CN111555339B - 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 PDF

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CN111555339B
CN111555339B CN202010117266.XA CN202010117266A CN111555339B CN 111555339 B CN111555339 B CN 111555339B CN 202010117266 A CN202010117266 A CN 202010117266A CN 111555339 B CN111555339 B CN 111555339B
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admittance
voltage
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CN111555339A (en
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郭焕
刘敏
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Jinan University
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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
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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

Converter grid-connected general sequence impedance model for stability analysis and modeling method
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 large number of distributed power inverters and the distribution network,”IEEE Trans.Power Electron.,vol.19,no.6,pp.1586–1593,Nov.2004.
[2]J.Sun,“Impedance-based stability criterion for grid-connected inverters,”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-Based stability 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 instability assessment 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 based power systems:concept,modeling,and analysis,”IEEE Trans.smart grid.,to be published soon.
[6]X.Wang,F.Blaabjerg,W.Wu,“Modeling and analysis of harmonic stability in an AC power-electronics-based power system,”IEEE Trans.Power Electron.,vol.29,no.12,pp.6421–6432,Dec.2014.
[7]B.Wen,D.Boroyevich,R.Burgos,P.Mattavelli,and Z.Shen,“Small signal stability analysis of three-phase ac systems in the presence of constant power loads based on measured d-q frame impedances,”IEEE Trans.Power Electron.,vol.30,no.10,pp.5952–5963,Oct.2015.
[8]L.Harnefors,M.Bongiorno,and S.Lundberg,“Input-admittance calculation 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 of grid-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 grid connect 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 phase domain impedance modeling of grid-connected converters”,IEEE Trans.Power Electron.,vol.31,no.10,pp.6792–6796,Oct.2016.
[12]Ch.Zhang,X.Cai,A.Rygg and M.Molinas,“Sequence Domain SISO Equivalent 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 of three-phase grid-connected converter using harmonic transfer matrices,”IEEE Trans.Energy Convers.,vol.33,no.2,pp.627-638,June,2018.
[14]L.Xu,L.Fan,and Z.Miao,“DC impedance-model based resonance analysis 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 HVDC system stability analysis and control design,”in Proc.Int.Conf.Power Electron.,Hiroshima,Japan,May 2014,pp.967–974.
[16]D.Lu,X.Wang,F.Blaabjerg,“Impedance-based analysis of DC-link voltage dynamics in voltage source converters”,IEEE Trans.Power Electron.,to be published soon.
[17]S.Shah,L.Persa,“Impedance modeling of three-phase voltage source converters 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 and Modeling 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);
Figure GDA0003298809340000051
the direct current side admittance model of the converter is an admittance matrix Yac(s), the specific matrix element is formula (2);
Figure GDA0003298809340000052
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);
Figure GDA0003298809340000053
Figure GDA0003298809340000054
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
Figure GDA0003298809340000061
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 transfer admittance from the direct current disturbance component of the converter to the negative sequence disturbance component is obtained; 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 alternating current 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 isnp1(s) is the coupling function one between the negative-positive sequences of the outer loop; 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;
Figure GDA0003298809340000063
and
Figure GDA0003298809340000064
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;
Figure GDA0003298809340000062
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; wherein,
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 impedance 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 phase voltage of the common connection point a 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 is represented as
Figure GDA0003298809340000081
The DC side voltage of the converter composed of a DC component and a disturbance component is expressed as
Figure GDA0003298809340000082
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
Figure GDA0003298809340000083
Wherein, thetamAnd
Figure GDA00032988093400000811
respectively at a frequency of omegamThe amplitude and phase of the electrical angle perturbation;
the Park transformation and the Park inverse transformation specifically include: tracking electrical angle taking into account phase locked loop PLLThe influence on DQ coordinate transformation is obtained by obtaining the complex space vector form of Park transformation under the condition of small signal disturbance
Figure GDA0003298809340000084
Also, the inverse Park transform takes the form of a complex space vector
Figure GDA0003298809340000085
Wherein T isk1And TR1Respectively representing Park transformation and inverse transformation equations under the condition of no small signal disturbance
Figure GDA0003298809340000086
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
