CN106953348A - A kind of Power network fault calculation method containing back-to-back DC power transmission - Google Patents

Abstract

The invention discloses a kind of Power network fault calculation method containing back-to-back (BTB) direct current transportation, comprise the steps：Input the systematic parameter and control parameter of back-to-back transmission system；Determine the exchange of failure side network topology structure and failure boundary, the network topology structure of non-faulting top-cross streaming system, the constraint equation of the straight-flow system of both sides；Set up the Inverter circuit switch function model of the straight-flow system at two endsWith voltage switch function model；Combination failure top-cross stream constraint equation, direct current constraint equation and transverter switch function solve failure side power frequency busbar voltage；Iterative calculation, exits calculating beyond maximum magnitude when variable error meets calculating requirement or iterations, exports BTB systems two ends AC network change of current bus power-frequency voltage result of calculation.Calculating speed of the present invention is fast, the degree of accuracy is high, strong applicability, has very strong engineering practical value in terms of the AC network calculation of fault and its setting value order of relay protection containing back-to-back DC power transmission.

Description

A kind of Power network fault calculation method containing back-to-back DC power transmission

Technical field

The present invention relates to the research field of electric power system fault computational methods, and in particular to one kind contains back-to-back DC power transmission Power network fault calculation method.

Background technology

As voltage class and construction scale are the western Shandong back-to-back DC engineering of the first in the world compared with similar projects Put into operation, indicate that the application of the back-to-back engineering of China enters the new stage.As between bulk power grid asynchronous networking it is important Mode, back-to-back DC can effectively reduce both sides and connect influencing each other between power network；However, compared with customary DC, the back of the body Backrest direct current is due to without DC power transmission line so that the electrical link between its rectification and inversion is close, thus both sides AC system Between there is certain failure interaction.I.e. when side AC network breaks down, pass through the friendship with back-to-back DC system The interaction of stream-DC-AC, offside power network will be influenceed by certain.Therefore, power network event of the research containing back-to-back DC Barrier computational methods will establish important foundation for the accident analysis of such power network.

Failure interaction and its accident analysis problem have obtained the extensive of experts and scholars all the time between ac and dc systemses Concern, related research work has been carried out for straight-flow system modeling to fault calculation methods for transmission etc..On straight-flow system model, There is research to establish the transverter model based on switch function；Further research work then considers DC control system Failure response, establishes straight-flow system Equivalent Model；The calculation of fault of alternating current-direct current power network can be realized using these models.But on Stating research, to be all based on customary DC transmission line of electricity longer, and only this side current conversion station is impacted during the AC network failure of side, And opposite side current conversion station is substantially unaffected this precondition.It is electric due to back-to-back DC rectifier and inverter Closely, the above-mentioned analysis method for considering failure side current conversion station is not particularly suited for back-to-back DC power transmission system for system.And mesh The preceding research for back-to-back DC then focuses primarily upon analysis and optimization to engineering proposal research and control system, exchange Side protective value analysis and the back-to-back DC commutation failure analysis of causes etc., there is no and be related to the alternating current-direct current containing back-to-back DC Electric network fault is analyzed.Therefore, it is necessary to propose a kind of Power network fault calculation method containing back-to-back DC power transmission.

The content of the invention

It is a primary object of the present invention to fill up the blank of this research field, overcome the shortcoming and deficiency of prior art, carry Go out a kind of Power network fault calculation method containing back-to-back DC power transmission.

In order to achieve the above object, the present invention uses following technical scheme：

A kind of Power network fault calculation method containing back-to-back DC power transmission, comprises the steps：

S1, the back-to-back transmission system of input systematic parameter and control parameter；

S2, form by the network topology structure and failure boundary condition of failure top-cross streaming system the constraint of failure top-cross streaming system Equation, is formed the AC system constraint equation of the side by the network topology structure of non-faulting top-cross streaming system, by the direct current of both sides The direct current constraint equation that control characteristic is set up between its DC side DC voltage and DC current respectively；

S3, failure side and non-faulting side change of current busbar voltage areWherein k is the secondary of interative computation Number；Whole variables are put with initial value, i.e. failure side and change of current busbar voltage in non-faulting side is

S4, set up according to AC power-frequency voltage, DC side current dc component and initial trigger angle voltage x current switch Function model, obtains the switch function of voltage, electric currentWith

S5, by failure side power frequency busbar voltageThe voltage of failure side straight-flow system is tried to achieve with reference to transverter switch function DC componentAnd second harmonic componentSo as to try to achieve the fundamental component of DC side electric currentAnd second harmonic component

S6, with reference to transverter switch function and non-faulting top-cross stream constraint equation try to achieve non-faulting side power frequency busbar voltageAnd thus correct the fundamental component of DC sideAnd second harmonic component

S7, try to achieve the electric current that DC side is injected into the AC network of failure side

S8, the electric current in the AC network of injection failure sideThe exchange constraint equation of combination failure side can try to achieve exchange Try to achieve failure side change of current busbar voltage

S9, judgementWithDifference andWithDifference whether be satisfied by convergence Condition, if being unsatisfactory forSubstitute into respectivelyAnd S4~S9 steps are repeated, until Restrain or reach that maximum iteration backed off after random is calculated, and export result of calculation.

