Extended impedance modal analysis method and device for internal dynamics of network-forming inverter

Abstract

The invention provides an extended impedance modal analysis method for internal dynamics of a network-forming inverter. The method comprises the following steps: splitting an overall impedance model under a global coordinate system to obtain first impedance, second impedance and third impedance, and respectively calculating through measurement fitting; calculating a first participation factor and a second participation factor according to the first impedance, the second impedance and the third impedance by adopting a modal analysis method of an impedance model, and normalizing the first participation factor and the second participation factor to obtain a first participation ratio and a second participation ratio; determining a key control loop influencing the stability of the power system according to the first participation ratio and the second participation ratio; and the control parameters of the key control loop are adjusted based on the explicit parameter participation factors so as to enhance system damping and improve system stability. According to the analysis method provided by the invention, the root cause of influence of different controllers in the network-building type inverter on the system stability is effectively identified, and the problem of extension impedance participation degree evaluation of dominant dynamics of the different controllers in the network-building type inverter is effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic stability of power systems, and in particular to an extended impedance modal analysis method and device for internal dynamics of a grid-connected inverter. Background Art

[0002] The large-scale integration of grid-forming inverters (GFMs) has greatly changed the dynamic characteristics of power systems, which has aroused widespread concern about the instability of power systems caused by the interaction between GFMs and power grids. At the same time, the interactive coupling between controllers of different time scales within GFMs makes stability analysis more complicated. Understanding the dynamic behavior of GFMs is crucial to solving potential stability problems. Therefore, it is urgent to develop new modeling and analysis frameworks to solve the ever-changing and complex stability problems. Since inverters are usually only provided with impedance models that describe the characteristics of voltage and current ports, which have gray box or black box characteristics, it is often necessary to make a reasonable assessment of the impact of different controllers of grid-forming inverters on stability in practice, so as to locate the key control loops and key control parameters that affect the system, so as to effectively optimize the control parameters of grid-forming inverters to achieve the purpose of improving system stability. At present, there is no analysis method for the internal dynamics of grid-forming inverters. Summary of the invention

[0003] In view of the problems existing in the prior art, the present invention proposes an extended impedance modal analysis method for the internal dynamics of a grid-type inverter, reveals the interaction relationship between different control loops inside the grid-type inverter, and realizes the dominant dynamics positioning of the internal dynamics of the grid-type inverter based on this analysis method, which has certain guiding significance for the current gray box modal analysis of the internal dynamics of the grid-type inverter.

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

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

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

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

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

[0009] Normalizing and converting the first participation factor and the second participation factor based on the participation ratio to obtain a first participation ratio and a second participation ratio respectively;

[0010] Determine the key dynamics affecting the stability of the power system according to the first participation ratio and the second participation ratio; the key dynamics is the electromagnetic dynamics or the synchronous dynamics;

[0011] Critical control loops of the power system are determined based on the key dynamics.

[0012] Furthermore, the first participation factor and the second participation factor are normalized and converted based on the participation ratio to obtain the first participation ratio and the second participation ratio respectively.

[0013] respectively calculating the absolute value of the first participation factor and the absolute value of the second participation factor of a single grid-connected inverter;

[0014] Obtaining an overall factor according to the sum of the absolute value of the first participation factor and the absolute value of the second participation factor;

[0015] Based on the power system, obtaining a sum of the overall factors according to the sum of the overall factors;

[0016] Obtaining the first participation ratio according to the proportion of the first participation factor in the sum of the overall factors;

[0017] The second participation ratio is obtained according to the proportion of the second participation factor in the sum of the overall factors.

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

[0019] Furthermore, after obtaining the control loop affecting the stability of the power system, the participation factor of the control parameter is calculated according to the small signal impedance model of the whole system and the overall impedance model.

[0020] Furthermore, the step of calculating the control parameter participation factor is:

[0021] Based on the control loop of the power system, the control parameter is partially differentiated according to the overall impedance model to construct a sensitivity equation; the control parameter includes the first control parameter and the second control parameter; the first control parameter is a control parameter reflecting electromagnetic dynamics in a single grid-type inverter, and the second control parameter is a control parameter reflecting synchronous dynamics in a single grid-type inverter;

[0022] Based on the electromagnetic dynamics, partially differentiating the first control parameter according to the overall impedance in the global coordinate system to obtain a sensitivity equation for the first control parameter;

[0023] Based on the synchronous dynamics, obtaining a sensitivity equation of a second control parameter according to the overall impedance in the global coordinate system;

[0024] The sensitivity equation and the sensitivity equation of the first control parameter are combined to obtain the participation factor of the first control parameter, or the sensitivity equation and the sensitivity equation of the second control parameter are combined and solved to obtain the participation factor of the second control parameter.

[0025] Furthermore, the control loop that dominates the electromagnetic dynamics is a voltage control loop, and the voltage control loop adopts a voltage-current double closed loop.

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

[0027] Furthermore, the control loop that dominates the synchronous 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 a power frequency synchronization loop low-pass filter time constant and a power frequency synchronization loop droop gain.

