Switched capacitor resonant converter state trajectory control method and controller

Abstract

The application discloses a state trajectory control method of a switched capacitor resonant converter, and comprises the following steps: step 1: setting the switching sequence of the switching mode of the switched capacitor resonant converter in the boosting process; establishing a state trajectory model of the boosting process, and drawing a total state trajectory diagram; step 2: determining the switching condition of each switching mode according to the drawn total state trajectory diagram; step 3: setting the resonant inductor and the switching capacitor of the switched capacitor resonant converter, and calculating the maximum peak-to-peak value of the resonant current and the maximum peak-to-peak value of the resonant voltage in the boosting process; step 4: selecting the electronic components, setting the switching parameters I SN and the constraint condition of R M1N ; and step 5: assembling the switched capacitor resonant converter, and controlling the switched capacitor resonant converter through a control system. The application can improve the operation time ratio of the boosting mode in each switching cycle, and improve the dynamic response speed.

Description

Technical Field

[0001] This invention relates to the field of resonant converter control technology, specifically to a method and controller for controlling the state trajectory of a switched capacitor resonant converter. Background Technology

[0002] Existing research has achieved relatively mature results in topology optimization, soft-switching implementation, efficiency improvement and high-frequency design of switched capacitor resonant converters. However, in the field of output voltage control technology, the research focus is still on steady-state performance optimization, and a complete theoretical and technical system that takes into account dynamic performance improvement, dedicated controller design and voltage and current peak constraints during boost start-up has not yet been formed.

[0003] Current linear control strategies for switched-capacitor resonant converters primarily focus on output voltage regulation. These methods typically establish an average mathematical model based on the converter's steady-state operating characteristics, assuming periodic changes in system state variables and neglecting output capacitor voltage ripple, thus approximating the output voltage as a constant. Controllers designed based on this model can guarantee good steady-state regulation and high control accuracy near the rated operating point. However, when the converter experiences dynamic conditions such as boost startup, sudden load changes, or step changes in reference values, the controller cannot effectively constrain the capacitor charging and discharging behavior, causing the system state to deviate from the ideal evolution path.

[0004] Various advanced control schemes generally suffer from complex control structures and difficult parameter tuning, and require high circuit precision, making it difficult to simultaneously achieve wide-range voltage regulation, rapid start-up, and stable control. While they can achieve high operating efficiency and dynamic performance under specific conditions, they generally suffer from complex control structures, high algorithm implementation costs, and difficult parameter tuning. These control strategies often rely on accurate circuit parameter identification and high-frequency state sampling, making them sensitive to device parameter deviations, parasitic parameter fluctuations, and load changes, and placing high demands on circuit hardware precision and controller computing power. Under wide input voltage ranges and variable load conditions, problems such as decreased control loop stability and limited dynamic response speed easily occur, especially during the start-up phase, which is prone to resonant current and capacitor voltage overshoot, making it difficult to effectively balance wide-range voltage regulation, rapid and smooth start-up, and stable control. In contrast, state trajectory control, based on large-signal geometric analysis, has advantages such as fast dynamic response, strong robustness, and ease of digital implementation, which meets the core requirement of switched-capacitor resonant converters for fast dynamic performance. However, existing state trajectory control methods for switched-capacitor resonant converters still have shortcomings in the design of mode switching sequences.

[0005] Furthermore, existing research cannot calculate the peak-to-peak values ​​of the resonant voltage and resonant current during the boost start-up process based on key parameters in the switching conditions. This results in a lack of quantitative data on the voltage and current stress of power devices, which can easily lead to safety hazards such as overvoltage and overcurrent, reducing the stability and reliability of system operation. It also results in overly conservative device selection, increasing converter size and hardware costs, while reducing power density and practical value, making it difficult to meet the stringent requirements of high-end applications such as new energy power generation and communication power supplies for efficient and miniaturized power supply systems. Summary of the Invention

[0006] This invention aims to solve the technical problems existing in the prior art, and innovatively proposes a state trajectory control method and controller for a switched capacitor resonant converter, which can increase the proportion of the running time of the boost mode in each switching cycle and improve the dynamic response speed.

[0007] To achieve the above objectives, the present invention provides a state trajectory control method for a switched capacitor resonant converter, comprising the following steps:

[0008] Step 1: Set the switching mode switching sequence of the switched capacitor resonant converter during the boost process; establish a state trajectory model of the boost process, and plot it on v according to the switching mode switching sequence of the boost process. out -i L The overall state trajectory diagram of each switching mode on the state plane, and the plotted on v CrN -i LN The overall state trajectory diagram of each switching mode on the state plane, v out For the output voltage, i L For resonant current, v CrN To standardize the switched capacitor voltage, i LN The standard resonant current is used; the switching sequence of the boost process is set as Mode2, Mode3, Mode4, Mode1.

[0009] Step 2: Based on the drawing in v out -i L State plane and v CrN -i LN The overall state trajectory diagram of the state plane determines the switching conditions of each switching mode;

[0010] Step 2-1: Set the switching conditions for the switching modes during the boost process of the switched capacitor resonant converter; select the switching parameters. and ,in, The maximum forward resonant current for Mode1 and Mode3 The standardized value, For the set v CrN -iLN The radius of Mode1's trajectory on the plane;

[0011] Step 2-1-1: Determine the switching condition from Mode 2 to Mode 3; the switching condition from Mode 2 to Mode 3 is when... and ,in, To standardize the resonant current, The maximum forward resonant current for Mode1 and Mode3 The standardized value, To standardize the switched capacitor voltage, v CrNQ The trajectory of Mode2 in the first cycle and trajectory i LN = I SN The standardized resonant voltage value at the intersection point;

[0012] Step 2-1-2: Determine the switching conditions from Mode 3 to Mode 4; the switching conditions from Mode 3 to Mode 4 are as follows: ;in, To standardize the resonant current, This is the maximum negative resonant current of Mode 3;

[0013] Step 2-1-3: Determine the switching conditions from Mode 4 to Mode 1; the switching conditions from Mode 4 to Mode 1 are as follows: or ; To standardize the resonant current, For the set v CrN -i LN The radius of the trajectory of Mode1 on the plane. Standardized switched capacitor voltage;

[0014] Step 2-1-4: Determine the switching conditions from Mode 1 to Mode 2; the switching conditions from Mode 1 to Mode 2 are as follows: ;in, To standardize the resonant current, The maximum forward resonant current for Mode1 and Mode3 The standardized value;

[0015] Step 3: Set the resonant inductor and switched capacitor of the switched capacitor resonant converter, and calculate the maximum peak-to-peak value of the resonant current and the maximum peak-to-peak value of the resonant voltage during the boost process;

[0016] Step 4: Select the electronic components of the switched capacitor resonant converter based on the maximum peak-to-peak value of the resonant current and the maximum peak-to-peak value of the resonant voltage during the boost process, and set the switching parameter I. SN and R M1NConstraints;

[0017] Step 5: Construct a switched capacitor resonant converter and control the switched capacitor resonant converter through a control system.

[0018] In the above scheme, step 1 also includes the following:

[0019] Step 1-1: For the equivalent circuits corresponding to each dominant switching mode of the switched capacitor resonant converter, establish and solve the large-signal nonlinear differential equations of the converter based on Kirchhoff's voltage law (KVL) and current law (KCL).

[0020] The modal differential equations are as follows:

[0021] Mode 1:

[0022] ;

[0023] in, Indicates the resonant current The first derivative, Indicates resonant inductance. This represents the voltage across the resonant capacitor. Indicates the input voltage. This represents the first derivative with respect to the voltage across the resonant capacitor. Indicates the resonant capacitor. Indicates the resonant current. Indicates the output voltage. This represents the first derivative with respect to the output voltage. Indicates the resistance of the load. Indicates the output capacitance;

[0024] Mode2:

[0025] ;

[0026] Mode3:

[0027] ;

[0028] Mode4:

[0029] ;

[0030] Solve for its value in v out -i L The natural trajectory equations for each switching mode in the state plane are as follows:

[0031] Mode 1:

[0032] ;

[0033] Mode2:

[0034] ;

[0035] Mode3:

[0036] ;

[0037] Mode4:

[0038] ;

[0039] in, Indicates the resonant current. This represents the instantaneous value of the resonant current at the initial moment of the current mode. Indicates the resonant capacitor. Indicates resonant inductance. This represents the instantaneous value of the switched capacitor voltage at the initial moment of the current mode. Indicates the input voltage. Indicates the resistance of the load. Indicates the output capacitance; This represents the instantaneous value of the output voltage at the initial moment of the current mode. Indicates the output voltage;

[0040] Step 1-2: Select the standardized switched capacitor voltage and standardized resonant current To control variables, construct the converter modes at v CrN -i LN The trajectory equation on the state plane is as follows:

[0041] Mode 1: ;

[0042] Mode2: ;

[0043] Mode3: ;

[0044] Mode4: ;

[0045] in, To standardize the switched capacitor voltage, and , For the standardized resonant current, and , Z represents the resonant current. r This represents the characteristic impedance of a series resonant circuit. , Indicates resonant inductance. Indicates the resonant capacitor. Indicates the voltage transformation ratio. , Indicates the input voltage. Indicates the output voltage;

[0046] The switching mode switching sequence during the boost process is plotted on v. out -i L The overall state trajectory diagram of each switching mode on the state plane, and the plotted on v CrN -i LN The overall state trajectory diagram of each switching mode on the state plane.

