CN111525611B - Subsynchronous oscillation analysis method of doubly-fed grid-connected system considering frequency coupling effect - Google Patents
Subsynchronous oscillation analysis method of doubly-fed grid-connected system considering frequency coupling effect Download PDFInfo
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- H—ELECTRICITY
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- H—ELECTRICITY
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The subsynchronous oscillation analysis method of the doubly-fed grid-connected system is used for considering the frequency coupling effect; firstly, inputting fan parameters, running states and grid-connected parameters of a doubly-fed grid-connected system; secondly, establishing an external impedance analysis model of the doubly-fed wind turbine based on a harmonic linearization method, wherein the main innovation point is that the frequency coupling effect of the output harmonic current of the doubly-fed wind turbine under single-frequency harmonic voltage disturbance is considered, and the external impedance analysis model of the wind turbine is deduced under different running states according to two running states of the doubly-fed wind turbine; then, combining grid-connected parameters to give 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 poles of the calculated system characteristic equation; the invention quantitatively reveals the subsynchronous oscillation mechanism of the double-fed grid-connected system, and can quantitatively analyze the subsynchronous oscillation stability of the target double-fed grid-connected system.
Description
Technical Field
The invention belongs to the field of power systems, relates to the field of stability analysis of doubly-fed fan grid-connected systems, and particularly relates to a doubly-fed grid-connected system subsynchronous oscillation analysis method considering frequency coupling effects.
Background
The proportion of the new energy and the electric energy access system is gradually increased, so that new challenges are brought to the safe and stable operation of the electric power system, and the problems of stability such as subsynchronous oscillation and the like are involved. At present, the doubly-fed wind power generator is widely applied to the field of new energy power generation, and the grid-connected external power supply of the doubly-fed wind power plant becomes a main mode for realizing large-scale development and utilization of wind energy. The grid-connected external power transmission energy of the doubly-fed wind power plant often adopts a transmission line series compensation technology, so that the electric distance is shortened, the electric energy transmission capacity is improved, and the stability of a power system is improved. However, because of the specificity of doubly-fed fan control and construction, this large-scale, remote, point-to-network power delivery via series compensation lines may present another stability problem, subsynchronous oscillation. Along with the construction of a large-scale wind power base in China, modeling, analysis and inhibition measures of subsynchronous oscillation induced by doubly-fed wind power grid connection are all problems to be solved urgently. The research on the subsynchronous oscillation problem of the double-fed wind turbine generator system grid connection has important significance for defining and perfecting the subsynchronous oscillation mechanism of the fan.
The impedance method is based on a small signal disturbance method, impedance models of the doubly-fed fan and the alternating-current power grid are respectively established, the stability of the grid-connected system is judged by utilizing a Nyquist stability criterion, and the difficulty and the key point of the method are that a small signal impedance analysis formula of the doubly-fed fan is obtained.
Disclosure of Invention
In order to solve the problem of the double-fed wind field grid-connected subsynchronous oscillation, the invention aims to provide a double-fed grid-connected system subsynchronous oscillation analysis method which takes the frequency coupling effect into account, a double-fed fan small signal impedance analysis model which takes the frequency coupling effect into account is established based on a harmonic linearization method, the impedance model difference of the double-fed fan under different running states is taken into account, the frequency coupling effect of harmonic current output by the double-fed fan under single-frequency harmonic voltage disturbance is taken into account, the frequency coupling quantitative relation of the harmonic current is output, and finally a pole criterion equation of a target system is deduced, so that subsynchronous stability of the system is judged, and subsynchronous oscillation characteristics of the double-fed grid-connected system are comprehensively analyzed.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
the subsynchronous oscillation analysis method of the doubly-fed grid-connected system considering the frequency coupling effect comprises the following steps:
step 1: inputting parameters of doubly-fed fans
The parameters of the following doubly-fed grid-connected system are obtained, including: grid-connected voltage V of fan 1 Phase locked loop PI parameter K pp ，K pi Rotor-side converter current inner loop PI parameter K p ，K i ，K d Frequency omega of fan operation rotating shaft r Resistor R of power transmission system L Inductance L L Inductance L of transformer T Series compensation capacitor C L ；
Step 2: establishing a doubly-fed type fan external impedance analysis model
Building a doubly-fed type fan external impedance analysis model based on a harmonic linearization method, and obtaining fan operation rotating shaft frequency omega according to the step 1 r Judging whether the fan is in a subsynchronous operation state or a supersynchronous operation state, specifically:
when the power grid voltage has disturbance, only positive sequence disturbance is considered, and the A-phase voltage is set as:
v sa (t)＝V 1 cos(ω 1 t+θ v )+V p cos(ω p t+θ vp ) (1)
wherein V is 1 、V p The power frequency and the disturbance voltage amplitude are respectively; omega 1 、ω p The power frequency and the disturbance voltage frequency are respectively; θ v 、θ vp The power frequency and the disturbance voltage phases are respectively.
