A small signal stability analysis method for grid-connected off-grid data centers

Abstract

This invention discloses a method for small-disturbance stability analysis of grid-connected and off-grid data centers, belonging to the field of stability analysis technology. The method includes the following steps: S1, constructing the data center power supply system; S2, constructing the dynamic admittance matrix of the DC network and the transfer function of the converter; S3, determining the reconstructed admittance matrix and the reconstructed transfer function; S4, determining the dominant oscillation mode based on the reconstructed transfer function. This invention equates the dynamic differences between different converters to the series and parallel impedance forms of the connected network. Therefore, all converters have the same transfer function, and the system retains its original dynamic characteristics. Through the principle of similarity transformation, the full-order state-space model is equivalent to multiple decoupled low-order system equations, thereby achieving efficient and accurate calculation of small-disturbance stability analysis for grid-connected and off-grid data centers.

Description

Technical Field

[0001] This invention belongs to the field of stability analysis technology, specifically relating to a small-interference stability analysis method for on-grid and off-grid data centers. Background Technology

[0002] Existing research mostly ignores some dynamic characteristics of converters to achieve model order reduction for high-order systems. In large systems, errors from multiple converters can lead to significant deviations in the analysis results. When performing small-disturbance stability analysis on grid-connected and off-grid data centers, the high order of the full-order state-space model makes analysis difficult, and mainstream model order reduction methods often ignore some dynamic characteristics, resulting in errors. Furthermore, as the system model increases, an excessive number of converters can still lead to the curse of dimensionality.

[0003] To address the above shortcomings, this invention provides a universally applicable method for reducing the order of stability in small-disturbance systems. By transforming the differences in dynamic characteristics between converters into network differences, and combining similarity transformation theory, the method achieves model order reduction and accurate calculation for full-order systems. Summary of the Invention

[0004] To address the above problems, this invention proposes a small-interference stability analysis method for connected and off-grid data centers.

[0005] The technical solution of this invention is: a method for small-interference stability analysis of on-grid and off-grid data centers, comprising the following steps:

[0006] S1. Construct a data center power supply system;

[0007] S2. Based on the data center power supply system, construct the dynamic admittance matrix of the DC network and the transfer function of the converter;

[0008] S3. Connect the converter's dynamic differential equivalent impedance to the DC network, determine the reconstructed admittance matrix based on the dynamic admittance matrix of the DC network, and reconstruct the converter's transfer function based on the reconstructed admittance matrix to determine the reconstructed transfer function.

[0009] S4. Determine the dominant oscillation mode based on the reconstructed transfer function.

[0010] Furthermore, in S1, the expression for the AC-DC converter in the data center power supply system is:

[0011] ;

[0012] in, This represents the port voltage of the k-th AC-DC converter. This represents the open-loop transfer function model of the k-th AC-DC converter. This represents the port current of the k-th AC-DC converter. This represents the first coefficient value of the numerator polynomial of the k-th transfer function. Let represent the second coefficient value of the numerator polynomial of the k-th transfer function. Let represent the value of the third coefficient of the numerator polynomial of the k-th transfer function. This represents the fourth coefficient value of the numerator polynomial of the k-th transfer function. This represents the first coefficient value of the denominator polynomial of the k-th transfer function. This represents the second coefficient value of the denominator polynomial of the k-th transfer function. This represents the value of the third coefficient of the denominator polynomial of the k-th transfer function. This represents the fourth coefficient value of the denominator polynomial of the k-th transfer function. This represents the fifth coefficient value of the denominator polynomial of the k-th transfer function. Represents complex frequency;

[0013] In S1, the expression for the DC-DC converter in the data center power supply system is:

[0014] ;

[0015] in, This represents the port voltage of the j-th DC-DC converter. This represents the open-loop transfer function model of the j-th DC-DC converter. This represents the port current of the j-th DC-DC converter. This represents the first coefficient value of the numerator polynomial of the j-th transfer function. Let represent the second coefficient value of the numerator polynomial of the j-th transfer function. This represents the value of the third coefficient of the numerator polynomial of the j-th transfer function. This represents the fourth coefficient value of the numerator polynomial of the j-th transfer function. This represents the first coefficient value of the denominator polynomial of the j-th transfer function. This represents the second coefficient value of the denominator polynomial of the j-th transfer function. This represents the value of the third coefficient of the denominator polynomial of the j-th transfer function. This represents the fourth coefficient value of the denominator polynomial of the j-th transfer function. This represents the fifth coefficient value of the denominator polynomial of the j-th transfer function;

[0016] In S1, the expression for the data center load model in the data center power supply system is:

[0017] ;

[0018] in, This represents the port voltage of the t-th DC data center load. This represents the port current of the t-th DC data center load. Let represent the open-loop transfer function model of the t-th DC data center load.

