CN115563921A - Method and system for determining fault transient electric quantity of flexible direct current transmission line - Google Patents
Method and system for determining fault transient electric quantity of flexible direct current transmission line Download PDFInfo
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Abstract
The invention discloses a method for determining fault transient electric quantity of a flexible direct current transmission line, which comprises the following steps: constructing an MMC equivalent circuit during interelectrode short circuit according to the MMC converter station circuit parameters; establishing an equivalent model of two ports of the direct current transmission line in a complex frequency domain according to the acquired transmission line parameters; obtaining a direct current fault transient expression under a complex frequency domain according to an MMC equivalent circuit and a direct current transmission line two-port equivalent model when the interelectrode is in short circuit; the method and the device can accurately give the overall trend of the transient process after the fault. The calculation process is simple and convenient, and the complicated modeling simulation process in the traditional simulation method is avoided. Meanwhile, the wave generation process when the overhead line fails can be well reflected. The method can accurately express the overall development trend of fault current flowing through the protection installation position after the fault occurs and before the converter station is locked, and has positive significance on the fault current suppression and protection setting design of the MMC-HVDC system.
Description
Technical Field
The invention belongs to the technical field of flexible direct current transmission, and particularly relates to a method and a system for determining fault transient electric quantity of a flexible direct current transmission line.
Background
Currently, a modular multi-level converter (MMC) has the advantages of convenience in control, low switching frequency, small harmonic, modularized design and the like, and is one of common topologies in flexible direct-current transmission engineering. The overhead line is a main mode for a modular multilevel converter (MMC-HVDC) system to carry out high-power electric energy transmission, but has a long transmission distance; and the direct exposure is in the environment, and the use of overhead line leads to the increase of straight line fault probability, seriously threatens the safe and stable operation of power system.
The switching of sub-module in MMC is non-linear, and electromagnetic transient process is complicated when trouble, uses simulation software (for example PSCAD/EMTDC) to simulate usually in the engineering, and nevertheless the following limitation exists in the simulation calculation: the direct current engineering has high complexity and difficult modeling; (2) The simulation system has limited scale, and the simulation is respectively carried out aiming at different fault types and fault positions, so that the simulation time is long, and the efficiency is low. Therefore, in order to accurately and efficiently analyze the transient process after the fault, the analytic calculation of the fault current becomes the focus of attention in the field of control protection.
In the current research on the short-circuit fault current calculation of the power transmission line, a centralized parameter model is usually adopted to enable the power transmission line to be equivalent to an RL series branch, the processing mode enables a direct-current system after the short-circuit fault to be equivalent to a linear circuit composed of a resistor, an inductor, a capacitor and a direct-current power supply, and on the basis, the linear circuit is solved through a circuit theory column equation. But the influence of distributed capacitance is neglected, and the propagation delay and the specific wave process of the line fault cannot be reflected.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for determining the fault transient electric quantity of the flexible direct-current transmission line, which can accurately determine the fault transient electric quantity of the direct-current transmission line.
The technical problem to be solved by the invention is realized by the following technical scheme:
in a first aspect, a method for determining fault transient electrical quantity of a flexible direct current transmission line is provided, which includes:
constructing an MMC equivalent circuit during interelectrode short circuit according to the MMC converter station circuit parameters;
establishing an equivalent model of two ports of the direct current transmission line in a complex frequency domain according to the acquired transmission line parameters;
obtaining a direct-current fault transient expression under a complex frequency domain according to an MMC equivalent circuit and two-port equivalent models of a direct-current transmission line during interelectrode short circuit;
and performing Laplace transform on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.
With reference to the first aspect, further, the constructing an inter-pole short-circuit time MMC equivalent circuit according to the MMC converter station circuit parameters includes:
obtaining MMC circuit parameters including bridge arm resistance R arm Bridge arm inductance L arm Smoothing reactor inductance L fw Sub-module on-resistance R on And sub-module capacitance C SM ；
An RCL series circuit is constructed according to the obtained MMC converter station circuit parameters and is used as an MMC equivalent circuit during interelectrode short circuit, wherein the resistance is R eq Inductance is L eq A capacitor is C eq ；
And N is the number of the upper bridge arm series submodule and the lower bridge arm series submodule of each phase of the MMC.
