Resonant converter optimization method and system based on fmincon function

Abstract

The application discloses a resonant converter optimization method and system based on an fmincon function, which first determines transformer ratio and maximum and minimum values of converter output voltage DC gain; then converts an LLC resonant converter into an equivalent circuit, and deduces the converter output voltage DC gain as a first constraint condition; and establishes a converter loss model according to the equivalent circuit; analyzes the condition for realizing ZVS (Zero Voltage Switching) of a switching tube as a second constraint condition; finally, an optimization design function fmincon is called to perform optimization design on the resonant converter parameters. The loop power consumption of the converter is taken as an evaluation index for the resonant converter parameter design, the output voltage DC gain and the condition for realizing ZVS of the switching tube are taken as constraint conditions, the LLC resonant converter parameters are comprehensively evaluated, the LLC resonant converter parameters are obtained, which make all indexes of the converter reach the best balance, and the overall performance of the converter is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power electronics, in particular to a resonant converter optimization method and system based on fmincon function. BACKGROUND

[0002] The development trend of switching power supply is high switching frequency, high power density and small size. Increasing the switching frequency of the converter can reduce the size of the transformer, but the increase of switching frequency will cause the switching loss to increase significantly, and the output efficiency of the power supply will also decrease significantly. In order to reduce the switching loss, the resonant circuit is usually used to make the switching device of the converter operate in a soft switching state. LLC resonant converter is improved on the basis of traditional second-order LC resonant converter by adding a parallel resonant inductor. Compared with the traditional series and parallel resonant converter, the LLC resonant converter has obvious improvement in characteristics. In recent years, the LLC resonant converter with soft switching characteristics and wide gain range has become a popular topology in power converter research, and has been successfully applied to different power supply products to realize high-performance DC / DC conversion. How to effectively optimize the parameters to make the LLC resonant converter fully exert its advantages and make the working frequency, loop loss and output voltage DC gain of the converter reach the best balance has been a difficult problem. Unreasonable parameter design will directly affect the overall performance of the system. SUMMARY

[0003] The present application aims to overcome the above technical deficiencies and provide a resonant converter optimization method and system based on fmincon function, which solves the problem of unreasonable parameter design affecting the overall performance of the switching power supply system.

[0004] To achieve the above technical purpose, the present application provides a resonant converter optimization method based on fmincon function, which includes the following steps:

[0005] Obtain the performance parameters of the LLC resonant converter, determine the transformer ratio and the maximum and minimum values of the converter output voltage DC gain;

[0006] The LLC resonant converter is converted into an equivalent circuit by using the fundamental analysis method, and the converter output voltage DC gain is derived as the first constraint condition;

[0007] According to the equivalent circuit, a converter loss model is established;

[0008] The condition for the switching tube to realize ZVS is analyzed as the second constraint condition;

[0009] The optimization design function fmincon is called, the total loss of the transformer is taken as an objective function, the transformer output voltage DC gain and the condition of realizing ZVS of the switch tube are taken as constraint conditions, and the LLC resonant converter parameters are found when the total loss of the transformer is minimum under the constraint conditions.

[0010] The application further provides a resonant converter optimization system based on the fmincon function, which comprises the following functional modules.

[0011] The parameter determination module is used for acquiring the performance parameters of the LLC resonant converter, and determining the transformer ratio and the maximum and minimum values of the transformer output voltage DC gain.

[0012] The equivalent circuit transformation module is used for transforming the LLC resonant converter into an equivalent circuit by using the fundamental wave analysis method, and deriving the transformer output voltage DC gain as the first constraint condition.

[0013] The loss model establishment module is used for establishing the transformer loss model according to the equivalent circuit.

[0014] The condition analysis module is used for analyzing the condition of realizing ZVS of the switch tube as the second constraint condition.

[0015] The optimization design module is used for calling the optimization design function fmincon, taking the total loss of the transformer as an objective function, taking the transformer output voltage DC gain and the condition of realizing ZVS of the switch tube as constraint conditions, and finding the LLC resonant converter parameters when the total loss of the transformer is minimum under the constraint conditions.

