WO2022226709A1 - 考虑功率控制的永磁同步风机接入弱电网稳定性分析方法 - Google Patents

考虑功率控制的永磁同步风机接入弱电网稳定性分析方法 Download PDF

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WO2022226709A1
WO2022226709A1 PCT/CN2021/089735 CN2021089735W WO2022226709A1 WO 2022226709 A1 WO2022226709 A1 WO 2022226709A1 CN 2021089735 W CN2021089735 W CN 2021089735W WO 2022226709 A1 WO2022226709 A1 WO 2022226709A1
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grid
side converter
generator
machine
power
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PCT/CN2021/089735
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English (en)
French (fr)
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于淼
刘佳宁
陆玲霞
韦巍
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浙江大学
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Priority to PCT/CN2021/089735 priority Critical patent/WO2022226709A1/zh
Priority to US17/556,839 priority patent/US11988696B2/en
Publication of WO2022226709A1 publication Critical patent/WO2022226709A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G01R19/25—Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
    • G01R19/2513—Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging
    • 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
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • H02J3/0012—Contingency detection
    • 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
    • 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
    • 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
    • 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

Definitions

  • the invention relates to a stability analysis method for a permanent magnet synchronous fan connected to a weak grid considering the influence of power control, and belongs to the field of stability analysis of a new energy power generation system in a power system.
  • Permanent magnet synchronous wind turbine (PMSG) has the advantages of high energy conversion efficiency, good operation reliability and strong controllability, and the proportion of installed capacity continues to increase.
  • PMSG Permanent magnet synchronous wind turbine
  • a suitable maximum power tracking algorithm must be adopted, among which the disturbance observation method does not need to measure the wind speed and has good practical value.
  • the perturbation observation method contains nonlinear discontinuous links, which makes the traditional small-signal stability analysis methods difficult to apply.
  • Conventional stability analysis methods generally ignore the power control loop based on the perturbation observation method.
  • the description function method can well complete the modeling of nonlinear elements and the stability analysis of the system.
  • the present invention proposes a stability analysis method for a permanent magnet synchronous fan connected to a weak grid considering the influence of power control, which fully considers the nonlinear links in the power loop and improves the accuracy of stability analysis.
  • the invention aims to propose a stability analysis method for a permanent magnet synchronous wind turbine connected to a weak power grid considering the influence of power control.
  • the permanent magnet synchronous fan includes a wind turbine, a generator, a machine-side converter, a DC capacitor, a grid-side converter, a filter, a machine-side converter controller and a grid-side converter controller.
  • the generator-side converter controller includes a power loop, a speed loop, and a generator-side current loop;
  • the grid-side converter controller includes a voltage loop and a grid-side current loop.
  • the present invention adopts following technical scheme:
  • Step 1 Obtain the main parameters of the permanent magnet synchronous fan, and establish the wind turbine, generator and machine-side converter, machine-side converter controller, DC capacitor, grid-side converter and filter, and grid-side converter respectively.
  • the mathematical model of the wind turbine controller is linearized in the dq coordinate system, and the steady-state operating parameters are calculated to obtain the wind turbine, generator and machine-side converter, machine-side converter controller, DC capacitor, grid-side converter. Small-signal models of converters and filters, grid-side converter controllers.
  • Step 2 Based on the description function method, the power loop in the machine-side converter controller is modeled, and its mathematical expression is
  • ⁇ is the power loop disturbance step size
  • T p is the power loop control period
  • P ref is the reference value of the output power of the permanent magnet synchronous fan
  • P is the output power of the permanent magnet synchronous fan
  • P n is the permanent magnet synchronous fan at the current sampling time n.
  • P n-1 is the output power of the permanent magnet synchronous fan at the last sampling time
  • ⁇ g is the generator speed
  • ⁇ g,n is the generator speed at the current sampling time
  • ⁇ g,n-1 is the generator speed at the previous sampling time.
  • the symbolic function in the formula can be modeled by the description function, and the description function is
  • A represents the amplitude of the input signal
  • Step 3 Considering the influence of the AC weak grid, the linear part of the weak grid and the small-signal model of the power ring mode are combined with the small-signal model of the permanent magnet synchronous fan established in step 1, and the transfer function G(s) of the linear part of the system is deduced.
  • Step 4 Draw G(s) and -1/N(A) curves in the complex plane, and analyze the stability of the system based on the description function method.
  • the specific method is that if G(s) contains the right half-plane pole, the system must not Stable; if G(s) does not contain the right half-plane pole, the system stability is judged by the relationship between the G(s) trajectory and the -1/N(A) trajectory:
  • G(j ⁇ ) G Re ( ⁇ )+jG Im ( ⁇ )
  • G Re represents the complex real part
  • G Im represents the complex imaginary part
  • ⁇ 0 is the oscillation angular frequency
  • a 0 is the oscillation amplitude ;
  • step 1 the small-signal models of the wind turbine, the generator, the machine-side converter, and the machine-side converter controller are established as follows:
  • J is the moment of inertia of the equivalent lumped mass block of the wind turbine and the generator
  • T m is the mechanical torque of the generator
  • T e is the electromagnetic torque of the generator
  • s is the parameter introduced by the Laplace change.
  • the electromagnetic torque of the generator is the electromagnetic torque of the generator.
  • n p is the number of pole pairs of the generator
  • i qr is the stator current of the q-axis generator
  • ⁇ f is the permanent magnet flux linkage of the generator.
  • the mechanical torque of the generator is the mechanical torque of the generator.
  • K cpr and K cir are the proportional and integral parameters of the PI control of the machine-side current loop, respectively.
  • K ⁇ p and K ⁇ i are the proportional and integral parameters of the speed loop PI control, respectively.
