CN114284998B - Four-winding induction filter transformer winding impedance matching method and system - Google Patents
Four-winding induction filter transformer winding impedance matching method and system Download PDFInfo
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- CN114284998B CN114284998B CN202111333458.5A CN202111333458A CN114284998B CN 114284998 B CN114284998 B CN 114284998B CN 202111333458 A CN202111333458 A CN 202111333458A CN 114284998 B CN114284998 B CN 114284998B
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Abstract
The embodiment of the invention provides a winding impedance matching method and system for a four-winding induction filter transformer, wherein a mathematical decoupling model of the four-winding induction filter transformer is established based on a single-phase circuit model of the transformer according to a multi-winding voltage transfer theory, a magnetomotive balance principle and a kirchhoff current-voltage theorem, an expression of network side current of the four-winding induction filter transformer is obtained, and impedance conditions required by the four-winding induction filter transformer are obtained through analysis; by utilizing a multi-winding voltage transfer theory and a magnetic potential balance principle, a mathematical decoupling model related to the network side current of the transformer is obtained, a network side current expression is calculated, and the dual zero impedance condition of the four-winding induction filter transformer is obtained according to the expression analysis.
Description
Technical Field
The embodiment of the invention relates to the technical field of induction filtering, in particular to a method and a system for impedance matching of a winding of a four-winding induction filtering transformer.
Background
The current generated by electronic equipment such as a rectifier, an inverter and the like in each half cycle is not in proportional relation with the applied voltage, so that a non-sinusoidal distortion waveform is presented, a large amount of higher harmonics are generated in a power system by the equipment, the running condition of a power grid is deteriorated to a great extent, the harmonic pollution of the power grid is serious, and the harmonics circulate in a transformer, so that the service life of the transformer is shortened, the system loss is increased, and even system faults can be caused.
The induction filtering is an effective power filtering method, a newly added filtering winding is designed through special impedance matching, reverse magnetic flux induced by load harmonic magnetic flux on the side of the filtering winding is offset, and load harmonic is damped on the filtering side and cannot be transmitted to the transformer network side.
The winding impedance matching method is to obtain the impedance design condition required by damping load harmonic current by analyzing the expression of the network side current and the load current. The existing impedance matching design method of the induction filter transformer is mainly used for a three-winding induction filter transformer, and four windings are rarely involved; and when a transformer equivalent circuit model is established, loads are mostly equivalent to current sources, and the method is low in accuracy and effectiveness.
Disclosure of Invention
The embodiment of the invention provides a winding impedance matching method and system for a four-winding induction filter transformer, which are used for solving the problems that when a transformer equivalent circuit model is established in the prior art, loads are mostly equivalent to current sources, and the existing induction filter transformer impedance matching design method is low in accuracy and effectiveness.
In order to solve the above technical problem, in a first aspect, an embodiment of the present invention provides a winding impedance matching method for a four-winding induction filter transformer, where the four-winding induction filter transformer is arranged in a four-winding manner, and the four-winding induction filter transformer includes a first winding, a second winding, a third winding, and a fourth winding; the first winding is a net side winding and adopts a star connection method; the second winding is a filter winding and adopts a delta connection method; the third winding is a load winding and adopts a star connection method; the fourth winding is a load winding and adopts a delta connection method; the method comprises the following steps:
determining the terminal voltage of each winding based on a single-phase circuit model of a transformer and a multi-winding voltage transfer theory, and determining the current-voltage relationship between the windings based on a magnetomotive balance principle and a kirchhoff current-voltage theorem; establishing a mathematical decoupling model of the four-winding induction filter transformer;
and determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model, and determining the impedance required by the four-winding induction filter transformer based on the network side current.
Preferably, the expression of the terminal voltage of each winding is as follows:
in the above formula, U 1 、U 2 、U 3 、U 4 The terminal voltages of the first winding, the second winding, the third winding and the fourth winding are respectively; i is 1 ～I 4 Respectively obtaining end currents of a first winding, a second winding, a third winding and a fourth winding; e is the main magnetic flux induced electromotive force; m is a group of xy X =1,2,3,4, y =1,2,3,4 for mutual inductance between windings x, y; l is a radical of an alcohol 1 ～L 4 Self-inductance of the first winding, the second winding, the third winding and the fourth winding respectively; r 1 ～R 4 Respectively the resistances of the first winding, the second winding, the third winding and the fourth winding.
