CN115360753A - LCL type grid-connected inverter system optimization method based on fractional order differential compensator - Google Patents
LCL type grid-connected inverter system optimization method based on fractional order differential compensator Download PDFInfo
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Abstract
The invention belongs to the field of robustness control of a new energy grid-connected inverter system, and provides an LCL type grid-connected inverter system optimization method based on a fractional order differential compensator. Firstly, establishing an LCL type grid-connected inverter system mathematical model based on a fractional order differential compensator; obtaining the relation between the reverse resonance peak frequency of the system and the impedance of the power grid according to a mathematical model of the system; then, obtaining a parameter design condition of the fractional order differential compensator by analyzing a resonance zero pole of an open-loop transfer function of the inverter system; substituting the parameter design condition into a fractional order differential compensator expression to obtain a fractional order differential compensator parameter design result; and obtaining a fitting frequency band and a fitting order design result of the fractional order differential compensator according to the frequency domain characteristic and the fitting characteristic of the fractional order differential. Finally, the system has enough phase margin to adapt to the change of the weak power grid, and the robustness of the system in the weak power grid is improved.
Description
Technical Field
The invention belongs to the field of robustness control of a new energy grid-connected inverter system, and particularly relates to an LCL type grid-connected inverter system optimization method based on a fractional order differential compensator.
Background
With the exhaustion of conventional fossil energy and the increase of environmental pollution, renewable energy sources such as photovoltaic and wind power generation have received much attention. The main development and utilization approach of renewable energy sources is distributed power generation, and grid-connected inverters are widely concerned as core devices for connecting power generation systems and power grids.
In order to ensure that the grid-connected current meets the requirements of relevant standards, a mode of cascading an inverter with an L filter or an LC filter is often adopted, but the mode can cause the filter inductor to be large in size and high in manufacturing cost. At present, the common practice is to use an LCL filter instead of the LCL filter, so as to achieve the purpose of effectively reducing the volume and obtaining better performance. However, the LCL filter as a third-order system has a resonance peak at a specific frequency, which may cause the network-access current to oscillate, and thus, the control is difficult. To address this problem, there are three active damping methods commonly used at present: a capacitance current and grid-connected current double closed-loop control method is based on a filter and current regulator series connection method and a system order reduction method. The system order reduction method can reduce the system order from three orders to one order, greatly reduces the control difficulty of the system, and is widely applied due to simple and flexible parameter design and higher control bandwidth.
The system order reduction method can obtain good control effect under the condition of neglecting system delay. However, in a practical digital control system, time delay is inevitable, which greatly affects the robustness of the system and becomes sensitive to the impedance of the power grid, making the application difficult. Therefore, on the basis of the system order reduction method, how to compensate the system delay can not only retain the advantages of the original method, but also enhance the system stability, and becomes a problem to be solved urgently.
Disclosure of Invention
The invention aims to provide an LCL type grid-connected inverter system optimization method based on a fractional order differential compensator, which aims to compensate the digital delay of a system and solve the problem of poor robustness of a grid-connected system in a digital control system.
Considering that the fractional order controller has better control effect and wider application range, the invention introduces the fractional order differential compensator on the optimization problem of the LCL type grid-connected inverter system and realizes the optimization of the control performance by utilizing the unique fitting characteristic of the fractional order differential compensator.
The technical scheme adopted by the invention is as follows: the LCL type grid-connected inverter system optimization method based on the fractional order differential compensator comprises the following steps:
establishing an LCL type grid-connected inverter system mathematical model based on a fractional order differential compensator;
obtaining the relation between the reverse resonance peak frequency of the system and the impedance of the power grid according to a mathematical model of the system;
analyzing a resonance zero-pole of an open-loop transfer function of the inverter system to obtain a parameter design condition of the fractional order differential compensator;
and substituting the parameter design condition into the expression of the fractional order differential compensator to obtain the parameter design result of the fractional order differential compensator.
