CN108347058A - The stability judging method and device of the grid-connected sub-synchronous oscillation of double-fed fan motor unit - Google Patents
The stability judging method and device of the grid-connected sub-synchronous oscillation of double-fed fan motor unit Download PDFInfo
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Abstract
本发明涉及双馈风电机组的并网次同步振荡的稳定性判断方法和装置,该方法包括:根据双馈风电机组的定子a相电压、定子a相电流以及转子a相电流,来设置双馈风电机组的定子的正序谐波电压和正序谐波电流;根据正序谐波电压和正序谐波电流来确定电流调节环节的输出电压表达式;根据正序谐波电压、正序谐波电流、以及输出电压表达式来建立双馈风电机组的定子侧阻抗解析表达式,以得到双馈风电机组侧阻抗特性;建立电网侧阻抗模型,以得到电网侧阻抗特性;建立双馈风电机组侧阻抗特性和电网侧阻抗特性的特征函数方程;以及对特征函数方程进行求解,以定量判断双馈风电机组的振荡频率和阻尼水平。根据该方法和装置能够定量判断振荡频率和阻尼水平。
The invention relates to a method and device for judging the stability of grid-connected sub-synchronous oscillation of a doubly-fed wind turbine. The positive-sequence harmonic voltage and positive-sequence harmonic current of the stator of the wind turbine; determine the output voltage expression of the current regulation link according to the positive-sequence harmonic voltage and positive-sequence harmonic current; , and the output voltage expression to establish the analytical expression of the stator side impedance of the DFIG to obtain the side impedance characteristics of the DFIG; establish the grid side impedance model to obtain the impedance characteristics of the grid side; establish the side impedance of the DFIG characteristic and the characteristic function equation of the grid side impedance characteristic; and solve the characteristic function equation to quantitatively judge the oscillation frequency and damping level of the doubly-fed wind turbine. According to the method and device, the oscillation frequency and damping level can be judged quantitatively.
Description
技术领域technical field
本发明涉及新能源电力系统次同步振荡分析领域,具体涉及一种双馈风电机组的并网次同步振荡的稳定性判断方法和装置。The invention relates to the field of subsynchronous oscillation analysis of new energy power systems, in particular to a method and device for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine.
背景技术Background technique
双馈风电机组(DFIG,Double-Fed Induction Generator)作为一种清洁能源发电技术获得了广泛应用,其并入电网后在一些特殊工况下会发生次同步功率振荡,这会严重威胁电网及风电机组的安全,这种事故在国内外屡有发生。Double-fed wind turbine (DFIG, Double-Fed Induction Generator) has been widely used as a clean energy power generation technology. After it is integrated into the grid, subsynchronous power oscillation will occur under some special conditions, which will seriously threaten the grid and wind power. The safety of the unit, such accidents have occurred frequently at home and abroad.
为了解决上述问题,研究了如下这些方法。In order to solve the above problems, the following methods have been studied.
状态空间分析法以互联系统在时域中的小信号状态空间模型为基础,分析模型的根轨迹,从而判断互联系统的稳定性。The state-space analysis method is based on the small-signal state-space model of the interconnected system in the time domain, and analyzes the root locus of the model to judge the stability of the interconnected system.
阻抗分析法是将互联系统简化成理想电压源与端口等效阻抗串联的戴维南电路模型、以及理想电流源与端口等效阻抗并联的诺顿电路模型,然后根据互联子系统之间的输出阻抗关系来进行稳定性和稳定裕度分析。这种基于阻抗的分析方法只要求互联系统端口的两端的等效阻抗特性已知,并且等效阻抗特性可经过计算或测量得到。与复杂的状态空间分析法的信息需求相比,利用阻抗分析法进行稳定性判断更简便,并且更适用于控制复杂的风电机组并网系统。The impedance analysis method is to simplify the interconnection system into the Thevenin circuit model in which the ideal voltage source is connected in series with the equivalent impedance of the port, and the Norton circuit model in which the ideal current source is connected in parallel with the equivalent impedance of the port, and then according to the output impedance relationship between the interconnection subsystems Perform stability and stability margin analysis. This impedance-based analysis method only requires that the equivalent impedance characteristics at both ends of the interconnection system port be known, and the equivalent impedance characteristics can be obtained through calculation or measurement. Compared with the information requirements of the complex state space analysis method, it is easier to use the impedance analysis method to judge the stability, and it is more suitable for controlling the complex wind turbine grid-connected system.
在三相交流互联系统等效阻抗模型的基础上利用奈奎斯特(Nyquist)判据即可对互联系统的稳定性进行判定。互联子系统可分别等效为电压源子系统和电流源子系统,从而得到各子系统的等效输出阻抗、以及电压源子系统与电流源子系统的输出阻抗之比。如果该输出阻抗比满足Nyquist判据,即输出阻抗比的Nyquist曲线轨迹不绕过复平面上的点(-1,0),则三相交流互联系统稳定;如果输出阻抗比的Nyquist曲线轨迹离点(-1,0)越远,则稳定裕度越大,越难失稳;靠近点(-1,0)的部分,离得越近,则越容易失稳,并且在三相交流互联系统耦合点容易发生谐波谐振。已有的Nyquist判据仅适用于简化系统(等效的单机无穷大系统)的稳定性分析,并且只能给出定性的结果(稳定或者不稳定),而不能给出定量的稳定性指标。On the basis of the equivalent impedance model of the three-phase AC interconnection system, the stability of the interconnection system can be judged by using the Nyquist criterion. The interconnected subsystems can be equivalent to the voltage source subsystem and the current source subsystem respectively, so as to obtain the equivalent output impedance of each subsystem and the ratio of the output impedance of the voltage source subsystem to the current source subsystem. If the output impedance ratio satisfies the Nyquist criterion, that is, the Nyquist curve trajectory of the output impedance ratio does not go around the point (-1,0) on the complex plane, then the three-phase AC interconnection system is stable; if the Nyquist curve trajectory of the output impedance ratio is away from The farther the point (-1,0) is, the greater the stability margin is, and the more difficult it is to lose stability; the closer the part is to the point (-1,0), the easier it is to lose stability, and in the three-phase AC interconnection System coupling points are prone to harmonic resonance. The existing Nyquist criterion is only suitable for the stability analysis of simplified systems (equivalent single-machine infinite systems), and can only give qualitative results (stable or unstable), but cannot give quantitative stability indicators.
发明内容Contents of the invention
有鉴于此,本发明提出了一种双馈风电机组的并网次同步振荡的稳定性判断方法和装置。In view of this, the present invention proposes a method and device for judging the stability of grid-connected sub-synchronous oscillation of a doubly-fed wind turbine.
根据本发明的一方面,提供了一种双馈风电机组的并网次同步振荡的稳定性判断方法,包括:根据所述双馈风电机组的定子a相电压、定子a相电流以及转子a相电流,来设置所述双馈风电机组的定子的正序谐波电压和正序谐波电流;根据所述正序谐波电压和所述正序谐波电流来确定电流调节环节的输出电压表达式;根据所述正序谐波电压、所述正序谐波电流、以及所述输出电压表达式来建立所述双馈风电机组的定子侧阻抗解析表达式,以得到双馈风电机组侧阻抗特性;建立电网侧阻抗模型,以得到电网侧阻抗特性;建立所述双馈风电机组侧阻抗特性和所述电网侧阻抗特性的特征函数方程;以及对所述特征函数方程进行求解,以定量判断所述双馈风电机组的振荡频率和阻尼水平。According to one aspect of the present invention, a method for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine is provided, including: according to the stator a-phase voltage, stator a-phase current and rotor a-phase of the doubly-fed wind turbine current to set the positive sequence harmonic voltage and positive sequence harmonic current of the stator of the doubly-fed wind turbine; determine the output voltage expression of the current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current ; According to the positive-sequence harmonic voltage, the positive-sequence harmonic current, and the output voltage expression, an analytical expression of the stator side impedance of the double-fed wind turbine is established to obtain the impedance characteristics of the double-fed wind turbine ; establish a grid-side impedance model to obtain the grid-side impedance characteristics; establish the characteristic function equations of the DFIG-side impedance characteristics and the grid-side impedance characteristics; and solve the characteristic function equations to quantitatively determine the Oscillation frequency and damping level of the DFIG described above.
