A transformerless model of large power grid dc bias risk assessment method

Abstract

The present application relates to DC bias risk assessment technology, specifically relates to a kind of transformerless model large-scale power grid DC bias risk assessment method, including obtaining the latitude and longitude information and grounding resistance R i Of n power stations, i=1, …,n Information, obtains n×n order substation grounding conductance matrix [Y gg ]:L i Line resistance information i=1, …,l is sorted, and l×l order bus-line conductance matrix [Y bb ]:DC current distribution modeling without transformer is carried out;DC current distribution without transformer is solved;When obtaining [I ac ] data from power grid, the risk of DC bias is determined according to the specific transformer parameters.The method greatly reduces the calculation scale and complexity of DC bias risk assessment model, can form the calculation result of DC current distribution in priority without considering the specific parameters of transformer, and realizes the DC bias risk assessment of transformer by substituting the calculation result into the specific transformer model.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of direct current bias risk assessment, and particularly relates to a transformerless model large power grid direct current bias risk assessment method. BACKGROUND

[0002] Transformer direct current bias risk is a new type of electromagnetic compatibility problem after large-scale application of direct current transmission. Short circuit fault is inevitable in direct current transmission, and after the fault, monopole blocking operation is usually adopted. At this time, the load current will directly pass through the direct current grounding electrode into the ground, resulting in direct current intrusion problem of the alternating current power grid around the direct current grounding electrode. Due to the existence of direct current in the power grid, the transformer core will be saturated. Actual operation shows that even if only a few A of direct current flows through the transformer winding, it is enough to cause the phenomenon of core saturation of the transformer. In the running condition, the core of the transformer is in the working state of symmetrical positive and negative half cycle magnetic density. Once the core saturation occurs, the working magnetic density of the transformer will deviate to one side, thereby causing the half cycle excitation current to increase sharply, inducing harmonic, vibration, noise and overheating and other problems. The direct current bias seriously endangers the safe operation of the power system, and also greatly shortens the service life of the transformer. Running experience shows that the power grid is seriously endangered by large-scale direct current bias, and has to adopt the method of installing neutral point grounding capacitor to manage the direct current bias risk, which consumes a lot of manpower and material resources.

[0003] The root cause of the wide range of power grid direct current bias harm caused by the direct current grounding electrode lies in the uneven ground potential distribution caused by the direct current grounding electrode. The specific performance of the power grid direct current bias harm is that the power grid is connected with substations far away from each other through transmission lines, and the neutral point of the high-voltage transformer in the substation is directly grounded; a mutual current channel is formed between the ground and the power grid, and part of the direct current of the direct current transmission will be "attracted" from the ground to the power system; the direct current flows through the transformer winding, causing the core of the transformer to be saturated, thereby causing the half cycle saturation phenomenon of the transformer excitation, that is, the direct current bias harm.

[0004] The direct current bias risk of large power grid needs to be assessed by means of the direct current distribution field-circuit coupling model of the power grid. Specifically, the node voltage analysis method of the direct current distribution field-circuit coupling model can be written as follows:

[0005] [F]=[Y][V] (1)

[0006] Wherein, [F] is the current injection matrix of the nodes of the power grid, [Y] is the node conductance matrix, and [V] is the node voltage column vector:

[0007]

[0008] Wherein, [V b ] is the bus node voltage column vector, [Vn ] is the column vector of bus node voltage, [V g ] is the column vector of substation grounding node voltage. The matrix relationship of the three with the column vector of node voltage [V] is:

[0009] [V b ] = [H b ][V] (3)

[0010] [V n ] = [H n ][V] (4)

[0011] [V g ] = [H g ][V] (5) Wherein, [H b ] is the association matrix of bus node voltage column vector and node voltage column vector, [H n ] is the association matrix of transformer neutral point node voltage column vector and node voltage column vector, [H g ] is the association matrix of substation grounding node voltage column vector and node voltage column vector.

[0012] In formula (1), the node conductance matrix of the node voltage analysis model of direct current distribution can be written as the following form:

[0013]

[0014] Wherein, [Y bb ] is the conductance matrix between bus nodes, which is the branch conductance of line acting on bus nodes; [Y bn ] is the conductance matrix between bus nodes and transformer neutral point nodes, [Y nb ] = [Y bn ], which is the branch conductance of transformer winding acting on bus nodes; [Y bg ] = [Y gb ] = 0, which is that the bus and the substation grounding node are electrically insulated; [Y nn ] is the conductance matrix between transformer neutral point nodes, which is the branch conductance of transformer winding acting on transformer neutral point nodes; [Y ng ] is the conductance matrix between transformer neutral point nodes and substation grounding nodes, [Y ng ] = [Y gn ], which is the branch conductance of transformer winding acting on substation grounding nodes; [Y gg ] is the substation grounding conductance matrix, which is the substation grounding conductance acting on substation grounding nodes.

