CN116418049B - 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 PDFInfo
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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
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 stationaryαβAnd accurately drooping and controlling the admittance model of the three-phase grid-connected inverter under the coordinate system. 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;
（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;
（2）
wherein ,is thatαβA certain amount of electricity in the coordinate system,x α andx β respectively of the electric quantityαβA component;x dq andThe conversion relation of (2) is: and，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:
（4）
wherein ,，，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:，，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，。
further, the step 3 includes the following steps:
step 31: external circuit partαβTransfer function and variable conversion in coordinate systemdqUnder a coordinate system;
（5）
（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;representation ofαβA steady state value of an electrical quantity in the coordinate system,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:
（7）
wherein ,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 andThe 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:
，
，
in the formula ：representing the steady state value of the modulation voltage +.>Representing steady state value of inverter output voltage, +.>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:
（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 vectorSAndthe expression of (2) is:
（9）
wherein ,u odq representation ofdqA complex vector expression of the inverter output voltage in the coordinate system,u odq ＝u od ＋ju oq ；representation ofu odq Conjugation of->；i odq Representation ofdqA complex vector expression of the inverter output current in the coordinate system,i odq ＝i od ＋ji oq ；representation ofi odq Conjugation of->；
Then get the instantaneous active powerP r And reactive powerQ r Is expressed as:
（10）
step 42: linearizing the active power and reactive power expression small signals, wherein the expression is as follows:
（11）
wherein ,ΔP r and ΔQ r Respectively represent active powerP r And reactive powerQ r A small signal disturbance component of (2);andseparate tableu odq andSteady state values of (2); deltau odq andRespectively representu odq andA small signal disturbance component of (2);i odq,0 andRespectively representi odq andSteady state values of (2); deltai odq andRespectively representi odq andA 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:
（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),representing the voltage reference value of the inner loop control system +.>Small signal disturbance component.
Bringing equation (11) into equation (12) yields:
（13）
（14）
wherein ,representing deltaθAnd deltaP r Is used for the transfer function of (a),G du (s) Representation->And deltaQ r Is a transfer function of (2); and is also provided with。
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):
（15）
wherein ,G 1 (s) Representing deltau odq Andis used for the transfer function of (a),G 2 (s) The expression +.> 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 andThe expression of which is as follows:
（16）
Δu odq the expression form of the conjugate complex vector of (a) is as follows:
（17）
wherein ,representation-> and Δu odq Is>Representation-> andIs used for the transfer function of (a),representation-> 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 system2 admittance matrix:
（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 voltageRelation of Y dq3 (s) Representing the disturbance of the output current>And output voltage disturbance deltau odq Relation of Y dq4 (s) Conjugation indicating output current disturbance quantityConjugate with output voltage disturbance quantity->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:
（19）
wherein,and->Respectively representing the output currents of the inverterαβComplex vector representation and conjugate thereof under a coordinate system;And->Respectively represent the output voltage of the inverterαβComplex vector representation and conjugate thereof under a coordinate system; index operator->The product of complex conjugate vector introduces the frequency coupling effect of VSC for one frequencyωWill produce a frequency of +.>Frequency coupling vector, Y 1 Representation ofαβOutput current disturbance quantity in coordinate system>Disturbance with output voltage->Is a relationship of (2); y is Y 2 Indicating the disturbance of the output current->And coupling voltage disturbance quantity->Is a relationship of (2); y is Y 3 Indicating the disturbance of the coupling current +.>And output voltage disturbance amount->Is a relationship of (2); y is Y 4 Indicating the disturbance of the coupling current +.>And coupling voltage disturbance quantity->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 conventional sequence impedance model in the static coordinate system does not consider the coupling effect between positive and negative sequencesThe invention establishes a static stateαβThe 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 powerSAndform 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 is 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 voltage control link gainK 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 a frequency coupling effect mechanism of the droop control three-phase grid-connected inverter, and analyzes the influence of the parameters of the inner loop control system and the outer loop control system on the output admittance characteristic and the frequency coupling effect of the 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;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:
（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,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 voltageAnd->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;And->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:
（2）
the conversion relation between the two is as follows:and->，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. 4Andu idq a complex vector representation representing the inverter output reference voltage and the modulation voltage;G u (s) AndG i (s) A complex vector representation representing the transfer functions of the voltage control link and the current control link of the inner loop control system;And->Representing coordinate transformation operators，And->Impedance of filter inductance and capacitance, respectively, +.>，And->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;And->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:
（4）
wherein:，，C f andL f a filter capacitor and a filter inductor, respectively. Based ondqCoordinate systemαβThe conversion relation of the coordinate system is as follows:，；
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，。
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:
（5）
（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 describedαβIn the coordinate systemConversion of variables and transfer functions 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: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;、And->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:
（7）
wherein,G V (s) Representing deltau odq Andthe 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:
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:
（8）
FIG. 6 is a complex in-plane complex power vectorSAndS * in the form of (a), wherein the complex power vectorSThe expression is:
（9）
can obtain instantaneous active powerP r And reactive powerQ r Is expressed as:
（10）
small signal linearization of equation (10) yields:
（11）
the small signal relationship for the droop control loop shown in fig. 2 is:
（12）
bringing equation (11) into equation (12) yields:
（13）
（14）
wherein: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):
（15）
wherein,G 1 (s) Representing deltau odq Andis used for the transfer function of (a),G 2 (s) The expression +.>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->The expression of which is as follows: />
（16）
Δu odq The expression form of the conjugate complex vector is as follows:
（17）
wherein,representation->And deltau odq Is>Representation->And->Is used for the transfer function of (a),representation->And deltai odq Is a transfer function of (a).
From equation (15) and equation (17)dq2 of output voltage and output current in coordinate system2 admittance matrix:
（18）
(2) From the following componentsdqCoordinate systemαβThe conversion relation of the coordinate system can be thatdqAdmittance matrix conversion of coordinate system toαβCoordinate system:
（19）
index operatorThe product of complex conjugate vector introduces the frequency coupling effect of VSC for a frequency ofωWill produce a frequency of +.>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>Disturbance with output voltage->Is a relationship of (2); y is Y 2 Indicating the disturbance of the output current->And coupling voltage disturbance quantity->Is a relationship of (2); y is Y 3 Indicating the disturbance of the coupling current +.>And output voltage disturbance amount->Is a relationship of (2); y is Y 4 Indicating the disturbance of the coupling current +.>And the coupling voltage disturbance quantityIs 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 of10 -4 Reactive power droop coefficientn2->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 droopCoefficients ofmInfluence 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 FIGS. 10-14, it can be derived that the cut-off frequency including the Low Pass Filter (LPF)ω 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 (3)
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;
the step 2 comprises the following steps:
step 21: control system for inner ringCoordinate system Down and->The electrical quantity under the coordinate system is expressed in the form of complex vector;
（1）
wherein,is->Certain electric quantity in coordinate system, +.>And->Respectively the electric quantity +.>A component;An 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;
（2）
wherein,is->Certain electric quantity in coordinate system, +.>And->Respectively the electric quantity +.>A component;and->The conversion relation of (2) is:And->，Is 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 systemAnd->The complex vector form of (a) is:
，（3）
wherein,representing the imaginary part as 0;
filter capacitance and filter inductance in coordinate systemTransfer function->And->The complex vector forms of (a) are respectively:
，（4）
wherein,，，and->A filter capacitor and a filter inductor respectively;
based onCoordinate systemConversion relation of coordinate systemThe transfer functions of the filter capacitor and the filter inductor under the coordinate system are as follows:，，is the fundamental angular frequency;
time delay transfer function of digital control systemComprising a sampling period +.>And a pulse width modulation delay of half the sampling frequency, expressed as:，；
Step 3: external circuit partTransfer function and variable conversion in coordinate system to +.>In the coordinate system, buildA complex vector small signal model of an inner loop control and external circuit part which are unified under a coordinate system;
the step 3 comprises the following steps:
step 31: external circuit partTransfer function and variable conversion in coordinate system to +.>Under a coordinate system;
（5）
（6）
wherein,representation->Steady-state value of certain electric quantity under coordinate system, < >>Representation->Small signal disturbance quantity of the electric quantity under a coordinate system;Representing the coordinate transformation angle +.>Is a small signal disturbance quantity;Representation->Steady-state value of certain electric quantity under coordinate system, < >>Representation->Small signal disturbance quantity of the electric quantity under a coordinate system;
step 32: small signal linearization of variables in a system, and establishmentA complex vector model of an inner loop control and an external circuit part which are unified under a coordinate system;
small signal disturbance quantity of inverter output voltageThe expression is:
（7）
wherein,indicating the small signal disturbance quantity of the voltage reference value of the inner loop control system,/->The small signal disturbance quantity of the output current of the inverter is represented;) Representation->And->Transfer function between->Representation ofAnd->Transfer function between->Representation->And->A transfer function therebetween; the expressions are respectively:
,
，
，
wherein:representing the steady state value of the modulation voltage +.>Representing steady state value of inverter output voltage, +.>Representing a steady state value of the filter inductor current;
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 obtainThe 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 +.>In the coordinate system.