对于上述方法,在一种可能的实现方式中,分别根据以下公式(1-1)、(1-2)和(1-3)来确定所述定子a相电压、所述定子a相电流以及所述转子a相电流,For the above method, in a possible implementation manner, the stator a-phase voltage, the stator a-phase current and The rotor phase a current,
其中,Vsa(f)表示所述定子a相电压,f表示频率,V1表示公共耦合点正序基波电压幅值,Vp表示所述正序谐波电压的电压幅值,分别表示对应分量的初始相角,f1、fp分别表示对应频率,Wherein, V sa (f) represents the phase a voltage of the stator, f represents the frequency, V represents the amplitude of the positive-sequence fundamental wave voltage at the common coupling point, and V represents the voltage amplitude of the positive-sequence harmonic voltage, represent the initial phase angles of the corresponding components respectively, f 1 and f p represent the corresponding frequencies respectively,
Isa(f)表示所述定子a相电流,I1表示公共耦合点正序基波电流幅值,Ip表示所述正序谐波电流的电流幅值,分别表示对应分量的初始相角,I sa (f) represents the stator a-phase current, I represents the magnitude of the positive-sequence fundamental wave current at the common coupling point, and Ip represents the current magnitude of the positive-sequence harmonic current, denote the initial phase angles of the corresponding components, respectively,
Ira(f)表示所述转子a相电流,Ir1、Irp分别表示对应正序基波、谐波的转子电流幅值,分别表示对应分量的初始相角,fr表示转子转动频率,fs表示转差频率。I ra (f) represents the phase a current of the rotor, I r1 and I rp represent the rotor current amplitude corresponding to the positive sequence fundamental wave and harmonic, respectively, Respectively represent the initial phase angle of the corresponding component, f r represents the rotor rotation frequency, f s represents the slip frequency.
对于上述方法,在一种可能的实现方式中,根据以下公式(1-4)来确定所述输出电压表达式,For the above method, in a possible implementation manner, the output voltage expression is determined according to the following formula (1-4),
其中,V(s)表示输出电压,s=j2πf,Hri(s)=kip+kii/s,kip和kii分别表示电流调节器的比例系数和积分系数,Krd(s)表示转子侧dq控制策略中的解耦系数,Vp(s)表示所述正序谐波电压,HPLL(s)表示包括PI调节器和积分器的锁相环的传递函数,Vr0表示转子电压稳态分量幅值,Vdc表示直流电容电压幅值。Among them, V(s) represents the output voltage, s=j2πf, H ri (s)=kip+kii/s, kip and kii represent the proportional coefficient and integral coefficient of the current regulator respectively, K rd (s) represents the rotor side dq The decoupling coefficient in the control strategy, V p (s) represents the positive sequence harmonic voltage, H PLL (s) represents the transfer function of the phase-locked loop including the PI regulator and integrator, V r0 represents the amplitude of the rotor voltage steady-state component, and V dc represents the amplitude of the DC capacitor voltage.
对于上述方法,在一种可能的实现方式中,根据以下公式(1-5)来建立所述双馈风电机组的定子侧阻抗解析表达式,For the above method, in a possible implementation manner, an analytical expression of the stator side impedance of the DFIG is established according to the following formula (1-5):
其中,Ztp(s)表示所述双馈风电机组侧阻抗特性,Lls表示定子绕组的漏感,L′lr表示转子绕组的漏感,Rs表示定子绕组的电阻,R′r表示转子绕组的电阻,σ(s)表示双馈异步感应发电机转子转差系数,表示双馈异步感应发电机的定子侧绕组与转子侧绕组的等效匝比,ω1表示基频角速度。Among them, Z tp (s) represents the side impedance characteristic of the DFIG, L ls represents the leakage inductance of the stator winding, L′ lr represents the leakage inductance of the rotor winding, R s represents the resistance of the stator winding, and R′ r represents the rotor The resistance of the winding, σ(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator, Indicates the equivalent turn ratio of the stator side winding and the rotor side winding of the doubly-fed asynchronous induction generator, and ω 1 represents the fundamental frequency angular velocity.
对于上述方法,在一种可能的实现方式中,根据以下公式(1-6)来建立所述电网侧阻抗模型,For the above method, in a possible implementation manner, the grid side impedance model is established according to the following formula (1-6):
其中,Zsp(s)表示所述电网侧阻抗特性,R表示电网中的等效电阻,L表示电网中的等效电感,C表示电网中的等效串联电容。Wherein, Z sp (s) represents the impedance characteristic of the grid side, R represents the equivalent resistance in the power grid, L represents the equivalent inductance in the power grid, and C represents the equivalent series capacitance in the power grid.
对于上述方法,在一种可能的实现方式中,根据以下公式(1-7)来建立所述双馈风电机组侧阻抗特性和所述电网侧阻抗特性的特征函数方程,For the above method, in a possible implementation manner, the characteristic function equations of the DFIG-side impedance characteristics and the grid-side impedance characteristics are established according to the following formula (1-7),
Zsp(s)+Ztp(s)=0 (1-7)。Z sp (s) + Z tp (s) = 0 (1-7).
对于上述方法,在一种可能的实现方式中,对所述特征函数方程进行求解,以定量判断所述双馈风电机组的振荡频率和阻尼水平,包括:For the above method, in a possible implementation manner, the characteristic function equation is solved to quantitatively judge the oscillation frequency and damping level of the doubly-fed wind turbine, including:
对公式(1-7)进行求解,以得到所述特征函数方程的共轭根λ1,2=α±jβ,Formula (1-7) is solved to obtain the conjugate root λ 1,2 =α±jβ of the characteristic function equation,
其中,虚部β决定所述双馈风电机组的振荡频率,实部α决定所述双馈风电机组的阻尼水平。Wherein, the imaginary part β determines the oscillation frequency of the DFIG, and the real part α determines the damping level of the DFIG.
根据本发明的另一方面,提供一种双馈风电机组的并网次同步振荡的稳定性判断装置,包括:正序谐波电压和电流设置单元,用于根据所述双馈风电机组的定子a相电压、定子a相电流以及转子a相电流,来设置所述双馈风电机组的定子的正序谐波电压和正序谐波电流;输出电压表达式确定单元,用于根据所述正序谐波电压和所述正序谐波电流来确定电流调节环节的输出电压表达式;定子侧阻抗解析表达式建立单元,用于根据所述正序谐波电压、所述正序谐波电流、以及所述输出电压表达式来建立所述双馈风电机组的定子侧阻抗解析表达式,以得到双馈风电机组侧阻抗特性;电网侧阻抗模型建立单元,用于建立电网侧阻抗模型,以得到电网侧阻抗特性;特征函数方程建立单元,用于建立所述双馈风电机组侧阻抗特性和所述电网侧阻抗特性的特征函数方程;以及振荡频率和阻尼水平判断单元,用于对所述特征函数方程进行求解,以定量判断所述双馈风电机组的振荡频率和阻尼水平。According to another aspect of the present invention, a device for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine is provided, including: a positive sequence harmonic voltage and current setting unit for A-phase voltage, stator a-phase current and rotor a-phase current are used to set the positive-sequence harmonic voltage and positive-sequence harmonic current of the stator of the doubly-fed wind turbine; the output voltage expression determination unit is used to determine the positive sequence according to the positive sequence The harmonic voltage and the positive sequence harmonic current are used to determine the output voltage expression of the current regulation link; the stator side impedance analytical expression establishment unit is used for according to the positive sequence harmonic voltage, the positive sequence harmonic current, and the output voltage expression to establish the stator side impedance analytical expression of the DFIG to obtain the DFIG side impedance characteristics; the grid side impedance model establishment unit is used to establish the grid side impedance model to obtain Grid-side impedance characteristics; a characteristic function equation establishing unit for establishing the characteristic function equations of the DFIG-side impedance characteristics and the grid-side impedance characteristics; and an oscillation frequency and damping level judging unit for determining the characteristic The function equation is solved to quantitatively judge the oscillation frequency and damping level of the doubly-fed wind turbine.
