CN113268944A - Broadband modeling method and system of high-coupling split reactor - Google Patents
Broadband modeling method and system of high-coupling split reactor Download PDFInfo
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Abstract
The invention provides a broadband modeling method and a broadband modeling system for a high-coupling split reactor, wherein the broadband modeling method comprises the following steps of: establishing an ideal coupling reactor sub-model; calculating stray capacitance of each winding in turn unit according to parameters of the high-coupling split reactor; obtaining terminal equivalent capacitance at two ends of each winding of the high-coupling split reactor according to the stray capacitance of each winding in turn; short-circuiting each odd terminal at the upper end, each even terminal at the upper end, each odd terminal at the lower end and each even terminal at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding; and adding the obtained terminal capacitor matrix corresponding to the four-port network to an ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor. The modeling method provided by the invention has certain advantages in accuracy and modeling complexity.
Description
Technical Field
The invention belongs to the field of power electronic circuit simulation, and particularly relates to a broadband modeling method and system of a high-coupling split reactor.
Background
In recent years, with the rapid development of power systems, the short-circuit current level of the system is increased rapidly, and the continuous increase of the short-circuit current level causes serious consequences to a power grid, so that the development of the power systems is restricted. Therefore, effective measures must be taken to limit the short-circuit fault current.
The fault current limiter based on the high-coupling split reactor has the advantages of small current-sharing working condition loss, strong current-limiting capability, excellent economy and the like, and has important application in the aspect of limiting short-circuit fault current of a power system. The core component of the fault current limiter based on the high-coupling split reactor is the high-coupling split reactor. The high-coupling split reactor is composed of two oppositely and tightly coupled arm coils and is generally in a hollow structure. When two arms of the high-coupling split reactor are connected to a power system at the same time, the fault current limiter works in a current equalizing working condition and presents very low impedance; when the single arm of the high-coupling split reactor is disconnected and only one arm is connected into the power system, the fault current limiter works under the current-limiting working condition, presents very large impedance and can effectively limit the fault current.
In the design stage of the fault current limiter, the influence of the fault current limiter on a power system and the requirement of the power system on the insulation level of a reactor are mainly researched through a simulation method. Therefore, the establishment of a stable and accurate model can ensure that an accurate conclusion is obtained. The high-coupling split reactor model and the modeling method in the traditional technology have poor accuracy.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a broadband modeling method and a broadband modeling system for a high-coupling split-core reactor, and aims to solve the problem that the high-coupling split-core reactor model and the modeling method in the prior art are poor in accuracy.
In order to achieve the above object, in a first aspect, the present invention provides a broadband modeling method for a high-coupling split reactor, the method is used for establishing a broadband model of the high-coupling split reactor, the broadband model of the high-coupling split reactor includes an ideal coupling reactor sub-model and a terminal equivalent capacitance, and the method includes the following steps:
establishing an ideal coupling reactor submodel, wherein the ideal coupling reactor submodel is used for simulating a high-coupling split reactor without stray capacitance and stray inductance influence;
calculating stray capacitance of each winding in turn unit according to parameters of the high-coupling split reactor; the stray capacitance comprises turns and mutual capacitance between the turns and capacitance to ground;
obtaining terminal equivalent capacitance at two ends of each winding of the high-coupling split reactor according to the stray capacitance of each winding in turn;
short-circuiting each odd terminal at the upper end, each even terminal at the upper end, each odd terminal at the lower end and each even terminal at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding;
and adding the obtained terminal capacitor matrix corresponding to the four-port network to an ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor.
In an alternative example, the stray capacitance of each winding in turns is calculated according to parameters of the high-coupling split reactor, specifically:
the wire turns of the same envelope are regularly arranged, and the adjacent turns mutually have a capacitance CaAnd a capacitance to groundCdRespectively as follows:
the adjacent wire turns with the same enveloping height have a mutual capacitance CbComprises the following steps:
in the formula, epsilon0Dielectric constant of vacuum,. epsilonjRelative dielectric constant of insulation, ra、waAverage radius of wire turns and radial length of wire, hbAnd d is the turn-to-turn distance, and h is the height of the turns to ground.