Preferably, after determining the terminal voltage of each winding based on a single-phase circuit model of the transformer and a multi-winding voltage transfer theory, the method further comprises determining a voltage drop expression of each winding and a filter winding:
setting a short-circuit resistance R between winding x and winding y kxy ＝R x +R y Short-circuit reactance of X kxy ＝ω(L x +L y -M xy -M yx ) Then short circuit impedance Z kxy ＝R kxy +jX kxy (ii) a Setting the equivalent leakage impedance of winding x to Z xyz ＝(Z kxy +Z kxz -Z kyz ) /2, and Z is present kxy ＝Z kyx 、Z xyz ＝Z xzy X =1,2,3,4, y =1,2,3,4, z =1,2,3,4, and x ≠ y ≠ z; the voltage drop expression of each winding and the filter winding is simplified as follows:
preferably, the current-voltage relationship among the windings of the four-winding induction filter transformer is as follows:
I 1 +I 2 +I 3 +I 4 ＝0
in the above formula, U s Is the power grid background voltage; i is L3 、I L4 The load equivalent current sources are a third winding and a fourth winding; z grid Is the system equivalent impedance; z is a linear or branched member f Is the equivalent impedance of the filter device; z L3 、Z L4 Load equivalent impedance of the third winding and the fourth winding; the first winding side power grid is equivalent to the equivalent impedance of a grid side voltage source series system; the filtering device of the second winding is a group of single-tuned filters with full-tuning design, and the equivalent impedance is filtering equivalent impedance; the loads connected with the third winding and the fourth winding are equivalent to load current source parallel load equivalent impedance through the Noton's theorem.
Preferably, the establishing of the mathematical decoupling model of the four-winding induction filter transformer specifically includes:
obtaining the network side current I of the four-winding induction filter transformer based on the current-voltage relational expression among the windings of the four-winding induction filter transformer and the voltage drop expression of the windings and the filter winding 1 Related mathematical decoupling models:
preferably, the grid side current I 1 The expression is as follows:
preferably, determining the impedance required by the four-winding induction filter transformer based on the grid-side current specifically includes:
at harmonic Z f Under the condition of 0, the catalyst contains I L3 、I L4 Is expressed as a value of 0, is,so as to eliminate the influence of the load harmonic current on the power grid;
let Z L3 [Z 214 Z 234 -Z 213 (Z L4 +Z k24 )]、Z L4 [Z 213 Z 234 -Z 214 (Z L3 +Z k23 )]Is 0 and satisfies Z 213 ＝Z 214 =0; obtaining a network side current expression after impedance matching:
in a second aspect, an embodiment of the present invention provides a winding impedance matching system for a four-winding induction filter transformer, where the four-winding induction filter transformer is arranged in a four-winding manner, and the four-winding induction filter transformer includes a first winding, a second winding, a third winding, and a fourth winding; the first winding is a net side winding and adopts a star connection method; the second winding is a filter winding and adopts a delta connection method; the third winding is a load winding and adopts a star connection method; the fourth winding is a load winding and adopts a delta connection method; the system comprises:
the mathematical decoupling model establishing module is used for determining the terminal voltage of each winding based on a single-phase circuit model of the transformer and a multi-winding voltage transfer theory and determining the current-voltage relation among the windings based on a magnetic potential balance principle and a kirchhoff current-voltage theorem; establishing a mathematical decoupling model of the four-winding induction filter transformer;
and the impedance matching module is used for determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model and determining the impedance required by the four-winding induction filter transformer based on the network side current. In a third aspect, an embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor executes the computer program to implement the steps of the method for matching impedance of windings of a four-winding inductive-filter transformer according to the embodiment of the first aspect of the present invention.
In a fourth aspect, embodiments of the present invention provide a non-transitory computer-readable storage medium, on which a computer program is stored, the computer program, when executed by a processor, implementing the steps of the four-winding inductive filter transformer winding impedance matching method according to embodiments of the first aspect of the present invention.
