Equivalent Modeling Method of Magnetic Valve Type Controllable Shunt Reactor Based on Magnetic Circuit Decomposition

Abstract

The present invention discloses an equivalent modeling method for a magnetic valve type controllable shunt reactor based on magnetic circuit decomposition, which solves the deficiencies of the prior art and includes the following steps: Step 1, obtain the basic information of the magnetic valve reactor and establish an equivalent magnetic circuit of the magnetically excited reactor; Step 2, write the expressions of the working circuit and the control circuit through the equivalent magnetic circuit of the magnetically excited reactor, and solve the magnetic flux changes of the two core columns and each current quantity; Step 3, obtain an equivalent structure diagram according to the magnetic flux changes of the two core columns and each current quantity, and analyze the equivalent structure relationship according to the equivalent structure diagram; Step 4, perform magnetic circuit decomposition in the equivalent structure diagram, and decompose the magnetic circuit into several magnetic circuit models according to the structure of the magnetic valve reactor; Step 5, analyze the characteristics of each magnetic circuit model and select the corresponding electrical model to equivalent each magnetic circuit model.

Description

Technical Field

[0001] The present invention relates to the field of digital simulation modeling, and particularly to an equivalent modeling method for a magnetic valve type controllable shunt reactor based on magnetic circuit decomposition. Background Art

[0002] The magnetic valve type controllable shunt reactor (MCR), this new type of reactor is favored by the power department because its capacity can be continuously and smoothly adjusted, it can meet the environment where grid parameters change frequently, and it has good economy and high reliability. In the power system, it is used for dynamic reactive power compensation at various voltage levels, and can also be used in the magnetically controlled soft start process of high-voltage motors, automatic arc suppression coils and supporting devices in the power system, electrified railway systems, etc., so it has very great application potential.

[0003] The simplest and most effective method to analyze the dynamic characteristics of a magnetic valve type controllable shunt reactor is to construct an accurate electromagnetic transient model. Different from a transformer, the magnetic circuit structure of an MCR is more complex, with AC-DC hybrid operation, and the iron core works in the saturation region, which determines that it cannot be simply replaced by an equivalent transformer, and there is no ready-made component library in existing simulation software for calling. Currently, the model research on magnetic valve reactors is relatively single. Only an equivalent circuit diagram is obtained based on its working principle, and a simple physical model is built. This model can only study the characteristics of the magnetic valve reactor as a whole externally, but cannot focus on its internal change characteristics, and has great limitations.

[0004] The magnetic circuit decomposition method is a method proposed by relevant scholars for the simulation modeling of ultra-high voltage magnetically controlled shunt reactors. This method analyzes the mathematical model of the magnetically controlled reactor, and based on the idea of magnetic circuit decomposition, according to the different reactor structures, the magnetic circuit is decomposed into several segments, and each segment of the magnetic circuit can be equivalent to a conventional saturated transformer and a saturated reactor. The principle of this modeling method is clear and easy to implement.

[0005] Compared with the ultra-high voltage magnetically controlled reactor, the magnetic valve type controllable shunt reactor has a more complex structure, so the latter's model cannot be directly applied. However, due to the certain similarity in their working principles, therefore, the magnetic valve type controllable shunt reactor can be modeled based on the idea of magnetic circuit decomposition, so as to better study its internal and external characteristics. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings in the prior art and provide an equivalent modeling method for a magnetic valve type controllable shunt reactor based on magnetic circuit decomposition.

[0007] The purpose of the present invention is realized through the following technical solutions:

[0008] An equivalent modeling method for a magnetic valve type controllable shunt reactor based on magnetic circuit decomposition includes the following steps:

[0009] Step 1: Obtain the basic information of the magnetic valve reactor and establish the equivalent magnetic circuit of the magnetic valve reactor.

[0010] Step 2: Write the expressions of the working circuit and the control circuit through the equivalent magnetic circuit of the magnetic valve reactor, and solve the magnetic flux changes and each current quantity of the two core columns.

[0011] Step 3: Obtain the equivalent structure diagram according to the magnetic flux changes and each current quantity of the two core columns, and analyze the equivalent structure relationship according to the equivalent structure diagram.