And obtaining a fitting frequency band and a fitting order design result of the fractional order differential compensator according to the frequency domain characteristic and the fitting characteristic of the fractional order differential.
Preferably, the LCL grid-connected inverter system mathematical model based on the fractional order differential compensator is the following open-loop transfer function, which is expressed by a first expression:
in the above formula, L 1 Is an inverter side inductor, L 2 A network side inductor and a filter capacitor, and R d For damping resistance, the impedance of the grid at the PCC is pure inductance L g Beta and 1-beta are current weighting coefficients, K PWM ＝v in /v tri The representation represents the voltage amplification of the inverter, v tri Is the amplitude of the triangular carrier, v in Representing the input DC bus voltage of the inverter, G f (s) is a PCC voltage feedforward function, G d (s) represents a digital delay element, and the transfer function of the digital delay element is a second expression:
wherein, T s Represents the sampling time of the system;
G i (s) a PI current regulator, the mathematical expression being a third expression;
wherein, K p Is a proportionality coefficient, K r Is an integration time constant;
get G f (s) and β satisfy the fourth expression and the fifth expression, respectively:
G c (s) is a fractional order differential compensator, and the mathematical expression is a sixth expression:
G c (s)＝Ks μ ,μ∈(0,1)
where K is the differential time constant and μ is the order of the differentiation.
Preferably, the step of obtaining the relationship between the system inverse resonance peak frequency and the grid impedance according to the system mathematical model includes:
substituting the fourth expression and the fifth expression into the first expression to obtain a seventh expression of the open-loop transfer function of the inverter system:
the open-loop transfer function of the inverter has a pair of conjugate resonance zero points, and the conjugate resonance zero points cause the appearance of a reverse resonance peak in the amplitude-frequency characteristic;
setting the amplitude of the molecular resonance term of the seventh expression to zero, so as to obtain an eighth expression:
can be obtained with L g The changed inverse resonance frequency is a ninth expression:
visible inverse resonance frequency f rx As the grid impedance changes, the grid tie system robustness decreases as the grid impedance increases.
Preferably, the step of analyzing a resonant zero pole of an open-loop transfer function of the inverter system to obtain a design condition of a fractional order differential compensator parameter includes:
as can be seen from the seventh expression, the root cause of the failure to eliminate the resonant zero pole is 1-G c (s)G d (s)；
To make 1-G c (s)G d (s) an amplitude approximately equal to zero at the reverse resonance frequency, a fractional order differential compensator G c (s) at f rx-min At an amplitude of 1, and an open-loop transfer function of the inverter at f rx-min There is a phase jump, and in order to maintain the stability of the grid-connected system, the fractional order differential compensator is in f rx-min The provided leading phase angle can completely offset the delay digital delay link G d (s) an introduced phase lag;
therefore, the parameter design condition of the fractional order differential compensator is set to the tenth expression:
wherein f is rx-min The reverse resonance frequency corresponding to the maximum value of the impedance of the power grid.
Preferably, the step of obtaining a parameter design result of the fractional order differential compensator by substituting the parameter design condition into the fractional order differential compensator expression includes:
for fractional order differential compensator transfer function G c (s), let s = j ω, then
Substituting the tenth expression to obtain an eleventh expression:
finally, the parameter design result of the fractional order differential compensator is obtained as a twelfth expression:
where K is the differential time constant and μ is the order of the differentiation.
Preferably, the step of obtaining a fitting frequency band and a fitting order design result of the fractional order differential compensator according to the frequency domain characteristic and the fitting characteristic of the fractional order differential comprises:
according to the frequency domain characteristic and the fitting characteristic of the fractional order differential, the fitting frequency band of the fractional order differential compensator is set to [10Hz,100000Hz ], and N =5 is selected in the fitting order.
According to another aspect of the present invention, the present invention also provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the computer program executes any one of the methods for optimizing the LCL grid-connected inverter system based on the fractional order differential compensator.
The technical scheme provided by the invention has the following beneficial effects:
1. the stability of the LCL type grid-connected inverter system in the digital system is improved.
