CN113253055A - Flexible direct-current power grid line short-circuit fault current calculation method - Google Patents
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Abstract
The invention provides a method for calculating short-circuit fault current of a flexible direct-current power grid line. The method is based on a time-sharing complex frequency domain circuit model of the hybrid direct current breaker, and the fault current of each branch of the flexible direct current power grid with the metal return line under the action of the hybrid direct current breaker is calculated by time-sharing solution of a fault network matrix equation in a complex frequency domain. The method of the invention expresses the network structure and key equipment of the flexible direct current power grid in a complex frequency domain in a matrix form, and has visual image and high transplantation degree.
Description
Technical Field
The invention relates to the field of flexible direct-current power grids, in particular to a method for calculating short-circuit fault current of a flexible direct-current power grid line.
Background
The flexible direct current transmission technology is an effective means for solving large-capacity and long-distance power transmission and realizing modern power transmission. Due to the advantages of flexible and independent adjustment of active power and reactive power, the flexible direct current transmission technology is widely applied to large-scale renewable energy transmission. The flexible direct-current power grid is a novel grid structure power grid which utilizes the existing alternating-current and direct-current power transmission and distribution equipment to transmit active power in a direct-current mode, and meanwhile, direct-current lines are interconnected into a network in a direct-current field, and the flexible direct-current power grid has wide application prospects in fields with increasingly urgent requirements for large-scale new energy grid-connected power generation, large-capacity remote power transmission and the like. The short-circuit fault of the flexible direct-current power grid line causes the fault current to increase rapidly and exceed the upper limit value of the tolerant current of the power electronic device, so that the converter station and even the whole direct-current power grid are stopped. Therefore, the short-circuit fault of the flexible direct-current power grid line is one of the decisive factors limiting the further development of the flexible direct-current power grid. The analysis and calculation of the short-circuit fault current can accurately describe the development trend of the fault current, provide stress indexes for direct-current power grid equipment, and are necessary to perform the analysis and calculation of the short-circuit fault of the flexible direct-current power grid.
However, the existing fault current analysis and calculation method for the direct current power grid has the following defects: the direct-current power grid fault current calculation method relates to matrix differential calculation or node static equivalence, the calculation complexity is high, and the static equivalence process is relatively complicated; at present, natural response of fault current is mostly calculated by a direct current power grid fault current analysis method, and the on-off response of the fault current of the direct current power grid under the action of a hybrid direct current breaker is not considered.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for calculating short-circuit fault current of a flexible direct-current power grid line. In order to achieve the purpose of the invention, the technical scheme of the invention is as follows.
A method for calculating short-circuit fault current of a flexible direct-current power grid line comprises the following steps:
establishing an equivalent complex frequency domain model of the flexible direct current power grid,
establishing a basic cut set matrix Q for representing a fault network of a flexible direct current power grid with metal return wiresf,
Determining a connected graph corresponding to the flexible direct current power grid fault network with the metal return wire, determining a tree and a directed graph of the connected graph, and determining a basic cut set C according to the tree and the directed graphkAnd its direction;
let each row of the basic cut set matrix correspond to a basic cut set CkEach column corresponding to a branch bjThen its element qkjComprises the following steps:
calculating the short-circuit fault current frequency domain quantity I of the flexible direct-current power grid line by adopting the formula (1)b(s);
Ib(s)=Yb(s)Ub(s)+Yb(s)Us(s)-Is(s) (1)
Wherein, Ub(s) is a complex frequency domain branch voltage column vector, Y, of the flexible direct current power grid fault network with the metal return lineb(s) is a branch admittance matrix of the flexible DC grid fault network with metallic return lines, Is(s) is a branch current source column vector, U, of the flexible direct current power grid fault network with the metal return linesAnd(s) is a branch voltage source column vector of the flexible direct current power grid fault network with the metal return line.
Preferably, the flexible direct current power grid equivalent complex frequency domain model comprises a converter equivalent complex frequency domain model, an overhead line equivalent complex frequency domain model and a hybrid direct current breaker equivalent complex frequency domain model; the converter complex frequency domain model is equivalent to an RLC series complex frequency domain model, the overhead line complex frequency domain model is equivalent to an RL series complex frequency domain model, and the hybrid direct-current breaker equivalent complex frequency domain model is equivalent to a resistor model and a constant-voltage source model in sequence in a time-interval mode.
