CN113452007B - Neutral point direct current calculation method for transformer of urban power grid - Google Patents
Neutral point direct current calculation method for transformer of urban power grid Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention discloses a direct current calculation method for a neutral point of a transformer of an urban power grid, which is characterized by respectively establishing direct current resistance network models of the subway and the urban power grid based on topological structures of the subway and the urban power grid, and realizing direct current resistance network model coupling based on the connection relation of the subway and an urban power grid grounding system; and assigning the resistance in the resistance network model by using the related electrical parameters of the subway and the urban power grid, and calculating the node voltage of the model based on the circuit principle so as to calculate and obtain the direct current of the neutral point of the main transformer. The calculation method provided by the invention is based on topological structures and electrical parameters of the metro and urban power grids, takes the metro train position and traction current distribution into consideration, realizes the direct current calculation of the main transformer neutral point, and has important significance for evaluating and identifying the direct current magnetic bias of the main transformer of the urban power grid.
Description
Technical Field
The invention belongs to the field of stable operation of power systems, and particularly relates to a neutral point direct-current calculation method for an urban power grid transformer.
Background
The subway adopts a direct current traction power supply system, and a steel rail is used as a traction backflow path. However, since the rail is not completely insulated from ground, the return current leaks out of the rail due to the rail potential, creating stray currents. Leaked subway stray current enters an urban power grid to cause the phenomenon of main transformer direct current magnetic biasing. At present, a main transformer direct current magnetic biasing phenomenon occurs in a plurality of urban power grids such as Beijing, Guangzhou, Shenzhen and Changsha, and the time for increasing the main transformer direct current magnetic biasing current is consistent with the subway running time. The direct current magnetic biasing phenomenon of the main transformer causes the aggravation of main transformer vibration, the increase of abnormal sound, the increase of harmonic content and the increase of local temperature rise, and the conditions of vibration and shedding of a main transformer insulating part, winding burning loss, protection misoperation and the like are caused in serious conditions, so that the safe and stable operation of an urban power grid is seriously influenced.
At present, the direct current of a main transformer neutral point in a power grid is mainly calculated aiming at the conditions of direct current single-pole grounding or bipolar unbalanced grounding and the like. The direct current grounding electrode is equivalent to a direct current source, the power grid is equivalent to a direct current resistance network, and the voltage and the current of each node of the direct current resistance network are calculated by utilizing the circuit principle to obtain the direct current of the neutral point of the main transformer. However, unlike the dc ground electrode having fixed, e.g., location and determined, ground current, the location and distribution characteristics of stray current leakage in the subway are affected by the train operation conditions, the electrical parameters of the equipment, and the soil resistivity distribution, and cannot be directly equivalent to a current source having a fixed location and amplitude. Meanwhile, unlike the condition that the direct current grounding electrode grounding current invades the urban power grid through the ground, the subway and the urban power grid are distributed in a staggered mode, and the complex grounding conductor provides a low-resistance path for the subway stray current to invade the urban power grid. Therefore, the existing method for calculating the direct current bias current of the main transformer cannot be completely suitable for calculating the direct current distribution of the neutral points of the main transformer of the urban power grid.
Disclosure of Invention
Aiming at the problems, the invention provides a direct current calculation method for a neutral point of an urban power grid transformer, which can realize direct current calculation of the neutral point of a main transformer by considering subway line topology and train operation conditions.
The invention discloses a neutral point direct current calculation method of an urban power grid transformer, which comprises the following steps of:
step 1: the method comprises the steps of obtaining geographic information of an urban subway station, related electrical parameters of a traction system and a backflow system, a train position and traction current, and obtaining geographic information of a transformer substation in an urban power grid, a main wiring diagram of the transformer substation, related electrical parameters of a transformer and a line.
Step 2: and establishing a direct-current resistance network model of the subway and the urban power grid.
And step 3: and (5) assigning model parameters, and calculating the voltage of each node of the direct-current resistance network model of the urban power grid.
And 4, step 4: and establishing an impedance matrix of a bus and a neutral point node of the urban power grid transformer, and calculating the direct current of the neutral point of the main transformer.
