CN113595430B - Three-loop controller of LCL type grid-connected inverter and parameter design method thereof - Google Patents
Three-loop controller of LCL type grid-connected inverter and parameter design method thereof Download PDFInfo
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- H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
- H02M7/539—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency
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Abstract
The invention provides a three-loop controller of an LCL type grid-connected inverter and a parameter design method thereof. The method comprises the steps of firstly establishing a mathematical model of the LCL grid-connected inverter, constructing a three-ring controller, calculating an equivalent admittance model of the inverter, and improving the stability of the system by taking the total goal that admittance has no non-passive region within the switching frequency. The grid impedance factor containing the capacitance is considered in the grid-connected control of the photovoltaic power station, so that a theoretical basis can be provided for analyzing the dense access stability of the inverter under the new energy station, and meanwhile, an important guide is provided for designing the grid-connected inverter under the weak grid.
Description
Technical Field
The invention relates to the field of current control of grid-connected inverters, in particular to a parameter design method for a three-loop controller of an LCL type grid-connected inverter.
Background
With the increase in power demand and concern about environmental issues, voltage source grid-connected inverter (VSI) systems have been widely adopted in recent years. The voltage-type inverter system transmits renewable energy to a power grid through an output filter. The VSI functions to convert dc voltage obtained from renewable energy sources into ac voltage, at the output of which there is a filter connection to process the ac voltage and inject a high quality sinusoidal current into the grid. Typically, there are two filters (L and LCL) used to reduce the switching harmonics of the current injected into the grid. The third-order LCL filter is the most widely used topology because it has the following advantages: the circuit can work at a lower switching frequency, better attenuate higher harmonics and have lower current ripples in the current injected into the power grid. However, there is a resonance problem inside the LCL filter, and a corresponding damping is required to suppress the internal resonance. At present, the resonance suppression problem can be solved by realizing passive damping through connecting LCL filter elements in series or in parallel, and active damping can also be realized by adopting a proper closed-loop control method by using a virtual resistance concept. Although passive damping is simple and low cost, it introduces additional power loss and degrades the harmonic attenuation performance of the LCL filter; the active damping method provides better damping performance at the expense of increased control complexity.
Meanwhile, equipment such as long-distance transmission point lines, transformers and the like cause the power grid to have weak power grid characteristics, and time-varying power grid impedance seriously threatens the stable operation of the system. When the photovoltaic inverter is connected to a weak grid, the change of the grid impedance changes the output impedance of the system at a Point of Common Coupling (PCC), the inverter output impedance and the grid impedance may interact with each other, the stability of the system is reduced, a resonance phenomenon may be caused in a severe case, and even a fault-free trip may be caused. Therefore, studying the interaction between the photovoltaic inverter and the power grid and how to suppress the generation of the resonance is a hot point in the field of photovoltaic power generation. However, the filter parameter design process is complex and the power grid impedance changes greatly, so that the wide application of the proposed control method is limited by the volatile effect. Therefore, it is necessary to design the controller reasonably and suppress the influence of the grid impedance under the premise of considering the grid impedance, especially under the condition that the ground capacitance exists in the grid.
The method for analyzing the external stability of the inverter system can be roughly divided into a time-domain state space method and a frequency-domain impedance method. The state space model is used for researching the stability of the system, the influence of the change of the internal state variable of the system on the internal stability of the system is essentially revealed, and the method is simple in stability analysis of the control process and time-domain design of system parameters. However, it is not sufficient and convenient for an inverter system with parameter drift due to the need for detailed system parameters, whereas the nyquist stability criterion is described by evaluating the stability of the system using an impedance-based method by studying the termination characteristics of the system, i.e. whether the ratio of the inverter output impedance to the grid impedance meets the requirements. Stability analysis methods based on impedance have been widely used in recent years.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a three-loop controller of an LCL type grid-connected inverter and a parameter design method thereof.
The invention provides a three-loop controller of an LCL type grid-connected inverter, which comprises an inverter, an inverter side current detection module, an LCL filter, a filter capacitor voltage detection module, a grid-connected side current detection module, a grid-connected point voltage detection module, a coordinate conversion module, a phase-locked loop module, an SVPWM module, an inner ring inverter side current control module, a middle ring capacitor voltage control module and an outer ring current control module, wherein:
the input end of the inverter is connected with a direct-current voltage source, the output end of the inverter is connected with the input end of the LCL filter, and the output end of the LCL filter is connected with a power grid;
an inverter side current detection module and a grid side current detection module are respectively arranged on an inverter side and a grid side of the LCL filter, a filter capacitor voltage detection module is arranged at a filter capacitor of the LCL filter, a grid-connected point voltage detection module is arranged at a grid-connected point, and the inverter side current detection module and the grid-connected point voltage detection module are connected to the input end of the coordinate conversion module; the grid-connected point voltage detection module is connected to the phase-locked loop module; the phase-locked loop module is connected to the outer loop current control module;
the inner ring inverter side current control module, the middle ring capacitor voltage control module and the outer ring power grid current control module are sequentially connected in series;
the output end of the coordinate conversion module is connected with the input end of the three-loop controller; the output of the three-loop controller is connected with the input of the SVPWM module, and the output of the SVPWM module is connected with the control end of the inverter.