[0016] Compared with the prior art, the application takes the loop power consumption of the transformer as an evaluation index of resonant converter parameter design, takes the output voltage DC gain and the condition of realizing ZVS of the switch tube as constraint conditions, comprehensively evaluates the LLC resonant converter parameters, obtains the LLC resonant converter parameters that make the working frequency, loop loss, output voltage DC gain and other indexes of the transformer reach the best balance, and effectively improves the overall performance of the transformer. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flow block diagram of the resonant converter optimization method based on the fmincon function according to the embodiment of the application;

[0018] Figure 2 is a circuit principle diagram of the LLC resonant converter;

[0019] Figure 3 is an equivalent circuit diagram of the LLC resonant converter;

[0020] Figure 4 is a DC gain curve diagram under different K values;

[0021] Figure 5 is a DC gain curve diagram at different Q values;

[0022] Figure 6 is a working waveform diagram of the LLC resonant converter when f s = f r .

[0023] Figure 7 is a working state waveform diagram of the LLC resonant converter when f m < f s < f r .

[0024] Figure 8 is a module schematic diagram of the resonant converter optimization system based on the fmincon function according to the embodiment of the present application. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0026] As shown in Figure 1 , the embodiment of the present application provides a resonant converter optimization method based on the fmincon function, which comprises the following steps:

[0027] S1, obtaining the performance parameters of the LLC resonant converter, determining the transformer turns ratio and the maximum and minimum values of the converter output voltage DC gain.

[0028] The circuit schematic diagram of the LLC resonant converter is shown in Figure 2 , and the performance parameters of the LLC resonant converter include: the minimum input voltage V inmin , the maximum input voltage V inmax , the rated input voltage V in , the rated output voltage V o , the rated output current I o , the rated power P o , the load resistance R o , the transformer turns ratio N, the switching frequency f s , the resonant frequency f r , the dead time T d , the junction capacitance of the switch tube C j ; the transformer turns ratio N and the maximum M max and minimum M min values of the converter output voltage DC gain are preliminarily determined by the converter performance parameters.

[0029] The transformer turns ratio N is:

[0030]

[0031] maximum output voltage DC gain M max is:

[0032]

[0033] minimum output voltage DC gain M min is:

[0034]

[0035] converter first resonant frequency f r is:

[0036]

[0037] converter second resonant frequency f m is:

[0038]

[0039] converter switching frequency f s , the analysis of the converter operating mode, it is known that, when f m <f s <f r , the resonant network works in inductive region, resonant capacitor C r , resonant inductor L r , excitation inductance L m involved in the resonance, the converter can achieve rectifier diode zero current turn-off (ZCS) and switch tube zero voltage turn-on (ZVS) in this mode; when f s >f r , the primary switch tube can achieve ZVS, but the rectifier diode is hard off, there is a reverse recovery problem; when f s =f r , the resonant network works in full resonance state, due to the clamping effect of the transformer in the converter, the voltage across the excitation inductance is always stable at NV o , the system gain is independent of the load, only related to the transformer ratio N, the system can achieve ZVS switch tube and ZCS rectifier diode. When the switching frequency f s of LLC resonant network works near the resonant frequency f r , the circuit has the highest conversion efficiency, which is also its best working area.

[0040] S2, the fundamental analysis method is used to convert the LLC resonant converter into an equivalent circuit, and the output voltage DC gain of the converter is derived as the first constraint condition.

[0041] Specifically, the fundamental harmonic analysis (FHA) is used to analyze the resonant converter, and it is assumed that the converter only relies on the fundamental component of the switching frequency for energy transmission, and each part is equivalent to a sinusoidal circuit. The nonlinear resonant conversion circuit is simplified and equivalent to a linear circuit for analysis. The equivalent circuit diagram of the LLC resonant converter is shown in Figure 3 In the full-bridge structure, the voltage v AB after the switching network inverter is a square wave with an amplitude of V in , and the starting time of the positive direction is 0. After Fourier decomposition of v AB , the following can be obtained:

[0042]

[0043] Where ω s = 2πf s is the angular frequency of the driving signal.

[0044] The fundamental component expression of v AB is:

[0045]

[0046] The effective value of the fundamental component is V AB1 , and its size is:

[0047]

[0048] The load effect of the rectifier output network on the resonant network can be equivalent to a resistance R e :

[0049]

[0050] The normalized inductance K value is:

[0051]

[0052] The normalized frequency f n is:

[0053]

[0054] The quality factor Q of the circuit is:

[0055]

[0056] Where ω = 2πf r .

