Single-phase multi-winding transformer electromagnetic transient modeling simulation method

Abstract

Embodiments of the present application provide a single-phase multi-winding transformer electromagnetic transient modeling simulation method, relating to the technical field of transformers. The method comprises: S1: constructing a complete electromagnetic transient simulation model of a single-phase N-winding transformer by setting the number of windings N, and simulating the saturation characteristics of the transformer by injecting current into the transformer port; S2: constructing an expression of the electromagnetic transient simulation model of the single-phase multi-winding transformer; S3: constructing a calculation formula of the injected current I s (t) of the transformer port; and S4: performing electromagnetic transient simulation of the single-phase multi-winding transformer. The method can improve the dynamic characteristics and numerical stability of the model.

Description

Technical Field

[0001] This invention relates to the field of transformer technology, and more specifically, to a method for electromagnetic transient modeling and simulation of a single-phase multi-winding transformer. Background Technology

[0002] The equivalent circuit diagram of the electromagnetic transient model of an existing transformer is as follows: Figure 1 As shown, the electromagnetic transient model of a single-phase two-winding transformer includes two mutually coupled windings, and the voltages of these windings can be expressed as:

[0003]

[0004] In the formula, v1 and v2 are the voltages of winding 1 and winding 2, respectively, and L 11 and L 22 These are the self-inductances of winding 1 and winding 2, respectively, L 12 and L 21 These refer to the mutual inductance between windings. Since mutual coupling is mutual, therefore, L 12 and L 21 equal.

[0005] To determine the current, we can transform the above equation to obtain:

[0006]

[0007] In the formula, i1 and i2 are the currents of winding 1 and winding 2, respectively.

[0008] Expanding the above equation, we get:

[0009]

[0010] Using the trapezoidal integral, and rearranging it into the form of the sum of historical and instantaneous terms:

[0011]

[0012] Among them, I h1 (t-Δt) represents the historical current of winding 1 at time (t-Δt):

[0013]

[0014] Similarly, i2(t) can also be expressed in a similar way, and the models represented by these equations are as follows: Figure 2 As shown.

[0015] In summary, the traditional electromagnetic transient model of a single-phase transformer discretizes the single-phase transformer, gives a pre-set step size Δt, and then solves the node voltage equation step by step. Within each solution step, the branch elements are described by the functional relationship between DC current and node voltage.

[0016] Thus, the traditional electromagnetic transient modeling method for single-phase transformers does not consider the transformer's saturation characteristics and core losses. Furthermore, for multi-winding transformer models, a new model needs to be rebuilt for each additional winding, limiting flexibility. Summary of the Invention

[0017] The present invention aims to provide an electromagnetic transient modeling and simulation method for single-phase multi-winding transformers, which can improve the dynamic characteristics and numerical stability of the model.

[0018] The embodiments of the present invention can be implemented as follows:

[0019] This invention provides a method for electromagnetic transient modeling and simulation of a single-phase multi-winding transformer, the method comprising:

[0020] S1: By setting the number of windings N, a complete electromagnetic transient simulation model of a single-phase N-winding transformer is constructed, and the saturation characteristics of the transformer are simulated by injecting current into the transformer port.

[0021] S2: Expression for constructing an electromagnetic transient simulation model of a single-phase multi-winding transformer;

[0022] S3: Construct the injected current I at the transformer port s The formula for calculating (t);

[0023] S4: Perform electromagnetic transient simulation of a single-phase multi-winding transformer.

[0024] The beneficial effects of the electromagnetic transient modeling and simulation method for single-phase multi-winding transformers provided in this invention include:

[0025] An improved electromagnetic transient modeling method for traditional single-phase transformers is proposed. By setting the number of windings N, a complete electromagnetic transient model of a single-phase N-winding transformer can be automatically constructed, simulating transformer saturation characteristics by injecting current into the transformer ports. This electromagnetic transient modeling method for single-phase multi-winding transformers is more flexible and accurate than traditional methods, and further improves the model's dynamic characteristics and numerical stability. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is the equivalent circuit of a single-phase, dual-winding transformer.

[0028] Figure 2 This is the discretized equivalent circuit of a two-winding transformer.