In an optional example, the terminal equivalent capacitance at two ends of each winding of the high-coupling split-core reactor is obtained according to the stray capacitance of each winding in turn, specifically:
determining an inductance matrix:
Ci0＝βi1+βi2+…+βii+…+βin
Cij＝-βij(i≠j)
Ci0capacitance to ground of turns of number i, CijThe mutual capacitance between the turns of the number i and the number j is the capacitance; beta is aijThe inductance of the ith turn coil and the jth turn coil;
solving an inductance matrix beta based on the ground capacitance and the mutual capacitance; if one high-coupling split reactor has n turns of coils, the beta is an n-order matrix;
determining a terminal inductance matrix:
γ＝ξTβξ
wherein gamma is a terminal inductance matrix, is a xi terminal coefficient matrix, and is xikIs a matrix of winding coefficients of number k, nkThe number of turns of the k winding is;
the k-winding has two terminals: t is t2k-1And t2k(ii) a The terminal capacitance of the k winding includes t2k-1Self-terminal capacitance of (1)2kSelf-terminated capacitance of t2k-1Capacitor with terminal
Is equal to the sum, t, of all elements of the 2k-1 th row in the terminal inductance matrix gamma2kCapacitor with terminal
Equal to the sum of all elements of the 2 k-th row in the terminal inductance matrix gamma;
the mutual terminal capacitance between the winding No. k and the winding No. l is as follows:
wherein the content of the first and second substances,
is the mutual terminal capacitance between the terminal on the winding of the number k and the terminal on the winding of the number l,
the mutual terminal capacitance between the upper terminal of the k winding and the lower terminal of the l winding,
the mutual terminal capacitance between the lower terminal of the k winding and the upper terminal of the l winding,
is the mutual terminal capacitance between the lower terminal of the k winding and the lower terminal of the l winding, gamma2k-1,2l-1Terminal inductance, γ, between terminals on winding k and winding l2k-1,2lTerminal inductance between the upper terminal of winding No. k and the lower terminal of winding No. l, γ2k,2l-1Terminal inductance, γ, between the lower terminal of winding No. k and the upper terminal of winding No. l2k,2lThe terminal inductance between the lower terminal of the winding No. k and the lower terminal of the winding No. l is obtained; l is not equal to k;
the terminal equivalent capacitance at two ends of the k winding comprises: the terminal capacitance of the k winding and the mutual terminal capacitance between the k winding and the l winding.
In an optional example, short-circuiting each odd terminal at the upper end, short-circuiting each even terminal at the upper end, short-circuiting each odd terminal at the lower end and short-circuiting each even terminal at the lower end of each winding terminal of the high-coupling split-reactor to form a four-port network; and obtaining a terminal capacitance matrix corresponding to the four-port network based on terminal equivalent capacitances at two ends of each winding, specifically:
and obtaining a terminal capacitor matrix corresponding to the four-port network by using a circuit theory principle.
In an alternative example, when the high-coupling split reactor includes four windings, the terminal capacitance matrix C of the four-port network is:
the terminal capacitance matrix C of the four-port network is:
wherein the content of the first and second substances,
the self-capacitance of the terminal on the No. 1 terminal or the No. 1 winding,
is the self-capacitance of the terminal under the No. 2 terminal or the No. 1 winding,
the self capacitance of the terminal on the No. 3 terminal or the No. 2 winding,
the self capacitance of the terminal under the No. 4 terminal or the No. 2 winding,
the self capacitance of the terminal on the No. 5 terminal or the No. 3 winding,
is the self capacitance of the lower terminal of the No. 6 terminal or the No. 3 winding,
the self capacitance of the terminal on the No. 7 terminal or the No. 4 winding,
the capacitor is a self-contained capacitor of a No. 8 terminal, namely a No. 4 winding lower terminal;
subscripts u and v of the subscript t belong to integers from 1 to 8, and are mutual terminal capacitances between any u-terminal and v-terminal.
In a second aspect, the present invention provides a broadband modeling system for a high-coupling split reactor, the system being configured to establish a broadband model of the high-coupling split reactor, the broadband model of the high-coupling split reactor including an ideal coupling reactor sub-model and a terminal equivalent capacitance, the system including:
the ideal reactor model establishing unit is used for establishing an ideal coupling reactor sub-model, wherein the ideal coupling reactor sub-model is used for simulating a high-coupling splitting reactor without stray capacitance and stray inductance influence;
the stray capacitance calculation unit is used for calculating the stray capacitance of each winding in turn unit according to the parameters of the high-coupling split reactor; the stray capacitance comprises turns and mutual capacitance between the turns and capacitance to ground;
the terminal equivalent capacitance determining unit is used for obtaining terminal equivalent capacitances at two ends of each winding of the high-coupling split reactor according to the stray capacitance of each winding in turn;
the terminal capacitor matrix determining unit is used for short-circuiting each odd terminal at the upper end, each even terminal at the upper end, each odd terminal at the lower end and each even terminal at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding;
and the broadband model determining unit is used for adding the obtained terminal capacitance matrix corresponding to the four-port network to the ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor.
