CN116317489A - Boost PFC converter stepless cooperative control method and system based on super local model - Google Patents

Boost PFC converter stepless cooperative control method and system based on super local model Download PDF

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CN116317489A
CN116317489A CN202310405497.4A CN202310405497A CN116317489A CN 116317489 A CN116317489 A CN 116317489A CN 202310405497 A CN202310405497 A CN 202310405497A CN 116317489 A CN116317489 A CN 116317489A
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output voltage
representing
current
pfc converter
boost pfc
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李红梅
潘晨
张恒果
杨利国
赵浩楠
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Hefei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters
    • H02M1/088—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters for the simultaneous control of series or parallel connected semiconductor devices
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/42—Circuits or arrangements for compensating for or adjusting power factor in converters or inverters
    • H02M1/4208—Arrangements for improving power factor of AC input
    • H02M1/4258—Arrangements for improving power factor of AC input using a single converter stage both for correction of AC input power factor and generation of a regulated and galvanically isolated DC output voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
    • H02M3/1582—Buck-boost converters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

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Abstract

The invention relates to a Boost PFC converter stepless cooperative control method and a system based on a super local model, which solve the defect that the average value of output voltage has static errors compared with the prior art. The invention comprises the following steps: boost PFC converter data and average filtering processing; establishing a super local model and carrying out load current estimation; generating a cascade-free cooperative control duty cycle control law; stepless coordinated control of Boost PFC converters. The invention can effectively improve the steady-state control precision of the output voltage of the Boost PFC converter, has the technical advantages of simple control structure and strong load disturbance resistance under the abrupt change of load power, and comprehensively improves the dynamic control performance and steady-state operation performance of the Boost PFC converter.

Description

Boost PFC converter stepless cooperative control method and system based on super local model
Technical Field
The invention relates to the technical field of Boost PFC converters, in particular to a stepless coupling cooperative control method and a stepless coupling cooperative control system for a Boost PFC converter based on a super local model.
Background
In order to meet international standards and grid guidelines for harmonic requirements of power devices to access the grid, power factor correction (Power Factor Correction, PFC) converters have gained research attention. The Boost PFC converter is a main circuit topology for realizing power factor correction in the middle-high power occasion due to the advantages of small size, light weight, high efficiency, small conduction loss and the like. For Boost PFC circuits, the control strategy is typically based on a double closed loop structure, consisting of a low bandwidth voltage outer loop and a high bandwidth current inner loop. The traditional Boost PFC converter voltage control system mainly designs a PI voltage controller based on a mathematical model of the converter, and limits the passing of double frequency voltage ripple by taking measures of actively reducing bandwidth. However, when the load changes, the PI voltage control with low bandwidth can cause the dynamic response of the output voltage of the system to be slow, generate large overshoot, require long stabilization time, increase circuit loss and even damage circuit elements.
In order to realize low harmonic distortion of input current when a Boost PFC converter is in a steady state and ensure rapid convergence of output voltage when in a dynamic state, chinese patent CN112350565B adopts a cascade model-free predictive control system to design control of a voltage outer ring and a current inner ring, wherein the voltage outer ring indirectly maintains the stability of the output voltage of the converter in a mode of providing a reference value for the current inner ring, and the dynamic performance of the whole system is influenced in a mode of indirectly controlling the output voltage due to lower bandwidth of an external voltage control loop; the Boost PFC converter has the defects of component conduction voltage drop, resistance loss, switching loss and the like, and the cascade model-free control system has the defect of poor steady-state control precision. In addition, the control system needs to adopt a double-closed-loop cascade control structure of a current inner ring and a voltage outer ring, and the control structure is complex.
The cooperative control is used as a control method with great potential, has the characteristics of simple control structure and flexible realization, and can improve the steady-state precision of the output voltage of the system by changing the design of macro variables. Because of the difference of steady-state control precision of different control strategies, one difficulty faced by cooperative control is manifold design. The control of the Boost PFC converter input voltage and input current directly affects the system control performance, so the most classical manifold design is to design the manifold as a linear combination of the output voltage error term and the inductor current error term. In view of the fact that the Boost PFC converter is affected by factors such as component conduction voltage drop, resistance loss and switching loss in actual operation, a static error exists in an output voltage average value based on cooperative control of a traditional macro-variable design, therefore, an integral term of the output voltage error is added on the basis of the traditional macro-variable design, and the problem that the static error exists in the output voltage average value due to the influence of factors such as component conduction voltage drop, resistance loss and switching loss is solved. The cascade-free cooperative control can effectively improve the steady-state control precision of the output voltage of the Boost PFC converter, has the technical advantages of simple control structure and strong load disturbance resistance under the sudden change of load power, and comprehensively improves the dynamic control performance and steady-state operation performance of the Boost PFC converter.
Disclosure of Invention
The invention aims to solve the defects that in the prior art, a double closed loop cascade control structure adopting a current inner loop and a voltage outer loop is complex, the dynamic performance of the whole system is influenced in an indirect control mode of the output voltage due to lower bandwidth of an external voltage control loop, and static errors exist in the average value of the output voltage caused by the influences of factors such as component conduction voltage drop, resistance loss and switching loss, and the like, and provides a Boost PFC converter stepless cascade cooperative control method based on a super local model.
In order to achieve the above object, the technical scheme of the present invention is as follows:
a Boost PFC converter stepless cooperative control method based on a super local model comprises the following steps:
11 Boost PFC converter data and average filtering process: acquiring parameters of a Boost PFC converter, wherein the parameters comprise a Boost inductor L, an output capacitor C, a resistive load R, a freewheeling diode D and a power switch tube S, establishing an average state space equation of the Boost PFC converter in a continuous conduction mode, and filtering double frequency ripple waves of an output voltage by using an average filtering module;
12 Building a super local model and carrying out load current estimation: based on the average state space equation of the single-phase Boost PFC converter, the uncertain part F of the super-local model of the output voltage is utilized v Uncertainty part F of inductor current superlocal model i Reference inductor current amplitude
Figure BDA0004181217820000021
Duty cycle coefficient alpha i Reference inductance current amplitude coefficient alpha v Establishing a super local model of output voltage and inductance current of the Boost PFC converter; estimating a load current by using a load current estimation module;
13 Generation of a tandem free cooperative control duty cycle control law): based on a super-local model of the Boost PFC converter, developing macro-variable design comprising an output voltage error term, an inductance current error term and an output voltage error integral term, and designing a dynamic evolution equation for converging a system to a manifold; and generating a duty ratio control law of stepless coordinated control by means of the designed dynamic evolution equation and the duty ratio required to be satisfied by the system operation;
14 Tandem free cooperative control of Boost PFC converter): and modulating the duty ratio control signal by using a PWM (pulse-width modulation) module to obtain a power switch device driving signal S [ k ] of a kth period, and controlling the action of a power switch tube S of the Boost PFC converter to realize stepless coordinated control of the Boost PFC converter based on the super local model.