It is preferred that, in step S2, the sequence network equation in the non-faulting top-cross stream constraint equation is as follows：

And then formula (2) is shown for failure boundary conditional equation.

Formula (1), (2) constitute failure top-cross stream constraint equation.In the formula of the above two,AndRespectively event Hinder positive sequence, negative phase-sequence and the zero-sequence component of side change of current bus fundamental frequency voltages.For the electric current positive-sequence component of AC network equivalent power supply,Respectively DC side is injected into the Fundamental-frequency Current positive sequence and negative sequence component of AC network；WithRespectively Positive-sequence component, negative sequence component and the zero-sequence component of fault current at failure；

For non-faulting side exchange constraint equation can be obtained according to the topological structure and principle of stacking of its AC network as Lower expression formula：

In formula (3),ForAC network power frequency order impedance matrix during independent role,ForDuring independent role AC network power frequency positive sequence admittance matrix.

For the direct current set up respectively between its DC side DC voltage and DC current according to the DC control characteristic of both sides Constraint equation is expressed as follows：

I_di0=f_i(U_di0) (4)

I_dr0=f_r(U_dr0) (5)

In formula (4), (5), U_di0、I_di0、U_dr0、I_dr0The DC component of rectification side DC voltage and electric current is expressed as, The DC voltage of inverter side and the DC component of electric current, subscript " i " and " r " wherein in following table represent inverter side and rectification respectively Side；U_d0、I_d0Then refer to the voltage DC component and current dc component of straight-flow system.

It is preferred that, in step S3, k is the number of times of interative computation, and when calculation error is unsatisfactory for requiring, k values Jia 1, is continued Cycle calculations.

It is preferred that, in step S4, built according to AC power-frequency voltage, DC side current dc component and initial trigger angle Vertical voltage x current switch function model, the calculating of the transverter voltage x current switch function power frequency order components is specific as follows：

A) according to the definition of Park Transformation, change of current bus can be converted to a, b, c three-phase voltage by positive and negative, residual voltage：

In formula (6),Respectively the fundamental frequency phase voltage of a, b, c phase of change of current bus, a=e^j2π/3.By phase Voltage and then try to achieve corresponding fundamental frequency line voltageWithAnd then obtain the skew of synchronizing voltage phase

WillWithThe α components and β components of commutation voltage are represented respectively, are counted by formula (7) Calculate：

The phase of DC control system synchronizing voltage can be tried to achieve using the α components and β components of commutation voltage

WillPhase angle bePhase angle bePhase angle beIt can be calculated by following formula The phase offset of synchronizing voltage

In formula (9),For ca phases and the phase offset of synchronizing voltage,Phase for ab phases and synchronizing voltage is inclined Move,For bc phases and the phase offset of synchronizing voltage；

B) according to AC power-frequency voltageWithDC side current dc component I_d0And initial trigger angle α₀, calculate converter valve turn on delay angle θ_mn, actual Trigger Angle α_mnWith actual angle of overlap μ_mn；

Turn on delay angle θ_mnComputing formula be：

In formula (10), xy=ab, bc, ca, wherein a, b, c represent the phase in three-phase respectively, similarly hereinafter；

Actual Trigger Angle α_xyComputing formula be：

In formula (10) and (11), all angles are with delayed for just, advanced is negative；

Angle of overlap μ during xy two-phase commutations_xyComputing formula be：

μ_xy=cos^-1(cosα_xy-2X_rI_d0/U_xy1)-α_xy (12)

In formula (12), X_rFor the commutating reactance of straight-flow system transverter；

C) according to θ_xy、α_xyAnd μ_xyThree-phase voltage current switching waveform is made, Fu is utilized by the three-phase voltage current waveform In leaf-size class number derive each order component of voltage x current switch function：

In formula (13) and (14),Respectively k order components of three-phase voltage switch function, Respectively k order components of three-phase current switch function, k=0,1,2,3 ..., T is 2 π；

