Method for establishing three-phase model of open YNd connection distribution transformer

Abstract

The application discloses a kind of open YNd connection distribution transformer three-phase model establishing method, according to the relationship of connection group respectively establishing open YNd1 and YNd1, open YNd3 and YNd3, open YNd5 and YNd5, open YNd7 and YNd7, open YNd9 and YNd9, open YNd11 and YNd11, the contact matrix is established under different contact phase condition The contact of voltage (current) correlation matrix of various group open YNd connection transformer and the voltage (current) correlation matrix of corresponding group YNd connection transformer is established, with the help of the node admittance matrix formation method of YNd connection transformer, the node admittance matrix of various group open YNd connection transformer under different contact phase condition can be obtained. In this way, the problem that the node admittance matrix of open YNd connection transformer is manually derived is solved, and the efficiency of open YNd connection transformer three-phase modeling is improved.

Description

Technical Field

[0001] This invention relates to a method for establishing a three-phase model of a transformer, and more particularly to a method for establishing a three-phase model of an open-type YNd-connected distribution transformer used in three-phase power flow calculation of a distribution network. Background Technology

[0002] A power distribution system is a network system that directly distributes electrical energy to end users, consisting of distribution lines, distribution transformers, distribution voltage regulators, distribution switches, distribution capacitors, and distribution loads. Power system analysis first requires establishing appropriate models for each component in the system. Unlike the three-phase symmetrical operation of high-voltage transmission networks, the loads and network of distribution networks may be asymmetrical. Therefore, power flow calculations for distribution networks should consider the characteristics of three-phase asymmetry and perform three-phase power flow calculations. Thus, three-phase power flow calculations for distribution networks require establishing three-phase models of each component of the distribution network.

[0003] In single-phase power flow calculations, three-phase transformers use a single-phase transformer model, where only the transformer turns ratio and impedance are typically considered. However, in three-phase power flow calculations for distribution networks, the transformer model is much more complex. It must consider not only the transformer turns ratio but also the connection method and group of the transformer windings, as well as whether the neutral point is grounded. A three-phase transformer has three windings on both the primary and secondary sides. There are two ways to connect the beginning and end of these three-phase windings and extend them to the three-phase starting points: one is to connect one end of each of the three-phase windings together and extend the other end, called a star connection; the other is to connect the beginning of one phase winding to the end of another phase winding in sequence to form a triangle, called a delta connection.

[0004] The primary and secondary windings of a three-phase transformer can be connected in either a star or delta configuration. National standards stipulate that when the windings are connected in a star configuration, they are labeled Y (primary winding) and y (secondary winding); when the neutral point is led out, they are labeled YN or yn. When the windings are connected in a delta configuration, they are labeled D (primary winding) and d (secondary winding). The connection group designation of a three-phase transformer is represented by the clock sequence number of the phase difference. The new national standard uses the phase difference of the corresponding phase voltage phasors of the primary and secondary sides to determine the connection group. The primary phase voltage phasor is used as a reference to point to clock 0, and the clock point pointed to by the corresponding secondary phase voltage phasor is the connection group designation of the three-phase transformer. The virtual neutral point of the delta configuration is the center of the delta. When the primary and secondary sides of a three-phase transformer are connected in the manner of Yy, YNy, Yyn, YNyn, Dd, the even-numbered connection points are 0, 2, 4, 6, 8, and 10; when the primary and secondary sides are connected in the manner of Yd, YNd, Dy, Dyn, the odd-numbered connection points are 1, 3, 5, 7, 9, and 11. This results in 54 possible transformer connection groups.

[0005] When modeling a three-phase transformer, considering that the voltage change is small during normal operation, the power consumption of the excitation circuit also changes little and can be combined with the load power for unified consideration. Therefore, the excitation circuit is generally not included in the modeling of a three-phase transformer.

