GB2616187A - Alternating current-direct current power grid harmonic coupling modeling method and system - Google Patents

Alternating current-direct current power grid harmonic coupling modeling method and system Download PDF

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GB2616187A
GB2616187A GB2308557.4A GB202308557A GB2616187A GB 2616187 A GB2616187 A GB 2616187A GB 202308557 A GB202308557 A GB 202308557A GB 2616187 A GB2616187 A GB 2616187A
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harmonic
power grid
transformer
model
power
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GB202308557D0 (en
Inventor
Yang Peihong
Cao Yang
Liu Wanfu
Dang Wei
Jing Huiying
Diao Fengxin
Sun Rui
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Electric Power Res Institute Of State Grid East Inner Mongolia Electric Power Co Ltd
Inner Mongolia Univ Of Science And Technology
Inner Mongolia University of Science and Technology
State Grid Eastern Inner Mongolia Power Co Ltd
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Electric Power Res Institute Of State Grid East Inner Mongolia Electric Power Co Ltd
Inner Mongolia Univ Of Science And Technology
Inner Mongolia University of Science and Technology
State Grid Eastern Inner Mongolia Power Co Ltd
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Publication of GB202308557D0 publication Critical patent/GB202308557D0/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H02J2003/365—Reducing harmonics or oscillations in HVDC
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

Abstract

The present invention provides an alternating current-direct current power grid harmonic coupling modeling method and system. The method comprises: acquiring historical data of an induced ground electric field when a geomagnetic storm occurs; constructing an alternating current power grid transformer harmonic source model, a direct current power grid converter transformer harmonic source model, a direct current power grid converter bridge harmonic source model, a direct current power grid harmonic network model, and an alternating current power grid harmonic network model according to the historical data of the induced ground electric field during the geomagnetic storm; and constructing an alternating current-direct current power grid harmonic coupling model on the basis of the alternating current power grid transformer harmonic source model, the direct current power grid converter transformer harmonic source model, the direct current power grid converter bridge harmonic source model, the direct current power grid harmonic network model, and the alternating current power grid harmonic network model. According to the present invention, by constructing the alternating current-direct current power grid harmonic coupling model, alternating current-direct current power grid harmonic distribution under the influence of a geomagnetic induced current can be obtained, thereby helping to establish defensive measures for transformer damage and large-area power outage caused by magnetic biasing of the geomagnetic induced current in a power grid.

Description

ALTERNATING CURRENT-DIRECT CURRENT POWER GRID HARMONIC
COUPLING MODELING METHOD AND SYSTEM
[0001] This patent application claims the benefit and priority of Chinese Patent Application No. 202111332714.9, entitled "MODELING METHOD AND SYSTEM FOR COUPLING HARMONICS IN AC AND DC POWER GRIDS" filed on November 11, 2021, the disclosure of which is incorporated by reference herein in its entirety.
TECHNICAL FIELD
[0002] The present invention relates to a technology field of Alternating Current (AC) and Direct Current (DC) power grids, in particular to a modeling method and system for coupling harmonics in the AC and DC power grids.
BACKGROUND ART
[0003] Power grids with voltage levels of 735kV and 760kV using quad bundled conductors with 400mm2 have been built in Canada and the United States, respectively. Due to relatively small resistance per unit length of conductors in the power grids with the voltage levels of 735kV and 760kV, Geomagnetic Induced Current (GIC) generated by a geomagnetic storm in the power grids with the voltage levels of 735kV and 760kV is relatively large. The GIC caused by the strong geomagnetic storm occurred on March 13, 1989 in the power grids with the voltage levels of 735kV and 760kV of North America, and harmonics and reactive power consumption derived from this GIC damaging on transformers increases interference, inducing a major outage in the power grid with the voltage level of 735kV in Quebec, Canada, and causing more than 60 power transmission lines and transformer protection devices in substations to trip in succession in North America. Multiple station transformers have been permanently damaged in the United States due to excessive temperature rise caused by the harmonics [0004] With a rapid development of Chinese economy, resistance of wires in a part of power grids with a voltage level of 500kV and above in China becomes increasingly small. In particular, power transmission lines with 500 kV matching ultra-high voltage (UHV) AC and 1 DC power grids also adopt quad bundled conductors with 630mm2 and 720mm2, resulting in low resistance of the power transmission line. According to intensity of the geomorphic storm on March 13, 1989, a geomagnetic storm with the same or similar intensity of the geomagnetic storm occurred on March 13, 1989 will cause the GIC of Huainan and Shanghai Station with 1000kV to reach a level of 700A. Compared with GIC data of the power grids in North American and China, it can be seen that, with the development of large-scale power grids, China has become a country with the highest risk of disasters caused by the geomagnetic storms on the power grids in the world. Considering that China's UHV AC and DC power grids have large and complex scales, a response mechanism of transformer cluster harmonic interference caused by GIC generated by the geomagnetic storms damaging the UHV AC and DC power grids and propagation characteristics and laws of the cluster harmonic interference in the AC and DC power grids are new issues that have not been studied at present.