The frequency domain expression is: fundamental componentPositive sequence disturbance voltage->
F may be present in the park transform due to frequency coupling effects p And frequency 2f 1 -f p Error of (2):
wherein: θ PLL For phase-locked loop output angle H PLL (s)＝(K pp +K pi /s)/s，K pp ，K pi Phase locked loop proportional and integral constants, respectively.
When the voltage on the power grid side exists f p When in harmonic wave, the fan grid-connected point current simultaneously has f p And 2f 1 -f p Harmonic current of frequency, set the corresponding rotor current time domain expression as:
i ra (t)＝I r1 cos[(ω 1 -ω m )t+θi i ]+I rp cos[(ω p -ω m )t+θ rp ]+I rp2 cos[(2ω 1 -ω p -ω m )t+θ rp2 ] (3)
wherein I is r1 、I rp 、I rp2 The rotor fundamental frequency, the disturbance current and the corresponding coupling frequency current amplitude are respectively; θ i 、θ rp 、θ rp2 Respectively the initial phases of the three; omega m Is the rotating speed of the rotating shaft.
Rolling the formula (3) and the formula (2)The product is ignored, and the dq-axis rotor current I after park transformation can be obtained rd 、I rq Frequency domain expression:
according to the control strategy of the inner ring of the doubly-fed wind turbine rotor-side converter, current disturbance can be generated on the dq axis of the rotor by reference voltage U rd,ref 、U rq,ref The above causes the following disturbances:
wherein: h r (s)＝K p +K i S, where K p ，K i The proportional and integral constants of the inner loop of the current, respectively. K (K) d To a feed-forward constant that eliminates dq axis coupling.
The frequency component in the analysis formula (5) is known to contain a DC component and. + -. (f) p -f 1 ) Frequency component V rd,ref [f p -f 1 ]、V rq，ref [f p -f 1 ]. Considering the dc component U of the dq-axis current at the steady state operating point rd 、U rq With reference value V rd,ref [dc]、V rq,ref [dc]Equal, then the two component expressions are respectively:
the three-phase voltage reference value is obtained by the coordinate inverse transformation of the dq axis voltage reference value, and the SPWM input A-phase reference voltage V can be obtained by convolution ra,ref The frequency domain expression is:
ignoring power electronics switching dynamics errors, the doubly fed wind machine rotor output voltage can be considered equal to the reference voltage, namely:
according to the circuit structure of the doubly-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
Wherein R is s 、R r 、L s 、L r The stator and rotor resistance and the low-cost rotor inductance of the doubly-fed wind turbine are respectively; k is the turns ratio of stator and rotor; sigma (sigma) p (s) is the corresponding slip; i.e sa 、i sb 、i sc Respectively stator three-phase currents.
Considering that the stator voltage contains only f p A harmonic voltage component, in which the above is rewritten to contain only f p Frequency domain expression of the components:
1) When the disturbance voltage on the stator side of the doubly-fed wind machine is induced to the rotor winding, when f p ＜f m When the phase sequence of disturbance voltage induced in the rotor winding is negative sequence; 2) The output angle of the phase-locked loop at the rotor side of the doubly-fed wind turbine is theta 1 -θ m The blower therefore exhibits different external impedance characteristics for different operating conditions.