In an optional example, the stray capacitance calculating unit calculates the stray capacitance of each winding in turn unit according to parameters of the high-coupling split reactor, specifically:
the wire turns of the same envelope are regularly arranged, and the adjacent turns mutually have a capacitance CaAnd a capacitance to ground CdRespectively as follows:
the adjacent wire turns with the same enveloping height have a mutual capacitance CbComprises the following steps:
in the formula, epsilon0Dielectric constant of vacuum,. epsilonjRelative dielectric constant of insulation, ra、waAverage radius of wire turns and radial length of wire, hbAnd d is the turn-to-turn distance, and h is the height of the turns to ground.
In an optional example, the terminal equivalent capacitance determining unit obtains the terminal equivalent capacitance at the two ends of each winding of the high-coupling split-core reactor according to the stray capacitance of each winding in turn, specifically:
determining an inductance matrix:
Ci0＝βi1+βi2+…+βii+…+βin
Cij＝-βij(i≠j)
Ci0capacitance to ground of turns of number i, CijThe mutual capacitance between the turns of the number i and the number j is the capacitance; beta is aijThe inductance of the ith turn coil and the jth turn coil;
solving an inductance matrix beta based on the ground capacitance and the mutual capacitance; if one high-coupling split reactor has n turns of coils, the beta is an n-order matrix;
determining a terminal inductance matrix:
γ＝ξTβξ
wherein gamma is a terminal inductance matrix, is a xi terminal coefficient matrix, and is xikIs a matrix of winding coefficients of number k, nkThe number of turns of the k winding is;
the k-winding has two terminals: t is t2k-1And t2k(ii) a The terminal capacitance of the k winding includes t2k-1Self-terminal capacitance of (1)2kSelf-terminated capacitance of t2k-1Capacitor with terminal
Is equal to the sum, t, of all elements of the 2k-1 th row in the terminal inductance matrix gamma2kCapacitor with terminal
Equal to the sum of all elements of the 2 k-th row in the terminal inductance matrix gamma;
the mutual terminal capacitance between the winding No. k and the winding No. l is as follows:
wherein the content of the first and second substances,
is the mutual terminal capacitance between the terminal on the winding of the number k and the terminal on the winding of the number l,
the mutual terminal capacitance between the upper terminal of the k winding and the lower terminal of the l winding,
the mutual terminal capacitance between the lower terminal of the k winding and the upper terminal of the l winding,
is the mutual terminal capacitance between the lower terminal of the k winding and the lower terminal of the l winding, gamma2k-1,2l-1Terminal inductance, γ, between terminals on winding k and winding l2k-1,2lTerminal inductance between the upper terminal of winding No. k and the lower terminal of winding No. l, γ2k,2l-1Terminal inductance, γ, between the lower terminal of winding No. k and the upper terminal of winding No. l2k,2lThe terminal inductance between the lower terminal of the winding No. k and the lower terminal of the winding No. l is obtained; l is not equal to k;
the terminal equivalent capacitance at two ends of the k winding comprises: the terminal capacitance of the k winding and the mutual terminal capacitance between the k winding and the l winding.
In an optional example, the terminal capacitance matrix determining unit obtains a terminal capacitance matrix corresponding to the four-port network by using a circuit theory principle.
