CN111555339A - Converter grid-connected general sequence impedance model for stability analysis and modeling method - Google Patents
Converter grid-connected general sequence impedance model for stability analysis and modeling method Download PDFInfo
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Abstract
The invention relates to a converter grid-connected general sequence impedance model for stability analysis and a modeling method. The circuit stability of alternating current and direct current sides can be analyzed based on the converter grid-connected general sequence impedance model, the deduced general sequence impedance model is suitable for various converters based on DQ coordinate transformation control structures, any converter grid-connected sequence impedance with a specific control structure can be obtained conveniently through the model, the application range is wide, and the use is flexible and convenient. In addition, the modeling method can be used for deducing a current transformer grid-connected general model based on other coordinate structures.
Description
Technical Field
The invention belongs to the technical field of grid-connected stability analysis of power devices, and particularly relates to a converter grid-connected general sequence impedance model for stability analysis and a modeling method.
Background
The converter has wide application in the fields of distributed energy, electric traction, high-voltage direct-current transmission, flexible alternating-current transmission systems and the like, and the application of the converter becomes more and more extensive along with the application of renewable energy and the development of modern power systems. Converters are generally used as intermediate units between ac and dc circuits, and thus play an important role in the characteristics of the interconnection expansion and stability of power systems (see documents [1] to [6 ]).
Up to now, engineers and researchers usually study the impedance characteristics of the current transformer on the basis of small signal analysis, so as to further analyze and judge the system stability. DQ domain impedance is described in documents [7] to [9 ]; document [10] describes a converter sequence impedance translated to the ac side, where the coupling between the positive-sequence and negative-sequence components is neglected; in documents [11] to [13], the coupling between the positive and negative sequence components is also reflected in the impedance model.
However, the applicant found that:
1. the converter impedance model is derived on the basis of a specific control design, so that the model is only suitable for the converter with the specific control structure. For example: the models in references [10] to [13] include only DQ current control; another example is: the documents [17] to [18] discuss a converter impedance model with internal current control and external dc voltage control, and the analysis results are basically only applicable to the specific control structure.
2. The impedance model of the current transformer is derived based on a specific control design, so that the model and the related derivation are only suitable for the current transformer with the specific control structure. Once the control strategy and method are changed, even locally, the impedance model is usually re-derived and constructed. The limitations of these models hinder the general solution of the stability analysis of the power system and the research and development thereof, thereby limiting the application and popularization thereof. In a converter grid-connected system, the frequency conversion of disturbance signals and the coupling action among multi-phase, multi-sequence and AC/DC networks make the establishment of an impedance model more complicated. However, the current transformer impedance model only adapted to a specific control structure is time-consuming and labor-consuming in stability and related analysis. The convenience of use is greatly reduced.
3. Neither the DQ impedance nor the sequence impedance model described above has taken into account the coupling between dc and ac circuits in depth, and although documents [14] to [15] discuss modeling of dc side impedance, neglecting ac system dynamic response, document [16] also introduces the effect of dc voltage control on system stability, and more recently documents [17] to [18] discuss the phenomenon of ac-dc circuit coupling through a power converter.
The relevant literature states that:
[1]J.H.Enslin and P.J.Heskes，“Harmonic interaction between a largenumber of distributed power inverters and the distribution network，”IEEETrans.Power Electron.，vol.19，no.6，pp.1586-1593，Nov.2004.
[2]J.Sun，“Impedance-based stability criterion for grid-connectedinverters，”IEEE Trans.Power Electron.，vol.27，no.11，pp.3075-3078，Nov. 2011.
[3]L.Harnefors，X.Wang，A.G.Yepes and F.Blaabjerg，“Passivity-Basedstability assessment of grid-connected VSCs-an overview，”IEEE J.Emerg.Sel.Topics Power Electron.，vol.4，no.1，pp.116-125，March 2016.
[4]Y.Wang，X.Wang，F.Blaagjerg，and Z.Chen，“Harmonic instabilityassessment using state-space modeling and participation analysis in inverter-fed power systems，”IEEE Trans.Ind.Electron.，vol.64，no.1，pp.806-6796，Oct.2016.
[5]X.Wang，F.Blaabjerg，“Harmonic stability in power electronic basedpower systems：concept，modeling，and analysis，”IEEE Trans.smart grid.，to bepublished soon.
[6]X.Wang，F.Blaabjerg，W.Wu，“Modeling and analysis of harmonicstability in an AC power-electronics-based power system，”IEEE Trans.PowerElectron.，vol.29，no.12，pp.6421-6432，Dec.2014.
[7]B.Wen，D.Boroyevich，R.Burgos，P.Mattavelli，and Z.Shen，“Small signalstability analysis of three-phase ac systems in the presence of constantpower loads based on measured d-q frame impedances，”IEEE Trans.PowerElectron.，vol.30，no.10，pp.5952-5963，Oct.2015.
[8]L.Harnefors，M.Bongiorno，and S.Lundberg，“Input-admittancecalculation and shaping for controlled voltage-source converter，”IEEE Trans.Ind.Electron.，vol.54，no.6，pp.3323-3334，Dec.2007
[9]X.Wang，L.Harnefors，and F.Blaabjerg，“Unified impedance model ofgrid-connected voltage-source converters”，IEEE Trans.Power Electron.，vol. 33，no.2，pp.1775-1787，Feb.2014.
[10]M.Cespedes and J.Sun，“Impedance modeling and analysis of gridconnect voltage-source converters”IEEE Trans.Power Electron.，vol.29，no.3，pp.1254-1261，Mar.2014.
