CN113162117B - Method for designing bandwidth of grid-connected inverter controller under weak grid - Google Patents

Abstract

The invention discloses a bandwidth design method of a grid-connected inverter controller under a weak grid, and belongs to the field of electric power control. The bandwidth design method includes: sampling, first giving the open-loop transfer function of the current control loop of the grid-connected inverter, then obtaining the amplitude of the open-loop transfer function of the current control loop, and finally combining the Nyquist stability criterion to give the weak current The restriction relationship between the bandwidth of the current control loop under the grid and the bandwidth of the phase-locked loop is completed, so as to complete the parameter design of the current control loop and the phase-locked loop controller. This method quantitatively gives the restriction relationship and value range of the design bandwidth of the current control loop and the phase-locked loop bandwidth under the weak grid condition, which can effectively solve the inconsistency caused by the interaction of the grid-connected inverter system under the weak grid condition. stability issues.

Description

A bandwidth design method of grid-connected inverter controller in weak grid

technical field

The invention relates to a bandwidth design method of a grid-connected inverter controller, in particular to a bandwidth design method of a grid-connected inverter controller under a weak grid, and belongs to the field of electric power control.

Background technique

Since the 21st century, with the rapid development of wind energy, solar energy and other forms of power generation, more and more renewable energy has been integrated into the large power grid through power electronic interfaces. Very weak network characteristics. The stability of grid-connected inverter system under weak power grid is one of the most important issues in the current research on the stability of systems including power electronics grid-connected interfaces and has the most practical application significance. In a very weak grid system formed by a high proportion of power electronic grid-connected interfaces, the phase-locked loop and the control system usually interact and cause system instability. Therefore, how to solve the instability of grid-connected inverter system under weak grid due to the interaction of control loops is a crucial issue.

Titled "Research Review of Stability Analysis of Grid-connected VSC System under Weak Connection Conditions" (Wang Xubin, Du Wenjuan, Wang Haifeng. Review of Grid-connected VSC System Stability Analysis under Weak Connection Conditions [J]. Chinese Journal of Electrical Engineering, 2018, 38 (06): 1593-1604+1895.) The article revealed the instability mechanism of the grid-connected inverter system under the weak grid from the perspective of the interaction of the grid-connected inverter control system, and pointed out that the grid-connected inverter under the weak grid The stability of the system is mainly related to the control system of the grid-connected inverter. The interaction between the phase-locked loop and the power/voltage outer loop and the current inner loop will cause the system to fall into instability. The more prominent the interaction between systems, the less stable the system is.

Entitled "Analysis of D-Q small-signal impedance of grid-tied inverters" (Wen Bo, Boroyevich D, Burgos R, et al. Analysis of D-Q small-signal impedance of grid-tied inverters [J]. IEEE Transactions on Power Electronics, 2016, 31(1): 675-687) The article analyzes the dynamic influence of the phase-locked loop on the current inner loop under the weak grid by establishing the impedance small signal model of the grid-connected inverter system. Because the phase-locked loop brings negative damping effect to the system, which makes the system unstable, and it is pointed out that when the control bandwidth of the phase-locked loop and the current inner loop is gradually approached in a weak grid, the interaction between them will be further strengthened. The small-signal stability of the system in the weak grid can be improved by optimizing the control parameters of the phase-locked loop and the current inner loop, but no specific controller parameter design and optimization scheme is given.

The title is "Analysis and Research on the Interaction Mechanism of Phase-locked Loop and Current Inner Loop When Flexible DC Transmission Connects to Weak AC Power Grid" (Wu Guanglu, Zhou Xiaoxin, Wang Shanshan, Liang Jun, Zhao Bing, Wang Tiezhu, Li Yingbiao, Yang Yanchen. Flexible DC Transmission Connection Analytical research on the interaction mechanism between phase-locked loop and current inner loop when entering weak AC power grid The expression of the current inner loop control transfer function of the grid-connected inverter under the influence of the loop, the influence of the grid strength on the interaction between the PLL and the current inner loop is analyzed from the analytical point of view, and it is pointed out that the smaller the PLL bandwidth is in the weak grid The more conducive to the stability of the current inner loop control, but this article only analyzes the interaction mechanism between the phase-locked loop and the current inner loop from a qualitative point of view, and gives the design idea of the phase-locked loop bandwidth, but does not give a specific method from a quantitative point of view. Phase-locked loop bandwidth design method.