SUMMARY
[0005] The present invention intends to provide a modeling method and system for coupling harmonics in AC and DC power grids to achieve calculation and analysis of harmonic distributions in the AC and DC power grids under an influence of Geomagnetic Induced Current (GIC), thereby improving a predictive ability of a harmonic risk caused by the GIC in the power grids [0006] In order to achieve the above effect, the invention provides the following solutions [0007] A modeling method for coupling harmonics in Alternating Current (AC) and Direct Current (DC) power grids, includes: [0008] acquiring historical data of an induced geoelectric field during a geomagnetic storm, [0009] establishing a harmonic source model of a transformer in the AC power grid, a harmonic source model of a converter transformer in the DC power grid, a harmonic source model of a converter bridge in the DC power grid, a harmonic network model of the DC power grid and a harmonic network model of the AC power grid, based on the historical data of the induced geoelectric field during the geomagnetic storm; and [0010] establishing a harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid.
100111 In an embodiment, the harmonic source model of the transformer in the AC power grid is- = (1/1 -
V
[0012] where -1-c, is a Geomagnetic Induced Current (GIC) from a node i to a node j; and are voltage values at the node i and the node j, respectively; ' = G-IELGwhere E is the induced geoelectric field, and 4/ is a distance of a power transmission line from the G node i to the node j; and is a admittance matrix [0013] In an embodiment, a GIC harmonic source model of the converter bridge in the DC power grid is: IT = kr nexp(j(p+If " )T/nexp[j((p" ±11-I] 6 6 [0014] where I is a harmonic current; kT is a ratio of a no-load phase voltage at a valve side to a phase voltage at a grid side of the transformer, (/)-is a phase, /-is an effective value of the harmonic current; n is a harmonic order, and n=1 2m ± 1, where m is a constant, with a maximum value of 15, and m=1, 2, ..*.
[0015] In an embodiment, the harmonic network model of the DC power grid is: = 01
P
27 a e, po D 1= Wupo f (n)+J -(o(n)(In-+1712) 27 2h [0016] where I', and 1-ki are self impedance and mutual impedance per unit length of a DC linerespectively; r0is resistance of the DC line; PH is vacuum permeability; f(n) is a 3 frequency, 69(n) is an angular frequency, h is a height of a conductor from ground, a"-i is a = Vask-I M an equivalent radius of bundled conductors, eq, where k is the number of the bundled conductors, a is a radius of the bundled conductors s is a side length of a regular Ic (2sin)k-1
M -
polygon formed by the bundled conductors, and and Tc, are constant coefficients, and D is a geometric mean distance of lines 100171 In an embodiment, the harmonic network model of the AC power grid is: Y (n) = Z c(n) Z. shy / c (n) Zc(n)sl1(72)' Z (2)thy(n) v Z 100181 where Y(n) is a network matrix; c( and ' '''' are a first function and a second \I z(n)y(n) Zem= 1 z(n)/y(n) z(n) function, respectively, where * y (a) = and Y(n) are a =r+jo(n)L yw=g+fro(n)C, r and 0 are third function and a forth function, respectively, ,t, resistance and conductance, respectively, (900 is an angular frequency at an nth harmonic, and L and C are inductance and capacitance, respectively.
100191 In an embodiment, establishing the harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid, includes: [0020] superposing currents output from the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid and the harmonic source model of the converter bridge in the DC power grid, to obtain a harmonic current injection amount; 100211 determining a harmonic coupling admittance matrix based on the harmonic network model of the DC power grid and the harmonic network model of the AC power grid; [0022] superposing voltages output from the harmonic source model of the transformer in the AC power grid and the harmonic source model of the converter bridge in the DC power grid, to obtain a harmonic node voltage vector; and [0023] establishing the harmonic coupling model of the AC and DC power grids, based on the harmonic current injection amount, the harmonic coupling admittance matrix and the harmonic node voltage vector.
[0024] In an embodiment, the harmonic coupling model of the AC and DC power grids is:
YNUN
[0025] where is the harmonic current injection amount, including harmonic current injections of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid; Yiv is the harmonic coupling admittance matrix, including a harmonic network of the AC power grid and a harmonic network of the DC power grid; and ON is the harmonic node voltage vector, including node harmonic voltages of the transformer in the AC power grid, a transformer in the DC power grid and the converter bridge in the DC power grid.
[0026] A modeling system for coupling harmonics in Alternating Current (AC) and Direct Current (DC) power grids, includes: [0027] a historical data acquisition module, configured to acquire historical data of an induced geoelectric field during a geomagnetic storm; [0028] an induced geoelectric field model establishment module, configured to establish a harmonic source model of a transformer in the AC power grid, a harmonic source model of a converter transformer in the DC power grid, a harmonic source model of a converter bridge in the DC power grid, a harmonic network model of the DC power grid and a harmonic network model of the AC power grid, based on the historical data of the induced geoelectric field during the geomagnetic storm, and [0029] a harmonic coupling model establishment module for the AC and DC power grids, configured to establish a harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid 100301 In an embodiment, the harmonic source model of the transformer in the AC power grid is: = (P; )(1,7 100311 where is a Geomagnetic Induced Current (GIC) from a node i to a node j, and are voltage values at the node i and the node jrespectively; = ""71EL0GJJwhere E is the induced geoelectric field, and '7 is a distance of a power transmission line from the node i to the node j; and u is a admittance matrix.
