CN108808669A - The Dynamic Phasors modeling method of HVDC transmission system transverter - Google Patents
The Dynamic Phasors modeling method of HVDC transmission system transverter Download PDFInfo
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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
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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
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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
- 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]
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- 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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Abstract
The invention discloses a kind of Dynamic Phasors modeling methods of HVDC transmission system transverter, it is according to the first-order dynamic phasor of transverter phase voltage, DC current zeroth order Dynamic Phasors and DC current second order Dynamic Phasors, and the Trigger Angle of DC control system, calculate practical Trigger Angle, turn on delay angle and the angle of overlap of each converter valve in transverter；It is calculated according to the practical Trigger Angle of each converter valve, turn on delay angle and angle of overlap in transverter and obtains three-phase voltage switch function and three-phase current switch function；By three-phase voltage switch function and three-phase current switch function, and it is decomposed on the basis of determining characteristic harmonics to alternating voltage and DC current progress order components, the dynamic phasor model of transverter is established, the method for the present invention can effectively improve model accuracy, reduce calculation amount.
Description
Technical field
The present invention relates to a kind of Dynamic Phasors modeling method of HVDC transmission system transverter, more specifically one
Kind is applied in unbalanced fault, a kind of HVDC transmission system change of current of alternating current-direct current combined hybrid system dynamic analysis
The Dynamic Phasors modeling method of device.
Background technology
Because its advantage in terms of long-distance and large-capacity power transmission is used widely, this makes directly high voltage dc transmission technology
Streaming system is modeled as the research emphasis in the field.Transverter is as the most important device of straight-flow system, the accuracy of model
Directly determine the validity of straight-flow system modeling.Transverter is as typical discrete switch element, in the huge of electric system
Under limitation with complexity and calculation scale and time, it is difficult to it is imitative to carry out the detailed electromagnetic transient modeling comprising valve process
Very, ignoring the simplified model of dynamic characteristic will make model lack accuracy.Dynamic Phasors as the improvement to quasi steady state method,
Derived from traditional mean value method, derived based on the corresponding time-varying Fourier coefficient of state variable for reflecting element dynamic characteristic
A kind of modeling method, precision is between QSS models and EMPT models, can be certain in Design & Analysis of System
Detailed time-domain model is replaced in research range, and the complexity of model can change according to the needs of analysis.
Being applied to the modeling method of the transverter dynamic phasor model under system asymmetric operation state in the prior art is
By fundametal component, commutation component and component is corrected according to influence construction of the asymmetric three-phase commutation voltage to transverter switch motion
The voltage and current switch function of composition is allowed to be suitable for the various operating conditions of ac and dc systems and fault condition；However it exchanges
When system asymmetrical three-phase, can transverter alternating current-direct current side generate each harmonic, especially 2 subharmonic current of DC side usually compared with
Greatly, more serious or when DC side equivalent harmonic wave impedance is smaller in asymmetric situation, the amplitudes of 2 subharmonic currents even close to
DC component, large error can be brought by ignoring its influence.