[0047] In the above scheme, step 2 also includes:

[0048] Step 2-2: Set the switching sequence and switching conditions of the switching modes in the steady-state regulation process of the switched capacitor resonant converter;

[0049] The switching sequence of the switching modes in the steady-state regulation process is Mode1, Mode2, Mode3, Mode4;

[0050] The switching condition from Mode 1 to Mode 2 in the steady-state adjustment process is as follows: ;in, To standardize the resonant current, Indicates the maximum forward resonant current of Mode1 and Mode3. The standardized value;

[0051] The switching condition from Mode 3 to Mode 4 during the steady-state regulation process is as follows: ;

[0052] The switching condition from Mode 2 to Mode 3 during the steady-state regulation process is as follows: ;in, Indicates the output voltage. Indicates the reference voltage. To standardize the switched capacitor voltage, To standardize the resonant current, Indicates resonant inductance. Indicates the resonant capacitor. Indicates the output capacitor. Indicates the magnitude of the load resistance.

[0053] The switching condition from Mode 4 to Mode 1 during the steady-state regulation process is as follows: .

[0054] In the above scheme, step 3 also includes the following steps:

[0055] Step 3-1: Calculate the peak value of the positive resonant current during the first switching mode cycle;

[0056] The calculation is performed using the following formula:

[0057] ;

[0058] in, This represents the maximum value of the positive resonant current during the first switching mode cycle. This represents the maximum value of the positive normalized resonant current during the first switching mode cycle. Indicates the input voltage. Indicates resonant inductance. Indicates the resonant capacitance;

[0059] Step 3-2: Calculate the peak value of the forward resonant voltage during the first switching mode cycle;

[0060] The calculation is performed using the following formula:

[0061] ;

[0062] in, This represents the peak value of the positive resonant voltage during the first switching mode cycle. Indicates the maximum forward resonant current of Mode1 and Mode3. The square of the standardized value;

[0063] Step 3-3: Calculate the maximum peak-to-peak value of the resonant current during the first switching mode cycle;

[0064] Set parameters The maximum value of the reverse resonant current during the first switching mode cycle is given by the x-coordinate of the intersection point of the Mode4 and Mode1 state trajectories. ≥ 1, calculate the peak-to-peak value of the resonant current in the first cycle using the following formula. :

[0065] ;

[0066] ;

[0067] in, This represents the peak-to-peak value of the resonant current during the first cycle. Indicates resonant inductance. Indicates the resonant capacitor. Indicates the input voltage. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. This represents the maximum value of the positive resonant current during the first switching mode cycle;

[0068] like If the value is less than 1, the peak-to-peak value of the resonant current in the first cycle can be calculated using the following formula. :

[0069] ;

[0070] ;

[0071] in, This represents the peak-to-peak value of the resonant current during the first cycle. Indicates resonant inductance. Indicates the resonant capacitor. Indicates the input voltage. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. The maximum forward resonant current for Mode1 and Mode3 The standardized value;

[0072] Steps 3-4: Calculate the maximum peak-to-peak value of the resonant voltage during the first switching mode cycle;

[0073] Calculate using the following formula

[0074] ;

[0075] in, This represents the maximum peak-to-peak value of the resonant voltage during the first switching mode cycle. Indicates the input voltage. The maximum forward resonant current for Mode1 and Mode3 The standardized value, Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane.

[0076] In the above scheme: the switching parameters mentioned in step 4 The constraints are as follows:

[0077] ;

[0078] ;

[0079] in, This represents the rated voltage of the switched capacitor. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. Indicates the input voltage. The maximum forward resonant current for Mode1 and Mode3 The standardized value; The peak value of the reverse normalized switched capacitor voltage for Mode 1;

[0080] Switch parameters The constraints are .

[0081] In the above scheme: Step 5 controls the start-up process by first acquiring the output voltage. If the acquired output voltage... Less than the reference voltage Then, the switched capacitor resonant converter is dynamically adjusted to boost voltage.

[0082] If the output voltage is collected at startup Greater than or equal to the reference voltage Therefore, the switched capacitor resonant converter is first subjected to voltage reduction dynamic adjustment, and then to steady-state adjustment.

[0083] In the above scheme: during boost dynamic adjustment, the switching is performed according to the switching mode switching sequence set in step 1, and the working state during boost dynamic adjustment includes initial state, state2, state5, state6, state7 and state8, where state2 and state5 are Mode2, state6 is Mode3, state7 is Mode4 and state8 is Mode1; and state5, state6, state7 and state8 form an outer adjustment loop cycle mode.

[0084] The control process begins by transitioning from the initial state (Initial) to state 2, then instantly jumps to state 5. The positive resonant current charges the output capacitor, causing the output voltage to rise steadily. This occurs when the trajectory simultaneously satisfies… and When the constraint conditions are met, the state switches to state6, after which the resonant current completes the polarity reversal;

[0085] When the state trajectory meets the switching conditions When the state switches to state7, the resonant circuit continues to transfer energy to the load side, further increasing the output voltage.

[0086] When the switching conditions are met or When the state switches to state 8, the system completes the reversal of the resonant current again, and the switching condition is met. When the state machine switches to state5, it completes one cycle of state switching during the dynamic process;

[0087] When the output voltage reaches the reference voltage, the system cycles through states 8, 5, 6, and 7 in that order. At this point, the switching condition from state 5 to state 6 becomes... The switching condition from state7 to state8 becomes .

[0088] In the above scheme: the working states during the dynamic adjustment of the voltage reduction include Initial, state1, state2, state3, state4, state5, state6, state7 and state8, where state2 and state5 are Mode2, state3 and state6 are Mode3, state4 and state7 are Mode4, and state1 and state8 are Mode1.

[0089] The control process starts from the initial state and enters the inner regulation loop cycle mode. The inner regulation loop cycle mode switches sequentially according to the state sequence of state4, state3, state2 and state1, so that the output voltage gradually decreases until the output voltage equals the reference voltage. Then, it switches from state4 to state7, and switches sequentially according to the state sequence of state8, state5, state6 and state7 to perform steady-state regulation.

[0090] This invention also provides a state trajectory controller for a switched-capacitor resonant converter, including a control system for implementing the state trajectory control method in the above-described technical solution. The control system includes a signal acquisition circuit, an FPGA main control unit, and an isolation drive module. The signal acquisition circuit is used to acquire the resonant current, switched capacitor voltage, output voltage, and load current of the switched-capacitor resonant converter. The signal acquisition output terminal of the signal acquisition circuit is connected to the signal acquisition output terminal of the FPGA main control unit. The control output terminal of the FPGA main control unit is connected to the drive signal output terminal of the isolation drive circuit. The first drive output terminal of the isolation drive circuit is connected to the gate of switch S1, the second drive output terminal of the isolation drive circuit is connected to the gate of switch S2, the third drive output terminal of the isolation drive circuit is connected to the gate of switch S3, and the fourth drive output terminal of the isolation drive circuit is connected to the gate of switch S4. The isolation drive circuit controls the corresponding switch according to the drive signal of the FPGA main control unit to achieve adjustment of different switching modes.

[0091] In summary, the beneficial effects of this invention are as follows: By setting the mode-2 of boosting the resonant current and output voltage as the initial mode for startup, and optimizing the mode sequence (changing the dynamic adjustment process mode sequence from 1, 2, 3, 4 to 2, 3, 4, 1), and correspondingly resetting the switching conditions, the operating time proportion of the boost mode in each switching cycle is effectively increased while ensuring normal commutation of the resonant current. This significantly improves the dynamic response speed of the converter from the trajectory planning perspective. Based on the designed state trajectory, quantitative calculation formulas for the resonant voltage, resonant current, and switching parameters during startup are derived, providing theoretical support for the rational selection of power devices and the design of safety margins. This effectively improves the operational safety and applicability of switched-capacitor resonant converters in high-frequency, high-power-density application scenarios. Furthermore, addressing the shortcomings of existing state trajectory control research, such as the inability to quantitatively calculate the peak-to-peak values ​​of the resonant voltage and resonant current during startup and the lack of theoretical basis for device selection, this invention conducts research on the peak characteristic analysis of the resonant voltage and resonant current during startup and the parameter design criteria. Based on the established normalized state-plane trajectory of vCrN-iLN, considering the trajectory switching characteristics of current commutation mode and boost mode, analytical expressions for the peak-to-peak values ​​of resonant voltage and resonant current during startup are derived, and peak-to-peak values ​​and switching parameters are established. and Based on the quantitative calculation relationship, and combined with the switching capacitor withstand voltage constraint and trajectory intersection constraint, a parameter design criterion that balances dynamic performance and device safety was formulated. Quantitative calculation of voltage and current stress during startup was achieved, providing theoretical support for power device selection and voltage and current stress margin design. Attached Figure Description

[0092] Figure 1 In (a), v is the switching mode sequence of the boost process set by the present invention. out -i L State plane trajectory diagram, (b) is the v of the switching mode sequence of the boost process set by the present invention. CrN -i LN The state plane trajectory diagram (c) is the output voltage state trajectory diagram of the switching mode sequence of the boost process set by the present invention.