Preferably, the complex frequency domain branch voltage column vector U is calculated by using the formula two (2)b(s):
Wherein, UtAnd(s) is a complex frequency domain tree branch voltage column vector of the flexible direct current power grid fault network with the metal return line. Preferably, the branch voltage source column vector U is calculated by adopting the formula three (3)s(s):
Us=Lbidc(ti)+uc(ti)/s-Uarr(s) (3)
Wherein, Us(s) variable branch voltage source column vector, Uarr(s) is the branch residual voltage column vector, tiIs the i stage time, Uarr(s) is the branch residual voltage column vector, idc(ti) For branch short-circuit fault current time domain quantity uc(ti) Is the branch current capacitance voltage, LbAnd(s) is a branch inductive reactance matrix.
Preferably, the branch current capacitance voltage u is calculated by the formula four (4)c(ti):
uc(ti)=L-1(Cb(s)Ib(s)) (4)
Wherein, Cb(s) is a branch capacitive reactance matrix, L-1Is an inverse laplace transform.
Preferably, the time domain quantity i of the short-circuit fault current of the branch circuit is calculated by adopting the formula five (5)dc(ti):
idc(ti)=L-1(Ib(s)) (5)
Preferably, the branch residual voltage column vector U is calculated by adopting the formula six (6)arr(s):
Wherein, URESIs the residual voltage of the lightning arrester.
Preferably, the complex frequency domain tree branch voltage column vector U is calculated by adopting the formula seven (7)t(s):
Yc(s)Ut(s)=Ic(s) (7)
Wherein, Ic(s) is flexible direct current with metallic returnSecant current source column vector, Y, of a network fault networkcAnd(s) is a cut-set admittance matrix of the flexible direct current power grid fault network with the metal return wire.
Preferably, the cutset current source column vector I is calculated using equation (8)c(s):
Ic(s)=Qf[Is(s)-Yb(s)Us(s)] (8)。
Preferably, the cut-set admittance matrix Y is calculated using equation (9)c(s):
Compared with the prior art, the invention has the beneficial technical effects that: the method is based on a converter station, an overhead line and a composite frequency domain equivalent model of the hybrid direct-current circuit breaker, and solves a fault network matrix equation in a time-sharing mode in a complex frequency domain according to a time-sharing composite frequency domain circuit model of the hybrid direct-current circuit breaker to calculate the fault current of each branch of the flexible direct-current power grid with the metal return wire under the action of the hybrid direct-current circuit breaker. The method of the invention expresses the network structure and key equipment of the flexible direct current power grid in a complex frequency domain in a matrix form, is visual in image and high in transplantation degree, and is convenient for a computer to solve.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.
FIG. 1 is a flow chart of a flexible direct current power grid line short circuit fault current calculation;
fig. 2 is a schematic diagram of a short-circuit energy dissipation process of a hybrid dc breaker in a flexible dc power grid.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments.
As shown in fig. 1, the method for calculating a short-circuit fault current of a flexible direct-current power grid line according to the embodiment includes:
establishing a flexible direct-current power grid equivalent complex frequency domain model, wherein the flexible direct-current power grid equivalent complex frequency domain model comprises a converter equivalent complex frequency domain model, an overhead line equivalent complex frequency domain model and a hybrid direct-current breaker equivalent complex frequency domain model; the converter complex frequency domain model is equivalent to an RLC series complex frequency domain model, the overhead line complex frequency domain model is equivalent to an RL series complex frequency domain model, and the hybrid direct-current breaker equivalent complex frequency domain model is equivalent to a resistor model and a constant-voltage source model in sequence in a time-interval mode.