The combination of the formula (8) and the formula (12) takes the external impedance Z of the doubly-fed fan into consideration p ＝-V p /I p The external impedance Z of the doubly-fed wind turbine in the sub-synchronous frequency band can be deduced p1 、Z p2 An expression.
For subsynchronous operating states (θ 1 ＞θ m )：
For the super-synchronous operating state (θ 1 ＜θ m )：
When theta is as 1 ＝θ m In this case, the expression (13) and the expression (14) are equal. In contrast to the rotor-side converter, the grid-side converter has little effect on the subsynchronous harmonic impedance of the wind turbine, and is therefore not considered here.
Step 3: calculating sub-synchronous oscillation frequency coupling component of doubly-fed system
Under the disturbance of single-frequency harmonic voltage, the doubly-fed fan outputs harmonic current with frequency coupling effect, namely when the fan grid-connected point exists at the frequency f p Positive sequence disturbance voltage V of (2) p When the output current contains f p And about power frequency f 1 Symmetrical 2f 1 -f p The specific calculation steps are as follows:
for frequency f p As can be seen from the following equations (13) and (14), the output current at the corresponding frequency is:
since the point of connection contains f only p The voltage at the frequency, therefore, satisfies the following relationship for the output voltage at the complementary frequency:
wherein I is p2 For corresponding coupling frequency currents in the stator, sigma p2 And(s) is the slip corresponding to the coupled frequency component.
Simultaneously with formulas (13) and (14), V is eliminated p The coupling frequency 2f can be obtained by arrangement 1 -f p The current of (2) is:
coupling frequency feedback quantity I of similarly available network side converter gp2 [2f 1 -f p ]The method comprises the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,
wherein L is inductance at the outlet of the grid-side converter; h g 、K gd The control parameters of an inner ring in the grid-side converter are used; i 1 Outputting steady-state power frequency voltage for the grid-side converter; u is the stator power frequency steady-state voltage.
The coupling current component is:
I G_p2 [2f 1 -f p ]＝I p2 [2f 1 -f p ]+I gp2 [2f 1 -f p ] (20)
equations (17), (18), (20) describe the quantitative relationship of frequency coupling of the doubly fed blower output current components. After the amplitude and frequency of the disturbance voltage are determined, the output current of the coupling frequency can be calculated according to equation (20), respectively.
Step 4: deriving pole criterion equation corresponding to target system by combining grid-connected parameters
Deducing a specific pole criterion equation F(s) corresponding to the target system according to the external impedance analysis 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 equivalent circuit can obtain the fan output current as follows:
I g (s) is grid-connected current, and the equivalent of the doubly-fed fan is an ideal current source I(s) and output impedance Z p (s) parallel connection, and the power grid is equivalent to an ideal voltage source U g (s) and grid-tie impedance Z g (s) series connection.
Considering that both systems can operate independently and stably, the stability of equation (18) depends on the second term on the right of the equation, i.e., 1/(1+Z) g (s)/Z p (s)), similar to a forward channel gain of 1, a negative feedback channel gain of Z g (s)/Z p The closed loop transfer function of(s), as known from the stability theory, is that the pole criterion equation of the doubly-fed grid-connected system is:
taking the case that the fan is in a subsynchronous operation state, the fan is connected with the grid through a transformer, a power transmission line and a series compensation capacitor, and then a specific pole criterion equation of the target system is as follows:
wherein:
Z g (s)＝R L +s(L T +L L )+1/sC L (24)
step 5: determining subsynchronous oscillation stability of doubly-fed grid-connected system according to poles
And (3) calculating a system pole by the system pole criterion equation deduced in the step (4) so as to quantitatively judge the stability of the subsynchronous oscillation of the system.
