CN117477643A - Inverter bifurcation control method based on state variable period difference feedback - Google Patents

Inverter bifurcation control method based on state variable period difference feedback Download PDF

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CN117477643A
CN117477643A CN202311437519.1A CN202311437519A CN117477643A CN 117477643 A CN117477643 A CN 117477643A CN 202311437519 A CN202311437519 A CN 202311437519A CN 117477643 A CN117477643 A CN 117477643A
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尹志红
陆益民
黄险峰
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Guangxi University
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    • H—ELECTRICITY
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    • 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
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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
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Abstract

The invention discloses an inverter bifurcation control method based on state variable period difference feedback, which belongs to the technical field of bifurcation control of power electronic converters, and comprises the following steps: establishing a discrete mapping model of the inverter by adopting a stroboscopic mapping method based on a quasi-static idea, and solving a Jacobian matrix at a balance point; drawing a locus of change of characteristic values of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs, and entering the next step when bifurcation occurs; let the difference between the initial value and the final value of the state variable of the inverter in the switching period be deltaThe difference between the initial value and the final value of a given reference signal in a switching period is delta ref Taking delta as a feedback signal, and combining delta with delta ref The control signals are obtained through a proportion link after comparison; the control signal is overlapped with the original PI regulating current control signal of the inverter to obtain a new control signal, and the new control signal is applied to the inverter to enable the inverter to resume steady state operation.

Description

Inverter bifurcation control method based on state variable period difference feedback
Technical Field
The invention relates to the technical field of bifurcation control of power electronic converters, in particular to an inverter bifurcation control method based on state variable period difference feedback.
Background
DC-AC inverters, which have the function of converting direct current into alternating current of any desired frequency, are an important and common power electronic converter, and have been widely used in micro-grids, distributed power generation systems, uninterruptible power supply systems, and other various power electronic systems. Meanwhile, as a typical nonlinear non-autonomous system, an inverter has a complex bifurcation behavior. At present, research on a bifurcation behavior control method of a power electronic converter is mainly focused on a DC-DC converter, and a certain result is achieved. The existing DC-DC converter bifurcation control method is mainly divided into a feedback control method and a non-feedback control method. The feedback control method mainly comprises a target shooting method [1], an active backstepping control method [2], a self-adaptive observer control method [3], a self-adaptive sliding mode control method [4], a time delay feedback control method [5], an extended time delay feedback control method [6] and the like, and the non-feedback control method comprises a disturbance control method [7-8] and a slope compensation method [9]. These methods all have a good control of the bifurcation behavior in the DC-DC converter, and so the scholars try to use some of them for the bifurcation control of the DC-AC inverter. The literature [10-11] introduces a time delay feedback control method into the bifurcation control of a DC-AC inverter. The method takes the difference value between the state variables of adjacent switching periods as a control signal, and can inhibit bifurcation behavior in the inverter to a certain extent. However, the DC-AC inverter is different from the DC-DC converter, and the state variables of adjacent switching periods of the inverter are not equal, so that the control signal always exists, which can cause disturbance to the inverter and affect the original dynamic response and steady-state precision of the inverter. The literature [12] introduces a disturbance control method based on a filter into the bifurcation control of a voltage controlled inverter, and the result shows that the slow-scale bifurcation behavior in the inverter can be effectively inhibited, but the fast-scale bifurcation cannot be controlled, the selection basis of a control coefficient is not given, the determination can only be realized by a trial-and-error method, and the practicability is limited. The reference [13] uses the slope compensation method for the bifurcation control of the peak current control inverter, and the result shows that the method can effectively control the fast-scale bifurcation, however, the method needs to add a control signal to interfere the system, the control signal always exists, and the original dynamics characteristic of the system can be changed. From the above analysis, the existing bifurcation control method of the DC-AC inverter causes disturbance to the inverter, and has problems that the control coefficient is difficult to determine, and the like. Therefore, there is a need for an inverter bifurcation control method based on state variable period difference feedback. Reference is made to:
[1]Ned J.Corron,Shawn D.Pethel.(2013)“Experimental targeting of chaos via controlled symbolic dynamics.”Physics Letters A,313.3(2003):192-197.
[2]M.T.Yassen.(2006)“Controlling,synchronization and tracking chaotic Liu system using active backstepping design.”Physics Letters A,360.4-5(2007):582-587.
[3]A Rodriguez,J.De León R.Femat,and C.Hernández-Rosales.“A dynamic parameter estimator to control chaos with distinct feedback schemes.”Communications in Nonlinear Science and Numerical Simulation,14.12(2009):4280-4291.
[4]Mehdi Roopaei,Bijan Ranjbar Sahraei,and Tsung-Chih Lin.(2015)“Adaptive sliding mode control in a novel class of chaotic systems.”Communications in Nonlinear Science and Numerical Simulation,15.12(2015):4158-4170.
[5]Wei Ma,Lei Wang,Rui Zhang,Jiahong Li,Zhiming Dong,Yihui Zhang,Min Hu,and Shuxi Liu.(2019)“HopfBifurcation and Its Control in the One-Cycle Controlled Cuk Converter.”IEEE Transactions on Circuits and Systems II:Express Briefs,66.8(2019):1411-1415.
