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

Method for designing bandwidth of grid-connected inverter controller under weak grid Download PDF

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CN113162117B
CN113162117B CN202110520856.1A CN202110520856A CN113162117B CN 113162117 B CN113162117 B CN 113162117B CN 202110520856 A CN202110520856 A CN 202110520856A CN 113162117 B CN113162117 B CN 113162117B
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刘芳
刘威
李研
徐韫钰
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Hefei University of Technology
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Abstract

The invention discloses a method for designing the bandwidth of a grid-connected inverter controller under a weak power grid, and belongs to the field of power control. The bandwidth design method comprises the following steps: sampling, namely giving an open-loop transfer function of a current control loop of the grid-connected inverter, solving the amplitude of the open-loop transfer function of the current control loop, and finally giving a restriction relation between the bandwidth of the current control loop and the bandwidth of a phase-locked loop under a weak power grid by combining a Nyquist stability criterion, thereby completing parameter design of the current control loop and the phase-locked loop controller. The method quantitatively gives the restriction relation and the value range of the design bandwidth of the current control loop and the bandwidth of the phase-locked loop under the condition of weak power grid, and can effectively solve the problem of instability of a grid-connected inverter system caused by interaction under the condition of the weak power grid.

Description

Method for designing bandwidth of grid-connected inverter controller under weak grid
Technical Field
The invention relates to a method for designing the bandwidth of a controller of a grid-connected inverter, in particular to a method for designing the bandwidth of a controller of a grid-connected inverter in a weak power grid, and belongs to the field of power control.
Background
Since the 21 st century, with the rapid development of various power generation forms such as wind energy and solar energy, more and more renewable energy sources are incorporated into a large power grid through power electronic interfaces, power electronic grid-connected interface systems are becoming high-scale day by day, and power grids gradually exhibit extremely weak grid characteristics. The stability of a grid-connected inverter system under a weak power grid is one of the most concerned and most significant problems in the stability research of a system containing a power electronic grid-connected interface at present and having practical application significance. In an extremely weak power grid system formed by a high-proportion power electronic grid-connected interface, a phase-locked loop and a control system usually interact to cause system instability. Therefore, how to solve the instability of the grid-connected inverter system under the weak grid due to the interaction of the control loops is a crucial problem.
An article entitled analysis and research review of stability of grid-connected VSC system under weak connection condition (Wang Xun, Du Wen Juan, Wang Haifeng.) analysis and research review of stability of grid-connected VSC system under weak connection condition [ J ]. Chinese Motor engineering reports, 2018, 38 (06): 1593-.
An article entitled Analysis of D-Q small-signal impedance of grid-ended inverters (Wen Bo, Boroyvich D, Burgos R, et al, Analysis of D-Q small-signal impedance of grid-ended inverters [ J ]. IEEE Transactions on Power Electronics, 2016, 31 (1): 675) 687) analyzes the dynamic effect of a phase-locked loop under a weak grid on a current inner loop by establishing an impedance small-signal model of a grid-connected inverter system, which article considers that the phase-locked loop under the weak grid is destabilized by a negative damping effect on the system, and simultaneously points out that the interaction between the phase-locked loop and the current inner loop control loop is further strengthened when the phase-locked loop and the current inner loop control bandwidth gradually approach under the weak grid, and can further improve the small-signal stability of the system under the weak grid by optimizing the current inner loop control parameters, but no specific controller parameter design and optimization scheme is given.
An article entitled analysis research on interaction mechanism of phase-locked loop and current inner loop when flexible direct current power transmission is connected into a weak alternating current power grid (Wuguanlu, West Suiyu, Kingson, Liqun, soldier, King iron post, Liying Biao, Yangxian, Yangxue.) analysis research on interaction mechanism of phase-locked loop and current inner loop when flexible direct current power transmission is connected into a weak alternating current power grid [ J ]. China Motor engineering Proc, 2018, 38 (09): 2622 + 2633+2830.) deduces an expression of a current inner loop control transfer function of a grid-connected inverter when the influence of the power grid strength and the phase-locked loop is considered, analyzes the influence of the power grid strength on the interaction of the phase-locked loop and the current inner loop from the analysis angle, and indicates that the smaller the bandwidth of the phase-locked loop under the weak power grid is more favorable for the stability of the current inner loop control, but analyzes the interaction mechanism of the phase-locked loop and the current inner loop at the qualitative angle and gives a design idea of the bandwidth of the phase-locked loop, and a method for designing the bandwidth of the phase-locked loop is not particularly provided from a quantitative point of view.