[0006] In a power transmission network, because the three-phase loads and the network are symmetrical, the voltage (or current) at all points in the transmission system is also symmetrical. That is, the magnitudes of the three-phase voltages (or currents) are equal, the phase difference between any two phases is 120°, phase B lags phase A by 120°, and phase C lags phase B by 120°. During analysis and calculation, the voltage (or current) of a single phase (e.g., phase A) can be calculated using a single-phase equivalent circuit, and the voltages (or currents) of the other two phases can be directly calculated based on the symmetry. In a single-phase equivalent circuit, the three-phase transformer model only includes the transformer turns ratio and equivalent impedance.

[0007] In power distribution networks, due to the asymmetry of three-phase loads and the network, the voltage (or current) at various points in the distribution system is also not symmetrical. Therefore, a three-phase circuit model must be used for analysis and calculation. In the three-phase equivalent circuit, the three-phase transformer model must consider not only the transformer turns ratio and equivalent impedance, but also the connection method and group of the primary and secondary windings of the transformer.

[0008] There are two methods for establishing a three-phase transformer model: the symmetrical component method and the correlation matrix method. If the three-phase parameters of the transformer are symmetrical, the symmetrical component method is more convenient; however, if the three-phase parameters are asymmetrical and the three-phase sequence cannot be decoupled, the symmetrical component method becomes very difficult. The correlation matrix method, on the other hand, is independent of whether the three-phase parameters are symmetrical, and the derivation process is simple and convenient, facilitating program implementation. The principle of establishing a three-phase transformer model based on the correlation matrix method will be briefly introduced below.

[0009] Three-phase transformer model as follows Figure 1 As shown, the power consumed by the excitation circuit does not vary significantly and can be combined with the load power for unified consideration. Therefore, the three-phase modeling of a transformer generally does not include the parameter G of the excitation circuit. T Considering only the series admittance Y T Modeling.

[0010] Three-phase transformers typically have a common core, resulting in coupling between the windings. The voltage vector U of the three-phase winding branches of a three-phase transformer is... b and current vector I b The relationship between them can be described by the original admittance matrix of the three-phase transformer, as shown in the following equation:

[0011] I b =Y p U b (1)

[0012] In the formula, It is the column vector of transformer winding branch currents. This is the column vector of transformer winding branch voltages. Subscripts 1, 2, and 3 represent the primary winding, and subscripts 4, 5, and 6 represent the secondary winding. Y p The original admittance matrix of a three-phase transformer is expressed as:

[0013]

[0014] In the formula, the equivalent admittance per phase of the three-phase transformer is:

[0015] y = 1 / z = 1 / (r + jx) (3)

[0016] In the formula, z, r, and x are the equivalent impedance, equivalent resistance, and equivalent leakage reactance of each phase winding of the three-phase transformer, respectively.

[0017] Consider as Figure 2 The model shown is a three-phase transformer with a non-standard turns ratio. The original admittance matrix Y of the three-phase transformer is shown. p Represented as:

[0018]

[0019] In the formula, α0 is the non-standard turns ratio of the primary winding, which is the ratio of the rated voltage of the primary winding to the reference value of the primary phase voltage, and β0 is the non-standard turns ratio of the secondary winding, which is the ratio of the rated voltage of the secondary winding to the reference value of the secondary phase voltage.

[0020] In actual power distribution networks, the non-standard turns ratio of a three-phase transformer with an equivalent star connection is known, and its relationship with the non-standard turns ratio of the three-phase transformer windings is as follows:

[0021] When the primary side is a neutral-grounded star connection or a neutral-ungrounded star connection, it is as follows:

[0022] α0=α (5)

[0023] In the formula, α is the non-standard turns ratio of the primary side of the three-phase transformer with equivalent star connection, and is the ratio of the rated value of the primary phase voltage to the reference value of the primary phase voltage.

[0024] When the original side is a triangle, it is:

[0025]

[0026] When the secondary side is a neutral-grounded star connection or a neutral-ungrounded star connection, it is as follows:

[0027] β0=β (7)

[0028] In the formula, β is the non-standard turns ratio of the equivalent star connection of the secondary side of the three-phase transformer, which is the ratio of the rated value of the secondary phase voltage to the reference value of the secondary phase voltage.

