CN108429252B - Method for calculating contribution short-circuit current of alternating current system during direct current fault of multi-terminal alternating current-direct current hybrid power distribution network - Google Patents

Method for calculating contribution short-circuit current of alternating current system during direct current fault of multi-terminal alternating current-direct current hybrid power distribution network Download PDF

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CN108429252B
CN108429252B CN201810127261.8A CN201810127261A CN108429252B CN 108429252 B CN108429252 B CN 108429252B CN 201810127261 A CN201810127261 A CN 201810127261A CN 108429252 B CN108429252 B CN 108429252B
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direct current
converter station
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CN108429252A (en
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祁晓敏
裴玮
肖浩
孔力
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State Grid Jiangsu Electric Power Co Ltd
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Institute of Electrical Engineering of CAS
State Grid Jiangsu Electric Power Co Ltd
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    • 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
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • 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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected 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
    • 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]
    • 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
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • 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 invention relates to a method for calculating contribution short-circuit current of an alternating current system during direct current fault of a multi-terminal alternating current-direct current hybrid power distribution network, which comprises the following steps: 101. the equivalent circuit of the alternating current and direct current hybrid power distribution network after the direct current interelectrode short-circuit fault is provided aiming at the fault current characteristics of the direct current line after the interelectrode short-circuit fault and the contribution of the alternating current system to the fault current. The equivalent circuit consists of an alternating current voltage source 301, an alternating current system equivalent resistor 302, an alternating current system equivalent inductor 303, a converter station direct current side capacitor 206, direct current line resistors 304 and 306 and direct current line inductors 305 and 307; 102. deducing an analytical expression of contribution of the short-circuit current of the alternating current system according to the analysis in the step 101; 103. and (4) providing a method for calculating the contribution short-circuit current of the alternating current system when the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network occurs according to the analysis in the step 102, and calculating a steady-state average value, transient peak time and a transient peak value of the method.

Description

Method for calculating contribution short-circuit current of alternating current system during direct current fault of multi-terminal alternating current-direct current hybrid power distribution network
Technical Field
The invention relates to a method for calculating contribution short-circuit current of an alternating current system during direct current fault of a multi-terminal alternating current and direct current hybrid power distribution network, and belongs to the technical field of alternating current and direct current hybrid power distribution networks.
Background
With the increase of global environmental pollution and energy crisis, the use of renewable energy sources such as wind energy, solar energy and the like to replace traditional fossil energy for power generation becomes a research hotspot of countries in the world. The wide grid connection of renewable energy sources puts higher requirements on technologies such as control and protection of an alternating current power distribution network, and the traditional alternating current power distribution network initially faces huge challenges in the aspects of distributed power supply access, load diversification, large and complicated grid structure and the like. The direct current power distribution network has certain advantages in the aspects of consuming distributed energy, reducing the energy conversion times and the like, but the current purpose of completely replacing the alternating current power distribution mode is not realistic. Therefore, from the perspective of utilizing the existing ac distribution network resources and the advantages of the dc distribution network, the ac/dc hybrid distribution network will become one of the important forms of the future distribution network. In the running process of the alternating-current and direct-current hybrid power distribution network, after a direct-current system line has a short-circuit fault, the alternating-current system can generate certain influence and contribution to the direct-current short-circuit current, and detailed research needs to be carried out aiming at the influence mechanism of the alternating-current system on the direct-current short-circuit current and the calculation method of the contribution short-circuit current of the alternating-current system, so that the influence of the alternating-current system on the direct-current system is determined, and a theoretical basis is laid for system fault.