Establishing a basic cut set matrix Q for representing a fault network of a flexible direct current power grid with metal return wiresf,
Determining a connected graph G corresponding to the flexible direct current power grid fault network with the metal return wire, determining a tree T and a directed graph of the connected graph G, and determining a basic cut set C according to the tree T and the directed graphkAnd its direction;
let each row of the basic cut set matrix correspond to a basic cut set CkEach column corresponding to a branch bjThen its element qkjComprises the following steps:
calculating the short-circuit fault current frequency domain quantity I of the flexible direct-current power grid line by adopting the formula (1)b(s);
Ib(s)=Yb(s)Ub(s)+Yb(s)Us(s)-Is(s) (1)
Wherein, Ib(s) is a complex frequency domain branch current column vector, U, of the flexible direct current power grid fault network with the metal return lineb(s) is a flexible straight wire with a metal loopComplex frequency domain branch voltage column vector, Y, of a galvanic network fault networkb(s) is a branch admittance matrix of the flexible DC grid fault network with metallic return lines, Is(s) is a branch current source column vector of the flexible direct current power grid fault network with the metal return line, and us(s) is a branch voltage source column vector of the flexible direct current power grid fault network with the metal return line; s represents a complex frequency domain quantity.
By tree branch voltage Ut(s) establishing a basic cut-set matrix equation of an original flexible direct-current power grid before the hybrid direct-current circuit breaker is disconnected, wherein the whole fault disconnection process is divided into the following steps according to the disconnection time of the hybrid direct-current circuit breaker: and in the limiting process (before the hybrid direct-current circuit breaker is switched on and off) and the dissipating process (after the hybrid direct-current circuit breaker is switched on and off), the equivalent complex frequency domain model of the hybrid direct-current circuit breaker is taken as a resistance model and used for analyzing the short-circuit fault current of the flexible direct-current power grid line in the limiting process. In particular, the amount of the solvent to be used,
calculating complex frequency domain branch voltage column vector U by adopting formula two (2)b(s):
Wherein, UtAnd(s) is a complex frequency domain tree branch voltage column vector of the flexible direct current power grid fault network with the metal return line. Calculating branch voltage source column vector U by adopting formula three (3)s(s)U:
Us=Lbidc(ti)+uc(ti)/s-Uarr(s) (3)
Wherein, Us(s) variable branch voltage source column vector, Uarr(s) is the branch residual voltage column vector, tiIs the i stage time, Uarr(s) is the branch residual voltage column vector, idc(ti) For branch short-circuit fault current time domain quantity uc(ti) Is the branch current capacitance voltage, LbAnd(s) is a branch inductive reactance matrix.
Calculating branch current capacitance voltage u by adopting formula four (4)c(ti):
uc(ti)=L-1(Cb(s)Ib(s)) (4)
Wherein, Cb(s) is a branch capacitive reactance matrix, L-1Is an inverse laplace transform.
Calculating time domain quantity i of short-circuit fault current of branch circuit by adopting formula five (5)dc(ti):
idc(ti)=L-1(Ib(s)) (5)
Calculating branch residual voltage column vector U by adopting formula six (6)arr(s):
Wherein, URESIs the residual voltage of the lightning arrester.
Calculating the complex frequency domain tree branch voltage column vector U by adopting the formula seven (7)t(s):
Yc(s)Ut(s)=Ic(s) (7)
Wherein, Ic(s) is a secant current source array vector, Y, of a flexible DC power grid fault network with metallic return linescAnd(s) is a cut-set admittance matrix of the flexible direct current power grid fault network with the metal return wire.
Calculating the column vector I of the current source of the cut set by adopting the formula eight (8)c(s):
Ic(s)=Qf[Is(s)-Yb(s)Us(s)] (8)
Calculating cut-set admittance matrix Y by adopting formula nine (9)c(s):
Taking an equivalent complex frequency domain model of the hybrid direct current breaker as a constant voltage source model URESAnd/s, correcting a basic cut set matrix equation of the original flexible direct-current power grid to analyze the short-circuit fault current of the flexible direct-current power grid line in the dissipation process. The correction method comprises dividing the dissipation processCalculating the intermediate variable branch voltage source column vector UsAnd(s) solving the current of each branch and the capacitor voltage of each branch by taking the original flexible direct-current power grid fault network matrix equation as a reference, and outputting the fault current of each stage.
As shown in fig. 2, according to the sequence of the hybrid dc circuit breakers at both ends of the fault line, the short-circuit energy dissipation process of the hybrid dc circuit breaker in the flexible dc power grid can be divided into 4 stages. And (4) converting the complex frequency domain current into a time domain current by the aid of inverse Laplace transformation of fault current output of each stage.
