A small signal modeling and device for LCC-HVDC system

Abstract

The present invention relates to the field of power transmission technology and discloses a small-signal modeling and device for an LCC-HVDC system. Starting from the commutation process of the converter, the present invention uses the node voltage method to derive the transfer function between the converter's AC voltage, DC current, delayed trigger angle, and the AC current, DC voltage, and commutation overlap angle. Furthermore, based on the converter's signal block diagram, the small-signal AC admittance model of the converter at a certain stable operating point is derived. The present invention solves the technical problem of how to implement small-signal modeling of an LCC-HVDC system that takes into account the converter valve damping circuit. The constructed small-signal admittance model has high accuracy.

Description

Technical Field

[0001] The present invention relates to the field of power transmission technology, and in particular to a small signal modeling and device for an LCC-HVDC system. Background Art

[0002] Grid-commutated converter-type high-voltage direct current (HVDC) systems are widely used in scenarios such as grid interconnection and long-distance, high-capacity power transmission. In LCC-HVDC systems, due to the leakage reactance of the converter transformer, the valve current cannot immediately return to zero, and commutation cannot be completed instantaneously. This leads to overlapping commutation, where all three valves are simultaneously conducting. Characterizing and processing this overlapping commutation process is key to achieving accurate modeling.

[0003] In practical LCC-HVDC projects, a damping circuit (hereinafter referred to as the valve damping circuit) is connected in parallel across the converter valve to limit transient overvoltages and excessive voltage change rates caused by voltage oscillations when the thyristors turn off. However, current small-signal modeling of LCC-HVDC systems does not consider the valve damping circuit, and its impact on converter small-signal modeling is uncertain. Therefore, establishing a converter model that considers the valve damping circuit is of great significance. Summary of the Invention

[0004] The present invention provides an LCC-HVDC system small signal modeling and device, which solves the technical problem of how to implement the LCC-HVDC system small signal modeling considering the converter valve damping circuit.

[0005] It can be seen from the above technical solutions that the present invention has the following advantages:

[0006] A first aspect of the present invention provides a small signal modeling method for an LCC-HVDC system, comprising:

[0007] According to the circuit structure of the converter connected to the converter valve damping circuit, analytical equations representing the relationship between various variables in the converter during the commutation phase and the non-commutation phase are constructed respectively.

[0008] The constructed analytical equation is processed to obtain an analytical equation representing the relationship between various variables of the converter within a commutation cycle;

[0009] Linearizing an analytical equation characterizing a relationship between variables of the converter within a commutation cycle at a steady-state operating point, and deriving a small-signal transfer function matrix having a first parameter set as input and a second parameter set as output, wherein the first parameter set includes variables of the three-phase AC voltage on the secondary side of the converter in a dq coordinate system, a DC current, and a delayed trigger angle, and the second parameter set includes variables of the three-phase AC current on the secondary side of the converter in a dq coordinate system, a DC voltage, and a commutation overlap angle;

[0010] According to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system, a small signal admittance model is derived.

[0011] According to one implementation of the first aspect of the present invention, the analytical equations representing the relationships between the variables of the converter in the commutation phase and the non-commutation phase are constructed according to the circuit structure of the converter connected to the converter valve damping circuit, respectively, including:

[0012] According to the converter circuit structure in the commutation stage, an analytical equation is constructed to characterize the relationship between various variables in the converter in the commutation stage, including:

[0013] The electrical analytical equation of the converter during the commutation phase is constructed as follows:

[0014]

[0015] The node voltage equation of the converter during the commutation phase is constructed as follows:

[0016]

[0017] According to the converter circuit structure in the non-commutation phase, an analytical equation is constructed to characterize the relationship between the various variables of the converter in the non-commutation phase, including:

[0018] The electrical analytical equation of the converter in the non-commutation stage is constructed as follows:

[0019]

[0020] The node voltage equation of the converter in the non-commutation stage is constructed as follows:

[0021]

[0022] In formulas (1) to (6), i C is the current in the damping circuit branch, V + is the DC output positive voltage of the converter, V - is the negative voltage of the DC output of the converter, V3 is the ground voltage of the connection point between the two damping circuit branches of phase c in the non-commutation phase, v a is the AC voltage of phase a on the secondary side of the converter, v b is the AC voltage of phase b on the secondary side of the converter, v c is the AC voltage of phase c on the secondary side of the converter, i a is the AC current of phase a on the secondary side of the converter, i b is the AC current of phase b on the secondary side of the converter, i c is the AC current of phase c on the secondary side of the converter, L c is the equivalent leakage reactance of the converter transformer, i dcis the DC current, V dc is the DC voltage, R is the damping resistance of the converter valve, C is the damping capacitance of the converter valve, and s represents an imaginary number.

[0023] According to an achievable manner of the first aspect of the present invention, the processing of the constructed analytical equation includes:

[0024] Convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the commutation stage into the variable V in the dq coordinate system. d and V q , and solve it to get the expression of DC voltage in the commutation stage;

[0025] Convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the non-commutation stage into the variable V in the dq coordinate system. d and V q , and solve it to get the expression of DC voltage in the non-commutation stage;

[0026] Based on the obtained expression, the DC voltage in the commutation phase and the non-commutation phase is averaged to obtain the analytical equation of the DC voltage in a commutation cycle:

[0027]

[0028] Where V dc Represents the DC voltage within a commutation cycle, α is the delayed trigger angle, is the voltage phase of phase a, Indicates the voltage phase of phase a at the start of commutation, Indicates the voltage phase of phase a at the end of commutation, V dc1 is the DC voltage during the commutation phase, V dc2 is the DC voltage during the non-commutation phase.

[0029] According to an achievable manner of the first aspect of the present invention, the processing of the constructed analytical equation includes:

[0030] Perform Park transformation on equation (1) in the electrical analytical equation of the converter in the commutation stage, and perform Laplace transformation on the obtained expression to obtain the frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the commutation stage;

[0031] Perform Park transformation on equation (5) in the electrical analytical equation of the converter in the non-commutation phase, and perform Laplace transformation on the obtained expression to obtain the frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the non-commutation phase;

[0032] Based on the obtained frequency domain expression, the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation phase and the non-commutation phase are averaged to obtain the analytical equation of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system during a commutation cycle:

[0033]

[0034] Where, I d and I q is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system within a commutation cycle, I d1 and I q1 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation phase, I d2 and I q2 is the variable of the three-phase AC current on the secondary side of the converter in the non-commutation stage in the dq coordinate system.

