CN116418049A - Accurate admittance modeling method for sagging-controlled three-phase grid-connected inverter - Google Patents

Accurate admittance modeling method for sagging-controlled three-phase grid-connected inverter Download PDF

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CN116418049A
CN116418049A CN202310674463.5A CN202310674463A CN116418049A CN 116418049 A CN116418049 A CN 116418049A CN 202310674463 A CN202310674463 A CN 202310674463A CN 116418049 A CN116418049 A CN 116418049A
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CN116418049B (en
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王顺亮
刘海军
马俊鹏
冯麟
刘天琪
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Sichuan 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
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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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 discloses a droop control three-phase grid-connected inverter accurate admittance modeling method, which introduces a complex vector modeling method and is staticαβAn accurate sag control three-phase grid-connected inverter admittance model is established under a coordinate system, and the main implementation process is as follows: splitting a sagging control system of the three-phase grid-connected inverter into an inner ring control system and an outer ring control system; establishing a single-input single-output structure complex vector small signal model of an inner loop control system and an external circuit; establishing a complex vector small signal model of an outer loop control system; and establishing a complete complex vector small signal admittance model of the sagging control three-phase grid-connected inverter. The model built by the invention can accurately describe the output admittance characteristics of the sagging control three-phase grid-connected inverter, and can reveal the frequency coupling effect mechanism caused by the asymmetric structure of the sagging control system.

Description

Accurate admittance modeling method for sagging-controlled three-phase grid-connected inverter
Technical Field
The invention relates to the field of small signal modeling of a sagging-controlled three-phase grid-connected inverter, in particular to a method for accurately modeling admittance of the sagging-controlled three-phase grid-connected inverter.
Background
With the vigorous development of new energy power generation technology in recent years, a grid-connected inverter is widely used as an energy transmission interface between a power grid and new energy, and the grid-connected inverter and other power electronic equipment are applied to the power grid in a large scale, so that a great challenge is brought to the stable operation of a power system. The power electronic converter is highly nonlinear and operates in a very wide frequency band, so that the modeling and stability analysis method is different from the traditional power equipment, and the impedance analysis method has the advantages of definite physical meaning, convenience in measurement and verification and the like, and is widely applied to the modeling and analysis of an AC/DC converter.
The grid-connected inverter widely adopts a sagging control structure in a parallel operation mode, and two current impedance modeling methods for the sagging control three-phase grid-connected inverter are as follows: of synchronous rotating coordinate systemdqShaft impedance/admittance model and three-phase restabcThe coordinate system adopts a sequence impedance model of a harmonic linearization method. Is built up indqThe physical meaning of the impedance/admittance model in the coordinate system is not clear enough and the impedance is not easy to measure; three-phase restabcThe physical meaning of the sequence impedance model established by adopting the harmonic linearization mode under the coordinate system is relatively clear and convenient to measure, but the frequency coupling relation between positive and negative sequences caused by an asymmetric link of a control system is not considered, and the modeling is more complicated by considering phase sequence coupling.
Complex frequency coupling effects exist among links in the sagging control system of the three-phase grid-connected inverter, the existing modeling method is not complete enough for structural consideration of the sagging control system, so that the established impedance/admittance model of the sagging control three-phase grid-connected inverter is not accurate enough, and theoretical analysis of the frequency coupling effects caused by asymmetry of the sagging control system is not comprehensive enough.
Disclosure of Invention
Aiming at the problems, the invention provides a droop control three-phase grid-connected inverter accurate admittance modeling method, which introduces a complex vector modeling method to unify positive and negative sequence components to obtain synchronous rotationdqIn the coordinate system and stationaryαβAccurate sagging control three-phase grid-connected inverse under coordinate systemAnd a transformer admittance model. The technical proposal is as follows:
a droop control three-phase grid-connected inverter accurate admittance modeling method comprises the following steps:
step 1: splitting a sagging control system of the three-phase grid-connected inverter into an inner ring control system and an outer ring control system; the outer loop control system comprises a power calculation link, a low-pass filtering link and a droop control link; the inner loop control system comprises a voltage control link and a current control link;
step 2: establishing a single-input single-output structure complex vector model of an inner loop control system and an external circuit;
step 3: external circuit partαβTransfer function and variable conversion in coordinate systemdqIn the coordinate system, builddqA complex vector small signal model of an inner loop control and external circuit part which are unified under a coordinate system;
step 4: establishing a complex vector expression of active power and reactive power, and linearizing small signals of the active power and reactive power expression to obtain a complex vector small signal model of an outer loop control system;
step 5: combining the complex vector small signal model of the inner loop control and the external circuit in the step 3 and the complex vector small signal model of the outer loop control system in the step 4 to obtaindqThe coordinate system sags to control the complete small signal admittance model of the three-phase grid-connected inverter, and the small signal admittance model is transferred to the three-phase grid-connected inverter through coordinate transformationαβIn the coordinate system.