[0093] Figure 2 This is a circuit diagram of the switched capacitor resonant converter of the present invention.

[0094] Figure 3 It is the equivalent circuit of the four dominant switching modes of the switched capacitor resonant converter.

[0095] Figure 4 This is a system diagram of the control system of the present invention.

[0096] Figure 5 This invention starts at v out <V refA schematic diagram of the state machine structure.

[0097] Figure 6 This invention starts at v out >V ref A schematic diagram of the state machine structure.

[0098] Figure 7 It is the natural state trajectory of the vout-iL state plane of the switched capacitor resonant converter.

[0099] Figure 8 In (a), the switching mode sequence of the boost process set by the present invention is shown in v. out -i L (a) A schematic diagram of the trajectories of Mode2 and Mode3 within the first switching mode cycle on the state plane; (b) The switching mode sequence of the boost process set by this invention in v CrN -i LN A schematic diagram of the Mode2 and Mode3 trajectories that meet the constraints during the first switching mode cycle on the state plane; (c) is a diagram of the switching mode sequence of the boost process set by the present invention in v CrN -i LN A schematic diagram of the Mode2 and Mode3 trajectories within the first switching mode cycle on the state plane.

[0100] Figure 9 In (a), the switching mode sequence of the boost process set by the present invention is shown in v. out -i L (a) A schematic diagram of the trajectories of Mode2, Mode3, and Mode4 within the first switching mode cycle on the state plane; (b) A schematic diagram of the switching mode sequence of the boost process set in this invention in v CrN -i LN A schematic diagram of the trajectories of Mode2, Mode3, and Mode4 that meet the constraints during the first switching mode cycle on the state plane.

[0101] Figure 10 In (a), the switching mode sequence of the boost process set by the present invention is shown in v. out -i L (a) A schematic diagram of the trajectories of Mode2, Mode3, Mode4, and Mode1 within the first switching mode cycle on the state plane; (b) A schematic diagram of the switching mode sequence of the boost process set by the present invention in v CrN -i LN (c) A schematic diagram of the trajectories of Mode2, Mode3, Mode4 and Mode1 that meet the constraints during the first switching mode cycle on the state plane; CrN -iLN A schematic diagram of the Mode4 trajectory and Mode1 trajectory during the first switching mode cycle on the state plane.

[0102] Figure 11 In (a), the switching mode sequence of the boost process set by the present invention is shown in v. out -i L (a) A schematic diagram of the trajectories of Mode2, Mode3, Mode4, and Mode1 within the first switching mode cycle on the state plane; (b) A schematic diagram of the switching mode sequence of the boost process set by the present invention in v CrN -i LN A schematic diagram of the trajectories of Mode2, Mode3, Mode4 and Mode1 that meet the constraints during the first switching mode cycle on the state plane.

[0103] Figure 12 (a) is the output voltage trajectory diagram of the existing trajectory control method, and (b) is the output voltage trajectory diagram of the switching mode sequence of the boost process set by the present invention.

[0104] Figure 13 The switching mode sequence of the boost process set in this invention is in v CrN -i LN A schematic diagram of the trajectory of the first switching mode cycle on the state plane.

[0105] Figure 14 For in v CrN -i LN A schematic diagram of the trajectories of Mode4 and Mode1 on the state plane.

[0106] Figure 15 The switching mode sequence of the boost process set for this invention is in v CrN -i LN A schematic diagram of the trajectory of the second switching mode cycle on the state plane.

[0107] Figure 16 A schematic diagram of the state trajectory of the subsequent cycles of the switching mode sequence in the boost process set for this invention. Detailed Implementation

[0108] The present invention will be further described below with reference to the embodiments and accompanying drawings:

[0109] like Figures 1-5 As shown, a state trajectory control method for a switched capacitor resonant converter, applicable to a symmetrical dual half-bridge structure switched capacitor resonant converter, includes the following steps:

[0110] Step 1: Set the switching mode switching sequence of the switched capacitor resonant converter during the boost process; establish a state trajectory model of the boost process, and plot it on v according to the switching mode switching sequence of the boost process. out -i L The overall state trajectory diagram of each switching mode on the (output voltage-resonant current) state plane, and the diagram plotted on v CrN -i LN (Standardized switched capacitor voltage - standardized resonant current) Overall state trajectory diagram of each switching mode on the state plane; the boost process is the stage where the output voltage is less than the reference voltage;

[0111] Step 1-1: For the equivalent circuits corresponding to each dominant switching mode of the switched capacitor resonant converter, establish and solve the large-signal nonlinear differential equations of the converter based on Kirchhoff's Voltage Law (KVL) and Current Law (KCL); the differential equations for each mode are as follows:

[0112] The differential equation for Mode1 is: (2.1);

[0113] in, Indicates the resonant current The first derivative, Indicates resonant inductance. This represents the voltage across the resonant capacitor. Indicates the input voltage. This represents the first derivative with respect to the resonant capacitor voltage. Indicates the resonant capacitor. Indicates the resonant current. Indicates the output voltage. This represents the first derivative with respect to the output voltage. Indicates the resistance of the load. Indicates the output capacitance;

[0114] The differential equation for Mode2 is: (2.2);

[0115] The differential equation for Mode3 is: (2.3);

[0116] The differential equation for Mode 4 is: (2.4);

[0117] Solve for its value in v out -i L The natural trajectory equations for each switching mode in the state plane are as follows:

[0118] Mode 1: (2.5);

[0119] Mode2: (2.6);

[0120] Mode3: (2.7);

[0121] Mode4: (2.8);

[0122] in, Indicates the resonant current. This represents the instantaneous value of the resonant current at the initial moment of the current mode. Indicates the resonant capacitor. Indicates resonant inductance. This represents the instantaneous value of the switched capacitor voltage at the initial moment of the current mode. Indicates the input voltage. Indicates the resistance of the load. Indicates the output capacitance; This represents the instantaneous value of the output voltage at the initial moment of the current mode. Indicates the output voltage;

[0123] According to equations (2.5) to (2.8), the four switching modes of the converter at v out -i L Natural trajectories on the state plane, such as Figure 7 As shown. Modes 1 and 3 are both used to reverse the resonant current, and their natural trajectory is a sinusoidal decay curve affected by load discharge. Its amplitude is related to the initial state. , Correlation, frequency and initial state Correlation, i.e., phase and initial state , and All are related. Mode 2 and Mode 4, as the core modes for establishing the output voltage, exhibit natural state trajectories as elliptical curves, with their centers located at points (V...). in -v Cr ,0) and point (v) Cr At point 1). During the Mode2 and Mode4 operating phases, the series resonant branch is connected to the output-side load. The resonant current not only participates in the resonant energy exchange but also determines the charging and discharging process of the output capacitor, thus having a direct impact on the dynamic changes of the output voltage.

[0124] Specifically, during Mode 2 operation, when the resonant current is positive, energy is transferred from the resonant branch to the output side, the output capacitor receives charging current, its stored energy increases, and thus the output voltage gradually rises. When the resonant current is negative, the output capacitor releases energy into the resonant branch, is in a discharging state, and the output voltage decreases accordingly.

[0125] Similarly, during Mode 4 operation, due to the change in circuit connections, the energy flow between the resonant current and the output capacitor is opposite to that in Mode 2. When the resonant current is negative, the resonant branch transfers energy to the output side, the output capacitor is charged, and the output voltage increases. When the resonant current is positive, the output capacitor releases energy outward, and the output voltage decreases.

[0126] Therefore, the trend of output voltage variation is not only related to the magnitude of the resonant current, but also closely related to its polarity. By reasonably controlling the polarity and duration of the resonant current during Mode 2 and Mode 4, the charging and discharging process of the output capacitor can be rapidly adjusted, thereby guiding the system state to evolve along a predetermined trajectory and eventually converge to the target equilibrium point.

[0127] Step 1-2: Select the standardized switched capacitor voltage and standardized resonant current To control variables, construct the converter modes at v CrN -i LN The trajectory equation on the state plane is as follows:

[0128] Mode 1: (2.9);

[0129] Mode2: (2.10);

[0130] Mode3: (2.11);

[0131] Mode4: (2.12);

[0132] in, To standardize the switched capacitor voltage, and , For the standardized resonant current, and , Z represents the resonant current. r This represents the characteristic impedance of a series resonant circuit. , Indicates resonant inductance. Indicates the resonant capacitor. Indicates the voltage transformation ratio. , Indicates the input voltage. This indicates the output voltage.