The pole of the target system can be calculated according to the equation (22), and according to the stability theory, the imaginary part of the pole represents the possible oscillation angular frequency, and the real part represents the corresponding system damping. Because the equation order is higher, a plurality of poles can be calculated, and poles with corresponding frequencies near the power frequency need to be removed when screening is performed. The 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 adopted, and the system is stable; the real part is greater than zero, negative damping, and the system is at risk of subsynchronous oscillations. Meanwhile, according to the absolute value of the real part, the risk degree of subsynchronous oscillation of the system can be quantitatively evaluated.
Compared with the prior art, the invention has the following advantages:
the invention discloses a subsynchronous oscillation analysis method of a doubly-fed grid-connected system considering frequency coupling effect. Firstly, inputting fan parameters, running states and grid-connected parameters of a doubly-fed grid-connected system; secondly, establishing an external impedance analysis model of the doubly-fed wind turbine based on a harmonic linearization method, wherein the main innovation point is that the frequency coupling effect of the output harmonic current of the doubly-fed wind turbine under single-frequency harmonic voltage disturbance is considered, and the external impedance analysis model of the wind turbine is deduced under different running states according to two running states of the doubly-fed wind turbine; then, deriving a pole criterion expression suitable for a characteristic equation of the doubly-fed grid-connected system by combining grid-connected parameters; and finally, judging the subsynchronous oscillation stability of the target system according to the poles of the calculated system characteristic equation. The invention quantitatively reveals the subsynchronous oscillation mechanism of the double-fed grid-connected system, and can quantitatively analyze the subsynchronous oscillation stability of the target double-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 grid-connected system.
Fig. 3 is a block diagram of a doubly-fed grid-tie system.
FIG. 4 is a graph of doubly fed fan subsynchronous impedance calculation versus sweep frequency; fig. 4 (a) shows a subsynchronous operation state, and fig. 5 (b) shows a supersynchronous operation state.
Fig. 5 is an output current at harmonic voltage disturbance, wherein: fig. 5 (a) is an amplitude, and fig. 5 (b) is a phase.
Fig. 6 is a diagram of current flow at system subsynchronous oscillation, wherein: fig. 6 (a) is a waveform, and fig. 6 (b) is an FFT.
Detailed Description
The invention will be described in further detail with reference to the drawings and examples.
As shown in FIG. 1, the invention relates to a frequency coupling effect-based subsynchronous oscillation analysis method for a double-fed grid-connected system, which comprises the following steps:
step 1: inputting parameters of doubly-fed fans
The parameters of the following doubly-fed grid-connected system are obtained, including: grid-connected voltage V of fan 1 Phase locked loop PI parameter K pp ，K pi Rotor-side converter current inner loop PI parameter K p ，K i ，K d Frequency omega of fan operation rotating shaft r Resistor R of power transmission system L Inductance L L Inductance L of transformer T Series compensation capacitor C L 。
Step 2: establishing a doubly-fed type fan external impedance analysis model
The grid-connected double-fed fan mainly comprises an induction motor, a rotor side converter, a phase-locked loop and the like.
When there is a disturbance in the grid voltage (only positive sequence disturbance is considered), let the a-phase voltage be:
v sa (t)＝V 1 cos(ω 1 t+θ v )+V p cos(ω p t+θ vp ) (1)
the frequency domain expression is: fundamental componentPositive sequence disturbance voltage->
F may be present in the park transform due to frequency coupling effects p And frequency 2f 1 -f p Error of (2):
wherein: h PLL (s)＝(K pp +K pi /s)/s，K pp ，K pi Phase locked loop proportional and integral constants, respectively.
Practical simulation shows that when the voltage on the power grid side exists f p When in harmonic wave, the fan grid-connected point current simultaneously has f p And 2f 1 -f p Harmonic current of frequency. Accordingly, the corresponding rotor current time domain expression is set as follows:
i ra (t)＝I r1 cos[(ω 1 -ω m )t+θ i ]+I rp cos[(ω p -ω m )t+θ rp ]+I rp2 cos[(2ω 1 -ω p -ω m )t+θ rp2 ] (3)
convolving equation (3) with equation (2), ignoring the quadratic term, yields a park-transformed rotor current dq-axis frequency domain expression:
according to the doubly-fed wind turbine rotor-side converter inner ring control strategy, the current disturbance causes the following disturbances on the rotor dq-axis reference voltage:
wherein: h r (s)＝K p +K i S, where K p ，K i The proportional and integral constants of the inner loop of the current, respectively.K d To a feed-forward constant that eliminates dq axis coupling.
