CN111525611A - Frequency coupling effect-considering doubly-fed grid-connected system subsynchronous oscillation analysis method - Google Patents

Frequency coupling effect-considering doubly-fed grid-connected system subsynchronous oscillation analysis method Download PDF

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CN111525611A
CN111525611A CN202010340956.1A CN202010340956A CN111525611A CN 111525611 A CN111525611 A CN 111525611A CN 202010340956 A CN202010340956 A CN 202010340956A CN 111525611 A CN111525611 A CN 111525611A
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CN111525611B (en
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舒进
张涛
都劲松
杨俊�
牛坤
蒋昊
马晋辉
蒋成文
王靖程
乔越
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Xian Thermal Power Research Institute Co Ltd
Huaneng Group Technology Innovation Center Co Ltd
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Huaneng Group Technology Innovation Center Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

A frequency coupling effect is considered, and a sub-synchronous oscillation analysis method of a double-fed grid-connected system is adopted; firstly, inputting fan parameters, running states and grid-connected parameters of a double-fed grid-connected system; secondly, establishing a double-fed fan external impedance analytical model based on a harmonic linearization method, wherein the main innovation point is that the frequency coupling effect of harmonic current output by the double-fed fan under single-frequency harmonic voltage disturbance is considered, and the external impedance analytical model of the fan is derived under different operating states according to the two operating states of the double-fed fan; then, combining grid-connected parameters, and giving a pole criterion expression suitable for a characteristic equation of the doubly-fed grid-connected system; finally, judging the subsynchronous oscillation stability of the target system according to the calculated poles of the system characteristic equation; the method quantitatively reveals the subsynchronous oscillation mechanism of the doubly-fed grid-connected system, and can quantitatively analyze the subsynchronous oscillation stability of the target doubly-fed grid-connected system.

Description

Frequency coupling effect-considering doubly-fed grid-connected system subsynchronous oscillation analysis method
Technical Field
The invention belongs to the field of electric power systems, relates to the field of stability analysis of a double-fed fan grid-connected system, and particularly relates to a method for analyzing sub-synchronous oscillation of the double-fed grid-connected system by considering a frequency coupling effect.
Background
The proportion of new energy electric energy access systems is gradually increased, and new challenges are brought to the safe and stable operation of the power system, wherein the new challenges include stability problems such as subsynchronous oscillation and the like. At present, a double-fed wind driven generator is widely applied in the field of new energy power generation, and double-fed wind power plant grid-connected electric energy delivery becomes a main mode for realizing large-scale development and utilization of wind energy. The grid-connected and outcoming electric energy of the double-fed wind power plant usually adopts a power transmission line series compensation technology to shorten the electric distance, improve the electric energy transmission capacity and improve the stability of an electric power system. However, because of the control and structural specificity of the doubly-fed wind turbine, another stability problem, subsynchronous oscillation, may be caused by the large-scale, long-distance, point-to-point network power transmission from the outside through the series compensation circuit. With the construction of large-scale wind power bases in China, the modeling, analysis and suppression measures of subsynchronous oscillation induced by double-fed wind power grid connection become problems to be solved urgently. The method has important significance for determining and perfecting the fan subsynchronous oscillation mechanism by researching the subsynchronous oscillation problem of the grid connection of the doubly-fed wind turbine generator set.
The impedance method is based on a small signal disturbance method, impedance models of a doubly-fed fan and an alternating current power grid are respectively established, and the stability of a grid-connected system is judged by utilizing a Nyquist stability criterion.
Disclosure of Invention
In order to solve the problem of the sub-synchronous oscillation of the doubly-fed wind field grid-connected system, the invention aims to provide a method for analyzing the sub-synchronous oscillation of the doubly-fed grid-connected system considering the frequency coupling effect.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the method for analyzing the subsynchronous oscillation of the doubly-fed grid-connected system considering the frequency coupling effect comprises the following steps of:
step 1: inputting double-fed fan parameters
Obtaining the following parameters of the doubly-fed grid-connected system, including: fan grid-connected voltage V1Phase-locked loop PI parameter Kpp，KpiAnd a current inner ring PI parameter K of the rotor side converterp，Ki，KdFan running shaft frequency omegarAnd a resistance R of the power transmission systemLInductor LLTransformer inductance LTSeries compensation capacitor CL；
Step 2: establishing an external impedance analytical model of a doubly-fed fan
Establishing a double-fed fan external impedance analytical model based on a harmonic linearization method, and operating the rotating shaft frequency omega of the fan obtained in the step 1rJudging whether the fan is in a sub-synchronous running state or a super-synchronous running state, specifically:
when the grid voltage has disturbance, only the positive sequence disturbance is considered, and the A phase voltage is set as follows:
vsa(t)＝V1cos(ω1t+θv)+Vpcos(ωpt+θvp) (1)
in the formula, V1、VpRespectively power frequency and disturbance voltage amplitude; omega1、ωpRespectively power frequency and disturbance voltage frequency; thetav、θvpPower frequency and disturbance voltage phase, respectively.
