CN115207968B - Method for improving stability margin of photovoltaic grid-connected inverter under weak current network - Google Patents
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Abstract
The invention relates to the technical field of stability of a photovoltaic grid-connected inverter under a weak current network, in particular to a method for improving stability margin of the photovoltaic grid-connected inverter under the weak current network; the invention discloses a method for improving stability margin of a photovoltaic grid-connected inverter under a weak power grid, which comprises the following steps: s1: modeling output admittance of a grid-connected inverter system comprising a complex coefficient filter phase-locked loop structure (CCF-PLL) and Grid Voltage Feedforward (GVF); s2: performing stability analysis on the output admittance model established in the S1 to obtain that the instability of the system under a weak current network is caused by leading the phase of the system to be advanced due to negative admittance introduced by GVF; s3: aiming at the problem of S2, the total output admittance phase of the inverter is subjected to hysteresis correction by using an all-pass filter, so that the stability margin of the system under a weak current network is improved, and the stability of the system is enhanced.
Description
Technical Field
The invention relates to the technical field of stability of a photovoltaic grid-connected inverter under a weak current network, in particular to a method for improving stability margin of the photovoltaic grid-connected inverter under the weak current network.
Background
Longer transmission lines and more transformation devices exist between the existing photovoltaic power generation and a power grid, and as seen from a public coupling point of a grid-connected inverter, grid impedance with resistance inductance exists, so that stable operation of a grid system is affected. Under the condition of weak network, a positive feedback channel of feedforward of the traditional power grid voltage proportion is coupled with the grid-connected current inner loop through power grid impedance, so that the stability margin of the system is reduced.
From the above, it can be seen that the grid-connected inverter may have excessive grid impedance under the weak grid, which results in a decrease in the phase margin of the inverter system, and affects the stable operation of the system. Therefore, how to improve the stability margin of the photovoltaic grid-connected inverter under the weak grid is a problem that needs to be solved by the skilled person.
In the prior art, as disclosed in publication number CN111245017a, the method is named as a method for controlling the feedforward of the capacitor voltage of the grid-connected inverter under the weak current network, by using the current i 1 at the inversion side to perform feedback control and using the capacitor voltage u C to perform phase locking, active damping and feedforward compensation, the capacitor voltage feedforward control system of the grid-connected inverter under the weak current network is obtained; the obtained capacitor voltage feedforward control system is subjected to active damping negative feedback design under a weak current network, and the capacitor voltage feedforward control system is subjected to capacitor voltage feedforward compensation control strategy design, however, the grid-connected inverter of the patent is easy to generate overlarge grid impedance under the weak current network, so that the phase margin of the inverter system is reduced, and the stable operation of the system is influenced.
Disclosure of Invention
Aiming at the technical problems, the invention provides a method for improving the stability margin of a photovoltaic grid-connected inverter under a weak current network, which uses an all-pass filter to carry out hysteresis correction on the total output admittance phase of the inverter, improves the stability margin of a system under the weak current network and enhances the stability of the system.
The invention adopts the following specific technical scheme:
a method for improving stability margin of a photovoltaic grid-connected inverter under a weak current network comprises the following steps:
S1: simplifying the whole system into a Thevenin equivalent circuit, connecting a power grid side with an inverter side through PCC to obtain an inverter equivalent output admittance Y i(s), a CCF-PLL admittance Y p(s), a GVF admittance Y v(s), and the expressions of the admittances are respectively:
Wherein G f、Gc、G1、G2、GPLL、GCCF is a shorthand form of G f(s)、Gc(s)、G1(s)、G2(s)、GPLL(s)、GCCF(s), G f(s) is traditional power grid voltage proportion feedforward, G c(s) is a quasi-proportion resonant controller parameter, G 1(s)、G2(s) is an equivalent transformed transfer function in a current loop, G PLL(s) is a transfer function of SRF-PLL, G CCF(s) is a transfer function of CCF, I r is a grid-connected current I g reference value, the amplitude of the reference value is given from outside, and H 1 is a feedback coefficient of I g;
according to the above established Thevenin equivalent circuit, the expression of the total output admittance Yo(s) of the inverter system is:
Yo(s)＝Yp(s)+Yi(s)+Yv(s)
The total output admittance Y o1(s) without GVF is expressed as:
Yo1(s)＝Yp(s)+Yi(s)
When the GVF is known by combining the two formulas of the total output admittance when the GVF is not calculated by the data analysis, the system is stable, and after the GVF is added, the phase margin of the system is negative, so that the stability of the system is seriously influenced, and the negative influence caused by the GVF needs to be reduced.