At present, some theoretical researches are carried out at home and abroad aiming at the mechanism and the calculation method of short-circuit current contribution of an alternating current system after a direct current system fails. In the mechanism of contribution of short-circuit current by an alternating current system, low-voltage bipolar direct-current microgrid fault analysis and protection scheme, which is written in power grid technology 2016, volume 40, phase 3 in Liuxin stamen, Xiaxian, Sun autumn and the like, analyzes characteristics of short-circuit fault between direct-current poles, but does not relate to research on a multi-terminal system. Yang J, Fletcher J E, O' Reilly J and so on, in IEEE Transactions on Industrial Electronics 2012, volume 59, phase 10, "Short-Circuit and group Fault analysis and Location in VSC-Based DC Network Cables" analyze Fault current characteristics of different stages of Short Circuit Fault between direct current lines, and provide corresponding Fault current expressions, but only analyze a single-ended system, and do not consider contributions of a plurality of converter stations. In terms of a method for calculating the contribution of the short-circuit current of the alternating-current system, li bin and heyday, a differential equation set of the contribution of the short-circuit current of the alternating-current system after the direct-current fault of the direct-current power distribution network is given in "flexible direct-current power distribution system fault analysis and current limiting method" written in "chinese electro-mechanical engineering journal" 2015, volume 35, phase 12, but a solution method is not proposed. An International Standard IEC 61660, entitled Short-Circuit Currents in DC automatic Installations in Power Plants and bases in 1997, 6.A direct-current Short-Circuit current steady-state value, peak value and peak time engineering calculation formula of a single converter station is provided, and no calculation is carried out for the contribution of an alternating-current system. A method for calculating a characteristic value of a Short-Circuit current by using a Second-Order system to approximate a system after a fault is proposed by Picres C L, Nabeta S I, Cardoso J R and the like in IET Power Electronics, 2008 volume 1, No. 3, and Second-Order Model for Remote and Close-up Short-Circuit fault Currents on DC Traction Supply, but the method aims at a single-end system and does not relate to the research of a multi-end system.
In short, most of the existing research is carried out on a single-ended system, and the method is not suitable for a multi-ended system. And the existing research does not provide a practical calculation method for contribution of an alternating current system to short-circuit current.
Disclosure of Invention
The purpose of the invention is as follows: the method for calculating the contribution short-circuit current of the alternating current system during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network is simple and easy to operate, can realize the prediction of the fault current level during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network, ensures the reliable operation of the system, and can ensure the calculation accuracy under various conditions.
The technical scheme of the invention is as follows: a method for calculating short-circuit current contribution of an alternating current system during direct current fault of a multi-terminal alternating current and direct current hybrid power distribution network comprises the following steps:
step 101: aiming at the fault current characteristics of a single converter station and the contribution of an alternating current system to the fault current after the interpolar short circuit fault of the direct current line occurs, an equivalent circuit of the alternating current-direct current hybrid power distribution network after the direct current interpolar short circuit fault is constructed;
step 102: establishing an analytical expression of contribution short-circuit current of the alternating current system at different fault stages according to the equivalent circuit obtained in the step 101; the different fault stages refer to a direct current capacitor discharge and an alternating current system feed-in stage;
step 103: and calculating the contribution short-circuit current of the alternating current system when the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network occurs according to the analytical expressions obtained in the step 102 in different fault stages and by combining the equivalent circuit constructed in the step 101, wherein the contribution short-circuit current comprises a steady-state average value, a transient peak time and a transient peak value.
Each step is specifically described as follows:
1. in the step 101, an equivalent circuit after a direct-current interelectrode short circuit fault of the alternating-current and direct-current hybrid power distribution network occurs reflects a current loop of a capacitor discharge stage and a current loop of an alternating-current system feed-in stage;
the equivalent circuit is composed of an alternating current voltage source 301, an alternating current system equivalent resistor 302, an alternating current system equivalent inductor 303, a converter station direct current side capacitor 206, direct current line resistors 304 and 306 and direct current line inductors 305 and 307. The converter station dc side capacitor 206, the dc link resistors 304, 306 and the dc link inductors 305, 307 are connected in series to form a current loop at the dc capacitor discharge stage. An alternating current voltage source 301, an alternating current system equivalent resistor 302 and an alternating current system equivalent inductor 303 are connected in series to form a current loop of an alternating current system feed-in stage; and a current loop in the discharging stage of the direct current capacitor and a current loop in the feeding stage of the alternating current system are connected in parallel to form a fault equivalent circuit of the system.
