CN113644836B - Robust control method suitable for LCL type grid-connected inverter - Google Patents

Robust control method suitable for LCL type grid-connected inverter Download PDF

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CN113644836B
CN113644836B CN202110854577.9A CN202110854577A CN113644836B CN 113644836 B CN113644836 B CN 113644836B CN 202110854577 A CN202110854577 A CN 202110854577A CN 113644836 B CN113644836 B CN 113644836B
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filter capacitor
voltage
grid
filter
positive feedback
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CN113644836A (en
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刘钊
徐魁
荣国灿
方城
马超
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Jiangsu Nanzi Tonghua Smart Energy Co ltd
Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/539—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency
    • H02M7/5395—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency by pulse-width modulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241—The oscillation concerning frequency
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • H02J2300/24—The renewable source being solar energy of photovoltaic origin
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

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  • Power Engineering (AREA)
  • Inverter Devices (AREA)

Abstract

The invention provides a robust control method suitable for an LCL type grid-connected inverter, which is characterized in that when a system is in a critical condition, namely the resonant frequency of an LCL filter is equal to 1/6 of sampling frequency, and the LCL type grid-connected inverter based on output current and filter capacitor current feedback is no longer in a stable state, the system can be kept stable under the critical condition by introducing filter capacitor voltage positive feedback. In addition, because the voltage of the Common connection Point (PCC) is in a proportional relation with the voltage of the filter capacitor, the positive feedback of the voltage of the filter capacitor can be replaced by the feedforward of the PCC voltage, so that the problem of increasing the sensor caused by introducing the positive feedback of the voltage of the filter capacitor is solved. By introducing PCC voltage feedforward, the system can be stabilized under all values of grid-connected inductance. The invention only increases the calculated amount of system control, and has no other additional economic investment.