S2: according to the expression of the Thevenin equivalent circuit established in the S1 and the total output admittance Yo (S) of the inverter system, deriving and transforming to obtain a grid-connected current expression as follows:
Yo is a shorthand form of Yo(s), yo is total output admittance of the inverter system, Y g is grid resistance, and u g is grid voltage;
As shown by the analysis of the ideal grid-connected system, the system has enough phase margin at the intersection frequency f c of the output impedance of the grid-connected inverter and the impedance of the power grid, and the phase margin is expressed as follows:
In the middle of The phase of the power grid admittance Y g and the phase of the inverter output admittance Y inv under the power grid impedance intersection frequency f c respectively; and analyzing according to the phase margin expression and the total output admittance of the inverter system, and obtaining that the instability of the system under a weak power grid is caused by the leading negative admittance of the GVF.
S3: correcting the phase of the total output admittance of the inverter by using an all-pass filter, and designing control parameters for improving the stability margin of the system under a weak current network, wherein the transfer function of the all-pass filter is as follows:
The k is a fixed amplitude gain in a full frequency section, k is taken as 1, the amplitude of the improved system is prevented from being influenced, and a is a phase compensation coefficient;
at this time, after the advanced feed-forward link is added, the expression of the voltage feedforward admittance is:
G AF is a shorthand version of G AF.
The all-pass filter is added into the branch of G f(s), so that the phase of Y v(s) is corrected, and the phase margin of the inverter under a weak current network is improved.
Preferably, in the davin equivalent circuit of the step S1, the grid-connected current i g (S) is expressed as follows:
where u pcc is the common-point voltage.
Preferably, the expression of the conventional grid voltage ratio feedforward G f (S) in the step S1 is 1/k pwm,kpwm, which is the inverter gain.
Preferably, the expression of the quasi-proportional resonance controller parameter G c (S) in the step S1 is:
Gc(s)＝kp+2krωis/(s2+2ωis+ω0 2)
where k p is the proportionality coefficient of G c(s), k r is the resonance coefficient of G c(s), and ω i is the bandwidth coefficient of Gc(s).
Preferably, the expressions based on the equivalent transformed transfer function G 1(s)、G2 (S) in the current loop in step S1 are respectively:
Wherein k c、Cf and S are respectively the feedback coefficient of capacitance current, capacitance and Laplacian, and L 1、L2 is respectively the inverter side inductance and the network side inductance of the filter.
Preferably, the expression based on the transfer function G PLL (S) of the SRF-PLL in step S1 is:
Where k pp is the scaling factor of the phase-locked loop, k pi is the integration factor of the phase-locked loop, and ω 0 is the fundamental angular frequency.
Preferably, the expression based on the transfer function G CCF (S) of CCF in step S1 is:
Where k CCF is denoted as the complex coefficient filter adaptation coefficient.
Preferably, the phase margin in the step S2 is in the expressionAt-90 ° in the full band, the expression of the phase margin can be transformed into:
As can be seen from the above description, And the stability of the grid-connected inverter can be ensured only when the angle is smaller than 90 degrees.
Preferably, in the step S3, the phase correction is performed in the specific frequency band by adjusting the value of the parameter a, where the parameter a has the expression:
Where f is the compensation frequency point, θ is the hysteresis compensation angle, and as known from the above equation, the phase correction can be performed in a specific frequency band by adjusting the value of the parameter a.
A photovoltaic power grid system adopts the method for improving the stability margin of a photovoltaic grid-connected inverter under the weak power grid.