[0019] Furthermore, S2 includes the following sub-steps:

[0020] S21. Based on the data center power supply system, construct the dynamic admittance matrix of the DC network;

[0021] S22. Based on the dynamic admittance matrix of the DC network and the data center load model of the data center power supply system, determine the transfer function between the converter output current and the port voltage.

[0022] S23. Based on the DC-DC converter of the data center power supply system and the transfer function between the converter output current and the port voltage, construct the transfer function of the DC network;

[0023] S24. Using any source-side converter in the data center power supply system as a reference converter, obtain the transfer function of the reference converter;

[0024] S25. Determine the transfer function of all converters based on the transfer function of the reference converter.

[0025] Furthermore, in S21, the expression for the dynamic admittance matrix of the DC network is:

[0026] ;

[0027] in, This indicates the outflow current of the power supply side converter. This represents the current flowing into the DC system from the load terminal. The admittance matrix of a DC network is represented. This represents the admittance matrix between the source-side converter nodes. This represents the first admittance matrix between the source-side converter node and the load node. This represents the second admittance matrix between the source-side converter node and the load node. This represents the first admittance matrix between the source-side converter nodes and the passive nodes. This represents the second admittance matrix between the source-side converter nodes and the passive nodes. This represents the admittance matrix between load nodes. This represents the first admittance matrix between passive nodes and load nodes. This represents the second admittance matrix between passive nodes and load nodes. This represents the admittance matrix between passive nodes. This indicates the converter port voltage. This represents the port voltage flowing into the DC system from the load end. This represents the DC voltage at a passive node in a DC network.

[0028] In S22, by eliminating the current flowing into the DC system from the load end, the port voltage flowing into the DC system from the load end, and the DC voltage at the passive nodes of the DC network, the transfer function between the converter output current and the port voltage is obtained, and its expression is:

[0029] ;

[0030] ;

[0031] Y l (s)=diag[R l1 -1 ···R lT -1 ] T ;

[0032] in, Indicates elimination , and The expression for the transfer function between the converter output current and the port voltage is then obtained. Let R represent a diagonal matrix consisting of the reciprocals of the load transfer function, and let diag[·] denote a diagonal matrix. l1 R represents the first load transfer function. lT Let T represent the load transfer function of the Tth generation, where T indicates that there are T loads in the system.

[0033] In S23, the expression for the transfer function of the DC network is:

[0034] ;

[0035] R o (s)=diag[R o1 ···R o(M+N) ];

[0036] Among them, R o (s) represents the diagonal matrix composed of the source-side converters. R represents the identity matrix. o1 R represents the transfer function of the first converter. o(M+N) This represents the transfer function of the (M+N)th converter;

[0037] In S24, the transfer function of the reference converter The expression is:

[0038] ;

[0039] in, This represents the numerator polynomial of the transfer function of the reference converter. Denotes the denominator polynomial of the transfer function of the reference converter. This represents the value of the first coefficient in the numerator polynomial. This represents the value of the second coefficient in the numerator polynomial. This represents the value of the third coefficient in the numerator polynomial. This represents the value of the fourth coefficient in the numerator polynomial. This represents the value of the first coefficient in the denominator polynomial. This represents the value of the second coefficient in the denominator polynomial. This represents the value of the third coefficient in the denominator polynomial. This represents the value of the fourth coefficient in the denominator polynomial. This represents the value of the fifth coefficient in the denominator polynomial. Represents complex frequency;

[0040] In S25, the transfer function of the j-th converter The expression is:

[0041] ;

[0042] in, Indicates the first differential equivalent impedance, This represents the second differential equivalent impedance. This represents the transfer function of the reference converter.

[0043] Furthermore, S3 includes the following sub-steps:

[0044] S31. Connect the equivalent impedance of the converter's dynamic difference to the DC network of the data center power supply system to form a reconfigured DC system;

[0045] S32. Construct the reconstruction admittance matrix for the reconstructed DC system;

[0046] S33. Based on the reconstructed admittance matrix, determine the transfer function between the converter output current and the port voltage after the DC network is reconstructed;

[0047] S34. Based on the transfer function between the converter output current and port voltage after DC network reconstruction, construct the reconstruction transfer function.

