CN110676874B - Direct-drive fan subsynchronous oscillation electrical quantity analysis method considering frequency coupling effect - Google Patents
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Abstract
The invention discloses a direct-drive fan subsynchronous oscillation electrical quantity analysis method considering frequency coupling effect, which comprises the steps of firstly, inputting parameters of a direct-drive fan to be analyzed, and establishing a simplified model of the direct-drive fan; secondly, establishing an external impedance analytical model of the direct-drive fan based on a harmonic linearization method, wherein the establishing process mainly accounts for the frequency coupling effect of the output harmonic current of the direct-drive fan under the single-frequency harmonic voltage disturbance; then, applying single frequency f to the direct-drive fan grid-connected point p Disturbing harmonic voltage, calculating f in output current p And 2f 1 ‑f p Harmonic components, which give an analytical expression of the frequency coupling relation of the output current, and comprehensively analyze the subsynchronous oscillation response characteristic of the direct-drive fan; the invention discloses a subsynchronous oscillation electrical quantity coupling response mechanism of the direct-drive fan under harmonic voltage disturbance quantitatively, and the quantitative relation among the subsynchronous oscillation electrical quantity coupling response mechanism, the subsynchronous oscillation electrical quantity coupling response mechanism and the direct-drive fan can be given only by inputting parameters of the direct-drive fan.
Description
Technical Field
The invention belongs to the field of power systems, relates to the field of stability analysis of direct-drive fans, and particularly relates to a direct-drive fan subsynchronous oscillation electrical quantity analysis method considering a frequency coupling effect.
Background
The proportion of the new energy electric energy access system is gradually increased, and new challenges are brought to the safe and stable operation of the electric power system, wherein the new challenges include the stability problems of subsynchronous oscillation and the like. Meanwhile, the specific gravity of the direct-drive wind turbine generator in the fan type is also improved year by year, and the direct-drive wind turbine generator brings a brand-new subsynchronous oscillation challenge after being connected to a power grid. On the premise that the back-to-back double PWM converters isolate the machine network side and do not carry out series compensation and external transmission, subsynchronous oscillation still occurs after the direct-drive wind turbine generator is connected into the system. The novel subsynchronous oscillation is obviously different from subsynchronous oscillation of a traditional thermal power steam turbine unit and a double-fed wind turbine unit in the aspects of mechanism and suppression measures. With the construction of large-scale wind power bases in China, the modeling, analysis and suppression measures of subsynchronous oscillation induced by direct-drive wind power integration become problems to be solved urgently. The method for researching the subsynchronous oscillation problem of the grid connection of the direct-drive wind turbine generator has important significance for determining and perfecting the subsynchronous oscillation mechanism of the fan, making a corresponding inhibition strategy, improving the grid connection performance of the direct-drive fan and ensuring the safety and stability of a power system.
The impedance method is an analysis method for researching the grid-connected stability of the direct-drive fan, which is emerging in recent years, and is based on a small signal disturbance method, impedance models of the direct-drive fan and an alternating current power grid are respectively established, and the stability of the grid-connected direct-drive fan is judged by utilizing a Nyquist stability criterion.