The frequency domain expression is as follows: fundamental component
Figure BDA0002468445300000021
Positive sequence disturbance voltage
Figure BDA0002468445300000022
Due to frequency coupling effects, f will exist in the park transformationpAnd frequency 2f1-fpError of (2):
Figure BDA0002468445300000023
in the formula: thetaPLLFor phase-locked loop output angle, HPLL(s)＝(Kpp+Kpi/s)/s，Kpp，KpiRespectively phase-locked loop proportional and integral constants.
When the grid-side voltage is present fpWhen harmonic waves exist, the fan grid-connected point current simultaneously exists fpAnd 2f1-fpAnd (3) setting a corresponding rotor current time domain expression as the harmonic current of the frequency:
ira(t)＝Ir1cos[(ω1-ωm)t+θii]+Irpcos[(ωp-ωm)t+θrp]+Irp2cos[(2ω1-ωp-ωm)t+θrp2](3)
in the formula Ir1、Irp、Irp2Respectively the rotor fundamental frequency, the disturbance current and the corresponding coupling frequency current amplitude; thetai、θrp、θrp2The initial phases of the three are respectively; omegamThe rotating speed of the rotating shaft.
The equation (3) is convolved with the equation (2), and the park transformation dq axis rotor current I can be obtained by neglecting the quadratic small termrd、IrqAnd a frequency domain expression:
Figure BDA0002468445300000031
according to the inner ring control strategy of the converter at the rotor side of the doubly-fed wind turbine, the current disturbance can be at the reference voltage U of the dq axis of the rotorrd,ref、Urq,refThe following disturbances are caused:
Figure BDA0002468445300000032
in the formula: hr(s)＝Kp+KiS, wherein Kp，KiProportional and integral constants for the current inner loop, respectively. KdTo a feed forward constant for eliminating dq axis coupling.
The frequency component in the formula (5) is known to contain a DC component and ± (f)p-f1) Frequency component Vrd,ref[fp-f1]、Vrq，ref[fp-f1]. Considering the DC component U of the dq-axis current at the steady-state operating pointrd、 UrqWith its reference value Vrd,ref[dc]、Vrq,ref[dc]Equal, then the two component expressions are:
Figure BDA0002468445300000033
Figure BDA0002468445300000034
the three-phase voltage reference value is obtained by inverse coordinate transformation of dq axis voltage reference value, and SPWM input A phase reference voltage V can be obtained by convolutionra,refThe frequency domain expression is:
Figure BDA0002468445300000035
Figure BDA0002468445300000041
neglecting the dynamic error of the switch of the power electronic device, the output voltage of the rotor of the doubly-fed wind turbine can be considered to be equal to the reference voltage, namely:
Figure BDA0002468445300000042
according to the circuit structure of the double-fed fan, the stator voltage, the output current and the rotor voltage can be obtained according to the circuit law and the motor induction relation
Figure BDA0002468445300000043
In the formula, Rs、Rr、Ls、LrThe resistance and the low-high rotor inductance of the stator and the rotor of the double-fed fan are respectively; k is the stator-rotor turn ratio; sigmap(s) is the corresponding slip; i.e. isa、isb、iscThe stator three-phase currents are respectively.
Considering that the stator voltage contains only fpHarmonic voltage component, rewriting the above formula to contain only fpFrequency domain expression of components:
Figure BDA0002468445300000044
1) when a disturbance voltage on the stator side of the doubly-fed wind turbine is induced to the rotor winding,when f isp＜fmWhen the rotor is in a neutral state, the phase sequence of the induced disturbance voltage in the rotor winding is a negative sequence; 2) the output angle of the double-fed fan rotor side phase-locked loop is theta1-θmTherefore, the external impedance characteristics exhibited by the fan are different for different operating conditions.
The combined vertical type (8) and the formula (12) consider that the external impedance of the doubly-fed wind turbine is Zp＝-Vp/IpThen the external impedance Z of the doubly-fed wind turbine in the sub-synchronous frequency band can be deducedp1、Zp2And (5) expressing.
For sub-synchronous operating conditions (theta)1＞θm)：
Figure BDA0002468445300000051
For super-synchronous operating condition (theta)1＜θm)：
Figure BDA0002468445300000052
When theta is1＝θmIn this case, the formula (13) and the formula (14) are equal. Compared with the rotor-side converter, the grid-side converter has almost no influence on the subsynchronous harmonic impedance of the wind turbine, so that the grid-side converter is not considered here.
