Converter stability domain determination method based on amplitude phase isoline

Abstract

The invention provides a converter stability domain determination method based on an amplitude phase contour line. The method comprises the following steps: S1, drawing a Nyquist curve based on a loop gain transfer function of a converter and mapping the Nyquist curve to an amplitude-frequency plane and a phase-frequency plane; s2, converting the amplitude-frequency plane and the phase-frequency plane into an amplitude-phase isoline plane by considering the change of the short-circuit ratio; s3, an amplitude contour line and a phase contour line are drawn in the amplitude phase contour line plane, all intersecting points of the two contour lines are found out, auxiliary lines parallel to the axis are drawn in the amplitude phase contour line plane through the points, and the amplitude phase contour line plane is divided into a plurality of intervals through the auxiliary lines; s4, in the interval formed by the auxiliary lines, if any line parallel to the axis is in the range and has no intersection point, the system is stable in the power grid strength interval; otherwise, the system is unstable.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of converter control, and particularly relates to a method for determining a stable region of a converter based on amplitude-phase contour lines. BACKGROUND

[0002] Grid-connected inverter (GCI) is a key interface between renewable energy and power grid, and its performance directly determines the performance of the power generation system. At present, the mainstream GCIs generally use Si-based power devices (such as Si IGBT). However, Si-based devices face the inherent contradiction between device loss and switching frequency. Especially in high-power scenarios, in order to maximize the conversion efficiency, the switching frequency is usually limited to several kilohertz. Therefore, the harmonic content of the output current of the Si-based GCI is greatly increased, and the power quality is seriously deteriorated. To alleviate this contradiction, new wide-bandgap devices (such as SiC MOSFET) are expected to significantly improve the dynamic performance and output quality of GCI due to their low conduction loss and high switching speed. However, the cost of SiC devices increases rapidly with the current level. In addition, the voltage level and reliability of existing commercial SiC devices are still difficult to meet the requirements of MVA-level high-power scenarios, and multiple SiC modules are usually used in parallel to meet the capacity requirements. The large number of parallel units greatly increases the system complexity, and the system development cycle and cost increase significantly.

[0003] Under this background, Si / SiC hybrid switching frequency inverter (HSFI) provides a new technical path for breaking through the inherent limitations of single devices and balancing performance and cost. The typical structure of HSFI is composed of a large-power Si IGBT main unit (MU) and a small-power SiC MOSFET auxiliary unit (SU) in parallel, as shown in Figure 16 . Among them, the MU efficiently handles most of the load power at a low switching frequency, and the SU accurately compensates the low-frequency ripple of the main unit at a high switching frequency, thereby combining high capacity and low harmonic output characteristics.

[0004] Although HSFI has made significant progress in device configuration and control strategy design, its system-level grid-connected adaptability still lacks in-depth research. Especially in the context of high penetration of distributed generation, HSFI is often connected to the public grid through long-distance lines, and such systems usually exhibit weak grid characteristics, that is, the grid impedance cannot be ignored and has a large variation range. Existing literature has extensively studied the stability problems of traditional multi-inverter systems, such as internal stability analysis, GCI-grid interaction behavior modeling, heterogeneous inverter system coupling mechanism and collaborative operation optimization strategy, etc. However, the MU and SU in HSFI share a unified controller, and their control links are tightly coupled, making the response path of the system to grid disturbances more complex. There is still a lack of systematic evaluation of the stability of inverter systems under varying grid impedance. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a converter stability domain determination method based on amplitude-phase contour lines, to quantitatively evaluate the stability of the converter system under varying grid impedance.

[0006] To solve the above technical problems, the present application adopts the following technical method: a converter stability domain determination method based on amplitude-phase contour lines, comprising: Step S1, based on the loop gain transfer function of the converter, draw a Nyquist curve, and map the Nyquist curve to the amplitude-frequency plane and the phase-frequency plane; Step S2, considering the change of the system short-circuit ratio, convert the obtained amplitude-frequency plane and phase-frequency plane into a two-variable amplitude-phase contour plane; Step S3, draw the amplitude contour and the phase contour in the amplitude-phase contour plane, find all the intersection points of the two contours, and record the number of intersection points as N, where the nth intersection point is represented by the short-circuit ratio, n=1, 2…N, and the amplitude-phase contour plane is drawn through the points , , , , , , auxiliary lines parallel to the axis, which divide the amplitude-phase contour plane into multiple intervals; Step S4, determine the system stability domain according to the interval condition divided in step S3; In the interval composed of the auxiliary line and the auxiliary line : if any line parallel to the axis is within the range of , the system is stable; otherwise, the system is unstable.Neither of them has intersection point, which means the system is stable in the grid strength interval . Both of them are 0, which means the system is stable in the grid strength interval . Otherwise, the number of the encirclements of the point by the Nyquist curve in the grid strength interval , is at least one, which means the system is unstable in the grid strength interval .

[0007] Further, the converter is a HSFI.

[0008] Still further, the loop gain transfer function of the HSFI is determined by the following method: Step S101, determining the analytical function relationship between the system operating point variables and the grid strength by using short-circuit ratio; Step S102, determining the system equivalent output current and its complex conjugate expression according to the HSFI body output impedance and the AC grid equivalent impedance; Step S103, constructing the equivalent single-input single-output model of the HSFI system from the system equivalent output current and its complex conjugate expression, and obtaining the loop gain transfer function of the system.