Further, step 1 specifically comprises:
s11: recording the total quantity N of subway lines and the quantity of the subway stations containing the traction substation is N1The total number of the subway vehicle sections and the parking lots is n2The number of subway main stations is A, the terminal station of the longest subway line is selected as the origin point, a coordinate system is established,recording the coordinate W ═ W of each subway station1(x1,y1)，w2(x2,y2)，…，wN(xN,yN)]Recording the coordinate B ═ B of the subway main station1(x1,y1)，b2(x2,y2)，…，bA(xA,yA)]Recording the distance L between adjacent subway stations as L1，L2，…，LN-1]The internal resistance r of the traction substation and the DC supply voltage grade of the subway are VrThe direct current resistance r of a single steel rail per kilometer1Per kilometer of rail resistance to earth r2The direct current resistance per kilometer of a contact network, the direct current resistance per kilometer of a subway through ground wire, the direct current resistance per kilometer of a 35kV cable armor, the length of a 35kV electric cable, and the grounding resistance r of a station and a field sectiong1The distance between the station section and the station entering the station section is La＝[l1，l2，…，ln2](ii) a Equivalent resistance r of station steel rail limiting deviceovEquivalent resistance r of unidirectional conducting deviced(ii) a The number of running trains in the subway line is n, the positions of the trains in the subway line and the traction current I of the trains are recordedt＝[I1，I2，…，In]。
S12: recording the total number M of the urban power grid transformer substations and the number M of the neutral point grounding autotransformers1The number of the neutral point grounding three-winding transformers is m2The coordinate D of each transformer substation is ═ D1(x1,y1)，d2(x2,y2)，…，dM(xM,yM)]High voltage winding DC resistance of transformer, medium voltage winding resistance of transformer, DC resistance per kilometer of three-phase transmission line r6The number of loops of the line, the direct current resistance per kilometer of an overhead ground wire, the direct current resistance per kilometer of a three-phase transmission cable core, the number of loops of the transmission cable, the direct current resistance per kilometer of a cable armor, the grounding resistance of a transformer substation, and the transmission line H between the transformer substations ═ H1，h2，…，hp]The distance of transmission cable between each city power grid transformer substation is [ g ]1，g2，…，gq]。
S13: recording the length of a 110kV cable of a subway traction main station and the longitudinal direct current resistance r of each kilometer of a three-phase cable armor layer10。
Further, step 2 specifically comprises:
s21: according to the topology of the subway line, the subway line is equivalent to a direct current resistance network model of a centralized parameter, the model comprises an uplink/downlink contact network, a steel rail, a through ground wire and a reference ground structure, and the total number of model nodes is Nm＝2×n1+A+2×N+2×n+2×n2In the model, an uplink/downlink contact network structure model comprises traction substation nodes and train nodes, and a steel rail structure model comprises station nodes, train nodes, vehicle sections and parking lot nodes; the through ground wire structure model comprises station nodes, vehicle sections and parking lot nodes, and direct current resistances between vertical adjacent nodes in the contact network, the steel rail and the through ground wire structure model are equal to the distance between the contact network, the steel rail and the through ground wire and the distance between every kilometer of the direct current resistance multiplied by the adjacent nodes.
S22: the subway traction substation is equivalent to a structure of a direct-current resistance parallel direct-current source, the structure is connected between a node of a contact net traction substation and a node of a steel rail traction substation, the direct-current resistance value is r, and the parallel current source is VrR; direct current transition resistance R2 ═ R between rail station node and through ground wire node in subway line2/([L1，L1，L2，…，LN-1]/2)+r2/([L1，L2，…，LN-1，LN-1]/2), the transition resistance between the rail node of the vehicle section and the parking lot and the through ground wire node is 0.35, and the rail limiting device of the station section and the parking lot is equivalent to a direct current resistor rovThe parallel connection is connected between a rail station node and a through ground wire node and is connected with R2 in parallel; the resistance between the field section steel rail node and the station steel rail node is rd+r1×LaAnd 2, connecting the nodes of the ground wire penetrated by the subway main station and the nodes of the traction substation through cable armor layers, wherein the resistances among the nodes are that the stations, the field sections and the main station grounding system are equivalent to voltage source series direct current resistances, and the direct current resistance is rg1The voltage source is [ U ]1，U2，…，UN+n2+A]Is connected toBetween the through ground wire node of the station and the field section and the reference ground node, the train is equivalent to a direct current source, and the current source current is train traction current ItAnd connecting the traction net train node with the steel rail train node.