Optionally, the inverter inverts the direct current into a three-phase alternating current according to the three-loop controller module;
the inverter side current detection module acquires a three-phase alternating current signal output by the inverter side and inputs the three-phase alternating current signal into the inner ring of the three-ring controller;
the grid-connected side current detection module is used for acquiring a three-phase current signal output by a grid-connected side and inputting the three-phase current signal to the outer ring of the three-ring controller;
the filter capacitor voltage detection module is used for acquiring a three-phase alternating voltage signal of the capacitor and inputting the three-phase alternating voltage signal into the middle ring of the three-ring controller;
and the grid-connected point voltage detection module is used for collecting a three-phase alternating current voltage signal of a power grid and inputting the signal into the phase-locked loop for grid-connected phase locking.
Optionally, the phase-locked loop module generates a reference angle signal according to the three-phase alternating-current voltage signal of the power grid side detected by the instantaneous grid-connected point voltage detection module, and the reference angle signal is input to the three-loop controller for grid-connected phase locking.
Optionally, the coordinate conversion module performs coordinate transformation on the three-phase ac voltage and current signals detected by all the detection modules to a two-phase stationary coordinate system.
Optionally, the inner-ring inverter-side current control module receives the signal from the coordinate conversion module and the output of the middle-ring capacitor voltage module, outputs the signal to the SVPWM, and injects active damping to the inverter-side inductor to enhance the system stability.
Optionally, the intermediate-loop capacitor voltage control module receives the signal from the coordinate conversion module and the output of the outer-loop current control module, and outputs the signal to the inner-loop inverter side current control module, and active damping is injected into the filter capacitor to enhance system stability.
Optionally, the outer-loop power grid current control module receives the signal from the coordinate conversion module and a given reference current signal, outputs the signal to the middle-loop capacitor voltage control module, injects active damping to the grid-side inductor to enhance system stability, and tracks a grid-connected current given value.
In a second aspect of the present invention, a method for designing parameters of a three-loop controller of an LCL grid-connected inverter is provided, including:
s1, according to a three-loop controller structure, considering SVPWM (space vector pulse width modulation) calculation time delay, establishing a mathematical model, and combining the mathematical model to respectively calculate an inner loop closed loop transfer function, a middle loop transfer function and an outer loop transfer function;
s2, based on the transfer function of the S1, a system admittance model of the LCL type grid-connected inverter is established, and the output admittance helps to analyze the system stability so as to determine active damping parameters r injected by the outer ring, the middle ring and the outer ring power grid current control module 1 、r 2 、r 3 A range of (d);
s3, simplifying the relation among variables of the system admittance model of the S2 according to the structure of the three-loop controller, and calculating a closed-loop transfer function X of the current control module at the side of the inner-loop inverter and an equivalent output admittance Y of the current control module at the side of the inner-loop inverter;
s4, according to the inner ring closed loop transfer function of the S1, the time delay is approximated by first order differential and converted into a second order system, and the damping r injected by the current control module at the side of the inner ring inverter is simplified 3 The design of (2);
s5, admittance Y of the output of the whole inverter system o (s) conversion from complex to frequency domain Y o (jw) wherein the transfer function of the delay is developed using the Euler equation to obtain Y o (jw) real part of (jw) where Y o (jw) the admittance is passive with a real part greater than zero;
s6, designing r according to passivity theory 2 ,r 3 When the parameters are needed to ensure that the real part of the output admittance is always larger than zero, r 3 Obtaining the critical damping ratio, and firstly, setting the active damping r injected by the current control module of the outer ring power grid 1 The frequency, the real part value and the active damping r injected by the middle-loop capacitance voltage control module in the parameter to be determined are drawn 2 Three-dimensional graph of (a) between (b), r 2 Is selected from the portion where the real part of the admittance is all greater than zero within the switching frequency; in the same way, determine r 3 、r 2 Plotting the frequency, the real part value and the parameter r to be determined 1 Three-dimensional graph of (a) between (b), r 1 Is selected from the portion where the real part of the admittance is all greater than zero within the switching frequency.
The method takes the LCL type grid-connected inverter as a research object, and determines the parameters of the controller by analyzing the passivity of the output admittance. Firstly, a three-ring controller is constructed, on the basis, an equivalent admittance model of the inverter is calculated, and the stability of the system is improved by taking the total goal that admittance does not have a non-passive area in the switching frequency.
