CN110543739B - Circuit simulation model of overhead power transmission line - Google Patents
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Abstract
The invention discloses a circuit simulation model of an overhead power transmission line, which is used for describing a transmission line system consisting of n conducting wires and the ground, wherein each conducting wire corresponds to a transmission line voltage equation and a transmission line current equation; each lead comprises a first inductor and a first resistor which are connected in series and is grounded through two grounding branches, wherein one grounding branch is connected with a grounding admittance in series, and the other grounding branch is connected with a grounding capacitor in series; any two wires are connected through two coupling branches, wherein a mutual admittance is connected in series on one coupling branch, and a mutual capacitance is connected in series on the other coupling branch; meanwhile, any two leads are connected by two back-to-back transformers, the common connection side of the two transformers is connected with a common branch in parallel, and the common branch is formed by connecting a second resistor and a second inductor in series; wherein n is more than or equal to 2. The invention adopts the passive basic circuit elements to construct the simulation model of the actual overhead transmission line, so that the simulation model is simplified and convenient to calculate.
Description
Technical Field
The invention relates to the technical field of power system simulation modeling, in particular to a circuit simulation model of an overhead power transmission line.
Background
In the field of electric power technology, a circuit simulation method is generally adopted to analyze the operation states of an electric power system under various different working conditions and grasp the operation characteristics of the electric power system, the basic principle is that circuit elements for equipment for producing, transmitting, converting, storing and consuming electric energy in an electric network are expressed, the elements are connected into a complete circuit network according to the topological structure of the electric network, and then the electric characteristics of voltage, current and power at a concerned position in the network are obtained by solving through numerical values or an analytical method according to the basic principle of the circuit.
The overhead transmission line is one of basic elements of a power system, but in the existing circuit simulation research, the overhead transmission line is not simply modeled, so that a simulation model is complex and is troublesome to calculate.
Disclosure of Invention
The embodiment of the invention aims to provide a circuit simulation model of an electric overhead transmission line, which is used for constructing a simulation model of an actual overhead transmission line by adopting common passive circuit elements such as resistors, inductors and the like, so that the simulation model is simplified and is convenient to calculate.
In order to achieve the above object, an embodiment of the present invention provides a circuit simulation model for an overhead power transmission line, where the circuit simulation model is used to describe a transmission line system including n conducting wires and the ground, and in the transmission line system, each conducting wire corresponds to a transmission line voltage equation and a transmission line current equation; in the circuit simulation model, each conducting wire comprises a first inductor and a first resistor which are connected in series and is grounded through two grounding branches, wherein one grounding branch is connected with a ground admittance in series, and the other grounding branch is connected with a ground capacitor in series; any two wires are connected through two coupling branches, wherein a mutual admittance is connected in series on one coupling branch, and a mutual capacitance is connected in series on the other coupling branch; meanwhile, any two leads are connected by two back-to-back transformers, the common connection side of the two transformers is connected with a common branch in parallel, and the common branch is formed by connecting a second resistor and a second inductor in series; wherein n is more than or equal to 2.
Preferably, the transformation ratios of both of the transformers are 1:1.
Preferably, the resistance value of the first resistor isWherein r' ii Is the unit resistance of said first resistance of wire i, Δ z is the wire length of wire i, r ii Is the unit self-resistance of the wire i unit length, r ik Is the unit mutual resistance between the wire i and the wire k, and r ik =r ki ,1<i≤n,1<k≤n,i≠k。
Preferably, the inductance value of the first inductor isWherein l' ii Unit inductance of the first inductance of conductor i,/ ii Is the unit self-inductance of the wire i unit length,/ ik Is the unit mutual inductance between the conducting wire i and the conducting wire k, and l ik =l ki 。
Preferably, the resistance value of the second resistor is the product of the unit mutual resistance of the unit length between the two corresponding wires and the length of the wire.
Preferably, the inductance of the second inductor is a product of a unit mutual inductance per unit length between two corresponding conductive lines and a length of the conductive line.
Preferably, the admittance value of the ground admittance is the product of the unit length of the conducting wire and the length of the conducting wire, and the capacitance value of the ground capacitance is the product of the unit length of the conducting wire and the length of the conducting wire.