According to the winding impedance matching method and system for the four-winding induction filter transformer, a mathematical decoupling model of the four-winding induction filter transformer is established based on a single-phase circuit model of the transformer according to a multi-winding voltage transfer theory, a magnetomotive balance principle and a kirchhoff current-voltage theorem, an expression of network side current of the four-winding induction filter transformer is obtained, and impedance conditions required by the four-winding induction filter transformer are obtained through analysis; by utilizing a multi-winding voltage transfer theory and a magnetic potential balance principle, a mathematical decoupling model related to the network side current of the transformer is obtained, a network side current expression is calculated, and the dual zero impedance condition of the four-winding induction filter transformer is obtained according to the expression analysis.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a flow chart of a four-winding inductive filter transformer winding impedance matching method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a single-phase circuit model of a four-winding induction filter transformer according to an embodiment of the invention;
fig. 3 is a schematic physical structure diagram according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the embodiment of the present application, the term "and/or" is only one kind of association relationship describing an associated object, and means that three relationships may exist, for example, a and/or B may mean: a exists alone, A and B exist simultaneously, and B exists alone.
The terms "first" and "second" in the embodiments of the present application are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, the terms "comprise" and "have", as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a system, product or apparatus that comprises a list of elements or components is not limited to only those elements or components but may alternatively include other elements or components not expressly listed or inherent to such product or apparatus. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless explicitly specifically limited otherwise.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
The existing impedance matching design method of the induction filter transformer is mainly used for a three-winding induction filter transformer, and four windings are rarely involved; and when a transformer equivalent circuit model is established, loads are mostly equivalent to current sources, and the method is low in accuracy and effectiveness.
Therefore, the embodiment of the invention provides a winding impedance matching method and system for a four-winding induction filter transformer, which utilize a multi-winding voltage transfer theory and a magnetomotive force balance principle to obtain a mathematical decoupling model related to the network side current of the transformer, calculate a network side current expression, and analyze according to the expression to obtain the dual zero impedance condition of the four-winding induction filter transformer. The following description and description will proceed with reference being made to various embodiments.
Fig. 1 is a diagram illustrating a winding impedance matching method for a four-winding induction filter transformer according to an embodiment of the present invention, where the four-winding induction filter transformer is arranged in a four-winding manner, and includes a first winding, a second winding, a third winding, and a fourth winding; the first winding is a net side winding and adopts a star connection method; the second winding is a filter winding and adopts a delta connection method; the third winding is a load winding and adopts a star connection method; the fourth winding is a load winding and adopts a delta connection method; the method comprises the following steps:
determining the terminal voltage of each winding based on a single-phase circuit model of a transformer and a multi-winding voltage transfer theory, and determining the current-voltage relation between each winding based on a magnetomotive balance principle and a kirchhoff current-voltage theorem; establishing a mathematical decoupling model of the four-winding induction filter transformer;
and determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model, and determining the impedance required by the four-winding induction filter transformer based on the network side current.
In the embodiment, based on a single-phase circuit model of the transformer, a mathematical decoupling model of the four-winding induction filter transformer is established according to a multi-winding voltage transfer theory, a magnetic potential balance principle and a kirchhoff current-voltage theorem, an expression of the network side current of the four-winding induction filter transformer is obtained, and impedance conditions required by the four-winding induction filter transformer are obtained through analysis; by utilizing a multi-winding voltage transfer theory and a magnetic potential balance principle, a mathematical decoupling model related to the network side current of the transformer is obtained, a network side current expression is calculated, and the dual zero impedance condition of the four-winding induction filter transformer is obtained according to the expression analysis.
As shown in fig. 2, the first winding side grid is equivalent to a grid side voltage source series system equivalent impedance; the filtering device of the second winding is a group of single-tuned filters with full-tuning design, and the equivalent impedance is filtering equivalent impedance; and the loads connected with the third winding and the fourth winding are equivalent to load current source parallel load equivalent impedance through the Noton theorem, and all variables are converted to the primary winding side for calculation.