[0029] A device for implementing the extended impedance modal analysis method of the internal dynamics of the grid-type inverter, comprising a modeling unit, a calculation unit and an analysis unit;

[0030] The modeling unit:

[0031] Used to: construct the overall impedance model of a single grid-type inverter in the global coordinate system based on the control structure of the grid-type inverter;

[0032] Used to split the overall impedance model to obtain a first impedance, a second impedance and a third impedance;

[0033] The computing unit:

[0034] Used to calculate the first impedance, the second impedance and the third impedance respectively through measurement fitting based on the single grid-type inverter;

[0035] For calculating a first participation factor and a second participation factor according to the first impedance, the second impedance and the third impedance by using a modal analysis method of an impedance model based on the power system where the grid-type inverter is located;

[0036] for normalizing and converting the first participation factor and the second participation factor based on the participation ratio to obtain a first participation ratio and a second participation ratio respectively;

[0037] The analysis unit:

[0038] for determining key dynamics affecting the stability of the power system according to the first participation ratio and the second participation ratio;

[0039] for determining key control loops of the power system based on the key dynamics.

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

[0041] 1. The analysis method provided by the present invention performs impedance splitting on the grid-type inverter, and then proposes an equivalent overall participation factor to evaluate the degree of participation of electromagnetic dynamics and synchronous dynamics dominated by different controllers, thereby effectively identifying the fundamental reasons why different controllers inside the grid-type inverter affect the system stability.

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

[0043] 3. The analysis method provided by the present invention is applicable to power systems containing a high proportion of grid-type inverters, and the stability of the system can be effectively improved according to the explicit parameter participation factors in different controllers of the grid-type inverters.

[0044] 4. The analysis method proposed in the present 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 this port. The calculation is simple and has good practical engineering application value. It can quickly and conveniently evaluate the fundamental reasons inside the grid-type inverter that affect the system stability, and has certain guiding significance for the current gray box modal analysis of the internal dynamics of the grid-type inverter. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of a small signal impedance model of the whole system in an embodiment of the present invention;

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

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

[0048] Figure 4 The impedance Bode diagram of an embodiment of the present invention;

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

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

[0051] Figure 7 It is an impedance differential operation diagram of an embodiment of the present invention;

[0052] Figure 8 This is a schematic diagram of the busbar system 14 transformed in Example 1 of the present invention;

[0053] Fig. 9 It is a pole distribution diagram of the modified 14-busbar system in Example 1 of the present invention;

[0054] Fig.10 The comparison diagram of the evaluation results of different modes of the 14-bus system modified in Example 1 of the present invention, (a) is mode 1, (b) is mode 2, (c) is mode 3, and (d) is mode 4;

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

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

[0057] Fig.13 The comparison diagram of the evaluation results of different modes of the 68-bus system in the calculation example 2 of the present invention, (a) is mode 1, (b) is mode 2, (c) is mode 3, and (d) is mode 4;

[0058] Fig.14 Schematic diagram of pole distribution of the 68 busbar system before and after parameter adjustment in Example 2 of the present invention;

[0059] Fig.15 It is a flow chart of the extended impedance modal analysis method of the internal dynamics of the grid-type inverter of the present invention. DETAILED DESCRIPTION

[0060] By the end of June 2024, the installed capacity of wind power and solar power generation connected to the grid in China will reach 470 million kilowatts and 710 million kilowatts respectively. New energy represented by wind power and photovoltaic power generation will be connected to the grid on a large scale through power electronic equipment such as grid-connected inverters. The level of power electronics in the grid will continue to improve, and "high proportion of new energy" and "high proportion of power electronic equipment" have become the inevitable trend of the development of my country's power system.

[0061] Modal Analysis Based on the State-spaceModel (MASS) is an important method that uses linear algebra to determine the key factors of the system. 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 scale of the mathematical model, which in turn increases the difficulty of modal analysis. In addition, state-space modeling requires detailed models and specific parameters for each system component. Since inverters are usually only provided with impedance models that describe the characteristics of the voltage and current ports, which have gray box or black box characteristics, the applicability of MASS for GFM stability analysis remains to be explored. MASS requires the system to be a white box model, so it is not suitable for scenarios where grid-type inverters can often only be provided with gray box or even black box models.

[0062] Recently, the full system dynamic matrix analyzes system stability by embedding the coordinate system dynamics of the inverter. On this basis, the Modal Analysis based on Impedance Model (MAI) method can evaluate the contribution of each power device to the oscillation mode at the device level. In addition, the corresponding parameter PF can also provide suggestions for improving system damping. However, unlike MASS, MAI considers the inverter as a whole element, which limits its ability to find the dominant dynamics of the system at the control loop or state variable level.

[0063] Gaining insight into the root causes of system instability within the GFM is crucial for targeted improvements in system stability. A method called port mapping provides a new perspective for analyzing stability issues caused by different causes. In addition, the extended impedance model enables the separation of different dynamics within the GFM by introducing additional degrees of freedom, but has certain limitations in practical applications. Decomposing different control loops into equivalent circuit elements allows stability analysis of the internal dynamics of the inverter. However, the decomposition of the synchronous control loop remains to be explored.

