Extended Impedance Mode Analysis Method and Apparatus for Internal Dynamics of Grid-Type Inverters

Abstract

This invention provides an extended impedance modal analysis method for the internal dynamics of a grid-connected inverter, comprising the following steps: decomposing the global impedance model in a global coordinate system to obtain a first impedance, a second impedance, and a third impedance, and calculating them separately through measurement fitting; employing the modal analysis method of the impedance model, calculating a first participation factor and a second participation factor based on the first impedance, the second impedance, and the third impedance, and normalizing them to obtain a first participation ratio and a second participation ratio; determining the key control loops affecting power system stability based on the first participation ratio and the second participation ratio; and adjusting the control parameters of the key control loops based on the explicit parameter participation factors to enhance system damping and improve system stability. The analysis method provided by this invention effectively identifies the root causes of the impact of different controllers on system stability within a grid-connected inverter, and effectively solves the problem of assessing the degree of extended impedance participation in the dominant dynamics of different controllers within a grid-connected inverter.

Description

Technical Field

[0001] This invention relates to the field of power system dynamic stability technology, specifically to an extended impedance mode analysis method and apparatus for the internal dynamics of a grid-connected inverter. Background Technology

[0002] The large-scale integration of grid-forming inverters (GFMs) has drastically altered the dynamic characteristics of power systems, drawing widespread attention to the instability caused by the interaction between GFMs and the grid. Furthermore, the interactive coupling between controllers at different time scales within the GFM further complicates stability analysis. Understanding the dynamic behavior of GFMs is crucial for addressing potential stability issues. Therefore, there is an urgent need to develop new modeling and analysis frameworks to solve these ever-changing and complex stability problems. Since inverters are typically provided only with impedance models describing voltage and current port characteristics, exhibiting gray-box or black-box behavior, it is often necessary to reasonably assess the impact of different controllers on stability in grid-forming inverters to pinpoint critical control loops and parameters affecting the system. This allows for effective tuning and optimization of the grid-forming inverter control parameters to improve system stability. Currently, there are no analytical methods specifically addressing the internal dynamics of grid-forming inverters. Summary of the Invention

[0003] This invention addresses the problems existing in the prior art by proposing an extended impedance mode analysis method for the internal dynamics of a grid-connected inverter. This method reveals the interaction relationships between different control loops within the grid-connected inverter and enables the dominant dynamic positioning of the internal dynamics of the grid-connected inverter based on this analysis method. This has certain guiding significance for the current gray-box mode analysis of the internal dynamics of grid-connected inverters.

[0004] To achieve the above objectives, the technical solution adopted by this invention is as follows: an extended impedance mode analysis method for the internal dynamics of a grid-connected inverter, comprising the following steps:

[0005] Based on the control structure of the grid-type inverter, a global impedance model of a single grid-type inverter in the global coordinate system is constructed.

[0006] The overall impedance model is decomposed to obtain a first impedance, a second impedance, and a third impedance; the first impedance is the equivalent impedance of the single grid-type inverter reflecting electromagnetic dynamics, the second impedance is the equivalent impedance of the single grid-type inverter reflecting the coupling effect of electromagnetic dynamics and synchronous dynamics, and the third impedance is the equivalent impedance of the single grid-type inverter reflecting synchronous dynamics.

[0007] Based on the single grid-type inverter, the first impedance, the second impedance, and the third impedance are calculated respectively by measurement and fitting.

[0008] Based on the power system where the grid-connected inverter is located, the modal analysis method of the impedance model is used to calculate the first participation factor and the second participation factor according to the first impedance, the second impedance and the third impedance; the first participation factor is the equivalent overall participation factor of the electromagnetic dynamics in the single grid-connected inverter; the second participation factor is the equivalent overall participation factor of the synchronization dynamics in the single grid-connected inverter.

[0009] Based on the participation ratio, the first participation factor and the second participation factor are normalized and converted to obtain the first participation ratio and the second participation ratio, respectively.

[0010] The key dynamics affecting the stability of the power system are determined based on the first participation ratio and the second participation ratio; the key dynamics are either the electromagnetic dynamics or the synchronization dynamics.

[0011] The critical control loop of the power system is determined based on the critical dynamics.

[0012] Further, the steps for normalizing and converting the first participation factor and the second participation factor based on the participation ratio to obtain the first participation ratio and the second participation ratio respectively are as follows:

[0013] Calculate the absolute value of the first participation factor and the absolute value of the second participation factor for each individual grid-connected inverter;

[0014] The overall factor is obtained by summing the absolute values ​​of the first participating factor and the second participating factor.

[0015] Based on the power system, the sum of the overall factors is obtained by summing the overall factors;

[0016] The first participation ratio is obtained based on the proportion of the first participating factor in the sum of all factors.

[0017] The second participation ratio is obtained based on the proportion of the second participation factor in the sum of all factors.

[0018] Furthermore, the impedance model is a small-signal impedance model of the entire power system constructed based on the power system.

[0019] Furthermore, after obtaining the control loop that affects the stability of the power system, the participation factors of the control parameters are calculated based on the small-signal impedance model of the whole system and the overall impedance model.

[0020] Further, the steps for calculating the participation factor of the control parameters are as follows:

[0021] Based on the control loop of the power system, a sensitivity equation is constructed by performing partial differential calculations on the control parameters according to the overall impedance model; the control parameters include the first control parameter and the second control parameter; the first control parameter is a control parameter reflecting electromagnetic dynamics in a single grid-connected inverter, and the second control parameter is a control parameter reflecting synchronization dynamics in a single grid-connected inverter;

[0022] Based on the electromagnetic dynamics, the sensitivity equation of the first control parameter is obtained by performing partial differentiation on the first control parameter according to the global impedance in the global coordinate system.

[0023] Based on the aforementioned synchronization dynamics, the sensitivity equation for the second control parameter is obtained according to the global impedance in the global coordinate system.

[0024] The participation factor of the first control parameter can be obtained by simultaneously solving the sensitivity equation and the sensitivity equation of the first control parameter, or the participation factor of the second control parameter can be obtained by simultaneously solving the sensitivity equation and the sensitivity equation of the second control parameter.