[0057] According to the equivalent circuit of the LLC resonant converter, the expression of the converter output voltage DC gain M is:

[0058]

[0059] Figure 4 DC gain curves for different K values when Q = 0.2. It can be seen that the smaller the K value, the greater the DC gain, and the narrower the frequency modulation range. This means that the gain of the circuit can be flexibly controlled and adjusted by changing the switching frequency within a narrow range. The quality factor Q value and the resonant frequency f r Under certain conditions, the smaller the K value, the smaller the excitation inductance L m If L m is too small, it will cause the current ripple flowing through the excitation inductance to be too large, thereby increasing the energy circulation and conduction loss. Therefore, the K value should not be too high or too low, and should be selected within a reasonable range, generally between 2 and 6.

[0060] The original definition of the quality factor Q is the ratio of reactive power to active power. In the resonant cavity, Q is proportional to the reactive power, and the reactive power is proportional to the circulating current amplitude. Therefore, increasing Q means increasing the circulating current, which will increase the conduction power loss and reduce the efficiency of the converter. From the expression of the quality factor Q, under the condition that L r and C r are determined, the value of Q depends on the size of the load. When the load is heavy, the Q value of the circuit is high, and when the load is light, the Q value is low. For example, Figure 5 is the DC gain curve for different Q values when k = 4. The area enclosed by the two dashed lines is the gain variation range determined by M max and M min . By observing Figure 5 , it can be seen that the larger the Q value, the lower the DC gain of the system, and when the Q value is very large, the system will not meet the system voltage gain requirement. When the Q value is very small, the DC gain will become very large, the peak value of the gain curve and the slope of the curve will increase, and small frequency changes will cause large voltage gain changes, affecting the stability of the system. The appropriate Q value should be selected according to the maximum gain M max to achieve the specified output range.

[0061]

[0062] M(f nmin ) is the normalized minimum operating frequency f nmin corresponding to the maximum DC gain actually achievable by the LLC resonant converter, and M(f nmax ) is the normalized maximum operating frequency f nmax corresponding to the minimum DC gain actually achievable by the LLC resonant converter. In order to ensure the constancy of the output voltage under wide-range input voltage, the voltage gain of the designed resonant network should be within the allowed switching frequency range, and then the following constraint condition is obtained:

[0063] M(f nmin )≥M max

[0064] M(f nmax )≤M min

[0065] S3、According to the equivalent circuit, a transformer loss model is established.

[0066] The LLC resonant converter can realize ZVS of the switching tube and ZCS of the rectifier diode, and the loss of the converter is mainly the on-state loss P Q_con , the off-state loss P Q_off of the switching tube and the on-state loss P D_con of the rectifier diode.

[0067] The expression of the on-state loss P Q_con of the switching tube is:

[0068]

[0069] Wherein, f s is the switching frequency of the converter, R ds is the on-state resistance of the switching tube, i r (t) is the instantaneous value of the resonant current, T s is the switching period.

[0070] The expression of the off-state loss P Q_off of the switching tube is:

[0071] P Q_off =f s V in (I r0 t fall +2C j V in )

[0072] Wherein, V in is the rated input voltage, t fall is the current falling time of the switching tube, C j is the junction capacitance of the switching tube, and I r0 is the initial value of the resonant current.

[0073] The expression of the on-state loss P D_con of the rectifier diode is:

[0074]

[0075] Wherein, V dio is the on-state voltage drop of the rectifier diode, R dio is the on-state resistance of the rectifier diode, and i D(t) is the difference between the resonant current and the magnetizing current i m (t).

[0076] 1) When f s = f r , the working state waveform of the LLC resonant converter is shown in Figure 6 .

[0077] When the LLC resonant converter works at the resonant point, in the first half cycle, the resonant current instantaneous value i r (t) is expressed as:

[0078]

[0079] The magnetizing current instantaneous value i m (t) is expressed as:

[0080]

[0081] Where I r0 is the initial value of the resonant current, I m0 is the initial value of the magnetizing current, and V Cr0 is the initial value of the resonant capacitor voltage, which is expressed as:

[0082]

[0083]

[0084] i D (t) is the difference between the resonant current and the magnetizing current i m (t), which is expressed as:

[0085]

[0086] 2) When f m <f s <f r , the working state waveform of the LLC resonant converter is shown in Figure 7 .

[0087] In the first half cycle, the resonant current instantaneous value i r (t) is expressed as:

[0088]

[0089] Where T s is the switching period, I r1 and I m1 are the resonant current value and the magnetizing current value at t1, respectively, and V Cr1 is the resonant capacitor voltage value, which is expressed as:

[0090]

[0091]

[0092]

[0093] The total loss P of the converter in the above two modes can be expressed as:

[0094] P = P Q_con + P Q_off + P D_con = f(K, Q, L m , f n ).

