Non-monotonous control method for gain of CLLC resonant converter

Abstract

The invention provides a gain non-monotonous control method for a CLLC resonant converter, and the method comprises the steps: 1, taking a primary side resonant capacitor, a secondary side resonant capacitor, a primary side resonant inductor current and a secondary side resonant inductor current as state variables, building a time domain model, and solving a minimum working frequency value under different loads; 2, when the CLLC resonant converter works, the output voltage and the load current of the CLLC resonant converter are detected, and the load state is judged; 3, if the load is light, the system is in a normal working mode; step 4, if the load is heavy load, the system enters a gain non-monotonous working mode; the system calculates the corresponding minimum frequency under the current condition by calculating the magnitude of the load current, and limits the PI output result above the minimum frequency; and step 5, the system gives a driving signal of a switching tube of the CLLC resonant converter. According to the method, the gain non-monotonous control is realized by reasonably improving the PI control strategy.

Description

Technical Field

[0001] The present application relates to the technical field of power electronic converters, and in particular to a method for controlling non-monotonic gain of a CLLC resonant converter. Background Art

[0002] At present, society has entered an era of high energy consumption. The use of fossil energy has gradually increased, and the impact on the earth's ecological environment has become more serious. Therefore, energy issues and the goal of achieving carbon neutrality have attracted widespread attention. In the field of new energy, although renewable energy such as wind power and solar energy has developed rapidly, its proportion in total energy consumption is still small, and it may cause harmonic pollution to the power grid. In terms of energy application, the number of electric new energy vehicles has increased significantly, even exceeding that of traditional gasoline vehicles. The battery energy storage characteristics of electric vehicles have brought new ideas for optimizing the power system.

[0003] V2G (Vehicle to Grid) technology makes full use of the energy storage characteristics of electric vehicle batteries as a distributed energy storage device to balance the fluctuations of renewable energy generation and optimize grid operation. The development of this technology helps to manage energy more efficiently, improve energy utilization efficiency, and promote sustainable development. In V2G systems, bidirectional DC / DC converters are key power conversion devices. The DC / DC converters in on-board chargers are mainly used to achieve voltage matching, control charging and discharging power, and electrical isolation, while also ensuring bidirectional power flow. Therefore, these converters need to meet requirements such as high efficiency and high power density, and the design is difficult. The bidirectional CLLC resonant converter is a common bidirectional isolated DC / DC topology. It realizes bidirectional symmetrical power flow based on the LLC resonant converter, and has the advantages of a wide soft switching range, high working efficiency, low control complexity, and no magnetic balance problems.

[0004] Since the CLLC resonant converter has one more resonant element than the LLC resonant converter, the CLLC resonant converter has two gain peaks in the under-resonance region under heavy load, which will cause the gain to be non-monotonic under heavy load, and the use of traditional PI modulation will cause loss of control. However, the current research on this feature of the CLLC resonant converter is not in-depth enough, and there is a lack of effective methods to prevent the gain from being non-monotonic. Summary of the invention

[0005] The present application provides a method for controlling gain non-monotonicity of a CLLC resonant converter, which can be used to solve the technical problem of lack of effective methods for preventing gain non-monotonicity.

[0006] The present application provides a non-monotonic gain control method for a CLLC resonant converter, the method comprising:

[0007] Step 1: Use the primary side resonant capacitor u Cr1 , secondary side resonant capacitor uCr2 , the primary side resonant inductor current i Lr1 , the secondary side resonant inductor current i Lr2 As a state variable, a time domain model is established to solve the minimum frequency value under different loads;

[0008] Step 2, when the CLLC resonant converter is working, detecting the output voltage and load current of the CLLC resonant converter, and judging the load state;

[0009] Step 3: According to step 2, if the load is light, the system is in normal working mode;

[0010] Step 4: According to step 2, if the load is heavy, the system enters a gain non-monotonic working mode; and limits the working frequency to a minimum frequency value under the current load;

[0011] Step 5: According to step 3 and step 4, the system gives a driving signal for the switch tube of the CLLC resonant converter.

