CN113179017A - Half-bridge type bidirectional DC-DC converter control loop compensation method - Google Patents

Half-bridge type bidirectional DC-DC converter control loop compensation method Download PDF

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CN113179017A
CN113179017A CN202110571214.4A CN202110571214A CN113179017A CN 113179017 A CN113179017 A CN 113179017A CN 202110571214 A CN202110571214 A CN 202110571214A CN 113179017 A CN113179017 A CN 113179017A
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voltage
current
loop
converter
transfer function
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郭颖娜
成欢
马昭
宋久旭
白思思
王淇民
孙锐
刘海峰
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Xian Shiyou University
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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
    • 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
    • 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

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  • Power Engineering (AREA)
  • Dc-Dc Converters (AREA)

Abstract

The invention discloses a compensation method for a control loop of a half-bridge bidirectional DC-DC converter, which comprises the steps of firstly establishing mathematical models of the half-bridge bidirectional DC-DC converter in different modes, and respectively deducing transfer functions of inductive current and output voltage to control variables and transfer functions of the output voltage to the inductive current in a BOOST mode and a BUCK mode; then designing a voltage and current double closed loop feedback control strategy based on a PI controller, and designing power circuit parameters of a half-bridge type bidirectional DC-DC converter; and finally, combining a system transfer function in a BOOST mode and a BUCK mode, an open-loop transfer function of a voltage and current double closed-loop feedback control system and power circuit parameters to obtain the double closed-loop half-bridge type bidirectional DC-DC converter added with double-loop compensation. The invention solves the problems of low power utilization rate and poor system power quality caused by distributed power supply intermittency and load fluctuation in the prior art.

Description

Half-bridge type bidirectional DC-DC converter control loop compensation method
Technical Field
The invention belongs to the technical field of bidirectional DC-DC converter control loop compensation, and particularly relates to a compensation method for a control loop of a half-bridge type bidirectional DC-DC converter.
Background
In recent years, with rapid progress of distributed power supplies and energy storage technologies and gradual increase of direct current load proportion, a direct current microgrid capable of integrating various distributed power supplies, loads, energy storage devices and energy conversion devices has received wide attention in domestic and foreign industries and academic circles. The distributed power supply has the characteristics of intermittence, easy fluctuation and large influence by weather conditions, and the problems of voltage fluctuation of a direct-current bus and the like caused when various loads are connected into a direct-current micro-grid system. Therefore, the reasonable use, distribution and storage of the energy are very important. In order to solve the above problems, an energy storage system including a bidirectional DC-DC converter is an indispensable link. The half-bridge type bidirectional DC-DC converter is used as one of the bidirectional DC-DC converters and has the advantages of simple topological structure and control mode, small voltage and current stress of a switching element, high transmission efficiency and the like. Therefore, the bidirectional flow of electric energy can be realized by reasonably controlling the half-bridge type bidirectional DC-DC converter, the peak clipping and valley filling effects are achieved, the voltage fluctuation can be inhibited, and the purposes of effectively improving the utilization rate of the distributed power supply and the electric energy quality of the system are achieved.
Disclosure of Invention
The invention aims to provide a compensation method for a control loop of a half-bridge bidirectional DC-DC converter, which solves the problems of low power utilization rate and poor system power quality caused by intermittent distributed power supply and load fluctuation in the prior art.
The technical scheme adopted by the invention is that the compensation method of the control loop of the half-bridge bidirectional DC-DC converter is implemented according to the following steps:
step 1, establishing mathematical models of a half-bridge bidirectional DC-DC converter in different modes, and respectively deducing transfer functions of inductive current and output voltage to control variables and transfer functions of output voltage to inductive current in a BOOST mode and a BUCK mode;
step 2, designing a voltage and current double closed loop feedback control strategy based on a PI controller, and controlling the half-bridge type bidirectional DC-DC converter to still ensure stable output under the condition of disturbance;
step 3, designing power circuit parameters of the half-bridge type bidirectional DC-DC converter;
and 4, combining the system transfer function in the BOOST mode and the BUCK mode obtained in the step 1, the open-loop transfer function of the voltage and current double closed-loop feedback control system obtained in the step 2 and the power circuit parameters obtained in the step 3, designing voltage and current loop PI parameters of the half-bridge type bidirectional DC-DC converter system, substituting the designed voltage and current loop PI parameters into the voltage and current double closed-loop feedback control strategy in the step 2, and obtaining the double-loop compensated double-closed-loop type bidirectional DC-DC converter.
The present invention is also characterized in that,
the step 1 is implemented according to the following steps:
step 1.1, a method for averaging variables in a switching period is adopted, namely, a variable x (T) is defined in the switching period TsMean value of
Figure BDA0003082652250000021
Comprises the following steps:
Figure BDA0003082652250000022
wherein:
Figure BDA0003082652250000023
representing the variable x (T) during the switching period TsAverage value of (d); t issRepresents a switching cycle; x (t) denotes a certain of the switching convertersA variable; t represents a time variable; τ represents an integral variable;
step 1.2, when the BOOST converter works in a continuous conduction mode CCM, the converter circuit is divided into two stages in a steady state, and the time intervals of the two stages are respectively set as follows: [ t, t + d ]1(t)Ts]And [ t + d1(t)Ts,t+Ts]Then the voltage v of the inductor in the converter circuitL(t) and a capacitance current iC(t) are respectively expressed as:
Figure BDA0003082652250000031
wherein: v. ofL(t) represents an inductor voltage; l represents an inductance; i.e. iL(t) represents an inductor current; v. ofg(t) represents a battery side voltage; v. ofo(t) represents a direct current bus side voltage; d1(t) represents the BOOST mode duty cycle;
Figure BDA0003082652250000032
wherein: i.e. iC(t) represents a capacitance current; c1Represents the direct current bus side capacitance; r1Representing a load resistance;
step 1.3, when the converter meets the low-frequency assumption and the small ripple assumption, vg(t)、vo(t) and iL(t) approximating the value over the entire switching period interval by the average value of the switching period
Figure BDA0003082652250000033