[0064] Modal Analysis Based on the State-space Model (MASS) requires the system to be a white box model, so it is not suitable for scenarios where grid-forming inverters (GFM) can only be provided with gray box or even black box models. The technical problem to be solved by the present disclosure is to conduct gray box participation evaluation on the dynamics dominated by different controllers inside the grid-forming inverter. Specifically: Based on the idea of ​​impedance splitting, 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). The overall PF characterizing ED and SD is proposed to evaluate the degree of participation of different control loops, and an explicit parameter participation factor (PF) is proposed to improve unstable oscillation modes. The gray box modal analysis of the internal dynamics of the grid-forming inverter is realized. The purpose of the present invention is to quickly locate the controller inside the grid-type inverter that plays a dominant role in system stability, and propose an extended impedance modal analysis method for the internal dynamics of the grid-type inverter, namely the extended MAI (Extend Modal Analysis based on Impedance Model, EMAI) method.

[0065] In order to clearly illustrate the technical features of this solution, this solution is described below through a specific implementation method.

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

[0067] Based on the power system where the grid-connected inverter is located Figure 1 The small signal impedance model of the whole system is shown in the figure. The total number of buses in the power system is n, and Z N is the node impedance matrix of the whole system network. The source impedance models of all meshed inverters need to align their coordinate systems to the global coordinate system before connection. Then, the admittance of the meshed inverter connected to bus m in the global DQ coordinate system is for:

[0068]

[0069] Where YmDD , Y mDQ , Y mQD and Y mQQ They are The four components of is the impedance of the grid-type inverter connected to bus m in the global DQ coordinate system, where m is the bus number;

[0070] according to Figure 1 The closed-loop feedback relationship shown in the figure is the dynamic admittance matrix Y of the whole system in the global DQ coordinate system. w for:

[0071] Y w =(E 2n +Y DQ Z N ) -1 Y DQ (2)

[0072] In the formula, E 2n is the identity matrix of order 2n, Y DQ It is the admittance matrix of the grid-shaped inverters connected to all buses in the whole system in the global DQ coordinate system;

[0073] The disturbance of the ith eigenvalue in the power system control loop is:

[0074]

[0075] In the formula, Δλ i is the disturbance of the ith eigenvalue in the power system, Y wm In λ i The remainder, Y wm is the block matrix corresponding to the four elements in rows 2m-1 to 2m and columns 2m-1 to 2m, λ i is the i-th eigenvalue in the power system control loop, i is the eigenvalue number, * indicates the conjugate transpose of the matrix, <,> is the Frobenius inner product, for The disturbance, ε m Normalized scalar, PF m is the overall participation factor of GFMm to the ith eigenvalue in the power system, where GFMm is the grid-connected inverter connected to bus m;

[0076] Based on the control structure of the grid-type inverter, the overall 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 given. In the figure, R fis the resistance of the LC filter circuit, L f is the inductance of the LC filter circuit and C f is the capacitance of the LC filter circuit. is the capacitor voltage, is the capacitor voltage reference value. As mentioned above, the power frequency synchronization loop adopts droop control with a low-pass filter, and the voltage control loop adopts a voltage and current double closed loop. When the frequency reference signal of the grid-type inverter is constant, it can be obtained Figure 3 The positive and negative sequence equivalent circuits corresponding to the voltage control loop shown.

[0078] Figure 3 In this case, s is the Laplace operator; ω0 is the reference angular frequency; Z L+ The equivalent impedance of the positive branch of the filter inductor, Z L- is the equivalent impedance of the negative branch of the filter inductor, Y C+ The equivalent impedance of the positive branch of the filter capacitor, Z L- is the equivalent impedance of the negative branch of the filter capacitor, Z PI+ is the equivalent impedance of the current control loop (CCL) positive circuit PI control, Z PI+ is the equivalent impedance of the negative circuit PI control of the current control loop, K pi is the proportional gain of the current control loop PI control, K ii is the integral gain of the current control loop PI control; Y PIv+ is the equivalent admittance of the positive circuit PI control of the voltage control loop (VCL), Y PIv- is the equivalent admittance of the negative circuit PI control of the voltage control loop, K pv is the proportional gain of the voltage control loop PI control, K iv is the integral gain of the voltage control loop PI control; Z CDi+ is the equivalent impedance of the cross-decoupling control of the positive circuit of the current control loop, Z CDi- is the equivalent impedance of the negative circuit cross-decoupling control of the current control loop, Y CDv+ is the equivalent admittance of the positive circuit cross-decoupling control of the voltage control loop, Y CDv- is the equivalent admittance of the negative circuit cross-decoupling control of the voltage control loop; Z Vi+ is the equivalent impedance of the positive circuit controlled by the current virtual impedance, Z Vi- is the equivalent impedance of the current virtual impedance control negative circuit, R Vi is the resistance controlled by the current virtual impedance, X Vi is the inductor controlled by the current virtual impedance; Y Vv+ is the equivalent admittance of the positive circuit controlled by the voltage virtual admittance, Y Vv- is the equivalent admittance of the negative circuit controlled by the voltage virtual admittance, R Vvis the voltage virtual impedance controlled resistor, X Vv is the inductor controlled by voltage virtual impedance; Y Fv+ is the equivalent admittance of the voltage feedforward impedance controlled positive circuit, Y Fv- is the equivalent admittance of the voltage feedforward impedance controlled negative circuit; F v is the voltage feed-forward gain; Z Fi+ is the equivalent impedance corresponding to the positive circuit of current feedforward control, Z Fi- is the equivalent impedance corresponding to the negative circuit of current feedforward control, F i is the current feedforward gain; Y i+ is the positive circuit equivalent admittance of the current control loop, Y i- is the equivalent admittance of the negative circuit of the current control loop, Y v+ is the positive circuit equivalent admittance of the voltage control loop, Y v- is the equivalent admittance of the negative circuit of the voltage control loop, Z o+ is the total equivalent impedance of the positive circuit, Z o- is the total equivalent impedance of the negative circuit, is the total equivalent impedance of positive and negative sequences; G del is the control delay, T s is the sampling period; G i+ is the current control loop positive circuit gain, G i- is the negative circuit gain of the current control loop, G v+ is the voltage control loop positive circuit gain, G v- is the negative circuit gain of the voltage control loop;