Invention content
The present invention is to provide a kind of high voltage direct current suitable under unbalanced fault to avoid above-mentioned the deficiencies in the prior art
The Dynamic Phasors modeling method of transmission system transverter, according to the commutation process of transverter under three-phase asymmetric operating state,
The influence of 2 subharmonic of DC side is considered in the calculating of angle of overlap, and inessential harmonic wave is ignored according to phasesequence component analysis and simplifies mould
The calculating process of type reduces calculation amount to improve model accuracy；
The present invention is to solve technical problem to adopt the following technical scheme that：
The characteristics of Dynamic Phasors modeling method of HVDC transmission system transverter of the present invention is to carry out as follows：
Step 1, voltage calculate；
Step 1.1, in time interval τ, τ ∈ (t-T0, t], sampling respectively obtains Converter DC-side electric current id(t) and
Transverter exchange side phase voltage ua(t)、ub(t) and uc(t), it is calculated using formula (1) and obtains each line voltage amplitude of transverter exchange side
umn(t)：
umn(t)=um(t)-un(t) (1),
In formula (1), m=a, b or c, n=a, b or c, difference corresponding A phase, B phases and C phases, mn=ab, bc or ca are described to change
It refers to HVDC transmission system DC current importation to flow device DC side, and transverter exchange side refers to D.C. high voltage transmission system
System alternating voltage importation；
Step 1.2, for the transverter exchange side phase voltage u obtained in step 1.1mn(t) side line electricity is exchanged with transverter
Press um(t), it is converted respectively using discrete Fourier transform and obtains transverter exchange side phase voltage first-order dynamic phasor<Um>1With change
Flow device exchange side line voltage first-order dynamic phasor<Umn>1；
Step 2 obtains phase offset；
Step 2.1, using formula (2) by transverter exchange side line voltage first-order dynamic phasor<Uab>1、<Ubc>1With<Uca>1It is logical
It crosses coordinate transform and obtains commutation voltage α componentsAnd commutation voltage β components
By commutation voltage α componentsWith commutation voltage β componentsExpansion is expressed as respectively：WithUαAnd UβIt is the amplitude of commutation voltage α components and commutation voltage β components respectively,WithRespectively commutation electricity
Press the phase of α components and commutation voltage β components；
Step 2.2 calculates DC control system synchronizing voltage phase in acquisition HVDC transmission system using formula (3)
Step 2.3, the phase that each line voltage when unbalanced fault occurs according to AC system, are calculated separately using formula (4)
Obtain the phase offset of synchronizing voltage：
In formula (4),WithEach line voltage U when corresponding as unbalanced fault occursca、UabAnd UbcPhase
Position,WithIt is each line voltage U to correspondca、UabAnd UbcAlternate synchronizing voltage phase offset.
Step 3 calculates practical Trigger Angle：
Sampling obtains the Trigger Angle instruction α that DC control system is sent out0, calculated using formula (5) and obtain three-phase converter valve
Commutation deviation angle θmnWith practical Trigger Angle αmn：
Angle of overlap between the transverter three-phase converter valve of step 4, calculating meter and second harmonic；
Step 4.1, for the Converter DC-side electric current i for sampling acquisition in step 1.1d(t) discrete fourier change is carried out
It changes, obtains the zeroth order Dynamic Phasors of Converter DC-side electric current respectively<Id>0With second order Dynamic Phasors<Id>2；
Step 4.2 calculates the angle of overlap μ between obtaining transverter three-phase converter valve using formula (6)mn：
In formula (6), XrFor transverter equivalence to the reactance value of valve side,For DC current second harmonic initial phase；
Step 5 establishes transverter improvement switch function model：
Step 5.1, by threephase switch function SmIt is launched into each component, is respectively：Fundametal component Sj, correct component SgmWith change
Phase component Sμm, the commutation component SμmIncluding voltage commutation component SuμmWith current commutation component Siμm；
Each component is launched by step 5.2 using Fourier space：Sj(ω t), Sg(ωt,θmn), Suμ(ωt,
μmn) and Siμ(ωt,μmn)；
Step 5.3, the commutation deviation angle θ according to three-phase converter valvemn, practical Trigger Angle αmn, changing between three-phase converter valve
Phase angle μmn, initial commutation device switch function model S ' is established using formula (7)umWith S 'im：
Step 5.4 is corrected by doing lag in phase to initial commutation device switch function model, by voltage switch function