According to the voltage transfer theory of the multi-winding transformer, the expression of the terminal voltage of each winding is as follows:
in the above formula, U 1 、U 2 、U 3 、U 4 The terminal voltages of the first winding, the second winding, the third winding and the fourth winding are respectively; i is 1 ～I 4 Respectively obtaining end currents of a first winding, a second winding, a third winding and a fourth winding; e is the induced electromotive force of the main magnetic flux; m xy X =1,2,3,4, y =1,2,3,4 for mutual inductance between windings x, y; l is 1 ～L 4 Self-inductance of the first winding, the second winding, the third winding and the fourth winding respectively; r 1 ～R 4 Respectively the resistances of the first winding, the second winding, the third winding and the fourth winding.
Subtracting the latter equation from each formula in the formula (1) to obtain a voltage drop expression of each winding and the filter winding, and determining the voltage drop expression of each winding and the filter winding:
setting a short-circuit resistance R between winding x and winding y kxy ＝R x +R y Short-circuit reactance of X kxy ＝ω(L x +L y -M xy -M yx ) Then short circuit impedance Z kxy ＝R kxy +jX kxy (ii) a Setting the equivalent leakage impedance of winding x to Z xyz ＝(Z kxy +Z kxz -Z kyz ) /2, and Z is present kxy ＝Z kyx 、Z xyz ＝Z xzy X =1,2,3,4, y =1,2,3,4, z =1,2,3,4, and x ≠ y ≠ z; the voltage drop expression of each winding and the filter winding is simplified as follows:
preferably, the current-voltage relationship among the windings of the four-winding induction filter transformer is as follows:
I 1 +I 2 +I 3 +I 4 ＝0 (4)
in the above formula, U s Is the power grid background voltage; i is L3 、I L4 The load equivalent current sources are a third winding and a fourth winding; z grid Is the system equivalent impedance; z f Is the equivalent impedance of the filter device; z L3 、Z L4 Load equivalent impedance of the third winding and the fourth winding; wherein the content of the first and second substances,
based on the current-voltage relation among the windings of the four-winding induction filter transformer and the voltage drop expression of the windings and the filter winding, namely, carrying formulas 4 and 5 into formula 3, and eliminating U 1 、U 2 、I 2 、I 3 、I 4 Parallel shift arrangement is carried out to obtain the network side current I of the four-winding induction filter transformer 1 Related mathematical decoupling models:
the current I at the network side can be obtained by the determinant correlation knowledge after the determinant transformation 1 The expression is as follows:
the following analysis can be made by using the derived network side current expression of the four-winding induction filter transformer: firstly, under harmonic conditions, in order to implement an inductive filtering technique, eliminating the effect of the load harmonic current on the grid, I 1 I in the expression L3 、I L4 The components should all be 0.
Then, according to the filter characteristics, Z is set under harmonic conditions f To be 0, make I L3 、I L4 Component (I) is 0 L3 、I L4 Is expressed as 0), and the remainder Z is L3 [Z 214 Z 234 -Z 213 (Z L4 +Z k24 )]、 Z L4 [Z 213 Z 234 -Z 214 (Z L3 +Z k23 )]Should also be 0, wherein Z L3 、Z L4 Is not 0 and is difficult to determine, so Z needs to be satisfied 213 ＝Z 214 ＝0。
And (7) carrying the analyzed condition into formula (7), so as to obtain a network side current expression after impedance matching:
as can be seen from the expression, the load harmonic current is completely damped and cannot be transmitted to the grid side.
The impedance matching calculation method utilizes a multi-winding voltage transfer theory and a magnetic potential balance principle to obtain a mathematical decoupling model related to the network side current of the transformer, calculates a network side current expression, and obtains a dual zero impedance condition of the four-winding induction filter transformer according to the expression.
The embodiment of the invention also provides a winding impedance matching system of the four-winding induction filter transformer, based on the winding impedance matching method of the four-winding induction filter transformer in the embodiments, the four-winding induction filter transformer is arranged in a four-winding mode, and the four-winding induction filter transformer comprises a first winding, a second winding, a third winding and a fourth winding; the first winding is a net side winding and adopts a star connection method; the second winding is a filter winding and adopts a delta connection method; the third winding is a load winding and adopts a star connection method; the fourth winding is a load winding and adopts a delta connection method; the system comprises:
the mathematical decoupling model establishing module is used for determining the terminal voltage of each winding based on a single-phase circuit model of the transformer and a multi-winding voltage transfer theory and determining the current-voltage relation among the windings based on a magnetic potential balance principle and a kirchhoff current-voltage theorem; establishing a mathematical decoupling model of the four-winding induction filter transformer;
and the impedance matching module is used for determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model and determining the impedance required by the four-winding induction filter transformer based on the network side current.
