WO2023010659A1 - 一种弱电网条件下的并网变流器控制环路稳定判据 - Google Patents

一种弱电网条件下的并网变流器控制环路稳定判据 Download PDF

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WO2023010659A1
WO2023010659A1 PCT/CN2021/119220 CN2021119220W WO2023010659A1 WO 2023010659 A1 WO2023010659 A1 WO 2023010659A1 CN 2021119220 W CN2021119220 W CN 2021119220W WO 2023010659 A1 WO2023010659 A1 WO 2023010659A1
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grid
phase
current
connected converter
transfer function
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French (fr)
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刘芳
刘威
徐韫钰
汪浩东
李研
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合肥工业大学
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    • 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
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • 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
    • 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
    • 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
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Definitions

  • the invention relates to a control loop stability criterion of a grid-connected converter, in particular to a control loop stability criterion of a grid-connected converter under the condition of a weak grid, and belongs to the field of electric power control.
  • Analytical methods such as state space averaging can judge system stability, but they cannot directly guide the design of each loop of the controller through indicators such as stability margin, which brings certain difficulties to the design of stable operation of grid-connected converters in weak grids.
  • the technical problem to be solved by the present invention is to overcome the limitations of the above-mentioned various technical solutions, and to provide a control loop stability criterion of a grid-connected converter under a weak grid condition in view of the aforementioned two problems.
  • the present invention provides a control loop stability criterion of a grid-connected converter under the condition of a weak grid.
  • the control loop of the grid-connected converter includes a current control loop and a phase-locked loop. The steps are as follows:
  • Step 1 Obtain the output current I g of the grid-connected converter and the output voltage U g of the grid-connected converter by sampling, and give the expressions of the grid impedance link G 1 (s) of the grid-connected converter, and The expression of the closed-loop transfer function G 2 (s) of the phase-locked loop of the grid-connected converter and the expression of the closed-loop transfer function G 3 (s) of the current control loop of the grid-connected converter without considering the influence of the phase-locked loop;
  • L grid is the inductance component of grid impedance
  • R grid is the resistance component of grid impedance
  • ⁇ is the damping ratio of the phase-locked loop
  • ⁇ pll is the control bandwidth of the phase-locked loop
  • G CL is the transfer function of the proportional and integral link of the current control loop
  • G main is the transfer function of the filter link of the grid-connected converter
  • Step 2 give the expression of the open-loop transfer function G IL (s) of the current control loop of the grid-connected converter considering the influence of the phase-locked loop;
  • step 3 the expression of the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop is given, and the open-loop transfer function G IL (s) of the current control loop in step 2 is calculated at the same time Constant deformation;
  • G IL (s) G pll_grid (s) ⁇ G 3 (s)
  • G current (s) 1/G 3 (s), recorded as the current control loop criterion transfer function of the grid-connected converter without considering the influence of the phase-locked loop;
  • Step 4 according to the transfer functions of each link given in the previous three steps, further give the control loop stability criterion of the grid-connected converter under the weak grid condition;
  • Step 4.1 calculate the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop and the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop ) phase expression and amplitude expression in the frequency domain;
  • the amplitude and phase of the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop in the frequency domain are respectively recorded as the combined amplitude A pll_gird ( ⁇ ), combined phase ⁇ pll_gird ( ⁇ ) , the expressions of combined amplitude A pll_gird ( ⁇ ) and combined phase ⁇ pll_gird ( ⁇ ) are:
  • ⁇ is the rotation angular frequency in the frequency domain
  • the amplitude and phase of the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop in the frequency domain are respectively recorded as the current amplitude A current ( ⁇ ) and the current phase ⁇ current ( ⁇ ), the expressions of current amplitude A current ( ⁇ ) and current phase ⁇ current ( ⁇ ) are respectively:
  • G CL ( ⁇ ) is the expression of the current control loop proportional and integral link transfer function G CL in the frequency domain
  • is the expression of the current control loop proportional and integral link transfer function G CL in the frequency domain Amplitude
  • G main ( ⁇ ) is the expression of the transfer function G main of the filter link of the grid-connected converter in the frequency domain
  • is the expression of the transfer function G main of the filter link of the grid-connected converter in the frequency domain Amplitude
  • is the amplitude of 1+G CL ( ⁇ )G main ( ⁇ ) in frequency domain
  • ⁇ G CL ( ⁇ ) is G CL ( ⁇ ) in The phase in the frequency domain
  • ⁇ G main ( ⁇ ) is the phase of G main ( ⁇ ) in the frequency domain
  • ⁇ (1+G CL ( ⁇ )G main ( ⁇ )) is 1+G CL ( ⁇ )G main ( ⁇ ) phase in the frequency domain;
  • step 4.2 according to the amplitude expression and phase expression obtained in step 4.1, the control loop stability criterion of the grid-connected converter under the condition of weak grid is given: when the following two conditions of amplitude and phase are satisfied at the same time, It is determined that the grid-connected converter system is in a stable state, otherwise, the control loop of the grid-connected converter is determined to be in an unstable state;
  • control loop stability criterion of the grid-connected converter under the weak grid condition is:
  • phase difference between the combined phase ⁇ pll_gird ( ⁇ ) and the current phase ⁇ current ( ⁇ ) is 180°, and A current ( ⁇ 180° ) > A pll_gird ( ⁇ 180° ), the control loop amplitude of the grid-connected converter is determined Stablize;
  • the combined amplitude A pll_gird ( ⁇ ) is equal to the current amplitude A current ( ⁇ ), and ⁇ pll_gird ( ⁇ )- ⁇ current ( ⁇ )-180°>0, it is determined that the phase of the grid-connected converter control loop is stable ;
  • ⁇ 180° is the corresponding angular frequency when the difference between the combined phase ⁇ pll_gird ( ⁇ ) and the current phase ⁇ current ( ⁇ ) is 180°;
  • a current ( ⁇ 180° ) is the magnitude of the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop when the angular frequency is ⁇ 180° ;
  • a pll_gird ( ⁇ 180° ) is the magnitude of the combined transfer function of the grid impedance part of the grid-connected converter and the phase-locked loop at an angular frequency of ⁇ 180° ;
  • ⁇ is the corresponding angular frequency when the combined amplitude A pll_gird ( ⁇ ) is equal to the current amplitude A current ( ⁇ );
  • ⁇ current ( ⁇ inter ) is the phase of the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop at the angular frequency ⁇ inter;
  • ⁇ pll_grid ( ⁇ ) is the phase of the combined transfer function G pll_grid (s) of the grid impedance part of the grid- connected converter and the phase-locked loop at the angular frequency ⁇ ;
  • Step 4.3 according to the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop obtained in step 4.1 and the current control loop criterion transfer of the grid-connected converter without considering the influence of the phase-locked loop
  • Degree expression A M and phase margin expression P M
  • the control loop stability criterion proposed by the present invention takes the power grid strength into consideration. No matter how the power grid strength changes, the stability of the grid-connected converter system can be judged only by solving the closed-loop transfer function of each loop, and At the same time, the stability margin of the system can be solved accurately, which provides great convenience for the design of the controller parameters of the grid-connected converter under the weak grid.