[0029] Figure 3 A flowchart of the electromagnetic transient modeling and simulation method for a single-phase multi-winding transformer provided in an embodiment of the present invention;

[0030] Figure 4 The equivalent circuit diagram for the complete electromagnetic transient model of a single-phase N-winding transformer;

[0031] Figure 5 This is a flowchart for electromagnetic transient simulation of a single-phase multi-winding transformer. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0033] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0034] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0035] In the description of this invention, it should be noted that if terms such as "upper," "lower," "inner," or "outer" are used to indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed, they are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0036] Furthermore, the terms "first" and "second" are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0037] It should be noted that, where there is no conflict, the features in the embodiments of the present invention can be combined with each other.

[0038] Please refer to Figure 3 This embodiment provides a method for electromagnetic transient modeling and simulation of a single-phase multi-winding transformer (hereinafter referred to as the "method"). The method includes the following steps:

[0039] S1: By setting the number of windings N, a complete electromagnetic transient simulation model of a single-phase N-winding transformer (hereinafter referred to as the "model") is constructed, and the saturation characteristics of the transformer are simulated by injecting current into the transformer port.

[0040] Please see Figure 4 In the model, the equivalent circuit of the primary winding is composed of self-inductance, resistance, and leakage reactance connected in series and then connected in parallel with the excitation resistor and the injected current source. The secondary winding is composed of self-inductance, resistance, and leakage reactance connected in series and then connected in parallel with the excitation resistor.

[0041] exist Figure 4 In the middle, L1, L2, L3, L N These are the leakage reactances of windings 1 through N, used to simulate leakage flux; R1, R2, R3, R N These are the resistances of windings 1 through N, used to simulate copper losses; R 1nll R 2nll R 3nll R Nnll These are the excitation resistors for windings 1 through N, used to simulate no-load losses; I s (t) represents the current injected into the transformer port to simulate the saturation characteristics of the transformer.

[0042] S2: Expression for constructing the electromagnetic transient simulation model of a single-phase multi-winding transformer:

[0043] I(t)=GV(t)+AI(t-Δt)+BV(t-Δt)

[0044] Where I(t) and V(t) are the node current and node voltage of the single-phase multi-winding transformer at time t, respectively; I(t-Δt) and V(t-Δt) are the node current and node voltage of the single-phase multi-winding transformer at time (t-Δt), respectively; G is the admittance matrix; and A and B are the coefficient matrices.

[0045] The specific expressions for I(t) and V(t) are as follows:

[0046]

[0047] In the formula, i N (t) represents the current in winding N, i Nnll (t) represents the excitation current of winding N, v N (t) represents the voltage across winding N. The total current in winding N includes the current i in winding N. N (t), excitation current iNnll (t) and injection current I s (t).

[0048] The formulas for calculating matrices G, A, and B are as follows:

[0049]

[0050] Where g and b are both undetermined coefficients, and the injected current I s Solve for G in the formula for calculating (t). nll and B nll These are all excitation admittance matrices, expressed as follows:

[0051]

[0052] G rl B rl and A rl All are coefficient matrices, and the calculation formula is as follows:

[0053]

[0054] Where Δt is the simulation step size, i.e., the time of one time step, E is a diagonal matrix, and L... B -1 To calculate the leakage current reactance matrix for the primary windings 1 to N, R B To calculate the resistance matrix for the primary windings 1 to N, L B -1 With R B The calculation formula is as follows:

[0055]

[0056]

[0057] Wherein, coefficient a ij The calculation formula is as follows:

[0058]

[0059]

[0060] S3: Construct the injected current I at the transformer port s The formula for calculating (t) is:

[0061]

[0062]

[0063]

[0064]

[0065] C = I M (L A I M -Φ M +Φ K )

[0066]

[0067]

[0068] Φ K =KΦ M

[0069]

[0070] In the formula, A, B, C, and D are all undetermined coefficients, and Φ M Let Φ be the flux linkage at the inflection point of the Φ-I curve. K Φ is the maximum flux linkage in the Φ-I curve. S (t) represents the equivalent magnetic flux linkage injected into the current source at time t, I M Let T be the current at the inflection point of the Φ-I curve. mval L is the rated capacity of winding 1. A For air-core reactor, K is the per-unit value of the inflection point voltage, v1(t) is the voltage of winding 1 at time t, and V1 is the effective value of the rated voltage of winding 1.

[0071] All the above formulas together constitute the electromagnetic transient modeling method for single-phase multi-winding transformers. Compared with the traditional electromagnetic transient modeling method for transformers, the model proposed in this embodiment has higher numerical stability and is more in line with the nodal analysis framework used in electromagnetic transient simulation.

