CN118100172A - Multi-machine system transient stability limit excision time calculation method and related device - Google Patents
Multi-machine system transient stability limit excision time calculation method and related device Download PDFInfo
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Abstract
A method and a related device for calculating transient stability limit excision time of a multi-machine system are provided, wherein the method comprises the following steps: establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, wherein the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation; linearizing to obtain a corresponding VSC state equation and a network state equation respectively, and calculating a simultaneous state equation to obtain a state matrix of the system; calculating to obtain class 1 balance points of the system according to the balance points and the state matrix of the system; and according to the state matrix of the system and the class 1 balance points of the system, calculating to obtain a super tangent plane equation, bringing the fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as the estimated value of the limit cutting time of the corresponding fault when the continuous fault track and a certain tangent plane intersect first. The method effectively solves the problem that transient stability of the multi-machine system is difficult to evaluate.
Description
Technical Field
The invention relates to the technical field of safe and stable operation of power systems, in particular to a method and a related device for calculating transient stability limit removal time of a multi-machine system.
Background
The large-scale new energy base delivery and the rapid development of a large number of power electronic equipment applications lead to great changes in the composition structure and operation morphology of the power system: the intermittent and fluctuating performance of the new energy output leads to a significant increase in the uncertainty of the running mode of the power grid; the rotary inertia of the power supply is reduced, the frequency modulation voltage regulation capability is reduced, and the disturbance rejection capability and the active and reactive power balance capability of the system are reduced; the voltage tolerance and the frequency fluctuation capability of the new energy, DC and other equipment are far lower than those of the traditional equipment, the large-range chain reaction is easy to be caused under AC/DC faults, and the transient process is complex. The transient stability analysis method formed based on the characteristic cognition of the traditional alternating current system is difficult to adapt to the new power grid form and operation requirements.
The transient stability of the new energy single machine grid-connected system is analyzed by a Lyapunov function method, an energy function method, a bifurcation analysis and the like, however, the equivalent damping of single machine equipment depends on the system state, the transient stability calculation result after damping is ignored can be conserved or can be aggressive, the quantitative analysis is not facilitated, and strong mutual coupling effect exists among multiple machine systems, so that the existing method cannot be directly applied to the transient stability analysis of the multiple machine systems, and partial research is carried out on the transient stability analysis and the evaluation of the new energy power system based on numerical simulation, data driving and an artificial intelligent algorithm, but the method has certain requirements on the simulation environment, consumes time and cannot provide relevant indexes of transient stability margin. Overall, for transient stability analysis of a multi-machine grid-connected system, an effective quantitative evaluation analysis method is still lacking.
Therefore, it is needed to provide a quantitative calculation method for measuring the transient stability of the multi-machine system, which effectively solves the difficult problem of difficult assessment of the transient stability of the multi-machine system, quantitatively assesses the transient stability and stability margin of the multi-machine system, reveals the transient characteristics of the power system taking new energy as a main body, and provides effective basis for parameter setting and transient characteristic analysis of the protection device.
Disclosure of Invention
In order to solve the problems, the invention provides a method and a related device for calculating the transient stability limit removal time of a multi-machine system, which can judge the transient stability of the multi-machine system by calculating the limit removal time of the system after a fault, measure the transient stability margin of the multi-machine system, can be used for analyzing the transient typical instability phenomenon of the multi-machine system, can reveal the transient characteristics of the power system taking new energy as a main body, provide effective basis for the transient stability analysis and protection parameter setting of the power system taking new energy as the main body, and ensure the safe and stable operation of the power system taking new energy as the main body.
In order to achieve the above objective, in one aspect, the present invention provides a method for calculating transient stability limit removal time of a multi-machine system, comprising the following steps:
s1: establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, wherein the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation;
S2: linearizing the multi-VSC node dynamics model equation and the network model equation respectively to obtain a corresponding VSC state equation and a network state equation, and calculating to obtain a state matrix of the system by combining the VSC state equation and the network state equation through coordinate transformation and an input-output interface relation;
S3: calculating to obtain class 1 balance points of the system according to the balance points obtained in the step S1 and the state matrix of the system obtained in the step S2;
S4: and (3) according to the state matrix of the system obtained in the step (S2) and the class 1 balance points of the system obtained in the step (S3), calculating to obtain a super tangent plane equation, bringing fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as an estimated value of limit cutting time of corresponding faults when the continuous fault track is intersected with one tangent plane at first.