[0079] The total equivalent impedance Z in the dq coordinate system when the power frequency synchronization ring is not considered dq The total equivalent impedance of positive and negative sequences can be Conversion:

[0080]

[0081] In the formula, Z odd , Z odq , Z oqd , Z oqq Z dq Four components in the dq coordinate system;

[0082] As can be seen from the circuit diagram, the CCL integral controller is equivalent to a capacitor connected in series with the filter inductor branch, which makes the positive circuit equivalent admittance Y of the current control loop i+ And the equivalent admittance Y of the negative circuit of the current control loop i- When s=j0, it is 0, that is, Y i+ and Y i- is the external characteristic of the current source. The VCL integral controller is equivalent to the inductor connected in parallel to the filter capacitor branch, which makes the positive circuit equivalent admittance Y of the voltage control loop v+And the equivalent admittance Y of the negative circuit of the voltage control loop v- When s=j0, it is infinite, that is, Y v+ and Y v- is the external characteristic of the voltage source. Figure 4 The Z of GFM3 in Table 1 (GFM3 represents the grid-type inverter connected to bus 3, and the power impedance of all grid-type inverters must be aligned with the global coordinate system of the system) is given. dq Bode plot of the cross-decoupling control, virtual control, and feedforward control, all set to 0. The VCL integral controller makes Z dq The impedance amplitude is extremely small within the subsynchronous frequency band.

[0083] exist Figure 5 In, ω b represents the angular velocity of the system reference power supply, and θ m represents the angle of GFMm relative to the reference source, θ m0 represents the steady-state angle of GFMm relative to the reference source, and Δθ m It represents the angle deviation of GFMm relative to the reference source. When the power frequency synchronization loop PFL does not provide additional dynamics, that is, Δθ m =0, which means that the swing coordinate system and the steady-state coordinate system coincide.

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

[0085]

[0086] In the formula, is the d-axis voltage on the common connection point of GFMm, is the q-axis voltage on the common connection point of GFMm, is the d-axis voltage of GFMm in the rocking coordinate system, is the q-axis voltage of GFMm in the swing coordinate system, is the d-axis current at the common connection point of GFMm, is the q-axis current at the common connection point of GFMm, is the d-axis current of GFMm in the swing coordinate system, is the q-axis current of GFMm in the swing coordinate system, is the droop gain of GFMm; T mf =1 / f mf is the low-pass filter time constant of the power frequency synchronization loop of GFMm, f mf is the low-pass filter bandwidth of the power frequency synchronization loop of GFMm; H mi is the current-to-angle transfer function of GFMm; H mv is the voltage-to-angle transfer function of GFMm, ΔP mis the active power change of GFMm.

[0087] Depend on Figure 5 It can be seen that the voltage variable of GFMm is transformed from the swing coordinate system to the global coordinate system through coordinate transformation, and it is linearized in the equilibrium state. The voltage relationship is:

[0088]

[0089] Where U m0 represents the voltage at the common connection point of GFMm, is the coordinate transformation matrix of GFMm; is the voltage vector of GFMm in the swing coordinate system, is the voltage vector of GFMm in the global coordinate system, is the D-axis voltage of GFMm in the global coordinate system, is the Q-axis voltage of GFMm in the global coordinate system;

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

[0091]

[0092] In the formula, I m0 represents the current at the common connection point of GFMm, is the current vector of GFMm in the swing coordinate system, is the current vector of GFMm in the global coordinate system, is the D-axis current of GFMm in the global coordinate system, is the Q-axis current of GFMm in the global coordinate system;

[0093] The overall impedance model is split to obtain the first impedance, the second impedance and the third impedance; the first impedance is the equivalent impedance of a single grid-type inverter reflecting electromagnetic dynamics, the second impedance is the equivalent impedance of a single grid-type inverter reflecting the coupling effect of electromagnetic dynamics and synchronous dynamics, and the third impedance is the equivalent impedance of a single grid-type inverter reflecting synchronous dynamics; electromagnetic dynamics is the dynamics caused by the AC voltage loop and electrical geographical location of the grid-type inverter, and synchronous dynamics is the dynamics caused by power frequency synchronization of the grid-type 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]

[0096] In the formula, is the overall impedance of GFMm in the global coordinate system, E2 is the second-order unit matrix; Send current to the common connection point of GFMm; To characterize the equivalent impedance of electromagnetic dynamics ED, Figure 6 The equivalent impedance of electromagnetic dynamics ED

[0097] Generally, the voltage loop bandwidth is several hundred Hz. The subsynchronous frequency is much smaller than the voltage loop bandwidth, so ΔP in equation (5) m can be rewritten as:

[0098]

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

[0100]

[0101] also, Figure 4 The Bode plot shows Much smaller than H mi This further illustrates the rationality of simplification. m0 and H mi are matrices of order 2×1 and 1×2 respectively, so (E2+I m0 H mi ) -1 It can be written as (E2+I m0 ×1×H mi ) -1 , which can be simplified to (12) using the matrix inversion lemma of (11).