[11]M.K.Bakhshizadeh，X.Wang，F.Blaabjerg，et al，“Coupling in phasedomain impedance modeling of grid-connected converters”，IEEE Trans.PowerElectron.，vol.31，no.10，pp.6792-6796，Oct.2016.
[12]Ch.Zhang，X.Cai，A.Rygg and M.Molinas，“Sequence Domain SISOEquivalent Models of a Grid-Tied Voltage Source Converter System for Small-Signal stability Analysis”，IEEE Trans.Energy Convers.，vol.33，no.2， pp.741-748，June，2018.
[13]H.Nian，L.Chen，Y.Xu et al.，“Sequence domain impedance modeling ofthree-phase grid-connected converter using harmonic transfer matrices，” IEEETrans.Energy Convers.，vol.33，no.2，pp.627-638，June，2018.
[14]L.Xu，L.Fan，and Z.Miao，“DC impedance-model based resonanceanalysis of a VSC-HVDC system，”IEEE Trans.Power Del.，vol.30，no.3，pp. 1221-1230，Jun.2015.
[15]H.Liu，S.Shah，and J.Sun，“An impedance-based approach to HVDCsystem stability analysis and control design，”in Proc.Int.Conf.PowerElectron.，Hiroshima，Japan，May 2014，pp.967-974.
[16]D.Lu，X.Wang，F.Blaabjerg，“Impedance-based analysis of DC-linkvoltage dynamics in voltage source converters”，IEEE Trans.Power Electron.，tobe published soon.
[17]S.Shah，L.Persa，“Impedance modeling of three-phase voltage sourceconverters in dq，sequence，and phasor domains，”IEEE Trans.Energy Convers.，vol.32，no.3，pp.1139-1150，Sep.2017.
[18]I.Vieto，X.Du，H.Nian，and J.Sun，“Frequency-domain coupling in two-level VSC small-signal dynamics”，2017IEEE 18th Workshop on Control andModeling for Power Electronics(COMPEL)，pp.1，8，9-12July 2017.
disclosure of Invention
In order to solve the problems in the prior art, the invention provides a converter grid-connected general sequence impedance model which can analyze the circuit stability of an alternating current side and a direct current side, is suitable for various converters based on a DQ coordinate transformation control structure, can conveniently obtain any converter grid-connected sequence impedance with a specific control structure, has a wide application range and is flexible and convenient to use, and a modeling method of the converter grid-connected general sequence impedance model for stability analysis.
In order to solve the technical problems, the invention adopts the following technical scheme:
the converter grid-connected general sequence impedance model comprises a converter sequence impedance model and a converter grid-connected sequence impedance model, wherein the converter sequence impedance model comprises a converter AC side small signal admittance model and a DC side admittance model, and the converter grid-connected sequence impedance model comprises a converter grid-connected AC side lumped admittance model and a DC side lumped admittance model.
Further, the converter AC side small signal admittance model is admittance matrix YdcThe specific matrix element is formula (1);
the direct current side admittance model of the converter is an admittance matrix Yac(s), the specific matrix element is formula (2);
the alternating current side lumped admittance model of the converter grid connection is an admittance matrix Y'dc(s±jω1) The specific matrix element is a formula (3);
and also
The direct current side lumped admittance model of the converter is an admittance matrix Y'ac(s), the specific matrix element is formula (4);
Yac′(s)＝Ydd(s)[1-kac(s)](4)
and also
Wherein s is a Laplace function basic variable j omega1Is the fundamental frequency; y ispp(s+jω1) Admittance of a positive sequence disturbance component of the converter; y isnp(s+jω1) The transfer admittance from the positive sequence disturbance component to the negative sequence disturbance component of the converter is obtained; y ispn(s-jω1) Transfer admittance from a negative sequence disturbance component to a positive sequence disturbance component of the converter; y isdp(s+jω1) Transfer admittance from a direct current disturbance component of the converter to a positive sequence disturbance component; y isdn(s -jω1) The method is characterized in that the method is a transfer admittance from a direct current disturbance component to a negative sequence disturbance component of a converter; y isnn(s-jω1) Admittance of a negative sequence disturbance component of the converter; y iss(s+jω1) Positive sequence lumped admittance of an external alternating current circuit of the converter; y iss(s-jω1) Negative sequence lumped admittance of an external AC circuit of the converter; y isdd(s) a converter admittance with direct current side disturbance; y ispd(s) is the transfer admittance from the positive sequence disturbance of the AC side to the DC side; y isnd(s) is a transfer admittance from the negative sequence disturbance of the alternating current side to the direct current side of the converter; y ispd(s) is a transfer admittance from the positive sequence disturbance of the alternating current side to the direct current side of the converter; t isθ(s) is a transfer function of the phase-locked loop angular offset; t isi(s) is the transfer function of the positive sequence alternating current signal; t isv(s) is the transfer function of the positive sequence alternating voltage signal; t isd(s) is a direct current signal transfer function; t isnp1Is a coupling function one between outer loop negative-positive sequences; t isnp2(s) is a second coupling function between the negative-positive sequences of the outer loop; t isvn(s) is the transfer function of the negative sequence alternating voltage signal; t isin(s) is the transfer function of the negative sequence alternating current signal; t ispn(s) is the coupling function between the positive-negative sequences of the outer loop;
and
the phase angles of the fundamental voltage, the positive sequence voltage disturbance and the negative sequence voltage disturbance are respectively; kmIs the modulation index gain; kpp(s+jω1)、Kpn(s-jω1)、Knp(s+jω1) And; knn(s-jω1) Are respectively admittance Ypp(s+jω1)、Ypn(s-jω1)、Ynp(s+jω1) And Ynn(s-jω1) The ac-dc coupling coefficient of (a); v1Is the AC side group wave voltage of the converter; vdcThe direct current component of the direct current side voltage of the converter;
a current reference value of a D-Q coordinate of the converter is obtained; i isdcThe direct current component of the direct current side current of the converter; l is the transformer reactance with the top "→" representing the complex space vector of the variable.
