CN107069795A - A kind of bipolar short-circuit current computational methods of multiterminal MMC HVDC - Google Patents

A kind of bipolar short-circuit current computational methods of multiterminal MMC HVDC Download PDF

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CN107069795A
CN107069795A CN201710287491.6A CN201710287491A CN107069795A CN 107069795 A CN107069795 A CN 107069795A CN 201710287491 A CN201710287491 A CN 201710287491A CN 107069795 A CN107069795 A CN 107069795A
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mrow
mtd
current
mtr
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CN107069795B (en
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陈东
梅念
李高望
程炜
赵峥
刘思源
魏争
李探
陈钊
祝全乐
谭静
刘崇茹
谢国超
王宇
徐东旭
王洁聪
凌博文
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State Grid Corp of China SGCC
North China Electric Power University
State Grid Economic and Technological Research Institute
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State Grid Corp of China SGCC
North China Electric Power University
State Grid Economic and Technological Research Institute
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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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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]

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Locating Faults (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

The present invention relates to a kind of bipolar short-circuit current computational methods of multiterminal MMC HVDC, it is characterised in that comprises the following steps：1) equivalent capacitance, equivalent reactance and the substitutional resistance of single-ended MMC HVDC system converter stations failure equivalent circuit are calculated；2) discharge current of current conversion station after current conversion station locking is calculated；3) discharge current initial solution when each end current conversion station influences without other current conversion stations in multiterminal MMC HVDC systems is calculated；4) fault current actually flowed through on each DC line in multiterminal MMC HVDC systems is calculated；5) substitutional resistance and equivalent reactance that multiterminal MMC HVDC respectively hold current conversion station physical fault equivalent circuit are calculated；6) discharge current of each end current conversion station in multiterminal MMC HVDC systems is recalculated；7) repeat step 4)~6), calculate and obtain the discharge current value that multiterminal MMC HVDC systems respectively hold current conversion station to export.The present invention has certain accuracy and speed, and direct current network planning, dc circuit breaker type selecting have certain directive significance.

Description

A kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC
Technical field
It is double especially with regard to a kind of multiterminal MMC-HVDC the present invention relates to a kind of computational methods of power system fault current Pole short-circuit current computational methods.
Background technology
In recent years, with the development of Power Electronic Technique, the flexible direct current power transmission system based on turn-off device (voltage source converter HVDC, VSC-HVDC) with it without commutation failure, active reactive independent control, be easy to The advantages such as multiterminal power network are constituted, are more and more favored.Flexible direct current power transmission system is broadly divided into two, three-level converter With two kinds of technology paths of modularization multi-level converter (modular multi-level converter, MMC).Wherein module Change multilevel converter by its switching frequency is low, output waveform quality is good, excellent to the switch low, favorable expandability of coherence request etc. Point, the main trend developed as voltage source converter.
DC side fault clearance is always the important issue of direct current transportation research, and straight-flow system damping is small, and the response time is normal Number is small, and fault progression is fast, and control protection cooperation difficulty is big.DC side failure is again the most serious with intereelectrode short-circuit, using modularization When the straight-flow system of multilevel converter occurs bipolar short-circuit, all submodules can be discharged by trouble point, just be produced in several milliseconds Raw serious excessively stream, operation normal to relevant device produces very big impact.