  • control loop stability criterion proposed by the present invention greatly simplifies the solution process of the transfer function expression of the grid-connected converter system.
  • the method is simple, the physical meaning is clear and the accuracy is high.
  • Fig. 1 is the topological structure of the grid-connected converter of the present invention.
  • Fig. 1 is a topological diagram of a grid-connected converter in an embodiment of the present invention.
  • 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 grid.
  • the DC voltage source U dc is connected to the input terminal of the inverter through the filter capacitor C dc , and the output terminal 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 the grid impedance Inductive component L grid .
  • R grid is the resistance component corresponding to the grid impedance, which is recorded as the grid impedance resistance component R grid .
  • DC voltage source U dc 750V
  • rated capacity of the grid-connected inverter 30kVA
  • the present invention is a control loop stability criterion of a grid-connected converter under the condition of a weak grid.
  • the control loop of the grid-connected converter includes a current control loop and a phase-locked loop, and the steps are as follows:
  • Step 1 Obtain the output current I g of the grid-connected converter and the output voltage U g of the grid-connected converter by sampling, and give the expressions of the grid impedance link G 1 (s) of the grid-connected converter, and The expression of the closed-loop transfer function G 2 (s) of the phase-locked loop of the grid converter and the expression of the closed-loop transfer function G 3 (s) of the current control loop of the grid-connected converter without considering the influence of the phase-locked loop.
  • L grid is the inductance component of grid impedance
  • R grid is the resistance component of grid impedance
  • ⁇ is the damping ratio of the phase-locked loop
  • ⁇ pll is the control bandwidth of the phase-locked loop
  • G CL is the transfer function of the proportional and integral link of the current control loop
  • G main is the transfer function of the filter link of the grid-connected converter.
  • the output current I g of the grid-connected converter is 45A
  • the output phase voltage U g of the grid-connected converter is 220V
  • Step 2 give the expression of the open-loop transfer function G IL (s) of the current control loop of the grid-connected converter considering the influence of the phase-locked loop;
  • step 3 the expression of the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop is given, and the open-loop transfer function G IL (s) of the current control loop in step 2 is calculated at the same time Constant deformation;
  • G IL (s) G pll_grid (s) ⁇ G 3 (s)
  • G current (s) 1/G 3 (s), recorded as the current control loop criterion transfer function of the grid-connected converter without considering the influence of the phase-locked loop;
  • Step 4 according to the transfer functions of each link given in the previous three steps, further give the control loop stability criterion of the grid-connected converter under the weak grid condition;
  • Step 4.1 calculate the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop and the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop ) in the phase and magnitude expressions in the frequency domain.
  • the amplitude and phase of the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop in the frequency domain are respectively recorded as the combined amplitude A pll_gird ( ⁇ ), combined phase ⁇ pll_gird ( ⁇ ) , the expressions of combined amplitude A pll_gird ( ⁇ ) and combined phase ⁇ pll_gird ( ⁇ ) are:
  • ⁇ is the angular frequency of rotation in the frequency domain.
  • the amplitude and phase of the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop in the frequency domain are respectively recorded as the current amplitude A current ( ⁇ ) and the current phase ⁇ current ( ⁇ ), the expressions of current amplitude A current ( ⁇ ) and current phase ⁇ current ( ⁇ ) are respectively:
  • G CL ( ⁇ ) is the expression of the current control loop proportional and integral link transfer function G CL in the frequency domain
  • is the expression of the current control loop proportional and integral link transfer function G CL in the frequency domain Amplitude
  • G main ( ⁇ ) is the expression of the transfer function G main of the filter link of the grid-connected converter in the frequency domain
  • is the expression of the transfer function G main of the filter link of the grid-connected converter in the frequency domain Amplitude
  • is the amplitude of 1+G CL ( ⁇ )G main ( ⁇ ) in frequency domain
  • ⁇ G CL ( ⁇ ) is G CL ( ⁇ ) in The phase in the frequency domain
  • ⁇ G main ( ⁇ ) is the phase of G main ( ⁇ ) in the frequency domain
  • ⁇ (1+G CL ( ⁇ )G main ( ⁇ )) is 1+G CL ( ⁇ )G main ( ⁇ ) in the frequency domain.