[0032] In an embodiment, a GIC harmonic source model of the converter bridge in the DC power grid is = kr LnexpW,, )+Icr exp[j(q)"-n 6 6 100331 where is a harmonic current; kT is a ratio of a no-load phase voltage at a valve side to a phase voltage at a grid side of the transformer; C)77 is a phase; is an effective value of the harmonic current; n is a hannonic order, and n=12m ± 1, where m is a constant, with a maximum value of 15, and m=1, 2, ..* [0034] According to the detailed embodiments of the invention, the invention discloses following technical effects.
[0035] In the present invention, the harmonic coupling model of the AC and DC power grids is established, and is used to calculate and analyze the harmonic distributions in the AC and DC power grids under the influence of GIC, in order to obtain a response mechanism of transformer cluster harmonic interference in the AC and DC power grids, and then determine propagation characteristics and laws of the cluster harmonic interference in the AC and DC power grids Based on the propagation characteristics and laws of the cluster harmonic interference in the AC and DC power grids, the harmonic risk caused by the GIC in the power grids is predicted, further helping to establish preventive measures for transformer damages
IOW
IT
and large-scale power outage accidents caused by bias magnet of the GIC in the power grids.
BRIEF DESCRIPTION OF THE DRAWINGS
[0036] In order to more clearly illustrate the embodiments of the present invention or technical solutions in the conventional art, the accompanying drawings used in the embodiments will now be described briefly. It is obvious that the drawings in the following description are only some embodiments of the invention, and that those skilled in the art can obtain other drawings from these drawings without any creative efforts.
[0037] FIG. I is a flowchart of a modeling method for coupling harmonics in AC and DC power grids in an embodiment of the present invention; [0038] FIG. 2 is a flowchart of a modeling method for coupling harmonics in the AC and DC power grids based on Geomagnetic Induced Current (GIC) in an embodiment of the present invention; [0039] FIG. 3 is an equivalent circuit diagram of a GIC harmonic source model of a transformer in an AC power grid provided by an embodiment of the present invention; [0040] FIG. 4 is an equivalent circuit diagram of harmonic coupling in the AC and DC power grids in an embodiment of the present invention; and [0041] FIG. 5 is a schematic structure diagram of a modeling system for coupling harmonics in the AC and DC power grids in an embodiment of the present invention.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0042] In the following, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all the embodiments thereof Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without any creative efforts shall fall within the scope of the present invention [0043] The invention intends to provide a modeling method and system for coupling harmonics in AC and DC power grids to achieve calculation and analysis of harmonic distributions in the AC and DC power grids under an influence of Geomagnetic Induced Current (GIC), thereby improving a predictive ability of a harmonic risk caused by the GIC in the power grids [0044] For a better understanding of above intention, features and advantages of the present invention, the invention will be described in details by reference to the accompanying drawings and specific embodiments thereof.
[0045] FIG 1 is a flowchart of a modeling method for coupling harmonics in AC and DC power grids in an embodiment of the present invention. As shown in FIG. I, a modeling method for coupling harmonics in AC and DC power grids is provided in the present invention, which includes step 101 to step 103.
[0046] In step 101, historical data of an induced geoelectric field during a geomagnetic storm is acquired. Where, the historical data of the induced geoelectric field during the geomagnetic storm is relevant historical data of Geomagnetic Induced Current (GIC), including voltage value at a node, the induced geoelectric field, distance of a power transmission line, ratio of a no-load phase voltage at a valve side to a phase voltage at a grid side of a transformer, effective value of harmonic current, resistance, conductance, inductance, capacitance, impedance and so on.
[0047] In step 102, a harmonic source model of a transformer in the Alternating Current (AC) power grid, a harmonic source model of a converter transformer in the Direct Current (DC) power grid, a harmonic source model of a converter bridge in the DC power grid, a harmonic network model of the DC power grid and a harmonic network model of the AC power grid are established, based on the historical data of the induced geoelectric field during the geomagnetic storm [0048] In step 103, a harmonic coupling model of the AC and DC power grids is established, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid.
[0049] After step 103, the method further includes that the harmonic coupling model of the AC and DC power grids is utilized to obtain a response mechanism of transformer cluster harmonic interference in the AC and DC power grids, and determine propagation characteristics and laws of the cluster harmonic interference in the AC and DC power grids, thereby establishing bias magnetic defense in the power grid Transformer damages and large-scale power outage accidents caused by bias magnet of the GIC in the power grid are prevented by the bias magnetic defense.
[0050] The harmonic source model of the transformer in the AC power grid is: fuic = -,)G" 1" [0051] where /01/0" is a OTC from a node i to a node j; and " are voltage values at the V = G-1EL, G node i and the node j, respectively, ' " , where E is the induced geoelectric field,
L G
and "" is a distance of a power transmission line from the node i to the node j; and u s an admittance matrix.