From the above analysis, it can be seen that, at present, the stability problem of the grid-connected inverter system under the weak power grid has received extensive attention and research, and particularly, the instability mechanism and the control optimization method of the grid-connected inverter system under the weak power grid. Partial research has found that the instability edge of the grid-connected inverter system under the weak power grid is mainly caused by the interaction of a phase-locked loop and a current inner loop, and qualitatively provides some conclusions. If a controller bandwidth design method can be provided from a quantitative perspective, the instability problem of a grid-connected inverter system caused by the interaction of a controller under a weak power grid is solved, and the method has very important significance and value for perfecting and enriching the stability analysis theory of the grid-connected inverter and designing and applying the controller in actual engineering.
In summary, the following problems still exist in the prior art:
1. when the stability problem of a grid-connected inverter system under a weak power grid is analyzed, a lot of researches only qualitatively analyze the influence of the power grid strength and the interaction of a phase-locked loop and a current inner loop on the system stability, but no specific method is provided for solving the instability problem of the grid-connected inverter under the extremely weak power grid.
2. Most researches only propose to design the bandwidth of the phase-locked loop to be small enough to avoid the control bandwidth of a current loop as far as possible when solving the instability problem of a grid-connected inverter system caused by the interaction of a controller under a weak power grid, but do not quantitatively give the design range of the bandwidth of the phase-locked loop and need to be repeatedly tried and debugged.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the limitations of the various technical schemes, and to solve the two problems, the invention provides a method for designing the bandwidth of the grid-connected inverter controller under the weak grid.
The object of the invention is thus achieved. In order to solve the technical problem of the invention, the adopted technical scheme is as follows: a design method for a grid-connected inverter controller bandwidth under a weak grid includes a control bandwidth omega of a current control loopCLAnd control bandwidth omega of phase-locked looppllThe method comprises the following steps:
step 1, obtaining output current I of grid-connected inverter through samplinggdAnd the output voltage U of the grid-connected invertergdGiving an expression of an open-loop transfer function G(s) of a current control loop of the grid-connected inverter;
Figure BDA0003062759110000031
wherein L isgridAs a component of the network impedance inductance, RgridThe impedance resistance component of the power grid is shown, xi is the damping ratio of a phase-locked loop, and s is a Laplace operator;
step 2, giving an expression of an open-loop transfer function frequency domain G (j omega) of a current control loop of the grid-connected inverter,
Figure BDA0003062759110000032
wherein, omega is the frequency domain rotation angular frequency; j is an imaginary unit;
step 3, obtaining an expression of the open-loop transfer function frequency domain amplitude | G (j ω) | according to the expression of the open-loop transfer function frequency domain G (j ω) given in the step 2,
Figure BDA0003062759110000033
step 4, obtaining the maximum value of the frequency domain amplitude of the open-loop transfer function according to the expression of the frequency domain amplitude | G (j ω) | of the open-loop transfer function obtained in the step 3, and recording the maximum value | G (j ω) |max，
Figure BDA0003062759110000041
And 5, combining the step 4, setting the open-loop transfer function frequency domain amplitude | G (j omega) | of the current control loop of the grid-connected inverter to meet the following requirements for ensuring the system stability according to the Nyquist stability criterion:
Figure BDA0003062759110000042
namely: maximum | G (j ω) & gtnon & gtmaxThe limiting conditions are as follows:
Figure BDA0003062759110000043
step 6, calculating the maximum value | G (j ω) & gt obtained in step 5maxThe design criteria of the control bandwidth of the current control loop and the control bandwidth of the phase-locked loop are given;
control bandwidth omega of current control loopCLThe design criteria are: control bandwidth omega of current loop for suppressing noise around switching frequencyCLNot greater than switching angular frequency omega of grid-connected invertersw0.5 times of (i.e.. omega.)CL≤0.5ωsw；
Control bandwidth omega of phase-locked looppllThe design criteria are: controlling the bandwidth omega of a phase-locked looppllAnd current control loop control bandwidth omegaCLThe ratio of (b) is recorded as a ratio n, and the ratio n satisfies the following formula:
Figure BDA0003062759110000051
control bandwidth omega of current control loopCLAfter the determination, the value range of the ratio n under any power grid strength, namely the control bandwidth omega of the phase-locked loop is determined by the formulapllIs determined.