With reference to the first aspect, further, the establishing a two-port equivalent model of the dc transmission line in the complex frequency domain according to the obtained transmission line parameters includes:
obtaining transmission line parameters including transmission line unit length resistance R 0 Inductance L per unit length 0 Conductivity per unit length G 0 Capacitance per unit length C 0 And a transmission line distance L;
according to the transmission line parameters, the direct current transmission line model in the complex frequency domain is expressed by using a common differential equation as follows:
solving the formula (2) to obtain
Wherein,
x is the position variable, s is the Laplacian operator, gamma is the propagation coefficient, Z 1 Is wave impedance, U f 、U b Respectively a forward traveling wave and a backward traveling wave of the transmission line voltage; i is f 、I b The forward traveling wave and the backward traveling wave of the transmission line current are respectively, and U, I respectively represent the voltage current of the direct current transmission line under the complex frequency domain;
taking x =0 and x = l, respectively, and equating the dc transmission line to a two-port equivalent model, where port characteristics of the two-port equivalent model are expressed as follows:
wherein, U m 、U n Representing the voltages at the nodes at both ends of the transmission line, I, respectively m 、I n Respectively representing the current of nodes at two ends of a transmission line, and U is a node voltage vector;
the two-port equivalent model is represented by a current admittance matrix Y as:
with reference to the first aspect, further, the obtaining of the transient expression of the dc fault in the complex frequency domain includes:
when the interelectrode short circuit occurs, the inductance and the capacitance in the MMC equivalent circuit are subjected to Laplacian transformation to obtain the inductance voltage and the capacitance current under a complex frequency domain, as shown in the following formula:
V L (s)＝L eq sI L (s)-L eq i L (0 - ) (6)
I C (s)＝C eq sV C (s)-C eq v C (0 - ) (7)
wherein, V L (s)、I L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; v C (s)、I C (s) are respectively capacitance voltage and current in complex frequency domain; l is eq 、C eq Respectively an inductor and a capacitor of the MMC equivalent circuit during interelectrode short circuit; i.e. i L (0-)、v C (0-) is steady state direct current, voltage respectively;
constructing an inter-electrode fault equivalent circuit of the transmission line in a complex frequency domain;
establishing a node admittance matrix for the inter-transmission line fault equivalent circuit on the basis of a single transmission line admittance matrix in the inter-transmission line fault equivalent circuit;
obtaining a relation between current and voltage at two ends of the transmission line in a complex frequency domain according to a node admittance matrix established by the transmission line interpolar fault equivalent circuit and a direct current transmission line two-port equivalent model in the complex frequency domain, and obtaining an equation of the relation between voltage of each node and branch current according to the relation between the current and voltage at two ends of the transmission line in the complex frequency domain, actual circuit information and the termination condition of the transmission line;
and solving an equation of the relation between the voltage of each node and the current of the branch circuit to obtain a direct-current fault transient expression F(s) in a complex frequency domain.
With reference to the first aspect, further, the performing laplace transform on the dc fault transient expression in the complex frequency domain to obtain a time domain response includes:
laplace transformation is carried out on a direct current fault transient expression under a complex frequency domain by adopting the following formula
Wherein f (t) is a transient expression of the direct current fault in the time domain; s = σ + j ω, laplacian operator; j is an imaginary number, ω is a frequency, σ is any normal number, z = st, t is time;
using rational functions xi β.α (z) to function e z Carrying out Pade approximation to make the first alpha + beta +1 terms of the Taylor expansion equations equal and xi β.α The expression of (z) is as follows:
wherein, P β (z)、Q α (z) are respectively beta, alpha order polynomials, alpha-beta > 2;
using xi β.α (z) alternative e z Obtaining an approximate expression of f (t)
As shown in the following formula:
according to the leave theorem pair
And (3) performing integral calculation to obtain the time domain response of the direct current fault transient as shown in the following formula:
wherein z is i Is xi β.α Pole of (z), k i The residue corresponding to the pole.
In a second aspect, a system for determining a fault transient electrical quantity of a flexible direct current transmission line is provided, which includes:
the MMC equivalent circuit construction module is used for constructing an MMC equivalent circuit during the interelectrode short circuit according to the circuit parameters of the MMC converter station;
the direct current transmission line two-port equivalent model building module in the complex frequency domain is used for building a direct current transmission line two-port equivalent model in the complex frequency domain according to the acquired transmission line parameters;
the direct current fault transient expression acquisition module under the complex frequency domain is used for acquiring a direct current fault transient expression under the complex frequency domain according to the MMC equivalent circuit and the two-port equivalent model of the direct current transmission line during the interelectrode short circuit;
and the line fault transient electrical quantity determining module is used for performing Laplace transformation on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.