[0025] Furthermore, the control loop that dominates the electromagnetic dynamics is a voltage control loop, which employs a dual voltage and current closed loop.

[0026] Furthermore, the first control parameter includes the proportional gain of the PI controller of the voltage control loop and the integral gain of the PI controller of the voltage control loop.

[0027] Furthermore, the control loop that dominates the synchronization dynamics is a power frequency control loop, and the power frequency synchronization loop adopts droop control with a low-pass filter.

[0028] Furthermore, the second control parameter includes the low-pass filter time constant of the power frequency synchronization loop and the droop gain of the power frequency synchronization loop.

[0029] An apparatus for implementing an extended impedance mode analysis method for the internal dynamics of a grid-connected inverter, comprising a modeling unit, a calculation unit, and an analysis unit;

[0030] The modeling unit:

[0031] Used for: constructing an overall impedance model of a single grid-connected inverter in the global coordinate system based on the control structure of the grid-connected inverter;

[0032] This is used to decompose the overall impedance model to obtain the first impedance, the second impedance, and the third impedance;

[0033] The computing unit:

[0034] The first impedance, the second impedance, and the third impedance are calculated respectively by measurement fitting based on the single grid-type inverter;

[0035] The modal analysis method using an impedance model is used to calculate the first participation factor and the second participation factor based on the first impedance, the second impedance, and the third impedance in the power system where the grid-type inverter is located.

[0036] This is used to normalize and convert the first participation factor and the second participation factor based on the participation ratio, so as to obtain the first participation ratio and the second participation ratio respectively;

[0037] The analysis unit:

[0038] Used to determine the key dynamics affecting the stability of the power system based on the first participation ratio and the second participation ratio;

[0039] Used to determine the critical control loop of the power system based on the critical dynamics.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. The analysis method provided by this invention performs impedance decomposition on the grid-type inverter and then proposes an equivalent overall participation factor to evaluate the degree of participation of electromagnetic dynamics and synchronization dynamics dominated by different controllers, effectively identifying the root cause of the influence of different controllers on system stability within the grid-type inverter.

[0042] 2. The analysis method provided by this invention takes into account the influence of the interaction between different controllers inside the grid-type inverter, and effectively solves the problem of evaluating the gray box participation degree of the dominant dynamics of different controllers inside the grid-type inverter.

[0043] 3. The analysis method provided by this invention is applicable to power systems with a high proportion of grid-connected inverters, and can effectively improve system stability based on the explicit parameter participation factors in different controllers of the grid-connected inverters.

[0044] 4. The analysis method proposed in this invention cannot construct a state-space model of the entire system. It only requires the port impedance of the grid-type inverter and the equivalent impedance of the rest of the system at that port. The calculation is simple and has good practical engineering application value. It can quickly and conveniently evaluate the root causes of the internal dynamics of the grid-type inverter that affect the stability of the system. It has certain guiding significance for the gray box modal analysis of the internal dynamics of the current grid-type inverter. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the small-signal impedance model of the entire system in an embodiment of the present invention;

[0046] Figure 2 This is a structural diagram of a grid-type inverter in an embodiment of the present invention;

[0047] Figure 3 The equivalent circuit of GFM under constant voltage and frequency reference signal;

[0048] Figure 4 This is an impedance Bode plot of an embodiment of the present invention;

[0049] Figure 5 This is a schematic diagram of coordinate system transformation according to an embodiment of the present invention;

[0050] Figure 6 This is a schematic diagram of impedance transformation according to an embodiment of the present invention;

[0051] Figure 7 This is an impedance differentiation operation diagram according to an embodiment of the present invention;

[0052] Figure 8 This is a schematic diagram of the modified 14-bus system in Example 1 of this invention;

[0053] Figure 9 This is a schematic diagram of the pole distribution of the modified 14-bus system in Example 1 of this invention;

[0054] Figure 10 The following is a comparison chart of the evaluation results of different modes of the 14-bus system modification in Example 1 of this invention: (a) is mode 1, (b) is mode 2, (c) is mode 3, and (d) is mode 4.

[0055] Figure 11 The following are the oscillation waveforms of GFM2 and GFM3 in Example 1 of this invention: (a) d-axis voltage variable diagram of the dominant ED in GFM2, (b) q-axis voltage variable diagram of the dominant ED in GFM2, and (c) angular frequency variable diagram of the dominant SD in GFM3.

[0056] Figure 12 This is a schematic diagram of the modified 68 busbar system in Example 2 of this invention;

[0057] Figure 13 The following is a comparison chart of the evaluation results of different modes of the 68 busbar system modification in Example 2 of this invention: (a) is mode 1, (b) is mode 2, (c) is mode 3, and (d) is mode 4.

[0058] Figure 14 This is a schematic diagram of the pole distribution of the 68-bus system before and after parameter adjustment in Example 2 of this invention;

[0059] Figure 15 This is a flowchart illustrating the extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to the present invention. Detailed Implementation

[0060] Faced with the growing threat of depleted global fossil fuels and a worsening greenhouse effect, my country has set a strategic goal of "peaking carbon emissions by 2030 and achieving carbon neutrality by 2060." As of the end of June 2024, the installed capacity of grid-connected wind power and solar power nationwide reached 470 million kilowatts and 710 million kilowatts, respectively. New energy sources, represented by wind and solar power, are being connected to the power grid on a large scale through grid-connected inverters and other power electronic equipment. The level of power electronics in the power grid is continuously improving, and "high proportion of new energy" and "high proportion of power electronic equipment" have become an inevitable trend in the development of my country's power system.

[0061] Modal Analysis Based on the State-space Model (MASS) is an important method for determining key system factors using linear algebra. MASS uses participation factors (PF) to quantify the contribution of each state variable to a specific mode. However, the large-scale integration of GFM increases the size of the mathematical model, thus increasing the difficulty of modal analysis. Furthermore, state-space modeling requires detailed models and specific parameters for each system component. Since inverters are typically only provided with impedance models describing voltage and current port characteristics, exhibiting gray-box or black-box behavior, the applicability of MASS for GFM stability analysis remains to be explored. MASS requires a white-box system model, therefore it is not suitable for scenarios where grid-connected inverters often only provide gray-box or even black-box models.