Preferably, the admittance value of the transadmittance is a product of a unit transadmittance per unit length between the corresponding two wires and a wire length; the capacitance value of the mutual capacitance is the product of the unit mutual capacitance of the unit length between the two corresponding lead wires and the length of the lead wires.
Preferably, the transmission line voltage equation corresponding to each wire is
Wherein, V i (z, t) represents the voltage to ground at time t at the location of length z on conductor I, I i (z, t) represents the current at time t at a location on wire i of length z.
Preferably, the transmission line current equation corresponding to each wire is
Wherein, g ii Is the unit admittance to ground, g, of unit length of the wire i ik Is the unit mutual admittance between the wire i and the wire k, and g ik =g ki ,c ii A unit capacitance to ground of unit length of the conductor i, c ik Is the unit mutual capacitance between the conductive line i and the conductive line k, and c ik =c ki 。
Compared with the prior art, the circuit simulation model of the overhead power transmission line provided by the embodiment of the invention is simple and direct, simplifies the actual simulation model of the overhead power transmission line and facilitates calculation by utilizing basic passive circuit elements such as resistance, inductance, capacitance, admittance and the like and combining and building the circuit simulation model corresponding to the overhead power transmission line.
Drawings
FIG. 1 is a schematic diagram of a circuit simulation model of multi-phase transmission of an overhead power line provided by an embodiment of the present invention;
fig. 2 is a transmission line system composed of n conductive lines and a ground according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a basic multi-phase transmission circuit simulation model of an overhead power line according to one embodiment of the present invention;
fig. 4 is a schematic diagram of a circuit simulation model of single-phase power transmission of an overhead power line according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.
Referring to fig. 1, a schematic diagram of a circuit simulation model for multi-phase power transmission of an overhead power line according to an embodiment of the present invention, where the circuit simulation model is used to describe a transmission line system including n conducting wires and the ground, and in the transmission line system, each conducting wire corresponds to a transmission line voltage equation and a transmission line current equation; in the circuit simulation model, each conducting wire comprises a first inductor and a first resistor which are connected in series and is grounded through two grounding branches, wherein one grounding branch is connected with a ground admittance in series, and the other grounding branch is connected with a ground capacitor in series; any two wires are connected through two coupling branches, wherein a mutual admittance is connected in series on one coupling branch, and a mutual capacitance is connected in series on the other coupling branch; meanwhile, any two leads are connected by two back-to-back transformers, the common connection side of the two transformers is connected with a common branch in parallel, and the common branch is formed by connecting a second resistor and a second inductor in series; wherein n is more than or equal to 2.
It should be noted that an actual overhead power transmission line is a power line composed of a metal conductor, a tower, a metal fitting, and a lightning conductor, and is used as a power facility for transmitting electric energy. In the analysis of the power system, since only the transmission characteristics of the overhead power transmission line are considered, the actual overhead power transmission line can be abstracted into a transmission line system composed of n wires and the ground according to the geometric structure at this time, and the parallel direction of the wires is assumed to be the Z axis, as shown in fig. 2. As shown in fig. 2, the transmission line system includes n conductive lines, the conductive lines are parallel to the ground surface, and the n conductive lines are parallel to each other. The current flows along the wire and the earth. For an actual three-phase alternating-current power overhead transmission line, the number n of conducting wires is =3; for a direct current overhead transmission line, n =2; for single phase ac or dc overhead lines, n =1. However, this embodiment of the present invention addresses only the first two cases, i.e., n ≧ 2. The line voltage and the line current of the conductor are mathematically described in terms of the transmission line equation (otherwise known as telegraph equation). Each conductor (number i, i =1 … … n) corresponds to one transmission line voltage equation and one transmission line current equation, respectively. The corresponding equation set of the whole transmission line system (comprising n conducting wires and the ground) is composed of n transmission line voltage equations and n transmission line current equations, and the electrical characteristics of the transmission line system are completely described in the equation set.
Specifically, the circuit simulation model is used to describe a transmission line system composed of n conducting wires and the ground, wherein n ≧ 2, that is, FIG. 1 is equivalent to FIG. 2, and FIG. 1 describes FIG. 2 using a simulation model language. In a transmission line system, each wire corresponds to a transmission line voltage equation and a transmission line current equation. The final corresponding equation set of the whole transmission line system consists of n transmission line voltage equations and n transmission line current equations.