Disclosure of Invention
In order to solve the problem of the sub-synchronous oscillation of the grid-connected direct-drive wind field, the invention aims to provide a method for analyzing the sub-synchronous oscillation electrical quantity of a direct-drive fan considering the frequency coupling effect.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a direct-drive fan subsynchronous oscillation electrical quantity analysis method considering frequency coupling effect is characterized by comprising the following steps: establishing a direct-drive fan small-signal impedance analytical model considering a frequency coupling effect, and giving a frequency coupling quantitative relation of output harmonic current of the direct-drive fan under single-frequency harmonic voltage disturbance; the method is characterized in that: the method comprises the following steps:
step 1: inputting direct-drive fan parameters
The following parameters of the direct drive fan are obtained: fan grid-connected voltage V 1 The current output power frequency current I of the fan 1 Angle of power factor
Phase-locked loop PI parameter K p ，K i And current inner loop PI parameter K pi ，K ii The filter inductor L at the outlet of the inverter;
and 2, step: establishing simplified model of direct-drive fan
According to the structure of the direct-drive fan and the time scale characteristics of a control link, simplifying the direct-drive fan into a grid-connected inverter model: the wind turbine, the generator and the machine side converter are replaced by a direct current voltage source; power outer loop control of the grid-side converter is omitted; parameters required by the simplified model are obtained in the step 1;
and 3, step 3: establishing external impedance analytical model of direct-drive fan
The method is characterized in that a direct-drive fan external impedance analytical model is established based on a harmonic linearization method, and the establishment process mainly accounts for the frequency coupling effect of the output harmonic current of the direct-drive fan under the single-frequency harmonic voltage disturbance:
practical simulation shows that omega exists when the voltage of the power grid side exists p When harmonic wave exists, the output current of the inverter can simultaneously exist omega p And 2 omega 1 -ω p Harmonic current of frequencyThe inverter output current time domain expression is as follows:
in the formula i a (t) is instantaneous value of phase current A, I 1 、I p 、I p2 The amplitude of the power frequency current, the amplitude of the output current with the same frequency as the disturbance voltage and the amplitude of the complementary frequency output current are respectively; omega 1 、ω p 、2ω 1 -ω p The angular frequency of the power frequency current, the angular frequency with the same frequency as the disturbance voltage and the angular frequency of the output current with complementary frequency are respectively;
the initial phase of the power frequency current, the initial phase of the output current with the same frequency as the disturbance voltage and the initial phase of the complementary frequency output current are respectively;
similar to the definition of phasor in the circuit science, the frequency domain expressions of the output current with the same frequency as the disturbance voltage and the complementary frequency output current in the equation (3) are respectively as follows:
I p is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression; i is p2 Angular frequency 2w of output current being complementary frequency 1 -w p The output current frequency domain expression of (1);
and taking the frequency coupling effect into account, and obtaining a frequency domain expression of the input A-phase reference voltage of the pulse width modulator of the converter as follows:
in the formula: v aref [w p ]And V aref [2w 1 -w p ]Are respectively w p And 2w 1 -w p A phase a reference voltage frequency domain expression of frequency; wherein: s and j are the fundamental variables of complex operations in mathematics;
performing exponential operation; h i (s-jw 1 )＝K pi +K ii /(s-jw 1 ) Is the transfer function of the current inner loop PI regulator;
wherein
Is the transfer function of the phase locked loop;
is the frequency domain expression V of the positive sequence disturbance voltage p Conjugation of (1);
the converter using an averaging model, i.e. the output voltage V ga [w p ]Is equal to the reference voltage V aref [w p ](ii) a Because there is only one filter inductance between converter output voltage and the grid-connected point voltage, so their three satisfy:
sLI p ＝V ga [w p ]-V a [w p ] (12)
substituting formula (8) for formula (12) and connecting to external impedance Z of direct-drive fan p (s)＝-V p /I p The analytical expression of (a) is:
and 4, step 4: calculating the output current of the direct-drive fan under the single-frequency voltage disturbance
For w p As can be seen from equation (13), the disturbance voltage at a frequency corresponds to an output current at the frequency:
in the formula: v p Is a frequency domain expression of positive sequence disturbance voltage, Z p (jw p ) Is that the direct-drive fan is at an angular frequency w with the same frequency as the disturbance voltage p Impedance calculated according to the following equation (13), I p Is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression;
because the fan grid-connected point only contains w p Voltage of frequency, so angular frequency 2w of output current for complementary frequency 1 -w p Satisfies the following conditions:
V aref [2w 1 -w p ]＝V ga [2w 1 -w p ]＝j(2w 1 -w p )LI p2 (15)
substituting formula (9) and eliminating V by formula (13) p (s), there can be obtained:
the above formula reveals a single frequency omega p Under voltage disturbance, the inverter outputs omega p And 2 omega 1 -ω p A quantitative relationship of the coupled current components; i is p Is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression; i is p2 Angular frequency 2w of output current being complementary frequency 1 -w p The output current frequency domain expression of (1); when V is p After the determination, the output currents of the two coupling frequencies can be calculated according to the equations (14) and (16), respectively.