[0029] When the secondary side is a triangle connection, it is:

[0030]

[0031] Power flow calculations use node voltage U n and node injection current I n This reflects the node voltage U at each end of the three-phase transformer. n and node injection current I n The relationship is as follows:

[0032] I n =Y Tn U n (9)

[0033] In the formula, It is the column vector of nodal injection currents at each end of a three-phase transformer. This is the column vector of node voltages at each terminal of a three-phase transformer. Subscripts A, B, and C represent the nodes connected to the primary winding, and subscripts a, b, and c represent the nodes connected to the secondary winding. Tn It is the nodal admittance matrix of a three-phase transformer.

[0034] In equation (1), the admittance matrix Y of the three-phase transformer p It reflects the three-phase branch voltage U inside the three-phase transformer. b and branch current I b The admittance matrix of the relationship between them, through Y p The connection relationship with the three-phase transformer can be used to derive the node voltage U, which reflects the values ​​at each terminal of the three-phase transformer. n and node injection current I n The nodal admittance matrix Y of the relationship between them Tn .

[0035] Let the branch voltage of the three-phase transformer be U. b With node voltage U n The relationship between them is:

[0036] U b =CU n (10)

[0037] In the formula, C is the branch voltage U b With node voltage U n The correlation matrix is ​​called the voltage correlation matrix.

[0038] Considering the branch current I under normal circumstances b With node injection current I nThe current correlation matrix G is the transpose of the voltage correlation matrix C. Therefore, the nodal admittance matrix can be obtained from the original admittance matrix as follows:

[0039] Y Tn =C T Y p C (11)

[0040] In the formula, the superscript T denotes the transpose of the matrix.

[0041] There are 96 possible connection groups for three-phase transformers, with more than a dozen being common. It has been proven that the node admittance matrix of three-phase transformers within the same connection group is identical. There are 9 possible connections between the primary and secondary sides of the transformer: YNyn, YNy, YNd, Yyn, Yy, Yd, Dyn, Dy, and Dd. Each combination has 6 group designations, totaling 54 connection groups, which is quite a lot. Developing a three-phase power flow calculation program for a distribution network requires considering all these combinations, writing out their respective correlation matrices, and deriving the models for these 54 combinations—that is, writing out the formulas for the transformer node admittance matrices for these combinations. Manually deriving so many types of three-phase transformer models is tedious and prone to errors. Relevant literature only provides node admittance matrices for a portion of typical connection groups, and many of these contain errors. To design a complete three-phase power flow calculation program for a distribution network, the programmer needs to manually derive the three-phase models of transformers for each of these connection groups, which is very inconvenient and makes it difficult to guarantee the correctness of the derived transformer three-phase models. Therefore, Chinese patent CN202010071839.X proposes a method for establishing a three-phase transformer model based on the correlation matrix considering the neutral point, which simplifies the modeling process and includes the following steps:

[0042] A. Read the transformer primary winding connection method k1, secondary winding connection method k2, and transformer connection group number k3;

[0043] The primary winding connection method (k1) of a three-phase transformer has three types: YN, Y, and D. The secondary winding connection method (k2) has three types: yn, y, and d. The transformer connection group number (k3) is related to the primary and secondary winding connection combinations. When the primary and secondary winding connections are YNyn, YNy, Yyn, Yy, and Dd, k3 is 0, 2, 4, 6, 8, and 10. When the primary and secondary winding connections are YNd, Yd, Dyn, and Dy, k3 is 1, 3, 5, 7, 9, and 11.

[0044] B. Establish voltage correlation sub-matrices (12)-(14) reflecting the relationship between the branch voltage and node voltage of the three-phase transformer windings, as well as a constant matrix and a transformation matrix;

[0045] The voltage correlation sub-matrices are as follows:

[0046]

[0047]

[0048]

[0049] In the formula, C YN For the voltage correlation submatrix when the primary / secondary windings are connected in a grounded star configuration with clock 0, C Y For the voltage correlation submatrix when the primary / secondary windings are connected in an ungrounded star configuration with clock 0, C D The voltage correlation submatrix is ​​used when the primary / secondary windings are connected in a delta configuration with clock 1.