The Boost PFC converter data and average filtering process comprises the following steps:
21 Acquiring Boost PFC converter parameters;
22 Using formula (1) to establish a dynamic equation of inductance current of the single-phase Boost PFC converter operating in a continuous conduction mode;
Figure BDA0004181217820000031
wherein ,diL Dt represents a first derivative of the inductor current; l represents a boost inductance value; v in Representing input electricityPressing; v o Representing an output voltage; d represents a duty cycle control signal of the switching tube S;
23 Establishing an output voltage dynamic equation of the single-phase Boost PFC converter operating in a continuous conduction mode by adopting the formula (2);
Figure BDA0004181217820000032
wherein ,dvo Dt represents a first derivative of the output voltage; c represents an output capacitance value; i.e L Representing the inductor current; i.e o Representing the load current; d represents a duty cycle control signal of the switching tube S;
24 Using an average filter module to output voltage v o [k]Carrying out averaging treatment; obtaining the kth sampling period T by adopting the formula (3) k Average output voltage value V of (a) o [k]；
Figure BDA0004181217820000033
wherein ,Vo [mk]Representing an average output voltage value at a kth sampling point of an mth output voltage period; v o_m k An output voltage sampling value at a kth sampling point of an mth output voltage period;
Figure BDA0004181217820000041
an average voltage value representing a sum of output voltage sampling values at N sampling points of an mth output voltage period; v (V) o [(m-1)N]An average voltage value at an nth sampling point of an m-1 th output voltage period; v o_(m-1)k An output voltage sample value at a kth sample point of an m-1 th output voltage period; n is the sampling point number in one output voltage period set by a user; m is the number of output voltage cycles, m is a positive integer; i is an integer between 1 and N.
The building of the super local model and the load current estimation comprise the following steps:
31 According to the model-free control theory, the first-order super local model of the single-input single-output system is expressed as a formula (4);
Figure BDA0004181217820000042
wherein u and y represent the input and output of the system, respectively; alpha is a scale factor input by the system; f comprises a known part and an unknown part of the system;
32 Building a super-local model of the inductance current of the Boost PFC converter;
Figure BDA0004181217820000043
Figure BDA0004181217820000044
wherein ,diL Dt represents a first derivative of the inductor current; alpha i Representing the duty cycle coefficient; d represents a duty cycle control signal of the switching tube S; f (F) i Representing a known portion and an unknown portion of the inductor current superlocal model; c (C) i Representing an adjustable constant parameter; l (L) n A rated inductance value of the input inductance; l represents boost inductance; v in Representing an input voltage; v o Representing an output voltage;
33 When the switch tube S is set to be conducted, the freewheel diode does not work; when the switching tube S is turned off, the freewheeling diode works, and the freewheeling diode and the inductive current have the following expression relationship:
Figure BDA0004181217820000051
34 Assume that all signals in the output voltage state equation are averaged to eliminate the influence of the system double frequency ripple and to ignore the internal loss in the system, the average input power and the average output power are represented by the following equations:
Figure BDA0004181217820000052
wherein ,Pin Representing the average input power of the system; v (V) in Representing the magnitude of the input voltage;
Figure BDA0004181217820000053
representing the magnitude of the reference inductor current; p (P) o Representing the average output power of the system; />
Figure BDA00041812178200000511
Representing the magnitude of the reference output voltage; i D Representing the average diode current;
35 According to principle of conservation of power P in ＝P o Deriving an average diode current I D The expression of (2) is:
Figure BDA0004181217820000054
wherein ,ID Representing the average diode current; v (V) in Representing the magnitude of the input voltage;
Figure BDA0004181217820000055
representing the magnitude of the reference output voltage; />
Figure BDA0004181217820000056
Representing the magnitude of the reference inductor current;
36 Rearranging a dynamic equation (2) of the output voltage, the average state equation of the output voltage being expressed as:
Figure BDA0004181217820000057
wherein ,dvo Dt represents a first derivative of the output voltage; v (V) in Representing the magnitude of the input voltage; c represents an output capacitance;
Figure BDA00041812178200000512
representing the magnitude of the reference output voltage; />
Figure BDA0004181217820000058
Representing the magnitude of the reference inductor current; i.e o Representing the load current;
37 Building a super local model of the output voltage of the Boost PFC converter;
Figure BDA0004181217820000059
Figure BDA00041812178200000510
wherein ,dvo Dt represents a first derivative of the output voltage; alpha v Representing a reference inductor current magnitude coefficient;
Figure BDA0004181217820000061
representing the magnitude of the reference inductor current; f (F) v Representing a known portion and an unknown portion of the output voltage; c (C) v A control gain set to adjust the output voltage; v (V) in Representing the magnitude of the input voltage; c (C) n A rated capacitance value of the output capacitance; />
Figure BDA00041812178200000611
Representing the magnitude of the reference output voltage; c represents an output capacitance; i.e o Representing the load current;
38 Using differential algebra method to F i and Fv Estimated and used
Figure BDA0004181217820000062
and />
Figure BDA0004181217820000063
Representing the estimated value thereof to obtain an expression of formula (13)
Figure BDA0004181217820000064
wherein ,Ts Is a control period; t (T) F ＝n F T s For sliding window length, n F Is constant and set to 12; considered within a shorter sampling interval
Figure BDA0004181217820000065
and />
Figure BDA0004181217820000066
Is a constant whose derivative is approximately 0; v o (τ) represents the output voltage at τ; i.e L (τ) represents the inductor current at τ; d (τ) represents the duty cycle control signal at τ;
39 For rapidly generating the reference current amplitude, a complex trapezoidal formula and a differential algebra method are applied to realize the output current i o The estimated value expression of the obtained load current is as follows:
Figure BDA0004181217820000067
wherein ,
Figure BDA0004181217820000068
an estimated value representing the load current; t (T) F ＝n F T s Is the sliding window length; c represents an output capacitance; v o (τ) represents the output voltage at τ; i.e L (τ) represents the inductor current at τ; d (τ) represents the duty cycle control signal at τ.