Compared with the prior art, the invention has the following advantages:
the invention discloses a direct-drive fan subsynchronous oscillation electrical quantity analysis method considering a frequency coupling effect. Firstly, inputting parameters of a direct-drive fan to be analyzed, and establishing a simplified model of the direct-drive fan; secondly, the direct-drive fan external impedance analytical model is established based on a harmonic linearization method, and the main innovation point of the direct-drive fan external impedance analytical model is that the frequency coupling effect of the output harmonic current of the direct-drive fan under the single-frequency harmonic voltage disturbance is considered; finally, based on the analysis expression of the output current frequency coupling relation, the subsynchronous oscillation response characteristic of the direct-drive fan is comprehensively analyzed, and a theoretical basis is provided for researching the subsynchronous oscillation and supersynchronous oscillation coupling relation of the direct-drive fan.
Drawings
FIG. 1 is a flow chart of the present patent.
Fig. 2 is a schematic diagram of a direct-drive fan grid-connected simplified topological structure.
Fig. 3 is a graph of output current relationship under harmonic voltage disturbance, wherein fig. 3a is a comparison of amplitude relationship and fig. 3b is a comparison of phase relationship.
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 invention discloses a method for analyzing subsynchronous oscillation electrical quantity of a direct-drive fan considering frequency coupling effect, which comprises the following steps:
step 1: inputting direct-drive fan parameters
The following parameters of the direct-drive fan are obtained: fan grid-connected voltage V 1 The current output power frequency current I of the fan 1 Angle of power factor
Phase-locked loop PI parameter K p ，K i Current inner loop PI parameter K pi ，K ii And an inverter outlet filter inductor L.
Step 2: establishing simplified simulation model of direct-drive fan
The permanent magnet direct drive type fan stator side is generally connected to a power grid through a topology structure of back-to-back double PWM converters, so that the machine side is isolated from the grid side. The permanent magnet direct-drive fan injects large-capacity power into the power grid side, but the inertia of a power system is not remarkably improved, so that the problem of unstable unit operation is easily caused. When the secondary and super-synchronous oscillation of the direct-drive type fan is analyzed, if the simplified direct-drive wind power system is directly subjected to mathematical modeling, the complexity is high and is not necessary.
Therefore, by combining the above two points, a simplified model of the direct-drive blower suitable for the subsynchronous oscillation analysis is shown in fig. 2. v. of a ,v b ,v c Is a grid connection point three-phase voltage i a ,i b ,i c The three-phase current output by the fan is a time domain expression. The phase-locked loop PLL provides a reference angle for coordinate changes so that control of the fan can be performed in the dq coordinate system. As can be seen from the figure, the simplified wind turbine topology only includes the grid-side inverter GSC and the current inner loop control in the dq coordinate system. Due to power decoupling, I dref ,I qref The reference values of the active power and the reactive power can be respectively calculated. Actual output current i after coordinate transformation d ,i q The deviation from the reference value is compensated by a current controller (PI control) and current feedforward to obtain the reference value v of the output voltage dref ,v qref . The latter is transformed into a voltage reference value under a three-phase static coordinate system through coordinate inverse transformation, and provides a modulation wave signal for the inverter PWM modulation technology.
And step 3: establishing external impedance analytical model of direct-drive fan
The voltage of a fan grid-connected point contains angular frequency omega p Positive sequence voltage of (d):
in the formula, v a (t) is the A phase instantaneous voltage; v 1 Is the amplitude of the fundamental component, V p Is the amplitude of the disturbance component, ω 1 Is the angular frequency, omega, of the power frequency voltage p Is the disturbance voltage angular frequency;
is the initial phase of the perturbation voltage;
according to the definition of phasor in the circuit, the frequency domain expression of two voltages in equation (1) is: fundamental component V 1 ＝V 1 Positive sequence disturbance voltage
Due to frequency coupling effects, omega may exist in the park transformation p And 2 omega 1 -ω p Error in frequency:
in the formula: cos θ pll [w p ]And cos θ pll [2w 1 -w p ]Is the phase-locked angle theta pll Omega in (1) p And 2 omega 1 -ω p A frequency component;
is the transfer function of the phase-locked loop, s and j are basic variables of complex operation in mathematics, kp and Ki are proportional and integral constants of the phase-locked loop respectively,
is the frequency domain expression V of the positive sequence disturbance voltage p Conjugation of (1).
