阅读说明：本技术 一种适用于lcl型并网逆变器的鲁棒控制方法 (Robust control method suitable for LCL type grid-connected inverter ) 是由 刘钊 徐魁 荣国灿 方城 马超 于 2021-07-28 设计创作，主要内容包括：本发明提供了一种适用于LCL型并网逆变器的鲁棒控制方法,当系统处于临界条件,即LCL滤波器的谐振频率等于1/6采样频率,基于输出电流和滤波电容电流反馈的LCL型并网逆变器将不再处于稳定状态时,引入滤波电容电压正反馈可以使得系统在临界条件下也保持稳定。此外,由于公共连接点(Point of Common Coupking,PCC)电压与滤波电容电压成比例关系,可以用PCC电压前馈替代滤波电容电压正反馈,以此来减少引入滤波电容电压正反馈所带来的传感器增加问题。通过引入PCC电压前馈,系统可以在所有并网电感取值下达到稳定。本发明仅仅增加了系统控制的计算量,无其他额外经济投入。(The invention provides a robust control method suitable for an LCL type grid-connected inverter, when a system is in a critical condition, namely the resonant frequency of an LCL filter is equal to 1/6 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.)

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_cAnd filter capacitor current feedback coefficient K_aTo 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_vThe 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.

2. Method according to claim 1, characterized in that in step 1, the compensation network G_cBy adopting proportional control, the calculation formula is as follows:

G_c＝K_p＝K_pop＝ω_c(L₁+L₂)

in the formula, K_pIs a proportional gain factor, K_popFor optimum proportional gain factor, ω_cIs the system cut-off frequency, L₁,L₂Two filter inductance values for the LCL filter.

3. The method of claim 2, wherein in step 1, the filter capacitor current feedback factor K_aThe calculation formula is as follows:

in the formula, K_aopFor optimal feedback coefficient, intermediate variablef_sIs the sampling frequency.

4. The method according to claim 3, wherein in step 2, the filter capacitor voltage positive feedback is introduced, and the filter capacitor voltage positive feedback coefficient K is obtained through a root track of a system closed loop pole in a discrete domain_vIs chosen to enable the system to maintain a steady state under critical conditions, i.e., the LCL filter resonant frequency is equal to the 1/6 sampling frequency.

5. The method of claim 4, wherein in step 3, the PCC voltage is proportional to the filter capacitor voltage as follows:

in the formula (I), the compound is shown in the specification,in order to be the PCC voltage,for filtering the capacitor voltage, L_gFor the value of the inductance to be connected to the grid,is the grid voltage.

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 harmonic components injected into a power grid, and has small volume and low price, so that the LCL type grid-connected inverter has great advantages in grid-connected inverters.

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 system sampling frequency and a proportional controller is used, filter capacitance 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 the 1/6 system sampling frequency, the system is no longer stable, and at this time, the grid-connected inverter cannot work in a normal state, and the electric energy injected into the grid does not have higher electric energy quality.

Disclosure of Invention

The purpose of the invention is as follows: in order to solve the technical problems in the background art, the invention providesA robust control method suitable for an LCL type grid-connected inverter is provided, so that when grid-connected inductance is in a critical value, a grid-connected inverter system can also keep a stable state, and the method specifically comprises the following steps: in a grid-connected inverter control system, a compensation network G_cAnd filter capacitor current feedback K_aThe 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_cAnd filter capacitor current feedback coefficient K_aTo 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_vThe 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_cBy adopting proportional control, the calculation formula is as follows:

G_c＝K_p＝K_pop＝ω_c(L₁+L₂)

in the formula, K_pIs a proportional gain factor, K_popFor optimum proportional gain factor, ω_cIs the system cut-off frequency, L₁,L₂Two filter inductance values for the LCL filter.

In step 1, a filter capacitor current feedback coefficient K_aThe calculation formula is as follows:

in the formula, K_aopFor optimal feedback coefficient, intermediate variablef_sIs 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_vIs chosen to enable the system to maintain a steady state under critical conditions, i.e., the LCL filter resonant frequency is equal to the 1/6 sampling frequency.

In step 3, the proportional relationship between the PCC voltage and the filter capacitor voltage is as follows:

in the formula (I), the compound is shown in the specification,in order to be the PCC voltage,for filtering the capacitor voltage, L_gFor the value of the inductance to be connected to the grid,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_aopWhile changing L_gA schematic diagram of a root locus of a closed loop pole of a time system;

FIG. 4 shows that when K_p＝K_pop,K_a＝K_aop,L_g＝L_gcWhile changing K_vA schematic diagram of a root locus of a closed loop pole of a time system;

FIG. 5 shows a modification K_vA 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_gA 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:

wherein G is₁(z)，G₂(z)，G₃(z) discrete domain expressions representing the transfer functions of the respective modules in figure 2, respectively representing the filter capacitor current and the grid-connected current,respectively representing the inverter output voltage and the filter capacitor voltage, L₁，L₂Is a filter inductor, C is a filter capacitor, L_T＝L₁+L₂Resonant frequency of the systemT_sFor sampling time, transfer function G₃Zero point of (z)WhereinFrom 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(L₁+L₂)。

in the formula, K_pIs a proportional gain factor, K_popFor optimum proportional gain factor, ω_cThe system cutoff frequency.

When the resonant frequency is less than 1/6 sampling frequency, the optimal filter capacitor current feedback coefficient calculation formula is:

in the formula, K_aopIn order to optimize the feedback factor,f_sis the sampling frequency. Taking the sampling frequency f_s＝11.835KHz,L₁＝2.28mH,L₂1.5mH, and 4 muF, in this case, the critical grid-connected inductance L_gc4.19 mH. Make the root locus of the closed loop pole, as shown in FIG. 3, when L_g＝L_gcWhen the poles a and a' are located on a circle with | Z | ═ 1, the system is not stable.

Increasing positive feedback of capacitor voltage, and controlling system block diagram as shown in FIG. 2 when K_p＝K_pop,K_a＝K_aop,L_g＝L_gcChange of K_vMaking 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_vWhen 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_vIs as shown in FIG. 5, at this time, K_vThe 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 capacitance voltage positive feedback, an additional capacitance 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:

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_gWhen not equal to 0, PCC feedforwardIs equivalent toPositive feedback of the filter capacitor voltage, and knowing K_vffConstantly less than 1, satisfies K_vThe value range of (a).

When K is_p＝K_pop,K_a＝K_aopChanging the grid-connected inductance L when introducing PCC voltage feedforward_gThe 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_gAll located within the unit circle. The PCC voltage feedforward is introduced, so that the system can be applied to all grid-connected inductors L_gThe value taking is stable, and compared with the introduction of filter capacitor voltage feedforward, the PCC voltage can be directly obtained from the input signal of the PLL without adding a voltage sensor.

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

The simulation results are shown in FIG. 8, just beforeThe 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_g2Due to L_g＜L_gcI.e. the grid-connected inductance is smaller than the critical inductance, the system will be in a stable state at first. When t is 240ms, the grid-connected inductor 1 is not short-circuited, and the grid-connected inductor L is at the moment_g＝L_g1+L_g2And then L_g＝L_gcNamely, 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 the time t is 261ms,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.