Compared with the prior art, the invention has the following beneficial effects:
1. no matter how the power grid strength changes, the method can quantitatively give out the restriction relation between the current control loop of the grid-connected inverter system and the control bandwidth of the phase-locked loop which meet the system stability condition, provides great convenience for the design of the parameters of the grid-connected inverter controller under the weak power grid, and can effectively solve the instability problem caused by the interaction of the grid-connected inverter system under the weak power grid condition.
2. The complicated repeated trial and error steps are omitted, and the calculation method is simple and intuitive and has high practical value.
Drawings
Fig. 1 is a grid-tied inverter topology of the present invention.
Fig. 2 shows that the grid strength is SCR-3 and the current loop design bandwidth is ωCL942rad/s, the pll design bandwidth is ωpllWhen 1347rad/s, baud diagram of grid-connected inverter system g(s).
Fig. 3 shows that the power grid strength is SCR-3 and the current loop design bandwidth is ωCL942rad/s, the pll design bandwidth is ωpll1347rad/s, nyquist curve of the grid-connected inverter system g(s).
Fig. 4 shows that the grid strength is SCR ═ 1.5, and the current loop design bandwidth is ωCL942rad/s, the pll design bandwidth is ωpllWhen the power is 422rad/s, baud graph of the grid-connected inverter system G(s).
Fig. 5 shows that the power grid strength is SCR ═ 1.5, and the current loop design bandwidth is ωCL942rad/s, the pll design bandwidth is ωpllAnd when the speed is 422rad/s, the Nyquist curve of the grid-connected inverter system G(s).
FIG. 6 shows grid strength as SCR 1 and current loop design bandwidth as ωCL942rad/s, the pll design bandwidth is ωpllAnd (4) when the voltage is 263.4rad/s, a baud graph of the grid-connected inverter system G(s).
Fig. 7 shows that the grid strength is SCR 1 and the current loop design bandwidth is ωCL942rad/s, the pll design bandwidth is ωpll263.4rad/s, nyquist curve of the grid-connected inverter system g(s).
Detailed Description
Fig. 1 is a topology diagram of a grid-connected inverter in the embodiment of the present invention. As shown in FIG. 1, the topology of the present invention includes a DC voltage source UdcDC side filter capacitor CdcThe three-phase half-bridge inverter comprises a three-phase half-bridge inverter, an L filter and a three-phase alternating current power grid. DC voltage source UdcThrough a filter capacitor CdcIs connected to the input end of an inverter, the output end of the inverter is connected with a three-phase alternating current network through an L filter, LgridThe inductance component corresponding to the network impedance is recorded as the network impedance inductance component Lgrid。RgridThe resistance component corresponding to the network impedance is recorded as the network impedance resistance component Rgrid。
The relevant electrical parameters when the invention is implemented are set as follows: DC voltage source Udc750V, the rated capacity of the grid-connected inverter is 30kVA, and the effective value of the three-phase grid phase voltage is Ea＝Eb＝Ec220V, the system switching frequency is fsw10kHz, system sampling time T s100 mus, filter inductance L2 mH.
Referring to fig. 1, fig. 2, fig. 3, fig. 4, fig. 5, fig. 6 and fig. 7, as seen from fig. 1, the present invention provides a method for designing a bandwidth of a grid-connected inverter controller under a weak power grid, where the bandwidth includes a control bandwidth ω of a current control loopCLAnd control bandwidth omega of phase-locked looppllThe method comprises the following steps:
step 1, obtaining output current I of grid-connected inverter through samplinggdAnd the output voltage U of the grid-connected invertergdGiving an expression of an open-loop transfer function G(s) of a current control loop of the grid-connected inverter;
Figure BDA0003062759110000061
wherein L isgridAs a component of the network impedance inductance, RgridAnd the impedance resistance component of the power grid is shown, ξ is the damping ratio of the phase-locked loop, and s is a Laplace operator.
In the present embodiment, the output current I of the grid-connected invertergd45A, the output phase voltage U of the grid-connected invertergdThe damping ratio of the phase-locked loop is ξ 0.707.
