Small-signal modeling method for LCC-HVDC system and application

Abstract

This invention belongs to the field of linear periodic time-varying system modeling and analysis technology, and discloses a small-signal modeling method and application for LCC-HVDC systems. The method includes: constructing mathematical models of the segmented and continuous parts of the LCC-HVDC system based on its circuit topology within each operating interval, and integrating these models as the mathematical model of the LCC-HVDC system; linearizing the trajectory of this mathematical model to obtain its small-signal model within each operating interval; designing a small-signal model of the LCC-HVDC system during switching between adjacent operating intervals using the Filippov method; and combining the small-signal models of the LCC-HVDC system within each operating interval and the small-signal models at the switching time to constitute the small-signal model of the LCC-HVDC system, thus completing the small-signal modeling. This invention can accurately characterize the switching dynamics of the LCC-HVDC system, achieving accurate and low-complexity small-signal modeling of the LCC-HVDC system.

Description

Technical Field

[0001] This invention belongs to the field of linear periodic time-varying system modeling and analysis technology, and more specifically, relates to a small-signal modeling method and application of an LCC-HVDC system. Background Technology

[0002] Conventional direct current (LCC-HVDC) transmission systems have been widely used for long-distance, high-capacity power transmission due to their advantages such as low cost, high efficiency, and mature technology. However, with the increasing number of LCC-HVDC projects, the problem of broadband oscillation has become increasingly prominent.

[0003] Small-signal modeling of conventional DC transmission systems refers to establishing a mathematical model of the dynamic response characteristics of a conventional DC transmission system (LCC-HVDC) near its steady-state operating point using linearization methods. This model is used to analyze the system's response behavior to small disturbances. Accurate small-signal modeling is fundamental to stability analysis. As a typical thyristor-based power electronic device, the LCC-HVDC can only be turned on by a trigger pulse, while its turn-off depends on the grid voltage, resulting in a low switching frequency (typically several hundred hertz). Switching actions cause changes in the circuit topology, generating infinite characteristic harmonics on both the AC and DC sides. Furthermore, the leakage inductance of the commutation transformer hinders instantaneous commutation, leading to commutation overlap. These switching dynamics cause the LCC-HVDC to behave as a piecewise smooth, nonlinear, periodic, time-varying system, thus posing a significant challenge to small-signal modeling of the LCC-HVDC.

[0004] Quasi-steady-state models, as a type of small-signal model, are widely used in the stability analysis of LCC-HVDC. However, because quasi-steady-state models are based on state-space averaging, the switching dynamics are simplified, with only DC and fundamental components considered, leading to low accuracy. To more accurately characterize the switching dynamics of LCC-HVDC, small-signal modeling methods based on switching functions have been proposed. These methods use switching functions to describe the AC / DC side relationship and smooth non-differentiable points through Fourier series expansion. Various models have been developed within this framework, including dynamic phasor models, harmonic state-space models, and linear periodic time-varying models. However, these models essentially rely on Fourier series approximation to characterize the switching dynamics, typically requiring high-order expansions, resulting in high modeling complexity.

[0005] There is a DR disclosed in the prior art The small-signal modeling method for MMC HVDC systems has limitations. Because it uses a diode-based DR (Diode Redirector) as an uncontrolled device, it cannot be controlled and relies solely on natural commutation by the grid voltage. In contrast, the thyristor-based LCC (Limited Cylinder Carrier) as a semi-controlled device allows for thyristor conduction control through relevant control circuits. Therefore, the LCC exhibits more complex switching characteristics than the DR. Current technology can only accurately describe the switching dynamics of uncontrolled devices, and cannot accurately describe the switching dynamics of LCCs using semi-controlled devices. Summary of the Invention

[0006] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a small-signal modeling method and application for LCC-HVDC system, the purpose of which is to accurately characterize the switching dynamics of LCC-HVDC system and realize accurate and low-complexity small-signal modeling of LCC-HVDC system.