Practical simulation shows that omega exists when the voltage of the power grid side exists p When harmonic wave exists, the output current of the inverter can simultaneously exist omega p And 2 omega 1 -ω p The harmonic current of the frequency, the inverter output current time domain expression is as follows:
in the formula i a (t) is instantaneous value of phase current A, I 1 、I p 、I p2 The amplitude of the power frequency current, the amplitude of the output current with the same frequency as the disturbance voltage and the amplitude of the complementary frequency output current are respectively; omega 1 、ω p The angular frequency of the power frequency current and the angular frequency of the output current with the same frequency as the disturbance voltage are respectively;
the initial phase of the power frequency current, the initial phase of the output current with the same frequency as the disturbance voltage and the initial phase of the complementary frequency output current are respectively.
Similar to the definition of phasor in the circuit science, the frequency domain expressions of the output current with the same frequency as the disturbance voltage and the complementary frequency output current in the formula (3) are respectively as follows:
I p is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression; I.C. A p2 Angular frequency (2 w) of output current being complementary frequency 1 -w p ) Output current frequency domain expression of
Convolving equation (3) with equation (2), ignoring the quadratic terms, we can obtain the frequency domain expression of the park transformed current dq axis:
I d [w p -w 1 ]and I q [w p -w 1 ]Respectively, the frequency of the dq-axis current is w p -w 1 Of the frequency component, T p (jw p ) Is T p (s) wherein s = jw p Thus, the compound was obtained.
According to a PI decoupling control strategy of a current inner loop of a direct-drive fan, a dq-axis reference voltage expression is as follows:
in the formula: v dref And V qref Reference voltages, H, for d-and q-axes, respectively i (s)＝K pi +K ii Is the transfer function of the current inner loop PI regulator, K pi And K ii Respectively, the proportional and integral constants of the current inner loop regulator.
Considering that under a steady-state working point, the direct current component of the dq-axis current is equal to a reference value thereof; in addition, general formula(4) Can be substituted by formula (5) to obtain dref And V qref Also contains a frequency w p -w 1 Of the frequency component (c). DC component sum w p -w 1 The expressions of the frequency components are shown in equations (6) and (7), respectively:
the three-phase voltage reference value is obtained by inverse coordinate transformation of a dq axis voltage reference value, and the frequency domain expression of the A-phase reference voltage input by the pulse width modulator of the current transformer obtained by convolution is as follows:
in the formula: v aref [w p ]And V aref [2w 1 -w p ]Are respectively w p And 2w 1 -w p Phase a reference voltage frequency domain representation of frequency.
The PWM inverter adopts a simplified model, ignores the dynamic error of the switch and can consider that the output voltage is equal to the reference voltage.
In the formula: v ga [w p ]And V ga [2w 1 -w p ]Are respectively w p And 2w 1 -w p And the A phase of the frequency outputs a voltage frequency domain expression.
The output voltage of the inverter of the direct-drive fan passes through the filter inductor, andthe PCC points are connected. The instantaneous value v of the output voltage of the inverter can be easily obtained according to the circuit law ga 、v gb 、v gc Output current i a 、i b 、i c And PCC point voltage v a 、v b 、v c Satisfies the following conditions:
as shown in the formula (1), the PCC point voltage contains only the angular frequency w p At a frequency w p The frequency domain expression of equation (11) is as follows:
sLI p ＝V ga [w p ]-V a [w p ] (12)
equations (4), (8) and (10) are substituted into equation (12), and the direct-drive fan external impedance is defined as Z p (s)＝-V p (s)/I p (s), the expression of an external impedance analytical model of the grid-connected direct-drive type fan can be deduced as follows:
in the formula: h i (s-jw 1 )＝K pi +K ii /(s-jw 1 ) Is the aforementioned H i (s) displacement transformation.
And 4, step 4: calculating the output current of the fan under the single-frequency voltage disturbance
For w p As can be seen from equation (13), the disturbance voltage at a frequency corresponds to an output current at the frequency:
in the formula: v p Is a frequency domain expression of positive sequence disturbance voltage, Z p (jw p ) Is that the direct-drive fan has an angular frequency w with the same frequency as the disturbance voltage p Impedance calculated according to the following equation (13), I p Is at the same frequency as the disturbance voltageW of p And outputting a current frequency domain expression by frequency.