Figure GDA0003298809340000087
And is provided with
Figure GDA0003298809340000088
Wherein
Figure GDA0003298809340000089
And
Figure GDA00032988093400000810
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
Figure GDA0003298809340000091
Wherein k ismTo modulate the exponential gain, and from this equation
Figure GDA0003298809340000092
And
Figure GDA0003298809340000093
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
Figure GDA0003298809340000094
Wherein the admittance matrix Ydc(s±jω1) The small signal admittance model of the AC side of the converter has matrix elements as shown in the formula
Figure GDA0003298809340000101
The current disturbance component on the direct current side of the alternating current device is as the formula
Figure GDA0003298809340000102
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
Figure GDA0003298809340000103
And also
Figure GDA0003298809340000104
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
Figure GDA0003298809340000111
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
Figure GDA0003298809340000112
And also
Figure GDA0003298809340000113
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
Figure GDA0003298809340000114
The direct current side lumped admittance model Y of the converter can be further obtainedac'(s)＝Ydd(s)[1-kac(s)]Wherein
Figure GDA0003298809340000121
Furthermore, the circuit structure of the converter comprises a converter, a DQ conversion controller, a phase-locked loop and a PWM modulation chip, wherein the signal input end of the DQ conversion controller is connected with the alternating current side voltage and current measurement signal output end of the converter, the direct current side voltage measurement signal output end of the converter and the signal output end of the phase-locked loop; or the circuit structure of the converter comprises the converter, a DQ conversion controller and a PWM modulation chip, wherein the signal input end of the DQ conversion controller, the alternating current side voltage and current measurement signal output end and the direct current side voltage measurement signal output end of the converter are integrated, a phase-locked loop is integrated in the controller of the converter, so that a transfer function for tracking the electrical angle disturbance can be deduced, the transfer function replaces an SRF-PLL 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 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.
The converter AC side small signal admittance model is an admittance matrix YdcThe specific matrix element is formula (1);
Figure GDA0003298809340000141
the direct current side admittance model of the converter is an admittance matrix Yac(s), the specific matrix element is formula (2);
Figure GDA0003298809340000142
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);
Figure GDA0003298809340000143
and also
Figure GDA0003298809340000144
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
Figure GDA0003298809340000151
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 transfer admittance from the direct current disturbance component of the converter to the negative sequence disturbance component is obtained; 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 alternating current 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 isnp1(s) is the coupling function one between the negative-positive sequences of the outer loop; 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;
Figure GDA0003298809340000153
and
Figure GDA0003298809340000154
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;
Figure GDA0003298809340000152
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 the converter sequence impedance model and a modeling method of the converter grid-connected sequence impedance model. Wherein,
the modeling method of the converter sequence impedance model comprises the following steps:
step 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 and is expressed as
Figure GDA0003298809340000161
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
Figure GDA0003298809340000162
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
Figure GDA0003298809340000163
Wherein, thetamAnd
Figure GDA0003298809340000164
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
Figure GDA0003298809340000165
Also, the inverse Park transform takes the form of a complex space vector
Figure GDA0003298809340000166
Wherein T isk1And TR1Respectively representing Park transformation and inverse transformation equations under the condition of no small signal disturbance
Figure GDA0003298809340000167
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
Figure GDA0003298809340000171
And is provided with
Figure GDA0003298809340000172
Wherein
Figure GDA0003298809340000173
And
Figure GDA0003298809340000174
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
Figure GDA0003298809340000175
Wherein k ismTo modulate the exponential gain, and from this equation
Figure GDA0003298809340000176
And
Figure GDA0003298809340000181
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
Figure GDA0003298809340000182
Wherein the admittance matrix Ydc(s±jω1) The small signal admittance model of the AC side of the converter has matrix elements as shown in the formula
Figure GDA0003298809340000183
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
Figure GDA0003298809340000184
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
Figure GDA0003298809340000191
And also
Figure GDA0003298809340000192
Wherein, YacAnd(s) is a direct current side admittance model of the current transformer.