[0007] To achieve the above objectives, the present invention provides a small-signal modeling method for an LCC-HVDC system, comprising: Based on the circuit topology of the LCC-HVDC system in each operating section, mathematical models of its segmented and continuous parts are constructed, and the mathematical models of the segmented and continuous parts are integrated as the mathematical model of the LCC-HVDC system. The mathematical model of the segmented part is the mathematical model of the LCC in each operating section, and the operating section includes the commutation process and non-commutation process on the rectifier side and the inverter side. The mathematical model of the continuous part is the mathematical model of the rectifier station and inverter station control system, DC line and AC network in the LCC-HVDC system. On the overall steady-state operating cycle trajectory of the LCC-HVDC system, the mathematical model of the LCC-HVDC system is linearized to obtain the small-signal model of the LCC-HVDC system in each working interval. Using the Filippov method, a transition matrix is ​​designed for the LCC-HVDC system during the switching between adjacent working intervals, in order to characterize the small-signal model of the LCC-HVDC system at the switching time between adjacent working intervals. The small-signal model of the LCC-HVDC system in each working interval and the small-signal model at the switching time together constitute the small-signal model of the LCC-HVDC system, thus completing the small-signal modeling.

[0008] Furthermore, when the LCC is a 12-pulse LCC, the second... z -2 work zones to the 2nd z -1 shift matrix during work zone switching for:

[0009]

[0010] Among them, the subscript in the variable or , respectively representing the rectifier side or the inverter side; the 2nd z -2 working intervals represent non-commutation processes, the second... z -1 working interval represents the commutation process. z =1, …, 12; , These represent the state variables of the LCC-HVDC system. In the 2nd z -2 work zones, the 2nd z The time derivative within a working interval at the interval switching time is -1 The value, Indicates the 2nd z -2 work zones to the 2nd z -1 time of work zone switching; state variable , For the state variables of LCC, , These are the AC secondary currents of the LCC in YY and Y-Δ connections, respectively. "Y" represents a star connection, and "Δ" represents a delta connection. This refers to the DC side current of the rectifier or inverter station. For the state variables of the continuous part of the LCC-HVDC system, , , The output is a phase-locked loop PI integrator. This represents the output angle of the phase-locked loop in the rotating reference frame. This is the output of the low-pass filter integrator. The output of the PI integrator is controlled by DC current. The output of the PI integrator is controlled by DC voltage. State variables representing DC lines and AC networks; T Indicates transpose; It is a state variable dimensionality The power frequency rotational angular frequency, , These are the proportional coefficients for controlling DC current and DC voltage, respectively. Represents the identity matrix. express A 0 matrix; when 2 z When -2=0, ; 2nd z -1 workspace to the 2nd zThe transition matrix during work zone switching for:

[0011]

[0012] in, State variables of the LCC-HVDC system In the 2nd z The time derivative within each working interval at the interval switching time The value, Indicates the 2nd z -1 workspace to the 2nd z The moment of switching work zones; the 2nd z Each working interval represents a non-commutation process; This indicates finding the partial derivative. This is the commutation current.

[0013] Furthermore, the mathematical model of the LCC-HVDC system is as follows:

[0014] in, express The derivative, State variables of the LCC-HVDC system In the z Time derivative within each working interval, t xz Indicates the time of switching between work zones; express The derivative, Representing state variables in DC lines and AC networks Time derivative, , , They are respectively: , , For LCC AC primary side voltage, This refers to the DC side current of the rectifier station. This is the DC line voltage. express time; , The matrices representing the state-space equations of DC lines and AC networks. For the turns ratio of the commutation transformer, This is the current transformation matrix.

[0015] Furthermore, the small-signal model of the LCC-HVDC system in each operating interval is as follows:

[0016] in, , , for , , Small semaphores; for about The Jacobian matrix in the periodic trajectory The value of ; yes about The Jacobian matrix in the periodic trajectory The value that can be taken on.

[0017] Furthermore, the mathematical model of the LCC within each working interval is as follows:

[0018] in, These are the AC secondary voltages of the LCCs in YY and Y-Δ connections, respectively. Indicates the first z Differential equations corresponding to each working interval Indicate the output equation. This refers to the primary AC current of the LCC.

[0019] This invention also provides a stability analysis method for an LCC-HVDC system, comprising: Stability analysis is performed based on a small-signal model of the LCC-HVDC system; wherein the small-signal model is constructed using any of the small-signal modeling methods described above.

[0020] The present invention also provides a small-signal modeling system for an LCC-HVDC system, characterized in that it includes a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the small signal modeling method described above.

[0021] The present invention also provides a stability analysis system for an LCC-HVDC system, comprising a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the stability analysis method described above.

[0022] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the small-signal modeling method as described above, or / and the stability analysis method as described above.