Set up the order components of voltage x current switch functionWith

In formula (15) and (16),For m-n phase of abc three-phase voltage switch functions Amount；For its positive and negative sequence component；For n-m phasor of three-phase current switch function；For its positive and negative sequence component；M=0,1,2,3 ..., n=1,2,3 ..., a=e^j2π/3。

It is preferred that, in step S5, the relational expression of DC voltage is tried to achieve by exchange change of current busbar voltage and voltage switch function For：

In formula (17),For m phasor of DC voltage；Thus the voltage DC component of straight-flow system can be tried to achieveAnd second harmonic componentIt can divide with reference to direct current constraint equation (4), formula (5) in the hope of the fundamental frequency of DC side electric current AmountAnd the m subharmonic currents of DC side can be tried to achieve by following formula：

Z_d(m)The DC side equivalent harmonic wave impedance seen into for AC, wherein m=2 can be in the hope of the two of DC side electric current Order harmonic components

It is preferred that, in step S6, the relational expression for trying to achieve alternating current by DC current and current switch function is：

For non-faulting side, n=1 then has：

With reference to non-faulting side exchange constraint equation (3) can in the hope of non-faulting side change of current bus power-frequency voltageIt is possible thereby to reference to the specific steps for setting up switch function, non-faulting side voltage x current switch function is corrected, and then With reference to the fundamental component of calculation procedure amendment DC sideAnd second harmonic component

It is preferred that, in step S7, the electric current that DC side is injected into the AC network of failure side can be tried to achieve according to formula (19)

It is preferred that, in step S8, exchange can be tried to achieve according to formula (1), formula (2) and try to achieve failure side change of current busbar voltage

It is preferred that, in step S9, judgeWithDifference andWithDifference be It is no to be satisfied by the condition of convergence, if being unsatisfactory forSubstitute into respectivelyUnder carrying out afterwards Iterative calculation once, until meeting the condition of convergence or reaching that maximum iteration backed off after random is calculated, and exports result of calculation.

The present invention compared with prior art, has the following advantages that and beneficial effect：

1st, research object of the invention is the AC network containing back-to-back DC power transmission system, has been filled up containing back-to-back DC The blank of research, is the stable operation of BTB systems and its adjusting for relay protection in terms of transmission system AC network calculation of fault Cooperation is laid a good foundation.

2nd, present invention meter and the influence of failure top-cross direct current interphase interaction, at the same consider in side AC network therefore By the AC-DC with back-to-back DC system-exchange interaction during barrier, one caused to non-faulting side power network is fixed Ring.Push through journey by being passed back to and be iterated calculating to whole network, therefore the fault calculation methods for transmission can more realistic situation.

3rd, calculating speed of the present invention is fast, the degree of accuracy is high, in the AC network calculation of fault containing back-to-back DC power transmission system And its there is very strong engineering practical value in terms of the setting value order of relay protection.

Brief description of the drawings

Fig. 1 is the flow chart of the present invention；

Fig. 2 is back-to-back DC power transmission system pie graph of the present invention；

Fig. 3 (a) is the sequence diagrams of failure side AC network positive sequence after BTB systems AC network failure of the present invention；

Fig. 3 (b) is the sequence diagrams of failure top-cross stream electrical network negative phase-sequence after BTB systems AC network failure of the present invention；

Fig. 3 (c) is the sequence diagrams of failure side AC network zero sequence after BTB systems AC network failure of the present invention；

Fig. 3 (d) is the sequence diagrams of non-faulting side AC network positive sequence after BTB systems AC network failure of the present invention；

Fig. 3 (e) is the sequence diagrams of non-faulting top-cross stream electrical network negative phase-sequence after BTB systems AC network failure of the present invention；

Fig. 4 is straight-flow system control characteristic curve in the present embodiment.

Embodiment

With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited In this.

Embodiment

As shown in figure 1, a kind of Power network fault calculation method containing back-to-back DC power transmission of the present invention, implements process such as Under：

Step 1：Input the systematic parameter and control parameter of back-to-back transmission system.