And
Figure BDA0003082652250000034
in this case, the expressions (2) and (3) are expressed as follows:
Figure BDA0003082652250000035
Figure BDA0003082652250000036
wherein:
Figure BDA0003082652250000037
represents the average value of the inductor current in the switching period;
Figure BDA0003082652250000038
represents an average value of the battery side voltage in the switching period;
Figure BDA0003082652250000039
the average value of the voltage on the direct current bus side in a switching period is represented;
step 1.4, defining the average value of the switching period of each variable by adopting the formula (1), and then, obtaining the average value of the switching period of the inductive voltage
Figure BDA00030826522500000310
Comprises the following steps:
Figure BDA0003082652250000041
wherein:
Figure BDA0003082652250000042
represents the average value of the inductor voltage in the switching period;
if further consider that
Figure BDA0003082652250000043
And
Figure BDA0003082652250000044
approximately constant during a switching cycle, it follows from equation (6):
Figure BDA0003082652250000045
in the same way, according to electricityThe sectional expression of the capacitance current is obtained by the same analysis method
Figure BDA0003082652250000046
Comprises the following steps:
Figure BDA0003082652250000047
wherein:
Figure BDA0003082652250000048
represents the average value of the capacitance current in the switching period;
step 1.5, introducing low-frequency small signal disturbance near a static working point of the converter so as to carry out linearization processing on the converter, and inputting a variable v in the BOOST converterg(t), state variable iL(t)、vo(t) average variation
Figure BDA0003082652250000049
And
Figure BDA00030826522500000410
and a control variable d1(t) decomposing it into a sum of a direct current component and an alternating current small signal component, namely:
Figure BDA00030826522500000411
wherein: vg、IL、VoAnd D1A direct current component representing a corresponding variable;
Figure BDA00030826522500000412
and
Figure BDA00030826522500000413
an alternating current component representing a corresponding variable;
step 1.6, decomposing the average variables in the formulas (7) and (8) into the sum of corresponding direct current components and alternating current small signal components according to the formula (9) to obtain:
Figure BDA0003082652250000051
after the same terms are combined and arranged in the formula, the corresponding direct current terms are equal and the corresponding alternating current terms are equal, and the linear state equation of the alternating current small signal determined according to the working characteristics of the inductor and the capacitor can be obtained by omitting second-order tiny quantity as follows:
Figure BDA0003082652250000052
step 1.7, equation (11) is a second-order dynamic model of the BOOST converter circuit in the time domain in the CCM mode, the model is the basis of closed-loop feedback control design of the converter system, the equation obtained in equation (11) is subjected to the lagrange transformation, and the time domain model is transformed to the S domain to obtain the transfer function of the S domain of the BOOST converter:
Figure BDA0003082652250000053
wherein: s represents a dummy variable;
Figure BDA0003082652250000054
representing the alternating current component of the S-domain inductive current;
Figure BDA0003082652250000055
representing the alternating-current component of the voltage at the side of the S-domain direct-current bus;
Figure BDA0003082652250000056
representing the alternating-current component of the voltage of the storage battery side in the S domain;
Figure BDA0003082652250000057
representing the duty ratio alternating current component of the S-domain BOOST mode;
in the formula (12), the AC component of the battery side voltage in the S domain
Figure BDA0003082652250000058
Obtaining a corresponding transfer function of the BOOST converter in a CCM mode, and obtaining a transfer function G of the output voltage of the BOOST converter to a control variable in the CCM modevd1(s) is:
Figure BDA0003082652250000059
transfer function G of BOOST converter inductive current to control variable in CCM modeid1(s) is:
Figure BDA0003082652250000061
transfer function G of output voltage of BOOST converter to inductive current in CCM modevi1(s) is:
Figure BDA0003082652250000062
and similarly, obtaining a corresponding transfer function of the BUCK converter in the CCM mode, and obtaining a transfer function G of the output voltage of the BUCK converter to the control variable in the CCM modevd2(s) is:
Figure BDA0003082652250000063
wherein: c2Represents the battery side capacitance; r2Represents the battery-side equivalent resistance;
Figure BDA0003082652250000064
representing an S-domain BUCK mode duty ratio alternating current component;
transfer function G of BUCK converter inductive current to control variable in CCM modeid2(s) is:
Figure BDA0003082652250000065
transfer function G of output voltage of BUCK converter to inductive current in CCM modevi2(s) is:
Figure BDA0003082652250000066
the step 2 is implemented according to the following steps:
step 2.1, in the BOOST mode, the voltage outer ring is composed of a voltage sampling resistor R2And R3Forming a voltage sampling network, and collecting output voltage V in BOOST modeoObtaining a voltage signal V after resistance voltage division1And a reference voltage value VrefAfter comparison, the voltage is sent to a voltage controller VA via a compensation resistor R4、R5And a compensation capacitor C3The compensation network generates a voltage signal V after compensationVA1To obtain, the current inner ring is sampled by the current sampling resistor RSAcquiring the current value of the inductor to obtain a voltage feedback signal VRSAnd is connected with the voltage signal V generated by the voltage outer loopVA1After comparison, the voltage is sent to a current controller CA via a compensation resistor R6、R7And a compensation capacitor C4The compensation network generates a voltage signal V after compensationCA1Obtaining a voltage signal V after the current inner loop compensationCA1And sawtooth wave signal VMAfter comparison, a PWM control signal is generated, and the switching tube Q is controlled2The stability of the system is controlled by the change of the duty ratio, and similarly, a BUCK mode voltage and current double closed-loop compensation network is designed by using the same design method;
step 2.2, respectively obtaining an open loop transfer function of a voltage current loop of the half-bridge type bidirectional DC-DC converter and an open loop transfer function G of a current inner loop of the half-bridge type bidirectional DC-DC converter according to the converter system transfer functions deduced by the formulas (14), (15), (17) and (18)iop(s) is:
Figure BDA0003082652250000071
wherein: gpic(s) represents the transfer function of the current inner loop PI controller;
Figure BDA0003082652250000072
representing a transfer function of the PWM controller; vmRepresenting a sawtooth wave peak-to-peak value; gid(s) represents the transfer function of the inductor current to the control variable; hcRepresenting an inductor current sampling coefficient;
open-loop transfer function G of voltage outer ring of half-bridge type bidirectional DC-DC convertervop(s) is:
Figure BDA0003082652250000073
wherein: gpiv(s) represents the transfer function of the voltage outer loop PI controller; gvi(s) represents the transfer function of the output voltage to the inductor current; hvRepresenting the voltage sampling coefficient.