[6]B.ROBERT,M.FEKI,and H.H.C.IU.(2006)“CONTROL OF A PWM INVERTER USING PROPORTIONAL PLUS EXTENDED TIME-DELAYED FEEDBACK”.International Journal ofBifurcation and Chaos,16.1(2006):113-128.
[7]Anbukumar Kavitha,Govindarajan Uma.(2010)“Control of chaos in SEPIC DC-DC converter.”International Journal of Control,Automation and Systems,8.6(2010):1320-1329.
[8]Yufei Zhou,H.H.C.Iu,C.K.Tse and Jun-Ning Chen,"Controlling chaos in DC/DC converters using optimal resonant parametric perturbation,"2005IEEE International Symposium on Circuits and Systems(ISCAS),2005,pp.2481-2484Vol.3
[9]Bao Bo-Cheng,Xu Jian-Ping,and Liu Zhong.(2009)“Mode shift and stability control ofa current mode controlled buck-boost converter operating in discontinuous conduction mode with ramp compensation.”Chinese Physics B,18.11(2009):4742.
[10]H.H.C Iu,and B.Robert.(2003)“Control of chaos in a PWM current-mode H-bridge inverter using time-delayed feedback.”IEEE Transactions on Circuits and Systems I:Fundamental Theory andApplications,50.8(2003):1125-1129.
[11]Jinke Zhang,Xiaojie Wu,and Lvshuai Xing.(2016)“Bifurcation Analysis of Five-Level Cascaded H-Bridge Inverter Using Proportional-Resonant Plus Time-Delayed Feedback.”International Journal of Bifurcation and Chaos,26.11(2016):1630031.
[12]Weiguo Lu,Naikuan Zhao,Junke Wu,Abdelali El Aroudi and Luowei Zhou.(2015)“Filter-based perturbation control of low-frequency oscillation in voltage-mode H-bridge DC–AC inverter.”International Journal ofCircuit Theory and Applications,43.7(2015):866-874.
[13]Hu Nai-Hong,Zhou Yu-Fei,and Chen Jun-Ning.(2012)“Control of fast-scale bifurcation in single-phase SPWM inverter and its stability analysis”.ACTA PHYSICA SINICA,61.13(2012):130504.
disclosure of Invention
The main purpose of the application is to provide an inverter bifurcation control method based on state variable period difference feedback, so as to at least solve the problems that the bifurcation control method of a DC-AC inverter in the prior art can cause disturbance to the inverter and the control coefficient is difficult to determine, and expand the stable operation domain of the system on the premise of not changing the original dynamic characteristics of the system.
To achieve the above object, according to one aspect of the present application, there is provided an inverter bifurcation control method based on state variable period difference feedback, including:
according to state equations of a main circuit and a control circuit of the inverter, a discrete mapping model of the inverter is established by adopting a stroboscopic mapping method based on a quasi-static idea, and a Jacobian matrix of the discrete mapping model at a balance point is solved;
drawing a characteristic value change track graph of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs according to the change condition of the characteristic value along with bifurcation parameters, and entering the next step when bifurcation occurs;
let the difference between the initial value and the final value of the state variable of the inverter in the switching period be delta, and the difference between the initial value and the final value of the given reference signal in the switching period be delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison;
and superposing the control signal and an original PI regulating current control signal of the inverter to obtain a new control signal, and applying the new control signal to the inverter to restore the inverter to steady state operation.
Optionally, solving the jacobian matrix of the discrete mapping model at the balance point comprises the steps of:
according to the main circuit structure of the inverter, a main circuit state equation of the inverter in an nth switching period T is established,
according to the PI regulating current control circuit structure of the inverter, a state equation of the PI regulating current control circuit is established;
combining the state equation of the main circuit and the state equation of the PI regulating current control circuit, taking T as a sampling interval, and obtaining a discrete mapping model of the inverter system by adopting a stroboscopic mapping method based on a quasi-static idea;
and calculating the Jacobian matrix at the balance point according to the discrete mapping model.
Optionally, the main circuit state equation of the inverter in the nth switching period T is different according to the switching stateIn two forms, T 1 、T 2 The representation is specifically as follows:
wherein Q is 1 、Q 2 、Q 3 、Q 4 Is a switching device in the main circuit; l is inductance, i L (t) is the inductor current at time t, R L The power supply is a resistor load, and E is a direct-current side power supply; d, d n Is duty cycle, and represents the switching device Q in the nth switching period 1 Q 3 The on-time is proportional to the total switching period T.
Optionally, the state equation of the PI regulated current control circuit is expressed as:
wherein k is p 、k i Proportional control coefficient and integral control coefficient in PI regulating current control, v con (t) control signal generated for PI regulated current control at time t, i e (t) is the inductive current iL and the reference current i at the moment t ref Is a difference in (c).