[0035] According to an achievable manner of the first aspect of the present invention, the processing of the constructed analytical equation includes:

[0036] Combining equations (1) and (2) in the electrical analytical equations of the converter during the commutation phase, we can obtain:

[0037]

[0038] will i a The analysis is divided into three parts, the first part of which is 1a Affected by DC current, Part II 2a Affected by AC voltage, Part IIIi 3a Affected by the current in the damping circuit branch, the following equation is obtained:

[0039]

[0040]

[0041] Where, is the voltage phase of phase a;

[0042] Integrate both ends of equation (12) and combine represents the voltage phase of phase a at the start of commutation, and we can get:

[0043]

[0044] Where, represents the instantaneous DC current during the commutation phase, Indicates the DC current at the start of commutation;

[0045] will i 2a Using the variable i in the dq coordinate system 2d and i 2q Integrate both ends of equation (13) and combine We can get:

[0046]

[0047] Integrate both ends of equation (14) and combine We can get:

[0048]

[0049] Where, represents the damping circuit branch current during the commutation phase, Indicates the damping circuit branch current at the start of commutation;

[0050] At the end of commutation, the current in phase a is approximately equal to the DC current, that is:

[0051]

[0052] Where, is the commutation angle at the end of commutation, is the DC current at the end of commutation, is the current of phase a at the end of commutation, and They are the first, second and third parts of the a-phase current at the end of commutation.

[0053] According to an implementation of the first aspect of the present invention, linearizing the analytical equation characterizing the relationship between the variables of the converter within a commutation period at a steady-state operating point to derive a small signal transfer function matrix with the first parameter set as input and the second parameter set as output includes:

[0054] By linearizing Equations (3), (15), (16), (17), and (18) at the end of commutation and performing Laplace transform, we can obtain the following analytical equations for the commutation angle:

[0055]

[0056] Where ω0 is the system power frequency, α is the delayed trigger angle, and μ is the commutation overlap angle;

[0057] The analytical equations about the commutation angle are solved together to obtain a transfer function with the commutation overlap angle as the output.

[0058] According to one implementation of the first aspect of the present invention, linearizing the analytical equation characterizing the relationship between the variables of the converter within a commutation cycle at a steady-state operating point to derive a small signal transfer function matrix with the first parameter set as input and the second parameter set as output further includes:

[0059] The transfer function with the commutation overlap angle as the output is multiplied by the transfer function of the zero-order holder to obtain a modified transfer function with the commutation overlap angle as the output.

[0060] According to an achievable manner of the first aspect of the present invention, the converter circuit structure is a six-pulse converter circuit structure.

[0061] According to an implementation of the first aspect of the present invention, the derivation of the small signal admittance model according to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system includes:

[0062] Assume that the small signal transfer function matrix is:

[0063]

[0064] Where K 1x Indicates I d is the output transfer function, K 2x Indicates I q is the output transfer function, K 3x represents the transfer function with DC voltage as output, K 4x represents the transfer function with the commutation overlap angle as the output, x = 1, 2, 3, 4, represents the x-th column of the corresponding row of the transfer function matrix K;

[0065] In dq coordinates, the AC admittance is defined as follows:

[0066]

[0067] According to the structural diagram of the LCC-HVDC system, the transfer function G of the phase-locked loop is obtained. pll And the transfer function G of the constant voltage control link c They are:

[0068]

[0069] Where K ppll and K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop PI link, pudc and K iudc is the proportional coefficient and integral coefficient of the constant voltage control PI link, G m and T mParameters for constant voltage control measurement link;

[0070] The AC admittance coefficients in dq coordinate form are derived using Mason's formula as shown below:

[0071]

[0072] According to the relationship between the dq axis admittance and the αβ axis admittance, the expression of the αβ axis admittance is obtained:

[0073]

[0074] Where Y s (s) represents self-admittance, Y c (s) is the coupling admittance, Y c The conjugation of (s), Y s (s) conjugation.

[0075] A second aspect of the present invention provides a small-signal modeling device for an LCC-HVDC system, comprising:

[0076] A first processor is configured to construct, based on a circuit structure of a converter connected to a converter valve damping circuit, analytical equations representing relationships between variables of the converter in a commutation phase and a non-commutation phase;

[0077] A second processor is used to process the constructed analytical equation to obtain an analytical equation representing the relationship between various variables of the converter within a commutation cycle;

[0078] a third processor, configured to linearize, at a steady-state operating point, an analytical equation characterizing a relationship between variables of the converter within a commutation cycle, and derive a small-signal transfer function matrix having a first parameter set as input and a second parameter set as output, wherein the first parameter set includes variables of the three-phase AC voltage on the secondary side of the converter in a dq coordinate system, a DC current, and a delayed trigger angle, and the second parameter set includes variables of the three-phase AC current on the secondary side of the converter in a dq coordinate system, a DC voltage, and a commutation overlap angle;

[0079] The fourth processor is configured to derive a small signal admittance model according to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system.

[0080] According to an implementation of the second aspect of the present invention, the first processor is specifically configured to:

[0081] According to the converter circuit structure in the commutation stage, an analytical equation is constructed to characterize the relationship between various variables in the converter in the commutation stage, including:

[0082] The electrical analytical equation of the converter during the commutation phase is constructed as follows:

[0083]

[0084] The node voltage equation of the converter during the commutation phase is constructed as follows:

[0085]

[0086] According to the converter circuit structure in the non-commutation phase, an analytical equation is constructed to characterize the relationship between the various variables of the converter in the non-commutation phase, including:

[0087] The electrical analytical equation of the converter in the non-commutation stage is constructed as follows:

[0088]

[0089] The node voltage equation of the converter in the non-commutation stage is constructed as follows:

[0090]

[0091] In formulas (1) to (6), i C is the current in the damping circuit branch, V + is the DC output positive voltage of the converter, V - is the negative voltage of the DC output of the converter, V3 is the ground voltage of the connection point between the two damping circuit branches of phase c in the non-commutation phase, v a is the AC voltage of phase a on the secondary side of the converter, v b is the AC voltage of phase b on the secondary side of the converter, v c is the AC voltage of phase c on the secondary side of the converter, i a is the AC current of phase a on the secondary side of the converter, i b is the AC current of phase b on the secondary side of the converter, i c is the AC current of phase c on the secondary side of the converter, L c is the equivalent leakage reactance of the converter transformer, i dc is the DC current, V dc is the DC voltage, R is the damping resistance of the converter valve, C is the damping capacitance of the converter valve, and s represents an imaginary number.

[0092] According to an implementation of the second aspect of the present invention, the second processor includes:

[0093] The first processing unit is used to convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the commutation stage into a variable V in the dq coordinate system. d and V q, and solve it to get the expression of DC voltage in the commutation stage; convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the non-commutation stage into the variable V in the dq coordinate system d and V q , and solve it to get the expression of DC voltage in the non-commutation phase; according to the obtained expression, the DC voltage in the commutation phase and the non-commutation phase is averaged to get the analytical equation of DC voltage in one commutation cycle:

[0094]

[0095] Where V dc Represents the DC voltage within a commutation cycle, α is the delayed trigger angle, is the voltage phase of phase a, Indicates the voltage phase of phase a at the start of commutation, Indicates the voltage phase of phase a at the end of commutation, V dc1 is the DC voltage during the commutation phase, V dc2 is the DC voltage during the non-commutation phase.