Step 2：According to the structure and parameter of BTB system AC networks, for failure side AC network, with reference to AC system Network topology structure and failure boundary condition can set up what is determined by AC systemWithAC system constraint equation； For non-faulting side AC network, it can be set up with reference to the network structure of AC systemWithAC system constraint side Journey；And the direct current constraint side set up respectively between its DC side DC voltage and DC current according to the DC control characteristic of both sides Journey；Exchange constraint equation and direct current constraint equation specify that the function between AC voltage, electric current between DC voltage, electric current Relation；Sequence network equation in the non-faulting top-cross stream constraint equation is as follows：

And failure boundary conditional equation is then as shown in formula (2)：

Formula (1), (2) constitute failure top-cross stream constraint equation.In the formula of the above two,AndRespectively event Hinder positive sequence, negative phase-sequence and the zero-sequence component of side change of current bus fundamental frequency voltages.For the electric current positive-sequence component of AC network equivalent power supply,Respectively DC side is injected into the Fundamental-frequency Current positive sequence and negative sequence component of AC network.WithRespectively Positive-sequence component, negative sequence component and the zero-sequence component of fault current at failure.Can for the exchange constraint equation of non-faulting side Following expression is obtained according to the topological structure and principle of stacking of its AC network：

In formula (3),ForAC network power frequency order impedance matrix during independent role,ForDuring independent role AC network power frequency positive sequence admittance matrix.

For the direct current set up respectively between its DC side DC voltage and DC current according to the DC control characteristic of both sides Constraint equation is expressed as follows：

I_di0=f_i(U_di0) (4)

I_dr0=f_r(U_dr0) (5)

In formula (4) and (5), U_di0、I_di0、U_dr0、I_dr0The DC component of rectification side DC voltage and electric current is expressed as, The DC voltage of inverter side and the DC component of electric current, subscript " i " and " r " wherein in following table represent inverter side and rectification respectively Side, is such as omitted, i.e. U_d0、I_d0Then refer to the voltage DC component and current dc component of straight-flow system.

Step 3：K=0 is made, whole variables are put with initial value, including failure side and non-faulting side change of current busbar voltage

Step 4：Voltage x current is set up according to AC power-frequency voltage, DC side current dc component and initial trigger angle Switch function model.More specifically, the calculating of the transverter voltage x current switch function power frequency order components is specific as follows：

A) according to the definition of Park Transformation, change of current bus can be converted to a, b, c three-phase voltage by positive and negative, residual voltage：

In formula (6),Respectively the fundamental frequency phase voltage of a, b, c phase of change of current bus, a=e^j2π/3.Thus Try to achieve corresponding fundamental frequency line voltageWithAnd then obtain the skew of synchronizing voltage phase

IfWithThe α components and β components of commutation voltage are represented respectively, are calculated by formula (7)：

The phase of DC control system synchronizing voltage can be tried to achieve using the α components and β components of commutation voltage

IfPhase angle bePhase angle bePhase angle beIt can be counted by formula (9) Calculate the phase offset of synchronizing voltage

In formula (9),For ca phases and the phase offset of synchronizing voltage,Phase for ab phases and synchronizing voltage is inclined Move,For bc phases and the phase offset of synchronizing voltage；

B) according to AC power-frequency voltageWithDC side current dc component I_d0And initial trigger angle α₀, calculate converter valve turn on delay angle θ_mn, actual Trigger Angle α_mnWith actual angle of overlap μ_mn；

Turn on delay angle θ_mnComputing formula be：

In formula (10), xy=ab, bc, ca, wherein a, b, c represent the phase in three-phase respectively, similarly hereinafter；

Actual Trigger Angle α_xyComputing formula be：

In formula (10) and (11), all angles are with delayed for just, advanced is negative；

Angle of overlap μ during xy two-phase commutations_xyComputing formula be：

μ_xy=cos^-1(cosα_xy-2X_rI_d0/U_xy1)-α_xy (12)

In formula (12), X_rFor the commutating reactance of straight-flow system transverter；

C) according to θ_xy、α_xyAnd μ_xyThree-phase voltage current switching waveform is made, Fu is utilized by the three-phase voltage current waveform In leaf-size class number derive each order component of voltage x current switch function：

In formula (13) and (14),Respectively k order components of three-phase voltage switch function, Respectively k order components of three-phase current switch function, k=0,1,2,3 ..., T is 2 π；

Set up the order components of voltage x current switch functionWith

In formula (15) and (16),For m-n phase of abc three-phase voltage switch functions Amount；For its positive and negative sequence component；For n-m phasor of three-phase current switch function；For its positive and negative sequence component；M=0,1,2,3 ..., n=1,2,3 ..., a=e^j2π/3。

Step 5：The relational expression for trying to achieve DC voltage by exchange change of current busbar voltage and voltage switch function is：

In formula (17),For m phasor of DC voltage；Thus the voltage DC component of straight-flow system can be tried to achieveAnd second harmonic componentIt can divide with reference to direct current constraint equation (4), formula (5) in the hope of the fundamental frequency of DC side electric current AmountAnd the m subharmonic currents of DC side can be tried to achieve by following formula：

Z_d(m)The DC side equivalent harmonic wave impedance seen into for AC, makes the m=2 can be in the hope of the secondary of DC side electric current Harmonic component