[0050] like Figure 3 As shown, the definitions of the primary and secondary clocks are as follows: Assuming the primary windings AX, BY, and CZ of a three-phase transformer are arranged from left to right and the positive polarity is on sides A, B, and C, the transformer connection group number when the primary winding is connected in a star configuration is defined as the secondary clock. Under the above assumptions, if terminals X, Y, and Z of the primary winding are connected together in a star configuration, the primary clock is defined as 0; if the primary winding is connected in a delta configuration, with terminals A and Z, B and X, and C and Y connected respectively, the primary clock is defined as 1. The transformer group number is the difference between the secondary clock and the primary clock. The secondary clock is the sum of the transformer group number and the primary clock. If the resulting secondary clock is greater than or equal to 12, then 12 is subtracted to obtain the secondary clock.

[0051] A constant matrix is:

[0052] P = [-1 -1 -1] T (15)

[0053] A transformation matrix is ​​as follows:

[0054]

[0055] C. Establish the original admittance matrix Y of the three-phase transformer shown in equation (4). p And according to the connection method of the primary and secondary windings of the three-phase transformer, Y is modified according to formulas (5)-(8). p The transformation ratio of the array;

[0056] D. Let h = 0, m = 3, n = 3;

[0057] E. Determine if k1 is YN. If it is, proceed to step I.

[0058] F. Determine if k1 is Y. If it is Y, proceed to step H.

[0059] G, C p =CD h=1, proceed to step J;

[0060] H, let C p =C Y m=4, proceed to step J;

[0061] I. Let C p =C YN ;

[0062] J. Determine if k2 is d. If not, proceed to step L.

[0063] K, let C s0 =C D Proceed to step M;

[0064] L, let C s0 =C YN ;

[0065] M. Determine the secondary clock k0 based on the transformer connection group number k3 and the primary clock h.

[0066] k0 = mod(k3 + h, 12) (17)

[0067] In the formula, mod is the Matlab remainder function, which obtains the remainder after k3+h is divided by 12;

[0068] N, calculate q using the following formula;

[0069] q = floor(k0 / 2) (18)

[0070] In the formula, floor is the Matlab floor function, which obtains the integer part of k0 divided by 2;

[0071] O, let C s1 =C s0 T q ;

[0072] P. Determine if k2 is y. If not, proceed to step R.

[0073] Q, let C s =[C s1 P], n=4, proceed to step S;

[0074] R, let C s =C s1 ;

[0075] S. The voltage correlation matrix C of the transformer is formed according to the sub-matrices of the transformer voltage correlation matrix using equation (19);

[0076]

[0077] In the formula, O 3×m It is a 3×m zero matrix;

[0078] T, based on the original admittance matrix Y p The voltage correlation matrix C is derived from the symbolic operation of equation (20) to form the nodal admittance matrix Y of the three-phase transformer. Tn .

[0079] Y Tn =C T Y p C (20)

[0080] Chinese patent CN202010071839.X can automatically derive the nodal admittance matrix model of a three-phase transformer, solving the problem of time-consuming and laborious manual derivation of the three-phase model of a distribution transformer and improving the efficiency of obtaining the three-phase model. However, this patented method does not consider the three-phase modeling problem of open YNd connected distribution transformers, resulting in the need for manual derivation of the three-phase modeling of open YNd connected distribution transformers, which affects the efficiency of three-phase modeling of open YNd connected distribution transformers. Summary of the Invention

[0081] To address the aforementioned problems in existing technologies, this invention proposes a method for establishing a three-phase model of an open-type YNd-connected distribution transformer. This invention seeks the relationship between the node admittance matrix and the node admittance matrix of the open-type YNd-connected distribution transformer, and proposes a method for establishing a three-phase model of the open-type YNd-connected distribution transformer.

[0082] The basic idea of ​​this invention is as follows: Based on the connection groups, establish the relationships between open YNd1 and YNd1, open YNd3 and YNd3, open YNd5 and YNd5, open YNd7 and YNd7, open YNd9 and YNd9, and open YNd11 and YNd11 respectively. Then, using the nodal admittance matrix formation method for YNd-connected distribution transformers, the nodal admittance matrix of the open YNd-connected distribution transformer can be obtained. This solves the problem that manually deriving the nodal admittance matrix of open YNd-connected distribution transformers is cumbersome and prone to errors.