The generation of the stepless coordinated control duty ratio control law comprises the following steps:
41 Setting macro variable of the Boost PFC converter cooperative control system as linear combination of inductance current error term, error term of output voltage and integral term of output voltage error term, and macro variable design as shown in (15)
Figure BDA0004181217820000069
Wherein ψ represents the macro variables of the system; i.e L Representing the inductor current;
Figure BDA00041812178200000610
representing a reference inductor current; k1, k2 and k3 respectively represent control parameters of an inductance current error term, an output voltage error term and an output voltage error integral term;
42 Differentiating the macro variable to obtain an expression of formula (16);
Figure BDA0004181217820000071
where dψ/dt represents the differentiation of the macro-variables; di L Dt represents the derivative of the inductor current; dv o Dt represents the differentiation of the output voltage;
Figure BDA0004181217820000072
representing a reference output voltage; k1, k2 and k3 respectively represent control parameters of an inductance current error term, an output voltage error term and an output voltage error integral term;
43 The dynamic evolution equation for the convergence of the system to the manifold is set as shown in the formula (17):
Figure BDA0004181217820000073
where T represents the convergence time constant of the system towards the manifold surface, T >0；
Figure BDA0004181217820000078
A derivative representing the macro variable;
44 Solving the formulas (15) to (17) to obtain a duty ratio control law of stepless coordinated control as formula (18);
Figure BDA0004181217820000074
wherein d represents a duty cycle control signal; ψ represents the macro variable; k1, k2 and k3 respectively represent control parameters of an inductance current error term, an output voltage error term and an output voltage error integral term; t represents the convergence time constant of the system towards the manifold surface;
Figure BDA0004181217820000075
an estimate representing an uncertainty portion of the inductor current superlocal model; />
Figure BDA0004181217820000076
An estimated value representing an uncertain part of the output voltage superlocal model; alpha i Representing the duty cycle coefficient; alpha v Representing a reference inductor current magnitude coefficient;
45 If constraint is imposed on the duty cycle generated by equation (18), then there are:
Figure BDA0004181217820000077
wherein d is a duty ratio control signal of the switching tube S;
46 Unlike a cascade control system, which removes the voltage outer loop, the reference current amplitude is given by the average conservation of power principle:
Figure BDA0004181217820000081
wherein ,pin Representing the average input power; p is p o Representing the average output power;
Figure BDA0004181217820000082
representing the magnitude of the inductor current reference value;
Figure BDA0004181217820000083
representing a reference output voltage; v (V) in Representing the magnitude of the input voltage; i.e o Representing the load current, load current i o From the estimated value +. >
Figure BDA0004181217820000084
Approximation, but estimate +.>
Figure BDA0004181217820000085
Obtained by the load current estimator in equation (14);
47 To prove the stability of the stepless coordinated control system of the Boost PFC converter, a Lyapunov function is defined
Figure BDA0004181217820000086
Wherein V represents a Lyapunov function, and ψ represents a macro variable of the system;
48 Deriving V when
Figure BDA00041812178200000810
Negative timing, meeting convergence conditions;
Figure BDA0004181217820000087
wherein ,
Figure BDA0004181217820000088
differentiation as Lyapunov function;
because of T>0，ψ 2 > 0, therefore
Figure BDA0004181217820000089
The defined Lyapunov function meets the gradual convergence condition, and the stable operation of the Boost PFC converter system is realized through the proposed stepless cooperative control.
The system of the Boost PFC converter stepless cooperative control method based on the super local model comprises a single-phase Boost PFC converter main circuit and a stepless cooperative control system;
the main circuit of the single-phase Boost PFC converter comprises an uncontrolled rectifier bridge circuit and a Boost converter; the Boost converter comprises a Boost inductor L, a power switch tube S, a freewheel diode D, an output capacitor C and a resistive load R; one end of the Boost inductor L at the input side of the Boost converter is an input end of the Boost converter, and the other end of the Boost inductor L is respectively connected with the anode of the freewheel diode D and the drain electrode of the power switching tube S; the source electrode of the power switch tube S is grounded, and the grid electrode of the power switch tube S is connected with the output end of the PWM modulation module in the cascade model-free predictive control system; the cathode of the freewheeling diode D is connected with one end of the output capacitor C, and the other end of the output capacitor C is grounded; the resistive load R is connected in parallel to two ends of the output capacitor C;
The stepless coordinated control system comprises a PWM modulation module, a reference inductance current value generation module, a load current estimation module and a coordinated control module. The input end of the average filtering module is connected with the output end of the output voltage, and the output end of the average filtering module is connected with the input end of the stepless cooperative controller; the output end of the PWM modulation module is connected with the grid electrode of the power switch tube S; the output end of the reference current value generating module is connected with the input end of the cooperative controller; the input end of the cooperative controller is connected with a reference output voltage value, an inductance current reference value, an output voltage value and an inductance current value which are given by a user, and the output end of the cooperative controller is connected with the input end of the PWM modulation module.
Advantageous effects
Compared with the prior art, the stepless cooperative control method and system for the Boost PFC converter based on the super local model can effectively improve the steady-state control precision of the output voltage of the Boost PFC converter, and has the technical advantages of simple control structure and strong load disturbance resistance under abrupt change of load power, and the dynamic control performance and steady-state operation performance of the Boost PFC converter are comprehensively improved.
The invention designs a stepless linkage cooperative control system of a Boost PFC converter: (1) And an average filtering module is adopted to filter the frequency doubling ripple voltage in the output voltage of the single-phase Boost PFC converter, so that the reference inductance current amplitude generated by ripple voltage pollution is avoided, the calculation delay of a controller is reduced, and the system stability is enhanced. (2) Based on the established super local model of the output voltage and the inductance current of the single-phase Boost PFC converter running in the continuous conduction mode, the stepless cooperative controller is designed, the control structure of the system is simplified, and the robustness and the dynamic response speed of the system to the control of the output voltage are improved. (3) By improving the traditional cooperative control macro-variable design, the designed macro-variable not only comprises an output voltage error term and an inductance current error term, but also increases an integral term of the output voltage error, and improves the steady-state precision of the output voltage of the Boost PFC converter.
The invention designs a macro variable comprising an output voltage error item, an inductance current error item and an output voltage error integral item of the Boost PFC converter based on the establishment of the super-local model of the Boost PFC converter operated in a continuous conduction mode, and designs a dynamic evolution equation, thereby realizing the cooperative control of the inductance current and the output voltage through a cascade-free control structure, effectively improving the steady-state control precision of the output voltage of the Boost PFC converter, having the technical advantages of simple control structure and stronger load disturbance resistance under the abrupt change of load power, and comprehensively improving the dynamic control performance and steady-state operation performance of the Boost PFC converter.