With reference to the second aspect, further, the operation performed by the MMC equivalent circuit building module during the inter-electrode short circuit includes:
obtaining MMC circuit parameters including bridge arm resistance R arm Bridge arm inductance L arm Smoothing reactor inductance L fw Sub-module on-resistance R on And a sub-module capacitor C SM ；
An RCL series circuit is constructed according to the obtained MMC converter station circuit parameters and is used as an MMC equivalent circuit during interelectrode short circuit, wherein the resistance is R eq Inductance is L eq A capacitor is C eq ；
And N is the number of the upper bridge arm series submodule and the lower bridge arm series submodule of each phase of the MMC.
With reference to the second aspect, further, the operations performed by the module for constructing an equivalent model of two ports of a dc transmission line in a complex frequency domain include:
obtaining transmission line parameters including transmission line unit length resistance R 0 Inductance L per unit length 0 Conductivity per unit length G 0 Capacitance per unit length C 0 And a transmission line distance L;
according to the transmission line parameters, the direct current transmission line model in the complex frequency domain is expressed by using a common differential equation as follows:
solving the formula (2) to obtain
Wherein,
x is the position variable, s is the Laplacian operator, gamma is the propagation coefficient, Z 1 Is wave impedance, U f 、U b Respectively a forward traveling wave and a backward traveling wave of the transmission line voltage; i is f 、I b The forward traveling wave and the backward traveling wave of the transmission line current are respectively;
taking x =0 and x = l, respectively, and equating the dc transmission line to a two-port equivalent model, where the port characteristics of the two-port equivalent model are as follows:
wherein, U m 、U n Respectively representing the voltages at the nodes at the two ends of the transmission line, I m 、I n Respectively representing the current of nodes at two ends of a transmission line, and U is a node voltage vector;
the two-port equivalent model is represented by a current admittance matrix Y as:
with reference to the second aspect, further, the operation performed by the complex frequency domain dc fault transient expression obtaining module includes:
when in interelectrode short circuit, an inductor and a capacitor in the MMC equivalent circuit are subjected to Laplacian transformation to obtain the inductance voltage and the capacitance current under a complex frequency domain, as shown in the following formula:
V L (s)＝L eq sI L (s)-L eq i L (0 - ) (6)
I C (s)＝C eq sV C (s)-C eq v C (0 - ) (7)
wherein, V L (s)、I L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; v C (s)、I C (s) are respectively capacitance voltage and current in complex frequency domain; l is eq 、C eq Respectively an inductor and a capacitor of the MMC equivalent circuit during interelectrode short circuit; i.e. i L (0-)、v C (0 - ) Respectively, steady-state direct current and voltage;
constructing an inter-electrode fault equivalent circuit of the transmission line in a complex frequency domain;
establishing a node admittance matrix for the inter-transmission line fault equivalent circuit on the basis of a single transmission line admittance matrix in the inter-transmission line fault equivalent circuit;
obtaining a relation between current and voltage at two ends of the transmission line in a complex frequency domain according to a node admittance matrix established by the transmission line interpolar fault equivalent circuit and a direct current transmission line two-port equivalent model in the complex frequency domain, and obtaining an equation of the relation between voltage of each node and branch current according to the relation between the current and voltage at two ends of the transmission line in the complex frequency domain, actual circuit information and the termination condition of the transmission line;
and solving an equation of the relation between the voltage of each node and the current of the branch circuit to obtain a direct-current fault transient expression F(s) in a complex frequency domain.
With reference to the second aspect, further, the line fault transient electrical quantity determination module performs operations including:
laplace transformation is carried out on a direct current fault transient expression under a complex frequency domain by adopting the following formula
Wherein f (t) is a transient expression of the direct current fault in the time domain; s = σ + j ω, which is laplacian; j is an imaginary number, ω is a frequency, σ is any normal number, z = st, t is time;
using rational functions xi β.α (z) to function e z Perform a Pade approximation so that both TaylorThe first alpha + beta +1 term of the expansion is equal, ξ β.α The expression of (z) is as follows:
wherein, P β (z)、Q α (z) are respectively beta, alpha order polynomials, alpha-beta > 2;
using xi β.α (z) alternative e z Obtaining an approximate expression of f (t)
As shown in the following formula:
according to the leave theorem pair
And (3) performing integral calculation to obtain the time domain response of the direct current fault transient as shown in the following formula:
wherein z is i Is xi β.α Pole of (z), k i The residue corresponding to the pole.