Step 2.2 sawtooth Peak VmInductance current sampling coefficient H1 c1, voltage sampling coefficient Hv＝1。
In the step 3, the power circuit parameter design of the half-bridge type bidirectional DC-DC converter comprises a voltage V at the side of the direct current buso(ii) a Battery side voltage Vg(ii) a Switching frequency fs(ii) a A rated power P; an inductance L; DC bus side capacitor C1(ii) a Storage battery side capacitance C2(ii) a Load resistance R1(ii) a Storage battery equivalent resistance R2(ii) a DC component D of BOOST mode duty cycle1。
Step 4 is specifically implemented according to the following steps:
step 4.1, setting the system switching frequency fsCurrent loop crossing frequency fc1Frequency f of current loop turnn1Voltage outer loop crossing frequency fc2Voltage outer loop turning frequency fn2；
Step 4.2, the transfer function expression of the voltage current loop PI controller in the BOOST mode is as follows:
Figure BDA0003082652250000081
wherein: gpic1(s) represents the transfer function of the BOOST mode current inner loop PI controller; gpiv1(s) represents the transfer function of the BOOST mode voltage outer loop PI controller; kp1Denotes the current loop proportionality coefficient, Kp1＝R7/R6；Ki1Represents the current loop integral coefficient, Ki1＝1/R6C4；Kp2Representing the voltage outer loop proportionality coefficient, Kp2＝R5/R4；Ki2Representing the voltage outer loop integral coefficient, Ki2＝1/R4C3；
And 4.3, after PI compensation, the transfer function of the BOOST mode voltage and current loop is as follows:
Figure BDA0003082652250000082
wherein: giop1(s) represents the transfer function of the current loop after the BOOST mode PI compensation; gvop1(s) represents the transfer function of the voltage outer ring after the BOOST mode PI compensation;
step 4.4, combining the crossing frequency and the turning frequency of the voltage and current loop after PI compensation in the BOOST mode obtained in the step 4.1, and solving corresponding PI parameters according to a formula:
Figure BDA0003082652250000091
obtaining the current inner loop PI parameter K under the BOOST mode after bringing in the relevant numerical valuep1、Ki1(ii) a Voltage outer loop PI parameter Kp2、Ki2；
Step 4.5, designing the voltage-current loop crossing frequency and the turning frequency after PI compensation of the BUCK converter in the same way, and setting the current loop crossing frequency fc3Frequency f of current loop turnn3Voltage outer loop crossing frequency fc4Outer loop turning frequency of voltagefn4；
Step 4.6, under the BUCK mode, the transfer function expression of the voltage and current loop PI controller is as follows:
Figure BDA0003082652250000092
wherein: gpic2(s) represents a transfer function of the BUCK mode current inner loop PI controller; gpiv2(s) represents a transfer function of the BUCK mode voltage outer loop PI controller; kp3Denotes the current loop proportionality coefficient, Kp3＝R13/R12，R12、R13Representing a compensation resistance; ki3Represents the current loop integral coefficient, Ki3＝1/R12C6，C6Represents a compensation capacitance; kp4Representing the voltage outer loop proportionality coefficient, Kp4＝R11/R10，R10、R11Representing a compensation resistance; ki4Representing the voltage outer loop integral coefficient, Ki4＝1/R10C5，C5Represents a compensation capacitance;
and 4.7, after PI compensation, the transfer function of the BUCK mode voltage and current loop is as follows:
Figure BDA0003082652250000093
wherein: giop2(s) represents the transfer function of the current loop after the BUCK mode PI compensation; gvop2(s) represents the transfer function of the voltage loop after the BUCK mode PI compensation;
step 4.8, combining the crossing frequency and the turning frequency of the voltage current loop after PI compensation in the BUCK mode obtained in the step 4.5, and solving corresponding PI parameters according to a formula:
Figure BDA0003082652250000101
obtaining the current inner loop PI parameter K in the BUCK mode after bringing in the relevant numerical valuep3、Ki3(ii) a Voltage outer loop PI parameter Kp4、Ki4。
The compensation method has the beneficial effects that the compensation method for the control loop of the half-bridge bidirectional DC-DC converter aims at solving the problems that the existing distributed power supply has the characteristics of intermittence, easy fluctuation and large influence by weather conditions, and the voltage fluctuation of a direct current bus can be caused when various loads are connected into a direct current micro-grid system. The method comprises the steps of taking a half-bridge bidirectional DC-DC converter as a model, carrying out system analysis on the model, establishing small signal models of the converter under different working modes, deducing corresponding transfer functions, respectively selecting appropriate voltage rings and current rings to design a compensation network, respectively carrying out control loop PI parameter design on BUCK and BOOST circuits by using a theoretical analysis method, and verifying the rationality of the designed PI parameters by adopting a tool box SISOTOOL provided by MATLAB. A voltage and current double-closed-loop feedback control strategy based on a PI controller is designed to control a half-bridge type bidirectional DC-DC converter, and the problems of low power utilization rate and poor system power quality caused by distributed power supply intermittency and load fluctuation are solved.
