Modeling method of discontinuous conduction mode DC / DC converter based on signal flow graph method

Abstract

The present invention belongs to the field of power electronics technology, and discloses a modeling method of a discontinuous conduction mode DC / DC converter based on a signal flow graph method, and analyzes three modes of the discontinuous conduction mode DC / DC converter in steady state to obtain voltage and current waveforms at both ends of the energy storage inductor. When the DC / DC converter is a non-isolated converter, the corresponding energy storage inductor is a pure inductor type, which can be equivalent to a control current source with a duty cycle disturbance as the control variable and an internal resistance in parallel; when the DC / DC converter is an isolated converter and the transformer has energy storage, the corresponding transformer is a coupled inductor type, and is connected in parallel with an ideal transformer on the basis of the pure inductor. In the derivation process of the model, the present invention has a clear physical meaning starting from the essence of the small signal model; the Mersenne formula is directly used in the model calculation, which avoids the complex calculations in the traditional modeling method, and can effectively reduce the difficulty of modeling the discontinuous conduction mode DC / DC converter.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics and relates to a modeling method, in particular to a modeling method of a discontinuous conduction mode DC / DC converter based on a signal flow graph method. Background Art

[0002] Since its invention, switching power supplies have been widely used because of their small size, light weight and high efficiency. An ideal control loop is the basis for the ideal characteristics of a switching power supply, such as quickly suppressing input disturbances and maintaining a stable output voltage. The design of the control loop is based on an accurate small signal model of the converter.

[0003] There are three modeling methods for switching converters: basic modeling method, state space averaging method and switching element and switching network averaging method.

[0004] The basic modeling method divides the converter working in the continuous conduction mode into two states: on and off. The volt-ampere characteristics of the energy storage elements (inductors and capacitors) in the converter are weighted averaged by the proportion of the switch tube on and the proportion of the switch tube off, that is, the duty cycle D and 1-D; then, the small signal model of the converter can be obtained by applying disturbances and separating variables. The basic averaging method is converted into a matrix form with the inductor current and capacitor voltage as the energy storage elements as state variables, and the state space method can be obtained.

[0005] The switching element averaging method is similar to the basic modeling method in that the voltage and current across the switching element are averaged over a switching cycle; whereas the switching network averaging method treats the switching element and the freewheeling diode as a two-port network and averages the voltage and current of the network.

[0006] These modeling methods require averaging two states in the modeling of continuous conduction mode converters, which has the problems of large computational complexity and unclear physical meaning. In the modeling of discontinuous conduction mode converters, three states need to be averaged, which greatly increases the computational complexity of the modeling work. Summary of the invention

[0007] In order to solve the deficiencies of the prior art, the object of the present invention is to provide a small signal modeling method for a discontinuous conduction mode DC / DC converter based on a signal flow graph method with low computational complexity.

[0008] To achieve the above objectives, the present invention adopts the following technical solutions:

[0009] The modeling method of the discontinuous conduction mode DC / DC converter based on the signal flow graph method includes the following steps:

[0010] The three modes of the discontinuous conduction mode DC / DC converter in steady state are analyzed to obtain the voltage and current waveforms at both ends of the energy storage inductor. The three modes are Mode I: the switch tube is turned on and the freewheeling diode is turned off; Mode II: the switch tube is turned off and the freewheeling diode is turned on; Mode III: both the switch tube and the freewheeling diode are turned off.

[0011] When the DC / DC converter is a non-isolated converter, the corresponding energy storage inductor element is a pure inductor, which can be equivalent to the control variable being the duty cycle disturbance. The voltage controls the current source and the internal resistance in parallel; when the DC / DC converter is an isolated converter and the transformer has an energy storage function, the corresponding transformer is a coupled inductor type, and on the basis of the pure inductance, it is also connected in parallel with an ideal transformer.

[0012] Furthermore, for the energy storage inductor in the DC / DC converter, based on the current waveform in the discontinuous conduction mode, the time that the switch tube and the freewheeling diode are turned on due to the disturbance of the duty cycle is calculated as:

[0013]

[0014] Where D1 and D2 are the ratios of the conduction time of the switch tube and the freewheeling diode to the switching period T respectively.