[0015] In the DC current distribution model of large power grid, the parameters of transformer are difficult to be counted. The types of transformer can be divided into three kinds, which are analyzed as follows.

[0016] (1) Single-phase transformer. The model schematic diagram is shown in Figure 1 . Figure 1 Two substations use single-phase transformer, and the two substations are connected by line. nn ] and [Y bb ] need to add 1 / R t , and the elements of [Y nb ] and [Y bn ] need to add -1 / R t . Since the value of R t is unknown and the value is small (about 0.3 Ω per phase), if there is a significant error in R t , the calculation results of the model will deviate from the actual situation. In addition, since the neutral point of the transformer is directly grounded, the neutral point node of the transformer and the grounding node of the substation are actually the same node, and the model also needs to be merged.

[0017] (2) Ordinary double-winding / three-winding transformer. The model schematic diagram is shown in Figure 2 . Figure 2 The intermediate substation uses ordinary double-winding / three-winding transformer, and the bus is connected to other stations by line. Generally, if there is no DC bias magnetism risk, the substation will implement the operation mode of high-voltage side neutral point direct grounding, low-voltage side neutral point grounding through small resistance or no grounding. Figure 2 The given is another case, that is, the DC bias magnetism suppression mode of transformer neutral point capacitor isolation. [Y nn ] and [Y bb ] need to add 1 / R t , and the elements of [Y nb ] and [Y bn ] need to add -1 / R t . Since the value of R t is unknown and the value is small (about 0.3 Ω per phase), if there is a significant error in R t , the calculation results of the model will deviate from the actual situation. In addition, since the neutral point of the transformer may be directly grounded, in this case, the transformer neutral point node and the grounding node of the substation are actually the same node, and the model also needs to be merged. If the transformer neutral point adopts the neutral point isolation capacitor mode, in this case, the neutral point has no current flowing in / out, and the transformer neutral point node degenerates into an invalid node.

[0018] (3) Autotransformer. The model schematic diagram is shown in Figure 3 .Figure 3 The intermediate substation uses autotransformer, and the bus is connected to other stations through lines. Autotransformer is different from other transformers, which has two directly connected windings, i.e. common winding and series winding. In addition to [Y nn ] and [Y bb ], the corresponding elements need to add 1 / R t , the elements of [Y nb ] and [Y bn ] need to add -1 / R t , [Y nn ] must consider the DC resistance of series winding. Since R t is not clear, and its value is small (about 0.3 Ω / phase), if R t exists obvious error, it will lead to the deviation of the model calculation results from the actual, the modeling error of autotransformer is more serious than other transformers.

[0019] In addition, since the neutral point of autotransformer may take the way of direct grounding, in this case the transformer neutral point node and the substation grounding node are actually the same node, the model also needs to do node merging. If the neutral point of autotransformer takes the way of neutral point direct current capacitor, in this case the neutral point has no current in / out, the transformer neutral point node degenerates into an invalid node.

[0020] Finally, in formula (1), [F] is the node voltage column vector, and the specific expression is

[0021]

[0022] F b = 0 (8)

[0023] F n = 0 (9)

[0024]

[0025]

[0026] In the formula, [F b ] is the bus node injected current column vector, [F n ] is the transformer neutral point node injected current column vector, [F g ] is the substation grounding node injected current column vector, [M] is the mutual resistance matrix between substations, [M dc ] is the mutual resistance matrix between substations and DC grounding electrode, [I g ] is the column vector of substation grounding current, [I dc ] is the column vector of DC grounding electrode grounding current.

[0027] The combined equations (1) to (12) can be used to solve the DC current distribution field-circuit coupling model of the power grid. Currently, there are still some technical difficulties in implementing this model, especially when there is no way to obtain accurate transformer DC network parameters. Summary of the Invention

[0028] In response to the problems existing in the background technology, the present invention provides a method for directly using the topological relationship of the transformer to replace the specific transformer DC network model, thereby realizing the DC bias magnetic risk assessment of large-scale power grids without a transformer DC network model.