The frequency component in the analysis formula (5) is known to contain a DC component and. + -. (f) p -f 1 ) A frequency component. Considering that the dc component of the dq-axis current is equal to its reference value at the steady state operating point. The two component expressions are:
the three-phase voltage reference value is obtained by reversely transforming the dq axis voltage reference value through coordinates, and the SPWM input A-phase reference voltage frequency domain expression can be obtained by convolution as follows:
ignoring power electronics switching dynamics errors, the doubly fed wind machine rotor output voltage can be considered equal to the reference voltage, namely:
according to the circuit structure of the doubly-fed fan, the induction relation of the motor is combined according to the circuit law, and the stator voltage, the output current and the rotor voltage can be obtained, so that the following conditions are satisfied:
considering that the stator voltage contains only f p A harmonic voltage component, in which the above is rewritten to contain only f p Frequency domain expression of the components:
note that: 1) When the disturbance voltage on the stator side of the doubly-fed wind machine is induced to the rotor winding, when f p ＜f m When the phase sequence of disturbance voltage induced in the rotor winding is negative sequence; 2) The output angle of the phase-locked loop at the rotor side of the doubly-fed wind turbine is theta 1 -θ m The blower therefore exhibits different external impedance characteristics for different operating conditions.
The combination of the formula (8) and the formula (12) takes the external impedance Z of the doubly-fed fan into consideration p ＝-V p /I p The external impedance expression of the doubly-fed wind machine in the subsynchronous frequency band can be deduced. When theta is as 1 ＝θ m When Z is p1 ＝Z p2 。
For subsynchronous operating states (θ 1 ＞θ m )：
For the super-synchronous operating state (θ 1 ＜θ m )：
Step 3: calculating sub-synchronous oscillation frequency coupling component of doubly-fed system
For frequency f p As can be seen from the following equations (13) and (14), the output current at the corresponding frequency is:
since the point of connection contains f only p Voltage of frequency, thereforeFor output voltages of complementary frequencies, the following relation is satisfied:
simultaneously with formulas (13) and (14), V is eliminated p The coupling frequency 2f can be obtained by arrangement 1 -f p The current of (2) is:
the coupling frequency feedback quantity of the network side converter can be obtained by the same method as the following:
wherein, the liquid crystal display device comprises a liquid crystal display device,
the coupling current component is:
I G_p2 [2f 1 -f p ]＝I p2 [2f 1 -f p ]+I gp2 [2f 1 -f p ] (20)
it can be seen that equations (17), (18), (20) describe the quantitative relationship of frequency coupling of the doubly fed blower output current components. After the amplitude and frequency of the disturbance voltage are determined, the output current of the coupling frequency can be calculated according to equation (20), respectively.
Step 4: deriving pole criterion equation corresponding to target system by combining grid-connected parameters
Fig. 2 is a small-signal equivalent circuit diagram of a current source grid-connected system analyzed by adopting an impedance method, and the small-signal equivalent circuit diagram is suitable for analyzing the stability of a target system researched by the invention. U (U) PCC (s) is the voltage of the grid-connected point of the fan, I g (s) is grid-connected current, and the equivalent of the doubly-fed fan is an ideal current source I(s) and output impedance Z p (s) parallel connection, and the power grid is equivalent to an ideal voltage source U g (s) and grid-tie impedance Z g (s) series connection.