[0012] Furthermore, in step 1, the time domain model is established to solve the frequency boundary of the mode, that is, the minimum operating frequency, as follows:

[0013] Step 11, confirming the CLLC resonant converter parameters;

[0014] CLLC resonant converter topology, including switches S1–S8, anti-parallel diode D S1 –D S8 And the parasitic capacitance C oss1 –C oss8 ; Primary side resonant inductor L r1 , primary side resonant capacitor C r1 , transformer excitation inductance L m , transformer with a turns ratio of n:1, secondary side resonant inductor L r2 , secondary side resonant capacitor C r2 , output capacitor C s , DC input voltage U in And output resistance R; resonant inductor L r1 , L r2 , resonant capacitor C r1 , C r2 and a transformer with a turns ratio of n:1 forming a resonant cavity of a CLLC resonant converter;

[0015] DC input voltage U in The positive electrode is connected to the source of the primary side switch tubes S1 and S3 at the same time; the DC input voltage U in The negative electrode is connected to the drain of the primary side switch tubes S2 and S4 at the same time; the output capacitor C s In parallel with the output resistor R;

[0016] Step 12: Establish a time domain model of the CLLC resonant converter and derive the CLLC resonant converter i by using time domain analysis. Lr1N ,i Lr2N ,u Cr1N ,u Cr2N Sub-resonant time domain expressions;

[0017] Step 13, solving the boundary conditions of the CLLC resonant converter;

[0018] Step 14, solving for the frequency boundary.

[0019] Further, step 11, confirming the CLLC resonant converter parameters, includes:

[0020] The CLLC resonant converter operates at the series resonant frequency f of the two components on the primary side. r , the series resonant frequency of the two elements is as follows:

[0021]

[0022] Where, L r1 is the primary side resonant inductance, C r1 is the primary side resonant capacitor; the voltage variable of the CLLC resonant converter is based on the input voltage U in Standardize all current variables according to U in / Z r Normalize to unit, where Z r is the primary side resonant inductance L r1 and the primary side resonant capacitor C r1 Characteristic impedance:

[0023]

[0024] Further, in step 12, a time domain model of a CLLC resonant converter is established, and the CLLC resonant converter i is derived by using time domain analysis. Lr1N ,i Lr2N ,u Cr1N ,u Cr2N Sub-resonant time domain expressions; including:

[0025] When the CLLC resonant converter is in PO mode, assuming that the O mode excitation current does not change; solve the CLLC resonant converter under the under-resonance PO mode i Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per unit expression of is:

[0026] P mode i under sub-resonant heavy load Lr1N ,i Lr2N ,u Cr1N,u Cr2N The per-unit expression is as follows:

[0027]

[0028] where ω r is the angular frequency of the resonant converter, ω k1 =k1ω r is the second angular frequency of the resonant converter, k=L m / L r1 , L m is the magnetizing inductance of the transformer, L r1 is the primary side resonant inductance; M output voltage U o The per unit value M = U in / nU o , f n The per-unit value of the operating frequency is f n =f s / f r , R is the output resistance;

[0029] O mode under sub-resonant heavy load Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per-unit expression is as follows:

[0030]

[0031] where u Cr1N (0.5T r ) is 0.5T r The per-unit value of the primary side resonant capacitor voltage at time i Lr1N (0.5T r ) is 0.5T r The per-unit value of the primary side resonant inductor current at the moment, u Cr2N (0.5T r ) is 0.5T r The per-unit value of the secondary side resonant capacitor voltage at moment ; based on the derivation of the time domain expression of the sub-resonant region of the CLLC resonant converter.