[0133] Set the switching mode switching sequence of the boost process to Mode2, Mode3, Mode4, Mode1; plot the switching mode switching sequence on v according to the boost process. out-i L The overall state trajectory diagram of each switching mode on the state plane, as shown below. Figure 1 As shown in a, and plotted in v CrN -i LN The overall state trajectory diagram of each switching mode on the state plane, as shown below. Figure 1 As shown in b. Figure 1 c is a schematic diagram of the output voltage trajectory under the switching mode control of the boost process set in this technical solution.

[0134] Step 2: Based on the drawing in v out -i L State plane and v CrN -i LN The overall state trajectory diagram of the state plane determines the switching conditions of each switching mode;

[0135] Step 2-1: Set the switching conditions for the switching modes during the boost process of the switched capacitor resonant converter; select the switching parameters. and ,in, The maximum forward resonant current for Mode1 and Mode3 The standardized value, For the set v CrN -i LN The radius of Mode1's trajectory on the plane;

[0136] Step 2-1-1: Determine the switching condition from Mode 2 to Mode 3; the switching condition from Mode 2 to Mode 3 is when... and When Mode 2 is used as the initial mode, it can directly and rapidly increase the output voltage, resonant voltage, and resonant current, achieving rapid start-up of the converter. Therefore, using Mode 2 as the initial mode of the converter, the trajectory starts from point O and moves along the elliptical trajectory of Mode 2, resulting in a rapid increase in resonant current and output voltage. Figure 8 As shown in Figure a, let point a1 be the intersection of the first cycle from Mode2 to Mode3. When the state trajectory crosses boundary I... LN =I SN Upon reaching it again, the converter then switches from Mode 2 to Mode 3. This allows for more efficient use of the high current peak in the elliptical trajectory of Mode 2, enabling rapid charging of the switched capacitor. Therefore, the switching condition from Mode 2 to Mode 3 is: (2.13); where, switching parameter I SN The value of I is related to the output voltage boost speed in Mode2. SN If I is too small, the converter's output voltage will rise slowly; if I is too small... SNIf the value is too high, the resonant current will exceed the rated value of the power devices, causing overcurrent damage and affecting the reliable operation of the converter. Therefore, I SN The selection of the appropriate current requires a balance between dynamic response speed and hardware safety margin. During the first switching mode cycle after the converter starts, the initial resonant current of Mode2 is 0, while in subsequent switching cycles, the initial resonant current of Mode2 remains constant at I. SN If only equation (2.13) is used as the criterion for switching from Mode2 to Mode3, the trajectory of Mode2 in the first cycle of the converter will be... Figure 8 In C, the shaded area of ​​Mode 3 switches to Mode 3 earlier. Therefore, an additional switching condition for switching from Mode 2 to Mode 3 is introduced: (2.14). Among them, The trajectory of Mode2 in the first cycle and i LN = I SN The standardized resonant voltage value at the intersection of the first cycle. Then the trajectory from Mode 2 to Mode 3 that satisfies the switching conditions is as follows: Figure 8 As shown in Figure b. In the accompanying drawings of this technical solution, trajectory curves of the same color belong to the state trajectory of the same mode; the solid line segments of each trajectory represent the parts actually traversed by the switched-capacitor resonant converter during operation, while the dashed line segments represent the sections where the switched-capacitor resonant converter no longer operates after switching to the next mode.

[0137] The point reached by the motion trajectory of Mode2 during the first switching mode cycle of the converter ( , I SN When the output voltage is relatively small, the voltage conversion ratio M≈0, and the trajectory radius of Mode2 is 1-M≈1, we can obtain... , among which, I SN The maximum forward resonant current I of Mode1 and Mode3 S The standardized value;

[0138] Step 2-1-2: Determine the switching conditions from Mode 3 to Mode 4; the switching conditions from Mode 3 to Mode 4 are as follows: After the converter enters Mode 3, as analyzed above, the resonant current needs to undergo a polarity reversal from positive to negative through Mode 3, so that the negative polarity i in the subsequent Mode 4... L The output capacitor is charged, causing the output voltage to rise. Let point b1 be the intersection of the first cycles of Mode3 and Mode4, as shown below. Figure 9 As shown in b, when the state trajectory reaches boundary I along the Mode3 trajectory LN =-I SN When the converter switches from Mode 3 to Mode 4, the switching condition is: (2.15);

[0139] Step 2-1-3: Determine the switching condition from Mode4 to Mode1;

[0140] The switching condition from Mode4 to Mode1 is or ;

[0141] After the converter enters Mode4, the resonant current is of negative polarity, the LC resonant circuit releases energy to the output capacitor and the load, and the voltage of the resonant capacitor decreases accordingly. As shown in Figure 10 b, when the state trajectory reaches the intersection point c1 of the first cycle of Mode4 and Mode1, the converter switches from Mode4 to Mode1, and the switching condition is: (2.16);

[0142] Wherein, the switching parameter R M1N determines the radius of the trajectory arc in Mode1, and the value of R M1N directly affects the peak-to-peak values of the resonant capacitor voltage and the resonant current during the startup process of the converter. Wherein, the center of the trajectory of Mode4 in the v CrN -i LN state plane gradually shifts rightward along the horizontal axis as the output voltage increases, and the radius of the corresponding arc gradually decreases as the number of startup cycles increases. In subsequent cycles, the trajectory of Mode4 may present a situation as shown in Figure 10 c indicated by S N+1 , resulting in the state trajectory failing to meet the switching condition (2.16), that is, the trajectory of Mode4 cannot intersect with the preset trajectory of Mode1. Therefore, in order to ensure the continuity of trajectory switching, an additional switching condition from Mode4 to Mode1 is introduced: (2.17);

[0143] Step 2-1-4: Determine the switching condition from Mode1 to Mode2;

[0144] The switching condition from Mode1 to Mode2 is ; after the converter enters Mode1, the variation process of the resonant current is opposite to that in Mode3, the resonant current i LN first attenuates to 0, and then increases in the positive direction. As shown in Figure 11 , when the state trajectory reaches the intersection point d1 of the first cycle of Mode1 and Mode2, the resonant current in Mode1 rises to I SN , the converter switches from Mode1 to Mode2, and the switching condition is: (2.18);

[0145] This completes the first startup cycle. Subsequent startup processes will cycle according to the mode switching sequence of Mode2, Mode3, Mode4, and Mode1, with the switching conditions remaining unchanged during startup, until the output voltage reaches the reference voltage, at which point the converter enters the steady-state regulation process.

[0146] Step 2-2: Set the switching sequence and conditions for the switching modes during the steady-state regulation process of the switched-capacitor resonant converter. The switching sequence for the switching modes during the steady-state regulation process is Mode1, Mode2, Mode3, Mode4. The switching condition from Mode1 to Mode2 during the steady-state regulation process is as follows: The switching condition from Mode 3 to Mode 4 during the steady-state regulation process is as follows: The switching condition from Mode 2 to Mode 3 during the steady-state regulation process is as follows: (2.19), the switching condition from Mode 4 to Mode 1 in the steady-state regulation process is: (2.20).

[0147] First, Mode2 is set as the initial startup mode, replacing Mode1 used in the existing switched-capacitor resonant converter control scheme. Analysis of the equivalent circuits of each mode shows that Mode2 can directly achieve a rapid increase in output voltage during the initial startup process, while Mode1 has a weak effect on output voltage increase. If Mode1 is used as the initial startup mode, a certain amount of time is required to increase the resonant current until the converter switches to Mode2, at which point the output voltage begins to increase, resulting in a slow startup process. Using Mode2 as the initial mode allows the output voltage, resonant voltage, and resonant current to rise rapidly and synchronously, achieving rapid converter startup. The optimized mode sequence cycles according to the period "Mode2, Mode3, Mode4, Mode1".

[0148] At the same time, while ensuring the normal commutation of the resonant current, the trajectory of Mode2 occupies its v. out -i L The design utilizes a larger proportion of the arc segments in the elliptical natural state trajectory on the state plane, and this trajectory continues to operate until the current decreases after reaching the peak of the resonant current. This design fully leverages the large resonant current to charge the output capacitor, while simultaneously increasing the proportion of Mode2's operating time within a single switching cycle, thereby effectively improving the dynamic response speed. Given that Mode1 and Mode3 are only used for resonant current commutation, the traditional state trajectory control scheme, with its balanced proportion of each mode, leads to Mode1 and Mode3 operating for an excessive proportion within the switching cycle, limiting the dynamic response speed.

[0149] First, the output voltage cycles through "Mode2, Mode3, Mode4, Mode1" until it reaches the reference voltage. Then, the output voltage trajectory follows the pattern "Mode1, Mode2, Mode3, Mode1". Figure 12 As shown in b. Figure 12 Figure 'a' shows the output voltage trajectory of the existing trajectory control method. Through the aforementioned optimized design strategy, the output voltage increment within a single cycle is increased, the number of switching cycles required for the output voltage to reach the reference value is reduced, the time for the output voltage to approach the reference value is shortened, and the dynamic response speed of the converter is further improved.