Optionally, combining the state equation of the main circuit and the state equation of the PI-regulated current control circuit, using T as a sampling interval, obtaining a discrete mapping model of the inverter system based on a quasi-static idea by using a stroboscopic mapping method, and calculating according to the discrete mapping model to obtain a jacobian matrix at a balance point, where the jacobian matrix comprises:
let i be based on quasi-static idea with T as sampling interval ref (t)＝I m sin(ωnT)，i ref (t) as a reference input, and obtaining an expression of a discrete mapping model of the inverter system by using a stroboscopic mapping method, wherein the expression is as follows:
wherein i is L(n) An inductance current value of the nth switching period, R L For resistive load, v con(n) The control signal is the control signal of the nth switching period, and E is a direct-current side power supply;
in the above formula:
U n-1 ＝k p I m ωcos(ω(n-1)T)+k i I m sin(ω(n-1)T)
from (4) i can be obtained L(n) 、v con(n-1) 、d n Corresponding balance point I LQ 、V conQ 、D Q ：
Taking the system state vector as X n ＝[i L(n) i L(n-1) v con(n-1) ] T Order-making
k p 、k i Respectively a proportional control coefficient and an integral control coefficient in PI regulating current control, R L Is a resistive load;
then, the jacobian matrix at the equilibrium point is obtained:
optionally, determining whether bifurcation occurs is: when all characteristic values of the Jacobian matrix at the balance point are in the unit circle, the system keeps running stably; when one or more characteristic values pass through the unit circle, and other characteristic values are in the unit circle, the system is branched.
Optionally, the method further comprises: establishing a discrete mapping model of the inverter after the inverter bifurcation control method based on the state variable period difference feedback is introduced, and solving a Jacobian matrix of the discrete mapping model at a balance point; based on the Jacobian matrix at the balance point, drawing a track graph of the change of the characteristic value of the Jacobian matrix along with the bifurcation parameter after bifurcation control is introduced, and judging whether the inverter resumes steady state operation according to the change condition of the characteristic value along with the bifurcation parameter, thereby verifying the effectiveness of the bifurcation control method of the inverter based on the state variable period difference feedback.
According to still another aspect of the present application, there is also provided an inverter bifurcation control device based on state variable period difference feedback, including:
the Jacobian matrix solving module is used for establishing a discrete mapping model of the inverter by adopting a stroboscopic mapping method based on a quasi-static idea according to state equations of a main circuit and a control circuit of the inverter and solving a Jacobian matrix of the discrete mapping model at a balance point;
the bifurcation judging module is used for drawing a characteristic value change track graph of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs according to the change condition of the characteristic value along with bifurcation parameters, and sending a signal to the control signal processing module when bifurcation occurs;
a control signal processing module for making the difference between the initial value and the final value of the state variable of the inverter in the switching period be delta after the bifurcation judging module judges that bifurcation occurs, and giving a reference signal in the switching periodThe difference between the initial value and the final value is delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison;
and the new control signal generation module is used for superposing the control signal and the original PI regulating current control signal of the inverter to obtain a new control signal, and then applying the new control signal to the inverter to restore the inverter to steady state operation.
According to an aspect of the present application, there is provided a computer readable storage medium, wherein the computer readable storage medium includes a stored program, and when the program runs, the device in which the computer readable storage medium is controlled to execute any one of the inverter bifurcation control methods based on state variable period difference feedback.
According to yet another aspect of the present application, an electronic device includes a memory and a processor, wherein the memory stores a computer program, and the processor is configured to execute any one of the inverter bifurcation control methods based on state variable period difference feedback by the computer program.
Compared with the prior art, the invention has the following beneficial effects:
1. by applying the technical scheme, according to the state equations of a main circuit and a control circuit of the inverter, a discrete mapping model of the inverter is established by adopting a stroboscopic mapping method based on a quasi-static thought, and a Jacobian matrix of the discrete mapping model at a balance point is solved; drawing a characteristic value change track graph of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs according to the change condition of the characteristic value along with bifurcation parameters, and entering the next step when bifurcation occurs; let the difference between the initial value and the final value of the state variable of the inverter in the switching period be delta, and the difference between the initial value and the final value of the given reference signal in the switching period be delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison; adjusting the control signal and the original PI of the inverterAnd finally, applying the new control signal to the inverter to restore the inverter to steady state operation. The invention can avoid complex calculation of the control coefficient determining process, effectively control the bifurcation behavior of the inverter, obviously reduce the harmonic content, enlarge the stable operation area of the inverter and not change the original dynamics property of the system.
2. In the inverter bifurcation control method based on state variable period difference feedback, the value range of the proportional control coefficient of the proportional link can be rapidly screened based on the necessary condition of inverter stability, namely, the modules of all characteristic values of the Jacobian matrix at the balance point after bifurcation control are ensured to be less than 1, the value range of the proportional control coefficient can be rapidly screened by means of MATLAB programming, and the complex calculation of the control coefficient determining process can be avoided.
3. Applying a new control signal to the inverter to restore the inverter to steady operation, and when the system is restored to steady state, delta and delta ref Equally, the proposed control method does not work, enabling the system to maintain the original kinetic properties.