[0102] (a+bd -1 c) -1 =a -1 -a -1 b(d+ca -1 b) -1 ca -1 (11)

[0103] Where a, b, c, and d are arbitrary matrices that are compatible in dimension and conform to the matrix multiplication rules.

[0104] (E2+I m0 ×1×H mi ) -1 =E2-I m0 (1+H mi I m0 ) -1 H mi (12)

[0105] Substituting equation (12) into equation (10), we notice that Hmi I m0 is a scalar, U m0 H mi Written as (1+H mi I m0 )(1+H mi I m0 ) - 1 U m0 H mi It is convenient to merge and simplify, and the final formula (10) is It is broken down into three parts.

[0106]

[0107] In the formula, K mS is the coefficient matrix related to steady-state power of GFMm, K mUU is the coefficient matrix related to GFMm and voltage; represents the equivalent power caused by the PFL parameters of GFMm; U m is the voltage measured at the common connection point of GFMm, P m is the active power measured by GFMm at the common connection point, Q m is the reactive power measured by GFMm at the point of common connection.

[0108] The first part, i.e. 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, the second impedance, is affected by the coupling effect between VCL and PFL. The decomposition of can be rewritten as .

[0109]

[0110] Based on a single grid-type inverter, the first impedance, the second impedance and the third impedance are respectively calculated by measuring and fitting;

[0111] It can be calculated by measuring the fit and Disconnect the PFL control loop, i.e. set the PFL frequency reference signal to a constant value or droop gain Set it to zero, and you can Separation and exist The unknown variable is and T mf . Due to K mS and K mUUare not zero, so we can solve the equation by calculating the appropriate frequency point and T mf At this point, we can calculate by measuring the fit three parts.

[0112] Based on the power system where the grid-type inverter is located, the modal analysis method of the impedance model is adopted 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 a single grid-type inverter, and the first participation factor that characterizes the degree of participation in the electromagnetic dynamics is calculated by the first impedance and the second impedance The second participation factor is the equivalent overall participation factor of synchronous dynamics in a single grid-type inverter. The second participation factor that characterizes the degree of participation in synchronous dynamics is composed of the second impedance and the third impedance caused by common

[0113] Perform differential operation on formula (13), and the calculation process diagram is as follows: Figure 7 shown.

[0114]

[0115] In the formula, represents the equivalent power caused by the PFL parameters of GFMm; ε me express The degree of disturbance, ε ms express degree of disturbance.

[0116] The combination of (3) and (15) can provide more in-depth identification of the dynamics that have the greatest impact on the power system.

[0117]

[0118] In the formula, PF me1 is the equivalent overall participation factor of the first control parameter in GFMm to the ith eigenvalue in the power system, PF ms1 is the equivalent overall participation factor of the second control parameter in GFMm to the ith eigenvalue in the power system, i.e., PF me1 Reflects the equivalent overall participation factor of the voltage control loop VCL, PF ms1 reflects the equivalent overall participation factor of the power frequency synchronization loop PFL. It is worth noting that PF me1 by and The joint influence of PF ms1 is and As a result of the interaction of. Since voltage control is essentially a voltage and current double closed loop, 1 / 2 is the conversion factor of impedance participation in the EMAI method;

[0119] The first participation factor and the second participation factor are normalized and converted based on the participation ratio to obtain a first participation ratio and a second participation ratio respectively, the steps are:

[0120] Calculating the absolute value of the first participation factor and the absolute value of the second participation factor of a single grid-connected inverter respectively;

[0121] The overall factor is obtained by summing the absolute value of the first participation factor and the absolute value of the second participation 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 according to the proportion of the first participation factor in the sum of the overall factors;

[0124] The second participation ratio is obtained according to the proportion of the second participation factor in the sum of the overall factors.

[0125]

[0126] In the formula, PR me1 is the first participation ratio, PR ms1 is the second participation ratio;

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

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

[0129] When PR me1 ≥PR ms1 When , the electromagnetic dynamics dominated by the voltage control loop plays a dominant role in the influence on 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 PR me1 <PR ms1 When , the synchronous dynamics dominated by the power frequency synchronization loop plays a dominant role in the influence on the stability of the power system, that is, the control loop that affects the stability of the power system is the synchronous dynamics control loop dominated by the power frequency synchronization loop;

[0131] According to the system characterization of different grid-type inverter ED and SD characteristics PRme1 and PR ms1 The value of is used to locate the dominant controller corresponding to the key dynamics affecting the system stability. The factors affecting the system stability are narrowed down to specific controllers, so as to further optimize the control parameters of the key controllers to effectively improve the system stability. PR is used to normalize the participation 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] The value of the participation factor PF of each control parameter in the key controller indicates the direction in which the dominant eigenvalue of the system will change when the corresponding control parameter is increased. The decrease in the real part of the system eigenvalue indicates an increase in the system damping, so the control parameter with the largest absolute value of the real part of the adjustment parameter participation factor PF is selected. If the real part of the PF value is positive, the corresponding control parameter value is reduced, and vice versa, if the real part of the PF value is negative, the corresponding control parameter value is increased. This achieves the purpose of increasing the system damping and improving the system stability.