S′umWith current switch function S 'imUnified Expression is S 'm, establish the transverter switch function improved model S as shown in formula (8)m：
Step 5.5 obtains three-phase voltage switch function S using discrete Fourier transform by formula (9)umIt is switched with three-phase current
Function SimQ rank Dynamic Phasors forms：
In formula (9),<sum>qFor three-phase voltage switch function SumQ rank Dynamic Phasors,<sim>qLetter is switched for three-phase current
Number SimQ rank Dynamic Phasors；
Step 6 carries out order components decomposition to each component：
Step 6.1, the q rank Dynamic Phasors that positive and negative sequence voltage switch function and current switch function are calculated using formula (10)：
In formula (10), h=ej2π/3,For the q rank Dynamic Phasors of positive and negative sequence voltage switch function,For the q rank Dynamic Phasors of positive and negative sequence current switch function；
Step 6.2, (p-q) rank dynamic phase that transverter exchange side three-phase voltage positive and negative sequence component is calculated using formula (11)
Amount<u+>p-qWith<u->p-q：
In formula (11), p, q are arbitrary nonzero integer, and p ≠ q,<ua>p-q、<ub>p-qWith<uc>p-qRespectively change of current busbar
A, (p-q) rank Dynamic Phasors of B, C three-phase voltage；
Step 7, the dynamic phasor model for constructing transverter：
Step 7.1 calculates the Dynamic Phasors for obtaining ac-side current and DC voltage using formula (12)：
In formula (12),<i+>kWith<i->kThe respectively k rank Dynamic Phasors of the positive and negative order components of transverter ac-side current,<ud
>pFor the p rank Dynamic Phasors of Converter DC-side voltage,<id>k-qIt is that the transverter that is calculated by discrete Fourier transform is straight
Flow (k-q) rank Dynamic Phasors of side electric current；
Step 7.2 is based on that the analysis of moment uncharacteristic harmonics occurs to not failure, and the alternating current of transverter exchange side includes
Fundamental wave and 3 order harmonic components, DC side DC voltage include DC quantity and 2 order harmonic components, what foundation was characterized by formula (13)
The dynamic phasor model of transverter：
The characteristics of Dynamic Phasors modeling method of HVDC transmission system transverter of the present invention, lies also in：It is each in formula (7)
Correct component Sgm, voltage commutation component SuμmWith current commutation component SiμmIt is respectively：
Sga=Sg(ωt-π/3,θab)-Sg(ωt-π/3,θca),
Sgb=Sg(ωt-π/3,θbc)-Sg(ωt-π/3,θab),
Sgc=Sg(ωt-π/3,θca)+Sg(ωt-π/3,θbc),
Suμa=Suμ(ωt-π/3-θab,μab)-Suμ(ωt+π/3-θca,θca),
Suμb=-Suμ(ωt-θbc,θbc)-Suμ(ωt-π/3-θab,θab),
Suμc=Suμ(ωt+π/3-θca,θca)-Suμ(ωt-θbc,θbc),
Siμa=Siμ(ωt-π/3-θab,μab)-Siμ(ωt+π/3-θca,μca),
Siμb=-Siμ(ωt-θbc,μbc)-Siμ(ωt-π/3-θab,μbc),
Siμc=Siμ(ωt+π/3-θca,μca)-Siμ(ωt-θbc,μbc),
Wherein：θcaFor CA two-phase commutations when A phase converter valves commutation deviation angle, θabFor AB two-phase commutations when B phase converter valves
Commutation deviation angle, θbcFor BC two-phase commutations when C phase converter valves commutation deviation angle.
Compared with the prior art, the present invention has the beneficial effect that：
1, the influence of 2 subharmonic of DC side is considered in the calculating of angle of overlap due to the present invention, it is not right in commutation voltage
When title, the second harmonic of larger component can be generated in Converter DC-side, the amplitude of second harmonic component even can be big when serious
In DC component.The size of DC current is directly related with the commutation duration, secondary between out of phase converter valve when commutation
Harmonic current can play the role of commutation DC current superposition or counteracting.Therefore, between calculating transverter three-phase converter valve
Angle of overlap when, consider DC side second harmonic current influence it is very necessary, breach the Dynamic Phasors of traditional angle of overlap
Computational methods effectively improve model accuracy；
2, the steady-state analysis of electric system unbalanced fault generally uses sequence component analysis method, the present invention to be changed by establishing
The order components model for flowing device is convenient for carrying out united analysis to entire ac and dc systems；
3, due to the present invention, using phasesequence component analysis, moment uncharacteristic harmonics do not occur for failure, based on humorous to straight-flow system
Wave studies the uncharacteristic harmonics voltage low one it can be shown that 12 pulse converters of the uncharacteristic harmonics voltage ratio n=1 of n >=1
A order of magnitude.Therefore it can ignore inessential harmonic wave, low order uncharacteristic harmonics only be considered, to enormously simplify the calculating of model
Process, and ensure model accuracy enough, and calculation amount is greatly decreased.
