Design method of bidirectional DC-DC converter

Abstract

The invention relates to a design method of a bidirectional DC-DC converter, which comprises a charging state and a discharging state, and is characterized in that when a train is pulled or accelerated, a traction motor needs higher power, the converter is equivalent to a boost chopper, current flows to a direct current side and charges a direct current bus, and when the train runs in an idle mode, the converter stops working and is in a standby holding state; when the train brakes or slows down, the traction motor feeds back a device to the direct-current power grid, so that the voltage of the overhead line system is increased, the converter is equivalent to a step-down chopper, energy is absorbed from a direct-current bus, input data is few, calculation is simple, and design results are more accurate.

Description

Technical Field

[0001] The invention relates to application technology of electrical equipment, and in particular to a design method of a bidirectional DC-DC converter. Background Art

[0002] With the rapid economic development, the power supply quality requirements of the power industry are getting higher and higher, and the electricity consumption is increasing year by year. The traditional thermal power generation method can no longer meet the development and needs of society. At the same time, due to the increasingly prominent environmental problems caused by thermal power generation and the enhancement of people's environmental awareness, the power industry has ushered in new challenges and opportunities. The rapid development of smart grids has provided new ideas and methods for the power industry. Smart grids are a new type of power grid structure with the advantages of strong self-healing, high safety and reliability. It encourages mutual "communication" between the user demand side and the power market supply side to achieve sustainable development of economy, energy and environment.

[0003] In recent years, new energy sources, mainly distributed power sources, have developed rapidly, providing ways and methods to solve the energy crisis. Distributed power sources include large-scale renewable energy sources such as wind power, solar energy, and tidal energy, which are inexhaustible and highly flexible. However, these renewable energy sources are affected by the natural environment (weather, sunshine time, etc.), and the power generation is extremely irregular, with great randomness and uncertainty, which brings great hidden dangers to the grid connection or island operation of distributed power generation. In recent years, various countries have begun to regard energy storage and the development of new resources that can replace traditional energy as important directions for energy development, and energy conservation and environmental protection have become the development theme. As a DC conversion technology in energy conversion, bidirectional DC-DC converters have become the research object of more and more scholars at home and abroad, especially in the fields of rail transportation, wind energy and new energy, and electric vehicles. It has received extensive attention and research. It is precisely because the bidirectional conversion technology based on storage devices (lithium battery packs, supercapacitors, etc.) can theoretically achieve good energy management. In recent years, energy storage technology has become an effective way to solve the uncertainty and randomness of distributed power generation in rail transportation, wind power, computers, electric vehicles, etc. Summary of the invention

[0004] One of the purposes of the present invention is to provide a design method for a bidirectional DC-DC converter, which can provide a design circuit for a bidirectional DC-DC converter.

[0005] A second object of the present invention is to provide a design method for a bidirectional DC-DC converter, which can provide a parameter calculation for an ice melting technology design method with less input data and simple calculation.

[0006] A third object of the present invention is to provide a design method for a bidirectional DC-DC converter, which makes the calculation process faster and the design result more accurate than a simple experimental method.

[0007] The object of the present invention is achieved by providing a design method of a bidirectional DC-DC converter, which is characterized by comprising: an energy absorption circuit for absorbing traction network energy, a charging circuit for charging a load, a switching circuit for the bidirectional DC-DC converter, and a control circuit for controlling the bidirectional DC-DC converter, When the train is pulling or accelerating, the traction motor needs a large power. The control circuit controls the switching circuit of the bidirectional DC-DC converter to be equivalent to a boost chopper, which works in the charging state mode. The current flows to the DC side to charge the DC bus. When the train is coasting, the control circuit controls the switching circuit of the bidirectional DC-DC converter to stop working, and the switching circuit of the bidirectional DC-DC converter is in a standby holding state; When the train brakes or decelerates, the traction motor feeds back energy to the DC grid, increasing the overhead line voltage. The switching circuit of the bidirectional DC-DC converter is equivalent to a step-down chopper, which is in a discharge mode and absorbs energy from the DC bus.