In a third aspect of the present invention, a parameter design apparatus for a three-ring controller is provided, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the parameter design method when executing the computer program.
In a fourth aspect of the present invention, there is provided a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the parameter design method.
Compared with the prior art, the embodiment of the invention has at least one of the following beneficial effects:
the invention provides a three-loop controller based on passivity theory and a parameter design method thereof, which can realize that the output admittance in the switching frequency is passive and can ensure that:
(1) The internal resonance of the LCL filter is suppressed and the internal stability is maintained.
(2) The interaction resonance between the power grid admittance and the inverter output admittance does not influence the stability of an inverter system, and the external stability is ensured; in the control structure, the differentiation link of the outer ring can expand the bandwidth of the controller, and cannot influence the external stability, and in addition, the steady-state error is zero in the system transmission; in the aspect of parameter design, the parameter selection of the inner ring is designed according to the critical damping ratio of a second-order system, and the second-order system is ideally, compared with an underdamping condition and an overdamping condition, under the critical damping condition, the time required by the system to approach the balance from the motion is shortest. In conclusion, the method has the advantages of simple parameter design, fast dynamic response and small steady-state error, and theoretically, the system stability is not influenced by the impedance of an external power grid.
The grid impedance factor containing the capacitance is considered in the grid-connected control of the photovoltaic power station, so that a theoretical basis can be provided for analyzing the dense access stability of the inverter under the new energy station, and meanwhile, an important guide is provided for designing the grid-connected inverter under the weak grid.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
fig. 1 is a diagram showing a conventional grid-connected inverter.
FIG. 2 is a block diagram of a three-cycle controller according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a system admittance model according to an embodiment of the present invention;
FIG. 4 shows an embodiment of the present invention 1 Frequency, real part of admittance and parameter r =15 2 A relationship diagram of (a);
FIG. 5 shows an embodiment of the present invention 2 Frequency, real part of admittance and parameter r when =0.2 1 A relationship diagram of (1);
FIG. 6 shows an embodiment of the present invention 1 And r 2 Under the value taking, an internal stability zero-pole diagram is obtained;
FIG. 7 is a flowchart of a parameter design method according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the concept of the invention. All falling within the scope of the invention.
According to the passivity theory, when the output impedance or admittance of the inverter is always passive in a frequency domain, the ratio of the output impedance of the inverter to the impedance of the power grid inevitably meets the stability requirement, and the resonance between the internal impedance of the system and the impedance of the power grid can be effectively avoided even under the complex impedance of the power grid, so that the passivity of the output impedance is designed to be very meaningful. The embodiment of the invention provides a three-loop controller of an LCL type grid-connected inverter based on an passivity theory and a parameter design method thereof.
Referring to fig. 2, a three-loop controller of an LCL type grid-connected inverter according to an embodiment of the present invention specifically includes an inverter, an inverter-side current detection module, an LCL filter, a filter capacitor voltage detection module, a grid-connected side current detection module, a grid-connected point voltage detection module, a coordinate conversion module, a phase-locked loop module, an SVPWM module, an inner-loop inverter-side current control module, a middle-loop capacitor voltage control module, and an outer-loop network current control module, where: the input end of the inverter is connected with a direct-current voltage source, the output end of the inverter is connected with the input end of the LCL filter, and the output end of the LCL filter is connected with the power grid; an inverter side current detection module and a grid side current detection module are respectively arranged on an inverter side and a grid side of the LCL filter, a filter capacitor voltage detection module is arranged at a filter capacitor of the LCL filter, a grid-connected point voltage detection module is arranged at a grid-connected point, and the inverter side current detection module and the grid-connected point voltage detection module are connected to the input end of the coordinate conversion module; the voltage detection module of the grid-connected point is connected to the phase-locked loop module; the phase-locked loop module is connected to the outer loop current control module; the inner ring inverter side current control module, the middle ring capacitor voltage control module and the outer ring power grid current control module are sequentially connected in series; the output end of the coordinate conversion module is connected with the input end of the three-ring controller; the output of the three-loop controller is connected with the input of the SVPWM module, and the output of the SVPWM module is connected with the control end of the inverter.
The present embodiment relates to the above respective portions:
direct current voltage source: providing a direct current voltage source;
an inverter: inverting the direct current into three-phase alternating current according to the controller module;
inverter side current detection module: the system is used for acquiring a three-phase alternating current signal output by an inverter side;
grid-connected side current detection module: for collecting three-phase current signals output by electric network side
The filter capacitor voltage detection module: the device is used for acquiring a three-phase alternating voltage signal of a capacitor;
and a grid connection point voltage detection module: three-phase alternating voltage signal for collecting power grid
A phase-locked loop module: generating a reference angle signal according to the instantaneous three-phase alternating current voltage signal at the power grid side;
a coordinate conversion module: coordinate transformation of three-phase alternating voltage and current signals to two-phase stationary coordinate system
And an SVPWM module: carrying out space vector modulation;
the inner ring inverter side current control module injects active damping on the inverter side inductor;
middle ring electric capacity voltage control module: injecting active damping into the filter capacitor;
outer ring electric wire netting current control module: injecting active damping on a network side inductor, and tracking a given value of grid-connected current;
a power grid module: providing three-phase alternating current and directly providing the three-phase alternating current by an alternating current power grid;
LCL filter: the filter is connected by inductance-capacitance-inductance T type to form LCL type filter.