[0095] S4, analyze the condition of the switch tube to realize ZVS as the second constraint condition.

[0096] LLC resonant converter has the advantages of high switching frequency, high power density and high efficiency. The basis of these advantages is that the switch tube must be able to realize soft switching, i.e. ZVS, and that the input current of the resonant network must lag the input voltage (i.e. working in the inductive operating area) is a necessary condition for realizing ZVS but not a sufficient condition. The size of the dead zone (in order to prevent the upper and lower switches of the full-bridge or half-bridge from being turned on at the same time, a dead zone needs to be added in the drive of the complementary conduction switch) will also affect whether the switch tube can realize ZVS. This is because during the dead zone time, the current is continued through the other set of switches, and during the current continuation process, the parasitic capacitance of the switch tube and the parasitic capacitance in parallel with the resonant network need to be charged and discharged, which is called commutation. The commutation process must be completed within the dead zone time, otherwise the switch tube ZVS cannot be realized.

[0097] During the dead zone time of the upper and lower switches in one bridge arm, the resonant current lags behind the input square wave voltage, and the inductive load current cannot change abruptly, so the current direction does not change, but the voltage drops from V in to 0. This current charges and discharges the parasitic capacitance, and since the dead zone time is very short, the current is considered to be constant during this time. This current must complete the above process within the dead zone time, i.e. the current must be greater than the charging and discharging current required by the parasitic capacitance.

[0098]

[0099] where I p is the size of the resonant current at t , which is equal to the peak value of the excitation current; C j is the junction capacitance of the switch tube, and T d is the dead zone time.

[0100] When the switching frequency f s is equal to the resonant frequency f r , the peak value of the excitation current can be expressed as:

[0101]

[0102] Therefore, the excitation inductance L m The constraint condition is:

[0103]

[0104] S5, calling the optimization design function fmincon, taking the total loss of the transformer as the objective function, taking the DC gain of the transformer output voltage and the condition of realizing ZVS of the switch tube as the constraint condition, and finding the LLC resonant transformer parameters satisfying the constraint condition and the minimum total loss of the transformer.

[0105] The fmincon function in the MATLAB optimization toolbox is a function for solving the minimum value of a multivariable, constrained, nonlinear function, and is suitable for solving local optimization and global optimization problems. Taking the total loss of the transformer as the objective function, taking the DC gain M of the transformer output voltage and the condition of realizing ZVS of the switch tube as the constraint condition, and the optimization target is to find the LLC resonant transformer parameters satisfying the constraint condition and the minimum total loss of the transformer.

[0106] The optimization problem can be described as

[0107]

[0108] Wherein, x is a vector group, and Ω is the value range of x.

[0109] x=[K,Q,L m ,f n ]

[0110] Running the optimization function, the optimal design parameters under the constraint condition are obtained.

[0111] The present application provides a resonant converter optimization design method based on fmincon function, which takes the loop power consumption of the transformer as the evaluation index of resonant converter parameter design, takes the DC gain of the output voltage and the condition of realizing ZVS of the switch tube as the constraint condition, and comprehensively evaluates the LLC resonant converter parameters, so as to obtain the LLC resonant converter parameters that make the working frequency, loop loss, output voltage DC gain and other indicators of the transformer reach the best balance, and effectively improve the overall performance of the transformer.

[0112] Based on the above-mentioned resonant converter optimization method based on fmincon function, the present application further provides a resonant converter optimization system based on fmincon function, as shown in Figure 8 The system comprises the following functional modules:

[0113] The parameter determining module 10 is configured to acquire performance parameters of the LLC resonant converter, and determine the transformer ratio and the maximum and minimum values of the converter output voltage DC gain.

[0114] The equivalent circuit converting module 20 is configured to convert the LLC resonant converter into an equivalent circuit by using the fundamental wave analysis method, and derive the converter output voltage DC gain as a first constraint condition.

[0115] The loss model establishing module 30 is configured to establish a converter loss model according to the equivalent circuit.

[0116] The condition analyzing module 40 is configured to analyze the condition of realizing ZVS of the switching tube as a second constraint condition.

[0117] The optimization design module 50 is configured to call an optimization design function fmincon, take the total loss of the converter as a target function, take the converter output voltage DC gain and the condition of realizing ZVS of the switching tube as constraint conditions, and find the LLC resonant converter parameters satisfying the constraint conditions and having the minimum total loss of the converter.

[0118] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the system, device and unit described above can refer to the corresponding processes in the foregoing method embodiments, which will not be described here.