[0008] The switching circuit of the bidirectional DC-DC converter includes an inductor L, an absorption capacitor C1, a switch device S1, a switch device S2, a filter inductor L1 and a filter capacitor C2. The absorption capacitor C1 and the filter capacitor C2 form a series circuit. The series circuit formed by the absorption capacitor C1 and the filter capacitor C2 is electrically connected in series between the low voltage end of the inductor L and the negative end of the circuit. The switch device S1 and the switch device S2 form a series controllable switch and are connected to both ends of the absorption capacitor C1 and the filter capacitor C2. The switch device S1 and the switch device S2 are field effect tubes. The source of the switching device S1 is electrically connected to the drain of the switching device S2, and the drain of the switching device S1 is electrically connected to the low voltage end of the inductor L and the electrical connection point of the absorption capacitor C1; the source of the switching device S2 is electrically connected to the negative end of the circuit; the series connection point of the switching device S1 and the switching device S2 is electrically connected to the series connection point of the absorption capacitor C1 and the filter capacitor C2 and one end of the filter inductor L1, and the filter inductor L1 is simultaneously connected in series with the load capacitor to the negative end of the circuit; the gates of the switching device S1 and the switching device S2 are respectively electrically connected to the I / O control end of the control circuit.

[0009] The charging state mode is formed when the control circuit receives a detection signal or a working command when the train brakes or decelerates, so that the switch devices S1 and S2 of the switching circuit of the bidirectional DC-DC converter are in the working state. When the train absorbs the energy of the traction network and brakes, the control circuit controls the switching circuit of the bidirectional DC-DC converter to work in the charging state; the energy is transmitted unidirectionally from the traction network to the load. At this time, one of the switch devices S2 of the switching circuit of the bidirectional DC-DC converter is turned off, and the other switch device S1 is periodically turned on and off; the traction motor feeds back to the DC power grid device to increase the voltage of the contact network, and the converter is equivalent to a step-down chopper to absorb energy from the DC bus.

[0010] The discharge state mode is: when the train is pulling or accelerating, the traction motor needs a larger power, and the converter is equivalent to a boost chopper. When the train is pulling or leaving the station, the switching circuit of the bidirectional DC-DC converter works in the discharge state. At this time, the switch device S1 is turned off, and the switch device S2 is periodically turned on and off, and the current flows to the DC side to charge the DC bus.

[0011] The switching circuit of the bidirectional DC-DC converter has the same circuits in the charging state mode and the discharging state mode, and the mathematical model and control strategy of the charging state and the analysis process of the mathematical model and control strategy of the discharging state are the same.

[0012] The purpose and advantage of the present invention are: the present invention realizes bidirectional control of charging and amplification by controlling two switches S1 and S2 of the switching circuit of the bidirectional DC-DC converter, and makes the DC-DC converter adjustable and accurate by different control of the two switches S1 and S2. In order to make the output current of the constant current source of the bidirectional DC-DC converter stable and continuously adjustable, the PWM control principle is adopted for adjustment. The hardware control part itself forms a closed-loop control loop to adjust the voltage to make it constant within the accuracy range.

[0013] The bidirectional DC-DC converter is functionally equivalent to a combination of the charging (Buck) state and the discharging (Boost) state.

[0014] When absorbing the braking energy of the traction network train, the bidirectional DC-DC converter works in the charging state, and the bidirectional DC-DC converter is controlled to realize unidirectional energy transmission. At this time, the switch device S2 is turned off, and the switch device S1 is periodically turned on and off; similarly, when the train is traction or leaving the station, the bidirectional DC-DC converter works in the discharging state. At this time, the switch device S1 is turned off, and the switch device S2 is periodically turned on and off. Due to the structural characteristics of the bidirectional DC-DC converter, the two switch states are the same, indicating different energy flow directions. The mathematical model and control strategy of the charging state are analyzed, and the analysis process of the discharge state is similar, and a unified control strategy for the bidirectional DC-DC converter can be obtained.

[0015] The present invention will be further described below in conjunction with the accompanying drawings of the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of a bidirectional DC-DC converter of the present invention; Figure 2 It is the schematic diagram of the charging state operation system; Figure 3 This is the schematic diagram of the system operating in the discharge state.