In the above embodiment of the present invention, when each module operates:
the direct current voltage source serves as an input power source for the inverter, the inverter inverts direct current into square wave signals, and the square wave signals are filtered by the LCL filter to obtain sinusoidal alternating current which is transmitted to the power grid module to realize the grid connection function; in the process, a current signal, a capacitance voltage signal, a power grid side current signal and a grid-connected point voltage signal on the inverter side need to be acquired, coordinate transformation is carried out on the signals, the power grid voltage signal is used for phase locking in the coordinate transformation process, and the signals after the coordinate transformation are output to an inner ring inverter side current control module, a middle ring capacitance voltage control module and an outer ring power grid voltage control module; and (3) transmitting an output signal of the inner ring control module to the SVPWM module for modulation, transmitting a modulated pulse signal to the inverter, and controlling the inversion process of the inverter.
In this embodiment, the internal resonance of the LCL filter is suppressed and the internal is stable.
Referring to fig. 7, in another embodiment of the present invention, a method for designing parameters of a three-loop controller of an LCL grid-connected inverter according to the above embodiment includes the following steps:
s1, according to a three-loop controller structure, considering SVPWM (space vector pulse width modulation) calculation delay, establishing a mathematical model, and respectively calculating an inner loop closed loop transfer function, a middle loop transfer function and an outer loop transfer function by combining the mathematical model;
in this step, the mathematical model is as follows:
in the above formula: the balance point of the controller state variable is represented by the upper table, E represents the active damping injected into the inner ring inverter side current control module, F represents the active damping injected into the middle ring capacitance voltage control module, G represents the active damping and differential feedforward injected into the outer ring grid current control module, ZOH represents the zero order keeper, E -1.0Ts The modulation delay in SVPWM is shown, and a two-phase static coordinate system is shown by subscript alpha beta; l is a radical of an alcohol 2e Indicating L in the actual circuit 2 Given a reference value, R, in a three-ring controller 2e Representing R in the actual circuit 2 A given reference value in a three-loop controller; i.e. i 1 Is through the inductance L 1 Current of (i) 2 Is a current flowing through the inductor L 2 Current of (u) C Is the voltage across the filter capacitor C, v pcc Is the grid-connected point voltage, u is the inverter output voltage.
In this step, the inner loop closed loop transfer function is as follows:
in this step, the middle loop transfer function is as follows:
in this step, the outer loop transfer function is as follows:
in the above formula: x represents the closed-loop transfer function of the current control module at the inner ring inverter side, Y represents the equivalent output admittance of the current control module at the inner ring inverter side, D represents the complex frequency domain impedance of the inductor at the inverter side in the LCL filter, B represents the complex frequency domain impedance of the filter capacitor in the LCL filter, the state variable balance point of the controller is represented by the table, F represents the active damping injected into the voltage control module of the middle ring capacitor, G represents the active damping and differential feedforward injected into the current control module of the outer ring grid, ZOH represents the zero-order keeper, e -1.0Ts The modulation delay in SVPWM is shown, and a two-phase static coordinate system is shown by subscript alpha beta; i.e. i 1 Is through the inductance L 1 Current of (i) 2 Is a current flowing through the inductor L 2 Current of (u) C Is the voltage across the filter capacitor C, v pcc Is the grid-connected point voltage, u is the inverter output voltage.
S2, establishing an LCL type grid-connected inverter and closed-loop control system admittance model based on the transfer function of the S1, outputting admittance to help analyze system stability so as to determine active damping parameters r injected by outer-loop, middle-loop and outer-loop power grid current control modules 1 、r 2 、r 3 A range of (d);
in this step, the system admittance model has the following system admittance matrix:
s3, simplifying the relation among variables of the system admittance model of the S2 according to the structure of the three-loop controller, and calculating the closed-loop transfer function of the current control module at the inner ring inverter side and the equivalent output admittance of the current control module at the inner ring inverter side;
in the step, after simplification:
in the above formula: g o Representing the closed loop transfer function, Y, of the entire grid-connected inverter system o The equivalent output admittance of the whole inverter system is represented, X represents the closed-loop transfer function of the current control module at the side of the inner ring inverter, Y represents the equivalent output admittance of the current control module at the side of the inner ring inverter, B represents the complex frequency domain impedance of the filter capacitor in the LCL filter, the state variable balance point of the controller is represented by the table, F represents the active damping injected into the voltage control module of the middle ring capacitor, G represents the active damping and differential feedforward injected into the current control module of the outer ring power grid, and the two-phase static coordinate system is represented by a subscript alpha beta; i.e. i 2 Is a current flowing through the inductor L 2 Current of v pcc Is the dot-on-dot voltage.