Mainly there are three classes for the more generally acknowledged method of DC side fault clearance both at home and abroad at present：AC circuit breaker, the change of current The DC Line Fault isolating power and dc circuit breaker of device itself.It is slower using AC circuit breaker response speed, 2-3 is needed at the soonest DC side serious excessively stream in individual cycle, this time；Restarting for system needs time cooperation after simultaneous faults excision, and process is multiple Miscellaneous, recovery time is longer.The DC Line Fault isolating power of transverter itself is the topological structure using transverter, former using possessing Phragma from submodule, such as full-bridge submodule (full-bridge sub-module, FBSM), clamped Shuangzi module (clamp Double sub-module, CDSM) etc..But in general, such a method can increase switching device, although with preferable event Barrier passes through characteristic, but needs all equal lockings of current conversion station, can reduce power supply reliability.Meanwhile, using Fault Isolation function Transverter topological structure, it is still desirable to configure breaker, to cut off permanent fault circuit, recovers the operation of other regular links, because This this method can additionally increase expense.It is the product of high voltage DC breaker using the major technology bottleneck of dc circuit breaker Change, and the expensive cost of dc circuit breaker, thus need the mutual of Electric Power Network Planning and parameter designing and dc circuit breaker capacity Coordinate.DC side fault clearance ability be used as weigh DC transmission system important indicator, it has also become project planning it is important because Element.DC side failure requires that dc circuit breaker, current conversion station protect interoperation in 10ms after occurring, therefore is also required to substantial amounts of event Hinder emulation testing.And at this stage, flexible DC power transmission engineering develops to multi-terminal high-voltage Large Copacity direction, it is numerous to be related to submodule, Emulation is slow.Therefore analysis is carried out to DC bipolar short trouble mechanism and quickly calculated to primary system parameter designing, direct current Breaker type selecting has directive significance.
The content of the invention
In view of the above-mentioned problems, it is an object of the invention to provide a kind of bipolar short-circuit current calculating sides of multiterminal MMC-HVDC Method, it is adaptable to the multiterminal MMC-HVDC system dcs side based on half-bridge submodule (half-bridge sub-module, HBSM) Failure, computational accuracy is high, and calculating speed is fast, has certain directive significance to direct current network planning, dc circuit breaker type selecting.
To achieve the above object, the present invention takes following technical scheme：A kind of bipolar short trouble electricity of multiterminal MMC-HVDC Flow calculation methodologies, it is characterised in that comprise the following steps：1) to the DC side failure of the single-ended MMC-HVDC systems based on HBSM Analyzed, i.e., equivalence is carried out to the discharge loop before current conversion station locking, obtain the equivalent capacitance C of the failure equivalent circuiteq, etc. It is worth reactance LeqWith substitutional resistance Req；2) according to obtained equivalent capacitance, equivalent inductance and substitutional resistance, current conversion station locking is calculated The discharge current of current conversion station afterwards；3) use and step 1) and step 2) identical method, to respectively being held in multiterminal MMC-HVDC systems Discharge loop progress when current conversion station influences without other current conversion stations etc. is worth to primary fault equivalent circuit, according to each primary fault The equivalent reactance and substitutional resistance of equivalent circuit, calculating obtain respectively holding current conversion station in multiterminal MMC-HVDC systems without other current conversion stations Discharge current during influence, is used as the initial solution of each end current conversion station discharge current in multiterminal MMC-HVDC systems；4) according to multiterminal DC side failure occurs in MMC-HVDC systems relevant position and the initial solution of each end current conversion station discharge current, calculating are obtained The fault current actually flowed through on each DC line in multiterminal MMC-HVDC systems；5) respectively held according in multiterminal MMC-HVDC systems The fault current actually flowed through on intercouple relation and each DC line of current conversion station, obtains each end current conversion station direct current transmission Line substitutional resistance and equivalent reactance, and then obtain each end current conversion station physical fault equivalent circuit substitutional resistance and equivalent reactance；6) According to step 5) in obtain the substitutional resistance and equivalent reactance of each end current conversion station physical fault equivalent circuit, recalculate multiterminal The discharge current of each end current conversion station in MMC-HVDC systems；7) repeat step 4)~6), calculated using the method for alternating iteration Into multiterminal MMC-HVDC systems, the discharge current value of failure each end current conversion station outlet after occurring.
The step 1) in, the equivalent capacitance C of the failure equivalent circuiteq, equivalent reactance LeqWith substitutional resistance ReqMeter Calculating formula is：
Wherein, C is the capacitance of submodule capacitor, and n is each bridge arm submodule number, R1For bridge arm substitutional resistance, L1For Bridge arm current-limiting reactor, L2For flat ripple reactance, R3For DC link substitutional resistance, L3For the equivalent reactance of DC link, Rf For fault resstance.