[0150] Step 3: Set the resonant inductor and switched capacitor of the switched capacitor resonant converter, and calculate the maximum peak-to-peak value of the resonant current and the maximum peak-to-peak value of the resonant voltage during the startup process;

[0151] Step 3-1: Calculate the peak value of the forward resonant current during the first switching mode cycle; since the converter starts from a zero state in the first switching mode cycle, the initial value of the resonant current is 0, and in subsequent cycles the resonant current increases by I... SN Entering Mode 2 with an initial value, the trajectory shape of Mode 2 in the first switching mode cycle differs significantly from that in subsequent cycles. Therefore, it is necessary to analyze Mode 2 separately for the first switching mode cycle at v. CrN -i LN Trajectory on the state plane.

[0152] The calculation is performed using the following formula: (3.1);

[0153] in, This represents the maximum value of the positive resonant current during the first switching mode cycle. This represents the maximum value of the positive normalized resonant current during the first switching mode cycle. Indicates the input voltage. Indicates resonant inductance. Indicates the resonant capacitance;

[0154] Mode2 in v CrN -i LN The state trajectory on the state plane is given by equation (2.10), which is a circle centered at (1-M, 0). Initially, M = 0, v CrN = 0, i LN= 0, at this time the corresponding trajectory is a circle with center (1, 0) and radius 1. As the output voltage increases, the value of M gradually increases, the center 1-M will shift to the left accordingly, and the trajectory radius will also change accordingly. When the normalized resonant voltage value in Mode2 is equal to the value of the trajectory center point 1-M, the maximum positive resonant current corresponding to the Mode2 trajectory in the first cycle can be determined, and the coordinates of this point are set as (v CrNa i LNmax1 At this point, 1 - M = v CrNa Due to v in the initial startup phase out The value is small. The value of 1-M can be approximated as 1, and the trajectory starts from v. CrN -i LN Starting from the origin of the state plane, after approximation, during Mode 2 of the first switching mode cycle, the center of the trajectory is point (1, 0), and the radius is 1. During the startup process of the switched-capacitor resonant converter, the maximum value of the normalized forward resonant current is the radius of the circular trajectory, i.e., the maximum value of the normalized forward resonant current i. LNmax1 = 1. Through the above derivation process, the formula for calculating the maximum value of the forward resonant current in the first cycle can be obtained as follows: ;

[0155] During the mode switching process of the switched capacitor resonant converter, when the set switching condition i is met... LN ≤I SN During the first switching mode cycle, the converter will switch from Mode 2 to Mode 3, and the mode switching process occurs during v. CrN -i LN Trajectories on the state plane as follows Figure 13 As shown. Let the coordinates of the switching point from Mode 2 to Mode 3 in the first switching mode cycle be (v... CrNb , I SN Because during the first switching cycle, the switching point (v) CrNb , I SN The corresponding output voltage is relatively small, but it still satisfies the condition 1-M ≈ 1. After approximation, the switching point (v) CrNb , I SN The following conditions must be met: (3.2);

[0156] Solving equation (3.2) yields the standardized resonant capacitor voltage. The expression is as follows: (3.3);

[0157] During the converter mode switching process, it can be seen from the switching condition (2.14) that the normalized resonant current i LN = I SN The point of intersection with the right side of the Mode2 track is used as the switching point. That is... This provides initial conditions for subsequent calculations of the maximum resonant voltage value.

[0158] Step 3-2: Calculate the peak value of the forward resonant voltage during the first switching mode cycle;

[0159] The calculation is performed using the following formula: (3.4); When the running trajectory of Mode3 meets the switching condition i LN ≤ -I SN At this time, the converter will switch from Mode 3 to Mode 4. For example... Figure 12 As shown, let the switching point be (v CrNc -I SN Because of point (v) CrNb , I SN ) and point (v) CrNc -I SN ) is symmetric about the horizontal axis, therefore v CrNc The following conditions must be met: (3.5); As can be seen from equation (2.9), in v CrN -i LN On the state plane, the trajectory of Mode 1 is a circle centered at (1, 0), providing initial conditions for subsequent calculations of the maximum resonant current. When equation (2.16) or (2.17) is satisfied, the converter will switch from Mode 4 to Mode 1, as follows. Figure 13 As shown, the coordinates of the corresponding mode switching point at this time are set as (v CrNd i LNd During the first switching mode cycle, the center coordinates of the Mode4 state trajectory are (M, 0). Since the output voltage increase mainly occurs in Modes 2 and 4, when the converter just enters Mode 4 in the first cycle, the value of M is located at the midpoint of Mode 2 (v). CrNb , I SN When the values ​​of M are almost the same, as analyzed above, M ≈ 0. From the switching condition (2.16), the trajectory radius of Mode4 is... During the first switching mode cycle, the trajectories of Mode1 and Mode4 satisfy the following conditions:

[0160] (3.6);

[0161] (3.7);

[0162] Solving equations (3.6) and (3.7) simultaneously, the x-coordinate of the intersection point of the Mode4 and Mode1 state trajectories can be determined as follows: (3.8);

[0163] Step 3-3: Calculate the maximum peak-to-peak value of the resonant current during the first switching mode cycle; from equation (2.16), it can be seen that the lowest point of the natural trajectory of Mode1 is at v CrN -i LN The coordinates on the state plane are (1, -R) M1N To determine the extreme current value during mode switching, it is necessary to further determine the switching point between Mode 4 and Mode 1 (v). CrNd i LNd The positional relationship of v relative to the lowest point is given in equation (3.9). CrNd Comparing the value of with 1, the converter's operating conditions can be divided into the following two positional relationships, determining the maximum value of the reverse normalized resonant current within the first switching mode cycle under different conditions. When v CrNd ≥ 1, that is, it satisfies At times, such as Figure 14 As shown, the switching point (v) CrNd i LNd ) is located at point (1, R) M1N On or to the right of ). The converter can reach the point (1, -R) on the operating trajectory of Mode 1. M1N The maximum value of the reverse normalized resonant current during the first switching mode cycle is -R. M1N .

[0164] Set parameters The maximum value of the reverse resonant current during the first switching mode cycle is given by v. CrNd ≥ 1, calculate the peak-to-peak value of the resonant current in the first cycle using the following formula. :

[0165] (3.9);

[0166] (3.10);

[0167] If v CrNd < 1, meaning it satisfies At that time, the switching point (v) CrNd i LNd ) is located at point (1, -R) M1N The left side of ) . The trajectory of Mode1 cannot pass through the point (1, -R) M1N In this case, the maximum value of the reverse normalized resonant current is determined by the switching point current i between Mode 4 and Mode 1. LNdThe decision is made by calculating the peak-to-peak value of the resonant current during the first cycle using the following formula. :

[0168] (3.11);

[0169] (3.12);

[0170] in, This represents the peak-to-peak value of the resonant current during the first cycle. Indicates resonant inductance. Indicates the resonant capacitor. Indicates the input voltage. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. The maximum forward resonant current for Mode1 and Mode3 The standardized value;

[0171] Steps 3-4: Calculate the maximum peak-to-peak value of the resonant voltage during the first switching mode cycle; after the state trajectory enters Mode 1 at the switching point, it will run along a circular trajectory centered at (1, 0). When the normalized resonant current i LN When =0, the state trajectory of Mode1 intersects the horizontal axis at the resonant voltage boundary point (v). CrNfmax ,0). According to the switching condition (2.16), the radius of the Mode1 trajectory is Based on geometric relationships, the normalized resonant voltage boundary value in the Mode1 trajectory at this time is: (3.13).

[0172] The peak-to-peak value of the resonant voltage during the first switching mode cycle can be obtained, and its expression is as follows: (3.14);

[0173] Equations (3.10), (3.12), and (3.14) represent the peak-to-peak values ​​of the resonant current and resonant capacitor voltage with respect to the state switching parameter I during the first switching mode cycle. SN With R M1N The analytical expression for this can be obtained. By appropriately adjusting the above switching parameters, the maximum peak-to-peak value of the resonant variable can be adjusted. And I... SN The physical meaning is the normalized resonant current value from Mode 1 to Mode 2 and from Mode 2 to Mode 3.

[0174] The starting point of the dynamic trajectory at the end of the first switching cycle and the beginning of the second switching cycle is set as (v). CrNE I SNThe maximum resonant current point of Mode2 during the second switching cycle is set to (v). CrNF i LNmax3 At the end of the first switching cycle, the change in output voltage. for:

[0175] (3.15);

[0176] And there are: (3.16);

[0177] Based on geometric relationships, it can be derived that: (3.17); where v CrNF The x-coordinate is the point where the resonant current of Mode2 reaches its maximum value during the second switching cycle.