[0017] In the figure, 1. energy absorption circuit; 2. switching circuit of bidirectional DC-DC converter; 3. charging circuit; 4. control circuit; 5. traction network; 6. load; 7. DC bus. DETAILED DESCRIPTION

[0018] The following will describe the implementation methods of the present invention in detail with reference to the accompanying drawings and examples, so as to fully understand how the present invention applies technical means to solve technical problems and achieve the implementation process of technical effects and implement them accordingly.

[0019] like Figure 1 , Figure 2 and Figure 3 As shown, the present invention relates to a design method of a bidirectional DC-DC converter, which is characterized by comprising: an energy absorption circuit 1 for absorbing traction network energy, a charging circuit 3 for charging a load 6, a switching circuit 2 for the bidirectional DC-DC converter, and a control circuit 4 for controlling the bidirectional DC-DC converter, When the train is towing or accelerating, the traction motor needs a large power, and the control circuit 4 controls the switching circuit 2 of the bidirectional DC-DC converter to be equivalent to a boost chopper, which works in the charging state mode, and the current flows to the DC side to charge the DC bus 7; When the train is coasting, the control circuit 4 controls the switching circuit 2 of the bidirectional DC-DC converter to stop working, and the switching circuit 2 of the bidirectional DC-DC converter is in a standby holding state; When the train brakes or decelerates, the traction motor feeds back energy to the DC grid, increasing the overhead line voltage. The switching circuit 2 of the bidirectional DC-DC converter is equivalent to a step-down chopper, which is in a discharge state mode and absorbs energy from the DC bus 7.

[0020] The switching circuit 2 of the bidirectional DC-DC converter includes an inductor L, an absorption capacitor C1, a switch device S1, a switch device S2, a filter inductor L1 and a filter capacitor C2. The absorption capacitor C1 and the filter capacitor C2 form a series circuit. The series circuit formed by the absorption capacitor C1 and the filter capacitor C2 is electrically connected in series between the low voltage end of the inductor L and the negative end of the circuit. The switch device S1 and the switch device S2 form a series controllable switch and are connected to both ends of the absorption capacitor C1 and the filter capacitor C2. The switch device S1 and the switch device S2 are field effect tubes. The source of the switching device S1 is electrically connected to the drain of the switching device S2, and the drain of the switching device S1 is electrically connected to the low voltage end of the inductor L and the electrical connection point of the absorption capacitor C1; the source of the switching device S2 is electrically connected to the negative end of the circuit; the series connection point of the switching device S1 and the switching device S2 is electrically connected to the series connection point of the absorption capacitor C1 and the filter capacitor C2 and one end of the filter inductor L1, and the filter inductor L1 is simultaneously connected in series with the load capacitor to the negative end of the circuit; the gates of the switching device S1 and the switching device S2 are respectively electrically connected to the I / O control end of the control circuit 4.

[0021] like Figure 2 As shown, the charging state mode in the present invention is formed when the control circuit 4 obtains a detection signal or a working command when the train brakes or decelerates, and the switch device S1 and the switch device S2 of the switching circuit 2 of the bidirectional DC-DC converter are in the working state. When the train brakes by absorbing the energy of the traction network 5, the control circuit 4 controls the switching circuit 2 of the bidirectional DC-DC converter to work in the charging state; the energy is transmitted unidirectionally from the traction network 5 to the load 6. At this time, one of the switch devices S2 of the switching circuit 2 of the bidirectional DC-DC converter is turned off, and the other switch device S1 is periodically turned on and off; the traction motor feeds back to the DC power grid to increase the contact network voltage, and the converter is equivalent to a step-down chopper, which absorbs energy from the DC bus 7.

[0022] like Figure 3 As shown, the discharge state mode in the present invention is: when the train is being pulled or accelerated, the traction motor requires a larger power, and the converter is equivalent to a step-up chopper. When the train is being pulled or leaving the station, the switching circuit 2 of the bidirectional DC-DC converter operates in the discharge state. At this time, the switch device S1 is turned off, and the switch device S2 is periodically turned on and off, and the current flows to the DC side to charge the DC bus 7.