Further, the step 2 includes the following steps:
step 21: control system for inner ringdqCoordinate system lower sumαβThe electrical quantity under the coordinate system is expressed in the form of complex vector;
Figure SMS_1
（1）
wherein ,x dq is thatdqA certain amount of electricity in the coordinate system,x d andx q respectively of the electric quantitydqA component;jan imaginary unit which is an imaginary part in the complex vector;
step 22: external circuit part, particularly including filter inductance, filter capacitance and delay module of digital control systemαβThe transfer function in the coordinate system is expressed in the form of complex vector;
Figure SMS_2
（2）
wherein ,
Figure SMS_3
is thatαβA certain amount of electricity in the coordinate system,x α andx β respectively of the electric quantityαβA component;x dq and />
Figure SMS_4
The conversion relation of (2) is: />
Figure SMS_5
and />
Figure SMS_6
，θIs the angle of the coordinate transformation;
step 23: connecting the inner loop control system with an external circuit part through a delay module and a coordinate transformation module, and converting a multi-input multi-output system structure of the inner loop control system and the external circuit part into a complex vector model of a single-input single-output structure;
transfer functions of voltage control link and current control link in inner loop control systemG u (s) and G i (s) The complex vector form of (a) is:
G u (s)＝G u (s)＋j0，G i (s)＝G i (s)＋j0（3）
wherein ,j0 represents an imaginary part of 0;
αβtransfer function of filter capacitor and filter inductor in coordinate systemG C,αβ (s) and G L,αβ (s) The complex vector forms of (a) are respectively:
Figure SMS_7
（4）
wherein ,
Figure SMS_8
，/>
Figure SMS_9
，C f andL f a filter capacitor and a filter inductor respectively;
based ondqCoordinate systemαβConversion relation of coordinate systemdqThe transfer functions of the filter capacitor and the filter inductor under the coordinate system are as follows:
Figure SMS_10
，/>
Figure SMS_11
，ω 0 is the fundamental angular frequency;
time delay transfer function of digital control systemG d (s) includes a sampling periodT s And a pulse width modulation delay of half the sampling frequency, expressed as:G d (s)＝G d (s)＋j0，
Figure SMS_12
。
further, the step 3 includes the following steps:
step 31: external circuit partαβTransfer function and variable conversion in coordinate systemdqUnder a coordinate system;
Figure SMS_13
（5）
Figure SMS_14
（6）
wherein ,x dq,0 representation ofdqSteady state value, delta, of certain electric quantity under coordinate systemx dq Representation ofdqThe small signal disturbance quantity delta of the electric quantity under the coordinate systemθRepresenting the angle of transformation of coordinatesθIs a small signal disturbance quantity;
Figure SMS_15
representation ofαβA steady state value of an electrical quantity in the coordinate system,
Figure SMS_16
representation ofαβThe small signal disturbance quantity of the electric quantity under the coordinate system;
step 32: small signal linearization of variables in a system, and establishmentdqA complex vector model of an inner loop control and an external circuit part which are unified under a coordinate system;
small signal disturbance delta of inverter output voltageu odq The expression is:
Figure SMS_17
（7）
wherein ,
Figure SMS_18
representing the voltage reference value small signal disturbance quantity delta of the inner loop control systemi odq The small signal disturbance quantity of the output current of the inverter is represented;G V (s) Representing deltau odq and />
Figure SMS_19
The transfer function between the two is chosen to be the same,G I (s) Representing deltau odq and Δi odq The transfer function between the two is chosen to be the same,G θ (s) Representing deltau odq and ΔθTransfer functions between the two are expressed as follows:
Figure SMS_20
，
Figure SMS_21
，
Figure SMS_22
in the formula ：
Figure SMS_23
representing the steady state value of the modulation voltage +.>
Figure SMS_24
Representing steady state value of inverter output voltage, +.>
Figure SMS_25
Representing the steady state value of the filter inductor current.
Further, the step 4 includes the following steps:
step 41: establishing active powerP r And reactive powerQ r Complex vector expression of (2)
Active powerP r And reactive powerQ r The expression of (2) is:
Figure SMS_26
（8）
wherein ,u od andu oq representing the output voltage of an inverter VSCdqA component;i od andi oq representing the output current of an inverter VSCdqA component;
complex in-plane complex power vectorSAnd
Figure SMS_27
the expression of (2) is:
Figure SMS_28
（9）
wherein ,u odq representation ofdqA complex vector expression of the inverter output voltage in the coordinate system,u odq ＝u od ＋ju oq ；
Figure SMS_29
representation ofu odq Conjugation of->
Figure SMS_30
；i odq Representation ofdqA complex vector expression of the inverter output current in the coordinate system,i odq ＝i od ＋ji oq ；/>
Figure SMS_31
representation ofi odq Conjugation of->
Figure SMS_32
；
Then get the instantaneous active powerP r And reactive powerQ r Is expressed as:
Figure SMS_33
（10）
step 42: linearizing the active power and reactive power expression small signals, wherein the expression is as follows:
Figure SMS_34
（11）
wherein ,ΔP r and ΔQ r Respectively represent active powerP r And reactive powerQ r A small signal disturbance component of (2);
Figure SMS_37
and
Figure SMS_40
separate tableu odq and />
Figure SMS_42
Steady state values of (2); deltau odq and />
Figure SMS_36
Respectively representu odq and />
Figure SMS_39
A small signal disturbance component of (2);i odq,0 and />
Figure SMS_41
Respectively representi odq and />
Figure SMS_43
Steady state values of (2); deltai odq and />
Figure SMS_35
Respectively representi odq and />
Figure SMS_38
A small signal disturbance component of (2);
step 43: obtaining a complex vector small signal model of the outer loop control system
The small signal relationship for the droop control loop is:
Figure SMS_44
（12）
wherein ,G LF (s) Representing the transfer function of the low-pass filtering element,mrepresenting the active power droop coefficient,nrepresenting the reactive power droop coefficient, deltaθRepresenting the angle of transformation of coordinatesθIs used for the small signal disturbance quantity of the (a),
Figure SMS_45
representing the voltage reference value of the inner loop control system +.>
Figure SMS_46
Small signal scramblingA dynamic component.