The above-mentioned embodiments are only specific embodiments of the present application, and are used for illustrating the technical solutions of the present application, but not limiting the same, and the scope of the present application is not limited thereto, and although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope disclosed in the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the present disclosure, which should be construed in light of the above teachings. Are intended to be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. A method for calculating short-circuit fault current of a flexible direct-current power grid line is characterized by comprising the following steps:
establishing an equivalent complex frequency domain model of the flexible direct current power grid,
establishing a basic cut set matrix Q for representing a fault network of a flexible direct current power grid with metal return wiresf,
Determining a connected graph corresponding to the flexible direct current power grid fault network with the metal return wire, determining a tree and a directed graph of the connected graph, and determining a basic cut set C according to the tree and the directed graphkAnd its direction;
let each row of the basic cut set matrix correspond to a basic cut set CkEach column pairCorresponding to a branch bjThen its element qkjComprises the following steps:
calculating the short-circuit fault current frequency domain quantity I of the flexible direct-current power grid line by adopting the formula (1)b(s);
Ib(s)=Yb(s)Ub(s)+Yb(s)Us(s)-Is(s) (1)
Wherein Ub(s) is a complex frequency domain branch voltage column vector of the flexible direct current power grid fault network with the metal return line, Yb(s) is a branch admittance matrix of the flexible DC grid fault network with metallic return lines, Is(s) is a branch current source column vector, U, of the flexible direct current power grid fault network with the metal return linesAnd(s) is a branch voltage source column vector of the flexible direct current power grid fault network with the metal return line.
2. The method for calculating the short-circuit fault current of the flexible direct-current power grid line according to claim 1, wherein the flexible direct-current power grid equivalent complex frequency domain model comprises a converter equivalent complex frequency domain model, an overhead line equivalent complex frequency domain model and a hybrid direct-current breaker equivalent complex frequency domain model; the converter complex frequency domain model is equivalent to an RLC series complex frequency domain model, the overhead line complex frequency domain model is equivalent to an RL series complex frequency domain model, and the hybrid direct-current breaker equivalent complex frequency domain model is equivalent to a resistor model and a constant-voltage source model in sequence in a time-interval mode.
3. The method for calculating the short-circuit fault current of the flexible direct-current power grid line with the metallic return wire according to claim 2, wherein a complex frequency domain branch voltage column vector U is calculated by adopting a formula two (2)b(s):
Wherein, UtAnd(s) is a complex frequency domain tree branch voltage column vector of the flexible direct current power grid fault network with the metal return line.
4. The method for calculating the short-circuit fault current of the flexible direct-current power grid line according to claim 3, wherein a branch voltage source column vector U is calculated by adopting a formula III (3)s(s):
Us=Lbidc(ti)+uc(ti)/s-Uarr(s) (3)
Wherein, Us(s) variable branch voltage source column vector, Uarr(s) is the branch residual voltage column vector, tiIs the i stage time, Uarr(s) is the branch residual voltage column vector, idc(ti) For a time domain quantity of short-circuit fault current of a branch circuit, uc(ti) Is the branch current capacitance voltage, LbAnd(s) is a branch inductive reactance matrix.
5. The method for calculating the short-circuit fault current of the flexible direct-current power grid line according to claim 4, wherein the branch current capacitor voltage u is calculated by adopting a formula four (4)c(ti):
uc(ti)=L-1(Cb(s)Ib(s)) (4)
Wherein, Cb(s) is a branch capacitive reactance matrix, L-1Is an inverse laplace transform.
6. The method for calculating the short-circuit fault current of the flexible direct-current power grid line according to claim 5, wherein a formula five (5) is adopted to calculate a branch short-circuit fault current time domain quantity idc(ti):
idc(ti)=L-1(Ib(s)) (5)。
8. The method for calculating the short-circuit fault current of the flexible direct-current power grid line according to claim 7, wherein a complex frequency domain tree branch voltage column vector U is calculated by adopting a formula of seven (7)t(s):
Yc(s)Ut(s)=Ic(s) (7)
Wherein, Ic(s) is a secant current source array vector, Y, of a flexible DC power grid fault network with metallic return linescAnd(s) is a cut-set admittance matrix of the flexible direct current power grid fault network with the metal return wire.
9. The method for calculating the short-circuit fault current of the flexible direct-current power grid line according to claim 8, wherein a cut-and-collect current source column vector I is calculated by adopting formula (8)c(s):
Ic(s)=Qf[Is(s)-Yb(s)Us(s)] (8)。
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