The step 2) in, the computational methods of the discharge current of current conversion station comprise the following steps after locking：
1. according to obtained equivalent capacitance Ceq, equivalent inductance LeqWith substitutional resistance Req, calculate failure and occur moment failure etc. It is worth the DC current in circuit, calculation formula is；
In formula：UDCFor DC side monopole voltage-to-ground, I0For inductive current initial value, δ1For damping time constant, and δ1= Req/(2Leq)；ω is angular frequency, andα is to write a Chinese character in simplified form, and：
2. failure occurs in moment failure equivalent circuit the control system parameter in single-ended MMC-HVDC systems DC current is modified, and obtains the discharge current of failure equivalent circuit after failure occurs, and calculation formula is：
In formula：IMAXFor fault current peak value；And
3. the discharge current of failure equivalent circuit obtains the current value at locking moment after being occurred according to failure, after locking The initial value of current conversion station discharge current, and then the discharge current of current conversion station after locking is obtained, calculation formula is：
In formula, δ2=Req/Leq, I1For DC current in locking moment DC line.
The step 4) in, the fault current actually flowed through on each DC line in multiterminal MMC-HVDC systems is：
In formula, I1~I4The discharge current of respectively each current conversion station outlet,It is actual on respectively each DC line The fault current flowed through, l1-l5For each bar DC line length, l is the total length of DC line, i.e. l=l1+l2+l3+l4+l5。
The step 5) in, each end current conversion station DC link substitutional resistance R3With equivalent reactance L3Calculation formula be：
In formula, RL1~RL5The resistance of respectively each DC line, LL1~LL5The reactance of respectively each DC line, The fault current actually flowed through on respectively each DC line.
The present invention is due to taking above technical scheme, and it has advantages below：1st, labor of the present invention is based on HBSM Single-ended MMC-HVDC systems, DC side occur bipolar intereelectrode short-circuit failure when, the influence factor of DC line excessively stream is disclosed Relation between overcurrent amplitude, time and primary system parameter, control system.2nd, the present invention is straight by single-ended MMC-HVDC systems The computational methods of stream side fault current are extended in multiterminal element power network, and current conversion station is respectively held for calculating multiterminal MMC-HVDC systems Fault current, computational accuracy is high, and calculating speed is fast, and simultaneous faults, which is calculated, does not need substantial amounts of off-line simulation, and suitable for not Homeomorphism multiterminal power network.Thus the present invention can be widely applied to the calculating of multiterminal MMC-HVDC system dcs side fault current In.
Brief description of the drawings
Fig. 1 is the three-phase topological structure of MMC in the single-ended MMC-HVDC systems based on HBSM；
Fig. 2 is the failure equivalent circuit of MMC before current conversion station locking；
Fig. 3 is the end MMC-HVDC power network schematic diagrames of parallel connection type four；
Fig. 4 is the failure equivalent circuit of MMC1 in four end MMC-HVDC；
Fig. 5 is MTDC transmission system calculation of fault flow；
Fig. 6 (a) is the simulation result and result of calculation pair of MMC1 discharge current in four end MMC-HVDC in the present embodiment Than figure；
Fig. 6 (b) is the simulation result and result of calculation pair of MMC2 discharge current in four end MMC-HVDC in the present embodiment Than figure；
Fig. 6 (c) is the simulation result and result of calculation pair of MMC3 discharge current in four end MMC-HVDC in the present embodiment Than figure；
Fig. 6 (d) is the simulation result and result of calculation pair of MMC4 discharge current in four end MMC-HVDC in the present embodiment Than figure.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
The present invention provides a kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC, comprises the following steps：
1) to the single-ended MMC-HVDC systems based on HBSM (half-bridge submodule, half-bridge sub-module, HBSM) The DC side failure of system is analyzed, i.e., carry out equivalence to the discharge loop before current conversion station locking, obtain the failure equivalent circuit Equivalent capacitance Ceq, equivalent reactance LeqWith substitutional resistance Req。
As shown in figure 1, being the three-phase topological structure schematic diagram of MMC in the single-ended MMC-HVDC systems based on HBSM.The MMC It is made up of the bridge arm of three-phase six, each bridge arm includes a current-limiting reactor and n submodule, and the current-limiting reactor and n sub- module levels Connection connection.Each submodule includes 2 igbt T1、T2, 2 inverse parallel sustained diodes1、D2With one Direct current capacitors C.Single-ended current conversion station MMC is in normal operation, two igbt T in each submodule1And T2Alternating is led It is logical so as to generate n+1 level staircase waveforms in AC per 2n submodule of phase, while remaining straight per n submodule is mutually put into altogether Flow voltage constant.