S23: according to the topological structure of the urban power grid, the urban power grid is equivalent to a direct-current resistance network model with centralized parameters, the model comprises transformer bus nodes and transformer substation grounding nodes, and the total number of the nodes is Nn＝M+2×m1+m2The resistance between bus nodes of each transformer substation is equal to the longitudinal direct current resistance of a three-phase power transmission line or cable per kilometer multiplied by the length of the power transmission line or cable/the number of the power transmission line or cable returns, and the resistance between ground nodes of each transformer substation is equal to the longitudinal direct current resistance of an overhead ground wire or cable armor per kilometer multiplied by the length of the power transmission line or cable/the number of the power transmission line or cable returns; the resistance between the bus nodes of the autotransformer is the direct-current resistance of the high-voltage winding of the autotransformer, the resistance between the bus nodes of the autotransformer and the grounding node of the transformer substation is the direct-current resistance of the medium-voltage winding of the transformer, and the resistance between the bus nodes and the grounding node of the three-winding transformer is the sum of the direct-current resistances of the high-voltage winding and the medium-voltage winding of the transformer; the grounding node of the transformer substation is connected with the large ground node through a direct current resistor r and a voltage sourceg2The voltage source is [ U ]1，U2，…，UM]。
S24: based on the cable armouring connection relation between the grounding networks of the subway main station and the urban power grid substation, the subway direct-current resistance network model and the urban power grid direct-current resistance network model are coupled, and the total number of model nodes is NA＝Nm+NnThe direct current resistance between the main station grounding node in the subway direct current resistance network model and the grounding node of the city power grid direct current resistance network model substation is equal to the length x r of the 110kV cable of the subway traction main station10。
Further, step 3 specifically comprises:
s31: determining model node admittance matrix Y according to direct current resistance between model nodes, wherein the size of the Y matrix is NA×NA(ii) a Determining the model current excitation I, I matrix size NA×NANon-train node in matrix and traction power transformationThe station node current excitations are all 0; determining an association matrix H of ground nodes and model nodesg，HgMatrix size NA×(N+n2+ a + M), the value is 1 when the model node and the ground node are the same node, and the rest are 0; determining model ground node ground resistance matrix Gg，GgMatrix size of N + N2+ a + M, the value being the dc resistance between the ground node and the reference ground node; the transimpedance matrix between the grounding nodes is Mg, and the size of the Mg matrix is (N + N)2+A+M)×(N+n2+ A + M); the grounding nodes are connected in series with a voltage source matrix U, and the size of the U matrix is N + N2+ A + M, the value of which is [ U ] the voltage of each grounding node in series1，U2，…，UN+n2+A+M](ii) a Ground node voltage V of transformer substationM，VMThe matrix size is M.
S32: based on the matrix, calculating the equivalent current matrix J of the model grounding nodeg＝GgU, model node current matrix J ═ I + HgJg(ii) a The node voltage V and the node current J meet YV-J; the ground node has a voltage of Vg＝(Hg)TV，VgAnd ground node ground current IgSatisfy the relation Ig＝Gg(Vg-U); the node voltage V and the model current excitation I satisfy the relationship: v ═ E ((E + H)gGgMgHg T)Y-HgGgMgGgHg T)(E+HgGgMgHg T)I。
S33: default subway steel rail limiting device and one-way conduction device are not conducted, rov＝105Ω，rd＝105Omega, calculating the node voltage according to the relation between the node voltage and the model current excitation; judging whether the voltage of the rail station node exceeds 120V or not, and if so, determining the node rov＝10-5Omega; calculating the voltage of the field section steel rail node-the voltage of the station steel rail node, and if the value is more than 0.8V or less than-8V, then rd＝10-5Omega; the model node voltage is recalculated.