[0134] The steps to calculate the control parameter participation factor are:

[0135] Based on the control loop of the power system, the control parameters are partially differentiated according to the overall impedance model to construct a sensitivity equation; 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-type inverter, and the second control parameter is a control parameter reflecting synchronous dynamics in a single grid-type inverter; preferably, the control loop that dominates electromagnetic dynamics is a voltage control loop, and the voltage control loop adopts a voltage-current double closed loop, and 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 a parameter reflecting the power frequency synchronization loop in the power system, preferably, the control loop that dominates synchronous dynamics is a power frequency control loop, and the power frequency synchronization loop adopts a droop control with a low-pass filter, and the second control parameter includes the power frequency synchronization loop low-pass filter time constant and the power frequency synchronization loop droop gain;

[0136] Equivalent overall impedance Sensitivity of any control parameter ρ of different control loops inside the grid-connected inverter It can be used to determine the main parameters affecting the system dynamics.

[0137]

[0138] It is difficult to obtain analytically using conventional methods. Conventional methods use numerical differences to replace partial derivative calculations, but the numerical differences are required to be small enough, which sometimes leads to unexpected errors.

[0139] exist Based on the three parts, we can get Explicit expression of , and then solve:

[0140] Based on electromagnetic dynamics, that is, when the key control loop is a voltage control loop, a sensitivity equation of the first control parameter is obtained by partially differentiating the first control parameter according to the overall impedance in the global coordinate system;

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

[0142]

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

[0144]

[0145] Therefore, the proportional gain of the PI controller of VCL in GFMm is Sensitivity and integral gain The sensitivities are:

[0146]

[0147] Based on synchronous dynamics, that is, when the key control loop is the 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]

[0150] Therefore, the impedance sensitivity of PFL in GFMm is T mf and The impedance sensitivities are:

[0151]

[0152] When the key control loop is a voltage control loop, the sensitivity equation and the sensitivity equation of the first control parameter are combined to obtain the participation factor of the first control parameter, or when the key control loop is a power frequency control loop, the sensitivity equation and the sensitivity equation of the second control parameter are combined and solved to obtain the participation factor of the second control parameter.

[0153] For any bus-connected grid-connected inverter in the power system, based on the dominant controller, i.e. the key control loop and the overall impedance The explicit parameter participation factor is calculated and the explicit parameter sensitivity is determined to enhance the damping of the power system; the explicit parameter sensitivity characterizes the influence of the sensitivity of the control parameter in the overall impedance on the dominant characteristic value of the power system dynamics.

[0154] The embodiment of the present invention also provides a device for implementing an extended impedance modal analysis method for internal dynamics of a grid-type inverter, comprising a modeling unit, a calculation unit, and an analysis unit;

[0155] Modeling unit:

[0156] It is used to construct the overall impedance model of a single grid-type inverter in a global coordinate system based on the control structure of the grid-type inverter;

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

[0158] Computational Unit:

[0159] Used to calculate the first impedance, the second impedance and the third impedance respectively through measurement fitting based on a single grid-type inverter;

[0160] It 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 based on the power system where the grid-type inverter is located, using the modal analysis method of the impedance model;

[0161] Used to normalize and convert 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;

[0162] Analysis unit:

[0163] for determining key dynamics affecting the stability of the power system according to a first participation ratio and a second participation ratio;

[0164] Used to identify critical control loops of power systems based on key dynamics.

[0165] The following two systems of different scales are used as examples to explore the performance of the proposed EMAI method. In order to show the comparison with the existing MASS evaluation method, Example 1 and Example 2 also use the MAI method and MASS method to calculate the results respectively. That is:

[0166] When the MAI method is used for calculation, based on the small signal impedance model of the whole system constructed by the power system, the overall participation factor PF of a single grid-connected inverter to the characteristic value in the power system is calculated using formula (3): m ; Then calculate the overall participation ratio according to formula (24), that is, the participation degree PR of a single grid-connected inverter in the influence of power system stability m ;

[0167]

[0168] The participation of ED and SD can also be evaluated from the state variable participation factors using the MASS method. To distinguish it from the method proposed in this disclosure, the subscript 2 is used to represent the participation factors obtained by the MASS method for characterizing the participation of ED and SD, i.e., PF me2 To obtain the equivalent overall participation factor of the first control parameter in GFMm to the ith eigenvalue in the power system using the MASS method, PF ms2 To obtain the equivalent overall participation factor of the second control parameter in GFMm to the i-th eigenvalue in the power system using the MASS method;

[0169]

[0170] In the formula, is the PF of the d-axis inductor current of GFMm in the dq coordinate system, is the PF of the q-axis inductor current of GFMm in the dq coordinate system, is the PF of the PI controller integrator in the d-axis current control loop CCL of GFMm in the dq coordinate system, is the PF of the PI controller integrator in the q-axis CCL of GFMm in the dq coordinate system; is the PF of the d-axis capacitance voltage of GFMm in the dq coordinate system, is the PF of the q-axis capacitor voltage of GFMm in the dq coordinate system, is the PF of the PI controller integrator in the q-axis VCL of GFMm in the dq coordinate system, is the PF of the PI controller integrator in the q-axis VCL of GFMm in the dq coordinate system; PF mθ PF and PF representing the angle variable of the PFL of GFMm mω is the PF of the filter state variable of GFMm.