  • the superscript c represents the dq coordinate system of the machine-side converter controller. It is the reference value of generator speed. Linearizing it, the small-signal model of the machine-side converter controller can be obtained as
  • step 1 the process of establishing the small signal model is as follows:
  • C dc is the DC capacitor
  • i dc1 is the grid-side DC current
  • i dc2 is the machine-side DC current
  • i dg is the grid-side converter AC port d
  • q-axis currents d dg
  • d qg is the output duty ratio of the grid-side converter controller in the dq coordinate system.
  • u dc is the DC voltage
  • i dr , i qr are the generator stator currents in the d and q coordinate systems, respectively
  • d dr , d qr are the output duty ratios of the controller of the machine-side converter in the dq coordinate system, which are linearized , the small-signal model of the DC capacitance can be obtained as
  • step 1 the process of establishing the small-signal model of the grid-side converter and the grid-side converter controller is as follows:
  • L f is the filter inductance
  • ⁇ is the power frequency angular frequency
  • ⁇ 100 ⁇ rad/s
  • i dg and i qg are the d and q-axis currents of the AC ports of the grid-side converter, respectively
  • d dg and d qg are the dq coordinates
  • u dc is the DC voltage
  • u dg and u qg are the d and q-axis voltages of the grid-connected points, respectively.
  • K cpg and K cig are the proportional and integral parameters of the grid-side current loop PI control, respectively.
  • K vp and K v9 are the proportional parameter and integral parameter of the grid-side voltage loop PI control, respectively, and U dcref is the DC voltage reference value.
  • a phase-locked loop is used to keep the wind turbine synchronized with the grid.
  • the superscript c represents the grid-side converter controller dq coordinate system. Linearizing the model, the small-signal model of the grid-side converter controller can be obtained as
  • phase-locked loop dynamics should also be considered in the grid-side converter, and its mathematical model is
  • K ppll and K ipll are the proportional and integral parameters of the phase-locked loop PI controller, respectively, is the q-axis voltage of the grid-connected point in the dq coordinate system of the grid-side converter controller. Linearizing it, we get
  • variables ⁇ x d and ⁇ x q can represent grid-side converter output currents ⁇ i dg , ⁇ i qg , grid-connected point voltages ⁇ u dg , ⁇ u qg or grid-side controller output duty ratios ⁇ d dg , ⁇ d qg , represents the steady-state component of the corresponding variable
  • the small-signal model of the phase-locked loop can be derived, that is,
  • step 3 is specifically:
  • the AC weak grid is represented by the series equivalent inductance of an ideal voltage source, and its mathematical model is established as
  • L g is the equivalent inductance of the weak grid
  • u ds and u qs are the ideal voltage source voltages of the d and q axes, respectively
  • idg and i qg are the d and q axis currents of the AC ports of the grid-side converter, respectively.
  • the output power of the permanent magnet synchronous fan is
  • T f represents the power sampling filter period
  • 1/(1+T f s) is the power sampling filter delay
  • 1/(1+1.5T ps ) is the controller and PWM delay.
  • the present invention applies the description function method to the stability analysis of the grid-connected system of the permanent magnet synchronous fan, fully considers the nonlinear links in the power loop based on the disturbance observation method, and overcomes the inability of the traditional small signal analysis method to apply to discontinuous , the problem of nonlinear links.
  • the description function method can quantitatively calculate the oscillation frequency and amplitude, which provides an important basis for oscillation prevention and suppression.
  • Figure 1 shows the topological structure of permanent magnet synchronous fan (A) and its controller structure (B and D are coordinate transformation, C is phase-locked loop, E is machine-side converter controller, and F is grid-side converter controller )
  • FIG. 2 shows the distribution of G(s) poles
  • Fig. 3 is the curve of G(s) and -1/N(A) when the value of L g is changed
  • FIG. 1 The topological structure of the permanent magnet synchronous fan according to the present invention and its controller are shown in FIG. 1 , including a wind turbine, a generator, a machine-side converter, a DC capacitor, a grid-side converter, and a filter.
  • the wind turbine captures wind energy and converts it into mechanical energy.
  • Both the machine-side converter and the grid-side converter are two-level voltage source converters.
  • the machine-side converter converts the alternating current output from the permanent magnet synchronous generator into direct current.
  • the grid-side converter inverts the DC power into a power-frequency AC power and connects it to the grid.
  • the generator-side converter controller includes power loop (P&O), speed loop (H ⁇ ), and generator-side current loop (H cr );
  • the grid-side converter controller includes voltage loop (H v ) and grid side current loop (H cg ).
  • PLL phase-locked loop
  • abc/dq and dq/abc coordinate transformation link
  • the main parameters of the permanent magnet synchronous fan are obtained as shown in Table 1, and the wind turbine, the generator and the machine-side converter, the machine-side converter controller, and the DC capacitor are respectively established.
  • s is the parameter introduced by the Laplace change
  • J is the moment of inertia of the equivalent lumped mass block of the wind turbine and generator
  • ⁇ g is the rotational speed of the generator
  • T m is the mechanical torque of the generator
  • T e is the electromagnetic field of the generator.
  • n p is the number of pole pairs of the generator
  • ⁇ f is the permanent magnet flux linkage of the generator
  • B t is the linearization constant of the mechanical torque of the wind turbine.
  • R s and L s are the generator rotor resistance and armature inductance respectively
  • ⁇ e is the rotor electrical angular velocity
  • ⁇ e n p ⁇ g .
  • i dr , i qr are the generator stator currents in the dq coordinate system
  • d dr , d qr are the output duty ratios of the machine-side converter controller in the dq coordinate system
  • u dc is the DC voltage.