Step 6：The relational expression for trying to achieve alternating current by DC current and current switch function is：

For non-faulting side, n=1 is made, then is had：

With reference to non-faulting side exchange constraint equation (3) can in the hope of non-faulting side change of current bus power-frequency voltageIt is possible thereby to reference to the specific steps for setting up switch function, non-faulting side voltage x current switch function is corrected, and then The fundamental component I of calculation procedure amendment DC side_d(0)And second harmonic component

Step 7：The electric current that DC side is injected into the AC network of failure side can be tried to achieve according to formula (19)According to formula (1), formula (2) can try to achieve exchange and try to achieve failure side change of current busbar voltage

Step 8：JudgeWithDifference andWithDifference whether be satisfied by receive Hold back condition, if being unsatisfactory forSubstitute into respectivelyIteration next time is carried out afterwards Calculate, until meeting the condition of convergence or reaching that maximum iteration backed off after random is calculated, and export result of calculation.

Fig. 2 is is back-to-back DC power transmission system pie graph in the present invention, back-to-back DC power transmission system as seen from the figure Main element includes change of current bus, converter power transformer, rectifier and the inverter at two ends, while matching somebody with somebody on the ac bus at two ends For more complete wave filter and reactive power compensator.Do not have transmission line of electricity between rectification side and inverter side, only pass through flat ripple Reactor is connected.

The present embodiment establishes Lingbao BTB HVDC Engineering straight-flow system model based on PSCAD/EMTDC.Lingbao City Back-to-back rated capacity is 360MW, and grade of rated voltage is 120kV, and rated current is 3000A, and smoothing reactor is 120mH, rectification side change of current busbar voltage is 330kV, and inverter side change of current busbar voltage is 220kV.For Fig. 2 BTB system knots Composition, failure side and non-faulting side AC network sequence diagrams such as Fig. 3 (a) -3 are can obtain in a certain top-cross stream grid collapses (e) show.In Fig. 3 (a) -3 (e),AndRespectively the positive sequence of failure side change of current bus fundamental frequency voltages, negative phase-sequence and Zero-sequence component.For the electric current positive-sequence component of AC network equivalent power supply,Respectively DC side is injected into failure side The Fundamental-frequency Current positive sequence and negative sequence component of AC network.WithThe positive-sequence component of fault current respectively at failure, Negative sequence component and zero-sequence component.Respectively DC side be injected into failure side AC network Fundamental-frequency Current positive sequence and Negative sequence component.In Fig. 3 (a) -3 (e), the parameter of BTB systems is： Unit is kV； Unit Ω.

DC control system characteristic curve in the present embodiment is as shown in Figure 4.Can be with for the control function of different zones Represented with piecewise function.Fine line A-I in figure is that rectifier runs on minimum trigger angle α_minInversion side controller during control Steady curve, heavy line A-Z is invertor operation in determining shut-off angle γ₀The stable state fortune of rectification side controller during control Row characteristic curve.Therefore, the constraint equation expression of the DC voltage of straight-flow system and electric current is as follows：

Rectification side：

The exchange constraint equation and direct current constraint equation of system can be set up according to above-mentioned parameter.K=0 is made, sets complete Portion's variable initial value is steady-state operation value, i.e., DC voltage is U_d=1.0, DC current is I_d=1.0 (perunit values).

Progressively calculated according to step 4~step 9, step-up error is no more than for front and rear change of current busbar voltage difference twice 0.001, the result of calculation of this computational methods is calculated by successive ignition.

Example one：It is set to rectification side AC network change of current bus and occurs singlephase earth fault, fault resstance is respectively 30 Ω、50Ω；Two-phase short-circuit fault, fault resstance is respectively 30 Ω, 50 Ω；Line to line fault earth fault, fault resstance is respectively 30 Ω, 70 Ω, calculate positive sequence, negative phase-sequence and the residual voltage of stable state change of current bus after failure, this algorithm result of calculation and PSCAD/ The simulation result of EMTDC simulation softwares is as shown in table 1.

Lingbao City's back-to-back DC model rectification side unbalanced fault change of current busbar voltage of table 1 is calculated and simulation result

Example two：It is set to inverter side AC network change of current bus and occurs singlephase earth fault, fault resstance is respectively 50 Ω、70Ω；Two-phase short-circuit fault, fault resstance is respectively 50 Ω, 70 Ω；Line to line fault earth fault, fault resstance is respectively 50 Ω, 70 Ω, calculate positive sequence, negative phase-sequence and the residual voltage of stable state change of current bus after failure, this algorithm result of calculation and PSCAD/ The simulation result of EMTDC simulation softwares is as shown in table 2.