[0023] The present invention also provides a computer program product, comprising a computer program that, when the computer program is run on a computer, causes the computer to execute the small signal modeling method described above, or / and to execute the stability analysis method described above.

[0024] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) The small-signal model of the LCC-HVDC system constructed in this invention establishes a segmented mathematical model of the LCC based on the circuit topology and switching of the LCC-HVDC system during commutation and non-commutation processes. Compared with existing modeling methods based on state-space averaging or switching function forms, the modeling method of this invention can more accurately reflect the switching dynamics of the LCC-HVDC system in each working interval (commutation and non-commutation processes). Furthermore, by connecting adjacent working intervals (switching between commutation and non-commutation processes) through a transition matrix, the constructed small-signal model of the LCC-HVDC system can accurately reflect the switching dynamics during the switching of each working interval and adjacent working intervals. Moreover, this invention does not require Fourier series expansion approximation processing, nor does it require using the commutation overlap angle to characterize the commutation process. The system order remains consistent with the original LCC-HVDC system order, resulting in lower modeling complexity.

[0025] (2) Furthermore, with DR Unlike the MMC HVDC system, this invention specifically designs a transition matrix for switching from non-commutation process to commutation process and from commutation process to non-commutation process to connect adjacent working intervals, which can accurately reflect the switching state of the LCC-HVDC system.

[0026] Overall, this invention can accurately characterize the switching dynamics of LCC-HVDC systems and achieve accurate and low-complexity small-signal modeling of LCC-HVDC systems. This has guiding significance for the design of relevant control parameters and the optimization of operating parameters, and helps to improve the stability of LCC-HVDC systems and ensure the safe and stable operation of power systems. Attached Figure Description

[0027] Figure 1 This is a flowchart of a small-signal modeling and stability analysis method for LCC-HVDC systems provided in Embodiment 1 of the present invention; Figure 2 This is a structural diagram of the LCC-HVDC system in Embodiment 1 of the present invention; Figure 3 This is a control structure diagram of the LCC-HVDC system in Embodiment 1 of the present invention; Figure 4 This is a system structure diagram of the 12-pulse LCC in Embodiment 1 of the present invention; Figure 5 This is the original mathematical model of the LCC-HVDC system in Embodiment 1 of the present invention within one cycle; Figure 6 This is a segmented small-signal model of the LCC-HVDC system in one cycle of the present invention, as described in Embodiment 1 of the present invention. Figure 7 This is a comparison of the time-domain response results of DC current in the LCC-HVDC electromagnetic transient simulation and the piecewise small-signal model; Figure 8 This is a comparison chart of the time-domain response results of AC voltage amplitude in LCC-HVDC electromagnetic transient simulation and piecewise small-signal model. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0029] Example 1 according to Figure 1 As shown, this embodiment of the invention provides a small-signal modeling method suitable for LCC-HVDC systems, comprising the following steps: S1. Based on the circuit topology of the LCC-HVDC system in each operating section, the original mathematical model of each segment (each operating section) on the rectifier side and inverter side is obtained; wherein, the operating section of the LCC-HVDC system includes the LCC commutation process and the non-commutation process.

[0030] Taking a 12-pulse LCC as an example, such as Figure 2 As shown, the original mathematical model of the segmented part of the LCC-HVDC system includes a 12-pulse LCC on both the rectifier and inverter sides; in other embodiments, the LCC can also be a 6-pulse bridge.

[0031] The original segmented mathematical model for the 12-pulse LCC on both the rectifier and inverter sides includes two categories: commutation processes and non-commutation processes. Under normal operating conditions, the commutation and non-commutation processes of the 12-pulse LCC alternate, thus dividing the entire power frequency cycle into 24 intervals, including 12 commutation processes and 12 non-commutation processes. Since there are too many expressions for these 24 intervals, this embodiment of the invention provides an example expression for one interval from each of the two processes; the expressions for the remaining intervals can be obtained similarly.