[0032] Further, step 13, solving the boundary conditions of the CLLC resonant converter, includes:

[0033] There are OPO / PO / PON / PN modes in the under-resonance region of the CLLC resonant converter; the OPO / PO mode gain is monotonic, the overloaded PON mode has an improvement to enter the non-monotonic gain range, and the overloaded PN mode will definitely enter the non-monotonic gain range; first calculate the frequency and load range conditions for entering the PON and PN modes;

[0034] The boundary between the PO mode and the PON mode is described as follows: the resonant capacitor will not be overcharged before the end of the O mode, causing the secondary side diode to turn on prematurely; similarly, for the PON mode and the PN mode, the resonant capacitor will not be overcharged before the end of the N mode, which will cause the secondary side diode to turn on prematurely; based on this, the following relationship equation is derived:

[0035]

[0036] Where T s is the actual period of the resonant converter, T r is the resonant period of the resonant converter, M output voltage U o The per unit value M = U in / nU o ,u Cr1N (0.5T s ) is 0.5T s The voltage value of the first resonant capacitor on the primary side at the moment, u Cr2N (0.5T s ) is 0.5T s The per unit value of the voltage of the second resonant capacitor on the primary side at the moment, u Cr1N (0.5T s ) is 0.5T s The per unit voltage value of the first resonant capacitor on the primary side at the moment, u Cr2N (0.5T s ) is 0.5T s The per-unit value of the voltage of the second resonant capacitor on the primary side at this moment.

[0037] Furthermore, step 14, solving the frequency boundary, includes:

[0038] Time domain analysis shows that part of the PON mode exhibits monotonic gain, while the other part exhibits non-monotonic gain. The boundary between the PO mode and the PON mode is calculated to avoid the non-monotonic gain region and maintain a certain margin. The frequency boundary between the PO mode and the PON mode is obtained as:

[0039]

[0040] where f s is the actual operating frequency, I o is the output current, f r is the resonant frequency, Z r is the characteristic impedance of the resonant converter, and n is the transformer ratio;

[0041] That is, the minimum operating frequency of the CLLC resonant converter is:

[0042]

[0043] When the frequency f s When the frequency f is greater than the minimum value, the resonant converter operates in the gain monotonic mode; s When it is less than the minimum value, the resonant converter operates in a non-monotonic mode.

[0044] Further, in step 4, according to step 2, if the load is heavy, the system enters a gain non-monotonic working mode; and limits the working frequency to a minimum frequency value under the load, including:

[0045] According to step 2, if it is overloaded, the system enters a gain non-monotonic working mode;

[0046] The system calculates the corresponding minimum frequency under the current situation by calculating the load current, and limits the operating frequency to above the minimum frequency.

[0047] The gain non-monotonic control method proposed in the present invention effectively prevents the gain non-monotonicity caused by the two gain peaks in the CLLC resonant converter itself, and its analysis and control are simple. Through the improved PI control, the CLLC resonant converter is prevented from entering the non-monotonic gain range, thereby causing the possibility of control imbalance, thereby improving the reliability of the CLLC resonant converter. At the same time, the proposed control method can also effectively reduce the load shedding time and overshoot, so this control method is not only highly versatile, but also has excellent control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a circuit diagram of a CLLC resonant converter which is a controlled object of the present invention.

[0049] Figure 2 It is a schematic diagram of the under-resonance working waveform of the CLLC resonant converter of the present invention.

[0050] Figure 3 It is a schematic diagram of the non-monotonic gain range of the CLLC resonant converter of the present invention.

[0051] Figure 4 It is a schematic diagram of the PO-PON-PN modal gain interval analysis of the present invention.

[0052] Figure 5 It is a schematic diagram of the traditional PI switching heavy load control stage of the CLLC resonant converter of the present invention.

[0053] Figure 6 It is a schematic diagram of the traditional PI boost voltage control stage of the CLLC resonant converter of the present invention.

[0054] Figure 7 It is a schematic diagram of the improved PI control flow of the present invention.

[0055] Figure 8 It is a comparison diagram of the control gain of the present invention and the traditional PI control.

[0056] Fig. 9 This is the simulation waveform of the traditional PI during the loading process.

[0057] Fig.10 This is the resonant waveform of the traditional PI after gain imbalance during the loading process.

[0058] Fig.11 It is a simulation waveform diagram of the control method in the present invention during the loading process.