[0096] According to an implementation of the second aspect of the present invention, the second processor includes:

[0097] The second processing unit is used to perform a Park transform on equation (1) in the electrical analytical equation of the converter in the commutation stage, and perform a Laplace transform on the obtained expression to obtain a frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the commutation stage; perform a Park transform on equation (5) in the electrical analytical equation of the converter in the non-commutation stage, and perform a Laplace transform on the obtained expression to obtain a frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the non-commutation stage; based on the obtained frequency domain expression, average the variables of the three-phase AC current on the secondary side of the converter in the commutation stage and the non-commutation stage in the dq coordinate system to obtain an analytical equation of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system within a commutation period:

[0098]

[0099] Where, I d and I q is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system within a commutation cycle, I d1 and I q1 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation phase, I d2 and I q2is the variable of the three-phase AC current on the secondary side of the converter in the non-commutation stage in the dq coordinate system.

[0100] According to an implementation of the second aspect of the present invention, the second processor includes a third processing unit, and the third processing unit is specifically configured to:

[0101] Combining equations (1) and (2) in the electrical analytical equations of the converter during the commutation phase, we can obtain:

[0102]

[0103] will i a The analysis is divided into three parts, the first part of which is 1a Affected by DC current, Part II 2a Affected by AC voltage, Part IIIi 3a Affected by the current in the damping circuit branch, the following equation is obtained:

[0104]

[0105] Where, is the voltage phase of phase a;

[0106] Integrate both ends of equation (12) and combine represents the voltage phase of phase a at the start of commutation, and we can get:

[0107]

[0108] Where, represents the instantaneous DC current during the commutation phase, Indicates the DC current at the start of commutation;

[0109] will i 2a Using the variable i in the dq coordinate system 2d and i 2q Integrate both ends of equation (13) and combine We can get:

[0110]

[0111] Integrate both ends of equation (14) and combine We can get:

[0112]

[0113] Where, represents the damping circuit branch current during the commutation phase, Indicates the damping circuit branch current at the start of commutation;

[0114] At the end of commutation, the current in phase a is approximately equal to the DC current, that is:

[0115]

[0116] Where, is the commutation angle at the end of commutation, is the DC current at the end of commutation, is the current of phase a at the end of commutation, and They are the first, second and third parts of the a-phase current at the end of commutation.

[0117] According to an achievable manner of the second aspect of the present invention, the third processor is specifically configured to:

[0118] By linearizing Equations (3), (15), (16), (17), and (18) at the end of commutation and performing Laplace transform, we can obtain the following analytical equations for the commutation angle:

[0119]

[0120] Where ω0 is the system power frequency, α is the delayed trigger angle, and μ is the commutation overlap angle;

[0121] The analytical equations about the commutation angle are solved together to obtain a transfer function with the commutation overlap angle as the output.

[0122] According to an implementation of the second aspect of the present invention, the third processor is further specifically configured to:

[0123] The transfer function with the commutation overlap angle as the output is multiplied by the transfer function of the zero-order holder to obtain a modified transfer function with the commutation overlap angle as the output.

[0124] According to an achievable manner of the second aspect of the present invention, the converter circuit structure is a six-pulse converter circuit structure.

[0125] According to an implementation of the second aspect of the present invention, the fourth processor is specifically configured to:

[0126] Assume that the small signal transfer function matrix is:

[0127]

[0128] Where K 1x Indicates I d is the output transfer function, K 2x Indicates I q is the output transfer function, K3x represents the transfer function with DC voltage as output, K 4x represents the transfer function with the commutation overlap angle as the output, x = 1, 2, 3, 4, represents the x-th column of the corresponding row of the transfer function matrix K;

[0129] In dq coordinates, the AC admittance is defined as follows:

[0130]

[0131] According to the structural diagram of the LCC-HVDC system, the transfer function G of the phase-locked loop is obtained. pll And the transfer function G of the constant voltage control link c They are:

[0132]

[0133] Where K ppll and K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop PI link, pudc and K iudc is the proportional coefficient and integral coefficient of the constant voltage control PI link, G m and T m Parameters for constant voltage control measurement link;

[0134] The AC admittance coefficients in dq coordinate form are derived using Mason's formula as shown below:

[0135]

[0136] According to the relationship between the dq axis admittance and the αβ axis admittance, the expression of the αβ axis admittance is obtained:

[0137]

[0138] Where Y s (s) represents self-admittance, Y c (s) is the coupling admittance, Y c The conjugation of (s), Y s (s) conjugation.

[0139] Based on the circuit structure of a converter connected to a converter valve damping circuit, the present invention constructs analytical equations that characterize the relationships between various variables of the converter in the commutation phase and the non-commutation phase, respectively. The constructed analytical equations are processed to obtain analytical equations that characterize the relationships between various variables of the converter within a commutation cycle. The analytical equations that characterize the relationships between various variables of the converter within a commutation cycle are linearized at a steady-state operating point to derive a small-signal transfer function matrix with a first parameter set as input and a second parameter set as output. The first parameter set includes the variables of the three-phase AC voltage on the secondary side of the converter in a dq coordinate system, the DC current, and the delayed trigger angle, and the second parameter set includes the variables of the three-phase AC current on the secondary side of the converter in a dq coordinate system, the DC voltage, and the commutation overlap angle. Based on the small-signal transfer function matrix, a small-signal admittance model is derived according to the structural block diagram of the LCC-HVDC system. The present invention fills the gap in how to implement small-signal modeling of an LCC-HVDC system when a converter valve damping circuit is included. The constructed small-signal model has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0140] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0141] Figure 1 A flowchart of a small signal modeling method for an LCC-HVDC system provided in an optional embodiment of the present invention;

[0142] Figure 2 A structural diagram of a six-pulse converter provided in an optional embodiment of the present invention;

[0143] Figure 3 A circuit structure diagram of a converter in a commutation phase according to an optional embodiment of the present invention;

[0144] Figure 4 A circuit diagram of a converter in a non-commutation phase according to an optional embodiment of the present invention;

[0145] Figure 5 A diagram showing the relationship between AC and DC voltages provided in an optional embodiment of the present invention;

[0146] Figure 6 A structural block diagram of a control system provided for an optional embodiment of the present invention;

[0147] Figure 7A structural block diagram of a system considering the effects of control links provided in an optional embodiment of the present invention;

[0148] Figure 8 A structural diagram of the inverter side of a Cigre conventional DC transmission system standard test model provided as an optional embodiment of the present invention;

[0149] Figure 9 Y provided in an optional embodiment of the present invention s (s) Comparison chart between theoretical value and scan value;

[0150] Figure 10 Y provided in an optional embodiment of the present invention c (s) Comparison chart between theoretical value and scan value;

[0151] Figure 11 K provided by an optional embodiment of the present invention pudc Schematic diagram of the characteristic root locus of ZgYac when =0.7506;

[0152] Figure 12 K provided by an optional embodiment of the present invention pudc Schematic diagram of the characteristic root locus of ZgYac when =12;

[0153] Figure 13 K provided by an optional embodiment of the present invention pudc Schematic diagram of simulation verification results from 0.7506 steps to 12;

[0154] Figure 14 This is a structural block diagram of a small-signal modeling device for an LCC-HVDC system provided in an optional embodiment of the present invention.