  • K cpr and K cir are the proportional and integral parameters of the PI control of the machine-side current loop, respectively.
  • K ⁇ p and K ⁇ i are the proportional and integral parameters of the speed loop PI control, respectively. is the reference value of the generator speed, is the steady-state value of the rotor electrical angular velocity, and the superscript c represents the dq coordinate system of the converter controller.
  • C dc is the DC capacitance
  • i dg and i qg are the d and q-axis currents of the AC ports of the grid-side converter, respectively
  • d dg and d qg are the output duty ratios of the grid-side converter controller in the dq coordinate system.
  • L f is the filter inductance
  • ⁇ is the power frequency angular frequency
  • ⁇ 100 ⁇ rad/s
  • i dg , i qg are the d and q-axis currents of the AC port of the grid-side converter, respectively
  • d dg , d qg are the dq coordinate system off-grid
  • the output duty ratio of the side converter controller, u dg and u qg are the d and q-axis voltages of the grid-connected points, respectively.
  • K cpg and K cig are the proportional and integral parameters of the grid-side current loop PI control, respectively.
  • K vp and K vi are the proportional parameters and integral parameters of the grid-side voltage loop PI control, respectively.
  • K ppll and K ipll are the proportional parameter and integral parameter of the phase-locked loop PI controller, respectively.
  • the second step is to model the power loop in the controller of the machine-side converter based on the description function method.
  • the mathematical model is
  • the symbolic function in the formula can be modeled by the description function, and the description function is
  • the third step is to consider the influence of AC weak grid, the weak grid model is
  • the fourth step is to analyze the system stability.
  • G(s) and -1/N(A) intersect, indicating that the system is in a critically stable state at this time.
  • the DC component is 0.6889MW, the corresponding oscillation frequency is 19.5Hz, and the amplitude is 58kW, which is basically consistent with the theoretical analysis results;
  • the DC component is 0.6889MW, the corresponding oscillation frequency is 19.5Hz, and the amplitude is 53kW , which is basically consistent with the theoretical analysis results.
  • the simulation results verify the validity and accuracy of the analysis method.

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Abstract

本发明涉及一种考虑功率控制影响的永磁同步风机接入弱电网稳定性分析方法。新能源发电多采用扰动观察法进行最大功率跟踪，其中的非线性不连续环节导致稳定性分析困难。本发明基于描述函数法分析了永磁同步风机接入弱电网系统的稳定性，充分考虑了功率环中的非线性不连续环节，使分析结果更加精确。同时，描述函数法是一种可以量化地计算振荡功率和幅值的方法，本发明的分析方法能够为振荡抑制及控制器设计提供良好参照。

Description

考虑功率控制的永磁同步风机接入弱电网稳定性分析方法 技术领域
本发明涉及一种考虑功率控制影响的永磁同步风机接入弱电网稳定性分析方法，属于电力系统中新能源发电系统稳定性分析领域。
背景技术
可再生能源发电占比不断提升，风力发电装机容量持续增长，风机并网系统的稳定运行成为重要问题。永磁同步风电机组(PMSG)具有能量转换效率高、运行可靠性好、可控性强的优势，装机占比持续提高。为了更好地利用风能，必须采用合适的最大功率跟踪算法，其中扰动观察法无需测量风速，具有较好的实用价值。然而，扰动观察法隐含非线性不连续环节，导致传统的小信号稳定性分析方法难以适用，常规的稳定性分析方法一般忽视基于扰动观察法的功率控制环。描述函数法可以很好地完成非线性环节建模和系统的稳定性分析，其基本思想是，当系统满足一定假设条件时，在正弦输入作用下，系统非线性环节的输出可用一次谐波分量来近似表示，从而获得非线性环节的近似等效频率特性。因此，本发明基于描述函数法提出一种考虑功率控制影响的永磁同步风机接入弱电网稳定性分析方法，充分考虑功率环中的非线性环节，提高稳定性分析的精确性。