[0015] The increment of the inductor stored charge during a switching cycle is calculated as

[0016]

[0017] Among them I peak It is the maximum value of the current flowing through the inductor when the switch is on.

[0018] The increased charge can be equivalent to a current source in one switching cycle

[0019]

[0020] Where V L It is the voltage across the inductor when the switch is turned on.

[0021] The internal resistance of the controlled current source is calculated using the imposed perturbation method:

[0022]

[0023] Where L M is the inductance of the inductor, V Applied is the duration of the voltage applied to the inductor L.

[0024] Furthermore, because there is a period D3×T=[1-(D1+D2)]×T during a switching cycle when neither the switch tube nor the freewheeling diode is conducting, the energy storage inductor changes due to the duty cycle. The current formed can be transmitted to the load end, so the freewheeling diode branch can be equivalent to a branch with a gain of 1, where D3 is the ratio of the time when the switch tube and the freewheeling diode are not conducting to the switching period T.

[0025] Furthermore, the output filter capacitor branch in the converter is directly equivalent to the impedance 1 / sC in the complex frequency domain.

[0026] Furthermore, the process of establishing the converter signal flow graph is as follows: establishing an equivalent model of the inductor, from the duty cycle Start by building a gain of The branch of the switch tube and the freewheeling diode conduction time increment is obtained The connection gain is branch to obtain the current of the controlled current source.

[0027] Furthermore, determine whether the DC / DC converter is an isolated converter. If it is a non-isolated converter, the energy storage inductor is a pure inductor type and there is no need to convert voltage and current. If the converter is isolated and the transformer stores energy, the transformer is a coupled inductor type and voltage and current conversion is required.

[0028] Furthermore, based on the established converter signal flow graph, the Mason formula is directly used to complete the calculation of the duty cycle to output transfer function.

[0029] Compared with the prior art, the present invention clarifies the physical meaning of the model from the essence of the small signal model during the derivation of the model; directly uses the Mersenne formula in the calculation of the model, avoiding the complex calculations in the traditional modeling method, and can effectively reduce the difficulty of modeling the discontinuous conduction mode DC / DC converter. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0031] Figure 1 It is an equivalent model of a pure inductive energy storage inductor.

[0032] Figure 2 It is an equivalent model of coupled inductor type energy storage inductor.

[0033] Figure 3 It is the inductor current waveform in the discontinuous conduction mode DC / DC converter.

[0034] Figure 4It is the circuit structure of a flyback converter.

[0035] Figure 5 Figure 2 is a typical waveform (a) of a discontinuous conduction mode flyback converter and an equivalent circuit (bd) of different modes, where b is mode I, c is mode II, and d is mode III.

[0036] Figure 6 This is the circuit for calculating the equivalent internal resistance of an inductor (a) and the waveform of the inductor current (b).

[0037] Figure 7 It is the signal flow diagram of the flyback converter transformer model.

[0038] Figure 8 It is the signal flow diagram of the flyback converter.

[0039] Fig. 9 It is a flyback converter simulation model.

[0040] Fig.10 These are the amplitude-frequency characteristics (a) and phase-frequency characteristics (b) of the flyback converter. DETAILED DESCRIPTION

[0041] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0042] The small signal modeling method of the discontinuous current mode converter based on the signal flow graph method uses the characteristics of the mainstream DC / DC converter that it stores energy during the on-time of the switch tube and transfers the stored energy to the output end in the off state. It directly uses a controlled current source to equate the change in inductor current caused by the duty cycle disturbance. It mainly includes the following steps:

[0043] The three modes of the discontinuous conduction mode DC / DC converter in steady state are analyzed, namely, the switch tube is turned on and the freewheeling diode is turned off, the switch tube is turned off and the freewheeling diode is turned on, and both the switch tube and the freewheeling diode are turned off, and the voltage and current waveforms at both ends of the energy storage inductor are obtained.