Description of the drawings
Fig. 1 is six pulse conversion devices topology diagrams in the present invention；
Fig. 2 a and Fig. 2 b are the on-delay condition schematic diagram of converter valve under different situations in the present invention；
Fig. 3 falls into a trap for the present invention and the angle of overlap calculation flow chart of DC current second harmonic；
Fig. 4 is that each component schematic diagram of switch function model is improved in the present invention；
Fig. 5 is that each component Overlay schematic diagram of switch function model is improved in the present invention.
Specific implementation mode
The Dynamic Phasors modeling method of the present embodiment mesohigh DC transmission system transverter is to carry out as follows：
Step 1, voltage calculate：
Step 1.1, in time interval τ, τ ∈ (t-T0, t], sampling respectively obtains Converter DC-side electric current id(t) and
Transverter exchange side phase voltage ua(t)、ub(t) and uc(t), it is calculated using formula (1) and obtains each line voltage amplitude of transverter exchange side
umn(t)：
umn(t)=um(t)-un(t) (1),
In formula (1), m=a, b or c, n=a, b or c, difference corresponding A phase, B phases, C phases, mn=ab, bc or ca are described to change
It refers to HVDC transmission system DC current importation to flow device DC side, and transverter exchange side refers to D.C. high voltage transmission system
System alternating voltage importation.
Step 1.2, for the transverter exchange side phase voltage u obtained in step 1.1mn(t) side line electricity is exchanged with transverter
Press um(t), it is converted respectively using discrete Fourier transform and obtains transverter exchange side phase voltage first-order dynamic phasor<Um>1With change
Flow device exchange side line voltage first-order dynamic phasor<Umn>1, obtain Dynamic Phasors using discrete Fourier transform and specifically refer to：For
N points discrete series { x [l] }1≤l≤N, calculate the k rank Dynamic Phasors for obtaining x<x>kFor：Wherein, e is
The truth of a matter of natural logrithm, j are imaginary unit, and N indicates sampling number, wherein 1≤l≤N.
Step 2 obtains phase offset：
Phase offset refers to：When asymmetrical three-phase failure, unbalanced fault can cause change of current busbar three-phase voltage uneven
Weighing apparatus, leads to null offset, this can cause the practical angle of overlap of each phase different, is actually turned on the moment and can also shift.
Step 2.1, using formula (2) by transverter exchange side line voltage first-order dynamic phasor<Uab>1、<Ubc>1With<Uca>1It is logical
It crosses coordinate transform and obtains the α components of commutation voltageAnd the β components of commutation voltage
By the α components of commutation voltageWith β componentsExpansion is expressed as respectively：
Wherein, UαAnd UβIt is the amplitude of commutation voltage α components and commutation voltage β components respectively,WithRespectively commutation voltage α components
With the phase of commutation voltage β components.
DC control system is protected for the control of HVDC transmission system in step 2.2, HVDC transmission system,
Calculated synchronizing voltage phaseThe reference phase of DC control system output can be obtained, and then is transverter
Trigger pulse is provided, the phase for obtaining DC control system synchronizing voltage is calculated using formula (3)
Step 2.3, the phase that each line voltage when unbalanced fault occurs according to AC system, are calculated separately using formula (4)
Obtain the phase offset of synchronizing voltage：
In formula (4),WithEach line voltage U when corresponding as unbalanced fault occursca、UabAnd UbcPhase
Position,WithIt is each line voltage U to correspondca、UabAnd UbcAlternate synchronizing voltage phase offset.
Step 3 calculates practical Trigger Angle：
Fig. 1 show the topology diagram of six pulse conversion devices, and six pulse conversion devices are made of three bridges, Mei Geqiao
There are upper bridge arm and lower bridge arm, the converter valve of thyristor composition is in series on each bridge arm, three-phase converter valve is the core of transverter
Heart component part controls respective turn-on instant, realizes that transverter is whole by applying trigger pulse respectively to this six converter valves
Stream or the function of inversion.When unbalanced fault occurs, transverter will be operate in asymmetric state, and three-phase angle of overlap is unequal,
Three-phase angle of overlap is unequal and the turn-on instant of converter valve will also shift, and phase difference and converter valve triggering moment occurs
Offset needs to calculate converter valve turn on delay angle and practical Trigger Angle at this time.