100521 a GIC harmonic source model of the converter bridge in the DC power grid s: I = k,, I nexp(frp ")+k, I nexpU (q) "-n + ] 6 6 [0053] where is the harmonic current kT is the ratio of the no-load phase voltage at the valve side to the phase voltage at the grid side of the transformer; (73-is the phase; is the effective value of the harmonic current; n is a harmonic order, and n=12m ± 1, where m is a constant, with a maximum value of 15, and m=1, 2..*.
[0054] The harmonic network model of the DC power grid is: (11 ± WiiPof (11))±1 (9(n)(in -211 + 27 a eq Po P = Wi2P0.1.(n)+/ -co(n)(1n -+Vi2) [0055] where and are self impedance and mutual impedance per unit length of a DC line, respectively is resistance of the DC line; /10 is vacuum permeability; f(n) is a frequency; 6)(T) is an angular frequency; h is a height of a conductor from ground; a"0 is a = { ask-iAJ an equivalent radius of bundled conductors, eq, where k is the number of the bundled conductors, a is a radius of the bundled conductors s is a side length of a regular
M -(2sin
polygon formed by the bundled conductors, and 12 and 12 are constant coefficients, and D is a geometric mean distance of lines.
[0056] The harmonic network model of the AC power grid is: 1 1 Z thy c(n) (n) Z)Shr (y)l Zc shv I Zc(n) th y(n)1 oo [0057] where Y(n) is a network matrix; Zc" and 21(') are a first function and a second function, respectively, where " = z(n)y(n) Z = z(n)/y(n) (n) and Y(n) are a third function and a forth function, respectively, =r +J. y =g+jonir, r and g are resistance and conductance, respectively, (9(n) is an angular frequency at an nth harmonic, and L and C are inductance and capacitance, respectively.
[0058] The step 103 specifically includes the following steps: [0059] superposing currents output from the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid and the harmonic source model of the converter bridge in the DC power grid to obtain a harmonic current injection amount; [0060] determining a harmonic coupling admittance matrix based on the harmonic network model of the DC power grid and the harmonic network model of the AC power grid; [0061] superposing voltages output from the harmonic source model of the transformer in the AC power grid and the harmonic source model of the converter bridge in the DC power grid to obtain a harmonic node voltage vector; and [0062] establishing the harmonic coupling model of the AC and DC power grids based on the harmonic current injection amount, the harmonic coupling admittance matrix and the harmonic node voltage vector.
100631 The harmonic coupling model of the AC and DC power grids is YVUN- 100641 where IN is the harmonic current injection amount, including harmonic current injections of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid; YN is the harmonic coupling admittance matrix, including a harmonic network of the AC power grid and a harmonic network of the DC power grid; and ON is the harmonic node voltage vector, including node harmonic voltages of the transformer in the AC power grid, a transformer in the DC power grid and the converter bridge in the DC power grid.
100651 FIG. 2 is a flowchart of a modeling method for coupling harmonics in the AC and DC power grids based on GIC in an embodiment of the present invention. As shown in FIG. 2, the present invention provides a modeling method for coupling harmonics in the AC and DC power grids considering GIC. The GIC distributions of transformer winding in the AC power grid and converter transformer winding in the DC power grid are calculated based on the historical typical values of the induced geoelectric field caused by the geomagnetic storm. DC bias magnetic characteristics of the transformer in the AC power grid and the converter transformer in the DC power grid are analyzed. The harmonic source models of the transformer in the AC power grid and the converter transformer in the DC power grid are established. Meanwhile, for the side of the DC power grid, it is also necessary to consider inherent harmonic characteristics of the converter bridge and establish the harmonic source model of the converter bridge. A harmonic parameter network model of the DC power grid is established, to further establish the harmonic coupling model of the AC and DC power grids by combining the harmonic source model of the transformer in the AC power grid with an equivalent harmonic model of the DC power grid. The present invention can provide a theoretical basis for harmonic control in AC and DC power grids under weather disasters to improve the ability of the power grids to resist disaster risks, ensuring the safe operation of the power grids 100661 Specifically, the present invention considers the modeling method for coupling harmonics in the Alternating Current and Direct Current (AC and DC) power grids, which includes: [0067] establishing a Geomagnetic Induced Current (GIC) harmonic source model of a transformer in AG power grid.
[0068] The GIC distribution of the AG power grid is calculated based on the historical typical values of the induced geoelectric field caused by the geomagnetic storm. The specific calculation model is as follows.
[0069] The GIC value between any two points in the grid is: iGic=(V,-Vi)G", [0070] where, the node voltage Vi is V= , GyEL",Gu [0071] where, Gal is the admittance matrix, E is the induced geoelectric field, V/km, and Lei is the distance of the power transmission line, km [0072] When GIC in the AC power grid flows through the transformer winding, a half-wave saturation phenomenon of the transformer can be caused. As can be seen from the ampere's circuital law: Ni=HI, [0073] where, lVis the number of winding turns, i is a winding current, His a magnetic field intensity, and / is an effective length of a magnetic circuit of an iron core.
[0074] GIC, a quasi direct current, is processed as a direct current in the present invention. After the DC current flows through the transformer winding, a DC magnetic flux is generated. Meanwhile, the current I in ampere's circuital law is composed of direct current and alternating current. The ampere's circuital law under the action of GIC is: NI=H1.