[0044] DC / DC converters can be divided into two categories, isolated converters and non-isolated converters. Buck converters, Boost converters, and Buck-Boost converters are all non-isolated converters, and the corresponding energy storage inductors are pure inductors, while flyback converters are isolated converters, and the corresponding energy storage inductors are coupled inductors.

[0045] The energy storage inductor in the non-isolated DC / DC converter is a pure inductive type, and the control variable can be used as the duty cycle disturbance The voltage controlled current source (VCCS) and the internal resistance are connected in parallel to be equivalent, such as Figure 1 As shown; the energy storage inductor in the isolated DC / DC converter is a coupled inductor type, and an ideal transformer needs to be connected in parallel on the basis of the pure inductor equivalent circuit, as shown Figure 2 shown.

[0046] The waveform of the inductor current in the discontinuous conduction mode DC / DC converter is as follows: Figure 3 As shown, the duty cycle disturbance can be calculated to increase the time for the switch tube and the freewheeling diode to be turned on:

[0047]

[0048] Where D1 and D2 are the ratios of the conduction time of the switch tube and the freewheeling diode to the switching period T respectively.

[0049] The increment of the inductor stored charge during a switching cycle can be calculated as

[0050]

[0051] I peak is the maximum value of the current flowing through the inductor when the switch is on. The added charge can be equivalent to the following current source in one switching cycle:

[0052]

[0053] V in the formula L It is the voltage across the inductor when the switch is turned on.

[0054] The internal resistance of the controlled current source can be calculated using the imposed perturbation method:

[0055]

[0056] In the formula, L M is the inductance of the inductor, V Applied is the duration of the voltage applied to the inductor L.

[0057] The modeling of the branch where the freewheeling diode D is located is another key point of the modeling work. Because in a switching cycle, there is a period D3×T=[1-(D1+D2)]×T when the switch tube and the freewheeling diode are not conducting, the energy storage inductor changes due to the duty cycle The resulting current can be transferred to the load end, so the freewheeling diode can be equivalent to a branch with a gain of 1.

[0058] For an isolated DC / DC converter, the corresponding energy storage inductor is a coupled inductor type, which is connected in parallel with an ideal transformer on the basis of the pure inductor to be equivalent.

[0059] The capacitor branch in the converter can be equivalent to the capacitor impedance 1 / sC in the complex frequency domain. The model established in this way is directly a small signal model in the complex frequency domain; the transformer in the converter, such as the forward converter, can be equivalent to an ideal transformer.

[0060] The specific converter modeling process is to establish an equivalent model of the inductor, from the duty cycle Start by building a gain of The branch of the switch tube and the freewheeling diode conduction time increment is obtained The connection gain is The branch of the controlled current source is connected to the inductor branch to obtain the current of the controlled current source. Determine whether the converter is an isolated converter. If it is, the voltage and current are converted according to the characteristics of the transformer; if it is not, the inductor branch is directly connected to the freewheeling diode branch.

[0061] Based on the converter signal flow graph established previously, the Mason formula in the automatic control principle can be used directly to complete the calculation of duty cycle to output transfer function, etc.

[0062] The present invention is specifically described below by taking a flyback converter as an example:

[0063] The circuit structure of the flyback converter (the transformer in the flyback converter is a coupled inductor type) is as follows Figure 4 As shown, V in is the input of the converter, T r For transformer, the excitation inductance L can be used m It is equivalent to an ideal transformer with a transformation ratio of N in parallel, D is a freewheeling diode, C o is the output capacitor, R is the load, Q is the switch tube, V o is the output voltage.

[0064] According to the on and off states of the flyback converter switch tube and the freewheeling diode, the intermittent conduction mode can be equivalent to three working states, such as Figure 5 b, c and d, and then the transformer T r The input current and output current waveforms are as follows: Figure 5 i in a Lm and i sec .

[0065] Converting the current on the secondary side of the transformer to the primary side, we can get Figure 3 The steady-state current of the magnetizing inductor, I priPkis the maximum current flowing through the excitation inductor, D1 is the on-duty cycle of the switch, and D2 is the on-duty cycle of the freewheeling diode.