Further, step 4 specifically includes:
s41: the resistance matrix of the bus node of the transformer and the grounding node of the transformer substation is phi, and the matrix size of phi is m1+m2(ii) a The voltage of a bus node of the transformer is VΦNode voltage V of bus bar of transformerΦAnd the voltage V of the grounding node of the transformer substationgNeutral point direct current I of main transformernSatisfies the following conditions: i isn＝Φ(VΦ-Vg)。
S42: based on the results of the node voltage calculations, based on In＝Φ(VΦ-Vg) And calculating the direct current of the neutral point of the main transformer.
The beneficial technical effects of the invention are as follows:
the method comprises the steps of firstly, effectively modeling a main transformer direct-current magnetic biasing current source by considering an actual subway line structure, a train operation position and traction current distribution.
And secondly, realizing equivalent modeling of the direct-current resistance network of the urban power grid based on the topological structure of the urban power grid and the connection relation between the subway and the transformer substation grounding system of the urban power grid.
And thirdly, calculating the direct current magnetic bias current of the main transformer of the urban power grid, and providing model support for analyzing the distribution of the direct current magnetic bias condition of the main transformer of the urban power grid.
Drawings
Fig. 1 is a structure diagram of a direct current resistance network of a subway and an urban power grid.
In the figure: firstly, a traction substation contact network node is added; secondly, a steel rail node of the traction substation; third, station through ground wire nodes (station grounding nodes); fourthly, the reference ground node; fifth, a station steel rail joint; sixthly, connecting the contact net of the train; seventhly, connecting the train steel rails; eighthly, connecting the field section steel rail nodes; a, a transformer substation grounding node; b-220 kV bus node; c-500 kV bus node. r isdown-downlink catenary resistance; r isup-uplink catenary resistance; r-internal resistance of traction substation; vr-traction substation voltage; rr-rail resistance; rm-through ground resistance; rw-rail to through ground transition resistance; rov-rail stop device resistance; rdResistance of unidirectional conducting device；Rg-a ground resistance; u shapeg-ground potential; rT-the transformer winding dc resistance; rL-transmission line/cable dc resistance; rf-overhead earth wire dc resistance; rca-cable armouring direct current resistance.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
The invention discloses a neutral point direct current calculation method of an urban power grid transformer, which comprises the following steps of:
step 1: the method comprises the steps of obtaining geographic information of an urban subway station, related electrical parameters of a traction system and a backflow system, a train position and traction current, and obtaining geographic information of a transformer substation in an urban power grid, a main wiring diagram of the transformer substation, related electrical parameters of a transformer and a line.
S11: recording the total quantity N of subway lines and the quantity of the subway stations containing the traction substation is N1The total number of the subway vehicle sections and the parking lots is n2The number of subway main stations is A, the terminal station of the longest subway line is selected as the origin, a coordinate system is established, and the coordinates W of the station of each subway is recorded as [ W ═ W1(x1,y1)，w2(x2,y2)，…，wN(xN,yN)]Recording the coordinate B ═ B of the subway main station1(x1,y1)，b2(x2,y2)，…，bA(xA,yA)]Recording the distance L between adjacent subway stations as L1，L2，…，LN-1]The internal resistance r of the traction substation and the DC supply voltage grade of the subway are VrThe direct current resistance r of a single steel rail per kilometer1Per kilometer of rail resistance to earth r2The direct current resistance per kilometer of a contact network, the direct current resistance per kilometer of a subway through ground wire, the direct current resistance per kilometer of a 35kV cable armor, the length of a 35kV electric cable, and the grounding resistance r of a station and a field sectiong1The distance between the station section and the station entering the station section is La＝[l1，l2，…，ln2](ii) a Equivalent resistance r of station steel rail limiting deviceovOne way ofEquivalent resistance r of conducting deviced(ii) a The number of running trains in the subway line is n, the positions of the trains in the subway line and the traction current I of the trains are recordedt＝[I1，I2，…，In]。
S12: recording the total number M of the urban power grid transformer substations and the number M of the neutral point grounding autotransformers1The number of the neutral point grounding three-winding transformers is m2The coordinate D of each transformer substation is ═ D1(x1,y1)，d2(x2,y2)，…，dM(xM,yM)]High voltage winding DC resistance of transformer, medium voltage winding resistance of transformer, DC resistance per kilometer of three-phase transmission line r6The number of loops of the line, the direct current resistance per kilometer of an overhead ground wire, the direct current resistance per kilometer of a three-phase transmission cable core, the number of loops of the transmission cable, the direct current resistance per kilometer of a cable armor, the grounding resistance of a transformer substation, and the transmission line H between the transformer substations ═ H1，h2，…，hp]The distance of transmission cable between each city power grid transformer substation is [ g ]1，g2，…，gq]。
S13: recording the length of a 110kV cable of a subway traction main station and the longitudinal direct current resistance r of each kilometer of a three-phase cable armor layer10。
Step 2: and establishing a direct current resistance network model of the subway and the urban power grid (as shown in figure 1).