The beneficial effects of the invention are as follows:
According to the invention, through carrying out output admittance modeling on a grid-connected inverter system comprising a complex coefficient filter phase-locked loop (CCF-PLL) structure and a Grid Voltage Feedforward (GVF), and carrying out stability analysis on the output admittance modeling, the problem that the system phase is advanced due to negative admittance introduced by the GVF is solved by adopting an all-pass filter to carry out hysteresis correction on the total output admittance phase of the inverter on the basis that the system phase is advanced due to the negative admittance introduced by the GVF is obtained, the stability margin of the system under the weak grid is improved, and the system stability is enhanced.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a diagram showing a structure of a single-phase LCL grid-connected inverter provided by the invention;
FIG. 2 is a diagram of a single inverter grid-tie circuit model;
FIG. 3 is a diagram showing an inverter grid-connected equivalent circuit model;
FIG. 4 is a diagram showing the total output admittance of the grid-connected inverter;
FIG. 5 is a block diagram illustrating the control of a grid-tie inverter with improved GVF;
FIG. 6 is a diagram showing the Bode diagram of an all-pass filter when a takes different values;
FIG. 7 (a) is a Bode diagram of the modified grid voltage Yv_AF(s);
FIG. 7 (b) is a Bode diagram of the grid voltage Yv(s) before modification;
FIG. 8 is a diagram of the overall output admittance of the inverter system after grid voltage improvement;
FIG. 9 (a) is a graph of the inverter grid-tie current waveform before grid voltage improvement;
FIG. 9 (b) is a graph showing the grid-tie current spectrum before grid voltage improvement;
FIG. 10 (a) is a graph showing the waveform of the grid-connected inverter current after grid voltage improvement;
FIG. 10 (b) is a graph showing the grid-tied current spectrum after grid voltage improvement.
Detailed Description
The present invention is further illustrated and described below with reference to examples, which are not intended to be limiting in any way.
Example 1
The embodiment of the invention discloses a method for improving the stability margin of a photovoltaic grid-connected inverter, and the technical scheme is further explained below by combining with a specific technical background.
Referring to fig. 1, in the single-phase LCL grid-connected inverter structure, inductor L 1, capacitor C f, and inductor L 2 form an LCL filter. I 1 is the current of L 1, I c is the current of C f, k c is the feedback coefficient of I c, H 1 is the feedback coefficient of grid-connected current I g, gc(s) is a quasi-proportional resonant controller parameter, U dc is direct current voltage, U pcc is the voltage at the common coupling point, I r is the reference value of I g, the amplitude is given by the outside and is always I r, and the phase angle is synchronous with the phase angle of U pcc through a phase-locked loop. Z g is the grid impedance, and Z g＝sLg is recorded assuming that Z g is purely inductive.
A method for improving stability margin of a photovoltaic grid-connected inverter under a weak current network comprises the following steps:
S1: referring to fig. 2 on the basis of fig. 1, fig. 2 is a model of a single inverter grid-connected circuit, and the whole system is simplified into a davin equivalent circuit, wherein the grid-connected current i g(s) has the expression:
An inverter grid-connected equivalent circuit model is established according to the formula (1) and is shown in fig. 3. The inverter equivalent output admittance Yi(s), CCF-PLL admittance Yp(s), GVF admittance Yv(s) are expressed as:
Wherein G f、Gc、G1、G2、GPLL、GCCF is a shorthand form of G f(s)、Gc(s)、G1(s)、G2(s)、GPLL(s)、GCCF(s), G f(s) is traditional power grid voltage proportion feedforward, an expression of a power grid voltage feedforward link G f(s) is 1/k pwm,Gc(s) and is expressed as a quasi-proportion resonance controller parameter, G 1(s)、G2(s) is a transfer function after equivalent transformation in a current loop, G PLL(s) is a transfer function of SRF-PLL, and G CCF(s) is a transfer function of CCF; the expression of G 1(s)、G2(s) is:
wherein k c、Cf and S are respectively the feedback coefficient of capacitance current, capacitance and Laplacian, and L 1、L2 is respectively the inverter side inductance and the network side inductance of the filter;
preferably, the expression of G PLL(s)、GCCF(s)、Gc(s) is:
Gc(s)＝kp+2krωis/(s2+2ωis+ω0 2) (9)
where k pp is the proportionality coefficient of the phase-locked loop, k pi is the integral coefficient of the phase-locked loop, ω 0 is the fundamental angular frequency, k p is the proportionality coefficient of G c(s), k r is the resonance coefficient of G c(s), ω i is the bandwidth coefficient of Gc(s).
