Robust stability analysis method for network-following construction type series-parallel multi-infeed system

Abstract

The invention relates to a quantitative evaluation method for robust stability of a hybrid multi-infeed system constructed with a network. The quantitative evaluation method comprises the following steps: S1, constructing a hybrid multi-infeed system model; s2, enabling the series-parallel multi-infeed system to be equivalent to an equivalent network construction subsystem and an equivalent network following subsystem, and respectively calculating a generalized short-circuit ratio as a power grid strength quantitative index; s3, selecting a nominal system model, and determining a critical value of small interference stability of a nominal system through the dominant feature root locus; s4, drawing a frequency domain characteristic curve of the uncertainty perturbation singular value, and determining an uncertainty perturbation upper bound; and S5, drawing a complementary sensitivity peak curve when the decoupled nominal system is connected to alternating current networks with different power grid intensities, and quantifying a critical value and a margin of robust stability under a power grid intensity perspective by combining an uncertainty perturbation upper bound. Compared with the prior art, the robust small-interference stability quantitative evaluation method is creatively provided, and technical support can be provided for coordinated optimization configuration and safe and stable operation of the high-proportion new energy grid-connected system.

Description

Technical Field

[0001] The present invention relates to the field of new energy power systems, and in particular to a robust stability analysis method for a grid-connected hybrid multi-feedback system. Background Art

[0002] With the increasing penetration of new energy sources such as wind power and photovoltaic power, the power system is transforming into a new power system dominated by power electronic equipment. The control method of new energy grid-connected equipment (i.e., converter) with power electronics as the interface significantly affects the stability of the system. At present, the converter mostly adopts the grid-following (GFL) control method, relying on the phase-locked loop to track the AC voltage of the grid connection point to achieve synchronization. When the grid-following converter is connected to a weak grid with a low short-circuit ratio, the strong coupling between the phase-locked loop and the grid is prone to phase-lock failure and subsynchronous oscillation instability. In contrast, the grid-forming (GFM) converter adopting the power synchronization strategy can actively establish and support the grid voltage and frequency, and has good adaptability to weak grids, but may have the risk of low-frequency oscillation instability in strong grids with high short-circuit ratios. The gradual introduction of grid-forming converters will form a grid-following hybrid multi-feed system. Studies have shown that the configuration of grid-forming converters can effectively improve the subsynchronous frequency band oscillation problem of the hybrid multi-feed system, but it will increase the risk of low-frequency oscillation instability.

[0003] The dynamic external characteristics of grid-following devices and grid-forming devices in hybrid multi-infeed systems are very different, and the coupling mechanism between devices and between devices and AC power grids is complex. Existing studies often assume that the external characteristics of grid-following or grid-forming converters in hybrid multi-infeed systems are consistent. However, in actual hybrid multi-infeed systems, not only are there differences in external characteristics between converters with different control modes (strong heterogeneity), but converters using the same control mode are also usually "heterogeneous" (weak heterogeneity). It is necessary to combine the decoupling idea of ​​the dominant oscillation mode of grid-following / grid-forming converters and modern robust control theory to analyze the influence of uncertainty "perturbations" that characterize the heterogeneous characteristics of devices on the system. Existing studies on hybrid multi-infeed systems often ignore the impact of uncertainty, and their theories are based on the assumption that the external characteristics of grid-following (grid-forming) converters are similar.

[0004] Therefore, at this stage, there is an urgent need for a robust stability quantitative evaluation method suitable for the complex dynamic characteristics of hybrid multi-input systems. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method for quantitatively evaluating the robust stability of a grid-connected hybrid multi-feedback system. A method for quantitatively evaluating the robust small-disturbance stability is creatively proposed, which can provide technical support for the coordinated optimization configuration and safe and stable operation of a high-proportion new energy grid-connected system.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system includes the following steps:

[0008] S1. Construct a multiplicative perturbation model of a hybrid multi-input system;

[0009] S2. Equivalently divide the hybrid multi-infeed system into an equivalent grid-forming subsystem and an equivalent grid-following subsystem, calculate the generalized short-circuit ratio of the equivalent grid-forming subsystem and the equivalent grid-following subsystem respectively, and use the generalized short-circuit ratio as a quantitative indicator of grid strength;

[0010] S3, select the nominal system model and determine the critical value of the nominal system small disturbance stability by drawing the dominant characteristic root locus;

[0011] S4, draw the frequency domain characteristic curve of the uncertainty perturbation singular value and determine the upper bound of the uncertainty perturbation;

[0012] S5. Draw the complementary sensitivity peak curve when the decoupled nominal system is connected to the AC network with different grid strengths, and quantify the critical value and margin of robust stability from the perspective of grid strength in combination with the uncertainty perturbation upper bound.