In an alternative example, when the high-coupling split reactor includes four windings, the terminal capacitance matrix C of the corresponding four-port network determined by the terminal capacitance matrix determining unit is:
the terminal capacitance matrix C of the four-port network is:
wherein the content of the first and second substances,
the self-capacitance of the terminal on the No. 1 terminal or the No. 1 winding,
is the self-capacitance of the terminal under the No. 2 terminal or the No. 1 winding,
the self capacitance of the terminal on the No. 3 terminal or the No. 2 winding,
the self capacitance of the terminal under the No. 4 terminal or the No. 2 winding,
the self capacitance of the terminal on the No. 5 terminal or the No. 3 winding,
is the self capacitance of the lower terminal of the No. 6 terminal or the No. 3 winding,
the self capacitance of the terminal on the No. 7 terminal or the No. 4 winding,
the capacitor is a self-contained capacitor of a No. 8 terminal, namely a No. 4 winding lower terminal;
subscripts u and v of the subscript t belong to integers from 1 to 8, and are mutual terminal capacitances between any u-terminal and v-terminal.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
the invention provides a broadband modeling method and a broadband modeling system for a high-coupling split reactor, wherein the high-coupling split reactor modeling method based on a terminal capacitor comprises the following steps: establishing an ideal coupling reactor sub-model simulating the influence of no stray parameters, calculating mutual capacitance and capacitance to ground between turns according to design parameters of the high-coupling splitting reactor, enabling the stray capacitance taking the turns as a unit to be equivalent to two ends of each winding of the high-coupling splitting reactor, combining multiple winding terminals to form a four-terminal network, obtaining a stray capacitance matrix corresponding to the four-port network, and adding the obtained terminal capacitance to the ideal coupling reactor model to obtain a high-coupling splitting reactor terminal capacitance broadband model. The modeling method provided by the invention has certain advantages in accuracy and modeling complexity.
Drawings
FIG. 1 is a flowchart of a broadband modeling method for a high-coupling split reactor according to an embodiment of the present invention;
fig. 2 is a flow chart of modeling a broadband model of a high-coupling split-reactor based on a terminal capacitor according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a terminal merging circuit according to an embodiment of the present invention;
FIG. 4 is a broadband model of a terminal capacitance-based high-coupling split reactor provided by an embodiment of the present invention;
fig. 5 is a schematic diagram of a broadband modeling system of a high-coupling split reactor according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method is used for establishing the high-coupling split reactor terminal capacitance broadband model. The broadband model of the high-coupling split reactor comprises an ideal coupling reactor model and a terminal equivalent capacitance. The modeling object of the high-coupling split reactor modeling method provided by the embodiment of the application is the high-coupling split reactor which is a four-end element with two arms in counter coupling and is greatly influenced by stray capacitance and stray inductance under high frequency.
Fig. 1 is a flowchart of a broadband modeling method for a high-coupling split reactor according to an embodiment of the present invention, as shown in fig. 1, including the following steps:
s101, establishing an ideal coupling reactor sub-model, wherein the ideal coupling reactor sub-model is used for simulating a high-coupling split reactor without stray capacitance and stray inductance influence;
s102, calculating stray capacitance of each winding in turn according to parameters of the high-coupling split reactor; the stray capacitance comprises turns and mutual capacitance between the turns and capacitance to ground;
s103, obtaining terminal equivalent capacitances at two ends of each winding of the high-coupling split-core reactor according to the stray capacitance of each winding in turn;
s104, short-circuiting each odd terminal at the upper end, each even terminal at the upper end, each odd terminal at the lower end and each even terminal at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding;
and S105, adding the obtained terminal capacitor matrix corresponding to the four-port network to the ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor.
In an alternative example, the stray capacitance of each winding in turns is calculated according to parameters of the high-coupling split reactor, specifically:
the wire turns of the same envelope are regularly arranged, and the adjacent turns mutually have a capacitance CaAnd a capacitance to ground CdRespectively as follows:
the adjacent wire turns with the same enveloping height have a mutual capacitance CbComprises the following steps:
in the formula, epsilon0Dielectric constant of vacuum,. epsilonjRelative dielectric constant of insulation, ra、waAverage radius of wire turns and radial length of wire, hbIs the mean axis of the wireThe radial length d is the turn-to-turn distance and h is the height of the turns to ground.