对于上述装置,在一种可能的实现方式中,所述正序谐波电压和电流设置单元分别根据以下公式(1-1)、(1-2)和(1-3)来确定所述定子a相电压、所述定子a相电流以及所述转子a相电流,For the above device, in a possible implementation, the positive sequence harmonic voltage and current setting unit determines the stator a-phase voltage, the stator a-phase current and the rotor a-phase current,
其中,Vsa(f)表示所述定子a相电压,f表示频率,V1表示公共耦合点正序基波电压幅值,Vp表示所述正序谐波电压的电压幅值,分别表示对应分量的初始相角,f1、fp分别表示对应频率,Wherein, V sa (f) represents the phase a voltage of the stator, f represents the frequency, V represents the amplitude of the positive-sequence fundamental wave voltage at the common coupling point, and V represents the voltage amplitude of the positive-sequence harmonic voltage, represent the initial phase angles of the corresponding components respectively, f 1 and f p represent the corresponding frequencies respectively,
Isa(f)表示所述定子a相电流,I1表示公共耦合点正序基波电流幅值,Ip表示所述正序谐波电流的电流幅值,分别表示对应分量的初始相角,I sa (f) represents the stator a-phase current, I represents the magnitude of the positive-sequence fundamental wave current at the common coupling point, and Ip represents the current magnitude of the positive-sequence harmonic current, denote the initial phase angles of the corresponding components, respectively,
Ira(f)表示所述转子a相电流,Ir1、Irp分别表示对应正序基波、谐波的转子电流幅值,分别表示对应分量的初始相角,fr表示转子转动频率,fs表示转差频率。I ra (f) represents the phase a current of the rotor, I r1 and I rp represent the rotor current amplitude corresponding to the positive sequence fundamental wave and harmonic, respectively, Respectively represent the initial phase angle of the corresponding component, f r represents the rotor rotation frequency, f s represents the slip frequency.
对于上述装置,在一种可能的实现方式中,所述输出电压表达式确定单元根据以下公式(1-4)来确定所述输出电压表达式,For the above device, in a possible implementation manner, the output voltage expression determining unit determines the output voltage expression according to the following formula (1-4),
其中,V(s)表示输出电压,s=j2πf,Hri(s)=kip+kii/s,kip和kii分别表示电流调节器的比例系数和积分系数,Krd(s)表示转子侧dq控制策略中的解耦系数,Vp(s)表示所述正序谐波电压,HPLL(s)表示包括PI调节器和积分器的锁相环的传递函数,Vr0表示转子电压稳态分量幅值,Vdc表示直流电容电压幅值。Among them, V(s) represents the output voltage, s=j2πf, H ri (s)=kip+kii/s, kip and kii represent the proportional coefficient and integral coefficient of the current regulator respectively, K rd (s) represents the rotor side dq The decoupling coefficient in the control strategy, V p (s) represents the positive sequence harmonic voltage, H PLL (s) represents the transfer function of the phase-locked loop including the PI regulator and integrator, V r0 represents the amplitude of the rotor voltage steady-state component, and V dc represents the amplitude of the DC capacitor voltage.
对于上述装置,在一种可能的实现方式中,所述定子侧阻抗解析表达式建立单元根据以下公式(1-5)来建立所述双馈风电机组的定子侧阻抗解析表达式,For the above device, in a possible implementation manner, the stator-side impedance analytical expression establishment unit establishes the stator-side impedance analytical expression of the doubly-fed wind turbine according to the following formula (1-5),
其中,Ztp(s)表示所述双馈风电机组侧阻抗特性,Lls表示定子绕组的漏感,L′lr表示转子绕组的漏感,Rs表示定子绕组的电阻,R′r表示转子绕组的电阻,σ(s)表示双馈异步感应发电机转子转差系数,表示双馈异步感应发电机的定子侧绕组与转子侧绕组的等效匝比,ω1表示基频角速度。Among them, Z tp (s) represents the side impedance characteristic of the DFIG, L ls represents the leakage inductance of the stator winding, L′ lr represents the leakage inductance of the rotor winding, R s represents the resistance of the stator winding, and R′ r represents the rotor The resistance of the winding, σ(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator, Indicates the equivalent turn ratio of the stator side winding and the rotor side winding of the doubly-fed asynchronous induction generator, and ω 1 represents the fundamental frequency angular velocity.
对于上述装置,在一种可能的实现方式中,所述电网侧阻抗模型建立单元根据以下公式(1-6)来建立所述电网侧阻抗模型,For the above device, in a possible implementation manner, the grid-side impedance model establishing unit establishes the grid-side impedance model according to the following formula (1-6),
其中,Zsp(s)表示所述电网侧阻抗特性,R表示电网中的等效电阻,L表示电网中的等效电感,C表示电网中的等效串联电容。Wherein, Z sp (s) represents the impedance characteristic of the grid side, R represents the equivalent resistance in the power grid, L represents the equivalent inductance in the power grid, and C represents the equivalent series capacitance in the power grid.
对于上述装置,在一种可能的实现方式中,所述特征函数方程建立单元根据以下公式(1-7)来建立所述双馈风电机组侧阻抗特性和所述电网侧阻抗特性的特征函数方程,For the above device, in a possible implementation manner, the characteristic function equation establishment unit establishes the characteristic function equations of the DFIG-side impedance characteristics and the grid-side impedance characteristics according to the following formula (1-7) ,
Zsp(s)+Ztp(s)=0 (1-7)。Z sp (s) + Z tp (s) = 0 (1-7).
对于上述装置,在一种可能的实现方式中,所述振荡频率和阻尼水平判断单元用于:For the above device, in a possible implementation manner, the oscillation frequency and damping level judging unit is used for:
对公式(1-7)进行求解,以得到所述特征函数方程的共轭根λ1,2=α±jβ,Formula (1-7) is solved to obtain the conjugate root λ 1,2 =α±jβ of the characteristic function equation,
其中,虚部β决定所述双馈风电机组的振荡频率,实部α决定所述双馈风电机组的阻尼水平。Wherein, the imaginary part β determines the oscillation frequency of the DFIG, and the real part α determines the damping level of the DFIG.
根据本发明实施例的双馈风电机组的并网次同步振荡的稳定性判断方法和装置,能够建立双馈风电机组详细的机端阻抗模型,考虑了dq/abc坐标变换、dq轴内外环控制、直流电容电压变化等环节,并且基于双馈风电机组侧阻抗特性和电网侧阻抗特性的特征函数方程根,给出了双馈风电机组并网次同步振荡稳定性量化判断方法,并且能够定量判断振荡频率和阻尼水平。According to the method and device for judging the stability of grid-connected subsynchronous oscillation of DFIG according to the embodiments of the present invention, a detailed machine-end impedance model of DFIG can be established, taking dq/abc coordinate transformation and dq-axis inner and outer loop control into consideration , DC capacitor voltage change and other links, and based on the characteristic function equation root of the DFIG side impedance characteristics and the grid side impedance characteristics, a quantitative judgment method for the grid-connected sub-synchronous oscillation stability of the DFIG is given, and it can be quantitatively judged Oscillation frequency and damping level.
根据下面参考附图对示例性实施例的详细说明,本发明的其它特征及方面将变得清楚。Other features and aspects of the present invention will become apparent from the following detailed description of exemplary embodiments with reference to the accompanying drawings.
附图说明Description of drawings
包含在说明书中并且构成说明书的一部分的附图与说明书一起示出了本发明的示例性实施例、特征和方面,并且用于解释本发明的原理。The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the invention and together with the description, serve to explain the principles of the invention.
图1示出根据本发明一实施例的双馈风电机组的并网次同步振荡的稳定性判断方法的流程图。Fig. 1 shows a flow chart of a method for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine according to an embodiment of the present invention.
图2示出双馈感应风电机组的常规转子电流闭环控制的基本结构的示意图。Fig. 2 shows a schematic diagram of the basic structure of conventional rotor current closed-loop control of a doubly-fed induction wind turbine.
图3示出并网电网端口阻抗的示意图。Fig. 3 shows a schematic diagram of grid-connected grid port impedance.
图4示出双馈风电机组并网等效阻抗模型的示意图。Fig. 4 shows a schematic diagram of a grid-connected equivalent impedance model of a doubly-fed wind turbine.
图5示出基于PSCAD/ETMDC的时域仿真计算的示意图。FIG. 5 shows a schematic diagram of time domain simulation calculation based on PSCAD/ETMDC.
图6示出对时域波形的频谱分析结果的示意图。FIG. 6 shows a schematic diagram of the spectrum analysis results of the time-domain waveform.
图7示出根据本发明一实施例的双馈风电机组的并网次同步振荡的稳定性判断装置的结构框图。Fig. 7 shows a structural block diagram of a device for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine according to an embodiment of the present invention.