  • step 4.2 according to the amplitude expression and phase expression obtained in step 4.1, the control loop stability criterion of the grid-connected converter under the condition of weak grid is given: when the following two conditions of amplitude and phase are satisfied at the same time, It is determined that the grid-connected converter system is in a stable state, otherwise, the control loop of the grid-connected converter is determined to be in an unstable state;
  • control loop stability criterion of the grid-connected converter under the weak grid condition is:
  • phase difference between the combined phase ⁇ pll_gird ( ⁇ ) and the current phase ⁇ current ( ⁇ ) is 180°, and A current ( ⁇ 180° ) > A pll_gird ( ⁇ 180° ), the control loop amplitude of the grid-connected converter is determined Stablize;
  • the combined amplitude A pll_gird ( ⁇ ) is equal to the current amplitude A current ( ⁇ ), and ⁇ pll_gird ( ⁇ )- ⁇ current ( ⁇ )-180°>0, it is determined that the phase of the grid-connected converter control loop is stable ;
  • ⁇ 180° is the corresponding angular frequency when the difference between the combined phase ⁇ pll_gird ( ⁇ ) and the current phase ⁇ current ( ⁇ ) is 180°;
  • a current ( ⁇ 180° ) is the magnitude of the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop when the angular frequency is ⁇ 180° ;
  • a pll_gird ( ⁇ 180° ) is the magnitude of the combined transfer function of the grid impedance part of the grid-connected converter and the phase-locked loop at an angular frequency of ⁇ 180° ;
  • ⁇ is the corresponding angular frequency when the combined amplitude A pll_gird ( ⁇ ) is equal to the current amplitude A current ( ⁇ );
  • ⁇ current ( ⁇ inter ) is the phase of the current control loop criterion transfer function G current (s) of the grid-connected converter without considering the influence of the phase-locked loop at the angular frequency ⁇ inter;
  • ⁇ pll_grid ( ⁇ ) is the phase of the combined transfer function G pll_grid (s) of the grid impedance part of the grid- connected converter and the phase-locked loop at the angular frequency ⁇ ;
  • Step 4.3 according to the combined transfer function G pll_grid (s) of the grid impedance part of the grid-connected converter and the phase-locked loop obtained in step 4.1 and the current control loop criterion transfer of the grid-connected converter without considering the influence of the phase-locked loop
  • Degree expression A M and phase margin expression P M
  • the control bandwidth of the phase-locked loop can be selected through the design method of the grid-connected converter controller under a weak grid, and then the system can be determined according to the stability criterion of the control loop Stability and stability margin, the following lists three situations when the phase-locked loop control bandwidth takes different values in this case:
  • the output current waveform of the grid-connected converter system is shown in Figure 7. It can also be seen from the output current waveform that the system is unstable under this condition.
  • the abscissa in FIG. 7 represents the time t in seconds, and the ordinate represents the output current I g of the grid-connected converter in A.
  • the control bandwidth of the phase-locked loop can be selected through the design method of the grid-connected converter controller under a weak grid, and then the system can be determined according to the stability criterion of the control loop Stability and stability margin, the following also lists three situations when the PLL control bandwidth takes different values in this case:
  • the output current waveform of the grid-connected converter system is shown in Figure 13. It can also be seen from the output current waveform that the system is unstable under this condition.
  • the abscissa in FIG. 13 represents the time t in seconds, and the ordinate represents the output current I g of the grid-connected converter in A.

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Abstract

本发明公开了一种弱电网条件下的并网变流器控制环路稳定判据，属于电力控制领域。该方法包括：采样，先求出并网变流器各个控制环路的传递函数表达式，进一步得到表征系统稳定性能的传递函数表达式，然后再根据该传递函数求出其幅值和相位表达式，并给出弱电网条件下的并网变流器控制环路稳定判据和系统的稳定裕度表达式。该控制环路稳定判据物理意义明确，运用简单，能够快速且准确的判断出并网变流器系统在弱电网条件下的稳定性，对指导控制器参数的设计也具有重要意义。

Description

一种弱电网条件下的并网变流器控制环路稳定判据
本申请主张2021年08月05日申请的申请号为202110899076.2的“一种弱电网条件下的并网变流器控制环路稳定判据”的优先权，原受理机构为中国。
技术领域
本发明涉及一种并网变流器控制环路稳定判据，尤其是一种弱电网条件下的并网变流器控制环路稳定判据，属于电力控制领域。
背景技术
近年来，随着煤、石油等传统化石能源日益枯竭，全球能源问题正面临着严峻的考验，越来越多的可再生能源通过电力电子接口并入大电网，电力电子并网接口系统逐渐呈现高比例特性。因此，含高比例电力电子并网接口的电力系统稳定性逐渐成为日益关注的重要问题，尤其是弱电网条件下的并网变流器稳定性问题。在高比例电力电子并网接口形成的弱电网系统中，如何寻求简单、快速且能够准确判断系统稳定性的方法是一个极其有价值的问题，并对进一步指导控制器参数的设计也具有十分重要的意义。
题为《“双高”电力系统稳定性的新问题及分类探讨》(谢小荣，贺静波，毛航银，李浩志.“双高”电力系统稳定性的新问题及分类探讨[J].中国电机工程学报，2021，41(02)：461-475.)的文章指出，在能源转型和科技进步的推动下，电力系统逐渐呈现高比例可再生能源和高比例电力电子设备的特征，随之而来带来的电力系统稳定性问题也日益复杂，如电力电子设备之间及其与电网之间相互作用引起的宽频带振荡以及控制器之间的交互影响等，尤其是弱电网条件下的失稳问题，是目前备受关注的重要问题之一。
题为《并网逆变器小信号建模方法对比及其适用性分析》(刘倪，张昌华，段雪，陈昕，陈树恒，刘群英.并网逆变器小信号建模方法对比及其适用性分析[J].电力系统自动化，2018，42(23)：134-141.)的文章介绍了状态空间模型在并网变流器系统中的应用，但是在采用状态空间方法进行稳定性分析时，若要最后得到完整地系统模型，则需要获取并网变流器和电网组成单元的所有参数，而在含高比例电力电子接口的并网变流器系统中，系统组成单元结构和参数随时都会发生变化，这就将会使得系统的稳定性分析过程变得繁琐复 杂。
题为《Small-signal stability analysis of three-phase AC systems in the presence of constant power loads based on measured d-q frame impedances》(Wen Bo，Boroyevich D，Burgos R，et al.Small-signal stability analysis of three-phase AC systems in the presence of constant power loads based on measured d-q frame impedances[J].IEEE Transactions on Power Electronics，2015，30(10)：5952-5963.)(《基于dq阻抗的三相交流系统恒功率负载下的小信号稳定性分析》(温博，布鲁耶威驰-德，布鲁格斯-仁，等.基于dq阻抗的三相交流系统恒功率负载下的小信号稳定性分析[J].电力电子，2015，30(10)：5952-5963.))的文章介绍了阻抗稳定性理论基础，讨论了三相并网变流器的阻抗稳定性分析方法和阻抗稳定判据的应用，阻抗分析方法将并网变流器和电网视为两个独立的子系统，分别建立各自的阻抗模型，最后根据两者的阻抗比值借助奈奎斯特判据来分析系统稳定性。阻抗分析法相比状态空间法虽能有效简化系统稳定性分析，但是当变流器控制结构和控制器参数等发生变化时，其变流器侧阻抗模型需要重新推导，过程也相对繁琐且易出错。
由以上分析可见，目前关于含有高比例电力电子并网接口的电力系统稳定性问题已受到了广泛的关注和研究，尤其是弱电网条件下并网变流器系统的稳定性问题。部分研究利用推导系统完整的状态空间模型或阻抗模型来分析稳定性，这些方法都能够全面且相对准确的展示系统的稳定状态，但是推导过程都相对复杂。如果能够提出一种简单的稳定性分析方法，仅建立控制环路各自的传递函数模型，最后通过组合就能得到表征系统稳定性能的表达式，从而进一步指导控制器参数设计，这无论对于完善和丰富并网变流器的稳定性分析理论，还是实际工程应用，都将具有十分重要的意义和价值。
综上所述，现有技术中还存在着以下问题：
1、采用阻抗分析或者状态空间平均方法分析弱电网下并网变流器的稳定性，在系统控制结构发生变化时需要重新推导其数学模型，过程繁琐复杂。
2、状态空间平均等分析方法可以判断系统稳定性，但不能通过稳定裕量等指标直接指导控制器的各环路设计，这给并网变流器的弱电网稳定运行设 计带来一定困难。
发明内容
本发明要解决的技术问题为克服上述各种技术方案的局限性，针对前述两个问题，提供一种弱电网条件下的并网变流器控制环路稳定判据。
本发明的目的是这样实现的。本发明提供了一种弱电网条件下的并网变流器控制环路稳定判据，所述并网变流器的控制环路包括电流控制环和锁相环，步骤如下：
步骤1，通过采样得到并网变流器的输出电流I g和并网变流器的输出电压U g，并分别给出并网变流器电网阻抗环节G 1(s)的表达式、并网变流器锁相环闭环传递函数G 2(s)的表达式和并网变流器不考虑锁相环影响的电流控制环闭环传递函数G 3(s)的表达式；
并网变流器电网阻抗环节G 1(s)的表达式如下：
Figure PCTCN2021119220-appb-000001
其中，s为拉普拉斯算子，L grid为电网阻抗电感分量，R grid为电网阻抗电阻分量；
并网变流器锁相环闭环传递函数G 2(s)的表达式如下：
Figure PCTCN2021119220-appb-000002
其中，ξ为锁相环的阻尼比，ω pll为锁相环的控制带宽；
并网变流器不考虑锁相环影响的电流控制环闭环传递函数G 3(s)的表达式G 3(s)如下：
Figure PCTCN2021119220-appb-000003
其中，G CL为电流控制环比例及积分环节传递函数，G main为并网变流器滤波环节传递函数；
步骤2，给出并网变流器考虑锁相环影响的电流控制环开环传递函数G IL(s)的表达式；
Figure PCTCN2021119220-appb-000004