[0178] Similar to the analysis method for Mode2 during the first switching cycle, the maximum resonant current at this time is equal to the trajectory radius of Mode2. At point (v... CrNE I SN At point ), the radius of the trajectory can be obtained from geometric relationships as . Therefore, the maximum positive value of the resonant current during the second switching cycle for: (3.18);

[0179] Substituting equations (3.16) and (3.17) into (3.18) and rearranging, we get:

[0180] (3.19);

[0181] That is, the maximum forward resonant current of Mode2 during the second switching cycle. The expression is as follows: (3.20);

[0182] in, Indicates the resonant capacitor. Indicates the output capacitor. The maximum forward resonant current for Mode1 and Mode3 The standardized value, For the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. This represents the input voltage. In summary, after determining the configuration of parameters such as the resonant inductance and switched capacitor of the converter, the maximum peak-to-peak value of the resonant current during startup can be calculated using equations (3.10) and (3.12), and the maximum peak-to-peak value of the resonant voltage during startup can be calculated using equation (3.14). The switching parameter I can be adjusted in the controller code.SN With R M1N By adjusting the parameter values, the peak values ​​of voltage and current in the resonant circuit can be reduced, thereby reducing the constraints on component selection and achieving a better balance between performance and cost.

[0183] When the number of switching cycles is n (n>1), the trajectory radius in Mode2 .because and The value of decreases as the number of cycles n increases. Therefore, the trajectory radius in Mode2 also decreases as the number of switching cycles increases, and the trajectory arc gradually moves downwards towards the horizontal axis. Thus, it can be concluded that the maximum resonant current value corresponding to Mode2 in the second switching cycle is greater than the peak resonant current value of Mode2 in all subsequent switching cycles.

[0184] The peak value of the first cycle resonant current i Lmax1 Designed to handle peak and maximum values ​​throughout the startup process, it can inject significant energy into the circuit during the initial startup phase, directly driving a rapid rise in the output voltage. Simultaneously, by configuring I... SN With R M1N Parameters that make the peak value of the second-cycle resonant current i Lmax3 < i Lmax1 Furthermore, the peak current continues to decline steadily after the second cycle, forming a control logic of high energy injection in the first cycle and stable convergence of current in subsequent cycles.

[0185] This design relies on the peak current of the first cycle to achieve efficient energy input, allowing the output voltage to quickly approach the reference value during startup. Then, through the gradual decrease in current in subsequent cycles, overshoot is avoided when the output voltage approaches the reference value, resulting in a significant improvement in dynamic response. And when i Lmax3 > i Lmax1 At this time, insufficient energy injection and slow output voltage rise may occur during the initial startup phase. Furthermore, if the current in subsequent cycles is too high, it will further increase the voltage stabilization time, significantly reducing the overall dynamic response efficiency. Therefore, the following conditions need to be met: (3.21);

[0186] in, Indicates the resonant capacitor. Indicates the output capacitor. The maximum forward resonant current for Mode1 and Mode3 The standardized value, For the set v CrN -i LN The radius of the Mode 1 trajectory on the plane; this condition limits the subsequent voltage peak, improves the energy injection in the early stage of startup, and enhances the dynamic response speed.

[0187] At the same time, by combining the switching condition (2.13) with equation (2.10) and... Substituting the values ​​into the solution, we can obtain the normalized resonant voltage when entering Mode 3 in subsequent cycles as follows: ,in, For a switching mode cycle number of n (n > 2), the trajectory radius in Mode2 is... This represents the voltage conversion ratio during the nth switching mode cycle. Correspondingly, it represents the maximum normalized resonant voltage value of Mode 3 in that cycle. As the number of cycles n increases, the voltage decreases. The trajectory in Mode 1 remains basically unchanged in different cycles. Therefore, the peak-to-peak value of the resonant voltage in the first switching mode cycle is the maximum value in the entire startup process.

[0188] Furthermore, because the starting and ending points of the trajectory in Mode3 are symmetrical about the horizontal axis, such as Figure 16 As shown, when the number of switching cycles is n, the initial normalized resonant voltage values ​​of Mode4 and Mode3 are the same, both being [value missing]. .

[0189] Depend on Figure 16 Analysis shows that when the switching point between Mode4 and Mode1 in the first cycle (v CrNd i LNd ) is located in (1, -R M1N When the right side coincides with the point, the maximum reverse normalized resonant current value in the subsequent period n is less than or equal to the point on the right. When the switching point between Mode4 and Mode1 in the first cycle (v CrNd i LNd ) is located in (1, -R M1N When on the left, combine equations (2.9) and (2.12) and... Substitute the values ​​to solve.

[0190] The standardized resonant voltage at the switching point between Mode4 and Mode1 in the nth switching cycle can be obtained as follows: Its value varies with It decreases as it increases. At this time, in Mode 1, v... CrN On the trajectory segment with a value < 1, the value of the normalized resonant current decreases as the value of the resonant voltage decreases. Therefore, in the two cases analyzed above, the maximum value of the reverse resonant current of Mode4 in the first cycle is the maximum value during the entire startup process.

[0191] Step 4: Select other electronic components for the switched capacitor resonant converter based on the maximum peak-to-peak values ​​of the resonant current and resonant voltage during startup, and set the switching parameter I. SN and R M1NThe constraints; where the switching parameter I SN and R M1N The constraints are as follows: (3.22); (3.23);

[0192] Among them, V rating R represents the rated voltage of the switched capacitor. M1N For the set v CrN -i LN The radius of the trajectory of Mode1 on the plane, and ; This represents the peak value of the reverse normalized switched capacitor voltage for Mode 1.

[0193] Among them, the switching parameter R M1N The value of v directly determines the intersection state of the two state trajectories, Mode4 and Mode1, and its reasonableness is the core prerequisite for the two trajectories to achieve effective intersection. The three critical intersection conditions for the two circular trajectories corresponding to Mode4 and Mode1 are as follows. In v CrN -i LN Within the state plane, during the first switching mode cycle, M has a smaller value, and the center of the Mode4 trajectory (M, 0) is close to the origin. When the resonant current satisfies equation (2.15), the system switches from Mode3 to Mode4. If the trajectory radius of Mode1 is at this time... If the value is too small, the state trajectories of Mode1 and Mode4 will have no intersection, and the converter will be unable to achieve normal mode switching. When the state trajectories of Mode4 and Mode1 are exactly tangent, the switching point (v) from Mode3 to Mode4 is... CrNc i LNc The state happens to fall on the trajectory of Mode 1, and the corresponding critical trajectory radius is... =1. Therefore, to ensure that the trajectories of Mode 1 and Mode 4 intersect and achieve stable mode switching, the trajectory radius R is 1. M1N Must meet ;

[0194] Step 5: Based on the selected resonant inductor, switched capacitor, and other electronic components, construct a switched capacitor resonant converter and control it through a control system. The control system includes a signal acquisition circuit, an FPGA main control unit, and an isolation drive module. The signal acquisition circuit is used to acquire the resonant current, switched capacitor voltage, output voltage, and load current of the switched capacitor resonant converter. The signal acquisition circuit's acquisition signal output terminal is connected to the FPGA main control unit's acquisition signal output terminal. The FPGA main control unit's control output terminal is connected to the isolation drive circuit's drive signal output terminal. The first drive output terminal of the isolation drive circuit is connected to the gate of switch S1, the second drive output terminal is connected to the gate of switch S2, the third drive output terminal is connected to the gate of switch S3, and the fourth drive output terminal is connected to the gate of switch S4. The isolation drive circuit controls the corresponding switch according to the drive signal from the FPGA main control unit to achieve adjustment of different switching modes.

[0195] At startup, the output voltage is first acquired. If the acquired output voltage is less than the reference voltage, the switched capacitor resonant converter is first dynamically adjusted by boosting, and then adjusted by steady state. The working states during the dynamic boost adjustment include Initial, state2, state5, state6, state7 and state8, where state2 and state5 are Mode2, state6 is Mode3, state7 is Mode4 and state8 is Mode1. The external adjustment loop cycle mode is formed by state5, state6, state7 and state8.

[0196] The control process begins by transitioning from the initial state (Initial) to state 2, then instantly jumping to state 5. The forward resonant current charges the output capacitor, causing the output voltage to steadily increase. When the trajectory simultaneously satisfies the constraints of equations (2.13) and (2.14), the state switches to state 6, after which the resonant current completes its polarity reversal. When the state trajectory satisfies the switching condition (2.15), the state switches to state 7, at which point the resonant circuit continues to transfer energy to the load side, further increasing the output voltage. When either switching condition (2.16) or (2.17) is met, the state switches to state 8, and the system completes the resonant current reversal again. When the resonant current satisfies the switching condition (2.18), the state machine switches to state 5, completing one cycle of state switching during the dynamic process.

[0197] When the output voltage reaches the reference voltage, the state switches cyclically in the order of state8, state5, state6, and state7. During the steady-state adjustment process, the switching condition from state5 to state6 becomes (2.19), and the switching condition from state7 to state8 becomes (2.20).