[0032] Taking the commutation process with VT156 / 56 turned on as an example, the topology of the LCC-HVDC system during this commutation process is as follows: Figure 4 As shown by the red solid line, the original mathematical relationship is as follows: (1) (2) Among them, subscript or , respectively representing variables on the rectifier side or the inverter side (in this embodiment of the invention, the subscript of the variable is...) Both represent variables on the rectifier side. Both represent variables on the contravariant side, for example, Reference or , Reference or , Reference or , Reference or etc), , ( j = a , b , c (Representing phases A, B, and C) are YY and Y-Δ connections respectively (combinations of primary and secondary winding connection methods for the LCC; "Y" represents star connection, and "Δ" represents delta connection). LCC AC secondary voltage. i gxa1 , i gxc2 These represent the phase A current on the AC secondary side of the YY-connected LCC and the phase C current on the AC secondary side of the Y-Δ-connected LCC, respectively. L x For the leakage inductance of the commutation transformer in the LCC-HVDC system, L dcx , R dcx These are the inductance and resistance of the DC lines in the rectifier or inverter station, respectively.u dc This is the DC line voltage. express time.

[0033] i gxj1 , i gxj2 ( j = a , b , c The residual current in the rectifier or inverter station and the DC side current. i dcx It can be used i gxa1 and i gxc1 Export as follows: (3) (4) Taking the VT16 / 56 conduction process as an example, the topology of the LCC-HVDC system during this commutation process is as follows: Figure 4 As shown by the blue dashed line, the original mathematical relationship is as follows: (5) i gxj1 , i gxj2 ( j = a , b , c The residual current in the rectifier or inverter station and the DC side current. It can be used i gxa1 Export as follows: (6) (7) Integrating the AC / DC dynamic equations across all 24 intervals, i.e., equations (1) to (7), the original mathematical models for each commutation and non-commutation interval of the LCC-HVDC on both the rectifier and inverter sides can be expressed as follows: (8) in, These are the state variables of the LCC on the rectifier or inverter side. express The derivative, T Indicates transpose. , These represent the AC secondary currents of the LCC in a YY connection and the LCC in a Y-Δ connection, respectively.i gx1 =[ i gxa1 i gxb1 i gxc1 ] T , i gx2 =[ i gxa2 i gxb2 i gxc2 ] T State variables The dimension is 7. Represent the differential equations corresponding to each working interval. z Indicates the first z In this embodiment of the invention, there are several work areas. z =1, ..., 24, the total number of working intervals is determined according to the structure of LCC. These are the AC secondary voltages of the LCCs in YY and Y-Δ connections, respectively. , ; This indicates the instant of switching between work zones. For the primary side current of the LCC, This is the output equation.

[0034] Depending on the connection method of the LCC transformer (YY connection and Y-Δ connection), the AC secondary voltage of the LCC... u gx1 , u gx2 and AC primary side current i gx satisfy: (9) in, For LCC AC primary side voltage, For the turns ratio of the commutated transformer, the voltage transformation matrix and current transformation matrix To introduce a 30° phase shift, the transformation matrix is ​​as follows: (10) S2, based on the circuit topology of the LCC-HVDC system, obtains the original mathematical model of its continuous part. Furthermore, for step S2, as... Figure 2 and Figure 3As shown, the original mathematical model of the continuous part of the LCC-HVDC system includes the control systems of the rectifier station and inverter station, DC lines, and AC lines. Many existing works have already provided detailed models of these components, so they will not be repeated here. This embodiment of the invention provides a mathematical model corresponding to its continuous part.

[0035] The control systems of rectifier stations and inverter stations, such as Figure 3 As shown, its original mathematical model can be expressed as: (11) in, This represents the state variables of the LCC control system on the rectifier side or inverter side. For the rectifier side (variable subscript) ), for For the inverse side (variable subscript) ), for , express The derivative, The output is a phase-locked loop PI integrator. This represents the output angle of the phase-locked loop in the rotating reference frame. This is the output of the low-pass filter integrator. The output of the PI integrator is controlled by DC current. The output of the PI integrator is controlled by DC voltage. Represent the corresponding differential equation. The output is... , The output angle of the phase-locked loop in the stationary reference frame. The conduction angle of the LCC thyristor. For the corresponding output equation; for the rectifier side, , For the inverter side, , .

[0036] The original mathematical model of DC lines and AC networks can be expressed as: (12) in, Represents the state variables of the DC line and AC network, and the inputs of the DC line and AC network are... The output is . , , , These are four matrices representing the state-space equations of DC lines and AC networks, respectively.