发明内容
本发明旨在提出一种考虑功率控制影响的永磁同步风机接入弱电网稳定性分析方法。所述永磁同步风机包括风力机、发电机、机侧变流器、直流电容、网侧变流器、滤波器、机侧变流器控制器和网侧变流器控制器。机侧变流器控制器中，包含功率环，转速环，机侧电流环；网侧变流器控制器中，包含电压环和网侧电流环。
本发明采用如下技术方案：
步骤一：获取永磁同步风机的主要参数，分别建立风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器的数学模型，并在dq坐标系下进行线性化，计算稳态运行参数，得到风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器的小信号模型。
步骤二：基于描述函数法，对机侧变流器控制器中的功率环进行建模，其数学表达式为
Figure PCTCN2021089735-appb-000001
其中，ε为功率环扰动步长，T p为功率环控制周期，P ref为永磁同步风机输出功率参考值， P表示永磁同步风机输出功率，P n为当前采样时刻n的永磁同步风机输出功率，P n-1为上一采样时刻永磁同步风机输出功率，ω g表示发电机转速，
Figure PCTCN2021089735-appb-000002
表示发电机转速的参考值，ω g,n为当前采样时刻发电机转速，ω g,n-1为上一采样时刻发电机转速。sgn(x)为符号函数，当x≥0时，sgn(x)＝1，当x<0时，sgn(x)＝-1。考虑实际永磁同步风机的功率-转速曲线，可以认为
Figure PCTCN2021089735-appb-000003
其中，ω mpp表示最大功率点处的发电机转速。进而功率环模型可简化为
Figure PCTCN2021089735-appb-000004
式中的符号函数可以采用描述函数进行建模，其描述函数为
Figure PCTCN2021089735-appb-000005
式中A表示输入信号的幅值。
步骤三：考虑交流弱电网影响，将弱电网、功率环模小信号模型的线性部分与步骤一中建立的永磁同步风机小信号模型联立，推导系统线性部分的传递函数G(s)。
步骤四：在复平面中绘制G(s)与-1/N(A)曲线，基于描述函数法分析系统稳定性，具体方法为，若G(s)包含右半平面极点，则系统必不稳定；若G(s)不包含右半平面极点，则通过G(s)轨迹与-1/N(A)轨迹的关系判断系统稳定性：
a、若G(s)曲线不包围-1/N(A)曲线，则系统是稳定的，不发生振荡；
b、若G(s)曲线与-1/N(A)曲线相交，则系统是临界稳定的，此时系统发生恒幅恒频振荡，可以通过下式计算振荡的频率和幅值
Figure PCTCN2021089735-appb-000006
其中，G(jω)＝G Re(ω)+jG Im(ω)，G Re表示求取复数实部，G Im表示求取复数虚部，ω 0为振荡角频率，A 0为振荡幅值；
c、若G(s)曲线包围-1/N(A)曲线，则系统是不稳定的。
进一步地，步骤一中，风力机、发电机及机侧变流器、机侧变流器控制器的小信号模型建立如下：
建立风力机的数学模型为
sJω g＝T m-T e-Bω g
式中，J为风力机和发电机的等效集中质量块转动惯量，T m为发电机机械转矩，T e为发电机电磁转矩，B为自阻尼系数，此处认为B＝0，s为拉普拉斯变化引入的参变量。对该模型进行线性化可得
sJΔω g＝ΔT m-ΔT e
发电机的电磁转矩为
Figure PCTCN2021089735-appb-000007
n p为发电机极对数，i qr为q轴发电机定子电流，ψ f为发电机永磁体磁链。对该式进行线性化可得
Figure PCTCN2021089735-appb-000008
发电机的机械转矩为
T m＝B tω g
式中，
Figure PCTCN2021089735-appb-000009
为风力机机械转矩线性化常数，ω g *为发电机转速稳态值，在平衡点处为特定常数。对该式线性化可得
ΔT m＝B tΔω g
由此可得风力机小信号模型，
Figure PCTCN2021089735-appb-000010
令
Figure PCTCN2021089735-appb-000011
则Δω g＝G iqω·Δi dqr，Δω e＝n pG iqω·Δi dqr。
发电机及机侧变流器的数学模型为
Figure PCTCN2021089735-appb-000012
式中，R s、L s分别为发电机转子电阻和电枢电感，ω e为转子电角速度，ω e＝n pω g。i dr、i qr为dq坐标系下发电机定子电流，d dr、d qr为dq坐标系下机侧变流器控制器输出占空比，u dc为直流电压。对该模型进行线性化，可得发电机及机侧变流器的小信号模型为
Figure PCTCN2021089735-appb-000013
其中，
Figure PCTCN2021089735-appb-000014
Figure PCTCN2021089735-appb-000015
大写字母及上标*表示对应小写变量的稳态分量，Δ表示对应变量的小信 号分量。
建立机侧变流器控制器的数学模型为
Figure PCTCN2021089735-appb-000016
其中，
Figure PCTCN2021089735-appb-000017
K cpr、K cir分别为机侧电流环PI控制的比例参数和积分参数，
Figure PCTCN2021089735-appb-000018
K ωp、K ωi分别为转速环PI控制的比例参数和积分参数。上标c表示机侧变流器控制器dq坐标系。
Figure PCTCN2021089735-appb-000019
为发电机转速的参考值。对其进行线性化，可得机侧变流器控制器的小信号模型为
Figure PCTCN2021089735-appb-000020
其中，
Figure PCTCN2021089735-appb-000021
Figure PCTCN2021089735-appb-000022
为转子电角速度稳态值。受转速扰动影响，动态过程中机侧变流器控制器的dq坐标系将与发电机dq坐标系存在相角差。发电机电角度为
θ e＝n pω g/s
对其进行线性化，可得
Figure PCTCN2021089735-appb-000023
式中，
Figure PCTCN2021089735-appb-000024
由此，机侧变流器控制器dq坐标系与发电机dq坐标系之间变量的转换关系为
Figure PCTCN2021089735-appb-000025
其中，
Figure PCTCN2021089735-appb-000026
则机侧变流器控制器的小信号模型为
Figure PCTCN2021089735-appb-000027
进一步地，步骤一中，小信号模型建立过程如下：