[0012] Step 4: Conduct magnetic circuit decomposition in the equivalent structure diagram, and decompose the magnetic circuit into several magnetic circuit models according to the structure of the magnetic valve reactor.

[0013] Step 5: Analyze the characteristics of each magnetic circuit model, and select the corresponding electrical model to equivalent each magnetic circuit model.

[0014] Preferably, in step 2, the specific process of writing the expression of the working circuit is as follows:

[0015] First, determine the electromagnetic equation of the magnetic valve reactor, and the electromagnetic equation is used to describe the electromagnetic characteristics of the magnetic valve reactor:

[0016]

[0017] Add the first two equations of the electromagnetic equation, that is, Make a sum to obtain the expression of the working circuit as follows:

[0018]

[0019] The working circuit and the control circuit of the magnetic valve reactor are mutually coupled, and the coupling relationship changes with the trigger angle and time. Considering that the value of δ is very small, the second term on the right side of the above equation can be ignored, and the following formula is obtained:

[0020]

[0021] From the above simplification process, it can be seen that by ignoring δ, the decoupling of the working circuit and the control circuit is realized, thereby simplifying the structure. Analyze and study the working circuit and the control circuit separately, and then use the superposition principle to superimpose the current in the control circuit into the working circuit to realize the equivalence of the two windings.

[0022] Preferably, in step 2, the specific process of writing the expression of the control circuit is as follows:

[0023] Subtract the first two equations of the electromagnetic equation, that is, Make a difference to obtain the expression of the control circuit as follows:

[0024]

[0025] When the magnetic valve reactor is working, a voltage is introduced from the power grid side to the control coil of δN turns to supply power to the control circuit.

[0026] Preferably, the specific content of step 3 is as follows:

[0027] Through the above equivalent derivation of the working circuit and control circuit of the magnetic valve reactor, its equivalent structure diagram can be drawn, and the equivalent structure is as follows:

[0028] For the working circuit, there is

[0029]

[0030] For the control circuit, there is

[0031]

[0032] Parameter description:

[0033]

[0034] Preferably, the specific content of step 4 is as follows:

[0035] Denote the current of each winding branch as i pq , the voltage as u pq , the induced electromotive force as e pq , the leakage inductance as L pq , the resistance as r pq , the number of winding turns as N pq ; the subscript P = 1 of the above variables represents the winding of the left core column, and p = 2 represents the winding of the right core column; the subscript q = 1 corresponds to the working winding, and q = 2 corresponds to the control winding; the magnetic field strength H m , the magnetic flux φ m , the magnetic path length l m The subscript m of represents the magnetic path number. The first magnetic path is the magnetic path of the left core column l 1 part, the second magnetic path is the magnetic path of the right core column l 2 part, the third magnetic path is the magnetic path of the left side post and the left upper and lower yokes l 3 part, the fourth magnetic path is the magnetic path of the right side post and the right upper and lower yokes l 4 part, the fifth magnetic path is the magnetic path of the middle upper yoke and the middle lower yoke (l 5 ) two parts;

[0036] Write the winding voltage equation according to the positive direction of the determined physical quantity as:

[0037]

[0038]

[0039]

[0040]

[0041] Applying Kirchhoff's second law of magnetic circuit to write the node equation as:

[0042] Φ 1 = Φ 3 + Φ 5 (11)

[0043] Φ 4 = Φ 2 + Φ 5 (12)

[0044] Applying Kirchhoff's second law of magnetic circuit to write the node equation as:

[0045] H 1 l 1 + H 3 l 3 = N 11 i 11 + N 12 i 12 (13)

[0046] H 2 l 2 + H 4 l 4 = N 21 i 21 - N 22 i 22 (14)

[0047] H 3 l 3 = H 4 l 4 + H 5 l 5 (15)

[0048] Next, the magnetic circuit decomposition method is used for modeling:

[0049] Split the first magnetic circuit and the third magnetic circuit, and let

[0050] i 12 = i' 12 + i'' 12 (16)

[0051] Then Equation (13) can be split into:

[0052] H 1 l 1 = N 11 i 11 + N12 i′ 12 (17)