And step 3: calculating subsynchronous oscillation frequency coupling component of doubly-fed system
Under the single-frequency harmonic voltage disturbance, the double-fed fan outputs harmonic current with frequency coupling effect, namely, when the fan grid-connected point has frequency fpPositive sequence disturbance voltage VpWhen f is included in the output currentpAnd about power frequency f1Symmetrical 2f1-fpThe specific calculation steps of the harmonic component of (a) are as follows:
for the frequency fpAs can be seen from equations (13) and (14), the output current corresponding to the frequency is:
Figure BDA0002468445300000053
since the grid-connected point contains only fpThe voltage of a frequency, so for an output voltage of complementary frequency, the following relation is satisfied:
Figure BDA0002468445300000054
in the formula Ip2For corresponding coupled frequency currents in the stator, σp2And(s) is the slip ratio corresponding to the coupling frequency component.
In conjunction with formulae (13) and (14), with elimination of VpArranged to obtain a coupling frequency 2f1-fpThe current of (a) is:
Figure BDA0002468445300000061
the coupling frequency feedback quantity I of the grid-side converter can be obtained in the same waygp2[2f1-fp]Comprises the following steps:
Figure BDA0002468445300000062
wherein the content of the first and second substances,
Figure BDA0002468445300000063
in the formula, L is the inductance at the outlet of the grid-side converter; hg、KgdControlling parameters for an inner ring in the grid-side converter; i is1Outputting steady-state power frequency voltage for the grid-side converter; u is stator power frequency steady state voltage.
The coupling current component is then:
IG_p2[2f1-fp]＝Ip2[2f1-fp]+Igp2[2f1-fp](20)
equations (17), (18) and (20) describe the quantitative relation of the frequency coupling of the output current components of the doubly-fed wind turbine. When the amplitude and the frequency of the disturbance voltage are determined, the output current of the coupling frequency can be calculated according to the formula (20).
And 4, step 4: pole criterion equation corresponding to target system is deduced by combining grid-connected parameters
Deducing a specific pole criterion equation F(s) corresponding to the target system according to the double-fed fan external impedance analytical expression deduced in the step 3 and the grid-connected parameters obtained in the step 1; the method comprises the following specific steps:
when the stability of the system is analyzed, the output current of the fan, which can be obtained by the equivalent circuit, is as follows:
Figure BDA0002468445300000064
Ig(s) is grid-connected current, and the doubly-fed wind turbine is equivalent to an ideal current source I(s) and an output impedance Zp(s) parallel connection, the power grid is equivalent to an ideal voltage source Ug(s) and grid-connection impedance Zg(s) in series.
Considering that both systems can operate stably independently, the stability of equation (18) depends on the second term on the right of the equation, i.e., 1/(1+ Z)g(s)/Zp(s)), similarly to a forward channel gain of 1 and a negative feedback channel gain of Zg(s)/ZpThe closed loop transfer function of(s) is known from the stability theory, and the pole judgment data equation of the doubly-fed grid-connected system is as follows:
Figure BDA0002468445300000071
taking the fan in the sub-synchronous operation state as an example, if the fan is connected to the grid through a transformer, a power transmission line and a series compensation capacitor, the specific pole criterion equation of the target system is as follows:
Figure BDA0002468445300000072
wherein:
Zg(s)＝RL+s(LT+LL)+1/sCL(24)
Figure BDA0002468445300000073
and 5: judging the subsynchronous oscillation stability of the doubly-fed grid-connected system according to the pole
And 4, calculating a system pole according to the system pole criterion equation deduced in the step 4, and further quantitatively judging the subsynchronous oscillation stability of the system.
And (3) calculating the pole of the target system according to the equation (22), wherein the imaginary part of the pole represents the possible oscillation angular frequency and the real part represents the corresponding system damping according to the stability theory. Because the order of the equation is higher, a plurality of poles may be calculated, and the poles with the corresponding frequency near the power frequency need to be removed during screening. Possible oscillation frequency of the system can be calculated according to the pole imaginary part, if the pole real part is smaller than zero, positive damping is achieved, and the system is stable; the real part is larger than zero and is negative damping, and the system has the risk of subsynchronous oscillation. Meanwhile, the risk degree of the subsynchronous oscillation of the system can be quantitatively evaluated according to the magnitude of the absolute value of the real part.