2. In step 103, the calculation of the short-circuit current can be divided into two stages, i.e., a dc capacitor discharge stage and an ac system feed-in stage;
3. in step 103, the alternating current system contributes an analytical expression of the short-circuit current in different fault stages, including a fault voltage and current expression in a capacitor discharge stage and a fault current expression in an alternating current system feed-in stage:
Figure BDA0001573886220000031
Figure BDA0001573886220000032
wherein i is the number of the converter station, UdciFor the converter station i direct-current side capacitor voltage ii0_iFor fault currents in the respective converter stations, R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。CdiIs the dc side capacitance of each converter station. Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3Equivalent resistance and equivalent inductance for the dc lines of the converter station 3. i.e. iCiDischarging current, i, for the DC-side capacitors of each converter stationsiSupplying a direct short-circuit current, C, to the direct side for the alternating system of each converter stationdiFor the direct-current side capacitance, t, of the converter station i0Time of occurrence of the fault, t1iThe moment when the discharge of the capacitors of the respective converter stations is finished, i.e. the moment when the ac system current starts to be fed into the dc side.
4. In step 103, the fault characteristic values of the short-circuit current contributed by the alternating-current system include a steady-state average value, a transient peak time and a transient peak.
5. In step 103, the steady-state average value of the short-circuit current contributed by the ac system is obtained by the following equations (3) to (6):
Figure BDA0001573886220000033
Figure BDA0001573886220000034
Figure BDA0001573886220000035
Figure BDA0001573886220000036
wherein i is the number of the converter station,
Figure BDA0001573886220000037
for each current conversionSteady state average value of short circuit current contributed by station AC system, ZiImpedance, Z, for feeding short-circuit current loops to the AC system of each converter stationfFor the contribution of the faulty DC line terminal to the impedance of the short-circuit current loop fed into the AC system, NiFor the transformation ratio, V, of the transformers of each converter stationsiFor each converter station AC system phase voltage, RsiFor each converter station AC system equivalent resistance, LsiFor each converter station AC system equivalent inductance, LtiFor each AC system transformer equivalent inductance, LriFor the inductance, R, at the AC outlet of each converter station1＝Rd1_1，L1＝Ld1_1，R2＝Rd2，L2＝Ld2，R3＝Rd3，L3＝Ld3。Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and the equivalent inductance, omega, of the direct current line of the converter station 3siIs the ac system angular frequency.
6. In step 103, the peak time of the short-circuit current contributed by the ac system is obtained by the following equations (7) to (8):
Figure BDA0001573886220000041
γi＝arctan[(U0iω0iCdi sinβi)/(U0iω0iCdi cosβi-I0i)] (8)
wherein, tsipTransient peak time, gamma, contributing short circuit current to an AC systemiIs the system equivalent phase angle when the transient peak arrives. t is t0In order to determine the time at which the failure occurred,i＝Rip/2Lip，
Figure BDA0001573886220000042
βi＝arctan(ωi/i)。U0i、I0ithe initial values of the converter station capacitor voltage and the line current at the moment of the fault occurrence are respectively. R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of each converter station.
7. In step 103, the transient peak value of the short-circuit current contributed by the ac system is obtained by equation (9):
Figure BDA0001573886220000043
wherein isipTransient peak, t, contributing short-circuit current to the AC systemsipContributes to the transient peak time of the short circuit current for the ac system,i＝Rip/2Lip，
Figure BDA0001573886220000044
t0for the time of occurrence of a fault, U0iAnd the initial value of the capacitor voltage of the converter station is the moment of failure occurrence. R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of each converter station.
Compared with the prior art, the invention has the advantages that: the invention provides a calculation method for effectively calculating the characteristic value of short-circuit current contributed by an alternating current system without solving a multivariate differential equation set based on theoretical analysis of a mechanism of short-circuit current contributed by the alternating current system when a direct current fault occurs in a multi-terminal alternating current and direct current hybrid power distribution network, the calculation process is simple and easy to implement, the prediction of the fault current level when the direct current fault occurs in the multi-terminal alternating current and direct current hybrid power distribution network can be realized, the design of a system control strategy and a protection scheme is guided, the reliable operation of the system is ensured, the influence of transition resistance and fault distance on the method is small, and the calculation precision can be ensured under various conditions.