[0083] The technical solution of the present invention is as follows: A method for establishing a three-phase model of an open-type YNd-connected distribution transformer, comprising the following steps:

[0084] A. Read the transformer primary winding connection method k1, secondary winding connection method k2, transformer connection group number k3, and open phase sequence number o of the open YNd transformer;

[0085] The primary winding connection method (k1) of a three-phase transformer has three types: YN, Y, and D. The secondary winding connection method (k2) has three types: yn, y, and d. The transformer connection group designation (k3) is related to the primary and secondary winding connection combinations. When the primary and secondary winding connections are YNyn, YNy, Yyn, Yy, and Dd, k3 is 0, 2, 4, 6, 8, and 10. When the primary and secondary winding connections are YNd, Yd, Dyn, and Dy, k3 is 1, 3, 5, 7, 9, and 11. The value of the disconnected phase sequence number (o) of an open YNd transformer is 1, 2, and 3, representing the disconnection of phases A, B, and C, respectively.

[0086] B. Establish two voltage correlation sub-matrices that reflect the relationship between the branch voltages and node voltages of a three-phase transformer winding. C. YN C D It also includes a constant matrix P, a transformation matrix T, and an opening matrix E;

[0087] The voltage correlation sub-matrices are as follows:

[0088]

[0089]

[0090] In the formula, C YN For the voltage correlation submatrix when the primary / secondary windings are connected in a grounded star configuration with clock 0, C D The voltage correlation submatrix is ​​used when the primary / secondary windings are connected in a delta configuration with clock 1.

[0091] The constant matrix is:

[0092] P = [-1 -1 -1] T (twenty three)

[0093] The transformation matrix is:

[0094]

[0095] The breaking matrix is:

[0096]

[0097] C. Establish the original admittance matrix Y of the three-phase transformer shown in equation (4). p And according to the connection method of the primary and secondary windings of the three-phase transformer, Y is modified according to formulas (5)-(8). p Matrix scaling;

[0098] D. Let h = 0, m = 3, n = 3;

[0099] E. Determine if k1 is YN. If it is, proceed to step I.

[0100] F. Determine if k1 is Y. If it is Y, proceed to step H.

[0101] G, let C p =C D h=1, proceed to step J;

[0102] H, let C p =[C YN P], m=4, proceed to step J;

[0103] I. Let C p =C YN ;

[0104] J. Determine if k2 is d. If not, proceed to step L.

[0105] K, let C s0 =C D Proceed to step M;

[0106] L, let C s0 =C YN ;

[0107] M. Determine if o belongs to the set {1,2,3}. If not, proceed to step N. If o belongs to the set {1,2,3}, then let the diagonal element E of matrix E be... oo =0, let C p =E·C p C s0 =E·C s0 ;

[0108] N. Determine the secondary clock k0 based on the transformer connection group number k3 and the primary clock h:

[0109] k0 = mod(k3 + h, 12) (26)

[0110] In the formula, mod is the Matlab remainder function, which obtains the remainder after k3+h is divided by 12;

[0111] O. Find q using the following formula;

[0112] q = floor(k0 / 2) (27)

[0113] In the formula, floor is the Matlab floor function, which obtains the integer part of k0 divided by 2;

[0114] P, let C s1 =C s0 T q ;

[0115] Q. Determine if k2 is y. If not, proceed to step S.