Bringing equation (11) into equation (12) yields:
Figure SMS_47
（13）
Figure SMS_48
（14）
wherein ,
Figure SMS_49
representing deltaθAnd deltaP r Is used for the transfer function of (a),G du (s) Representation->
Figure SMS_50
And deltaQ r Is a transfer function of (2); and is also provided with
Figure SMS_51
。
Further, the step 5 includes the following steps:
step 5.1: based on the built two control system models of the inner ring and the outer ring, the method obtainsdqAnd (3) a complete small signal model of the coordinate system sag control three-phase grid-connected inverter system is obtained by inputting the formula (13) and the formula (14) into an output voltage expression formula (7):
Figure SMS_52
（15）
wherein ,G 1 (s) Representing deltau odq And
Figure SMS_53
is used for the transfer function of (a),G 2 (s) The expression +.>
Figure SMS_54
and ΔθDelta after similar term simplification is replaced and combined by a formula (13) and a formula (14) respectivelyu odq and Δi odq Is a new expression of the transfer function of (c),G 3 (s) Representing deltau odq and />
Figure SMS_55
The expression of which is as follows:
Figure SMS_56
（16）
Δu odq the expression form of the conjugate complex vector of (a) is as follows:
Figure SMS_57
（17）
wherein ,
Figure SMS_58
representation->
Figure SMS_59
and Δu odq Is>
Figure SMS_60
Representation->
Figure SMS_61
and />
Figure SMS_62
Is used for the transfer function of (a),
Figure SMS_63
representation->
Figure SMS_64
and Δi odq Is a transfer function of (a).
Derived from equation (15) and equation (17)dq2 of output voltage and output current in coordinate system
Figure SMS_65
Figure SMS_65
2 admittance matrix:
Figure SMS_66
（18）
wherein ,Y dq1 (s) Representation ofdqOutput current disturbance delta under coordinate systemi odq And output voltage disturbance deltau odq Relation of Y dq2 (s) Indicating the disturbance delta of the output currenti odq Conjugate with the disturbance of output voltage
Figure SMS_67
Relation of Y dq3 (s) Representing the disturbance of the output current>
Figure SMS_68
And output voltage disturbance deltau odq Relation of Y dq4 (s) Conjugation indicating output current disturbance quantity
Figure SMS_69
Conjugate with output voltage disturbance quantity->
Figure SMS_70
Is a relationship of (2);
step 5.2: from the following componentsdqCoordinate systemαβThe conversion relation of the coordinate system is todqAdmittance matrix conversion of coordinate system toαβCoordinate system:
Figure SMS_71
（19）
wherein,
Figure SMS_75
and->
Figure SMS_77
Respectively representing the output currents of the inverterαβComplex vector representation and conjugate thereof under a coordinate system; />
Figure SMS_83
And->
Figure SMS_74
Respectively represent the output voltage of the inverterαβComplex vector representation and conjugate thereof under a coordinate system; index operator->
Figure SMS_78
The product of complex conjugate vector introduces the frequency coupling effect of VSC for one frequencyωWill produce a frequency of +.>
Figure SMS_81
Frequency coupling vector, Y 1 Representation ofαβOutput current disturbance quantity in coordinate system>
Figure SMS_84
Disturbance with output voltage->
Figure SMS_72
Is a relationship of (2); y is Y 2 Indicating the disturbance of the output current->
Figure SMS_76
And coupling voltage disturbance quantity->
Figure SMS_82
Is a relationship of (2); y is Y 3 Indicating the disturbance of the coupling current +.>
Figure SMS_85
And output voltage disturbance amount->
Figure SMS_73
Is a relationship of (2); y is Y 4 Indicating the disturbance of the coupling current +.>
Figure SMS_79
And coupling voltage disturbance quantity->
Figure SMS_80
Is a relationship of (3).
Compared with the prior art, the invention has the beneficial effects that:
1) The invention is based on complex vector modeling methodαβAn accurate admittance model of the sagging control three-phase grid-connected inverter is established under a coordinate system, and the problems are solveddqThe impedance model in the coordinate system has no definite physical meaning and is not easy to measure;
2) The traditional sequence impedance model under the static coordinate system does not consider the coupling effect between positive and negative sequences, and the static is established by the inventionαβThe complex vector admittance model under the coordinate system has comprehensive consideration factors, and positive and negative sequence components are unified into a complex vector, so that the frequency coupling effect caused by the asymmetry of the sagging control system can be revealed.
Drawings
Fig. 1 is a block diagram of a droop-controlled three-phase grid-connected inverter.
Fig. 2 is a block diagram of the outer loop control system.
Fig. 3 is a block diagram of the inner loop control system.
FIG. 4 is a block diagram of the complex vector form of the inner loop control system and the external circuit portion.
FIG. 5 is a schematic view of a displaydqAnd a small signal model block diagram of the inner loop control system and an external circuit part under the coordinate system.
FIG. 6 is complex vector powerSAnd
Figure SMS_86
form of the invention.
Fig. 7 is a small signal model of the outer loop control system.
Fig. 8 is a relationship between VSC output voltage and current.
FIG. 9 (a) is a diagram of Y in the established admittance model 1 Is verified by the amplitude and phase of the signal.
FIG. 9 (b) is Y in the established admittance model 2 Is verified by the amplitude and phase of the signal.
FIG. 9 (c) is Y in the established admittance model 3 Is verified by the amplitude and phase of the signal.
FIG. 9 (d) is Y in the established admittance model 4 Is verified by the amplitude and phase of the signal.
FIG. 10 (a) shows the LPF cut-off frequencyω c ) VSC output admittance profile at change:Y 1 amplitude and phase response results of (a).
FIG. 10 (b) shows the LPF cut-off frequencyω c ) VSC output admittance profile at change: y is Y 2 Amplitude and phase response results of (a).
FIG. 10 (c) shows the LPF cut-off frequencyω c ) VSC output admittance profile at change: y is Y 3 Amplitude and phase response results of (a).
FIG. 10 (d) shows the LPF cut-off frequencyω c ) VSC output admittance profile at change: y is Y 4 Amplitude and phase response results of (a).
FIG. 11 (a) shows the active power droop factormVSC output admittance profile at change: y is Y 1 Amplitude and phase response results of (a).
FIG. 11 (b) shows the active power droop factormVSC output admittance profile at change: y is Y 2 Amplitude and phase response results of (a).
FIG. 11 (c) shows the active power droop factormVSC output admittance profile at change: y is Y 3 Amplitude and phase response results of (a).