[0023] The switching circuit characteristics of the bidirectional DC-DC converter are that the circuits in the charging state mode and the discharging state mode are the same, but the two switching states are different and the energy flow directions are different.

[0024] The analysis process of the mathematical model and control strategy of the charging state is similar to that of the mathematical model and control strategy of the discharging state, and a unified control strategy of the switching circuit 2 of the bidirectional DC-DC converter can be obtained.

[0025] The present invention adopts a state space averaging method to derive a signal model of a switching circuit 2 of a bidirectional DC-DC converter.

[0026] In the charging state, such as Figure 2 As shown, select the state variable: inductor current i L， Ideal terminal voltage U2; switch S1 conduction period is set to 0 ~ dT, the state differential equation of the circuit can be written as follows: (L L / dt+i L r+u SC -u1=0@C SC du SC / dt=i L ) Formula 1 That is: L / dt=-r / L i L -1 / Lu SC +1 / L u1@du SC / dt=1 / C SC i L ) Formula 2 Write equation 2 in matrix form: [(di L / dt@du SC / dt)]=[(-r / L&-1 / L@1 / C SC &0)][(i L @u SC )]+[(1 / L@0)]u1 Formula 3 Let χ=[(i L @u SC )],χ ̇=[(di L / dt@du SC / dt)], A 充电_1 =[(-r / L&-1 / L@1 / C SC &0)],B 充电_1 =[(1 / L@0)], Then formula 3 can be expressed as: χ ̇=A 充电_1 χ+B 充电_1 u1 type 4 u SC is the low-voltage side terminal voltage of the bidirectional DC-DC converter, as the output variable, from the circuit relationship we can know: U2=ri L +u SC =[(r@1)]^r [(i L @u SC Formula 5 Remember C充电_1 =[(r@1)]^r, y=u2, then Equation 5 can be expressed as: y=C 充电_1 χ Formula 6 When the switch device S1 is turned off, the state differential equation can be obtained: {L L / dt+i L r+u SC =0@C SC du SC / dt=i L Formula 7 That is: L / dt=-r / Li L -1 / Lu SC @du SC / dt=1 / C SC i L Formula 8 [(di L / dt@du SC / dt)]=[(-r / L&-1 / L@1 / C SC &0)][(i L @u SC )] Formula 9 Note A 充电_2 =[(-r / L&-1 / L@1 / C SC &0)],B 充电_2 =[(0@0)], then Equation 9 can be expressed as: χ ̇=A 充电_2 χ+B 充电_2 u1 Formula 10 The output variable u2 is still expressed in the same form as in equation 6, then: y=C 充电_2 χ Formula 11 Among them, C 充电_2 =[(r@1)]^r, by averaging the state equations 4 and 6 when the switch device is turned on and the state equations 10 and 11 when the switch device is turned off, according to the on-time and off-time, the average model of the converter running in the charging state space can be obtained: χ ̇=A 充电 χ+B 充电 u1@y=C 充电 χ Formula 12 Where: A 充电 =dA 充电_1 +d ̇A 充电_2 =d[(-r / L&-1 / L@1 / CSC &0)]+(1-d)[(-r / L&-1 / L@1 / C SC &0)] =[(-r / L&-1 / L@1 / C SC &0)] Formula 13 B 充电 =dB 充电_1 +d ̇B 充电_2 =d[(1 / L@0)]+(1-d)[(0@0)] =[(d / L@0)] Equation 14 C 充电 =dC 充电_1 +d ̇C 充电_2 =d[(r@1)]^r+(1-d)[(r@1)]^r =[(r@1)]^r Formula 15 Applying disturbance to the basic state average equation 12, each instantaneous value is decomposed into the sum of the steady-state value and the disturbance, u1=U1+(u1) ̇, i L =I L +(i L ) ̇, u SC =U SC +(u SC ) ̇, d ̇=D ̇+d ̇, d ̇=D ̇-d ̇, χ=X+χ ̇, y=Y+y ̇; then the state equation containing the disturbance is Laplace transformed to obtain the state space average equation describing the dynamic low-frequency small signal behavior of the converter: (χ ̇(s)=〖(sE-A 充电 )〗^(-1) B 充电 (u1 ) ̇(s)+(sE-A 充电 )^(-1) [(1 / L@0)] U1 d ̇(s)@y ̇(s)=C 充电 〖(sE-A 充电 )〗^(-1) B 充电 (u1 ) ̇(s)+C 充电 (sE-A 充电 )^(-1) [(1 / L@0)] U1 d ̇(s)) Eq. 16 From this, the small signal transfer functions from input to state variable, control to state variable, input to output, and control to output can be obtained as follows: ├ (χ ̇(s)) / ((u1) ̇(s) )┤|_(d ̇(s)=0)=[(├ (i L ) ̇ / ((u1) ̇(s))┤|_(d ̇(s)=0)@├ (u SC ) ̇ / ((u1) ̇(s))┤|_(d ̇(s)=0))]=[((DC SC s) / (LC SC s^2+rDC SC s+1)@D / (LC SC s^2+rC SC s+1))] Formula 17 ├ (χ ̇(s)) / d(s) ┤|_((u1) ̇(s)=0)=[(├ (i L ) ̇ / (d ̇(s))┤|_((u1) ̇(s)=0)@├(u SC ) ̇ / (d ̇(s))┤|_((u1) ̇(s)=0))]=[((C SC sU1) / (LC SC s^2+rC SC s+1)@U1 / (LC SC s^2+rC SC s+1))] Formula 18 ├ (y ̇(s)) / ((u1) ̇(s))┤|_(d ̇(s)=0)=├ ((u2) ̇(s)) / ((u1) ̇(s))┤|_(d ̇(s)=0)=D(rC SC s+1) / (LC SC s^2+rC SC s+1) Formula 19 ├ (y ̇(s)) / (d ̇(s) )┤|_((u1) ̇(s)=0)=├ ((u2) ̇(s)) / (d ̇(s))┤|_((u1) ̇(s)=0)=(U1(rC SC s+1)) / (LC SC s^2+rC SC s+1) Formula 20 When the train is coasting, the converter stops working and is in a standby holding state.