[0155] Reference numerals:

[0156] 1 - first processor; 2 - second processor; 3 - third processor; 4 - fourth processor. DETAILED DESCRIPTION

[0157] The embodiments of the present invention provide a small-signal modeling system and a device thereof for LCC-HVDC system, which are used to solve the technical problem of how to implement small-signal modeling of LCC-HVDC system considering the damping circuit of converter valves.

[0158] In order to make the purpose, features, and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only 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 making creative work are within the scope of protection of the present invention.

[0159] In the embodiments of the present application, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance.

[0160] A first embodiment of the present invention provides a small signal modeling method for an LCC-HVDC system taking into account a converter valve damping loop.

[0161] See also Figure 1 , Figure 1 A flowchart of a small signal modeling method for an LCC-HVDC system provided by an embodiment of the present invention is shown.

[0162] An embodiment of the present invention provides a small-signal modeling method for an LCC-HVDC system, comprising:

[0163] Step S1: According to the circuit structure of the converter connected to the converter valve damping circuit, analytical equations are constructed to characterize the relationship between various variables of the converter in the commutation phase and the non-commutation phase.

[0164] The converter circuit structure connected to the converter valve damping circuit includes a converter circuit structure during the commutation phase and a converter circuit structure during the non-commutation phase. During step S1, an analytical equation characterizing the relationship between various variables of the converter during the commutation phase is constructed based on the converter circuit structure during the commutation phase, and an analytical equation characterizing the relationship between various variables of the converter during the non-commutation phase is constructed based on the converter circuit structure during the non-commutation phase.

[0165] In actual engineering, multi-pulse converters are often used to achieve AC-DC conversion. The basic structure of a multi-pulse converter is a six-pulse converter. As a specific implementation, this embodiment constructs the above analytical equation based on the circuit structure of a six-pulse converter. After considering the converter valve damping circuit, the circuit structure of the six-pulse converter is as follows: Figure 2 shown. Figure 2 In, v a ,v b ,v c is the three-phase AC voltage on the secondary side of the converter, i a ,i b ,i c is the three-phase AC current on the secondary side of the converter, L cis the equivalent leakage reactance of the converter transformer, i dc is the DC current, V dc is the DC voltage, R is the damping resistance of the converter valve, C is the damping capacitance of the converter valve, and v1, v2, v3, v4, v5, and v6 represent the converter valves.

[0166] The commutation period of the six-pulse converter is π / 3. In each commutation period, the physical quantities change periodically. Therefore, the relationship between the physical quantities can be determined by analyzing a commutation period. Figure 2 In the process of switching from the converter valve v2 to the converter valve v4, the circuit structures of the converter in the switching stage and the non-switching stage are as follows: Figure 3 and Figure 4 As shown. In the commutation stage, since the voltages across each damping circuit are equal, the currents through each damping circuit branch are also equal. Therefore, the currents of each damping circuit branch are uniformly set to i C .

[0167] When constructing analytical equations, according to Figure 3 It can be seen that in the commutation stage, the electrical analytical equation of the converter in the commutation stage can be constructed as follows:

[0168]

[0169] Where i C is the current in the damping circuit branch, V + is the DC output positive voltage of the converter, V - is the negative voltage of the DC outlet of the converter;

[0170] The node voltage equation of the converter during the commutation phase can be constructed as follows:

[0171]

[0172] In the formula, s represents an imaginary number.

[0173] according to Figure 4 It can be seen that in the non-commutation stage, the analytical equation that can be constructed to characterize the relationship between the various variables of the converter in the commutation stage is:

[0174]

[0175] Where V3 is the ground voltage at the connection point between the two damping circuit branches of phase c during the non-commutation phase;

[0176] The node voltage equation of the converter in the non-commutation phase can be constructed as follows:

[0177]

[0178] In the formula, s represents an imaginary number.

[0179] The coordinate origin is set as the moment when the phase a voltage reaches its peak value. The relationship between the AC and DC voltage waveforms in a commutation cycle is as follows: Figure 5 As shown. Use Replace the time t for subsequent analysis and record the commutation angle at the start of commutation as The commutation angle at the end of commutation is Then they satisfy:

[0180]

[0181] Step S2: Process the constructed analytical equation to obtain an analytical equation that characterizes the relationship between various variables of the converter within a commutation cycle.

[0182] The three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the commutation stage is converted into the variable V in the dq coordinate system. d and V q , and solve it, we can get:

[0183]

[0184] Where V dc1 Indicates the DC voltage during the commutation phase;

[0185] Convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the non-commutation stage into the variable V in the dq coordinate system. d and V q , and solve it, we can get:

[0186]

[0187] Where V dc2 Indicates the DC voltage in the non-commutation stage;

[0188] By averaging the DC voltage within a commutation cycle, we can obtain the expression for the DC voltage within a commutation cycle:

[0189]

[0190] Where α is the delayed trigger angle, Indicates the voltage phase of phase a at the start of commutation, Indicates the voltage phase of phase A at the end of commutation.

[0191] Among them, the electrical analytical equation of the converter in the commutation stage is subjected to Park transformation (1), and the result is:

[0192]

[0193] Where, I d1 and I q1 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation stage, and ω0 is the system power frequency;

[0194] Solve I based on Laplace transform d1 and I q1 Frequency domain expression of :

[0195]

[0196] Perform Park transformation on equation (5) in the electrical analytical equation of the converter in the non-commutation phase to obtain:

[0197]

[0198] Where, I d2 and I q2 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the non-commutation phase;

[0199] Solve I based on Laplace transform d2 and I q2 Frequency domain expression of :

[0200]

[0201] The average value of the three-phase AC current on the secondary side of the converter in the dq coordinate system within a commutation cycle is obtained, and the corresponding expression is:

[0202]

[0203] Where, I d and I q is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system within one commutation cycle.