Lingbao City's back-to-back DC model inverter side unbalanced fault change of current busbar voltage of table 2 is calculated and simulation result

Knowable to upper Tables 1 and 2, this algorithm is different in not homonymy failure, homonymy different type failure and same fault The equal very little of error between result of calculation and simulation model simulation value under transition resistance, thus illustrates that this computational methods is calculated accurate Degree is high, can be suitably used for various short troubles, and calculating speed is fast, is a kind of stronger electricity containing back-to-back DC power transmission of practicality Net fault calculation methods for transmission.

Above-described embodiment is preferably embodiment, but embodiments of the present invention are not by above-described embodiment of the invention Limitation, other any Spirit Essences without departing from the present invention and the change made under principle, modification, replacement, combine, simplification, Equivalent substitute mode is should be, is included within protection scope of the present invention.

Claims (9)

1. a kind of Power network fault calculation method containing back-to-back DC power transmission, it is characterised in that comprise the steps：

S1, the back-to-back transmission system of input systematic parameter and control parameter；

S2, failure top-cross streaming system constraint side formed by the network topology structure and failure boundary condition of failure top-cross streaming system Journey, is formed the AC system constraint equation of the side by the network topology structure of non-faulting top-cross streaming system, by the direct current control of both sides The direct current constraint equation that characteristic processed is set up between its DC side DC voltage and DC current respectively；

S3, failure side and non-faulting side change of current busbar voltage areWherein k is the number of times of interative computation；To complete Portion's variable puts initial value, i.e. failure side and change of current busbar voltage in non-faulting side is

S4, voltage x current switch function set up according to AC power-frequency voltage, DC side current dc component and initial trigger angle Model, obtains the switch function of voltage, electric currentWith

S5, by failure side power frequency busbar voltageThe voltage DC of failure side straight-flow system is tried to achieve with reference to transverter switch function ComponentAnd second harmonic componentSo as to try to achieve the fundamental component of DC side electric currentAnd second harmonic component

S6, with reference to transverter switch function and non-faulting top-cross stream constraint equation try to achieve non-faulting side power frequency busbar voltageAnd thus correct the fundamental component of DC sideAnd second harmonic component

S7, try to achieve the electric current that DC side is injected into the AC network of failure side

S8, the electric current in the AC network of injection failure sideThe exchange constraint equation of combination failure side can try to achieve exchange and try to achieve Failure side change of current busbar voltage

S9, judgementWithDifference andWithDifference whether be satisfied by the condition of convergence, If being unsatisfactory forSubstitute into respectivelyAnd repeat S4~S9 step, until convergence or Reach that maximum iteration backed off after random is calculated, and export result of calculation.

2. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 1, it is characterised in that step In rapid S2, the sequence network equation in the non-faulting top-cross stream constraint equation is as follows：

$\left\{\begin{array}{c}{\stackrel{\·}{U}}_{F1}^{+}=f_1({\stackrel{\·}{I}}_{Fs}^{+},{\stackrel{\·}{I}}_{F1}^{+},{\stackrel{\·}{I}}_f^{+})\\ {\stackrel{\·}{U}}_{F1}^{-}=f_2({\stackrel{\·}{I}}_{F1}^{-},{\stackrel{\·}{I}}_f^{-})\\ {\stackrel{\·}{U}}_{F1}^0=f_3\left({\stackrel{\·}{I}}_f^0\right)\end{array}\right.---\left(1\right)$

And failure boundary conditional equation is then as shown in formula (2)：

$f_4({\stackrel{\·}{U}}_{F1}^{+},{\stackrel{\·}{U}}_{F1}^{-},{\stackrel{\·}{U}}_{F1}^0,{\stackrel{\·}{I}}_f^{+},{\stackrel{\·}{I}}_f^{-},{\stackrel{\·}{I}}_f^0)=0---\left(2\right)$

Formula (1), (2) constitute failure top-cross stream constraint equation；In the formula of the above two,AndRespectively failure side Positive sequence, negative phase-sequence and the zero-sequence component of change of current bus fundamental frequency voltages；For the electric current positive-sequence component of AC network equivalent power supply,Respectively DC side is injected into the Fundamental-frequency Current positive sequence and negative sequence component of AC network；WithRespectively Positive-sequence component, negative sequence component and the zero-sequence component of fault current at failure；

It can be obtained for the exchange constraint equation of non-faulting side according to the topological structure and principle of stacking of its AC network such as following table Up to formula：