The modeling method of the converter grid-connected sequence impedance 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
Figure GDA0003298809340000193
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
Figure GDA0003298809340000201
And also
Figure GDA0003298809340000202
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
Figure GDA0003298809340000203
The direct current side lumped admittance model Y of the converter can be further obtainedac'(s)＝Ydd(s)[1-kac(s)]Wherein
Figure GDA0003298809340000204
Furthermore, as shown in fig. 2, the circuit structure of the converter includes a converter 1, a DQ converter controller 2, a phase-locked loop 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-locked loop 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 phase-locked loop 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 phase locked loop 3 according to the present invention may also be programmed in the controller of the converter 1 in the form of program code, that is: 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 the circuit stability of an alternating current side and a 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) When the Nyquist criterion is met, the alternating current network is kept stable, and the deduced general sequence impedance model is suitable for various DQ coordinate transformation-based controlsThe method is used for constructing the current transformer, and can be used for deriving a current transformer grid-connected general model based on other coordinate structures 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. The three control structures are 1) alternating current control, 2) direct current voltage control and 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
Figure GDA0003298809340000211
Wherein Hi(s) is the current controller transfer function,
Figure GDA0003298809340000221
and
Figure GDA0003298809340000226
representing converter operating conditions.
Then according to the formula
Figure GDA0003298809340000222
A formula
Figure GDA0003298809340000223
And the transfer function of the control loop
Figure GDA0003298809340000224
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
Figure GDA0003298809340000225
If AC voltage feedforward is not adopted, T in the formulav(s) and Tvn(s) substituting 0 to obtain admittance matrix elements of formula
Figure GDA0003298809340000231
Wherein Y isdp(s+jω1) And Ydn(s-jω1) Remain unchanged.
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
Figure GDA0003298809340000232
Taking into account the power balance between converter input and output
Figure GDA0003298809340000233
A formula
Figure GDA0003298809340000234
And the transfer function of the control loop can be obtained
Figure GDA0003298809340000235
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
Figure GDA0003298809340000236
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 is given for this AC voltage feed forward free case, and case 1 and case2 final equation (equation obtained by substituting transfer function of control loop into each element in matrix element equation of AC side small signal admittance model) in converter admittance and 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 for stability analysis 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 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.
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);
Figure FDA0003298809330000011
the direct current side admittance model of the converter is an admittance matrix Yac(s), the specific matrix element is formula (2);
Figure FDA0003298809330000012
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);
Figure FDA0003298809330000021
and also
Figure FDA0003298809330000022
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
Figure FDA0003298809330000023
Wherein s is Laplace functionNumber basic variable j ω1Is 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 transfer admittance from the direct current disturbance component of the converter to the negative sequence disturbance component is obtained; 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 alternating current 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 isnp1(s) is the coupling function one between the negative-positive sequences of the outer loop; 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;
Figure FDA0003298809330000031
and
Figure FDA0003298809330000032
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;
Figure FDA0003298809330000033
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 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 impedance 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
Figure FDA0003298809330000041
The DC side voltage of the converter composed of a DC component and a disturbance component is expressed as
Figure FDA0003298809330000042
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
Figure FDA0003298809330000043
Wherein, thetamAnd
Figure FDA0003298809330000044
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
Figure FDA0003298809330000045
Similarly, Park inverse transforms complex space vector forms into
Figure FDA0003298809330000051
Wherein T isk1And TR1Respectively representing Park transformation and inverse transformation equations under the condition of no small signal disturbance
Figure FDA0003298809330000052
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
Figure FDA0003298809330000053
And is provided with
Figure FDA0003298809330000054
Wherein
Figure FDA0003298809330000055
And
Figure FDA0003298809330000056
complex space of positive sequence disturbance component and negative sequence disturbance component of modulation coefficient respectivelyVector, Ti(s) and Tin(s) transfer functions of positive-sequence and negative-sequence alternating current signals, 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
Figure FDA0003298809330000057
Wherein k ismTo modulate the exponential gain, and from this equation
Figure FDA0003298809330000058
And
Figure FDA0003298809330000059
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
Figure FDA0003298809330000061
Wherein the admittance matrix Ydc(s±jω1) The small signal admittance model of the AC side of the converter has matrix elements as shown in the formula
Figure FDA0003298809330000062
The current disturbance component on the direct current side of the alternating current device is as the formula
Figure FDA0003298809330000063
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
Figure FDA0003298809330000064
And also
Figure FDA0003298809330000071
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
Figure FDA0003298809330000072
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
Figure FDA0003298809330000073
And also
Figure FDA0003298809330000074
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
Figure FDA0003298809330000081
The direct current side lumped admittance model Y of the converter can be further obtainedac'(s)＝Ydd(s)[1-kac(s)]Wherein
Figure FDA0003298809330000082
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 phase-locked loop (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 phase-locked loop (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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