[0059] Fig.12 It is a resonant waveform diagram of the control method in the present invention after the loading process. DETAILED DESCRIPTION

[0060] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0061] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0062] Step 1: Use the primary side resonant capacitor u Cr1 , secondary side resonant capacitor u Cr2 , the primary side resonant inductor current i Lr1 , the secondary side resonant inductor current i Lr2 As a state variable, a time domain model is established to solve the frequency boundary of the mode;

[0063] Step 2, when the CLLC resonant converter is working, detecting the output voltage and load current of the CLLC resonant converter, and judging the load state;

[0064] Step 3: According to step 2, if the load is light, the system is in normal working mode;

[0065] Step 4: According to step 2, if the load is heavy, the system enters the gain non-monotonic working mode; the system calculates the minimum frequency corresponding to the current situation by calculating the load current, and limits the PI output result to above the minimum frequency;

[0066] Step 5: According to step 3 and step 4, the system gives a driving signal for the switch tube of the CLLC resonant converter.

[0067] In a further embodiment, in step 1, the steps of establishing a time domain model to solve the frequency boundary of the mode, i.e., the minimum operating frequency, are as follows:

[0068] Step 11, confirm the CLLC resonant converter parameters: Figure 1 It is a CLLC resonant converter topology, including switch tubes S1–S8, anti-parallel diode D S1 –D S8And the parasitic capacitance C oss1 –C oss8 ; Primary side resonant inductor L r1 , primary side resonant capacitor C r1 , transformer excitation inductance L m , transformer with a turns ratio of n:1, secondary side resonant inductor L r2 , secondary side resonant capacitor C r2 , output capacitor C s , DC input voltage U in And output resistance R; resonant inductor L r1 , L r2 , resonant capacitor C r1 , C r2 and a transformer with a turns ratio of n:1 forming a resonant cavity of a CLLC resonant converter;

[0069] DC input voltage U in The positive electrode is connected to the source of the primary side switch tubes S1 and S3 at the same time; the DC input voltage U in The negative electrode is connected to the drain of the primary side switch tubes S2 and S4 at the same time; the output capacitor C s In parallel with the output resistor R.

[0070] The CLLC resonant converter operates at the series resonant frequency f of the two components on the primary side. r , where the series resonant frequency of the two components is as follows:

[0071]

[0072] Where, L r1 is the primary side resonant inductance, C r1 is the primary side resonant capacitor; the voltage variable of the CLLC resonant converter is based on the input voltage U in Standardize all current variables according to U in / Z r Normalize to unit, where Z r is the primary side resonant inductance L r1 and the primary side resonant capacitor C r1 Characteristic impedance:

[0073]

[0074] Step 12: Establish a time domain model of the CLLC resonant converter and derive the CLLC resonant converter i by using time domain analysis. Lr1N ,i Lr2N ,u Cr1N ,u Cr2N Sub-resonant time domain expressions;

[0075] When the CLLC resonant converter is in PO mode, assuming that the O mode excitation current does not change; solve the CLLC resonant converter under the under-resonance PO mode i Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per unit expression of is:

[0076] P mode i under sub-resonant heavy load Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per-unit expression is as follows:

[0077]

[0078] where ω r is the angular frequency of the resonant converter, ω k1 =k1ω r is the second angular frequency of the resonant converter, k=L m / L r1 , L m is the magnetizing inductance of the transformer, L r1 is the primary side resonant inductance; M output voltage U o The per unit value M = U in / nU o , f n The per-unit value of the operating frequency is f n =f s / f r , R is the output resistance;

[0079] O mode under sub-resonant heavy load Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per-unit expression is as follows:

[0080]

[0081] where u Cr1N (0.5T r ) is 0.5T r The per-unit value of the primary side resonant capacitor voltage at time i Lr1N (0.5T r ) is 0.5T r The per-unit value of the primary side resonant inductor current at the moment, u Cr2N (0.5T r ) is 0.5T r The per-unit value of the secondary side resonant capacitor voltage at the moment; based on the derivation of the time domain expression of the sub-resonant region of the CLLC resonant converter. Its working waveform is as follows Figure 2 .