[0075] The present invention adopts a hyperbolic function to fit the magnetizing curve, namely: H=rsh(31), [0076] where, B is magnetic flux density, x and y are parameters related to a magnetizing orientation of the iron core, and sh() represents a hyperbolic function [0077] The magnetic flux density under the action of GIC is: B = K -4) = A -K - )=-K ( sirifot+W pc)
A A
[0078] where, A is an effective area of the iron core, K is a magnetic leakage coefficient, tD is a magnetic flux, and Om' , °pc, and (Dm respectively represent an AC flux, a DC flux, and a main flux.
100791 Under the action of GIC, an exciting current of the transformer under no load is: Ix Ky I =sincot+q)," ) [
N A
I x Ky Ky. )sh(J}K cl) sinwei - )ch(-1)",sincot)+ch( Ky [six!
A A
[0080] where, -Ky(I) is related to transformer design and is a constant in the present Am invention as a design parameter,and 0, is also a constant with the geoelectric field E is constant [0081] The harmonic components of the exciting current under the action of GIC can be Ky obtained by Fourier series expansion of sh( -cromsi Ky n CD 0 and ch(-cicsin ot)
A A
respectively, [0082] The obtained exciting current under the action of GIC is describe as: i" = viL I,sin(not + (p") [0083] where, n is a harmonic order, and (on is a phase.
[0084] The GIC harmonic source model of the transformer is further established by taking the exciting current in as a current source to replace an exciting branch in the transformer model.
[0085] The establishment of the GIC harmonic source model of the converter transformer in the DC power grid is consistent with the method for modeling the GIC harmonic source of the transformer in the AC power grid, and will not be repeated here.
[0086] The GIC harmonic source model of the converter transformer in the DC power grid is established.
[0087] The characteristic harmonic is established by adopting a double 12-pulse converter bridge structure, and the mathematical model is as follows: = krInexp(j(p" )+kT/ nexp[j((pn ±211-6 6 [0088] where, kT is the ratio of the no-load phase voltage at the valve side to the phase ) i voltage at the grid side of the transformer; (j) is s the phase, / is the effective value of the harmonic current, 11= 12m ± 1, and m=1,2,...
[0089] The harmonic network model of the DC power grid is established [0090] Under the action of harmonics, the self impedance and mutual impedance per unit length of the DC line can be expressed as: = W ±ilitio.i(n))±j (0(n)(Inh +V1) 27 a 1 e<1 Wi2P0.1(1)±.1 o(n)(in +Vi2) 27 2h 100911 where, re is the resistance of the DC line, p is the vacuum permeability, An) is the frequency, co(n) is the angular frequency, h is the height of the conductor from the ground, cie" is the equivalent radius of the bundled conductors, and Wi1, Wi2, VII, and l'12 are constant coefficients, respectively.
100921 The calculation formula for the equivalent radius of the bundled conductors is: a = a 5,k -1 A4 ey [0093] where, Al= A. is the number of the bundled conductors, a is the radius (2sin)1,-1 of the bundled conductors, and s is the side length of the regular polygon formed by the bundled conductors.
[0094] The harmonic network model of the AC power grid is established [0095] The model of the AC line is presented in the form of an admittance matrix, specifically: Ze (117(n)1 Zc( sh7()1 1 1 Z(n) shy(n)' / Z(fl)thy(fl)1 n Y(n) = [0096] where, 10,) = z(n)y(n) Z, (,) = ,Jz(n)/y(n) ()=rtle)(11)L yg±jo(n)C (n) is the angular frequency at the n harmonic, r is the resistance, g is the conductance, L is the inductance, and C is the capacitance.
[0097] In the AC power grid, in the model of the transformer under the action of harmonics, only L in the equivalent circuit parameters is adjusted, that is, under the nth harmonics, the inductance increases by el times, while the other parameters remain unchanged.
[0098] In the AC power grid, L and C in the model parameters, for the models of compensation devices and filtering devices under the action of harmonics, are adjusted, that is, under the nth harmonics, the inductance L increases by n times, the capacitance C increases by 1/n times, and the other parameters remain unchanged.
[0099] The harmonic coupling model of the AC and DC power grids is established.
[0100] Coupling modeling is performed by adopting the admittance matrix. In the present invention, the geomagnetic induction current is injected into the neutral points of the transformer in the AC power grid and the converter transformer in the DC power grid, causing DC bias magnetic of the transformers, thereby generating harmonics. Meanwhile, the converter bridge in the DC power grid, as a characteristic harmonic source, can also cause harmonic distribution in the power grid. To this end, there are three harmonic sources in the AC and DC power grids to calculate the harmonic distributions of the power grids. At this point, a general formula can be used to describe the specific model: IN 172V UN [0101] where, iN is the harmonic current injection amount, including harmonic current injections of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid; Yiv is the harmonic coupling admittance matrix, including the networks of the AC power grid and the DC power grid, and 6, is the harmonic node voltage vector, including node harmonic voltages of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid.