Drawings
FIG. 1 is a process sequence diagram of the present invention;
FIG. 2 is a control block diagram of a Boost PFC converter tandem free cooperative control;
FIG. 3 is a steady-state simulated waveform diagram of input voltage and input current of the tandem free cooperative control system at an output power of 1000 w;
FIG. 4 is a steady-state simulation waveform diagram of input voltage and input current of the stepless coordinated control system at an output power of 600 w;
FIG. 5 is a steady-state simulated waveform diagram of the input voltage and input current of the tandem free control system at an output power of 300 w;
FIG. 6 is a dynamic simulation waveform diagram of the output voltage and input current of the stepless coordinated control system with load power of 1000w stepped to 500 w;
FIG. 7 is a dynamic simulation waveform diagram of the output voltage and input current of the stepless coordinated control system with load power of 500w stepped to 1000 w;
FIG. 8 is a waveform diagram of steady-state experiment of input voltage and input current of the stepless coordinated control system at a load power of 1000 w;
FIG. 9 is a waveform diagram of steady-state experiment of input voltage and input current of the stepless coordinated control system at a load power of 500 w;
FIG. 10 is a graph of a dynamic experimental waveform of the output voltage and input current of a stepless coordinated control system with a load power of 1000w stepped to 500 w;
FIG. 11 is a dynamic simulation waveform diagram of the output voltage and input current of a stepless coordinated control system with a load power of 500w stepped to 1000 w;
fig. 12 is a power factor versus graph of a Boost PFC converter for different load powers and different control methods.
Detailed Description
For a further understanding and appreciation of the structural features and advantages achieved by the present invention, the following description is provided in connection with the accompanying drawings, which are presently preferred embodiments and are incorporated in the accompanying drawings, in which:
as shown in fig. 1, the stepless cooperative control method of the Boost PFC converter based on the super local model disclosed by the invention designs macro variables through a stepless cooperative control strategy, and uniformly manages inductance current and output errors, and aims to simplify a system control structure and make up for the influence of insufficient dynamic response performance caused by indirectly lifting a reference value for a current inner loop by a voltage outer loop in a cascading scheme. Which comprises the following steps:
Step one, boost PFC converter data and average filtering processing: the method comprises the steps of obtaining parameters of a Boost PFC converter, wherein the parameters comprise a Boost inductance L, an output capacitor C, a resistive load R, a freewheeling diode D and a power switch device S, establishing an average state space equation of the Boost PFC converter in a continuous conduction mode, and filtering double frequency ripple waves of output voltage by using an average filtering module.
(1) Boost PFC converter parameters are obtained.
(2) Establishing a dynamic equation of an inductance current of the single-phase Boost PFC converter operating in a continuous conduction mode by adopting the formula (1);
Figure BDA0004181217820000111
wherein ,diL Dt represents a first derivative of the inductor current; l represents a boost inductance value; v in Representing an input voltage; v o Representing an output voltage; d represents the duty cycle control signal of the switching tube S. The method comprises the steps of carrying out a first treatment on the surface of the
(3) Establishing a dynamic equation of output voltage of the single-phase Boost PFC converter operating in a continuous conduction mode by adopting the formula (2);
Figure BDA0004181217820000112
wherein ,dvo Dt represents a first derivative of the output voltage; c represents an output capacitance value; i.e L Representing the inductor current; i.e o Representing the load current; d represents the duty cycle control signal of the switching tube S.
(4) Output voltage v by means of average filter module o [k]Carrying out averaging treatment; obtaining the kth sampling period T by adopting the formula (3) k Average output voltage value V of (a) o [k]；
Figure BDA0004181217820000113
wherein ,Vo [mk]Representing an average output voltage value at a kth sampling point of an mth output voltage period; v o_mk An output voltage sampling value at a kth sampling point of an mth output voltage period;
Figure BDA0004181217820000121
an average voltage value representing a sum of output voltage sampling values at N sampling points of an mth output voltage period; v (V) o [(m-1)N]Average voltage at nth sampling point of (m-1) th output voltage periodA value; v o_(m-1)k An output voltage sample value at a kth sample point of an m-1 th output voltage period; n is the sampling point number in one output voltage period set by a user; m is the number of output voltage cycles, m is a positive integer; i is an integer between 1 and N.
Secondly, building a super local model and carrying out load current estimation: based on the average state space equation of the single-phase Boost PFC converter, the uncertain part F of the super-local model of the output voltage is utilized v Uncertainty part F of inductor current superlocal model i Reference inductor current amplitude
Figure BDA0004181217820000122
Duty cycle coefficient alpha i Reference inductor current amplitude coefficient alpha v Establishing a super local model of output voltage and inductance current of the Boost PFC converter; the load current is estimated using a load current estimation module.
(1) According to the model-free control theory, a first-order super local model of the single-input single-output system is expressed as a formula (4);
Figure BDA0004181217820000123
wherein u and y represent the input and output of the system, respectively; alpha is a proportionality coefficient input by the system; f contains an uncertainty part of the system.
(2) Establishing a super-local model of inductance current of the Boost PFC converter;
Figure BDA0004181217820000124
Figure BDA0004181217820000125
wherein ,diL Dt represents a first derivative of the inductor current; alpha i Representing the duty cycle coefficient; d represents a duty cycle control signal of the switching tube S; f (F) i An uncertainty portion representing an inductor current superlocal model; c (C) i Control gain set to represent inductor current; l (L) n A rated inductance value of the input inductance; l represents boost inductance; v in Representing an input voltage; v o Representing the output voltage.
(3) When the switching tube S is set to be conductive, the freewheeling diode does not work; when the switching tube S is turned off, the freewheeling diode works, and the freewheeling diode and the inductive current have the following expression relationship:
Figure BDA0004181217820000131
(4) Assume that all signals in the output voltage state equation are subjected to averaging processing to eliminate the influence caused by the system double frequency ripple and ignore internal loss in the system, and the average input power and the average output power are represented by the following equations:
Figure BDA0004181217820000132
wherein ,Pin Representing the average input power of the system; v (V) in Representing the magnitude of the input voltage;
Figure BDA0004181217820000133
representing the magnitude of the reference inductor current; p (P) o Representing the average output power of the system; />
Figure BDA0004181217820000139
Representing a reference output voltage magnitude; i D Representing the average diode current.