Compared with the prior art, the invention has the following advantages:
the invention discloses a method for analyzing sub-synchronous oscillation of a double-fed grid-connected system by considering frequency coupling effect. Firstly, inputting fan parameters, running states and grid-connected parameters of a double-fed grid-connected system; secondly, establishing a double-fed fan external impedance analytical model based on a harmonic linearization method, wherein the main innovation point is that the frequency coupling effect of harmonic current output by the double-fed fan under single-frequency harmonic voltage disturbance is considered, and meanwhile, the external impedance analytical model of the fan is derived under different operating states according to two operating states of the double-fed fan; secondly, combining grid-connected parameters, and deducing a pole criterion expression suitable for a characteristic equation of the doubly-fed grid-connected system; and finally, judging the subsynchronous oscillation stability of the target system according to the calculated poles of the system characteristic equation. The method quantitatively reveals the subsynchronous oscillation mechanism of the doubly-fed grid-connected system, and can quantitatively analyze the subsynchronous oscillation stability of the target doubly-fed grid-connected system.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a small-signal equivalent circuit diagram of a current source type grid-connected system.
Fig. 3 is a block diagram of a doubly-fed grid-connected system.
FIG. 4 is a diagram of doubly-fed fan subsynchronous impedance calculation and frequency sweep comparison; fig. 4(a) shows the sub-synchronous operation state, and fig. 4(b) shows the super-synchronous operation state.
FIG. 5 is output current under harmonic voltage disturbance, where: fig. 5(a) is amplitude, and fig. 5(b) is phase.
FIG. 6 is the current for subsynchronous oscillation of the system, where: fig. 6(a) is a waveform, and fig. 6(b) is FFT.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in fig. 1, the present invention is a method for analyzing sub-synchronous oscillation of a doubly-fed grid-connected system considering a frequency coupling effect, including the following steps:
step 1: inputting double-fed fan parameters
Obtaining the following parameters of the doubly-fed grid-connected system, including: fan grid-connected voltage V1Phase-locked loop PI parameter Kpp，KpiAnd a current inner ring PI parameter K of the rotor side converterp，Ki，KdFan running shaft frequency omegarAnd a resistance R of the power transmission systemLInductor LLTransformer inductance LTSeries compensation capacitor CL。
Step 2: establishing an external impedance analytical model of a doubly-fed fan
The grid-connected double-fed fan mainly comprises an induction motor, a rotor side converter, a phase-locked loop and the like.
When the grid voltage has disturbance (only considering positive sequence disturbance), the A-phase voltage is set as:
vsa(t)＝V1cos(ω1t+θv)+Vpcos(ωpt+θvp) (1)
the frequency domain expression is as follows: fundamental component
Figure BDA0002468445300000081
Positive sequence disturbance voltage
Figure BDA0002468445300000082
Due to frequency coupling effects, f will exist in the park transformationpAnd frequency 2f1-fpError of (2):
Figure BDA0002468445300000091
in the formula: hPLL(s)＝(Kpp+Kpi/s)/s，Kpp，KpiPhase-locked loop proportional and integral constants, respectively.
Practical simulation shows that when the voltage of the power grid side exists fpWhen harmonics exist, the current of the grid-connected point of the fan can simultaneously exist fpAnd 2f1-fpHarmonic currents of frequency. Accordingly, the corresponding rotor current time domain expression is set as follows:
ira(t)＝Ir1cos[(ω1-ωm)t+θi]+Irpcos[(ωp-ωm)t+θrp]+Irp2cos[(2ω1-ωp-ωm)t+θrp2](3)
and (3) convolving the equation (3) with the equation (2), and neglecting a quadratic small term to obtain a park transformed rotor current dq axis frequency domain expression:
Figure BDA0002468445300000092
according to the inner ring control strategy of the converter at the rotor side of the doubly-fed wind turbine, the current disturbance can cause the following disturbance on the reference voltage of the dq axis of the rotor:
Figure BDA0002468445300000093
in the formula: hr(s)＝Kp+KiS, wherein Kp，KiProportional and integral constants for the current inner loop, respectively. KdTo a feed forward constant for eliminating dq axis coupling.
The frequency component in the formula (5) is known to contain a DC component and ± (f)p-f1) A frequency component. Considering the steady state operating point, the dc component of the dq-axis current is equal to its reference value. Then the two component expressions are:
Figure BDA0002468445300000094
Figure BDA0002468445300000095
the three-phase voltage reference value is obtained by inverse coordinate transformation of a dq axis voltage reference value, and an SPWM input A-phase reference voltage frequency domain expression obtained by convolution is as follows:
Figure BDA0002468445300000101
Figure BDA0002468445300000102
neglecting the dynamic error of the switch of the power electronic device, the output voltage of the rotor of the doubly-fed wind turbine can be considered to be equal to the reference voltage, namely:
Figure BDA0002468445300000103
according to the circuit structure of the double-fed fan and the combination of the circuit law and the motor induction relation, the requirements among the stator voltage, the output current and the rotor voltage can be obtained:
Figure BDA0002468445300000104
considering that the stator voltage contains only fpHarmonic voltage component, rewriting the above formula to contain only fpFrequency domain expression of components:
Figure BDA0002468445300000105
note that: 1) when disturbance voltage on the stator side of the doubly-fed wind turbine is induced to the rotor winding, when fp＜fmThe phase sequence of the induced disturbance voltage in the rotor winding is negative; 2) the output angle of the double-fed fan rotor side phase-locked loop is theta1-θmTherefore, the external impedance characteristics exhibited by the fan are different for different operating conditions.