As shown in Fig. 2 being the failure equivalent circuit of discharge loop before current conversion station locking.The present invention is at analysis fault current peak Ignore the effect of control system during value, it is believed that per 2n sub- block coupled in series electric discharges of phase, equivalent capacitance CeqBy 2n be often in series Electric capacity and the bridge arm of parallel three phase are calculated, substitutional resistance ReqWith equivalent reactance LeqBy the equivalent electricity of 2 bridge arms being often in series Resistance is calculated with 2 current-limiting reactors, the bridge arm of parallel three phase and discharge loop.Specifically calculation formula is：
Wherein, C is the capacitance of submodule capacitor, and n is each bridge arm submodule number, R1For bridge arm substitutional resistance, L1For Bridge arm current-limiting reactor, L2For flat ripple reactance, R3For DC link substitutional resistance, L3For the equivalent reactance of DC link, Rf For fault resstance.
The primary condition of current conversion station locking prior fault equivalent circuit is：
In formula, UDCFor DC side monopole voltage-to-ground, I0For inductive current initial value, uCFor equivalent capacitance both end voltage, iL To flow through the electric current of equivalent inductance.
2) according to obtained equivalent capacitance Ceq, equivalent inductance LeqWith substitutional resistance Req, calculate current conversion station after current conversion station locking Discharge current.
The computational methods of the discharge current of current conversion station comprise the following steps after locking：
1. according to obtained equivalent capacitance Ceq, equivalent inductance LeqWith substitutional resistance Req, calculate failure and occur moment failure etc. It is worth the DC current in circuit.
For the electric capacity discharge regime before locking, if moment t=0 occurs for failure, now, whole failure equivalent circuit is Know the second order underdamped oscillation discharge process of primary condition.According to primary condition and equivalent capacitance Ceq, equivalent reactance LeqAnd equivalence Resistance Req, the calculation formula for obtaining the DC line fault electric current i in failure equivalent circuit is：
In formula (5), δ1For damping time constant, and δ1=Req/(2Leq)；ω0For resonance angular frequency, andω is angular frequency, and(R is met under normal circumstanceseq/(2Leq))2＜ (the L of ＜ 1/eqCeq), so there is ω=ω0, β=pi/2.
Formula (5) abbreviation can be obtained：
In formula,
2. failure occurs in moment failure equivalent circuit the control system parameter in single-ended MMC-HVDC systems DC current is modified, and obtains the discharge current of failure equivalent circuit after failure occurs.
Control system is still in effect after failure occurs, and control system does not interfere with fault current peak value, but can influence failure Current calculation slope of a curve, according to simulation comparison, the present invention reduces the slope of calculated curve simultaneously on the basis of formula (6) Ignore exponential damping, the discharge current for obtaining failure equivalent circuit after failure occurs is：
In formula, IMAXFor fault current peak value, and
3. the discharge current of failure equivalent circuit obtains the current value at locking moment after being occurred according to failure, after locking The initial value of current conversion station discharge current, and then obtain the discharge current of current conversion station after locking.
Inductance freewheeling period after locking, inductive current can not be mutated, therefore afterflow is led in a period of time after locking Upper and lower bridge arm inverse parallel fly-wheel diode is caused still to turn on.Freewheel current is decayed to after zero, and reversely, now handing over occurs in bridge arm current Streaming system constitutes three-phase uncontrollable rectifier bridge by inverse parallel fly-wheel diode, but generally protects and moved before this Make, therefore calculating now can be ignored.If DC current is I in locking moment DC line1, then current conversion station is put after locking Electric current is：
δ in formula2=Req/Leq。
3) use and step 1) and step 2) identical method, to each end current conversion station in multiterminal MMC-HVDC systems without other Current conversion station influence when discharge loop carry out etc. be worth to primary fault equivalent circuit, according to each primary fault equivalent circuit etc. It is worth reactance and substitutional resistance, calculates the electric discharge obtained when each end current conversion station influences without other current conversion stations in multiterminal MMC-HVDC systems Electric current, is used as the initial solution of each end current conversion station discharge current in multiterminal MMC-HVDC systems.