[0029] To solve the above technical problems, the present invention adopts the following technical solution: a large-scale power grid DC bias magnetic risk assessment method without a transformer model, comprising the following steps:

[0030] Step 1: Obtain the latitude and longitude information and ground resistance R of n power stations i , i=1,…,n information, calculate the n×n order substation grounding conductivity matrix [Y gg ]:

[0031]

[0032] Among them, diag() represents the vector The diagonal matrix formed;

[0033] If the substation grounding resistance measurement data is collected, there are:

[0034] R i =R iM (13)

[0035] Where R iM Measure the ground resistance data for substations;

[0036] If the substation ground resistance measurement data cannot be collected and the substation soil is considered to be uniform, the following will occur:

[0037]

[0038] Where, ρ i is the uniform soil rate of the substation local area, A is the total area of ​​the grounding grid;

[0039] If the ground resistance measurement data of the substation is not collected, the soil at the substation is considered to be horizontally stratified if:

[0040]

[0041] Where, ρ i0 is the local surface soil rate of the substation, α and β are the complex image size and position of the layered soil, respectively, z iis the buried depth of the grounding grid, ρ1…ρ d are the earth resistivity of each layer, h1…h d-1 are the thickness of each layer of the earth;

[0042] Use the complex mirror method to calculate the following Green's function:

[0043]

[0044] Where r1 is the distance from the substation to the DC grounding electrode, I is the ground current flowing into the substation, z is the buried depth of the substation grounding grid, z0 is the buried depth of the DC grounding electrode, J0 is the first-order zero-order Bessel function, λ is the integral variable, ρ1…ρ d are the earth resistivity of each layer, h1…h d-1 are the thickness of each layer of the earth;

[0045] The complex mirror method is to use the complex mirror fitting formula (17) of the F function to achieve the solution;

[0046]

[0047] Where k is the number of complex images, α and β are the size and position of the complex images respectively; Substituting equation (17) into equation (16) can derive equation (15);

[0048] Step 2: Arrange the line resistance L of the circuit i , i=1,…,l information, find the l×l order bus-line conductance matrix [Y bb ]:

[0049]

[0050] Among them, [A l ] is the correlation matrix between the l×n-order line and busbar; [A l ] The busbar element corresponding to the starting point of the line is -1, the busbar element corresponding to the end point of the line is 1, and the rest of the elements in the same row are 0; [A l ] T For [A l ] transpose operation;

[0051] Step 3: Modeling the DC current distribution without a transformer;

[0052] Step 3.1: Rewrite the DC current distribution field-circuit coupling model as follows:

[0053] [F g ]=([Y bb ]+[Y gg ])[V g ] (19)

[0054] where [F g ] is the column vector of injected current at the grounding nodes of the substation; [V g ] is the column vector of voltage at the grounding nodes of the substation;

[0055] Step 3.2, recalculate [F g ] according to the definition:

[0056]

[0057] where [F g ] is the column vector of injected current at the grounding nodes of the substation;

[0058] Step 3.3, recalculate [V g ] according to the definition:

[0059]

[0060] where [M] is the mutual resistance matrix between the substations, [M dc ] is the mutual resistance matrix between the substations and the DC grounding electrode, [I g ] is the column vector of ground current at the substations, [I dc ] is the column vector of ground current at the DC grounding electrode;

[0061] Step 3.4, calculate [M] according to formula (15):

[0062] The formula for calculating the mutual resistance M(i, j) between the i-th substation and the j-th substation is:

[0063]

[0064] where ρ i0 is the local surface soil resistivity of the i-th substation, ρ j0 is the local surface soil resistivity of the j-th substation, and α and β are the complex mirror size and position of the layered soil, respectively, and r2 is the distance between the i-th substation and the j-th substation;

[0065] Step 3.5, calculate [M dc ] according to formula (15):

[0066]

[0067] where r3 is the distance between the i-th substation and the DC grounding electrode;

[0068] Step 4, solve the DC current distribution without transformer;

[0069] Solve [V g ] by simultaneously solving formulas (12)-(23), and further solve the branch current [Iac ]:

[0070]

[0071] Step 5, when obtaining [I ac ] data from the power grid, the risk of DC bias is determined according to specific transformer parameters:

[0072] (1) Single-phase transformer:

[0073] [I1]=[A1][I ac ] (25) In the formula, [A1] is the correlation matrix of single-phase transformer winding current and branch current;

[0074] (2) Double-winding / three-winding transformer:

[0075] [I 23 ]=[A 23 ][I ac ] (24)

[0076] In the formula, [A 23 ] is the correlation matrix of double-winding / three-winding transformer winding current and branch current;

[0077] (3) Autotransformer:

[0078] [I a ]=[A a ][I ac ] (27)

[0079] In the formula, [A a ] is the correlation matrix of autotransformer winding current and branch current.