A modeling method of a converter grid-connected general sequence impedance model for stability analysis comprises a modeling method of a converter sequence impedance model and a modeling method of a converter grid-connected sequence impedance model; the modeling method of the converter sequence impedance model comprises the following steps:
s101, defining a phase voltage of a common connection point A, wherein the phase voltage of the common connection point A consists of a basic positive sequence voltage component, a positive sequence disturbance voltage component, a negative sequence disturbance voltage component and a zero sequence disturbance voltage component;
s102, defining the direct-current side voltage of the converter, wherein the direct-current side voltage of the converter consists of a direct-current component and a current disturbance component;
s103, deducing tracking electrical angle disturbance of the phase-locked loop according to the defined converter alternating voltage disturbance, and carrying out Park transformation and Park inverse transformation to obtain a complex space vector of a converter modulation coefficient disturbance component;
s104, defining a universal transfer function of a converter control link based on alternating voltage, current, direct voltage and current, deriving a complex function space vector of alternating current disturbance according to an average model of a voltage source converter, and further obtaining a positive sequence component and a negative sequence component of the alternating current disturbance, so that a converter alternating-current side small signal admittance model is obtained from a mutual relation of the alternating voltage disturbance and the alternating current disturbance;
s105, obtaining a direct current side disturbance current according to the converter alternating current side small signal admittance model and a current disturbance component of the direct current side of the alternating current device, and obtaining a converter direct current side admittance model from the direct current side disturbance current;
the modeling method of the converter grid-connected sequence anti-resistance model comprises the following steps:
s201, obtaining a direct-current side disturbance voltage according to the lumped admittance at the direct-current side of the converter and the direct-current side disturbance current obtained in S105;
s202, substituting the direct-current side disturbance voltage into the alternating-current disturbance positive sequence component and the alternating-current disturbance negative sequence component obtained in the S104 to obtain an alternating-current side lumped admittance model of the converter grid connection;
and S203, further obtaining a direct current side lumped admittance model of the converter according to the alternating current side lumped admittance model of the converter grid connection.
Further, the public connection point A phase consisting of a basic positive sequence voltage component, a positive sequence disturbance voltage component, a negative sequence disturbance voltage component and a zero sequence disturbance voltage componentThe voltage is expressed as
The DC side voltage of the converter composed of a DC component and a disturbance component is expressed as
ωp＝ωd+ω1，ωn＝ωd-ω1(ii) a And by taking a synchronous reference coordinate phase-locked loop as an example, deducing tracking electrical angle disturbance of the phase-locked loop under the condition of alternating voltage small signal disturbance as
Wherein, thetamAnd
respectively at a frequency of omegamThe amplitude and phase of the electrical angle perturbation;
the Park transformation and the Park inverse transformation specifically include: considering the influence of a phase-locked loop PLL tracking electrical angle on DQ coordinate transformation, the complex space vector form of Park transformation under the condition of small signal disturbance is obtained
Also, the inverse Park transform takes the form of a complex space vector
Meanwhile, considering the influence of tracking electrical angle disturbance of a phase-locked loop on Park transformation and Park inverse transformation thereof under the condition of small signal disturbance, the complex space vector of the disturbance component of the modulation coefficient of the current transformer can be finally obtained as the formula
And is provided with
Wherein
And
complex space vectors, T, of positive-sequence and negative-sequence disturbance components, respectively, of the modulation coefficienti(s) and Tin(s) transfer functions for positive-sequence and negative-sequence AC current signals, respectively (other voltage and current signal transfer functions are similarly represented, and reference values in AC voltage, AC current, DC voltage and DQ coordinates are denoted below with the designations "v", "i", "d" and "x", respectively), Tnp1(s)、Tnp2(s)、 Tpn1(s) and Tpn2(s) represents the coupling function between the positive and negative sequences of the voltage, respectively, for the outer loop kvFor the AC voltage feed-forward gain, kdFor the current transformer inductor current decoupling gain, j0 represents the frequency of the dc signal in the control loop;
the average model of the voltage source converter is expressed as
Wherein k ismTo modulate the exponential gain, and from this equation
And
The current disturbance component on the direct current side of the alternating current device is as the formula
The disturbance current at the DC side obtained according to the current disturbance component at the DC side of the AC device and the small signal admittance model at the AC side of the current transformer is
And also
Wherein, Yac(s) is a converter direct current side admittance model;
the method for obtaining the direct current side disturbance current according to the lumped admittance at the direct current side of the converter and the direct current side disturbance current obtained in the step S105 comprises the following steps: if the lumped admittance at the DC side of the converter is denoted as Yd(jωm) The obtained DC side disturbance current is further expressed as
The DC side disturbance voltage V obtained from the equationd(s)；
The method comprises the following steps of substituting the direct-current side disturbance voltage into the alternating-current disturbance positive sequence component and the alternating-current disturbance negative sequence component obtained in the step S104 to obtain an alternating-current side lumped admittance model of the converter grid connection, and specifically comprises the following steps: will be straightCurrent side disturbance voltage Vd(s) substituting into the positive sequence component and negative sequence component of AC current disturbance to obtain
And also
Wherein, matrix Y'dcThe method comprises the following steps that an alternating current side lumped admittance model of a converter grid connection is formed;
obtaining a DC side lumped admittance model of the converter according to the AC side lumped admittance model of the converter grid connection, which specifically comprises the following steps: slave type
Further, the circuit structure of the converter comprises a converter, a DQ conversion controller, a lock-up ring and a PWM modulation chip, wherein the signal input end of the DQ conversion controller is connected with the AC side voltage and current measurement signal output end of the converter, the DC side voltage measurement signal output end of the converter and the signal output end of the phase-locked loop, the signal input end of the PWM modulation chip is connected with the signal output end of the DQ conversion controller, the signal input end of the lock-up ring is connected with the AC side voltage and current signal output end of the converter or the circuit structure of the converter comprises a converter, a DQ conversion controller and a PWM modulation chip, the signal input end of the DQ conversion controller is connected with the AC side voltage and current measurement signal output end of the converter and the DC side voltage measurement signal output end of the converter, and the phase-locked loop is integrated in the controller of the converter, and the SRF-PLL transfer function is replaced by the transfer function, and the signal input end of the PWM modulation chip is connected with the signal output end of the DQ conversion controller.