步骤3，给出并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的表达式，并同时对步骤2中的电流控制环开环传递函数G IL(s)进行恒等变形；
并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的表达式如下：
Figure PCTCN2021119220-appb-000005
电流控制环开环传递函数G IL(s)的恒等变形结果如下：
G IL(s)＝G pll_grid(s)×G 3(s)
＝G pll_grid(s)/(1/G 3(s))
＝G pll_grid(s)/G current(s)
其中：G current(s)＝1/G 3(s)，记为并网变流器不考虑锁相环影响的电流控制环判据传递函数；
步骤4，根据前面3个步骤中给出的各环节传递函数，进一步给出弱电网条件下并网变流器控制环路稳定判据；
步骤4.1，求出并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)与并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的相位表达式和幅值表达式；
将并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)在频域中的幅值、相位分别记为组合幅值A pll_gird(ω)、组合相位ψ pll_gird(ω)，组合幅值A pll_gird(ω)和组合相位ψ pll_gird(ω)的表达式分别为：
Figure PCTCN2021119220-appb-000006
其中，ω为频域旋转角频率；
将并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的幅值、相位分别记为电流幅值A current(ω)、电流相位ψ current(ω)，电流幅值A current(ω)和电流相位ψ current(ω)的表达式分别为：
Figure PCTCN2021119220-appb-000007
式中，G CL(ω)为电流控制环比例及积分环节传递函数G CL在频域内的表达式，|G CL(ω)|为电流控制环比例及积分环节传递函数G CL在频域内的幅值，G main(ω)为并网变流器滤波环节传递函数G main在频域内的表达式，|G main(ω)|为并网变流器滤波环节传递函数G main在频域内的幅值，|1+G CL(ω)G main(ω)|为1+G CL(ω)G main(ω)在频域内的幅值，∠G CL(ω)为G CL(ω)在频域内的相位，∠G main(ω)为G main(ω)在频域内的相位，∠(1+G CL(ω)G main(ω))为1+G CL(ω)G main(ω)在频域内的相位；
步骤4.2，根据步骤4.1中求出的幅值表达式和相位表达式，给出弱电网条件下的并网变流器控制环路稳定判据：同时满足以下幅值和相位2个条件时，认定并网变流器系统处于稳定状态，否则，认定并网变流器控制环路处于非稳定状态；
所述弱电网条件下并网变流器控制环路稳定判据为：
组合相位ψ pll_gird(ω)与电流相位ψ current(ω)的相位差为180°，且A current(ω 180°)＞A pll_gird(ω 180°)，认定并网变流器控制环路幅值稳定；
组合幅值A pll_gird(ω)和电流幅值A current(ω)相等，且ψ pll_gird(ω 交)-ψ current(ω 交)-180°＞0，认定并网变流器控制环路相位稳定；
当并网变流器控制环路同时满足幅值稳定和相位稳定时，则认定整个并网变流器稳定；
其中，
ω 180°为组合相位ψ pll_gird(ω)与电流相位ψ current(ω)的差值为180°时对应的角频率；
A current(ω 180°)为角频率ω 180°时并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)的幅值；
A pll_gird(ω 180°)为角频率ω 180°时并网变流器电网阻抗部分和锁相环的组合传递函数的幅值；
ω 交为组合幅值A pll_gird(ω)与电流幅值A current(ω)相等时对应的角频率；
ψ current(ω 交)为角频率ω 交时并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)的相位；
ψ pll_grid(ω 交)为角频率ω 交时并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的相位；
步骤4.3，根据步骤4.1中求出的并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)与并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的相位表达式和幅值表达式，再结合步骤4.2给出的控制环路稳定判据，给出弱电网条件下并网变流器系统的幅值裕度表达式A M和相位裕度表达式P M：
Figure PCTCN2021119220-appb-000008
与现有技术相比，本发明的有益效果如下：
1、本发明提出的控制环路稳定判据将电网强度考虑在内，无论电网强度如何变化，仅通过求解各个环路的闭环传递函数，就能够判断并网变流器系统的稳定性，并同时可以准确求解出系统的稳定裕度，为弱电网下并网变流器控制器参数的设计提供了巨大的方便。
2、相比其它的稳定性判别方法，本发明提出的控制环路稳定判据大大简化了并网变流器系统传递函数表达式的求解过程，方法简单、物理意义清晰 且准确性高。
附图说明
图1是本发明的并网变流器拓扑结构。
图2是电网强度为SCR＝1.5，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝64.5rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图。
图3是电网强度为SCR＝1.5，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝64.5rad/s时，并网变流器的输出电流I g的仿真波形图。
图4是电网强度为SCR＝1.5，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝320.4rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图。
图5是电网强度为SCR＝1.5，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝320.4rad/s时，并网变流器的输出电流I g的仿真波形图。
图6是电网强度为SCR＝1.5，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝452.3rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图。
图7是电网强度为SCR＝1.5，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝452.3rad/s时，并网变流器的输出电流I g的仿真波形图。
图8是电网强度为SCR＝1.1，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝32.3rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图。
图9是电网强度为SCR＝1.1，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝32.3rad/s时，并网变流器的输出电流I g的仿真波形图。