S4, according to the inner ring closed loop transfer function of the S1, the time delay is approximated by first order differentiation and is converted into a second order system, and the damping r injected by the current control module at the side of the inner ring inverter is simplified 3 The design of (2);
s5, admittance Y of the output of the whole inverter system o (s) by Y o (jw) wherein the transfer function of the delay is expanded by the Euler equation to obtain Y o (jw) real part of (wherein Y) o (jw) the real part is more than zero admittance is passive;
s6, designing r according to a passivity theory 2 ,r 3 When the parameters are needed to ensure that the real part of the output admittance is always larger than zero, r 3 The critical damping ratio is obtained, and the active damping r injected by the current control module of the outer ring power grid is given 1 The frequency, the real part value and the active damping r injected by the middle-loop capacitance voltage control module in the parameter to be determined are drawn 2 Three-dimensional graph of (a) between, r 2 Is selected from the portion where the real part of the admittance is all greater than zero within the switching frequency; in the same way, determine r 3 、r 2 Plotting the frequency, the real value and the parameter r to be determined 1 Three-dimensional graph of (a) between, r 1 Ranging from the real part of the admittanceAll parts of the switching frequency greater than zero are selected.
In the embodiment, the interaction resonance between the power grid admittance and the inverter output admittance does not influence the stability of an inverter system, and the external part is stable; in the control structure, the differential link of the outer ring can expand the bandwidth of the controller, and the external stability is not influenced, and in addition, the steady-state error is zero in the aspect of system transmission; in the aspect of parameter design, the parameter selection of the inner ring is designed according to the critical damping ratio of a second-order system, and the second-order system is ideally, compared with an underdamping condition and an overdamping condition, under the critical damping condition, the time required by the system to approach the balance from the motion is shortest.
In some preferred embodiments, based on the above embodiments, before performing S1, a three-loop controller may be constructed, including:
s001, establishing a system circuit model by applying kirchhoff voltage and current law according to the structure of the LCL type grid-connected inverter;
s002, converting the three-phase static coordinate system of the system circuit model established in the S001 into a two-phase static coordinate system, and performing Laplace transformation;
and S003, combining the transformation result obtained in the S002 to construct a three-ring controller.
The structure of the three-loop controller is obtained in the above mode, and a mathematical model is built according to the structure.
In a preferred embodiment, when executing S001, applying kirchhoff' S voltage-current law to build a system circuit model is as follows:
L 1 is an inverter side inductor, L 2 Is a network side inductor, C is a filter capacitor, L g As inductance of the grid, C g For grid capacitance, U dc DC output voltage i 1 Is a current flowing through the inductor L 1 Current of (i) 2 Is a current flowing through the inductor L 2 Current of R 1 Is an inductance L 1 Parasitic resistance of R 2 Is L 2 Impedance of u C Is the voltage across the filter capacitor C, v pcc Is the grid-connected point voltage, u is the inverter output voltage.
In a preferred embodiment, when performing S002, the method further includes:
in the above equation, the two-phase stationary coordinate system is represented by a subscript α β, s represents a laplacian operator, a represents a complex frequency domain impedance of an inverse grid-connected inductor in the LCL filter, B represents a complex frequency domain impedance of a filter capacitor in the LCL filter, and D represents a complex frequency domain impedance of an inverter-side inductor in the LCL filter.
In another embodiment, the present invention further provides a parameter design apparatus for a three-ring controller, including a memory and a processor, where the memory stores a computer program, and the processor implements the parameter design method in any one of the above embodiments when executing the computer program.
In another embodiment, the present invention further provides a computer-readable storage medium, on which a computer program is stored, which, when executed by a processor, implements the parameter design method in any of the above embodiments.
In order to better understand the parameter design method of the LCL filter three-loop controller in the above embodiments of the present invention, the following description is made in conjunction with the above technical features and specific embodiments, but the following embodiments are not intended to limit the present invention.