Further, the phase-locked loop is a phase-locked loop which can derive a transfer function for tracking the electrical angle disturbance and replace the SRF-PLL transfer function with the transfer function.
Further, the phase-locked loop is a synchronous reference coordinate system phase-locked loop.
The invention mainly has the following beneficial effects:
the circuit stability of an alternating current side and a direct current side can be analyzed based on the converter grid-connected general sequence impedance model, the deduced general sequence impedance model is suitable for various converters based on a DQ coordinate transformation control structure, and the derivation of the converter grid-connected general model based on other coordinate structures can be deduced by the modeling method; the converter grid-connected general sequence impedance model for stability analysis can conveniently obtain any converter grid-connected sequence impedance with a specific control structure, and has the advantages of wide application range, flexible use and convenience.
Drawings
Fig. 1 is a schematic flow chart of a modeling method of a converter grid-connected general sequence impedance model for stability analysis according to an embodiment of the invention;
fig. 2 is a schematic circuit structure diagram of a converter in the modeling method of the converter grid-connected general sequence impedance model for stability analysis according to the embodiment of the present invention;
fig. 3 is a schematic diagram of a phase-locked loop in the circuit configuration of the current transformer;
FIG. 4 is a schematic structural diagram of the converter grid-connected general sequence impedance model for stability analysis according to the present invention, which adopts AC current control;
FIG. 5 is a schematic structural diagram of a converter grid-connected general sequence impedance model for stability analysis according to the present invention, which adopts DC current control;
FIG. 6 shows the AC-side lumped admittances Y for case 1, case 2 and verification of the inventionpp′(s+jω1) And Ynn′(s-jω1)A graph of the model calculation result and the time domain simulation result of (1);
FIG. 7 shows the AC-side lumped admittances Y for case 1, case 2 and verification of the inventionnp′(s+jω1) And Ypn′(s-jω1) A graph of the model calculation result and the time domain simulation result of (1);
FIG. 8 shows the DC-side lumped admittance Y of case 1, case 2 and verification of the present inventionac'(s) and converter admittance Ydd(s) a graph of model calculation results and time domain simulation results.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The converter grid-connected general sequence impedance model for stability analysis comprises a converter sequence impedance model and a converter grid-connected sequence impedance model, wherein the converter sequence impedance model comprises a converter alternating current side small signal admittance model and a direct current side admittance model, and the converter grid-connected sequence impedance model comprises a converter grid-connected alternating current side lumped admittance model and a direct current side lumped admittance model.
The converter AC side small signal admittance model is an admittance matrix YdcThe specific matrix element is formula (1);
the direct current side admittance model of the converter is an admittance matrix Yac(s), the specific matrix element is formula (2);
the alternating current side lumped admittance model of the converter grid connection is an admittance matrix Y'dc(s±jω1) The specific matrix element is a formula (3);
and also
The direct current side lumped admittance model of the converter is an admittance matrix Y'ac(s), the specific matrix element is formula (4);
Yac′(s)＝Ydd(s)[1-kac(s)](4)
and also
Wherein s is a Laplace function basic variable j omega1Is the fundamental frequency; y ispp(s+jω1) Admittance of a positive sequence disturbance component of the converter; y isnp(s+jω1) The transfer admittance from the positive sequence disturbance component to the negative sequence disturbance component of the converter is obtained; y ispn(s-jω1) Transfer admittance from a negative sequence disturbance component to a positive sequence disturbance component of the converter; y isdp(s+jω1) Transfer admittance from a direct current disturbance component of the converter to a positive sequence disturbance component; y isdn(s -jω1) The method is characterized in that the method is a transfer admittance from a direct current disturbance component to a negative sequence disturbance component of a converter; y isnn(s-jω1) Admittance of a negative sequence disturbance component of the converter; y iss(s+jω1) Positive sequence lumped admittance of an external alternating current circuit of the converter; y iss(s-jω1) Negative sequence lumped admittance of an external AC circuit of the converter; y isdd(s) a converter admittance with direct current side disturbance; y ispd(s) is the transfer admittance from the positive sequence disturbance of the AC side to the DC side; y isnd(s) is a transfer admittance from the negative sequence disturbance of the alternating current side to the direct current side of the converter; y ispd(s) is a transfer admittance from the positive sequence disturbance of the alternating current side to the direct current side of the converter; t isθ(s) transmission of phase-locked loop angular offsetA transfer function; t isi(s) is the transfer function of the positive sequence alternating current signal; t isv(s) is the transfer function of the positive sequence alternating voltage signal; t isd(s) is a direct current signal transfer function; t isnp1Is a coupling function one between outer loop negative-positive sequences; t isnp2(s) is a second coupling function between the negative-positive sequences of the outer loop; t isvn(s) is the transfer function of the negative sequence alternating voltage signal; t isin(s) is the transfer function of the negative sequence alternating current signal; t ispn(s) is the coupling function between the positive-negative sequences of the outer loop;
and
the phase angles of the fundamental voltage, the positive sequence voltage disturbance and the negative sequence voltage disturbance are respectively; kmIs the modulation index gain; kpp(s+jω1)、Kpn(s-jω1)、Knp(s+jω1) And; knn(s-jω1) Are respectively admittance Ypp(s+jω1)、Ypn(s-jω1)、Ynp(s+jω1) And Ynn(s-jω1) The ac-dc coupling coefficient of (a); v1Is the AC side group wave voltage of the converter; vdcThe direct current component of the direct current side voltage of the converter;
a current reference value of a D-Q coordinate of the converter is obtained; i isdcThe direct current component of the direct current side current of the converter; l is the transformer reactance with the top "→" representing the complex space vector of the variable.