[0037] S3 integrates the original mathematical models of the continuous and piecewise parts to obtain the final original mathematical model of the LCC-HVDC system. Furthermore, for step S3, the original mathematical model of LCC-HVDC includes the continuous part in S1 and the piecewise part in S2. Through algebraic transformations, the continuous and piecewise parts are eliminated. , , , , The general formula for the original mathematical model of the LCC-HVDC system can be expressed as: (13) in, These are the state variables of the LCC on the rectifier or inverter side. express The derivative, subscript or , representing the variables on the rectifier side or the inverter side, respectively. Represents the rectifier-side state variables In the z Time derivative within each working interval, Represents the state variables on the inverter side In the z Time derivative within each working interval; This refers to all state variables of the entire LCC-HVDC system; For the continuous part of the state variables, Representing state variables in DC lines and AC networks Time derivative, , , , They are respectively , , The abbreviation of, i.e. The original mathematical model of the entire LCC-HVD system is as follows: Figure 5 As shown.

[0038] S4. Based on the trajectory linearization method, the small-signal model of the continuous part of the LCC-HVDC system within the segmented intervals is obtained. Furthermore, for step S4, by ignoring the switching moments, the original mathematical model of the LCC-HVDC system (formula (13)) is linearized on the overall steady-state operating cycle trajectory of the LCC-HVDC system, resulting in the small-signal model of the LCC-HVDC system within the segmented intervals: (14) Where Δ represents the small semaphore. for about The Jacobian matrix in the periodic trajectory The value that can be taken on. yes about The Jacobian matrix in the periodic trajectory The value that can be taken on.

[0039] In step S5, based on Filippov's theory, the small-signal model of the LCC-HVDC system at the switching moment is obtained, including two types: switching from non-commutation to commutation and switching from commutation to non-commutation. Furthermore, in step S5, the switching causes abrupt changes in the state variables related to the rectifier and inverter-side LCCs in the LCC-HVDC small-signal model at the switching moment. Based on Filippov's theory, the state variables before and after the switching moment can be related by a transition matrix, which describes the influence of the switching dynamics and represents the small-signal model at the switching moment.

[0040] For LCC-HVDC, in this embodiment of the invention, two types of transition matrices are designed using the Filippov method. The first type is the transition matrix for switching from a non-commutation process to a commutation process. Considering two 6-pulse LCC pulses with equal intervals and a phase shift of 30°, when the second... z -2 working intervals are non-commutation processes (corresponding to even-numbered working intervals), the 2nd... z -1 working intervals represent the commutation process (corresponding to odd-numbered working intervals). In this case, the transition matrix during the switch from a non-commutation process to a commutation process can be represented as: (15) (16) in, , These represent the non-commutation processes on the rectifier side and inverter side, respectively (2nd...). z -2 working intervals) to commutation process (2nd) z The transition matrix during switching between -1 working intervals; z =1, …, 12, It is a state variable dimensionality , These represent the instants at which the rectifier and inverter sides switch their operating ranges, i.e., from the 2nd... z -2 workspaces switched to the 2nd z -1 working interval time; yes The abbreviation for state variable In the 2nd z The time derivative within a working interval at time -1 t x(2z-2)The value of, i.e. , Representing state variables respectively In the 2nd z -1 work zone, 2nd z -The time derivative within the two working intervals at the switching time t x(2z-2) The value of . When 2 z When -2=0 (z=1, corresponding to...), , ), . , These are the proportional coefficients for controlling DC current and DC voltage, respectively, and are empirically determined values. The rotational angular frequency is the power frequency. express( n o +14) × ( n o +14) dimensional identity matrix, express A zero matrix. , These represent the outputs of the low-pass filter integrators on the rectifier and inverter sides, respectively. The output of the PI integrator is controlled by DC current. The output is controlled by a DC voltage-controlled PI integrator.

[0041] The second type is the transition matrix when switching from commutation to non-commutation. Its characteristic is that the commutation current crosses zero, the 2z-1th working interval is the commutation process, and the 2zth working interval is the non-commutation process. In this case, the transition matrix when switching from commutation to non-commutation can be expressed as: (17) (18) in, , These represent the commutation processes on the rectifier side and the inverter side, respectively (2nd...). z -1 working interval) to non-commutation process (2nd) z The transition matrix during switching between (each working interval); z =1, …, 12, in the formula , Representing state variables respectively In the 2nd z -1 work zone, 2nd z The time derivative within each working interval at the interval switching time t x(2z-1) The value; This indicates the partial derivative; The commutation current on the rectifier side or inverter side can be represented as follows in this embodiment of the invention: (19) S6, integrating the small-signal models within the segmented intervals and at the switching moments, finally obtains the overall segmented small-signal model of the LCC-HVDC system. Furthermore, for step S6, combining the small-signal model of the LCC-HVDC within the segmented intervals shown in formula (14), and the small-signal models at the switching moments shown in formulas (15)-(18), the overall segmented small-signal model of the LCC-HVDC system can be obtained, such as... Figure 6 As shown. It can be seen that within each interval, it is described by formula (14), and the transition matrix connects the two segmented intervals before and after the switching time.