[0009] Still further, the construction process of the HSFI body output impedance is as follows: 1) determining the current control strategy of the HSFI The system operates in direct parallel mode under weak grid, and the MU and the SU operate independently in peer-to-peer structure; the system operates in harmonic compensation mode under strong grid, the MU operates at low switching frequency, and the SU dynamically compensates the harmonics introduced by the MU and corrects the fundamental tracking error of the MU after filtering the high-frequency components of the output current of the MU through the filter inductance; the current control process of the system is as follows: calculating the voltage phase angle: collecting the PCC voltage of the system ; current control of the MU: setting the system output current reference value , collecting the output current of the MU ; calculating the current reference value of the MU according to the system output current reference value and the power distribution ratio ; comparing and and performing PI control to obtain the internal potential reference value of the MU After PWM processing, a pulse signal is generated to drive the MU switch tube to operate; (1) SU current control: total output current of the acquisition system and SU output current ; According to the system output current reference value Calculate the current reference value of SU ; When the system works in harmonic compensation mode, select the following formula (2) to calculate ,Compare and And perform PI control to obtain the internal potential reference value of SU ; When the system works in direct parallel mode, choose the following formula (3) to calculate ,Compare and And perform PI control to obtain the internal potential reference value of SU ;Will After PWM processing, a pulse signal is generated to drive the SU switch tube to operate; (2) (3) 2) Based on the system’s current control process, a small-signal model of the HSFI system in harmonic compensation mode is constructed to determine the overall frequency domain characteristics of the system in this mode, as shown in the following equation: (4) (5) (6) (7) (8) (9) Where, Small disturbance of system output current; and are the small disturbances of the output currents of MU and SU respectively; A small disturbance of the system output current reference value; is a small disturbance of the grid connection point voltage; for conjugation of; is the PI parameter of the MU current controller; is the delay value of MU; is the voltage feedforward coefficient of MU; is the system base frequency; is the filter inductance of MU; is the transfer function of the phase-locked loop; is the steady-state value of MU output current; is the steady-state value of the grid-connected point voltage; is the steady-state value of MU output voltage; is the filter impedance of MU; is the PI parameter of the SU current controller; is the delay value of SU; is the voltage feedforward coefficient of SU; is the filter inductance of SU; is the steady-state value of SU output current; is the steady-state value of SU output voltage; is the filter impedance of SU; 3) Based on the system’s current control process, a small-signal model of the HSFI system in direct parallel mode is constructed to determine the overall frequency domain characteristics of the system in this mode, as shown in the following equation: (10) (11) (12) (13) (14) 4) Based on the overall frequency domain characteristics of the HSFI system in harmonic compensation mode and direct parallel mode, the output impedance expression of the HSFI body is unified as follows: (15) in, represent or ; represent or ; represent or .

[0010] Preferably, the loop gain transfer function of the HSFI is for: (16) (17) (18) (19) Where, 、 、 They are 、 , the conjugate of the AC grid equivalent impedance; the AC grid filter capacitance impedance; the AC grid line impedance.

[0011] The amplitude-phase contour-based converter stability domain determination method provided by the application focuses on the converter operating point migration caused by the grid impedance variation, establishes a whole model of the converter grid-connected system containing the grid-side impedance, analyzes the stability boundary of the HSFI in two operating modes, and based on the complex vector impedance modeling method, the remodeling effect of the SU on the whole admittance characteristics of the system is determined, and the mode switching critical threshold is quantitatively evaluated in combination with the stability criterion based on the stability domain. Further, the application can depict the system stability boundary under the dynamic change of the grid strength, make up for the limitations of the traditional Nyquist criterion in multivariable analysis, quantitatively analyze the stability boundary of the converter grid-connected system in two operating modes, and provide a reliable critical standard for subsequent double-mode switching of the converter. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 Fig. 2 is a Nyquist curve trend chart of the HSFI system under different grid strengths (in the figure, (a) is a frequency domain characteristic chart of the HSFI system in the harmonic compensation mode; (b) is a frequency domain characteristic chart of the HSFI system in the direct parallel mode); Figure 2 Fig. 3 is a time domain simulation waveform chart of the HSFI system in two control modes under different grid strengths (in the figure, (a) is an output waveform chart of the HSFI system in the harmonic compensation mode; (b) is an output waveform chart of the HSFI system in the direct parallel mode); Figure 3 Fig. 4 is a mapping relationship chart of the Nyquist diagram and the amplitude-phase contour diagram (in the figure, (a) is a schematic diagram of four cases of the open-loop transfer function Nyquist diagram; (b) is a schematic diagram of the Nyquist curve in (a) mapped to the amplitude-frequency plane and the phase-frequency plane; (c) is a schematic diagram of the amplitude contour and the phase contour in (b) drawn in the plane); Figure 4 Fig. 5 is a flowchart of the amplitude-phase contour-based converter stability domain determination method involved in the application; Figure 5 Fig. 6 is a schematic diagram of the steady-state operating point migration trajectory of the HSFI system when the grid strength changes; Figure 6 ​​​​Schematic diagram of the control structure of HSFI in the present invention (in the figure, (a) is a schematic diagram of the current control structure in harmonic compensation mode; (b) is a schematic diagram of the current control structure in direct parallel mode); Figure 7 Schematic diagram of the overall small signal impedance model of HSFI in the present invention; Figure 8 Schematic diagram of the SISO model of HSFI in the present invention; Figure 9 Schematic diagram of amplitude and phase contours in Example 1 of the present invention; Figure 10 Graphs showing the amplitude and phase characteristics of HSFI in harmonic compensation mode according to Example 2 of the present invention ((a) shows the three-dimensional amplitude-frequency characteristic; (b) shows the three-dimensional phase-frequency characteristic; and (c) shows the amplitude and phase contours). Figure 11 Graphs showing the amplitude-phase characteristics of HSFI in direct parallel mode according to Example 3 of the present invention ((a) shows the three-dimensional amplitude-frequency characteristic; (b) shows the three-dimensional phase-frequency characteristic; and (c) shows the amplitude-phase contours). Figure 12 Schematic diagram of the stability region of the HSFI system in the output current-grid strength plane of the present invention; Figure 13 In the embodiment of the present invention The system output current waveform under different load conditions; Figure 14 In the embodiment of the present invention The system output current waveform under different load conditions; Figure 15 In the embodiment of the present invention The system output current waveform under different load conditions; Figure 16 This is the topology diagram of the Si and SiC mixed-frequency parallel inverter system. DETAILED DESCRIPTION