[0013] Preferably, the multiplicative perturbation model of the parallel-parallel multi-infeed system specifically includes:

[0014] Nominal system equipment side:

[0015]

[0016] Where: Y GFL (s) indicates the dynamics of network-based devices, Y PLL (s) is the nominal grid-type converter admittance, Y GFM (s) represents the dynamics of networking equipment, Y GF (s) is the nominal grid-type converter admittance, S1 and S2 are diagonal matrices consisting of the capacity ratios of the grid-type converter and the grid-type converter, respectively. is the Kronecker product, e Jθ and e -Jθ is the coordinate transformation matrix between the global coordinate system and the local coordinate system, and θ represents the steady-state phase angle difference between the two coordinate systems;

[0017] Nominal system network side:

[0018]

[0019] Where: Y multi_grid(s) represents the network side dynamics, the B matrix is ​​the node admittance matrix of the AC network, N is the number of converter feeding nodes (the internal nodes in the network have been eliminated by the Kron Reduction method), ω0 is the nominal frequency of the system, and τ is the R / L ratio of the line;

[0020] Uncertainty perturbation:

[0021]

[0022] Wherein, Δ1(s) is the block diagonal matrix composed of the perturbations corresponding to the n grid-type converters in the hybrid system, Δ2(s) is the block diagonal matrix composed of the perturbations corresponding to the m grid-type converters in the hybrid system, diag represents the block diagonal matrix, Δ PLL,i (s)(i=1,K,n) is the perturbation corresponding to the i-th grid-type converter, Δ GF,j (s)(j=1,K,m) is the perturbation corresponding to the jth grid-connected converter, is the device admittance matrix of the ith grid-type converter in the actual hybrid system in the global coordinate system, is the device admittance matrix of the jth grid-type converter in the actual hybrid system in the global coordinate system.

[0023] Preferably, by dividing the dynamics of the hybrid multi-feed system equipment, the hybrid multi-feed system is equivalent to an equivalent network-building subsystem and an equivalent network-following subsystem, specifically:

[0024] The equivalent network subsystem The closed-loop dynamics are:

[0025]

[0026]

[0027]

[0028] in: is the admittance matrix of the grid-connected converter considering the uncertainty on the equipment side, B redv is the equivalent network node admittance matrix after kron reduction, # indicates that a control closed loop is formed between the device dynamics on the left and the network dynamics on the right, gSCR v Equivalent Network Subsystem The generalized short-circuit ratio describes the low-frequency grid strength of the hybrid system, and eig(·) is the function for calculating the eigenvalue of the matrix ·.

[0029] The equivalent network subsystem The closed-loop dynamics are:

[0030]

[0031] B redp =B 11

[0032]

[0033] in: is the admittance matrix of the grid-connected converter considering the uncertainty on the equipment side, B redp To delete the submatrix corresponding to the rows and columns of the grid-type converter nodes in matrix B, gSCR p Equivalent network subsystem The generalized short-circuit ratio describes the grid strength of the hybrid system in the subsynchronous frequency band, and Δλ(s) is the perturbation caused by the dynamics of the grid-connected converter in the equivalent network.

[0034] Preferably, the hybrid multi-feed system adopts a robust stability criterion based on the small gain theorem to perform robust stability judgment, specifically:

[0035] If the uncertainty perturbation Δ(s) H ∞ If the norm has an upper bound, then the sufficient condition for the robust stability of the hybrid multi-input system is:

[0036] 1) The nominal system of the equivalent subsystem is small-disturbance stable, that is:

[0037]

[0038] Among them: gSCR v Equivalent Network Subsystem The generalized short-circuit ratio, CgSCR v gSCR is the critical value of the small interference stability of the nominal system in the low frequency band. p Equivalent network subsystem The generalized short-circuit ratio, CgSCR p It is the critical value of small interference stability of the nominal system in the sub-synchronous frequency band;

[0039] 2) The grid-following / grid-building converter's ability to support grid voltage meets the robust stability conditions:

[0040]

[0041] Among them: CRgSCR v is the critical robust generalized short-circuit ratio in the low frequency band, CRgSCR p is the critical robust generalized short-circuit ratio in the subsynchronous band.