[0048] Furthermore, in S32, the expression for reconstructing the admittance matrix is:

[0049] ;

[0050] Y l (s)=diag[R l1-1 ···R lT -1 ] T ;

[0051] in, This indicates the outflow current of the power supply side converter. This represents the admittance matrix between source-side converter nodes after considering the differential equivalent impedance. This represents the first admittance matrix between the source-side converter node and the load node after considering the differential equivalent impedance. This represents the second admittance matrix between the source-side converter node and the load node, taking into account the differential equivalent impedance. This represents the admittance matrix between load nodes after considering the differential equivalent impedance. A diagonal matrix consisting of the reciprocals of the load transfer function. This represents the first admittance matrix between the passive node and the load node after considering the differential equivalent impedance. This represents the second admittance matrix between the passive node and the load node after considering the differential equivalent impedance. This represents the first admittance matrix between the source-side converter nodes and passive nodes after considering the differential equivalent impedance. This represents the second admittance matrix between the source-side converter nodes and passive nodes, taking into account the differential equivalent impedance. This represents the admittance matrix between passive nodes after considering the differential equivalent impedance. This indicates the converter port voltage. This represents the port voltage flowing into the DC system from the load end. R represents the DC voltage at a passive node in a DC network, diag[·] represents a diagonal matrix, and R l1 R represents the first load transfer function. lT This represents the T-th load transfer function;

[0052] In S33, the expression for the transfer function between the converter output current and the port voltage after DC network reconfiguration is:

[0053] ;

[0054] ;

[0055] in, This indicates the outflow current of the power supply side converter. This represents the reconstructed equivalent network admittance matrix. Indicates the converter port voltage;

[0056] In S34, the expression for reconstructing the transfer function is:

[0057] ;

[0058] ;

[0059] in, Let E represent the diagonal matrix consisting of the transfer functions of the reference converter, and let E represent the identity matrix. This represents the transfer function of the reference converter.

[0060] Furthermore, S4 includes the following sub-steps:

[0061] S41. Substitute the complex frequency into the reconstructed transfer function and use the similarity transformation method to reduce the full-order model to a lower-order system.

[0062] S42. Based on the low-order system, determine the dominant oscillation mode.

[0063] Furthermore, in S41, the expression for reducing the full-order model to a lower-order system is:

[0064] ;

[0065] in, express An invertible matrix composed of the left eigenvectors, This represents a diagonal matrix consisting of the transfer functions of the reference converter. Indicates will Substitution The obtained network admittance array, This represents the transfer function of the reference converter. The angular velocity represents the oscillation frequency, and E represents the identity matrix. Represents a diagonal matrix. express The real part of the i-th eigenvalue express The imaginary part of the i-th eigenvalue, where j represents the imaginary unit. Represents complex frequency;

[0066] In S42, the expression for the reduced-order calculation equations for the oscillation mode is:

[0067] ;

[0068] in, express The real part of the first eigenvalue, express The imaginary part of the first eigenvalue. express The real part of the Mth eigenvalue express The imaginary part of the Mth eigenvalue Indicates will Substitution The obtained network admittance array.

[0069] The beneficial effects of this invention are: This invention equates the dynamic differences of different converters to the series and parallel impedance forms of the access network, so that all converters have the same transfer function and the system retains its original dynamic characteristics. Through the principle of similarity transformation, the full-order state-space model is equivalent to multiple decoupled low-order system equations, thereby realizing efficient and accurate calculation of small-disturbance stability analysis of grid-connected and off-grid data centers. Attached Figure Description

[0070] Figure 1 A flowchart for a small-interference stability analysis method for on-grid and off-grid data centers;

[0071] Figure 2 This is a schematic diagram of the DC system.

[0072] Figure 3 A schematic diagram illustrating the dynamic differences of the converter;

[0073] Figure 4 A schematic diagram of DC network reconfiguration;

[0074] Figure 5 A schematic diagram of a DC system containing a large-scale data center;

[0075] Figure 6 This is a schematic diagram showing the changing trend of the dominant oscillation mode under operating condition 1 when the power changes. Detailed Implementation

[0076] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0077] like Figure 1 As shown, this invention provides a method for small-interference stability analysis of on-grid and off-grid data centers, comprising the following steps:

[0078] S1. Construct a data center power supply system;

[0079] S2. Based on the data center power supply system, construct the dynamic admittance matrix of the DC network and the transfer function of the converter;

[0080] S3. Connect the converter's dynamic differential equivalent impedance to the DC network, determine the reconstructed admittance matrix based on the dynamic admittance matrix of the DC network, and reconstruct the converter's transfer function based on the reconstructed admittance matrix to determine the reconstructed transfer function.

[0081] S4. Determine the dominant oscillation mode based on the reconstructed transfer function.

[0082] Obtain the data center power supply system structure model, such as Figure 2 As shown, there are two operating conditions: Condition 1, when the power grid is operating normally, the AC power grid supplies power to the data center through the AC-DC converter, and the input and output signals of the converter are the converter port current I, respectively. oj With voltage U oj Condition 2: During a grid fault, the AC grid is disconnected, and the energy storage device supplies power to the data center through a DC-DC converter. The converter's input and output signals are the converter port current I0 and I0, respectively. ok With voltage U ok Without loss of generality, load models for AC-DC converters, DC-DC converters, and data centers are established separately.