In an optional example, the terminal equivalent capacitance at two ends of each winding of the high-coupling split-core reactor is obtained according to the stray capacitance of each winding in turn, specifically:
determining an inductance matrix:
Ci0＝βi1+βi2+…+βii+…+βin
Cij＝-βij(i≠j)
Ci0capacitance to ground of turns of number i, CijThe mutual capacitance between the turns of the number i and the number j is the capacitance; beta is aijThe inductance of the ith turn coil and the jth turn coil;
solving an inductance matrix beta based on the ground capacitance and the mutual capacitance; if one high-coupling split reactor has n turns of coils, the beta is an n-order matrix;
determining a terminal inductance matrix:
γ＝ξTβξ
wherein gamma is a terminal inductance matrix, is a xi terminal coefficient matrix, and is xikIs a matrix of winding coefficients of number k, nkThe number of turns of the k winding is;
the k-winding has two terminals: t is t2k-1And t2k(ii) a The terminal capacitance of the k winding includes t2k-1Self-terminal capacitance of (1)2kSelf-terminated capacitance of t2k-1Capacitor with terminal
Is equal to the sum, t, of all elements of the 2k-1 th row in the terminal inductance matrix gamma2kCapacitor with terminal
Equal to the sum of all elements of the 2 k-th row in the terminal inductance matrix gamma;
the mutual terminal capacitance between the winding No. k and the winding No. l is as follows:
wherein the content of the first and second substances,
is the mutual terminal capacitance between the terminal on the winding of the number k and the terminal on the winding of the number l,
the mutual terminal capacitance between the upper terminal of the k winding and the lower terminal of the l winding,
the mutual terminal capacitance between the lower terminal of the k winding and the upper terminal of the l winding,
is the mutual terminal capacitance between the lower terminal of the k winding and the lower terminal of the l winding, gamma2k-1,2l-1Terminal inductance, γ, between terminals on winding k and winding l2k-1,2lTerminal inductance between the upper terminal of winding No. k and the lower terminal of winding No. l, γ2k,2l-1Terminal inductance, γ, between the lower terminal of winding No. k and the upper terminal of winding No. l2k,2lThe terminal inductance between the lower terminal of the winding No. k and the lower terminal of the winding No. l is obtained; l is not equal to k;
the terminal equivalent capacitance at two ends of the k winding comprises: the terminal capacitance of the k winding and the mutual terminal capacitance between the k winding and the l winding.
In an optional example, short-circuiting each odd terminal at the upper end, short-circuiting each even terminal at the upper end, short-circuiting each odd terminal at the lower end and short-circuiting each even terminal at the lower end of each winding terminal of the high-coupling split-reactor to form a four-port network; and obtaining a terminal capacitance matrix corresponding to the four-port network based on terminal equivalent capacitances at two ends of each winding, specifically:
and obtaining a terminal capacitor matrix corresponding to the four-port network by using a circuit theory principle.
In an alternative example, when the high-coupling split reactor includes four windings, the terminal capacitance matrix C of the four-port network is:
the terminal capacitance matrix C of the four-port network is:
wherein the content of the first and second substances,
the self-capacitance of the terminal on the No. 1 terminal or the No. 1 winding,
is the self-capacitance of the terminal under the No. 2 terminal or the No. 1 winding,
the self capacitance of the terminal on the No. 3 terminal or the No. 2 winding,
the self capacitance of the terminal under the No. 4 terminal or the No. 2 winding,
the self capacitance of the terminal on the No. 5 terminal or the No. 3 winding,
is the self capacitance of the lower terminal of the No. 6 terminal or the No. 3 winding,
the self capacitance of the terminal on the No. 7 terminal or the No. 4 winding,
the capacitor is a self-contained capacitor of a No. 8 terminal, namely a No. 4 winding lower terminal;
subscripts u and v of the subscript t belong to integers from 1 to 8, and are mutual terminal capacitances between any u-terminal and v-terminal.
Fig. 2 is a flow chart of modeling a broadband model of a high-coupling split-reactor based on a terminal capacitor according to an embodiment of the present invention; as shown in fig. 2, includes:
and establishing an ideal coupling reactor model, wherein the ideal coupling reactor model is used for simulating the high coupling split reactor without the influence of stray capacitance and stray inductance.
And calculating mutual capacitance and capacitance to ground between turns of each winding according to the parameters of the high-coupling split reactor.
And obtaining the terminal equivalent capacitance at the two ends of each winding of the high-coupling split reactor according to the stray capacitance taking turns as units.
And short-circuiting the multi-winding terminal to form a four-port network and obtaining a terminal capacitor matrix corresponding to the four-port network.
And adding the obtained four-port stray capacitance parameters to an ideal coupling reactor model to obtain a high-coupling split reactor terminal capacitance broadband model.
FIG. 3 is a schematic diagram of a terminal merging circuit according to an embodiment of the present invention; as shown in fig. 3, the upper terminals, i.e. t1 and t5, of each odd-numbered winding of the high-coupling split-reactor are shorted to form a No. 1 terminal, and the lower terminals, i.e. t2 and t6, are shorted to form a No. 2 terminal; the upper terminals, namely t3 and t7, of the even-numbered windings are short-circuited to form a No. 3 terminal, and the lower terminals, namely t4 and t8, are short-circuited to form a No. 4 terminal, so that a four-port network is formed. t1-t8 correspond to terminals No. 1 to No. 8 before the high-coupling split reactor terminals are merged, respectively.