(5) According to the principle of conservation of power P in ＝P o Deriving an average diode current I D The expression of (2) is:
Figure BDA0004181217820000134
wherein ,ID Representing the average diode current; v (V) in Representing the magnitude of the input voltage;
Figure BDA00041812178200001310
representing a reference output voltage magnitude; />
Figure BDA0004181217820000135
Representing the magnitude of the reference inductor current.
(6) Rearranging a dynamic equation (2) of the output voltage, wherein an average state equation of the output voltage is expressed as:
Figure BDA0004181217820000136
wherein ,dvo Dt represents a first derivative of the output voltage; v (V) in Representing the magnitude of the input voltage; c represents an output capacitance;
Figure BDA00041812178200001311
representing a reference output voltage magnitude; />
Figure BDA0004181217820000137
Representing the magnitude of the reference inductor current; i.e o Representing the load current.
(7) Establishing a super local model of the output voltage of the Boost PFC converter;
Figure BDA0004181217820000138
Figure BDA0004181217820000141
wherein ,dvo Dt represents a first derivative of the output voltage; alpha v Representing a reference inductor current magnitude coefficient;
Figure BDA0004181217820000149
representing the magnitude of the reference inductor current; f (F) v An uncertainty section representing an output voltage superlocal model; c (C) v A control gain set to adjust the output voltage; v (V) in Representing the magnitude of the input voltage; c (C) n A rated capacitance value of the output capacitance; />
Figure BDA00041812178200001410
Representing the magnitude of the reference output voltage; c represents an output capacitance; i.e o Representing the load current.
(8) Using differential algebra method to F i and Fv Estimated and used
Figure BDA0004181217820000142
and />
Figure BDA0004181217820000143
Representing the estimated value thereof to obtain an expression of formula (13)
Figure BDA0004181217820000144
wherein ,Ts Is a control period; t (T) F ＝n F T s For sliding window length, n F Is constant and set to 12; considered within a shorter sampling interval
Figure BDA0004181217820000145
and />
Figure BDA0004181217820000146
Is a constant whose derivative is approximately 0; v o (τ) represents the output voltage at τ; i.e L (τ) represents the inductor current at τ; d (τ) represents the duty cycle control signal at τ.
(9) For rapidly generating the reference current amplitude, a complex trapezoidal formula and a differential algebra method are applied to realize the output current i o The estimated value of the obtained load current is expressed as follows:
Figure BDA0004181217820000147
wherein ,
Figure BDA0004181217820000148
an estimated value representing the load current; t (T) F ＝n F T s Is the sliding window length; c represents an output capacitance; v o (τ) represents the output voltage at τ; i.e L (τ) represents the inductor current at τ; d (τ) represents the duty cycle control signal at τ.
Thirdly, generating a stepless coordinated control duty ratio control law: based on a super-local model of the Boost PFC converter, developing macro-variable design comprising an output voltage error term, an inductance current error term and an integral term of the output voltage error, and designing a dynamic evolution equation for converging a system to a manifold; and the duty ratio control law of stepless coordinated control is generated by the related dynamic evolution equation and the duty ratio required to be satisfied by the system operation.
(1) The macro variable of the Boost PFC converter cooperative control system is set as the linear combination of an inductance current error term, an output voltage error term and an integral term of the output voltage error term, and the macro variable is designed as shown in the specification (15)
Figure BDA0004181217820000151
Wherein ψ represents the macro variables of the system; i.e L Representing the inductor current;
Figure BDA0004181217820000152
representing a reference inductor current; k1, k2, k3 represent the control parameter coefficients of the inductor current error term, the output voltage error term, and the output voltage error integral term, respectively.
(2) Differentiating the macro variable to obtain an expression of formula (16);
Figure BDA0004181217820000153
where dψ/dt represents the differentiation of the macro-variables; di L Dt represents the derivative of the inductor current; dv o Dt represents the differentiation of the output voltage;
Figure BDA0004181217820000154
representing a reference output voltage; k1, k2, k3 represent the control parameter coefficients of the inductor current error term, the output voltage error term, and the output voltage error integral term, respectively.
(3) The dynamic evolution equation for setting the system to converge towards the manifold is shown in the formula (17):
Figure BDA0004181217820000155
where T represents the convergence time constant of the system towards the manifold surface, T>0；
Figure BDA0004181217820000156
Representing the derivative of the macro variable.
(4) Solving the formulas (15) to (17) to obtain a duty ratio control law of stepless coordinated control as formula (18);
Figure BDA0004181217820000157
wherein d represents a duty cycle control signal; ψ represents the macro variable; k1, k2 and k3 respectively represent control parameter coefficients of an inductance current error term, an output voltage error term and an output voltage error integral term; t systems tend to converge time constants for the manifold facets;
Figure BDA0004181217820000158
An estimate representing an uncertainty portion of the super-local model of the inductor current; />
Figure BDA0004181217820000159
Representing output electricityAn estimate of the uncertain part of the super local model of the pressure; alpha i Representing the duty cycle coefficient; alpha v Representing the reference inductor current magnitude coefficient.
(5) Constraint on the duty cycle generated by equation (18) is:
Figure BDA0004181217820000161
where d is the control signal of the duty cycle.
(6) Unlike a cascade control system, which removes the voltage outer loop, the reference current amplitude is given by the average conservation of power principle:
Figure BDA0004181217820000162
wherein ,pin Representing the average input power; p is p o Representing the average output power;
Figure BDA0004181217820000163
representing a reference inductor current magnitude;
Figure BDA0004181217820000164
representing a reference output voltage; v (V) in Representing the magnitude of the input voltage; i.e o Representing the load current, load current i o From the estimated value +.>
Figure BDA0004181217820000165
Approximation, but estimate +.>
Figure BDA0004181217820000166
Obtained by the load current estimator in equation (14). />
(7) In order to prove the stability of the stepless tandem cooperative control system of the Boost PFC converter, a Lyapunov function is defined
Figure BDA0004181217820000167
Where V represents the lyapunov function and ψ represents the macro variables of the system.
(8) Deriving V when
Figure BDA00041812178200001611
Negative timing, meeting convergence conditions;
Figure BDA0004181217820000168
wherein ,
Figure BDA0004181217820000169
differentiation as Lyapunov function;
because of T>0，ψ 2 > 0, therefore
Figure BDA00041812178200001610
The defined Lyapunov function meets the gradual convergence condition, and the fact that the proposed stepless cooperative control realizes stable operation of the Boost PFC converter system is proved.
Step four, stepless coordinated control of the Boost PFC converter: and modulating the duty ratio control signal by using a PWM (pulse-width modulation) module to obtain a power switch device driving signal S [ k ] of a kth period, and controlling the action of a power switch device S of the Boost PFC converter to realize stepless coordinated control of the Boost PFC converter based on the super local model.
