CN108347058A - The stability judging method and device of the grid-connected sub-synchronous oscillation of double-fed fan motor unit - Google Patents

Abstract

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

Method and device for judging the stability of grid-connected subsynchronous oscillation of doubly-fed wind turbines

technical field

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.

Background technique

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.

In order to solve the above problems, the following methods have been studied.

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.

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.

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.

Contents of the invention

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.

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.

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,

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,

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,

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.

For the above method, in a possible implementation manner, the output voltage expression is determined according to the following formula (1-4),

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.

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):

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.

For the above method, in a possible implementation manner, the grid side impedance model is established according to the following formula (1-6):

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.

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),

Z _sp (s) + Z _tp (s) = 0 (1-7).

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:

Formula (1-7) is solved to obtain the conjugate root λ _1,2 =α±jβ of the characteristic function equation,

Wherein, the imaginary part β determines the oscillation frequency of the DFIG, and the real part α determines the damping level of the DFIG.

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.

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,

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,

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,

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.

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),

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.

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),

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.

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),

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.

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) ,

Z _sp (s) + Z _tp (s) = 0 (1-7).

For the above device, in a possible implementation manner, the oscillation frequency and damping level judging unit is used for:

Formula (1-7) is solved to obtain the conjugate root λ _1,2 =α±jβ of the characteristic function equation,

Wherein, the imaginary part β determines the oscillation frequency of the DFIG, and the real part α determines the damping level of the DFIG.

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.

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.

Description of drawings

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.

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.

Fig. 2 shows a schematic diagram of the basic structure of conventional rotor current closed-loop control of a doubly-fed induction wind turbine.

Fig. 3 shows a schematic diagram of grid-connected grid port impedance.

Fig. 4 shows a schematic diagram of a grid-connected equivalent impedance model of a doubly-fed wind turbine.

FIG. 5 shows a schematic diagram of time domain simulation calculation based on PSCAD/ETMDC.

FIG. 6 shows a schematic diagram of the spectrum analysis results of the time-domain waveform.

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.

Detailed ways

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.

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.

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.

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.

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:

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;

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;

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;

Step S130, establishing a grid-side impedance model to obtain grid-side impedance characteristics;

Step S140, establishing the characteristic function equations of the impedance characteristics of the DFIG side impedance characteristics and the grid side impedance characteristics; and

Step S150, solving the characteristic function equation to quantitatively judge the oscillation frequency and damping level of the DFIG.

First, the basic structure of the doubly-fed wind turbine system is explained.

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.

According to the characteristics of doubly-fed wind turbines, the following basic circuit relationship of the system in phase coordinates can be obtained.

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.

Based on the description of the above basic structure, the above steps S100 to S150 will be specifically described below.

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.

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.

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).

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.

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).

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.

Correspondingly, the expression of the rotor phase a current in the frequency domain can be shown in formula (1-3).

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.

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.

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.

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.

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.

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.

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).

U _dr ＝-H _ri (s) i _rd -K _rd i _rq (1-15)

U _qr ＝-H _ri (s)i _rq +K _rd i _rd (1-16)

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.

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.

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.

in:

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:

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).

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.

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.

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.

The specific derivation process is described as follows.

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:

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.

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:

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.

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.

For the above step S130, a grid-side impedance model is established.

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.

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).

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.

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.

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).

Z _sp (s) + Z _tp (s) = 0 (1-7)

Next, in step S150 , quantitative determination of stability is performed based on the root of the impedance characteristic function in the static coordinate system.

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:

◆Get the conjugate root of the impedance characteristic equation: λ _1,2 ＝α±jβ;

◆ 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.

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.

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.

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 .

Table 1 Basic parameters of DFIG

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.

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.

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.

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,

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,

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,

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.

In a possible implementation manner, the output voltage expression determining unit 11 determines the output voltage expression according to the following formula (1-4),

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.

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),

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.

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),

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.

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),

Z _sp (s) + Z _tp (s) = 0 (1-7).

In a possible implementation manner, the oscillation frequency and damping level judging unit 15 is configured to:

Formula (1-7) is solved to obtain the conjugate root λ _1,2 =α±jβ of the characteristic function equation,

Wherein, the imaginary part β determines the oscillation frequency of the DFIG, and the real part α determines the damping level of the DFIG.

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.

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.

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.

Claims (14)

1. A method for judging stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator is characterized by comprising the following steps:

setting positive sequence harmonic voltage and positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator;

determining an output voltage expression of a current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current;

establishing a stator side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain a side impedance characteristic of the doubly-fed wind turbine generator;

establishing a power grid side impedance model to obtain a power grid side impedance characteristic;

establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; and

and solving the characteristic function equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator.

2. The method according to claim 1, characterized in that the stator-a phase voltage, the stator-a phase current and the rotor-a phase current are determined according to the following equations (1-1), (1-2) and (1-3), respectively,

wherein, V_sa(f) Representing the stator a phase voltage, f representing the frequency,V₁representing the positive sequence fundamental voltage amplitude, V, of the point of common coupling_pRepresents a voltage magnitude of the positive sequence harmonic voltage,respectively representing the initial phase angles, f, of the corresponding components₁、f_pRespectively, the corresponding frequencies are represented by,

I_sa(f) representing the stator a phaseThe current is applied to the surface of the substrate,I₁representing the positive sequence fundamental current amplitude, I, of the point of common coupling_pRepresents the current magnitude of the positive sequence harmonic current,respectively represent the initial phase angles of the corresponding components,

I_ra(f) showing the phase a current of the rotor,I_r1、I_rprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,respectively representing the initial phase angles, f, of the corresponding components_rRepresenting the rotor rotation frequency, f_sRepresenting slip frequency.