[0082] Step 13, solve the boundary conditions of the CLLC resonant converter: According to Figure 3 , the CLLC resonant converter is prone to enter the gain non-monotonic range when overloaded, causing loss of control and easily causing damage to the equipment. Because a method is needed to control the gain non-monotonic range. There are OPO / PO / PON / PN modes in the sub-resonant region of the CLLC resonant converter; among them, the OPO / PO mode gain is monotonic, and the overloaded PON mode has an improvement to enter the non-monotonic gain range, and the overloaded PN mode will definitely enter the non-monotonic gain range; therefore, first calculate the frequency and load range conditions for entering the PON and PN modes;

[0083] The boundary between the PO mode and the PON mode is described as follows: the resonant capacitor will not be overcharged before the end of the O mode, causing the secondary side diode to turn on prematurely; similarly, for the PON mode and the PN mode, the resonant capacitor will not be overcharged before the end of the N mode, which will cause the secondary side diode to turn on prematurely; based on this, the following relationship equation is derived:

[0084]

[0085] Where T s is the actual period of the resonant converter, T r is the resonant period of the resonant converter, M output voltage U o The per unit value M = U in / nU o ,u Cr1N (0.5T s ) is 0.5T s The voltage value of the first resonant capacitor on the primary side at the moment, u Cr2N (0.5T s ) is 0.5T s The per unit value of the voltage of the second resonant capacitor on the primary side at the moment, u Cr1N (0.5T s ) is 0.5T s The per unit voltage value of the first resonant capacitor on the primary side at the moment, u Cr2N (0.5T s ) is 0.5T s The per-unit value of the voltage of the second resonant capacitor on the primary side at this moment.

[0086] Step 14, solve the frequency boundary: Time domain analysis shows that part of the PON mode presents monotonic gain, while the other part presents non-monotonic gain; calculate the boundary of the PO mode and the PON mode to avoid the non-monotonic gain area and maintain a certain margin; the frequency boundary between the PO mode and the PON mode is obtained as:

[0087]

[0088] where f s is the actual operating frequency, I o is the output current, f r is the resonant frequency, Z r is the characteristic impedance of the resonant converter, and n is the transformer ratio;

[0089] That is, the minimum operating frequency of the CLLC resonant converter is:

[0090]

[0091] When the frequency f s When the frequency f is greater than the minimum value, the resonant converter operates in the gain monotonic mode; s When it is less than the minimum value, the resonant converter operates in a non-monotonic mode.

[0092] Step 2, when the CLLC resonant converter is working, detecting the output voltage and load current of the CLLC resonant converter, and judging the load state;

[0093] Step 3: According to step 2, determine the load state. If it is light load, the system is in normal working mode.

[0094] Step 4: According to step 2, the load state is determined. If it is overloaded, the system enters the gain non-monotonic control mode. The system calculates the corresponding minimum frequency in this case by calculating the load current and limits the PI output result to above the minimum frequency.

[0095] Step 5: According to step 3 and step 4, the system gives a driving signal for the switch tube of the CLLC resonant converter.

[0096] Step 4 is as follows: Due to the hysteresis of traditional PI control, it will cause value overshoot and may also enter the gain non-monotonic area, such as Figure 5 and Figure 6 . Figure 5 Indicates the hysteresis when switching loads, Figure 6 Indicates the hysteresis phenomenon when switching voltage. The hysteresis phenomenon is mainly reflected in that, due to the influence of the output capacitor, when the output frequency is shedding, the change of the output voltage will be slower than the change of the frequency, which will cause the frequency to overshoot easily, and then enter the gain non-monotonic area. Therefore, it is necessary to limit the frequency of the PI control calculation. This limit is obtained from the above analysis and calculation. In order to ensure that the resonant converter works in the PO mode, the operating frequency f s To limit the size, it is necessary to limit the frequency of calculation, and this limit is obtained by the above analysis and calculation of the present invention.

[0097] Let the resonant converter operate at the frequency f corresponding to the loads By using the output current I o As a feedback variable. However, when the output value of the PI controller reaches the set cutoff level, the PI controller is still calculating and generating output. When the output voltage reaches the set value, since the actual output of the PI controller has exceeded the set value, it needs to be adjusted to return to the set value. This requires a long feedback calculation time. In order to make the CLLC resonant converter switch loads or voltages faster, an additional controller S is designed. c , when the frequency reaches the minimum value, S c Set to 1, the PI controller stops working until the output voltage reaches the set value (U o,set ). Its control method is as follows Figure 7 shown. Figure 8 The difference between the traditional PI and the non-monotonic control method proposed by the present invention is shown in FIG. The traditional PI control enters into gain imbalance.