[0102] Specifically, the main process of this modeling method is as follows. The distributions of GIC in the power grids and the magnitude of GIC flowing through the transformer winding in the AC power grid and converter transformer winding in the DC power grid are calculated. The harmonic source model of the transformer in the AC power grid and the harmonic source model of the converter transformer in the DC power grid are calculated based on the magnitude of GIC. In the invention, the converter bridge is modeled by adopting characteristic harmonic in consideration that the converter bridge in the DC power grid itself is also a harmonic source. Through the network models of the AC and DC power grids, the harmonic source of the transformer in the AC power grid, the harmonic source of the converter transformer in the DC power grid and the harmonic source of the converter bridge in the DC power grid are associated to establish the harmonic coupling model of the AC and DC power grids, and the overall modeling process is shown in FIG. 2. [0103] The calculation of GIC distributions in the power grids is based on the induced geoelectric field caused by the geomagnetic storm. The size of the induced geoelectric field is related to the intensity of the geomagnetic storm, and the larger the intensity of the geomagnetic storm, the greater the magnitude of GIC in the power grids. The maximum value of Dst of the geomagnetic storm inducing the major outage in the power grid in Quebec, Canada, on March 13, 1989 was -548 nT. The maximum index value of Dst of the geomagnetic storm occurred on November 9, 2004 was -282nT, the geomagnetic storm caused the strong vibration and noise of the transformer in the Guangdong Ling'ao Nuclear Power Plant, the actual GIC peak value of the neutral point of the transformer was as high as 75.5A, and the continuous average value in 1 minute is also over 50A. Since the harmonic is only related to the magnitude of GIC of the transformer winding, rather than the duration, the analysis of the power grid harmonic benefits under the geomagnetic storm should be done according to the most severe extent. In the invention, three induction geoelectric fields with different magnitudes, namely 1V/km, 2V/km and 3V/km, are selected when the GIC distribution of the power grid is calculated. The 3V/km geoelectric field is basically close to the geomagnetic storm inducing the major outage of the power grid in Quebec, Canada, on March 13, 1989.
101041 The magnitudes of GIC of all transformer windings in the AC power grid and the magnitudes of G1C of all converter transformer windings in the DC power grid are further obtained based on the GIC distribution in the power grid, namely: kici= ( [0105] where, [ince is the magnitude of the GIC of the transformer winding, V, is the node induced voltage at the high voltage end of the transformer winding, Ito is the induced ground voltage, and G, is the conductivity of the transformer winding.
[0106] Based on the magnitude of the GIC of the transformer winding and the DC bias magnetic characteristics of the transformer, the exciting current of the transformer in the AC power grid and the converter transformer in the DC power grid are calculated. The calculation result thereof is described as: /nsin(mot + [0107] where, n is the harmonic order, and (Pn is the phase.
[0108] The exciting branch is replaced with the exciting current source according to the transformer equivalent model to complete the establishment of the GIC harmonic source model of the transformer.
[0109] The harmonic source model is established by the converter bridge, in the DC power grid, adopting characteristic harmonics, specifically: 21 21 = krI,"exp(Jon)+Icr "exp[j(c -6 6 101101 where, lo is the ratio of the no-load phase voltage at the valve side to the phase voltage at the grid side of the transformer, (Pn is the phase, 1(n) is the effective value of the harmonic current, and n=12m ± 1, m=1,2, [0111] The harmonic coupling model is established by combining the harmonic network models of the AC power grid and the DC power grid based on the harmonic source models, which is described as: i" = [0112] where, I, is the harmonic current injection amount, including harmonic current injections of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid; YN is the harmonic coupling admittance matrix, including the networks of the AC power grid and the DC power grid; and ON is the harmonic node voltage vector, including node harmonic voltages of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid.
[0113] As for the GIC harmonic source mod& of the transformer, the GIC harmonic source is modeled by the transformer equivalent circuit. In the present invention, a T-type equivalent circuit of transformer is adopted to replace the exciting branch in an original equivalent circuit with the exciting current source. The exciting current source is calculated by DC bias magnetic of the transformer, which is also the cause and source of harmonic generation in the power grids under the action of GIC. At this point, the exciting current is used as a known value to calculate the harmonic distribution. In FIG. 2, RI and Li represent the resistance and inductance parameters of the primary winding of the transformer, and R2 and L2 represent the resistance and inductance parameters of the secondary winding of the transformer. During harmonic calculation, parameters of transformer winding and parameters of the power grid are combined, and corresponding models are established according to the method for modeling the harmonic networks of the power grids, so that basic parameter data is provided for the coupling modeling of the harmonics in the AC and DC power grids.
[0114] In the process of coupling harmonics in the AC and DC power grids, because the geomagnetic storm causing GIC occurs almost simultaneously in the world, GIC with different magnitudes will flow through transformers with neutral points directly grounded in the power grids. These transformers are all harmonic sources. Meanwhile, because the neutral points of the converter transformers in the DC power grid are also directly grounded, and the GIC can also be injected into the converter transformer windings through the AC power grid, the converter transformers of the DC transmission system are all harmonic sources. Furthermore, the converter bridge in the DC system is also a source of harmonics in the power grid. In the present invention, due to the switching characteristics of the converter device, characteristic harmonics are adopted for modeling. In the present invention, under the influence of GIC, three types of harmonic sources exist in the AC and DC power grids. The three types of harmonic sources are taken as the excitations of the AC and DC power grids to perform modeling of the harmonics coupling. A schematic network diagram of the modeling of coupling the AC and DC multi-harmonic sources is shown in FIG. 4.