[0198] If the output voltage acquired at startup is greater than or equal to the reference voltage, the switched capacitor resonant converter first undergoes buck dynamic regulation, followed by steady-state regulation. The operating states during buck dynamic regulation include Initial, state1, state2, state3, state4, state5, state6, state7, and state8. State2 and state5 are Mode 2, state3 and state6 are Mode 3, state4 and state7 are Mode 4, and state1 and state8 are Mode 1. The control process starts from the initial state (Initial) and enters the inner regulation loop cyclic mode. The inner regulation loop cyclic mode sequentially switches between states 4, 3, 2, and 1, gradually decreasing the output voltage until it equals the reference voltage. Then, it enters the outer regulation loop cyclic mode (state7) from state 4, and performs steady-state regulation by sequentially switching between states 8, 5, 6, and 7.

[0199] The circuit of the switched capacitor resonant converter is as follows: Figure 2 As shown, this is a symmetrical dual half-bridge structure, including the drain of the switching transistor S1 connected to the input voltage V. in Positive electrode and buffer capacitor C s1 At one end, the source of the switching transistor S1 is connected to a buffer capacitor C. s1 The other end, the drain of the switching transistor S2, and the buffer capacitor C s2 One end and inductor L r One end, inductor L r The other end is connected to the switched capacitor C. r Positive terminal; the source of switching transistor S2 is connected to a buffer capacitor C. s2 The other end, output capacitor C out Positive terminal, drain of switching transistor S3, buffer capacitor C s3 One end is connected to the load resistor R, and the source of the switching transistor S3 is connected to the buffer capacitor C. s3 At the other end, the switched capacitor C r The negative terminal is connected to the drain of the switching transistor S4, and the source of the switching transistor S4 is connected to the other end of the load resistor R and the output capacitor C. out Negative terminal and input voltage V inNegative terminal. The converter has four switching modes: Mode1, Mode2, Mode3, and Mode4. The equivalent circuits for each mode are as follows: Figure 3 As shown. In Mode 1, switches S1 and S4 are on, while switches S2 and S3 are off. At this time, the input power supply and resonant inductor L... r and switched capacitor C r This forms a closed loop. In this mode, the output capacitor C out The load R is discharged independently to maintain the stability of the output voltage. When the resonant current i L When i > 0, the input power supply charges the LC resonant circuit, and the resonant current rises rapidly. L When the voltage is less than 0, the LC resonant circuit feeds energy back to the input power supply, and the resonant energy gradually decreases. Mode 1 is mainly responsible for the polarity reversal of the resonant current and does not directly contribute to the establishment of the output voltage. In Mode 2, switches S1 and S3 are turned on, while switches S2 and S4 are turned off. At this time, the input power supply and the resonant inductor L... r and switched capacitor C r This forms a closed loop. When the resonant current i L When >0, the input power supply and the resonant circuit simultaneously supply power to the output capacitor C. out Powered by the load R, the output voltage is quickly established. When i L When the voltage is less than 0, the output capacitor will feed energy back to the resonant circuit and the input side, which is detrimental to output voltage regulation. Mode 2 is one of the core modes for the converter to quickly establish the output voltage. In Mode 3, switches S2 and S3 are turned on, while switches S1 and S4 are turned off. At this time, the resonant inductor L... r With switched capacitor C r This forms an LC resonant circuit. When the resonant current i L When i > 0, energy is transferred from the resonant inductor to the switched capacitor, which stores energy. L When the voltage is less than 0, the switched capacitor discharges, feeding energy back to the resonant inductor. Mode 3 has no external energy input or output; it is only used for rapid reversal of the resonant current, preparing for the next stage of power supply to the output side. In Mode 4, switches S2 and S4 are turned on, while switches S1 and S3 are turned off. At this time, the resonant inductor L... r Switched capacitor C r With the output capacitor C on the output side out The load R forms a closed loop. When the resonant current i L When i < 0, the LC resonant circuit releases the stored energy to the output side, charging the output capacitor, and the output voltage is quickly established. LWhen the output voltage is greater than 0, the energy of the output capacitor is fed back to the resonant circuit, causing the output voltage to drop. Mode 4 is another key mode for the rapid establishment of the converter's output voltage. The working principle of the control system is as follows: when the switched capacitor resonant converter is in operation, the acquisition circuit obtains the output voltage v at the output terminal. out With load current i Load And simultaneously acquire the resonant current i in the resonant circuit L and the switched capacitor voltage v Cr The analog signals are processed by signal detection and conditioning circuits and converted into digital signals. The detected signals are compared with the signals in the planned trajectory. The FPGA main control chip generates corresponding switching drive commands based on the control logic set by the finite state machine. Subsequently, the isolation drive module amplifies these drive signals to control the switching transistors of the main switched capacitor resonant converter to turn on and off.

[0200] To verify the effectiveness of the state trajectory control scheme designed in this paper, an experimental prototype of a switched-capacitor resonant converter with an input voltage of 200V and an output voltage of 100V / 10A was built. The steady-state switching period Tsw was set to a range of 30μs to 80μs. Based on the design requirements of the converter under rated operating conditions, specific parameter designs were completed for the key components of the converter.

[0201] For a switched-capacitor resonant converter to achieve soft-switching operation, the switching frequency must be higher than the resonant frequency. The hardware platform built in this paper has a lower limit for the switching frequency fsw = 12.5kHz. To ensure the converter always operates above the resonant frequency fr, the resonant inductor L... r With switched capacitor C r The parameters must meet the following requirements. (4.6).

[0202] According to equation (4.6), in order to make the system's natural resonant frequency reach fr = 10kHz, the resonant inductor and the switched capacitor are respectively taken as L. r =27μH, C r =9.4μF.

[0203] Table 1 Experimental Parameters of Switched-Capacitor Resonant Converter

[0204]

[0205] When the steady-state switching period Tsw is set between 30μs and 80μs, the maximum timing difference Ts between the upper and lower half-bridges of the steady-state switched capacitor resonant converter is 33.8μs. According to the output voltage ripple calculation formula:

[0206] (4.7)

[0207] Based on the design specification of 1% maximum output voltage ripple, and by combining equation (4.7), it can be seen that the output capacitor C out The value should be no less than 336μF. Finally, the key parameter values ​​for the switched capacitor resonant converter are shown in Table 1.

Claims

1. A method for controlling the state trajectory of a switched capacitor resonant converter, characterized in that, Includes the following steps: Step 1: Set the switching mode switching sequence of the switched capacitor resonant converter during the boost process; establish a state trajectory model of the boost process, and plot it on v according to the switching mode switching sequence of the boost process. out -i L The overall state trajectory diagram of each switching mode on the state plane, and the plotted on v CrN -i LN The overall state trajectory diagram of each switching mode on the state plane, v out For the output voltage, i L For resonant current, v CrN To standardize the switched capacitor voltage, i LN This is the standardized resonant current; The switching sequence of the switching modes during the boost process is set to Mode2, Mode3, Mode4, and Mode1. Step 2: Based on the drawing in v out -i L State plane and v CrN -i LN The overall state trajectory diagram of the state plane determines the switching conditions of each switching mode; Step 2-1: Set the switching conditions for the switching modes during the boost process of the switched capacitor resonant converter; Select switching parameters and ,in, The maximum forward resonant current for Mode1 and Mode3 The standardized value, For the set v CrN -i LN The radius of Mode1's trajectory on the plane; Step 2-1-1: Determine the switching conditions from Mode 2 to Mode 3; The condition for switching from Mode 2 to Mode 3 is when and ,in, To standardize the resonant current, The maximum forward resonant current for Mode1 and Mode3 The standardized value, To standardize the switched capacitor voltage, v CrNQ The trajectory of Mode2 in the first cycle and trajectory i LN = I SN The standardized resonant voltage value at the intersection point; Step 2-1-2: Determine the switching conditions from Mode 3 to Mode 4; The condition for switching from Mode 3 to Mode 4 is: ;in, To standardize the resonant current, This is the maximum negative resonant current of Mode 3; Step 2-1-3: Determine the switching conditions from Mode4 to Mode1; The switching condition from Mode 4 to Mode 1 is: or ; To standardize the resonant current, For the set v CrN -i LN The radius of the trajectory of Mode1 on the plane. Standardized switched capacitor voltage; Step 2-1-4: Determine the switching conditions from Mode1 to Mode2; The switching condition from Mode1 to Mode2 is: ;in, To standardize the resonant current, The maximum forward resonant current for Mode1 and Mode3 The standardized value; Step 3: Set the resonant inductor and switched capacitor of the switched capacitor resonant converter, and calculate the maximum peak-to-peak value of the resonant current and the maximum peak-to-peak value of the resonant voltage during the boost process; Step 4: Select the electronic components of the switched capacitor resonant converter based on the maximum peak-to-peak value of the resonant current and the maximum peak-to-peak value of the resonant voltage during the boost process, and set the switching parameter I. SN and R M1N Constraints; Step 5: Construct a switched capacitor resonant converter and control the switched capacitor resonant converter through a control system.