$\left\{\begin{array}{c}{\stackrel{\·}{U}}_{N1}^{+}=Z_{N1}^{+}{\stackrel{\·}{I}}_{N1}^{+}+Y_{NS1}^{+}{\stackrel{\·}{E}}_{Ns}\\ {\stackrel{\·}{U}}_{N1}^{-}=Z_{N1}^{-}{\stackrel{\·}{I}}_{N1}^{-}\end{array}\right.---\left(3\right)$

In formula (3),ForAC network power frequency order impedance matrix during independent role,ForExchanged during independent role Power network power frequency positive sequence admittance matrix；

For setting up the constraint of the direct current between its DC side DC voltage and DC current respectively according to the DC control characteristic of both sides Equation is expressed as follows：

I_di0=f_i(U_di0) (4)

I_dr0=f_r(U_dr0) (5)

With in (4), (5), U_di0、I_di0、U_dr0、I_dr0It is expressed as the DC component of rectification side DC voltage and electric current, inversion The DC voltage of side and the DC component of electric current, subscript " i " and " r " wherein in following table represent inverter side and rectification side respectively； U_d0、I_d0Then refer to the voltage DC component and current dc component of straight-flow system.

3. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 1, it is characterised in that step In rapid S3, k is the number of times of interative computation, and when calculation error is unsatisfactory for requiring, k values Jia 1, continue cycling through calculating.

4. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 1, it is characterised in that step In rapid S4, voltage x current switch function is set up according to AC power-frequency voltage, DC side current dc component and initial trigger angle Model, the calculating of the transverter voltage x current switch function power frequency order components is specific as follows：

A) according to the definition of Park Transformation, change of current bus can be converted to a, b, c three-phase voltage by positive and negative, residual voltage：

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{a1}\\ {\stackrel{\·}{U}}_{b1}\\ {\stackrel{\·}{U}}_{c1}\end{array}\right]=\left[\begin{array}{ccc}1& 1& 1\\ a^2& a& 1\\ a& a^2& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_1^{+}\\ {\stackrel{\·}{U}}_1^{-}\\ {\stackrel{\·}{U}}_1^0\end{array}\right]---\left(6\right)$

In formula (6),Respectively the fundamental frequency phase voltage of a, b, c phase of change of current bus, a=e^j2π/3；By phase voltage And then try to achieve corresponding fundamental frequency line voltageWithAnd then obtain the skew of synchronizing voltage phase

WillWithThe α components and β components of commutation voltage are represented respectively, are calculated by following formula (7)：

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{\mathrm{\α}}\\ {\stackrel{\·}{U}}_{\mathrm{\β}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{ca1}\\ {\stackrel{\·}{U}}_{ab1}\\ {\stackrel{\·}{U}}_{bc1}\end{array}\right]---\left(7\right)$

The phase of DC control system synchronizing voltage can be tried to achieve using the α components and β components of commutation voltage

WillPhase Angle Table be shown asPhase Angle Table be shown asPhase Angle Table be shown asBy formula (9) The phase offset of synchronizing voltage can be calculated

In formula (9),For ca phases and the phase offset of synchronizing voltage,For ab phases and the phase offset of synchronizing voltage,For bc phases and the phase offset of synchronizing voltage；

B) according to AC power-frequency voltageWithDC side current dc component I_d0And initial trigger angle α₀, meter Calculate converter valve turn on delay angle θ_mn, actual Trigger Angle α_mnWith actual angle of overlap μ_mn；

Turn on delay angle θ_mnComputing formula be：

In formula (10), xy=ab, bc, ca, wherein a, b, c represent the phase in three-phase respectively, similarly hereinafter；

Actual Trigger Angle α_xyComputing formula be：

In formula (10) and (11), all angles are with delayed for just, advanced is negative；

Angle of overlap μ during xy two-phase commutations_xyComputing formula be：

μ_xy=cos^-1(cosα_xy-2X_rI_d0/U_xy1)-α_xy (12)

In formula (12), X_rFor the commutating reactance of straight-flow system transverter；

C) according to θ_xy、α_xyAnd μ_xyThree-phase voltage current switching waveform is made, Fourier is utilized by the three-phase voltage current waveform Series derives each order component of voltage x current switch function：

$\left\{\begin{array}{c}{\stackrel{\·}{S}}_{Uak}=\frac{1}{T}{\∫}_0^T{s}_{Ua}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{Ubk}=\frac{1}{T}{\∫}_0^T{s}_{Ub}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{Uck}=\frac{1}{T}{\∫}_0^T{s}_{Uc}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\end{array}\right.---\left(13\right)$