[0062] Recently, whole-system dynamic matrix analysis (MASS) has been used to analyze system stability through coordinate system dynamics embedded in the inverter. Building upon this, Modal Analysis based on Impedance Model (MAI) can assess the contribution of each power supply device to oscillation modes at the device level. Furthermore, the corresponding parameter PF can provide suggestions for improving system damping. However, unlike MASS, MAI treats the inverter as a single, monolithic component, which limits its ability to identify the dominant system dynamics at the control loop or state variable level.

[0063] A deep understanding of the root causes of system instability within the GFM is crucial for targeted improvements in system stability. A method known as port mapping offers a new perspective for analyzing stability problems caused by various factors. Furthermore, the extended impedance model achieves separation of different dynamics within the GFM by introducing additional degrees of freedom, but it has certain limitations in practical applications. Decomposing different control loops into equivalent circuit elements allows for stability analysis of the inverter's internal dynamics. However, the decomposition of the synchronous control loop remains to be explored.

[0064] Modal Analysis Based on the State-space Model (MASS) requires a white-box model of the system, making it unsuitable for grid-forming inverters (GFMs), which often only provide gray-box or even black-box models. This disclosure addresses the technical problem of gray-box participation evaluation of the dynamics dominated by different controllers within a grid-forming inverter. Specifically, based on the concept of impedance decomposition, the dynamics of the grid-forming inverter are divided into electromagnetic dynamics (ED) dominated by the Voltage Control Loop (VCL) and synchronous dynamics (SD) dominated by the Power Frequency Synchronization Loop (PFL). An overall Power Factor (PF) characterizing ED and SD is proposed to evaluate the participation degree of different control loops, and an explicit Participation Factor (PF) is proposed to improve unstable oscillation modes. Gray-box modal analysis of the internal dynamics of the grid-forming inverter is thus achieved. The purpose of this invention is to quickly locate the controller inside a grid-connected inverter that plays a dominant role in system stability, and to propose an extended impedance mode analysis method for the internal dynamics of a grid-connected inverter, namely the extended MAI (Extend Modal Analysis based on Impedance Model, EMAI) method.

[0065] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.

[0066] See Figure 15 This embodiment provides an extended impedance mode analysis method for the internal dynamics of a grid-connected inverter, including the following steps: constructing a small-signal impedance model of the entire power system based on the power system;

[0067] Based on the power system where the grid-type inverter is located Figure 1 The small-signal impedance model of the entire system is shown below. The total number of buses in the power system is... n , This is the node impedance matrix of the entire system network. Before connection, the power supply impedance models of all grid-connected inverters need to align their respective coordinate systems to the global coordinate system. Therefore, the bus in the global DQ coordinate system... m Admittance of the connected grid inverter for:

[0068] (1)

[0069] In the formula, , , and They are respectively The four components, The generatrix in the global DQ coordinate system m The impedance of the connected grid-type inverter. m The busbar number;

[0070] according to Figure 1 The closed-loop feedback relationship is shown, and the dynamic admittance matrix of the entire system in the global DQ coordinate system is also shown. for:

[0071] (2)

[0072] In the formula, 2 n An identity matrix of order 1. This is the admittance matrix of the grid inverter formed by connecting all buses of the entire system in the global DQ coordinate system.

[0073] The first in the power system control loop The perturbation of each eigenvalue is:

[0074] (3)

[0075] In the formula, For the first in the power system The perturbation of each eigenvalue for exist Take the number of places to leave. The dynamic admittance matrix of the entire system in the global DQ coordinate system Middle 2 m -1 to 2 m line and 2 m -1 to 2 m The block matrix corresponding to the four elements in the column, The first in the power system control loop 1 eigenvalue, The eigenvalue index is represented by *, where * indicates the conjugate transpose of the matrix. For Frobenius inner product, for The amount of disturbance. For normalization scalar, For GFM m For the first in the power system The overall participation factor of each eigenvalue, GFM m busbar mConnected grid-type inverters;

[0076] Based on the control structure of the grid-type inverter, a global impedance model of a single grid-type inverter in the global coordinate system is constructed.

[0077] Figure 2 The control structure of the grid-connected inverter is shown in the figure. It is the resistor in the LC filter circuit. The inductance of the LC filter circuit and It is the capacitor in the LC filter circuit. It is the capacitor voltage. This is the capacitor voltage reference value. As mentioned earlier, the power frequency synchronization loop uses droop control with a low-pass filter, and the voltage control loop uses a dual voltage and current closed loop. When the frequency reference signal of the grid-connected inverter is constant, we can obtain... Figure 3 The positive and negative sequence equivalent circuits corresponding to the voltage control loop are shown.

[0078] Figure 3 middle, s It is the Laplace operator; The reference angular frequency; The equivalent impedance of the positive branch of the filter inductor. It is the equivalent impedance of the negative branch of the filter inductor. The equivalent impedance of the positive branch of the filter capacitor. It is the equivalent impedance of the negative branch of the filter capacitor. It is the equivalent impedance of the positive circuit PI control of the current control loop (CCL). It is the equivalent impedance controlled by the PI controller in the negative circuit of the current control loop. It is the proportional gain controlled by the PI loop of the current control loop. It is the integral gain of the PI control in the current control loop; It is the equivalent admittance of the positive circuit PI control of the voltage control loop (VCL). It is the equivalent admittance of the PI control in the negative circuit of the voltage control loop. It is the proportional gain controlled by the PI control of the voltage control loop. It is the integral gain of the voltage control loop PI control; It is the equivalent impedance of the positive circuit cross-decoupling control of the current control loop. It is the equivalent impedance of the cross-decoupling control of the negative circuit of the current control loop. It is the equivalent admittance of the voltage control loop positive circuit cross-decoupling control. It is the equivalent admittance of the voltage control loop negative circuit cross-decoupling control; It is the equivalent impedance of the positive circuit controlled by the virtual impedance of the current. It is the equivalent impedance of the negative circuit controlled by the virtual impedance of the current. It is a resistor controlled by the virtual impedance of the current. It is an inductor controlled by the virtual impedance of the current; It is the equivalent admittance of the positive circuit controlled by the voltage virtual admittance. It is the equivalent admittance of the negative circuit controlled by the voltage virtual admittance. It is a resistor controlled by voltage virtual impedance. It is an inductor controlled by voltage virtual impedance; It is the equivalent admittance of the voltage feedforward impedance-controlled positive circuit. It is the equivalent admittance of the voltage feedforward impedance-controlled negative circuit; It is the voltage feedforward gain; It is the equivalent impedance corresponding to the positive circuit of the current feedforward control. It is the equivalent impedance corresponding to the current feedforward controlled negative circuit. It is the current feedforward gain; It is the equivalent admittance of the positive circuit of the current control loop. It is the equivalent admittance of the negative circuit of the current control loop. It is the equivalent admittance of the positive circuit of the voltage control loop. It is the equivalent admittance of the negative circuit of the voltage control loop. This is the total equivalent impedance of the positive circuit. This is the total equivalent impedance of the negative circuit. The total equivalent impedance is for both positive and negative sequences; It controls the delay. It is the sampling period; It is the gain of the positive circuit of the current control loop. It is the gain of the negative circuit of the current control loop. It is the gain of the positive circuit of the voltage control loop. It is the gain of the negative circuit of the voltage control loop;