Further, the step S1 specifically includes: establishing a multi-VSC node dynamics model, wherein when only the phase-locked loop dynamics is considered, the node dynamics model of the VSC is represented by a second-order dynamic differential equation:
Where u tq,i represents the q-axis component of the terminal voltage ut, i at the PLL control dq coordinate of the ith VSC, x pll,i is the output of the phase-locked loop integrator of the ith VSC, phi i represents the angular difference between the phase-locked loop output of the ith VSC and the reference coordinate, and k p_pll,i and k i_pll,i represent the proportional and integral coefficients of the PLL, respectively;
Establishing a network model, neglecting the dynamic state of alternating current time scale, describing the network by using a node admittance matrix, expressing the load by using constant admittance, and leading the load into the node admittance matrix to obtain a network model equation:
Wherein I s and I vsc represent injection current vectors of the balance node and the VSC node, respectively, U s and U vsc represent node voltage vectors of the balance node and the VSC node, respectively, and the network node hybrid matrix M is represented by the following formula:
Wherein Yra, yrb, yrc, yrd are four components of the network node hybrid matrix that take into account the load impedance;
And (3) obtaining a differential algebraic equation of the power electronic multi-VSC grid-connected system by combining the formula (1.1) and the formula (1.2), enabling the right side of the differential algebraic equation to be zero, and further solving to obtain a balance point of the system.
Further, the step S2 specifically includes: performing modularized treatment on each VSC by adopting a blocking connection method, linearizing each VSC at a balance point, and selecting proper input and output variables to form a VSC state equation of a VSC submodule system;
Linearizing a network model equation, selecting the same input and output variables as VSC, and forming a network state equation of a network submodule system;
and transforming the respective input and output variables of the VSC sub-module system and the network sub-module system into a unified coordinate system through coordinate transformation, and according to the input and output interface relation, establishing a VSC state equation and a network state equation of each VSC sub-module system, and calculating to obtain a state matrix of the system.
Further, the step S3 specifically includes: and (3) calculating characteristic roots of the balance points obtained in the step (S1) according to the state matrix of the system obtained in the step (S2), and selecting the balance points with only 1 positive characteristic roots as class 1 balance points of the system.
Further, the step S4 specifically includes: obtaining a super tangent plane equation of the system according to the state matrix of the system obtained in the step S2 and the class 1 balance points of the system obtained in the step S3:
where φ is the angular difference of the phase-locked loop, x pll is the output of the phase-locked loop integrator, φ 1 is the steady state value of φ at the equilibrium point, y 1 is the coefficient of the super-tangent plane equation, y 1 T is the transpose of y 1;
According to a state matrix J of the system, calculating coefficients of a super tangent plane equation:
Wherein μ is the only positive feature root in class 1 equilibrium points, J T is the transpose of the state matrix J;
Bringing the specific value of the fault track into a super-tangent plane equation (1.5), and when the sign of the value of the function F changes, considering that the system fault track passes through the super-tangent plane, meeting the requirements of
And delta t is the system numerical simulation time step, and the time t corresponding to the intersection point is taken as the estimated value of the limit cutting time of the corresponding fault.
In another aspect, the present invention provides a device for calculating transient stability limit removal time of a multi-computer system, including:
The system comprises a first processor, a second processor and a third processor, wherein the first processor is used for establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, and the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation;
The second processor is used for linearizing the multi-VSC node dynamics model equation and the network model equation respectively to obtain a corresponding VSC state equation and a network state equation, and the VSC state equation and the network state equation are combined through coordinate transformation and an input-output interface relation to calculate to obtain a state matrix of the system;
the third processor is used for calculating and obtaining class 1 balance points of the system according to the balance points obtained by the first processor and the state matrix of the system obtained by the second processor;
And the fourth processor is used for calculating and obtaining a super-tangent plane equation according to the state matrix of the system obtained by the second processor and the class 1 balance point of the system obtained by the third processor, bringing the fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as the estimated value of the limit cutting time of the corresponding fault when the continuous fault track and one tangent plane are intersected firstly.