具体实施方式Detailed ways
以下将参考附图详细说明本发明的各种示例性实施例、特征和方面。附图中相同的附图标记表示功能相同或相似的元件。尽管在附图中示出了实施例的各种方面,但是除非特别指出,不必按比例绘制附图。Various exemplary embodiments, features, and aspects of the invention will be described in detail below with reference to the accompanying drawings. The same reference numbers in the figures indicate functionally identical or similar elements. While various aspects of the embodiments are shown in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
在这里专用的词“示例性”意为“用作例子、实施例或说明性”。这里作为“示例性”所说明的任何实施例不必解释为优于或好于其它实施例。The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as superior or better than other embodiments.
另外,为了更好的说明本发明,在下文的具体实施方式中给出了众多的具体细节。本领域技术人员应当理解,没有某些具体细节,本发明同样可以实施。在一些实例中,对于本领域技术人员熟知的方法、手段、元件和电路未作详细描述,以便于凸显本发明的主旨。In addition, in order to better illustrate the present invention, numerous specific details are given in the specific embodiments below. It will be understood by those skilled in the art that the present invention may be practiced without certain of the specific details. In some instances, methods, means, components and circuits well known to those skilled in the art have not been described in detail in order to highlight the gist of the present invention.
通常,双馈风电机组的定子侧直接接入电网,并且由转子侧变流器来控制定子端的转矩、功率、输出电流等电气量,从而使风电机组满足运行要求。因此,转子侧变流器的控制对发电机定子侧的输出阻抗有较大的影响。同时,为了简化阻抗建模过程,并突出关注的重点,假设转子侧变流器的直流电压稳定无波动,即双馈电机的两个变流器间相互解耦且输出电压与指令电压一致。在这种假设下进行本发明的阻抗建模。本发明的主要过程将在下面详细说明。Usually, the stator side of the double-fed wind turbine is directly connected to the grid, and the rotor-side converter controls the torque, power, output current and other electrical quantities at the stator end, so that the wind turbine can meet the operating requirements. Therefore, the control of the rotor-side converter has a greater impact on the output impedance of the generator stator side. At the same time, in order to simplify the impedance modeling process and highlight the focus of attention, it is assumed that the DC voltage of the rotor-side converter is stable and has no fluctuations, that is, the two converters of the DFIG are decoupled from each other and the output voltage is consistent with the command voltage. The impedance modeling of the present invention is performed under this assumption. The main process of the present invention will be described in detail below.
图1示出根据本发明一实施例的双馈风电机组的并网次同步振荡的稳定性判断方法的流程图。如图1所示,该方法包括以下步骤:Fig. 1 shows a flow chart of a method for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine according to an embodiment of the present invention. As shown in Figure 1, the method includes the following steps:
步骤S100、根据双馈风电机组的定子a相电压、定子a相电流以及转子a相电流,来设置双馈风电机组的定子的正序谐波电压和正序谐波电流;Step S100 , according to the stator a-phase voltage, stator a-phase current and rotor a-phase current of the doubly-fed wind turbine, set the positive-sequence harmonic voltage and positive-sequence harmonic current of the stator of the doubly-fed wind turbine;
步骤S110、根据正序谐波电压和正序谐波电流来确定电流调节环节的输出电压表达式;Step S110, determining the output voltage expression of the current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current;
步骤S120、根据正序谐波电压、正序谐波电流、以及输出电压表达式来建立双馈风电机组的定子侧阻抗解析表达式,以得到双馈风电机组侧阻抗特性;Step S120, according to the positive sequence harmonic voltage, positive sequence harmonic current, and output voltage expressions, an analytical expression of the stator side impedance of the DFIG is established to obtain the side impedance characteristics of the DFIG;
步骤S130、建立电网侧阻抗模型,以得到电网侧阻抗特性;Step S130, establishing a grid-side impedance model to obtain grid-side impedance characteristics;
步骤S140、建立双馈风电机组侧阻抗特性和电网侧阻抗特性的特征函数方程;以及Step S140, establishing the characteristic function equations of the impedance characteristics of the DFIG side impedance characteristics and the grid side impedance characteristics; and
步骤S150、对特征函数方程进行求解,以定量判断双馈风电机组的振荡频率和阻尼水平。Step S150, solving the characteristic function equation to quantitatively judge the oscillation frequency and damping level of the DFIG.
首先,说明双馈风电机组系统的基本结构。First, the basic structure of the doubly-fed wind turbine system is explained.
图2示出双馈感应风电机组的常规转子电流闭环控制的基本结构的示意图。其中usabc=[usa usb usc]T,usa、usb、usc为定子abc三相静止坐标系电压;isabc=[isa isb isc]T,isa、isb、isc为定子abc三相静止坐标系电流;usa、usb、usc为电网侧逆变器中的公共耦合点电压va、vb、vc。usdq=[usd usq]T,usd、usq为同步旋转d/q坐标系中的定子电压;isdq=[isd isq]T,isd、isq为在同步旋转d/q坐标系中的定子电流。urabc=[ura urb urc]T,ura、urb、urc为在转子三相坐标系中的电压;irabc=[ira irb irc]T,ira、irb、irc为在转子三相坐标系中的电流;urdq=[urdurq]T,urd、urq为同步旋转d/q坐标系中的转子电压;irdq=[ird irq]T,ird、irq为同步旋转d/q坐标系中的转子电流。ωr为转子角速度;θPLL、ωPLL为电网电压的相位角及电网电压的角频率。Fig. 2 shows a schematic diagram of the basic structure of conventional rotor current closed-loop control of a doubly-fed induction wind turbine. Among them, u sabc =[ usa u sb u sc ] T , usa , us sb , us sc are the voltages of stator abc three-phase stationary coordinate system; i sabc =[ isa i sb i sc ] T , isa , isb , i sc is the stator abc three-phase static coordinate system current; u sa , u sb , u sc are the common coupling point voltages v a , v b , v c in the grid side inverter. u sdq =[u sd u sq ] T , u sd , u sq are stator voltages in the synchronous rotation d/q coordinate system; i sdq =[i sd i sq ] T , i sd , i sq are synchronous rotation d Stator currents in the /q coordinate system. u rabc =[u ra u rb u rc ] T , u ra , u rb , u rc are voltages in the rotor three-phase coordinate system; i rabc =[i ra i rb i rc ] T , i ra , i rb , i rc is the current in the rotor three-phase coordinate system; u rdq =[u rd u rq ] T , u rd , u rq are the rotor voltage in the synchronous rotation d/q coordinate system; i rdq =[i rd i rq ] T , i rd , i rq are the rotor current in the synchronously rotating d/q coordinate system. ω r is the angular velocity of the rotor; θ PLL and ω PLL are the phase angle of the grid voltage and the angular frequency of the grid voltage.
根据双馈风电机组特性,可得出系统在相坐标下的如下的基本电路关系。According to the characteristics of doubly-fed wind turbines, the following basic circuit relationship of the system in phase coordinates can be obtained.
其中,ψsabc=[ψsa ψsa ψsa]T,ψrabc=[ψra ψra ψra]T,ψsa、ψsb、ψsc和ψra、ψrb、ψrc分别为双馈感应发电机定和转子三相绕组磁链,Ke为定子与转子的匝数比,Rs、Rr、Lss、Lsr、Lrs、Lrr为折算到定子侧后的定子和转子电路参数,并且Lss、Lsr、Lrs、Lrr为发电机定子与转子之间的自感、互感。Among them, ψ sabc = [ψ sa ψ sa ψ sa ] T , ψ rabc = [ψ ra ψ ra ψ ra ] T , ψ sa , ψ sb , ψ sc and ψ ra , ψ rb , ψ rc are double-fed induction Generator stator and rotor three-phase winding flux linkage, K e is the turns ratio of stator and rotor, R s , R r , L ss , L sr , L rs , L rr are the stator and rotor circuits converted to the stator side Parameters, and L ss , L sr , L rs , L rr are the self-inductance and mutual inductance between the generator stator and rotor.
基于上述基本结构的说明,以下将具体说明上述步骤S100~S150。Based on the description of the above basic structure, the above steps S100 to S150 will be specifically described below.