建立直流电容的数学模型为
sC dcu dc＝i dc2-i dc1＝1.5(d dri dr+d qri qr)-1.5(d dgi dg+d qgi qg)
式中，C dc为直流电容，i dc1为网侧直流电流，i dc2为机侧直流电流，i dg、i qg分别为网侧 变流器交流端口d、q轴电流，d dg、d qg为dq坐标系下网侧变流器控制器输出占空比。u dc为直流电压，i dr、i qr分别为d、q坐标系发电机定子电流，d dr、d qr为dq坐标系下机侧变流器控制器输出占空比，对其进行线性化，可得直流电容小信号模型为
Figure PCTCN2021089735-appb-000028
式中，
Figure PCTCN2021089735-appb-000029
大写字母及上标*表示对应小写变量的稳态分量，Δ表示对应变量的小信号分量。
进一步地，步骤一中，所述网侧变流器、网侧变流器控制器的小信号模型建立过程如下：
建立网侧变流器及滤波器的数学模型为
Figure PCTCN2021089735-appb-000030
式中，L f为滤波电感，ω为工频角频率，ω＝100πrad/s，i dg、i qg分别为网侧变流器交流端口d、q轴电流，d dg、d qg为dq坐标系下网侧变流器控制器输出占空比，u dc为直流电压，u dg、u qg分别为并网点d、q轴电压。对该模型进行线性化，可得网侧变流器及滤波器的小信号模型为
Figure PCTCN2021089735-appb-000031
其中，
Figure PCTCN2021089735-appb-000032
大写字母及上标*表示对应小写变量的稳态分量，Δ表示对应变量的小信号分量。
建立网侧变流器控制器的数学模型为
Figure PCTCN2021089735-appb-000033
其中，
Figure PCTCN2021089735-appb-000034
K cpg、K cig分别为网侧电流环PI控制的比例参数和积分参数，
Figure PCTCN2021089735-appb-000035
K vp、K v9分别为网侧电压环PI控制的比例参数和积分参数，U dcref为直流电压参考值。在网侧变流器控制器中，采用锁相环使风机与电网保持同步。上标c表示网侧变流器控制器dq坐标系。对该模型进行线性化，可得网侧变流器控制器的小信号模型为
Figure PCTCN2021089735-appb-000036
其中，
Figure PCTCN2021089735-appb-000037
此外，网侧变流器中还应考虑锁相环动态，其数学模型为
Figure PCTCN2021089735-appb-000038
其中，
Figure PCTCN2021089735-appb-000039
K ppll、K ipll分别为锁相环PI控制器的比例参数和积分参数，
Figure PCTCN2021089735-appb-000040
为网侧变流器控制器dq坐标系下的并网点q轴电压。对其进行线性化，可得
Figure PCTCN2021089735-appb-000041
其中，系统dq坐标系与控制器dq坐标系存在一定偏差，二者之间可以通过如下方程相互转换
Figure PCTCN2021089735-appb-000042
式中变量Δx d、Δx q可以表示网侧变流器输出电流Δi dg、Δi qg、并网点电压Δu dg、Δu qg或网侧控制器输出占空比Δd dg、Δd qg，
Figure PCTCN2021089735-appb-000043
表示对应变量的稳态分量
Figure PCTCN2021089735-appb-000044
Figure PCTCN2021089735-appb-000045
由此可推导出锁相环小信号模型，即
Δθ＝G pll·Δu qg
其中，
Figure PCTCN2021089735-appb-000046
从而可以得出控制器dq坐标系与系统dq坐标系之间的关系为
Figure PCTCN2021089735-appb-000047
其中，
Figure PCTCN2021089735-appb-000048
则网侧变流器控制器的小信号模型转变为
Figure PCTCN2021089735-appb-000049
进一步地，步骤三具体为：
交流弱电网采用理想电压源串联等效电感表示，建立其数学模型为
Figure PCTCN2021089735-appb-000050
式中，L g为弱电网等效电感，u ds、u qs分别为d、q轴理想电压源电压，i dg、i qg分别为 网侧变流器交流端口d、q轴电流。将该式线性化，可得
Z g·Δi dqg＝Δu dqg
式中，
Figure PCTCN2021089735-appb-000051
永磁同步风机的输出功率为
P＝1.5(i dgu dg+i qgu qg)
将该式线性化可得
Figure PCTCN2021089735-appb-000052
式中，
Figure PCTCN2021089735-appb-000053
结合前述永磁同步风机并网系统各部分模型的线型部分，可得系统线性部分传递函数G(s)为
Figure PCTCN2021089735-appb-000054
Figure PCTCN2021089735-appb-000055
Figure PCTCN2021089735-appb-000056
Figure PCTCN2021089735-appb-000057
Figure PCTCN2021089735-appb-000058
Figure PCTCN2021089735-appb-000059
Figure PCTCN2021089735-appb-000060
Figure PCTCN2021089735-appb-000061
Figure PCTCN2021089735-appb-000062
式中，T f表示功率采样滤波器周期，1/(1+T fs)为功率采样滤波器延时，1/(1+1.5T ps)为控制器及PWM延时。
与现有技术相比，本发明的优点在于：
(1)本发明将描述函数法应用于永磁同步风机并网系统稳定性分析中，充分考虑基于扰动观察法的功率环中的非线性环节，克服了传统小信号分析法无法适用于不连续、非线性环节的问题。
(2)当系统处于临界稳定状态时，发生恒幅恒频振荡。描述函数法可以量化地计算振荡 频率和幅值，为振荡预防和抑制提供了重要依据。
附图说明
图1为永磁同步风机拓扑结构(A)及其控制器结构(B、D为坐标变换，C为锁相环，E为机侧变流器控制器，F为网侧变流器控制器)
图2为G(s)极点分布图
图3为改变L g值时G(s)与-1/N(A)曲线
图4为L g＝0.1mH时的仿真验证波形(a)与FFT频谱分析(b)
图5为L g＝0.4mH时的仿真验证波形(a)与FFT频谱分析(b)
具体实施方式