[0053] H 3 l 3 =N 12 i″ 12 (18)

[0054] Split the second magnetic circuit and the fourth magnetic circuit, and let

[0055] i 22 =i′ 22 +i″ 22 (19)

[0056] Then Equation (14) can be split into:

[0057] H 2 l 2 =N 21 i 21 -N 22 i′ 22 (20)

[0058] H 4 l 4 =-N 22 i″ 22 (21)

[0059] Equation (15) can be split into:

[0060] H 5 l 5 =N 12 i″ 12 +N 22 i″ 22 (22)

[0061] Through the above process, the magnetic circuit decomposition of the magnetically controlled shunt reactor is completed. The original magnetic circuit is decomposed into five segments, so as to perform equivalence on the original magnetic circuit.

[0062] Preferably, step 5 is specifically as follows: According to the equations (7)-(10) and equations (16)-(22), the magnetically controlled shunt reactor can be split into five parts (T1-T5), where T1 represents the left core column (p) of the reactor core of each phase, T2 represents the right core column (q), T3 represents the left side column and the left upper and lower yokes, T4 represents the right side column and the right upper and lower yokes. The electromagnetic characteristics of the model before and after splitting are the same, and all equations of (7)-(22) are satisfied; only the core saturation and iron loss need to be considered for each segment of the core magnetic circuit.

[0063] The beneficial effects of the present invention are as follows: Based on the idea of magnetic circuit decomposition, an equivalent model of the magnetically controlled shunt reactor is established, overcoming the limitation that the existing model can only simulate the external characteristics. It has the characteristics of clear principle, simple modeling, accurate model, and strong engineering applicability, and is suitable for the electromagnetic transient simulation calculation of power systems containing magnetically controlled shunt reactors. The present invention lays a foundation for analyzing and studying the steady-state and transient conditions of magnetically controlled reactors, and can better represent their electrical characteristics. At the same time, the model has certain advantages in internal fault simulation, especially in turn-to-turn fault simulation, and is a simple and effective modeling method for studying the fault characteristics of magnetically controlled reactors. Brief Description of the Drawings

[0064] Figure 1 is the structural schematic diagram of the magnetically controlled shunt reactor of the present invention;

[0065] Figure 2 is the equivalent structural diagram of the magnetically controlled shunt reactor;

[0066] Figure 3 is the magnetic circuit decomposition diagram of the magnetically controlled shunt reactor;

[0067] Figure 4 is the equivalent five-segment magnetic circuit model diagram of the magnetically controlled shunt reactor. Detailed Embodiment

[0068] The present invention will be further described below with reference to the drawings and embodiments.

[0069] Embodiment:

[0070] An equivalent modeling method for a magnetically controlled shunt reactor based on magnetic circuit decomposition includes the following steps:

[0071] Step 1: Obtain the basic information of the magnetically controlled reactor, as Figure 1 shown, and establish an equivalent magnetic circuit of the magnetically controlled reactor;

[0072] Step 2: Write the expressions of the working circuit and the control circuit through the equivalent magnetic circuit of the magnetically controlled reactor, and solve the magnetic flux changes and each current quantity of the two core columns;

[0073] Step 3: Obtain the equivalent structural diagram according to the magnetic flux changes and each current quantity of the two core columns, and analyze the equivalent structural relationship according to the equivalent structural diagram;

[0074] Step 4: Perform magnetic circuit decomposition in the equivalent structural diagram, and decompose the magnetic circuit into several magnetic circuit models according to the structure of the magnetically controlled reactor;

[0075] Step 5: Analyze the characteristics of each magnetic circuit model, and select the corresponding electrical model to equivalent each magnetic circuit model.