As shown in fig. 1, the modeling method of the converter grid-connected general sequence impedance model for stability analysis includes a modeling method of a converter sequence impedance model and a modeling method of a converter grid-connected sequence impedance model. Wherein the content of the first and second substances,
the modeling method of the converter sequence impedance model comprises the following steps:
s101, defining a phase voltage of a public connection point A, wherein the public connection point A is a phase voltageThe common connection point A-phase voltage is composed of a basic positive sequence voltage component, a positive sequence disturbance voltage component, a negative sequence disturbance voltage component and a zero sequence disturbance voltage component, and is expressed as
S102, defining the direct-current side voltage of the converter, wherein the direct-current side voltage of the converter consists of a direct-current component and a current disturbance component and is expressed as
ωp＝ωd+ω1，ωn＝ωd-ω1。
S103, deducing tracking electrical angle disturbance of the phase-locked loop according to the defined converter alternating voltage disturbance, and carrying out Park transformation and Park inverse transformation to obtain a complex space vector of a converter modulation coefficient disturbance component; the method specifically comprises the following steps: for example, a Synchronous Reference Frame phase-locked loop (Synchronous Reference Frame PLL) is used to derive tracking electrical angle disturbance of the phase-locked loop under the condition of AC voltage small signal disturbance as
Wherein, thetamAnd
respectively at a frequency of omegamThe amplitude and phase of the electrical angle perturbation; the Park transformation and the Park inverse transformation specifically include: considering the influence of a phase-locked loop PLL tracking electrical angle on DQ coordinate transformation, the complex space vector form of Park transformation under the condition of small signal disturbance is obtained
Also, the inverse Park transform takes the form of a complex space vector
Wherein T isk1And TR1Respectively in the absence of small signal disturbancesPark transform and inverse transform equations
Converter control based on DQ coordinate transformation, its ac current and ac voltage signal transmission paths can be described as: alternating current signal → Park transformation → control algorithm → Park inverse transformation → modulation coefficient, and the transmission path of the direct current signal is similar to the alternating current signal, except that the Park transformation is not required to be applied; meanwhile, considering the influence of tracking electrical angle disturbance of a phase-locked loop on Park transformation and Park inverse transformation thereof under the condition of small signal disturbance, the complex space vector of the disturbance component of the modulation coefficient of the current transformer can be finally obtained as the formula
And is provided with
Wherein
And
complex space vectors, T, of positive-sequence and negative-sequence disturbance components, respectively, of the modulation coefficienti(s) and Tin(s) transfer functions for positive-sequence and negative-sequence AC current signals, respectively (other voltage and current signal transfer functions are similarly represented, and reference values in AC voltage, AC current, DC voltage and DQ coordinates are denoted below with the designations "v", "i", "d" and "x", respectively), Tnp1(s)、Tnp2(s)、 Tpn1(s) and Tpn2(s) represents the coupling function between the positive and negative sequences of the voltage, respectively, for the outer loop kvFor the AC voltage feed-forward gain, kdFor the current transformer inductor current decoupling gain, j0 represents the frequency of the dc signal in the control loop.
S104, defining a universal transfer function of a converter control link based on alternating voltage, current, direct voltage and current, deducing and obtaining a complex function space vector of alternating current disturbance according to an average model of a voltage source converter, and further obtaining a positive sequence component and a negative sequence component of the alternating current disturbance, so that a converter alternating current side small signal admittance model is obtained from the mutual relation of the alternating voltage disturbance and the alternating current disturbance; the method specifically comprises the following steps:
the average model of the voltage source converter is expressed as
Wherein k ismTo modulate the exponential gain, and from this equation
And
S105, obtaining a direct current side disturbance current according to the converter alternating current side small signal admittance model and a current disturbance component of the direct current side of the alternating current device, and obtaining a converter direct current side admittance model from the direct current side disturbance current; the method specifically comprises the following steps:
the current disturbance component on the direct current side of the alternating current device is as the formula
The disturbance current at the DC side obtained according to the current disturbance component at the DC side of the AC device and the small signal admittance model at the AC side of the current transformer is
And also
Wherein, YacAnd(s) is a direct current side admittance model of the current transformer.
