CN112952901A - Distributed stability analysis method for multi-fan grid-connected system - Google Patents

Distributed stability analysis method for multi-fan grid-connected system Download PDF

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CN112952901A
CN112952901A CN202110168509.7A CN202110168509A CN112952901A CN 112952901 A CN112952901 A CN 112952901A CN 202110168509 A CN202110168509 A CN 202110168509A CN 112952901 A CN112952901 A CN 112952901A
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grid
side converter
permanent magnet
controller
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CN112952901B (en
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刘佳宁
于淼
赵竞涵
陆玲霞
韦巍
亢朋朋
王衡
李渝
孙谊媊
印欣
宋朋飞
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Zhejiang University ZJU
State Grid Xinjiang Electric Power Co Ltd
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Zhejiang University ZJU
State Grid Xinjiang Electric Power Co Ltd
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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
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention relates to a distributed stability analysis method for a multi-fan grid-connected system, which comprises the steps of firstly carrying out mathematical modeling on a permanent magnet synchronous fan, wherein the mathematical modeling comprises mathematical models of a permanent magnet synchronous generator, a machine side converter and a controller thereof, a grid side converter and a controller thereof, and a filter, and carrying out Park transformation and linearization at a steady-state operation point to obtain a dq coordinate system admittance model of a single permanent magnet synchronous fan. And multiplying the admittance model by the network equivalent impedance model to construct a system contrast matrix, and drawing a characteristic curve of the system contrast matrix. And drawing a concentric circle curve of the number of the parallel-connected fans according to the requirement, and analyzing the stability of the multi-fan grid-connected system by comparing the relation between the system characteristic curve and the concentric circle curve. The method is based on the basic principle of an impedance analysis method, and has better engineering practice value. The stability of the whole system is analyzed through the relation between the impedance characteristic of a single fan and the number of the grid-connected units, the scale increase of the wind power plant can be better coped with, meanwhile, the analysis process is simplified, and repeated analysis is avoided.

Description

Distributed stability analysis method for multi-fan grid-connected system
Technical Field
The invention relates to a distributed stability analysis method for a multi-fan grid-connected system, and belongs to the field of stability analysis of power systems and new energy power generation systems.
Background
In recent years, with the rapid development of renewable energy sources, the installed capacity of wind power generation is continuously improved, and the total installed capacity of wind power generation in China reaches 2.23 hundred million kilowatts by 9 months in 2020. The centralized wind power plant is a main form of collecting and sending out wind power generation, and each wind power plant is usually provided with dozens or even hundreds of wind power generation units, so that a multi-fan grid-connected system is formed. The permanent magnet synchronous wind turbine generator system (PMSG) has the advantages of high energy conversion efficiency, good operation reliability and strong controllability, and the installed proportion is continuously improved. However, the PMSG uses the inverter as a grid-connected interface, and when the strength of the power grid at the interface is weak, an oscillation instability accident is easy to occur, and the safe and stable operation of the power grid is seriously threatened. The stability analysis method of the multi-fan grid-connected system mainly comprises a state space method and an impedance analysis method. The state space method needs to obtain a refined model of the global information construction system, which is difficult to implement in reality. Meanwhile, when the scale of the wind power plant is continuously increased, parameters needing to be calculated are multiplied, and the stability analysis faces the problem of dimension disaster. In contrast, the impedance analysis method can be realized by deducing a system fine model, and can also be used for obtaining the system impedance characteristics through impedance measurement to complete stability analysis, so that the method has higher engineering practice value. However, the traditional impedance analysis method also cannot solve the problem of the increase of the scale of the wind power plant, and when the number of the wind turbines is increased, the impedance of the wind power plant needs to be modeled again, so that repeated analysis is caused.
Disclosure of Invention
The invention provides a distributed stability analysis method aiming at multi-fan grid connection based on the basic principle of an impedance analysis method.
The invention adopts the following technical scheme:
the method comprises the following steps: the method comprises the steps of obtaining main parameters of the permanent magnet synchronous fan, establishing mathematical models of a permanent magnet synchronous generator, a machine side converter and a controller thereof, a direct current capacitor, a grid side converter and a controller thereof and a filter, and equivalently converting the models to a dq coordinate system by using Park conversion. Linearizing the model at a steady-state operation point, and calculating a steady-state operation parameter to obtain an admittance model Y of a dq coordinate system of the permanent magnet synchronous fanPMSG。
Step two: obtaining the equivalent impedance of the grid-connected point network and equivalently converting the equivalent impedance into a dq coordinate system to obtain a network impedance equivalent model Z of the dq coordinate systemg。
Step three: obtaining a system return matrix of L(s) ═ ZgYPMSGLet its characteristic function be λ1(s)、λ2(s) plotting λ in the complex plane as s moves along the standard Nyquist contour in the complex plane1(s)、λ2(s) a trajectory.