The invention has the beneficial effects that: the invention can accurately give the overall trend of the transient process after the fault. The calculation process is simple and convenient, and the complicated modeling simulation process in the traditional simulation method is avoided. Meanwhile, the wave generation process when the overhead line fails can be well reflected. The method can accurately express the overall development trend of fault current flowing through the protection installation position after the fault occurs and before the converter station is locked, and has positive significance on the fault current suppression and protection setting design of the MMC-HVDC system.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a main circuit structure of an MMC-HVDC system suitable for use in the present invention;
FIG. 3 is a schematic diagram of an MMC equivalent circuit in the inter-electrode short circuit of the present invention;
FIG. 4 is a schematic diagram of an equivalent model of two ports of a DC transmission line in complex frequency domain according to the present invention;
fig. 5 is a schematic diagram of an equivalent circuit of an interpolar fault of a transmission line of an MMC-HVDC system in a complex frequency domain.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
For better understanding of the present invention, the related art in the technical solution of the present invention is explained below.
Example 1
As shown in fig. 1-5, fig. 1 is a main circuit structure diagram of an MMC-HVDC system, and it should be noted that the MMC-HVDC system is a two-terminal ac system, an MMC converter station, and devices in the total converter station of the MMC-HVDC system and the dc transmission line mainly include a converter transformer, an ac filter, a smoothing reactor, and a converter. The MMC-HVDC system converts three-phase alternating current into direct current through a converter station in a rectifying mode, and then the MMC converter station is transmitted to another converter station through a direct current transmission line to be inverted into the three-phase alternating current in a power transmission mode. The MMC current station comprises an MMC current station, a bridge arm reactor, a bridge arm current station and a bridge arm power station, wherein each phase of upper and lower bridge arms of the MMC current station is respectively formed by connecting N half-bridge sub-modules and bridge arm reactors in series, and each half-bridge SM comprises two IGBTs, a follow current diode group and an energy storage capacitor; two ends of the direct current line are connected with the smoothing reactor. When the system normally operates, the total number of the input SMs of the upper bridge arm and the lower bridge arm of each phase in the MMC at any time is not changed and is N (half of the total SM of each phase), and the direct-current voltage keeps stable. And the corresponding output alternating voltage can be obtained by controlling the distribution of the N input SMs between the upper bridge arm and the lower bridge arm.
Referring to fig. 2, the method for calculating the fault transient electrical quantity of the flexible direct current transmission line based on the inverse numerical laplace transform provided by the present invention includes:
step S1: and establishing an MMC equivalent circuit when an interelectrode short circuit is formed according to the circuit parameters of the MMC converter station in the MMC-HVDC system and determining the parameters of the MMC equivalent circuit. The specific process is as follows:
step S1.1: obtaining MMC circuit parameters including bridge arm resistance R arm Bridge arm inductance L arm Smoothing reactor inductance L fw Submodule on-resistance R on Sub-module capacitor C SM . Each phase of the MMC is obtained by connecting N submodules in series, wherein N is a positive integer larger than 1.
Step S1.2: establishing an MMC equivalent circuit and determining equivalent circuit parameters when the interelectrode is in short circuit, wherein the equivalent circuit model is an RLC series circuit, and the resistance is R eq Inductance is L eq Capacitor C eq 。
It can be understood that after an inter-electrode short circuit occurs in a transmission line in an MMC-HVDC system, power transmission is stopped between a sending end converter station and a receiving end converter station, and an SM capacitor in an input state discharges to a fault point through a bridge arm, which is equivalent to a three-phase short circuit fault. In a period of time before the converter station is locked, the number of the SM put into the converter station is kept unchanged to be N, the control system hardly influences short-circuit current, and the MMC can be equivalent to an RLC series circuit.
It should be noted that the equivalent resistance R in the equivalent circuit of the MMC converter station eq Equivalent inductance L eq And an equivalent capacitance C eq The following formula can be calculated from the MMC circuit parameters:
step S2: establishing an equivalent two-port network model of the direct current transmission line in a complex frequency domain, and specifically comprising the following steps of:
step S2.1: obtaining transmission line parameters including resistance per unit length R 0 Inductance L per unit length 0 Conductivity per unit lengthG 0 Capacitance per unit length C 0 And a transmission line distance L. m and n are the serial numbers of the end nodes at two ends (head end and tail end) of the transmission line.