FIG. 11 (d) shows the active power droop factormVSC output admittance profile at change: y is Y 4 Amplitude and phase response results of (a).
FIG. 12 (a) is a reactive power droop coefficientnVSC output admittance profile at change: y is Y 1 Amplitude and phase response results of (a).
FIG. 12 (b) is a reactive power droop coefficientnVSC output admittance profile at change: y is Y 2 Amplitude and phase response results of (a).
FIG. 12 (c) is a reactive power droop coefficientnVSC output admittance profile at change: y is Y 3 Amplitude and phase response results of (a).
FIG. 12 (d) is a reactive power droop coefficientnVSC output admittance profile at change: y is Y 4 Amplitude and phase response results of (a).
FIG. 13 (a) shows the voltage control step upBenefit (benefit)K up VSC output admittance profile at change: y is Y 1 Amplitude and phase response results of (a).
FIG. 13 (b) shows the gain of the voltage control linkK up VSC output admittance profile at change: y is Y 2 Amplitude and phase response results of (a).
FIG. 13 (c) shows the gain of the voltage control linkK up VSC output admittance profile at change: y is Y 3 Amplitude and phase response results of (a).
FIG. 13 (d) shows the gain of the voltage control linkK up VSC output admittance profile at change: y is Y 4 Amplitude and phase response results of (a).
FIG. 14 (a) shows the gain of the current control loopK ip VSC output admittance profile at change: y is Y 1 Amplitude and phase response results of (a).
FIG. 14 (b) shows the gain of the current control loopK ip VSC output admittance profile at change: y is Y 2 Amplitude and phase response results of (a).
FIG. 14 (c) shows the gain of the current control loopK ip VSC output admittance profile at change: y is Y 3 Amplitude and phase response results of (a).
FIG. 14 (d) shows the gain of the current control loopK ip VSC output admittance profile at change: y is Y 4 Amplitude and phase response results of (a).
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. The invention considers the complete system structure of the sagging control three-phase grid-connected inverter, establishes a detailed sagging control three-phase grid-connected inverter admittance model, introduces a complex vector modeling method to unify positive and negative sequence components, and obtains synchronous rotationdqIn the coordinate system and stationaryαβAnd accurately drooping and controlling the admittance model of the three-phase grid-connected inverter under the coordinate system. The model reveals the frequency coupling effect mechanism of the sagging control three-phase grid-connected inverter, and analyzes the internalInfluence of loop control and outer loop control system parameters on output admittance characteristics and frequency coupling effects of a three-phase grid-connected inverter. The specific implementation process is as follows:
step 1: the sagging control system of the three-phase grid-connected inverter is divided into an inner ring control system and an outer ring control system
(1) The three-phase grid-connected inverter based on droop control is shown in a structural block diagram in fig. 1, a control system is divided into an outer loop control system and an inner loop control system, the outer loop control system comprises three parts of a power calculation link, a Low Pass Filter (LPF) link and a droop control link, and the inner loop control system comprises two parts of a voltage control link and a current control link.
In fig. 1:U dc representing the dc voltage of the dc side of the inverter;L f andC f respectively representing the inductance and the capacitance of the filtering link;u g 、L g andR g respectively representing the phase voltage of the power grid, the equivalent inductance and the equivalent resistance of the power grid side;u oa/b/c andi oa/b/c respectively representing the three-phase alternating voltage and the three-phase alternating current output by the inverter;i la/b/c three-phase alternating current representing a filter inductance;i od/q andu od/q representing the inverter output current and output voltage, respectivelydqThe component(s) of the composition,i ld/q representing the filtered inductor currentdqA component;PandQrespectively representing active power and reactive power;u id/q representing the modulated voltagedqA component;
Figure SMS_87
representing the voltage reference value of the inner loop control linkdqA component; abc/dq represents the link of the coordinate transformation,θan angle representing the coordinate transformation; SPWM represents a sinusoidal pulse width modulation element.
(2) Fig. 2 is a block diagram of the outer loop control system, in which the relation between the parameters is:
Figure SMS_88
（1）
wherein:mandnrepresenting the real and reactive power droop coefficients respectively,P ref andQ ref which are the real and reactive power reference values respectively,P r andQ r respectively the instantaneous values of active and reactive power,
Figure SMS_89
andu 0 the fundamental angular frequency and the voltage of the PCC point respectively,G LF (s) Is the transfer function of the low pass filter element (LPF),θis the angle of the coordinate transformation.
(3) FIG. 3 is a block diagram of an inner loop control system with inputs including a reference voltage
Figure SMS_90
And->
Figure SMS_91
Inverter VSC output voltageu od Andu oq inductor currenti ld Andi lq ；G u (s)=K up +K ui /sandG i (s)=K ip the transfer functions of the voltage control link and the current control link in the inner loop control system respectively,K up 、K ui representing the proportional gain and integral gain of the Voltage Control Link (VCL) of the inner loop control system respectively,K ip a Current Control Link (CCL) proportional gain for the inner loop control system; />
Figure SMS_92
And->
Figure SMS_93
Respectively the reference values of the filter inductance currentdqA component;u id andu iq respectively of modulated voltagedqThe component(s) of the composition,ωindicating the angular frequency of rotation. dq/abc & PWM means coordinate transformation and PWM modulation link, pulse means trigger Pulse.
Step 2: building single-input single-output structure complex vector model of inner loop control system and external circuit
(1) Control system for inner ringdqThe electrical quantity in the coordinate system is expressed in the form of complex vectors.
(2) External circuit part, particularly including filter inductance, filter capacitance and delay module of digital control systemαβThe transfer function in the coordinate system is expressed in the form of complex vectors.
Complex vectors can be represented asA+jBIn the form of (a) and (b),dqcoordinate system lower sumαβComplex vectors in the coordinate system can be expressed as:
Figure SMS_94
（2）
the conversion relation between the two is as follows:
Figure SMS_95
and->
Figure SMS_96
，θIs the angle of the coordinate transformation.