Step four: analyzing the stability of the system: the sufficient requirements for system stability can be summarized as: l(s) does not contain a right half-plane pole; l(s) does not encompass at least the (-1,0) point.
Further, in the first step, models of the permanent magnet synchronous generator and the machine side converter are obtained first, and an equivalent admittance Y is usedMAnd (4) showing. Y isMForm a DC equivalent admittance Y together with a DC capacitordcAnd then combining a mathematical model of a network side converter and a filter to obtain a final dq coordinate system admittance model Y of the permanent magnet synchronous fanPMSG. The machine side converter is a two-level voltage source type converter, converts alternating current output by the permanent magnet synchronous generator into direct current and controls torque of the direct current. Obtaining the equivalent admittance Y of the permanent magnet synchronous generator and the machine side converterMThe process of (2) is as follows:
the frequency domain mathematical model of the permanent magnet synchronous generator and the machine side converter is as follows:
Figure BDA0002938348980000021
in the formula, Rs、LsRotor resistance and armature inductance, omega, of a permanent magnet synchronous generatoreAs the electrical angular velocity of the rotor, idr、iqrStator currents, psi, of dq coordinate system, respectivelyfIs a permanent magnet flux linkage, ddr、dqrRespectively, the output duty ratio u of the converter controller under the dq coordinate systemdcIs a direct current voltage, and s is a complex parameter introduced by Laplace transform. Linearizing the model to obtain a small signal model of
Figure BDA0002938348980000022
Wherein,
Figure BDA0002938348980000023
capital letters and superscripts denote steady-state components of the corresponding variables, and Δ denotes small-signal components of the corresponding variables.
The controller model of the machine side converter is
Figure BDA0002938348980000024
Wherein,
Figure BDA0002938348980000025
Kcpr、Kcirproportional and integral parameters, I, of the machine side current loop PI controller, respectivelydrref、IqrrefD-axis and q-axis current reference values, respectively. Linearizing it to obtain a small signal model of the machine side converter controller as
Figure BDA0002938348980000026
Wherein,
Figure BDA0002938348980000027
and side direct current idc2Can be expressed as
Figure BDA0002938348980000028
Linearizing it to obtain
Figure BDA0002938348980000031
Wherein,
Figure BDA0002938348980000032
therefore, the permanent magnet synchronous generator and the machine side converter model can use the equivalent admittance YMIs shown, i.e.
Figure BDA0002938348980000033
Wherein, Δ idc2Is made into a machineThe small signal component of the side dc current, I is the identity matrix,
Figure BDA0002938348980000034
further, obtaining the DC equivalent admittance YdcThe process is as follows: the DC capacitance model is
sCdcudc＝idc2-idc1
Wherein, CdcIs a DC capacitor, idc1Is the grid side direct current. Linearizing the signal to obtain a small signal model of DC capacitor
sCdcΔudc＝Δidc2-Δidc1＝-ΔudcYM-Δidc1
The impedance characteristic of the DC bus is influenced by the PMSM, the machine side converter and the DC capacitor, so that the three models can be combined and expressed by an equivalent admittance, namely a DC equivalent admittance YdcThe expression is
Figure BDA0002938348980000035
Further, a final permanent magnet synchronous fan dq coordinate system admittance model Y is obtained by combining a mathematical model of a grid-side converter and a filterPMSGThe process is as follows: the grid-side converter is also a two-level voltage source type converter, is externally connected with a single inductance filter, inverts direct current into power frequency alternating current and then is connected into a power grid. The established mathematical model is specifically as follows:
Figure BDA0002938348980000036
wherein L isfFor filter inductance, ω is power frequency angular frequency, ω ═ 100 π rad/s, idg、iqgD, q-axis currents at AC port of grid-side converterdg、dqgFor the output duty ratio u of the grid side converter controller under dq coordinate systemdg、uqgThe voltage of the grid connection point d and the q axis are respectively. Linearizing the model to obtain a small signal model of the grid-side converter and the filter
Figure BDA0002938348980000037
Wherein,
Figure BDA0002938348980000038
the network side converter controller model is
Figure BDA0002938348980000041
Wherein,
Figure BDA0002938348980000042