[0083] In this embodiment of the invention, in S1, the expression for the AC-DC converter in the data center power supply system is:

[0084] ;

[0085] in, This represents the port voltage of the k-th AC-DC converter. This represents the open-loop transfer function model of the k-th AC-DC converter. This represents the port current of the k-th AC-DC converter. This represents the first coefficient value of the numerator polynomial of the k-th transfer function. Let represent the second coefficient value of the numerator polynomial of the k-th transfer function. Let represent the value of the third coefficient of the numerator polynomial of the k-th transfer function. This represents the fourth coefficient value of the numerator polynomial of the k-th transfer function. This represents the first coefficient value of the denominator polynomial of the k-th transfer function. This represents the second coefficient value of the denominator polynomial of the k-th transfer function. This represents the value of the third coefficient of the denominator polynomial of the k-th transfer function. This represents the fourth coefficient value of the denominator polynomial of the k-th transfer function. This represents the fifth coefficient value of the denominator polynomial of the k-th transfer function. Represents complex frequency;

[0086] In S1, the expression for the DC-DC converter in the data center power supply system is:

[0087] ;

[0088] in, This represents the port voltage of the j-th DC-DC converter. This represents the open-loop transfer function model of the j-th DC-DC converter. This represents the port current of the j-th DC-DC converter. This represents the first coefficient value of the numerator polynomial of the j-th transfer function. Let represent the second coefficient value of the numerator polynomial of the j-th transfer function. This represents the value of the third coefficient of the numerator polynomial of the j-th transfer function. This represents the fourth coefficient value of the numerator polynomial of the j-th transfer function. This represents the first coefficient value of the denominator polynomial of the j-th transfer function. This represents the second coefficient value of the denominator polynomial of the j-th transfer function. This represents the value of the third coefficient of the denominator polynomial of the j-th transfer function. This represents the fourth coefficient value of the denominator polynomial of the j-th transfer function. This represents the fifth coefficient value of the denominator polynomial of the j-th transfer function;

[0089] In S1, the expression for the data center load model in the data center power supply system is:

[0090] ;

[0091] in, This represents the port voltage of the t-th DC data center load. This represents the port current of the t-th DC data center load. Let represent the open-loop transfer function model of the t-th DC data center load.

[0092] In this embodiment of the invention, S2 includes the following sub-steps:

[0093] S21. Based on the data center power supply system, construct the dynamic admittance matrix of the DC network;

[0094] S22. Based on the dynamic admittance matrix of the DC network and the data center load model of the data center power supply system, determine the transfer function between the converter output current and the port voltage.

[0095] S23. Based on the DC-DC converter of the data center power supply system and the transfer function between the converter output current and the port voltage, construct the transfer function of the DC network;

[0096] S24. Using any source-side converter in the data center power supply system as a reference converter, obtain the transfer function of the reference converter;

[0097] S25. Determine the transfer function of all converters based on the transfer function of the reference converter.

[0098] In this embodiment of the invention, S21, taking operating condition 1 as an example, based on the DC network interconnection structure and system line parameters, the following is obtained: Figure 2 The dynamic admittance matrix of a DC network. The expression for the dynamic admittance matrix of a DC network is:

[0099] ;

[0100] in, This indicates the outflow current of the power supply side converter. This represents the current flowing into the DC system from the load terminal. The admittance matrix of a DC network is represented. This represents the admittance matrix between the source-side converter nodes. This represents the first admittance matrix between the source-side converter node and the load node. This represents the second admittance matrix between the source-side converter node and the load node. This represents the first admittance matrix between the source-side converter nodes and the passive nodes. This represents the second admittance matrix between the source-side converter nodes and the passive nodes. This represents the admittance matrix between load nodes. This represents the first admittance matrix between passive nodes and load nodes. This represents the second admittance matrix between passive nodes and load nodes. This represents the admittance matrix between passive nodes. This indicates the converter port voltage. This represents the port voltage flowing into the DC system from the load end. This represents the DC voltage at a passive node in a DC network.

[0101] Where I o =[ΔI o1 ···ΔI o(M) ] T U o = [ΔU o1 ···ΔU o(M) ] T These are the outflow current and port voltage of the power supply-side converter, respectively. l =[ΔI l1 ···ΔI lT ] T and U l =[ΔU l1 ···ΔU lT ] T U represents the current flowing into the DC system from the load terminal and the port voltage, respectively. p =[ΔU p1 ···ΔU pF ] TIt is the DC voltage at a passive node (without power input) in a DC network.

[0102] In S22, the transfer function equations of the data center load are combined to eliminate the sub-load voltage U. l and passive node voltage U p This yields information only about the converter output current I. o and port voltage U o The transfer function between them.