[0098] Fig. 9 The simulation diagram of the traditional PI control method in the loading process is given. When the light load is switched to the heavy load, the output voltage of the CLLC resonant converter gradually decreases and cannot return to the set voltage of 480V. It enters the gain non-monotonic range and the output state of the resonant converter is unstable. Fig.10 The specific resonant current waveform after load shedding is shown. It can be seen that the resonant current completely enters the PN state, the excitation current is no longer clamped, its waveform is no longer regular, and the converter efficiency drops sharply.

[0099] Fig.11 The simulation diagram of the non-monotonic gain control method proposed in the present invention during the loading process is given. When the light load is switched to the heavy load, the output voltage of the CLLC resonant converter initially decreases, and then returns to the set voltage of 480V, and the output state of the resonant converter is stable. Fig.12 The specific resonant current waveform after load shedding is shown. It can be seen that the resonant current enters the PO state, the excitation current is clamped, and its waveform is regular, ensuring the converter efficiency.

[0100] The control method provided by the present application has simple calculation, small error and no need for additional devices, realizes the control of a wide range of converter voltage, reduces the influence of non-monotonic gain, and improves the working performance of the converter.

[0101] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A non-monotonic gain control method for a CLLC resonant converter, characterized in that: The method comprises: Step 1: Use the primary side resonant capacitor u Cr1 , secondary side resonant capacitor u Cr2 , the primary side resonant inductor current i Lr1 , the secondary side resonant inductor current i Lr2 As a state variable, a time domain model is established to solve the minimum frequency value under different loads; Step 2, when the CLLC resonant converter is working, detecting the output voltage and load current of the CLLC resonant converter, and judging the load state; Step 3: According to step 2, if the load is light, the system is in normal working mode; Step 4: According to step 2, if the load is heavy, the system enters a gain non-monotonic working mode; and limits the working frequency to a minimum frequency value under the current load; Step 5: According to step 3 and step 4, the system gives a driving signal for the switch tube of the CLLC resonant converter.

2. The method according to claim 1, characterized in that Step 1: Establish a time domain model to solve the frequency boundary of the mode, that is, the minimum operating frequency. The steps are as follows: Step 11, confirming the CLLC resonant converter parameters; CLLC resonant converter topology, including switches S1–S8, anti-parallel diode D S1 –D S8 And the parasitic capacitance C oss1 –C oss8 ; Primary side resonant inductor L r1 , primary side resonant capacitor C r1 , transformer excitation inductance L m , transformer with a turns ratio of n:1, secondary side resonant inductor L r2 , secondary side resonant capacitor C r2 , output capacitor C s , DC input voltage U in And output resistance R; resonant inductor L r1 , L r2 , resonant capacitor C r1 , C r2 and a transformer with a turns ratio of n:1 forming a resonant cavity of a CLLC resonant converter; DC input voltage U in The positive electrode is connected to the source of the primary side switch tubes S1 and S3 at the same time; the DC input voltage U in The negative electrode is connected to the drain of the primary side switch tubes S2 and S4 at the same time; the output capacitor C s In parallel with the output resistor R; Step 12: Establish a time domain model of the CLLC resonant converter and derive the CLLC resonant converter i by using time domain analysis. Lr1N ,i Lr2N ,u Cr1N ,u Cr2N Sub-resonant time domain expressions; Step 13, solving the boundary conditions of the CLLC resonant converter; Step 14, solving for the frequency boundary.