[0013] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0014] Before explaining the present invention, it is worth mentioning that based on the equivalent single-input single-output (SISO) model of the HSFI grid-connected system, the impact of grid strength changes on the frequency domain stability of the HSFI system is analyzed in detail. Figure 1 Shows the different grid strengths (i.e. short circuit ratio The Nyquist curve of the HSFI system is shown in Fig. 2. The system parameters are listed in Table 1.

[0015] Table 1. System parameters of the HSFI system .

[0016] With the increase of , the system stability in both operating modes decreases. However, due to the introduction of an additional feedback channel in the harmonic compensation mode, it is more sensitive to the change of grid strength. When decreases to 0.75 (extremely weak grid condition), the Nyquist curve in the harmonic compensation mode has surrounded the critical point , indicating that the system is unstable. In contrast, the system in the direct parallel mode remains stable, indicating that it has stronger adaptability to grid disturbances.

[0017] Figure 2 Further, time-domain simulation waveforms of the HSFI system in the two control modes under different grid strength conditions are shown, including the dynamic response of output current and output power. In the strong grid condition ( = 5) and the weak grid condition ( = 2 and = 1), the current and power responses in both modes tend to be stable, and the system presents good dynamic performance. However, in the extremely weak grid condition where decreases to 0.75, the output current in the harmonic compensation mode appears sustained divergent oscillation, and the power response also has obvious unstable fluctuations, indicating that the system is dynamically unstable; while in the direct parallel mode, although the system also appears short-term oscillation disturbance, it presents an asymptotic convergence stable trend overall. This phenomenon is consistent with the frequency-domain analysis result. Figure 1

[0018] The above results also show that the dynamic migration of the operating point significantly affects the system stability, and the method of drawing Nyquist curves point by point is not only inefficient, but also difficult to comprehensively cover all operating conditions. In addition, the traditional Nyquist stability criterion is applicable to the case where the grid strength is fixed, and it is difficult to depict the system stability under the change of two variables (frequency and grid strength). Therefore, the present application proposes a converter stability region criterion based on amplitude-phase contour lines, which comprehensively analyzes the stability boundary under the migration of the operating point by means of the distribution law of the contour lines on the plane.

[0019] In the single-variable case (fixed ), the stability of the loop gain can be judged by the Nyquist criterion. The sufficient and necessary condition for stability is: (20) ​Where Z is the number of closed-loop poles in the right half plane (RHP), P is the number of open-loop poles in the RHP, and N is Depend on Change to hour Counterclockwise around the point The net number of circles, and Respectively Counterclockwise and clockwise orbit points The open-loop transfer function Surround Point There are four situations, such as Figure 3 (a) In which, cases 1 and 2 are clockwise, and cases 3 and 4 are counterclockwise.

[0020] The Nyquist curve can be mapped to the amplitude-frequency plane and the phase-frequency plane, such as Figure 3 (b) is shown. The mapping relationship is as follows: (twenty one) in, and They are Observe the four typical surround situations and find that There is a mapping relationship between the Bode diagram and the Nyquist diagram as shown in Table 2. For Case 1 and Case 2, the clockwise rotation in the Nyquist plane is equivalent to Frequency region ( Figure 3 (b) The shaded area Crossing with a negative slope ( is an odd number). Similarly, for Cases 3 and 4, the counterclockwise rotation in the Nyquist plane is equivalent to Frequency region ( Figure 3 (b) The shaded area Crossing with a positive slope .

[0021] When considering When changes occur, the mapping relationship shown in formula (21) needs to be expanded into a two-variable function: (twenty two) Amplitude contours and phase contours Drawn on In the plane, such as Figure 3 (c) In the figure, the solid arrow indicates the direction of phase increase, which is point to .

[0022] For any specified , make a line through the point and with Axis-parallel directed auxiliary lines , whose direction is frequency Increase the direction. Through the auxiliary line The direction of crossing the red line defines the crossing type: (1) Crossing in the same direction: Auxiliary lines at the crossing point The direction is consistent with the phase increase direction, such as Figure 3 (c) as shown in cases 3 and 4; (2) Reverse crossing: Auxiliary line at the crossing point The direction is opposite to the phase increase direction, such as Figure 3 (c) is shown in cases 1 and 2.