[0076] In the aforesaid Step 2, the specific expression for formulating the working circuit is as follows:

[0077] Firstly, determine the electromagnetic equation of the magnetic valve reactor, which is used to describe the electromagnetic characteristics of the magnetic valve reactor:

[0078]

[0079] Add the first two equations of the electromagnetic equation, that is, add to obtain the following expression for the working circuit:

[0080]

[0081] The working circuit and the control circuit of the magnetic valve reactor are mutually coupled, and the coupling relationship changes with the trigger angle and time. Considering that the value of δ is very small, the second term on the right side of the above equation can be ignored, resulting in the following equation:

[0082]

[0083] As can be seen from the above simplification process, by ignoring δ, the decoupling of the working circuit and the control circuit is achieved, thereby simplifying the structure. Analyze and study the working circuit and the control circuit separately, and then use the superposition principle to superimpose the current in the control circuit into the working circuit to achieve the equivalence of the two windings.

[0084] In the aforesaid Step 2, the specific expression for formulating the control circuit is as follows:

[0085] Subtract the first two equations of the electromagnetic equation, that is, subtract to obtain the following expression for the control circuit:

[0086]

[0087] When the magnetic valve reactor is operating, the control coil of δ turns introduces voltage from the power grid side to supply power to the control circuit

[0088] The aforesaid Step 3 is specifically as follows:

[0089] Through the equivalent derivation of the working circuit and the control circuit of the magnetic valve reactor above, its equivalent structure diagram can be drawn, as Figure 2 shown. The equivalent structure is as described below:

[0090] For the working circuit, there is

[0091]

[0092] For the control circuit, there is

[0093]

[0094] Parameter description:

[0095]

[0096] The specific content of step 4 is as follows:

[0097] The iron core structure of the magnetic valve reactor consists of two iron cores in the middle and yokes on the left and right sides. Coils are wound around the two iron cores in the middle (see Figure 1 ). During normal operation, two parts of current flow through the windings of the magnetic valve reactor. One part is the working (alternating current) current, and the other part is the control (direct current) current. The magnetic circuit of the magnetic valve reactor can be decomposed into an alternating current magnetic circuit and a direct current magnetic circuit. Among them, the alternating current magnetic circuit is generated by the exciting current of the working winding, while the direct current magnetic circuit is generated by the exciting current of the control winding.

[0098] The magnitudes of the alternating magnetic fluxes generated by the working windings in the two iron cores are the same, but the directions are opposite. Therefore, only one iron core column can form a closed magnetic circuit with the adjacent yoke, and no loop will be formed between the two iron core columns; the magnitudes of the direct magnetic fluxes generated by the control windings in the two iron core columns are the same, but the directions are opposite, forming a closed magnetic circuit between the two iron core columns. See the magnetic circuit flow diagram in Figure 1 .

[0099] Through the above, the equivalent structure of the magnetic valve type controllable shunt reactor is established. Next, its magnetic circuit is analyzed to obtain the magnetic circuit decomposition diagram of the magnetic valve type controllable shunt reactor, as shown in Figure 3 .

[0100] Denote the branch currents of each winding as i pq , the voltage as u pq , the induced electromotive force as e pq , the leakage inductance as L pq , the resistance as r pq , and the number of turns of the winding as N pq ; the subscript P = 1 of the above variables represents the winding of the left core column, and p = 2 represents the winding of the right core column; the subscript q = 1 corresponds to the working winding, and q = 2 corresponds to the control winding; the subscript m of the magnetic field strength H m , magnetic flux φ m , and magnetic path length l m represents the magnetic path number. The first magnetic path is the magnetic path of the left core column l 1 part, the second magnetic path is the magnetic path of the right core column l 2 part, the third magnetic path is the magnetic path of the left side post and the left upper and lower yokes l 3 part, the fourth magnetic path is the magnetic path of the right side post and the right upper and lower yokes l 4 part, and the fifth magnetic path is the magnetic path of the middle upper yoke and the middle lower yoke (l 5 );

[0101] Write the winding voltage equation according to the determined positive direction of the physical quantity as follows:

[0102]

[0103]

[0104]

[0105]

[0106] Apply Kirchhoff's second law of the magnetic circuit to write the node equation as follows:

[0107] Φ 1 = Φ 3 + Φ 5 (11)

[0108] Φ 4 = Φ 2 + Φ 5 (12)

[0109] Apply Kirchhoff's second law of the magnetic circuit to write the node equation as follows:

[0110] H 1 l 1 + H 3 l 3 = N 11 i 11 + N 12 i 12 (13)