对于上述步骤S100,根据定子a相电压、定子a相电流和转子a相电流来设定双馈风电机组的机端定子的正序谐波电压Vp和正序谐波电流Ip,并建立参照系。For the above step S100, set the positive-sequence harmonic voltage Vp and positive-sequence harmonic current Ip of the machine terminal stator of the DFIG according to the stator a-phase voltage, stator a-phase current and rotor a-phase current, and establish a reference frame.
具体而言,通常基于谐波线性化方法对双馈风电机组的阻抗进行建模,通过在风电机组三相机端电压叠加一个小扰动,计算输出电流,然后通过电压小扰动与输出电流的比值得到机端阻抗特性。Specifically, the impedance of the double-fed wind turbine is usually modeled based on the harmonic linearization method. The output current is calculated by superimposing a small disturbance on the three-phase terminal voltage of the wind turbine, and then obtained by the ratio of the small voltage disturbance to the output current Terminal impedance characteristics.
在双馈风机系统在给定工作点运行时,为推导转子侧输出阻抗,假设公共耦合点(Point of Common Coupling,PCC)电压含有基频正序电压和正序谐波电压。此时,在一种可能的实现方式中,定子a相电压在频域的表达式可以如式(1-1)所示。When the double-fed fan system is running at a given operating point, in order to derive the output impedance of the rotor side, it is assumed that the point of common coupling (Point of Common Coupling, PCC) voltage contains fundamental frequency positive sequence voltage and positive sequence harmonic voltage. At this time, in a possible implementation manner, the expression of the phase a voltage of the stator in the frequency domain may be as shown in formula (1-1).
式中,Vsa(f)为定子a相电压,f为频率,分别表示从时域的正弦量转换到频域的对应频率冲激分量,这与逆变器中的分量一致。V1为公共耦合点正序基波电压幅值,Vp为正序谐波电压的电压幅值,分别为对应分量的初始相角,f1、fp分别为对应频率。In the formula, V sa (f) is the phase voltage of the stator a, f is the frequency, Respectively represent the conversion from the sinusoidal quantity in the time domain to the corresponding frequency impulse component in the frequency domain, which is consistent with the component in the inverter. V 1 is the amplitude of the positive sequence fundamental wave voltage at the common coupling point, V p is the voltage amplitude of the positive sequence harmonic voltage, are the initial phase angles of the corresponding components, and f 1 and f p are the corresponding frequencies.
在定子的正序谐波电压Vp的作用下,定子的电流会产生同频率的正序谐波电流Ip。定子的a相电流在频域的表达式如式(1-2)所示。Under the action of the positive sequence harmonic voltage Vp of the stator, the current of the stator will generate a positive sequence harmonic current Ip of the same frequency. The expression of the a-phase current of the stator in the frequency domain is shown in formula (1-2).
其中,Isa(f)为定子a相电流,I1为公共耦合点正序基波电流幅值,Ip为正序谐波电流的电流幅值,分别为对应分量的初始相角。Among them, I sa (f) is the stator a-phase current, I 1 is the amplitude of the positive sequence fundamental wave current at the common coupling point, I p is the current amplitude of the positive sequence harmonic current, are the initial phase angles of the corresponding components, respectively.
相应地,转子a相电流在频域的表达式可以如式(1-3)所示。Correspondingly, the expression of the rotor phase a current in the frequency domain can be shown in formula (1-3).
其中,Ira(f)为转子a相电流,Ir1、Irp对应正序基波、谐波的转子电流幅值,分别为对应分量的初始相角,fr为转子转动频率,fs为转差频率。Among them, I ra (f) is the phase a current of the rotor, I r1 and I rp correspond to the rotor current amplitude of positive sequence fundamental wave and harmonic, are the initial phase angles of the corresponding components, f r is the rotor rotation frequency, and f s is the slip frequency.
由此,可以根据上述公式(1-1)、(1-2)和(1-3)确定出双馈风电机组的定子a相电压、定子a相电流和转子a相电流,从而进一步根据定子a相电压、定子a相电流和转子a相电流来设置正序谐波电压Vp和正序谐波电流Ip。Therefore, according to the above formulas (1-1), (1-2) and (1-3), the stator a-phase voltage, stator a-phase current and rotor a-phase current of the doubly-fed wind turbine can be determined, so that further according to the stator A-phase voltage, stator a-phase current and rotor a-phase current to set positive sequence harmonic voltage Vp and positive sequence harmonic current Ip.
对于上述步骤S110,根据正序谐波电压Vp和正序谐波电流Ip来推导电流调节环节输出电压表达式。For the above step S110, the output voltage expression of the current regulation link is derived according to the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip.
具体而言,首先,根据定子侧的正序谐波电压Vp和正序谐波电流Ip,可以根据以下公式推导得到转子侧的电流表达式。Specifically, firstly, according to the positive-sequence harmonic voltage Vp and the positive-sequence harmonic current Ip on the stator side, the current expression on the rotor side can be derived according to the following formula.
其中,Vp(s)为定子的正序谐波电压,其是变量s的函数,其中s=j2πf。此外,如下表达式成立。where Vp (s) is the positive sequence harmonic voltage of the stator, which is a function of the variable s, where s=j2πf. In addition, the following expression holds.
其中,HPLL(s)表示包括PI调节器和积分器的锁相环的传递函数,并且其可以表示为其中,kpp、kpi分别为锁相环比例系数和积分系数。转子各分量在转换坐标系时使用的角度为θPLL-θr,其中θPLL为电网电压的相位角,θr为转子位置角。in, H PLL (s) represents the transfer function of a phase-locked loop including a PI regulator and an integrator, and it can be expressed as Among them, k pp and k pi are the phase-locked loop proportional coefficient and integral coefficient respectively. The angle used by each component of the rotor when transforming the coordinate system is θ PLL -θ r , where θ PLL is the phase angle of the grid voltage, and θ r is the rotor position angle.
在转子侧的d/q控制经过电流调节环节后,得到转子侧变换器的输出电压d/q轴指令值,表达式如式(1-15)、(1-16)所示。After the d/q control on the rotor side passes through the current regulation link, the output voltage d/q axis command value of the rotor side converter is obtained, and the expressions are shown in equations (1-15) and (1-16).
Udr=-Hri(s)ird-Krdirq (1-15)U dr =-H ri (s) i rd -K rd i rq (1-15)
Uqr=-Hri(s)irq+Krdird (1-16)U qr =-H ri (s)i rq +K rd i rd (1-16)
式中,Hri(s)=kip+kii/s,其为转子电流调节传递函数,采用比例积分(Proportional Integral,PI)控制,kip、kii分别为电流调节器的比例系数、积分系数,Krd为转子侧dq控制策略中的解耦系数。In the formula, H ri (s)=kip+kii/s, which is the rotor current regulation transfer function, adopts proportional integral (PI) control, kip and kii are the proportional coefficient and integral coefficient of the current regulator respectively, K rd is the decoupling coefficient in the dq control strategy on the rotor side.
转子电流调节器输出的转子电压d/q指令值再通过以下表达式(1-17)而dq/abc坐标变换至abc相。The rotor voltage d/q command value output by the rotor current regulator is converted to the abc phase by the following expression (1-17) and the dq/abc coordinates.
其中,Ud0、Uq0为双馈风电机组在额定工作状态下的电流调节器输出的直流稳态值,其与系统额定工作点有关。Among them, U d0 and U q0 are the DC steady-state values output by the current regulator of the doubly-fed wind turbine in the rated working state, which are related to the rated working point of the system.
其中:in:
由此,最终可推导得到转子侧变换器的输出电压的各分量在abc相坐标系下的正序分量:Thus, the positive sequence components of each component of the output voltage of the rotor-side converter in the abc phase coordinate system can be finally derived:
其中,可以通过V(s)来表示Ura、Urb和Urc中的任一个的值。此外,Vr0为转子电压稳态分量幅值,Vdc为直流电容电压幅值(直流母线电压幅值)。Wherein, the value of any one of U ra , U rb and U rc can be represented by V(s). In addition, V r0 is the amplitude of the steady-state component of the rotor voltage, and V dc is the amplitude of the DC capacitor voltage (the amplitude of the DC bus voltage).