The combined vertical type (8) and the formula (12) consider that the external impedance of the doubly-fed wind turbine is Zp＝-Vp/IpAnd then, an external impedance expression of the doubly-fed wind turbine in the sub-synchronous frequency band can be deduced. When theta is1＝θmWhen Z isp1＝Zp2。
For sub-synchronous operating conditions (theta)1＞θm)：
Figure BDA0002468445300000111
For super-synchronous operating condition (theta)1＜θm)：
Figure BDA0002468445300000112
And step 3: calculating subsynchronous oscillation frequency coupling component of doubly-fed system
For the frequency fpAs can be seen from equations (13) and (14), the output current corresponding to the frequency is:
Figure BDA0002468445300000113
since the grid-connected point contains only fpThe voltage of a frequency, so for an output voltage of complementary frequency, the following relation is satisfied:
Figure BDA0002468445300000114
in conjunction with formulae (13) and (14), with elimination of VpArranged to obtain a coupling frequency 2f1-fpThe current of (a) is:
Figure BDA0002468445300000115
similarly, the coupling frequency feedback quantity of the network side converter is obtained as follows:
Figure BDA0002468445300000116
wherein the content of the first and second substances,
Figure BDA0002468445300000117
the coupling current component is then:
IG_p2[2f1-fp]＝Ip2[2f1-fp]+Igp2[2f1-fp](20)
it can be seen that the equations (17), (18), (20) describe the quantitative relationship of the frequency coupling of the doubly-fed fan output current components. When the amplitude and the frequency of the disturbance voltage are determined, the output current of the coupling frequency can be calculated according to the formula (20).
And 4, step 4: pole criterion equation corresponding to target system is deduced by combining grid-connected parameters
Fig. 2 is a diagram of a small-signal equivalent circuit of a current source type grid-connected system analyzed by an impedance method, and it is noted that this is suitable for the stability analysis of a target system studied by the present invention. U shapePCC(s) is the fan grid-connected point voltage, Ig(s) is grid-connected current, and the doubly-fed wind turbine is equivalent to an ideal current source I(s) and an output impedance Zp(s) parallel connection, the power grid is equivalent to an ideal voltage source Ug(s) and grid-connection impedance Zg(s) in series.
When analyzing the stability of the system shown in fig. 3, the fan output current obtained according to the equivalent circuit is:
Figure BDA0002468445300000121
considering that both systems can operate stably independently, the stability of equation (18) depends on the second term on the right of the equation, i.e., 1/(1+ Z)g(s)/Zp(s)). Similar to a forward channel gain of 1, the negative feedback channel gain is Zg(s)/Zp(s) closed loop transfer function. According to the stability theory, the pole judgment data equation of the doubly-fed grid-connected system is as follows:
Figure BDA0002468445300000122
taking the fan in the sub-synchronous operation state as an example, if the fan is connected to the grid through a transformer, a power transmission line and a series compensation capacitor, the specific pole criterion equation of the target system is as follows:
Figure BDA0002468445300000123
fig. 3 shows a diagram of a doubly-fed grid-connected system, where:
Zg(s)＝RL+s(LT+LL)+1/sCL(24)
Figure BDA0002468445300000131
and 5: judging the subsynchronous oscillation stability of the doubly-fed grid-connected system according to the pole
And (4) calculating the pole of the target system according to the equation (25), wherein the imaginary part of the pole represents the possible oscillation angular frequency and the real part represents the corresponding system damping according to the stability theory. And during screening, the poles of the corresponding frequency near the power frequency need to be removed. Possible oscillation frequency of the system can be calculated according to the pole imaginary part, and if the pole real part is smaller than zero, the system is stable; the real part is greater than zero and the system is at risk of subsynchronous oscillation. Meanwhile, the risk degree of the subsynchronous oscillation of the system can be quantitatively evaluated according to the magnitude of the absolute value of the real part.
For verificationThe correctness of the analysis is verified by simulation according to the following parameters: 50Hz fundamental voltage amplitude V1690V, perturbation voltage: vp＝0.96ej(-1)(ii) a Current inner loop PI parameter Kp＝0.6，K i10; phase-locked loop control parameters: kpp＝500，Kpi500; reference value of rotor current Ir,ref＝0.1723ej(-1.87)(ii) a Rotor voltage reference value: u shaper,ref＝0.2302ej(-1.25)Rotation speed of the rotation shaft (per unit value): 0.8. and (3) injecting disturbance voltages with different frequencies into the grid-connected point of the doubly-fed fan within the range of the secondary synchronous frequency band of the doubly-fed fan (0-30Hz), and comparing the obtained frequency sweep result with the calculation result of the formula (13), for example, as shown in fig. 4 (a).