Kcpg、Kcigrespectively are a proportional parameter and an integral parameter of a network side current loop PI controller,
Figure BDA0002938348980000043
Kvp、Kviproportional and integral parameters, U, of the network side voltage loop PI controller, respectivelydcrefIs a dc voltage reference. In the grid-side converter controller, a phase-locked loop is adopted to keep the fan and the power grid synchronous. Under the dynamic influence of the phase-locked loop, a certain deviation exists between the controller phase angle and the real system phase angle, so that a small deviation occurs between a system dq coordinate system and a controller dq coordinate system. To distinguish between the two, the grid-side converter controller dq coordinate system is denoted by the superscript c. The model is linearized to obtain a small signal model of the grid-side converter controller
Figure BDA0002938348980000044
Wherein,
Figure BDA0002938348980000045
in addition, the dynamic of the phase-locked loop should be considered in the network side converter, and the model is
Figure BDA0002938348980000046
Wherein,
Figure BDA0002938348980000047
Kppll、Kipllrespectively, a proportional parameter and an integral parameter of the phase-locked loop PI controller. Linearizing it to obtain
Figure BDA0002938348980000048
The dq coordinate system of the system has a certain deviation from the dq coordinate system of the controller, and the two can be mutually converted by the following equation
Figure BDA0002938348980000049
In the formula, the variable Δ xd、ΔxqCan represent the output current delta i of the grid-side converterdg、ΔiqgGrid connection point voltage delta udg、ΔuqgOr network side controller output duty ratio delta ddg、Δdqg，
Figure BDA00029383489800000412
Representing the steady state component of the corresponding variable.
From this, a phase-locked loop small-signal model can be derived, i.e.
Δθ＝Gpll·Δuqg
Wherein,
Figure BDA00029383489800000410
it can thus be derived that the relationship between the controller dq coordinate system and the system dq coordinate system is
Figure BDA00029383489800000411
Wherein,
Figure BDA0002938348980000051
and the network side direct current idc1Can be expressed as
Figure BDA0002938348980000052
Linearizing it to obtain
Figure BDA0002938348980000053
Wherein,
Figure BDA0002938348980000054
the permanent magnet synchronous fan can be represented by an equivalent admittance, i.e.
Δidqg＝YPMSG·Δudqg
YPMSGIs an admittance model of a dq coordinate system of the permanent magnet synchronous fan, and the expression is
Figure BDA0002938348980000055
Wherein,
Figure BDA0002938348980000056
Figure BDA0002938348980000057
and I is an identity matrix.
Further, in the second step, the network equivalent impedance model is
Figure BDA0002938348980000058
Wherein s is a complex parameter introduced by Laplace transform, ω is power frequency angular frequency, ω is 100 π rad/s, LgIs the network equivalent inductance.
Further, in the third step, the system contrast matrix is L ═ ZgYPMSGL is a 2X 2 matrix, let us assume
Figure BDA0002938348980000059
Its characteristic function lambda1(s)、λ2(s) can be obtained by the following equation.
Figure BDA00029383489800000510
In step four, if the characteristic locus of l(s) does not enclose the point (-1/k,0), and k (k is 1,2,3 …) is the number of fans connected in parallel in the system, the maximum number of fans connected in parallel in the system is k.
Further, the acquisition of the (-1/k,0) point is performed by: and if the number of the fans connected in parallel in the system is k (k is 1,2 and 3 …), the complex plane origin is taken as the center of a circle, 1/k is taken as the radius to draw a circle, and the intersection point of the circle and the negative real axis is (-1/k, 0).
Compared with the prior art, the invention has the advantages that:
(1) based on the basic principle of an impedance analysis method, the impedance characteristic of the fan can be deduced through a mathematical model and can also be obtained through impedance measurement in an actual system, and the method has a good engineering practice value.
(2) The invention discloses a distributed stability analysis method, which can analyze the overall stability of a multi-fan grid-connected system by only obtaining the impedance characteristic of one fan and analyze the influence of fan parameters and the number of parallel fans on the stability of the system. The method can better solve the problem of dimension disaster caused by the scale increase of the wind power plant, and meanwhile, the analysis process is simplified, and repeated analysis is avoided.