此外,在式(1-4)中,第一项分量为正序转差频率,主要起到使双馈风机对外输出电流和功率的作用;第二项为因正序谐波分量的存在而产生的转子侧变换器的输出电压谐波输出,频率为正序谐波频率减去转速,其与锁相环参数、电流环参数、额定工作点以及定子侧电压谐波分量等都有关系。In addition, in formula (1-4), the first component is the positive sequence slip frequency, which mainly plays the role of making the double-fed fan output current and power; the second component is the positive sequence harmonic component. The output voltage harmonic output of the rotor-side converter generated is the positive-sequence harmonic frequency minus the rotational speed, which is related to the phase-locked loop parameters, current loop parameters, rated operating point, and stator-side voltage harmonic components.
由此,可以通过正序谐波电压Vp和正序谐波电流Ip来推导出电流调节环节输出电压表达式。Thus, the output voltage expression of the current regulation link can be derived from the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip.
对于上述步骤S120,可以根据正序谐波电压Vp、正序谐波电流Ip、以及输出电压表达式V(s)来建立双馈风电机组的定子侧阻抗解析表达式(建立双馈异步感应发电机定子/转子频率折算及阻抗解析表达式),以得到双馈风电机组侧阻抗特性。For the above step S120, the stator side impedance analytical expression of the DFIG can be established according to the positive-sequence harmonic voltage Vp, the positive-sequence harmonic current Ip, and the output voltage expression V(s) (establishing the DFIG asynchronous induction power generation Stator/rotor frequency conversion and impedance analysis expression) to obtain the side impedance characteristics of doubly-fed wind turbines.
具体推导过程阐述如下。The specific derivation process is described as follows.
基于单相表示的异步感应发电机定子侧和转子侧关系,发电机转子转差系数为:Based on the relationship between the stator side and the rotor side of the asynchronous induction generator represented by a single phase, the slip coefficient of the generator rotor is:
其中,isa、isb、isc为定子abc三相电流,usa、usb、usc为定子abc三相电压,ira、irb、irc为转子三相电流,ura、urb、urc为转子三相电压。Lls是定子绕组的漏感,L′lr是折算后的转子绕组漏感,Rs是定子绕组的电阻,R′r是折算后的转子绕组的电阻,σ(s)为双馈异步感应发电机转子转差系数,为感应发电机定子侧绕组与转子侧绕组的等效匝比。Among them, i sa , isb , i sc are three-phase currents of stator abc, u sa , u sb , u sc are three-phase voltages of stator abc, i ra , i rb , i rc are three-phase currents of rotor, u ra , u rb and u rc are the three-phase voltages of the rotor. L ls is the leakage inductance of the stator winding, L′ lr is the converted leakage inductance of the rotor winding, R s is the resistance of the stator winding, R′ r is the converted resistance of the rotor winding, σ(s) is the double-fed asynchronous induction Generator rotor slip coefficient, is the equivalent turns ratio of the induction generator stator side winding to the rotor side winding.
由于转子侧阻抗和定子侧阻抗并联,因此统一归算到定子侧。当双馈风电机组在额定电压下进行正常并网工作时,若电网中含有正序电压谐波时,端口会存在相应的正序电流谐波,此时电压谐波比电流谐波相量就得到了该频率下的正序阻抗特性(即,双馈风电机组侧阻抗特性):Since the impedance on the rotor side and the impedance on the stator side are connected in parallel, they are collectively attributed to the stator side. When the doubly-fed wind turbine is normally connected to the grid at the rated voltage, if the grid contains positive-sequence voltage harmonics, there will be corresponding positive-sequence current harmonics at the port. At this time, the ratio of voltage harmonics to current harmonic phasors is The positive-sequence impedance characteristics at this frequency (that is, the impedance characteristics of the doubly-fed wind turbine side) are obtained:
其中,Ztp(s)表示双馈风电机组侧阻抗特性,Lls表示定子绕组的漏感,L′lr表示转子绕组的漏感,Rs表示定子绕组的电阻,R′r表示转子绕组的电阻,σ(s)表示双馈异步感应发电机转子转差系数,表示双馈异步感应发电机的定子侧绕组与转子侧绕组的等效匝比,ω1表示基频角速度。Among them, Z tp (s) represents the impedance characteristic of the DFIG side, L ls represents the leakage inductance of the stator winding, L′ lr represents the leakage inductance of the rotor winding, R s represents the resistance of the stator winding, R′ r represents the resistance of the rotor winding Resistance, σ(s) represents the rotor slip coefficient of doubly-fed asynchronous induction generator, Indicates the equivalent turn ratio of the stator side winding and the rotor side winding of the doubly-fed asynchronous induction generator, and ω 1 represents the fundamental frequency angular velocity.
由此,通过上述步骤S120,可以得到建立双馈风电机组的定子侧阻抗解析表达式,以得到双馈风电机组侧阻抗特性Ztp(s)。Thus, through the above step S120, an analytical expression of the stator-side impedance of the doubly-fed wind turbine can be established to obtain the impedance characteristic Z tp (s) of the doubly-fed wind turbine.
对于上述步骤S130,建立电网侧阻抗模型。For the above step S130, a grid-side impedance model is established.
为了通用性,电网侧假定为经串补送出系统,如图3所示,示出了并网电网端口阻抗的示意图。For the sake of generality, the grid side is assumed to be sent out through series compensation, as shown in Figure 3, which shows a schematic diagram of the grid-connected grid port impedance.
在一种可能的实现方式中,可以根据以下公式(1-6)来建立电网侧阻抗模型,从而最终得到电网阻抗特性(即,并网电网端口阻抗特性)。In a possible implementation manner, a grid-side impedance model may be established according to the following formula (1-6), so as to finally obtain grid impedance characteristics (ie, grid-connected grid port impedance characteristics).
其中,Zsp(s)表示电网侧阻抗特性,R表示电网中的等效电阻,L表示电网中的等效电感,C表示电网中的等效串联电容。Among them, Z sp (s) represents the impedance characteristic of the grid side, R represents the equivalent resistance in the power grid, L represents the equivalent inductance in the power grid, and C represents the equivalent series capacitance in the power grid.
对于上述步骤S140和步骤S150,可以利用上述公式(1-5)和(1-6)来建立特征函数方程,并求解该特征函数方程的根来实现基于静止坐标系的阻抗特性函数根的稳定性量化判据。For the above step S140 and step S150, the above formulas (1-5) and (1-6) can be used to establish the characteristic function equation, and solve the root of the characteristic function equation to realize the stability of the root of the impedance characteristic function based on the static coordinate system Quantitative criteria.
图4示出双馈风电机组并网等效阻抗模型的示意图。如图4所示,当双馈风电机组并入电网时,电网阻抗模型由Zsp(s)表示,其表示电网侧阻抗特性(即,电网用理想电压源串联等效阻抗);双馈风电机组的阻抗模型由Ztp(s)表示,其表示双馈风电机组侧阻抗特性(即,双馈风电机组侧一般用理想电流源并联等效阻抗)。此外,在图4中,还示出了电流表Is(s)和电压表Vs(s),以测量电流I(s)和电压V(s)。然后,根据以下公式(1-7)来建立特征函数方程。Fig. 4 shows a schematic diagram of a grid-connected equivalent impedance model of a doubly-fed wind turbine. As shown in Figure 4, when the DFIG is connected to the grid, the grid impedance model is represented by Z sp (s), which represents the grid-side impedance characteristics (that is, the grid uses an ideal voltage source in series with the equivalent impedance); DFIG The impedance model of the unit is represented by Z tp (s), which represents the impedance characteristics of the DFIG side (that is, the DFIG side generally uses an ideal current source in parallel with the equivalent impedance). In addition, in FIG. 4 , an ammeter I s (s) and a voltmeter V s (s) are also shown to measure the current I(s) and the voltage V(s). Then, the characteristic function equation is established according to the following formula (1-7).
Zsp(s)+Ztp(s)=0 (1-7)Z sp (s) + Z tp (s) = 0 (1-7)
接着,在步骤S150中,基于静止坐标系阻抗特性函数根来进行稳定性量化判断。Next, in step S150 , quantitative determination of stability is performed based on the root of the impedance characteristic function in the static coordinate system.