3. The method according to claim 2, characterized in that the output voltage expression is determined according to the following equations (1-4),

where V(s) represents the output voltage, s-j 2 pi f, H_ri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, K_rd(s) represents the decoupling coefficient in the rotor-side dq control strategy, V_p(s) represents the positive sequence harmonic voltage,H_PLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, V_r0Representing the magnitude of the steady-state component of the rotor voltage, V_dcRepresenting dc capacitor voltageThe amplitude value.

4. The method according to claim 3, characterized in that the stator side impedance analytical expression of the doubly-fed wind turbine is established according to the following equations (1-5),

wherein Z is_tp(s) represents the doubly-fed wind turbine side impedance characteristic, L_lsIndicating leakage inductance of the stator winding, L_l′_rIndicating leakage inductance of the rotor winding, R_sRepresenting the resistance of the stator winding, R_r' represents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator₁Representing the fundamental angular velocity.

5. The method according to claim 4, characterized in that the grid-side impedance model is established according to the following equations (1-6),

wherein Z is_sp(s) represents the impedance characteristic of the power 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.

6. The method according to claim 5, characterized in that the characteristic function equations of the doubly-fed wind turbine side impedance characteristic and the grid side impedance characteristic are established according to the following equations (1-7),

Z_sp(s)+Z_tp(s)＝0 (1-7)。

7. the method of claim 6, wherein solving the eigenfunction equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator comprises:

solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation_1,2＝α±jβ，

the imaginary part β determines the oscillation frequency of the doubly-fed wind turbine generator, and the real part α determines the damping level of the doubly-fed wind turbine generator.

8. The utility model provides a doubly-fed wind turbine generator system's stability of sub-synchronous oscillation that is incorporated into power networks judges device which characterized in that includes:

the positive sequence harmonic voltage and current setting unit is used for setting the positive sequence harmonic voltage and the positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator;

the output voltage expression determining unit is used for determining an output voltage expression of the current regulating link according to the positive sequence harmonic voltage and the positive sequence harmonic current;

the stator side impedance analytical expression establishing unit is used for establishing a stator side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the side impedance characteristic of the doubly-fed wind turbine generator;

the power grid side impedance model establishing unit is used for establishing a power grid side impedance model so as to obtain the power grid side impedance characteristic;

the characteristic function equation establishing unit is used for establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; and

and the oscillation frequency and damping level judging unit is used for solving the characteristic function equation so as to quantitatively judge the oscillation frequency and the damping level of the double-fed wind turbine generator.

9. The apparatus of claim 8, wherein 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 according to the following equations (1-1), (1-2), and (1-3), respectively,

wherein, V_sa(f) Representing the stator a phase voltage, f representing the frequency,V₁representing the positive sequence fundamental voltage amplitude, V, of the point of common coupling_pRepresents a voltage magnitude of the positive sequence harmonic voltage,respectively representing the initial phase angles, f, of the corresponding components₁、f_pRespectively, the corresponding frequencies are represented by,

I_sa(f) showing the phase a current of the stator,I₁representing the positive sequence fundamental current amplitude, I, of the point of common coupling_pRepresents the current magnitude of the positive sequence harmonic current,respectively represent the initial phase angles of the corresponding components,

I_ra(f) showing the phase a current of the rotor,I_r1、I_rprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,respectively representing the initial phase angles, f, of the corresponding components_rRepresenting the rotor rotation frequency, f_sRepresenting slip frequency.

10. The apparatus according to claim 9, wherein the output voltage expression determination unit determines the output voltage expression according to the following equations (1-4),

where V(s) represents the output voltage, s-j 2 pi f, H_ri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, K_rd(s) represents the decoupling coefficient in the rotor-side dq control strategy, V_p(s) represents the positive sequence harmonic voltage,H_PLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, V_r0Representing the magnitude of the steady-state component of the rotor voltage, V_dcRepresenting the dc capacitor voltage magnitude.

11. The apparatus of claim 10, wherein the stator side impedance analytical expression establishing unit establishes the stator side impedance analytical expression of the doubly-fed wind turbine generator according to the following equation (1-5),

wherein，Z_tp(s) represents the doubly-fed wind turbine side impedance characteristic, L_lsIndicating leakage inductance of the stator winding, L_l′_rIndicating leakage inductance of the rotor winding, R_sRepresenting the resistance of the stator winding, R_r' represents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator₁Representing the fundamental angular velocity.

12. The apparatus according to claim 11, wherein the grid-side impedance model establishing unit establishes the grid-side impedance model according to the following equations (1-6),

wherein Z is_sp(s) represents the impedance characteristic of the power 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.

13. The apparatus according to claim 12, wherein the characteristic function equation establishing unit establishes characteristic function equations of the doubly-fed wind turbine side impedance characteristic and the grid side impedance characteristic according to the following equations (1-7),

Z_sp(s)+Z_tp(s)＝0 (1-7)。

14. the apparatus of claim 13, wherein the oscillation frequency and damping level determination unit is configured to:

solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation_1,2＝α±jβ，

the imaginary part β determines the oscillation frequency of the doubly-fed wind turbine generator, and the real part α determines the damping level of the doubly-fed wind turbine generator.