[0204] Further,

[0205] Combining equations (1) and (2) in the electrical analytical equations of the converter during the commutation phase, we can obtain:

[0206]

[0207] will i a The analysis is divided into three parts, the first part of which is 1a Affected by DC current, Part II 2a Affected by AC voltage, Part IIIi 3a Affected by the current in the damping circuit branch, the following equation is obtained:

[0208]

[0209] Where, is the voltage phase of phase a;

[0210] Integrate both ends of equation (12) and combine represents the voltage phase of phase a at the start of commutation, and we can get:

[0211]

[0212] Where, represents the instantaneous DC current during the commutation phase, Indicates the DC current at the start of commutation;

[0213] will i 2a Using the variable i in the dq coordinate system 2d and i 2q Integrate both ends of equation (13) and combine We can get:

[0214]

[0215] Integrate both ends of equation (14) and combine We can get:

[0216]

[0217] Where, represents the damping circuit branch current during the commutation phase, Indicates the damping circuit branch current at the start of commutation;

[0218] At the end of commutation, the current in phase a is approximately equal to the DC current, that is:

[0219]

[0220] Where, is the commutation angle at the end of commutation, is the DC current at the end of commutation, is the current of phase a at the end of commutation, and They are the first, second and third parts of the a-phase current at the end of commutation.

[0221] Step S3: linearize the analytical equation characterizing the relationship between the variables of the converter within a commutation cycle at a steady-state operating point, and derive a small signal transfer function matrix with a first parameter set as input and a second parameter set as output, wherein the first parameter set includes the variables of the three-phase AC voltage on the secondary side of the converter in the dq coordinate system, the DC current, and the delayed trigger angle; and the second parameter set includes the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system, the DC voltage, and the commutation overlap angle.

[0222] The analytical equation of the DC voltage within the one commutation period is linearized at a steady-state operating point to obtain a transfer function with the DC voltage as output.

[0223] The analytical equation of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system within the said commutation period is linearized to obtain the value of I d The transfer function of the output and I q is the output transfer function.

[0224] Furthermore, by linearizing Equations (3), (15), (16), (17), and (18) at the end of commutation and performing Laplace transform, we can obtain the following analytical equations for the commutation angle:

[0225]

[0226] Where ω0 is the system power frequency, α is the delayed trigger angle, and μ is the commutation overlap angle;

[0227] The analytical equations about the commutation angle are solved together to obtain a transfer function with the commutation overlap angle as the output.

[0228] Furthermore, in actual physical systems, the commutation overlap angle is not a continuously changing quantity, but is sampled and held every π / 3 angles. Therefore, it is necessary to multiply the transfer function with the commutation overlap angle as the output by the transfer function of the zero-order holder to achieve the correction of the transfer function with the commutation overlap angle as the output.

[0229] Among them, the transfer function of the zero-order holder is:

[0230]

[0231] Where, T s is the sampling period, which is 1 / 6 of the system basic period.

[0232] In this embodiment, by performing correction processing on the transfer function with the commutation overlap angle as the output, the accuracy of the constructed small signal transfer function moment can be improved.

[0233] Taking the variables of the three-phase AC voltage on the secondary side of the converter in the dq coordinate system, the DC current and the delayed trigger angle as input, the input vector in the small disturbance form is shown as follows:

[0234] ΔU=[ΔV d ΔV q Δi dc Δα] T

[0235] Where ΔU represents the input vector, V d 、V q is the variable of the three-phase AC voltage on the secondary side of the converter in the dq coordinate system, i dc is the DC current, α is the delayed trigger angle, and T represents the transposition;

[0236] Taking the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system, the DC voltage, and the commutation overlap angle as output, the output vector in the small disturbance form is shown as follows:

[0237] ΔY=[ΔI d ΔI q ΔV dc Δμ] T

[0238] Where ΔY represents the output vector, I d , I q is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system, V dc represents the DC voltage, μ represents the commutation overlap angle;

[0239] The focus of this application is to analyze the commutation process while considering the damping circuit and establish the relationship between the input vector ΔU and the output vector ΔY in the complex frequency domain. The relationship between the input vector ΔU and the output vector ΔY is described using a 4×4 matrix K, as shown in the following formula:

[0240]

[0241] Where K 1x Indicates I d is the output transfer function, K 2x Indicates I q is the output transfer function, K 3x represents the transfer function with DC voltage as output, K 4x represents the transfer function with the commutation overlap angle as the output, x = 1, 2, 3, 4, and represents the x-th column of the corresponding row of the transfer function matrix K.

[0242] For the twelve-pulse converter, since its DC voltage and AC current are twice that of the six-pulse converter, the relationship between the transfer function matrix of the twelve-pulse converter and the transfer function matrix of the six-pulse converter is:

[0243]

[0244] Where, the superscript K represents the converter pulsation number.

[0245] Similarly, the converter transfer function matrix with other pulsation numbers can also be obtained based on the multiple relationship between DC voltage and AC current.

[0246] Therefore, the method of the present application can be applied to multi-pulse converters, has high flexibility and wide applicability.

[0247] Step S4: deriving a small signal admittance model according to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system.

[0248] The converter is a nonlinear element. When a d-axis voltage disturbance is injected into the AC side, both the d-axis current and the q-axis current are disturbed simultaneously. Therefore, in the dq coordinate, the AC admittance is defined as follows:

[0249]

[0250] When constant voltage control and SRF phase-locked loop are used, the control system structure diagram is as follows Figure 6 shown. Figure 6 middle, is the frequency domain formula of Park transform, K ppll and K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop PI link, pudc and K iudc is the proportional coefficient and integral coefficient of the constant voltage control PI link, G m and T m Parameters for constant voltage control measurement link;

[0251] Depend on Figure 6 The transfer function G of the phase-locked loop can be obtained pll And the transfer function G of the constant voltage control link c They are:

[0252]

[0253] After considering the role of the control link, when ΔV d or ΔV q When a disturbance occurs, the signal transmission path inside the converter is as follows Figure 7As shown, the Mason formula can be used to derive the AC admittance coefficients in the dq coordinate form as shown below:

[0254]

[0255] According to the relationship between the dq axis admittance and the αβ axis admittance, the expression of the αβ axis admittance can be obtained:

[0256]

[0257] Where Y s (s) is the self-admittance, Y c (s) is the coupling admittance, Y c The conjugation of (s), Y s conjugation of (s);

[0258] The expression of the αβ-axis admittance shows that, in the three-phase stationary coordinate system, when a voltage disturbance with a frequency of ω is injected into the AC side, not only a current disturbance with the same frequency is generated, but also a current disturbance with a frequency of 2ω0-ω.

[0259] The specific expressions of self-admittance, coupled admittance and corresponding conjugate are as follows:

[0260]

[0261] At this point, the LCC-HVDC small signal admittance model considering the converter valve damping circuit is completed.

[0262] Take the inverter parameters and AC filter group parameters as shown in Table 1 and Table 2, according to Figure 8 The test model shown in the figure performs frequency sweep verification on the small signal admittance model. The results are shown in the figure. Figure 9 and Figure 10 shown.

[0263] Table 1:

[0264]

[0265] Table 2:

[0266]

[0267] Depend on Figure 9 and Figure 10 It can be seen that after considering the damping circuit, Y s (s) The theoretical value maintains a high degree of agreement with the value without considering the damping circuit in the frequency band less than 150Hz, and improves the agreement with the scan value in the frequency band greater than 150Hz; after considering the damping circuit, Y cThe theoretical value (s) agrees better with the value without the damping circuit at frequencies above 500 Hz. Therefore, considering the damping circuit can effectively improve the accuracy of the AC admittance model in the medium and high frequency ranges.