The multiple input multiple output system (MIMO) shown in fig. 3 can be converted to a single input single output system (SISO) as shown in fig. 4 based on a complex vector method. FIG. 4 is divided into two parts, the left part representingdqThe complex vector model of the inner loop control system in the coordinate system, while the right part representsαβAn external circuit complex vector model under a coordinate system. In FIG. 4
Figure SMS_99
Andu idq a complex vector representation representing the inverter output reference voltage and the modulation voltage;G u (s) AndG i (s) Complex vector representing transfer functions of voltage control link and current control link of inner loop control systemA quantity representation form; />
Figure SMS_102
And->
Figure SMS_104
The coordinate transformation operator is represented by a coordinate transformation operator,
Figure SMS_98
and->
Figure SMS_100
Impedance of filter inductance and capacitance, respectively, +.>
Figure SMS_103
，/>
Figure SMS_106
And->
Figure SMS_97
Respectively representing the output voltage, the output current and the filter inductance current of the inverterαβComplex vector form under the coordinate system;G d (s) A complex vector representation representing the delay element; />
Figure SMS_101
And->
Figure SMS_105
Respectively representαβComplex vector form of filter inductance and filter capacitance transfer function in coordinate system.
The transfer functions of the voltage control loop and the current control loop in the inner loop control system of FIG. 4G u (s) AndG i (s) The complex vector form of (a) is:
G u (s)＝G u (s)＋j0，G i (s)＝G i (s)＋j0（3）
in FIG. 4G C,αβ (s) AndG L,αβ (s) Transfer functions of the filter capacitor and the filter inductor are respectively:
Figure SMS_107
（4）
wherein:
Figure SMS_108
，/>
Figure SMS_109
，C f andL f a filter capacitor and a filter inductor, respectively. Based ondqCoordinate systemαβThe conversion relation of the coordinate system is as follows: />
Figure SMS_110
，/>
Figure SMS_111
；
G d (s) represents the time delay transfer function of the digital control system, including a sampling period [ ]T s ) The calculated delay and the pulse width modulation delay of half the sampling frequency can be expressed as:G d (s)＝G d (s)＋j0，
Figure SMS_112
。
step 3: performing small signal linearization on the model established in the step 2 at a steady-state point
（1）dqCoordinate systemαβThe complex vector small signaling method under the coordinate system comprises the following steps:
Figure SMS_113
（5）
Figure SMS_114
（6）
wherein,x dq,0 represents steady state value, deltax dq Indicating the disturbance quantity of small signals, deltaθRepresenting the angle of transformation of coordinatesθIs a small signal disturbance amount.
The external circuit in FIG. 4 will be describedαβConversion of variables and transfer functions in a coordinate System todqIn the coordinate system, builddqA complex vector small signal model of the unified inner loop control and external circuit portion in the coordinate system is shown in fig. 5. In fig. 5:
Figure SMS_115
representing the voltage reference value small signal disturbance quantity delta of the inner loop control systemθRepresenting the angle of transformation of coordinatesθIs a small signal disturbance quantity; deltau odq 、Δi odq And deltau odq Representation ofdqThe small signal disturbance quantity of the output voltage, the output current and the modulation voltage of the inverter under the coordinate system; />
Figure SMS_116
、
Figure SMS_117
And->
Figure SMS_118
Respectively representdqModulating voltage, inverter output voltage under a coordinate system, and filtering steady-state values of inductance current;G L (s) AndG C (s) Representation ofdqTransfer functions of filter inductance and filter capacitance in a coordinate system.
Obtaining output voltage deltau odq The expression is:
Figure SMS_119
（7）
wherein,G V (s) Representing deltau odq And
Figure SMS_120
the transfer function between the two is chosen to be the same,G I (s) Representing deltau odq And deltai odq The transfer function between the two is chosen to be the same,G θ (s) Representing deltau odq And deltaθA transfer function therebetween; the expressions are respectively:
Figure SMS_121
Figure SMS_122
Figure SMS_123
step 4: building complex vector small signal model of outer loop control system
Active powerP r And reactive powerQ r The expression of (2) is:
Figure SMS_124
（8）
FIG. 6 is a complex in-plane complex power vectorSAndS * in the form of (a), wherein the complex power vectorSThe expression is:
Figure SMS_125
（9）
can obtain instantaneous active powerP r And reactive powerQ r Is expressed as:
Figure SMS_126
（10）
small signal linearization of equation (10) yields:
Figure SMS_127
（11）
the small signal relationship for the droop control loop shown in fig. 2 is:
Figure SMS_128
（12）
bringing equation (11) into equation (12) yields:
Figure SMS_129
（13）
Figure SMS_130
（14）
wherein:
Figure SMS_131
a small signal model of the outer loop control system as shown in fig. 7 can be obtained.
Step 5: establishing a complete complex vector small signal admittance model of a sagging control three-phase grid-connected inverter
(1) Based on the built two control system models of the inner ring and the outer ring, the method obtainsdqThe complete small signal model of the three-phase grid-connected inverter system controlled by the coordinate system sag can be obtained by inputting the formula (13) and the formula (14) into an output voltage expression formula (7):
Figure SMS_132
（15）
wherein,G 1 (s) Representing deltau odq And
Figure SMS_133
is used for the transfer function of (a),G 2 (s) The expression +.>
Figure SMS_134
And deltaθDelta after similar term simplification is replaced and combined by a formula (13) and a formula (14) respectivelyu odq And deltai odq Is a new expression of the transfer function of (c),G 3 (s) Representing deltau odq And->
Figure SMS_135
The expression of which is as follows:
Figure SMS_136
（16）
Δu odq the expression form of the conjugate complex vector is as follows:
Figure SMS_137
（17）
wherein,
Figure SMS_138
representation->
Figure SMS_139
And deltau odq Is>
Figure SMS_140
Representation->
Figure SMS_141
And->
Figure SMS_142
Is used for the transfer function of (a),
Figure SMS_143
representation->
Figure SMS_144
And deltai odq Is a transfer function of (a).