S21: according to the topology of the subway line, the subway line is equivalent to a direct current resistance network model of a centralized parameter, the model comprises an uplink/downlink contact network, a steel rail, a through ground wire and a reference ground structure, and the total number of model nodes is Nm＝2×n1+A+2×N+2×n+2×n2In the model, an uplink/downlink contact network structure model comprises traction substation nodes and train nodes, and a steel rail structure model comprises station nodes, train nodes, vehicle sections and parking lot nodes; the through ground wire structure model comprises station nodes, vehicle sections and parking lot nodes, and direct current resistances between vertical adjacent nodes in the contact network, the steel rail and the through ground wire structure model are equal to the distance between the contact network, the steel rail and the through ground wire and the distance between every kilometer of the direct current resistance multiplied by the adjacent nodes.
S22: the subway traction substation is equivalent to a structure of a direct-current resistance parallel direct-current source, the structure is connected between a node of a contact net traction substation and a node of a steel rail traction substation, the direct-current resistance value is r, and the parallel current source is VrR; direct current transition resistance R2 ═ R between rail station node and through ground wire node in subway line2/([L1，L1，L2，…，LN-1]/2)+r2/([L1，L2，…，LN-1，LN-1]/2), the transition resistance between the rail node of the vehicle section and the parking lot and the through ground wire node is 0.35, and the rail limiting device of the station section and the parking lot is equivalent to a direct current resistor rovThe parallel connection is connected between a rail station node and a through ground wire node and is connected with R2 in parallel; the resistance between the field section steel rail node and the station steel rail node is rd+r1×LaAnd 2, connecting the nodes of the ground wire penetrated by the subway main station and the nodes of the traction substation through cable armor layers, wherein the resistances among the nodes are that the stations, the field sections and the main station grounding system are equivalent to voltage source series direct current resistances, and the direct current resistance is rg1The voltage source is [ U ]1，U2，…，UN+n2+A]Connecting the station and field section through ground wire node with the reference ground node, wherein the train is equivalent to a direct current source, and the current source current is train traction current ItAnd connecting the traction net train node with the steel rail train node.
S23: according to the topological structure of the urban power grid, the urban power grid is equivalent to a direct-current resistance network model with centralized parameters, the model comprises transformer bus nodes and transformer substation grounding nodes, and the total number of the nodes is Nn＝M+2×m1+m2The resistance between bus nodes of each transformer substation is equal to the longitudinal direct current resistance of a three-phase power transmission line or cable per kilometer multiplied by the length of the power transmission line or cable/the number of the power transmission line or cable returns, and the resistance between ground nodes of each transformer substation is equal to the longitudinal direct current resistance of an overhead ground wire or cable armor per kilometer multiplied by the length of the power transmission line or cable/the number of the power transmission line or cable returns; the resistance between the bus nodes of the autotransformer is the direct current resistance of the high-voltage winding of the autotransformer, and the resistance between the bus nodes of the autotransformer and the grounding node of the transformer substation is changedThe resistance between the bus node and the ground node of the three-winding transformer is the sum of the direct-current resistances of the high-voltage winding and the medium-voltage winding of the transformer; the grounding node of the transformer substation is connected with the large ground node through a direct current resistor r and a voltage sourceg2The voltage source is [ U ]1，U2，…，UM]。
S24: based on the cable armouring connection relation between the grounding networks of the subway main station and the urban power grid substation, the subway direct-current resistance network model and the urban power grid direct-current resistance network model are coupled, and the total number of model nodes is NA＝Nm+NnThe direct current resistance between the main station grounding node in the subway direct current resistance network model and the grounding node of the city power grid direct current resistance network model substation is equal to the length x r of the 110kV cable of the subway traction main station10。
And step 3: and (5) assigning model parameters, and calculating the voltage of each node of the direct-current resistance network model of the urban power grid.