Specifically, the present embodiment provides a method for designing parameters of an LCL filter three-loop controller considering stability of an inverter under a capacitive weak grid, including the following steps:
step 1: according to the structure of the LCL type grid-connected inverter, a system circuit model is established by applying kirchhoff voltage and current law;
in this embodiment, a structure diagram of the grid-connected inverter is shown in fig. 1, and specific parameters are set as follows:
L 1 =1.2mH is inverter side inductance, L 2 =1.2mH network side inductance, C =6uF filter capacitance, L g =4.8mH is the grid inductance, C g =2uF is grid capacitance, U dc =350V dc output voltage, three-phase mains phase voltage u g Has an effective value of 110V, i 1 Is a current flowing through the inductor L 1 Current of (i) 2 Is a current flowing through the inductor L 2 Current of (R), R 1 =0.1 Ω is inductance L 1 Parasitic resistance of R 2 =0.1 Ω is L 2 Parasitic resistance of u C The voltage at two ends of a filter capacitor C, u is the output voltage of an inverter, vpcc is the voltage of a grid-connected point, the switching frequency and the sampling frequency are both 10kHz, and a system circuit model is established by applying kirchhoff voltage and current law:
and 2, step: converting the three-phase static coordinate system of the system circuit model established in the step S1 into a two-phase static coordinate system (indicated by subscript alpha beta), and performing Laplace transform:
and step 3: combining the transformation result obtained in the S2, constructing a three-loop controller, considering SVPWM (space vector pulse width modulation) calculation delay, and establishing a mathematical model;
specifically, a three-loop controller as shown in FIG. 2 is constructed, L in FIG. 2 2e Indicating L in the actual circuit 2 Given reference value, R, in a three-ring controller 2e Representing R in the actual circuit 2 Given a reference value in a three-loop controller, considering that SVPWM calculates the delay time to be 1 beat, and adopting a Zero Order keeper (ZOH) to establish a mathematical model analysis parameter r 1 ,r 2 ,r 3 Selecting the range:
and 4, step 4: calculating inner loop closed loop transfer function
And 5: further calculation of the Ring transfer function from step 4
Step 6: further calculation of the outer loop transfer function from step 5
And 7: based on the steps 3-5, an LCL type grid-connected inverter and closed-loop control system admittance model is established, and output admittance helps to analyze system stability and determine damping parameter r 1 、r 2 、r 3 A range of (d);
in this step, the equivalent circuit admittance model is composed of an equivalent dc power supply and an equivalent output admittance, as shown in fig. 3, the system admittance matrix is as follows
And 8: according to the passive three-loop controller structure of FIG. 2, the relation between variables is simplified, and G is calculated o (s) and Y o (s)
And step 9: according to the step 4, the time delay is approximated by first order differential according to the inner loop closed loop transfer function, and is converted into a second order system, so that the inner loop parameter r is simplified 3 Design of (d), designing the parameter r according to the critical damping ratio 3 ；
According to the step 4, the delay is approximated by first order differential according to the inner loop transfer function, and is converted into a second order system, so that the inner loop parameter r is simplified 3 The design of the second-order system generally requires that the inner ring has higher response speed than the middle ring and the outer ring when the three-ring system is designed, and the second-order system has the advantages that under the ideal condition, compared with the under-damping condition and the over-damping condition, under the critical damping condition, the shortest time required by the system to approach the balance from the motion is ensuredSo design the parameter r according to the critical damping ratio 3 。
In the parameter design of the embodiment, the parameter selection of the inner ring is designed according to the critical damping ratio of the second-order system, and the second-order system is ideally, compared with the under-damping condition and the over-damping condition, under the critical damping condition, the time required by the system to approach the balance from the motion is shortest.
Step 10: converting Y in step 8 o (s) by Y o (jw) where the transfer function of the delay is developed with Euler's formula and Y is acquired using the calculation software Wolfram MATHETAMTICA o (jw) real part of (jw) where Y o The admittance is passive when the real part of (jw) is greater than zero.
Step 11: according to the passivity theory, when the inverter output admittance is always passive, the power grid impedance can not generate mutual resonance with the inverter output impedance any longer, so that the design r is carried out 2 ,r 3 The parameters need to ensure that the real part of the output admittance is always larger than zero. Due to, r 3 =2 obtained from critical damping ratio, assuming r 1 In the case of =15, the frequency, the real part of the admittance, and the parameter r to be determined are plotted 2 Three-dimensional graph of (a) between (b), r 2 Is selected from the portion where the real part of the admittance is all greater than zero within the switching frequency, as shown in fig. 4.
Step 12: same as step 11, r 3 Obtained by critical damping, r 2 Obtained from step 11 as 0.2, the frequency, the real part of the admittance and the parameter r to be determined are plotted 1 Three-dimensional graph of (a) between (b), r 1 Is selected from the portion whose real part is all greater than zero within the switching frequency, as shown in fig. 5.
In the embodiment, the interaction resonance between the power grid admittance and the inverter output admittance does not influence the stability of the inverter system, and the external part is stable; in the aspect of a control structure, the bandwidth of the controller can be expanded through a differential link of an outer ring, the influence on the external stability is avoided, and in addition, the steady-state error is zero in the transfer function of the closed-loop control system of the LCL type grid-connected inverter.