As shown in fig. 1, the circuit simulation model can be divided into four areas i, ii, iii, and iv, and in the area i, each wire includes a first inductor and a first resistor connected in series; in the IV area, each wire is grounded through two grounding branches, wherein one grounding branch is connected with a grounding admittance in series, and the other grounding branch is connected with a grounding capacitor in series; in the area III, any two wires are connected through two coupling branches, wherein one coupling branch is connected with a mutual admittance in series, and the other coupling branch is connected with a mutual capacitor in series; in the area II, any two wires are connected by two back-to-back transformers, the public connection side of the two transformers is connected with a common branch in parallel, and the common branch is formed by connecting a second resistor and a second inductor in series.
Such a circuit simulation model formed by using basic circuit elements is generally called a lumped parameter model because parameters such as self-inductance, self-resistance, mutual inductance, mutual resistance, admittance to ground, capacitance to ground, mutual capacitance between wires, mutual admittance between wires, and the like in a transmission line equation are expressed by being lumped in the basic elements.
It should be noted that, when the power system is analyzed by circuit simulation, the entire content of the power system includes that each part in the power system is expressed by circuit elements, and then a circuit network is constructed. The invention only relates to the part of the overhead power transmission line, and the simulation of the power system can be realized only when the part is put into a complete circuit network.
According to the embodiment of the invention, basic passive circuit elements such as resistors, inductors, capacitors, admittances and the like are utilized to build the circuit simulation model corresponding to the overhead power transmission line in a combined mode, so that the method is simple and direct, the simulation model of the actual overhead power transmission line is simplified, and calculation is convenient.
As an improvement of the scheme, the transformation ratio of the two transformers is 1:1.
Specifically, in the circuit simulation model, the transformer in fig. 1 is an ideal transformer, and the transformation ratio of both transformers is 1:1.
As a modification of the above, the first resistor has a resistance value ofWherein r' ii Is the unit resistance of said first resistance of wire i, Δ z is the wire length of wire i, r ii Is the unit self-resistance of the wire i unit length, r ik Is the unit mutual resistance between the wire i and the wire k, and r ik =r ki ,1<i≤n,1<k≤n,i≠k。
Specifically, the resistance value of the first resistor is determined by the self-resistance of the wire and the mutual resistance between the wire and other wires, and the calculation formula isWherein r' ii Is the unit resistance of the first resistance of the wire i, Δ z is the wire length of the wire i, r ii Is the unit self-resistance of the wire i unit length, r ik Is the unit mutual resistance between the wire i and the wire k, and r ik =r ki ,1<i≤n,1<k≤n,i≠k。
As an improvement of the above, the inductance value of the first inductor isWherein l' ii Unit inductance of the first inductance of conductor i,/ ii Is the unit self-inductance of the wire i unit length,/ ik Is the unit mutual inductance between the conducting wire i and the conducting wire k, and l ik =l ki 。
Specifically, the inductance of the first inductor is determined by the self-inductance of the conductive line and the mutual inductance between the conductive line and other conductive lines, and is calculated by the formulaWherein l' ii Unit inductance being the first inductance of the conductor i,/ ii Is the unit self-inductance of the wire i unit length,/ ik Is the unit mutual inductance between the conducting wire i and the conducting wire k, and l ik =l ki 。
As an improvement of the above solution, the resistance value of the second resistor is a product of a unit mutual resistance per unit length between the two corresponding wires and a wire length.
Specifically, the resistance value of the second resistor is the product of the unit mutual resistance per unit length between the two corresponding wires and the length of the wire, see the area ii in fig. 1, that is, the resistance value of the second resistor is r ij Δ z; wherein r is ij Is the unit mutual resistance between the conducting wire i and the conducting wire j, and r ij =r ji ,1<j≤n,i≠j。
As an improvement of the above solution, an inductance value of the second inductor is a product of a unit mutual inductance per unit length between the two corresponding wires and a wire length.