Step 2, giving an expression of an open-loop transfer function frequency domain G (j omega) of a current control loop of the grid-connected inverter,
Figure BDA0003062759110000062
wherein, omega is the frequency domain rotation angular frequency; j is an imaginary unit.
Step 3, obtaining an expression of the open-loop transfer function frequency domain amplitude | G (j ω) | according to the expression of the open-loop transfer function frequency domain G (j ω) given in the step 2,
Figure BDA0003062759110000071
step 4, obtaining the maximum value of the frequency domain amplitude of the open-loop transfer function according to the expression of the frequency domain amplitude | G (j ω) | of the open-loop transfer function obtained in the step 3, and recording the maximum value | G (j ω) |max，
Figure BDA0003062759110000072
And 5, combining the step 4, setting the open-loop transfer function frequency domain amplitude | G (j omega) | of the current control loop of the grid-connected inverter to meet the following requirements for ensuring the system stability according to the Nyquist stability criterion:
Figure BDA0003062759110000073
namely: maximum | G (j ω) & gtnon & gtmaxThe limiting conditions are as follows:
Figure BDA0003062759110000074
step 6, calculating the maximum value | G (j ω) & gt obtained in step 5maxThe design criteria of the control bandwidth of the current control loop and the control bandwidth of the phase-locked loop are given.
Control bandwidth omega of current control loopCLThe design criteria are: control bandwidth omega of current loop for suppressing noise around switching frequencyCLNot greater than switching angular frequency omega of grid-connected invertersw0.5 times of (i.e.. omega.)CL≤0.5ωsw。
In this embodiment, the control bandwidth ω of the current loopCL＝150×2πrad/s＝942rad/s。
Control bandwidth omega of phase-locked looppllThe design criteria are as follows: controlling the bandwidth omega of a phase-locked looppllAnd current control loop control bandwidth omegaCLThe ratio of (A) is recorded as a ratio n, and the ratio n satisfies the following formula:
Figure BDA0003062759110000081
control bandwidth omega of current control loopCLAfter the determination, the value range of the ratio n under any power grid strength, namely the control bandwidth omega of the phase-locked loop is determined by the formulapllIs determined.
In the embodiment, three situations of the grid-connected inverter system in the weak grid environment are implemented in total:
the first situation is as follows: the short-circuit ratio of the grid-connected inverter system is SCR (selective catalytic reduction) 3, and the grid impedance inductance component Lgrid5.1mH, the grid impedance resistance component Rgrid0.16 Ω. When the control bandwidth of the current loop is determined as ωCLAfter 942rad/s, the ratio n is less than or equal to 1.43, and then the design range of the pll control bandwidth is:
ωpll≤nωCL＝1.43×942rad/s＝1347rad/s。
in summary, the design bandwidth of the current-taking control loop is omegaCLTaking the design bandwidth of the phase-locked loop as omega for 942rad/spllAfter substituting G (j ω) into 1347rad/s, a bode plot and a nyquist curve of the transfer function of the current control loop can be obtained as shown in fig. 2 and fig. 3. Wherein, fig. 2 is a bode diagram, the upper and lower parts in the diagram are respectively an amplitude frequency curve and a phase frequency curve in the bode diagram, the abscissa indicates angular frequency in rad/s, the ordinate of the amplitude frequency curve indicates amplitude in dB, the ordinate of the phase frequency curve indicates phase in deg; fig. 3 is a nyquist curve with the abscissa representing the real axis and the ordinate representing the imaginary axis. It can be observed that the system is in a critical steady state at this time.
The second situation: the short-circuit ratio of the grid-connected inverter system is 1.5 of SCR, and the grid impedance inductance component Lgrid10.2mH, the grid impedance resistance component Rgrid0.32 Ω. When the control bandwidth of the current loop is determined as ωCLAfter 942rad/s, the ratio n is less than or equal to 0.4478, and the design range of the pll control bandwidth is: omegapll≤nωCL＝0.4478×942rad/s＝422rad/s。
In summary, the current-taking control loop is designed to have a bandwidth ωCLTaking the design bandwidth omega of the phase-locked loop as 942rad/spllAfter substituting G (j ω) for 422rad/s, a bode plot and a nyquist curve of the transfer function of the current control loop can be obtained as shown in fig. 4 and 5. Wherein, fig. 4 is a bode diagram, the upper and lower parts in the diagram are respectively an amplitude frequency curve and a phase frequency curve in the bode diagram, the abscissa indicates angular frequency in rad/s, the ordinate of the amplitude frequency curve indicates amplitude in dB, the ordinate of the phase frequency curve indicates phase in deg; fig. 5 is a nyquist curve with the abscissa representing the real axis and the ordinate representing the imaginary axis. It can be observed that the system is in a critical steady state at this time.