[0079] Without considering power frequency synchronization loop dq Overall equivalent impedance in coordinate system It can be determined by the total equivalent impedance of positive and negative sequence. Conversion:

[0080] (4)

[0081] In the formula, , , , They are respectively exist dq The four components of a coordinate system;

[0082] As shown in the circuit diagram, the CCL integral controller is equivalent to a capacitor connected in series in the filter inductor branch, which makes the equivalent admittance of the current control loop positive circuit... Equivalent admittance of current control loop negative circuit exist s= When j0 is 0, that is... and The characteristics are those of a current source. The VCL integral controller is equivalent to an inductor connected in parallel with the filter capacitor branch, which makes the equivalent admittance of the voltage control loop positive circuit... Equivalent admittance of voltage control loop negative circuit exist s= When j0 is infinity, that is... and This refers to the external characteristics of the voltage source. Figure 4 Table 1 provides the GFM3 (GFM3 represents the grid-connected inverters on bus 3; the power supply impedances of all grid-connected inverters must be aligned with the system's global coordinate system). The Bode plot is obtained where cross-decoupling control, virtual control, and feedforward control are all set to 0. The VCL integral controller enables... The impedance amplitude is extremely small in the subsynchronous frequency band.

[0083] exist Figure 5 middle, This represents the angular velocity of the system reference power supply, while GFM m Relative to the reference source, GFM m Relative to the steady-state angle of the reference source, and GFM m Angular deviation relative to the reference source. When the power frequency synchronization loop (PFL) does not provide additional dynamics, i.e. This means that the oscillating coordinate system and the steady-state coordinate system coincide.

[0084] The small-signal transfer function of the power frequency synchronization loop (PFL) is:

[0085] (5)

[0086] In the formula, For GFM m On public connection points d shaft voltage, For GFM m On public connection points q shaft voltage, GFM in the rocking coordinate system m of d shaft voltage, GFM in the rocking coordinate system m of q shaft voltage, For GFM m On public connection pointsd shaft current, For GFM m On public connection points q shaft current, GFM in the rocking coordinate system m of d shaft current, GFM in the rocking coordinate system m of q shaft current, It is GFM m droop gain; =1 / It is GFM m The power frequency synchronization loop low-pass filter time constant It is GFM m The power frequency synchronization loop low-pass filter bandwidth; It is GFM m The transfer function of current to angle; It is GFM m The voltage-to-angle transfer function, For GFM m The change in active power.

[0087] Depend on Figure 5 It can be seen that GFM is transformed by coordinate transformation. m The voltage variable is transformed from the oscillating coordinate system to the global coordinate system and linearized in equilibrium. The voltage relationship is as follows:

[0088] (6)

[0089] In the formula, GFM m Voltage at the point of common coupling, It is GFM m The coordinate transformation matrix; GFM in the rocking coordinate system m voltage vector, GFM in global coordinate system m voltage vector, GFM in global coordinate system m of D shaft voltage, GFM in global coordinate system m of Q Shaft voltage;

[0090] The formula for current is similar to that for voltage:

[0091] (7)

[0092] In the formula, GFM m The current at the point of common coupling, GFM in the rocking coordinate system m The current vector, GFM in global coordinate system m current vector, GFM in global coordinate system m of D shaft current, GFM in global coordinate system m of Q shaft current;

[0093] The overall impedance model is decomposed to obtain the first impedance, the second impedance, and the third impedance. The first impedance is the equivalent impedance of a single grid-connected inverter reflecting electromagnetic dynamics. The second impedance is the equivalent impedance of a single grid-connected inverter reflecting the coupling effect of electromagnetic dynamics and synchronization dynamics. The third impedance is the equivalent impedance of a single grid-connected inverter reflecting synchronization dynamics. Electromagnetic dynamics refers to the dynamics caused by the AC voltage loop and electrical geographical location of the grid-connected inverter. Synchronization dynamics refers to the dynamics caused by the power frequency synchronization of the grid-connected inverter.

[0094] Considering the power frequency synchronization loop (PFL) in the global coordinate system, the overall impedance of the global coordinate system is: Figure 6 of :

[0095] (8)

[0096] In the formula, GFM in global coordinate system m Overall impedance, E 2 is a second-order identity matrix; =[ ] T For GFM m The common connection point supplies external current; To characterize the equivalent impedance of an electromagnetic dynamic ED, it is Figure 6 The equivalent impedance characterizing the electromagnetic dynamics ED ;

[0097] Typically, the voltage loop bandwidth is several hundred hertz, within the voltage loop bandwidth =0. The secondary synchronization frequency is much smaller than the voltage loop bandwidth, so in equation (5) It can be rewritten as:

[0098] (9)

[0099] Therefore, equation (8) can be rewritten as:

[0100] (10)

[0101] also, Figure 4 The Bode plot can be derived much smaller This conclusion further illustrates the rationale for the simplification. Because I m0 and H mi These are matrices of order 2×1 and 1×2, respectively. Therefore ( E 2+ I m0 H mi ) -1 It can be written as ( E 2+ I m0 ×1× H mi ) -1 This can be simplified to equation (12) using the matrix inversion lemma of equation (11).