In analyzing the stability of the system shown in fig. 3, the fan output current is obtained according to the equivalent circuit as follows:
considering that both systems can operate independently and stably, the stability of equation (18) depends on the second term on the right of the equation, i.e., 1/(1+Z) g (s)/Z p (s)). Similar to a forward channel gain of 1, the negative feedback channel gain is Z g (s)/Z p (s) closed loop transfer function. The stability theory shows that the pole criterion equation of the doubly-fed grid-connected system is as follows:
taking the case that the fan is in a subsynchronous operation state, the fan is connected with the grid through a transformer, a power transmission line and a series compensation capacitor, and then a specific pole criterion equation of the target system is as follows:
the structure of the doubly-fed grid-connected system is shown in fig. 3, wherein:
Z g (s)＝R L +s(L T +L L )+1/sC L (24)
step 5: determining subsynchronous oscillation stability of doubly-fed grid-connected system according to poles
The pole of the target system can be calculated according to the equation (25), and according to the stability theory, the imaginary part of the pole represents the possible oscillation angular frequency, and the real part represents the corresponding system damping. And poles with corresponding frequencies near the power frequency need to be removed during screening. Calculating possible oscillation frequency of the system according to the pole imaginary part, and stabilizing the system if the pole real part is smaller than zero; the real part is greater than zero and the system is at risk of subsynchronous oscillations. Meanwhile, according to the absolute value of the real part, the risk degree of subsynchronous oscillation of the system can be quantitatively evaluated.
To verify the correctness of the above analysis, a simulation verification was performed according to the following parameters: 50Hz fundamental voltage amplitude V 1 =690V, perturbation voltage: v (V) p ＝0.96e j(-1) The method comprises the steps of carrying out a first treatment on the surface of the Current inner loop PI parameter K p ＝0.6，K i =10; phase-locked loop control parameters: k (K) pp ＝500，K pi =500; rotor current reference value I r,ref ＝0.1723e j(-1.87) The method comprises the steps of carrying out a first treatment on the surface of the Rotor voltage reference value: u (U) r,ref ＝0.2302e j(-1.25) Rotating shaft rotation speed (per unit value): 0.8. disturbance voltages with different frequencies are injected into the doubly-fed fan grid-connected point within the doubly-fed fan sub-synchronous frequency range (0-30 Hz), and the obtained frequency sweeping result and the calculated result of the formula (13) are compared, for example, as shown in fig. 4 (a).
Changing the operation of the doubly-fed wind turbine into the super-synchronous operation state, and having the fundamental voltage amplitude V of 50Hz 1 =690V, current inner loop PI parameter: K p ＝1.5，K i =0.004; phase-locked loop control parameters: k (K) pp ＝0.05，K pi =0.002; rotor current reference value I r,ref ＝7.635e j(1.3183) The method comprises the steps of carrying out a first treatment on the surface of the Rotor voltage reference value: u (U) r,ref ＝3.575e j(-2.281) Rotating shaft rotation speed (per unit value): 1.2. disturbance voltages with different frequencies are injected into the doubly-fed fan grid-connected point within the doubly-fed fan sub-synchronous frequency range (0-30 Hz), and the obtained frequency sweeping result and the calculated result of the formula (14) are compared, for example, as shown in fig. 4 (b).
As can be seen from FIG. 4, the frequency sweep result is consistent with the calculation result, so that the invention calculates the analysis impedance of different operation states within the range of the sub-synchronous frequency band (0-30 Hz) of the doubly fed fan correctly.
Taking the above sub-synchronous operation state as an example, the disturbance frequency is set: 7Hz, substituting the parameters into the formula (13), and calculating to obtain 7Hz output current with the same frequency as the disturbance voltage, wherein the 7Hz output current is as follows:
I p (f p )＝18∠2.57A (26)
substituting the above result into equation (20), the output current with a coupling frequency of 93Hz can be calculated as:
I p2 (2f 1 -f p )＝4.1∠0.21A (27)
simulation results show that when the disturbance voltage of 7Hz exists in the PCC point, the harmonic component of 7/93Hz exists in the output current, and the amplitude and the phase are shown in the figures (a) and (b) respectively.