Based on the same concept, an embodiment of the present invention further provides an entity structure schematic diagram, as shown in fig. 3, the server may include: a processor (processor) 810, a communication Interface 820, a memory 830 and a communication bus 840, wherein the processor 810, the communication Interface 820 and the memory 830 communicate with each other via the communication bus 840. Processor 810 may invoke logic instructions in memory 830 to perform the steps of the four-winding inductive filter transformer winding impedance matching method as described in the various embodiments above. Examples include:
determining the terminal voltage of each winding based on a single-phase circuit model of a transformer and a multi-winding voltage transfer theory, and determining the current-voltage relationship between the windings based on a magnetomotive balance principle and a kirchhoff current-voltage theorem; establishing a mathematical decoupling model of the four-winding induction filter transformer;
and determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model, and determining the impedance required by the four-winding induction filter transformer based on the network side current.
In addition, the logic instructions in the memory 830 may be implemented in software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as independent products. Based on such understanding, the technical solution of the present invention or a part thereof which substantially contributes to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Based on the same concept, embodiments of the present invention further provide a non-transitory computer-readable storage medium, which stores a computer program, where the computer program includes at least one code, where the at least one code is executable by a master control device to control the master control device to implement the steps of the four-winding inductive filter transformer winding impedance matching method according to the embodiments. Examples include:
determining the terminal voltage of each winding based on a single-phase circuit model of a transformer and a multi-winding voltage transfer theory, and determining the current-voltage relationship between the windings based on a magnetomotive balance principle and a kirchhoff current-voltage theorem; establishing a mathematical decoupling model of the four-winding induction filter transformer;
and determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model, and determining the impedance required by the four-winding induction filter transformer based on the network side current.
Based on the same technical concept, the embodiment of the present application further provides a computer program, which is used to implement the above method embodiment when the computer program is executed by the main control device.
The program may be stored in whole or in part on a storage medium packaged with the processor, or in part or in whole on a memory not packaged with the processor.
Based on the same technical concept, the embodiment of the present application further provides a processor, and the processor is configured to implement the above method embodiment. The processor may be a chip.
In summary, according to the winding impedance matching method and system for the four-winding induction filter transformer provided by the embodiments of the present invention, based on a single-phase circuit model of the transformer, a mathematical decoupling model of the four-winding induction filter transformer is established according to a multi-winding voltage transfer theory, a magnetomotive balance principle and a kirchhoff current-voltage theorem, an expression of a network-side current of the four-winding induction filter transformer is obtained, and an impedance condition required by the four-winding induction filter transformer is obtained through analysis; by utilizing a multi-winding voltage transfer theory and a magnetic potential balance principle, a mathematical decoupling model related to the network side current of the transformer is obtained, a network side current expression is calculated, and the dual zero impedance condition of the four-winding induction filter transformer is obtained according to the expression analysis.
The embodiments of the present invention can be arbitrarily combined to achieve different technical effects.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the procedures or functions described in accordance with the present application are generated, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (e.g., coaxial cable, fiber optic, digital subscriber line) or wirelessly (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that incorporates one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk), among others.