[0023] Therefore, the number of turns can be determined by Auxiliary lines within the range Crossing The number of isolines is determined. The number of same-direction crossings and reverse-direction crossings are and , then the necessary and sufficient conditions for stability shown in formula (20) can be equivalently expressed as: (twenty three) Table 2 compares Figure 3 The morphological characteristics of Nyquist diagrams, Bode diagrams and amplitude-phase contour diagrams in different situations. It should be noted that the stability criterion based on amplitude and phase contours proposed in the present invention is the stability criterion of Nyquist criterion in The proposed method is a strict mapping within the plane, rather than a simple extension of the Bode plot to the three-dimensional region. Existing methods for stability analysis using Bode plots only consider the phase relationship at each crossover frequency, while ignoring the amplitude and phase derivatives. Therefore, the correct analysis results are only obtained for cases 2 or 3.

[0024] Table 2 Mapping relationship between Nyquist plot and amplitude-phase contour plot .

[0025] From the above, we can see that, focusing on the problem of converter operating point migration caused by grid impedance changes, an overall model of the converter grid-connected system including grid-side impedance is established. On this basis, a method for determining the converter stability domain based on amplitude-phase contours is proposed. This method can characterize the system stability boundary under dynamic changes in grid strength, making up for the limitations of the traditional Nyquist criterion in multivariable analysis. Furthermore, the stability boundary of the converter grid-connected system under two operating modes is quantitatively analyzed, and then the critical conditions for the subsequent dual-mode switching of the converter can be clarified, providing a theoretical basis for the design of the dual-mode switching strategy. Based on this,Figure 4 As shown, the application provides a converter stability domain determination method based on amplitude-phase contour lines, which specifically comprises the following four steps.

[0026] Step S1, draw a Nyquist curve based on the loop gain transfer function of the converter, and map the Nyquist curve to the amplitude-frequency plane and the phase-frequency plane.

[0027] Impedance / admittance method stability analysis usually needs to be based on a specific steady-state operating point. However, under the influence of high proportion of renewable energy access and high load uncertainty, the grid strength shows obvious time-varying characteristics, making it difficult for the converter grid-connected system to maintain a constant steady-state operating point. Therefore, the analytical mapping relationship between the grid strength and the system operating point is established, and the system modeling and stability analysis containing the operating point dynamic migration effect are carried out accordingly.

[0028] The converter in the application can be a GCI using Si-based power devices or new wide bandgap devices, or a HSFI using Si IGBT and SiC MOSFET hybrid frequency inverters. In the embodiment, when the converter is a HSFI, the loop gain transfer function of the HSFI is determined by the following method: Step S101, determine the analytical function relationship between the system operating point variable and the grid strength by using the short circuit ratio to represent the grid strength.

[0029] The grid strength is measured by the short circuit ratio (SCR), which is defined as the ratio of the AC side short circuit capacity P N to the rated capacity of the device P , denoted as . Considering a purely inductive grid line, the SCR is expressed as: (24) (25) where is the fundamental angular frequency of the grid; is the line inductance; U N is the rated voltage.

[0030] In a typical renewable energy grid-connected scenario, the inverter usually adopts the maximum power point tracking and voltage-oriented control strategy based on the phase-locked loop. Therefore, the PCC voltage U o and the output current I o only contain the active components U od and I od at steady state. Based on the power relationship, the grid voltage U g is expressed as a function of the PCC voltage and the output current: (26) where, is the AC grid line impedance.

[0031] In the time scale of current loop, the grid voltage amplitude U gm is considered as a constant, i.e., o (27) (28) where, is the steady-state value of grid voltage d-axis component; is the steady-state value of grid voltage q-axis component; By combining equations (26)-(28) and substituting into the SCR definition, the analytical function relationship between HSFI operating point variables and grid strength is obtained: (29) Figure 5 shows the migration trajectory of HSFI system steady-state operating point when the grid strength changes. As can be seen from the figure, as the grid strength increases (i.e. increases), increases, while decreases. This operating point migration effect poses a challenge to system stability and must be considered in dynamic modeling.

[0032] Step S102, according to the output impedance of the HSFI body and the equivalent impedance of the AC grid, the equivalent output current of the system and its complex conjugate expression are determined.

[0033] S1021, the output impedance of the HSFI body is determined.

[0034] 1) Determine the current control strategy of HSFI As shown in Figure 16 , the HSFI is composed of Si-based main variable current unit (Main Unit, MU) and SiC-based sub variable current unit (Sub Unit, SU), and the two are connected in parallel through inductance filters L1 and L2 to the point of common coupling (Point of Common Coupling, PCC). The total output current of the system is composed of the output current of MU and SU respectively and , that is .