2. The adaptability of the LCL type grid-connected inverter system to the impedance of the power grid is improved, and the robustness of the system is improved.
Drawings
The invention will be further described with reference to the following drawings and examples, wherein:
fig. 1 is an execution flowchart of an LCL-type grid-connected inverter system optimization method based on a fractional order differential compensator according to an embodiment of the present invention;
FIG. 2 is a topological structure of an LCL type grid-connected inverter system based on a fractional order differential compensator in the embodiment of the invention;
fig. 3 is a control block diagram of an LCL type grid-connected inverter system based on a fractional order differential compensator in the embodiment of the present invention;
FIG. 4 is a Bode diagram of a fractional order differential compensator in an embodiment of the present invention;
FIG. 5 is a system open loop Bode diagram of an LCL type grid-connected inverter system based on a fractional order differential compensator when the impedance of a power grid changes in the embodiment of the invention;
fig. 6 is a closed loop system root trace diagram of an LCL type grid-connected inverter system based on a fractional order differential compensator in the embodiment of the present invention;
fig. 7 is a grid-connected voltage and current waveform diagram of an LCL type grid-connected inverter system based on a fractional order differential compensator according to an embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Referring to fig. 1, the method for optimizing an LCL-type grid-connected inverter system based on a fractional order differential compensator according to the embodiment of the present invention includes the following steps:
s10: establishing an LCL type grid-connected inverter system mathematical model based on a fractional order differential compensator;
s20: obtaining the relation between the reverse resonance peak frequency of the system and the impedance of the power grid according to a mathematical model of the system; (ii) a
S30: analyzing a resonance zero-pole of an open-loop transfer function of the inverter system to obtain a parameter design condition of the fractional order differential compensator;
s40: substituting the parameter design condition into a fractional order differential compensator expression to obtain a fractional order differential compensator parameter design result;
s50: and obtaining a fitting frequency band and a fitting order design result of the fractional order differential compensator according to the frequency domain characteristic and the fitting characteristic of the fractional order differential.
As shown in fig. 2, a mathematical model is established according to the topology structure diagram of the system of fig. 2, and a control structure diagram of the system is shown in fig. 3.
In an embodiment of the present invention, the implementation manner of step S10 is:
an LCL type grid-connected inverter system mathematical model based on a fractional order differential compensator is constructed, and the open-loop transfer function of the mathematical model is as follows:
in the above formula, L 1 Is an inverter-side inductor, L 2 A network side inductor and a filter capacitor, and R d For damping the resistance, the grid impedance at the Point of Common Coupling (PCC) is a pure inductance L g . Beta and 1-beta are current weighting coefficients, K PWM ＝v in /v tri (v in Representing the input DC bus voltage, v, of the inverter tri Is a triangular carrier amplitude) represents the inverter voltage amplification. G i (s) is a PI current regulator, G f (s) is a PCC voltage feed forward function. G d (s) represents a digital delay element, where T s Representing the sampling time of the system, the transfer function is:
G i (s) denotes a PI current regulator, K p Is a proportion systemNumber, K r Is the integration time constant.
Get G f (s) and β satisfy the following design:
G c (s) is a fractional order differential compensator, K is a differential time constant, and μ is an order.
G c (s)＝Ks μ ,μ∈(0,1) (6)
It should be noted that the system grid impedance L g The weak grid degree of the system is closely related, and for convenience of subsequently explaining embodiments, a formula of the short-circuit current ratio SCR is given to represent the strong and weak degree of the grid:
wherein, I SC Representing the magnitude of the effective value of the short-circuit current, I N Indicating the magnitude of the rated current, P, of the inverter output o For rated power of the system, omega o Is the fundamental angular frequency. The smaller the value of the SCR, the stronger the level of the weak grid, and if the value of the SCR is greater than 25, the grid is called a strong grid, and if the SCR is less than 10, the grid is called a weak grid. L is g Is in linear relation with SCR and can utilize the network impedance L g The change of the voltage is used for reflecting the strength of the power grid. In this embodiment, the set parameters are as shown in table 1, and SCR =25, so that the critical grid impedance of the strong grid is L g-strong =1mH. Let SCR =10, obtain the critical grid impedance of the weak grid as L g-weak ＝2.6mH。
Table 1 table of parameters of examples
In the above embodiment, according to the above system model, the change of the system stability when the system operates in a weak grid can be compared by changing the grid impedance.