[0042] Preferably, the uncertainty perturbation upper bound quantifies the margin of robust stability from the perspective of power grid strength, specifically:

[0043]

[0044] Where: η1 is the robust stability margin of the low frequency band, η2 is the robust stability margin of the subsynchronous frequency band, CRgSCR v is the critical robust generalized short-circuit ratio in the low frequency band, CRgSCR p is the critical robust generalized short circuit ratio of the subsynchronous frequency band, gSCR v Equivalent Network Subsystem Generalized short circuit ratio, gSCR p Equivalent network subsystem The generalized short-circuit ratio.

[0045] Preferably, the nominal system model is selected, and the critical value of the nominal system small disturbance stability is determined by drawing the dominant characteristic root locus, specifically: the nominal system model is selected, and the critical value CgSCR of the nominal network type system small disturbance stability is determined by the dominant characteristic root locus in the low frequency band v , the critical value CgSCR of small disturbance stability of nominal grid-following system is determined by the dominant characteristic root locus of subsynchronous frequency band p .

[0046] Preferably, the generalized short-circuit ratio is used as a quantitative index of grid strength, specifically: according to the characteristic root decoupling theory of the generalized short-circuit ratio, the isomorphic N-feed system is dynamically characterized by N independent single-feed systems, and the generalized short-circuit ratio gSCR is used to characterize the grid strength of the weakest single-feed system. For the grid-following system, For a networked system, Among them, SCR i Corresponding to the short-circuit ratio of the i-th single-feed system.

[0047] Preferably, the step of drawing the frequency domain characteristic curve of the singular value of the uncertainty perturbation and determining the upper bound of the uncertainty perturbation is specifically as follows: according to the maximum modulus theorem, drawing the frequency domain characteristic curve of the singular value of the uncertainty perturbation Δ(s), and determining the H of the uncertainty perturbation Δ(s) by the peak value of the frequency domain characteristic curve. ∞ The upper bound of the norm is calculated as:

[0048]

[0049] Among them, δ p is the inverse of the upper bound of the perturbation Δ1(s), δ v is the reciprocal of the upper bound of the perturbation Δ2(s), sup represents the maximum value, σ max [·] is the maximum singular value of matrix ·.

[0050] Preferably, the drawing of the complementary sensitivity peak curve when the decoupled nominal system is connected to AC networks with different grid strengths includes:

[0051] Establish an explicit relationship between complementary sensitivity and short-circuit ratio SCR:

[0052]

[0053] Where: Y C (s) is the unified representation of the admittance matrix of the grid-following and grid-forming converters, The matrix SB -1 The i-th eigenvalue of corresponds to the inverse of the short-circuit ratio of the i-th single-feed system after decoupling; W is the eigenvector matrix, and there is a similar diagonal transformation: κ2(W) is the spectral condition number of the matrix W. When SB -1 When it is a symmetric matrix, κ2(W)=1;

[0054] The generalized short-circuit ratio gSCR is used to characterize the grid strength of the weakest single-feed system. The explicit relationship between the generalized short-circuit ratio and the complementary sensitivity peak is:

[0055]

[0056] Where gSCR is the generalized short-circuit ratio of the homogeneous multi-infeed system. For the homogeneous multi-infeed grid-following system, For a homogeneous multi-input grid system,

[0057] Preferably, the drawing of the complementary sensitivity peak curve when the decoupled nominal system is connected to an AC network with different grid strengths, and combining the uncertainty perturbation upper bound to quantify the critical value of robust stability from the perspective of grid strength, specifically includes:

[0058] Plot the weakest single-feed system connected to different generalized short-circuit ratios gSCR after the nominal grid-following system is decoupled p The complementary sensitivity peak curve of the AC system, where the critical robust generalized short-circuit ratio CRgSCR in the subsynchronous frequency band is p The corresponding ordinate is δ p / κ2(W p ) when the generalized short-circuit ratio gSCR p The corresponding calculation expression is:

[0059]

[0060] Where: W p To expand the admittance matrix The eigenvector matrix of .

[0061] Plot the weakest single-feed system connected to different generalized short-circuit ratios gSCR after decoupling of the nominal grid-type system v The complementary sensitivity peak curve of the AC system, where the low-frequency critical robust generalized short-circuit ratio CRgSCRv The corresponding ordinate is δ v / κ2(W v ) when the generalized short-circuit ratio gSCR v The corresponding calculation expression is:

[0062]

[0063] Where: W v To expand the admittance matrix The eigenvector matrix of .