Step S2.2: in a complex frequency domain, a transmission line model is established and expressed by ordinary differential equations.
The transmission line is represented by the following partial differential equation system in the time domain:
where u and i represent the voltage and current of the transmission line in the time domain, respectively.
And performing Laplace transformation on the partial differential equation set in the time domain, wherein the transmission line model in the complex frequency domain can be expressed as follows by adopting an ordinary differential equation:
u, I represents the voltage and current of the transmission line in the complex frequency domain, respectively.
Step S2.3: solving the transmission line model ordinary differential equation under the complex frequency domain to obtain a general solution as follows:
in the formula,
is the propagation coefficient; ,
is the wave impedance. U shape f 、U b Respectively a forward traveling wave and a backward traveling wave of the transmission line voltage; i is f 、I b Respectively a forward traveling wave and a backward traveling wave of the transmission line current; x is a position variable.
Step S2.4: let x =0, x = l, i.e. the transmission line head and end nodes m, n. The transmission line in the complex frequency domain is equivalent to a two-port network, and the port characteristics of the two-port network are described by an admittance matrix.
Specifically, taking x =0 and x = l, respectively, the relationship between two ends of the transmission line in the complex frequency domain can be expressed as:
regarding the electrical characteristics of both ends of the transmission line, the transmission line in the complex frequency domain is regarded as a two-port network, and the port characteristics can be expressed by the form of a transmission parameter matrix as follows:
deriving according to the above formula, when the transmission parameter matrix adopts admittance matrix, the two-port network port characteristics are expressed as:
in the formula u m 、u n The first and the last nodes m, n of the transmission line, i m 、i n The first and the last nodes m and n of the transmission line respectively, the equivalent model of the two ports of the direct current transmission line is expressed as follows through a transmission line current admittance matrix Y:
and step S3: and calculating the direct current fault transient under a complex frequency domain. The specific process is as follows:
step S3.1: after the MMC equivalent circuit is established in the step S1 during the interelectrode short circuit, the inductance in the equivalent circuit is L eq Capacitor C eq The laplace transform is performed to obtain the following expressions in the complex frequency domain:
V L (s)＝L eq sI L (s)-L eq i L (0 - ) (9)
I C (s)＝C eq sV C (s)-C eq v C (0 - ) (10)
in the formula V L (s)、I L (s) transmission line inductance, voltage, current in complex frequency domain, respectively; v C (s)、I C And(s) are the voltage and the current of the transmission line capacitance in the complex frequency domain respectively. i.e. i L (0 - )、v C (0 - ) For steady state dc current, voltage, it can be expressed as:
in the formula of U dc 、I dc MMC direct current voltage and current in a steady state are respectively.
In a complex frequency domain, an inductor is represented by a Norton equivalent circuit; the capacitance is represented by a Thevenin equivalent circuit.
Step S3.2: and establishing an equivalent circuit of the fault between transmission lines of the MMC-HVDC system in a complex frequency domain, wherein a circuit diagram is shown in figure 4. The nodes of the circuit in the figure are numbered (node-1 to node-6). The voltage at each node is recorded as U n (s), subscript n is node number; the current of each branch is marked as I nm And(s), wherein n and m in the subscript are the serial numbers of the nodes at the two ends of the branch connection respectively.
Step 3.3: admittance matrix Y in a single transmission line nm On the basis, a node admittance matrix is established for the DC system transmission line interelectrode fault equivalent circuit, which comprises the following steps:
matrix Y Trans Middle Y nm,k I.e. transmission line admittance matrix Y nm The kth element in (1).
Step S3.4: and S2, the equivalent two-port network model of the transmission line obtained in the step reflects the relation between the current and the voltage at the two ends of the transmission line in the complex frequency domain through the admittance matrix. According to actual circuit information and the termination condition of the transmission line, an equation representing the relation between each node voltage and branch current is obtained by adopting a node analysis method as follows:
step S3.5: according to the MMC equivalent circuit obtained in the step S1 and the inductance and capacitance expression in the complex frequency domain obtained in the step S3.1, introducing boundary conditions as follows:
in the formula Z eq,L ＝R eq,L +L eq,L s+1/C eq,L s，Z eq.R ＝R eq.R +L eq.R s+1/C eq.R s。R eq,L 、L eq,L 、C eq,L And R eq.R 、L eq,R 、C eq,R Equivalent resistance, inductance and capacitance in equivalent circuits of the converter stations at the left end and the right end are respectively. Step S3.6: and solving an equation (13)) representing the relation between the voltage of each node and the branch current to obtain a direct-current fault transient expression F(s) in a complex frequency domain.