[0268] Furthermore, the accuracy of the model is verified through small perturbation stability analysis.

[0269] According to the generalized Nyquist stability criterion, the stability of an interconnected system can be determined by the characteristic roots of the open-loop transfer matrix ZgYac. When the characteristic root locus of ZgYac does not enclose the point (-1, j0) on the complex plane, the system is stable; otherwise, the system is unstable. In this embodiment, Yac is defined as the αβ-axis AC admittance from the converter toward the DC side; Zg is defined as the AC grid impedance, which is the parallel result of the AC filter bank impedance and the AC source impedance, as shown in the following equation:

[0270]

[0271] The effectiveness of the model in judging small disturbance stability is verified by changing the constant voltage controller parameters. pudc =0.7506, K iudc =18.3824, the characteristic root locus of ZgYac is drawn as follows Figure 11 As shown, it is obvious that the trajectory does not surround the point (-1, j0). According to the criterion, the system is stable at this time. pudc =12, K iudc =18.3824, the characteristic root locus of ZgYac is as follows Figure 12 As shown in Figure 2, the characteristic root locus surrounds the point (-1, j0). According to the criterion, the system is unstable at this time, and the corresponding frequencies when the characteristic root locus crosses the negative real axis are -14.52 Hz and 114.67 Hz respectively.

[0272] Schilling K in PSCAD pudc =0.7506, K iudc =18.3824, at t=4s, K pudc Step to 12, and get the simulation result of phase a voltage at PCC point as follows Figure 13 As shown in the figure, the waveform of the phase a voltage at the PCC point is stable before 4 seconds, and the amplitude does not change significantly. Therefore, the system is in a stable operating state, which is consistent with the theoretical analysis results. After 4 seconds, the amplitude of the phase a voltage at the PCC point gradually increases, and the system begins to oscillate. The FFT analysis of the oscillating voltage after 4 seconds shows that the oscillation frequencies are 15Hz and 115Hz, which are basically consistent with the theoretical results and verify the accuracy of the model.

[0273] A second embodiment of the present invention provides a small-signal modeling device for an LCC-HVDC system taking into account a converter valve damping circuit.

[0274] See also Figure 14 , Figure 14 The figure shows a structural block diagram of a small-signal modeling device for an LCC-HVDC system provided by an embodiment of the present invention.

[0275] An embodiment of the present invention provides a small-signal modeling device for an LCC-HVDC system, comprising:

[0276] The first processor 1 is configured to construct analytical equations representing the relationships between various variables of the converter in a commutation phase and a non-commutation phase, respectively, according to a circuit structure of the converter connected to a converter valve damping circuit;

[0277] The second processor 2 is configured to process the constructed analytical equation to obtain an analytical equation representing the relationship between the variables of the converter within a commutation cycle;

[0278] a third processor 3, configured to linearize, at a steady-state operating point, an analytical equation characterizing a relationship between variables of the converter within a commutation cycle, and derive a small-signal transfer function matrix having a first parameter set as input and a second parameter set as output, wherein the first parameter set includes variables of the three-phase AC voltage on the secondary side of the converter in a dq coordinate system, a DC current, and a delayed trigger angle, and the second parameter set includes variables of the three-phase AC current on the secondary side of the converter in a dq coordinate system, a DC voltage, and a commutation overlap angle;

[0279] The fourth processor 4 is configured to derive a small signal admittance model according to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system.

[0280] In one implementation, the first processor 1 is specifically configured to:

[0281] According to the converter circuit structure in the commutation stage, an analytical equation is constructed to characterize the relationship between various variables in the converter in the commutation stage, including:

[0282] The electrical analytical equation of the converter during the commutation phase is constructed as follows:

[0283]

[0284] The node voltage equation of the converter during the commutation phase is constructed as follows:

[0285]

[0286] According to the converter circuit structure in the non-commutation phase, an analytical equation is constructed to characterize the relationship between the various variables of the converter in the non-commutation phase, including:

[0287] The electrical analytical equation of the converter in the non-commutation stage is constructed as follows:

[0288]

[0289] The node voltage equation of the converter in the non-commutation stage is constructed as follows:

[0290]

[0291] In formulas (1) to (7), i C is the current in the damping circuit branch, V + is the DC output positive voltage of the converter, V - is the negative voltage of the DC output of the converter, V3 is the ground voltage of the connection point between the two damping circuit branches of phase c in the non-commutation phase, v a is the AC voltage of phase a on the secondary side of the converter, v b is the AC voltage of phase b on the secondary side of the converter, v c is the AC voltage of phase c on the secondary side of the converter, i a is the AC current of phase a on the secondary side of the converter, i b is the AC current of phase b on the secondary side of the converter, i c is the AC current of phase c on the secondary side of the converter, L c is the equivalent leakage reactance of the converter transformer, i dc is the DC current, V dc is the DC voltage, R is the damping resistance of the converter valve, C is the damping capacitance of the converter valve, and s represents an imaginary number.

[0292] In one implementation, the second processor 2 includes:

[0293] The first processing unit is used to convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the commutation stage into a variable V in the dq coordinate system. d and V q , and solve it to get the expression of DC voltage in the commutation stage; convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the non-commutation stage into the variable V in the dq coordinate system d and V q , and solve it to get the expression of DC voltage in the non-commutation phase; according to the obtained expression, the DC voltage in the commutation phase and the non-commutation phase is averaged to get the analytical equation of DC voltage in one commutation cycle:

[0294]

[0295] Where V dcRepresents the DC voltage within a commutation cycle, α is the delayed trigger angle, is the voltage phase of phase a, Indicates the voltage phase of phase a at the start of commutation, Indicates the voltage phase of phase a at the end of commutation, V dc1 is the DC voltage during the commutation phase, V dc2 is the DC voltage during the non-commutation phase.

[0296] In one implementation, the second processor 2 includes:

[0297] The second processing unit is used to perform a Park transform on equation (1) in the electrical analytical equation of the converter in the commutation stage, and perform a Laplace transform on the obtained expression to obtain a frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the commutation stage; perform a Park transform on equation (5) in the electrical analytical equation of the converter in the non-commutation stage, and perform a Laplace transform on the obtained expression to obtain a frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the non-commutation stage; based on the obtained frequency domain expression, average the variables of the three-phase AC current on the secondary side of the converter in the commutation stage and the non-commutation stage in the dq coordinate system to obtain an analytical equation of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system within a commutation period:

[0298]

[0299] Where, I d and I q is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system within a commutation cycle, I d1 and I q1 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation phase, I d2 and I q2 is the variable of the three-phase AC current on the secondary side of the converter in the non-commutation stage in the dq coordinate system.