From equation (15) and equation (17)dq2 of output voltage and output current in coordinate system
Figure SMS_145
Figure SMS_145
2 admittance matrix:>
Figure SMS_146
（18）
(2) From the following componentsdqCoordinate systemαβThe conversion relation of the coordinate system can be thatdqAdmittance matrix conversion of coordinate system toαβCoordinate system:
Figure SMS_147
（19）
index operator
Figure SMS_149
The product of complex conjugate vector introduces the frequency coupling effect of VSC for a frequency ofωWill produce a frequency of +.>
Figure SMS_153
The frequency coupling vector, the detailed relationship between output voltage and current is shown in FIG. 8, Y 1 Representation ofαβOutput current disturbance quantity in coordinate system>
Figure SMS_156
Disturbance with output voltage->
Figure SMS_150
Is a relationship of (2); y is Y 2 Indicating the disturbance of the output current->
Figure SMS_152
And coupling voltage disturbance quantity->
Figure SMS_155
Is a relationship of (2); y is Y 3 Indicating the disturbance of the coupling current +.>
Figure SMS_157
And output voltage disturbance amount->
Figure SMS_148
Is a relationship of (2); y is Y 4 Indicating the disturbance of the coupling current +.>
Figure SMS_151
And coupling ofAmount of voltage disturbance
Figure SMS_154
Is a relationship of (3).
The technical route proposed by the present invention is now verified for this embodiment.
First, the main parameters of this embodiment are as follows: grid phase voltageU g Active power reference value=310VP ref 7kW of reactive powerQ ref 0var, switching frequencyf w At 20kHz, fundamental frequencyf 0 50Hz, filter inductanceL f 2mH, filter capacitorC f Is 15uF, DC voltageU dc 600V power supply inductanceL g 1mH, power supply resistanceR g 0.1 omega, active power droop coefficientmIs 8 of
Figure SMS_158
10 -4 Reactive power droop coefficientn2->
Figure SMS_159
10 -3 。
The accuracy of the established admittance model was verified using frequency scanning, the verification results of which are shown in fig. 9. Wherein FIG. 9 (a) shows Y in the established admittance model 1 Is shown in FIG. 9 (b) is Y 2 Is shown in FIG. 9 (c) is Y 3 Is shown in FIG. 9 (d) is Y 4 Is verified by the amplitude and phase of the signal.
FIG. 10 shows the cut-off frequency of different low pass filtersω c ) The effect on the output admittance of the VSC, where FIG. 10 (a) isω c Y at the time of change 1 The amplitude and phase response results of (b) of FIG. 10 areω c Y at the time of change 2 The amplitude and phase response results of (c) of FIG. 10 areω c Y at the time of change 3 The amplitude and phase response results of (d) of FIG. 10 areω c Y at the time of change 4 Amplitude and phase response results of (a).
FIG. 11 is a graph of different active power droop coefficientsmInfluence on the output admittance of the VSC, wherein fig. 11 (a) ismY at the time of change 1 The amplitude and phase response results of (b) of FIG. 11 aremY at the time of change 2 The amplitude and phase response results of (c) of FIG. 11 aremY at the time of change 3 The amplitude and phase response results of (d) of FIG. 11 aremY at the time of change 4 Amplitude and phase response results of (a).
FIG. 12 is a graph of different reactive power droop coefficientsnInfluence on the output admittance of the VSC, wherein fig. 12 (a) isnY at the time of change 1 The amplitude and phase response results of (b) of FIG. 12 arenY at the time of change 2 The amplitude and phase response results of (c) of FIG. 12 arenY at the time of change 3 The amplitude and phase response results of (d) of FIG. 12 arenY at the time of change 4 Amplitude and phase response results of (a).
FIG. 13 is a voltage control link proportional gainK up The effect of the variation on the output admittance of the VSC, where FIG. 13 (a) isk up Y at the time of change 1 The amplitude and phase response results of (b) of FIG. 13 arek up Y at the time of change 2 The amplitude and phase response results of (c) of FIG. 13 arek up Y at the time of change 3 The amplitude and phase response results of (d) of FIG. 13 areK up Y at the time of change 4 Amplitude and phase response results of (a).
FIG. 14 is a current control link proportional gainK ip The effect of the variation on the output admittance of the VSC, where FIG. 14 (a) isk ip Y at the time of change 1 The amplitude and phase response results of (b) of FIG. 14 arek ip Y at the time of change 2 The amplitude and phase response results of (c) of FIG. 14 arek ip Y at the time of change 3 The amplitude and phase response results of (d) of FIG. 14 areK ip Y at the time of change 4 Amplitude and phase response results of (a).
From FIG. 10-FIG. 14 shows the cut-off frequency of a filter (LPF) comprising a low pass filterω c ) Droop coefficients of active and reactive powermAndnthe coupling effect of frequency is caused, but has less effect on the positive and negative sequence admittances of the droop control three-phase grid-connected inverter. The proportional gain of the voltage control link has little influence on the positive and negative sequence admittance and the frequency coupling of the low frequency band, but the proportional gain of the current control link has obvious influence on the positive and negative sequence admittance and the frequency coupling phenomenon of the low frequency band.
Finally, the above embodiments are only illustrative of the technical solution of the invention and are not limiting. It is intended that all such insubstantial changes or modifications from the invention as described herein be covered by the scope of the appended claims.