[0171] Similarly, in order to normalize the participation factor, the PF with a subscript of 1 in equation (17) is me1 Modified to PF me2 PF ms1 Modified to PF ms2 , which are used to calculate the second participation ratio and the third participation ratio respectively using the MASS method.

[0172] Calculation example 1

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

[0174] Table 1 14-bus system inverter parameters

[0175]

[0176] Transform 14 busbar system such as Figure 8 Bus 1 is set as an infinite bus. Buses 2, 3, 6 and 8 are connected to GFMs. The parameters of all GFMs are given in Appendix 1. The system pole distribution is shown in Fig. 9 As shown. Modes 1, 2, 3 and 4 are four modes at different frequencies, namely 2π(-1.23+j12.33), 2π(-3.90+j4.55), 2π(-10.62+j36.97) and 2π(-2.64+j42.95). The participation ratio PR calculation results of different methods are shown in Fig.10 As shown in Table 2-5.

[0177] Fig.10 The bars of almost the same height in different modes show that the three methods have the same overall evaluation effect on the participation of all GFMs. Obviously, although MAI can make an overall assessment of the participation of GFMs, it cannot capture the dominant dynamics of a single GFM. In contrast, the EMAI proposed in this paper can not only identify the interaction between various GFMs and the power grid, but also provide the complex coupling mechanism between the different dynamics within each GFM. This provides system operators with a broader perspective to maintain and enhance system stability. The results of the EMAI method and the MASS method are highly similar, which further verifies the effectiveness of the EMAI method. In addition, the overall evaluation results of EMAI on GFM in mode 1 are closer to the evaluation structure of MASS than MAI, which illustrates the superiority of the EMAI method. In addition, Fig.10 It also shows that the dominant dynamics in each GFM gradually shifts from ED to SD as the frequency of the oscillation mode decreases.

[0178] Table 2 14-bus system mode 1PR

[0179]

[0180] Table 3 14-bus system mode 2PR

[0181]

[0182] Table 4 14-bus system mode 3PR

[0183]

[0184] Mode 1 is the weakest damped among the four modes, so it is easier to be excited to oscillate. Figure 8It shows that GFM2 is closer to the infinite bus than GFM3. Due to the strong grid instability of GFM, GFM2 may participate in Mode 1 to a greater extent than GFM3, and disturbances in the infinite bus may have a greater impact on GFM2. Fig.10 (a) shows that GFM3 has a higher overall participation in mode 1 than GFM2, among which the SD ratio of GFM3 is very high, which is mainly due to the larger droop coefficient of GFM's PFL in Table 1. The SD ratio of GFM2 is higher than that of GFM3. At 0.1 seconds, the voltage of the infinite bus is 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 shown in Fig.11 As shown in the figure, the voltage waveform oscillation amplitude of GFM2 is larger, which indicates that GFM2 dominates ED, while the frequency waveform oscillation amplitude of GFM3 is larger, which indicates that GFM3 dominates SD. Fig.10 (a) is consistent, so the EMAI method can accurately capture the dominant situations of the internal dynamics of different GFMs, which fully demonstrates the effectiveness of the proposed EMAI method.

[0185] Table 5 14-bus system mode 4PR

[0186]

[0187] Calculation example 2

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

[0189] Table 6 68 bus system inverter parameters

[0190]

[0191] Fig.12 The topology of the modified 68 bus is given, where bus 1 and 16 are set as infinite bus, bus 2-15 are connected to synchronous machine, and the rest of GFM are dispersedly connected to different bus. Mode 1, 2, 3 and 4 are four modes at different frequencies, namely 2π(-1.56+j35.29), 2π(-0.69+j16.66), 2π(-0.64+j12.23) and 2π(-1.22+j8.08). As shown in Table 6, the parameters of all GFMs are the same. Fig.13Tables 8-11 give 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 the same, and the participation evaluation results of the EMAI method and the MASS method for different dynamics within the 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 mode decreases, the dominant dynamics of all GFMs gradually change from ED to SD.

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

[0193]

[0194] Table 8 68 bus system mode 1PR

[0195]

[0196] Table 9 68 bus system mode 2PR

[0197]

[0198] Fig.13 In the evaluation results of mode 2 2π(-0.69+j16.66) in (b), GFM50 and GFM51 show high participation, so it is considered to adjust the control parameters of GFM50 and GFM51 to optimize the damping of this mode. The PF parameters of GFM50 and GFM51 are shown in Table 7.