[0300] In one implementation, the second processor 2 includes a third processing unit, and the third processing unit is specifically configured to:

[0301] Combining equations (1) and (2) in the electrical analytical equations of the converter during the commutation phase, we can obtain:

[0302]

[0303] will i a The analysis is divided into three parts, the first part of which is1a Affected by DC current, Part II 2a Affected by AC voltage, Part IIIi 3a Affected by the current in the damping circuit branch, the following equation is obtained:

[0304]

[0305] Where, is the voltage phase of phase a;

[0306] Integrate both ends of equation (12) and combine represents the voltage phase of phase a at the start of commutation, and we can get:

[0307]

[0308] Where, represents the instantaneous DC current during the commutation phase, Indicates the DC current at the start of commutation;

[0309] will i 2a Using the variable i in the dq coordinate system 2d and i 2q Integrate both ends of equation (13) and combine We can get:

[0310]

[0311] Integrate both ends of equation (14) and combine We can get:

[0312]

[0313] Where, represents the damping circuit branch current during the commutation phase, Indicates the damping circuit branch current at the start of commutation;

[0314] At the end of commutation, the current in phase a is approximately equal to the DC current, that is:

[0315]

[0316] Where, is the commutation angle at the end of commutation, is the DC current at the end of commutation, is the current of phase a at the end of commutation, and They are the first, second and third parts of the a-phase current at the end of commutation.

[0317] In one achievable manner, the third processor 3 is specifically configured to:

[0318] By linearizing Equations (3), (15), (16), (17), and (18) at the end of commutation and performing Laplace transform, we can obtain the following analytical equations for the commutation angle:

[0319]

[0320] Where ω0 is the system power frequency, α is the delayed trigger angle, and μ is the commutation overlap angle;

[0321] The analytical equations about the commutation angle are solved together to obtain a transfer function with the commutation overlap angle as the output.

[0322] In one achievable manner, the third processor 3 is further specifically configured to:

[0323] The transfer function with the commutation overlap angle as the output is multiplied by the transfer function of the zero-order holder to obtain a modified transfer function with the commutation overlap angle as the output.

[0324] In one achievable manner, the converter circuit structure is a six-pulse converter circuit structure.

[0325] In one achievable manner, the fourth processor 4 is specifically configured to:

[0326] Assume that the small signal transfer function matrix is:

[0327]

[0328] Where K 1x Indicates I d is the output transfer function, K 2x Indicates I q is the output transfer function, K 3x represents the transfer function with DC voltage as output, K 4x represents the transfer function with the commutation overlap angle as the output, x = 1, 2, 3, 4, represents the x-th column of the corresponding row of the transfer function matrix K;

[0329] In dq coordinates, the AC admittance is defined as follows:

[0330]

[0331] According to the structural diagram of the LCC-HVDC system, the transfer function G of the phase-locked loop is obtained. pll And the transfer function G of the constant voltage control link c They are:

[0332]

[0333] Where K ppll and K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop PI link, pudc and K iudc is the proportional coefficient and integral coefficient of the constant voltage control PI link, G m and T m Parameters for constant voltage control measurement link;

[0334] The AC admittance coefficients in dq coordinate form are derived using Mason's formula as shown below:

[0335]

[0336] According to the relationship between the dq axis admittance and the αβ axis admittance, the expression of the αβ axis admittance is obtained:

[0337]

[0338] Where Y s (s) represents self-admittance, Y c (s) is the coupling admittance, Y c The conjugation of (s), Y s (s) conjugation.

[0339] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the devices and units described above can refer to the corresponding processes in the aforementioned method embodiments, and the specific beneficial effects of the devices and units described above can refer to the corresponding beneficial effects in the aforementioned method embodiments, which will not be repeated here.

[0340] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units described is merely a logical function division, and other division methods may be used in actual implementation.

[0341] In addition, the various units in the various embodiments of the present invention may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0342] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A small signal modeling method for an LCC-HVDC system, characterized in that: include: According to the circuit structure of the converter connected to the converter valve damping circuit, analytical equations are constructed to characterize the relationship between various variables of the converter in the commutation stage and the non-commutation stage respectively; including: according to the circuit structure of the converter in the commutation stage, analytical equations are constructed to characterize the relationship between various variables of the converter in the commutation stage, and the electrical analytical equation of the converter in the commutation stage is constructed as follows: The node voltage equation of the converter during the commutation phase is constructed as follows: According to the converter circuit structure in the non-commutation stage, an analytical equation is constructed to characterize the relationship between the various variables in the non-commutation stage. The electrical analytical equation of the converter in the non-commutation stage is constructed as follows: The node voltage equation of the converter in the non-commutation stage is constructed as follows: In formulas (1) to (6), i C is the current in the damping circuit branch, V + is the DC output positive voltage of the converter, V - is the negative voltage of the DC output of the converter, V3 is the ground voltage of the connection point between the two damping circuit branches of phase c in the non-commutation phase, v a is the AC voltage of phase a on the secondary side of the converter, v b is the AC voltage of phase b on the secondary side of the converter, v c is the AC voltage of phase c on the secondary side of the converter, i a is the AC current of phase a on the secondary side of the converter, i b is the AC current of phase b on the secondary side of the converter, i c is the AC current of phase c on the secondary side of the converter, L c is the equivalent leakage reactance of the converter transformer, i dc is the DC current, V dc is the DC voltage, R is the damping resistance of the converter valve, C is the damping capacitance of the converter valve, and s represents an imaginary number; The constructed analytical equation is processed to obtain an analytical equation that represents the relationship between various variables of the converter within a commutation cycle; Linearizing an analytical equation characterizing a relationship between variables of the converter within a commutation cycle at a steady-state operating point, and deriving a small-signal transfer function matrix having a first parameter set as input and a second parameter set as output, wherein the first parameter set includes variables of the three-phase AC voltage on the secondary side of the converter in a dq coordinate system, a DC current, and a delayed trigger angle, and the second parameter set includes variables of the three-phase AC current on the secondary side of the converter in a dq coordinate system, a DC voltage, and a commutation overlap angle; According to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system, a small signal admittance model is derived.

2. The LCC-HVDC system small signal modeling method according to claim 1, characterized in that: The processing of the constructed analytical equation includes: Convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the commutation stage into the variable V in the dq coordinate system. d and V q , and solve it to get the expression of DC voltage in the commutation stage; Convert the three-phase AC voltage on the secondary side of the converter in the node voltage equation of the converter in the non-commutation stage into the variable V in the dq coordinate system. d and V q , and solve it to get the expression of DC voltage in the non-commutation stage; Based on the obtained expression, the DC voltage in the commutation phase and the non-commutation phase is averaged to obtain the analytical equation of the DC voltage in a commutation cycle: Where V dc Represents the DC voltage within a commutation cycle, α is the delayed trigger angle, is the voltage phase of phase a, Indicates the voltage phase of phase a at the start of commutation, Indicates the voltage phase of phase a at the end of commutation, V dc1 is the DC voltage during the commutation phase, V dc2 is the DC voltage during the non-commutation phase.