Note that the fundamental component amplitude in fig. 5 (a) is outside the vertical axis range, and its amplitude is marked in the figure. For clarity, other component phases than 7/93Hz in FIG. 5 (b) have been filtered out. It can be seen that the magnitudes of the 7/93Hz currents are about 0.017kA and 0.004kA, respectively, and the phases are about 2.6 and 0.2, respectively, consistent with the calculations of equations (26) and (27).
In order to verify a pole criterion equation corresponding to a target system in the formula (23), the parameters of the power transmission system with high voltage level are calculated to 35kV, the resistance is 27.55 omega, the inductance is 0.63948H, the series compensation capacitance is 720uF, the proportion parameters of the wind power system are adjusted to 0.65, the short-circuit impedance of a 35/0.69kV transformer is 0.065, and other conditions are not changed. The pole at this time of the system is calculated according to equation (25) as: 0.266+j29.4. An oscillation of 29.4/(2pi) =5.16 Hz may occur in a system obtainable from pole calculations.
Simulation is carried out on a PSCAD platform, and line current and FFT thereof are obtained as shown in figure 6:
as can be seen from FIG. 6, the critical oscillation of the system is about 5Hz, and the oscillation frequency is consistent with the calculation result of the pole criterion equation.
In summary, the invention discloses a subsynchronous oscillation analysis method of a doubly-fed grid-connected system considering frequency coupling effect. Firstly, establishing an external impedance analysis model of a doubly-fed fan based on a harmonic linearization method, wherein the main innovation point is that the frequency coupling effect of harmonic current output by the doubly-fed fan under single-frequency harmonic voltage disturbance is considered, and simultaneously, according to two running states of the doubly-fed fan, the external impedance analysis model of the fan is deduced under different running states; then deriving 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 poles of the calculated system characteristic equation. The invention quantitatively reveals the subsynchronous oscillation mechanism of the double-fed grid-connected system, and can quantitatively analyze the subsynchronous oscillation stability of the target double-fed grid-connected system.
Claims (2)
1. The subsynchronous oscillation analysis method 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 doubly-fed fan;
the parameters of the following doubly-fed grid-connected system are obtained, including: grid-connected voltage V of fan 1 Phase locked loop PI parameter K pp ，K pi Rotor-side converter current inner loop PI parameter K p ，K i Feedforward constant K to cancel dq axis coupling d Frequency omega of fan operation rotating shaft r Resistor R of power transmission system L Inductance L L Inductance L of transformer T Series compensation capacitor C L The method comprises the steps of carrying out a first treatment on the surface of the Step 2: establishing a doubly-fed type fan external impedance analysis model;
building a doubly-fed type fan external impedance analysis model based on a harmonic linearization method, and obtaining fan operation rotating shaft frequency omega according to the step 1 r Judging whether the fan is in a subsynchronous operation state or a supersynchronous operation state;
step 3: calculating the subsynchronous oscillation frequency coupling component of the doubly-fed system;
step 4: deriving 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 external impedance analysis expression deduced in the step 2 and the grid-connected parameters obtained in the step 1;
step 5: judging the subsynchronous oscillation stability of the doubly-fed grid-connected system according to the poles;
calculating a pole of a target system according to a stability theory, wherein an imaginary part of the pole represents possible oscillation angular frequency, and a real part represents corresponding system damping; because the equation order is high, a plurality of poles can be calculated, and poles with corresponding frequencies near the power frequency need to be removed when screening is performed;
the 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 adopted, and the system is stable; the real part is larger than zero, negative damping is adopted, and the system has the risk of subsynchronous oscillation; meanwhile, according to the absolute value of the real part, the risk degree of subsynchronous oscillation of the system can be quantitatively evaluated.