Claims

1. A design method for a bidirectional DC-DC converter, characterized in that: include: An energy absorption circuit (1) for absorbing energy of the traction network, a charging circuit (3) for charging a load (6), a switching circuit (2) for a bidirectional DC-DC converter, and a control circuit (4) for controlling the bidirectional DC-DC converter, When the train is being pulled or accelerated, the traction motor requires a relatively large power, and the control circuit (4) controls the switching circuit (2) of the bidirectional DC-DC converter to be equivalent to a step-up chopper, which works in a charging state mode, and the current flows to the DC side to charge the DC bus (7); When the train is coasting, the control circuit (4) controls the switching circuit (2) of the bidirectional DC-DC converter to stop working, and the switching circuit (2) of the bidirectional DC-DC converter is in a standby holding state; When the train brakes or decelerates, the traction motor feeds back energy to the DC grid, causing the overhead line voltage to increase. The switching circuit (2) of the bidirectional DC-DC converter is equivalent to a step-down chopper and is in a discharge state mode, absorbing energy from the DC bus (7).

2. The design method of a bidirectional DC-DC converter according to claim 1, characterized in that: The switching circuit (2) of the bidirectional DC-DC converter comprises an inductor L, an absorption capacitor C1, a switch device S1, a switch device S2, a filter inductor L1 and a filter capacitor C2, wherein the absorption capacitor C1 and the filter capacitor C2 form a series circuit, the series circuit formed by the absorption capacitor C1 and the filter capacitor C2 is electrically connected in series between the low voltage end of the inductor L and the negative end of the circuit, the switch device S1 and the switch device S2 form a series controllable switch and are connected between the absorption capacitor C1 and the filter capacitor C2; the switch device S1 and the switch device S2 are field effect transistors, and the switch device S1 and the switch device S2 are field effect transistors. The source of the switching device S1 is electrically connected to the drain of the switching device S2, and the drain of the switching device S1 is electrically connected to the low voltage end of the inductor L and the electrical connection point of the absorption capacitor C1; the source of the switching device S2 is electrically connected to the negative end of the circuit; the series connection point of the switching device S1 and the switching device S2 is electrically connected to the series connection point of the absorption capacitor C1 and the filter capacitor C2 and one end of the filter inductor L1, and the filter inductor L1 is simultaneously connected in series with the load capacitor to the negative end of the circuit; the gates of the switching device S1 and the switching device S2 are electrically connected to the I / O control end of the control circuit (4) respectively.