The modeling method of the converter grid-connected sequence anti-resistance model comprises the following steps:
s201, obtaining a direct current side disturbance voltage according to the lumped admittance of the direct current side of the converter and the direct current side disturbance current obtained in the S105; the method specifically comprises the following steps: if the lumped admittance at the DC side of the converter is denoted as Yd(jωm) The obtained DC side disturbance current is further expressed as
The DC side disturbance voltage V obtained from the equationd(s)。
S202, substituting the direct-current side disturbance voltage into the alternating-current disturbance positive sequence component and the alternating-current disturbance negative sequence component obtained in the S104 to obtain an alternating-current side lumped admittance model of the converter grid connection; the method specifically comprises the following steps: disturbing the voltage V at the DC sided(s) substituting into the positive sequence component and negative sequence component of AC current disturbance to obtain
And also
Wherein, matrix Y'dcThe method is an alternating current side lumped admittance model of the converter grid connection.
S203, further solving a direct-current side lumped admittance model of the converter according to the alternating-current side lumped admittance model of the converter grid connection; the method specifically comprises the following steps: slave type
Furthermore, as shown in fig. 2, the circuit structure of the converter includes a converter 1, a DQ converter controller 2, a lock ring 3 and a PWM modulation chip 4, wherein a signal input terminal of the DQ converter controller 2 is connected to an ac side voltage and current measurement signal output terminal of the converter 1, a dc side voltage measurement signal output terminal and a signal output terminal of the phase lock ring 3, a signal input terminal of the PWM modulation chip 4 is connected to a signal output terminal of the DQ converter controller 2, and a signal input terminal of the lock ring 3 is connected to an ac side voltage signal output terminal of the converter 1; the phase-locked loop 3 is a phase-locked loop that can derive a transfer function for tracking electrical angle disturbances and replace the SRF-PLL transfer function with this transfer function, such as the synchronous reference frame phase-locked loop shown in fig. 3.
Of course, the lock collar 3 according to the invention can also be programmed in the form of program code in the control unit of the converter 1, namely: the circuit structure of the converter comprises a converter 1, a DQ conversion controller 2 and a PWM modulation chip 4, wherein a signal input end of the DQ conversion controller 2, an alternating current side voltage and current measurement signal output end and a direct current side voltage measurement signal output end of the converter 1 are integrated, a phase-locked loop is integrated in the controller of the converter 1, so that a transfer function for tracking electric angle disturbance can be deduced, the transfer function replaces an SRF-PLL transfer function, and a signal input end of the PWM modulation chip 4 is connected with a signal output end of the DQ conversion controller 2.
The converter grid-connected general sequence impedance model can be used for analyzing alternating currentThe circuit stability on the side and on the direct current side, namely: according to the criterion of impedance stability (reference [2 ]]) When admittance ratio Yd(s)/Yac'(s) the DC circuit remains stable when the Nyquist criterion is met; also, if the admittance ratio Y ispp′(s+jω1)/Ys(s+jω1) And Ynn′(s-jω1)/Ys(s-jω1) The Nyquist criterion is met, the alternating current network is kept stable, the deduced general sequence impedance model is suitable for various converters based on the DQ coordinate transformation control structure, and the derivation of the converter grid-connected general model based on other coordinate structures can be deduced through the modeling method.
And through the converter grid-connected general sequence impedance model for stability analysis, any converter grid-connected sequence impedance with a specific control structure can be obtained very conveniently, and the model has the advantages of wide application range, flexible use and convenience. The converter grid-connected general sequence impedance model is further explained by the grid-connected admittance of the voltage source converter with three control structures. These three control structures are: 1) alternating current control, 2) direct voltage control, 3) alternating current power control.
1) Case 1: AC current control
An ac current control arrangement as shown in fig. 4, whereby the transfer function of the control loop is obtained as
Wherein Hi(s) is the current controller transfer function,
and
representing converter operating conditions.
Then according to the formula
A formula
And the transfer function of the control loop
And substituting the transfer function of the control loop into each element in a matrix element formula of a converter AC side small signal admittance model to obtain
2) Case 2: DC voltage control
The DC voltage control structure shown in FIG. 5, thereby obtaining a control loop with a transfer function of
In addition Ypp(s+jω1)，Ynp(s+jω1)，Ynn(s-jω1) And Ypn(s-jω1) In accordance with case 1, reference [17]]The impedance modeling under the condition of no AC voltage feedforward is given, and the transformer admittance in the expression finally obtained by case 1 and case 2 (namely, the expression obtained by substituting the transfer function of the control loop into each element in the matrix element expression of the AC side small signal admittance model of the current transformer) and the document [17]]The same as in (1).
3) Authentication
The correctness of the derived converter admittance is verified by taking a 20MW voltage source converter as an example, and the model calculation result is compared with the time domain simulation result, wherein the time domain simulation result is shown by points and the model calculation result is shown by lines.
As shown in fig. 6-8, line A, B, C represents case 1, case 2, and verification 3, respectively, where fig. 6 and 7 are ac-side lumped admittances Ypp′(s+jω1)，Ynn′(s-jω1)，Ynp′(s+jω1) And Ypn′(s-jω1) Amplitude and phase of (1), AC-side lumped admittance Ypp′(s+jω1) As a solid line, AC-side lumped admittance Ynn′(s-jω1) As a dotted line, FIG. 8 shows a DC-side lumped admittance Yac'(s) amplitude and phase, DC-side lumped admittance Yac'(s) is a solid line, converter admittance Ydd(s) is a dotted line. From fig. 5-8 it is shown that model prediction is consistent with simulation results, verifying that the lumped admittances derived from the generic admittance for stability analysis are correct, and thus verifying the correctness of the generic model.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (8)
1. The converter grid-connected general sequence impedance model is characterized by comprising a converter sequence impedance model and a converter grid-connected sequence impedance model, wherein the converter sequence impedance model comprises a converter alternating current side small signal admittance model and a direct current side admittance model, and the converter grid-connected sequence impedance model comprises a converter grid-connected alternating current side lumped admittance model and a direct current side lumped admittance model.