Drawings
Fig. 1 shows a permanent magnet synchronous fan topology (a) and its controller structure (B, D is coordinate transformation, C is a phase-locked loop, E is a machine-side converter controller, and F is a grid-side converter controller);
FIG. 2 is a system signature trace;
FIG. 3 is a system characteristic trace and parallel number concentric circle curve;
FIG. 4 is a distribution diagram of L(s) poles.
Detailed Description
The topological structure of the permanent magnet synchronous fan and the controller thereof are shown in figure 1 and comprise a permanent magnet synchronous generator, a machine side converter, a direct current capacitor, a network side converter and a filter. The machine side converter and the grid side converter are both two-level voltage source type converters, wherein the machine side converter converts alternating current output by the permanent magnet synchronous generator into direct current, and the grid side converter inverts the direct current into power frequency alternating current to be incorporated into a power grid. The machine side converter and the grid side converter adopt a vector control method under a dq coordinate system, and the three-phase voltage and current of abc is converted into voltage and current under a d axis and a q axis through dq conversion. In the machine side converter, a current loop PI controller is used for controlling an output current to track a reference value. In the grid-side converter, a voltage loop PI controller is used for controlling the direct-current voltage to be constant, a current loop PI controller is used for controlling the output current, and a phase-locked loop (PLL) is used for acquiring a grid phase angle. The invention will be further described with reference to a specific embodiment:
in one embodiment of the present invention, the main parameters of the system are shown in table 1.
TABLE 1 Main parameters of the System
Figure BDA0002938348980000061
Figure BDA0002938348980000071
In the embodiment of the invention, in the first step, main parameters (table 1) of the permanent magnet synchronous fan are obtained, and the fan, the machine side converter and the grid side converter are establishedAnd (4) a mathematical model, namely equivalently converting the model into a dq coordinate system by using Park transformation. Linearizing the model at a steady-state operation point, and calculating a steady-state operation parameter to obtain an admittance model Y of a dq coordinate system of the permanent magnet synchronous fanPMSG。
Figure BDA0002938348980000072
Wherein,
Figure BDA0002938348980000073
Figure BDA0002938348980000074
Figure BDA0002938348980000075
Figure BDA0002938348980000076
Figure BDA0002938348980000077
Figure BDA0002938348980000078
Figure BDA0002938348980000079
Figure BDA00029383489800000710
Ydc＝sCdc+YM
Figure BDA00029383489800000711
Figure BDA00029383489800000712
Figure BDA00029383489800000713
Kcpg、Kcigrespectively are a proportional parameter and an integral parameter of a network side current loop PI controller,
Figure BDA00029383489800000714
Kvp、Kviproportional parameters and integral parameters of a network side voltage loop PI controller are respectively set;
Figure BDA00029383489800000715
Figure BDA0002938348980000081
Kppll、Kipllrespectively, a proportional parameter and an integral parameter of the phase-locked loop PI controller.
Capital letters and superscripts indicate steady state components of the corresponding variables, and are calculated as follows.
Figure BDA0002938348980000082
In the embodiment of the invention, the second step is to obtain the equivalent impedance of the grid-connected point network and equivalently convert the equivalent impedance into a dq coordinate system to obtain a network impedance equivalent model Z of the dq coordinate systemg。
Figure BDA0002938348980000083
In an embodiment of the present invention, the third step,admittance model Y according to dq coordinate system of permanent magnet synchronous fanPMSGAnd network impedance equivalent model ZgObtaining a system return matrix of L(s) ═ ZgYPMSGLet its characteristic function be λ1(s)、λ2(s) suppose
Figure BDA0002938348980000084
Its characteristic function lambda1(s)、λ2(s) can be obtained by the following equation.
Figure BDA0002938348980000085
Plotting λ in the complex plane as s moves along the standard Nyquist contour in the complex plane1(s)、λ2The(s) trajectory is shown in fig. 2.
In the fourth step of the present invention, if the number of fans connected in parallel in the system is k (k is 1,2,3 …), the point of intersection between the circle and the negative real axis is (-1/k,0) and the circle is drawn with the origin of the complex plane as the center of the circle and 1/k as the radius, where the maximum value of k is 4, and the concentric circle curve is shown in fig. 3.