[0035] ​According to the different control modes of MU and SU, HSFI has two typical operation modes: harmonic compensation mode and direct parallel mode. In practical application, the grid impedance is significantly fluctuated by many factors such as fault and grid-connected capacity, which leads to the significant change of grid strength in different scenarios. In order to enhance the grid adaptability of HSFI system, the application proposes to adopt direct parallel mode when the system is in weak grid, to suppress the influence of grid disturbance on system stability by reducing the coupling of control loop, and the basic principle of direct parallel mode is the same as that of traditional GCI, and MU and SU run independently in peer-to-peer structure. When the system is in strong grid, harmonic compensation mode is adopted to give full play to the advantages of HSFI in power quality and efficiency, and the core idea of harmonic compensation mode is to integrate the low cost and high current carrying capacity of Si device and the high frequency and high precision control ability of SiC device, to realize the collaborative optimization of system efficiency and power quality. Specifically: MU is used to bear the main load power: MU adopts Si IGBT device with low cost and high current carrying capacity, and bears most of the active power in the system. In order to reduce switching loss, it works at a low switching frequency; SU is used to improve the output current quality: SU adopts SiC MOSFET device with excellent switching characteristics, which is mainly used to compensate the low-frequency harmonic components introduced by MU in real time, so as to improve the total harmonic distortion performance of the output current. Since SU only bears a small amount of power, high-frequency operation has limited impact on the overall efficiency and cost of the system.

[0036] The above control mode not only improves the stable operation ability of the system in complex grid environment, but also builds a flexible control framework suitable for various scenarios.

[0037] The control target of HSFI system is to make the total output current accurately track its reference value , that is . In order to achieve this goal, HSFI adopts different control strategies in two operation modes, and the control structure is shown in Figure 6 . Among them, the alternating current grid is represented by the Thevenin equivalent circuit composed of voltage source and Z g in series; the output voltages of MU and SU are and .

[0038] In order to unify subsequent modeling and analysis, the power distribution ratio between MU and SU is defined as : (30) wherein and are and reference value.

[0039] Current control process in harmonic supplement mode: In harmonic compensation mode, MU operates at a low switching frequency and its output current After filtering out the high-frequency components by the filter inductor L1, the main components are the fundamental components. and low-frequency harmonic components To ensure the waveform quality of the system output current, SU needs to dynamically compensate for the harmonics introduced by MU. Its output current is expressed as: (31) Among them, the fundamental component Used to correct fundamental tracking error and harmonic components It is used to compensate for the harmonic current caused by MU. Therefore, the control objectives of MU and SU are expressed as: (32) The corresponding control structure is as follows Figure 6 (a) shows: acquisition system Perform phase-locked control to obtain the voltage phase angle , set the system output current reference value , collect the output current of MU ; Calculate the current reference value of MU according to formula (32) ;Compare and And send it to the current controller CC1 of MU for PI control to obtain the internal potential reference value of MU ;Will After PWM processing, a pulse signal is generated to drive the MU switch tube to operate. The total output current of the acquisition system ; Calculate the current reference value of SU according to formula (32) ;Compare and And send it to the SU current controller CC2 for PI control to obtain the internal potential reference value of SU ;Will After PWM processing, a pulse signal is generated to drive the SU switch tube to operate.

[0040] Current control process in direct parallel mode: When the system operates in direct parallel mode, MU and SU operate independently in a peer-to-peer structure, each bearing a certain proportion of the total output current. At this time, SU and MU each track their reference values ​​to meet: (33) Since SU is no longer responsible for harmonic compensation, in order to ensure the power quality of the system output current, the switching frequency of MU needs to be appropriately increased to compensate for the decline in harmonic suppression capability. The corresponding control structure is as follows Figure 6 (b) shows: acquisition system Perform phase-locked control to obtain the voltage phase angle , set the system output current reference value , collect the output current of MU ; Calculate the current reference value of MU according to formula (33) ;Compare and And send it to the current controller CC1 of MU for PI control to obtain the internal potential reference value of MU ;Will After PWM processing, a pulse signal is generated to drive the MU switch. The output current of SU is collected. ; Calculate the current reference value of SU according to formula (33) ;Compare and And send it to the SU current controller CC2 for PI control to obtain the internal potential reference value of SU ;Will After PWM processing, a pulse signal is generated to drive the SU switch tube to operate.

[0041] 2) Based on the system's current control process, a small signal model of the HSFI system in harmonic compensation mode is constructed to determine the overall frequency domain characteristics of the system in this mode.

[0042] 1. Coordinate Description Due to the dynamic characteristics of the phase-locked loop (PLL), the system involves two different dq rotating coordinate systems: the system coordinate system (denoted by the superscript "s") defined by the grid voltage, and the controller coordinate system (denoted by the superscript "c") defined by the phase synchronization control algorithm. The following relationship exists between small perturbations of any physical quantity in these two coordinate systems: (34) in, and are the small disturbance variables in the controller coordinate system and the system coordinate system, respectively, Represents phase synchronization dynamics. Consider a typical synchronous rotating reference frame PLL (Synchronous Reference Frame PLL, SRF-PLL), It is given by: (35) Among them, X0 is the steady-state value of the corresponding physical quantity, is the dynamic response of the phase-locked loop output phase angle to voltage disturbance: (36) in, is the small disturbance of the grid-connected point voltage, for The conjugate of ; s is the differential operator, , is the response frequency; is the d-axis component of the steady-state value of the grid voltage.

[0043] 2. Power circuit dynamics Both MU and SU use L-type filters, with inductance values ​​of L1 and L2 and parasitic resistance values ​​of R1 and R2 respectively. In the system coordinate system, the voltage disturbance on the filter is and Expressed as: (37) in, and is the filter impedance, is the system base frequency.

[0044] 3. Controller dynamics In order to achieve the current control target described in Equation (32), the current controllers (CC1 and CC2) of MU and SU both adopt PI control in the dq coordinate system, and their small disturbance response relationship is as follows: (38) Where, and are small disturbances of the modulation signals of MU and SU respectively, and is a PI controller, and is the voltage feed-forward coefficient.