It can be seen from the above analysis that the stability of grid-connected inverter systems in weak grids has received extensive attention and research, especially the instability mechanism and control optimization methods of grid-connected inverter systems in weak grids. Some studies have found that the main reason for the instability of grid-connected inverter systems in weak grids is the interaction between the phase-locked loop and the current inner loop, and some qualitative conclusions are given. If a controller bandwidth design method can be proposed from a quantitative point of view, and then to solve the instability problem caused by the interaction of the controller in the weak grid to the grid-connected inverter system, this will not matter for the improvement and enrichment of grid-connected inverters. The stability analysis theory, or the controller design application in practical engineering, will have very important significance and value.

To sum up, the following problems still exist in the prior art:

1. When analyzing the stability of the grid-connected inverter system in the weak grid, many studies only qualitatively analyze the influence of the grid strength and the interaction between the phase-locked loop and the current inner loop on the system stability. A specific method is proposed to solve the instability problem of grid-connected inverters in extremely weak grids.

2. Most of the researches only propose to design the bandwidth of the phase-locked loop to be small enough to avoid the control of the current loop as much as possible when solving the instability problem caused by the interaction of the controller in the weak grid. bandwidth, but the design range of the phase-locked loop bandwidth is not quantitatively given, which requires repeated trial and error.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to overcome the limitations of the above-mentioned various technical solutions, aiming at the above-mentioned two problems, to provide a bandwidth design method of a grid-connected inverter controller in a weak grid.

The object of the present invention is achieved in this way. In order to solve the technical problem of the present invention, the adopted technical scheme is: a method for designing the bandwidth of a grid-connected inverter controller in a weak grid, the bandwidth includes the control bandwidth ω _CL of the current control loop and the control bandwidth of the phase-locked loop ω _pll , the steps are as follows:

Step 1, obtain the output current I _gd of the grid-connected inverter and the output voltage U _gd of the grid-connected inverter through sampling, and give the expression of the open-loop transfer function G(s) of the current control loop of the grid-connected inverter Mode;

Among them, L _grid is the inductive component of grid impedance, R _grid is the resistance component of grid impedance, ξ is the damping ratio of the phase-locked loop, and s is the Laplace operator;

Step 2, give the expression of the open-loop transfer function frequency domain G(jω) of the current control loop of the grid-connected inverter,

Among them, ω is the frequency domain rotation angular frequency; j is the imaginary unit;

Step 3, according to the expression of the frequency domain G(jω) of the open-loop transfer function given in step 2, the expression of the frequency-domain amplitude |G(jω)| of the open-loop transfer function is obtained,

Step 4, according to the expression of the open-loop transfer function frequency-domain amplitude |G(jω)| obtained in step 3, obtain the maximum value of the open-loop transfer function frequency-domain amplitude, and record it as the maximum value |G(jω) | _max ,

Step 5, combined with step 4, and then according to the Nyquist stability criterion, in order to ensure the stability of the system, the open-loop transfer function frequency domain amplitude of the current control loop of the grid-connected inverter |G(jω)| should satisfy :

That is: the limit of the maximum value |G(jω)| _max is:

Step 6, according to the limiting condition of the maximum value |G(jω)| _max obtained in step 5, the design criteria of the control bandwidth of the current control loop and the control bandwidth of the phase-locked loop are given;

The design criterion for the control bandwidth ω _CL of the current control loop is: in order to suppress the noise near the switching frequency, the control bandwidth ω _CL of the current loop is not greater than 0.5 times the switching angular frequency ω _sw of the grid-connected inverter, that is, ω _CL ≤0.5ω _sw ;

The design criterion for the control bandwidth ω _pll of the phase-locked loop is: the ratio of the phase-locked loop control bandwidth ω _pll and the current control loop control bandwidth ω _CL is recorded as the ratio n, and the ratio n satisfies the following formula:

After the control bandwidth ω _CL of the current control loop is determined, the value range of the ratio n under any grid strength is determined by the above formula, that is, the value range of the control bandwidth ω _pll of the phase-locked loop is determined.