Specifically, the inductance value of the second inductor is the product of the unit mutual inductance per unit length between the two corresponding wires and the length of the corresponding wire, see the area ii in fig. 1, that is, the inductance value of the second inductor is l ij Δ z; wherein l ij Is the unit mutual inductance between the conducting wire i and the conducting wire j, and l ij =l ji ,1<j≤n,,i≠j。
As a modification of the above solution, the admittance value of the ground admittance is a product of a unit of ground admittance per unit length of the conductive wire and a length of the conductive wire, and the capacitance value of the ground capacitance is a product of a unit of ground capacitance per unit length of the conductive wire and a length of the conductive wire.
Specifically, the admittance value of the ground admittance is the product of the unit length of the conductive line and the length of the conductive line, and the capacitance value of the ground capacitance is the product of the unit length of the conductive line and the length of the conductive line, see in particular the region iv of fig. 1, i.e. the admittance value of the ground admittance is g ii Δ z, wherein g ii Is the unit admittance to ground of unit length of the wire i; capacitance value of the capacitor to ground is c ii Δ z, wherein c ii Which is the capacitance per unit length of conductor i to ground.
As an improvement of the above solution, an admittance value of the transadmittance is a product of a unit transadmittance per unit length between the two corresponding wires and a wire length; the capacitance value of the mutual capacitance is the product of the unit mutual capacitance of the unit length between the two corresponding lead wires and the length of the lead wires.
Specifically, referring to the area iii of fig. 1, the admittance value of the transadmittance is the product of the unit transadmittance per unit length between the corresponding two wires and the wire length, i.e., the admittance value of the transadmittance is g ij Δ z, wherein g ij Is the unit mutual admittance of unit length between the conducting wire i and the conducting wire j; the capacitance value of the mutual capacitance is the product of the unit mutual capacitance of the unit length between the two corresponding wires and the length of the wire, that is, the capacitance value of the mutual capacitance is c ij Δ z, wherein, c ij Is the unit mutual capacitance per unit length between the conductive line i and the conductive line j.
As an improvement of the scheme, the transmission line voltage equation corresponding to each wire is
Wherein, V i (z, t) represents the voltage to ground at time t at the location of length z on conductor I, I i (z, t) represents a wirei current at time t at a location of length z.
It should be noted that the circuit simulation model in fig. 1 is derived and determined from fig. 3, fig. 3 is a schematic diagram of a basic circuit simulation model for multi-phase power transmission of an overhead power transmission line according to an embodiment of the present invention, and the model in fig. 3 can be also divided into four regions i, ii, iii, and iv, where a resistance element and an inductance element of each conductor in the region i respectively correspond to a self-resistance and a self-inductance of a conductor in a simulation model of a single-phase power transmission line; the capacitance element and the admittance element of each wire in the IV area respectively correspond to the ground capacitance and the ground susceptance of the wire in the single-phase power transmission line simulation model; the III area expresses the mutual admittance among the leads and the mutual capacitance among the leads; region II expresses the mutual resistance and mutual inductance between the conductors by using a transverse voltage source E ij (z, t) and E ji (z, t) is expressed, E ij (z, t) represents the lateral voltage generated by wire j versus wire i at the location of length z and at time t. The transverse voltage source has the formula
In order to express the transverse voltage source by adopting a passive basic circuit element, the area II is changed into the area I by adopting two back-to-back transformers to connect any two leads, the common connecting side of the two transformers is connected with a common branch circuit in parallel, the common branch circuit is formed by a second resistor and a second inductor, and the area I is changed into the area I by connecting a self resistor and the self inductor in series and connecting a first resistor and a first inductor in series; the areas III and IV are kept unchanged, so that the effect that the circuit simulation model of the multiphase transmission line system is expressed by adopting all basic elements is achieved, namely, the diagram 3 is converted into the diagram 1 for expression.