[0111] H 2 l 2 + H 4 l 4 = N 21 i 21 - N 22 i 22 (14)

[0112] H 3 l 3 = H 4 l 4 + H 5 l 5 (15)

[0113] Next, use the magnetic circuit decomposition method for modeling:

[0114] Split the first magnetic circuit and the third magnetic circuit, and let

[0115] i 12 = i′ 12 + i″ 12 (16)

[0116] Then Equation 13 can be split into:

[0117] H 1 l 1 = N 11 i 11 + N 12 i′ 12 (17)

[0118] H 3 l 3 = N 12 i″ 12 (18)

[0119] Split the second magnetic circuit and the fourth magnetic circuit, and let

[0120] i 22 = i′ 22 + i″ 22 (19

[0121] Then Equation 14 can be split into:

[0122] H 2 l 2 = N 21 i 21 - N 22 i′ 22 (20)

[0123] H 4 l 4 = N 22 i″ 22 (21)

[0124] Equation 15 can be split into:

[0125] H 5 l 5 = N 12 i″ 12 + N 22 i″ 22 (22)

[0126] Through the above process, the magnetic circuit decomposition of the magnetic valve type controllable shunt reactor is completed. The original magnetic circuit is decomposed into five segments, so as to perform equivalence on the original magnetic circuit.

[0127] Such as Figure 4As shown in the figure, the specific steps of Step 5 are as follows: According to the equations (7)-(10) and equations (16)-(22), the magnetic valve type controllable shunt reactor can be split into five parts (T1-T5), where T1 represents the left core column (p) of the reactor core of each phase, T2 represents the right core column (q), T3 represents the left side column and the upper and lower yokes on the left, T4 represents the right side column and the upper and lower yokes on the right. The electromagnetic characteristics of the model before and after splitting are the same and satisfy all the equations of (7)-(22); for each section of the core magnetic circuit, only the core saturation and iron loss need to be considered.

[0128] In summary, the principle of this modeling method is clear, the modeling is flexible, and the applicable range is wide. The key lies in that there is no need to develop a magnetic valve reactor model separately, which is easy to implement. In addition to being able to accurately simulate the external characteristics of the magnetic valve reactor under various transient and steady-state conditions, it has unique advantages in internal fault simulation, especially in winding turn-to-turn fault simulation, providing necessary technical support for protection configuration and setting.

[0129] The above-described embodiments are only a preferred solution of the present invention and do not impose any form of limitation on the present invention. There are other variations and modifications without exceeding the technical solutions described in the claims.

Claims

1. Equivalent modeling method of magnetically controlled shunt reactor based on magnetic circuit decomposition, Characterized in that, It includes the following steps: Step 1, obtain the basic information of the magnetic valve reactor, and establish the equivalent magnetic circuit of the magnetically energized reactor; Step 2, write the expressions of the working circuit and the control circuit through the equivalent magnetic circuit of the magnetically energized reactor, and solve the magnetic flux changes and various current quantities of the two core columns; Step 3, obtain the equivalent structure diagram according to the magnetic flux changes and various current quantities of the two core columns, and analyze the equivalent structure relationship according to the equivalent structure diagram; Step 4, perform magnetic circuit decomposition in the equivalent structure diagram, and decompose the magnetic circuit into several magnetic circuit models according to the structure of the magnetic valve reactor; Step 5, analyze the characteristics of each magnetic circuit model, and select the corresponding electrical model to equivalent each magnetic circuit model; In the said Step 2, the specific process of writing the expression of the working circuit is: First, determine the electromagnetic equation of the magnetic valve reactor, and the electromagnetic equation is used to describe the electromagnetic characteristics of the magnetic valve reactor: Adding the first two electromagnetic equations, that is, adding yields the following expression for the working circuit: The working circuit and the control circuit of the magnetic valve reactor are mutually coupled, and the coupling relationship changes with the trigger angle and time. Considering that the value of δ is very small, the second term on the right side of the above formula can be ignored, and the following formula is obtained: From the above simplification process, it can be seen that by ignoring δ, the decoupling of the working circuit and the control circuit is realized, thus simplifying the structure. The working circuit and the control circuit are analyzed and studied separately, and then the superposition principle is used to superimpose the current in the control circuit into the working circuit to realize the equivalence of the two windings; In the said Step 2, the specific process of writing the expression of the control circuit is: Subtract the first two electromagnetic equations, that is, Take the difference to obtain the expression of the control loop as follows: When the magnetic valve reactor works, the control coil of δN turns introduces voltage from the grid side to supply power to the control circuit.