Fig. 4 is a broadband model of a terminal capacitance-based high-coupling split-reactor according to an embodiment of the present invention. As shown in fig. 4, the broadband model of the high-coupling split-core reactor is a 10-capacitor model, which includes an ideal high-coupling split-core reactor model and 10 terminal equivalent capacitors, and by adding the 10 terminal equivalent capacitors, the model can exhibit high-frequency band characteristics.
Fig. 5 is a schematic diagram of a broadband modeling system of a high-coupling split reactor according to an embodiment of the present invention, as shown in fig. 5, including:
an ideal reactor model establishing unit 510, configured to establish an ideal coupling reactor sub-model, where the ideal coupling reactor sub-model is used to simulate a high-coupling split reactor without stray capacitance and stray inductance;
a stray capacitance calculation unit 520, configured to calculate, according to parameters of the high-coupling split reactor, a stray capacitance of each winding in turn units; the stray capacitance comprises turns and mutual capacitance between the turns and capacitance to ground;
a terminal equivalent capacitance determining unit 530, configured to obtain terminal equivalent capacitances at two ends of each winding of the high-coupling split-core reactor according to the stray capacitance of each winding in turns;
the terminal capacitor matrix determining unit 540 is used for short-circuiting the odd-numbered terminals at the upper end, the even-numbered terminals at the upper end, the odd-numbered terminals at the lower end and the even-numbered terminals at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding;
and a broadband model determining unit 550, configured to add the obtained terminal capacitance matrix corresponding to the four-port network to the ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor.
It is understood that the detailed functions of each unit in fig. 5 can refer to the description in the foregoing method embodiment, and are not described herein again.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A broadband modeling method of a high-coupling split reactor is characterized by being used for building a broadband model of the high-coupling split reactor, wherein the broadband model of the high-coupling split reactor comprises an ideal coupling reactor sub-model and a terminal equivalent capacitance, and the method comprises the following steps:
establishing an ideal coupling reactor submodel, wherein the ideal coupling reactor submodel is used for simulating a high-coupling split reactor without stray capacitance and stray inductance influence;
calculating stray capacitance of each winding in turn unit according to parameters of the high-coupling split reactor; the stray capacitance comprises turns and mutual capacitance between the turns and capacitance to ground;
obtaining terminal equivalent capacitance at two ends of each winding of the high-coupling split reactor according to the stray capacitance of each winding in turn;
short-circuiting each odd terminal at the upper end, each even terminal at the upper end, each odd terminal at the lower end and each even terminal at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding;
and adding the obtained terminal capacitor matrix corresponding to the four-port network to an ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor.
2. The broadband modeling method according to claim 1, wherein the stray capacitance of each winding in turns is calculated according to parameters of the high-coupling split-reactor, specifically:
the wire turns of the same envelope are regularly arranged, and the adjacent turns mutually have a capacitance CaAnd a capacitance to ground CdRespectively as follows:
the adjacent wire turns with the same enveloping height have a mutual capacitance CbComprises the following steps:
in the formula, epsilon0Dielectric constant of vacuum,. epsilonjRelative dielectric constant of insulation, ra、waAverage radius of wire turns and radial length of wire, hbAnd d is the turn-to-turn distance, and h is the height of the turns to ground.