Further, after the above parameters are obtained, step 13 may be included: checking the selected r 1 ,r 2 ,r 3 Whether or not internal stability, r, is satisfied 1 ＝15,r 2 ＝0.2,r 3 The =2 zero-pole diagram is shown in fig. 6, and the system is stable.
According to the embodiment of the invention, the capacitive power grid impedance factor is considered in the grid-connected control of the photovoltaic power station, so that the output admittance in the switching frequency is passive, and the internal resonance of the LCL filter can be inhibited and the internal stability is ensured. The method has the advantages of simple parameter design, fast dynamic response and small steady-state error, and theoretically, the system stability is not influenced by the impedance of an external power grid.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The above-described preferred features may be used in any combination without conflict with each other.
Claims (9)
1. A parameter design method for a three-ring controller of an LCL type grid-connected inverter is characterized by comprising the following steps:
the three-loop controller of the LCL type grid-connected inverter comprises an inverter, an inverter side current detection module, an LCL filter, a filter capacitor voltage detection module, a grid-connected side current detection module, a grid-connected point voltage detection module, a coordinate conversion module, a phase-locked loop module, an SVPWM module, an inner ring inverter side current control module, a middle ring capacitor voltage control module and an outer ring grid current control module, wherein:
the input end of the inverter is connected with a direct-current voltage source, the output end of the inverter is connected with the input end of the LCL filter, and the output end of the LCL filter is connected with a power grid;
the LCL filter comprises a coordinate conversion module, an inverter side current detection module, a grid side current detection module, a filter capacitor voltage detection module, a grid-connected point voltage detection module and a grid-connected point voltage detection module, wherein the inverter side and the grid-connected side of the LCL filter are respectively provided with the inverter side current detection module and the grid-connected point current detection module; the grid-connected point voltage detection module is connected to the phase-locked loop module; the phase-locked loop module is connected to the outer loop power grid current control module;
the inner ring inverter side current control module, the middle ring capacitor voltage control module and the outer ring power grid current control module are sequentially connected in series;
the output end of the coordinate conversion module is connected with the input end of the three-loop controller; the output of the three-loop controller is connected with the input of an SVPWM module, and the output of the SVPWM module is connected with the control end of the inverter;
the parameter design method comprises the following steps:
s1, according to a three-loop controller structure, considering SVPWM (space vector pulse width modulation) calculation delay, establishing a mathematical model, and respectively calculating an inner loop closed loop transfer function, a middle loop transfer function and an outer loop transfer function by combining the mathematical model;
s2, based on the transfer function of the S1, a system admittance model of the LCL type grid-connected inverter is established, and the output admittance helps to analyze the system stability so as to determine the active damping parameter r injected by the current control modules of the outer ring, the middle ring and the inner ring of the power grid 1 、r 2 、r 3 A range of (d);
s3, simplifying the relation among variables of the system admittance model of the S2 according to the structure of the three-loop controller, and calculating a closed-loop transfer function X of the current control module at the side of the inner-loop inverter and an equivalent output admittance Y of the current control module at the side of the inner-loop inverter;
s4, according to the inner ring closed loop transfer function of the S1, the time delay is approximated by first order differentiation and is converted into a second order system, and the damping r injected by the current control module at the side of the inner ring inverter is simplified 3 Designing (1);
s5, admittance Y of the output of the whole inverter system o (s) conversion from complex frequency domain to frequency domain Y o (jw) wherein the transfer function of the delay is developed using the Euler equation to obtain Y o (jw) real part of (wherein Y) o (jw) the real part is more than zero admittance is passive;
s6, designing r according to a passivity theory 2 ,r 3 Guaranteed output when parameters are usedThe real part of admittance is always greater than zero, r 3 Obtaining the critical damping ratio, and firstly, setting the active damping r injected by the current control module of the outer ring power grid 1 The frequency, the real part value and the active damping r injected by the ring capacitance voltage control module in the parameter to be determined are drawn 2 Three-dimensional graph of (a) between, r 2 Is selected from the portion where the real part of the admittance is all greater than zero within the switching frequency; in the same way, determine r 3 、r 2 Plotting the frequency, the real value and the parameter r to be determined 1 Three-dimensional graph of (a) between (b), r 1 Is selected from the portion where the real part of the admittance is all greater than zero within the switching frequency.
2. The parameter design method for the three-loop controller of the LCL-type grid-connected inverter according to claim 1, wherein the inverter inverts the direct current into a three-phase alternating current according to the three-loop controller module;
the inverter side current detection module acquires a three-phase alternating current signal output by the inverter side and inputs the three-phase alternating current signal into the inner ring of the three-ring controller;
the grid-connected side current detection module is used for acquiring a three-phase current signal output by a grid-connected side and inputting the three-phase current signal to the outer ring of the three-ring controller;
the filter capacitor voltage detection module collects three-phase alternating current voltage signals of the capacitor and inputs the three-phase alternating current voltage signals into the middle ring of the three-ring controller;
and the grid-connected point voltage detection module is used for collecting a three-phase alternating current voltage signal of a power grid and inputting the signal into the phase-locked loop for grid-connected phase locking.