Compared with the prior art, the beneficial effects of the present invention are as follows:

1. No matter how the strength of the power grid changes, the present invention can quantitatively provide the constraint relationship between the current control loop and the control bandwidth of the phase-locked loop of the grid-connected inverter system that meets the system stability conditions, so as to provide grid-connected inverters under weak grid conditions. The design of the parameters of the inverter controller provides great convenience and can effectively solve the instability problem caused by the interaction of the grid-connected inverter system under weak grid conditions.

2. The tedious steps of trial and error are omitted, and the calculation method is simple and intuitive, and has strong practical value.

Description of drawings

Fig. 1 is the topology structure of the grid-connected inverter of the present invention.

Figure 2 is the Bode plot of grid-connected inverter system G(s) when the grid strength is SCR=3, the design bandwidth of the current loop is ω _CL = 942rad/s, and the design bandwidth of the phase-locked loop is ω _pll = 1347rad/s .

Figure 3 shows the Nyquis of grid-connected inverter system G(s) when the grid strength is SCR=3, the design bandwidth of the current loop is ω _CL =942rad/s, and the design bandwidth of the phase-locked loop is ω _pll =1347rad/s special curve.

Figure 4 is the Bode plot of grid-connected inverter system G(s) when the grid strength is SCR=1.5, the design bandwidth of the current loop is ω _CL = 942rad/s, and the design bandwidth of the phase-locked loop is ω _pll = 422rad/s .

Figure 5 shows the Nyquis of grid-connected inverter system G(s) when the grid strength is SCR=1.5, the design bandwidth of the current loop is ω _CL = 942rad/s, and the design bandwidth of the phase-locked loop is ω _pll = 422rad/s special curve.

Figure 6 shows the baud rate of grid-connected inverter system G(s) when the grid strength is SCR=1, the design bandwidth of the current loop is ω _CL = 942rad/s, and the design bandwidth of the phase-locked loop is ω _pll = 263.4rad/s picture.

Figure 7 shows the Nyquity of the grid-connected inverter system G(s) when the grid strength is SCR=1, the design bandwidth of the current loop is ω _CL = 942rad/s, and the design bandwidth of the phase-locked loop is ω _pll = 263.4rad/s Sterling curve.

Detailed ways

FIG. 1 is a topology diagram of a grid-connected inverter in an embodiment of the present invention. As shown in FIG. 1 , the topology of the present invention includes a DC voltage source U _dc , a DC side filter capacitor C _dc , a three-phase half-bridge inverter, an L filter and a three-phase AC power grid. The DC voltage source U _dc is connected to the input end of the inverter through the filter capacitor C _dc , and the output end of the inverter is connected to the three-phase AC grid through the L filter. L _grid is the inductance component corresponding to the grid impedance, which is recorded as grid impedance. Inductive component L _grid . R _grid is the resistance component corresponding to the grid impedance, denoted as the grid impedance resistance component R _grid .

The relevant electrical parameters in the implementation of the present invention are set as follows: the DC voltage source U _dc =750V, the rated capacity of the grid-connected inverter is 30kVA, the effective value of the phase voltage of the three-phase grid is E _a =E _b =E _c =220V, the system switch The frequency is f _sw =10kHz, the sampling time of the system is T _s =100μs, and the filter inductance value L=2mH.

Referring to Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6 and Fig. 7, it can be seen from Fig. 1 that the present invention provides a bandwidth design method of a grid-connected inverter controller under a weak grid. Including the control bandwidth ω _CL of the current control loop and the control bandwidth ω _pll of the phase-locked loop, the steps are as follows:

Step 1, obtain the output current I _gd of the grid-connected inverter and the output voltage U _gd of the grid-connected inverter through sampling, and give the expression of the open-loop transfer function G(s) of the current control loop of the grid-connected inverter Mode;

Among them, L _grid is the inductive component of the grid impedance, R _grid is the resistance component of the grid impedance, ξ is the damping ratio of the phase-locked loop, and s is the Laplace operator.

In this embodiment, the output current I _gd =45A of the grid-connected inverter, the output phase voltage U _gd =220V of the grid-connected inverter, and the damping ratio of the phase-locked loop is ξ=0.707.