3. The method according to claim 2, characterized in that Step 11, confirming the CLLC resonant converter parameters, including: The CLLC resonant converter operates at the series resonant frequency f of the two components on the primary side. r , the series resonant frequency of the two elements is as follows: Where, L r1 is the primary side resonant inductance, C r1 is the primary side resonant capacitor; the voltage variable of the CLLC resonant converter is based on the input voltage U in Standardize all current variables according to U in / Z r Normalize to unit, where Z r is the primary side resonant inductance L r1 and the primary side resonant capacitor C r1 Characteristic impedance:

4. The method according to claim 2, characterized in that: Step 12: Establish a time domain model of the CLLC resonant converter and derive the CLLC resonant converter i by using time domain analysis. Lr1N ,i Lr2N ,u Cr1N ,u Cr2N Sub-resonant time domain expressions; include: When the CLLC resonant converter is in PO mode, assuming that the O mode excitation current does not change; solve the CLLC resonant converter under the under-resonance PO mode i Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per unit expression of is: P mode i under sub-resonant heavy load Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per-unit expression is as follows: where ω r is the angular frequency of the resonant converter, ω k1 =k1ω r is the second angular frequency of the resonant converter, k=L m / L r1 , L m is the magnetizing inductance of the transformer, L r1 is the primary side resonant inductance; M output voltage U o The per unit value M = U in / nU o , f n The per-unit value of the operating frequency is f n =f s / f r , R is the output resistance; O mode under sub-resonant heavy load Lr1N ,i Lr2N ,u Cr1N ,u Cr2N The per-unit expression is as follows: where u Cr1N (0.5T r ) is 0.5T r The per-unit value of the primary side resonant capacitor voltage at time i Lr1N (0.5T r ) is 0.5T r The per-unit value of the primary side resonant inductor current at the moment, u Cr2N (0.5T r ) is 0.5T r The per-unit value of the secondary side resonant capacitor voltage at moment ; based on the derivation of the time domain expression of the sub-resonant region of the CLLC resonant converter.

5. The method according to claim 2, characterized in that: Step 13, solving the boundary conditions of the CLLC resonant converter, including: There are OPO / PO / PON / PN modes in the under-resonance region of the CLLC resonant converter; the OPO / PO mode gain is monotonic, the overloaded PON mode has an improvement to enter the non-monotonic gain range, and the overloaded PN mode will definitely enter the non-monotonic gain range; first calculate the frequency and load range conditions for entering the PON and PN modes; The boundary between the PO mode and the PON mode is described as follows: the resonant capacitor will not be overcharged before the end of the O mode, causing the secondary side diode to turn on prematurely; similarly, for the PON mode and the PN mode, the resonant capacitor will not be overcharged before the end of the N mode, which will cause the secondary side diode to turn on prematurely; based on this, the following relationship equation is derived: Where T s is the actual period of the resonant converter, T r is the resonant period of the resonant converter, M output voltage U o The per unit value M = U in / nU o ,u Cr1N (0.5T s ) is 0.5T s The voltage value of the first resonant capacitor on the primary side at the moment, u Cr2N (0.5T s ) is 0.5T s The per unit value of the voltage of the second resonant capacitor on the primary side at the moment, u Cr1N (0.5T s ) is 0.5T s The per unit voltage value of the first resonant capacitor on the primary side at the moment, u Cr2N (0.5T s ) is 0.5T s The per-unit value of the voltage of the second resonant capacitor on the primary side at this moment.

6. The method according to claim 2, characterized in that Step 14, solving the frequency boundary, includes: Time domain analysis shows that part of the PON mode exhibits monotonic gain, while the other part exhibits non-monotonic gain. The boundary between the PO mode and the PON mode is calculated to avoid the non-monotonic gain region and maintain a certain margin. The frequency boundary between the PO mode and the PON mode is obtained as: where f s is the actual operating frequency, I o is the output current, f r is the resonant frequency, Z r is the characteristic impedance of the resonant converter, and n is the transformer ratio; That is, the minimum operating frequency of the CLLC resonant converter is: When the frequency f s When the frequency f is greater than the minimum value, the resonant converter operates in the gain monotonic mode; s When it is less than the minimum value, the resonant converter operates in a non-monotonic mode.

7. The method according to claim 2, characterized in that Step 4: According to step 2, if the load is heavy, the system enters a non-monotonic gain operation mode; and limits the operating frequency to a minimum frequency value under the load, including: According to step 2, if it is overloaded, the system enters a gain non-monotonic working mode; The system calculates the corresponding minimum frequency under the current situation by calculating the load current, and limits the operating frequency to above the minimum frequency.

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