4) relevant position occurred according to DC side failure in multiterminal MMC-HVDC systems and each end current conversion station electric discharge electricity The initial solution of stream, calculates the fault current for obtaining actually flowing through on each DC line in multiterminal MMC-HVDC systems.
As shown in figure 3, the present invention introduces multiterminal MMC-HVDC systems by taking four end ring net formula parallel connection MMC-HVDC systems as an example Bipolar short-circuit current computational methods.In four end ring net formula parallel connection MMC-HVDC systems, including MMC1~MMC4 totally 4 changes of current Stand, if failure occurs between MMC3 and MMC4, each DC line length is respectively l1~l5, the electric discharge electricity of each current conversion station outlet Stream is respectively I1~I4.During the bipolar short trouble of generation, often holding between current conversion station and trouble point has two paths, per paths The discharge current component flowed through is Ii' and Ii" (i=1,2,3,4), if the impedance of each DC line unit length is identical, according to simultaneously Connection shunting can obtain each discharge current component Ii'、Ii" with each end current conversion station outlet discharge current IiRelation, while consider electric discharge electricity Stream is the superposition of each current conversion station discharge current component on the DC line, according to the reference direction of each electric current, you can obtain each The relation of discharge current and each DC line electric current of end current conversion station outlet is：
In formula, I1~I4The discharge current of respectively each current conversion station outlet, IL1~IL5It is actual on respectively each DC line The fault current flowed through, l is the total length of DC line, i.e. l=l1+l2+l3+l4+l5。
5) according to actual on intercouple relation and each DC line that current conversion station is respectively held in multiterminal MMC-HVDC systems The fault current flowed through, obtains each end current conversion station DC link substitutional resistance and equivalent reactance, and then obtain each end current conversion station The substitutional resistance R of physical fault equivalent circuiteqWith equivalent reactance Leq。
As shown in figure 4, being the failure Equivalent Circuit figure of MMC1 in Fig. 3.Due to each end change of current in multiterminal MMC-HVDC systems Station is mutually coupled, and electric current is not only point of current conversion station outlet discharge current in one end on the DC line on each DC line Amount, but four end current conversion stations export the synthesis of discharge current component, therefore in the equivalent line impedance of every one end current conversion station simultaneously Join reverse current source, to represent the actual electric current flowed through of the circuit, equivalent impedance is circuit actual current and this current conversion station at this The ratio of line discharge current component and the product of line impedance.Now the DC link substitutional resistance of each end current conversion station, etc. Value reactance is respectively：
In formula, RL1~RL5The resistance of respectively each DC line, LL1~LL5The reactance of respectively each DC line, IL1~ IL5The fault current actually flowed through on respectively each DC line.
The DC link substitutional resistance of obtained each end current conversion station, equivalent reactance are substituted into formula (2) and (3), you can Obtain the substitutional resistance R of each end change of current station failure equivalent circuit in multiterminal MMC-HVDC systemseqWith equivalent reactance Leq。
6) according to step 5) in obtain the substitutional resistance R of each end current conversion station physical fault equivalent circuiteqAnd equivalent reactance Leq, recalculate the discharge current of each end current conversion station in multiterminal MMC-HVDC systems.
7) repeat step 4)~6), and calculated and obtained in multiterminal MMC-HVDC systems using the method for alternating iteration, failure hair The discharge current value of each end current conversion station outlet after life.