1. Further, the first processor is specifically configured to: establishing a multi-VSC node dynamics model, wherein when only the phase-locked loop dynamics is considered, the node dynamics model of the VSC is represented by a second-order dynamic differential equation:
Where u tq,i represents the q-axis component of the terminal voltage ut, i at the PLL control dq coordinate of the ith VSC, x pll,i is the output of the phase-locked loop integrator of the ith VSC, phi i represents the angular difference between the phase-locked loop output of the ith VSC and the reference coordinate, and k p_pll,i and k i_pll,i represent the proportional and integral coefficients of the PLL, respectively;
Establishing a network model, neglecting the dynamic state of alternating current time scale, describing the network by using a node admittance matrix, expressing the load by using constant admittance, and leading the load into the node admittance matrix to obtain a network model equation:
Wherein I s and I vsc represent injection current vectors of the balance node and the VSC node, respectively, U s and U vsc represent node voltage vectors of the balance node and the VSC node, respectively, and the network node hybrid matrix M is represented by the following formula:
Wherein Yra, yrb, yrc, yrd are four components of the network node hybrid matrix that take into account the load impedance;
The simultaneous expression (1.1) and the expression (1.2) obtain a differential algebraic equation of the power electronic multi-VSC grid-connected system, the right side of the differential algebraic equation is made to be zero, and then the balance point of the system is obtained by solving
2. Further, the second processor is specifically configured to: performing modularized treatment on each VSC by adopting a blocking connection method, linearizing each VSC at a balance point, and selecting proper input and output variables to form a VSC state equation of a VSC submodule system;
Linearizing a network model equation, selecting the same input and output variables as VSC, and forming a network state equation of a network submodule system;
and transforming the respective input and output variables of the VSC sub-module system and the network sub-module system into a unified coordinate system through coordinate transformation, and according to the input and output interface relation, establishing a VSC state equation and a network state equation of each VSC sub-module system, and calculating to obtain a state matrix of the system.
Further, the third processor is specifically configured to: and calculating characteristic roots of the balance points obtained by the first processor according to the state matrix of the system obtained by the second processor, and selecting the balance points with only 1 positive characteristic root as class 1 balance points of the system.
3. Further, the fourth processor is specifically configured to: obtaining a super tangential plane equation of the system according to the state matrix of the system obtained by the second processor and the class 1 balance point of the system obtained by the third processor:
where φ is the angular difference of the phase-locked loop, x pll is the output of the phase-locked loop integrator, φ 1 is the steady state value of φ at the equilibrium point, y 1 is the coefficient of the super-tangent plane equation, y 1 T is the transpose of y 1;
According to a state matrix J of the system, calculating coefficients of a super tangent plane equation:
Wherein μ is the only positive feature root in class 1 equilibrium points, J T is the transpose of the state matrix J;
Bringing the specific value of the fault track into a super-tangent plane equation (1.5), and when the sign of the value of the function F changes, considering that the system fault track passes through the super-tangent plane, meeting the requirements of
And delta t is the system numerical simulation time step, and the time t corresponding to the intersection point is taken as the estimated value of the limit cutting time of the corresponding fault.
Compared with the prior art, the invention has the following beneficial effects:
Aiming at the problem that the transient stability and stability margin of a novel power system taking new energy as a main body are difficult to quantitatively calculate and analyze, the method for calculating the transient stability limit cutting time based on the stability domain super-tangent plane is provided, the limit cutting time of the multi-machine system after the fault can be calculated, the transient stability of the multi-machine system can be estimated through the limit cutting time, the stability margin of the multi-machine system can be quantitatively measured, the problem that the transient stability of the multi-machine system is difficult to estimate is effectively solved, and an effective basis is provided for transient stability analysis and protection parameter setting of the novel power system taking new energy as the main body.