3. The LCC-HVDC system small signal modeling method according to claim 1, characterized in that: The processing of the constructed analytical equation includes: Perform Park transformation on equation (1) in the electrical analytical equation of the converter in the commutation stage, and perform Laplace transformation on the obtained expression to obtain the frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the commutation stage; Perform Park transformation on equation (5) in the electrical analytical equation of the converter in the non-commutation phase, and perform Laplace transformation on the obtained expression to obtain the frequency domain expression of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system in the non-commutation phase; Based on the obtained frequency domain expression, the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation phase and the non-commutation phase are averaged to obtain the analytical equation of the variables of the three-phase AC current on the secondary side of the converter in the dq coordinate system during a commutation cycle: Where, I d and I q is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during a commutation cycle, I d1 and I q1 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the commutation phase, I d2 and I q2 is the variable of the three-phase AC current on the secondary side of the converter in the dq coordinate system during the non-commutation stage.

4. The LCC-HVDC system small signal modeling method according to claim 1, characterized in that: The processing of the constructed analytical equation includes: Combining equations (1) and (2) in the electrical analytical equations of the converter during the commutation phase, we can obtain: will i a The analysis is divided into three parts, the first part of which is 1a Affected by DC current, Part II 2a Affected by AC voltage, Part IIIi 3a Affected by the current in the damping circuit branch, the following equation is obtained: Where, is the voltage phase of phase a; Integrate both ends of equation (12) and combine represents the voltage phase of phase a at the start of commutation, and we can get: Where, represents the instantaneous DC current during the commutation phase, Indicates the DC current at the start of commutation; will i 2a Using the variable i in the dq coordinate system 2d and i 2q Integrate both ends of equation (13) and combine We can get: Integrate both ends of equation (14) and combine We can get: Where, represents the damping circuit branch current during the commutation phase, Indicates the damping circuit branch current at the start of commutation; At the end of commutation, the current in phase a is approximately equal to the DC current, that is: Where, is the commutation angle at the end of commutation, is the DC current at the end of commutation, is the current of phase a at the end of commutation, and They are the first, second and third parts of the a-phase current at the end of commutation.

5. The LCC-HVDC system small signal modeling method according to claim 3, characterized in that: The analytical equation characterizing the relationship between the variables of the converter in one commutation cycle is linearized at a steady-state operating point to derive a small signal transfer function matrix with the first parameter set as input and the second parameter set as output, including: By linearizing Equations (3), (15), (16), (17), and (18) at the end of commutation and performing Laplace transform, we can obtain the following analytical equations for the commutation angle: Where ω0 is the system power frequency, α is the delayed trigger angle, and μ is the commutation overlap angle; The analytical equations about the commutation angle are solved together to obtain a transfer function with the commutation overlap angle as the output.

6. The LCC-HVDC system small signal modeling method according to claim 5, characterized in that: The step of linearizing the analytical equation representing the relationship between the variables of the converter within a commutation cycle at a steady-state operating point to derive a small signal transfer function matrix with the first parameter set as input and the second parameter set as output further includes: The transfer function with the commutation overlap angle as the output is multiplied by the transfer function of the zero-order holder to obtain a modified transfer function with the commutation overlap angle as the output.

7. The LCC-HVDC system small signal modeling method according to claim 1, characterized in that: The converter circuit structure is a six-pulse converter circuit structure.

8. The LCC-HVDC system small signal modeling method according to claim 1, characterized in that: The small signal admittance model is derived according to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system, including: Assume that the small signal transfer function matrix is: Where K 1x Indicates I d is the output transfer function, K 2x Indicates I q is the output transfer function, K 3x represents the transfer function with DC voltage as output, K 4x represents the transfer function with the commutation overlap angle as the output, x = 1, 2, 3, 4, represents the x-th column of the corresponding row of the transfer function matrix K; In dq coordinates, the AC admittance is defined as follows: According to the structural diagram of the LCC-HVDC system, the transfer function G of the phase-locked loop is obtained. pll And the transfer function G of the constant voltage control link c They are: Where K ppll and K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop PI link, pudc and K iudc is the proportional coefficient and integral coefficient of the constant voltage control PI link, G m and T m Parameters for constant voltage control measurement link; The AC admittance coefficients in dq coordinate form are derived using Mason's formula as shown below: According to the relationship between the dq axis admittance and the αβ axis admittance, the expression of the αβ axis admittance is obtained: Where Y s (s) represents self-admittance, Y c (s) is the coupling admittance, Y c The conjugation of (s), Y s (s) conjugation.

9. A small signal modeling device for an LCC-HVDC system, characterized in that: include: The first processor is configured to construct analytical equations for characterizing the relationships between various variables of the converter in a commutation phase and a non-commutation phase, respectively, based on a circuit structure of the converter connected to a converter valve damping circuit. The analytical equations include: constructing analytical equations for characterizing the relationships between various variables of the converter in the commutation phase based on the circuit structure of the converter in the commutation phase, wherein the electrical analytical equations of the converter in the commutation phase are: According to the converter circuit structure in the non-commutation stage, an analytical equation is constructed to characterize the relationship between the various variables in the non-commutation stage. The electrical analytical equation of the converter in the non-commutation stage is constructed as follows: The node voltage equation of the converter in the non-commutation stage is constructed as follows: In formulas (1) to (6), i C is the current in the damping circuit branch, V + is the DC output positive voltage of the converter, V - is the negative voltage of the DC output of the converter, V3 is the ground voltage of the connection point between the two damping circuit branches of phase c in the non-commutation phase, v a is the AC voltage of phase a on the secondary side of the converter, v b is the AC voltage of phase b on the secondary side of the converter, v c is the AC voltage of phase c on the secondary side of the converter, i a is the AC current of phase a on the secondary side of the converter, i b is the AC current of phase b on the secondary side of the converter, i c is the AC current of phase c on the secondary side of the converter, L c is the equivalent leakage reactance of the converter transformer, i dc is the DC current, V dc is the DC voltage, R is the damping resistance of the converter valve, C is the damping capacitance of the converter valve, and s represents an imaginary number; A second processor is used to process the constructed analytical equation to obtain an analytical equation representing the relationship between various variables of the converter within a commutation cycle; a third processor, configured to linearize, at a steady-state operating point, an analytical equation characterizing a relationship between variables of the converter within a commutation cycle, and derive a small-signal transfer function matrix having a first parameter set as input and a second parameter set as output, wherein the first parameter set includes variables of the three-phase AC voltage on the secondary side of the converter in a dq coordinate system, a DC current, and a delayed trigger angle, and the second parameter set includes variables of the three-phase AC current on the secondary side of the converter in a dq coordinate system, a DC voltage, and a commutation overlap angle; The fourth processor is configured to derive a small signal admittance model according to the small signal transfer function matrix and the structural block diagram of the LCC-HVDC system.

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