Step 2, give the expression of the open-loop transfer function frequency domain G(jω) of the current control loop of the grid-connected inverter,

Among them, ω is the frequency domain rotation angular frequency; j is the imaginary unit.

Step 3, according to the expression of the frequency domain G(jω) of the open-loop transfer function given in step 2, the expression of the frequency-domain amplitude |G(jω)| of the open-loop transfer function is obtained,

Step 4, according to the expression of the open-loop transfer function frequency-domain amplitude |G(jω)| obtained in step 3, obtain the maximum value of the open-loop transfer function frequency-domain amplitude, and record it as the maximum value |G(jω) | _max ,

Step 5, combined with step 4, and then according to the Nyquist stability criterion, in order to ensure the stability of the system, the open-loop transfer function frequency domain amplitude of the current control loop of the grid-connected inverter |G(jω)| should satisfy :

That is: the limit of the maximum value |G(jω)| _max is:

Step 6: According to the limiting condition of the maximum value |G(jω)| _max obtained in step 5, the design criteria of the control bandwidth of the current control loop and the control bandwidth of the phase-locked loop are given.

The design criterion for the control bandwidth ω _CL of the current control loop is: in order to suppress the noise near the switching frequency, the control bandwidth ω _CL of the current loop is not greater than 0.5 times the switching angular frequency ω _sw of the grid-connected inverter, that is, ω _CL ≤0.5ω _sw .

In this embodiment, the control bandwidth of the current loop ω _CL =150×2πrad/s=942rad/s.

The design criterion for the control bandwidth ω _pll of the phase-locked loop is: the ratio of the phase-locked loop control bandwidth ω _pll and the current control loop control bandwidth ω _CL is recorded as the ratio n, and the ratio n satisfies the following formula:

After the control bandwidth ω _CL of the current control loop is determined, the value range of the ratio n under any grid strength is determined by the above formula, that is, the value range of the control bandwidth ω _pll of the phase-locked loop is determined.

In this embodiment, a total of three situations of the grid-connected inverter system in the weak grid environment are implemented:

Case 1: The short-circuit ratio of the grid-connected inverter system is SCR=3, the grid impedance inductance component L _grid = 5.1mH, and the grid impedance resistance component R _grid = 0.16Ω. When the control bandwidth of the current loop is determined as ω _CL = 942rad/s, the ratio n≤1.43 can be obtained, so the design range of the control bandwidth of the phase-locked loop can be obtained as:

ω _pll ≦nω _CL =1.43×942rad/s=1347rad/s.

To sum up, take the design bandwidth of the current control loop as ω _CL = 942rad/s, and take the design bandwidth of the phase-locked loop as ω _pll = 1347rad/s, after substituting G(jω), the Bode plot and the transfer function of the current control loop can be obtained. The Nyquist curves are shown in Figure 2 and Figure 3. Among them, Figure 2 is the Bode plot, the upper and lower parts of the figure are the amplitude-frequency curve and the phase-frequency curve in the Bode plot, respectively, the abscissa represents the angular frequency, the unit is rad/s, and the ordinate of the amplitude-frequency curve represents the amplitude , the unit is dB, the ordinate of the phase-frequency curve represents the phase, and the unit is deg; Figure 3 is the Nyquist curve, the abscissa represents the real axis, and the ordinate represents the imaginary axis. Through observation, it can be found that the system is in a critically stable state at this time.

Case 2: The short-circuit ratio of the grid-connected inverter system is SCR=1.5, the grid impedance inductance component L _grid =10.2mH, and the grid impedance resistance component R _grid =0.32Ω. When the control bandwidth of the current loop is determined as ω _CL = 942rad/s, the ratio n≤0.4478 can be obtained, so the design range of the control bandwidth of the phase-locked loop can be obtained as: ω _pll ≤nω _CL =0.4478×942rad/s =422rad/s.

To sum up, take the design bandwidth of the current control loop ω _CL = 942rad/s, and take the design bandwidth of the phase-locked loop ω _pll = 422 rad/s, after substituting in G(jω), you can get the Bode plot and Nyquiw of the transfer function of the current control loop The Sterling curve is shown in Figure 4 and Figure 5. Among them, Figure 4 is the Bode plot, the upper and lower parts of the figure are the amplitude-frequency curve and the phase-frequency curve in the Bode plot, respectively, the abscissa represents the angular frequency, the unit is rad/s, and the ordinate of the amplitude-frequency curve represents the amplitude , the unit is dB, the ordinate of the phase-frequency curve represents the phase, and the unit is deg; Figure 5 is the Nyquist curve, the abscissa represents the real axis, and the ordinate represents the imaginary axis. Through observation, it can be found that the system is in a critically stable state at this time.