Drawings
FIG. 1 is a flowchart of a method for calculating transient stability limit removal time of a multi-machine system according to an embodiment of the present invention;
Fig. 2 is a schematic topology diagram of a three-machine nine-node system according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, a method for calculating transient stability limit removal time of a multi-machine system according to an embodiment of the present invention includes the following steps:
s1: establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, wherein the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation;
The step S1 specifically comprises the following steps: establishing a multi-VSC node dynamics model, wherein when only the phase-locked loop dynamics are considered, the node dynamics model of the VSC can be expressed by a second-order dynamic differential equation:
where u tq,i represents the q-axis component of the terminal voltage ut, i at the PLL control dq coordinate of the ith VSC, x pll,i is the output of the phase-locked loop integrator of the ith VSC, phi i represents the angular difference between the phase-locked loop output of the ith VSC and the reference coordinate, and k p_pll,i and k i_pll,i represent the proportional and integral coefficients of the PLL, respectively.
For the balance nodes in the system, an infinite voltage source is used for analysis simplicity.
A network model is established, the dynamic state of alternating current time scale is ignored, the network can be described by a node admittance matrix, the load is represented by constant admittance, and the constant admittance is imported into the node admittance matrix, so that a network model equation can be obtained:
Wherein I s and I vsc represent injection current vectors of the balance node and the VSC node, respectively, U s and U vsc represent node voltage vectors of the balance node and the VSC node, respectively, and the network node hybrid matrix M may be represented by the following formula:
Wherein Yra, yrb, yrc, yrd are four components of the network node hybrid matrix that take into account the load impedance.
And (3) obtaining a differential algebraic equation of the power electronic multi-VSC grid-connected system by combining the formula (1.1) and the formula (1.2), enabling the right side of the differential algebraic equation to be zero, and further solving to obtain a balance point of the system.
S2: linearizing a multi-VSC node dynamics model equation and a network model equation respectively to obtain a corresponding state equation, and calculating a state matrix J of the system by combining the VSC state equation and the network state equation through coordinate transformation and an input-output interface relation;
The step S2 specifically comprises the following steps: performing modularized treatment on each VSC by adopting a blocking connection method, linearizing each VSC at a balance point, and selecting proper input and output variables to form a VSC state equation of a VSC submodule system;
Linearizing a network model equation, selecting the same input and output variables as VSC, and forming a network state equation of a network submodule system;
and transforming the respective input and output variables of the VSC submodule system and the network submodule system into a unified coordinate system through coordinate transformation, and according to the input and output interface relation, establishing each VSC submodule equation (VSC equation of state and network equation of state) in a combined mode, and calculating to obtain a state matrix J of the system.
S3: calculating to obtain class 1 balance points of the system according to the balance points obtained in the step S1 and the state matrix of the system obtained in the step S2;
The step S3 specifically comprises the following steps: and (3) calculating characteristic roots of the balance points obtained in the step (S1) according to the state matrix of the system obtained in the step (S2), and selecting the balance points with only 1 positive characteristic roots, namely the class-1 balance points of the system.
S4: according to the state matrix of the system obtained in the step S2 and the class 1 balance points of the system obtained in the step S3, calculating to obtain a super tangent plane equation of the system, bringing fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as an estimated value of limit cutting time of corresponding faults when a continuous fault track is intersected with one tangent plane at first.
The step S4 specifically comprises the following steps: according to the state matrix of the system obtained in the step S2 and the class 1 balance points of the system obtained in the step S3, the super tangent plane equation of the system can be obtained:
where φ is the angular difference of the phase-locked loop, x pll is the output of the phase-locked loop integrator, φ 1 is the steady state value of φ at the equilibrium point, y 1 is the coefficient of the super-tangent plane equation, y 1 T is the transpose of y 1;
from the state matrix J of the system, the coefficients of the hyper-tangential plane equations can be calculated:
Where μ is the only positive feature root in class 1 equilibrium point and J T is the transpose of the state matrix J.
The specific value of the fault track is brought into a super-tangent plane equation (1.5), when the sign of the value of the function F changes, the fault track of the system is considered to pass through the super-tangent plane, namely the condition that
The delta t is the system numerical simulation time step, the time t corresponding to the intersection point is taken as the estimated value of the limit cutting time of the corresponding fault, and it is worth noting that the stability domain is usually convex near the class 1 balance point, so that the intersection point between the fault track and the super-tangent plane is always outside the stability domain, namely the calculated result of the method is always slightly larger than the actual value, and the calculated result has better conservation in the system fault cutting and protection device parameter setting, and can ensure the stable operation of the system.