Drawings
FIG. 1 is a flow chart of a method for calculating the contribution of short-circuit current to an AC system according to the present invention;
FIG. 2 is a topological structure diagram of a multi-terminal radiation-shaped AC/DC hybrid power distribution network;
fig. 3 is an equivalent circuit diagram of a multi-terminal radiation-shaped alternating current and direct current hybrid power distribution network fault F1.
Detailed Description
The invention is further described below with reference to the accompanying drawings and the detailed description.
FIG. 1 is a flowchart of a method for calculating a short-circuit current contribution of an AC system according to the present invention. As can be seen from fig. 1, the present invention comprises the following steps: step 101: aiming at the fault current characteristics of a single converter station and the contribution of an alternating current system to the fault current after the interpolar short circuit fault of the direct current line occurs, an equivalent circuit of the alternating current-direct current hybrid power distribution network after the direct current interpolar short circuit fault is constructed; step 102: establishing an analytical expression of contribution short-circuit current of the alternating current system in a direct current capacitor discharge and alternating current system feed-in stage according to the equivalent circuit obtained in the step 101; step 103: and calculating the contribution short-circuit current of the alternating current system when the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network occurs according to the analytical expression obtained by deducting in the step 102 and by combining the equivalent circuit in the step 101, and calculating the steady-state average value, the transient peak time and the transient peak value.
1. Step 101: aiming at the fault current characteristics of a single converter station and the contribution of an alternating current system to the fault current after the interpolar short circuit fault of the direct current line occurs, an equivalent circuit after the direct current interpolar short circuit fault of the alternating current-direct current hybrid power distribution network is constructed:
fig. 2 is a schematic diagram of a topological structure of a multi-terminal radiation-shaped alternating current-direct current hybrid power distribution network, and the system comprises an alternating current system, a transformer, a converter station, a direct current line and the like. Equivalent power supply U for alternating current systems201. Equivalent inductance Ls202 and an equivalent resistance Rs203 are connected in series to be equivalent. The transformer adopts a grid side Yg and valve side delta connection method, the transformation ratio is N, and the equivalent inductance is Lt204. The converter station adopts a three-phase two-level voltage source type converter, and the inductance at the AC side is Lr205, the DC side capacitance of the converter station is Cdi206. The direct current side of the converter station adopts a capacitance midpoint grounding mode, and a direct current circuit is equivalent to the series connection of a resistor and an inductor. Three alternating current distribution networks are connected with a direct current distribution network through three converter stations and then are connected to a public connection point 0, and the converter station 1 adopts a constant direct current voltage and reactive power control mode to ensure the voltage stability of a direct current bus. The converter station 2 and the converter station 3 adopt a constant active power and constant reactive power control mode. The alternating current system and the direct current system can provide power support mutually, and flexible power supply of a plurality of areas is guaranteed. After any converter station fails and stops working, the rest part can continue to exchange power, the system reliability is high, and system capacity expansion is convenient to achieve.
Fig. 3 is an equivalent circuit diagram of the system of fig. 2 after an inter-electrode short fault F1 occurs. Wherein i is the number of the converter station 1, 2, 3, Usdi301 is the equivalent voltage source from the AC system equivalent to the DC side, Rsdi302 is the equivalent resistance from the AC system equivalent to the DC side, Lsdi3303 is the equivalent inductance from the AC system equivalent to the DC side, Rdi_iFor each converter station DC line equivalent resistance, Ldi_iFor each converter station DC line equivalent inductance, Rd1_0、Ld1_0For faulty line ends in the converter station 1Equivalent resistance and inductance. After the fault F1 occurs, the converter station IGBT latches immediately after detecting the fault, and the equivalent circuit diagram shows the fault characteristics of two phases of capacitor discharge and ac system current feed-in after the fault.
Current loop in capacitor discharge stage: as shown by the black solid line part in fig. 3, the dc-side capacitor of the converter station discharges rapidly through the loop formed by the dc line inductor and the resistor, and the dc current rises rapidly, and at this time, the dc fault current is mainly the capacitor discharge current.
The current loop of the feeding stage of the alternating current system is as follows: then, the capacitor discharge stages of the three converter stations are successively ended, and the ending time is t11、t12、t13When a three-phase short-circuit fault occurs on the alternating current side, the feed current of the alternating current system is increased and becomes the leading part of the short-circuit current. After a period of time, the system gradually enters a steady state, and the short-circuit current is still mainly determined by the current fed in by the alternating current system.