As shown in fig. 2, a system of the stepless cooperative control method of the Boost PFC converter based on the super local model is further provided, and the single-phase Boost PFC converter comprises a main circuit of the single-phase Boost PFC converter and the stepless cooperative control system.
The main circuit of the single-phase Boost PFC converter comprises an uncontrolled rectifier bridge circuit and a Boost converter, wherein the Boost converter comprises a Boost inductor L, a power switching device (tube) S, a freewheeling diode D, an output capacitor C and a resistive load R; one end of the Boost inductor L at the input side of the Boost converter is an input end of the Boost converter, and the other end of the Boost inductor L is respectively connected with the anode of the freewheel diode D and the drain electrode of the power switching device S; the source electrode of the power switch device S is grounded, and the grid electrode of the power switch device S is connected with the output end of a PWM modulation module in the cascade model-free predictive control system; the cathode of the freewheeling diode D is connected with one end of the output capacitor C, and the other end of the output capacitor C is grounded; the resistive load R is connected in parallel to two ends of the output capacitor C;
The stepless coordinated control system comprises a PWM modulation module, a reference inductance current value generation module, a load current estimation module and a coordinated control module. The input end of the average filtering module is connected with the output end of the output voltage, and the output end of the average filtering module is connected with the input end of the model-free prediction voltage controller; the output end of the PWM modulation module is connected with the grid electrode of the power switch device S; the output end of the reference current value generating module is connected with the input end of the cooperative controller; the input end of the cooperative controller is connected with a reference output voltage value, an inductance current reference value, an output voltage value and an inductance current value which are given by a user, and the output end of the cooperative controller is connected with the input end of the PWM modulation module.
In order to verify the effectiveness of the control method of the stepless coordinated control system, matlab/simulink simulation is carried out, and the specific process of the Matlab/simulink simulation is as follows:
and establishing a simulation model of the control system of the single-phase Boost PFC converter controlled by the stepless coordinated control shown in the figure 2 by Matlab/simulink software. The parameters of the main circuit of the converter are as follows: rated load power 1000W, AC input voltage 110V/50Hz, DC output voltage 300V, boost inductor 486 muH, output capacitor 990 muF, switching frequency 50kHz, n F Data window length n of (2) F The number of sampling points n=20 in the average filtering algorithm module.
The macro variable ψ will decay exponentially with the time constant T, after 3T-4T the system approaches the manifold and thereafter the system remains running on the manifold. Dynamic response time T of Boost PFC converter according to transient response process of system d About 0.16s, the time constant T has a value in the range of [ T ] d /4，T d /3]Therefore, the time constant T is 0.04. The macro-variable design mainly comprises three parameters: error of inductance currentThe difference coefficient k1, the output voltage error coefficient k2 and the voltage error integral coefficient k3. The coefficient k1 defines the magnitude of the inductor current weight factor in the macro-variable, the magnitude of which affects the waveform quality of the inductor current. When the system reaches the manifold surface, the proportion parameters of the system need to balance the output voltage and the inductance current control performance. When the relative proportion of the current error term coefficient is increased, the performance of the controller for tracking the reference value of the actual value of the inductance current is improved, but the tracking error of the output voltage is larger; when the relative proportion of the voltage error term coefficient is increased, the dynamic response speed of the controller to the output voltage is increased, but the waveform quality of the inductance current is affected; when the relative proportion of the output voltage error integral term coefficient increases, the controller increases the accuracy of the output voltage when reaching steady state. Through data debugging of multiple groups of simulation and experiments, k1, k2 and k3 are respectively set to be 1, 0.4 and 10.
The simulation result of the system through Matlab/Simulink is shown in figures 3-12; wherein i is ac Representing the input current of the converter; i.e ac ref A reference value representing the converter input current; v o Representing the output voltage of the converter. Fig. 3, fig. 4 and fig. 5 show waveforms of input voltage, input current and input current reference values when the load power is 1000w, 600w and 300w respectively under the stepless coordinated control scheme, it can be seen that the input current quality is improved to a certain extent, and the inductor current reference value is generated by adopting algebraic identification technology to estimate the inductor current on line and utilizing the principle of power conservation under the stepless coordinated control scheme based on super local model design. Because the influence of factors such as actual switching loss, conduction voltage drop and the like is considered, the inductor current reference value cannot be accurately generated, and steady-state errors are caused. The integral term of the output voltage error is added on the basis of designing the traditional macro-variable, so that the steady-state performance of the system is further improved.
FIG. 6 shows a dynamic simulation waveform diagram of output voltage and input current of the converter with load power of 1000w stepped to 500w under tandem free cooperative control; fig. 7 shows a dynamic simulation waveform diagram of the output voltage and input current of the converter with a load power of 500w stepped to 1000w under tandem free control. The method has the advantages that the output voltage recovery response speed is high, the stabilization time is short, the inductance current and the output voltage are uniformly managed under the stepless linkage cooperative control scheme based on the super-local model design, the influence of insufficient dynamic response caused by the fact that a voltage outer ring indirectly provides a reference value for a current inner ring under the traditional cascade control scheme is overcome, and the purpose of accelerating the dynamic response performance of a system is achieved.
FIG. 8 shows steady-state experimental waveforms of input voltage and input current of the tandem free cooperative control system at a load power of 1000 w; FIG. 9 is a waveform diagram of steady-state experiment of input voltage and input current of the stepless coordinated control system at a load power of 500 w; FIG. 10 is a graph showing a dynamic experimental waveform of the output voltage and input current of a stepless coordinated control system with a load power of 1000w stepped to 500 w; fig. 11 is a dynamic experimental waveform diagram showing the output voltage and input current of a tandem free cooperative control system with a load power of 500w stepped to 1000 w. Therefore, the experimental result is consistent with the simulation result, and the stepless coordinated control scheme based on the super local model has higher control precision and convergence rate, and combines the steady-state operation performance and the dynamic control performance of the Boost PFC converter system.
Fig. 12 shows the power factor of the Boost PFC converter input current for different control schemes. The stepless coordinated control scheme is better than the cascading model-free control and PI control scheme, particularly, when the low-power load is output, the stepless coordinated control obviously improves the power factor of the input current, and optimizes the current quality of the input current of the Boost converter.