One of ordinary skill in the art will appreciate that all or part of the processes in the methods of the above embodiments may be implemented by hardware related to instructions of a computer program, which may be stored in a computer-readable storage medium, and when executed, may include the processes of the above method embodiments. And the aforementioned storage medium includes: various media capable of storing program codes, such as ROM or RAM, magnetic or optical disks, etc.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (4)
1. A four-winding induction filter transformer winding impedance matching method is characterized in that the four-winding induction filter transformer is arranged in a four-winding mode and comprises a first winding, a second winding, a third winding and a fourth winding; the first winding is a net side winding and adopts a star connection method; the second winding is a filter winding and adopts a delta connection method; the third winding is a load winding and adopts a star connection method; the fourth winding is a load winding and adopts a delta connection method; characterized in that the method comprises:
determining the terminal voltage of each winding based on a single-phase circuit model of the transformer and a multi-winding voltage transmission theory, wherein the expression of the terminal voltage of each winding is as follows:
in the above formula, U 1 、U 2 、U 3 、U 4 The terminal voltages of the first winding, the second winding, the third winding and the fourth winding are respectively; i is 1 ～I 4 The current of the first winding end, the second winding end, the third winding end and the fourth winding end respectively; e is the induced electromotive force of the main magnetic flux; m xy X =1,2,3,4, y =1,2,3,4 for mutual inductance between windings x, y; l is 1 ～L 4 Self-inductance of the first winding, the second winding, the third winding and the fourth winding respectively; r 1 ～R 4 The resistors are respectively a first winding, a second winding, a third winding and a fourth winding;
determining a voltage drop expression of each winding and the filter winding:
setting a short-circuit resistance R between winding x and winding y kxy ＝R x +R y Short-circuit reactance of X kxy ＝ω(L x +L y -M xy -M yx ) Then short circuit impedance Z kxy ＝R kxy +jX kxy (ii) a Setting the equivalent leakage impedance of winding x to Z xyz ＝(Z kxy +Z kxz -Z kyz ) /2, and Z is present kxy ＝Z kyx 、Z xyz ＝Z xzy X =1,2,3,4, y =1,2,3,4, z =1,2,3,4, and x ≠ y ≠ z; the voltage drop expression of each winding and the filter winding is simplified as follows:
the current-voltage relation among the windings of the four-winding induction filter transformer is as follows:
I 1 +I 2 +I 3 +I 4 ＝0
in the above formula, U s Is the power grid background voltage; i is L3 、I L4 The load equivalent current sources are a third winding and a fourth winding; z grid Is the system equivalent impedance; z is a linear or branched member f Is the equivalent impedance of the filter device; z L3 、Z L4 Load equivalent impedance of the third winding and the fourth winding; the first winding side power grid is equivalent to the equivalent impedance of a grid side voltage source series system; the filtering device of the second winding is a group of single-tuned filters with full-tuning design, and the equivalent impedance is filtering equivalent impedance; the loads connected with the third winding and the fourth winding are equivalent to load current source parallel load equivalent impedance through the Noton theorem;
determining a current-voltage relation among windings based on a magnetic potential balance principle and a kirchhoff current-voltage theorem; and establishing a mathematical decoupling model of the four-winding induction filter transformer, which specifically comprises the following steps:
obtaining the network side current I of the four-winding induction filter transformer based on the current-voltage relational expression among the windings of the four-winding induction filter transformer and the voltage drop expression of the windings and the filter winding 1 Related mathematical decoupling models:
net side current I 1 The expression is as follows:
determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model, and determining the impedance required by the four-winding induction filter transformer based on the network side current, specifically comprising:
at harmonic Z f Under the condition of 0, the catalyst contains I L3 、I L4 The expression of (1) is 0 to eliminate the influence of load harmonic current on the power grid;
let Z L3 [Z 214 Z 234 -Z 213 (Z L4 +Z k24 )]、Z L4 [Z 213 Z 234 -Z 214 (Z L3 +Z k23 )]Is 0 and satisfies Z 213 ＝Z 214 =0; obtaining a network side current expression after impedance matching:
2. a four-winding induction filter transformer winding impedance matching system is characterized in that the four-winding induction filter transformer is arranged in a four-winding mode and comprises a first winding, a second winding, a third winding and a fourth winding; the first winding is a net side winding and adopts a star connection method; the second winding is a filter winding and adopts a delta connection method; the third winding is a load winding and adopts a star connection method; the fourth winding is a load winding and adopts a delta connection method; characterized in that the system comprises:
the mathematical decoupling model building module is used for determining the end voltage of each winding based on a single-phase circuit model of the transformer and a multi-winding voltage transmission theory, and the expression of the end voltage of each winding is as follows:
in the above formula, U 1 、U 2 、U 3 、U 4 The terminal voltages of the first winding, the second winding, the third winding and the fourth winding are respectively; I.C. A 1 ～I 4 Are respectively the firstThe winding, the second winding, the third winding and the fourth winding end current; e is the main magnetic flux induced electromotive force; m xy X =1,2,3,4, y =1,2,3,4 for mutual inductance between windings x, y; l is 1 ～L 4 Self-inductance of the first winding, the second winding, the third winding and the fourth winding respectively; r is 1 ～R 4 The resistors are respectively a first winding, a second winding, a third winding and a fourth winding;
determining a voltage drop expression of each winding and the filter winding:
setting a short-circuit resistance R between winding x and winding y kxy ＝R x +R y Short-circuit reactance of X kxy ＝ω(L x +L y -M xy -M yx ) Then short circuit impedance Z kxy ＝R kxy +jX kxy (ii) a Setting the equivalent leakage impedance of winding x to Z xyz ＝(Z kxy +Z kxz -Z kyz ) /2, and the presence of Z kxy ＝Z kyx 、Z xyz ＝Z xzy X =1,2,3,4, y =1,2,3,4, z =1,2,3,4, and x ≠ y ≠ z; the voltage drop expression of each winding and the filter winding is simplified as follows:
the current-voltage relation among the windings of the four-winding induction filter transformer is as follows:
I 1 +I 2 +I 3 +I 4 ＝0
in the above formula, U s Is the power grid background voltage; i is L3 、I L4 Load for third winding, fourth winding, etcAn effective current source; z grid Is the system equivalent impedance; z f Is the equivalent impedance of the filter device; z L3 、Z L4 Load equivalent impedance of the third winding and the fourth winding; the first winding side power grid is equivalent to the equivalent impedance of a grid side voltage source series system; the filtering device of the second winding is a group of single-tuned filters with full-tuning design, and the equivalent impedance is filtering equivalent impedance; the loads connected with the third winding and the fourth winding are equivalent to load current source parallel load equivalent impedance through the Noton theorem;
determining a current-voltage relation among windings based on a magnetic potential balance principle and a kirchhoff current-voltage theorem; and establishing a mathematical decoupling model of the four-winding induction filter transformer, which specifically comprises the following steps:
obtaining the network side current I of the four-winding induction filter transformer based on the current-voltage relational expression among the windings of the four-winding induction filter transformer and the voltage drop expression of the windings and the filter winding 1 Related mathematical decoupling models:
net side current I 1 The expression is as follows:
the impedance matching module is used for determining the network side current of the four-winding induction filter transformer based on the mathematical decoupling model and determining the impedance required by the four-winding induction filter transformer based on the network side current, and specifically comprises the following steps:
at harmonic Z f Under the condition of 0, the catalyst contains I L3 、I L4 Is expressed as 0 to eliminate the influence of the load harmonic current on the power grid;
let Z L3 [Z 214 Z 234 -Z 213 (Z L4 +Z k24 )]、Z L4 [Z 213 Z 234 -Z 214 (Z L3 +Z k23 )]Is 0 and satisfies Z 213 ＝Z 214 =0; obtaining a network side current expression after impedance matching:
3. an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs the steps of the method of impedance matching of windings of a four-winding inductive filter transformer as claimed in claim 1.
4. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor, performs the steps of the method of impedance matching of windings of a four-winding induction filter transformer according to claim 1.
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| CN105391069A (en) * | 2015-11-09 | 2016-03-09 | 国家电网公司 | Mathematic model of four-winding induction filtering transformer and equivalent circuit thereof |
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| CN108614949A (en) * | 2018-05-17 | 2018-10-02 | 湖南大学 | A kind of transformer integrated regulation and control filtering system harmonic current distribution calculation method |
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| CN105391069A (en) * | 2015-11-09 | 2016-03-09 | 国家电网公司 | Mathematic model of four-winding induction filtering transformer and equivalent circuit thereof |
| CN106324353A (en) * | 2016-08-17 | 2017-01-11 | 国家电网公司 | Inductive filtering converter transformer harmonic wave impedance measurement method and device |
| CN108614949A (en) * | 2018-05-17 | 2018-10-02 | 湖南大学 | A kind of transformer integrated regulation and control filtering system harmonic current distribution calculation method |
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