$\left\{\begin{array}{c}{\stackrel{\·}{S}}_{Iak}=\frac{1}{T}{\∫}_0^T{s}_{Ia}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{Ibk}=\frac{1}{T}{\∫}_0^T{s}_{Ib}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{Ick}=\frac{1}{T}{\∫}_0^T{s}_{Ic}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\end{array}\right.---\left(14\right)$

In formula (13) and (14),Respectively k order components of three-phase voltage switch function, Respectively k order components of three-phase current switch function, k=0,1,2,3 ..., T is 2 π；

Set up the order components of voltage x current switch functionWith

${\stackrel{\·}{S}}_{I(n-m)}^{\±}=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{S}}_{Ia(n-m)}\\ {\stackrel{\·}{S}}_{Ib(n-m)}\\ {\stackrel{\·}{S}}_{Ic(n-m)}\end{array}\right]---\left(15\right)$

${\stackrel{\·}{S}}_{U(m-n)}^{\±}=\[\begin{array}{ccc}{\stackrel{\·}{S}}_{Ua(m-n)}& {\stackrel{\·}{S}}_{Ub(m-n)}& {\stackrel{\·}{S}}_{Uc(m-n)}\end{array}\]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]---\left(16\right)$

In formula,For m-n phasor of abc three-phase voltage switch functions；For it just, Negative sequence component；For n-m phasor of three-phase current switch function；For its positive and negative sequence Component；M=0,1,2,3 ..., n=1,2,3 ..., a=e^j2π/3。

5. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 1, it is characterised in that In step S5, the relational expression for trying to achieve DC voltage by exchange change of current busbar voltage and voltage switch function is：

${\stackrel{\·}{U}}_{d\left(m\right)}=\underset{n}{\Σ}\[\begin{array}{cc}{\stackrel{\·}{S}}_{U(m-n)}^{+}& {\stackrel{\·}{S}}_{U(m-n)}^{-}\end{array}\]\left[\begin{array}{c}{\stackrel{\·}{U}}_{\left(n\right)}^{+}\\ {\stackrel{\·}{U}}_{\left(n\right)}^{-}\end{array}\right]---\left(17\right)$

In formula (17),For m phasor of DC voltage；Thus the voltage DC component of straight-flow system can be tried to achieveWith Second harmonic componentWith reference to direct current constraint equation (4), formula (5) can in the hope of DC side electric current fundamental component And the m subharmonic currents of DC side can be tried to achieve by following formula：

${\stackrel{\·}{I}}_{d\left(m\right)}={\stackrel{\·}{U}}_{d\left(m\right)}/Z_{d\left(m\right)}---\left(18\right)$

Z_d(m)The DC side equivalent harmonic wave impedance seen into for AC, wherein m=2 can be in the hope of the secondary humorous of DC side electric current Wave component

6. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 1, it is characterised in that In step S6, the relational expression for trying to achieve alternating current by DC current and current switch function is：

${\stackrel{\·}{I}}_{\left(n\right)}^{\±}=\underset{m}{\Σ}{\stackrel{\·}{S}}_{I(n-m)}^{\±}{\stackrel{\·}{I}}_{d\left(m\right)}---\left(19\right)$

For non-faulting side, n=1 then has：

$\left\{\begin{array}{c}{\stackrel{\·}{I}}_{N\left(1\right)}^{+}={\stackrel{\·}{S}}_{i1}^{+}{\stackrel{\·}{I}}_{d\left(0\right)}\\ {\stackrel{\·}{I}}_{N\left(1\right)}^{-}={\stackrel{\·}{S}}_{i(-1)}^{+}{\stackrel{\·}{I}}_{d\left(2\right)}\end{array}\right.---\left(20\right)$

With reference to non-faulting side exchange constraint equation (3) can in the hope of non-faulting side change of current bus power-frequency voltage It is possible thereby to reference to the specific steps for setting up switch function, amendment non-faulting side voltage x current switch function, and then combine calculating The fundamental component of step amendment DC sideAnd second harmonic component

7. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 6, it is characterised in that In step S7, the electric current that DC side is injected into the AC network of failure side can be tried to achieve according to formula (19)

8. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 2, it is characterised in that In step S8, exchange can be tried to achieve according to formula (1), formula (2) and try to achieve failure side change of current busbar voltage

9. a kind of Power network fault calculation method containing back-to-back DC power transmission according to claim 1, it is characterised in that In step S9, judgeWithDifference andWithDifference whether be satisfied by restrain bar Part, if being unsatisfactory forSubstitute into respectivelyIterative calculation next time is carried out afterwards, Until meeting the condition of convergence or reaching that maximum iteration backed off after random is calculated, and export result of calculation.