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] (1) The present invention clearly gives the action mechanism and analytical relationship between the generalized short-circuit ratio and the robust stability of the hybrid multi-infeed system. The larger the generalized short-circuit ratio of the equivalent grid-following subsystem, the stronger the supporting ability of the grid-following converter for the grid voltage and the better the robust stability of the subsynchronous frequency band. The smaller the generalized short-circuit ratio of the equivalent grid-following subsystem, the smaller the risk of low-frequency oscillation. That is, the proposed robust stability quantitative evaluation method is strictly based on mathematical derivation, calculation and simulation, and has higher reliability.

[0066] (2) The critical value of robust stability of the present invention is the short-circuit ratio of the critical stability of the weakest single-feed grid-following / grid-forming system taking into account uncertainty. Its calculation only involves 2×2-order matrix operations, avoiding the "curse of dimensionality" problem caused by high-order matrix operations, and the calculation is more convenient.

[0067] (3) The present invention characterizes the differences in the external characteristics of each converter by multiplicative uncertainty perturbation. The relationship between the nominal system complementary sensitivity peak and the grid strength is usually only related to the control method. It is also applicable to complex scenarios in which converters with different control parameters, control structures and operating modes exist in the system, and has a certain degree of universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a flow chart of the method of the present invention;

[0069] Figure 2 It is a flowchart of a specific embodiment of the present invention;

[0070] Figure 3 A schematic diagram of a multi-converter grid-connected system according to an embodiment of the present invention;

[0071] Figure 4 Schematic diagram of a multiplicative perturbation model of a parallel-parallel multi-input system in an embodiment of the present invention;

[0072] Figure 5 Schematic diagram of a hybrid multi-feed system model deconstruction method in an embodiment of the present invention;

[0073] Figure 6 A comparison diagram of the low-frequency band dominant characteristic root loci of the hybrid multi-feed system and its equivalent network subsystem in an embodiment of the present invention;

[0074] Figure 7 A comparison diagram of the dominant characteristic root loci of the subsynchronous frequency band of the hybrid multi-feed system and its equivalent tracking subsystem in an embodiment of the present invention;

[0075] Figure 8 is a distribution diagram of uncertainty perturbation versus frequency in an embodiment of the present invention;

[0076] Fig. 9 is a relationship diagram between the complementary sensitivity peak and gSCRp in an embodiment of the present invention;

[0077] Fig.10 Schematic diagram of critical robust stability of the equivalent network subsystem in an embodiment of the present invention. DETAILED DESCRIPTION

[0078] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0079] Example

[0080] like Figure 1 As shown, this embodiment provides a method for quantitatively evaluating the robust stability of a grid-connected hybrid multi-feedback system, and the method includes the following steps:

[0081] S1. Construct a multiplicative perturbation model of a hybrid multi-infeed system, and input the initial value of the rated capacity of the hybrid multi-infeed system and the original data such as the equivalent AC network line impedance;

[0082] S2. Equivalent the hybrid multi-infeed system to an equivalent grid-forming subsystem Σ1 and an equivalent grid-following subsystem Σ2, and calculate the generalized short-circuit ratio gSCR of the equivalent grid-forming subsystem and the equivalent grid-following subsystem respectively. v and gSCR p , taking the generalized short-circuit ratio as a quantitative indicator of power grid strength;

[0083] S3. Select the nominal system model and draw the dominant characteristic root locus through MATLAB simulation to determine the critical value of the nominal system's small disturbance stability. Specifically, determine the critical value CgSCR of the nominal network type system's small disturbance stability through the dominant characteristic root locus in the low frequency band. v, the critical value CgSCR of small disturbance stability of nominal grid-following system is determined by the dominant characteristic root locus of subsynchronous frequency band p ;

[0084] S4. Draw the frequency domain characteristic curve of the singular value of the uncertainty perturbation and determine the upper bound of the uncertainty perturbation. Specifically, draw the frequency domain characteristic curve of the singular value of the uncertainty perturbation Δ1(s) and Δ2(s) and determine the H of the perturbation. ∞ Norm upper bound δ p -1 and δ v -1 ;

[0085] S5. Draw the complementary sensitivity peak curve when the decoupled nominal system is connected to the AC network with different grid strengths, and combine the uncertainty perturbation upper bound to quantify the critical value and margin of robust stability from the perspective of grid strength. Specifically: Draw the decoupled nominal grid system connected to different gSCR v The complementary sensitivity peak curve of the AC system is used to solve the critical robust generalized short-circuit ratio CRgSCR in the low-frequency band. v and robust stability margin η1; plot the nominal grid-type system after decoupling connected to different gSCR p The complementary sensitivity peak curve of the AC system is used to solve the critical robust generalized short-circuit ratio CRgSCR in the subsynchronous frequency band. p and robust stability margin η2.