Drawings
FIG. 1 is a block diagram of a half-bridge bidirectional DC-DC converter topology;
FIG. 2(a) is an equivalent circuit diagram of BOOST converter stage 1;
FIG. 2(b) is an equivalent circuit diagram of BOOST converter stage 2;
FIG. 3(a) is a schematic diagram of a BOOST mode voltage current double closed loop compensation network;
FIG. 3(b) is a schematic diagram of a BUCK mode voltage current double closed loop compensation network;
FIG. 4(a) is a structural block diagram of a BOOST mode voltage and current double closed loop feedback control system;
FIG. 4(b) is a block diagram of a BUCK mode voltage and current double closed loop feedback control system;
FIG. 5(a) is a BOOST mode current inner loop Bode plot;
FIG. 5(b) is a BOOST mode voltage outer loop bode plot;
FIG. 6(a) is a BOOST mode current inner loop system step response plot;
FIG. 6(b) is a BOOST mode voltage outer loop system step response plot;
FIG. 7(a) is a BUCK mode current inner loop Bode diagram;
FIG. 7(b) is an outer loop bode plot of BUCK mode voltage;
FIG. 8(a) is a BUCK mode current inner loop system step response plot;
FIG. 8(b) is a step response graph of the BUCK mode voltage outer loop system;
FIG. 9 is a graph of voltage waveforms for a BUCK mode DC bus and battery;
FIG. 10(a) is a BOOST mode battery voltage and inductor current waveform diagram;
fig. 10(b) is a BOOST mode dc bus voltage and load current waveform diagram.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a compensation method for a control loop of a half-bridge bidirectional DC-DC converter, which is implemented according to the following steps:
step 1, establishing mathematical models of a half-bridge bidirectional DC-DC converter in different modes, and respectively deducing transfer functions of inductive current and output voltage to control variables and transfer functions of output voltage to inductive current in a BOOST mode and a BUCK mode, wherein the topological structure of the half-bridge bidirectional DC-DC converter is shown in figure 1;
the step 1 is implemented according to the following steps:
step 1.1, in order to solve the static operating point of the BOOST converter, it is necessary to eliminate the high-frequency switching ripple component of each variable in the converter, and usually a method of averaging the variables in one switching period is adopted, that is, a variable x (T) is defined in the switching period TsMean value of
Figure BDA0003082652250000121
Comprises the following steps:
Figure BDA0003082652250000122
wherein:
Figure BDA0003082652250000123
representing the variable x (T) during the switching period TsAverage value of (d); t issRepresents a switching cycle; x (t) represents a variable in the switching converter; t represents a time variable; τ represents an integral variable;
step 1.2, when the BOOST converter works in a continuous conduction mode CCM, the converter circuit is divided into two stages in a steady state, and the time intervals of the two stages are respectively set as follows: [ t, t + d ]1(t)Ts]And [ t + d1(t)Ts,t+Ts]And its equivalent circuit is shown in fig. 2(a) and fig. 2(b), the inductance voltage v in the converter circuitL(t) and a capacitance current iC(t) are respectively expressed as:
Figure BDA0003082652250000124
wherein: v. ofL(t) represents an inductor voltage; l represents an inductance; i.e. iL(t) represents an inductor current; v. ofg(t) represents a battery side voltage; v. ofo(t) represents a direct current bus side voltage; d1(t) represents the BOOST mode duty cycle;
Figure BDA0003082652250000125
wherein: i.e. iC(t) represents a capacitance current; c1Represents the direct current bus side capacitance; r1Representing a load resistance;
step 1.3, in order to eliminate the influence of the switching ripple, v is used when the converter meets the low-frequency assumption and the small-ripple assumptiong(t)、vo(t) and iL(t) approximating the value over the entire switching period interval by the average value of the switching period
Figure BDA0003082652250000126
And
Figure BDA0003082652250000127
in this case, the expressions (2) and (3) are expressed as follows:
Figure BDA0003082652250000131
Figure BDA0003082652250000132
wherein:
Figure BDA0003082652250000133
represents the average value of the inductor current in the switching period;
Figure BDA0003082652250000134
represents an average value of the battery side voltage in the switching period;
Figure BDA0003082652250000135
the average value of the voltage on the direct current bus side in a switching period is represented;
step 1.4, defining the average value of the switching period of each variable by adopting the formula (1), and then, obtaining the average value of the switching period of the inductive voltage
Figure BDA0003082652250000136
Comprises the following steps:
Figure BDA0003082652250000137
wherein:
Figure BDA0003082652250000138
represents the average value of the inductor voltage in the switching period;
if further consider that
Figure BDA0003082652250000139
And
Figure BDA00030826522500001310
approximately constant during a switching cycle, it follows from equation (6):
Figure BDA00030826522500001311
similarly, the average value of the switching period of the capacitance current is obtained by using the same analysis method according to the segmented expression of the capacitance current
Figure BDA00030826522500001312
Comprises the following steps:
Figure BDA00030826522500001313
wherein:
Figure BDA00030826522500001314
represents the average value of the capacitance current in the switching period;
step 1.5, introducing low-frequency small signal disturbance near a static working point of the converter so as to carry out linearization processing on the converter, and inputting a variable v in the BOOST converterg(t), state variable iL(t)、vo(t) average variation
Figure BDA0003082652250000141
And
Figure BDA0003082652250000142
and a control variable d1(t) decomposing it into a sum of a direct current component and an alternating current small signal component, namely:
Figure BDA0003082652250000143
wherein: vg、IL、VoAnd D1A direct current component representing a corresponding variable;
Figure BDA0003082652250000144
and
Figure BDA0003082652250000145
an alternating current component representing a corresponding variable;
step 1.6, decomposing the average variables in the formulas (7) and (8) into the sum of corresponding direct current components and alternating current small signal components according to the formula (9) to obtain:
Figure BDA0003082652250000146
after the same terms are combined and arranged in the formula, the corresponding direct current terms are equal and the corresponding alternating current terms are equal, and the linear state equation of the alternating current small signal determined according to the working characteristics of the inductor and the capacitor can be obtained by omitting second-order tiny quantity as follows:
Figure BDA0003082652250000147
step 1.7, equation (11) is a second-order dynamic model of the BOOST converter circuit in the time domain in the CCM mode, the model is the basis of closed-loop feedback control design of the converter system, the equation obtained in equation (11) is subjected to the lagrange transformation, and the time domain model is transformed to the S domain to obtain the transfer function of the S domain of the BOOST converter:
Figure BDA0003082652250000151
wherein: s represents a dummy variable;
Figure BDA0003082652250000152
representing the alternating current component of the S-domain inductive current;
Figure BDA0003082652250000153
representing the alternating-current component of the voltage at the side of the S-domain direct-current bus;
Figure BDA0003082652250000154
representing the alternating-current component of the voltage of the storage battery side in the S domain;
Figure BDA0003082652250000155
representing the duty ratio alternating current component of the S-domain BOOST mode;
in the formula (12), the AC component of the battery side voltage in the S domain
Figure BDA0003082652250000156
Obtaining a corresponding transfer function of the BOOST converter in a CCM mode, and obtaining a transfer function G of the output voltage of the BOOST converter to a control variable in the CCM modevd1(s) is:
Figure BDA0003082652250000157
transfer function G of BOOST converter inductive current to control variable in CCM modeid1(s) is:
Figure BDA0003082652250000158
transfer function G of output voltage of BOOST converter to inductive current in CCM modevi1(s) is:
Figure BDA0003082652250000159
and similarly, obtaining a corresponding transfer function of the BUCK converter in the CCM mode, and obtaining a transfer function G of the output voltage of the BUCK converter to the control variable in the CCM modevd2(s) is:
Figure BDA00030826522500001510
wherein: c2Represents the battery side capacitance; r2Represents the battery-side equivalent resistance;
Figure BDA00030826522500001511
representing an S-domain BUCK mode duty ratio alternating current component;
transfer function G of BUCK converter inductive current to control variable in CCM modeid2(s) is:
Figure BDA0003082652250000161
transfer function G of output voltage of BUCK converter to inductive current in CCM modevi2(s) is:
Figure BDA0003082652250000162