[0102] (11)

[0103] In the formula, a , b , c and d These are arbitrary matrices that are compatible matrices in terms of dimension and conform to the rules of matrix multiplication.

[0104] (12)

[0105] Substituting equation (12) into equation (10), we notice... It is a scalar, Written as For ease of merging and simplification, the final equation (10) is... It is broken down into three parts.

[0106] (13)

[0107] In the formula, K mS It is GFM m The coefficient matrix related to steady-state power, K mUU It is GFM m Voltage-related coefficient matrix; GFM m The equivalent power caused by the PFL parameters; U m It is GFM mThe voltage measured at the point of common coupling. P m It is GFM m Active power measured at the point of common coupling. Q m It is GFM m Reactive power measured at the point of common coupling.

[0108] The first part, namely the first impedance, is only related to the voltage control loop VCL. The third part, namely the third impedance, is only related to the power frequency synchronization loop (PFL), while The second part, namely the second impedance, is affected by the coupling effect between VCL and PFL. Therefore, The decomposition can be rewritten as follows.

[0109] (14)

[0110] Based on a single grid-type inverter, the first impedance, second impedance, and third impedance are calculated respectively through measurement and fitting.

[0111] It can be calculated by measurement and fitting. , and Disconnect the PFL control loop, that is, set the PFL frequency reference signal to a constant value or droop gain. Setting it to zero will allow you to... Separation and .exist In this context, the unknown variable is... and .because and Since none of them are zero, the solution can be found by calculating the equation at appropriate frequency points. and At this point, the result can be calculated through measurement and fitting. The three parts.

[0112] Based on the power system in which the grid-connected inverter is located, modal analysis using an impedance model is employed to calculate the first and second participation factors based on the first, second, and third impedances. The first participation factor is the equivalent overall participation factor of electromagnetic dynamics in a single grid-connected inverter, and the first participation factor characterizing the degree of electromagnetic dynamics participation is determined by the first impedance. Second impedance The second participation factor is the equivalent overall participation factor of the synchronization dynamics in a single grid-type inverter, which is jointly caused by the second impedance. and third impedance Caused by both;

[0113] The differential operation of equation (13) is illustrated in the following diagram: Figure 7 As shown.

[0114] (15)

[0115] In the formula, GFM m The equivalent power caused by the PFL parameters; express The degree of disturbance, express The degree of disturbance.

[0116] Combining equations (3) and (15) can provide a deeper understanding of the dynamics that have the greatest impact on the power system.

[0117] (16)

[0118] In the formula, For GFM m The first control parameter in the power system Equivalent overall participation factor for each eigenvalue For GFM m The second control parameter in the power system The equivalent total participation factor for each eigenvalue, i.e. This reflects the equivalent overall participation factor of the voltage control loop (VCL). This reflects the equivalent overall participation factor of the power-frequency synchronization loop (PFL). It is worth noting that... by and The combined influence of, and That is and The result of their interaction. Since voltage control is essentially a voltage-current dual closed loop, 1 / 2 is the impedance-based reduction factor in the EMAI method;

[0119] Based on the participation ratio, the first participation factor and the second participation factor are normalized and converted to obtain the first participation ratio and the second participation ratio, respectively. The steps are as follows:

[0120] Calculate the absolute values ​​of the first participation factor and the second participation factor for each individual grid-connected inverter.

[0121] The overall factor is obtained by summing the absolute values ​​of the first participating factor and the second participating factor.

[0122] Based on the power system, the sum of the overall factors is obtained by summing the overall factors;

[0123] The first participation ratio is obtained based on the proportion of the first participating factor in the total sum of factors.

[0124] The second participation ratio is obtained based on the proportion of the second participation factor in the total sum of factors.

[0125] (17)

[0126] In the formula, As the first participation ratio, The second participation ratio;

[0127] The first participation ratio reflects the degree of participation of electromagnetic dynamics dominated by the voltage control loop in the influence of power system stability in a single grid-connected inverter; the second participation ratio reflects the degree of participation of synchronization dynamics dominated by the power frequency synchronization loop in the influence of power system stability in a single grid-connected inverter.

[0128] The control loop affecting the stability of the power system is obtained by comparing the first participation ratio and the second participation ratio.

[0129] when At that time, the electromagnetic dynamics dominated by the voltage control loop plays a dominant role in the stability of the power system, that is, the control loop that affects the stability of the power system is the electromagnetic dynamics control loop dominated by the voltage control loop.

[0130] when At that time, the synchronization dynamics dominated by the power frequency synchronization loop play a dominant role in the stability of the power system, that is, the control loop that affects the stability of the power system is the synchronization dynamics control loop dominated by the power frequency synchronization loop.

[0131] Based on the ED and SD characteristics of inverters with different grid configurations in the system and The numerical values ​​are used to locate the dominant controller corresponding to the key dynamics affecting system stability. This narrows down the factors influencing system stability to specific controllers, allowing for further optimization of the control parameters of these key controllers to effectively improve system stability. PR is used to normalize the participating factors calculated by different methods.

[0132] After obtaining the control loop that affects the stability of the power system, the participation factors of the control parameters are calculated based on the small-signal impedance model and the overall impedance model of the whole system.

[0133] In the key controller, the factor PF for each control parameter indicates the direction in which increasing the corresponding control parameter will change the dominant eigenvalue of the system. A decrease in the real part of the system eigenvalue indicates an increase in system damping; therefore, the control parameter with the largest absolute value of the real part of the factor PF is selected for adjustment. If the real part of the PF value is positive, the corresponding control parameter value is decreased; conversely, if the real part of the PF value is negative, the corresponding control parameter value is increased. This achieves the goal of increasing system damping and improving system stability.