[0045] 4. Full system impedance model The modulation signals m1 and m2 are modulated by PWM to drive the inverter switching action. Considering the delay caused by digital control and PWM, the relationship between the modulation signal and the inverter output voltage is expressed as: (39) Among them, G d1 , G d2 is the delay link. For symmetrical regular modulation, the duration from sampling to update is one carrier cycle; the zero-order hold effect keeps the updated duty cycle constant, close to half the carrier cycle. Therefore, the total delay value is usually considered to be 1.5 carrier cycles, that is: (40) where T s1 and T s2 are the carrier periods of MU and SU, respectively.

[0046] Based on the above modeling, the overall small-signal impedance model of HSFI in the harmonic compensation mode is constructed, as shown in FIG. 3. According to the connection relationship between the modules in the figure, the small perturbation of the output current of MU and SU is represented as: Figure 7 (41) (42) (6) (8) (9) where, is the small perturbation of the system output current; and are the small perturbations of the output currents of MU and SU, respectively; is the small perturbation of the reference value of the system output current; is the small perturbation of the grid-connected point voltage; is the conjugate of ; is the PI parameter of the current controller of MU; is the delay value of MU; is the voltage feed-forward coefficient of MU; is the system fundamental frequency; is the filter inductance of MU; is the transfer function of the phase-locked loop; is the steady-state value of the output current of MU; is the steady-state value of the grid-connected point voltage; is the steady-state value of the output voltage of MU; is the filter impedance of MU; is the PI parameter of the current controller of SU; is the delay value of SU; is the voltage feed-forward coefficient of SU; is the filter inductance of SU; is the steady-state value of the output current of SU; is the steady-state value of the output voltage of SU; is the filter impedance of SU.

[0047] ​​​​It can be seen from equation (42) that the dynamic characteristics of SU are not only related to itself, but also affected by MU. This makes the overall impedance characteristics of HSFI different from traditional multi-inverter parallel system. Substituting equation (41) into equation (42), the small perturbation relationship between voltage and current of SU under the influence of MU is further obtained as: (43) (7) Superimposing equation (41) and equation (43), the overall frequency domain characteristics of HSFI system are obtained as: (4) (5) 3) According to the current control process of the system, the small signal model of HSFI system in direct parallel mode is constructed, and then the overall frequency domain characteristics of the system in this mode are determined.

[0048] In direct parallel mode, MU and SU adopt independent current control strategy, and the dynamic of their controllers is: (44) On this basis, the complex vector impedance models of MU and SU are respectively represented as: (45) (46) (12) (13) (14) It can be seen from equation (45) and equation (46) that in direct parallel mode, the dynamic characteristics of MU and SU are independent of each other, and there is no significant coupling between the control systems. Therefore, their frequency domain responses are also independent of each other and do not affect each other. This characteristic is in sharp contrast to the influence of SU on MU state in harmonic compensation mode, making the stability difference of the system in the two modes significant. Superimposing equation (45) and equation (46), the overall frequency domain characteristics of HSFI system in direct parallel mode are obtained as: (10) (11) 4) According to the overall frequency domain characteristics of HSFI system in harmonic compensation mode and direct parallel mode obtained above, the expression of the output impedance of HSFI can be unified as: (15) Wherein, represents or ; represents or ; represent or .

[0049] S1022, determine the equivalent impedance of the AC grid.

[0050] The AC grid can be equivalent to a parallel structure of filter capacitor impedance Z C and line impedance Z g : (47) wherein: (48) S1023, determine the equivalent output current of the system and its complex conjugate expression.

[0051] Substitute equation (48) into equation (47), ignore the current given value disturbance term and the grid voltage disturbance term , and set the equivalent impedance: (19) wherein, is the equivalent impedance of the AC grid; is the filter capacitor impedance of the AC grid; is the line impedance of the AC grid.

[0052] Thus, the equivalent output current of the system is: (49) Its complex conjugate expression is: (50) Step S103, construct the equivalent single-input single-output model of the HSFI system from the equivalent output current of the system and its complex conjugate expression, and obtain the loop gain transfer function of the system.

[0053] From equations (49) and (50), the equivalent single-input single-output (SISO) model of the HSFI grid-connected system can be constructed, as shown in Figure 8 According to Figure 8 , the loop gain transfer function of the HSFI is obtained : (16) (17) (18) In the formula, , , They are 、 、 The conjugation of .

[0054] The transfer function includes the dynamic migration effect of the operating point and can be used for stability judgment and margin assessment under different grid strengths.

[0055] Step S104: Draw a Nyquist curve based on the loop gain transfer function of the HSFI, and map the Nyquist curve to an amplitude-frequency plane and a phase-frequency plane.