In an embodiment of the present invention, in a fifth step, system stability is analyzed. First, an l(s) pole point diagram is drawn, as shown in fig. 4, it can be seen that l(s) does not include a right half-plane pole, and thus the first condition for system stability is satisfied. Next, as can be seen from fig. 3, the system characteristic curve encloses the point (-1/3,0), but does not enclose the point (-1/2,0), which indicates that the system remains stable when k is 2 under the current parameters. Furthermore, the maximum number of the fans which can be connected in parallel in the system is 2, namely if the number of the fans exceeds 2, the system is unstable, and if the number of the fans is less than or equal to 2, the system can keep stable operation.

Claims (8)

1. A distributed stability analysis method for a multi-fan grid-connected system is characterized by comprising the following steps:
the method comprises the following steps: acquiring main parameters of the permanent magnet synchronous fan, and establishing a permanent magnet synchronous generator, a machine side converter and a controller thereof, a direct current capacitor, a grid side converter and a control thereofAnd (3) a mathematical model of the device and the filter, wherein the model is equivalently converted into a dq coordinate system by using Park transformation. Linearizing the model at a steady-state operation point, and calculating a steady-state operation parameter to obtain an admittance model Y of a dq coordinate system of the permanent magnet synchronous fanPMSG。
Step two: obtaining the equivalent impedance of the grid-connected point network and equivalently converting the equivalent impedance into a dq coordinate system to obtain a network impedance equivalent model Z of the dq coordinate systemg。
Step three: admittance model Y according to dq coordinate system of permanent magnet synchronous fanPMSGAnd network impedance equivalent model ZgObtaining a system return matrix of L(s) ═ ZgYPMSGLet its characteristic function be λ1(s)、λ2(s) plotting λ in the complex plane as s moves along the standard Nyquist contour in the complex plane1(s)、λ2(s) a trajectory.
Step four: analyzing the stability of the system: sufficient requirements for system stability may be: l(s) does not contain a right half-plane pole; l(s) does not encompass at least the (-1,0) point.
2. The method of claim 1, wherein in the first step, the equivalent admittance Y is obtained according to the PMSM and machine side converter modelM。YMForm a DC equivalent admittance Y together with a DC capacitordcAnd then combining a mathematical model of a network side converter and a filter to obtain a final dq coordinate system admittance model Y of the permanent magnet synchronous fanPMSG. The machine side converter is a two-level voltage source type converter, converts alternating current output by the permanent magnet synchronous generator into direct current and controls torque of the direct current. Obtaining the equivalent admittance Y of the permanent magnet synchronous generator and the machine side converterMThe process of (2) is as follows:
the frequency domain mathematical model of the permanent magnet synchronous generator and the machine side converter is as follows:
Figure FDA0002938348970000011
in the formula, Rs、LsRotor resistance and armature inductance, omega, of a permanent magnet synchronous generatoreAs the electrical angular velocity of the rotor, idr、iqrStator currents, psi, of dq coordinate system, respectivelyfIs a permanent magnet flux linkage, ddr、dqrRespectively, the output duty ratio u of the converter controller under the dq coordinate systemdcIs a direct current voltage, and s is a complex parameter introduced by Laplace transform. Linearizing the model to obtain a small signal model of
Figure FDA0002938348970000012
Wherein,
Figure FDA0002938348970000013
capital letters and superscripts indicate steady-state components for corresponding lower case variables, and Δ indicates small signal components for corresponding variables.
The controller model of the machine side converter is
Figure FDA0002938348970000021
Wherein,
Figure FDA0002938348970000022
Kcpr、Kcirproportional and integral parameters, I, of the machine side current loop PI controller, respectivelydrref、IqrrefD-axis and q-axis current reference values, respectively. Linearizing it to obtain a small signal model of the machine side converter controller as
Figure FDA0002938348970000023
Wherein,
Figure FDA0002938348970000024
the permanent magnet synchronous generator and machine side converter model can use the equivalent admittance YMIs shown, i.e.