Claims (5)

1. The accurate admittance modeling method for the sagging-controlled three-phase grid-connected inverter is characterized by comprising the following steps of:
step 1: splitting a sagging control system of the three-phase grid-connected inverter into an inner ring control system and an outer ring control system; the outer loop control system comprises a power calculation link, a low-pass filtering link and a droop control link; the inner loop control system comprises a voltage control link and a current control link;
step 2: establishing a single-input single-output structure complex vector model of an inner loop control system and an external circuit;
step 3: external circuit partαβTransfer function and variable conversion in coordinate systemdqIn the coordinate system, builddqA complex vector small signal model of an inner loop control and external circuit part which are unified under a coordinate system;
step 4: establishing a complex vector expression of active power and reactive power, and linearizing small signals of the active power and reactive power expression to obtain a complex vector small signal model of an outer loop control system;
step 5: combining the complex vector small signal model of the inner loop control and the external circuit in the step 3 and the complex vector small signal model of the outer loop control system in the step 4 to obtaindqIn the coordinate systemThe sagging control three-phase grid-connected inverter is a complete small signal admittance model and is transferred to the three-phase grid-connected inverter through coordinate transformationαβIn the coordinate system.
2. The droop-controlled three-phase grid-connected inverter precise admittance modeling method according to claim 1, wherein said step 2 comprises the following steps:
step 21: control system for inner ringdqCoordinate system lower sumαβThe electrical quantity under the coordinate system is expressed in the form of complex vector;
Figure QLYQS_1
（1）
wherein,x dq is thatdqA certain amount of electricity in the coordinate system,x d andx q respectively of the electric quantitydqA component;jan imaginary unit which is an imaginary part in the complex vector;
step 22: external circuit part, particularly including filter inductance, filter capacitance and delay module of digital control systemαβThe transfer function in the coordinate system is expressed in the form of complex vector;
Figure QLYQS_2
（2）
wherein,
Figure QLYQS_3
is thatαβA certain amount of electricity in the coordinate system,x α andx β respectively of the electric quantityαβA component;x dq and->
Figure QLYQS_4
The conversion relation of (2) is: />
Figure QLYQS_5
And->
Figure QLYQS_6
，θIs the angle of the coordinate transformation;
step 23: connecting the inner loop control system with an external circuit part through a delay module and a coordinate transformation module, and converting a multi-input multi-output system structure of the inner loop control system and the external circuit part into a complex vector model of a single-input single-output structure;
transfer functions of voltage control link and current control link in inner loop control systemG u (s) AndG i (s) The complex vector form of (a) is:
G u (s)＝G u (s)＋j0，G i (s)＝G i (s)＋j0（3）
wherein,j0 represents an imaginary part of 0;
αβtransfer function of filter capacitor and filter inductor in coordinate system
Figure QLYQS_7
And->
Figure QLYQS_8
The complex vector forms of (a) are respectively:
Figure QLYQS_9
（4）
wherein,
Figure QLYQS_10
，/>
Figure QLYQS_11
，C f andL f a filter capacitor and a filter inductor respectively;
based ondqCoordinate systemαβConversion relation of coordinate systemdqIn the coordinate systemThe transfer function of the filter capacitor and the filter inductor is as follows:
Figure QLYQS_12
，/>
Figure QLYQS_13
，ω 0 is the fundamental angular frequency;
time delay transfer function of digital control systemG d (s) includes a sampling periodT s And a pulse width modulation delay of half the sampling frequency, expressed as:G d (s)＝G d (s)＋j0，
Figure QLYQS_14
。
3. the droop-controlled three-phase grid-connected inverter precise admittance modeling method according to claim 2, wherein said step 3 comprises the following steps:
step 31: external circuit partαβTransfer function and variable conversion in coordinate systemdqUnder a coordinate system;
Figure QLYQS_15
（5）
Figure QLYQS_16
（6）
wherein,x dq,0 representation ofdqSteady state value, delta, of certain electric quantity under coordinate systemx dq Representation ofdqSmall signal disturbance quantity of the electric quantity under a coordinate system; deltaθRepresenting the angle of transformation of coordinatesθIs a small signal disturbance quantity;
Figure QLYQS_17
representation ofαβA steady state value of an electrical quantity in the coordinate system,
Figure QLYQS_18
representation ofαβSmall signal disturbance quantity of the electric quantity under a coordinate system;
step 32: small signal linearization of variables in a system, and establishmentdqA complex vector model of an inner loop control and an external circuit part which are unified under a coordinate system;
small signal disturbance delta of inverter output voltageu odq The expression is:
Figure QLYQS_19
（7）
wherein,
Figure QLYQS_20
representing the voltage reference value small signal disturbance quantity delta of the inner loop control systemi odq The small signal disturbance quantity of the output current of the inverter is represented;G V (s) Representing deltau odq And->
Figure QLYQS_21
The transfer function between the two is chosen to be the same,G I (s) Representing deltau odq And deltai odq The transfer function between the two is chosen to be the same,G θ (s) Representing deltau odq And deltaθA transfer function therebetween; the expressions are respectively:
Figure QLYQS_22
，
Figure QLYQS_23
，
Figure QLYQS_24
，
wherein:
Figure QLYQS_25
representing the steady state value of the modulation voltage +.>
Figure QLYQS_26
Representing steady state value of inverter output voltage, +.>
Figure QLYQS_27
Representing the steady state value of the filter inductor current.