S31: determining model node admittance matrix Y according to direct current resistance between model nodes, wherein the size of the Y matrix is NA×NA(ii) a Determining the model current excitation I, I matrix size NA×NACurrent excitation of non-train nodes and traction substation nodes in the matrix is 0; determining an association matrix H of ground nodes and model nodesg，HgMatrix size NA×(N+n2+ a + M), the value is 1 when the model node and the ground node are the same node, and the rest are 0; determining model ground node ground resistance matrix Gg，GgMatrix size of N + N2+ a + M, the value being the dc resistance between the ground node and the reference ground node; the transimpedance matrix between the grounding nodes is Mg, and the size of the Mg matrix is (N + N)2+A+M)×(N+n2+ A + M); the grounding nodes are connected in series with a voltage source matrix U, and the size of the U matrix is N + N2+ A + M, the value of which is [ U ] the voltage of each grounding node in series1，U2，…，UN+n2+A+M](ii) a Ground node voltage V of transformer substationM，VMThe matrix size is M.
S32: based on the matrix, calculating the equivalent current of the model grounding nodeMatrix Jg＝GgU, model node current matrix J ═ I + HgJg(ii) a The node voltage V and the node current J meet YV-J; the ground node has a voltage of Vg＝(Hg)TV，VgAnd ground node ground current IgSatisfy the relation Ig＝Gg(Vg-U); the node voltage V and the model current excitation I satisfy the relationship: v ═ E ((E + H)gGgMgHg T)Y-HgGgMgGgHg T)(E+HgGgMgHg T)I。
S33: default subway steel rail limiting device and one-way conduction device are not conducted, rov＝105Ω，rd＝105Omega, calculating the node voltage according to the relation between the node voltage and the model current excitation; judging whether the voltage of the rail station node exceeds 120V or not, and if so, determining the node rov＝10-5Omega; calculating the voltage of the field section steel rail node-the voltage of the station steel rail node, and if the value is more than 0.8V or less than-8V, then rd＝10-5Omega; the model node voltage is recalculated.
And 4, step 4: and establishing an impedance matrix of a bus and a neutral point node of the urban power grid transformer, and calculating the direct current of the neutral point of the main transformer.
S41: the resistance matrix of the bus node of the transformer and the grounding node of the transformer substation is phi, and the matrix size of phi is m1+m2(ii) a The voltage of a bus node of the transformer is VΦNode voltage V of bus bar of transformerΦAnd the voltage V of the grounding node of the transformer substationgNeutral point direct current I of main transformernSatisfies the following conditions: i isn＝Φ(VΦ-Vg)。
S42: based on the results of the node voltage calculations, based on In＝Φ(VΦ-Vg) And calculating the direct current of the neutral point of the main transformer.