Because the fan grid-connected point only contains w p Voltage of frequency, so angular frequency 2w of output current for complementary frequency 1 -w p Satisfies the following conditions:
V aref [2w 1 -w p ]＝V ga [2w 1 -w p ]＝j(2w 1 -w p )LI p2 (15)
in the formula I p2 Angular frequency 2w of output current being complementary frequency 1 -w p The output current frequency domain expression of (1).
Substituting formula (9) and eliminating V by formula (13) p (s), there can be obtained:
I p2 angular frequency 2w of output current being complementary frequency 1 -w p The output current frequency domain expression of (1).
It can be seen that the above formula reveals a single frequency ω p Under voltage disturbance, the inverter outputs omega p And 2 omega 1 -ω p Quantitative relationship of the coupled current components. When the amplitude and the frequency of the disturbance voltage are determined, the output currents of the two coupling frequencies can be calculated according to the formula (14) and the formula (16), respectively.
Examples
In order to verify the correctness of the above formula, simulation verification is performed according to the following parameters: 50Hz fundamental voltage amplitude V 1 =566V, disturbance voltage:
disturbance frequency: 20Hz, current inner loop PI parameter K p ＝0.25，K i =355; phase-locked loop control parameters: k p ＝0.085，K i =32; current reference value I dref ＝1847,I qref =0; the inverter outlet filter inductance parameter L =0.15e-3H.
The parameters are substituted into the formula (14), and the 20Hz output current with the same frequency as the disturbance voltage can be calculated as follows:
I p ＝45∠2.75 A (17)
the output current at a coupling frequency of 80Hz can be calculated from equation (16) as:
I p2 ＝0.7754×45∠(3.063-2.75)＝35∠0.256 A (18)
the simulation result is shown in fig. 3, when 20Hz disturbance voltage exists at the grid-connected point of the fan, it can be seen that the output current of the fan has 20/80Hz harmonic components in addition to 50Hz power frequency components, and the amplitude and phase of the harmonic components are respectively shown in fig. 3a and fig. 3 b. Note that the fundamental component amplitude in FIG. 3a is outside the vertical axis range, and the actual output current follows the d-axis current reference I dref (ii) a For clarity, the other component phases in FIG. 3b, except 20/50/80Hz, have been filtered out. It can be seen that the amplitude and phase of the 20/80Hz current are consistent with the calculation results of the equations (17) and (18), and the correctness of the equations (14) and (16) is verified.
In summary, for a direct-drive fan with determined parameters, a single frequency ω exists at a machine-end grid-connected point p When the harmonic voltage is disturbed, the output current of the inverter can simultaneously exist omega p And 2 omega 1 -ω p The harmonic currents of the frequencies can be calculated according to equations (14) and (16), respectively.