[0072] S4: Perform electromagnetic transient simulation of a single-phase multi-winding transformer.

[0073] Please refer to Figure 5 The electromagnetic transient simulation of a single-phase multi-winding transformer includes the following steps:

[0074] S41: Determine the admittance matrix G and the coefficient matrices A and B.

[0075] S42: At the beginning of each time step, solve for the injected current I. s (t), node voltage V(t), update node current I(t), equivalent flux linkage Φ S (t).

[0076] S43: Let t = t + Δt.

[0077] S44: Determine if t > t end , where tend This is the deadline.

[0078] If t > t end The simulation ends when t ≤ t. end If so, then return to execute S42.

[0079] The beneficial effects of the electromagnetic transient modeling method for single-phase multi-winding transformers provided in this embodiment include:

[0080] The proposed electromagnetic transient modeling method for single-phase multi-winding transformers considers the transformer's saturation characteristics and core losses, thus ensuring stable simulation of the transformer and improving the calculation accuracy of traditional models. Furthermore, the electromagnetic transient modeling structure for single-phase multi-winding transformers is easy to implement, highly flexible, and expands the application scenarios of transformer components in electromagnetic transient simulation.

[0081] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for electromagnetic transient modeling and simulation of a single-phase multi-winding transformer, characterized in that, The method includes: S1: By setting the number of windings N, a complete electromagnetic transient simulation model of a single-phase N-winding transformer is constructed, and the saturation characteristics of the transformer are simulated by injecting current into the transformer port. S2: Expression for constructing an electromagnetic transient simulation model of a single-phase multi-winding transformer; S3: Construct the injected current I at the transformer port s The formula for calculating (t); S4: Perform electromagnetic transient simulation of a single-phase multi-winding transformer; In S2, the expression for the electromagnetic transient simulation model of the single-phase multi-winding transformer is as follows: Where I(t) and V(t) are the node current and node voltage of the single-phase multi-winding transformer at time t, respectively, and I(t-Δt) and V(t-Δt) are the node current and node voltage of the single-phase multi-winding transformer at time (t-Δt), respectively. Let be the admittance matrix. and It is a coefficient matrix; The expressions for I(t) and V(t) are as follows: In the formula, i N (t) represents the current in winding N, i Nnll (t) represents the excitation current of winding N, v N (t) represents the voltage of winding N; In S2, the formulas for calculating G, A, and B are as follows: Where g and b are both undetermined coefficients, and the injected current I s Solve for G in the formula for calculating (t). nll and B nll All are excitation admittance matrices, G rl B rl and A rl Both are coefficient matrices; In S2, G nll and B nll The expression is as follows: In the formula, R 1nll R 2nll R 3nll R Nnll These are the excitation resistors for windings 1 to N, used to simulate no-load losses; In S2, G rl B rl and A rl The calculation formula is as follows: Where Δt is the simulation step size, i.e., the time of one time step, E is a diagonal matrix, and L... B -1 To calculate the leakage current reactance matrix for the primary windings 1~N, R B This is the resistance matrix converted to the primary winding 1~N; In S3, the injected current I at the transformer port s The formula for calculating (t) is: In the formula, A, B, C, D, g, and b are all undetermined coefficients, and Φ K Φ is the maximum flux linkage in the Φ-I curve. S For the equivalent magnetic flux of the injected current source, L A V is the air-core reactor, and v1(t) is the voltage of winding 1 at time t.

2. The electromagnetic transient modeling and simulation method for a single-phase multi-winding transformer according to claim 1, characterized in that, In S1, the equivalent circuit of the primary winding in the electromagnetic transient simulation model is composed of self-inductance, resistance, and leakage reactance connected in series and then connected in parallel with the excitation resistor and the injected current source. The secondary winding is composed of self-inductance, resistance, and leakage reactance connected in series and then connected in parallel with the excitation resistor.

3. The electromagnetic transient modeling and simulation method for a single-phase multi-winding transformer according to claim 1, characterized in that, S4 include: S41: Determine the admittance matrix G and the coefficient matrices A and B; S42: At the beginning of each time step, solve for the injected current I. s (t), node voltage V(t), update node current I(t), equivalent flux linkage Φ S (t); S43: Let t = t + Δt; S44: Determine if t > t end , where t end The deadline; If t > t end The simulation ends when t ≤ t. end If so, then return to execute S42.

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