图10是电网强度为SCR＝1.1，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝193.7rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图。
图11是电网强度为SCR＝1.1，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝193.7rad/s时，并网变流器的输出电流I g的仿真波形图。
图12是电网强度为SCR＝1.1，电流环设计带宽为ω CL＝4750rad/s，锁相环 设计带宽为ω pll＝387.4rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图。
图13是电网强度为SCR＝1.1，电流环设计带宽为ω CL＝4750rad/s，锁相环设计带宽为ω pll＝387.4rad/s时，并网变流器的输出电流I g的仿真波形图。
具体实施方式
下面结合附图和具体实施例对本发明做进一步的说明。
图1是本发明实施例中的并网变流器的拓扑图。如图1所示，本发明的拓扑包括直流电压源U dc、直流侧滤波电容C dc、三相半桥式逆变器、L滤波器和三相交流电网。直流电压源U dc通过滤波电容C dc连接在逆变器的输入端，逆变器的输出端经过L滤波器和三相交流电网相连，L grid为电网阻抗对应的电感分量，记为电网阻抗电感分量L grid。R grid为电网阻抗对应的电阻分量，记为电网阻抗电阻分量R grid。
本发明实施时的有关电气参数设置如下：直流电压源U dc＝750V，并网逆变器额定容量为30kVA，三相电网相电压有效值为E a＝E b＝E c＝220V，系统开关频率为f sw＝10kHz，系统采样时间为T s＝100μs，滤波器滤波电感值L＝2mH。
本发明一种弱电网条件下的并网变流器控制环路稳定判据，所述并网变流器的控制环路包括电流控制环和锁相环，步骤如下：
步骤1，通过采样得到并网变流器的输出电流I g和并网变流器的输出电压U g，并分别给出并网变流器电网阻抗环节G 1(s)的表达式、并网变流器锁相环闭环传递函数G 2(s)的表达式和并网变流器不考虑锁相环影响的电流控制环闭环传递函数G 3(s)的表达式。
并网变流器电网阻抗环节G 1(s)的表达式如下：
Figure PCTCN2021119220-appb-000009
其中，s为拉普拉斯算子，L grid为电网阻抗电感分量，R grid为电网阻抗电阻分量。
并网变流器锁相环闭环传递函数G 2(s)的表达式如下：
Figure PCTCN2021119220-appb-000010
其中，ξ为锁相环的阻尼比，ω pll为锁相环的控制带宽。
并网变流器不考虑锁相环影响的电流控制环闭环传递函数G 3(s)的表达式G 3(s)如下：
Figure PCTCN2021119220-appb-000011
其中，G CL为电流控制环比例及积分环节传递函数，G main为并网变流器滤波环节传递函数。
在本实施例中，并网变流器的输出电流I g＝45A，并网变流器的输出相电压U g＝220V，电网阻抗电感分量分别取L grid＝10.2mH和L grid＝13.9mH两种情形，电网阻抗电阻分量分别取R grid＝0.32Ω和R grid＝0.436Ω两种情形。
在本实施例中，锁相环的阻尼比ξ＝0.707。
在本实施例中，并网变流器主电路的滤波电感L＝2mH，电流环的控制带宽ω CL＝4750rad/s。
步骤2，给出并网变流器考虑锁相环影响的电流控制环开环传递函数G IL(s)的表达式；
Figure PCTCN2021119220-appb-000012
步骤3，给出并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的表达式，并同时对步骤2中的电流控制环开环传递函数G IL(s)进行恒等变形；
并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的表达式如下：
Figure PCTCN2021119220-appb-000013
电流控制环开环传递函数G IL(s)的恒等变形结果如下：
G IL(s)＝G pll_grid(s)×G 3(s)
＝G pll_grid(s)/(1/G 3(s))
＝G pll_grid(s)/G current(s)
其中：G current(s)＝1/G 3(s)，记为并网变流器不考虑锁相环影响的电流控制环判据传递函数；
步骤4，根据前面3个步骤中给出的各环节传递函数，进一步给出弱电网条件下并网变流器控制环路稳定判据；
步骤4.1，求出并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)与并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的相位表达式和幅值表达式。
将并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)在频域中的幅值、相位分别记为组合幅值A pll_gird(ω)、组合相位ψ pll_gird(ω)，组合幅值A pll_gird(ω)和组合相位ψ pll_gird(ω)的表达式分别为：
Figure PCTCN2021119220-appb-000014
其中，ω为频域旋转角频率。
将并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的幅值、相位分别记为电流幅值A current(ω)、电流相位ψ current(ω)，电流幅值A current(ω)和电流相位ψ current(ω)的表达式分别为：
Figure PCTCN2021119220-appb-000015
式中，G CL(ω)为电流控制环比例及积分环节传递函数G CL在频域内的表达式，|G CL(ω)|为电流控制环比例及积分环节传递函数G CL在频域内的幅值，G main(ω)为并网变流器滤波环节传递函数G main在频域内的表达式，|G main(ω)|为并 网变流器滤波环节传递函数G main在频域内的幅值，|1+G CL(ω)G main(ω)|为1+G CL(ω)G main(ω)在频域内的幅值，∠G CL(ω)为G CL(ω)在频域内的相位，∠G main(ω)为G main(ω)在频域内的相位，∠(1+G CL(ω)G main(ω))为1+G CL(ω)G main(ω)在频域内的相位。
步骤4.2，根据步骤4.1中求出的幅值表达式和相位表达式，给出弱电网条件下的并网变流器控制环路稳定判据：同时满足以下幅值和相位2个条件时，认定并网变流器系统处于稳定状态，否则，认定并网变流器控制环路处于非稳定状态；
所述弱电网条件下并网变流器控制环路稳定判据为：
组合相位ψ pll_gird(ω)与电流相位ψ current(ω)的相位差为180°，且A current(ω 180°)＞A pll_gird(ω 180°)，认定并网变流器控制环路幅值稳定；
组合幅值A pll_gird(ω)和电流幅值A current(ω)相等，且ψ pll_gird(ω 交)-ψ current(ω 交)-180°＞0，认定并网变流器控制环路相位稳定；
当并网变流器控制环路同时满足幅值稳定和相位稳定时，则认定整个并网变流器稳定；
其中，
ω 180°为组合相位ψ pll_gird(ω)与电流相位ψ current(ω)的差值为180°时对应的角频率；
A current(ω 180°)为角频率ω 180°时并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)的幅值；
A pll_gird(ω 180°)为角频率ω 180°时并网变流器电网阻抗部分和锁相环的组合传递函数的幅值；
ω 交为组合幅值A pll_gird(ω)与电流幅值A current(ω)相等时对应的角频率；
ψ current(ω 交)为角频率ω 交时并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)的相位；