According to the established Thevenin equivalent circuit, the expression of the total output admittance Yo(s) of the inverter system is obtained as follows:
Yo(s)＝Yp(s)+Yi(s)+Yv(s) (10)
the expression of the output admittance Yo 1(s) without GVF is:
Yo1(s)＝Yp(s)+Yi(s) (11)
the total output admittance bode diagram of the grid-connected inverter is shown in fig. 4, which can be obtained according to the formulas (10) and (11).
S2: according to the expression of the Thevenin equivalent circuit established in the S1 and the total output admittance Yo (S) of the inverter system, deriving and transforming to obtain a grid-connected current expression as follows:
Yo is a shorthand form of Yo(s), yo is total output admittance of the inverter system, Y g is grid resistance, and u g is grid voltage;
In an ideal grid-tie system, the grid impedance is 0, and the inverter output current is determined by-Y oug, at which point the system is stable. However, in actual situations, due to the influence of parameters such as a power grid transmission cable and the like, the power grid impedance is not zero, the system stability condition is Y o/Yg, the nyquist stability criterion is met, the system has enough phase margin at the intersection frequency f c of the output impedance of the grid-connected inverter and the power grid impedance, and the expression of the phase margin is as follows:
In the middle of The phase of the power grid admittance Y g and the inverter output admittance Y inv under the power grid impedance intersection frequency f c are respectively, and due to/>At-90 ° in the full band, the expression of the phase margin can be transformed into:
As can be seen from the above description, The stability of the grid-connected inverter can be ensured only when the angle is smaller than 90 degrees;
And analyzing according to the phase margin expression and the total output admittance of the inverter system, and obtaining that the instability of the system under a weak power grid is caused by the leading negative admittance of the GVF. Specific analysis is combined with fig. 4, the phase margin of the total output admittance of the grid-connected inverter system is 54.2 degrees when the GVF is not considered under the weak power grid, and the system is stable; when GVF is considered, the phase margin of the total output admittance of the grid-connected inverter system is-8.8 degrees, the stability condition is not met, and the system is unstable. Therefore, after the GVF is added, the system phase margin is negative, which leads to the system phase advance, and seriously affects the system stability, so that the negative effect of the GVF needs to be reduced.
S3: according to step S2, it is known that the system is required to be stabilized, for this purpose, an all-pass filter is added to the branch of G f (S), the phase of Y v (S) is corrected, and the phase margin of the inverter under a weak current network is improved. Fig. 5 is an equivalent control block diagram of a grid-connected inverter after GVF improvement, where G AF(s) is an all-pass filter transfer function, and the expression is:
where k is the amplitude gain, k is 1, and a is the phase compensation coefficient;
Fig. 6 is a bode diagram of an all-pass filter. The amplitude of the full frequency band is 0dB, and the phase lag compensation of 0-180 degrees can be provided in a certain frequency band. The adjustment parameter a can be used for phase correction in a specific frequency band.
Where f is the compensation frequency point and θ is the hysteresis compensation angle.
Since Y v(s) has a maximum phase of 227 DEG (f min) in the phase advance frequency band, the phase frequency curve thereof monotonically decreases. Let f min be the compensation frequency point and according to the analysis, get θ= -160 °. F min =133 Hz, θ= -160 ° is substituted into expression (14) of parameter a, yielding a=0.0068.
After the advanced feed-forward link is added, the expression of the voltage feedforward admittance is as follows:
FIG. 7 (a) is a Bode diagram of modified GVF admittance Y v_AF(s). The phase of Y v_AF(s) at f min is 66.7 DEG, meeting the stability requirement.