[0042] In one specific embodiment, a system is built in MATLAB / Simulink as follows: Figure 2 The electromagnetic transient simulation model of the LCC-HVDC system is shown. For both the electromagnetic transient simulation model and the piecewise small-signal model of the LCC-HVDC system, a disturbance of 0.02 pu is applied to the DC voltage control reference value at 0.1 s, and the disturbance response results of the two models are compared. Figure 7 This is a comparison chart of the time-domain response results of DC current in the LCC-HVDC electromagnetic transient simulation model and the piecewise small-signal model. Figure 8 This is a comparison of the time-domain response results of the AC voltage amplitude in the LCC-HVDC electromagnetic transient simulation model and the piecewise small-signal model. The results show that the time-domain disturbance response results of the LCC-HVDC electromagnetic transient simulation model and the piecewise small-signal model constructed in this embodiment of the invention are basically consistent. This also verifies the accuracy of the piecewise small-signal modeling method for LCC-HVDC systems proposed in this invention.

[0043] Example 2 This invention provides a stability analysis method for an LCC-HVDC system, which performs stability analysis on a conventional DC transmission system based on a small-signal model constructed in Embodiment 1.

[0044] The relevant technical solutions are the same as above, and will not be repeated here.

[0045] Example 3 This invention provides a small-signal modeling device suitable for LCC-HVDC systems, comprising the following modules: The first processing module is used to process the circuit topology based on the LCC-HVDC system and obtain the original mathematical model of its segmented parts. The second processing module is used to process the circuit topology based on the LCC-HVDC system and obtain the original mathematical model of its continuous part. The third processing module is used to integrate the original mathematical models of the continuous and segmented parts to obtain the original mathematical model of the final LCC-HVDC system. The fourth processing module is used to obtain the small-signal model of the continuous part of the LCC-HVDC system within the segmented intervals based on the trajectory linearization method. The fifth processing module is used to obtain the small-signal model of the LCC-HVDC system at the switching moment based on Filippov theory, including two types: switching from non-commutation process to commutation process and switching from commutation process to non-commutation process. The sixth processing module is used to integrate the small-signal models within the segmented intervals and at the switching times, ultimately obtaining the overall segmented small-signal model of the LCC-HVDC system.

[0046] The specific implementation methods of each module are described in the corresponding steps of Embodiment 1 above, and will not be repeated here.

[0047] Example 4 This invention provides a small signal modeling system, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the small signal modeling method in Embodiment 1 above.

[0048] The relevant technical solutions are the same as above, and will not be repeated here.

[0049] Example 5 This invention provides a stability analysis system for an LCC-HVDC system, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the stability analysis method in Embodiment 2 above.

[0050] The relevant technical solutions are the same as above, and will not be repeated here.

[0051] Example 6 This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the methods in Embodiment 1 and / or Embodiment 2 described above.

[0052] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0053] The relevant technical solutions are the same as above, and will not be repeated here.

[0054] Example 7 This invention provides a computer program product, including a computer program that, when run on a computer, causes the computer to perform the steps of the methods described in Embodiment 1 and / or Embodiment 2.

[0055] The relevant technical solutions are the same as above, and will not be repeated here.

[0056] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of small-signal modeling of an LCC-HVDC system, characterized by, include: Based on the circuit topology of the LCC-HVDC system in each operating section, mathematical models of its segmented and continuous parts are constructed, and the mathematical models of the segmented and continuous parts are integrated as the mathematical model of the LCC-HVDC system. The mathematical model of the segmented part is the mathematical model of the LCC in each operating section, and the operating section includes the commutation process and non-commutation process on the rectifier side and the inverter side. The mathematical model of the continuous part is the mathematical model of the rectifier station and inverter station control system, DC line and AC network in the LCC-HVDC system. On the overall steady-state operating cycle trajectory of the LCC-HVDC system, the mathematical model of the LCC-HVDC system is linearized to obtain the small-signal model of the LCC-HVDC system in each working interval. Using the Filippov method, a transition matrix is ​​designed for the LCC-HVDC system during the switching between adjacent working intervals, in order to characterize the small-signal model of the LCC-HVDC system at the switching time between adjacent working intervals. The small-signal model of the LCC-HVDC system in each working interval and the small-signal model at the switching time together constitute the small-signal model of the LCC-HVDC system, thus completing the small-signal modeling.