Claims (1)
1. A direct-drive fan subsynchronous oscillation electrical quantity analysis method considering frequency coupling effect is characterized by comprising the following steps: establishing a direct-drive fan small-signal impedance analytical model considering a frequency coupling effect, and giving a frequency coupling quantitative relation of output harmonic current of the direct-drive fan under single-frequency harmonic voltage disturbance; the method is characterized in that: the method comprises the following steps:
step 1: inputting direct-drive fan parameters
The following parameters of the direct drive fan are obtained: fan grid-connected voltage V 1 The current output power frequency current I of the fan 1 Angle of power factor
Phase-locked loop PI parameter K p ，K i Current inner loop PI parameter K pi ，K ii The filter inductor L at the outlet of the inverter;
step 2: establishing simplified model of direct-drive fan
According to the structure of the direct-drive fan and the time scale characteristics of a control link, simplifying the direct-drive fan into a grid-connected inverter model: the wind turbine, the generator and the machine side converter are replaced by a direct current voltage source; power outer loop control of the grid-side converter is omitted; parameters required by the simplified model are obtained in the step 1;
and step 3: establishing external impedance analytical model of direct-drive fan
The method is characterized in that a direct-drive fan external impedance analytical model is established based on a harmonic linearization method, and the establishment process mainly accounts for the frequency coupling effect of the output harmonic current of the direct-drive fan under the single-frequency harmonic voltage disturbance:
practical simulation shows that omega exists when the voltage of the power grid side exists p When harmonic wave exists, the output current of the inverter can simultaneously exist omega p And 2 omega 1 -ω p The harmonic current of the frequency, the inverter output current time domain expression is as follows:
in the formula i a (t) is instantaneous value of phase current A, I 1 、I p 、I p2 The amplitude of the power frequency current, the amplitude of the output current with the same frequency as the disturbance voltage and the amplitude of the complementary frequency output current are respectively; omega 1 、ω p 、2ω 1 -ω p The angular frequency of the power frequency current, the angular frequency which is the same as the disturbance voltage in frequency and the angular frequency of the output current with complementary frequency are respectively;
the initial phase of the power frequency current, the initial phase of the output current with the same frequency as the disturbance voltage and the initial phase of the complementary frequency output current；
Similar to the definition of phasor in the circuit science, the frequency domain expressions of the output current with the same frequency as the disturbance voltage and the complementary frequency output current in the formula (3) are respectively as follows:
I p is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression; i is p2 Angular frequency 2w of output current being complementary frequency 1 -w p The output current frequency domain expression of (1);
and taking the frequency coupling effect into account, and obtaining a frequency domain expression of the input A-phase reference voltage of the pulse width modulator of the converter as follows:
in the formula: v aref [w p ]And V aref [2w 1 -w p ]Are respectively w p And 2w 1 -w p A phase a reference voltage frequency domain expression of frequency; wherein: s and j are the fundamental variables of complex operations in mathematics;
performing exponential operation; h i (s-jw 1 )＝K pi +K ii /(s-jw 1 ) Is the transfer function of the current inner loop PI regulator;
wherein
Is the transfer function of the phase locked loop;
is the frequency domain expression V of the positive sequence disturbance voltage p Conjugation of (2);
the converter using an averaging model, i.e. the output voltage V ga [w p ]Is equal to the reference voltage V aref [w p ](ii) a Because only one filter inductor exists between the output voltage of the converter and the voltage of the grid-connected point, the three satisfy the following conditions:
sLI p ＝V ga [w p ]-V a [w p ] (12)
the formula (8) is substituted into the formula (12), and the external impedance Z of the grid-connected direct-drive type fan p (s)＝-V p /I p The analytical expression of (a) is:
and 4, step 4: calculating the output current of the direct-drive fan under the single-frequency voltage disturbance
For w p As can be seen from equation (13), the disturbance voltage at a frequency corresponds to an output current at the frequency:
in the formula: v p Is a frequency domain expression of positive sequence disturbance voltage, Z p (jw p ) Is that the direct-drive fan is at an angular frequency w with the same frequency as the disturbance voltage p Impedance calculated according to the following equation (13), I p Is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression;
because the fan grid-connected point only contains w p Voltage of frequency, so angular frequency 2w of output current for complementary frequency 1 -w p Satisfies the following conditions:
V aref [2w 1 -w p ]＝V ga [2w 1 -w p ]＝j(2w 1 -w p )LI p2 (15)
substituting formula (9) and eliminating V by formula (13) p (s), there can be obtained:
the above formula reveals a single frequency omega p Under voltage disturbance, the inverter outputs omega p And 2 omega 1 -ω p A quantitative relationship of the coupled current components; i is p Is w at the same frequency as the disturbance voltage p A frequency output current frequency domain expression; i is p2 Angular frequency 2w of output current being complementary frequency 1 -w p The output current frequency domain expression of (1); when V is p After the determination, the output currents of the two coupling frequencies can be calculated according to the equations (14) and (16), respectively.
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| CN111641229B (en) * | 2020-06-16 | 2022-07-01 | 山东大学 | Wind power generation system output monitoring method and system based on extended harmonic domain model |
| CN112217203B (en) * | 2020-09-28 | 2022-11-25 | 西安热工研究院有限公司 | Direct-drive wind power plant subsynchronous oscillation equivalence method capable of keeping model structure |
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