And step S4: and after a direct-current fault transient expression under a complex frequency domain is obtained, frequency domain-time domain conversion is realized through numerical Laplace inverse transformation, and corresponding time domain response is obtained. The specific process is as follows:
step S4.1: after the direct current fault transient expression F (S) in the complex frequency domain is obtained by calculation in step S3, inverse laplace transform is performed on F (S), and the transform formula is expressed as:
in the formula, s = σ + j ω, which is a laplacian operator; 1; z = st.
Step S4.2: using rational functions xi β.α (z) to function e z Carrying out Pade approximation to make the first alpha + beta +1 terms of the Taylor expansion equations equal and xi β.α The expression of (z) is as follows:
in the formula, P β (z)、Q α (z) is a polynomial of the order of beta, alpha, respectively, alpha-beta > 2.
Step S4.3: using xi β.α (z) alternative formula e z An approximate expression of f (t) can be obtained
The following were used:
step S4.4: using the left theorem to
The time domain response of the direct current fault transient can be obtained by performing the following integral calculation.
In the formula z i Is xi n.m Pole of (z), k i The two may be complex numbers, which are the residues corresponding to the poles.
Example 2
The utility model provides a flexible direct current transmission line trouble transient state electrical quantity confirms system, includes:
the MMC equivalent circuit construction module is used for constructing an MMC equivalent circuit during the interelectrode short circuit according to the circuit parameters of the MMC converter station;
the direct current transmission line two-port equivalent model building module in the complex frequency domain is used for building a direct current transmission line two-port equivalent model in the complex frequency domain according to the acquired transmission line parameters;
the direct current fault transient expression acquisition module under the complex frequency domain is used for acquiring a direct current fault transient expression under the complex frequency domain according to the MMC equivalent circuit and the two-port equivalent model of the direct current transmission line during the interelectrode short circuit;
and the line fault transient electrical quantity determining module is used for performing Laplace transformation on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.
As will be appreciated by one skilled in the art, 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 flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams 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.
Claims (10)
1. A method for determining fault transient electric quantity of a flexible direct current transmission line is characterized by comprising the following steps:
constructing an MMC equivalent circuit during interelectrode short circuit according to the MMC converter station circuit parameters;
establishing an equivalent model of two ports of the direct current transmission line in a complex frequency domain according to the acquired transmission line parameters;
obtaining a direct-current fault transient expression under a complex frequency domain according to an MMC equivalent circuit and two-port equivalent models of a direct-current transmission line during interelectrode short circuit;
and performing Laplace transform on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.
2. The method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 1, wherein the step of constructing the inter-pole short-circuit-time MMC equivalent circuit according to the MMC converter station circuit parameters comprises the following steps:
obtaining MMC circuit parameters including bridge arm resistance R arm Bridge arm inductance L arm Smoothing reactor inductance L fw Submodule on-resistance R on And a sub-module capacitor C SM ；
An RCL series circuit is constructed according to the obtained MMC converter station circuit parameters and is used as an MMC equivalent circuit during interelectrode short circuit, wherein the resistance is R eq Inductance is L eq A capacitor of C eq ；
And N is the number of the MMC each-phase upper and lower bridge arm series sub-modules.