In a specific embodiment, a three-machine nine-node system shown in fig. 2 is built in MATLAB/Smulink, and the transient stability limit cutting time of the built three-machine nine-node system is calculated according to the multi-machine system transient stability limit cutting time calculation method provided by the embodiment of the invention.
Table 1 is a table showing the comparison of the calculated limit fault removal time results and MATLAB/Smulink simulation results of the method provided by the invention under different voltage drop degrees at the bus 1 of the three-machine nine-node system.
TABLE 1 Limit cut-off time at different voltage sag levels
It can be seen that, for faults when the voltage drops to 0.4pu, 0.3pu, 0.2pu, 0.1pu and 0, the method provided by the invention can effectively calculate the limit cutting time under different faults of the multi-computer system, and the calculated relative error of the limit cutting time is kept within 7%, so that the method has better calculation precision and can effectively measure the transient stability margin of the multi-computer system.
In summary, according to the calculation method provided by the embodiment of the invention, the limit cutting time of the multi-machine system under different voltage drop degrees can be obtained, the calculation accuracy is good, the transient stability of the multi-machine system can be quantitatively evaluated, and the transient stability margin of the multi-machine system can be effectively measured.
The second embodiment of the invention correspondingly provides a multi-machine system transient stability limit cutting time calculation device, which comprises the following steps:
The system comprises a first processor, a second processor and a third processor, wherein the first processor is used for establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, and the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation;
The second processor is used for linearizing the multi-VSC node dynamics model equation and the network model equation respectively to obtain a corresponding VSC state equation and a network state equation, and the VSC state equation and the network state equation are combined through coordinate transformation and an input-output interface relation to calculate to obtain a state matrix of the system;
the third processor is used for calculating and obtaining class 1 balance points of the system according to the balance points obtained by the first processor and the state matrix of the system obtained by the second processor;
And the fourth processor is used for calculating and obtaining a super-tangent plane equation according to the state matrix of the system obtained by the second processor and the class 1 balance point of the system obtained by the third processor, bringing the fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as the estimated value of the limit cutting time of the corresponding fault when the continuous fault track and one tangent plane are intersected firstly.
Compared with the prior art, the method and the system for calculating the transient stability limit cutting time of the multi-machine system have the following beneficial effects:
Aiming at the problem that the transient stability and stability margin of a novel power system taking new energy as a main body are difficult to quantitatively calculate and analyze, the method for calculating the transient stability limit cutting time based on the stability domain super-tangent plane is provided, the limit cutting time of the multi-machine system after the fault can be calculated, the transient stability of the multi-machine system can be estimated through the limit cutting time, the stability margin of the multi-machine system can be quantitatively measured, the problem that the transient stability of the multi-machine system is difficult to estimate is effectively solved, and an effective basis is provided for transient stability analysis and protection parameter setting of the novel power system taking new energy as the main body.
In another aspect, the present invention provides a system for calculating transient stability limit removal time of a multi-machine system based on a stability domain super-tangent plane, comprising: a computer readable storage medium and a processor;
The computer-readable storage medium is for storing executable instructions;
The processor is configured to read executable instructions stored in the computer readable storage medium, and execute the method for calculating the transient stability limit excision time of the multi-computer system based on the stability domain super-tangent plane according to the first aspect.
In another aspect, the present invention provides a non-transitory computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements the method for calculating a transient stability limit excision time of a multi-computer system based on a stability domain super tangential plane according to the first aspect.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (10)
1. A method for calculating transient stability limit excision time of a multi-machine system is characterized by comprising the following steps of: the method comprises the following steps:
s1: establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, wherein the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation;
S2: linearizing the multi-VSC node dynamics model equation and the network model equation respectively to obtain a corresponding VSC state equation and a network state equation, and calculating to obtain a state matrix of the system by combining the VSC state equation and the network state equation through coordinate transformation and an input-output interface relation;
S3: calculating to obtain class 1 balance points of the system according to the balance points obtained in the step S1 and the state matrix of the system obtained in the step S2;
S4: and (3) according to the state matrix of the system obtained in the step (S2) and the class 1 balance points of the system obtained in the step (S3), calculating to obtain a super tangent plane equation, bringing fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as an estimated value of limit cutting time of corresponding faults when the continuous fault track is intersected with one tangent plane at first.