[0103] By eliminating the current flowing into the DC system from the load end, the port voltage flowing into the DC system from the load end, and the DC voltage at the passive nodes of the DC network, the transfer function between the converter output current and the port voltage is obtained, and its expression is:

[0104] ;

[0105] ;

[0106] Y l (s)=diag[R l1 -1 ···R lT -1 ] T ;

[0107] in, Indicates elimination , and The expression for the transfer function between the converter output current and the port voltage is then obtained. Let R represent a diagonal matrix consisting of the reciprocals of the load transfer function, and let diag[·] denote a diagonal matrix. l1 R represents the first load transfer function. lT Let T represent the load transfer function of the Tth generation, where T indicates that there are T loads in the system.

[0108] In S23, the expression for the transfer function of the DC network is:

[0109] ;

[0110] R o (s)=diag[R o1 ···R o(M+N) ];

[0111] Among them, R o (s) represents the diagonal matrix composed of the source-side converters. R represents the identity matrix. o1 R represents the transfer function of the first converter. o(M+N) This represents the transfer function of the (M+N)th converter;

[0112] In S24, the transfer function of the reference converter The expression is:

[0113] ;

[0114] in, This represents the numerator polynomial of the transfer function of the reference converter. Denotes the denominator polynomial of the transfer function of the reference converter. This represents the value of the first coefficient in the numerator polynomial. This represents the value of the second coefficient in the numerator polynomial. This represents the value of the third coefficient in the numerator polynomial. This represents the value of the fourth coefficient in the numerator polynomial. This represents the value of the first coefficient in the denominator polynomial. This represents the value of the second coefficient in the denominator polynomial. This represents the value of the third coefficient in the denominator polynomial. This represents the value of the fourth coefficient in the denominator polynomial. This represents the value of the fifth coefficient in the denominator polynomial. Represents complex frequency;

[0115] In S25, such as Figure 3 As shown, based on the reference converter, the dynamic difference characteristics of the other converters can be equivalent to the series-parallel impedance ΔR connected to the DC network. o1.j (s), ΔR o2.j Therefore, all converters have the same dynamic characteristics and transfer function.

[0116] The transfer function of the j-th converter The expression is:

[0117] ;

[0118] in, Indicates the first differential equivalent impedance, This represents the second differential equivalent impedance. This represents the transfer function of the reference converter.

[0119] Modeling error is defined as:

[0120] .

[0121] In this embodiment of the invention, S3 includes the following sub-steps:

[0122] S31. Connect the equivalent impedance of the converter's dynamic difference to the DC network of the data center power supply system to form a reconfigured DC system;

[0123] S32. Construct the reconstruction admittance matrix for the reconstructed DC system;

[0124] S33. Based on the reconstructed admittance matrix, determine the transfer function between the converter output current and the port voltage after the DC network is reconstructed;

[0125] S34. Based on the transfer function between the converter output current and port voltage after DC network reconstruction, construct the reconstruction transfer function.

[0126] After obtaining the equivalent impedance of the converter's dynamic difference and connecting it to the DC network, a new network structure is formed, such as... Figure 4 As shown, considering the differences among all converters, i.e., considering ΔR o1.j (s) and ΔR o2.j (s) can be used to obtain the reconstructed admittance matrix.

[0127] In this embodiment of the invention, in S32, the expression for reconstructing the admittance matrix is:

[0128] ;

[0129] Y l (s)=diag[R l1 -1 ···R lT -1 ] T ;

[0130] in, This indicates the outflow current of the power supply side converter. This represents the admittance matrix between source-side converter nodes after considering the differential equivalent impedance. This represents the first admittance matrix between the source-side converter node and the load node after considering the differential equivalent impedance. This represents the second admittance matrix between the source-side converter node and the load node, taking into account the differential equivalent impedance. This represents the admittance matrix between load nodes after considering the differential equivalent impedance. A diagonal matrix consisting of the reciprocals of the load transfer function. This represents the first admittance matrix between the passive node and the load node after considering the differential equivalent impedance. This represents the second admittance matrix between the passive node and the load node after considering the differential equivalent impedance. This represents the first admittance matrix between the source-side converter nodes and passive nodes after considering the differential equivalent impedance. This represents the second admittance matrix between the source-side converter nodes and passive nodes, taking into account the differential equivalent impedance. This represents the admittance matrix between passive nodes after considering the differential equivalent impedance. This indicates the converter port voltage. This represents the port voltage flowing into the DC system from the load end. R represents the DC voltage at a passive node in a DC network, diag[·] represents a diagonal matrix, and R l1 R represents the first load transfer function. lT This represents the T-th load transfer function;

[0131] ΔY o1 (s)=diag[ΔR o1.j The rules for changing the coefficient matrix are as follows: After reconstruction, the network admittance value only needs to be modified by modifying the self-admittance of the i-th node connected to the converter and the w-th node connected to the i-th node, as well as the mutual admittance between the i-th and w-th nodes.