[0116] R, let C s =[C s1 P], n=4, proceed to step T;

[0117] S, let C s =C s1 ;

[0118] T, The voltage correlation matrix C of the transformer is formed according to the sub-matrices of the transformer voltage correlation matrix using equation (28);

[0119]

[0120] In the formula, O 3×m It is a 3×m zero matrix;

[0121] U, based on the original admittance matrix Y p The voltage correlation matrix C is derived from the symbolic operation of equation (29) to form the nodal admittance matrix Y of the three-phase transformer. Tn :

[0122] Y Tn =C T Y p C (29)

[0123] Compared with the prior art, the present invention has the following beneficial effects:

[0124] This invention establishes a relationship between the voltage (current) correlation matrix of an open-type YNd-connected transformer and the voltage (current) correlation matrix of a YNd-connected transformer. By utilizing the method for forming the nodal admittance matrix of a YNd-connected transformer, the nodal admittance matrix of the open-type YNd-connected distribution transformer can be obtained. This solves the problem that manually deriving the nodal admittance matrix of an open-type YNd-connected distribution transformer is tedious and prone to errors, thus improving the efficiency of three-phase modeling of open-type YNd-connected distribution transformers. Attached Figure Description

[0125] This invention has a total of appendices Figure 7 Zhang, of which:

[0126] Figure 1 This is a three-phase model diagram of a three-phase transformer.

[0127] Figure 2 This is a single-phase model diagram considering the non-standard turns ratio of a three-phase transformer.

[0128] Figure 3 This is the wiring diagram defining the primary clock of the transformer.

[0129] Figure 4 This is the wiring diagram for an IEEE 4-node system.

[0130] Figure 5This is a diagram showing the connection diagrams of different groups of open YNd-connected three-phase transformers and their corresponding YNd-connected three-phase transformers when phase C is disconnected (dashed lines indicate that phase is disconnected in the open YNd-connected transformer).

[0131] Figure 6 This is a flowchart of existing technology.

[0132] Figure 7 This is a flowchart of the present invention. Detailed Implementation

[0133] The following description, with reference to the accompanying drawings, uses an open YNd1 connected three-phase transformer as an example to further illustrate the derivation process of the transformer three-phase model of the present invention. The derived transformer model is then applied to the IEEE 4-node distribution network system for power flow calculation to verify the correctness of the established model.

[0134] according to Figure 7 The method shown is for establishing a three-phase model of an open YNd-connected distribution transformer to obtain... Figure 5 (a) shows the three-phase model of the open YNd1 transformer. The input transformer primary winding connection k1 is YN; the secondary winding connection k2 is d; the transformer connection group number k3 is 1; and the open / closed phase sequence number o of the open YNd transformer is 3.

[0135] Establish the initial admittance matrix Y of the three-phase transformer p And modify Y according to the connection method of the primary and secondary windings of the three-phase transformer. p The transformation ratio of the matrix yields:

[0136]

[0137] The voltage correlation submatrix C of the three-phase transformer with YNd1 connection p C s0 as follows:

[0138]

[0139]

[0140] The breaking matrix is:

[0141]

[0142] For a three-phase transformer with YNd1 connection, the primary clock h = 0 and the secondary clock k0 = 1, then q = 0. The voltage correlation matrix C of the three-phase transformer with YNd1 connection is given by the switching matrix E and the voltage correlation matrix C. p C s0 The voltage correlation submatrix C of the open YNd1 connected three-phase transformer is obtained. p C s0 as follows:

[0143]

[0144]

[0145]

[0146] The voltage correlation matrix C and current correlation matrix G of the open YNd1 connected three-phase transformer are obtained as follows:

[0147]

[0148]

[0149] according to Figure 5 (a) It can be seen that the relationship between the transformer winding branch voltage and the node voltage expressed by equation (37) and the relationship between the transformer winding branch current and the node current expressed by equation (38) are correct.

[0150] Finally, the nodal admittance matrix Y of the open YNd1 connected three-phase transformer is obtained. Tn for:

[0151]

[0152] In the formula, y is the equivalent admittance per phase of the three-phase transformer.

[0153] Wiring diagram of IEEE 4-node system as follows Figure 4 As shown, node 1 is a balanced node with a phase voltage amplitude of 7.2kV. The phase angles of phases A, B, and C are 0°, -120°, and 120°, respectively. Power flow calculations are performed using an open-type YNd1 step-down transformer with an unbalanced load. The power flow calculation method is the current deviation type rectangular coordinate Newton method, using per-unit values. The voltage reference value is the rated phase voltage, the power reference value is (100 / 3) MVA, and the convergence accuracy is 0.0001. Due to the singularity of the Jacobian matrix in the power flow calculation, a susceptance of 10 is added to each phase at each node. -6 The capacitance of S is very small. Since the capacitance value is very small, it does not affect the final calculation accuracy. As a comparison, the "Ladder Iterative Technique" method from William H. Kersting's "Distribution System Modeling and Analysis" was used to perform power flow calculations on the same example. This method uses a different power flow calculation method and transformer model than the method of this invention, which can verify the correctness of the transformer model in the method of this invention.