2. Step 102: establishing an analytical expression of contribution short-circuit current of the alternating current system in a direct current capacitor and an alternating current system feed-in stage according to the equivalent circuit obtained in the step 101:
and (3) a capacitor discharging stage: from fig. 3, the differential equation of the dc capacitor discharge loop of each converter station can be obtained as follows:
Figure BDA0001573886220000061
wherein i is the number of the converter station, UdciFor the converter station i direct-current side capacitor voltage ii0_iFor fault currents in the respective converter stations, R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。CdiIs the dc side capacitance of each converter station. Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0For failed DC line endsEquivalent resistance and inductance. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of the converter station i.
Solving the formula (1) to obtain the DC voltage U of each converter station at the capacitor discharge stagedciAnd line current ii0_iThe expression of (a) is:
Figure BDA0001573886220000062
Figure BDA0001573886220000063
wherein, UdciFor the converter station i direct-current side capacitor voltage ii0_iIs the fault current of each converter station.i＝Rip/2Lip，
Figure BDA0001573886220000064
βi＝arctan(ωi/i)。t0For the time of occurrence of a fault, U0i、I0iThe initial values of the converter station capacitor voltage and the line current at the moment of the fault occurrence are respectively. R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of each converter station.
And an alternating current system current feeding stage: the short-circuit current contributed to the dc side by a single ac system is:
isi＝isia>0+isib>0+isic>0 (4)
wherein i is the number of the converter station 1, 2, 3, isiContribution of a direct short-circuit current i to the direct current side for the alternating current system of each converter stationsia、isib、isicThe system phase currents are exchanged for the converter station.
During the whole inter-electrode short-circuit fault process, the fault current of the direct current line of each converter station can be expressed as follows:
Figure BDA0001573886220000071
ii0_ifor fault currents of the converter stations, iCiDischarging current, i, for the DC-side capacitors of each converter stationsiDC short-circuit current, t, contributing to the DC side for the AC system of each converter station0Time of occurrence of the fault, t1iThe moment when the discharge of the capacitors of the respective converter stations is finished, i.e. the moment when the ac system current starts to be fed into the dc side.
3. Step 103: calculating the contribution short-circuit current of the alternating current system when the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network occurs according to the analytical expression obtained by deducting in the step 102 and by combining the equivalent circuit in the step 101, wherein the contribution short-circuit current comprises a steady-state average value, a transient peak time and a transient peak value:
calculating the average value of the steady-state current: according to a calculation formula of the average value of short-circuit current contributed by the alternating current system of the single converter station, kirchhoff voltage and kirchhoff current law are deduced to obtain:
Figure BDA0001573886220000072
Figure BDA0001573886220000073
Figure BDA0001573886220000074
Figure BDA0001573886220000075
wherein i is the number of the converter station,
Figure BDA0001573886220000076
contribution of steady-state average value of short-circuit current, Z, to AC system of each converter stationiImpedance, Z, for feeding short-circuit current loops to the AC system of each converter stationfFor the contribution of the faulty DC line terminal to the impedance of the short-circuit current loop fed into the AC system, NiFor the transformation ratio, V, of the transformers of each converter stationsiFor each converter station AC system phase voltage, RsiFor each converter station AC system equivalent resistance, LsiFor each converter station AC system equivalent inductance, LtiFor each AC system transformer equivalent inductance, LriFor the inductance, R, at the AC outlet of each converter station1＝Rd1_1，L1＝Ld1_1，R2＝Rd2，L2＝Ld2，R3＝Rd3，L3＝Ld3。Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and the equivalent inductance, omega, of the direct current line of the converter station 3siIs the ac system angular frequency.
And (4) solving to obtain the average value of the short-circuit current contributed by the alternating current system of each converter station in the post-fault steady-state stage according to the formulas (6) to (9).