[0132] In S33, the expression for the transfer function between the converter output current and the port voltage after DC network reconfiguration is:

[0133] ;

[0134] ;

[0135] in, This indicates the outflow current of the power supply side converter. This represents the reconstructed equivalent network admittance matrix. Indicates the converter port voltage;

[0136] In S34, the expression for reconstructing the transfer function is:

[0137] ;

[0138] ;

[0139] in, Let E represent the diagonal matrix consisting of the transfer functions of the reference converter, and let E represent the identity matrix. This represents the transfer function of the reference converter.

[0140] In this embodiment of the invention, S4 includes the following sub-steps:

[0141] S41. Substitute the complex frequency into the reconstructed transfer function and use the similarity transformation method to reduce the full-order model to a lower-order system.

[0142] S42. Based on the low-order system, determine the dominant oscillation mode.

[0143] In this embodiment of the invention, in S41, the critical stability of the system is an important boundary for determining system instability. The system oscillation mode is as follows: In the critical oscillation mode, ε osc=0, and under weakly damped conditions In the above circumstances, The system oscillation frequency was obtained based on Fourier analysis. .

[0144] Substituting s into equation (12), by the principle of similarity transformation, the full-order model can be reduced to a low-order system of M-structure: The expression for reducing the full-order model to a low-order system is:

[0145] ;

[0146] in, express An invertible matrix composed of the left eigenvectors, This represents a diagonal matrix consisting of the transfer functions of the reference converter. Indicates will Substitution The obtained network admittance array, ω represents the transfer function of the reference converter. osc The angular velocity represents the oscillation frequency, and E represents the identity matrix. Represents a diagonal matrix. express The real part of the i-th eigenvalue express The imaginary part of the i-th eigenvalue, where j represents the imaginary unit. Represents complex frequency;

[0147] In S42, the expression for the reduced-order calculation equations for the oscillation mode is:

[0148] ;

[0149] in, express The real part of the first eigenvalue, express The imaginary part of the first eigenvalue. express The real part of the Mth eigenvalue express The imaginary part of the Mth eigenvalue Indicates will Substitution The obtained network admittance array.

[0150] Example structure as follows Figure 5This includes three AC-DC converters, three energy storage systems, and 9 representing the constant power load of the data center. The operating conditions of the DC data center can be divided into two categories according to whether the power grid is faulty: ① Operating condition 1: The power grid is working normally, and the mains power supplies the DC data center through the AC-DC converters, while the energy storage is in standby mode; ② Operating condition 2: The power grid fails, the line is disconnected, and the energy storage is in boost mode to supply power to the DC data center. This example assumes that the system is operating under operating condition 1, in which case the AC-DC converters are working and the DC-DC converters are disconnected.

[0151] The system parameters are shown in Table 1.

[0152] Table 1

[0153]

[0154] Based on the system parameters, the source-side converter transfer function can be obtained as follows:

[0155] ;

[0156] Selecting Ro1 as the reference converter, the equivalent series and parallel impedances are as follows:

[0157] ;

[0158] The DC voltage oscillation frequency of the system is obtained by Fourier analysis. Thus, the reconstructed value is obtained only for the converter output current I. o and port voltage V o Transfer function between:

[0159] ;

[0160] The calculation equation for the dominant oscillation mode is obtained as follows:

[0161] ;

[0162] The dominant oscillation mode is calculated from the equation, which gives the dominant oscillation mode s = -2.09 + 56.66. Therefore, the damping is greater than 0, and the system is stable.

[0163] The calculation results of the DC voltage oscillation mode of the dynamic reconfiguration model are shown when the data center load is increased in steps of 0.1 pu to 0.5 pu. For comparison and verification, a full-order linearized model is established for a large-scale DC data center system, and the eigenvalues ​​of the full-order state-space matrix are calculated. The calculation results of the dominant oscillation mode under the two operating conditions are as follows: Figure 6 . Figure 6In the diagram, the green solid circle represents the oscillation mode of the full-order model, and the blue solid circle represents the oscillation mode of the dynamic reduced-order model; the shaded area is the oscillation mode region of system instability; the solid line with arrows indicates the direction of movement of the DC system oscillation mode; the red dashed line is the boundary between the stable region and the unstable region; the area within the black elliptical dashed line represents the oscillation mode calculation results under the same load power condition.

[0164] As the load power gradually increases from 0.1 pu to 0.5 pu, the oscillation modes of the dynamically reconfigurable system under both operating conditions gradually shift from the left side of the imaginary axis to the right side of the imaginary axis in the complex plane, reaching an unstable state when the load power is 0.5 pu. As the oscillation modes gradually shift towards the critical oscillation, the calculation results of the dynamic order-reduced model gradually approach the calculation results of the oscillation modes of the full-order model. Furthermore, during the calculation process, the average calculation time of the full-order model is 8.55 s, while the average calculation time of the dynamic order-reduced model is 0.07 s. This indicates that the method proposed in this study not only effectively reduces the order of the system and improves the calculation speed, but also achieves high accuracy in the weakly damped case, demonstrating a high degree of consistency with the full-order model.