3. The design method of a bidirectional DC-DC converter according to claim 1, characterized in that: The charging state mode is formed when the control circuit (4) receives a detection signal or a working command when the train brakes or decelerates, and the switch device S1 and the switch device S2 of the switching circuit (2) of the bidirectional DC-DC converter are in the working state. When the train brakes by absorbing the energy of the traction network (5), the control circuit (4) controls the switching circuit (2) of the bidirectional DC-DC converter to work in the charging state; the unidirectional transmission of energy from the traction network (5) to the load (6) is realized, at which time one of the switch devices S2 of the switching circuit (2) of the bidirectional DC-DC converter is turned off, and the other switch device S1 is periodically turned on and off; the traction motor feeds back to the DC power grid device, so that the contact network voltage is increased, and the converter is equivalent to a step-down chopper, absorbing energy from the DC bus (7).

4. The design method of a bidirectional DC-DC converter according to claim 1, characterized in that: The discharge state mode is: when the train is being pulled or accelerated, the traction motor requires a relatively large power, and the converter is equivalent to a step-up chopper. When the train is being pulled or leaving the station, the switching circuit (2) of the bidirectional DC-DC converter operates in a discharge state, at which time the switch device S1 is turned off, the switch device S2 is periodically turned on and off, and the current flows to the DC side to charge the DC bus (7).

5. The design method of a bidirectional DC-DC converter according to claim 1, characterized in that: The switching circuit (2) of the bidirectional DC-DC converter has the same circuit configuration in the charging state mode and the discharging state mode, and the mathematical model and control strategy of the charging state and the mathematical model and control strategy analysis process of the discharging state are the same.

6. The design method of a bidirectional DC-DC converter according to claim 1, characterized in that: The analysis process of the mathematical model and control strategy of the charging state is the same as that of the mathematical model and control strategy of the discharging state.

