltage a of phase , the grid-connected current and the capacitor current at the grid connection point of the AC side have the following time-domain expressions:

[0105]

[0106]

[0107]

[0108] Where U g1 , U p , U po respectively represent the amplitudes of the fundamental frequency component, the perturbation component and the coupling component of the grid-connected voltage; φ p , φ po respectively represent the phases of the perturbation component and the coupling component of the grid-connected voltage, and it is usually considered that the initial phase of the fundamental frequency component is 0; I g1 , I p , I po respectively represent the amplitudes of the fundamental frequency component, the perturbation component and the coupling component of the grid-connected current; φ i1 , φ ip , φ ipo are the phases of the fundamental frequency component, the perturbation component and the coupling component of the grid-connected current; I c1 , I cp , I cpo respectively represent the amplitudes of the fundamental frequency component, the perturbation component and the coupling component of the capacitor current,φ ic1 , φ icp , φ icpo represent the phases of the fundamental frequency component, disturbance component, and coupling component of the capacitive current respectively; f p and f po represent the frequencies of the disturbance component and coupling component at the grid connection point respectively, and they satisfy f po = f p -2 f 1.

[0109] Furthermore, the grid-connected voltage u ga , the grid-connected current i ga and the capacitive current i ca after Fourier transform, the corresponding frequency-domain expressions are , and :

[0110]

[0111]

[0112]

[0113] Among them, ;

[0114] , ;

[0115] ;

[0116] According to a , b , c the phase angle relationship among the three phases, the frequency-domain expressions of the grid-connected voltage, grid-connected current, and capacitive current at the grid connection point for phase b phase, c phase can be obtained, which will not be elaborated here one by one.

[0117] As a multi-port power device, the frequency coupling component on the AC side of the inverter will be transferred to the DC port under the action of coordinate transformation. Therefore, in addition to the DC steady-state component on the DC side, it also contains a coupling component with a frequency of f p - f 1. At this time, the DC voltage and DC current The time-domain expression of

[0118]

[0119]

[0120] is as follows: U dc , U dcpo are respectively the fundamental-frequency component and the disturbance component of the DC-side capacitor voltage; φ dcpo is the phase of the disturbance component of the DC-side capacitor voltage; f dcpo = f p - f 1 is the frequency of the disturbance component; I pvdc , I pvdcpo are respectively the amplitudes of the fundamental-frequency component and the coupling component of the DC-side input current; φ dcipo is the phase of the DC-side input coupling component; is the frequency of the disturbance component of the DC-side, satisfying f dcpo = f p - f 1.

[0121] Furthermore, the DC voltage and the DC current are Fourier-transformed to obtain the corresponding frequency-domain expressions , which are as follows:

[0122]

[0123]

[0124] wherein, .

[0125] Step S3: Establish a DC voltage outer-loop control model according to the DC-side dynamic control strategy.

[0126] The DC-side dynamic control strategy is the MPPT dynamic control of the micro-source. It can be considered that there is a bus voltage disturbance component on the DC side. Because the input power of the micro-source is fixed, there is an input current disturbance component on the DC side. The relationship between the two is as follows:

[0127]

[0128] Among them, K is the ratio of the output voltage to the output current corresponding to the operating power point at a specific time section.

[0129] More specifically, the DC-side power and the AC-side power The time-domain expressions and frequency-domain expressions are:

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] Among them, L 1, L 2 are respectively the inverter-side inductor and the grid-side inductor of the LCL filter.

[0136] The filter capacitor C The capacitor voltages and the capacitor currents Satisfy:

[0137]

[0138]

[0139] According to the grid-connected voltage and the grid-connected current The AC-side output voltage and the output current of the inverter can be obtained as:

[0140]

[0141] Among them, L f = L 1 + L 2, L 1, L 2 are respectively the inverter-side inductor and the grid-side inductor of the LCL filter.