[0086] Next, the method of this embodiment is introduced in detail.

[0087] Firstly, a multiplicative perturbation model of the hybrid multi-infeed system considering equipment uncertainty is established. Figure 3 The multi-converter grid-connected system shown includes n grid-following converters (nodes 1 to n) and m grid-forming converters (nodes n+1 to N), and the dynamic external characteristics of each grid-following converter are different, and the dynamic external characteristics of each grid-forming converter are also different. The differences mainly come from the different control parameters, control structures and operating modes adopted by the converters.

[0088] Using the perturbation Δ(s) to represent the uncertainty on the device side, the multiplicative perturbation model of the hybrid multi-infeed system can be obtained, as follows: Figure 4 As shown in the figure, the model consists of the following three parts:

[0089] 1) Nominal system equipment side:

[0090]

[0091] Among them, Y GFL (s) indicates the dynamics of network-based devices, Y PLL (s) is the nominal grid-type converter admittance, YGFM (s) represents the dynamics of networking equipment, Y GF (s) is the nominal grid-type converter admittance, S1 and S2 are the diagonal matrices consisting of the capacity ratios of the grid-type converter and the grid-type converter, respectively, e Jθ and e -Jθ is the coordinate transformation matrix between the global coordinate system and the local coordinate system, and θ represents the steady-state phase angle difference between the two coordinate systems.

[0092] 2) Nominal system network side:

[0093]

[0094] Where: Y multi_grid (s) represents the network side dynamics, ω0 is the nominal frequency of the system, and τ is the R / L ratio of the line. The B matrix is ​​the node admittance matrix of the AC network, which can be expressed in blocks as follows:

[0095]

[0096] 3) Uncertainty perturbation:

[0097]

[0098] Wherein, Δ1(s) is the block diagonal matrix composed of the perturbations corresponding to the n grid-type converters in the hybrid system, Δ2(s) is the block diagonal matrix composed of the perturbations corresponding to the m grid-type converters in the hybrid system, diag represents the block diagonal matrix, Δ PLL,i (s)(i=1,K,n) is the perturbation corresponding to the i-th grid-type converter, Δ GF,j (s)(j=1,K,m) is the perturbation corresponding to the jth grid-connected converter, is the device admittance matrix of the ith grid-type converter in the actual hybrid system in the global coordinate system, is the device admittance matrix of the jth grid-type converter in the actual hybrid system in the global coordinate system.

[0099] Then, the grid-forming converter is dynamically merged into the equivalent network, such as Figure 5 As shown in Figure 1, the hybrid multi-infeed system is deconstructed into two subsystems dominated by a single type of converter on the device side. Since the closed-loop poles of the original hybrid multi-infeed system are the combination of the closed-loop poles of the two subsystems after deconstruction, it can be proved that the original hybrid multi-infeed system is stable if and only if the two subsystems are stable.

[0100] In order to make the robust stability analysis method based on the small gain theorem applicable to the two subsystems, it is also necessary to construct an equivalent heterogeneous multi-infeed grid-following / grid-forming system to approximate the dominant oscillation modes of the two subsystems Σ2 and Σ1, and quantify the grid voltage support capability of the grid-following / grid-forming converter for the hybrid multi-infeed system from the perspective of grid strength.

[0101] By performing Kron reduction on the network side, an equivalent network subsystem is obtained.

[0102]

[0103] in: is the admittance matrix of the grid-connected converter considering the uncertainty on the equipment side, B redv is the equivalent network node admittance matrix after kron reduction; gSCR v Equivalent Network Subsystem The generalized short-circuit ratio is also a quantitative indicator of the strength of the low-frequency power grid.