Claims (1)
1. A direct current calculation method for a neutral point of a transformer of an urban power grid is characterized by comprising the following steps:
step 1: acquiring geographic information of an urban subway station, related electrical parameters of a traction system and a reflux system, a train position and traction current, and acquiring geographic information of a transformer substation in an urban power grid, a main wiring diagram of the transformer substation, and related electrical parameters of a transformer and a line;
s11: recording the total quantity N of subway lines and the quantity of the subway stations containing the traction substation is N1The total number of the subway vehicle sections and the parking lots is n2The number of subway main stations is A, the terminal station of the longest subway line is selected as the origin, a coordinate system is established, and the coordinates W of the station of each subway is recorded as [ W ═ W1(x1,y1)，w2(x2,y2)，…，wN(xN,yN)]Recording the coordinate B ═ B of the subway main station1(x1,y1)，b2(x2,y2)，…，bA(xA,yA)]Recording the distance L between adjacent subway stations as L1，L2，…，LN-1]The internal resistance r of the traction substation and the DC supply voltage grade of the subway are VrThe direct current resistance r of a single steel rail per kilometer1Per kilometer of rail resistance to earth r2The direct current resistance per kilometer of a contact network, the direct current resistance per kilometer of a subway through ground wire, the direct current resistance per kilometer of a 35kV cable armor, the length of a 35kV electric cable, and the grounding resistance r of a station and a field sectiong1The distance between the station section and the station entering the station section is La＝[l1，l2，…，ln2](ii) a Equivalent resistance r of station steel rail limiting deviceovEquivalent resistance r of unidirectional conducting deviced(ii) a The number of running trains in the subway line is n, the positions of the trains in the subway line and the traction current I of the trains are recordedt＝[I1，I2，…，In]；
S12: recording the total number M of the urban power grid transformer substations and the number M of the neutral point grounding autotransformers1The number of the neutral point grounding three-winding transformers is m2The coordinate D of each transformer substation is ═ D1(x1,y1)，d2(x2,y2)，…，dM(xM,yM)]High voltage winding DC resistance of transformer, medium voltage winding resistance of transformer, DC resistance per kilometer of three-phase transmission line r6The number of loops of the line, the direct current resistance per kilometer of an overhead ground wire, the direct current resistance per kilometer of a three-phase transmission cable core, the number of loops of the transmission cable, the direct current resistance per kilometer of a cable armor, the grounding resistance of a transformer substation, and the transmission line H between the transformer substations ═ H1，h2，…，hp]The distance of transmission cable between each city power grid transformer substation is [ g ]1，g2，…，gq]；
S13: recording the length of a 110kV cable of a subway traction main station and the longitudinal direct current resistance r of each kilometer of a three-phase cable armor layer10；
Step 2: establishing a direct-current resistance network model of a subway and an urban power grid;
s21: according to the topology of the subway line, the subway line is equivalent to a direct current resistance network model of a centralized parameter, the model comprises an uplink/downlink contact network, a steel rail, a through ground wire and a reference ground structure, and the total number of model nodes is Nm＝2×n1+A+2×N+2×n+2×n2In the model, an uplink/downlink contact network structure model comprises traction substation nodes and train nodes, and a steel rail structure model comprises station nodes, train nodes, vehicle sections and parking lot nodes; the through ground wire structure model comprises station nodes, vehicle sections and parking lot nodes, and direct current resistances between longitudinal adjacent nodes in the contact network, the steel rail and the through ground wire structure model are equal to the distance between the contact network, the steel rail and the through ground wire and the distance between every kilometer of the direct current resistance multiplied by the adjacent nodes;
s22: the subway traction substation is equivalent to a structure of a direct-current resistance parallel direct-current source, the structure is connected between a node of a contact net traction substation and a node of a steel rail traction substation, the direct-current resistance value is r, and the parallel current source is VrR; direct current transition resistance R2 ═ R between rail station node and through ground wire node in subway line2/([L1，L1，L2，…，LN-1]/2)+r2/([L1，L2，…，LN-1，LN-1]/2), transition resistance between rail nodes and through ground wire nodes of vehicle section and parking lotIs 0.35, and the limiting device of the railway of the station and the field section is equivalent to a direct current resistor rovThe parallel connection is connected between a rail station node and a through ground wire node and is connected with R2 in parallel; the resistance between the field section steel rail node and the station steel rail node is rd+r1×LaAnd 2, connecting the nodes of the ground wire penetrated by the subway main station and the nodes of the traction substation through cable armor layers, wherein the resistances among the nodes are that the stations, the field sections and the main station grounding system are equivalent to voltage source series direct current resistances, and the direct current resistance is rg1The voltage source is [ U ]1，U2，…，UN+n2+A]Connecting the station and field section through ground wire node with the reference ground node, wherein the train is equivalent to a direct current source, and the current source current is train traction current ItConnecting the traction net train node with the steel rail train node;