step 2, analyzing the half-bridge bidirectional DC-DC converter to know that the PI controller can be adopted to improve the system performance, so that a voltage and current double-closed-loop feedback control strategy based on the PI controller is designed to control the half-bridge bidirectional DC-DC converter to still ensure stable output under the condition of disturbance;
the step 2 is implemented according to the following steps:
step 2.1, in the BOOST mode, the voltage outer ring is composed of a voltage sampling resistor R2And R3Forming a voltage sampling network, and collecting output voltage V in BOOST modeoObtaining a voltage signal V after resistance voltage division1And a reference voltage value VrefAfter comparison, the voltage is sent to a voltage controller VA via a compensation resistor R4、R5And a compensation capacitor C3The compensation network generates a voltage signal V after compensationVA1To obtain, the current inner ring is sampled by the current sampling resistor RSAcquiring the current value of the inductor to obtain a voltage feedback signal VRSAnd is connected with the voltage signal V generated by the voltage outer loopVA1After comparison, the voltage is sent to a current controller CA via a compensation resistor R6、R7And a compensation capacitor C4The compensation network generates a voltage signal V after compensationCA1Obtaining a voltage signal V after the current inner loop compensationCA1And sawtooth wave signal VMAfter comparison, a PWM control signal is generated, and the switching tube Q is controlled2The change of the duty ratio controls the stability of the system, and similarly, the BUCK mode voltage and current double closed loop compensation network is designed by using the same design method, schematic diagrams of the BUCK mode voltage and current double closed loop compensation network and structural block diagrams of the BUCK mode voltage and current double closed loop compensation network are shown in fig. 3(a) and fig. 3(b), and structural block diagrams are shown in fig. 4(a) and fig. 4(b),
step 2.2, respectively obtaining an open loop transfer function of a voltage current loop of the half-bridge type bidirectional DC-DC converter and an open loop transfer function G of a current inner loop of the half-bridge type bidirectional DC-DC converter according to the converter system transfer functions deduced by the formulas (14), (15), (17) and (18)iop(s) is:
Figure BDA0003082652250000171
wherein: gpic(s) represents the transfer function of the current inner loop PI controller;
Figure BDA0003082652250000172
representing a transfer function of the PWM controller; vmRepresenting a sawtooth wave peak-to-peak value; gid(s) represents the transfer function of the inductor current to the control variable; hcRepresenting an inductor current sampling coefficient;
open-loop transfer function G of voltage outer ring of half-bridge type bidirectional DC-DC convertervop(s) is:
Figure BDA0003082652250000173
wherein: gpiv(s) represents the transfer function of the voltage outer loop PI controller; gvi(s) represents the transfer function of the output voltage to the inductor current; hvRepresenting the voltage sampling coefficient.
Step 2.2 sawtooth Peak VmInductance current sampling coefficient H1 c1, voltage sampling coefficient Hv＝1。
Step 3, designing power circuit parameters of the half-bridge type bidirectional DC-DC converter;
step 3 is specifically implemented according to the following steps:
the parameters of the power circuit of the half-bridge type bidirectional DC-DC converter are designed as follows: voltage V at dc bus sideo30V; battery side voltage Vg12V; switching frequency f s20 kHz; rated power P is 96W; inductance L ═ 100 μ H; DC bus side capacitor C11000 μ F; storage battery side capacitance C2220 muF; load resistance R19.31 Ω; storage battery equivalent resistance R21.5 Ω; DC component D of BOOST mode duty cycle1＝0.6。
And 4, combining the system transfer function in the BOOST mode and the BUCK mode obtained in the step 1, the open-loop transfer function of the voltage and current double closed-loop feedback control system obtained in the step 2 and the power circuit parameters obtained in the step 3, designing voltage and current loop PI parameters of the half-bridge type bidirectional DC-DC converter system, substituting the designed voltage and current loop PI parameters into the voltage and current double closed-loop feedback control strategy in the step 2, and obtaining the double-loop compensated double-closed-loop type bidirectional DC-DC converter.
Step 4 is specifically implemented according to the following steps:
step 4.1, when the converter works in the BOOST mode, in order to ensure the stability of the system, the cross-over frequency of the current loop after PI compensation is generally taken as the switching frequency f when the PI parameter is designedsBetween 1/10 and 1/5, a system switching frequency fs20kHz, the current loop crossing frequency f is designed for this timec14kHz is taken, the turning frequency of a current loop PI controller is sufficiently smaller than the switching frequency of the current loop PI controller, and the turning frequency f of the current loop is designedn1500Hz is taken, and meanwhile, in order to ensure that the bandwidth of a current loop is higher than that of a voltage outer loop, the crossing frequency of the voltage outer loop is far lower than that of the current loop, and the voltage outer loop crossing frequency f is designed at this timec2Taking 100Hz, voltage outer ring turning frequency fn2Taking 10 Hz;
step 4.2, the transfer function expression of the voltage current loop PI controller in the BOOST mode is as follows:
Figure BDA0003082652250000181
wherein: gpic1(s) represents the transfer function of the BOOST mode current inner loop PI controller; gpiv1(s) represents the transfer function of the BOOST mode voltage outer loop PI controller; kp1Denotes the current loop proportionality coefficient, Kp1＝R7/R6；Ki1Represents the current loop integral coefficient, Ki1＝1/R6C4；Kp2Representing the voltage outer loop proportionality coefficient, Kp2＝R5/R4；Ki2Representing the voltage outer loop integral coefficient, Ki2＝1/R4C3；
And 4.3, after PI compensation, the transfer function of the BOOST mode voltage and current loop is as follows:
Figure BDA0003082652250000191
wherein: giop1(s) represents the transfer function of the current loop after the BOOST mode PI compensation; gvop1(s) represents the transfer function of the voltage outer ring after the BOOST mode PI compensation;
step 4.4, combining the crossing frequency and the turning frequency of the voltage and current loop after PI compensation in the BOOST mode obtained in the step 4.1, and solving corresponding PI parameters according to a formula:
Figure BDA0003082652250000192
after the correlation values are introduced, the following results are obtained: the PI parameter of the current inner loop is K under the BOOST modep1＝0.32、K i130; voltage outer loop PI parameter is Kp2＝0.5、Ki2＝97；
Step 4.5, designing the voltage-current loop crossing frequency and the turning frequency after PI compensation of the BUCK converter in the same way, wherein the current loop crossing frequency f is designed in the designc3Taking 3kHz and the turning frequency f of the current loopn3Taking 400Hz, voltage outer ring throughThe more frequency fc4Taking 300Hz, voltage outer ring turning frequency fn4Taking 30 Hz;
step 4.6, under the BUCK mode, the transfer function expression of the voltage and current loop PI controller is as follows:
Figure BDA0003082652250000193
wherein: gpic2(s) represents a transfer function of the BUCK mode current inner loop PI controller; gpiv2(s) represents a transfer function of the BUCK mode voltage outer loop PI controller; kp3Denotes the current loop proportionality coefficient, Kp3＝R13/R12，R12、R13Representing a compensation resistance; ki3Represents the current loop integral coefficient, Ki3＝1/R12C6，C6Represents a compensation capacitance; kp4Representing the voltage outer loop proportionality coefficient, Kp4＝R11/R10，R10、R11Representing a compensation resistance; ki4Representing the voltage outer loop integral coefficient, Ki4＝1/R10C5，C5Represents a compensation capacitance;
and 4.7, after PI compensation, the transfer function of the BUCK mode voltage and current loop is as follows:
Figure BDA0003082652250000201
wherein: giop2(s) represents the transfer function of the current loop after the BUCK mode PI compensation; gvop2(s) represents the transfer function of the voltage loop after the BUCK mode PI compensation;
step 4.8, combining the crossing frequency and the turning frequency of the voltage current loop after PI compensation in the BUCK mode obtained in the step 4.5, and solving corresponding PI parameters according to a formula:
Figure BDA0003082652250000202
bring-in correlationObtaining the following numerical values: the PI parameter of the current inner loop in the BUCK mode is Kp3＝0.07、K i3106; voltage outer loop PI parameter is Kp4＝0.05、Ki4＝298。
In order to verify the rationality of the designed PI parameters, the system characteristics after compensation can be reflected by drawing a system Bode diagram and a step response curve under different modes by adopting a tool box SISOTOOL provided by MATLAB.