[0142] According to the law of conservation of energy, it can be considered that the AC-side power and the DC-side power are equal, and the bus voltage disturbance component of the DC side is obtained as:

[0143]

[0144] Among them,

[0145]

[0146] Among them, s p1 =± ( j 2 πf p -j 2 πf 1 ), s p =±j 2 πf p , s p2 =± ( j 2 πf p -j 4 πf 1 ), s 1 =± 2 πf 1 ; The voltage of the inverter bridge arm U ina At the frequency ±f 1 The steady-state value is V il , and its conjugate value is V * il ; The current of the inverter bridge arm I ina At the frequency ±f 1 The steady-state value is I il , and its conjugate value is I * il .

[0147] Step S4, considering the small disturbance of the phase-locked loop, establish the inner loop control model of the AC current, and obtain the frequency-domain expressions of the grid-connected voltage and grid-connected current.

[0148] Refer to Figure 3 Schematic diagram of the measurement method of the grid-connected inverter admittance, select the synchronous reference frame phase-locked loop (SRF-PLL) to obtain the phase angle required for the Park coordinate transformation θ PLL , to achieve synchronization with the grid voltage. When small disturbances are not considered, the phase angle corresponding to the fundamental frequency f 1 is expressed as , satisfying ; When considering the small disturbance of the phase angle of the phase-locked loop output When the output angle satisfies ; Therefore, the coordinate transformation module can be To split, the splitting formula is:

[0149]

[0150] Furthermore, the expressions of grid voltage, grid current and capacitor current after the phase angle component transformation of the steady-state phase-locked loop are: , , for:

[0151]

[0152]

[0153]

[0154] Furthermore, considering the small perturbation of the phase angle Very small, grid-connected voltage dq Axis Component u gd , u gq , u gdu , u gqu The following relationship is satisfied in the time domain and frequency domain:

[0155]

[0156] Furthermore, in the steady state, the small perturbation of the phase angle is zero; in ( f p - f 1) and -( f p - f 1) At a frequency of for dq Axis Component u gq The transfer function of a small signal through a phase-locked loop is H PLL (s) income, including:

[0157]

[0158] Combining the above two equations, we can get:

[0159]

[0160] Then, the grid-connected voltage after considering the phase angle component transformation dq The frequency components of the d-axis are as follows:

[0161]

[0162]

[0163] Similarly, the grid-connected current and capacitor current dq The frequency components of the d-axis can be obtained.

[0164] The voltage disturbance signal on the DC side will be transmitted to the AC side through the DC voltage outer loop and PWM, H v ( s ) is the transfer function of the PI control of the DC voltage outer loop, that is H v ( s ) = K pdc + K idc / s ; H i ( s ) is the transfer function of the PI control of the grid current inner loop, that is H i ( s ) = K p + K i / s , then dq The frequency-domain expression of the voltage modulation component of the d-axis , is:

[0165]

[0166] Among them, D 0 and Q 0 are the steady-state values of the d-axis components of the leg voltage, respectively, and can be obtained according to the operation of the inverter main circuit at the steady-state operating point: dq

[0167]

[0168] Step S5: According to the convolution features of each component, use the simplified modeling method based on the superposition theorem to obtain the inverter sequence admittance model with multiple frequency coupling effects.

[0169] More specifically, referring to Figure 4 The flow chart of the simplified modeling method of the inverter sequence admittance shown, in the frequency domain, the dq The voltage modulation component of the d-axis includes the steady-state component without small disturbances​ , ; dq Perturbation components of the grid-connected current and capacitor current of the P-axis , ; Small-signal components introduced into the AC side after considering the DC side dynamics , . The steady-state components without small perturbations and the small-signal components introduced into the AC side after considering the DC side dynamics contain fewer perturbation vectors, and the convolution process is simple. dq The perturbation components of the grid-connected current and capacitor current of the P-axis contain many perturbation vectors, and due to dq the incomplete symmetry of the P-axis component signs, direct convolution would be very complex. In the frequency domain, dq the perturbation components of the grid-connected current and capacitor current of the P-axis are essentially obtained by performing a Park transformation on the abc phase current, and then performing another Park transformation to return to the abc αβ coordinate system. Therefore, their calculations can be directly expressed, and the voltage modulation components of each part dq on the P-axis can be expressed as:

[0170]

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] Where A and B are expressed as:

[0177]

[0178] According to the proposed simplified modeling method, the steady-state components without small perturbations transformed to the abc frequency-domain components in the αβ coordinate system can be directly written without calculation:

[0179]

[0180] In the frequency domain, dq the perturbation components of the grid-connected current and capacitor current of the P-axis can be obtained after one Park inverse transformation:

[0181]

[0182] The small-signal components introduced to the AC side after considering the DC-side dynamics After one Park inverse transformation, the following can be obtained:

[0183]

[0184] According to the superposition theorem, the expression of the main circuit of the inverter is:

[0185]

[0186]

[0187] The second-order admittance matrix expression of the output impedance model of the inverter considering the frequency coupling effect between AC and DC and the characteristics of the DC-side dynamic control strategy is:

[0188]

[0189] After arrangement, we have:

[0190]

[0191]

[0192] More specifically, the specific expressions of each parameter are:

[0193]

[0194]

[0195] Combining the above expressions, the admittance elements in the second-order admittance matrix of the inverter considering multiple frequency coupling effects can be derived Y 11 , Y 12 , Y 21 , Y 22 The expressions of:

[0196]

[0197]

[0198]

[0199]

[0200] Reference Figure 5The simulation verification diagram of each element of the second-order admittance matrix of the inverter shown. A time-domain simulation model of a three-phase photovoltaic grid-connected inverter is established using the PSCAD / EMTDC simulation software. By sweeping the frequency, the accuracy of the established inverter admittance model and the effectiveness of the proposed simplified modeling method are verified. It can be seen that the theoretical results are consistent with the simulation results, verifying the correctness of the model.

[0201] Step S6, based on the sequence admittance model of the inverter with multiple frequency coupling effects, the positive and negative sequence admittance models after equivalent decoupling of a single inverter are derived.

[0202] The sequence admittance model of the inverter considering multiple frequency coupling effects is equivalent decoupled, and the single-inverter system is equivalent to two subsystems of positive sequence and negative sequence. is the disturbance voltage source with the applied frequency of f p , is the reciprocal of the sum of the line impedance and the load impedance, and are the controlled current sources introduced by the positive and negative sequence coupling of the grid-following inverter, and satisfy the following relationship:

[0203]

[0204] Then the equivalent positive sequence impedance of a single inverter is:

[0205]

[0206] Similarly, the equivalent negative sequence impedance of a single inverter is:

[0207]

[0208] Step S7, based on the positive and negative sequence admittance models after equivalent decoupling of the single inverter, the positive and negative sequence admittance models of multiple inverters are derived, and the stability criterion of the multiple-inverter grid-connected system is established.

[0209] When m inverters with the same model parameters are grid-connected, then the expressions of the equivalent controlled sources j and of the th inverter satisfy the following relationship:

[0210]

[0211] It can be deduced that m the expressions of the positive and negative sequence aggregated impedances , of the

[0212]

[0213]

[0214] Then the system admittance seen by a certain grid-connected inverter looking outwards Y re Satisfies the following relationship:

[0215]

[0216] Wherein, Z cline Is the line impedance from each inverter to the grid connection point, Z load Is the load impedance.

[0217] Then the multi-inverter grid connection stability criterion considering various frequency coupling effects can be obtained as: the ratio of the equivalent grid impedance to the positive and negative sequence impedances of the inverter ( Z cline / m + Z load ) / Z scp And ( Z cline / m + Z load ) / Z scn Both satisfy the Nyquist criterion, and the multi-inverter grid connection system is stable.

[0218] A simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side proposed by the present invention can accurately establish a sequence admittance model considering various frequency coupling effects, greatly simplify the derivation process and reduce the computational complexity, and can comprehensively analyze the impact of inverter access on the stability of the AC power grid, with strong applicability.

[0219] Although the present invention has been disclosed as above by way of examples, it is not intended to limit the present invention. Any person with ordinary knowledge in the relevant technical field can make some modifications and refinements without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be subject to that defined by the appended patent application scope.