Drawings
In order to more clearly illustrate the technical solutions of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawing in the description below is only one embodiment of the present invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an inverter bifurcation control method based on state variable period difference feedback in accordance with an embodiment of the present invention;
fig. 2 is a main circuit configuration diagram of an inverter according to an embodiment of the present invention;
fig. 3 is a block diagram of an inverter control circuit according to an embodiment of the present invention, a solid line representing a PI regulated current control section, and a broken line representing an inverter bifurcation control section based on a state variable period difference feedback;
FIG. 4 is a bifurcation parameter k according to an embodiment of the present invention p Variation ofTime characteristic value lambda 1 ～λ 3 Is a trajectory graph of (1);
FIG. 5 shows the characteristic value lambda when the bifurcation parameter E is changed according to an embodiment of the present invention 1 ～λ 3 Is a trajectory graph of (1);
FIG. 6 is a bifurcation parameter k according to an embodiment of the present invention p ＝1.5，k 1 The characteristic value lambda is taken as-5 to 5 1 ～λ 3 Trace diagram of the mould;
fig. 7 shows the bifurcation parameters e=70v, k according to an embodiment of the present invention 1 The characteristic value lambda is taken as-5 to 5 1 ～λ 3 Trace diagram of the mould;
FIG. 8 is a diagram of k according to an embodiment of the present invention p The value of k is 0.8-2 1 After introducing inverter bifurcation control method based on state variable period difference feedback when= -0.6 1 ～λ 3 Is a trajectory graph of (1);
FIG. 9 shows E values of 40V-80V, k according to an embodiment of the present invention 1 After introducing inverter bifurcation control method based on state variable period difference feedback when= -0.3 1 ～λ 3 Is a trajectory graph of (1);
FIG. 10 (a) is a diagram of k according to an embodiment of the present invention p ＝1.5，k 1 After introducing inverter bifurcation control method based on state variable period difference feedback when in= -0.6, inductance current i L A waveform;
FIG. 10 (b) is a diagram of k according to an embodiment of the present invention p Inverter bifurcation control method i before introducing feedback based on state variable period difference when=1.5 L A waveform spectrum simulation calculation result;
FIG. 10 (c) is a diagram of k according to an embodiment of the present invention p ＝1.5，k 1 After introducing inverter bifurcation control method based on state variable period difference feedback when in= -0.6 L A waveform spectrum simulation calculation result;
fig. 11 (a) is e=70v, k according to an embodiment of the present invention 1 After introducing inverter bifurcation control method based on state variable period difference feedback when in= -0.3, inductance current i L A waveform;
fig. 11 (b) is e=according to an embodiment of the present inventionInductive current i before inverter bifurcation control method based on state variable period difference feedback is introduced at 70V L A waveform spectrum simulation calculation result;
fig. 11 (c) is e=70v, k according to an embodiment of the present invention 1 After introducing inverter bifurcation control method based on state variable period difference feedback when in= -0.3, inductance current i L And simulating a calculation result of the waveform spectrum.
Detailed Description
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
In order to make the present application solution better understood by those skilled in the art, the following description will be made in detail and with reference to the accompanying drawings in the embodiments of the present application, it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, shall fall within the scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate in order to describe the embodiments of the present application described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or device that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or device.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
Fig. 1 is a flowchart of an inverter bifurcation control method based on state variable period difference feedback according to an embodiment of the present invention, as shown in fig. 1, the method includes the steps of:
step S1: according to state equations of a main circuit and a control circuit of the inverter, a discrete mapping model of the inverter is established by adopting a stroboscopic mapping method based on a quasi-static idea, and a Jacobian matrix of the discrete mapping model at a balance point is solved;
step S2: based on the Jacobian matrix at the balance point, selecting a proportional control coefficient k in PI regulating current control p And the direct-current side voltage E is a bifurcation parameter, a track graph of the characteristic value of the Jacobian matrix along with the bifurcation parameter is calculated and drawn by means of MATLAB, whether bifurcation occurs or not is judged according to the change condition of the characteristic value along with the bifurcation parameter, and the next step is carried out when bifurcation occurs;
step S3: introducing state variable period difference feedback control for controlling bifurcation, i.e. making state variable inductor current i of inverter L The difference between the initial value and the final value in the switching period is delta, given the current reference signal i ref The difference between the initial value and the final value in the switching period is delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison;
step S4: and superposing the control signal and an original PI regulating current control signal of the inverter to obtain a new control signal, and applying the new control signal to the inverter to restore the inverter to steady state operation.
In the described embodiment, fig. 2 shows the main circuit structure of the inverter, the dc side power supply E is supplied, and the four legs are provided with switching devices Q with antiparallel diodes 1 -Q 4 Composition, R is obtained by inductance L filtering L Is a resistive load. Fig. 3 is a structural diagram of an inverter control circuit according to an embodiment of the present invention, in which a solid line in fig. 3 represents a PI regulated current control section, and a broken line represents an inverter bifurcation control section based on a state variable period difference feedback. The specific control process is as follows: inductor current i without added bifurcation control L With reference current i ref Is the difference i of (1) e Generating control signal v via PI regulation con Control signal v con And carrier signal v ramp After comparison, SPWM signals are generated by an SPWM generator to control two pairs of switching devices Q 1 Q 3 、Q 2 Q 4 Complementary conduction; after the bifurcation control is added, the state variable inductance current i of the inverter is made L The difference between the initial value and the final value in the switching period is delta, given the current reference signal i ref The difference between the initial value and the final value in the switching period is delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison; the proportion link needs to rapidly screen out the value range of the proportion control coefficient based on the necessary condition of inverter stability (all characteristic values need to be in a unit circle, namely, the modulus of all the characteristic values is smaller than 1); the control signal is overlapped with the original PI regulating current control signal to obtain a new control signal v con Will be a new control signal v con And carrier signal v ramp After comparison, SPWM signals are generated by an SPWM generator to control two pairs of switching devices Q 1 Q 3 、Q 2 Q 4 Complementary conduction.