After the grid voltage feedforward link is improved, the total output admittance of the inverter system is expressed as follows:
Yo_AF(s)＝Yp(s)+Yi(s)+Yv_AF(s) (16)
In conclusion, the method for improving the stability margin of the photovoltaic grid-connected inverter under the weak power grid improves the phase margin of the system, and further improves the stability of the grid-connected system.
Example 2
In order to verify the correctness of the proposed control method, matalab is adopted for simulation, a single-phase photovoltaic inverter system model is built in MATLAB/Simulink simulation software, and simulation parameters in the embodiment are shown in the following table:
The grid-connected current waveform and spectrum analysis of a single string photovoltaic inverter without applying/applying the active damping high frequency resonance suppression method are shown in fig. 10 (a) and 10 (b).
As can be seen from fig. 8, 9 (a) and 9 (b), after the all-pass filter is introduced into the grid voltage feed-forward channel, the grid-connected current distortion rate of the system is reduced by 94.2%, which indicates that the resonance of the inverter is effectively inhibited and the grid-connected current waveform is significantly improved.
The conventional GVF causes the inverter system to have a phase margin of-8.8 ° at scr=2, and the system is unstable, as known from fig. 4. As shown in fig. 9 (a) and 9 (b), after the conventional GVF is added, the grid-connected current i g(s) is distorted and distorted when scr=2, and the system is unstable. The result shows that under weak current network, the stability margin of the grid-connected inverter system adopting the CCF-PLL is reduced by the traditional GVF, and the instability of the system is aggravated along with the increase of the impedance of the power network.
As can be seen from fig. 8, the GVF is modified so that the phase margin of the inverter system at scr=2 is 34.2 °, and the system is stable. As shown in fig. 10 (a) and 10 (b), the distortion of the grid-connected current waveform is significantly improved after the GVF is added.
According to simulation analysis, the method for improving the stability margin of the photovoltaic grid-connected inverter under the weak current network provided by the invention has obvious effects of improving the phase margin of the system and enhancing the stability of the system.
Example 3
A photovoltaic grid-connected system adopts the method for improving the stability margin of a photovoltaic grid-connected inverter under a weak current network in the embodiment 1, models the output admittance of the grid-connected inverter system comprising a complex coefficient filter phase-locked loop structure (CCF-PLL) and Grid Voltage Feedforward (GVF), and performs stability analysis on the output admittance modeling to obtain that the instability of the system under the weak current network is caused by the lead of the system phase due to the negative admittance introduced by the GVF, and on the basis, an all-pass filter is adopted to perform hysteresis correction on the total output admittance phase of the inverter, so that the problem of lead of the system phase due to the negative admittance introduced by the GVF is solved, the stability margin of the system under the weak current network is improved, and the stability of the system is enhanced.
It is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.
Claims (9)
1. The method for improving the stability margin of the photovoltaic grid-connected inverter under the weak current network is characterized by comprising the following steps of:
S1: simplifying the whole system into a Thevenin equivalent circuit, connecting a power grid side with an inverter side through PCC to obtain an inverter equivalent output admittance of Y i(s), a CCF-PLL admittance of Y p(s) and a GVF admittance of Y v(s), wherein the admittances are expressed as follows:
Wherein G f、Gc、G1、G2、GPLL、GCCF is a shorthand form of G f(s)、Gc(s)、G1(s)、G2(s)、GPLL(s)、GCCF(s), G f(s) is traditional power grid voltage proportion feedforward, G c(s) is a quasi-proportion resonant controller parameter, G 1(s)、G2(s) is an equivalent transformed transfer function in a current loop, G PLL(s) is a transfer function of SRF-PLL, G CCF(s) is a transfer function of CCF, I r is a grid-connected current I g reference value, the amplitude of the reference value is given from outside, and H 1 is a feedback coefficient of I g;
according to the above established Thevenin equivalent circuit, the expression of the total output admittance Yo(s) of the inverter system is:
Yo(s)＝Yp(s)+Yi(s)+Yv(s)
The total output admittance Y o1(s) without GVF is expressed as:
Yo1(s)＝Yp(s)+Yi(s)；