Changing the ultra-synchronous running state of the double-fed fan during running and the 50Hz fundamental voltage amplitude V1690V, current inner loop PI parameter Kp＝1.5，Ki0.004; phase-locked loop control parameters: kpp＝0.05，Kpi0.002; reference value of rotor current Ir,ref＝7.635ej(1.3183)(ii) a Rotor voltage reference value: u shaper,ref＝3.575ej(-2.281)Rotation speed of the rotation shaft (per unit value): 1.2. and (3) injecting disturbance voltages with different frequencies into the grid-connected point of the doubly-fed fan within the subsynchronous frequency range (0-30Hz) of the doubly-fed fan, and comparing the obtained frequency sweep result with the calculation result of the formula (14), for example, as shown in fig. 4 (b).
As can be seen from FIG. 4, the frequency sweeping result is consistent with the calculation result, so that the method can correctly calculate the analytical impedance of the doubly-fed fan in different operation states within the subsynchronous frequency range (0-30 Hz).
Taking the subsynchronous operation state as an example, the disturbance frequency is set as follows: 7Hz, the parameters are substituted into the formula (13), and the 7Hz output current with the same frequency as the disturbance voltage can be calculated as follows:
Ip(fp)＝18∠2.57A (26)
by substituting the above results into equation (20), the output current with a coupling frequency of 93Hz can be calculated as:
Ip2(2f1-fp)＝4.1∠0.21A (27)
simulation results as shown in the following figure, when a disturbance voltage of 7Hz exists at the PCC point, it can be seen that a harmonic component of 7/93Hz exists at the same time in the output current, and the amplitude and phase are respectively shown in fig. 5(a), (b).
Note that the fundamental component amplitude in fig. 5(a) is outside the vertical axis range, and its amplitude has been marked in the figure. For clarity, the phase of the components of FIG. 5(b) other than 7/93Hz have been filtered out. It can be seen that the 7/93Hz current has an amplitude of about 0.017kA and 0.004kA, respectively, and a phase of about 2.6 and 0.2, respectively, consistent with the results of the equations (26), (27).
In order to verify a pole criterion equation corresponding to the target system in the formula (23), parameters of a power transmission system with a high voltage level are reduced to 35kV, the resistance is 27.55 omega, the inductance is 0.63948H, the series compensation capacitance is 720uF, the proportion parameter of the wind power system is adjusted to 0.65, the short-circuit impedance of a 35/0.69kV transformer is adjusted to 0.065, and other conditions are not changed. The pole at this time of the system is calculated according to the equation (25): 0.266+ j 29.4. According to the polar point calculation, the system may generate oscillation of 29.4/(2 pi) ═ 5.16 Hz.
Simulation is performed on a PSCAD platform, and the obtained line current and FFT thereof are shown in FIG. 6:
as can be seen from FIG. 6, at this time, the system is critically oscillated with an oscillation frequency of about 5Hz, which is consistent with the calculation result of the pole criterion equation.
In summary, the invention discloses a method for analyzing the sub-synchronous oscillation of a doubly-fed grid-connected system, which takes the frequency coupling effect into account. Firstly, establishing a double-fed fan external impedance analytical model based on a harmonic linearization method, wherein the main innovation point is that the frequency coupling effect of harmonic current output by a double-fed fan under single-frequency harmonic voltage disturbance is considered, and meanwhile, the external impedance analytical model of the double-fed fan is derived under different operation states according to two operation states of the double-fed fan; then, deriving a pole criterion expression suitable for the doubly-fed grid-connected system characteristic equation; and finally, judging the subsynchronous oscillation stability of the target system according to the calculated poles of the system characteristic equation. The method quantitatively reveals the subsynchronous oscillation mechanism of the doubly-fed grid-connected system, and can quantitatively analyze the subsynchronous oscillation stability of the target doubly-fed grid-connected system.