[0154] The calculated results of the voltage amplitude U at each node are shown in Table 1.

[0155] Table 1 Calculation results of voltage amplitude at each node

[0156]

[0157] As shown in Table 1, the calculated values ​​of phase voltage or line voltage at each node in the power flow calculation of the present invention and the comparative method are very similar, all within 0.5V.

[0158] The calculation results of the voltage phase angle δ at each node are shown in Table 2, with the A-phase voltage of node 1 as the reference phasor.

[0159] Table 2 Calculation results of voltage phase angle at each node

[0160]

[0161] As shown in Table 2, the phase angle calculation results of each node phase voltage or line voltage in the power flow calculation of the present invention and the comparative method are very similar, all within 0.01°.

[0162] The calculation results of the current amplitude I of each transmission line branch are shown in Table 3.

[0163] Table 3 Calculation results of current amplitude for each transmission line branch

[0164]

[0165] As shown in Table 3, the calculated current amplitudes of each transmission line branch calculated by the present invention and the comparative method are very similar, all within 0.03A.

[0166] Transmission line branch current phase angle The calculation results are shown in Table 4, with the A-phase voltage of node 1 as the reference phasor.

[0167] Table 4 Calculation results of phase angle of current in each transmission line branch

[0168]

[0169] As shown in Table 4, the phase angle calculation results of the current of each transmission line branch calculated by the present invention and the comparative method are very similar, both being less than 0.001°.

[0170] A comparison between the present invention and the comparative method shows that the calculated results of node voltage and branch current are very similar, indicating that the transformer model of the present invention is correct.

[0171] This invention can be implemented in any MATLAB programming language with symbolic computation capabilities, but it is recommended to use a newer version of the MATLAB language.