[0066] Apply a perturbation to the switch's on-duty cycle The conduction time increment of the switch tube and the freewheeling diode can be obtained as

[0067]

[0068] Then the increment of transformer excitation inductance current can be calculated as

[0069]

[0070] Due to the duty cycle The change of transformer excitation inductance L m To increase the stored charge, the change in charge is divided by the duty cycle disturbance during the switching period T. The increase in the conduction time of the switch tube and the output diode can be equivalent to a current source controlled by the duty cycle.

[0071] The circuit for calculating the equivalent internal resistance of a controlled current source using the applied voltage method is as follows: Figure 6 As shown, Z Lout is the equivalent internal resistance of the power supply, V T is the duration of applied voltage, and the inductance L M The stored charge is the area enclosed by the triangle in the figure.

[0072]

[0073] Then the current formed by the voltage applied to the inductor L in one switching cycle is

[0074]

[0075] The average value of the applied voltage in one switching cycle is v T(avg) =V T ×T L / T, the equivalent power supply internal resistance can be calculated as

[0076]

[0077] The equivalent current source and equivalent internal resistance are calculated to realize the modeling of the excitation inductance. In the equivalent excitation inductance modeling of the opposite-end transformer, the influence of the transformer must also be considered. A transformer with a transformation ratio of N:1 is connected in parallel at both ends of the non-ideal controlled current source to obtain the following: Figure 2 The equivalent model shown.

[0078] Next, we build a signal flow graph for the transformer to model the disturbance of duty cycle. Starting from, the gain of connecting the first branch is This can get the increment of the conduction time of the switch tube and the freewheeling diode Then connect the second branch gain to The second branch of the excitation inductor current is obtained. Finally, a branch with a gain of N is connected so that the disturbance of the excitation inductor current can be converted to the secondary current of the transformer.

[0079] In order to calculate the equivalent internal resistance of the controlled current source, it is also necessary to start from the secondary side of the transformer and assume that the voltage disturbance acting on the secondary side of the transformer is Starting from the voltage disturbance, a branch with a gain of N is connected to convert the disturbance on the secondary side to the excitation inductance to obtain the disturbance of the reflected voltage. According to the previous calculation, the voltage disturbance The connection gain is The branch is used to equalize the internal resistance of the controlled current source. After the previous calculation, the equivalent small signal model of the transformer is obtained, as shown in Figure 7 shown.

[0080] Next, the overall small signal model of the converter is established, and the secondary side current disturbance Connect the branch with a gain of 1 to be equivalent to the freewheeling diode branch. Figure 1 The structure of the flyback converter shows that the output filter capacitor C o It is in parallel with the load R, and the equivalent impedance can be used Equivalent, so that the output current disturbance and output voltage disturbances A branch with the above impedance as gain should be added.

[0081] Output voltage disturbance It will also be fed back to the excitation inductance, which is done by the disturbance of the secondary voltage of the transformer. To describe this effect, we create an output voltage disturbance Disturbance to the secondary voltage The gain of the branch is D2. In this way, the overall signal flow diagram of the flyback converter is established, as shown in Figure 8 shown.

[0082] according to Figure 8 The signal flow diagram shows that from the duty cycle disturbance d to the output voltage disturbance There is a forward path The gain of the forward path is

[0083]

[0084] There are also independent loops in the signal flow graph The gain of the loop is

[0085]

[0086] The transfer function from duty cycle to output is calculated using the Mason formula:

[0087]

[0088] in is the DC gain, is the turning frequency.

[0089] In order to verify the correctness of the application model, a simulation model of the flyback converter in discontinuous current mode was established using PSIM software (such as Fig. 9 The main parameters of the flyback converter are shown in Table 1.