[0115] FIG. 4 shows a DC line with both ends connected to the AC network. 177 and (2; respectively represent harmonic voltages at two ends of the DC line, If and 17 respectively represent harmonic injection currents caused by GIC of the transformer in the AC power grid. 17 and /7 respectively represent the harmonic injection currents caused by GIC of the converter transformer at both ends of the DC line. The harmonic sources are associated through the AC and DC networks and the harmonic coupling model is further established by utilizing an AC and DC network matrix.
[0116] FIG. 5 is a schematic structure diagram of a modeling system for coupling harmonics in AC and DC power grids in an embodiment of the present invention. In the present invention, the modeling system for coupling harmonics in the AC and DC power grids is provided, which includes: [0117] a historical data acquisition module 501, configured to acquire historical data of an induced geoelectric field during a geomagnetic storm 101181 an induced geoelectric field model establishment module 502, configured to establish a harmonic source model of a transformer in the Alternating Current (AC) power grid, a harmonic source model of a converter transformer in the Direct Current (DC) power grid, a harmonic source model of a converter bridge in the DC power grid, a harmonic network model of the DC power grid and a harmonic network model of the AC power grid, based on the historical data of the induced geoelectric field during the geomagnetic storm; and [0119] a harmonic coupling model establishment module for the AC and DC power grids 503, configured to establish a harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid [0120] The harmonic source model of the transformer in the AC power grid is: Tare (T: -)(1, / L- [0121] where Luc is a Geomagnetic Induced Current (GIC) from a node i to a node j, V = G-1 EL G and */ are voltage values at the node i and the node j respectively ' 1/ " , where
L
E is the induced geoelectric field, and is a distance of a power transmission line from the
G
node i to the node j; and // is a admittance matrix [0122] The GIC harmonic source model of the converter bridge in the DC power grid is: = ki, I "exp( M")+k, I expU 0), -n 11-6 711-6 [0123] where is a harmonic current, kT is a ratio of a no-load phase voltage at a valve side to a phase voltage at a grid side of the transformer, 'Pt' is a phase, in is an effective value of the harmonic current; n is a harmonic order, and n=12m I, where m is a constant, with a maximum value of 15, and m=1, 2, [0124] Various embodiments of the description have been described in a progressive way, each of which emphasizes the difference from the others, and among which the same and similar parts can be referred to each other. Because the system disclosed in the embodiments corresponds to the method disclosed in the embodiments, it is described relatively simply, and the relevant parts can be found in the description of the method.
[0125] The principles and implementations of the present invention have been described herein with specific examples, and the above embodiments are described for a better understanding of the methods and core concepts of the present invention, meanwhile, the detailed implementation and the application scope could be ameneded by those skilled in the art according to the teachings of this invention. In conclusion, the contents of the description should not be construed as limiting the invention.

Claims (10)

  1. CLAIMS1. A modeling method for coupling harmonics in Alternating Current (AC) and Direct Current (DC) power grids, comprising: acquiring historical data of an induced geoelectric field during a geomagnetic storm; establishing a harmonic source model of a transformer in the AC power grid, a harmonic source model of a converter transformer in the DC power grid, a harmonic source model of a converter bridge in the DC power grid, a harmonic network model of the DC power grid and a harmonic network model of the AC power grid, based on the historical data of the induced geoelectric field during the geomagnetic storm; and establishing a harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid.
  2. 2. The modeling method for coupling the harmonics in the AC and DC power grids according to claim 1, wherein the harmonic source model of the transformer in the AC power grid is: /are = -17)g,Iwherein "lc is a Geomagnetic Induced Current (GIC) from a node i to a node j; VV = G-IEL G 7 and V) are voltage values at the node, and the node j, respectively; 71 " wherein E is the induced geoelectric field, and is a distance of a power transmission line from the node i to the node j; and G '7 is a admittance matrix.
  3. 3 The modeling method for coupling the harmonics in the AC and DC power grids according to claim 2, wherein a GIC harmonic source model of the converter bridge in the DC power grid is: = kjnexp(kpn)-47/,,exp[j(Q" ± ] 6 6 wherein 1 is a harmonic current; kr is a ratio of a no-load phase voltage at a valve (p side to a phase voltage at a grid side of the transformer, n is a phase, /'7 is an effective value of the harmonic current; n is a harmonic order, and n=12m ± 1, wherein m is a constant, with a maximum value of 15, and m=1, 2, ..*.