[0056] Step S2, considering the change of the system short-circuit ratio, converting the obtained amplitude-frequency plane and phase-frequency plane into a dual-variable amplitude-phase contour plane; Step S3: Draw amplitude contour lines in the amplitude-phase contour line plane. and phase contours , find all the intersection points of the two contour lines, and record the number of intersection points as N, Indicates the short-circuit ratio of the nth intersection, n = 1, 2...N, passing through the points in the amplitude and phase contour plane 、 、…、 Painting and Axis-parallel auxiliary lines 、 、…、 ,These auxiliary lines divide the amplitude and phase contour plane into multiple intervals; Step S4, determining the system stability region according to the interval divided in step S3; On the auxiliary line With auxiliary lines In the interval composed of: if any one of Axis parallel lines within the scope of There is no intersection, which means that the Nyquist curve surrounds the point in the interval Number of laps and are all 0, so it can be determined that the grid strength range The internal system is stable; otherwise, it means that the Nyquist curve surrounds the point in this interval. Number of laps 、 At least one of them is not 0, in this grid strength range The internal system is unstable.

[0057] Example 1 Figure 9A typical amplitude and phase contour diagram is shown. Combined with this diagram, the stability region determination process using the criteria proposed in this invention is as follows: The first step is Drawing in a plane and Contour lines. Figure 9 Phase contours , amplitude contours . The area is Figure 9 Highlighted by shaded area.

[0058] The second step is to specify Draw auxiliary lines below , determine the intersection of the auxiliary line and the phase contour line. , draw a line through the point and with Axis-parallel auxiliary lines ,like Figure 9 . It can be seen that in Within the range, auxiliary line and The contour lines have no intersection. Therefore, it can be concluded that the Nyquist curve surrounds the point Number of laps and are all 0, the system is stable under this grid strength. Similarly, for any , past a point Auxiliary lines and The contour lines intersect at At the intersection point B, the auxiliary line The same direction as the phase increase direction. Therefore, it can be judged that the Nyquist curve surrounds the point Number of laps and , the system is unstable under this grid strength.

[0059] The third step is to determine the stability range. Based on the analysis in the second step, we know that in the power grid strength range The internal system is stable and within the grid strength range The internal system is unstable. 、 are the minimum and maximum values ​​of the power grid strength respectively. In this embodiment, 、 Take 0.5 and 6 respectively.

[0060] Example 2 Figure 10 The stable domain amplitude and phase characteristics of a HSFI in harmonic compensation mode are shown. Phase contours and The amplitude contours intersect at A(−138, 0.9), B(−108, 0.0), C(85, 0.8), D(325, 0.9), and E(315, 0.8). These intersections divide the SCR into three intervals: [0, 0.8), [0.8, 0.9), and [0,9, +∞). In these intervals, Auxiliary lines in the frequency region Crossing The net number of isolines is 1, 2, and 0 respectively. Therefore, the system stability threshold is K SCR =0.9.

[0061] Example 3 Figure 11 The stable domain amplitude and phase characteristics of a HSFI in direct parallel mode are shown. Phase contours and The amplitude contour lines intersect only at A(50, 0.6). This intersection divides the SCR into two intervals [0, 0.6) and [0.6, +∞). In these intervals, Auxiliary lines in the frequency region Crossing The net times of the contour lines are 1 and 0 respectively. Therefore, the system stability threshold is K scr =0.6.

[0062] In order to verify the effectiveness and superiority of the present invention, several typical working points were selected to test the stability of the system under two operating modes under different grid strengths and different load conditions. The middle mark covers three typical working conditions: strong power grid, weak power grid and very weak power grid. and They are the stability domain boundaries in harmonic compensation mode and direct parallel mode respectively. and Divide the plane into three regions: Region I: Both modes are stable, and harmonic compensation mode is recommended to achieve better power quality and efficiency; Region II: The system is in a weak grid condition and needs to switch to direct parallel mode to ensure stable operation; Region III: Both modes cannot operate stably, and advance scheduling or protective measures must be taken to prevent the system from entering an unstable state.

[0063] Figure 13 Shown in The current waveforms of the system under different output current reference values in the strong grid environment of

[0064] Figure 14 The operation state of the system in the weak grid environment of It can be observed that in the harmonic compensation mode, the system is obviously unstable when the output current reaches 1.25 p.u., which is manifested as a dramatic fluctuation of the current; while in the same condition, the system can maintain stable output in the direct parallel mode, which is consistent with the stable domain boundary obtained in the theoretical derivation.

[0065] Figure 15 The extremely weak grid environment of The results show that the system is unstable in the harmonic compensation mode when the output current reaches 0.5 p.u., while it can maintain stability when the load is less than 1.0 p.u. in the direct parallel mode.

[0066] The above phenomena are consistent with the stable domain prediction results in Figure 12 Therefore, the accuracy of the converter stable domain determination method based on the amplitude-phase contour line proposed in the present application is verified.

[0067] In summary, the converter stable domain determination method based on the amplitude-phase contour line proposed in the present application characterizes the multi-dimensional stable domain of the HSFI system, constructs the small perturbation impedance model of the system in the harmonic compensation and direct parallel control, and reveals the sensitivity of the system stability to the grid strength and operating point. Based on the equivalent impedance modeling, the stable domain determination method analyzes the stability boundary of the system in the two operating modes, so that the system can effectively identify whether the operating point is in the stable region, thereby providing a clear criterion for mode switching and enhancing the dynamic adaptability of the system.

[0068] The above embodiments are the preferred implementation of the present application, in addition to this, the present application can be implemented in other ways, without departing from the technical scheme concept of the present application, any obvious replacement is within the protection scope of the present application.

[0069] In order to make the person skilled in the art more convenient to understand the improvement of the present application relative to the prior art, some drawings and descriptions of the present application have been simplified, and some other elements have been omitted in the present application file for the sake of clarity, and the person skilled in the art should realize that these omitted elements can also constitute the content of the present application.