[0134] The steps for calculating the participation factor of control parameters are as follows:

[0135] Based on the control loop of the power system, a sensitivity equation is constructed by performing partial differential calculations on the control parameters according to the overall impedance model. The control parameters include a first control parameter and a second control parameter. The first control parameter is the control parameter reflecting electromagnetic dynamics in a single grid-connected inverter, and the second control parameter is the control parameter reflecting synchronization dynamics in a single grid-connected inverter. Preferably, the control loop that dominates electromagnetic dynamics is a voltage control loop, which adopts a voltage and current dual closed loop. The first control parameter includes the proportional gain of the PI controller of the voltage control loop and the integral gain of the PI controller of the voltage control loop. The second control parameter is the parameter reflecting the power frequency synchronization loop in the power system. Preferably, the control loop that dominates synchronization dynamics is a power frequency control loop, which adopts droop control with a low-pass filter. The second control parameter includes the low-pass filter time constant of the power frequency synchronization loop and the droop gain of the power frequency synchronization loop.

[0136] Equivalent overall impedance Any control parameter of different control loops within the grid-connected inverter Sensitivity It can be used to determine the main parameters that affect system dynamics.

[0137] (18)

[0138] It is difficult to obtain the result analytically using conventional methods. Conventional methods use numerical differences to replace partial derivative calculations, but numerical differences require to be small enough, which can sometimes lead to unpredictable errors.

[0139] exist Based on being broken down into three parts, we can obtain The explicit expression is then used to solve for:

[0140] Based on electromagnetic dynamics, when the key control loop is a voltage control loop, the sensitivity equation of the first control parameter is obtained by performing partial differentiation on the first control parameter according to the global impedance in the global coordinate system.

[0141] Here, we consider setting cross-decoupling, virtual control, and feedforward control to 0. First, we consider the parameters of VCL. From... Figure 7 It can be known that:

[0142] (19)

[0143] Since the PI controller of VCL is equivalent to the admittance connected in parallel with the filter capacitor, the impedance differential is converted into the admittance differential:

[0144] (20)

[0145] Therefore GFM m The proportional gain of the PI controller in VCL Sensitivity and integral gain The sensitivities are as follows:

[0146] (twenty one)

[0147] Based on synchronization dynamics, when the critical control loop is a power frequency control loop, the sensitivity equation of the second control parameter is obtained according to the overall impedance in the global coordinate system.

[0148] When considering the control parameters of PFL, the parameter sensitivity is only related to Related:

[0149] (twenty two)

[0150] Therefore, that is, GFM m Impedance sensitivity of PFL and The impedance sensitivities are respectively:

[0151] (twenty three)

[0152] When the critical control loop is a voltage control loop, the participation factor of the first control parameter is obtained by simultaneously solving the sensitivity equation and the sensitivity equation of the first control parameter. Alternatively, when the critical control loop is a power frequency control loop, the participation factor of the second control parameter is obtained by simultaneously solving the sensitivity equation and the sensitivity equation of the second control parameter.

[0153] For any bus-connected grid-type inverter in a power system, based on the dominant controller (i.e., the critical control loop) and the overall impedance... The explicit parameter participation factor is calculated to determine the explicit parameter sensitivity, which is used to enhance the damping of the power system. The explicit parameter sensitivity characterizes the influence of the sensitivity of the control parameters in the overall impedance on the dominant characteristic value of the power system dynamics.

[0154] This invention also provides an apparatus for implementing an extended impedance mode analysis method for the internal dynamics of a grid-connected inverter, comprising a modeling unit, a calculation unit, and an analysis unit;

[0155] Modeling Unit:

[0156] For control structures based on grid-connected inverters, construct an overall impedance model of a single grid-connected inverter in the global coordinate system;

[0157] Used to break down the overall impedance model to obtain the first impedance, second impedance, and third impedance;

[0158] Computational unit:

[0159] For use with a single grid-type inverter, the first impedance, second impedance, and third impedance are calculated by measurement fitting, respectively;

[0160] For power systems based on grid-connected inverters, a modal analysis method using an impedance model is employed to calculate the first participation factor and the second participation factor based on the first impedance, the second impedance, and the third impedance.

[0161] Used to normalize and convert the first participation factor and the second participation factor based on the participation ratio, so as to obtain the first participation ratio and the second participation ratio respectively;

[0162] Analysis Unit:

[0163] Used to determine the key dynamics affecting the stability of the power system based on the first participation ratio and the second participation ratio;

[0164] Used to identify critical control loops in a power system based on key dynamics.

[0165] The performance of the proposed EMAI method is explored below using two systems of different sizes as examples. To demonstrate the comparison with the existing MASS evaluation method, examples 1 and 2 also employ the MAI and MASS methods respectively.

[0166] When using the MAI method, based on the small-signal impedance model of the entire power system, equation (3) is used to calculate the overall participation factor of a single grid-connected inverter on the eigenvalues ​​of the power system. Then, calculate the overall participation ratio according to equation (24), which is the degree of participation of a single grid-connected inverter in the influence of power system stability. ;

[0167] (twenty four)

[0168] The participation of ED and SD can also be evaluated from state variable participation factors using the MASS method. To distinguish it from the method proposed in this disclosure, subscript 2 indicates the participation factors obtained using the MASS method, respectively used to characterize the participation of ED and SD. To obtain GFM using the MASS method m The first control parameter in the power system Equivalent overall participation factor for each eigenvalue To obtain GFM using the MASS method m The second control parameter in the power system Equivalent overall participation factor for each eigenvalue;

[0169] (25)

[0170] In the formula, for dq GFM in coordinate system m of d PF of shaft inductor current, for dq GFM in coordinate system m of q PF of shaft inductor current, for dq GFM in coordinate system m of d PF, in the PI controller integrator of the shaft current control loop (CCL) for dq GFM in coordinate system m of q PF of the PI controller integrator in the axis CCL; for dq GFM in coordinate system m of d pF of the shaft capacitance voltage for dq GFM in coordinate system m of q pF of the shaft capacitance voltage for dq GFM in coordinate system m of q PF of the PI controller integrator in the axis VCL for dq GFM in coordinate system m of q PF of the PI controller integrator in the axis VCL; GFM m The angle variables of PFL and PF For GFM m The filter state variable PF.

[0171] Similarly, in order to normalize the participation factor, the subscript 1 in equation (17) is used to... Modified to , Modified to This is used to calculate the second and third participation ratios obtained using the MASS method, respectively.