Referring to fig. 1, 2 and 3, step S1 establishes a discrete mapping model of the inverter by using a stroboscopic mapping method based on a quasi-static idea according to state equations of a main circuit and a control circuit of the inverter, and solves a jacobian matrix of the discrete mapping model at a balance point, wherein the steps include:
step S11, according to the main circuit of the inverter shown in FIG. 2, the main circuit equation of state of the inverter in the nth switching period T has two forms according to the different switching states, T is used 1 、T 2 The representation is specifically as follows:
wherein i is L (t) is the inductor current at time t; d, d n Is duty cycle, and represents the switching device Q in the nth switching period 1 Q 3 The on-time is proportional to the total switching period T.
In step S12, as can be seen from the solid line part of fig. 3, the state equation of the PI regulated current control circuit is expressed as:
wherein k is p 、k i Proportional control coefficient and integral control coefficient in PI regulating current control, v con (t) control signal generated for PI adjustment at time t, i e (t) inductor current i at time t L (t) and reference current i ref (t) difference.
Step S13, combining the state equation of the main circuit and the state equation of the PI regulating current control circuit, taking T as a sampling interval, and based on a quasi-static idea, letting i ref (t)＝I m sin (ωnT), obtaining a discrete mapping model of the inverter system by adopting a stroboscopic mapping method, and calculating to obtain the Jacobian matrix at the balance point according to the discrete mapping model.
Specifically, taking T as a sampling interval, and based on a quasi-static thought order i ref (t)＝I m sin (ωnT), i.e. i ref Is the reference input, the purpose of controlling the inverter is to hope the inductor current i L Can track i ref . Since the final build is a discrete mapping model, the reference input i ref Which is also represented discretized. So through i ref (t)＝I m sin (ωnt) to express a quasi-static based idea, it is considered that the current i is referenced in the nth switching period T ref Is unchanged. And then, a discrete mapping model expression of the inverter system is obtained by adopting a stroboscopic mapping method, wherein the expression is as follows:
wherein i is L(n) For the inductor current in the nth switching period, R L For resistive load, v con(n) Is a control signal in an nth switching period;
U n-1 ＝k p I m ωcos(ω(n-1)T)+k i I m sin(ω(n-1)T)
from (4) i can be obtained L(n) 、v con(n-1) 、d n Corresponding balance point I LQ 、V conQ 、D Q ：
Taking the system state vector as X n ＝[i L(n) i L(n-1) v con(n-1) ] T Order-making
Then, the jacobian matrix at the equilibrium point is obtained:
in the illustrated embodiment, the step S2 specifically includes the following steps:
s21, selecting P according to the Jacobian matrix at the balance pointI adjusting the proportional control coefficient k in the current control p And the direct-current side voltage E is a bifurcation parameter;
s22, calculating and drawing a change track of the characteristic value of the Jacobian matrix at the balance point when the bifurcation parameter is changed by means of MATLAB, and obtaining a change track graph of the characteristic value along with the bifurcation parameter;
s23, analyzing k by combining the characteristic value along with the bifurcation parameter change track diagram, namely the characteristic value change condition at the balance point p E, judging whether bifurcation occurs or not according to the influence of E on the system stability;
wherein, judge whether to take place the bifurcation and be: when all the characteristic values are in the unit circle, the system keeps running stably; when one or more characteristic values pass through the unit circle, and other characteristic values are in the unit circle, the system is branched.
Specifically, when taking k p E=50v for the bifurcation parameter; when E is taken as a bifurcation parameter, k p =1. Other circuit parameters are configured as in table 1.
Table 1 inverter parameter set point
From the characteristic equation det [ lambda I-J (X) Q )]The characteristic value lambda of the sample can be obtained by the method of (0) 1 ，λ 2 ，λ 3 . Drawing k by MATLAB calculation p I when increasing from 0.8 to 2 and E from 40V to 80V L Characteristic value lambda at positive peak 1 ，λ 2 ，λ 3 The change track of (a) is shown in fig. 4 and 5. Judging whether bifurcation occurs according to the change condition of the Jacobian matrix eigenvalue at the balance point along with bifurcation parameters: when all the characteristic values are in the unit circle, the system keeps running stably; when one or more characteristic values pass through the unit circle, and other characteristic values are in the unit circle, the system is branched. As can be seen from FIGS. 4 and 5, when k is p When=1.15 and e=57.7v, the characteristic value λ 1 Through a unit circle along the negative real axis, while the eigenvalue lambda 2 ，λ 3 All are in the unit circle, and the inverter appears at the momentThe bifurcation behavior is achieved. With k p And E, continuing to increase, and performing unstable operation after bifurcation of the system.