In summary, the proposed stepless coordinated control scheme based on the super local model can give consideration to both the dynamic control performance and the steady-state operation performance of the system.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention, which is defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. A Boost PFC converter stepless cooperative control method based on a super local model is characterized by comprising the following steps:
11 Boost PFC converter data and average filtering process: acquiring parameters of a Boost PFC converter, wherein the parameters comprise a Boost inductor L, an output capacitor C, a resistive load R, a freewheeling diode D and a power switch tube S, establishing an average state space equation of the Boost PFC converter in a continuous conduction mode, and filtering double frequency ripple waves of an output voltage by using an average filtering module;
12 Building a super local model and carrying out load current estimation: based on the average state space equation of the single-phase Boost PFC converter, the uncertain part F of the super-local model of the output voltage is utilized v Uncertainty part F of inductor current superlocal model i Reference inductor current amplitude
Figure FDA0004181217810000011
Duty cycle coefficient alpha i Reference inductance current amplitude coefficient alpha v Establishing a super local model of output voltage and inductance current of the Boost PFC converter; estimating a load current by using a load current estimation module;
13 Generation of a tandem free cooperative control duty cycle control law): based on a super-local model of the Boost PFC converter, developing macro-variable design comprising an output voltage error term, an inductance current error term and an output voltage error integral term, and designing a dynamic evolution equation for converging a system to a manifold; and generating a duty ratio control law of stepless coordinated control by means of the designed dynamic evolution equation and the duty ratio required to be satisfied by the system operation;
14 Tandem free cooperative control of Boost PFC converter): and modulating the duty ratio control signal by using a PWM (pulse-width modulation) module to obtain a power switch device driving signal S [ k ] of a kth period, and controlling the action of a power switch tube S of the Boost PFC converter to realize stepless coordinated control of the Boost PFC converter based on the super local model.
2. The method for tandem free control of a Boost PFC converter based on a super local model according to claim 1, wherein the processing of data and average filtering of the Boost PFC converter comprises the steps of:
21 Acquiring Boost PFC converter parameters;
22 Using formula (1) to establish a dynamic equation of inductance current of the single-phase Boost PFC converter operating in a continuous conduction mode;
Figure FDA0004181217810000012
wherein ,diL Dt represents a first derivative of the inductor current; l represents a boost inductance value; v in Representing an input voltage; v o Representing an output voltage; d represents a duty cycle control signal of the switching tube S;
23 Establishing an output voltage dynamic equation of the single-phase Boost PFC converter operating in a continuous conduction mode by adopting the formula (2);
Figure FDA0004181217810000021
wherein ,dvo Dt represents a first derivative of the output voltage; c represents an output capacitance value; i.e L Representing the inductor current; i.e o Representing the load current; d represents a duty cycle control signal of the switching tube S;
24 Using an average filter module to output voltage v o [k]Carrying out averaging treatment; obtaining the kth sampling period T by adopting the formula (3) k Average output voltage value V of (a) o [k]；
Figure FDA0004181217810000022
wherein ,Vo [mk]Representing an average output voltage value at a kth sampling point of an mth output voltage period; v o_mk An output voltage sampling value at a kth sampling point of an mth output voltage period;
Figure FDA0004181217810000023
An average voltage value representing a sum of output voltage sampling values at N sampling points of an mth output voltage period; v (V) o [(m-1)N]An average voltage value at an nth sampling point of an m-1 th output voltage period; v o_(m-1)k An output voltage sample value at a kth sample point of an m-1 th output voltage period; n is the sampling point number in one output voltage period set by a user; m is the number of output voltage cycles, m is a positive integer; i is an integer between 1 and N.
3. The superlocal model-based Boost PFC converter tandem free cooperative control method according to claim 1, wherein the establishing the superlocal model and the load current estimation include the steps of:
31 According to the model-free control theory, the first-order super local model of the single-input single-output system is expressed as a formula (4);
Figure FDA0004181217810000031
wherein u and y represent the input and output of the system, respectively; alpha is a scale factor input by the system; f comprises a known part and an unknown part of the system;
32 Building a super-local model of the inductance current of the Boost PFC converter;
Figure FDA0004181217810000032
Figure FDA0004181217810000033
wherein ,diL Dt represents a first derivative of the inductor current; alpha i Representing the duty cycle coefficient; d represents a duty cycle control signal of the switching tube S; f (F) i Representing a known portion and an unknown portion of the inductor current superlocal model; c (C) i Representing an adjustable constant parameter; l (L) n A rated inductance value of the input inductance; l represents boost inductance; v in Representing an input voltage; v o Representing an output voltage;
33 When the switch tube S is set to be conducted, the freewheel diode does not work; when the switching tube S is turned off, the freewheeling diode works, and the freewheeling diode and the inductive current have the following expression relationship:
Figure FDA0004181217810000034
34 Assume that all signals in the output voltage state equation are averaged to eliminate the influence of the system double frequency ripple and to ignore the internal loss in the system, the average input power and the average output power are represented by the following equations:
Figure FDA0004181217810000035
wherein ,Pin Representing the average input power of the system; v (V) in Representing the magnitude of the input voltage;
Figure FDA0004181217810000036
representing the magnitude of the reference inductor current; p (P) o Representing the average output power of the system; />
Figure FDA0004181217810000037
Representing the magnitude of the reference output voltage; i D Representing the average diode current;
35 According to principle of conservation of power P in ＝P o Deriving an average diode current I D The expression of (2) is:
Figure FDA0004181217810000041
wherein ,ID Representing the average diode current; v (V) in Representing the magnitude of the input voltage;
Figure FDA0004181217810000042
representing the magnitude of the reference output voltage;
Figure FDA0004181217810000043
representing the magnitude of the reference inductor current;
36 Rearranging a dynamic equation (2) of the output voltage, the average state equation of the output voltage being expressed as:
Figure FDA0004181217810000044
wherein ,dvo Dt represents a first derivative of the output voltage; v (V) in Representing the magnitude of the input voltage; c represents an output capacitance;
Figure FDA0004181217810000045
representing the magnitude of the reference output voltage; />
Figure FDA0004181217810000046
Representing the magnitude of the reference inductor current; i.e o Representing the load current;
37 Building a super local model of the output voltage of the Boost PFC converter;
Figure FDA0004181217810000047
Figure FDA0004181217810000048
wherein ,dvo Dt represents a first derivative of the output voltage; alpha v Representing a reference inductor current magnitude coefficient;
Figure FDA0004181217810000049
representing the magnitude of the reference inductor current; f (F) v Representing a known portion and an unknown portion of the output voltage; c (C) v A control gain set to adjust the output voltage; v (V) in Representing the magnitude of the input voltage; c (C) n A rated capacitance value of the output capacitance; />
Figure FDA00041812178100000410
Representing the magnitude of the reference output voltage; c represents an output capacitance; i.e o Representing the load current;
38 Using differential algebra method to F i and Fv Estimated and used
Figure FDA00041812178100000411
and />
Figure FDA00041812178100000412
Representing the estimated value thereof to obtain an expression of formula (13)
Figure FDA00041812178100000413
wherein ,Ts Is a control period; t (T) F ＝n F T s For sliding window length, n F Is constant and set to 12; considered within a shorter sampling interval
Figure FDA00041812178100000414
and />
Figure FDA00041812178100000415
Is a constant whose derivative is approximately 0; v o (τ) represents the output voltage at τ; i.e L (τ) represents the inductor current at τ; d (τ) represents the duty cycle control signal at τ;
39 For rapidly generating the reference current amplitude, a complex trapezoidal formula and a differential algebra method are applied to realize the output current i o The estimated value expression of the obtained load current is as follows:
Figure FDA0004181217810000051
wherein ,
Figure FDA0004181217810000052
an estimated value representing the load current; t (T) F ＝n F T s Is the sliding window length; c represents an output capacitance; v o (τ) represents the output voltage at τ; i.e L (τ) represents the inductor current at τ; d (τ) represents the duty cycle control signal at τ.