[0090] Table 1 Flyback converter parameters

[0091] Parameter name Parameter Value unit Input voltage Vin 24 V Output voltage Vout 12 V <![CDATA[Excitation inductance L m > 12.5 u <![CDATA[Transformation ratio N1 / N2]]> 1 <![CDATA[Leakage inductance L k > 0.15 u Switching frequency f 100 kHz Output filter capacitor C 66 uF Load resistance R 20 Ω <![CDATA[Duty cycle D1]]> 0.18

[0092] From the amplitude-frequency characteristics of the flyback converter ( Fig.10 (a)), it can be seen that the DC gain obtained by PSIM AC analysis is 36.55dB, and the DC gain of the application model is 36.65dB. The error between the two is negligible. In addition, the corner frequencies 219Hz and 214Hz obtained by PSIM simulation and the application model are consistent, which proves that the AC small signal model established by the application is correct. The phase-frequency characteristics of the application model and the amplitude-frequency characteristics obtained by PSIM software simulation ( Fig.10 (b)) is consistent throughout the entire simulation range, which also proves the correctness of the model and modeling method of this application.

[0093] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A modeling method for a discontinuous conduction mode DC / DC converter based on a signal flow graph method, characterized in that: The following steps are involved: The three modes of the discontinuous conduction mode DC / DC converter in steady state are analyzed to obtain the voltage and current waveforms at both ends of the energy storage inductor. The three modes are Mode I: the switch tube is turned on and the freewheeling diode is turned off; Mode II: the switch tube is turned off and the freewheeling diode is turned on; Mode III: both the switch tube and the freewheeling diode are turned off; When the DC / DC converter is a non-isolated converter, the corresponding energy storage inductor element is a pure inductor, which can be equivalent to the duty cycle disturbance as the control variable. The voltage-controlled current source and the internal resistance are connected in parallel; when the DC / DC converter is an isolated converter and the transformer has an energy storage function, the corresponding transformer is a coupled inductor type, and it is connected in parallel with an ideal transformer on the basis of the pure inductor; for the energy storage inductor in the DC / DC converter, according to the current waveform of the discontinuous conduction mode, the duty cycle disturbance causes the switch tube and the freewheeling diode to increase the conduction time. Where D1 and D2 are the ratios of the conduction time of the switch tube and the freewheeling diode to the switching period T respectively; The increment of the inductor stored charge in one switching cycle is calculated as Among them I peak is the maximum value of the current flowing through the inductor when the switch is on; The increased charge can be equivalent to the following current source in one switching cycle Where V L is the voltage across the inductor when the switch is turned on; The internal resistance of the controlled current source is calculated using the imposed perturbation method: Where L M is the inductance of the inductor, V Applied is the duration of the voltage applied to the inductor L.

2. The discontinuous conduction mode DC / DC converter modeling method based on the signal flow graph method according to claim 1 is characterized in that: Because there is a period D3×T=[1-(D1+D2)]×T during a switching cycle when neither the switch tube nor the freewheeling diode is conducting, the energy storage inductor changes due to the duty cycle. The current formed can be transmitted to the load end, so the freewheeling diode branch can be equivalent to a branch with a gain of 1, where D3 is the ratio of the time when the switch tube and the freewheeling diode are not conducting to the switching period T.

3. The discontinuous conduction mode DC / DC converter modeling method based on the signal flow graph method according to claim 1 is characterized in that: The output filter capacitor branch in the converter is directly equivalent to the impedance 1 / sC in the complex frequency domain.

4. The discontinuous conduction mode DC / DC converter modeling method based on the signal flow graph method according to claim 1 is characterized in that: The process of establishing the converter signal flow graph is as follows: Establish an equivalent model of the inductor, from the duty cycle Start by building a gain of The branch of the switch tube and the freewheeling diode conduction time increment is obtained The connection gain is branch to obtain the current of the controlled current source.

5. The discontinuous conduction mode DC / DC converter modeling method based on the signal flow graph method according to claim 4 is characterized in that: Determine whether the DC / DC converter is an isolated converter. If it is a non-isolated converter, the energy storage inductor is a pure inductor and does not need to be converted into voltage and current. If the converter is of isolated type and the transformer stores energy, and the transformer is of coupled inductor type, the voltage and current must be converted.

6. The discontinuous conduction mode DC / DC converter modeling method based on the signal flow graph method according to claim 4 is characterized in that: Based on the established converter signal flow graph, the Mason formula is directly used to complete the calculation of the duty cycle to output transfer function.

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