具体而言,对公式(1-7)进行求解,得到特征函数方程的根,根据特征函数方程的根可以判断系统的稳定性。具体判据为:Specifically, the formula (1-7) is solved to obtain the root of the characteristic function equation, and the stability of the system can be judged according to the root of the characteristic function equation. The specific criteria are:
◆得到阻抗特性方程的共轭根:λ1,2=α±jβ;◆Get the conjugate root of the impedance characteristic equation: λ 1,2 =α±jβ;
◆其中,虚部β决定了振荡频率ω;实部α决定了振荡发散或收敛及阻尼水平,当α>0时振荡发散,α越大振荡发散越快;当α<0时振荡收敛,α越大则收敛越快。◆ Among them, the imaginary part β determines the oscillation frequency ω; the real part α determines the oscillation divergence or convergence and damping level. When α>0, the oscillation diverges, and the larger the α, the faster the oscillation divergence; when α<0, the oscillation converges, and α The larger it is, the faster the convergence.
这样,根据本发明实施例的双馈风电机组的并网次同步振荡的稳定性判断方法,能够建立双馈风电机组详细的机端阻抗模型,考虑了dq/abc坐标变换、dq轴内外环控制、直流电容电压变化等环节,并且基于双馈风电机组侧阻抗特性和电网侧阻抗特性的特征函数方程根,给出了双馈风电机组并网次同步振荡稳定性量化判断方法,并且能够定量判断振荡频率和阻尼水平。In this way, according to the method for judging the stability of the grid-connected subsynchronous oscillation of the doubly-fed wind turbine in the embodiment of the present invention, a detailed machine-end impedance model of the doubly-fed wind turbine can be established, taking dq/abc coordinate transformation and dq-axis inner and outer loop control into consideration , DC capacitor voltage change and other links, and based on the characteristic function equation root of the DFIG side impedance characteristics and the grid side impedance characteristics, a quantitative judgment method for the grid-connected sub-synchronous oscillation stability of the DFIG is given, and it can be quantitatively judged Oscillation frequency and damping level.
以下将说明应用上述双馈风电机组并网次同步振荡稳定性量化判断方法来对设定的双馈风电机组进行计算分析。双馈风电机组的主电路、锁相环、控制器参数如表1所示。The calculation and analysis of the set doubly-fed wind turbines will be described below by applying the above-mentioned quantitative judgment method for the grid-connected subsynchronous oscillation stability of the doubly-fed wind turbines. The parameters of main circuit, phase-locked loop and controller of DFIG are shown in Table 1.
此外,设定双馈风电机组出力为1.0MW。针对以上双馈风电机组的基本参数,代入公式(1-5)得到双馈风电机组侧阻抗特性Ztp(s)。假定并网交流电网的等值电感为0.0011H,串补电容为100uF,得到电网侧阻抗特性Zsp(s)。最后,将双馈风电机组侧阻抗特性Ztp(s)和电网侧阻抗特性Zsp(s)代入Ztp(s)+Zsp(s)=0。计算特征函数方程的根得到振荡频率ω=4.1Hz,阻尼α=0.1s-1。In addition, set the output of the doubly-fed wind turbine as 1.0MW. Aiming at the above basic parameters of DFIG, substituting formula (1-5) to obtain the side impedance characteristic Z tp (s) of DFIG. Assuming that the equivalent inductance of the grid-connected AC grid is 0.0011H, and the series compensation capacitor is 100uF, the impedance characteristic Z sp (s) of the grid side is obtained. Finally, the impedance characteristic Z tp (s) of the DFIG side and the impedance characteristic Z sp (s) of the grid side are substituted into Z tp (s)+Z sp (s)=0. The root of the characteristic function equation is calculated to obtain the oscillation frequency ω=4.1Hz and the damping α=0.1s −1 .
表1双馈风电机组机的基本参数Table 1 Basic parameters of DFIG
为了验证双馈风电机组并网次同步振荡稳定性量化判断方法的正确性,在PSCAD软件或ETMDC软件上建立时域仿真模型。双馈风电机组内部电路参数及转子侧锁相、控制参数(即,双馈风电机组机基本参数)与表1一致。风机出力为1.0MW时,网侧逆变器与双馈风机转子侧变流器共用锁相环,在阻抗解析表达式中的对应参数参照表1中的锁相环参数。在这种系统参数下,在PSCAD上进行仿真,并进行时域对比分析,通过断路器在3s时将大小为100uF的串补电容投入,从而会发生次同步振荡。图5示出基于PSCAD/ETMDC的时域仿真计算的示意图。其中,图5的(a)示出电流的时域波形,以及图5的(b)示出功率的时域波形。图6示出对时域波形的频谱分析结果的示意图。其中,图6的(a)示出电流的频谱分析,以及图(6)的(b)示出功率的频谱分析。从图6的频谱分析可以看出,在3Hz处的谐波分量比较大,与理论分析基本吻合。In order to verify the correctness of the quantitative judgment method for grid-connected subsynchronous oscillation stability of doubly-fed wind turbines, a time-domain simulation model is established on PSCAD software or ETMDC software. The internal circuit parameters of the DFIG and the phase-locked and control parameters on the rotor side (that is, the basic parameters of the DFIG) are consistent with Table 1. When the output of the wind turbine is 1.0MW, the grid-side inverter and the rotor-side converter of the double-fed wind turbine share a phase-locked loop, and the corresponding parameters in the impedance analysis expression refer to the phase-locked loop parameters in Table 1. Under this system parameter, carry on the simulation on PSCAD, and carry on the comparative analysis in the time domain, through the circuit breaker in 3s when the size is 100uF series compensatory electric capacity puts in, thus will produce the synchronous oscillation. FIG. 5 shows a schematic diagram of time domain simulation calculation based on PSCAD/ETMDC. Among them, (a) of FIG. 5 shows the time-domain waveform of the current, and (b) of FIG. 5 shows the time-domain waveform of the power. FIG. 6 shows a schematic diagram of the spectrum analysis results of the time-domain waveform. Among them, (a) of FIG. 6 shows the spectrum analysis of the current, and (b) of FIG. 6 shows the spectrum analysis of the power. It can be seen from the spectrum analysis in Figure 6 that the harmonic component at 3Hz is relatively large, which is basically consistent with the theoretical analysis.
由此可见,本发明实施例提供的双馈风电机组并网次同步振荡稳定性量化判断方法是恰当的。It can be seen that the quantitative judgment method for grid-connected subsynchronous oscillation stability provided by the embodiment of the present invention is appropriate.
图7示出根据本发明一实施例的双馈风电机组的并网次同步振荡的稳定性判断装置的结构框图。如图7所示,双馈风电机组的并网次同步振荡的稳定性判断装置1包括:正序谐波电压和电流设置单元10,用于根据所述双馈风电机组的定子a相电压、定子a相电流以及转子a相电流,来设置所述双馈风电机组的定子的正序谐波电压和正序谐波电流;输出电压表达式确定单元11,用于根据所述正序谐波电压和所述正序谐波电流来确定电流调节环节的输出电压表达式;定子侧阻抗解析表达式建立单元12,用于根据所述正序谐波电压、所述正序谐波电流、以及所述输出电压表达式来建立所述双馈风电机组的定子侧阻抗解析表达式,以得到双馈风电机组侧阻抗特性;电网侧阻抗模型建立单元13,用于建立电网侧阻抗模型,以得到电网侧阻抗特性;特征函数方程建立单元14,用于建立所述双馈风电机组侧阻抗特性和所述电网侧阻抗特性的特征函数方程;以及振荡频率和阻尼水平判断单元15,用于对所述特征函数方程进行求解,以定量判断所述双馈风电机组的振荡频率和阻尼水平。Fig. 7 shows a structural block diagram of a device for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine according to an embodiment of the present invention. As shown in Fig. 7, the stability judging device 1 for the grid-connected subsynchronous oscillation of the doubly-fed wind turbine includes: a positive sequence harmonic voltage and current setting unit 10, which is used to set the phase a voltage of the stator of the doubly-fed wind turbine, stator a-phase current and rotor a-phase current to set the positive-sequence harmonic voltage and positive-sequence harmonic current of the stator of the doubly-fed wind turbine; the output voltage expression determination unit 11 is used to determine the positive-sequence harmonic voltage according to the and the positive-sequence harmonic current to determine the output voltage expression of the current regulation link; the stator side impedance analytical expression establishment unit 12 is used for according to the positive-sequence harmonic voltage, the positive-sequence harmonic current, and the The above output voltage expression is used to establish the stator side impedance analytical expression of the DFIG to obtain the DFIG side impedance characteristics; the grid side impedance model establishment unit 13 is used to establish the grid side impedance model to obtain the grid Side impedance characteristics; characteristic function equation establishment unit 14, used to establish the characteristic function equations of the side impedance characteristics of the DFIG and the grid side impedance characteristics; and an oscillation frequency and damping level judging unit 15, used to determine the The characteristic function equation is solved to quantitatively judge the oscillation frequency and damping level of the doubly-fed wind turbine.