Description

Robust control method suitable for LCL type grid-connected inverter
Technical Field
The invention belongs to the technical field of distributed power generation, and particularly relates to a robust control method suitable for an LCL type grid-connected inverter.
Background
Nowadays, distributed power generation technology is continuously developed along with increasing energy requirements, and research on an LCL type filter is widely researched in order to obtain good electric energy quality. Compared with the traditional filter, the LCL type filter can better reduce the harmonic component injected into the power grid, and has small volume and low price, so that the LCL type grid-connected inverter has great advantages in the grid-connected inverter.
However, the natural resonant frequency of the LCL type filter makes the current injected into the grid by the inverter difficult to control. The grid impedance is changed, which causes the resonant frequency of the LCL type grid-connected filter to be changed, which makes the whole system with the stabilizing controller unstable. To prevent this drawback, robust control is often used to control the system, and when the resonant frequency of the LCL type grid-connected filter is less than 1/6 of the system sampling frequency and a proportional controller is used, filter capacitor feedback is added to stabilize the system. However, when the grid-connected inductor is in a critical value, namely the resonant frequency of the LCL type grid-connected filter is equal to 1/6 of the sampling frequency of the system, the system is not stable any more, and at the moment, the grid-connected inverter cannot work in a normal state, and the electric energy injected into the power grid does not have higher electric energy quality any more.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the technical problems in the background art, the invention provides a robust control method suitable for an LCL type grid-connected inverter, so that a grid-connected inverter system can keep a stable state when grid-connected inductance is in a critical value, and the method specifically comprises the following steps: in a grid-connected inverter control system, a compensation network G c And filter capacitor current feedback K a The optimal design of (2); when the grid-connected inductor is in a critical value, the system is not stable any more, and filter capacitor voltage positive feedback is introduced; and replacing the positive feedback of the filter capacitor with the PCC voltage feedforward equivalence according to the proportional relation between the PCC voltage and the filter capacitor voltage.
The invention specifically comprises the following steps:
step 1, calculating a compensation network G based on a proportional controller c And filter capacitor current feedback coefficient K a Is determined by the optimal solution of (a) to (b),thus obtaining the current feedback of the optimal proportional controller and the optimal filter capacitor;
step 2, introducing filter capacitor voltage positive feedback under the current feedback of the optimal proportion controller and the optimal filter capacitor, and solving the filter capacitor voltage positive feedback coefficient K by drawing a root track of a system closed loop pole in a discrete domain v The value range enables the system to be stable under critical conditions;
and 3, equivalently replacing the filter capacitor voltage positive feedback with the PCC voltage feedforward according to the proportional relation between the PCC voltage and the filter capacitor voltage.
In step 1, the compensation network G c By adopting proportional control, the calculation formula is as follows:
G c ＝K p ＝K pop ＝ω c (L 1 +L 2 )
in the formula, K p Is a proportional gain factor, K pop For optimum proportional gain factor, ω c Is the system cut-off frequency, L 1 ,L 2 Two filter inductance values for the LCL filter.
In step 1, a filter capacitor current feedback coefficient K a The calculation formula is as follows:
Figure RE-GDA0003292656830000021
in the formula, K aop For optimal feedback coefficient, intermediate variable
Figure RE-GDA0003292656830000022
f s Is the sampling frequency.
In step 2, introducing filter capacitor voltage positive feedback, and solving a filter capacitor voltage positive feedback coefficient K through a root track of a system closed loop pole in a discrete domain v The value range of (a) enables the system to maintain a stable state under a critical condition, i.e., when the resonant frequency of the LCL filter is equal to 1/6 of the sampling frequency.
In step 3, the proportional relationship between the PCC voltage and the filter capacitor voltage is as follows:
Figure RE-GDA0003292656830000023
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0003292656830000024
in order to be the PCC voltage,
Figure RE-GDA0003292656830000025
for filtering the capacitor voltage, L g For the value of the inductance to be connected to the grid,
Figure RE-GDA0003292656830000026
is the grid voltage. Since the second term on the right of the equation is an external disturbance term and does not affect the system stability, it is considered as 0.
Compared with the prior art, the invention has the following obvious advantages: 1) When the grid-connected inductor is in a critical value, the LCL type grid-connected inverter can be stable; 2) The input quantity PCC voltage of the PLL can be directly used for equivalently replacing the filter capacitor voltage without increasing the number of the sensors, the calculated quantity of a control system is increased only a little, and the economic cost is saved.
Drawings
The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
FIG. 1 is a circuit topology diagram of a robust controlled LCL type grid-connected inverter applying the present invention;
FIG. 2 is a block diagram of a system transfer function;
FIG. 3 shows voltage positive feedback without filter capacitor and K p ＝K pop ,K a ＝K aop While changing L g A schematic diagram of a root locus of a closed loop pole of a time system;
FIG. 4 shows a graph of K p ＝K pop ,K a ＝K aop ,L g ＝L gc While changing K v A schematic diagram of a root locus of a closed loop pole of a time system;
FIG. 5 shows a modification K v A schematic diagram of maximum values of the mode values of the closed-loop poles;
FIG. 6 is a circuit topology diagram of an LCL grid-connected inverter when PCC voltage feedforward is introduced;
FIG. 7 shows the change of grid-connected inductance L when PCC voltage feedforward is introduced g A schematic diagram of a root locus of a closed loop pole of a time system;