[0199] Table 10 68 bus system mode 3PR

[0200]

[0201] Schedule 11 68 bus system mode 4PR

[0202]

[0203] From the real part of the parameter PF, it can be seen that increasing the proportional gain of the PI controller in VCL and reducing the droop coefficient in PFL are good ways to improve the system stability in different control loops. Fig.14 The pole distribution diagram of changing the droop gain of GFM50 and GFM51 from 0.001 to 0.0005 is given, in which the increase of mode 2 damping illustrates the effectiveness of the proposed parameter PF guidance 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, rather than to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions of the technical solution of the present invention by ordinary technicians in this field do not deviate from the essence and scope of the technical solution of the present invention.

Claims

1. An extended impedance modal analysis method for internal dynamics of a grid-connected inverter, characterized in that: The following steps are involved: Based on the control structure of the grid-type inverter, the overall impedance model of a single grid-type inverter in the global coordinate system is constructed; The overall impedance model is split to obtain a first impedance, a second impedance and a third impedance; the first impedance is an equivalent impedance of the single grid-type inverter reflecting electromagnetic dynamics, the second impedance is an equivalent impedance of the single grid-type inverter reflecting the influence of the coupling effect of electromagnetic dynamics and synchronous dynamics, and the third impedance is an equivalent impedance of the single grid-type inverter reflecting synchronous dynamics; Based on the single grid-type inverter, respectively calculating the first impedance, the second impedance and the third impedance by measurement fitting; Based on the power system where the grid-type inverter is located, a modal analysis method of an impedance model is used to calculate a first participation factor and a second participation factor according to the first impedance, the second impedance and the third impedance; the first participation factor is an equivalent overall participation factor of electromagnetic dynamics in the single grid-type inverter; The second participation factor is an equivalent overall participation factor of synchronous dynamics in the single grid-connected inverter; Normalizing and converting the first participation factor and the second participation factor based on the participation ratio to obtain a first participation ratio and a second participation ratio respectively; determining key dynamics affecting power system stability according to the first participation ratio and the second participation ratio; The key dynamics is the electromagnetic dynamics or the synchronous dynamics; Critical control loops of the power system are determined based on the key dynamics.

2. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 1, characterized in that: The steps of 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 are as follows: respectively calculating the absolute value of the first participation factor and the absolute value of the second participation factor of a single grid-connected inverter; Obtaining an overall factor according to the sum of the absolute value of the first participation factor and the absolute value of the second participation factor; Based on the power system, obtaining a sum of the overall factors according to the sum of the overall factors; Obtaining the first participation ratio according to the proportion of the first participation factor in the sum of the overall factors; The second participation ratio is obtained according to the proportion of the second participation factor in the sum of the overall factors.

3. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 1, characterized in that: The impedance model is a small signal impedance model of the entire system constructed based on the power system.

4. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 3, characterized in that: After obtaining the control loop affecting the stability of the power system, the participation factor of the control parameter is calculated according to the small signal impedance model of the whole system and the overall impedance model.

5. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 4, characterized in that: The steps of calculating the participation factor of the control parameter are: Based on the control loop of the power system, the control parameter is partially differentiated according to the overall impedance model to construct a sensitivity equation; the control parameter includes a first control parameter and a second control parameter; the first control parameter is a control parameter reflecting electromagnetic dynamics in a single grid-type inverter, and the second control parameter is a control parameter reflecting synchronous dynamics in a single grid-type inverter; Based on the electromagnetic dynamics, partially differentiating the first control parameter according to the overall impedance in the global coordinate system to obtain a sensitivity equation for the first control parameter; Based on the synchronous dynamics, obtaining a sensitivity equation of a second control parameter according to the overall impedance in the global coordinate system; The sensitivity equation and the sensitivity equation of the first control parameter are combined to obtain the participation factor of the first control parameter, or the sensitivity equation and the sensitivity equation of the second control parameter are combined and solved to obtain the participation factor of the second control parameter.

6. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 5, characterized in that: The control loop that dominates the electromagnetic dynamics is a voltage control loop, and the voltage control loop adopts a voltage-current double closed loop.

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

8. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 5, characterized in that: The control loop that dominates the synchronization dynamics is a power frequency control loop, which uses droop control with a low-pass filter.

9. The extended impedance modal analysis method for internal dynamics of a grid-connected inverter according to claim 8, characterized in that: The second control parameters include a power frequency synchronization loop low-pass filter time constant and a power frequency synchronization loop droop gain.

10. A device for implementing the extended impedance modal analysis method of internal dynamics of a grid-connected inverter according to any one of claims 1 to 9, characterized in that: It includes modeling unit, calculation unit and analysis unit; The modeling unit: Used to: construct the overall impedance model of a single grid-type inverter in the global coordinate system based on the control structure of the grid-type inverter; Used to split the overall impedance model to obtain a first impedance, a second impedance and a third impedance; The computing unit: Used to calculate the first impedance, the second impedance and the third impedance respectively through measurement fitting based on the single grid-type inverter; For calculating a first participation factor and a second participation factor according to the first impedance, the second impedance and the third impedance by using a modal analysis method of an impedance model based on the power system where the grid-type inverter is located; for normalizing and converting the first participation factor and the second participation factor based on the participation ratio to obtain a first participation ratio and a second participation ratio respectively; The analysis unit: for determining key dynamics affecting the stability of the power system according to the first participation ratio and the second participation ratio; for determining key control loops of the power system based on the key dynamics.

Images