2. The state trajectory control method for a switched capacitor resonant converter according to claim 1, characterized in that: Step 1 also Includes the following: Step 1-1: For the equivalent circuits corresponding to each dominant switching mode of the switched capacitor resonant converter, establish and solve the large-signal nonlinear differential equations of the converter based on Kirchhoff's voltage law (KVL) and current law (KCL). The modal differential equations are as follows: Mode 1: ； in, Indicates the resonant current The first derivative, Indicates resonant inductance. This represents the voltage across the resonant capacitor. Indicates the input voltage. This represents the first derivative with respect to the resonant capacitor voltage. Indicates the resonant capacitor. Indicates the resonant current. Indicates the output voltage. This represents the first derivative with respect to the output voltage. Indicates the resistance of the load. Indicates the output capacitance; Mode2: ； Mode3: ； Mode4: ； Solve for its value in v out -i L The natural trajectory equations for each switching mode in the state plane are as follows: Mode 1: ； Mode2: ； Mode3: ； Mode4: ； in, Represents the resonant current. This represents the instantaneous value of the resonant current at the initial moment of the current mode. Indicates the resonant capacitor. Indicates resonant inductance. This represents the instantaneous value of the switched capacitor voltage at the initial moment of the current mode. Indicates the input voltage. Indicates the resistance of the load. Indicates the output capacitor; This represents the instantaneous value of the output voltage at the initial moment of the current mode. Indicates the output voltage; Step 1-2: Select the standardized switched capacitor voltage and standardized resonant current To control variables, construct the converter modes at v CrN -i LN The trajectory equation on the state plane is as follows: Mode1: ; Mode2: ; Mode3: ; Mode4: ; in, To standardize the switched capacitor voltage, and , For the standardized resonant current, and , Z represents the resonant current. r This represents the characteristic impedance of a series resonant circuit. , Indicates resonant inductance. Indicates the resonant capacitor. Indicates the voltage transformation ratio. , Indicates the input voltage. Indicates the output voltage; Based on the switching mode switching sequence of the boost process, plotted on v out -i L The overall state trajectory diagram of each switching mode on the state plane, and the plotted on v CrN -i LN The overall state trajectory diagram of each switching mode on the state plane.

3. The state trajectory control method for a switched capacitor resonant converter according to claim 1, characterized in that: Step 2 also includes: Step 2-2: Set the switching sequence and switching conditions of the switching modes in the steady-state regulation process of the switched capacitor resonant converter; The switching sequence of the switching modes in the steady-state regulation process is Mode1, Mode2, Mode3, Mode4; The switching condition from Mode 1 to Mode 2 in the steady-state adjustment process is as follows: ;in, To standardize the resonant current, Indicates the maximum forward resonant current of Mode1 and Mode3. The standardized value; The switching condition from Mode 3 to Mode 4 during the steady-state regulation process is as follows: ; The switching condition from Mode 2 to Mode 3 during the steady-state regulation process is as follows: ;in, Indicates the output voltage. Indicates the reference voltage. To standardize the switched capacitor voltage, To standardize the resonant current, Indicates resonant inductance. Indicates the resonant capacitor. Indicates the output capacitor. Indicates the magnitude of the load resistance. The switching condition from Mode 4 to Mode 1 during the steady-state regulation process is as follows: .

4. The state trajectory control method for a switched capacitor resonant converter according to claim 1, characterized in that: Step 3 also includes the following steps: Step 3-1: Calculate the peak value of the positive resonant current during the first switching mode cycle; The calculation is performed using the following formula: ； in, This represents the maximum value of the positive resonant current during the first switching mode cycle. This represents the maximum value of the positive normalized resonant current during the first switching mode cycle. Indicates the input voltage. Indicates resonant inductance. Indicates the resonant capacitance; Step 3-2: Calculate the peak value of the forward resonant voltage during the first switching mode cycle; The calculation is performed using the following formula: ； in, This represents the peak value of the positive resonant voltage during the first switching mode cycle. Indicates the maximum forward resonant current of Mode1 and Mode3. The square of the standardized value; Step 3-3: Calculate the maximum peak-to-peak value of the resonant current during the first switching mode cycle; Set parameters The maximum value of the reverse resonant current during the first switching mode cycle is given by the x-coordinate of the intersection point of the Mode4 and Mode1 state trajectories. ≥ 1, calculate the peak-to-peak value of the resonant current in the first cycle using the following formula. : ； ； in, This represents the peak-to-peak value of the resonant current during the first cycle. Indicates resonant inductance. Indicates the resonant capacitor. Indicates the input voltage. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. This represents the maximum value of the positive resonant current during the first switching mode cycle; like If the value is less than 1, the peak-to-peak value of the resonant current in the first cycle can be calculated using the following formula. : ； ； in, This represents the peak-to-peak value of the resonant current during the first cycle. Indicates resonant inductance. Indicates the resonant capacitor. Indicates the input voltage. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. The maximum forward resonant current for Mode1 and Mode3 The standardized value; Steps 3-4: Calculate the maximum peak-to-peak value of the resonant voltage during the first switching mode cycle; Calculate using the following formula ； in, This represents the maximum peak-to-peak value of the resonant voltage during the first switching mode cycle. Indicates the input voltage. The maximum forward resonant current for Mode1 and Mode3 The standardized value, Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane.

5. The state trajectory control method for a switched capacitor resonant converter according to claim 1, characterized in that: The switching parameters described in step 4 The constraints are as follows: ； ； in, This represents the rated voltage of the switched capacitor. Indicates the set v CrN -i LN The radius of the trajectory of Mode 1 on the plane. Indicates the input voltage. The maximum forward resonant current for Mode1 and Mode3 The standardized value; The peak value of the reverse normalized switched capacitor voltage for Mode 1; Switch parameters The constraints are .

6. The state trajectory control method for a switched capacitor resonant converter according to claim 1, characterized in that: Step 5: During startup, the output voltage is first acquired. If the acquired output voltage... Less than the reference voltage Then, the switched capacitor resonant converter is dynamically adjusted to boost voltage. If the output voltage is collected at startup Greater than or equal to the reference voltage Therefore, the switched capacitor resonant converter is first subjected to voltage reduction dynamic adjustment, and then to steady-state adjustment.

7. The state trajectory control method for a switched capacitor resonant converter according to claim 6, characterized in that: During boost dynamic adjustment, the switching is performed according to the switching mode switching sequence set in step 1. The working states during boost dynamic adjustment include Initial, state2, state5, state6, state7, and state8, where state2 and state5 are Mode2, state6 is Mode3, state7 is Mode4, and state8 is Mode1. The outer adjustment loop cycle mode is formed by state5, state6, state7, and state8. The control process begins by transitioning from the initial state (Initial) to state 2, then instantly jumps to state 5. The positive resonant current charges the output capacitor, causing the output voltage to rise steadily. This occurs when the trajectory simultaneously satisfies… and When the constraint conditions are met, the state switches to state6, after which the resonant current completes the polarity reversal; When the state trajectory meets the switching conditions When the state switches to state7, the resonant circuit continues to transfer energy to the load side, further increasing the output voltage. When the switching conditions are met or When the state switches to state 8, the system completes the reversal of the resonant current again, and the switching condition is met. When the state machine switches to state5, it completes one cycle of state switching during the dynamic process; When the output voltage reaches the reference voltage, the system cycles through states 8, 5, 6, and 7 in that order. The switching condition from state 5 to state 6 is as follows: The switching condition from state7 to state8 is: .

8. The state trajectory control method for a switched capacitor resonant converter according to claim 6, characterized in that: The working states during the dynamic adjustment of the voltage reduction include Initial, state1, state2, state3, state4, state5, state6, state7 and state8, where state2 and state5 are Mode2, state3 and state6 are Mode3, state4 and state7 are Mode4, and state1 and state8 are Mode1. The control process starts from the initial state and enters the inner regulation loop cycle mode. The inner regulation loop cycle mode switches sequentially according to the state sequence of state4, state3, state2 and state1, so that the output voltage gradually decreases until the output voltage equals the reference voltage. Then, it switches from state4 to state7, and switches sequentially according to the state sequence of state8, state5, state6 and state7 to perform steady-state regulation.

9. A state trajectory controller for a switched capacitor resonant converter, characterized in that: The system includes a control system for implementing the state trajectory control method according to any one of claims 1 to 8. The control system includes a signal acquisition circuit, an FPGA main control unit, and an isolation drive module. The signal acquisition circuit is used to acquire the resonant current, switched capacitor voltage, output voltage, and load current of the switched capacitor resonant converter. The signal acquisition output terminal of the signal acquisition circuit is connected to the signal acquisition output terminal of the FPGA main control unit. The control output terminal of the FPGA main control unit is connected to the drive signal output terminal of the isolation drive circuit. The first drive output terminal of the isolation drive circuit is connected to the gate of the switch transistor S1, the second drive output terminal of the isolation drive circuit is connected to the gate of the switch transistor S2, the third drive output terminal of the isolation drive circuit is connected to the gate of the switch transistor S3, and the fourth drive output terminal of the isolation drive circuit is connected to the gate of the switch transistor S4. The isolation drive circuit controls the corresponding switch transistor according to the drive signal of the FPGA main control unit to achieve the adjustment of different switching modes.

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