2. The method for analyzing subsynchronous oscillation of a doubly-fed grid-connected system according to claim 1, wherein the step 2 is specifically as follows:
when the power grid voltage has disturbance, only positive sequence disturbance is considered, and the A-phase voltage is set as:
v sa (t)＝V 1 cos(ω 1 t+θ v )+V p cos(ω p t+θ vp )(1)
wherein V is 1 、V p The power frequency and the disturbance voltage amplitude are respectively; omega 1 、ω p The power frequency and the disturbance voltage frequency are respectively; θ v 、θ vp The phase of the power frequency and the disturbance voltage are respectively;
the frequency domain expression is: fundamental componentPositive sequence disturbance voltage->
F may be present in the park transform due to frequency coupling effects p And frequency 2f 1 -f p Error of (2):
wherein: θ PLL For phase-locked loop output angle H PLL (s)＝(K pp +K pi /s)/s，K pp ，K pi Phase-locked loop proportional and integral constants, respectively;
when the voltage on the power grid side exists f p When in harmonic wave, the fan grid-connected point current simultaneously has f p And 2f 1 -f p Harmonic current of frequency, set the corresponding rotor current time domain expression as:
i ra (t)＝I r1 cos[(ω 1 -ω m )t+θ i ]+I rp cos[(ω p -ω m )t+θ rp ]+I rp2 cos[(2ω 1 -ω p -ω m )t+θ rp2 ](3)
wherein I is r1 、I rp 、I rp2 The rotor fundamental frequency, the disturbance current and the corresponding coupling frequency current amplitude are respectively; θ i 、θ rp 、θ rp2 Respectively the initial phases of the three; omega m The rotating speed of the rotating shaft;
convolving equation (3) with equation (2), ignoring the quadratic term, and obtaining the parker transformed dq-axis rotor current I rd 、I rq Frequency domain expression:
according to the control strategy of the inner ring of the doubly-fed wind turbine rotor-side converter, current disturbance can be generated on the dq axis of the rotor by reference voltage U rd,ref 、U rq,ref The above causes the following disturbances:
wherein: h r (s)＝K p +K i S, where K p ，K i The proportional and integral constants of the inner loop of the current respectively; k (K) d To eliminate dq axis couplingA feed constant;
the frequency component in the analysis formula (5) is known to contain a DC component and. + -. (f) p -f 1 ) Frequency component V rd,ref [f p -f 1 ]、V rq,ref [f p -f 1 ]The method comprises the steps of carrying out a first treatment on the surface of the Considering the dc component U of the dq-axis current at the steady state operating point rd 、U rq With reference value V rd,ref [dc]、V rq,ref [dc]Equal, then the two component expressions are respectively:
the three-phase voltage reference value is obtained by the coordinate inverse transformation of the dq axis voltage reference value, and the SPWM input A-phase reference voltage V can be obtained by convolution ra,ref The frequency domain expression is:
ignoring power electronics switching dynamics errors, the doubly fed wind machine rotor output voltage can be considered equal to the reference voltage, namely:
according to the circuit structure of the doubly-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
Wherein R is s 、R r 、L s 、L r The stator and rotor resistance and the low-cost rotor inductance of the doubly-fed wind turbine are respectively; k is the turns ratio of stator and rotor; sigma (sigma) p (s) is the corresponding slip; i.e sa 、i sb 、i sc Respectively stator three-phase currents;
considering that the stator voltage contains only f p A harmonic voltage component, in which the above is rewritten to contain only f p Frequency domain expression of the components:
1) When the disturbance voltage on the stator side of the doubly-fed wind machine is induced to the rotor winding, when f p <f m When the phase sequence of disturbance voltage induced in the rotor winding is negative sequence; 2) The output angle of the phase-locked loop at the rotor side of the doubly-fed wind turbine is theta 1 -θ m Thus, the blower exhibits different external impedance characteristics for different operating conditions;
the combination of the formula (8) and the formula (12) takes the external impedance Z of the doubly-fed fan into consideration p ＝-V p /I p The external impedance Z of the doubly-fed wind turbine in the sub-synchronous frequency band can be deduced p1 、Z p2 An expression;
for subsynchronous operating states (θ 1 ＞θ m )：
For the super-synchronous operating state (θ 1 ＜θ m )：
When theta is as 1 ＝θ m When formula (13) and formula (14) are equal; in contrast to the rotor-side converter, the grid-side converter has little effect on the subsynchronous harmonic impedance of the wind turbine, and is therefore not considered here.
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