Transient current peak time calculation: let equation (2) be 0, the peak time of the short-circuit current contributed by the ac system is:
Figure BDA0001573886220000077
wherein, tsipTransient peak time, gamma, contributing short circuit current to an AC systemiIs the system equivalent phase angle when the transient peak arrives. t is t0In order to determine the time at which the failure occurred,i＝Rip/2Lip，
Figure BDA0001573886220000081
βi＝arctan(ωi/i)。U0i、I0ithe initial values of the converter station capacitor voltage and the line current at the moment of the fault occurrence are respectively. R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。Rdi、LdiFor discharging the equivalent resistance and inductance of the circuit for the DC capacitor after a fault, CdiIs the dc side capacitance of each converter station. Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line.
Transient current peak value calculation: from formula (3):
Figure BDA0001573886220000082
wherein isipTransient peak, t, contributing short-circuit current to the AC systemsipContributes to the transient peak time of the short circuit current for the ac system,i＝Rip/2Lip，
Figure BDA0001573886220000083
t0for the time of occurrence of a fault, U0iAnd the initial value of the capacitor voltage of the converter station is the moment of failure occurrence. R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0。Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0The terminal equivalent resistance and inductance of the fault direct current line. Rd2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of each converter station.
The results of calculating the short-circuit current contributed by the AC system when the DC fault occurs in the system by applying the method are shown in Table 1.
TABLE 1 comparison of the calculation results of the method with the simulation results for different transition resistances
Figure BDA0001573886220000084

Claims (6)

1. A method for calculating contribution short-circuit current of an alternating current system during direct current fault of a multi-terminal alternating current and direct current hybrid power distribution network is characterized by comprising the following steps: the calculation method comprises the following steps:
step 101: aiming at the fault current characteristics of a single converter station and the contribution of an alternating current system to the fault current after the interpolar short circuit fault of the direct current line occurs, an equivalent circuit of the alternating current-direct current hybrid power distribution network after the direct current interpolar short circuit fault is constructed;
step 102: establishing an analytical expression of contribution short-circuit current of the alternating current system at different fault stages according to the equivalent circuit obtained in the step 101; the different fault stages are two stages of direct current capacitor discharge and alternating current system feed-in;
step 103: calculating short-circuit current contributed by the alternating current system when the direct current fault of the multi-terminal alternating current-direct current hybrid power distribution network occurs according to the analytical expressions at different fault stages obtained in the step 102 and in combination with the equivalent circuit constructed in the step 101, wherein the short-circuit current comprises a steady-state average value, transient peak time and a transient peak;
the equivalent circuit after the short circuit fault between the direct current poles of the alternating current and direct current hybrid power distribution network in the step 101 reflects a current loop of a direct current capacitor discharging stage and an alternating current system feeding stage;
the equivalent circuit consists of an alternating current voltage source, an alternating current system equivalent resistor, an alternating current system equivalent inductor, a converter station direct current side capacitor, a first direct current line resistor, a second direct current line resistor, a first direct current line inductor and a second direct current line inductor; a direct current side capacitor, a first direct current line resistor, a second direct current line resistor, a first direct current line inductor and a second direct current line inductor of the converter station are connected in series to form a current loop in a direct current capacitor discharging stage; the alternating current voltage source, the alternating current system equivalent resistor and the alternating current system equivalent inductor are connected in series to form a current loop of the alternating current system feed-in stage; and a current loop in the discharging stage of the direct current capacitor and a current loop in the feeding stage of the alternating current system are connected in parallel to form a fault equivalent circuit of the system.
2. The method for calculating the contribution of the short-circuit current of the alternating current system during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network according to claim 1, characterized by comprising the following steps of: in step 103, the short-circuit current is calculated by two stages, i.e., dc capacitor discharge and ac system feed.