As shown in figure 5, entering because both discharge current and line current influence each other, therefore using the method for alternating iteration Row is calculated.The initial solution of the discharge current of each end current conversion station outlet first ignores the influence of other current conversion stations when calculating, by equivalent electricity Do not include parallel-current source in road to obtain.Each end current conversion station current maxima is determined by discharge loop, therefore is respectively held before current conversion station Result of calculation is less than ε (such as 10 twice afterwards-5) when exit iteration.
The inventive method is described further with reference to embodiment.In the present embodiment, built under PSCAD/EMTDC Four end MMC DC transmission system simulation models, topological structure are as shown in figure 3, each DC line length l1=226km, l2= 126km, l3=110km, l4=110km, l5=66km, DC line uses lumped parameter, and resistance per unit length R0=0.01 Ω/km, unit length inductance L0=1mH/km.Four end MMC-HVDC primary system parameters are as shown in table 1 below.
The end MMC-HVDC primary system parameters of table 1 four
During 1.5s, intereelectrode short-circuit failure occurs for MMC3 the and MMC4 midpoints in four end MMC-HVDC systems.Occur with failure Moment is t=0, the simulation result of each end current conversion station outlet discharge current and the fault current on DC line and result of calculation It is shown to such as Fig. 6 (a)~6 (d).
By contrast simulation result and result of calculation, multiterminal MMC-HVDC systems occurs the meter of intereelectrode short-circuit failure Calculator is for the good degree of accuracy.Moreover, calculation of fault is independent of off-line simulation, the substantial amounts of time is saved.For other topological shapes The multiterminal element power network of formula, different faults position, the method is applicable, and simple and direct effective.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although The present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that：It still may be used To be modified to the technical scheme described in foregoing embodiments, or equivalent substitution is carried out to which part technical characteristic, And these modification or replace, do not make appropriate technical solution essence depart from various embodiments of the present invention technical scheme spirit and Scope.

Claims (5)

1. a kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC, it is characterised in that comprise the following steps：
1) the DC side failure to the single-ended MMC-HVDC systems based on HBSM is analyzed, i.e., to the electric discharge before current conversion station locking Loop carries out equivalence, obtains the equivalent capacitance C of the failure equivalent circuiteq, equivalent reactance LeqWith substitutional resistance Req；
2) according to obtained equivalent capacitance, equivalent inductance and substitutional resistance, the discharge current of current conversion station after current conversion station locking is calculated；
3) use and step 1) and step 2) identical method, to each end current conversion station in multiterminal MMC-HVDC systems without other changes of current Progress of discharge loop when influenceing etc. of standing is worth to primary fault equivalent circuit, according to the equivalence electricity of each primary fault equivalent circuit Anti- and substitutional resistance, calculates the electric discharge electricity obtained when each end current conversion station influences without other current conversion stations in multiterminal MMC-HVDC systems Stream, is used as the initial solution of each end current conversion station discharge current in multiterminal MMC-HVDC systems；
4) the end current conversion station discharge current according to the relevant position of DC side failure generation in multiterminal MMC-HVDC systems and respectively Initial solution, calculates the fault current for obtaining actually flowing through on each DC line in multiterminal MMC-HVDC systems；
5) according to actually being flowed through on intercouple relation and each DC line of each end current conversion station in multiterminal MMC-HVDC systems Fault current, obtain each end current conversion station DC link substitutional resistance and equivalent reactance, and then it is actual to obtain each end current conversion station Failure equivalent circuit substitutional resistance and equivalent reactance；
6) according to step 5) in obtain the substitutional resistance and equivalent reactance of each end current conversion station physical fault equivalent circuit, recalculate The discharge current of each end current conversion station in multiterminal MMC-HVDC systems；
7) repeat step 4)~6), calculated and obtained in multiterminal MMC-HVDC systems using the method for alternating iteration, after failure occurs The discharge current value of each end current conversion station outlet.