And a, importing the system transfer functions in different modes into a SISOTOOL tool box, wherein the tool box can draw a baud graph and a root track graph of the system before compensation immediately and display the baud graph and the root track graph in real time.
And step b, adding a pole with a value of zero into the system root trace graph according to the nature of PI regulation in the system regulation page, and then adding a real zero. And substituting the designed PI parameter into the expression, adjusting the phase angle margin and the crossing frequency through a dragging curve, and simultaneously observing a system step response curve at the lower right corner to judge the overshoot and the response time of the system.
Step c, as can be seen from fig. 5(a) and 5(b), the phase margin of the current inner loop in the BOOST mode is 82 degrees, and the crossing frequency is 4 kHz; the phase margin of the voltage outer ring is 77.8 degrees, and the crossing frequency is 100 Hz; at the moment, the phase margin of the system is more than 45 degrees, the current loop crossing frequency is positioned at 1/10-1/5 of the switching frequency, the voltage loop crossing frequency is far less than the current loop crossing frequency, the design requirements of a general system are met, and the converter has good stability and dynamic response. Meanwhile, as can be seen from fig. 6(a) and 6(b), the overshoot of the corrected step response of the system is low, and the adjustment time is also short.
Step d, as can be seen from fig. 7(a) and 7(b), the phase margin of the current inner loop in the BUCK mode is 85.6 degrees, and the crossing frequency is 3 kHz; the phase margin of the voltage outer ring is 89.8 degrees, and the crossing frequency is 300 Hz; at the moment, the phase margin of the system is more than 45 degrees, the current loop crossing frequency is positioned at 1/10-1/5 of the switching frequency, the voltage loop crossing frequency is far less than the current loop crossing frequency, the design requirements of a general system are met, and the converter has good stability and dynamic response. Meanwhile, as can be seen from fig. 8(a) and 8(b), the overshoot of the corrected step response of the system is low, and the adjustment time is also short.
The MATLAB/Simulink is adopted to build a simulation model of the double closed-loop feedback control system of the half-bridge type bidirectional DC-DC converter, and the correctness of the control method is verified by analyzing the control effect of the voltage loop and the current loop on adverse factors such as voltage disturbance, load disturbance and the like. The simulation results are shown in fig. 9, 10(a) and 10 (b).
As can be seen from fig. 9, when the half-bridge bidirectional DC-DC converter operates in the BUCK mode, the DC bus voltage fluctuates at 0.5s, 1.0s, and 1.5s, and the battery voltage can be stabilized at 12V by the dual closed-loop feedback control strategy based on the PI controller. As can be seen from fig. 10(a) and 10(b), when the half-bridge bidirectional DC-DC converter operates in the BOOST mode, the load is suddenly reduced at 0.3s, the voltage of the battery rises while the inductor current drops, and the DC bus voltage slightly rises during the load jump but can quickly return to the voltage reference value, at which time the closed-loop regulation reduces the load current to maintain the DC bus voltage stable. On the contrary, when the load is suddenly applied for 0.5s, the voltage of the storage battery is reduced, the inductive current is increased, the voltage of the direct current bus is slightly reduced in the process of load jump, but the voltage can be quickly restored to the reference value, and at the moment, the closed-loop regulation can increase the load current to maintain the voltage of the direct current bus to be stable. Simulation results show that the compensation method for the control loop of the half-bridge bidirectional DC-DC converter provided by the invention has good control effect and meets design requirements.

Claims (6)

1. The compensation method for the control loop of the half-bridge bidirectional DC-DC converter is characterized by comprising the following steps:
step 1, establishing mathematical models of a half-bridge bidirectional DC-DC converter in different modes, and respectively deducing transfer functions of inductive current and output voltage to control variables and transfer functions of output voltage to inductive current in a BOOST mode and a BUCK mode;
step 2, designing a voltage and current double closed loop feedback control strategy based on a PI controller, and controlling the half-bridge type bidirectional DC-DC converter to still ensure stable output under the condition of disturbance;
step 3, designing power circuit parameters of the half-bridge type bidirectional DC-DC converter;
and 4, combining the system transfer function in the BOOST mode and the BUCK mode obtained in the step 1, the open-loop transfer function of the voltage and current double closed-loop feedback control system obtained in the step 2 and the power circuit parameters obtained in the step 3, designing voltage and current loop PI parameters of the half-bridge type bidirectional DC-DC converter system, substituting the designed voltage and current loop PI parameters into the voltage and current double closed-loop feedback control strategy in the step 2, and obtaining the double-loop compensated double-closed-loop type bidirectional DC-DC converter.