In general, the transmission line voltage equation for a multi-phase transmission line system, i.e., conductor i of fig. 3, is:
after transformation to fig. 1, the transmission line voltage equation for conductor i should be adjusted accordingly, but it should be noted thatThe two equations are equivalent, but are expressed differently. Since the resistance value of the first resistor in the region I in FIG. 1 is determined by the self-resistance of the conductive line and the mutual resistance between the conductive line and other conductive lines, the calculation formula isThe inductance value of the first inductor is determined by the self-inductance of the conducting wire and the mutual inductance between the conducting wire and other conducting wires, and the calculation formula isAnd flows through the mutual resistance r ij Comprises two parts I i (z, t) and I j (z, t) flowing through a mutual inductance l ij The current of (A) also comprises two parts I i (z, t) and I j (z, t), so there are two changes to the above formula, one is r in the formula ii I i (z,t)、/>Is changed into> Second is r in the formula ij I j (z,t)、/>Is transformed into r ij [I j (z,t)+I i (z,t)]、/>The derived formula becomes->Wherein, V i (z, t) represents the voltage to ground at time t at a location on conductor I of length z, I i (z, t) represents the current on the wire i at time t at a position of length z, r ii Is a wirei unit self-resistance per unit length, r in Is the unit mutual resistance between the conducting wire i and the conducting wire n, and r in =r ni ,l ii Is the unit self-inductance of the wire i unit length,/ in Is the unit mutual inductance between the conducting wire i and the conducting wire n, and l in =l ni 。
In the physical sense, r in the formula ij I j (z,t)、Is transformed into r ij [I j (z,t)+I i (z,t)]、It can be explained that the transverse voltage variation caused by mutual resistance and mutual inductance between the wires is determined by the sum of currents flowing through two interacting wires, and r is ij =r ji ,l ij =l ji Thus r is ij [I j (z,t)+I i (z,t)]、Meanwhile, the transverse voltage caused by the wire i on the wire j through mutual resistance and mutual inductance can be understood, and the sum of the currents of the wire i and the wire j can be considered to cause the same transverse voltage on the two wires through the mutual resistance and the mutual inductance between the two wires.
As an improvement of the scheme, the transmission line current equation corresponding to each wire is
Wherein, g ii Is the unit admittance to ground, g, of unit length of the wire i ik Is the unit mutual admittance between the wire i and the wire k, and g ik =g ki ,c ii A unit capacitance to ground of unit length of the conductor i, c ik Is the unit mutual capacitance between the conductive line i and the conductive line k, and c ik =c ki 。
Specifically, in the multi-phase transmission line system, the transmission line current equation corresponding to any one wire i is
Wherein, g ii Is the unit admittance to ground, g, of unit length of the wire i in Is the unit mutual admittance between the wire i and the wire n, and g in =g ni ,c ii A unit capacitance to ground of unit length of the conductor i, c in Is the unit mutual capacitance between the conductive line i and the conductive line n, and c in =c ni . Finally the multi-phase transmission line system contains n sets of transmission line current equations in this embodiment.
In order to further understand the above embodiment of the present invention, the embodiment of the present invention explains a single-phase transmission line simulation model, specifically referring to fig. 4, fig. 4 is a schematic diagram of a circuit simulation model for single-phase transmission of an overhead power line provided in an embodiment of the present invention, that is, the number of conductors in the circuit simulation model is 1, that is, the whole transmission line system is a single-phase transmission line system composed of one conductor and the ground. At this time, the value of the inductance L connected in series in the wire is the unit self-inductance L of the unit length of the wire 11 The product with the length of the conductor Δ z, i.e. L = L 11 Δ z; the value of the resistance R is the unit self-resistance R of the unit length of the lead 11 Product of the length of the conductor Δ z, i.e. R = R 11 Δ z; admittance to ground G 1 ground The value of (a) is the unit-to-ground admittance g of the unit length of the conductor 11 The product of the length of the conductor Δ z, i.e. G 1 ground =g 11 Δ z, capacitance to ground C 1 floor The value of (a) is the unit capacitance to ground (c) of the conductor unit length 11 The product of the length of the conductor Δ z, i.e. C 1 floor =c 11 Δ z. Because only a single transmission line is provided, the transmission line voltage equation does not contain mutual resistance among wires and mutual inductance among the wires, and the transmission line current equation does not contain mutual admittance among the wires and mutual capacitance among the wires.