In an embodiment of the present invention, the implementation manner of analyzing the relationship between the system reverse resonance peak frequency and the power grid impedance according to the system mathematical model in step S20 is specifically:
based on the design of equations (4) and (5), substituting into equation (1), the open-loop transfer function of the system is:
as can be seen from equation (8), there exists a pair of conjugate resonance zeros, which directly causes the occurrence of an inverse resonance peak in the amplitude-frequency characteristic. Further study on the frequency characteristics of the inverse resonance peak to make the amplitude of the molecular resonance term in equation (8) zero, i.e.
Can be obtained with L g The changed inverse resonant frequency is:
visible reverse resonant frequency f rx As the grid impedance changes. In order to fully analyze the working state of the system under different conditions, in this embodiment, the system is selectedWhen the system short circuit ratio SCR =5, obtaining the maximum value of the corresponding power grid impedance as L according to the formula (7) g-max =5.1mH, and the inverse resonance peak frequency at that time is obtained by substituting the equation (10) with the minimum value f rx-min ＝773.1Hz。
In the above embodiment, based on the analysis of S20, the relation between the resonance peak frequency and the grid impedance is obtained.
In step S30, according to the system mathematical model, the resonant zero-pole of the open-loop transfer function of the inverter system is analyzed, and the implementation manner of obtaining the parameter design condition of the fractional order differential compensator is specifically as follows:
as can be seen from the formula (8), the root of the failure to cancel the resonance zero-pole is 1-G c (s)G d (s) the effect of the digital delay on the system can be eliminated by making this term 0. Thus, the compensator parameters can be analyzed in terms of both amplitude-frequency and phase-frequency characteristics.
As can be seen from the analysis of the previous step, the robustness of the grid-connected system decreases as the grid impedance increases, so that in the parameter design of the embodiment, L is set only for the case where the grid impedance is maximum g-max =5.1mH, and the reverse resonance frequency at this time is f rx-min ＝773.1Hz。
To make 1-G c (s)G d The amplitude of(s) is approximately equal to 0 at the inverse resonance frequency, compensator G c (s) at f rx-min The amplitude of (b) should be 1. In addition, the inverter open loop transfer function is at f rx-min There is a phase jump, and in order to maintain the stability of the grid-connected system, the lead compensator is at f rx-min It is necessary to provide a sufficiently large leading phase angle to completely cancel the delay element G d (s) the phase lag introduced, from which the following parametric design conditions can be derived from the above analysis:
in an embodiment of the present invention, in step S40, according to the derivation and conclusion of steps S20 and S30, the obtained parameter design condition is substituted into the fractional order differential compensator expression to obtain an implementation manner of a parameter design result of the fractional order differential compensator, which is specifically implemented as follows:
for fractional order differential compensator transfer function G c (s), let s = j ω, then
Substituting equation (11) with:
finally obtaining the parameter design result of the fractional order differential compensator:
it should be noted that, because the fractional order differential term cannot be directly implemented, a polynomial of a high-order integer term is usually adopted to fit the fractional order differential term in engineering, and the frequency domain response of the fractional order differential term can be approximated to an original fractional order model in a specific frequency band, so that the selection of the fitting frequency band and the fitting order needs to be explained in the aspect of the implementation of the fractional order. When the fractional order is approximately fitted, partial loss exists near two ends of a fitting frequency band, so that an ideal set value cannot be achieved, and the fitting frequency band needs to be set to be larger in order not to influence the compensation effect.