2. The method for calculating the transient stability limit excision time of the multiple computer systems according to claim 1, wherein the method comprises the following steps: the step S1 specifically comprises the following steps: establishing a multi-VSC node dynamics model, wherein when only the phase-locked loop dynamics is considered, the node dynamics model of the VSC is represented by a second-order dynamic differential equation:
Where u tq,i represents the q-axis component of the terminal voltage ut, i at the PLL control dq coordinate of the ith VSC, x pll,i is the output of the phase-locked loop integrator of the ith VSC, phi i represents the angular difference between the phase-locked loop output of the ith VSC and the reference coordinate, and k p_pll,i and k i_pll,i represent the proportional and integral coefficients of the PLL, respectively;
Establishing a network model, neglecting the dynamic state of alternating current time scale, describing the network by using a node admittance matrix, expressing the load by using constant admittance, and leading the load into the node admittance matrix to obtain a network model equation:
；
Wherein I s and I vsc represent injection current vectors of the balance node and the VSC node, respectively, U s and U vsc represent node voltage vectors of the balance node and the VSC node, respectively, and the network node hybrid matrix M is represented by the following formula:
；
Wherein Yra, yrb, yrc, yrd are four components of the network node hybrid matrix that take into account the load impedance;
And (3) obtaining a differential algebraic equation of the power electronic multi-VSC grid-connected system by combining the formula (1.1) and the formula (1.2), enabling the right side of the differential algebraic equation to be zero, and further solving to obtain a balance point of the system.
3. The method for calculating the transient stability limit excision time of the multiple computer systems according to claim 1, wherein the method comprises the following steps: the step S2 specifically comprises the following steps: performing modularized treatment on each VSC by adopting a blocking connection method, linearizing each VSC at a balance point, and selecting proper input and output variables to form a VSC state equation of a VSC submodule system;
Linearizing a network model equation, selecting the same input and output variables as VSC, and forming a network state equation of a network submodule system;
and transforming the respective input and output variables of the VSC sub-module system and the network sub-module system into a unified coordinate system through coordinate transformation, and according to the input and output interface relation, establishing a VSC state equation and a network state equation of each VSC sub-module system, and calculating to obtain a state matrix of the system.
4. The method for calculating the transient stability limit excision time of the multiple computer systems according to claim 1, wherein the method comprises the following steps: the step S3 specifically comprises the following steps: and (3) calculating characteristic roots of the balance points obtained in the step (S1) according to the state matrix of the system obtained in the step (S2), and selecting the balance points with only 1 positive characteristic roots as class 1 balance points of the system.
5. The method for calculating the transient stability limit excision time of the multiple computer systems according to claim 1, wherein the method comprises the following steps: the step S4 specifically comprises the following steps: obtaining a super tangent plane equation of the system according to the state matrix of the system obtained in the step S2 and the class 1 balance points of the system obtained in the step S3:
；
where φ is the angular difference of the phase-locked loop, x pll is the output of the phase-locked loop integrator, φ 1 is the steady state value of φ at the equilibrium point, y 1 is the coefficient of the super-tangent plane equation, y 1 T is the transpose of y 1;
According to a state matrix J of the system, calculating coefficients of a super tangent plane equation:
；
Wherein μ is the only positive feature root in class 1 equilibrium points, J T is the transpose of the state matrix J;
Bringing the specific value of the fault track into a super-tangent plane equation (1.5), and when the sign of the value of the function F changes, considering that the system fault track passes through the super-tangent plane, meeting the requirements of
；
And delta t is the system numerical simulation time step, and the time t corresponding to the intersection point is taken as the estimated value of the limit cutting time of the corresponding fault.