2. The converter grid-connected general sequence impedance model for stability analysis according to claim 1, wherein the converter AC side small signal admittance model is admittance matrix YdcThe specific matrix element is formula (1);
the direct current side admittance model of the converter is an admittance matrix Yac(s), the specific matrix element is formula (2);
the alternating current side lumped admittance model of the converter grid connection is an admittance matrix Y'dc(s±jω1) The specific matrix element is a formula (3);
and also
The direct current side lumped admittance model of the converter is an admittance matrix Y'ac(s), the specific matrix element is formula (4);
Yac′(s)＝Ydd(s)[1-kac(s)](4)
and also
Wherein s is a Laplace function basic variable j omega1Is the fundamental frequency; y ispp(s+jω1) Admittance of a positive sequence disturbance component of the converter; y isnp(s+jω1) The transfer admittance from the positive sequence disturbance component to the negative sequence disturbance component of the converter is obtained; y ispn(s-jω1) Transfer admittance from a negative sequence disturbance component to a positive sequence disturbance component of the converter; y isdp(s+jω1) Transfer admittance from a direct current disturbance component of the converter to a positive sequence disturbance component; y isdn(s-jω1) The method is characterized in that the method is a transfer admittance from a direct current disturbance component to a negative sequence disturbance component of a converter; y isnn(s-jω1) Admittance of a negative sequence disturbance component of the converter; y iss(s+jω1) Positive sequence lumped admittance of an external alternating current circuit of the converter; y iss(s-jω1) Negative sequence lumped admittance of an external AC circuit of the converter; y isdd(s) a converter admittance with direct current side disturbance; y ispd(s) is the transfer admittance from the positive sequence disturbance of the AC side to the DC side; y isnd(s) is a transfer admittance from the negative sequence disturbance of the alternating current side to the direct current side of the converter; y ispd(s) is a transfer admittance from the positive sequence disturbance of the alternating current side to the direct current side of the converter; t isθ(s) is a transfer function of the phase-locked loop angular offset; t isi(s) is the transfer function of the positive sequence alternating current signal; t isv(s) is the transfer function of the positive sequence alternating voltage signal; t isd(s) is a direct current signal transfer function; t isnp1Is a coupling function one between outer loop negative-positive sequences; t isnp2(s) is a second coupling function between the negative-positive sequences of the outer loop; t isvn(s) is the transfer function of the negative sequence alternating voltage signal; t isin(s) is the transfer function of the negative sequence alternating current signal; t ispn(s) is the coupling function between the positive-negative sequences of the outer loop;
and
the phase angles of the fundamental voltage, the positive sequence voltage disturbance and the negative sequence voltage disturbance are respectively; kmIs the modulation index gain; kpp(s+jω1)、Kpn(s-jω1)、Knp(s+jω1) And; knn(s-jω1) Are respectively admittance Ypp(s+jω1)、Ypn(s-jω1)、Ynp(s+jω1) And Ynn(s-jω1) The ac-dc coupling coefficient of (a); v1Is the AC side group wave voltage of the converter; vdcThe direct current component of the direct current side voltage of the converter;
a current reference value of a D-Q coordinate of the converter is obtained; i isdcThe direct current component of the direct current side current of the converter; l is the transformer reactance with the top "→" representing the complex space vector of the variable.
3. A modeling method of a converter grid-connected general sequence impedance model for stability analysis is characterized by comprising a modeling method of a converter sequence impedance model and a modeling method of a converter grid-connected sequence impedance model; wherein the content of the first and second substances,
the modeling method of the converter sequence impedance model comprises the following steps:
s101, defining a phase voltage of a common connection point A, wherein the phase voltage of the common connection point A consists of a basic positive sequence voltage component, a positive sequence disturbance voltage component, a negative sequence disturbance voltage component and a zero sequence disturbance voltage component;
s102, defining the direct-current side voltage of the converter, wherein the direct-current side voltage of the converter consists of a direct-current component and a current disturbance component;
s103, deducing tracking electrical angle disturbance of the phase-locked loop according to the defined converter alternating voltage disturbance, and carrying out Park transformation and Park inverse transformation to obtain a complex space vector of a converter modulation coefficient disturbance component;
s104, defining a universal transfer function of a converter control link based on alternating voltage, current, direct voltage and current, deriving a complex function space vector of alternating current disturbance according to an average model of a voltage source converter, and further obtaining a positive sequence component and a negative sequence component of the alternating current disturbance, so that a converter alternating-current side small signal admittance model is obtained from a mutual relation of the alternating voltage disturbance and the alternating current disturbance;
s105, obtaining a direct current side disturbance current according to the converter alternating current side small signal admittance model and a current disturbance component of the direct current side of the alternating current device, and obtaining a converter direct current side admittance model from the direct current side disturbance current;
the modeling method of the converter grid-connected sequence anti-resistance model comprises the following steps:
s201, obtaining a direct-current side disturbance voltage according to the lumped admittance at the direct-current side of the converter and the direct-current side disturbance current obtained in S105;
s202, substituting the direct-current side disturbance voltage into the alternating-current disturbance positive sequence component and the alternating-current disturbance negative sequence component obtained in the S104 to obtain an alternating-current side lumped admittance model of the converter grid connection;
and S203, further obtaining a direct current side lumped admittance model of the converter according to the alternating current side lumped admittance model of the converter grid connection.