2. a kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC as claimed in claim 1, it is characterised in that：Institute State step 1) in, the equivalent capacitance C of the failure equivalent circuiteq, equivalent reactance LeqWith substitutional resistance ReqCalculation formula be：
<mrow> <msub> <mi>C</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mi>C</mi> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </mfrac> <mo>,</mo> </mrow>
<mrow> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>L</mi> <mn>3</mn> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>R</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>R</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>R</mi> <mi>f</mi> </msub> <mo>,</mo> </mrow>
Wherein, C is the capacitance of submodule capacitor, and n is each bridge arm submodule number, R1For bridge arm substitutional resistance, L1For bridge arm Current-limiting reactor, L2For flat ripple reactance, R3For DC link substitutional resistance, L3For the equivalent reactance of DC link, RfFor event Hinder resistance.
3. a kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC as claimed in claim 1, it is characterised in that：Institute State step 2) in, the computational methods of the discharge current of current conversion station comprise the following steps after locking：
1. according to obtained equivalent capacitance Ceq, equivalent inductance LeqWith substitutional resistance Req, calculate failure and occur the equivalent electricity of moment failure DC current in road, calculation formula is；
<mrow> <mi>i</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mn>1</mn> </msub> <mi>t</mi> </mrow> </msup> <msqrt> <mrow> <mfrac> <mrow> <mn>4</mn> <msubsup> <mi>U</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mfrac> <mo>+</mo> <msubsup> <mi>I</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </msqrt> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
In formula：UDCFor DC side monopole voltage-to-ground, I0For inductive current initial value, δ1For damping time constant, and δ1=Req/ (2Leq)；ω is angular frequency, andα is to write a Chinese character in simplified form, and：
<mrow> <mi>&amp;alpha;</mi> <mo>=</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> <msub> <mi>U</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </mfrac> <msqrt> <mfrac> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <msub> <mi>C</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mfrac> </msqrt> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
2. the control system parameter in single-ended MMC-HVDC systems failure occurs the direct current in moment failure equivalent circuit Electric current is modified, and obtains the discharge current of failure equivalent circuit after failure occurs, and calculation formula is：
<mrow> <mi>i</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>/</mo> <mn>2</mn> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>i</mi> <mo>&lt;</mo> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>(</mo> <mi>i</mi> <mo>&amp;GreaterEqual;</mo> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
In formula：IMAXFor fault current peak value；And
3. the discharge current of failure equivalent circuit obtains the current value at locking moment after being occurred according to failure, is used as the change of current after locking Stand the initial value of discharge current, and then obtain the discharge current of current conversion station after locking, calculation formula is：
<mrow> <mi>i</mi> <mo>=</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mn>2</mn> </msub> <mi>t</mi> </mrow> </msup> <mo>,</mo> </mrow>
In formula, δ2=Req/Leq, I1For DC current in locking moment DC line.
4. a kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC as claimed in claim 1, it is characterised in that：Institute State step 4) in, the fault current actually flowed through on each DC line in multiterminal MMC-HVDC systems is：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mn>4</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <msub> <mi>l</mi> <mn>3</mn> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>l</mi> <mn>4</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>4</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>l</mi> <mn>4</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>l</mi> <mn>4</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>4</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>l</mi> <mn>4</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>4</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>l</mi> <mn>4</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>l</mi> <mn>3</mn> </msub> </mtd> <mtd> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>5</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>l</mi> <mn>3</mn> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>l</mi> <mn>4</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mn>4</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
In formula, I1~I4The discharge current of respectively each current conversion station outlet,Actually flowed through on respectively each DC line Fault current, l1-l5For each bar DC line length, l is the total length of DC line, i.e. l=l1+l2+l3+l4+l5。
5. a kind of bipolar short-circuit current computational methods of multiterminal MMC-HVDC as claimed in claim 1, it is characterised in that：Institute State step 5) in, each end current conversion station DC link substitutional resistance R3With equivalent reactance L3Calculation formula be：
<mrow> <msub> <mi>R</mi> <mn>3</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <mo>)</mo> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <msubsup> <mi>I</mi> <mn>1</mn> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>I</mi> <mn>1</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>
<mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <mo>)</mo> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <msubsup> <mi>I</mi> <mn>1</mn> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>5</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>I</mi> <mn>1</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>
In formula, RL1~RL5The resistance of respectively each DC line, LL1~LL5The reactance of respectively each DC line, Point The fault current that Wei actually do not flow through on each DC line.
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