3. The broadband modeling method according to claim 1, wherein the equivalent capacitance of the terminal at the two ends of each winding of the high-coupling split-core reactor is obtained according to the stray capacitance of each winding in turns, and specifically comprises:
determining an inductance matrix:
Ci0＝βi1+βi2+…+βii+…+βin
Cij＝-βij(i≠j)
Ci0capacitance to ground of turns of number i, CijThe mutual capacitance between the turns of the number i and the number j is the capacitance; beta is aijThe inductance of the ith turn coil and the jth turn coil;
solving an inductance matrix beta based on the ground capacitance and the mutual capacitance; if one high-coupling split reactor has n turns of coils, the beta is an n-order matrix;
determining a terminal inductance matrix:
γ＝ξTβξ
wherein gamma is a terminal inductance matrix, is a xi terminal coefficient matrix, and is xikIs a matrix of winding coefficients of number k, nkThe number of turns of the k winding is;
the k-winding has two terminals: t is t2k-1And t2k(ii) a The terminal capacitance of the k winding includes t2k-1Self-terminal capacitance of (1)2kSelf-terminated capacitance of t2k-1Capacitor with terminal
Is equal to the sum, t, of all elements of the 2k-1 th row in the terminal inductance matrix gamma2kCapacitor with terminal
Equal to the sum of all elements of the 2 k-th row in the terminal inductance matrix gamma;
the mutual terminal capacitance between the winding No. k and the winding No. l is as follows:
wherein the content of the first and second substances,
is the mutual terminal capacitance between the terminal on the winding of the number k and the terminal on the winding of the number l,
the mutual terminal capacitance between the upper terminal of the k winding and the lower terminal of the l winding,
the mutual terminal capacitance between the lower terminal of the k winding and the upper terminal of the l winding,
is the mutual terminal capacitance between the lower terminal of the k winding and the lower terminal of the l winding, gamma2k-1,2l-1Terminal inductance, γ, between terminals on winding k and winding l2k-1,2lTerminal inductance between the upper terminal of winding No. k and the lower terminal of winding No. l, γ2k,2l-1Terminal inductance, γ, between the lower terminal of winding No. k and the upper terminal of winding No. l2k,2lThe terminal inductance between the lower terminal of the winding No. k and the lower terminal of the winding No. l is obtained; l is not equal to k;
the terminal equivalent capacitance at two ends of the k winding comprises: the terminal capacitance of the k winding and the mutual terminal capacitance between the k winding and the l winding.
4. The broadband modeling method according to claim 1, characterized in that a four-port network is formed by short-circuiting the odd-numbered terminals at the upper end, the even-numbered terminals at the upper end, the odd-numbered terminals at the lower end and the even-numbered terminals at the lower end of each winding terminal of the high-coupling split-reactor; and obtaining a terminal capacitance matrix corresponding to the four-port network based on terminal equivalent capacitances at two ends of each winding, specifically:
and obtaining a terminal capacitor matrix corresponding to the four-port network by using a circuit theory principle.
5. The broadband modeling method of claim 4, wherein when a high-coupling split-reactor comprises four windings, the terminal capacitance matrix C of the four-port network is:
the terminal capacitance matrix C of the four-port network is:
wherein the content of the first and second substances,
the self-capacitance of the terminal on the No. 1 terminal or the No. 1 winding,
is the self-capacitance of the terminal under the No. 2 terminal or the No. 1 winding,
the self capacitance of the terminal on the No. 3 terminal or the No. 2 winding,
the self capacitance of the terminal under the No. 4 terminal or the No. 2 winding,
from terminal on winding No. 3, terminal No. 5There is a capacitance that is,
is the self capacitance of the lower terminal of the No. 6 terminal or the No. 3 winding,
the self capacitance of the terminal on the No. 7 terminal or the No. 4 winding,
the capacitor is a self-contained capacitor of a No. 8 terminal, namely a No. 4 winding lower terminal;
subscripts u and v of the subscript t belong to integers from 1 to 8, and are mutual terminal capacitances between any u-terminal and v-terminal.
6. A broadband modeling system for a high coupling split reactor, the system configured to build a broadband model of the high coupling split reactor, the broadband model of the high coupling split reactor including an ideal coupling reactor sub-model and a terminal equivalent capacitance, the system comprising:
the ideal reactor model establishing unit is used for establishing an ideal coupling reactor sub-model, wherein the ideal coupling reactor sub-model is used for simulating a high-coupling splitting reactor without stray capacitance and stray inductance influence;
the stray capacitance calculation unit is used for calculating the stray capacitance of each winding in turn unit according to the parameters of the high-coupling split reactor; the stray capacitance comprises turns and mutual capacitance between the turns and capacitance to ground;
the terminal equivalent capacitance determining unit is used for obtaining terminal equivalent capacitances at two ends of each winding of the high-coupling split reactor according to the stray capacitance of each winding in turn;
the terminal capacitor matrix determining unit is used for short-circuiting each odd terminal at the upper end, each even terminal at the upper end, each odd terminal at the lower end and each even terminal at the lower end of each winding terminal of the high-coupling split reactor to form a four-port network; obtaining a terminal capacitor matrix corresponding to the four-port network based on terminal equivalent capacitors at two ends of each winding;
and the broadband model determining unit is used for adding the obtained terminal capacitance matrix corresponding to the four-port network to the ideal coupling reactor model to obtain a broadband model of the high-coupling split reactor.