[0080] Compared with the prior art, the DC bias risk assessment model of the present application greatly reduces the calculation scale and complexity, can form the calculation result of DC current distribution preferentially without considering the specific parameters of the transformer, and the user can substitute the calculation result into the specific transformer model, so as to completely realize the DC bias risk assessment of the transformer. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 It is a model schematic diagram of a single-phase transformer;

[0082] Figure 2 It is a model schematic diagram of a common double-winding / three-winding transformer;

[0083] Figure 3 It is a model schematic diagram of an autotransformer;

[0084] Figure 4 It is a schematic diagram of a horizontal layered ground structure of an embodiment of the present application;

[0085] Figure 5 The latest geographical information connection diagram of an electric network in 2020 for an embodiment of the present application;

[0086] Figure 6 The line DC current distribution diagram of a 500kV network for an embodiment of the present application;

[0087] Figure 7 The line DC current distribution diagram near the DC pole for an embodiment of the present application. DETAILED DESCRIPTION

[0088] The technical solutions in the embodiments of the present application will be clearly and completely described in combination with the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0089] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0090] The present application will be further described in combination with specific embodiments, but is not limited by the embodiments.

[0091] In the model of a large power grid, the transformer model information cannot be completely and accurately counted. In the embodiment, the topological connection relationship is directly used to replace the transformer model to improve the AC power grid DC current distribution evaluation model, thereby forming a large power grid DC magnetic bias risk evaluation method without transformer model. The evaluation method of the large power grid DC current distribution without transformer model is helpful for large-scale transformer DC magnetic bias risk analysis and management.

[0092] The embodiment is realized by the following technical solutions. A large power grid DC magnetic bias risk evaluation method without transformer model, and the specific steps are as follows:

[0093] S1. Organize the latitude and longitude information and grounding resistance (R i ,i=1,…,n) information of n power stations:

[0094]

[0095] Wherein, [Y gg ] represents an n*n order power station grounding conductance matrix, diag() represents a diagonal matrix composed of a vector .

[0096] For the case with power station grounding resistance measurement data:

[0097] R i = R iM (13)

[0098] where R iM is the substation grounding resistance measurement data.

[0099] If the substation grounding resistance measurement data cannot be collected, and the substation local soil can be considered as homogeneous soil:

[0100]

[0101] where p i is the substation local homogeneous soil rate, and A is the total area of the grounding grid.

[0102] If the substation grounding resistance measurement data cannot be collected, and the substation local soil can be considered as horizontally layered soil:

[0103]

[0104] where p i0 is the substation local surface soil rate, and a and b are the complex image size and position of the layered soil respectively, z i is the burial depth of the grounding grid, p1…p d are the earth resistivity of each layer respectively, and h1…h d-1 are the thickness of each layer of earth respectively. The complex image method is usually used to calculate the Green's function in the following format:

[0105]

[0106] where r1 is the horizontal distance from the substation to the DC pole, I is the ground current flowing into the substation, z is the burial depth of the substation grounding grid, z0 is the burial depth of the DC grounding pole, J0 is the first kind of zero order Bessel function, l is the integral variable, p1…p d are the earth resistivity of each layer respectively, and h1…h d-1 are the thickness of each layer of earth respectively.

[0107] The complex image method is to use the complex image of F function to fit

[0108]

[0109] to realize the solution. In the formula, k is the number of complex images, and a and b are the size and position of the complex image respectively.

[0110] Substitute equation (17) into equation (16) to derive equation (15).

[0111] S2. Organize the line resistance (L i , i = 1, …, l) information of the line:

[0112]

[0113] where [Y bb ] represents an l x l bus-line conductance matrix, [A l ] is an l x n matrix of the association of lines and buses. In [A l ], the bus element corresponding to the start of the line is -1, the bus element corresponding to the end of the line is 1, and the remaining elements in the same row are 0. l T represents the transpose operation of [A l ].

[0114] S3. Perform transformerless DC current distribution modeling.