本发明所述永磁同步风机拓扑结构及其控制器如图1所示，包含风力机、发电机、机侧变流器、直流电容、网侧变流器、滤波器。风力机捕捉风能并转化为机械能，机侧变流器和网侧变流器均为两电平电压源型变换器，其中，机侧变流器将永磁同步发电机输出的交流电转换成直流电，网侧变流器将直流电逆变成工频交流电并入电网。机侧变流器和网侧变流器均采用dq坐标系下的矢量控制方法，通过dq变换将abc三相电压电流转换为d轴和q轴下的电压电流。机侧变流器控制器中，包含功率环(P&O)，转速环(H ω)，机侧电流环(H cr)；网侧变流器控制器中，包含电压环(H v)和网侧电流环(H cg)。此外，还包含锁相环(PLL)和坐标变换环节(abc/dq和dq/abc)。下面，结合具体实施例对本发明作进一步说明：
本发明的一个实施例中，系统的主要参数如表1所示。
表1 系统主要参数
Figure PCTCN2021089735-appb-000063
Figure PCTCN2021089735-appb-000064
在本发明的实施例中，第一步，获取永磁同步风机的主要参数如表1所示，分别建立风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器的数学模型，并在dq坐标系下进行线性化，计算稳态运行参数，得到风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器的小信号模型：
sJΔω g＝ΔT m-ΔT e
Figure PCTCN2021089735-appb-000065
ΔT m＝B tΔω g
Figure PCTCN2021089735-appb-000066
Figure PCTCN2021089735-appb-000067
Figure PCTCN2021089735-appb-000068
Figure PCTCN2021089735-appb-000069
Figure PCTCN2021089735-appb-000070
Figure PCTCN2021089735-appb-000071
Figure PCTCN2021089735-appb-000072
s为拉普拉斯变化引入的参变量，J为风力机和发电机的等效集中质量块转动惯量，ω g表示发电机转速，T m为发电机机械转矩，T e为发电机电磁转矩。n p为发电机极对数，ψ f为发电 机永磁体磁链，B t为风力机机械转矩线性化常数。
Figure PCTCN2021089735-appb-000073
Figure PCTCN2021089735-appb-000074
R s、L s分别为发电机转子电阻和电枢电感，ω e为转子电角速度，ω e＝n pω g。i dr、i qr为dq坐标系下发电机定子电流，d dr、d qr为dq坐标系下机侧变流器控制器输出占空比，u dc为直流电压。
Figure PCTCN2021089735-appb-000075
Figure PCTCN2021089735-appb-000076
K cpr、K cir分别为机侧电流环PI控制的比例参数和积分参数，
Figure PCTCN2021089735-appb-000077
K ωp、K ωi分别为转速环PI控制的比例参数和积分参数，
Figure PCTCN2021089735-appb-000078
为发电机转速的参考值，
Figure PCTCN2021089735-appb-000079
为转子电角速度稳态值，上标c表示变流器控制器dq坐标系。
Figure PCTCN2021089735-appb-000080
Figure PCTCN2021089735-appb-000081
Figure PCTCN2021089735-appb-000082
C dc为直流电容，i dg、i qg分别为网侧变流器交流端口d、q轴电流，d dg、d qg为dq坐标系下网侧变流器控制器输出占空比。
Figure PCTCN2021089735-appb-000083
Figure PCTCN2021089735-appb-000084
L f为滤波电感，ω为工频角频率，ω＝100πrad/s，i dg、i qg分别为网侧变流器交流端口d、q轴电流，d dg、d qg为dq坐标系下网侧变流器控制器输出占空比，u dg、u qg分别为并网点d、q轴电压。
Figure PCTCN2021089735-appb-000085
Figure PCTCN2021089735-appb-000086
K cpg、K cig分别为网侧电流环PI控制的比例参数和积分参数，
Figure PCTCN2021089735-appb-000087
Figure PCTCN2021089735-appb-000088
K vp、K vi分别为网侧电压环PI控制的比例参数和积分参数。
Figure PCTCN2021089735-appb-000089
Figure PCTCN2021089735-appb-000090
K ppll、K ipll分别为锁相环PI控制器的比例参数和积分参数。
大写字母及上标*表示对应变量的稳态分量，具体的计算方式如下。
Figure PCTCN2021089735-appb-000091
第二步，基于描述函数法，对机侧变流器控制器中的功率环进行建模，其数学模型为
Figure PCTCN2021089735-appb-000092
式中的符号函数可以采用描述函数进行建模，其描述函数为
Figure PCTCN2021089735-appb-000093
第三步，考虑交流弱电网影响，弱电网模型为
Z g·Δi dqg＝Δu dqg
式中，
Figure PCTCN2021089735-appb-000094
永磁同步风机的输出功率小信号模型为
Figure PCTCN2021089735-appb-000095
将弱电网模型、功率环模型的线性部分与步骤一中的永磁同步风机小信号模型联立，推导系统线性部分的传递函数G(s)为
Figure PCTCN2021089735-appb-000096
其中，
Figure PCTCN2021089735-appb-000097
Figure PCTCN2021089735-appb-000098
Figure PCTCN2021089735-appb-000099
Figure PCTCN2021089735-appb-000100
Figure PCTCN2021089735-appb-000101
Figure PCTCN2021089735-appb-000102
Figure PCTCN2021089735-appb-000103
Figure PCTCN2021089735-appb-000104
第四步，分析系统稳定性。首先绘G(s)极点图，如图2所示，可以看出G(s)不包含右半平面(实部大于0)极点，因此满足系统稳定的第一个条件。在复平面中绘制G(s)与-1/N(A)图像，如图3所示，G(s)与-1/N(A)相交，说明此时系统处于临界稳定状态。通过计算可知，当L g＝0.1mH时，系统的振荡频率约为129rad/s(20.5Hz)，振荡幅值约为61kW；当L g＝0.4mH时，系统的振荡频率约为131rad/s(20.9Hz)，振荡幅值约为56kW。当电网强度降低(L g增大)时，系统振荡幅值减小，说明在特定条件下，电网等效阻抗的增加有利于系统保持稳定。