In summary, the circuit simulation model of the overhead power transmission line provided by the embodiment of the invention is simple and direct, and the actual simulation model of the overhead power transmission line is simplified and is convenient to calculate by utilizing basic passive circuit elements such as resistance, inductance, capacitance, admittance and the like to build the circuit simulation model corresponding to the overhead power transmission line in a combined manner. Meanwhile, the circuit simulation model is applied to a complete circuit network, and the electrical characteristics of voltage, current and power at a concerned position in the circuit network can be obtained, so that the operation condition of the power system can be better known, the operation and design of the power system can be optimized, and the operation of the power system is more economic and reliable.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (9)
1. The circuit simulation model of the overhead power transmission line is characterized by being used for describing a transmission line system consisting of n conducting wires and the ground, wherein in the transmission line system, each conducting wire corresponds to a transmission line voltage equation and a transmission line current equation; in the circuit simulation model, each wire comprises a first inductor and a first resistor which are connected in series, and is grounded through two grounding branches, wherein one grounding branch is connected with a grounding admittance in series, and the other grounding branch is connected with a grounding capacitor in series; any two wires are connected through two coupling branches, wherein a mutual admittance is connected in series on one coupling branch, and a mutual capacitance is connected in series on the other coupling branch; meanwhile, any two leads are connected by two back-to-back transformers, the common connection side of the two transformers is connected with a common branch in parallel, and the common branch is formed by connecting a second resistor and a second inductor in series; wherein n is more than or equal to 2;
wherein the transmission line voltage equation corresponding to each wire is
Wherein, V i (z, t) represents the voltage to ground at time t at the location of length z on conductor I, I i (z, t) represents the current at time t at a position on wire i of length z; r is a radical of hydrogen ii Is the unit self-resistance of the wire i unit length, r ik Is the unit mutual resistance between the wire i and the wire k, and r ik =r ki ,1<i≤n,1<k≤n,i≠k;l ii Is the unit self-inductance of the wire i unit length, l ik Is the unit mutual inductance between the conducting wire i and the conducting wire k, and l ik =l ki 。
2. The circuit simulation model of the overhead power transmission line according to claim 1, wherein the transformation ratios of both of the transformers are 1:1.
3. The circuit simulation model of the overhead power transmission line according to claim 1, wherein the first resistor has a resistance value ofWherein r' ii Is the unit resistance of said first resistance of wire i, Δ z is the wire length of wire i, r ii Is the unit self-resistance of the wire i unit length, r ik Is the unit mutual resistance between the wire i and the wire k, and r ik =r ki ,1<i≤n,1<k≤n,i≠k。
4. The circuit simulation model of overhead power transmission line according to claim 3, wherein the inductance value of the first inductor isWherein l' ii Unit inductance of the first inductance of conductor i,/ ii Is the unit self-inductance of the wire i unit length,/ ik Is a unit mutual inductance between the conductive line i and the conductive line k, andl ik =l ki 。
5. the circuit simulation model of the overhead power transmission line according to claim 1, wherein the resistance value of the second resistor is a product of a unit mutual resistance per unit length between the two corresponding wires and a wire length.
6. The circuit simulation model of overhead power transmission line according to claim 1, wherein the inductance value of the second inductor is the product of the unit mutual inductance per unit length between the two corresponding wires and the wire length.
7. The circuit simulation model of overhead power transmission line according to claim 1, wherein the admittance value of the ground admittance is a product of a unit of ground admittance per unit length of the conductor and a conductor length, and the capacitance value of the ground capacitance is a product of a unit of ground capacitance per unit length of the conductor and a conductor length.
8. The circuit simulation model of overhead power transmission line according to claim 1, wherein the admittance value of the transadmittance is the product of the unit transadmittance per unit length between the corresponding two wires and the wire length; the capacitance value of the mutual capacitance is the product of the unit mutual capacitance of the unit length between the two corresponding lead wires and the length of the lead wires.
9. The circuit simulation model for an overhead electrical power transmission line according to claim 1, wherein the transmission line current equation for each of the conductors is
Wherein, g ii Is the unit admittance to ground, g, of unit length of the wire i ik Is the unit mutual admittance between the wire i and the wire k,and g is ik =g ki ,c ii A unit capacitance to ground of unit length of the conductor i, c ik Is the unit mutual capacitance between the conductive line i and the conductive line k, and c ik =c ki 。
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