Case three: the short-circuit ratio of the grid-connected inverter system is SCR (silicon controlled rectifier) 1, and the impedance inductance component of the power grid is Lgrid15.32mH, the grid impedance resistance component is Rgrid＝048 Ω. When the control bandwidth of the current loop is determined as ωCLAfter 942rad/s, the ratio n is less than or equal to 0.2795, and then the design range of the pll control bandwidth is: omegapll≤nωCL＝0.2795×942rad/s＝263.4rad/s。
In summary, the design bandwidth of the current-taking control loop is omegaCLTaking the design bandwidth of the phase-locked loop as omega for 942rad/spllThe baud plot and nyquist curve of the current control loop transfer function can be obtained by substituting G (j ω) at 263.4rad/s as shown in fig. 6 and 7. Wherein, fig. 6 is a bode diagram, the upper and lower parts in the diagram are respectively an amplitude frequency curve and a phase frequency curve in the bode diagram, the abscissa indicates angular frequency in rad/s, the ordinate of the amplitude frequency curve indicates amplitude in dB, the ordinate of the phase frequency curve indicates phase in deg; fig. 7 is a nyquist curve with the abscissa representing the real axis and the ordinate representing the imaginary axis. It can be observed that the system is in a critical steady state at this time.

Claims (1)

1. A design method for a grid-connected inverter controller bandwidth under a weak grid includes a control bandwidth omega of a current control loopCLAnd control bandwidth omega of phase-locked looppllThe method is characterized by comprising the following steps:
step 1, obtaining output current I of grid-connected inverter through samplinggdAnd the output voltage U of the grid-connected invertergdGiving an expression of an open-loop transfer function G(s) of a current control loop of the grid-connected inverter;
Figure FDA0003062759100000011
wherein L isgridAs a component of the network impedance inductance, RgridThe impedance resistance component of the power grid is shown, xi is the damping ratio of a phase-locked loop, and s is a Laplace operator;
step 2, giving an expression of an open-loop transfer function frequency domain G (j omega) of a current control loop of the grid-connected inverter,
Figure FDA0003062759100000012
wherein, omega is the frequency domain rotation angular frequency; j is an imaginary unit;
step 3, obtaining an expression of the open-loop transfer function frequency domain amplitude | G (j ω) | according to the expression of the open-loop transfer function frequency domain G (j ω) given in the step 2,
Figure FDA0003062759100000013
step 4, obtaining the maximum value of the frequency domain amplitude of the open-loop transfer function according to the expression of the frequency domain amplitude | G (j ω) | of the open-loop transfer function obtained in the step 3, and recording the maximum value | G (j ω) |max，
Figure FDA0003062759100000014
And 5, combining the step 4, setting the open-loop transfer function frequency domain amplitude | G (j omega) | of the current control loop of the grid-connected inverter to meet the following requirements for ensuring the system stability according to the Nyquist stability criterion:
Figure FDA0003062759100000021
namely: maximum | G (j ω) & gtnon & gtmaxThe limiting conditions are as follows:
Figure FDA0003062759100000022
step 6, calculating the maximum value | G (j ω) & gt obtained in step 5maxThe design criteria of the control bandwidth of the current control loop and the control bandwidth of the phase-locked loop are given;
control bandwidth omega of current control loopCLThe design criteria are: is composed ofSuppressing noise near the switching frequency, control bandwidth omega of the current loopCLNot greater than switching angular frequency omega of grid-connected invertersw0.5 times of (i.e.. omega.)CL≤0.5ωsw；
Control bandwidth omega of phase-locked looppllThe design criteria are: controlling the bandwidth omega of a phase-locked looppllAnd current control loop control bandwidth omegaCLThe ratio of (A) is recorded as a ratio n, and the ratio n satisfies the following formula:
Figure FDA0003062759100000023
control bandwidth omega of current control loopCLAfter the determination, the value range of the ratio n under any power grid strength, namely the control bandwidth omega of the phase-locked loop is determined through the formulapllIs determined.
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