ψ pll_grid(ω 交)为角频率ω 交时并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的相位；
步骤4.3，根据步骤4.1中求出的并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)与并网变流器不考虑锁相环影响的电流控制环判据传 递函数G current(s)在频域中的相位表达式和幅值表达式，再结合步骤4.2给出的控制环路稳定判据，给出弱电网条件下并网变流器系统的幅值裕度表达式A M和相位裕度表达式P M：
Figure PCTCN2021119220-appb-000016
在本实施例中，一共实施了并网变流器系统在弱电网条件下的两种情形：
情形一：并网变流器系统短路比为SCR＝1.5，电网阻抗电感分量为L grid＝10.2mH，电阻分量为R grid＝0.32Ω。当电流环的控制带宽确定为ω CL＝4750rad/s后，则可以通过弱电网下并网变流器控制器设计方法选定锁相环的控制带宽再根据控制环路稳定判据判定系统的稳定性及稳定裕度，下面列举了此种情形下锁相环控制带宽取不同值时的三种情况：
(1)当锁相环的控制带宽为ω pll＝64.5rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图如图2所示，图中上下两部分分别为波特图中的幅频曲线和相频曲线，横坐标均表示角频率，单位为rad/s，幅频曲线纵坐标表示幅值，单位为dB，相频曲线纵坐标表示相位，单位为deg。从图2中可以看出，ω 180°＝292rad/s，A current(ω 180°)＝0.0165dB，A pll_grid(ω 180°)＝-14.2dB，幅值裕度为A M＝A current(ω 180°)-A pll_grid(ω 180°)＝0.0165dB-(-14.2)dB＝14.2165dB＞0，幅值裕度大于0，幅值满足系统稳定条件且在全频带范围内A current(ω)恒大于A pll_gird(ω)，因此系统相位裕度始终满足条件，此时并网变流器系统的输出电流波形如图3所示，从输出电流波形也可以看出该条件下系统始终保持稳定。其中图3的横坐标表示时间t，单位为秒，纵坐标表示并网变流器的输出电流I g，单位为A。
(2)当锁相环的控制带宽为ω pll＝320.4rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图如图4所示，图中上下两部分分别为波特图中的幅频曲线和相频曲线，横坐标均表示角频率，单位为rad/s，幅频曲线纵坐标表示幅值，单位为dB，相频曲线纵坐标表示相位，单位为deg。从图4中可以看出，ω 180°＝999rad/s，A current(ω 180°)＝0.188dB，A pll_grid(ω 180°)＝-0.223dB，幅值裕度为A M＝A current(ω 180°)-A pll_grid(ω 180°)＝0.188dB-(-0.233)dB＝0.421dB＞0，幅值裕度相对较小但仍满足稳定条件，且在全频带范围内A current(ω)恒大于A pll_gird(ω)，因此系统 相位裕度始终满足条件，此时并网变流器系统的输出电流波形如图5所示，从输出电流波形也可以看出该条件下系统始终保持稳定。其中图5的横坐标表示时间t，单位为秒，纵坐标表示并网变流器的输出电流I g，单位为A。
(3)当锁相环的控制带宽为ω pll＝452.3rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图如图6所示，图中上下两部分分别为波特图中的幅频曲线和相频曲线，横坐标均表示角频率，单位为rad/s，幅频曲线纵坐标表示幅值，单位为dB，相频曲线纵坐标表示相位，单位为deg。从图6中可以看出，ω 180°＝1240rad/s，A current(ω 180°)＝0.29dB，A pll_grid(ω 180°)＝2.8dB，幅值裕度为A M＝A current(ω 180°)-A pll_grid(ω 180°)＝0.29dB-(2.8)dB＝-2.51dB＜0，幅值不满足系统稳定条件，且ω 交1＝381rad/s，ω 交2＝4290rad/s，系统相位裕度P M1＝ψ pll_gird(ω 交1)-ψ current(ω 交1)-180°＝54.43°＞0，P M2＝ψ pll_gird(ω 交2)-ψ current(ω 交2)-180°＝-38.2°＜0，因此相位也不满足系统稳定条件，其中ω 交1、ω 交2分别为A pll_gird(ω)和A current(ω)两次恰好相等时对应的第一个、第二个角频率，此时并网变流器系统的输出电流波形如图7所示，从输出电流波形也可以看出该条件下系统失稳。其中图7的横坐标表示时间t，单位为秒，纵坐标表示并网变流器的输出电流I g，单位为A。
情形二：并网变流器系统短路比为SCR＝1.1，电网阻抗电感分量为L grid＝13.9mH，电阻分量为R grid＝0.436Ω。当电流环的控制带宽确定为ω CL＝4750rad/s后，则可以通过弱电网下并网变流器控制器设计方法选定锁相环的控制带宽再根据控制环路稳定判据判定系统的稳定性及稳定裕度，下面同样列举了此种情形下锁相环控制带宽取不同值时的三种情况：
(1)当锁相环的控制带宽为ω pll＝32.3rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图如图8所示，图中上下两部分分别为波特图中的幅频曲线和相频曲线，横坐标均表示角频率，单位为rad/s，幅频曲线纵坐标表示幅值，单位为dB，相频曲线纵坐标表示相位，单位为deg。从图8中可以看出，ω 180°＝52rad/s，A current(ω 180°)＝0.001dB，A pll_grid(ω 180°)＝-16.1dB，幅值裕度为A M＝A current(ω 180°)-A pll_grid(ω 180°)＝0.001dB-(-16.1)dB＝16.101dB＞0，幅值满足系统稳定条件且在全频带范围内A current(ω)恒大于A pll_gird(ω)，因此相位也满足系统稳定条件，此时并网变流器系统的输出电流波形如图9所示，从输出电流波形也可 以看出该条件下系统始终保持稳定。其中图9的横坐标表示时间t，单位为秒，纵坐标表示并网变流器的输出电流I g，单位为A。
(2)当锁相环的控制带宽为ω pll＝193.7rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图如图10所示，图中上下两部分分别为波特图中的幅频曲线和相频曲线，横坐标均表示角频率，单位为rad/s，幅频曲线纵坐标表示幅值，单位为dB，相频曲线纵坐标表示相位，单位为deg。从图10中可以看出，ω 180°＝743rad/s，A current(ω 180°)＝0.106dB，A pll_grid(ω 180°)＝-1.94dB，幅值裕度为A M＝A current(ω 180°)-A pll_grid(ω 180°)＝0.106dB-(-1.94)dB＝2.046dB＞0，幅值裕度相对较小但仍满足系统稳定条件，在全频带范围内A current(ω)恒大于A pll_gird(ω)，因此相位也满足系统稳定条件，此时并网变流器系统的输出电流波形如图11所示，从输出电流波形也可以看出该条件下系统始终保持稳定。其中图11的横坐标表示时间t，单位为秒，纵坐标表示并网变流器的输出电流I g，单位为A。