Step S3 is to introduce an inverter bifurcation control method based on state variable period difference feedback for controlling bifurcation, namely, to make the state variable inductance current i of the inverter L The difference between the initial value and the final value in the switching period is delta, given the current reference signal i ref The difference between the initial value and the final value in the switching period is delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref And comparing and then obtaining a control signal through a proportion link. The ratio link needs to rapidly screen the value range of the ratio control coefficient based on the necessary condition of inverter stability, and the necessary condition of inverter stability is as follows: all eigenvalues must be within a unit circle, i.e. the modulus of all eigenvalues is less than 1.
As an optional embodiment, the method for controlling the bifurcation of the inverter based on the feedback of the state variable period difference further includes step S4, establishing a discrete mapping model of the inverter after the method for controlling the bifurcation of the inverter based on the feedback of the state variable period difference is introduced, and solving a jacobian matrix of the discrete mapping model at a balance point; based on the Jacobian matrix at the balance point, drawing a track graph of the change of the characteristic value of the Jacobian matrix along with the bifurcation parameter after bifurcation control is introduced, and judging whether the inverter resumes steady state operation according to the change condition of the characteristic value along with the bifurcation parameter, thereby verifying the effectiveness of the bifurcation control method of the inverter based on the state variable period difference feedback.
Specifically, to prove the effectiveness of the inverter bifurcation control method that introduces feedback based on the state variable period difference, a new control signal is applied to the inverter for verification. The bifurcation control is introduced as shown by the broken line in FIG. 3, wherein the bifurcation control proportional link control coefficient is denoted as k 1 . Based on the formula (4), the control signal v after the bifurcation control is introduced con The discrete mapping model of (a) is:
v con(n) ＝p 1 i L(n-1) +v con(n-1) +p 2 E+TU n-1 +k 1 (δ ref(n-1) -δ (n-1) ) (6)
wherein delta ref(n-1) For a given current reference signal i ref The difference between the initial value and the final value, delta, in the n-1 th switching period (n-1) Inductance current i for the state variable of the inverter L The difference between the initial value and the final value in the n-1 th switching period.
Delta in the above ref(n-1) ＝I m sin(ωnT)－I m sin[ω(n－1)T]，δ (n-1) ＝i L(n) －i L(n－1) . At this time, the jacobian matrix at the balance point of the inverter is:
proportional control coefficient k in bifurcation control 1 Has important influence on the control effect, in order to avoid directly solving k 1 Complex operations brought by value analysis of (a) are respectively firstly obtained by k p As is clear from fig. 4 and 5, the inverter is in an unstable state after the inverter is branched at this time, as shown in=1.5 and e=70v. Drawing k by MATLAB programming 1 The value range is-5 to 5 (the value range can be arbitrarily set), and k is 0.001 when the step length is 0.001 p The change traces of the three eigenvalue modes of the jacobian matrix (equation 7) when=1.5 and e=70 are shown in fig. 6 and 7. As can be seen from the enlarged view in fig. 6, k p When k=1.5 1 Within (-1.6, -0.55), the modulus of 3 eigenvalues is less than 1. As can be seen from the enlarged view in fig. 7, when e=70v, k is 1 Within (-1.1, -0.25), the modulus of 3 eigenvalues is less than 1. To be general, take k 1 = -0.6, draw k p1 The value range is [0.8,2 ]]The characteristic value trace variation is shown in fig. 8. Take K arbitrarily 1 = -0.3, drawing E with value range of [40v,80v]The characteristic value trace variation is shown in fig. 9. Fig. 8 and 9 show that all characteristic values are in a unit circle of a complex plane after the inverter bifurcation control method based on the state variable period difference feedback is introduced, and the system stably operates. The method for controlling the bifurcation of the inverter based on the feedback of the state variable period difference value can effectively control the bifurcation behavior in the inverter and enlarge the stable operation domain of the system.
FIGS. 10 and 11 show k, respectively p When=1.5, e=70v, t=0.06 s, the inverter introduces the inductor current i after the inverter bifurcation control method based on the feedback of the state variable period difference L Is a simulation result of (a). When k is p When=1.5, fig. 10 (a) shows that the waveform distortion before control is introduced, and the duty cycle of the inverter is 2T when viewed from the enlarged view, which indicates that the inverter is in the bifurcation state. When t=0.06 s, the waveform tends to be smooth after the bifurcation control of the invention is introduced, the working period of the inverter is recovered to T from the enlarged view, and the inverter is recovered to stably run. By comparing fig. 10 (b) and fig. 10 (c), it is understood that the waveform THD before control is introduced up to 11.11%, and that the harmonic wave mainly having a frequency concentrated around 10kHz (i.e., half of the switching frequency) is contained in addition to the fundamental component. After the control is introduced, the waveform THD is reduced to 3.41% and contains only a small number of harmonics of the switching frequency, in addition to the fundamental component. When e=70v, it can be seen from fig. 11 (a) that the waveform distortion before the control is introduced, the duty cycle of the inverter is 2T as seen from the enlarged view, which indicates that the inverter is also in the bifurcation state at this time, and when t=0.06 s, the waveform tends to be smooth after the bifurcation control is introduced, and the duty cycle of the inverter is restored to T as seen from the enlarged view. By comparing fig. 11 (b) and 11 (c), it is understood that the waveform THD before control is introduced up to 17.76%, and the waveform contains mainly harmonics around 10kHz in addition to the fundamental component. In addition, the harmonic wave with the frequency of 5kHz which is not easy to be perceived on the time domain waveform diagram is also contained. After control is introduced, the waveform THD is reduced to 4.48% with only a small number of harmonics of the switching frequency, in addition to the fundamental component. This means that the branching behavior in the inverter is effectively controlled after the branching control of the present invention is introduced.