FIG. 8 is a diagram of simulation results of the present invention.
Detailed Description
According to the LCL grid-connected inverter topology shown in fig. 1 in combination with the control method, the system transfer function block diagram shown in fig. 2 can be obtained, wherein the inverter is modeled as unity gain, and the transfer functions of other modules in the z domain are as follows:
Figure RE-GDA0003292656830000031
Figure RE-GDA0003292656830000032
Figure RE-GDA0003292656830000033
wherein G is 1 (z)，G 2 (z)，G 3 (z) discrete domain expressions representing the transfer functions of the respective modules in figure 2,
Figure RE-GDA0003292656830000034
Figure RE-GDA0003292656830000035
respectively representing the filter capacitor current and the grid-connected current,
Figure RE-GDA0003292656830000036
respectively representing the inverter output voltage and the filter capacitor voltage, L 1 ，L 2 Is a filter inductor, C is a filter capacitor, L T ＝L 1 +L 2 Resonant frequency of the system
Figure RE-GDA0003292656830000041
T s For sampling time, transfer function G 3 Zero point of (z)
Figure RE-GDA0003292656830000042
Wherein
Figure RE-GDA0003292656830000043
From the above equation, when the grid impedance changes, the system resonant frequency changes, and the system stability also changes.
Since PI and PR control is equivalent to proportional control at the cut-off frequency, the present invention employs proportional control, G c ＝K p . When the optimal compensation network is designed:
G c ＝K p ＝K pop ＝ω c (L 1 +L 2 )。
in the formula, K p Is a proportional gain factor, K pop For optimum proportional gain factor, ω c The system cutoff frequency.
When the resonant frequency is less than 1/6 of the sampling frequency, the optimal filter capacitor current feedback coefficient calculation formula is as follows:
Figure RE-GDA0003292656830000044
in the formula, K aop In order to optimize the feedback factor,
Figure RE-GDA0003292656830000045
f s is the sampling frequency. Taking the sampling frequency f s ＝11.835KHz,L 1 ＝2.28mH,L 2 =1.5mh, c =4 μ F, critical grid-connected inductance L gc =4.19mH. Make the root locus of the closed loop pole, as shown in FIG. 3, when L g ＝L gc When poles a and a' are located on a circle of | Z | =1, the system is not stable.
Increase the positive feedback of capacitor voltage, and system control frameWhen K is shown in FIG. 2 p ＝K pop ,K a ＝K aop ,L g ＝L gc Change of K v Making the root locus of the pole of the closed loop of the system as shown in FIG. 4, it can be seen that when K is v When the value is within a certain range, the closed-loop pole point falls in the unit circle, and the system is stable at the moment, which shows that the system is stable under the condition of critical grid-connected inductance by increasing the positive feedback of the capacitor voltage. E and E' in FIG. 4 determine K v Is shown in fig. 5, at this time, K v The value is in the range of (0,1.036), and the system is stable.
Although the system can be stabilized under the critical grid-connected inductance by increasing the positive feedback of the capacitor voltage, an additional capacitor voltage sensor is added, and the economic burden is increased. To improve this drawback, a PCC voltage feedforward equivalent is used instead of a capacitor voltage positive feedback. From the circuit topology of fig. 6, the PCC voltage expression:
Figure RE-GDA0003292656830000051
the second term on the right of the equation can be regarded as an external disturbance, does not affect the stability of the system, and is set to 0. The influence of the positive feedback of the capacitor voltage on the system stability is equivalent to the influence of the PCC voltage feedforward on the system stability. According to the above formula, when L g With 0, PCC feedforward is equivalent to
Figure RE-GDA0003292656830000052
Positive feedback of the filter capacitor voltage, and knowing K vff Constantly less than 1, satisfies K v The value range of (a).
When K is p ＝K pop ,K a ＝K aop Changing the grid-connected inductance L when introducing PCC voltage feedforward g The root locus of the closed loop pole of the system is shown in fig. 7, and it can be obviously seen that the pole of the system is positioned at any grid-connected inductor L g All located within the unit circle. The PCC voltage feedforward is introduced, so that the system can be applied to all grid-connected inductors L g The values are stable, and compared with the introduction of filter capacitor voltage feedforward, the voltage does not need to be increasedAnd the sensor can directly obtain the PCC voltage from the input signal of the PLL.
Examples
In order to verify the effectiveness of the robust control method suitable for the LCL type grid-connected inverter, a simulation model is built in MATLAB/Simulink, and the actual system parameters are as shown in the following table 1:
TABLE 1
Figure RE-GDA0003292656830000053
Figure RE-GDA0003292656830000061
The simulation results are shown in FIG. 8, just before
Figure RE-GDA0003292656830000062
The grid-connected inductor 1 is short-circuited, the grid-connected inductor 1 does not participate in the circuit operation, and the grid inductor L at the moment g ＝L g2 Due to L g ＜L gc I.e. the grid-connected inductance is smaller than the critical inductance, the system will be in a stable state at first. When t =240ms, the grid-connected inductor 1 is not short-circuited, and the grid-connected inductor L is at the moment g ＝L g1 +L g2 And then L g ＝L gc Namely, the grid-connected inductance is equal to the critical inductance, the system is no longer in a stable state, and it can be seen that when 240ms < t < 261ms, the output current has a high-frequency oscillation component and is continuously increased along with the lapse of time.
When t =261ms, the time is,
Figure RE-GDA0003292656830000063
namely, PCC voltage feedforward is introduced into the control system, it can be seen that high-frequency oscillation components in the output current can no longer exist when t is more than 261ms, and this also proves that the LCL type grid-connected inverter can be stabilized under critical inductance by adding the PCC voltage feedforward in closed-loop control. The robust control method is applicable to the LCL type grid-connected inverter.
The present invention provides a robust control method suitable for an LCL grid-connected inverter, and a number of methods and ways for implementing the technical solution are provided, the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, a number of improvements and modifications may be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (1)