Case 3: The short-circuit ratio of the grid-connected inverter system is SCR=1, the inductive component of the grid impedance is L _grid =15.32mH, and the resistance component of the grid impedance is R _grid =0.48Ω. When the control bandwidth of the current loop is determined as ω _CL = 942rad/s, the ratio n≤0.2795 can be obtained, then, the design range of the control bandwidth of the phase-locked loop can be obtained: ω _pll ≤nω _CL =0.2795×942rad/ s=263.4rad/s.

To sum up, take the design bandwidth of the current control loop as ω _CL = 942rad/s, and take the design bandwidth of the phase-locked loop as ω _pll = 263.4rad/s, after substituting G(jω), the Bode plot of the transfer function of the current control loop can be obtained and Nyquist curves are shown in Figure 6 and Figure 7. Among them, Figure 6 is a Bode plot. The upper and lower parts of the figure are the amplitude-frequency curve and the phase-frequency curve in the Bode plot, respectively. The abscissa represents the angular frequency, and the unit is rad/s. The ordinate of the amplitude-frequency curve represents the amplitude. , the unit is dB, the ordinate of the phase-frequency curve represents the phase, and the unit is deg; Figure 7 is the Nyquist curve, the abscissa represents the real axis, and the ordinate represents the imaginary axis. Through observation, it can be found that the system is in a critically stable state at this time.

Claims (1)

1. a method for designing the bandwidth of a grid-connected inverter controller under a weak power grid, the bandwidth comprises the control bandwidth ω _CL of the current control loop and the control bandwidth ω _pll of the phase-locked loop, and is characterized in that, the steps are as follows: Step 1, obtain the output current I _gd of the grid-connected inverter and the output voltage U _gd of the grid-connected inverter through sampling, and give the expression of the open-loop transfer function G(s) of the current control loop of the grid-connected inverter Mode;

Among them, L _grid is the inductive component of grid impedance, R _grid is the resistance component of grid impedance, ξ is the damping ratio of the phase-locked loop, and s is the Laplace operator; Step 2, give the expression of the open-loop transfer function frequency domain G(jω) of the current control loop of the grid-connected inverter,

Among them, ω is the frequency domain rotation angular frequency; j is the imaginary unit; Step 3, according to the expression of the frequency domain G(jω) of the open-loop transfer function given in step 2, the expression of the frequency-domain amplitude |G(jω)| of the open-loop transfer function is obtained,

Step 4, according to the expression of the open-loop transfer function frequency-domain amplitude |G(jω)| obtained in step 3, obtain the maximum value of the open-loop transfer function frequency-domain amplitude, and record it as the maximum value |G(jω) | _max ,

Step 5, combined with step 4, and then according to the Nyquist stability criterion, in order to ensure the stability of the system, the open-loop transfer function frequency domain amplitude of the current control loop of the grid-connected inverter |G(jω)| should satisfy :

That is: the limit of the maximum value |G(jω)| _max is:

Step 6, according to the limiting condition of the maximum value |G(jω)| _max obtained in step 5, the design criteria of the control bandwidth of the current control loop and the control bandwidth of the phase-locked loop are given; The design criterion for the control bandwidth ω _CL of the current control loop is: in order to suppress the noise near the switching frequency, the control bandwidth ω _CL of the current loop is not greater than 0.5 times the switching angular frequency ω _sw of the grid-connected inverter, that is, ω _CL ≤0.5ω _sw ; The design criterion for the control bandwidth ω _pll of the phase-locked loop is: the ratio of the control bandwidth ω _pll of the phase-locked loop to the control bandwidth ω _CL of the current control loop is recorded as the ratio n, and the ratio n satisfies the following formula:

After the control bandwidth ω _CL of the current control loop is determined, the value range of the ratio n under any grid strength is determined by the above formula, that is, the value range of the control bandwidth ω _pll of the phase-locked loop is determined.

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