Claims

1. A method for establishing a three-phase model of an open-type YNd-connected distribution transformer, characterized in that: Includes the following steps: A. Read the transformer primary winding connection method k1, secondary winding connection method k2, transformer connection group number k3, and open phase sequence number o of the open YNd transformer; The primary winding connection method (k1) of a three-phase transformer has three types: YN, Y, and D. The symbols YN, Y, and D represent the neutral-point grounded star connection, the neutral-point ungrounded star connection, and the delta connection of the primary winding, respectively. The secondary winding connection method (k2) has three types: yn, y, and d. The symbols yn, y, and d represent the neutral-point grounded star connection, the neutral-point ungrounded star connection, and the delta connection of the secondary winding, respectively. The transformer connection group number (k3) is related to the primary and secondary winding connection combinations. When the primary and secondary winding connections are YNyn, YNy, Yyn, Yy, and Dd, k3 is 0, 2, 4, 6, 8, and 10. When the primary and secondary winding connections are YNd, Yd, Dyn, and Dy, k3 is 1, 3, 5, 7, 9, and 11. The value of the disconnected phase sequence number (o) of an open YNd transformer is 1, 2, or 3, where 1, 2, and 3 represent the disconnection of phases A, B, and C, respectively. B. Establish two voltage correlation sub-matrices that reflect the relationship between the branch voltages and node voltages of a three-phase transformer winding. C. YN C D It also includes a constant matrix P, a transformation matrix T, and an opening matrix E; The voltage correlation sub-matrices are as follows: In the formula, C YN For the voltage correlation submatrix when the primary / secondary windings are connected in a grounded star configuration with clock 0, C D The voltage correlation submatrix for the primary / secondary windings when the clock is 1 in a delta connection; The primary and secondary clocks are defined as follows: Assuming the primary windings AX, BY, and CZ of a three-phase transformer are arranged from left to right and the positive polarity is on sides A, B, and C, the transformer connection group number when the primary winding is connected in a star configuration is defined as the secondary clock. Under the above assumptions, if the terminals X, Y, and Z of the primary winding are connected together in a star configuration, the primary clock is defined as 0. If the primary winding is connected in a delta configuration, with terminals A and Z, B and X, and C and Y connected respectively, the primary clock is defined as 1. The transformer group number is the difference between the secondary clock and the primary clock. The secondary clock is the sum of the transformer group number and the primary clock. If the resulting secondary clock is greater than or equal to 12, then 12 is subtracted to obtain the secondary clock. The constant matrix is: P＝[-1 -1 -1] T (3) In the formula, the superscript T denotes the transpose of the matrix; The transformation matrix is: The breaking matrix is: C. Establish the initial admittance matrix Y of the three-phase transformer. p As shown in equation (6), and Y is modified according to equations (8)-(11) based on the connection method of the primary and secondary windings of the three-phase transformer. p Matrix scaling; In the formula, α0 is the non-standard turns ratio of the primary winding, which is the ratio of the rated voltage of the primary winding to the reference value of the primary phase voltage; β0 is the non-standard turns ratio of the secondary winding, which is the ratio of the rated voltage of the secondary winding to the reference value of the secondary phase voltage; and y is the equivalent admittance per phase of the three-phase transformer, expressed as: y = 1 / z = 1 / (r + jx) (7) In the formula, z, r, and x are the equivalent impedance, equivalent resistance, and equivalent leakage reactance of each phase winding of a three-phase transformer, respectively; In actual power distribution networks, the non-standard turns ratio of a three-phase transformer with an equivalent star connection is known, and its relationship with the non-standard turns ratio of the three-phase transformer windings is as follows: When the primary side is a neutral-grounded star connection or a neutral-ungrounded star connection, it is as follows: α0＝α (8) In the formula, α is the non-standard turns ratio of the primary side of the three-phase transformer with equivalent star connection, and is the ratio of the rated value of the primary side phase voltage to the reference value of the primary side phase voltage. When the original side is a triangle, it is: When the secondary side is a neutral-grounded star connection or a neutral-ungrounded star connection, it is as follows: β0＝β (10) In the formula, β is the non-standard turns ratio of the equivalent star connection of the secondary side of the three-phase transformer, which is the ratio of the rated value of the secondary phase voltage to the reference value of the secondary phase voltage. When the secondary side is a triangle connection, it is: D. Let h = 0, m = 3, n = 3; E. Determine if k1 is YN. If it is, proceed to step I. F. Determine if k1 is Y. If it is Y, proceed to step H. G, let C p =C D h=1, proceed to step J; H, let C p =[C YN P], m=4, proceed to step J; I. Let C p =C YN ; J. Determine if k2 is d. If not, proceed to step L. K, let C s0 =C D Proceed to step M; L, let C s0 =C YN ; M. Determine if o belongs to the set {1,2,3}. If not, proceed to step N. If o belongs to the set {1,2,3}, then let the diagonal element E of matrix E be... oo =0, let C p =E·C p C s0 =E·C s0 ; N. Determine the secondary clock k0 based on the transformer connection group number k3 and the primary clock h: k0 = mod(k3 + h, 12) (12) In the formula, mod is the Matlab remainder function, which obtains the remainder after k3+h is divided by 12; O. Find q using the following formula; q = floor(k0 / 2) (13) In the formula, floor is the Matlab floor function, which obtains the integer part of k0 divided by 2; P, let C s1 =C s0 T q ; Q. Determine if k2 is y. If not, proceed to step S. R, let C s =[C s1 P], n=4, proceed to step T; S, let C s =C s1 ; T. Form the voltage correlation matrix C of the transformer based on each submatrix of the transformer voltage correlation matrix; In the formula, O 3×m It is a 3×m zero matrix; U, based on the original admittance matrix Y p The voltage correlation matrix C is used to derive the nodal admittance matrix Y of the three-phase transformer using symbolic operations. Tn : Y Tn =C T Y p C (15) Finish.

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