Claims

1. A simplified modeling method for the sequence admittance of an inverter considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side, characterized in that It includes the following steps: Step S1, determine the type of the main circuit filter and the control structure of the three-phase inverter grid-connected system; Step S2, based on the AC-DC frequency coupling effect and the AC-side frequency coupling effect, obtain the time-domain expressions and frequency-domain expressions of the AC-DC side voltages and currents; Step S3, establish a DC voltage outer-loop control model according to the DC-side dynamic control strategy; Step S4, considering the small disturbance of the phase-locked loop, establish an AC current inner-loop control model to obtain the frequency-domain expressions of the grid-connected voltage and grid-connected current; Step S5, according to the convolution characteristics of each component, use the simplified modeling method based on the superposition theorem to obtain the inverter sequence admittance model of various frequency coupling effects; Step S6, based on the inverter sequence admittance model of various frequency coupling effects, derive the positive and negative sequence admittance models after equivalent decoupling of the single-inverter system; Step S7, based on the positive and negative sequence admittance models after equivalent decoupling of the single-inverter system, derive the positive and negative sequence admittance models of the multi-inverter, and establish the stability criterion of the multi-inverter grid-connected system.

2. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side according to claim 1, wherein In the step S1, the outer loop of the inverter grid-connected system adopts DC voltage control, and the inner loop of the inverter grid-connected system adopts grid current and capacitor current control; the inverter is connected to the grid connection point through an LCL filter and then connected to the grid through the grid impedance.

3. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as described in claim 2, characterized in that In the step S2, a the grid-connected voltage of the phase , the grid-connected current and the capacitor current have the following time-domain expressions: Among them, U g1 , U p , U po respectively represent the amplitudes of the fundamental frequency component, disturbance component, and coupling component of the grid-connected voltage; φ p , φ po respectively represent the phases of the disturbance component and coupling component of the grid-connected voltage; I g1 , I p , I po respectively represent the amplitudes of the fundamental frequency component, disturbance component, and coupling component of the grid-connected current; φ i1 , φ ip , φ ipo respectively represent the phases of the fundamental frequency component, disturbance component, and coupling component of the grid-connected current; I c1 , I cp , I cpo respectively represent the amplitudes of the fundamental frequency component, disturbance component, and coupling component of the capacitor current, φ ic1 , φ icp , φ icpo respectively represent the phases of the fundamental frequency component, disturbance component, and coupling component of the capacitor current; f p and f po respectively represent the frequencies of the disturbance component and coupling component of the grid connection point, which satisfy f po = f p -2 f 1, f 1 is the fundamental frequency; The grid-connected voltage u ga , the grid-connected current i ga and the capacitor current i ca After Fourier transform, the corresponding frequency-domain expressions are , and : Among them, ; , ； ； The DC side includes a DC steady-state component and a coupling component with a frequency of f p - f 1. The time-domain expressions of the DC voltage and DC current of the DC side are as follows: Among them, U dc and U dcpo are respectively the fundamental frequency component and the disturbance component of the capacitor voltage on the DC side; φ dcpo is the phase of the disturbance component of the capacitor voltage on the DC side; I pvdc and I pvdcpo are respectively the amplitudes of the fundamental frequency component and the coupling component of the input current on the DC side; φ dcipo is the phase of the input coupling component on the DC side; is the frequency of the disturbance component on the DC side, satisfying f dcpo = f p - f 1; The DC voltage and the DC current are Fourier-transformed to obtain the corresponding frequency-domain expressions , which are as follows: Among them, .

4. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as claimed in claim 3, wherein In the step S3, the DC-side dynamic control strategy is the MPPT dynamic control of the micro-source, and there is a bus voltage disturbance component on the DC side. If the input power of the micro-source is fixed, there is an input current disturbance component on the DC side. The bus voltage disturbance component and the input current disturbance component have the following relationship: Among them, K is the ratio of the output voltage to the output current corresponding to the operating power point at a specific time section; According to the grid-connected voltage and the grid-connected current obtain the AC-side output voltage and output current of the inverter as follows: Among them, L f = L 1 + L 2, L 1, L 1 and 2 are respectively the inductor on the inverter side and the inductor on the grid side of the LCL filter; According to the law of conservation of energy, the bus voltage disturbance component of the DC side is obtained as follows: Wherein, Among them, s p1 =± ( j 2 πf p -j 2 πf 1 ), s p =±j 2 πf p , s p2 =± ( j 2 πf p -j 4 πf 1 ), s 1 =± 2 πf 1 ; The arm voltage of the inverter U ina At the frequency ±f 1 The steady-state value is V il , and its conjugate value is V * il ; The arm current of the inverter I ina At the frequency ±f 1 The steady-state value is I il , and its conjugate value is I * il .

5. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as described in claim 4, characterized in that, In the step S4, a synchronous reference frame phase-locked loop is selected to obtain the phase angle required for Park coordinate transformation , when small disturbances are not considered, the fundamental frequency f corresponding to 1 is the phase angle , satisfying ; When the small disturbance of the output phase angle of the phase-locked loop is , the output phase angle of the phase-locked loop satisfies ; Under steady-state conditions, through the phase angle component transformation of the phase-locked loop, the frequency-domain expressions of the grid-connected voltage, the grid-connected current, and the capacitor current are obtained , , are as follows: Then, for each frequency component of the dq axis of the grid-connected voltage after the phase angle component transformation , the expression is: The voltage disturbance signal on the DC side will be transmitted to the AC side through the DC voltage outer loop and PWM, H v ( s ) is the transfer function of the PI control of the DC voltage outer loop, that is, H v ( s ) = K pdc + K idc / s ; H i ( s ) is the transfer function of the PI control of the grid current inner loop, that is, H i ( s ) = K p + K i / s , then the frequency-domain expression of the voltage modulation component on the dq axis 、 is: Among them, D 0 and Q 0 are respectively the dq steady-state values of the axial components of the bridge arm voltage, and there is: 。 6. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as described in claim 5, characterized in that In the step S5, in the frequency domain, the dq voltage modulation component of the axis includes a steady-state component without small disturbances and dq the disturbance components of the grid-connected current and capacitor current of the axis, and the small-signal components introduced into the AC side after considering the DC-side dynamics; and the steady-state component without small disturbances and the small-signal components introduced into the AC side after considering the DC-side dynamics contain fewer disturbance vectors; the dq disturbance components of the grid-connected current and capacitor current of the dq axis contain many disturbance vectors, and the axis component signs have incomplete symmetry; The said dq The voltage modulation component of the shaft is expressed as: Wherein, Obtain the corresponding abc Components in the coordinate system are: According to the superposition theorem, the expression of the main circuit of the inverter is: Obtain the second-order admittance matrix expression of the inverter as: Among them, Y 11 , Y 12 , Y 21 , Y 22 are the admittance elements of the second-order admittance matrix.

7. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as described in claim 6, characterized in that, In the step S6, the equivalent positive sequence impedance of the single inverter is as follows: The equivalent negative-sequence impedance of the single inverter is as follows: 。 8. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as claimed in claim 7, wherein Connect m in parallel the inverters with the same model parameters, then the expressions of the equivalent controlled sources j and of the th inverter satisfy the following relationship: Obtained m Positive and negative sequence aggregation impedance of , The expression of is as follows: Then the system admittance seen by a certain grid-connected inverter looking outwards Y re satisfies the following relationship: Among them, Z cline is the line impedance from each inverter to the grid connection point, Z load is the load impedance.

9. The simplified modeling method of the inverter sequence admittance considering the frequency coupling effect between AC and DC and the frequency coupling effect on the AC side as claimed in claim 8, characterized in that In step S7, when multiple inverters form a multi-inverter grid-connected system, the stability criterion for the multi-inverter grid-connected system considering multiple frequency coupling effects is: the ratio of the equivalent grid impedance to the positive and negative sequence impedances of the inverter ( Z cline / m + Z load ) / Z scp and ( Z cline / m + Z load ) / Z scn both satisfy the Nyquist criterion, and the multi-inverter grid-connected system is stable.

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