7. The broadband modeling system of claim 6, wherein the stray capacitance calculating unit calculates the stray capacitance of each winding in turns according to parameters of the high-coupling split reactor, specifically:
the wire turns of the same envelope are regularly arranged, and the adjacent turns mutually have a capacitance CaAnd a capacitance to ground CdRespectively as follows:
the adjacent wire turns with the same enveloping height have a mutual capacitance CbComprises the following steps:
in the formula, epsilon0Dielectric constant of vacuum,. epsilonjRelative dielectric constant of insulation, ra、waAverage radius of wire turns and radial length of wire, hbAnd d is the turn-to-turn distance, and h is the height of the turns to ground.
8. The broadband modeling system according to claim 6, wherein the terminal equivalent capacitance determining unit obtains the terminal equivalent capacitance at the two ends of each winding of the high-coupling split-core reactor according to the stray capacitance of each winding in turns, specifically:
determining an inductance matrix:
Ci0＝βi1+βi2+…+βii+…+βin
Cij＝-βij(i≠j)
Ci0capacitance to ground of turns of number i, CijThe mutual capacitance between the turns of the number i and the number j is the capacitance; beta is aijThe inductance of the ith turn coil and the jth turn coil;
solving an inductance matrix beta based on the ground capacitance and the mutual capacitance; if one high-coupling split reactor has n turns of coils, the beta is an n-order matrix;
determining a terminal inductance matrix:
γ＝ξTβξ
wherein gamma is a terminal inductance matrix, is a xi terminal coefficient matrix, and is xikIs a matrix of winding coefficients of number k, nkThe number of turns of the k winding is;
the k-winding has two terminals: t is t2k-1And t2k(ii) a The terminal capacitance of the k winding includes t2k-1Self-terminal capacitance of (1)2kSelf-terminated capacitance of t2k-1Capacitor with terminal
Is equal to the sum, t, of all elements of the 2k-1 th row in the terminal inductance matrix gamma2kCapacitor with terminal
Equal to the sum of all elements of the 2 k-th row in the terminal inductance matrix gamma;
the mutual terminal capacitance between the winding No. k and the winding No. l is as follows:
wherein the content of the first and second substances,
is the mutual terminal capacitance between the terminal on the winding of the number k and the terminal on the winding of the number l,
the mutual terminal capacitance between the upper terminal of the k winding and the lower terminal of the l winding,
the mutual terminal capacitance between the lower terminal of the k winding and the upper terminal of the l winding,
is the mutual terminal capacitance between the lower terminal of the k winding and the lower terminal of the l winding, gamma2k-1,2l-1Terminal induction system between terminal on winding No. k and terminal on winding No. lNumber, gamma2k-1,2lTerminal inductance between the upper terminal of winding No. k and the lower terminal of winding No. l, γ2k,2l-1Terminal inductance, γ, between the lower terminal of winding No. k and the upper terminal of winding No. l2k,2lThe terminal inductance between the lower terminal of the winding No. k and the lower terminal of the winding No. l is obtained; l is not equal to k;
the terminal equivalent capacitance at two ends of the k winding comprises: the terminal capacitance of the k winding and the mutual terminal capacitance between the k winding and the l winding.
9. The broadband modeling system of claim 6, wherein the terminal capacitance matrix determining unit obtains the terminal capacitance matrix corresponding to the four-port network by using circuit theory principles.
10. The broadband modeling system of claim 9, wherein when a high-coupling split reactor includes four windings, the terminal capacitance matrix C of the corresponding four-port network determined by the terminal capacitance matrix determination unit is:
the terminal capacitance matrix C of the four-port network is:
wherein the content of the first and second substances,
the self-capacitance of the terminal on the No. 1 terminal or the No. 1 winding,
is the self-capacitance of the terminal under the No. 2 terminal or the No. 1 winding,
the self capacitance of the terminal on the No. 3 terminal or the No. 2 winding,
the self capacitance of the terminal under the No. 4 terminal or the No. 2 winding,
the self capacitance of the terminal on the No. 5 terminal or the No. 3 winding,
is the self capacitance of the lower terminal of the No. 6 terminal or the No. 3 winding,
the self capacitance of the terminal on the No. 7 terminal or the No. 4 winding,
the capacitor is a self-contained capacitor of a No. 8 terminal, namely a No. 4 winding lower terminal;
subscripts u and v of the subscript t belong to integers from 1 to 8, and are mutual terminal capacitances between any u-terminal and v-terminal.
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