2. The compensation method for the control loop of the half-bridge bidirectional DC-DC converter according to claim 1, wherein the step 1 is implemented by the following steps:
step 1.1, a method for averaging variables in a switching period is adopted, namely, a variable x (T) is defined in the switching period TsMean value of
Figure FDA0003082652240000011
Comprises the following steps:
Figure FDA0003082652240000012
wherein:
Figure FDA0003082652240000013
representing the variable x (T) during the switching period TsAverage value of (d); t issRepresents a switching cycle; x (t) represents a variable in the switching converter; t represents a time variable; τ represents an integral variable;
step 1.2, when the BOOST converter works in a continuous conduction mode CCM, the converter circuit is divided into two stages in a steady state, and the time intervals of the two stages are respectively set as follows: [ t, t + d ]1(t)Ts]And [ t + d1(t)Ts,t+Ts]Then the voltage v of the inductor in the converter circuitL(t) and a capacitance current iC(t) are respectively expressed as:
Figure FDA0003082652240000021
wherein: v. ofL(t) represents an inductor voltage; l represents an inductance; i.e. iL(t) represents an inductor current; v. ofg(t) represents a battery side voltage; v. ofo(t) represents a direct current bus side voltage; d1(t) represents the BOOST mode duty cycle;
Figure FDA0003082652240000022
wherein: i.e. iC(t) represents a capacitance current; c1Represents the direct current bus side capacitance; r1Representing a load resistance;
step 1.3, when the converter meets the low-frequency assumption and the small ripple assumption, vg(t)、vo(t) and iL(t) approximating the value over the entire switching period interval by the average value of the switching period
Figure FDA0003082652240000023
And
Figure FDA0003082652240000024
in this case, the expressions (2) and (3) are expressed as follows:
Figure FDA0003082652240000025
Figure FDA0003082652240000026
wherein:
Figure FDA0003082652240000027
represents the average value of the inductor current in the switching period;
Figure FDA0003082652240000028
represents an average value of the battery side voltage in the switching period;
Figure FDA0003082652240000029
the average value of the voltage on the direct current bus side in a switching period is represented;
step 1.4, defining the average value of the switching period of each variable by adopting the formula (1), and then, obtaining the average value of the switching period of the inductive voltage
Figure FDA0003082652240000031
Comprises the following steps:
Figure FDA0003082652240000032
wherein:
Figure FDA0003082652240000033
represents the average value of the inductor voltage in the switching period;
if further consider that
Figure FDA0003082652240000034
And
Figure FDA0003082652240000035
approximately constant during a switching cycle, it follows from equation (6):
Figure FDA0003082652240000036
similarly, the average value of the switching period of the capacitance current is obtained by using the same analysis method according to the segmented expression of the capacitance current
Figure FDA0003082652240000037
Comprises the following steps:
Figure FDA0003082652240000038
wherein:
Figure FDA0003082652240000039
represents the average value of the capacitance current in the switching period;
step 1.5, introducing low-frequency small signal disturbance near a static working point of the converter so as to carry out linearization processing on the converter, and inputting a variable v in the BOOST converterg(t), state variable iL(t)、vo(t) average variation
Figure FDA00030826522400000310
And
Figure FDA00030826522400000311
and a control variable d1(t) decomposing it into a sum of a direct current component and an alternating current small signal component, namely:
Figure FDA00030826522400000312
wherein: vg、IL、VoAnd D1A direct current component representing a corresponding variable;
Figure FDA00030826522400000313
and
Figure FDA00030826522400000314
an alternating current component representing a corresponding variable;
step 1.6, decomposing the average variables in the formulas (7) and (8) into the sum of corresponding direct current components and alternating current small signal components according to the formula (9) to obtain:
Figure FDA0003082652240000041
after the same terms are combined and arranged in the formula, the corresponding direct current terms are equal and the corresponding alternating current terms are equal, and the linear state equation of the alternating current small signal determined according to the working characteristics of the inductor and the capacitor can be obtained by omitting second-order tiny quantity as follows:
Figure FDA0003082652240000042
step 1.7, equation (11) is a second-order dynamic model of the BOOST converter circuit in the time domain in the CCM mode, the model is the basis of closed-loop feedback control design of the converter system, the equation obtained in equation (11) is subjected to the lagrange transformation, and the time domain model is transformed to the S domain to obtain the transfer function of the S domain of the BOOST converter:
Figure FDA0003082652240000043
wherein: s represents a dummy variable;
Figure FDA0003082652240000044
representing the alternating current component of the S-domain inductive current;
Figure FDA0003082652240000045
representing the alternating-current component of the voltage at the side of the S-domain direct-current bus;
Figure FDA0003082652240000046
representing the alternating-current component of the voltage of the storage battery side in the S domain;
Figure FDA0003082652240000047
representing the duty ratio alternating current component of the S-domain BOOST mode;
in the formula (12), the AC component of the battery side voltage in the S domain
Figure FDA0003082652240000048
Obtaining a corresponding transfer function of the BOOST converter in a CCM mode, and obtaining a transfer function G of the output voltage of the BOOST converter to a control variable in the CCM modevd1(s) is:
Figure FDA0003082652240000049
transfer function G of BOOST converter inductive current to control variable in CCM modeid1(s) is:
Figure FDA0003082652240000051
transfer function G of output voltage of BOOST converter to inductive current in CCM modevi1(s)：
Figure FDA0003082652240000052
And similarly, obtaining a corresponding transfer function of the BUCK converter in the CCM mode, and obtaining a transfer function G of the output voltage of the BUCK converter to the control variable in the CCM modevd2(s)：
Figure FDA0003082652240000053
Wherein: c2Represents the battery side capacitance; r2Represents the battery-side equivalent resistance;
Figure FDA0003082652240000054
representing an S-domain BUCK mode duty ratio alternating current component;
BUCK converter inductive current pair control variable in CCM modeTransfer function G ofid2(s)：
Figure FDA0003082652240000055
Transfer function G of output voltage of BUCK converter to inductive current in CCM modevi2(s)：
Figure FDA0003082652240000056
3. The compensation method for the control loop of the half-bridge bidirectional DC-DC converter according to claim 2, wherein the step 2 is implemented by the following steps:
step 2.1, in the BOOST mode, the voltage outer ring is composed of a voltage sampling resistor R2And R3Forming a voltage sampling network, and collecting output voltage V in BOOST modeoObtaining a voltage signal V after resistance voltage division1And a reference voltage value VrefAfter comparison, the voltage is sent to a voltage controller VA via a compensation resistor R4、R5And a compensation capacitor C3The compensation network generates a voltage signal V after compensationVA1To obtain, the current inner ring is sampled by the current sampling resistor RSAcquiring the current value of the inductor to obtain a voltage feedback signal VRSAnd is connected with the voltage signal V generated by the voltage outer loopVA1After comparison, the voltage is sent to a current controller CA via a compensation resistor R6、R7And a compensation capacitor C4The compensation network generates a voltage signal V after compensationCA1Obtaining a voltage signal V after the current inner loop compensationCA1And sawtooth wave signal VMAfter comparison, a PWM control signal is generated, and the switching tube Q is controlled2The stability of the system is controlled by the change of the duty ratio, and similarly, a BUCK mode voltage and current double closed-loop compensation network is designed by using the same design method;
step 2.2, transfer function of converter system derived from equation (14), equation (15), equation (17) and equation (18)Respectively obtaining an open loop transfer function G of a voltage current loop and an open loop transfer function G of a current inner loop of the half-bridge type bidirectional DC-DC converteriop(s) is:
Figure FDA0003082652240000061
wherein: gpic(s) represents the transfer function of the current inner loop PI controller;
Figure FDA0003082652240000062
representing a transfer function of the PWM controller; vmRepresenting a sawtooth wave peak-to-peak value; gid(s) represents the transfer function of the inductor current to the control variable; hcRepresenting an inductor current sampling coefficient;
open-loop transfer function G of voltage outer ring of half-bridge type bidirectional DC-DC convertervop(s) is:
Figure FDA0003082652240000063
wherein: gpiv(s) represents the transfer function of the voltage outer loop PI controller; gvi(s) represents the transfer function of the output voltage to the inductor current; hvRepresenting the voltage sampling coefficient.