The embodiment of the application also provides an inverter bifurcation control device based on state variable period difference feedback, and it should be noted that the inverter bifurcation control device based on state variable period difference feedback of the embodiment of the application can be used for executing the inverter bifurcation control method based on state variable period difference feedback provided by the embodiment of the application. The device is used for implementing the embodiments and the preferred embodiments, and is not described again. As used below, the term "module" may be a combination of software and/or hardware that implements a predetermined function. While the means described in the following embodiments are preferably implemented in software, implementation in hardware, or a combination of software and hardware, is also possible and contemplated.
The following describes an inverter bifurcation control device based on feedback of a state variable period difference provided in the embodiment of the present application.
The inverter bifurcation control device based on state variable period difference feedback comprises:
the Jacobian matrix solving module is used for establishing a discrete mapping model of the inverter by adopting a stroboscopic mapping method based on a quasi-static idea according to state equations of a main circuit and a control circuit of the inverter and solving a Jacobian matrix of the discrete mapping model at a balance point;
the bifurcation judging module is used for drawing a characteristic value change track graph of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs according to the change condition of the characteristic value along with bifurcation parameters, and sending a signal to the control signal processing module when bifurcation occurs;
a control signal processing module for making the difference between the initial value and the final value of the state variable of the inverter in the switching period be delta after the bifurcation judging module judges that bifurcation occurs, and giving the difference between the initial value and the final value of the reference signal in the switching period be delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison;
the new control signal generation module is used for superposing the control signal and the original PI regulating current control signal of the inverter to obtain a new control signal, and then applying the new control signal to the inverter to restore the inverter to steady state operation
The present invention is not limited to the above embodiments, but is to be accorded the widest scope consistent with the principles and other features of the present invention.
An embodiment of the present invention provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor is configured to execute the method for controlling the bifurcation of the inverter based on feedback of a state variable period difference value by using the computer program.
The embodiment of the invention provides equipment, which comprises a processor, a memory and a program stored in the memory and capable of running on the processor, wherein the processor realizes the steps of an inverter bifurcation control method based on at least state variable period difference feedback when executing the program.
The device herein may be a server, PC, PAD, cell phone, etc.
The present application also provides a computer program product adapted to perform a program of steps of an inverter bifurcation control method initialized with feedback based at least on a state variable period difference when executed on a data processing device.
It will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented in a general purpose computing device, they may be concentrated on a single computing device, or distributed across a network of computing devices, they may be implemented in program code executable by computing devices, so that they may be stored in a storage device for execution by computing devices, and in some cases, the steps shown or described may be performed in a different order than that shown or described herein, or they may be separately fabricated into individual integrated circuit modules, or multiple modules or steps of them may be fabricated into a single integrated circuit module. Thus, the present invention is not limited to any specific combination of hardware and software.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In one typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of non-volatile memory, random Access Memory (RAM), and/or nonvolatile memory in a computer-readable medium, such as Read Only Memory (ROM) or flash RAM. Memory is an example of a computer-readable medium.
Computer readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. Examples of storage media that can be used for storing information that can be accessed by a computing device include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disc read-only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises an element.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the same, but rather, various modifications and variations may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims (10)

1. An inverter bifurcation control method based on state variable period difference feedback, comprising:
according to state equations of a main circuit and a control circuit of the inverter, a discrete mapping model of the inverter is established by adopting a stroboscopic mapping method based on a quasi-static idea, and a Jacobian matrix of the discrete mapping model at a balance point is solved;
drawing a characteristic value change track graph of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs according to the change condition of the characteristic value along with bifurcation parameters, and entering the next step when bifurcation occurs;
let the difference between the initial value and the final value of the state variable of the inverter in the switching period be delta, and the difference between the initial value and the final value of the given reference signal in the switching period be delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison;
and superposing the control signal and an original PI regulating current control signal of the inverter to obtain a new control signal, and applying the new control signal to the inverter to restore the inverter to steady state operation.
2. The method for controlling the bifurcation of the inverter based on the feedback of the period difference of the state variables according to claim 1, wherein solving the jacobian matrix of the discrete mapping model at the balance point comprises the steps of:
according to the main circuit structure of the inverter, a main circuit state equation of the inverter in an nth switching period T is established,
according to the PI regulating current control circuit structure of the inverter, a state equation of the PI regulating current control circuit is established;
combining the state equation of the main circuit and the state equation of the PI regulating current control circuit, taking T as a sampling interval, and obtaining a discrete mapping model of the inverter system by adopting a stroboscopic mapping method based on a quasi-static idea;
and calculating the Jacobian matrix at the balance point according to the discrete mapping model.