[0172] Calculation example 1

[0173] The modified 14-bus system was used to verify that EMAI can fully capture the dominant dynamics within GFM under different conditions.

[0174] Table 1 Parameters of the 14-bus system inverter

[0175]

[0176] Upgrade the 14 busbar system, such as Figure 8 As shown. Bus 1 is set to an infinite bus. Buses 2, 3, 6, and 8 are connected to the GFM. Parameters for all GFMs are given in Appendix Table 1. The system pole distribution is as follows. Figure 9 As shown. Modes 1, 2, 3, and 4 are four modes operating at different frequencies, which are 2... π (-1.23+ j 12.33), 2 π (-3.90+ j 4.55), 2 π (-10.62+ j 36.97) and 2 π (-2.64+ j 42.95). The participation ratio (PR) calculation results for different methods are as follows: Figure 10 As shown in Table 2-5.

[0177] Figure 10 The bar charts of almost equal height across different modes indicate that the three methods achieve similar overall evaluation results for all GFM participation. Clearly, while MAI can provide a holistic assessment of GFM participation, it fails to capture the dominant dynamics of individual GFMs. In contrast, the proposed EMAI not only identifies the interactions between various GFMs and the grid but also provides insights into the complex coupling mechanisms between different dynamics within each GFM. This offers system operators a broader perspective for maintaining and enhancing system stability. The highly similar results between the EMAI and MASS methods further validate the effectiveness of the EMAI method. Furthermore, in Mode 1, the overall evaluation results of GFMs by EMAI are closer to the evaluation structure of MASS than those by MAI, demonstrating the superiority of the EMAI method. Figure 10It also indicates that as the frequency of the oscillation mode decreases, the dominant dynamics in each GFM gradually shift from ED to SD.

[0178] Table 2 14 Busbar System Mode 1 PR

[0179]

[0180] Table 3 14 Busbar System Mode 2 PR

[0181]

[0182] Table 4 14 Busbar System Mode 3 PR

[0183]

[0184] Mode 1 has the weakest damping among the four modes, making it easier to generate oscillations. Figure 8 The data shows that GFM2 is electrically closer to the infinite bus than GFM3. Due to the strong grid instability of GFM, GFM2 may participate more in Mode 1 than GFM3, and disturbances to the infinite bus may have a greater impact on GFM2. However, Figure 10 (a) indicates that GFM3 has a higher overall participation in mode 1 than GFM2, with GFM3 having a high SD proportion, mainly due to the larger droop factor of the PFL in GFM as shown in Table 1. GFM2 has a higher SD proportion than GFM3. At 0.1 seconds, with the voltage of the infinite bus set to a forced oscillation with an amplitude of 0.05 pu and the same frequency as mode 1, the oscillation waveforms of GFM2 and GFM3 are as follows: Figure 11 As shown. The voltage waveform of GFM2 has a larger oscillation amplitude, indicating that GFM2 dominates ED, while the frequency waveform of GFM3 has a larger oscillation amplitude, indicating that GFM3 dominates SD. Simulation results and Figure 10 The conclusions in (a) are consistent, therefore the EMAI method can accurately capture the dominant dynamics within different GFMs, which fully demonstrates the effectiveness of the proposed EMAI method.

[0185] Table 5 14 Busbar System Mode 4 PR

[0186]

[0187] Calculation example 2

[0188] The modified 68 bus system was used to verify the applicability of EMAI in large-scale power systems and the effectiveness of the proposed parameter PF in guiding improvements to system damping.

[0189] Table 6 Inverter Parameters for 68-Bus System

[0190]

[0191] Figure 12 A topology diagram for the modified 68-bus system is provided, where buses 1 and 16 are set as infinite buses, buses 2-15 are connected to synchronous machines, and the remaining GFMs are distributed and connected to different buses. Modes 1, 2, 3, and 4 are four modes operating at different frequencies, which are 2 π (-1.56+ j 35.29), 2 π (-0.69+ j 16.66), 2 π (-0.64+ j 12.23) and 2 π (-1.22+ j 8.08). As shown in Table 6, all GFM parameters are the same. Figure 13 Table 8-11 presents the participation evaluation results of the three methods for the four modes. The bar chart of PR shows that the overall participation results of the three methods are almost identical, and the participation evaluation results of the EMAI method and MASS method for different dynamics within GFM are also highly consistent, which fully demonstrates the applicability of the proposed method in large-scale power systems. Similarly, as the oscillation frequency of the selected modes decreases, the dominant dynamic of all GFMs gradually changes from ED to SD.

[0192] Table 7 Parameters PF of 68-bus system mode 2

[0193]

[0194] Table 868 Bus System Mode 1 PR

[0195]

[0196] Table 968 Bus System Mode 2 PR

[0197]

[0198] Figure 13 (b) Mode 2 π The evaluation results for (-0.69+j16.66) show that GFM50 and GFM51 are very high. Therefore, it is considered to adjust the control parameters of GFM50 and GFM51 to optimize the damping of this mode. The parameter PF of GFM50 and GFM51 is shown in Table 7.

[0199] Table 1068 Bus System Mode 3 PR

[0200]

[0201] Appendix 1168 Bus System Mode 4 PR

[0202]

[0203] As can be seen from the real part of parameter PF, increasing the proportional gain of the PI controller in VCL and reducing the droop coefficient in PFL are better ways to improve system stability in different control loops. Figure 14 The pole distribution plots of GFM50 and GFM51 with the droop gain changed from 0.001 to 0.0005 are given. The increase in mode 2 damping demonstrates the effectiveness of the proposed parameter PF in improving system stability.