3. The method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 1, wherein the establishing of the two-port equivalent model of the direct current transmission line in the complex frequency domain according to the acquired transmission line parameters comprises:
obtaining transmission line parameters including transmission line unit length resistance R 0 Inductance L per unit length 0 Conductivity per unit length G 0 Capacitance per unit length C 0 And a transmission line distance L;
according to the transmission line parameters, the direct current transmission line model in the complex frequency domain is expressed by using a common differential equation as follows:
solving the formula (2) to obtain
Wherein,
x is the position variable, s is the Laplacian operator, gamma is the propagation coefficient, Z 1 Is wave impedance, U f 、U b Respectively a transmission line voltage forward traveling wave and a transmission line voltage backward traveling wave; i is f 、I b The forward traveling wave and the backward traveling wave of the transmission line current are respectively;
taking x =0 and x = l, respectively, and equating the dc transmission line to a two-port equivalent model, where the port characteristics of the two-port equivalent model are as follows:
wherein, U m 、U n Respectively representing the voltages at the nodes at the two ends of the transmission line, I m 、I n Respectively representing transmissionsThe current of nodes at two ends of the line, U is a node voltage vector;
the two-port equivalent model is represented by a current admittance matrix Y as:
4. the method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 2, wherein the obtaining of the direct current fault transient expression in the complex frequency domain comprises:
when the interelectrode short circuit occurs, the inductance and the capacitance in the MMC equivalent circuit are subjected to Laplacian transformation to obtain the inductance voltage and the capacitance current under a complex frequency domain, as shown in the following formula:
V L (s)＝L eq sI L (s)-L eq i L (0 - ) (6)
I C (s)＝C eq sV C (s)-C eq v C (0 - ) (7)
wherein, V L (s)、I L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; v C (s)、I C (s) are respectively capacitance voltage and current in complex frequency domain; l is eq 、C eq Respectively an inductor and a capacitor of the MMC equivalent circuit during interelectrode short circuit; i.e. i L (0 - )、v C (0 - ) Respectively, steady-state direct current and voltage;
constructing an inter-electrode fault equivalent circuit of the transmission line in a complex frequency domain;
establishing a node admittance matrix for the inter-transmission line fault equivalent circuit on the basis of a single transmission line admittance matrix in the inter-transmission line fault equivalent circuit;
obtaining a relation between current and voltage at two ends of the transmission line in a complex frequency domain according to a node admittance matrix established by the transmission line interpolar fault equivalent circuit and a direct current transmission line two-port equivalent model in the complex frequency domain, and obtaining an equation of the relation between voltage of each node and branch current according to the relation between the current and voltage at two ends of the transmission line in the complex frequency domain, actual circuit information and the termination condition of the transmission line;
and solving an equation of the relation between the voltage of each node and the current of the branch circuit to obtain a direct-current fault transient expression F(s) in a complex frequency domain.
5. The method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 1, wherein the step of performing laplace transform on the direct current fault transient expression in the complex frequency domain to obtain a time domain response comprises the steps of:
laplace transformation is carried out on a direct current fault transient expression under a complex frequency domain by adopting the following formula
Wherein f (t) is a transient expression of the direct current fault in the time domain; s = σ + j ω, which is laplacian; j is an imaginary number, ω is a frequency, σ is any normal number, z = st, t is time;
using rational functions xi n.m (z) to function e z Carrying out Pade approximation to ensure that the first alpha + beta +1 terms of the Taylor expansion of the two are equal to each other, and xi n.m The expression of (z) is as follows:
wherein, P β (z)、Q α (z) are respectively beta, alpha order polynomials, alpha-beta > 2;
using xi β.α (z) alternative e z Obtaining an approximate expression of f (t)
As shown in the following formula:
according to the leave theorem pair
And (3) performing integral calculation to obtain the time domain response of the direct current fault transient as shown in the following formula:
wherein z is i Is xi β.α Pole of (z), k i The residue corresponding to the pole.
6. The utility model provides a flexible direct current transmission line trouble transient state electrical quantity confirms system which characterized in that includes:
the MMC equivalent circuit construction module is used for constructing an MMC equivalent circuit during the interelectrode short circuit according to the circuit parameters of the MMC converter station;
the direct current transmission line two-port equivalent model building module in the complex frequency domain is used for building a direct current transmission line two-port equivalent model in the complex frequency domain according to the acquired transmission line parameters;
the direct current fault transient expression acquisition module under the complex frequency domain is used for acquiring a direct current fault transient expression under the complex frequency domain according to the MMC equivalent circuit and the two-port equivalent model of the direct current transmission line during the interelectrode short circuit;
and the line fault transient electrical quantity determining module is used for performing Laplace transformation on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.
7. The system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the operations executed by the MMC equivalent circuit building module during the short circuit between the electrodes comprise:
obtaining MMC circuit parameters including bridge arm resistance R arm Bridge arm inductance L arm Smoothing reactor inductance L fw Submodule on-resistance R on And a sub-module capacitor C SM ；
According to the obtained MMC converter station circuit parametersEstablishing RCL series circuit as MMC equivalent circuit in interelectrode short circuit, wherein the resistance is R eq Inductance is L eq A capacitor is C eq ；
And N is the number of the upper bridge arm series submodule and the lower bridge arm series submodule of each phase of the MMC.