2. The droop-controlled three-phase grid-connected inverter precise admittance modeling method according to claim 1, wherein said step 4 comprises the following steps:
step 41: establishing active powerAnd reactive power->Complex vector expression of (2)
Active powerAnd reactive power->The expression of (2) is:
，（8）
wherein,and->Representing the output voltage of an inverter VSCdqA component;And->Representing the output current of an inverter VSCdqA component;
complex in-plane complex power vectorSAnd conjugate of the sameThe expression of (2) is:
，（9）
wherein,representation->A complex vector expression of the inverter output voltage in the coordinate system,；representation->Conjugation of->；Representation ofComplex vector expression of inverter output current in coordinate system,/->；Representation->Conjugation of->；
Then get the instantaneous active powerAnd reactive power->Is expressed as:
（10）
step 42: linearizing the active power and reactive power expression small signals, wherein the expression is as follows:
（11）
wherein,and->Respectively represent active power +>And reactive power->A small signal disturbance component of (2);and->Respectively indicate->And->Steady state values of (2);And->Respectively representAnd->A small signal disturbance component of (2);And->Respectively indicate->And->Steady state values of (2):and->Respectively indicate->And->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:
，（12）
wherein,representing the transfer function of the low-pass filtering element, < >>Representing the active power droop coefficient, +.>Representing the reactive power droop factor,/->Representing the angle of transformation of coordinatesθIs%>Representing the voltage reference value of the inner loop control system +.>A small signal disturbance component;
bringing equation (11) into equation (12) yields:
（13）
（14）
wherein,representation->And->Is>Representation->And->And>，。
3. the droop-controlled three-phase grid-connected inverter precise admittance modeling method according to claim 2, 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):
（15）
wherein,representation->And->Is>Expressed in the formula (7)And->The similar items are simplified by replacing and combining the formula (13) and the formula (14) respectively>Andnew transfer function expression of +.>Representation->And->The expression of which is as follows:
（16）
the expression form of the conjugate complex vector of (a) is as follows:
（17）
wherein,representation->And->Is>Representation->Andis>Representation->And->Is a transfer function of (2);
derived from equation (15) and equation (17)Output voltage and output current in coordinate system +.>Admittance matrix:
（18）
wherein,representation->Output current disturbance quantity in coordinate system>And the output voltage disturbanceIs a relationship of (2);Indicating the disturbance of the output current->Conjugate with the disturbance of output voltageIs a relationship of (2);Representing the disturbance of the output current>And the output voltage disturbanceIs a relationship of (2);Representing the disturbance of the output current>Conjugate to output voltage disturbanceIs a relationship of (2);
step 5.2: from the following componentsCoordinate System and->Conversion relation of coordinate system, will->Admittance matrix conversion of coordinate system toCoordinate system:
（19）
wherein,andrespectively representing the output currents of the inverterComplex vector representation form of disturbance quantity under coordinate system and conjugate thereof;andrespectively representing output voltages of the inverterComplex vector representation form of disturbance quantity under coordinate system and conjugate thereof; index operatorThe product of complex conjugate vector introduces the frequency coupling effect of VSC for one frequencyWill produce a frequency ofIs a function of the frequency coupling vector of (a),representation ofOutput current disturbance quantity under coordinate systemDisturbance with output voltageIs a relationship of (2);indicating the disturbance of the output currentAnd the coupling voltage disturbance quantityIs a relationship of (2);representing the disturbance quantity of the coupling currentAnd the output voltage disturbanceIs a relationship of (2);representing the disturbance quantity of the coupling currentAnd the coupling voltage disturbance quantityIs a relationship of (3).
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