S2: according to the expression of the Thevenin equivalent circuit established in the S1 and the total output admittance Yo (S) of the inverter system, deriving and transforming to obtain a grid-connected current expression as follows:
Yo is a shorthand form of Yo(s), yo is total output admittance of the inverter system, Y g is grid resistance, and u g is grid voltage;
As shown by the analysis of the ideal grid-connected system, the system has enough phase margin at the intersection frequency f c of the output impedance of the grid-connected inverter and the impedance of the power grid, and the phase margin is expressed as follows:
In the middle of The phase of the power grid admittance Y g and the phase of the inverter output admittance Y inv under the power grid impedance intersection frequency f c respectively; analyzing according to the phase margin expression and the total output admittance of the inverter system, and obtaining that the instability of the system under a weak power grid is caused by leading negative admittance of GVF to lead the phase of the system;
S3: correcting the phase of the total output admittance of the inverter by using an all-pass filter, and designing control parameters for improving the stability margin of the system under a weak current network, wherein the transfer function of the all-pass filter is as follows:
The k is a fixed amplitude gain in a full frequency section, k is taken as 1, the amplitude of the improved system is prevented from being influenced, and a is a phase compensation coefficient;
at this time, after the advanced feed-forward link is added, the expression of the voltage feedforward admittance is:
G AF is a shorthand version of G AF(s).
2. The method for improving the stability margin of a photovoltaic grid-connected inverter under a weak current network according to claim 1, wherein in the davin equivalent circuit of step S1, the grid-connected current i g (S) has the expression:
where u pcc is the common-point voltage.
3. The method for improving stability margin of a photovoltaic grid-connected inverter under a weak grid according to claim 1, wherein the expression of the conventional grid voltage ratio feedforward G f (S) in step S1 is 1/k pwm,kpwm, which is an inverter gain.
4. The method for improving the stability margin of a photovoltaic grid-connected inverter under a weak power grid according to claim 1, wherein the expression of the quasi-proportional resonant controller parameter G c (S) in the step S1 is:
Gc(s)＝kp+2krωis/(s2+2ωis+ω0 2)
where k p is the proportionality coefficient of G c(s), k r is the resonance coefficient of G c(s), and ω i is the bandwidth coefficient of Gc(s).
5. The method for improving the stability margin of a photovoltaic grid-connected inverter under a weak current network according to claim 1, wherein the expression of the transfer function G 1(s)、G2 (S) after the equivalent transformation in the current loop in step S1 is respectively:
Wherein k c、Cf and S are respectively the feedback coefficient of capacitance current, capacitance and Laplacian, and L 1、L2 is respectively the inverter side inductance and the network side inductance of the filter.
6. The method for improving stability margin of a photovoltaic grid-connected inverter under a weak current network according to claim 1, wherein the transfer function G PLL (S) of the SRF-PLL in step S1 is expressed as follows:
Where k pp is the scaling factor of the phase-locked loop, k pi is the integration factor of the phase-locked loop, and ω 0 is the fundamental angular frequency.
7. The method for improving stability margin of a photovoltaic grid-connected inverter under weak current network according to claim 1, wherein the expression based on the transfer function G CCF (S) of CCF in step S1 is:
Where k CCF is denoted as the complex coefficient filter adaptation coefficient.
8. The method for improving stability margin of photovoltaic grid-connected inverter under weak current network according to claim 1, wherein the phase margin in step S2 is expressed in the expressionAt-90 ° in the full band, the expression of the phase margin can be transformed into:
As can be seen from the above description, And the stability of the grid-connected inverter can be ensured only when the angle is smaller than 90 degrees.
9. The method for improving the stability margin of a photovoltaic grid-connected inverter under a weak power grid according to claim 1, wherein in the step S3, the phase correction is performed in a specific frequency band by adjusting the value of a parameter a, and the expression of the parameter a is as follows:
Where f is the compensation frequency point, θ is the hysteresis compensation angle, and as known from the above equation, the phase correction can be performed in a specific frequency band by adjusting the value of the parameter a.
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