2. The equivalent modeling method of magnetically controlled shunt reactor based on magnetic circuit decomposition according to claim 1, Characterized in that, The said Step 3 is specifically: Through the equivalent derivation of the working circuit and the control circuit of the magnetic valve reactor above, its equivalent structure diagram can be made, and the equivalent structure is as follows: For the working circuit, there is For the control circuit, there is Parameter description:

3. The equivalent modeling method of magnetically controlled shunt reactor based on magnetic circuit decomposition according to claim 2, Characterized in that, The said Step 4 is specifically: The current of each winding branch is i pq , voltage is u pq , the induced electromotive force is e pq , the leakage inductance is L pq , the resistance is r pq , the number of winding turns is N pq ; The subscript P=1 of the above variables represents the left core winding, and p=2 represents the right core winding; the subscript q=1 corresponds to the working winding, and q=2 corresponds to the control winding; the magnetic field intensity H m , magnetic flux φ m , magnetic circuit length l m The subscript m indicates the magnetic circuit number. The first magnetic circuit is the left core column l 1 Part of the magnetic circuit, the second magnetic circuit is the right core l 2 Part of the magnetic circuit, the third magnetic circuit is the left side column and the left upper and lower yoke l 3 Part of the magnetic circuit, the fourth magnetic circuit is the right side column and the right upper and lower yoke l 4 The fifth magnetic circuit is the middle upper yoke and the middle lower yoke (l 5 ) Two parts of the magnetic circuit; Write the winding voltage equation according to the positive direction of the determined physical quantity: Apply Kirchhoff's second law of magnetic circuit to write the node equation: Φ 1 = Φ 3 + Φ 5 (11) Φ 4 = Φ 2 + Φ 5 (12) Apply Kirchhoff's second law of magnetic circuit to write the node equation: H 1 l 1 +H 3 l 3 =N 11 i 11 +N 12 i 12 (13) H 2 l 2 +H 4 l 4 =N 21 i 21 -N 22 i 22 (14) H 3 l 3 = H 4 l 4 + H 5 l 5 (15) The following uses the magnetic circuit decomposition method for modeling: Split the first magnetic circuit and the third magnetic circuit, and let i 12 = i' 12 + i'' 12 (16) Then Equation 13 can be split into: H 1 l 1 =N 11 i 11 +N 12 i′ 12 (17) H 3 l 3 = N 12 i″ 12 (18) Split the second magnetic circuit and the fourth magnetic circuit, and let i 22 = i' 22 + i'' 22 (19) Then Equation 14 can be split into: H 2 l 2 =N 21 i 21 -N 22 i′ 22 (20) H 4 l 4 = -N 22 i″ 22 (21) Equation 15 can be split into: H 5 l 5 =N 12 i″ 12 +N 22 i″ 22 (22) Through the above process, the magnetic circuit decomposition of the magnetically controlled shunt reactor is completed, and the original magnetic circuit is decomposed into five segments, so as to equivalent the original magnetic circuit.

4. The equivalent modeling method of magnetically controlled shunt reactor based on magnetic circuit decomposition according to claim 3, Characterized in that, The specific content of step 5 is as follows: According to the equations (7) to (10) and equations (16) to (22), the magnetic valve type controllable shunt reactor can be split into five parts (T1 to T5), where T1 represents the left core column (p) of the reactor core of each phase, T2 represents the right core column (q), T3 represents the left side column and the left upper and lower yokes, T4 represents the right side column and the right upper and lower yokes. The electromagnetic characteristics of the model before and after splitting are the same and satisfy all the equations of (7) to (22); for the magnetic circuits of each section of the iron core, only the iron core saturation and iron loss need to be considered.

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