3. The method for designing parameters of a three-loop controller of an LCL-type grid-connected inverter according to claim 1,
the phase-locked loop module generates a reference angle signal according to the three-phase alternating current voltage signal of the power grid side detected by the instantaneous grid-connected point voltage detection module, and the reference angle signal is input to the three-loop controller for grid-connected phase locking;
and the coordinate conversion module is used for converting the three-phase alternating current voltage and current signals detected by all the detection modules into a two-phase static coordinate system.
4. The method for designing parameters of a three-loop controller of an LCL-type grid-connected inverter according to claim 1,
the inner ring inverter side current control module receives the signal from the coordinate conversion module and the output of the middle ring capacitor voltage module, outputs the signal to the SVPWM, and injects active damping on the inverter side inductor to enhance the system stability;
the middle-ring capacitor voltage control module receives the signal from the coordinate conversion module and the output of the outer-ring power grid current control module and outputs the signal to the inner-ring inverter side current control module, and active damping is injected into the filter capacitor to enhance the system stability;
and the outer loop power grid current control module receives the signal from the coordinate conversion module and a given reference current signal, outputs the signal to the middle loop capacitance voltage control module, injects active damping on the network side inductor to enhance the system stability, and tracks the given value of the grid-connected current.
5. The method for designing parameters of the three-loop controller of the LCL grid-connected inverter according to claim 1, wherein in the S1, the mathematical model is as follows:
in the above formula: the balance point of the controller state variable is represented by the upper table, E represents the active damping injected into the inner ring inverter side current control module, F represents the active damping injected into the middle ring capacitance voltage control module, G represents the active damping and differential feedforward injected into the outer ring grid current control module, ZOH represents the zero order keeper, E -1.0Ts The modulation delay in SVPWM is shown, and a two-phase static coordinate system is shown by subscript alpha beta; l is 2e Indicating L in the actual circuit 2 Given reference value, R, in a three-ring controller 2e Representing R in the actual circuit 2 A given reference value in a three-loop controller; i.e. i 1 Is a current flowing through the inductor L 1 Current of (i) 2 Is through the inductance L 2 Current of (u) C Is the voltage across the filter capacitor C, v pcc Is the grid-connected point voltage, u is the inverter output voltage.
6. The method for designing parameters of a three-loop controller of an LCL grid-connected inverter according to claim 1, wherein in S1:
the inner loop closed loop transfer function is as follows:
the middle ring transfer function is as follows:
the outer loop transfer function is as follows:
in the above formula: x represents the closed-loop transfer function of the current control module at the inner ring inverter side, Y represents the equivalent output admittance of the current control module at the inner ring inverter side, D represents the complex frequency domain impedance of the inductor at the inverter side in the LCL filter, A represents the complex frequency domain impedance of the inductor at the grid-connected side in the LCL filter, B represents the complex frequency domain impedance of the filter capacitor in the LCL filter, the balance point of the state variable of the controller is represented by the table, F represents the active damping injected into the voltage control module of the capacitor in the middle ring, G represents the active damping and the differential injected into the current control module of the outer ring grid, ZOH represents the zero-order retainer, e -1.0Ts The modulation delay in SVPWM is shown, and a two-phase static coordinate system is shown by subscript alpha beta; i.e. i 1 Is through the inductance L 1 Current of (i) 2 Is through the inductance L 2 Current of (u) C Is the voltage across the filter capacitor C, v pcc Is the grid-connected point voltage, u is the inverter output voltage.
7. The method according to claim 1, wherein in the S2, the system admittance matrix of the system admittance model is as follows:
in the step S3, after simplification:
in the above formula: g o Representing the closed loop transfer function, Y, of the entire grid-connected inverter system o Represents the equivalent output admittance of the whole inverter system, and X represents the side current of the inner ring inverterThe control module is used for controlling a closed-loop transfer function, Y represents an equivalent output admittance of a current control module at the side of an inner-loop inverter, A represents a complex frequency domain impedance of an inductor at the side of a grid in an LCL filter, B represents a complex frequency domain impedance of a filter capacitor in the LCL filter, a state variable balance point of a controller is represented by the table, F represents active damping injected into a voltage control module of a middle-loop capacitor, G represents active damping and differential feedforward injected into a current control module of an outer-loop power grid, and a two-phase static coordinate system is represented by a subscript alpha beta; i all right angle 2 Is a current flowing through the inductor L 2 Current of (v) pcc Is the dot-on-dot voltage.
8. A parametric design apparatus for a three-loop controller, comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the parametric design method of any one of claims 1 to 7 when executing the computer program.
9. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the parameter design method of any one of claims 1 to 7.
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