1. A robust control method suitable for an LCL type grid-connected inverter is characterized by comprising the following steps:
step 1, calculating a compensation network G based on a proportional controller c And filter capacitor current feedback coefficient K a To obtain the optimal proportional controller and the optimal filter capacitor current feedback;
step 2, introducing filter capacitor voltage positive feedback under the current feedback of the optimal proportional controller and the optimal filter capacitor, and calculating a filter capacitor voltage positive feedback coefficient K by drawing a root track of a system closed loop pole in a discrete domain v The value range enables the system to be stable under the critical condition;
step 3, according to the proportional relation between the PCC voltage and the filter capacitor voltage, replacing the filter capacitor voltage positive feedback with PCC voltage feedforward equivalence;
in step 1, the compensation network G c By adopting proportional control, the calculation formula is as follows:
G c ＝K p ＝K pop ＝ω c (L 1 +L 2 )
in the formula, K p Is a proportional gain factor, K pop For optimum proportional gain factor, ω c Is the system cut-off frequency, L 1 ,L 2 Two filter inductance values for the LCL filter;
in step 1, a filter capacitor current feedback coefficient K a The calculation formula is as follows:
Figure FDA0004016730700000011
in the formula, K aop For optimal feedback coefficient, intermediate variable
Figure FDA0004016730700000012
f s Is the sampling frequency;
in step 2, introducing filter capacitor voltage positive feedback, and solving a filter capacitor voltage positive feedback coefficient K through a root track of a system closed loop pole in a discrete domain v The value range of (2) enables the system to maintain a stable state under a critical condition, namely when the resonant frequency of the LCL filter is equal to 1/6 of the sampling frequency;
in step 3, the proportional relationship between the PCC voltage and the filter capacitor voltage is as follows:
Figure FDA0004016730700000013
in the formula (I), the compound is shown in the specification,
Figure FDA0004016730700000014
in order to be the PCC voltage,
Figure FDA0004016730700000015
for filtering the capacitor voltage, L g For the value of the inductance to be connected to the grid,
Figure FDA0004016730700000016
is the grid voltage.
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Citations (4)

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Publication number Priority date Publication date Assignee Title
CN102545266A (en) * 2012-02-09 2012-07-04 浙江大学 Method for controlling grid-connected inverter based on feed-forward compensation
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Publication number Priority date Publication date Assignee Title
CN102545266A (en) * 2012-02-09 2012-07-04 浙江大学 Method for controlling grid-connected inverter based on feed-forward compensation
CN108879782A (en) * 2018-08-01 2018-11-23 国网重庆市电力公司电力科学研究院 Gird-connected inverter optimal control method based on double-smoothing voltage feed-forward control
CN110233494A (en) * 2019-04-19 2019-09-13 南京航空航天大学 A kind of control method of grid-connected inverter of the specific component of degree n n feedforward of network voltage
CN110086171A (en) * 2019-05-05 2019-08-02 重庆大学 A kind of gird-connected inverter resonance suppressing method and device enhancing system rejection to disturbance ability

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