[0115] wherein the first step is to rewrite the DC current distribution field-circuit coupling model into the following form:

[0116] [F g ] = ([Y bb ] + [Y gg ])[V g ] (19)

[0117] wherein [F g ] is the column vector of the injection current of the grounding node of the substation.

[0118] The second step is to recalculate [F g ] according to the definition:

[0119]

[0120] wherein [F g ] is the column vector of the injection current of the grounding node of the substation.

[0121] The third step is to recalculate [V g ] according to the definition:

[0122]

[0123] wherein [M] is the mutual resistance matrix between the substations, [M dc ] is the mutual resistance matrix between the substations and the DC grounding electrode, [I g ] is the column vector of the grounding current of the substation, and [I dc ] is the column vector of the grounding current of the DC grounding electrode.

[0124] The fourth step is to calculate [M] based on formula (15):

[0125] The calculation formula of the mutual resistance M(i,j) between the i th substation and the j th substation is:

[0126] ​

[0127] where ρ i0 is the local surface soil rate of the i-th substation, ρ j0 is the local surface soil rate of the j-th substation, and α and β are the complex image size and location of the layered soil, respectively, and r2 is the distance between the i-th substation and the j-th substation.

[0128] In the fifth step, [M dc ] is calculated based on formula (15):

[0129]

[0130] where r3 is the distance between the i-th substation and the DC grounding electrode.

[0131] S4. Solve the DC current distribution without transformer.

[0132] Solve [V g ] by simultaneously solving formulae (12)-(23), and further solve the branch current [I ac ] according to the distribution of the node voltage:

[0133]

[0134] S5. After the power grid obtains the [I ac ] data, the risk of DC bias is determined according to the specific transformer parameters:

[0135] (1) Single-phase transformer:

[0136] [I1]=[A1][I ac ] (25) where [A1] is the correlation matrix of the winding current of the single-phase transformer and the branch current.

[0137] (2) Double-winding / three-winding transformer:

[0138] [I 23 ]=[A 23 ][I ac ] (26) where [A 23 ] is the correlation matrix of the winding current of the double-winding / three-winding transformer and the branch current.

[0139] (3) Autotransformer:

[0140] [I a ]=[A a ][I ac ] (27)

[0141] where [A a] is the correlation matrix between the autotransformer winding current and the branch current.

[0142] Example 1

[0143] The geographical wiring diagram of a power grid in 2020 is as follows Figure 5 The model has 197 power stations, including 6 1000kV UHV stations, 169 220kV stations, 22 500kV stations, and 445 lines in and around Hebei.

[0144] When the DC grounding electrode flows into the earth return operating current of 5kA, the DC current distribution of the power grid is calculated using this method. The calculation results of the power station line current around the DC electrode are shown in Figure 6 and Figure 7 ,The calculation results of relevant sites are shown in Table 1 and Table 2.

[0145] Table 1 Calculation results of surface potential

[0146] Power station Distance / km Ground potential / V 5A 55.29 5.218312 5B 31.92 13.21118 5C 66.74 3.742627 5D 65.27 3.890848 5E 130.12 1.379759 5F 31.94 13.19845 5G 67.03 3.714524 5H 69.64 3.477173 2A 30.90 13.88294 2B 12.38 41.70896 2C 30.56 14.11712 2D 23.19 20.82543 2E 22.23 21.99756 2F 24.25 19.62721 2G 33.26 12.39396 2H 35.83 11.00921

[0147] Table 2 Calculation results of line current

[0148] Line (start - end) Method / A Reference algorithm / A 5B - 5A 8.09 8.07 5D - 5B –7.19 –7.22 5C - 5D –2.51 –2.50 5E - 5D –10.45 –10.40 5D - 5F –4.39 –4.40 5H - 5F –15.80 –15.83 5G - 5F –11.52 –11.50 2B - 2A 19.46 19.49 2A - 5A 15.51 15.47 2B - 5A 21.64 21.66 5B - 2C 1.98 1.98 2D - 2C 9.02 9.00 2D - 2F –2.73 –2.75 2E - 2F –0.45 –0.45 2G - 2F –3.93 –3.92 2E - 2G –4.16 –4.17 5F - 2E –15.45 –15.41 2E - 2H 3.32 3.31

[0149] The results in Tables 1 and 2 demonstrate that the simplified method can accurately determine the surface potential distribution and is suitable for calculating DC current distribution in large power grids. Compared with publicly available benchmark methods, the absolute error of the line current calculation results is less than 1A, meeting the engineering application requirements for DC bias magnetic risk assessment and mitigation.