Fig. 2 a and Fig. 2 b show the on-delay situation of converter valve under different situations, and wherein Fig. 2 a show symmetric case
Under converter valve on-delay situation, Fig. 2 b show the converter valve on-delay situation in the case of asymmetry.
Sampling obtains the Trigger Angle instruction α that DC control system is sent out0, three-phase converter valve is calculated using formula (5)
Commutation deviation angle θmnWith practical Trigger Angle αmn：
Step 4 calculates angle of overlap between meter and the transverter three-phase converter valve of second harmonic：
Fig. 3 show angle of overlap calculation flow chart, in the calculating process of the angle of overlap between transverter three-phase converter valve, when
When commutation voltage asymmetry, the second harmonic of larger component, second harmonic component when serious can be generated in Converter DC-side
Amplitude is even larger than DC component.The size of DC current is directly related with the commutation duration, out of phase converter valve it
Between commutation when, second harmonic current can play the role of commutation DC current superposition or counteracting.Therefore, transverter three is being calculated
When angle of overlap between phase converter valve, it is necessary to take into account the influence of DC side second harmonic current.
Step 4.1, in same time interval τ, sampling obtains Converter DC-side electric current id(t), straight for transverter
Flow side electric current id(t) discrete Fourier transform is carried out, the zeroth order Dynamic Phasors of Converter DC-side electric current are respectively obtained<Id>0With
Second order Dynamic Phasors<Id>2；
Step 4.2 calculates the angle of overlap μ between obtaining transverter three-phase converter valve using formula (6)mn：
In formula (6), XrFor transverter equivalence to the reactance value of valve side,For DC current second harmonic initial phase.
Step 5 establishes transverter improvement switch function model：
Including the circuit of converter valve can indicate that corresponding linear circuit, each corresponding different valve conducting combination can be handled
For different linear circuits.Based on the piecewise combination of transverter different conditions, using switch function in the on off state for indicating valve
While can indicate to show different voltage and currents in commutation process respectively.Under normal circumstances when functional value is 1 and 0 difference
Correspondence is conductive and nonconductive, when functional value is between 0 to 1, then it represents that it is in the commutation stage, but under asymmetric situation,
The variation of switch function can many times be ignored.Improved switch function model is established herein, as shown in figure 4, processing switch
During function as, switch function is regarded to the superposition of fundametal component, amendment component and commutation component.In wherein Fig. 4 shown in (a)
For the oscillogram of fundametal component, it is the square that 1 width is 2/3 π that fundametal component, which is amplitude in switch motion not in any case,
Shape wave, (b) show the oscillogram for correcting component in Fig. 4, and it is the rectangular wave that 1 width is θ that correct component, which be amplitude, is used for the change of current
The variation of switch function waveform caused by the offset of valve turn-on instant, (c) and (d) show the oscillogram of commutation component in Fig. 4,
The waveform voltage electric current of commutation component is slightly different, but it is μ all to concentrate on stage and the width that the period starts.
Step 5.1, by threephase switch function SmIt is launched into each component, is respectively：Fundametal component Sj, correct component SgmWith
Commutation component Sμm, the commutation component SμmIncluding voltage commutation component SuμmWith current commutation component Siμm, it is illustrated in figure 5 each
The superposition schematic diagram of a component, (a) indicates fundametal component oscillogram in wherein Fig. 5, and (b) indicates fundametal component and correct in Fig. 5
The waveform diagram of component superposition, (c) indicates fundametal component, corrects component and the waveform diagram of commutation component superposition in Fig. 5.