3. The method for calculating the contribution of the short-circuit current of the alternating current system during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network according to claim 1, characterized by comprising the following steps of: in the step 102, the analytical expression of the direct-current capacitor discharge stage includes a fault voltage and current expression; the analytical expression of the feed-in stage of the alternating current system comprises a fault current expression;
wherein the fault voltage and current expressions of the discharge phase of the DC capacitor
Figure FDA0002587733400000011
The fault current expression of the alternating current system feed-in stage is as follows:
Figure FDA0002587733400000012
wherein i is the number of the converter station, UdciFor the converter station i the dc side capacitor voltage, also called the fault voltage at the dc capacitor discharge stage, i is 1, 2, 3, ii0_iFor fault currents in the respective converter stations, R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0，Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0For the end equivalent resistance and inductance, R, of a faulty DC lined2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and the equivalent inductance, i, of the direct current line of the converter station 3CiDischarging current, i, for the DC-side capacitors of each converter stationsiSupplying a direct short-circuit current, C, to the direct side for the alternating system of each converter stationdiIs the DC side capacitance, t, of the converter station i0Time of occurrence of the fault, t1iThe moment when the discharge of the capacitors of the respective converter stations is finished, i.e. the moment when the ac system current starts to be fed into the dc side.
4. The method for calculating the contribution of the short-circuit current of the alternating current system during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network according to claim 1, characterized by comprising the following steps of: in step 103, the steady state average value is obtained by equations (3) to (6):
Figure FDA0002587733400000021
Figure FDA0002587733400000022
Figure FDA0002587733400000023
Figure FDA0002587733400000024
wherein i is the number of the converter station, i is 1, 2, 3,
Figure FDA0002587733400000025
contribution of steady-state average value of short-circuit current, Z, to AC system of each converter stationiImpedance, Z, for feeding short-circuit current loops to the AC system of each converter stationfFor the contribution of the faulty DC line terminal to the impedance of the short-circuit current loop fed into the AC system, NiFor the transformation ratio, V, of the transformers of each converter stationsiFor each converter station AC system phase voltage, RsiFor each converter station AC system equivalent resistance, LsiFor each converter station AC system equivalent inductance, LtiFor each AC system transformer equivalent inductance, LriFor the inductance, R, at the AC outlet of each converter station1＝Rd1_1，L1＝Ld1_1，R2＝Rd2，L2＝Ld2，R3＝Rd3，L3＝Ld3，Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0For the end equivalent resistance and inductance, R, of a faulty DC lined2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and the equivalent inductance, omega, of the direct current line of the converter station 3siIs the ac system angular frequency.
5. The method for calculating the contribution of the short-circuit current of the alternating current system during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network according to claim 1, characterized by comprising the following steps of: in step 103, the transient peak time is obtained by equations (7) to (8):
Figure FDA0002587733400000026
γi＝arctan[(U0iω0iCdi sinβi)/(U0iω0iCdi cosβi-I0i)] (8)
wherein, tsipTransient peak time, gamma, contributing short circuit current to an AC systemiIs the equivalent phase angle of the system at the time of transient peak arrival, t0In order to determine the time at which the failure occurred,i＝Rip/2Lip，
Figure FDA0002587733400000031
βi＝arctan(ωi/i)，U0i、I0ithe initial values of the converter station capacitor voltage and the line current at the moment of the fault are respectively, and i is 1, 2 and 3; r1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0，Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0For the end equivalent resistance and inductance, R, of a faulty DC lined2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of each converter station.
6. The method for calculating the contribution of the short-circuit current of the alternating current system during the direct current fault of the multi-terminal alternating current and direct current hybrid power distribution network according to claim 1, characterized by comprising the following steps of: in step 103, the transient peak is obtained by equation (9):
Figure FDA0002587733400000032
wherein isipTransient peak, t, contributing short-circuit current to the AC systemsipContributes to the transient peak time of the short circuit current for the ac system,i＝Rip/2Lip，
Figure FDA0002587733400000033
t0for the time of occurrence of a fault, U0iFor the initial value of the capacitor voltage of the converter station at the time of the fault, i is 1, 2, 3, R1p＝Rd1_1，L1p＝Ld1_1，R2p＝Rd2+Rd1_0，L2p＝Ld2+Ld1_0，R3p＝Rd3+Rd1_0，L3p＝Ld3+Ld1_0；Rd1_1、Ld1_1Equivalent resistance and inductance R for the initial end of the direct current line with the fault of the converter station 1d1_0、Ld1_0For the end equivalent resistance and inductance, R, of a faulty DC lined2、Ld2For the equivalent resistance and the equivalent inductance, R, of the DC line of the converter station 2d3、Ld3For the equivalent resistance and inductance, C, of the DC line of the converter station 3diIs the dc side capacitance of each converter station.
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