[0150] The above are only preferred embodiments of the present invention and do not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the present invention specification should be included in the protection scope of the present invention.

Claims

1. A transformerless model of large power grid DC bias risk assessment method, characterized in that: The method comprises the following steps: Step 1, obtain the latitude and longitude information and grounding resistance R of n power stations i , i = 1, …, n information, obtain n x n order substation grounding conductance matrix [Y gg ] wherein diag() denotes a diagonal matrix composed of the vector b. If the substation grounding resistance measurement data is collected, then: R i = R iM (13) In the formula, R iM is the substation grounding resistance measurement data; If the substation grounding resistance measurement data is not collected, the substation is considered to be in homogeneous soil, and then: wherein p i is the local uniform soil rate of the substation, A is the total area of the grounding grid; If the substation grounding resistance measurement data is not collected, the substation is considered to be in horizontally layered soil, and then: wherein p i0 is the local surface soil rate of the substation, a and b are the complex mirror size and position of the layered soil, respectively, z i is the burial depth of the grounding grid, p1...p d are the earth resistivity of each layer, respectively, h1...h d-1 are the thickness of each layer of earth, respectively. The following Green's functions are calculated by using the complex mirror image method: In the formula, r1 is the distance from the substation to the DC grounding electrode, I is the ground current flowing into the substation, z is the burial depth of the substation grounding grid, z0 is the burial depth of the DC grounding electrode, J0 is the zero-order Bessel function of the first kind, λ is an integral variable, ρ1…ρ d are the resistivities of the earth of respective layers, h1…h d-1 are the thicknesses of the earth of respective layers; The complex mirror image method is to solve by using the complex mirror image fitting formula (17) of F function; In the formula, k is the number of complex mirror images, and α and β are the size and position of the complex mirror images respectively; the formula (15) can be derived by substituting the formula (17) into the formula (16); Step 2, adjusting the line resistance L of the line i , i = 1,..., l information, l x l order bus-line conductance matrix [Y bb ] is calculated: Wherein, [A l ] is the incidence matrix of the l x n order line and bus; [A l ]The bus element corresponding to the starting point of the line is-1, the bus element corresponding to the terminal of the line is 1, and the remaining elements in the same row are 0;[A l ] T is the transpose operation of [A l ] Step 3, transformerless direct current distribution modeling is performed; Step 3.1, rewrite the direct current distribution field circuit coupling model into the following form: [F g ] = ([Y bb ] + [Y gg ])[V g ] (19) where [F g ] is the substation ground node injected current column vector; [V g ] is the substation ground node voltage column vector; Step 3.2, recalculate [F g ] by definition. In the formula, [F g ] is the substation ground node injected current column vector; Step 3.3, Recalculate [V g ]: where [M] is the mutual resistance matrix between substations, [M dc ] is the mutual resistance matrix between substations and DC grounding electrodes, [I g ] is the ground current column vector of substations, [I dc ] is the ground current column vector of DC grounding electrodes; Step 3.4, calculate [M] according to formula (15): The calculation formula of mutual resistance M(i, j) between the i-th substation and the j-th substation is: wherein ρ i0 is the local surface soil rate of the i-th substation, ρ j0 is the local surface soil rate of the j-th substation, and α and β are the complex mirror size and position of the layered soil, respectively, and r2 is the distance between the i-th substation and the j-th substation. Step 3.5, Calculate [M] from formula (15) dc ]: In the formula, r3 is the distance between the i-th substation and the direct current grounding electrode; Step 4, transformerless direct current distribution solving is performed; Solving equations (12)~(23) simultaneously, we obtain the node voltages [V g ] and further the branch currents [I ac ] according to the distribution of the node voltages. Step 5, after obtaining [I ac ] data from the grid, the risk of DC bias is determined according to the specific transformer parameters: (1) Single-phase transformer: [I1] = [A1][I ac ] (25) In the formula, [A1] is the correlation matrix of single-phase transformer winding current and branch current; (2) Double-winding / three-winding transformer: [I 23 ]=[A 23 ][I ac ] (26) where [A 23 ] is the association matrix of the double / three-winding transformer winding currents and branch currents; (3) Autotransformer: [I a ]=[A a ][I ac ] (27) In the formula, [A a ] is the correlation matrix of the autotransformer winding current and the branch current.

Images