Step 5.2, the form that each component is launched into Fourier space using Fourier space：Sj(ω t), Sg(ωt,
θmn), Suμ(ωt,μmn), Siμ(ωt,μmn)：
Step 5.3, the commutation deviation angle θ according to three-phase converter valvemn, practical Trigger Angle αmn, changing between three-phase converter valve
Phase angle μmn, initial commutation device switch function model S ' is established using formula (7)umWith S 'im：
It is each to correct component S in formula (7)gm, voltage commutation component SuμmWith current commutation component SiμmIt is respectively：
Sga=Sg(ωt-π/3,θab)-Sg(ωt-π/3,θca),
Sgb=Sg(ωt-π/3,θbc)-Sg(ωt-π/3,θab),
Sgc=Sg(ωt-π/3,θca)+Sg(ωt-π/3,θbc),
Suμa=Suμ(ωt-π/3-θab,μab)-Suμ(ωt+π/3-θca,θca),
Suμb=-Suμ(ωt-θbc,θbc)-Suμ(ωt-π/3-θab,θab),
Suμc=Suμ(ωt+π/3-θca,θca)-Suμ(ωt-θbc,θbc),
Siμa=Siμ(ωt-π/3-θab,μab)-Siμ(ωt+π/3-θca,μca),
Siμb=-Siμ(ωt-θbc,μbc)-Siμ(ωt-π/3-θab,μbc),
Siμc=Siμ(ωt+π/3-θca,μca)-Siμ(ωt-θbc,μbc)；
Wherein：θcaFor CA two-phase commutations when A phase converter valves commutation deviation angle, θabFor AB two-phase commutations when B phase converter valves
Commutation deviation angle, θbcFor BC two-phase commutations when C phase converter valves commutation deviation angle.
In step 5.4, initial switch function model, by taking A phases as an example, it is believed that the fundametal component of A phase switch functions is to close
It is symmetrical in y-axis, and under normal conditions, this condition is ungratified, when DC control system exports locking phase, is being passed through
After crossing the delay of Trigger Angle command value, A phase valves when to CA commutations send out trigger pulse, i.e., switch letter relative to initial commutation device
Exponential model does lag correction in phase, and the switch function of other each phases is also required to correspondingly carry out phase shift transform.Voltage is opened
Close function S 'umWith current switch function S 'imUnified Expression is S 'm, establish the transverter switch function as shown in formula (8) and improve mould
Type Sm：
Step 5.5 obtains three-phase voltage switch function S using discrete Fourier transform by formula (9)umIt is switched with three-phase current
Function SimQ rank Dynamic Phasors forms：
In formula (9),<sum>qFor the q rank Dynamic Phasors of voltage switch function；<sim>qFor the q rank dynamics that electricity is switch function
Phasor；
Step 6 carries out order components decomposition to each component：
The steady-state analysis of electric system unbalanced fault generally uses sequence component analysis method, it is therefore necessary to establish the change of current
The order components model of device, consequently facilitating to the united analysis of entire ac and dc systems, since exchange residual voltage is to DC voltage
It does not influence, zero sequence voltage component can not considered, only need to establish three-phase voltage switch function vector sum alternating voltage positive-negative sequence
Component vector.
Step 6.1, the q rank Dynamic Phasors that positive and negative sequence voltage switch function and current switch function are calculated using formula (10)：
In formula (10), h=ej2π/3,For the q rank Dynamic Phasors of positive and negative sequence voltage switch function,For the q rank Dynamic Phasors of positive and negative sequence current switch function；
Step 6.2, (p-q) rank dynamic phase that transverter exchange side three-phase voltage positive and negative sequence component is calculated using formula (11)
Amount<u+>p-qWith<u->p-q：
In formula (11), p, q are arbitrary nonzero integer, and p ≠ q,<ua>p-q、<ub>p-qWith<uc>p-qRespectively change of current busbar
A, (p-q) rank Dynamic Phasors of B, C three-phase voltage.
Step 7, the dynamic phasor model for constructing transverter：
Step 7.1, construction transverter dynamic phasor model are specifically referred to according to the dynamic of aforementioned obtained DC side electric current
State phasor, the Dynamic Phasors of exchange side voltage, the Dynamic Phasors of the switch function of Converter DC-side voltage and current utilize formula
(12) Dynamic Phasors of ac-side current and DC voltage are calculated：
In formula (12),<i+>kWith<i->kThe respectively k rank Dynamic Phasors of the positive and negative order components of transverter ac-side current,<ud
>pFor the p rank Dynamic Phasors of Converter DC-side voltage,<id>k-qIt is that the transverter that is calculated by discrete Fourier transform is straight
Flow (k-p) rank Dynamic Phasors of side electric current.