Claims

1. A method for determining the converter stability region based on amplitude and phase contours, characterized in that: include: Step S1, drawing a Nyquist curve based on a loop gain transfer function of the converter, and mapping the Nyquist curve to an amplitude-frequency plane and a phase-frequency plane; Step S2, considering the change of the system short-circuit ratio, converting the obtained amplitude-frequency plane and phase-frequency plane into a dual-variable amplitude-phase contour plane; Step S3: Draw amplitude contour lines in the amplitude-phase contour line plane. and phase contours , find all the intersection points of the two contour lines, and record the number of intersection points as N, Indicates the short-circuit ratio of the nth intersection, n = 1, 2...N, passing through the points in the amplitude and phase contour plane 、 、…、 Painting and Axis-parallel auxiliary lines 、 、…、 ,These auxiliary lines divide the amplitude and phase contour plane into multiple intervals; Step S4, determining the system stability region according to the interval divided in step S3; On the auxiliary line With auxiliary lines In the interval composed of: if any one of Axis parallel lines within the scope of There is no intersection, which means that the Nyquist curve surrounds the point in the interval Number of laps and are all 0, so it can be determined that the power grid strength range The internal system is stable; otherwise, it means that the Nyquist curve surrounds the point in this interval. Number of laps 、 At least one of them is not 0, in this grid strength range The internal system is unstable.

2. The method for determining the converter stability region based on amplitude and phase contours according to claim 1, characterized in that: The converter is HSFI.

3. The method for determining the converter stability region based on amplitude and phase contours according to claim 2, characterized in that: The loop gain transfer function of the HSFI is determined using the following method: Step S101, using the short-circuit ratio to represent the grid strength, and determining the analytical function relationship between the system operating point variable and the grid strength; Step S102: determining the system equivalent output current and its complex conjugate expression based on the HSFI body output impedance and the AC grid equivalent impedance; Step S103 : constructing an equivalent single-input single-output model of the HSFI system based on the system equivalent output current and its complex conjugate expression, and obtaining the loop gain transfer function of the system.

4. The method for determining the converter stability region based on amplitude and phase contours according to claim 3, wherein: The process of constructing the HSFI body output impedance is as follows: 1) Determine the current control strategy of HSFI The system operates in direct parallel mode under weak grid conditions, with the MU and SU operating independently in a peer-to-peer structure. Under strong grid conditions, the system operates in harmonic compensation mode, with the MU operating at a low switching frequency. After the MU's output current is filtered out of high-frequency components by the filter inductor, the SU dynamically compensates for the harmonics introduced by the MU and corrects the MU's fundamental tracking error. The system's current control process is as follows: Calculate voltage phase angle: collect system PCC voltage Perform phase-locked control to obtain the voltage phase angle ; MU current control: set the system output current reference value , collect the output current of MU ; According to the system output current reference value and power distribution ratio Calculate the current reference value of MU ;Compare and And perform PI control to obtain the internal potential reference value of MU ;Will After PWM processing, a pulse signal is generated to drive the MU switch tube to operate; （1） SU current control: total output current of the acquisition system and SU output current ; According to the system output current reference value Calculate the current reference value of SU ; When the system works in harmonic compensation mode, select the following formula (2) to calculate ,Compare and And perform PI control to obtain the internal potential reference value of SU ; When the system works in direct parallel mode, choose the following formula (3) to calculate ,Compare and And perform PI control to obtain the internal potential reference value of SU ;Will After PWM processing, a pulse signal is generated to drive the SU switch tube to operate; （2） （3） 2) Based on the system’s current control process, a small-signal model of the HSFI system in harmonic compensation mode is constructed to determine the overall frequency domain characteristics of the system in this mode, as shown in the following equation: （4） （5） （6） （7） （8） （9） Where, Small disturbance of system output current; and are the small disturbances of the output currents of MU and SU respectively; A small disturbance of the system output current reference value; is a small disturbance of the grid connection point voltage; for conjugation of; is the PI parameter of the MU current controller; is the delay value of MU; is the voltage feedforward coefficient of MU; is the system base frequency; is the filter inductance of MU; is the transfer function of the phase-locked loop; is the steady-state value of MU output current; is the steady-state value of the grid-connected point voltage; is the steady-state value of MU output voltage; is the filter impedance of MU; is the PI parameter of the SU current controller; is the delay value of SU; is the voltage feedforward coefficient of SU; is the filter inductance of SU; is the steady-state value of SU output current; is the steady-state value of SU output voltage; is the filter impedance of SU; 3) Based on the system’s current control process, a small-signal model of the HSFI system in direct parallel mode is constructed to determine the overall frequency domain characteristics of the system in this mode, as shown in the following equation: （10） （11） （12） （13） （14） 4) Based on the overall frequency domain characteristics of the HSFI system in harmonic compensation mode and direct parallel mode, the output impedance expression of the HSFI body is unified as follows: （15） in, represent or ; represent or ; represent or .

5. The method for determining the converter stability region based on amplitude and phase contours according to claim 4, characterized in that: The loop gain transfer function of the HSFI for: （16） （17） （18） （19） Where, 、 、 They are 、 、 conjugation of; is the equivalent impedance of the AC grid; is the impedance of the AC grid filter capacitor; is the AC grid line impedance.

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