图4、图5分别为L g＝0.1mH、0.4mH时系统仿真及FFT频谱分析结果。图4中，直流分量为0.6889MW，对应振荡频率为19.5Hz，幅值为58kW，与理论分析结果基本一致；图5中，直流分量为0.6889MW，对应振荡频率为19.5Hz，幅值为53kW，与理论分析结果基本一致。仿真结果验证了所述分析方法的有效性和精确性。

Claims (5)

  1. 一种考虑功率控制影响的永磁同步风机接入弱电网稳定性分析方法，其特征在于，所述永磁同步风机包括风力机、发电机、机侧变流器、直流电容、网侧变流器、滤波器、机侧变流器控制器和网侧变流器控制器；机侧变流器控制器中，包含功率环，转速环，机侧电流环；网侧变流器控制器中，包含电压环和网侧电流环；该方法包括以下步骤：
    步骤一：获取永磁同步风机的主要参数，分别建立风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器的数学模型，并在dq坐标系下进行线性化，计算稳态运行参数，得到风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器的小信号模型；
    步骤二：基于描述函数法，对机侧变流器控制器中的功率环进行建模，其数学表达式为
    Figure PCTCN2021089735-appb-100001
    其中，ε为功率环扰动步长，T p为功率环控制周期，P ref为永磁同步风机输出功率参考值，P表示永磁同步风机输出功率，P n为当前采样时刻n的永磁同步风机输出功率，P n-1为上一采样时刻永磁同步风机输出功率，ω g表示发电机转速，
    Figure PCTCN2021089735-appb-100002
    表示发电机转速的参考值，ω g,n为当前采样时刻发电机转速，ω g,n-1为上一采样时刻发电机转速；sgn(x)为符号函数，当x≥0时，sgn(x)＝1，当x<0时，sgn(x)＝-1；考虑实际永磁同步风机的功率-转速曲线，则
    Figure PCTCN2021089735-appb-100003
    其中，ω mpp表示最大功率点处的发电机转速；进而功率环模型可简化为
    Figure PCTCN2021089735-appb-100004
    式中的符号函数可以采用描述函数进行建模，其描述函数为
    Figure PCTCN2021089735-appb-100005
    式中A表示输入信号的幅值；
    步骤三：考虑交流弱电网影响，将弱电网、功率环小信号模型的线性部分与步骤一中建立的小信号模型联立，推导系统线性部分的传递函数G(s)；
    步骤四：在复平面中绘制G(s)与-1/N(A)曲线，基于描述函数法分析系统稳定性，具体 方法为，若G(s)包含右半平面极点，则系统必不稳定；若G(s)不包含右半平面极点，则通过G(s)轨迹与-1/N(A)轨迹的关系判断系统稳定性：
    a、若G(s)曲线不包围-1/N(A)曲线，则系统是稳定的，不发生振荡；
    b、若G(s)曲线与-1/N(A)曲线相交，则系统是临界稳定的，此时系统发生恒幅恒频振荡，可以通过下式计算振荡的频率和幅值
    Figure PCTCN2021089735-appb-100006
    其中，G(jω)＝G Re(ω)+jG Im(ω)，G Re表示求取复数实部，G Im表示求取复数虚部，ω 0为振荡角频率，A 0为振荡幅值；
    c、若G(s)曲线包围-1/N(A)曲线，则系统是不稳定的。
  2. 如权利要求1所述方法，其特征在于，步骤一中，风力机、发电机及机侧变流器、机侧变流器控制器的小信号模型建立如下：
    建立风力机的数学模型为
    sJω g＝T m-T m-Bω g
    式中，J为风力机和发电机的等效集中质量块转动惯量，T m为发电机机械转矩，T e为发电机电磁转矩，B为自阻尼系数，此处认为B＝0，s为拉普拉斯变化引入的参变量；对该模型进行线性化可得
    sJΔω g＝ΔT m-ΔT e
    发电机的电磁转矩为
    Figure PCTCN2021089735-appb-100007
    n p为发电机极对数，i qr为q轴发电机定子电流，ψ f为发电机永磁体磁链。对该式进行线性化可得
    Figure PCTCN2021089735-appb-100008
    发电机的机械转矩为
    T m＝B tω g
    式中，
    Figure PCTCN2021089735-appb-100009
    为风力机机械转矩线性化常数，ω g *为发电机转速稳态值，在平衡点处为特定常数；对该式线性化可得
    ΔT m＝B tΔω g
    由此可得风力机小信号模型，
    Figure PCTCN2021089735-appb-100010
    令
    Figure PCTCN2021089735-appb-100011
    则Δω g＝G iqω·Δi dqr，Δω e＝n pG iqω·Δi dqr；
    建立发电机及机侧变流器的数学模型为
    Figure PCTCN2021089735-appb-100012
    式中，R s、L s分别为发电机转子电阻和电枢电感，ω e为转子电角速度，ω e＝n pω g；对该模型进行线性化，可得发电机及机侧变流器的小信号模型为
    Figure PCTCN2021089735-appb-100013
    其中，
    Figure PCTCN2021089735-appb-100014
    Figure PCTCN2021089735-appb-100015
    大写字母及上标*表示对应小写变量的稳态分量，Δ表示对应变量的小信号分量；
    建立机侧变流器控制器的数学模型为
    Figure PCTCN2021089735-appb-100016
    其中，
    Figure PCTCN2021089735-appb-100017
    K cpr、K cir分别为机侧电流环PI控制的比例参数和积分参数，
    Figure PCTCN2021089735-appb-100018
    K ωp、K ωi分别为转速环PI控制的比例参数和积分参数。上标c表示机侧变流器控制器dq坐标系；
    Figure PCTCN2021089735-appb-100019
    为发电机转速的参考值；对其进行线性化，可得机侧变流器控制器的小信号模型为
    Figure PCTCN2021089735-appb-100020
    其中，
    Figure PCTCN2021089735-appb-100021
    Figure PCTCN2021089735-appb-100022
    为转子电角速度稳态值；受转速扰动影响，动态过程中机侧变流器控制器的dq坐标系将与发电机dq坐标系存在相角差；发电机电角度为
    θ e＝n pω g/s
    对其进行线性化，可得
    Figure PCTCN2021089735-appb-100023
    式中，