[0104] Equivalent network subsystem The closed-loop dynamics are:

[0105]

[0106] B redp =B 11

[0107] SCR p =min[eig(S1 -1 B redp )]+Δλ(s)

[0108] in: is the admittance matrix of the grid-connected converter considering the uncertainty on the equipment side, B redp To delete the sub-matrix corresponding to the rows and columns of the grid-type converter nodes in matrix B; gSCR p Equivalent network subsystem The generalized short-circuit ratio is also a quantitative indicator of the grid strength in the subsynchronous frequency band; Δλ(s) is the perturbation caused by the dynamics of the grid-connected converter in the equivalent network, which can be ignored because the grid-connected converter usually has high admittance.

[0109] Figure 6 and Figure 7 The original hybrid multi-input system and its equivalent subsystem obtained through MATLAB simulation The comparison diagram of the dominant characteristic root loci in the low-frequency band / sub-synchronous frequency band shows that the dominant characteristic root loci are approximately fitted, indicating that the robust stability performance of the hybrid multi-feed system is characterized by its equivalent subsystem.

[0110] In order to reduce the conservatism of the robust stability criterion, the grid-following / grid-forming equipment that can minimize the perturbation is selected as the nominal model. According to the characteristic equation of the “weakest” single-feed grid-following / grid-forming system after decoupling the nominal grid-following / grid-forming system and the gSCR p / gSCR v Explicit relationship between:

[0111] c(s)=det(Y PLL (s)+gSCR p *F(s))

[0112] c(s)=det(Y GF (s)+gSCR v *F(s))

[0113] The dominant characteristic root locus of the subsynchronous frequency band / low frequency band of the nominal network-following / network-forming system is plotted on MATLAB. When the real part of the dominant characteristic root is 0, the system is considered to be critically stable with small disturbances, thus determining the critical value CgSCR of the nominal system with small disturbance stability. p / CgSCR v .

[0114] The robust stability quantitative evaluation process of the two equivalent subsystems is the same. For example, the device uncertainty perturbation is expressed as:

[0115]

[0116] in: Equivalent network subsystem The device admittance matrix of the i-th converter in the global coordinate system, e Jθ Y PLL (s)e -Jθ is the device admittance matrix in the global coordinate system of the nominal tracking system.

[0117] Analyze the above uncertainty perturbation and plot σ on MATLAB max [Δ PLL,i The distribution curve of (jω)] with frequency (such as Figure 8 As shown), determine the peak value of the perturbation and its inverse δ p .

[0118] The uncertainty perturbation Δ1(s) on the equipment side affects the critical value CgSCR of the small disturbance stability of the nominal grid-following system. p By inversely solving the following equation, the critical robust generalized short-circuit ratio CRgSCR can be obtained: p The explicit expression for is:

[0119]

[0120] The above solution process is equivalent to drawing the “weakest” single-feed system connected to different gSCRs after the nominal grid-type system is decoupled on MATLAB. p The complementary sensitivity peak curve of the AC system (such as Fig. 9 As shown), CRgSCR p The corresponding ordinate is δ p / κ2(W p ) p Value. Equivalent to the network subsystem The schematic diagram of critical robust stability is shown in Fig.10 .

[0121] The equivalent grid subsystem based on the generalized short-circuit ratio is obtained The robust stability and its critical value quantitative evaluation index can define the robust stability margin of the subsynchronous frequency band of the system as:

[0122] η2=gSCR p -CRgSCR p

[0123] Similarly, the equivalent network subsystem can be calculated Critical robust generalized short circuit ratio CRgSCR v , and quantify the system low-frequency robust stability margin:

[0124] η1=CRgSCR v -gSCR v

[0125] The simulation results show that the equivalent subsystem model constructed in this embodiment can fit the dominant characteristic root trajectory of the original hybrid multi-feedback system, so that the robust stability analysis of the complex system is simplified to the robust stability analysis of two subsystems. The robust stability quantitative evaluation method combining the generalized short-circuit ratio theory and the small gain theorem can not only take into account the uncertainty factors, but also simplify the high-order matrix solution problem to 2×2-order matrix solution, which greatly reduces the amount of calculation and has application value in practical engineering.