4. The modeling method of the converter grid-connected universal sequence impedance model for stability analysis according to claim 3, characterized in that the phase voltage of the common connection point A consisting of a basic positive sequence voltage component, a positive sequence disturbance voltage component, a negative sequence disturbance voltage component and a zero sequence disturbance voltage component is represented as
The DC side voltage of the converter composed of a DC component and a disturbance component is expressed as
ωp＝ωd+ω1，ωn＝ωd-ω1(ii) a And by taking a synchronous reference coordinate phase-locked loop as an example, deducing an alternating voltage small signal disturbance stripThe tracking electrical angle of the phase-locked loop under the part is disturbed as
Wherein, thetamAnd
respectively at a frequency of omegamThe amplitude and phase of the electrical angle perturbation;
the Park transformation and the Park inverse transformation specifically include: considering the influence of a phase-locked loop PLL tracking electrical angle on DQ coordinate transformation, the complex space vector form of Park transformation under the condition of small signal disturbance is obtained
Similarly, Park inverse transforms complex space vector forms into
Wherein T isk1And TR1Respectively representing Park transformation and inverse transformation equations under the condition of no small signal disturbance
Meanwhile, considering the influence of tracking electrical angle disturbance of a phase-locked loop on Park transformation and Park inverse transformation thereof under the condition of small signal disturbance, the complex space vector of the disturbance component of the modulation coefficient of the current transformer can be finally obtained as the formula
And is provided with
Wherein
And
complex space vectors, T, of positive-sequence and negative-sequence disturbance components, respectively, of the modulation coefficienti(s) and Tin(s) transfer functions for positive-sequence and negative-sequence AC current signals, respectively (other voltage and current signal transfer functions are similarly represented, and reference values in AC voltage, AC current, DC voltage and DQ coordinates are denoted below with the designations "v", "i", "d" and "x", respectively), Tnp1(s)、Tnp2(s)、Tpn1(s) and Tpn2(s) represents the coupling function between the positive and negative sequences of the voltage, respectively, for the outer loop kvFor the AC voltage feed-forward gain, kdFor the current transformer inductor current decoupling gain, j0 represents the frequency of the dc signal in the control loop;
the average model of the voltage source converter is expressed as
Wherein k ismTo modulate the exponential gain, and from this equation
And
further, a complex function space vector of alternating current disturbance can be obtained through derivation, and positive sequence components and negative sequence components of the alternating current disturbance are further obtained
The current disturbance component on the direct current side of the alternating current device is as the formula
The disturbance current at the DC side obtained according to the current disturbance component at the DC side of the AC device and the small signal admittance model at the AC side of the current transformer is
And also
Wherein, Yac(s) is a converter direct current side admittance model;
the method for obtaining the direct current side disturbance current according to the lumped admittance at the direct current side of the converter and the direct current side disturbance current obtained in the step S105 comprises the following steps: if the lumped admittance at the DC side of the converter is denoted as Yd(jωm) The obtained DC side disturbance current is further expressed as
The DC side disturbance voltage V obtained from the equationd(s)；
The method comprises the following steps of substituting the direct-current side disturbance voltage into the alternating-current disturbance positive sequence component and the alternating-current disturbance negative sequence component obtained in the step S104 to obtain an alternating-current side lumped admittance model of the converter grid connection, and specifically comprises the following steps: disturbing the voltage V at the DC sided(s) substituting into the positive sequence component and negative sequence component of AC current disturbance to obtain
And also
Wherein, matrix Y'dcThe method comprises the following steps that an alternating current side lumped admittance model of a converter grid connection is formed;
obtaining a DC side lumped admittance model of the converter according to the AC side lumped admittance model of the converter grid connection, which specifically comprises the following steps: slave type
The direct current side lumped admittance model Y of the converter can be further obtainedac′(s)＝Ydd(s)[1-kac(s)]Wherein
5. The modeling method of the converter grid-connected general sequence impedance model for stability analysis according to claim 3 or 4, characterized in that the circuit structure of the converter comprises a converter (1), a DQ converter controller (2), a lock-top ring (3) and a PWM modulation chip (4), the signal input end of the DQ converter controller (2) is connected with the AC side voltage and current measurement signal output end of the converter (1), the DC side voltage measurement signal output end and the signal output end of the phase-locked loop (3), the signal input end of the PWM modulation chip (4) is connected with the signal output end of the DQ converter controller (2), and the signal input end of the lock-top ring (3) is connected with the AC side voltage signal output end of the converter (1).
6. The modeling method of the converter grid-connected universal sequence impedance model for stability analysis according to claim 5, characterized in that the phase-locked loop (3) is a phase-locked loop which can derive a transfer function tracking electrical angle disturbance and replace the SRF-PLL transfer function with the transfer function.
7. The modeling method of the converter grid-connected general sequence impedance model for stability analysis according to claim 6, characterized in that the phase-locked loop (3) is a synchronous reference coordinate system phase-locked loop.
8. The modeling method of the converter grid-connected universal sequence impedance model for stability analysis according to claim 3 or 4, characterized in that the circuit structure of the converter comprises a converter (1), a DQ converter controller (2) and a PWM modulation chip (4), the signal input end of the DQ converter controller (2) is connected with the AC side voltage and current measurement signal output end and the DC side voltage and current measurement signal output end of the converter (1), and a phase-locked loop is integrated in the controller of the converter (1), so that a transfer function for tracking electrical angle disturbance can be derived therefrom and is used to replace the SRF-PLL transfer function, and the signal input end of the PWM modulation chip (4) is connected with the signal output end of the DQ converter controller (2).
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