3. The method according to claim 2, wherein the nth on is turned on according to a switching stateThe main circuit state equation of the inverter in the off period T has two forms, T is used 1 、T 2 The representation is specifically as follows:
wherein Q is 1 、Q 2 、Q 3 、Q 4 Is a switching device in the main circuit; l is inductance, i L (t) is the inductor current at time t, R L The power supply is a resistor load, and E is a direct-current side power supply; d, d n Is duty cycle, and represents the switching device Q in the nth switching period 1 Q 3 The on-time is proportional to the total switching period T.
4. The inverter bifurcation control method based on state variable period difference feedback according to claim 2, wherein the state equation of the PI regulated current control circuit is expressed as:
wherein k is p 、k i Proportional control coefficient and integral control coefficient in PI regulating current control, v con (t) control signal generated for PI regulated current control at time t, i e (t) inductor current i at time t L (t) and reference current i ref (t) difference.
5. The method for controlling the bifurcation of the inverter based on the feedback of the period difference of the state variables according to claim 2, wherein, by combining the state equation of the main circuit and the state equation of the PI-regulated current control circuit, with T as a sampling interval, a discrete mapping model of the inverter system is obtained by a stroboscopic mapping method based on a quasi-static idea, and the jacobian matrix at the balance point is calculated according to the discrete mapping model, comprising:
let i be based on quasi-static idea with T as sampling interval ref (t)＝I m sin(ωnT)，i ref (t) as a reference input, and obtaining an expression of a discrete mapping model of the inverter system by using a stroboscopic mapping method, wherein the expression is as follows:
wherein i is L(n) An inductance current value of the nth switching period, R L For resistive load, v con(n) The control signal is the control signal of the nth switching period, and E is a direct-current side power supply;
in the above formula:
U n-1 ＝k p I m ωcos(ω(n-1)T)+k i I m sin(ω(n-1)T)
from (4) i can be obtained L(n) 、v con(n-1) 、d n Corresponding balance point I LQ 、V conQ 、D Q ：
Taking system state vectorsIs X n ＝[i L(n) i L(n-1) v con(n-1) ] T Order-making
k p 、k i Respectively a proportional control coefficient and an integral control coefficient in PI regulating current control, R L Is a resistive load;
then, the jacobian matrix at the equilibrium point is obtained:
6. the method for controlling the bifurcation of the inverter based on the feedback of the period difference of the state variables according to claim 1, wherein the determining whether the bifurcation occurs is: when all characteristic values of the Jacobian matrix at the balance point are in the unit circle, the system keeps running stably; when one or more characteristic values pass through the unit circle, and other characteristic values are in the unit circle, the system is branched.
7. The inverter bifurcation control method based on state variable period difference feedback of claim 1, further comprising: establishing a discrete mapping model of the inverter after the inverter bifurcation control method based on the state variable period difference feedback is introduced, and solving a Jacobian matrix of the discrete mapping model at a balance point; based on the Jacobian matrix at the balance point, drawing a track graph of the change of the characteristic value of the Jacobian matrix along with the bifurcation parameter after bifurcation control is introduced, and judging whether the inverter resumes steady state operation according to the change condition of the characteristic value along with the bifurcation parameter, thereby verifying the effectiveness of the bifurcation control method of the inverter based on the state variable period difference feedback.
8. An inverter bifurcation control device based on state variable period difference feedback, comprising:
the Jacobian matrix solving module is used for establishing a discrete mapping model of the inverter by adopting a stroboscopic mapping method based on a quasi-static idea according to state equations of a main circuit and a control circuit of the inverter and solving a Jacobian matrix of the discrete mapping model at a balance point;
the bifurcation judging module is used for drawing a characteristic value change track graph of the Jacobian matrix along with bifurcation parameters based on the Jacobian matrix at the balance point, judging whether bifurcation occurs according to the change condition of the characteristic value along with bifurcation parameters, and sending a signal to the control signal processing module when bifurcation occurs;
a control signal processing module for making the difference between the initial value and the final value of the state variable of the inverter in the switching period be delta after the bifurcation judging module judges that bifurcation occurs, and giving the difference between the initial value and the final value of the reference signal in the switching period be delta ref Taking delta as a feedback signal, and combining the feedback signals delta and delta ref The control signals are obtained through a proportion link after comparison;
and the new control signal generation module is used for superposing the control signal and the original PI regulating current control signal of the inverter to obtain a new control signal, and then applying the new control signal to the inverter to restore the inverter to steady state operation.
9. A computer-readable storage medium, characterized in that the computer-readable storage medium includes a stored program, wherein the program, when run, controls a device in which the computer-readable storage medium is located to execute the inverter bifurcation control method based on the state variable period difference feedback according to any one of claims 1 to 7.
10. An electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to execute the state variable period difference feedback-based inverter bifurcation control method according to any one of claims 1 to 7 by means of the computer program.
CN202311437519.1A 2023-10-31 2023-10-31 Inverter bifurcation control method based on state variable period difference feedback Pending CN117477643A (en)

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