[0126] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system, characterized in that: The following steps are involved: S1. Construct a multiplicative perturbation model of a hybrid multi-input system; S2. Equivalently divide the hybrid multi-infeed system into an equivalent grid-forming subsystem and an equivalent grid-following subsystem, calculate the generalized short-circuit ratio of the equivalent grid-forming subsystem and the equivalent grid-following subsystem respectively, and use the generalized short-circuit ratio as a quantitative indicator of grid strength; S3, select the nominal system model and determine the critical value of the nominal system small disturbance stability by drawing the dominant characteristic root locus; S4, draw the frequency domain characteristic curve of the uncertainty perturbation singular value and determine the upper bound of the uncertainty perturbation; S5. Draw the complementary sensitivity peak curve when the decoupled nominal system is connected to the AC network with different grid strengths, and quantify the critical value and margin of robust stability from the perspective of grid strength in combination with the uncertainty perturbation upper bound.

2. According to claim 1, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: The multiplicative perturbation model of the hybrid multi-input system specifically includes: Nominal system equipment side: Where: Y GFL (s) indicates the dynamics of network-based devices, Y PLL (s) is the nominal grid-type converter admittance, Y GFM (s) represents the dynamics of networking equipment, Y GF (s) is the nominal grid-type converter admittance, S1 and S2 are diagonal matrices consisting of the capacity ratios of the grid-type converter and the grid-type converter, respectively. is the Kronecker product, e Jθ and e -Jθ is the coordinate transformation matrix between the global coordinate system and the local coordinate system, and θ represents the steady-state phase angle difference between the two coordinate systems; Nominal system network side: Where: Y multi_grid (s) represents the network side dynamics, the B matrix is ​​the node admittance matrix of the AC network, N is the number of converter feeding nodes, ω0 is the nominal frequency of the system, and τ is the R / L ratio of the line; Uncertainty perturbation: Where: Δ1(s) is the block diagonal matrix composed of the perturbations corresponding to the n grid-type converters in the hybrid system, Δ2(s) is the block diagonal matrix composed of the perturbations corresponding to the m grid-type converters in the hybrid system, diag represents the block diagonal matrix, Δ PLL,i (s), i = 1, ..., n is the perturbation corresponding to the i-th grid-type converter, Δ GF,j (s),j=1,...,m is the perturbation corresponding to the jth grid-connected converter, is the device admittance matrix of the ith grid-type converter in the actual hybrid system in the global coordinate system, is the device admittance matrix of the jth grid-type converter in the actual hybrid system in the global coordinate system.

3. According to claim 2, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: By dividing the dynamics of the hybrid multi-infeed system equipment, the hybrid multi-infeed system is equivalent to an equivalent grid-building subsystem and an equivalent grid-following subsystem, specifically: The equivalent network subsystem The closed-loop dynamics are: in: is the admittance matrix of the grid-connected converter considering the uncertainty on the equipment side, B redv is the equivalent network node admittance matrix after kron reduction, # indicates that a control closed loop is formed between the device dynamics on the left and the network dynamics on the right; gSCR v Equivalent Network Subsystem The generalized short-circuit ratio is used to describe the low-frequency power grid strength of the hybrid system; eig(·) is the function for calculating the eigenvalue of the matrix ·; The equivalent network subsystem The closed-loop dynamics are: B redp =B 11 in: is the admittance matrix of the grid-connected converter considering the uncertainty on the equipment side, B redp To delete the sub-matrix corresponding to the rows and columns of the grid-type converter nodes in matrix B; gSCR p Equivalent network subsystem The generalized short-circuit ratio is used to describe the grid strength of the hybrid system in the subsynchronous frequency band; Δλ(s) is the perturbation caused by the dynamics of the grid-connected converter in the equivalent network.

4. According to claim 3, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: The hybrid multi-input system adopts a robust stability criterion based on the small gain theorem to perform robust stability judgment, specifically: If the uncertainty perturbation Δ(s) H ∞ If the norm has an upper bound, then the sufficient condition for the robust stability of the hybrid multi-input system is: 1) The nominal system of the equivalent subsystem is small-disturbance stable, that is: Among them: gSCR v Equivalent Network Subsystem The generalized short-circuit ratio, CgSCR v gSCR is the critical value of small interference stability of the nominal system in the low frequency band. p Equivalent network subsystem The generalized short-circuit ratio, CgSCR p It is the critical value of small interference stability of the nominal system in the sub-synchronous frequency band; 2) The grid-following / grid-building converter's ability to support grid voltage meets the robust stability conditions: Among them, CRgSCR v is the critical robust generalized short-circuit ratio in the low frequency band, CRgSCR p is the critical robust generalized short-circuit ratio in the subsynchronous band.