4. The droop-controlled three-phase grid-connected inverter precise admittance modeling method according to claim 3, wherein said step 4 comprises the following steps:
step 41: establishing active powerP r And reactive powerQ r Complex vector expression of (2)
Active powerP r And reactive powerQ r The expression of (2) is:
Figure QLYQS_28
（8）
wherein,u od andu oq representing the output voltage of an inverter VSCdqA component;i od andi oq representing the output current of an inverter VSCdqA component;
complex in-plane complex power vectorSAnd conjugate of the same
Figure QLYQS_29
The expression of (2) is:
Figure QLYQS_30
（9）
wherein,u odq representation ofdqA complex vector expression of the inverter output voltage in the coordinate system,u odq ＝u od ＋ju oq ；
Figure QLYQS_31
representation ofu odq Conjugation of->
Figure QLYQS_32
；i odq Representation ofdqA complex vector expression of the inverter output current in the coordinate system,i odq ＝i od ＋ji oq ；/>
Figure QLYQS_33
representation ofi odq Conjugation of->
Figure QLYQS_34
；
Then get the instantaneous active powerP r And reactive powerQ r Is expressed as:
Figure QLYQS_35
（10）
step 42: linearizing the active power and reactive power expression small signals, wherein the expression is as follows:
Figure QLYQS_36
（11）
wherein delta isP r And deltaQ r Respectively represent active powerP r And reactive powerQ r A small signal disturbance component of (2);
Figure QLYQS_38
and->
Figure QLYQS_40
Respectively representu odq And->
Figure QLYQS_43
Steady state values of (2); deltau odq And->
Figure QLYQS_39
Respectively representu odq And->
Figure QLYQS_41
A small signal disturbance component of (2);i odq,0 and
Figure QLYQS_44
respectively representi odq And->
Figure QLYQS_45
Steady state values of (2): deltai odq And->
Figure QLYQS_37
Respectively representi odq And->
Figure QLYQS_42
A small signal disturbance component of (2);
step 43: obtaining a complex vector small signal model of the outer loop control system
The small signal relationship for the droop control loop is:
Figure QLYQS_46
（12）
wherein,G LF (s) Representing the transfer function of the low-pass filtering element,mrepresenting the active power droop coefficient,nrepresenting the reactive power droop coefficient, deltaθRepresenting the angle of transformation of coordinatesθIs used for the small signal disturbance quantity of the (a),
Figure QLYQS_47
representing an inner loop control system voltage reference
Figure QLYQS_48
A small signal disturbance component;
bringing equation (11) into equation (12) yields:
Figure QLYQS_49
（13）
Figure QLYQS_50
（14）
wherein,
Figure QLYQS_51
representing deltaθAnd deltaP r Is used for the transfer function of (a),G du (s) Representation->
Figure QLYQS_52
And deltaQ r And (2) transfer function of
Figure QLYQS_53
。
5. The droop-controlled three-phase grid-connected inverter precise admittance modeling method according to claim 4, wherein said step 5 comprises the following steps:
step 5.1: based on the built two control system models of the inner ring and the outer ring, the method obtainsdqAnd (3) a complete small signal model of the coordinate system sag control three-phase grid-connected inverter system is obtained by inputting the formula (13) and the formula (14) into an output voltage expression formula (7):
Figure QLYQS_54
（15）
wherein,G 1 (s) Representing deltau odq And
Figure QLYQS_55
is used for the transfer function of (a),G 2 (s) The expression +.>
Figure QLYQS_56
And deltaθDelta after similar term simplification is replaced and combined by a formula (13) and a formula (14) respectivelyu odq And deltai odq Is a new expression of the transfer function of (c),G 3 (s) Representing deltau odq And->
Figure QLYQS_57
The expression of which is as follows:
Figure QLYQS_58
（16）
Δu odq the expression form of the conjugate complex vector of (a) is as follows:
Figure QLYQS_59
（17）
wherein,
Figure QLYQS_60
representation->
Figure QLYQS_61
And deltau odq Is>
Figure QLYQS_62
Representation->
Figure QLYQS_63
And->
Figure QLYQS_64
Is>
Figure QLYQS_65
Representation->
Figure QLYQS_66
And deltai odq Is a transfer function of (2);
derived from equation (15) and equation (17)dq2 of output voltage and output current in coordinate system
Figure QLYQS_67
2 admittance matrix:
Figure QLYQS_68
（18）
wherein Y is dq1 (s) Representation ofdqOutput current disturbance delta under coordinate systemi odq And output voltage disturbance deltau odq Is the relation of Y dq2 (s) Indicating the disturbance delta of the output currenti odq Conjugate with the disturbance of output voltage
Figure QLYQS_69
Is the relation of Y dq3 (s) Representing the disturbance of the output current>
Figure QLYQS_70
And output voltage disturbance deltau odq Is the relation of Y dq4 (s) Representing the disturbance of the output current>
Figure QLYQS_71
Conjugate with output voltage disturbance quantity->
Figure QLYQS_72
Is a relationship of (2);
step 5.2: from the following componentsdqCoordinate systemαβThe conversion relation of the coordinate system is todqAdmittance matrix conversion of coordinate system toαβCoordinate system:
Figure QLYQS_73
（19）
wherein,
Figure QLYQS_76
and->
Figure QLYQS_80
Respectively representing the output currents of the inverterαβComplex vector representation form of disturbance quantity under coordinate system and conjugate thereof; />
Figure QLYQS_82
And->
Figure QLYQS_77
Respectively representing output voltages of the inverterαβComplex vector representation form of disturbance quantity under coordinate system and conjugate thereof; index operator->
Figure QLYQS_78
The product of complex conjugate vector introduces the frequency coupling effect of VSC for one frequencyωWill produce a frequency of +.>
Figure QLYQS_83
Frequency coupling vector, Y 1 Representation ofαβOutput current disturbance quantity under coordinate system
Figure QLYQS_86
Disturbance with output voltage->
Figure QLYQS_74
Is a relationship of (2); y is Y 2 Indicating the disturbance of the output current->
Figure QLYQS_81
And the coupling voltage disturbance quantity
Figure QLYQS_85
Is a relationship of (2); y is Y 3 Indicating the disturbance of the coupling current +.>
Figure QLYQS_87
And output voltage disturbance amount->
Figure QLYQS_75
Is a relationship of (2); y is Y 4 Indicating the disturbance of the coupling current +.>
Figure QLYQS_79
And coupling voltage disturbance quantity->
Figure QLYQS_84
Is a relationship of (3).
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