在一种可能的实现方式中,所述正序谐波电压和电流设置单元10分别根据以下公式(1-1)、(1-2)和(1-3)来确定所述定子a相电压、所述定子a相电流以及所述转子a相电流,In a possible implementation, the positive sequence harmonic voltage and current setting unit 10 determines the stator a-phase voltage according to the following formulas (1-1), (1-2) and (1-3) respectively , the stator a-phase current and the rotor a-phase current,
其中,Vsa(f)表示所述定子a相电压,f表示频率,V1表示公共耦合点正序基波电压幅值,Vp表示所述正序谐波电压的电压幅值,分别表示对应分量的初始相角,f1、fp分别表示对应频率,Wherein, V sa (f) represents the phase a voltage of the stator, f represents the frequency, V represents the amplitude of the positive-sequence fundamental wave voltage at the common coupling point, and V represents the voltage amplitude of the positive-sequence harmonic voltage, represent the initial phase angles of the corresponding components respectively, f 1 and f p represent the corresponding frequencies respectively,
Isa(f)表示所述定子a相电流,I1表示公共耦合点正序基波电流幅值,Ip表示所述正序谐波电流的电流幅值,分别表示对应分量的初始相角,I sa (f) represents the stator a-phase current, I represents the magnitude of the positive-sequence fundamental wave current at the common coupling point, and Ip represents the current magnitude of the positive-sequence harmonic current, denote the initial phase angles of the corresponding components, respectively,
Ira(f)表示所述转子a相电流,Ir1、Irp分别表示对应正序基波、谐波的转子电流幅值,分别表示对应分量的初始相角,fr表示转子转动频率,fs表示转差频率。I ra (f) represents the phase a current of the rotor, I r1 and I rp represent the rotor current amplitude corresponding to the positive sequence fundamental wave and harmonic, respectively, Respectively represent the initial phase angle of the corresponding component, f r represents the rotor rotation frequency, f s represents the slip frequency.
在一种可能的实现方式中,所述输出电压表达式确定单元11根据以下公式(1-4)来确定所述输出电压表达式,In a possible implementation manner, the output voltage expression determining unit 11 determines the output voltage expression according to the following formula (1-4),
其中,V(s)表示输出电压,s=j2πf,Hri(s)=kip+kii/s,kip和kii分别表示电流调节器的比例系数和积分系数,Krd(s)表示转子侧dq控制策略中的解耦系数,Vp(s)表示所述正序谐波电压,HPLL(s)表示包括PI调节器和积分器的锁相环的传递函数,Vr0表示转子电压稳态分量幅值,Vdc表示直流电容电压幅值。Among them, V(s) represents the output voltage, s=j2πf, H ri (s)=kip+kii/s, kip and kii represent the proportional coefficient and integral coefficient of the current regulator respectively, K rd (s) represents the rotor side dq The decoupling coefficient in the control strategy, V p (s) represents the positive sequence harmonic voltage, H PLL (s) represents the transfer function of the phase-locked loop including the PI regulator and integrator, V r0 represents the amplitude of the rotor voltage steady-state component, and V dc represents the amplitude of the DC capacitor voltage.
在一种可能的实现方式中,所述定子侧阻抗解析表达式建立单元12根据以下公式(1-5)来建立所述双馈风电机组的定子侧阻抗解析表达式,In a possible implementation manner, the stator-side impedance analytical expression establishment unit 12 establishes the stator-side impedance analytical expression of the doubly-fed wind turbine according to the following formula (1-5),
其中,Ztp(s)表示所述双馈风电机组侧阻抗特性,Lls表示定子绕组的漏感,L′lr表示转子绕组的漏感,Rs表示定子绕组的电阻,R′r表示转子绕组的电阻,σ(s)表示双馈异步感应发电机转子转差系数,表示双馈异步感应发电机的定子侧绕组与转子侧绕组的等效匝比,ω1表示基频角速度。Among them, Z tp (s) represents the side impedance characteristic of the DFIG, L ls represents the leakage inductance of the stator winding, L′ lr represents the leakage inductance of the rotor winding, R s represents the resistance of the stator winding, and R′ r represents the rotor The resistance of the winding, σ(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator, Indicates the equivalent turn ratio of the stator side winding and the rotor side winding of the doubly-fed asynchronous induction generator, and ω 1 represents the fundamental frequency angular velocity.
在一种可能的实现方式中,所述电网侧阻抗模型建立单元13根据以下公式(1-6)来建立所述电网侧阻抗模型,In a possible implementation manner, the grid-side impedance model establishing unit 13 establishes the grid-side impedance model according to the following formula (1-6),
其中,Zsp(s)表示所述电网侧阻抗特性,R表示电网中的等效电阻,L表示电网中的等效电感,C表示电网中的等效串联电容。Wherein, Z sp (s) represents the impedance characteristic of the grid side, R represents the equivalent resistance in the power grid, L represents the equivalent inductance in the power grid, and C represents the equivalent series capacitance in the power grid.
在一种可能的实现方式中,所述特征函数方程建立单元14根据以下公式(1-7)来建立所述双馈风电机组侧阻抗特性和所述电网侧阻抗特性的特征函数方程,In a possible implementation manner, the characteristic function equation establishment unit 14 establishes the characteristic function equations of the DFIG-side impedance characteristics and the grid-side impedance characteristics according to the following formula (1-7),
Zsp(s)+Ztp(s)=0 (1-7)。Z sp (s) + Z tp (s) = 0 (1-7).
在一种可能的实现方式中,所述振荡频率和阻尼水平判断单元15用于:In a possible implementation manner, the oscillation frequency and damping level judging unit 15 is configured to:
对公式(1-7)进行求解,以得到所述特征函数方程的共轭根λ1,2=α±jβ,Formula (1-7) is solved to obtain the conjugate root λ 1,2 =α±jβ of the characteristic function equation,
其中,虚部β决定所述双馈风电机组的振荡频率,实部α决定所述双馈风电机组的阻尼水平。Wherein, the imaginary part β determines the oscillation frequency of the DFIG, and the real part α determines the damping level of the DFIG.
本发明实施例的双馈风电机组的并网次同步振荡的稳定性判断装置1的具体功能及实现详见上述实施例所述,这里不再进行详细说明。The specific functions and implementation of the grid-connected sub-synchronous oscillation stability judging device 1 of the doubly-fed wind turbine in the embodiment of the present invention are detailed in the above-mentioned embodiments, and will not be described in detail here.
这样,根据本发明实施例的双馈风电机组的并网次同步振荡的稳定性判断装置,能够建立双馈风电机组详细的机端阻抗模型,考虑了dq/abc坐标变换、dq轴内外环控制、直流电容电压变化等环节,并且基于双馈风电机组侧阻抗特性和电网侧阻抗特性的特征函数方程根,给出了双馈风电机组并网次同步振荡稳定性量化判断方法,并且能够定量判断振荡频率和阻尼水平。In this way, the device for judging the stability of the grid-connected subsynchronous oscillation of the DFIG according to the embodiment of the present invention can establish a detailed machine-end impedance model of the DFIG, taking dq/abc coordinate transformation and dq-axis inner and outer loop control into consideration , DC capacitor voltage change and other links, and based on the characteristic function equation root of the DFIG side impedance characteristics and the grid side impedance characteristics, a quantitative judgment method for the grid-connected sub-synchronous oscillation stability of the DFIG is given, and it can be quantitatively judged Oscillation frequency and damping level.
以上已经描述了本发明的各实施例,上述说明是示例性的,并非穷尽性的,并且也不限于所披露的各实施例。在不偏离所说明的各实施例的范围和精神的情况下,对于本技术领域的普通技术人员来说许多修改和变更都是显而易见的。本文中所用术语的选择,旨在最好地解释各实施例的原理、实际应用或对市场中的技术的技术改进,或者使本技术领域的其它普通技术人员能理解本文披露的各实施例。Having described various embodiments of the present invention, the foregoing description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and alterations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles of the various embodiments, practical applications or technical improvements over technologies in the market, or to enable other persons of ordinary skill in the art to understand the various embodiments disclosed herein.
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