(3)当锁相环的控制带宽为ω pll＝387.4rad/s时，考虑锁相环影响的电流控制环开环传递函数G IL(s)的波特图如图12所示，图中上下两部分分别为波特图中的幅频曲线和相频曲线，横坐标均表示角频率，单位为rad/s，幅频曲线纵坐标表示幅值，单位为dB，相频曲线纵坐标表示相位，单位为deg。从图12中可以看出，ω 180°＝1130rad/s，A current(ω 180°)＝0.24dB，A pll_grid(ω 180°)＝4.14dB，幅值裕度为A M＝A current(ω 180°)-A pll_grid(ω 180°)＝0.24dB-4.14dB＝-3.9dB＜0，幅值不满足系统稳定条件，且ω 交1＝275rad/s，ω 交2＝5910ad/s，系统相位裕度P M1＝ψ pll_gird(ω 交1)-ψ current(ω 交1)-180°＝41.68°＞0，P M2＝ψ pll_gird(ω 交2)-ψ current(ω 交2)-180°＝-49.8°＜0，因此相位也不满足系统稳定条件，此时并网变流器系统的输出电流波形如图13所示，从输出电流波形也可以看出该条件下系统失稳。其中图13的横坐标表示时间t，单位为秒，纵坐标表示并网变流器的输出电流I g，单位为A。

Claims (1)

  1. 一种弱电网条件下的并网变流器控制环路稳定判据，所述并网变流器的控制环路包括电流控制环和锁相环，其特征在于，步骤如下：
    步骤1，通过采样得到并网变流器的输出电流I g和并网变流器的输出电压U g，并分别给出并网变流器电网阻抗环节G 1(s)的表达式、并网变流器锁相环闭环传递函数G 2(s)的表达式和并网变流器不考虑锁相环影响的电流控制环闭环传递函数G 3(s)的表达式；
    并网变流器电网阻抗环节G 1(s)的表达式如下：
    Figure PCTCN2021119220-appb-100001
    其中，s为拉普拉斯算子，L grid为电网阻抗电感分量，R grid为电网阻抗电阻分量；
    并网变流器锁相环闭环传递函数G 2(s)的表达式如下：
    Figure PCTCN2021119220-appb-100002
    其中，ξ为锁相环的阻尼比，ω pll为锁相环的控制带宽；
    并网变流器不考虑锁相环影响的电流控制环闭环传递函数G 3(s)的表达式G 3(s)如下：
    Figure PCTCN2021119220-appb-100003
    其中，G CL为电流控制环比例及积分环节传递函数，G main为并网变流器滤波环节传递函数；
    步骤2，给出并网变流器考虑锁相环影响的电流控制环开环传递函数G IL(s)的表达式；
    Figure PCTCN2021119220-appb-100004
    步骤3，给出并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s) 的表达式，并同时对步骤2中的电流控制环开环传递函数G IL(s)进行恒等变形；
    并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的表达式如下：
    Figure PCTCN2021119220-appb-100005
    电流控制环开环传递函数G IL(s)的恒等变形结果如下：
    G IL(s)＝G pll_grid(s)×G 3(s)
    ＝G pll_grid(s)/(1/G 3(s))
    ＝G pll_grid(s)/G current(s)
    其中：G current(s)＝1/G 3(s)，记为并网变流器不考虑锁相环影响的电流控制环判据传递函数；
    步骤4，根据前面3个步骤中给出的各环节传递函数，进一步给出弱电网条件下并网变流器控制环路稳定判据；
    步骤4.1，求出并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)与并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的相位表达式和幅值表达式；
    将并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)在频域中的幅值、相位分别记为组合幅值A pll_gird(ω)、组合相位ψ pll_gird(ω)，组合幅值A pll_gird(ω)和组合相位ψ pll_gird(ω)的表达式分别为：
    Figure PCTCN2021119220-appb-100006
    其中，ω为频域旋转角频率；
    将并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在 频域中的幅值、相位分别记为电流幅值A current(ω)、电流相位ψ current(ω)，电流幅值A current(ω)和电流相位ψ current(ω)的表达式分别为：
    Figure PCTCN2021119220-appb-100007
    式中，G CL(ω)为电流控制环比例及积分环节传递函数G CL在频域内的表达式，|G CL(ω)|为电流控制环比例及积分环节传递函数G CL在频域内的幅值，G main(ω)为并网变流器滤波环节传递函数G main在频域内的表达式，|G main(ω)|为并网变流器滤波环节传递函数G main在频域内的幅值，|1+G CL(ω)G main(ω)|为1+G CL(ω)G main(ω)在频域内的幅值，∠G CL(ω)为G CL(ω)在频域内的相位，∠G main(ω)为G main(ω)在频域内的相位，∠(1+G CL(ω)G main(ω))为1+G CL(ω)G main(ω)在频域内的相位；
    步骤4.2，根据步骤4.1中求出的幅值表达式和相位表达式，给出弱电网条件下的并网变流器控制环路稳定判据：同时满足以下幅值和相位2个条件时，认定并网变流器系统处于稳定状态，否则，认定并网变流器控制环路处于非稳定状态；
    所述弱电网条件下并网变流器控制环路稳定判据为：
    组合相位ψ pll_gird(ω)与电流相位ψ current(ω)的相位差为180°，且A current(ω 180°)＞A pll_gird(ω 180°)，认定并网变流器控制环路幅值稳定；
    组合幅值A pll_gird(ω)和电流幅值A current(ω)相等，且ψ pll_gird(ω 交)-ψ current(ω 交)-180°＞0，认定并网变流器控制环路相位稳定；
    当并网变流器控制环路同时满足幅值稳定和相位稳定时，则认定整个并网变流器稳定；
    其中，
    ω 180°为组合相位ψ pll_gird(ω)与电流相位ψ current(ω)的差值为180°时对应的角频率；
    A current(ω 180°)为角频率ω 180°时并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)的幅值；
    A pll_gird(ω 180°)为角频率ω 180°时并网变流器电网阻抗部分和锁相环的组合传 递函数的幅值；
    ω 交为组合幅值A pll_gird(ω)与电流幅值A current(ω)相等时对应的角频率；
    ψ current(ω 交)为角频率ω 交时并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)的相位；
    ψ pll_grid(ω 交)为角频率ω 交时并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)的相位；
    步骤4.3，根据步骤4.1中求出的并网变流器电网阻抗部分和锁相环的组合传递函数G pll_grid(s)与并网变流器不考虑锁相环影响的电流控制环判据传递函数G current(s)在频域中的相位表达式和幅值表达式，再结合步骤4.2给出的控制环路稳定判据，给出弱电网条件下并网变流器系统的幅值裕度表达式A M和相位裕度表达式P M：
    Figure PCTCN2021119220-appb-100008
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CN116505520B (zh) * 2023-06-26 2023-11-07 国网江西省电力有限公司电力科学研究院 一种光伏并网发电系统振荡抑制方法及系统

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