Step 7.2 is based on that the analysis of moment uncharacteristic harmonics occurs to not failure, and the alternating current of transverter exchange side includes
Fundamental wave and 3 order harmonic components, DC side DC voltage includes DC quantity and 2 order harmonic components, in straight-flow system harmonic study table
The uncharacteristic harmonics voltage order of magnitude lower of the 12 pulse transverters of the uncharacteristic harmonics voltage ratio n=1 of bright n >=1, therefore only
Consider that low order uncharacteristic harmonics voltage ensures model accuracy enough, and calculation amount can be greatly decreased.It establishes by formula (13) institute table
The dynamic phasor model of the transverter of sign：
The present invention is asymmetric in analysis AC system for current HVDC transmission system transverter dynamic phasor model
Precision deficiency and calculation amount problem bigger than normal when operation, it is proposed that a kind of transverter dynamic phase suitable for asymmetric operation situation
Measure modeling method, consider the commutation process of transverter in the case of asymmetry in detail, and ignored by order components decomposition it is unnecessary
Harmonic wave simplified model, the precision for effectively increasing model simultaneously, reduce calculation amount.
Claims (2)
1. a kind of Dynamic Phasors modeling method of HVDC transmission system transverter, it is characterized in that carrying out as follows：
Step 1, voltage calculate；
Step 1.1, in time interval τ, τ ∈ (t-T0, t], sampling respectively obtains Converter DC-side electric current id(t) and the change of current
Device exchange side phase voltage ua(t)、ub(t) and uc(t), it is calculated using formula (1) and obtains each line voltage amplitude u of transverter exchange sidemn
(t)：
umn(t)=um(t)-un(t) (1),
In formula (1), m=a, b or c, n=a, b or c, difference corresponding A phase, B phases and C phases, mn=ab, bc or ca, the transverter
DC side refers to HVDC transmission system DC current importation, and transverter exchange side refers to that HVDC transmission system is handed over
Flow voltage input section；
Step 1.2, for the transverter exchange side phase voltage u obtained in step 1.1mn(t) and transverter exchange side line voltage um
(t), it is converted respectively using discrete Fourier transform and obtains transverter exchange side phase voltage first-order dynamic phasor<Um>1And transverter
Exchange side line voltage first-order dynamic phasor<Umn>1；
Step 2 obtains phase offset；
Step 2.1, using formula (2) by transverter exchange side line voltage first-order dynamic phasor<Uab>1、<Ubc>1With<Uca>1Pass through seat
Mark transformation obtains commutation voltage α componentsAnd commutation voltage β components
By commutation voltage α componentsWith commutation voltage β componentsExpansion is expressed as respectively：WithUαAnd UβIt is the amplitude of commutation voltage α components and commutation voltage β components respectively,WithRespectively commutation electricity
Press the phase of α components and commutation voltage β components；
Step 2.2 calculates DC control system synchronizing voltage phase in acquisition HVDC transmission system using formula (3)
Step 2.3, the phase that each line voltage when unbalanced fault occurs according to AC system, acquisition is calculated separately using formula (4)
The phase offset of synchronizing voltage：
In formula (4),WithEach line voltage U when corresponding as unbalanced fault occursca、UabAnd UbcPhase,WithIt is each line voltage U to correspondca、UabAnd UbcAlternate synchronizing voltage phase offset.