In one embodiment of the present invention, in step S50, the fitting frequency band of the fractional order differential compensator is set to [10hz,100000hz ], and the fitting order is N =5, as shown in fig. 4.
According to the embodiment parameters in table 1, a system open loop transfer function bode graph is plotted when the grid impedance of the LCL type grid-connected inverter system based on the fractional order differential compensator changes from 0mH to 5.1mH, as shown in fig. 5. It can be seen that after the fractional order differential compensator is used, the frequency characteristic of the open-loop transfer function of the inverter system still has an inverse resonant peak, which is caused by the fact that the calculation error cannot be completely compensated, and the inverse resonant peak is associated with L g The larger the difference from 5.1mH, the larger the resonance peak amplitude will be. But the phase frequency characteristic before the resonance peak is compared with the traditional methodThe WAC method is greatly improved, the phase margin of the system is larger than 0, the system is in a stable state, and the robustness of the system is greatly improved.
From fig. 3 it can be deduced that the system is from i 2 (s) to
The expression of the closed-loop transfer function of (1) is:
when the grid impedance L g When changing from 0mH to 6mH, FIG. 6 is a root trace diagram of the closed-loop transfer function of the system incorporating the fractional order differential compensator (only the dominant pole is shown in the figure, with the direction of the arrow L g Increasing direction), it can be seen that all poles are located on the left half plane, the system is stable, and the system obtains better robustness.
In order to further verify the effectiveness of the method of the invention, the LCL type grid-connected inverter system of the embodiment was established. The system parameters are shown in table 1. The control method is realized on the basis of NI PXIE-1071 hardware in a ring experiment platform, is connected to a power analyzer through an external interface board to display a waveform, and measures and outputs a THD value of the side current of the power grid.
As shown in fig. 7, fig. 7 is an experimental waveform diagram of the grid-connected inverter when the method for optimizing the LCL type grid-connected inverter system based on the fractional order differential compensator according to the present invention is applied to different grid impedance values. It can be seen from the figure that when the impedance change of the power grid changes from 0mH to 5.1mH, the grid-connected inverter can stably work, higher grid-connected current quality is kept, and the method verifies that the system robustness of the LCL type grid-connected inverter system based on the fractional order differential compensator can be improved under the weak power grid.
As a preferred embodiment of the present invention, the present invention further provides an electronic device, where the electronic device includes a memory and a processor, and the memory stores a computer program, and when the computer program is executed by the processor, the method for optimizing an LCL-type grid-connected inverter system based on a fractional order differential compensator according to the foregoing embodiment is executed, and the same technical effect can be achieved, and therefore, details are not repeated here.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or system that comprises the element.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments. In the unit claims enumerating several means, several of these means can be embodied by one and the same item of hardware. The use of the words first, second, third and the like do not denote any order, but rather the words first, second and the like may be interpreted as indicating any order.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (7)
1. A LCL type grid-connected inverter system optimization method based on a fractional order differential compensator is characterized by comprising the following steps:
establishing an LCL type grid-connected inverter system mathematical model based on a fractional order differential compensator;
obtaining the relation between the reverse resonance peak frequency of the system and the impedance of the power grid according to a mathematical model of the system;
analyzing a resonance zero-pole of an open-loop transfer function of the inverter system to obtain a parameter design condition of the fractional order differential compensator;
substituting the parameter design condition into a fractional order differential compensator expression to obtain a fractional order differential compensator parameter design result;
and obtaining a fitting frequency band and a fitting order design result of the fractional order differential compensator according to the frequency domain characteristic and the fitting characteristic of the fractional order differential.