s23: according to the topological structure of the urban power grid, the urban power grid is equivalent to a direct-current resistance network model with centralized parameters, the model comprises transformer bus nodes and transformer substation grounding nodes, and the total number of the nodes is Nn＝M+2×m1+m2The resistance between bus nodes of each transformer substation is equal to the longitudinal direct current resistance of a three-phase power transmission line or cable per kilometer multiplied by the length of the power transmission line or cable/the number of the power transmission line or cable returns, and the resistance between ground nodes of each transformer substation is equal to the longitudinal direct current resistance of an overhead ground wire or cable armor per kilometer multiplied by the length of the power transmission line or cable/the number of the power transmission line or cable returns; the resistance between the bus nodes of the autotransformer is the direct-current resistance of the high-voltage winding of the autotransformer, the resistance between the bus nodes of the autotransformer and the grounding node of the transformer substation is the direct-current resistance of the medium-voltage winding of the transformer, and the resistance between the bus nodes and the grounding node of the three-winding transformer is the sum of the direct-current resistances of the high-voltage winding and the medium-voltage winding of the transformer; the grounding node of the transformer substation is connected with the large ground node through a direct current resistor r and a voltage sourceg2The voltage source is [ U ]1，U2，…，UM]；
S24: based on the cable armouring connection relation between the grounding networks of the subway main station and the urban power grid substation, the subway direct-current resistance network model and the urban power grid direct-current resistance network model are coupled, and the total number of model nodes is NA＝Nm+NnThe direct current resistance between the main station grounding node in the subway direct current resistance network model and the grounding node of the city power grid direct current resistance network model substation is equal to the length x r of the 110kV cable of the subway traction main station10；
And step 3: assigning model parameters, and calculating the voltage of each node of the direct-current resistance network model of the urban power grid;
s31: determining model node admittance matrix Y according to direct current resistance between model nodes, wherein the size of the Y matrix is NA×NA(ii) a Determining the model current excitation I, I matrix size NA×NACurrent excitation of non-train nodes and traction substation nodes in the matrix is 0; determining an association matrix H of ground nodes and model nodesg，HgMatrix size NA×(N+n2+ a + M), the value is 1 when the model node and the ground node are the same node, and the rest are 0; determining model ground node ground resistance matrix Gg，GgMatrix size of N + N2+ a + M, the value being the dc resistance between the ground node and the reference ground node; the transimpedance matrix between the grounding nodes is Mg, and the size of the Mg matrix is (N + N)2+A+M)×(N+n2+ A + M); the grounding nodes are connected in series with a voltage source matrix U, and the size of the U matrix is N + N2+ A + M, the value of which is [ U ] the voltage of each grounding node in series1，U2，…，UN+n2+A+M](ii) a Ground node voltage V of transformer substationM，VMThe matrix size is M;
s32: based on the matrix, calculating the equivalent current matrix J of the model grounding nodeg＝GgU, model node current matrix J ═ I + HgJg(ii) a The node voltage V and the node current J meet YV-J; the ground node has a voltage of Vg＝(Hg)TV，VgAnd ground node ground current IgSatisfy the relation Ig＝Gg(Vg-U); the node voltage V and the model current excitation I satisfy the relationship: v ═ E ((E + H)gGgMgHg T)Y-HgGgMgGgHg T)(E+HgGgMgHg T)I；
S33: default subway steel rail limiting device and one-way conduction device are not conducted, rov＝105Ω，rd＝105Omega, calculating the node voltage according to the relation between the node voltage and the model current excitation; judging whether the voltage of the rail station node exceeds 120V or not, and if so, determining the node rov＝10-5Omega; calculating the voltage of the field section steel rail node-the voltage of the station steel rail node, and if the value is more than 0.8V or less than-8V, then rd＝10-5Omega; recalculating the model node voltage;
and 4, step 4: establishing a bus and a neutral point node impedance matrix of the urban power grid transformer, and calculating the direct current of a neutral point of a main transformer;
s41: the resistance matrix of the bus node of the transformer and the grounding node of the transformer substation is phi, and the matrix size of phi is m1+m2(ii) a The voltage of a bus node of the transformer is VΦNode voltage V of bus bar of transformerΦAnd the voltage V of the grounding node of the transformer substationgNeutral point direct current I of main transformernSatisfies the following conditions: i isn＝Φ(VΦ-Vg)；
S42: based on the results of the node voltage calculations, based on In＝Φ(VΦ-Vg) And calculating the direct current of the neutral point of the main transformer.
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