  4. 4. The modeling method for coupling the harmonics in the AC and DC power grids according to claim 3, wherein the harmonic network model of the DC power grid is: z = (r 27 a ey W12120 (n)+1 0(n)(in -1) +Vi2) 27 2h wherein Z0and zm are self impedance and mutual impedance per unit length of a DC line, respectively; I. c is resistance of the DC I ne; Po is vacuum c h is a height of a permeability; ff o(n) i n) is a frequency, s an angular frequency conductor from ground, aaq is an equivalent radius of bundled conductors, a = as Ad eq, wherein k is a number of the bundled conductors, a is a radius of the bundled conductors, s is a side length of a regular polygon formed by the bundled = conductors, and (2S111)k1 I 2 and are constant coefficients,
  5. WIand D is a geometric mean distance of lines 5. The modeling method for coupling the harmonics in the AC and DC power grids according to claim 4, wherein the harmonic network model of the AC power grid is: Y(n) = thy(n)/ Zc( shyol 1 1 Z(n) shy(77) / Zc(n)thy(n) c wherein Y (n) is a network matrix; Zcol and 7(n) are a first function and a y 00 z(nly(n) second function, respectively, wherein = Z00 = z(n)/1(n) z(n) and y(n) are a third function and a forth function, respectively, z'")-r+16)(11)L =g +to (7)(1, r and g are resistance and conductance, respectively, a) (n) is an angular frequency at an nth harmonic, L and C are inductance and capacitance, respectively; and / is an effective length of a magnetic circuit of an iron core.
  6. 6. The modeling method for coupling the harmonics in the AC and DC power grids according to claim 5, wherein establishing the harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid, comprises: superposing currents output from the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid and the harmonic source model of the converter bridge in the DC power grid, to obtain a harmonic current injection amount; determining a harmonic coupling admittance matrix based on the harmonic network model of the DC power grid and the harmonic network model of the AC power grid; superposing voltages output from the harmonic source model of the transformer in the AC power grid and the harmonic source model of the converter bridge in the DC power grid, to obtain a harmonic node voltage vector; and establishing the harmonic coupling model of the AC and DC power grids, based on the harmonic current injection amount, the harmonic coupling admittance matrix and the harmonic node voltage vector.
  7. 7 The modeling method for coupling the harmonics in the AC and DC power grids according to claim 6, wherein the harmonic coupling model of the AC and DC power grids is: jA IC, wherein is the harmonic current injection amount, comprising harmonic current injections of the transformer in the AC power grid, the converter transformer in the DC power grid and the converter bridge in the DC power grid; 17.v is the harmonic coupling admittance matrix, comprising a harmonic network of the AC power grid and a harmonic network of the DC power grid; and UN is the harmonic node voltage vector, comprising node harmonic voltages of the transformer in the AC power grid, a transformer in the DC power grid and the converter bridge in the DC power grid.
  8. 8. A modeling system for coupling harmonics in Alternating Current (AC) and Direct Current (DC) power grids, comprising: a historical data acquisition module, configured to acquire historical data of an induced geoelectric field during a geomagnetic storm; an induced geoelectric field model establishment module, configured to establish a harmonic source model of a transformer in the AC power grid, a harmonic source model of a converter transformer in the DC power grid, a harmonic source model of a converter bridge in the DC power grid, a harmonic network model of the DC power grid and a harmonic network model of the AC power grid, based on the historical data of the induced geoelectric field during the geomagnetic storm; and a harmonic coupling model establishment module for the AC and DC power grids, configured to establish a harmonic coupling model of the AC and DC power grids, based on the harmonic source model of the transformer in the AC power grid, the harmonic source model of the converter transformer in the DC power grid, the harmonic source model of the converter bridge in the DC power grid, the harmonic network model of the DC power grid and the harmonic network model of the AC power grid
  9. 9. The modeling system for coupling the harmonics in the AC and DC power grids according to claim 8, wherein the harmonic source model of the transformer in the AC power grid is: 1.7 where n ich s a Geomagnetic Induced Current (GIC) from a node i to a node j; V and are voltage values at the node and the node j, respectively; Vi = Gi'EL G wherein E is the induced geoelectric field, and 1) is a distance of a powerGtransmission line from the node i to the node j, and is a admittance matrix
  10. 10. The modeling system for coupling the harmonics in the AC and DC power grids according to claim 9, wherein a GIC harmonic source model of the converter bridge in the DC power grid is: = "expy(p")+1c7,I "exp[j(Q"-nir +lc] 6 6 wherein I is a harmonic current; kir is a ratio of a no-load phase voltage at a valve side to a phase voltage at a grid side of the transformer; is a phase; in is an effective value of the harmonic current; n is a harmonic order, and n=12m ± 1, wherein m is a constant, with a maximum value of 15, and m=1, 2,
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CN108258682A (en) * 2018-01-11 2018-07-06 内蒙古科技大学 The control method and system of a kind of electric network geomagnetic induction current
CN113034002A (en) * 2021-03-26 2021-06-25 国网江苏省电力有限公司电力科学研究院 Method for analyzing small-disturbance voltage stability of power system by geomagnetic storm
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US20180145504A1 (en) * 2015-04-23 2018-05-24 New York University Reduction of geomagnetically induced currents
CN108258682A (en) * 2018-01-11 2018-07-06 内蒙古科技大学 The control method and system of a kind of electric network geomagnetic induction current
CN113034002A (en) * 2021-03-26 2021-06-25 国网江苏省电力有限公司电力科学研究院 Method for analyzing small-disturbance voltage stability of power system by geomagnetic storm
CN114117754A (en) * 2021-11-11 2022-03-01 国网内蒙古东部电力有限公司 AC/DC power grid harmonic coupling modeling method and system

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