2. The LCL type grid-connected inverter system optimization method based on the fractional order differential compensator according to claim 1, wherein the LCL type grid-connected inverter system mathematical model based on the fractional order differential compensator is the following open-loop transfer function, which is expressed by a first expression:
in the above formula, L 1 Is an inverter side inductor, L 2 A network side inductor and a filter capacitor, which together form an LCL inverter, R d For damping resistance, the grid impedance at the PCC is a pure inductance L g Beta and 1-beta are current weighting coefficients, K PWM ＝v in /v tri The representation represents the voltage amplification of the inverter, v tri Is the amplitude of the triangular carrier, v in Representing the input DC bus voltage, G, of the inverter f (s) is a PCC voltage feedforward function, G d (s) represents a digital delay element, and the transfer function of the digital delay element is a second expression:
wherein, T s Represents the sampling time of the system;
G i (s) represents a PI current regulator, the mathematical expression being a third expression;
wherein, K p Is a proportionality coefficient, K r Is the integration time constant;
get G f (s) and β satisfy the fourth expression and the fifth expression, respectively:
G c (s) is a fractional order differential compensator, and the mathematical expression is a sixth expression:
G c (s)＝Ks μ ,μ∈(0,1)
where K is the differential time constant and μ is the order of the differential.
3. The LCL type grid-connected inverter system optimization method based on fractional order differential compensator according to claim 2, wherein the step of obtaining the relation between the system inverse resonance peak frequency and the grid impedance according to the system mathematical model comprises:
substituting the fourth expression and the fifth expression into the first expression to obtain a seventh expression of the open-loop transfer function of the inverter system:
the open-loop transfer function of the inverter has a pair of conjugate resonance zero points, and the conjugate resonance zero points cause the appearance of a reverse resonance peak in the amplitude-frequency characteristic;
setting the amplitude of the molecular resonance term of the seventh expression to zero, so as to obtain an eighth expression:
can be obtained with L g The changed inverse resonance frequency is a ninth expression:
visible inverse resonance frequency f rx As the grid impedance changes, the grid tie system robustness decreases as the grid impedance increases.
4. The LCL type grid-connected inverter system optimization method based on the fractional order differential compensator according to claim 3, wherein the step of analyzing the resonance zero-pole of the open-loop transfer function of the inverter system to obtain the parameter design condition of the fractional order differential compensator comprises:
as can be seen from the seventh expression, the root cause of the failure to eliminate the resonant zero pole is 1-G c (s)G d (s)；
To make 1-G c (s)G d (s) is approximately equal to zero at the reverse resonant frequency, fractional order differential compensator G c (s) at f rx-min At an amplitude of 1, and an open-loop transfer function of the inverter at f rx-min There is a phase jump, in order to maintain the stability of the grid-connected system, the fractional order differential compensator is at f rx-min The provided leading phase angle can completely offset the delay digital delay link G d (s) an introduced phase lag;
therefore, the parameter design condition of the fractional order differential compensator is set to the tenth expression:
wherein f is rx-min The reverse resonance frequency corresponding to the maximum value of the impedance of the power grid.
5. The LCL type grid-connected inverter system optimization method based on the fractional order differential compensator according to claim 4, wherein the step of substituting the parameter design condition into the fractional order differential compensator expression to obtain the fractional order differential compensator parameter design result comprises:
for fractional order differential compensator transfer function G c (s), let s = j ω, then
Substituting the tenth expression to obtain an eleventh expression:
finally, the parameter design result of the fractional order differential compensator is obtained as a twelfth expression:
where K is the differential time constant and μ is the order of the differentiation.
6. The LCL type grid-connected inverter system optimization method based on the fractional order differential compensator according to claim 5, wherein the step of obtaining the fitting frequency band and the fitting order design result of the fractional order differential compensator according to the frequency domain characteristic and the fitting characteristic of the fractional order differential comprises:
and according to the frequency domain characteristic and the fitting characteristic of the fractional order differential, setting the fitting frequency band of the fractional order differential compensator to be [10Hz and 100000Hz ], and selecting N =5 in the fitting order.
7. An electronic device, characterized in that it comprises a memory and a processor, said memory having stored thereon a computer program which, when executed by said processor, performs the fractional order differential compensator-based LCL grid-connected inverter system optimization method according to any of claims 1-6.
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