Step 3 calculates practical Trigger Angle：
Sampling obtains the Trigger Angle instruction α that DC control system is sent out0, using formula (5) calculate obtain three-phase converter valve commutation it is inclined
Move angle θmnWith practical Trigger Angle αmn：
Angle of overlap between the transverter three-phase converter valve of step 4, calculating meter and second harmonic；
Step 4.1, for the Converter DC-side electric current i for sampling acquisition in step 1.1d(t) discrete Fourier transform is carried out, point
Not Huo get Converter DC-side electric current zeroth order Dynamic Phasors<Id>0With second order Dynamic Phasors<Id>2；
Step 4.2 calculates the angle of overlap μ between obtaining transverter three-phase converter valve using formula (6)mn：
In formula (6), XrFor transverter equivalence to the reactance value of valve side,For DC current second harmonic initial phase；
Step 5 establishes transverter improvement switch function model：
Step 5.1, by threephase switch function SmIt is launched into each component, is respectively：Fundametal component Sj, correct component SgmWith commutation point
Measure Sμm, the commutation component SμmIncluding voltage commutation component SuμmWith current commutation component Siμm；
Each component is launched by step 5.2 using Fourier space：Sj(ω t), Sg(ωt,θmn), Suμ(ωt,μmn) and
Siμ(ωt,μmn)；
Step 5.3, the commutation deviation angle θ according to three-phase converter valvemn, practical Trigger Angle αmn, angle of overlap between three-phase converter valve
μmn, initial commutation device switch function model S ' is established using formula (7)umWith S 'im：
Step 5.4 is corrected by doing lag in phase to initial commutation device switch function model, by voltage switch function S 'um
With current switch function S 'imUnified Expression is S 'm, establish the transverter switch function improved model S as shown in formula (8)m：
Step 5.5 obtains three-phase voltage switch function S using discrete Fourier transform by formula (9)umWith three-phase current switch function
SimQ rank Dynamic Phasors forms：
In formula (9),<sum>qFor three-phase voltage switch function SumQ rank Dynamic Phasors,<sim>qFor three-phase current switch function Sim
Q rank Dynamic Phasors；
Step 6 carries out order components decomposition to each component：
Step 6.1, the q rank Dynamic Phasors that positive and negative sequence voltage switch function and current switch function are calculated using formula (10)：
In formula (10), h=ej2π/3,For the q rank Dynamic Phasors of positive and negative sequence voltage switch function,For the q rank Dynamic Phasors of positive and negative sequence current switch function；
Step 6.2, (p-q) rank Dynamic Phasors that transverter exchange side three-phase voltage positive and negative sequence component is calculated using formula (11)<u+
>p-qWith<u->p-q：
In formula (11), p, q are arbitrary nonzero integer, and p ≠ q,<ua>p-q、<ub>p-qWith<uc>p-qThe respectively change of current busbar A, B, C
(p-q) rank Dynamic Phasors of three-phase voltage；
Step 7, the dynamic phasor model for constructing transverter：
Step 7.1 calculates the Dynamic Phasors for obtaining ac-side current and DC voltage using formula (12)：
In formula (12),<i+>kWith<i->kThe respectively k rank Dynamic Phasors of the positive and negative order components of transverter ac-side current,<ud>pFor
The p rank Dynamic Phasors of Converter DC-side voltage,<id>k-qIt is the transverter direct current being calculated by discrete Fourier transform
(k-q) rank Dynamic Phasors of side electric current；
Step 7.2 is based on that the analysis of moment uncharacteristic harmonics occurs to not failure, and the alternating current of transverter exchange side includes fundamental wave
With 3 order harmonic components, DC side DC voltage includes DC quantity and 2 order harmonic components, establishes the change of current characterized by formula (13)
The dynamic phasor model of device：
2. the Dynamic Phasors modeling method of HVDC transmission system transverter according to claim 1, it is characterized in that：Formula
(7) component S is respectively corrected ingm, voltage commutation component SuμmWith current commutation component SiμmIt is respectively：
Sga=Sg(ωt-π/3,θab)-Sg(ωt-π/3,θca),
Sgb=Sg(ωt-π/3,θbc)-Sg(ωt-π/3,θab),
Sgc=Sg(ωt-π/3,θca)+Sg(ωt-π/3,θbc),
Suμa=Suμ(ωt-π/3-θab,μab)-Suμ(ωt+π/3-θca,θca),
Suμb=-Suμ(ωt-θbc,θbc)-Suμ(ωt-π/3-θab,θab),
Suμc=Suμ(ωt+π/3-θca,θca)-Suμ(ωt-θbc,θbc),
Siμa=Siμ(ωt-π/3-θab,μab)-Siμ(ωt+π/3-θca,μca),
Siμb=-Siμ(ωt-θbc,μbc)-Siμ(ωt-π/3-θab,μbc),
Siμc=Siμ(ωt+π/3-θca,μca)-Siμ(ωt-θbc,μbc),
Wherein：θcaFor CA two-phase commutations when A phase converter valves commutation deviation angle, θabFor AB two-phase commutations when B phase converter valves change
Phase deviation angle, θbcFor BC two-phase commutations when C phase converter valves commutation deviation angle.
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