[0204] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. An extended impedance mode analysis method for the internal dynamics of a grid-connected inverter, characterized in that: Includes the following steps: Based on the control structure of a grid-connected inverter, a global impedance model of a single grid-connected inverter in the global coordinate system is constructed; the global impedance in the global coordinate system is: ； In the formula, GFM in global coordinate system m Overall impedance, GFM m busbar m The connected grid-type inverter, m The busbar number is the number of the busbar. It is GFM m The coordinate transformation matrix, To characterize the equivalent impedance of electromagnetic dynamics, GFM m Voltage at the point of common coupling, It is GFM m The transfer function of current to angle. It is GFM m The voltage-to-angle transfer function, E 2 is a second-order identity matrix; For GFM m The common connection point supplies external current; The overall impedance model is decomposed to obtain a first impedance, a second impedance, and a third impedance; the first impedance is the equivalent impedance of the single grid-type inverter reflecting electromagnetic dynamics, the second impedance is the equivalent impedance of the single grid-type inverter reflecting the coupling effect of electromagnetic dynamics and synchronous dynamics, and the third impedance is the equivalent impedance of the single grid-type inverter reflecting synchronous dynamics. ； In the formula, K mS It is GFM m The coefficient matrix related to steady-state power, K mUU It is GFM m Voltage-related coefficient matrix; GFM m The equivalent power caused by the power frequency synchronization loop parameters. Q m It is GFM m Reactive power measured at the point of common coupling. P m It is GFM m Active power measured at the point of common coupling. U m It is GFM m The voltage measured at the point of common coupling. For the Laplace operator, It is GFM m The power frequency synchronization loop low-pass filter time constant For GFM m droop gain, As the reference angular frequency, For GFM m On public connection points d shaft voltage, For GFM m On public connection points q shaft voltage, For GFM m On public connection points d shaft current, For GFM m On public connection points q shaft current; Based on the single grid-type inverter, the first impedance, the second impedance, and the third impedance are calculated respectively by measurement and fitting. Based on the power system where the grid-type inverter is located, the modal analysis method of the impedance model is used to calculate the first participation factor and the second participation factor according to the first impedance, the second impedance and the third impedance; the first participation factor is the equivalent overall participation factor of the electromagnetic dynamics in the single grid-type inverter; The second participation factor is the equivalent overall participation factor of the synchronization dynamics in the single grid-connected inverter; ； In the formula, For the first in the power system The perturbation of each eigenvalue For the characteristic value index, for exist The * indicates taking the residue at a given position, and * denotes taking the conjugate transpose of the matrix. For Frobenius inner product, In the global DQ coordinate system, the dynamic admittance matrix of the entire system is 2 m -1 to 2 m line and 2 m -1 to 2 m The block matrix corresponding to the four elements in the column, for The amount of disturbance. The generatrix in the global DQ coordinate system m The impedance of the connected grid-type inverter. The first in the power system control loop 1 eigenvalue, express The degree of disturbance, express The degree of disturbance, The first impedance, The second impedance, The third impedance, For GFM m The first control parameter in the power system Equivalent overall participation factor for each eigenvalue For GFM m The second control parameter in the power system Equivalent overall participation factor for each eigenvalue; Based on the participation ratio, the first participation factor and the second participation factor are normalized and converted to obtain the first participation ratio and the second participation ratio, respectively. ； In the formula, As the first participation ratio, As the second participation ratio, This represents the total number of busbars in the power system. The key dynamics affecting the stability of the power system are determined based on the first participation ratio and the second participation ratio; the key dynamics are either the electromagnetic dynamics or the synchronization dynamics. The critical control loop of the power system is determined based on the critical dynamics.

2. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 1, characterized in that: The impedance model is a small-signal impedance model of the entire power system.

3. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 2, characterized in that: After obtaining the control loop that affects the stability of the power system, the participation factor of the control parameters is calculated based on the small-signal impedance model of the whole system and the overall impedance model.

4. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 3, characterized in that: The steps for calculating the participation factor of the control parameter are as follows: Based on the control loop of the power system, a sensitivity equation is constructed by performing partial differentials on the control parameters according to the overall impedance model; the control parameters include a first control parameter and a second control parameter; the first control parameter is a control parameter reflecting electromagnetic dynamics in a single grid-connected inverter, and the second control parameter is a control parameter reflecting synchronization dynamics in a single grid-connected inverter; Based on the electromagnetic dynamics, the sensitivity equation of the first control parameter is obtained by performing partial differentiation on the first control parameter according to the global impedance in the global coordinate system. Based on the aforementioned synchronization dynamics, the sensitivity equation for the second control parameter is obtained according to the global impedance in the global coordinate system. The participation factor of the first control parameter can be obtained by simultaneously solving the sensitivity equation and the sensitivity equation of the first control parameter, or the participation factor of the second control parameter can be obtained by simultaneously solving the sensitivity equation and the sensitivity equation of the second control parameter.

5. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 4, characterized in that: The control loop that dominates the electromagnetic dynamics is a voltage control loop, which adopts a dual closed loop of voltage and current.

6. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 5, characterized in that: The first control parameter includes the proportional gain of the PI controller in the voltage control loop and the integral gain of the PI controller in the voltage control loop.

7. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 4, characterized in that: The control loop that dominates the synchronization dynamics is a power frequency control loop, and the power frequency synchronization loop adopts droop control with a low-pass filter.

8. The extended impedance mode analysis method for the internal dynamics of a grid-type inverter according to claim 7, characterized in that: The second control parameter includes the low-pass filter time constant of the power frequency synchronization loop and the droop gain of the power frequency synchronization loop.

9. An apparatus for implementing the extended impedance mode analysis method for the internal dynamics of a grid-type inverter as described in any one of claims 1-8, characterized in that: It includes modeling units, computation units, and analysis units; The modeling unit: Used for: constructing an overall impedance model of a single grid-connected inverter in the global coordinate system based on the control structure of the grid-connected inverter; This is used to decompose the overall impedance model to obtain the first impedance, the second impedance, and the third impedance; The computing unit: The first impedance, the second impedance, and the third impedance are calculated respectively by measurement fitting based on the single grid-type inverter; The modal analysis method using an impedance model is used to calculate the first participation factor and the second participation factor based on the first impedance, the second impedance, and the third impedance in the power system where the grid-type inverter is located. This is used to normalize and convert the first participation factor and the second participation factor based on the participation ratio, so as to obtain the first participation ratio and the second participation ratio respectively; The analysis unit: Used to determine the key dynamics affecting the stability of the power system based on the first participation ratio and the second participation ratio; Used to determine the critical control loop of the power system based on the critical dynamics.

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