[0119] In the foregoing embodiments, the description of each embodiment has its own emphasis, and the parts not described or recorded in detail in a certain embodiment can be referred to the relevant description of other embodiments.

[0120] Those skilled in the art can realize that the modules, units and / or method steps of each embodiment described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software mode depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0121] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A resonant converter optimization method based on the fmincon function, characterized in that, Includes the following steps: Obtain the performance parameters of the LLC resonant converter, and determine the transformer turns ratio and the maximum and minimum DC gain of the converter output voltage. The LLC resonant converter is transformed into an equivalent circuit using the fundamental wave analysis method, and the DC gain of the converter output voltage is derived as the first constraint condition. Based on the equivalent circuit, establish a converter loss model; The conditions for achieving ZVS by the switching transistor are analyzed and used as the second constraint. Call the optimization design function fmincon, take the total loss of the converter as the objective function, and take the DC gain of the converter output voltage and the conditions for the switching transistor to achieve ZVS as the constraints, and find the LLC resonant converter parameters that satisfy the constraints and minimize the total loss of the converter. The converter loss model includes the on-state loss and off-state loss of the switching transistors and the on-state loss of the rectifier diodes. The conduction loss of the switching transistor The expression is: in, For the converter switching frequency, The on-state resistance of the switching transistor is... This is the instantaneous value of the resonant current. For switching cycles; The turn-off loss of the switching transistor The expression is: in, The rated input voltage, The turn-off current drop time of the switching transistor. For the junction capacitance of the switching transistor, This is the initial value of the resonant current; The conduction loss of the rectifier diode The expression is: in, For the forward voltage drop of the rectifier diode, This is the on-resistance of the rectifier diode. This is the difference between the resonant current and the excitation current.

2. The resonant converter optimization method based on the fmincon function according to claim 1, characterized in that, The expression for the DC gain M of the converter output voltage is as follows: Where K is the normalized inductance value, and N is the transformer turns ratio. Q is the normalized frequency, and Q is the quality factor of the circuit.

3. The resonant converter optimization method based on the fmincon function according to claim 1, characterized in that, The expression for the total loss P of the converter is: Where K is the normalized inductance value, and Q is the quality factor of the circuit. For magnetizing inductance, This is the normalized frequency.

4. The resonant converter optimization method based on the fmincon function according to claim 1, characterized in that, The condition for the switching transistor to achieve ZVS is that it must complete the freewheeling process through another set of switching transistors within the dead time, and in the process of freewheeling, the parasitic capacitance of the switching transistor and the parasitic capacitance connected in parallel with the resonant network are charged and discharged.

5. The resonant converter optimization method based on the fmincon function according to claim 1, characterized in that, The second constraint is as follows: in, The magnitude of the resonant current at t=T / 2 is equal to the peak value of the excitation current; For the junction capacitance of the switching transistor, The rated input voltage, Dead time; in, For magnetizing inductance; This is the first resonant frequency of the converter.

6. A resonant converter optimization system based on the fmincon function, characterized in that, Includes the following functional modules: The parameter determination module is used to obtain the performance parameters of the LLC resonant converter and determine the transformer turns ratio and the maximum and minimum values ​​of the DC gain of the converter output voltage. The equivalent circuit transformation module is used to transform the LLC resonant converter into an equivalent circuit using the fundamental wave analysis method, and derive the DC gain of the converter output voltage as the first constraint condition. The loss model building module is used to build a converter loss model based on the equivalent circuit. The condition analysis module is used to analyze the conditions under which the switching transistor achieves ZVS, as the second constraint condition; The optimization design module is used to call the optimization design function fmincon, which takes the total loss of the converter as the objective function, and the DC gain of the converter output voltage and the conditions for the switching transistor to achieve ZVS as constraints, to find the LLC resonant converter parameters that minimize the total loss of the converter while satisfying the constraints. The converter loss model includes the on-state loss and off-state loss of the switching transistors and the on-state loss of the rectifier diodes. The conduction loss of the switching transistor The expression is: in, For the converter switching frequency, The on-state resistance of the switching transistor is... This is the instantaneous value of the resonant current. For switching cycles; The turn-off loss of the switching transistor The expression is: in, The rated input voltage, The turn-off current drop time of the switching transistor. For the junction capacitance of the switching transistor, This is the initial value of the resonant current; The conduction loss of the rectifier diode The expression is: in, For the forward voltage drop of the rectifier diode, This is the on-resistance of the rectifier diode. This is the difference between the resonant current and the excitation current.

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