Claims (4)

1. The method for analyzing the subsynchronous oscillation of the doubly-fed grid-connected system considering the frequency coupling effect is characterized by comprising the following steps of:
step 1: inputting parameters of a double-fed fan;
obtaining the following parameters of the doubly-fed grid-connected system, including: fan grid-connected voltage V1Phase-locked loop PI parameter Kpp，KpiAnd a current inner ring PI parameter K of the rotor side converterp，Ki，KdFan running shaft frequency omegarAnd a resistance R of the power transmission systemLInductor LLTransformer inductance LTSeries compensation capacitor CL；
Step 2: establishing a double-fed fan external impedance analytical model;
establishing a double-fed fan external impedance analytical model based on a harmonic linearization method, and operating the rotating shaft frequency omega of the fan according to the frequency obtained in the step 1rJudging whether the fan is in a sub-synchronous running state or a super-synchronous running state;
and step 3: calculating the subsynchronous oscillation frequency coupling component of the doubly-fed system;
and 4, step 4: deducing a pole criterion equation corresponding to the target system by combining the grid-connected parameters;
deducing a specific pole criterion equation F(s) corresponding to the target system according to the double-fed fan external impedance analytical expression deduced in the step 3 and the grid-connected parameters obtained in the step 1;
and 5: judging the subsynchronous oscillation stability of the doubly-fed grid-connected system according to the pole;
calculating a system pole by the system pole criterion equation deduced in the step 4 so as to quantitatively judge the subsynchronous oscillation stability of the system, namely calculating the pole of the target system, wherein according to the stability theory, the imaginary part of the pole represents possible oscillation angular frequency, and the real part represents corresponding system damping; because the order of the equation is higher, a plurality of poles can be calculated, and the poles with the corresponding frequency near the power frequency need to be removed during screening; possible oscillation frequency of the system can be calculated according to the pole imaginary part, if the pole real part is smaller than zero, positive damping is achieved, and the system is stable; the real part is larger than zero and is negative damping, so that the system has the risk of subsynchronous oscillation; meanwhile, the risk degree of the subsynchronous oscillation of the system can be quantitatively evaluated according to the magnitude of the absolute value of the real part.
2. The method for analyzing the subsynchronous oscillation of the doubly-fed grid-connected system in consideration of the frequency coupling effect according to claim 1, wherein the step 2 specifically comprises:
when the grid voltage has disturbance, only the positive sequence disturbance is considered, and the A phase voltage is set as follows:
vsa(t)＝V1cos(ω1t+θv)+Vpcos(ωpt+θvp) (1)
in the formula, V1、VpRespectively power frequency and disturbance voltage amplitude; omega1、ωpRespectively power frequency and disturbance voltage frequency; thetav、θvpPower frequency and disturbance voltage phases respectively;
the frequency domain expression is as follows: fundamental component
Figure FDA0002468445290000021
Positive sequence disturbance voltage
Figure FDA0002468445290000022
Due to frequency coupling effects, f will exist in the park transformationpAnd frequency 2f1-fpError of (2):
Figure FDA0002468445290000023
in the formula: thetaPLLFor phase-locked loop output angle, HPLL(s)＝(Kpp+Kpi/s)/s，Kpp，KpiPhase-locked loop proportion and integral constant respectively;
when the grid-side voltage is present fpWhen harmonic waves exist, the fan grid-connected point current simultaneously exists fpAnd 2f1-fpThe harmonic current of the frequency is set to be,setting a corresponding rotor current time domain expression as follows:
ira(t)＝Ir1cos[(ω1-ωm)t+θi]+Irpcos[(ωp-ωm)t+θrp]+Irp2cos[(2ω1-ωp-ωm)t+θrp2](3)
in the formula Ir1、Irp、Irp2Respectively the rotor fundamental frequency, the disturbance current and the corresponding coupling frequency current amplitude; thetai、θrp、θrp2The initial phases of the three are respectively; omegamThe rotating speed of the rotating shaft;
the equation (3) is convolved with the equation (2), and the park transformation dq axis rotor current I can be obtained by neglecting the quadratic small termrd、IrqAnd a frequency domain expression:
Figure FDA0002468445290000024
according to the inner ring control strategy of the converter at the rotor side of the doubly-fed wind turbine, the current disturbance can be at the reference voltage U of the dq axis of the rotorrd,ref、Urq,refThe following disturbances are caused:
Figure FDA0002468445290000025
in the formula: hr(s)＝Kp+KiS, wherein Kp，KiRespectively are the proportional constant and the integral constant of the current inner loop; kdA feed forward constant to cancel the dq axis coupling;
the frequency component in the formula (5) is known to contain a DC component and ± (f)p-f1) Frequency component Vrd,ref[fp-f1]、Vrq,ref[fp-f1](ii) a Considering the DC component U of the dq-axis current at the steady-state operating pointrd、UrqWith its reference value Vrd,ref[dc]、Vrq,ref[dc]Equal, then the two component expressions are:
Figure FDA0002468445290000031
Figure FDA0002468445290000032