8. The system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the operations executed by the direct current transmission line two-port equivalent model building module in the complex frequency domain comprise:
obtaining transmission line parameters including transmission line unit length resistance R 0 Inductance L per unit length 0 Conductivity per unit length G 0 Capacitance per unit length C 0 And a transmission line distance L;
according to the transmission line parameters, the direct current transmission line model in the complex frequency domain is expressed by using a common differential equation as follows:
solving the formula (2) to obtain
Wherein,
x is the position variable, s is the Laplacian operator, gamma is the propagation coefficient, Z 1 Is wave impedance, U f 、U b Respectively a transmission line voltage forward traveling wave and a transmission line voltage backward traveling wave; i is f 、I b The forward traveling wave and the backward traveling wave of the transmission line current are respectively, U, I respectively represent the direct current transmission under the complex frequency domainVoltage current of the transmission line;
taking x =0 and x = l, respectively, and equating the dc transmission line to a two-port equivalent model, where the port characteristics of the two-port equivalent model are as follows:
wherein, U m 、U n Respectively representing the voltages at the nodes at the two ends of the transmission line, I m 、I n Respectively representing the current of nodes at two ends of a transmission line, and U is a node voltage vector;
the two-port equivalent model is represented by a current admittance matrix Y as:
9. the system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the operation performed by the direct current fault transient expression obtaining module in the complex frequency domain comprises:
when the interelectrode short circuit occurs, the inductance and the capacitance in the MMC equivalent circuit are subjected to Laplacian transformation to obtain the inductance voltage and the capacitance current under a complex frequency domain, as shown in the following formula:
V L (s)＝L eq sI L (s)-L eq i L (0 - ) (6)
I C (s)＝C eq sV C (s)-C eq v C (0 - ) (7)
wherein, V L (s)、I L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; v C (s)、I C (s) are respectively capacitance voltage and current in complex frequency domain; l is eq 、C eq Respectively an inductor and a capacitor of the MMC equivalent circuit during interelectrode short circuit; i.e. i L (0 - )、v C (0 - ) Respectively, steady-state direct current and voltage;
constructing an inter-electrode fault equivalent circuit of the transmission line in a complex frequency domain;
establishing a node admittance matrix for the inter-transmission line fault equivalent circuit on the basis of a single transmission line admittance matrix in the inter-transmission line fault equivalent circuit;
obtaining a relation between current and voltage at two ends of the transmission line in a complex frequency domain according to a node admittance matrix established by the transmission line interpolar fault equivalent circuit and a direct current transmission line two-port equivalent model in the complex frequency domain, and obtaining an equation of the relation between voltage of each node and branch current according to the relation between the current and voltage at two ends of the transmission line in the complex frequency domain, actual circuit information and the termination condition of the transmission line;
and solving an equation of the relation between the voltage of each node and the current of the branch circuit to obtain a direct-current fault transient expression F(s) in a complex frequency domain.
10. The system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the line fault transient electrical quantity determination module performs operations including:
laplace transformation is carried out on a direct current fault transient expression under a complex frequency domain by adopting the following formula
Wherein f (t) is a transient expression of the direct current fault in the time domain; s = σ + j ω, which is laplacian; j is an imaginary number, ω is a frequency, σ is any normal number, z = st, t is time;
using rational functions xi β.α (z) to function e z Carrying out Pade approximation to make the first alpha + beta +1 terms of the Taylor expansion equations equal and xi β.α The expression of (z) is as follows:
wherein, P β (z)、Q α (z) is respectively beta, alpha-order multiThe formula, alpha-beta is more than 2;
using xi β.α (z) alternative e z Obtaining an approximate expression of f (t)
As shown in the following formula:
according to the leave theorem pair
And (3) performing integral calculation to obtain the time domain response of the direct current fault transient as shown in the following formula:
wherein z is i Is xi β.α Pole of (z), k i The residue corresponding to the pole.
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| CN116070569A (en) * | 2023-03-06 | 2023-05-05 | 西安热工研究院有限公司 | Frequency domain calculation method and system for discharge current of distributed parameter circuit |
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| CN115828819A (en) * | 2023-02-22 | 2023-03-21 | 西安热工研究院有限公司 | High-precision transmission line high-frequency coupling current calculation method and system |
| CN115828819B (en) * | 2023-02-22 | 2023-05-12 | 西安热工研究院有限公司 | High-frequency coupling current calculation method and system for high-precision transmission line |
| CN116070569A (en) * | 2023-03-06 | 2023-05-05 | 西安热工研究院有限公司 | Frequency domain calculation method and system for discharge current of distributed parameter circuit |
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