6. A multi-machine system transient stability limit cut-off time calculation device, comprising:
The system comprises a first processor, a second processor and a third processor, wherein the first processor is used for establishing a differential algebraic equation of the power electronic multi-VSC grid-connected system and obtaining a balance point of the system, and the differential algebraic equation comprises a multi-VSC node dynamics model equation and a network model equation;
The second processor is used for linearizing the multi-VSC node dynamics model equation and the network model equation respectively to obtain a corresponding VSC state equation and a network state equation, and the VSC state equation and the network state equation are combined through coordinate transformation and an input-output interface relation to calculate to obtain a state matrix of the system;
the third processor is used for calculating and obtaining class 1 balance points of the system according to the balance points obtained by the first processor and the state matrix of the system obtained by the second processor;
And the fourth processor is used for calculating and obtaining a super-tangent plane equation according to the state matrix of the system obtained by the second processor and the class 1 balance point of the system obtained by the third processor, bringing the fault track information of the system into all tangent plane equations, and taking the time corresponding to the intersection point as the estimated value of the limit cutting time of the corresponding fault when the continuous fault track and one tangent plane are intersected firstly.
7. The multi-machine system transient stability limit cut-off time calculation device of claim 6, wherein: the first processor is specifically configured to: establishing a multi-VSC node dynamics model, wherein when only the phase-locked loop dynamics is considered, the node dynamics model of the VSC is represented by a second-order dynamic differential equation:
；
Where u tq,i represents the q-axis component of the terminal voltage ut, i at the PLL control dq coordinate of the ith VSC, x pll,i is the output of the phase-locked loop integrator of the ith VSC, phi i represents the angular difference between the phase-locked loop output of the ith VSC and the reference coordinate, and k p_pll,i and k i_pll,i represent the proportional and integral coefficients of the PLL, respectively;
Establishing a network model, neglecting the dynamic state of alternating current time scale, describing the network by using a node admittance matrix, expressing the load by using constant admittance, and leading the load into the node admittance matrix to obtain a network model equation:
；
Wherein I s and I vsc represent injection current vectors of the balance node and the VSC node, respectively, U s and U vsc represent node voltage vectors of the balance node and the VSC node, respectively, and the network node hybrid matrix M is represented by the following formula:
；
Wherein Yra, yrb, yrc, yrd are four components of the network node hybrid matrix that take into account the load impedance;
And (3) obtaining a differential algebraic equation of the power electronic multi-VSC grid-connected system by combining the formula (1.1) and the formula (1.2), enabling the right side of the differential algebraic equation to be zero, and further solving to obtain a balance point of the system.
8. The multi-machine system transient stability limit cut-off time calculation device of claim 6, wherein: the second processor is specifically configured to: performing modularized treatment on each VSC by adopting a blocking connection method, linearizing each VSC at a balance point, and selecting proper input and output variables to form a VSC state equation of a VSC submodule system;
Linearizing a network model equation, selecting the same input and output variables as VSC, and forming a network state equation of a network submodule system;
and transforming the respective input and output variables of the VSC sub-module system and the network sub-module system into a unified coordinate system through coordinate transformation, and according to the input and output interface relation, establishing a VSC state equation and a network state equation of each VSC sub-module system, and calculating to obtain a state matrix of the system.
9. The multi-machine system transient stability limit cut-off time calculation device of claim 6, wherein: the third processor is specifically configured to: and calculating characteristic roots of the balance points obtained by the first processor according to the state matrix of the system obtained by the second processor, and selecting the balance points with only 1 positive characteristic root as class 1 balance points of the system.
10. The multi-machine system transient stability limit cut-off time calculation device of claim 6, wherein: the fourth processor is specifically configured to: obtaining a super tangential plane equation of the system according to the state matrix of the system obtained by the second processor and the class 1 balance point of the system obtained by the third processor:
；
where φ is the angular difference of the phase-locked loop, x pll is the output of the phase-locked loop integrator, φ 1 is the steady state value of φ at the equilibrium point, y 1 is the coefficient of the super-tangent plane equation, y 1 T is the transpose of y 1;
According to a state matrix J of the system, calculating coefficients of a super tangent plane equation:
；
Wherein μ is the only positive feature root in class 1 equilibrium points, J T is the transpose of the state matrix J;
Bringing the specific value of the fault track into a super-tangent plane equation (1.5), and when the sign of the value of the function F changes, considering that the system fault track passes through the super-tangent plane, meeting the requirements of
；
And delta t is the system numerical simulation time step, and the time t corresponding to the intersection point is taken as the estimated value of the limit cutting time of the corresponding fault.
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