the three-phase voltage reference value is obtained by inverse coordinate transformation of dq axis voltage reference value, and SPWM input A phase reference voltage V can be obtained by convolutionra,refThe frequency domain expression is:
Figure FDA0002468445290000033
Figure FDA0002468445290000034
neglecting the dynamic error of the switch of the power electronic device, the output voltage of the rotor of the doubly-fed wind turbine can be considered to be equal to the reference voltage, namely:
Figure FDA0002468445290000035
according to the circuit structure of the double-fed fan, the stator voltage, the output current and the rotor voltage can be obtained according to the circuit law and the motor induction relation
Figure FDA0002468445290000036
In the formula, Rs、Rr、Ls、LrThe resistance and the low-high rotor inductance of the stator and the rotor of the double-fed fan are respectively; k is the stator-rotor turn ratio; sigmap(s) is the corresponding slip; i.e. isa、isb、iscRespectively stator three-phase currents;
considering that the stator voltage contains only fpHarmonic voltage component, rewriting the above formula to contain only fpFrequency domain representation of the components:
Figure FDA0002468445290000041
1) when disturbance voltage on the stator side of the doubly-fed wind turbine is induced to the rotor winding, when fp＜fmThe phase sequence of the induced disturbance voltage in the rotor winding is negative; 2) the output angle of the double-fed fan rotor side phase-locked loop is theta1-θmTherefore, the external impedance characteristics of the fan are different for different running states;
the combined vertical type (8) and the formula (12) consider that the external impedance of the doubly-fed wind turbine is Zp＝-Vp/IpThen the external impedance Z of the doubly-fed wind turbine in the sub-synchronous frequency band can be deducedp1、Zp2An expression;
for sub-synchronous operating conditions (theta)1＞θm)：
Figure FDA0002468445290000042
For super-synchronous operating condition (theta)1＜θm)：
Figure FDA0002468445290000043
When theta is1＝θmWhen the formula (13) and the formula (14) are equal; compared with the rotor-side converter, the grid-side converter has almost no influence on the subsynchronous harmonic impedance of the wind turbine, so that the grid-side converter is not considered here.
3. The method for analyzing the subsynchronous oscillation of the doubly-fed grid-connected system in consideration of the frequency coupling effect according to claim 1, wherein the step 3 specifically comprises:
for the frequency fpAs can be seen from equations (13) and (14), the output current corresponding to the frequency is:
Figure FDA0002468445290000044
since the grid-connected point contains only fpThe voltage of a frequency, so for an output voltage of complementary frequency, the following relation is satisfied:
Figure FDA0002468445290000051
in the formula Ip2For corresponding coupled frequency currents in the stator, σp2(s) is the slip corresponding to the coupled frequency component;
in conjunction with formulae (13) and (14), with elimination of VpArranged to obtain a coupling frequency 2f1-fpThe current of (a) is:
Figure FDA0002468445290000052
the coupling frequency feedback quantity I of the grid-side converter can be obtained in the same waygp2[2f1-fp]Comprises the following steps:
Figure FDA0002468445290000053
wherein the content of the first and second substances,
Figure FDA0002468445290000054
in the formula, L is the inductance at the outlet of the grid-side converter; hg、KgdControlling parameters for an inner ring in a network side converter; i is1Outputting steady-state power frequency voltage for the grid-side converter; u is stator power frequency steady state voltage;
the coupling current component is then:
IG_p2[2f1-fp]＝Ip2[2f1-fp]+Igp2[2f1-fp](20)
the equations (17), (18) and (20) describe the quantitative relation of the frequency coupling of the output current components of the doubly-fed wind turbine; when the amplitude and the frequency of the disturbance voltage are determined, the output current of the coupling frequency can be calculated according to the formula (20).
4. The method for analyzing the subsynchronous oscillation of the doubly-fed grid-connected system in consideration of the frequency coupling effect according to claim 1, wherein the step 4 specifically comprises:
when the stability of the system is analyzed, the output current of the fan, which can be obtained by the equivalent circuit, is as follows:
Figure FDA0002468445290000055
Ig(s) is grid-connected current, and the doubly-fed wind turbine is equivalent to an ideal current source I(s) and an output impedance Zp(s) parallel connection, the power grid is equivalent to an ideal voltage source Ug(s) and grid-connection impedance Zg(s) in series;
considering that both systems can operate stably independently, the stability of equation (18) depends on the second term on the right side of the equation, i.e., 1/(1+ Z)g(s)/Zp(s)) similar to a forward channel gain of 1 and a negative feedback channel gain of Zg(s)/ZpThe closed loop transfer function of(s) is known from the stability theory, and the pole criterion equation of the doubly-fed grid-connected system is as follows:
Figure FDA0002468445290000061
taking the case that the fan is in a sub-synchronous operation state, if the fan is connected to the grid through the transformer, the transmission line and the series compensation capacitor, the specific pole criterion equation of the target system is as follows:
Figure FDA0002468445290000062
wherein:
Zg(s)＝RL+s(LT+LL)+1/sCL(24)
Figure FDA0002468445290000063
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