Figure FDA0002938348970000025
Wherein, Δ idc2Is the small signal component of the machine side direct current, I is the identity matrix,
Figure FDA0002938348970000026
3. the method of claim 2, wherein obtaining the dc equivalent admittance YdcThe process is as follows:
the DC capacitance model is expressed as
sCdcudc＝idc2-idc1
Wherein, CdcIs a DC capacitor, idc1Is the grid side direct current. Linearizing the signal to obtain a DC capacitance small signal model of
sCdcΔudc＝Δidc2-Δidc1＝-ΔudcYM-Δidc1
The impedance characteristic of the DC bus is influenced by the PMSM, the machine side converter and the DC capacitor, so that the three models can be combined and expressed by an equivalent admittance, namely a DC equivalent admittance YdcThe expression is
Figure FDA0002938348970000027
4. The method of claim 2, wherein a mathematical model of the grid-side converter and the filter is combined to obtain a final permanent magnet synchronous fan dq coordinate system admittance model YPMSGThe process is as follows:
the grid-side converter is also a two-level voltage source type converter, is externally connected with a single inductance filter, inverts direct current into power frequency alternating current and then is connected into a power grid. The established mathematical model is specifically as follows:
Figure FDA0002938348970000028
wherein L isfFor filter inductance, ω is power frequency angular frequency, ω ═ 100 π rad/s, idg、iqgD, q-axis currents at AC port of grid-side converterdg、dqgFor the output duty ratio u of the grid side converter controller under dq coordinate systemdg、uqgThe voltage of the grid connection point d and the q axis are respectively. Linearizing the model to obtain a small signal model of the grid-side converter and the filter
Figure FDA0002938348970000031
Wherein,
Figure FDA0002938348970000032
the network side converter controller model is
Figure FDA0002938348970000033
Wherein,
Figure FDA0002938348970000034
Kcigrespectively are a proportional parameter and an integral parameter of a network side current loop PI controller,
Figure FDA0002938348970000035
Kviproportional and integral parameters, U, of the network side voltage loop PI controller, respectivelydcrefIs a DC voltage referenceAnd (4) taking the value into consideration. In the grid-side converter controller, a phase-locked loop is adopted to keep the fan and the power grid synchronous. The superscript c denotes the grid-side converter controller dq coordinate system. The model is linearized to obtain a small signal model of the grid-side converter controller
Figure FDA0002938348970000036
Wherein,
Figure FDA0002938348970000037
in addition, the dynamic of the phase-locked loop should be considered in the network side converter, and the model is
Figure FDA0002938348970000038
Wherein,
Figure FDA0002938348970000039
Kppll、Kipllrespectively, a proportional parameter and an integral parameter of the phase-locked loop PI controller. Linearizing it to obtain
Figure FDA00029383489700000310
Wherein, there is certain deviation between the system dq coordinate system and the controller dq coordinate system, and the two can be converted into each other by the following equation
Figure FDA00029383489700000311
In the formula, the variable Δ xd、ΔxqCan represent the output current delta i of the grid-side converterdg、ΔiqgGrid connection point voltage delta udg、ΔuqgOr net side controller output dutyRatio deltaddg、Δdqg，
Figure FDA00029383489700000312
Representing the steady state component of the corresponding variable.
From this, a phase-locked loop small-signal model can be derived, i.e.
Δθ＝Gpll·Δuqg
Wherein,
Figure FDA0002938348970000041
it can thus be derived that the relationship between the controller dq coordinate system and the system dq coordinate system is
Figure FDA0002938348970000042
Wherein,
Figure FDA0002938348970000043
finally, the permanent magnet synchronous fan can be represented by an equivalent admittance, i.e.
Δidqg＝YPMSG·Δudqg
YPMSGIs an admittance model of a dq coordinate system of the permanent magnet synchronous fan, and the expression is
Figure FDA0002938348970000044
Wherein,
Figure FDA0002938348970000045
Figure FDA0002938348970000046
and I is an identity matrix.
5. The method of claim 1, wherein the equivalent impedance model of the network in step two is
Figure FDA0002938348970000047
Wherein s is a complex parameter introduced by Laplace transform, ω is power frequency angular frequency, ω is 100 π rad/s, LgIs the network equivalent inductance.
6. The method of claim 1, wherein the system contrast matrix in step three is L ═ ZgYPMSGL is a 2X 2 matrix, let us assume
Figure FDA0002938348970000048
Its characteristic function lambda1(s)、λ2(s) can be obtained by the following equation.
Figure FDA0002938348970000049
7. The method according to claim 1, wherein in step four, if the characteristic locus of l(s) does not enclose a point (-1/k,0), and k (k ═ 1,2, 3.) is the number of fans connected in parallel in the system, then the maximum number of fans connected in parallel in the system is k.
8. The method of claim 7, wherein the acquisition of the (-1/k,0) point is performed by: and if the number of the fans connected in parallel in the system is k (k is 1,2 and 3.), a circle is drawn by taking the origin of the complex plane as the center of the circle and 1/k as the radius, and the intersection point of the complex plane and the negative solid axis is (-1/k, 0).
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