2. The small-signal modeling method according to claim 1, characterized in that, When the LCC is a 12-pulse LCC, the 2nd z -2 operating interval to the 2nd z -1 operating interval transition jump matrix is: Among them, the subscript in the variable or , respectively representing the rectifier side or the inverter side; the 2nd z -2 working intervals represent non-commutation processes, the second... z -1 working interval represents the commutation process. z =1, …, 12; , These represent the state variables of the LCC-HVDC system. In the 2nd z -2 work zones, the 2nd z The time derivative within a working interval at the interval switching time is -1 The value, Indicates the 2nd z -2 work zones to the 2nd z -1 time of work zone switching; state variable , For the state variables of LCC, , These are the AC secondary currents of the LCC in YY and Y-Δ connections, respectively. "Y" represents a star connection, and "Δ" represents a delta connection. This refers to the DC side current of the rectifier or inverter station. For the state variables of the continuous part of the LCC-HVDC system, , , The output is a phase-locked loop PI integrator. This represents the output angle of the phase-locked loop in the rotating reference frame. This is the output of the low-pass filter integrator. The output of the PI integrator is controlled by DC current. The output of the PI integrator is controlled by DC voltage. State variables representing DC lines and AC networks; T Indicates transpose; It is a state variable dimensionality The power frequency rotational angular frequency, , These are the proportional coefficients for controlling DC current and DC voltage, respectively. Represents the identity matrix. express A 0 matrix; when 2 z When -2=0, ; 2nd z -1 workspace to the 2nd z The transition matrix during work zone switching for: in, State variables of the LCC-HVDC system In the 2nd z The time derivative within each working interval at the interval switching time The value, Indicates the 2nd z -1 workspace to the 2nd z The moment of switching work zones; the 2nd z Each working interval represents a non-commutation process; This indicates finding the partial derivative. This is the commutation current.

3. The small-signal modeling method according to claim 2, characterized in that, The mathematical model of the LCC-HVDC system is as follows: in, express The derivative of State variables of the LCC-HVDC system In the z Time derivative within each working interval, t xz Indicates the time of switching between work zones; express The derivative of State variables in DC lines and AC networks Time derivative, , , They are respectively: , , For LCC AC primary side voltage, This refers to the DC side current of the rectifier station. This is the DC line voltage. express time; , The matrices representing the state-space equations of DC lines and AC networks. For the turns ratio of the commutation transformer, This is the current transformation matrix.

4. The small-signal modeling method according to claim 3, characterized in that, The small-signal model of the LCC-HVDC system in each working interval is as follows: in, , , for , , Small semaphores; for about The Jacobian matrix in the periodic trajectory The value of ; yes about The Jacobian matrix in the periodic trajectory The value that can be taken on.

5. The small-signal modeling method according to claim 3, characterized in that, The mathematical model of the LCC in each working interval is as follows: in, These are the AC secondary voltages of the LCCs in YY and Y-Δ connections, respectively. Indicates the first z Differential equations corresponding to each working interval Indicate the output equation. This refers to the AC primary current of the LCC.

6. A stability analysis method for an LCC-HVDC system, characterized in that, include: Stability analysis is performed based on a small-signal model of the LCC-HVDC system; wherein the small-signal model is constructed using the small-signal modeling method described in any one of claims 1-5.

7. A small-signal modeling system for an LCC-HVDC system, characterized in that, Includes computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the small signal modeling method according to any one of claims 1-5.

8. A stability analysis system for an LCC-HVDC system, characterized in that, Includes computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the stability analysis method of claim 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the small-signal modeling method as described in any one of claims 1-5, or / and the stability analysis method as described in claim 6.

10. A computer program product, characterized in that, Includes a computer program that, when run on a computer, causes the computer to perform the small-signal modeling method according to any one of claims 1-5, or / and, the stability analysis method according to claim 6.

Images