4. The compensation method for the control loop of the half-bridge bidirectional DC-DC converter according to claim 3, wherein the step 2.2 is performed by using a sawtooth peak-to-peak VmInductance current sampling coefficient H1c1, voltage sampling coefficient Hv＝1。
5. The compensation method for the control loop of the half-bridge type bidirectional DC-DC converter according to claim 3, wherein in the step 3, the power circuit parameter design of the half-bridge type bidirectional DC-DC converter comprises a voltage V on the DC bus sideo(ii) a Battery side voltage Vg(ii) a Switching frequency fs(ii) a A rated power P; an inductance L; DC bus side capacitor C1(ii) a Storage battery side capacitance C2(ii) a Load resistance R1(ii) a Storage battery equivalent resistance R2(ii) a DC component D of BOOST mode duty cycle1。
6. The compensation method for the control loop of the half-bridge bidirectional DC-DC converter according to claim 5, wherein the step 4 is implemented by the following steps:
step 4.1, setting the system switching frequency fsCurrent loop crossing frequency fc1Frequency f of current loop turnn1Voltage outer loop crossing frequency fc2Voltage outer loop turning frequency fn2；
Step 4.2, the transfer function expression of the voltage current loop PI controller in the BOOST mode is as follows:
Figure FDA0003082652240000071
wherein: gpic1(s) represents the transfer function of the BOOST mode current inner loop PI controller; gpiv1(s) represents the transfer function of the BOOST mode voltage outer loop PI controller; kp1Denotes the current loop proportionality coefficient, Kp1＝R7/R6；Ki1Represents the current loop integral coefficient, Ki1＝1/R6C4；Kp2Representing the voltage outer loop proportionality coefficient, Kp2＝R5/R4；Ki2Representing the voltage outer loop integral coefficient, Ki2＝1/R4C3；
And 4.3, after PI compensation, the transfer function of the BOOST mode voltage and current loop is as follows:
Figure FDA0003082652240000072
wherein: giop1(s) represents the transfer function of the current loop after the BOOST mode PI compensation; gvop1(s) represents the transfer function of the voltage outer ring after the BOOST mode PI compensation;
step 4.4, combining the crossing frequency and the turning frequency of the voltage and current loop after PI compensation in the BOOST mode obtained in the step 4.1, and solving corresponding PI parameters according to a formula:
Figure FDA0003082652240000081
obtaining the current inner loop PI parameter K under the BOOST mode after bringing in the relevant numerical valuep1、Ki1(ii) a Voltage outer loop PI parameter is Kp2、Ki2；
Step 4.5, designing the voltage-current loop crossing frequency and the turning frequency after PI compensation of the BUCK converter in the same way, and setting the current loop crossing frequency fc3Frequency f of current loop turnn3Voltage outer loop crossing frequency fc4Voltage outer loop turning frequency fn4；
Step 4.6, under the BUCK mode, the transfer function expression of the voltage and current loop PI controller is as follows:
Figure FDA0003082652240000082
wherein: gpic2(s) represents a transfer function of the BUCK mode current inner loop PI controller; gpiv2(s) represents a transfer function of the BUCK mode voltage outer loop PI controller; kp3Denotes the current loop proportionality coefficient, Kp3＝R13/R12，R12、R13Representing a compensation resistance; ki3Represents the current loop integral coefficient, Ki3＝1/R12C6，C6Represents a compensation capacitance; kp4Representing the voltage outer loop proportionality coefficient, Kp4＝R11/R10，R10、R11Representing a compensation resistance; ki4Representing the voltage outer loop integral coefficient, Ki4＝1/R10C5，C5Represents a compensation capacitance;
and 4.7, after PI compensation, the transfer function of the BUCK mode voltage and current loop is as follows:
Figure FDA0003082652240000091
wherein: giop2(s) represents the transfer function of the current loop after the BUCK mode PI compensation; gvop2(s) represents the transfer function of the voltage loop after the BUCK mode PI compensation;
step 4.8, combining the crossing frequency and the turning frequency of the voltage current loop after PI compensation in the BUCK mode obtained in the step 4.5, and solving corresponding PI parameters according to a formula:
Figure FDA0003082652240000092
obtaining the current inner loop PI parameter K in the BUCK mode after bringing in the relevant numerical valuep3、Ki3(ii) a Voltage outer loop PI parameter is Kp4、Ki4。
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CN113783422B (en) * 2021-09-15 2023-11-21 四川科陆新能电气有限公司 Topological structure and method of bidirectional direct current converter
CN114070062A (en) * 2021-10-21 2022-02-18 合肥巨一动力***有限公司 Control method and device for three-phase interleaved Boost converter
CN114070062B (en) * 2021-10-21 2024-06-04 合肥巨一动力***有限公司 Control method and device for three-phase staggered parallel Boost converter
CN114513132A (en) * 2022-02-23 2022-05-17 合肥工业大学 Isolated half-bridge converter and modeling and loop parameter design method thereof
CN114513132B (en) * 2022-02-23 2024-03-12 合肥工业大学 Isolation half-bridge converter and modeling and loop parameter design method thereof

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