4. The method for tandem free control of a Boost PFC converter based on a super local model according to claim 1, wherein the generating of the tandem free control duty cycle control law includes the steps of:
41 Setting macro variable of the Boost PFC converter cooperative control system as linear combination of inductance current error term, error term of output voltage and integral term of output voltage error term, and macro variable design as shown in (15)
Figure FDA0004181217810000053
Wherein ψ represents the macro variables of the system; i.e L Representing the inductor current;
Figure FDA0004181217810000054
representing a reference inductor current; k1, k2 and k3 respectively represent control parameters of an inductance current error term, an output voltage error term and an output voltage error integral term;
42 Differentiating the macro variable to obtain an expression of formula (16);
Figure FDA0004181217810000055
Where dψ/dt represents the differentiation of the macro-variables; di L Dt represents the derivative of the inductor current; dv o Dt represents the differentiation of the output voltage;
Figure FDA0004181217810000056
representing a reference output voltage; k1, k2 and k3 respectively represent control parameters of an inductance current error term, an output voltage error term and an output voltage error integral term;
43 The dynamic evolution equation for the convergence of the system to the manifold is set as shown in the formula (17):
Figure FDA0004181217810000057
where T represents the convergence time constant of the system towards the manifold surface, T>0；
Figure FDA0004181217810000058
A derivative representing the macro variable;
44 Solving the formulas (15) to (17) to obtain a duty ratio control law of stepless coordinated control as formula (18);
Figure FDA0004181217810000061
wherein d represents a duty cycle control signal; ψ represents the macro variable; k1, k2, k3 represent an inductor current error term, an output voltage error term and an output, respectivelyOutputting control parameters of voltage error integral items; t represents the convergence time constant of the system towards the manifold surface;
Figure FDA0004181217810000062
an estimate representing an uncertainty portion of the inductor current superlocal model; />
Figure FDA0004181217810000063
An estimated value representing an uncertain part of the output voltage superlocal model; alpha i Representing the duty cycle coefficient; alpha v Representing a reference inductor current magnitude coefficient;
45 If constraint is imposed on the duty cycle generated by equation (18), then there are:
Figure FDA0004181217810000064
wherein d is a duty ratio control signal of the switching tube S;
46 Unlike a cascade control system, which removes the voltage outer loop, the reference current amplitude is given by the average conservation of power principle:
Figure FDA0004181217810000065
wherein ,pin Representing the average input power; p is p o Representing the average output power;
Figure FDA0004181217810000066
representing the magnitude of the inductor current reference value; />
Figure FDA0004181217810000067
Representing a reference output voltage; v (V) in Representing the magnitude of the input voltage; i.e o Representing the load current, load current i o From the estimated value +.>
Figure FDA0004181217810000068
Approximation, but estimate +.>
Figure FDA0004181217810000069
Obtained by the load current estimator in equation (14);
47 To prove the stability of the stepless coordinated control system of the Boost PFC converter, a Lyapunov function is defined
Figure FDA00041812178100000610
Wherein V represents a Lyapunov function, and ψ represents a macro variable of the system;
48 Deriving V when
Figure FDA00041812178100000611
Negative timing, meeting convergence conditions;
Figure FDA0004181217810000071
wherein ,
Figure FDA0004181217810000072
differentiation as Lyapunov function;
because of T>0，ψ 2 > 0, therefore
Figure FDA0004181217810000073
The defined Lyapunov function meets the gradual convergence condition, and the stable operation of the Boost PFC converter system is realized through the proposed stepless cooperative control.
5. The system of the superlocal model-based Boost PFC converter tandem free operation cooperative control method according to claim 1, wherein: the single-phase Boost PFC converter comprises a single-phase Boost PFC converter main circuit and a stepless cooperative control system;
The main circuit of the single-phase Boost PFC converter comprises an uncontrolled rectifier bridge circuit and a Boost converter; the Boost converter comprises a Boost inductor L, a power switch tube S, a freewheel diode D, an output capacitor C and a resistive load R; one end of the Boost inductor L at the input side of the Boost converter is an input end of the Boost converter, and the other end of the Boost inductor L is respectively connected with the anode of the freewheel diode D and the drain electrode of the power switching tube S; the source electrode of the power switch tube S is grounded, and the grid electrode of the power switch tube S is connected with the output end of the PWM modulation module in the cascade model-free predictive control system; the cathode of the freewheeling diode D is connected with one end of the output capacitor C, and the other end of the output capacitor C is grounded; the resistive load R is connected in parallel to two ends of the output capacitor C;
the stepless coordinated control system comprises a PWM modulation module, a reference inductance current value generation module, a load current estimation module and a coordinated control module. The input end of the average filtering module is connected with the output end of the output voltage, and the output end of the average filtering module is connected with the input end of the stepless cooperative controller; the output end of the PWM modulation module is connected with the grid electrode of the power switch tube S; the output end of the reference current value generating module is connected with the input end of the cooperative controller; the input end of the cooperative controller is connected with a reference output voltage value, an inductance current reference value, an output voltage value and an inductance current value which are given by a user, and the output end of the cooperative controller is connected with the input end of the PWM modulation module.
CN202310405497.4A 2023-04-17 2023-04-17 Boost PFC converter stepless cooperative control method and system based on super local model Pending CN116317489A (en)

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