[0165] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for small-interference stability analysis of grid-connected and off-grid data centers, characterized in that, Includes the following steps: S1. Construct a data center power supply system; S2. Based on the data center power supply system, construct the dynamic admittance matrix of the DC network and the transfer function of the converter; S3. Connect the converter's dynamic differential equivalent impedance to the DC network, determine the reconstructed admittance matrix based on the dynamic admittance matrix of the DC network, and reconstruct the converter's transfer function based on the reconstructed admittance matrix to determine the reconstructed transfer function. S4. Determine the dominant oscillation mode based on the reconstructed transfer function.

2. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 1, characterized in that, In S1, the expression for the AC-DC converter in the data center power supply system is: ； in, This represents the port voltage of the k-th AC-DC converter. This represents the open-loop transfer function model of the k-th AC-DC converter. This represents the port current of the k-th AC-DC converter. This represents the first coefficient value of the numerator polynomial of the k-th transfer function. Let represent the second coefficient value of the numerator polynomial of the k-th transfer function. Let represent the value of the third coefficient of the numerator polynomial of the k-th transfer function. This represents the fourth coefficient value of the numerator polynomial of the k-th transfer function. This represents the first coefficient value of the denominator polynomial of the k-th transfer function. This represents the second coefficient value of the denominator polynomial of the k-th transfer function. This represents the value of the third coefficient of the denominator polynomial of the k-th transfer function. This represents the fourth coefficient value of the denominator polynomial of the k-th transfer function. This represents the fifth coefficient value of the denominator polynomial of the k-th transfer function. Represents complex frequency; In S1, the expression for the DC-DC converter in the data center power supply system is: ； in, This represents the port voltage of the j-th DC-DC converter. This represents the open-loop transfer function model of the j-th DC-DC converter. This represents the port current of the j-th DC-DC converter. This represents the first coefficient value of the numerator polynomial of the j-th transfer function. Let represent the second coefficient value of the numerator polynomial of the j-th transfer function. This represents the value of the third coefficient of the numerator polynomial of the j-th transfer function. This represents the fourth coefficient value of the numerator polynomial of the j-th transfer function. This represents the first coefficient value of the denominator polynomial of the j-th transfer function. This represents the second coefficient value of the denominator polynomial of the j-th transfer function. This represents the value of the third coefficient of the denominator polynomial of the j-th transfer function. This represents the fourth coefficient value of the denominator polynomial of the j-th transfer function. This represents the fifth coefficient value of the denominator polynomial of the j-th transfer function; In S1, the expression for the data center load model in the data center power supply system is: ； in, This represents the port voltage of the t-th DC data center load. This represents the port current of the t-th DC data center load. Let represent the open-loop transfer function model of the t-th DC data center load.

3. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 1, characterized in that, S2 includes the following sub-steps: S21. Based on the data center power supply system, construct the dynamic admittance matrix of the DC network; S22. Based on the dynamic admittance matrix of the DC network and the data center load model of the data center power supply system, determine the transfer function between the converter output current and the port voltage. S23. Based on the DC-DC converter of the data center power supply system and the transfer function between the converter output current and the port voltage, construct the transfer function of the DC network; S24. Using any source-side converter in the data center power supply system as a reference converter, obtain the transfer function of the reference converter; S25. Determine the transfer function of all converters based on the transfer function of the reference converter.

4. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 3, characterized in that, In step S21, the expression for the dynamic admittance matrix of the DC network is: ； in, This indicates the outflow current of the power supply side converter. This represents the current flowing into the DC system from the load terminal. The admittance matrix of a DC network is represented. This represents the admittance matrix between the source-side converter nodes. This represents the first admittance matrix between the source-side converter node and the load node. This represents the second admittance matrix between the source-side converter node and the load node. This represents the first admittance matrix between the source-side converter nodes and the passive nodes. This represents the second admittance matrix between the source-side converter nodes and the passive nodes. This represents the admittance matrix between load nodes. This represents the first admittance matrix between passive nodes and load nodes. This represents the second admittance matrix between passive nodes and load nodes. This represents the admittance matrix between passive nodes. This indicates the converter port voltage. This represents the port voltage flowing into the DC system from the load end. This represents the DC voltage at a passive node in a DC network. In step S22, the current flowing into the DC system from the load end, the port voltage flowing into the DC system from the load end, and the DC voltage on the passive nodes of the DC network are eliminated to obtain the transfer function between the converter output current and the port voltage, the expression of which is: ； ； Y l (s)=diag[R l1 -1 ···R lT -1 ] T ; in, Indicates elimination , and The expression for the transfer function between the converter output current and the port voltage is then obtained. Let R represent a diagonal matrix consisting of the reciprocals of the load transfer function, and let diag[·] denote a diagonal matrix. l1 R represents the first load transfer function. lT Let T represent the load transfer function of the Tth generation, where T indicates that there are T loads in the system. In step S23, the expression for the transfer function of the DC network is: ； R o (s)=diag[R o1 ···R o(M+N) ]; Among them, R o (s) represents the diagonal matrix composed of the source-side converters. R represents the identity matrix. o1 R represents the transfer function of the first converter. o(M+N) This represents the transfer function of the (M+N)th converter; In S24, the transfer function of the reference converter The expression is: ； in, This represents the numerator polynomial of the transfer function of the reference converter. Denotes the denominator polynomial of the transfer function of the reference converter. This represents the value of the first coefficient in the numerator polynomial. This represents the value of the second coefficient in the numerator polynomial. This represents the value of the third coefficient in the numerator polynomial. This represents the value of the fourth coefficient in the numerator polynomial. This represents the value of the first coefficient in the denominator polynomial. This represents the value of the second coefficient in the denominator polynomial. This represents the value of the third coefficient in the denominator polynomial. This represents the value of the fourth coefficient in the denominator polynomial. This represents the value of the fifth coefficient in the denominator polynomial. Represents complex frequency; In S25, the transfer function of the j-th converter The expression is: ； in, Indicates the first differential equivalent impedance, This represents the second differential equivalent impedance. This represents the transfer function of the reference converter.

5. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 1, characterized in that, S3 includes the following sub-steps: S31. Connect the equivalent impedance of the converter's dynamic difference to the DC network of the data center power supply system to form a reconfigured DC system; S32. Construct the reconstruction admittance matrix for the reconstructed DC system; S33. Based on the reconstructed admittance matrix, determine the transfer function between the converter output current and the port voltage after the DC network is reconstructed; S34. Based on the transfer function between the converter output current and port voltage after DC network reconstruction, construct the reconstruction transfer function.

6. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 5, characterized in that, In step S32, the expression for reconstructing the admittance matrix is: ； Y l (s)=diag[R l1 -1 ···R lT -1 ] T ; in, This indicates the outflow current of the power supply side converter. This represents the admittance matrix between source-side converter nodes after considering the differential equivalent impedance. This represents the first admittance matrix between the source-side converter node and the load node after considering the differential equivalent impedance. This represents the second admittance matrix between the source-side converter node and the load node, taking into account the differential equivalent impedance. This represents the admittance matrix between load nodes after considering the differential equivalent impedance. A diagonal matrix consisting of the reciprocals of the load transfer function. This represents the first admittance matrix between the passive node and the load node after considering the differential equivalent impedance. This represents the second admittance matrix between the passive node and the load node after considering the differential equivalent impedance. This represents the first admittance matrix between the source-side converter nodes and passive nodes after considering the differential equivalent impedance. This represents the second admittance matrix between the source-side converter nodes and passive nodes, taking into account the differential equivalent impedance. This represents the admittance matrix between passive nodes after considering the differential equivalent impedance. This indicates the converter port voltage. This represents the port voltage flowing into the DC system from the load end. R represents the DC voltage at a passive node in a DC network, diag[·] represents a diagonal matrix, and R l1 R represents the first load transfer function. lT This represents the T-th load transfer function; In S33, the expression for the transfer function between the converter output current and the port voltage after DC network reconfiguration is: ； ； in, This indicates the outflow current of the power supply side converter. This represents the reconstructed equivalent network admittance matrix. Indicates the converter port voltage; In step S34, the expression for reconstructing the transfer function is: ； ； in, Let E represent the diagonal matrix consisting of the transfer functions of the reference converter, and let E represent the identity matrix. This represents the transfer function of the reference converter.

7. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 1, characterized in that, S4 includes the following sub-steps: S41. Substitute the complex frequency into the reconstructed transfer function and use the similarity transformation method to reduce the full-order model to a lower-order system. S42. Based on the low-order system, determine the dominant oscillation mode.

8. The method for small-interference stability analysis of on-grid and off-grid data centers according to claim 7, characterized in that, In S41, the expression for reducing the full-order model to a lower-order system is: ； in, express An invertible matrix composed of the left eigenvectors, This represents a diagonal matrix consisting of the transfer functions of the reference converter. Indicates will Substitution The obtained network admittance array, This represents the transfer function of the reference converter. The angular velocity represents the oscillation frequency, and E represents the identity matrix. Represents a diagonal matrix. express The real part of the i-th eigenvalue express The imaginary part of the i-th eigenvalue, where j represents the imaginary unit. Represents complex frequency; In S42, the expression for the reduced-order calculation equations of the oscillation mode is: ； in, express The real part of the first eigenvalue, express The imaginary part of the first eigenvalue. express The real part of the Mth eigenvalue express The imaginary part of the Mth eigenvalue Indicates will Substitution The obtained network admittance array.

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