7. The design method of a bidirectional DC-DC converter according to claim 6, characterized in that: In the charging state, select the state variable: inductor current i L， Ideal terminal voltage U2; switch S1 conduction period is set to 0 ~ dT, the state differential equation of the circuit can be written as follows: (L of L / dt+i L r+u SC -u1=0@C SC two SC / dt=i L ) formula 1 That is: (of L / dt=-r / L i L -1 / L u SC +1 / L u1@du SC / dt=1 / C SC the L ) formula 2 Write equation 2 in matrix form: [(di L / dt@du SC / dt)]=[(-r / L&-1 / L@1 / C SC &0)][(i L @u SC )]+[(1 / L@0)]u1 Equation 3 Note: [(i L @u SC )],χ ̇=[(di L / dt@du SC / dt)], A 充电_1 =[(-r / L&-1 / L@1 / C SC &0)],B 充电_1 =[(1 / L@0)], Then formula 3 can be expressed as: x ̇=A 充电_1 x+B 充电_1 u1 formula4 u SC is the low-voltage side terminal voltage of the bidirectional DC-DC converter, as the output variable, from the circuit relationship we can know: U2=ri L +u SC =[(r@1)]^r [(i L @u SC )] Formula 5 Remember C 充电_1 =[(r@1)]^r, y=u2, then Equation 5 can be expressed as: y=C 充电_1 x formula 6 When the switch device S1 is turned off, the state differential equation can be obtained: {L of L / dt+i L r+u SC =0@C SC two SC / dt=i L formula 7 That is: {di L / dt = -r / Li L -1 / Lu SC @du SC / dt = 1 / C SC i L Equation 8 [(di L / dt@du SC / dt)]=[(-r / L&-1 / L@1 / C SC &0)][(i L @u SC )] Equation 9 Note A 充电_2 =[(-r / L&-1 / L@1 / C SC &0)],B 充电_2 =[(0@0)], then Equation 9 can be expressed as: χ ̇=A 充电_2 χ + B 充电_2 u1 Equation 10 The output variable u2 is still expressed in the same form as in equation 6, then: y = C 充电_2 Formula 11 of χ Among them, C 充电_2 =[(r@1)]^r, by averaging the state equations 4 and 6 when the switch device is turned on and the state equations 10 and 11 when the switch device is turned off, according to the on-time and off-time, the average model of the converter running in the charging state space can be obtained: x ̇=A 充电 x+B 充电 u1@y=C 充电 x formula 12 Where: A 充电 =dA 充电_1 +d ̇A 充电_2 =d[(-r / L&-1 / L@1 / C SC &0)]+(1-d)[(-r / L&-1 / L@1 / C SC &0)] =[(-r / L&-1 / L@1 / C SC &0)] Formula 13 B 充电 =dB 充电_1 +d ̇B 充电_2 =d[(1 / L@0)]+(1-d)[(0@0)] =[(d / L@0)] Equation 14 C 充电 =dC 充电_1 +d ̇C 充电_2 =d[(r@1)]^r+(1-d)[(r@1)]^r =[(r@1)]^r Formula 15 Applying disturbance to the basic state average equation 12, each instantaneous value is decomposed into the sum of the steady-state value and the disturbance, u1=U1+(u1) ̇, i L =I L +(i L ) ̇, u SC =U SC +(u SC ) ̇, d ̇=D ̇+d ̇, d ̇=D ̇-d ̇, χ=X+χ ̇, y=Y+y ̇; then the state equation containing the disturbance is Laplace transformed to obtain the state space average equation describing the dynamic low-frequency small signal behavior of the converter: (χ ̇(s)=〖(sE - A 充电 )〗^(-1) B 充电 (u1 ) ̇(s)+(sE - A 充电 )^(-1) [(1 / L@0)] U1 d ̇(s)@y ̇(s)=C 充电 〖(sE - A 充电 )〗^(-1) B 充电 (u1 ) ̇(s)+C 充电 (sE - A 充电 )^(-1) [(1 / L@0)] U1 d ̇(s)) Equation 16 From this, the small signal transfer functions from input to state variable, control to state variable, input to output, and control to output can be obtained as follows: ├ (χ ̇(s)) / ((u1) ̇(s) )┤|_(d ̇(s)=0)=[(├ (i L ) ̇ / ((u1) ̇(s))┤|_(d ̇(s)=0)@├(u SC ) ̇ / ((u1) ̇(s))┤|_(d ̇(s)=0))]=[((DC SC s) / (LC SC s^2+rDC SC s+1)@D / (LC SC s^2+rC SC s+1))] Equation 17 ├ (χ ̇(s)) / d(s) ┤|_((u1) ̇(s)=0)=[(├ (i L ) ̇ / (d ̇(s))┤|_((u1) ̇(s)=0)@├(u SC ) ̇ / (d ̇(s))┤|_((u1) ̇(s)=0))]=[((C SC sU1) / (LC SC s^2+rC SC s+1)@U1 / (LC SC s^2+rC SC s+1))] Equation 18 ├ (y ̇(s)) / ((u1) ̇(s))┤|_(d ̇(s)=0)=├ ((u2) ̇(s)) / ((u1) ̇(s))┤|_(d ̇(s)=0)=D(rC SC s + 1) / (LC SC s^2 + rC SC s + 1) Equation 19 ├ (y ̇(s)) / (d ̇(s) )┤|_((u1) ̇(s)=0)=├ ((u2) ̇(s)) / (d ̇(s))┤|_((u1) ̇(s)=0)=(U1(rC SC s + 1)) / (LC SC s^2 + rC SC s + 1) Equation 20.

Images