5. According to claim 4, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: The uncertainty perturbation upper bound quantifies the margin of robust stability from the perspective of power grid strength, specifically: Where: η1 is the robust stability margin of the low frequency band, η2 is the robust stability margin of the subsynchronous frequency band, CRgSCR v is the critical robust generalized short-circuit ratio in the low frequency band, CRgSCR p is the critical robust generalized short circuit ratio of the subsynchronous frequency band, gSCR v Equivalent Network Subsystem Generalized short circuit ratio, gSCR p Equivalent network subsystem The generalized short-circuit ratio.

6. According to claim 4, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: The nominal system model is selected, and the critical value of the nominal system small disturbance stability is determined by drawing the dominant characteristic root locus. Specifically, the nominal system model is selected, and the critical value CgSCR of the nominal network type system small disturbance stability is determined by the dominant characteristic root locus in the low frequency band. v , the critical value CgSCR of small disturbance stability of nominal grid-following system is determined by the dominant characteristic root locus of subsynchronous frequency band p .

7. According to claim 4, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: The generalized short-circuit ratio is used as a quantitative indicator of grid strength. Specifically, according to the characteristic root decoupling theory of the generalized short-circuit ratio, the isomorphic N-feed system is dynamically characterized by N independent single-feed systems, and the generalized short-circuit ratio gSCR is used to characterize the grid strength of the weakest single-feed system. For the grid-following system, For a networked system, Among them, SCR i Corresponding to the short-circuit ratio of the i-th single-feed system.

8. According to claim 4, a method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system is characterized in that: The method of drawing the frequency domain characteristic curve of the singular value of the uncertainty perturbation and determining the upper bound of the uncertainty perturbation is specifically as follows: according to the maximum modulus theorem, drawing the frequency domain characteristic curve of the singular value of the uncertainty perturbation Δ(s), and determining the H of the uncertainty perturbation Δ(s) by the peak value of the frequency domain characteristic curve ∞ The upper bound of the norm is calculated as: Where: p is the inverse of the upper bound of the perturbation Δ1(s), δ v is the reciprocal of the upper bound of the perturbation Δ2(s), sup represents the maximum value, σ max [·] is the maximum singular value of matrix ·.

9. The method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system according to claim 8 is characterized in that: The drawing of the complementary sensitivity peak curve when the decoupled nominal system is connected to an AC network with different grid strengths includes: Establish an explicit relationship between complementary sensitivity and short-circuit ratio SCR: Where: Y C (s) is the unified representation of the admittance matrix of the grid-following and grid-forming converters, The matrix SB -1 The i-th eigenvalue of corresponds to the inverse of the short-circuit ratio of the i-th single-feed system after decoupling; W is the eigenvector matrix, and there is a similar diagonal transformation: κ2(W) is the spectral condition number of the matrix W. When SB -1 When it is a symmetric matrix, κ2(W)=1; The generalized short-circuit ratio gSCR is used to characterize the grid strength of the weakest single-feed system. The explicit relationship between the generalized short-circuit ratio and the complementary sensitivity peak is: Where: gSCR is the generalized short-circuit ratio of the homogeneous multi-infeed system. For the homogeneous multi-infeed grid-following system, For a homogeneous multi-input grid system, 10. The method for quantitatively evaluating robust stability of a grid-connected hybrid multi-feedback system according to claim 9, characterized in that: The method of drawing the complementary sensitivity peak curve when the decoupled nominal system is connected to the AC network with different grid strengths, and combining the uncertainty perturbation upper bound to quantify the critical value of robust stability from the perspective of grid strength, specifically includes: Plot the weakest single-feed system connected to different generalized short-circuit ratios gSCR after the nominal grid-following system is decoupled p The complementary sensitivity peak curve of the AC system, where the critical robust generalized short-circuit ratio CRgSCR in the subsynchronous frequency band is p The corresponding ordinate is δ p / κ2(W p ) when the generalized short circuit ratio gSCR p The corresponding calculation expression is: Where: W p To expand the admittance matrix The eigenvector matrix of Plot the weakest single-feed system connected to different generalized short-circuit ratios gSCR after decoupling of the nominal grid-type system v The complementary sensitivity peak curve of the AC system, where the low-frequency critical robust generalized short-circuit ratio CRgSCR v The corresponding ordinate is δ v / κ2(W v ) when the generalized short circuit ratio gSCR v The corresponding calculation expression is: Where: W v To expand the admittance matrix The eigenvector matrix of .

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