    Figure PCTCN2021089735-appb-100024
    由此，机侧变流器控制器dq坐标系与发电机dq坐标系之间变量的转换关系为
    Figure PCTCN2021089735-appb-100025
    其中，
    Figure PCTCN2021089735-appb-100026
    则机侧变流器控制器的小信号模型为
    Figure PCTCN2021089735-appb-100027
  3. 如权利要求2所述方法，其特征在于，步骤一所述直流电容的小信号模型建立过程如下：
    建立直流电容的数学模型为
    sC dcu dc＝i dc2-i dc1＝1.5(d dri dr+d qri qr)-1.5(d dgi dg+d qgi qg)
    式中，C dc为直流电容，i dc1为网侧直流电流，i dc2为机侧直流电流，对其进行线性化，可得直流电容小信号模型为
    Figure PCTCN2021089735-appb-100028
    式中，
    Figure PCTCN2021089735-appb-100029
    大写字母及上标*表示对应小写变量的稳态分量，Δ表示对应变量的小信号分量。
  4. 如权利要求3所述方法，其特征在于，步骤一所述网侧变流器及滤波器、网侧变流器控制器的小信号模型建立过程如下：
    建立网侧变流器及滤波器的数学模型为
    Figure PCTCN2021089735-appb-100030
    式中，L f为滤波电感，ω为工频角频率，ω＝100π rad/s，u dg、u qg分别为并网点d、q轴电压；对该模型进行线性化，可得网侧变流器及滤波器的小信号模型为
    Figure PCTCN2021089735-appb-100031
    其中，
    Figure PCTCN2021089735-appb-100032
    大写字母及上标*表示对应小写变量的稳态分量，Δ表示对应变量的小信号分量；
    建立网侧变流器控制器的数学模型为
    Figure PCTCN2021089735-appb-100033
    其中，
    Figure PCTCN2021089735-appb-100034
    K cpg、K cig分别为网侧电流环PI控制的比例参数和积分参数，
    Figure PCTCN2021089735-appb-100035
    K vp、K vi分别为网侧电压环PI控制的比例参数和积分参数，U dcref为直流电压参考值；在网侧变流器控制器中，采用锁相环使风机与电网保持同步；上标c表示网侧变流器控制器dq坐标系；对该模型进行线性化，可得网侧变流器控制器的小信号模型为
    Figure PCTCN2021089735-appb-100036
    其中，
    Figure PCTCN2021089735-appb-100037
    此外，网侧变流器中还应考虑锁相环动态，其数学模型为
    Figure PCTCN2021089735-appb-100038
    其中，
    Figure PCTCN2021089735-appb-100039
    K ppll、K ipll分别为锁相环PI控制器的比例参数和积分参数，
    Figure PCTCN2021089735-appb-100040
    为网侧变流器控制器dq坐标系下的并网点q轴电压；对其进行线性化，可得
    Figure PCTCN2021089735-appb-100041
    其中，系统dq坐标系与控制器dq坐标系存在一定偏差，二者之间可以通过如下方程相互转换
    Figure PCTCN2021089735-appb-100042
    式中变量Δx d、Δx q可以表示网侧变流器输出电流Δi dg、Δi qg、并网点电压Δu dg、Δu qg或网侧控制器输出占空比Δd dg、Δd qg，
    Figure PCTCN2021089735-appb-100043
    表示对应变量的稳态分量
    Figure PCTCN2021089735-appb-100044
    Figure PCTCN2021089735-appb-100045
    由此可推导出锁相环小信号模型，即
    Δθ＝G pll·Δu qg
    其中，
    Figure PCTCN2021089735-appb-100046
    从而可以得出控制器dq坐标系与系统dq坐标系之间的关系为
    Figure PCTCN2021089735-appb-100047
    其中，
    Figure PCTCN2021089735-appb-100048
    则网侧变流器控制器的小信号模型转变为
    Figure PCTCN2021089735-appb-100049
  5. 如权利要求4所述方法，其特征在于，所述步骤三具体为：
    交流弱电网采用理想电压源串联等效电感表示，建立其数学模型为
    Figure PCTCN2021089735-appb-100050
    式中，L g为弱电网等效电感，u ds、u qs分别为d、q轴理想电压源电压，i dg、i qg分别为网侧变流器交流端口d、q轴电流；将该式线性化，可得
    Z g·Δi dqg＝Δu dqg
    式中，
    Figure PCTCN2021089735-appb-100051
    永磁同步风机的输出功率为
    P＝1.5(i dgu dg+i qgu qg)
    将该式线性化可得
    Figure PCTCN2021089735-appb-100052
    式中，
    Figure PCTCN2021089735-appb-100053
    结合风力机、发电机及机侧变流器、机侧变流器控制器、直流电容、网侧变流器及滤波器、网侧变流器控制器小信号模型以及功率环线性部分，可得系统线性部分传递函数G(s)为
    Figure PCTCN2021089735-appb-100054
    Figure PCTCN2021089735-appb-100055
    Figure PCTCN2021089735-appb-100056
    Figure PCTCN2021089735-appb-100057
    Figure PCTCN2021089735-appb-100058
    Figure PCTCN2021089735-appb-100059
    Figure PCTCN2021089735-appb-100060
    Figure PCTCN2021089735-appb-100061
    Figure PCTCN2021089735-appb-100062
    式中，T f表示功率采样滤波器周期，1/(1+T fs)为功率采样滤波器延时，1/(1+1.5T ps)为控制器及PWM延时。
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