A method for active capacitor voltage balancing control of a flying capacitor seven-level soft-switching power amplifier

Abstract

The present invention discloses a method for active capacitor voltage balancing control of a flying capacitor seven-level soft-switching power amplifier. The method is based on a mathematical model of the power amplifier topology, analyzes its working state, the multi-level voltage and inductor current characteristics of the power amplifier, and studies the parameter characteristics of the trapezoidal filter inductor current. According to the conversion mechanism of the ten states of the soft switch, the six key time domains of the trapezoidal filter inductor current are dynamically allocated based on the constraints of the current circulation conduction path and the minimum error of the trapezoidal filter equivalent average current. Considering the initial value of the flying capacitor, the carrier phase shift modulation meets the initial voltage balance condition, and combined with the dynamically reconstructed trapezoidal filter current, the stability of the flying capacitor voltage in multiple switching cycles within the full operating range is achieved. The closed-loop simulation results show that the control strategy proposed in the present invention can effectively control the capacitor voltage balance and achieve high-precision current output.

Description

Technical Field

[0001] The present invention relates to a capacitor voltage active balancing control method, and in particular to a capacitor voltage active balancing control method for a flying capacitor seven-level soft switching power amplifier. Background Art

[0002] For many years, flying capacitor multi-level power amplifiers have been widely used in high-density, high-power power conversion applications because they can effectively reduce switch voltage stress and increase bus voltage levels. Due to the limitations of semiconductor switching devices, the introduction of flying capacitor multi-level power amplifiers can effectively increase the voltage level on the output side and achieve stable high-voltage output. Combined with the drive application of gradient coils, flying capacitor power amplifiers can be used in high-bandwidth, low-harmonic, and high-current output scenarios. In order for the power amplifier to stably generate multiple levels and maintain the voltage stress across each switch tube, additional methods are required to achieve flying capacitor voltage balance, which becomes the key to the stable operation of flying capacitor multi-level power amplifiers.

[0003] Modern scholars generally divide flying capacitor voltage balancing strategies into passive balancing and active balancing. Active balancing of flying capacitor voltage is generally achieved through duty cycle compensation or repeated switching. Previous literature (Capacitor voltage balancing in a 5-L full-bridge flying capacitor inverter) proposed a method of maintaining flying capacitor voltage balance by using a controller to modify the switching time duty cycle, such as Figure 1 This control scheme is based on the traditional multi-carrier control scheme. Although it solves the flying capacitor balance problem, its output current tracking capability and soft switching control capability are limited, making it difficult to meet the requirements of low harmonics and high output current in MRI systems. Summary of the Invention

[0004] This paper combines the stringent requirements of MRI with the unique characteristics of flying capacitor power topology to provide a method for active capacitor voltage balancing control in a flying capacitor seven-level soft-switching power amplifier. Based on the constraints of current loop conduction paths and minimizing the error in the equivalent average current of the trapezoidal filter, this method dynamically allocates the critical time domain of the trapezoidal filter inductor current, achieving high-precision current output and flying capacitor voltage balance. This method can be used to drive the gradient coils in magnetic resonance imaging systems, providing high-precision current.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for actively balancing capacitor voltage of a flying capacitor seven-level soft-switching power amplifier comprises the following steps:

[0007] Step 1: Establishment of the mathematical model of the ladder filter current:

[0008] In a single cycle of the trapezoidal filter current, there are two moments to choose to charge or discharge the flying capacitor. In order to ensure the feasibility of the trapezoidal filter shape, the resonant mode and switching characteristics of the soft switch are combined to optimize the distribution and obtain the trapezoidal filter current i Lf The slope equation is:

[0009]

[0010] Where α is [t0, t1], [t9, t 10 ] Time period ladder filter current i Lf The slope of β is the trapezoidal filter current i in the [t4, t6] period. Lf The slope of γ is the trapezoidal filter current i in the time period [t2, t3] and [t7, t8] Lf For phase α and phase β, select the highest level V dc and the lowest level -V dc As the required distribution level, for the level level corresponding to the intermediate stage part γ of the ladder filter current, the selected level uses the output voltage u out To determine, choose the output voltage u out The closest electrical level; u p Represents the AC side node voltage; L f Represents the inductance value of the filter inductor;

[0011] In the flying capacitor seven-level soft switching power amplifier topology, C r1 、C r2 、C r3 、C r4 、C r5 、C r6 、C r7 、C r8 、C r9 、C r10 、C r11 and C r12 As the resonant element of the filter current, the soft switching process of the switch tube is realized; based on the balance of the flying capacitor, an accurate mathematical model of the ladder filter current is established. The specific steps are as follows:

[0012] Step 1.1: Assume that the average value of equivalent current i ave >0 and γ>0, the commutation charge Q of the parallel resonant capacitor of a single MOSFET during the conversion process c It needs to be fully released. The minimum commutation current i is obtained according to the cross-sectional area (the area enclosed by the trapezoidal filter current) when the inductor current resonates and the corresponding slope α.LfL :

[0013]

[0014] In order to achieve ZVS at every switching point, the cross-sectional area of ​​the inductor current when it resonates must meet 2Q c , the resonance time interval is calculated according to the magnitude of the current;

[0015] Step 1.2: In order to ensure the stability of flying capacitor charging and discharging under different currents, an adjustable parameter is given to the time period [t7, t8], which is determined by the average current i ave Make adjustments to ensure there is enough mid-level state:

[0016]

[0017] Where, represents the time from t7 to t8; k0 is a variable parameter; t min is the minimum time length of the time period [t7, t8]; t rat is the actual parameter defined; i ave is the filter inductor current i in a single cycle Lf Equivalent value after filtering; comprehensive known minimum commutation current i LfL , the slopes of each time period (α, β, γ) and the above formula are used to derive the time interval [t5, t6] and i L The size of the negative half axis of the filter current is finally obtained in the controller. The complete description of the switching point value and time interval of the negative half axis of the filter current is obtained;

[0018] Step 1.3: There is no specific limit for the current value and time interval of the positive axis. An upper limit needs to be set:

[0019] i Lfh =-i LfL +k1·i ave

[0020] Where k1 is the variable coefficient;

[0021] Step 1.4: According to the charge equivalence principle, we get the following formula:

[0022] Q p -Q N =i ave (t p +t N )

[0023] Where Q p , Q N are respectively the positive and negative areas of the ladder filter current; t pRepresents the time from t0 to t5, that is, the time when the filter inductor current is positive; t N Represents t5 to t 10 The time size of the filter inductor current is negative;

[0024] Step 1.5: The current i at the transition point is known. Lfh , slopes α, β, γ and the magnitude and time interval of the negative half-axis current, combined with the charge equivalent equation, the filter current i in a single switching cycle is finally obtained. Lf A complete description of

[0025] Step 2: Calculate and reconstruct a complete description of the ladder filter current in a single cycle so that the charge and discharge of the capacitor are balanced in a single cycle. The specific steps are as follows:

[0026] Step 2.1: Based on the ladder filter current mathematical model, the charging charge Q of the flying capacitor in a single cycle is obtained. h and discharge charge Q f The expression:

[0027]

[0028] Where i h Represents the highest point of the ladder filter current; i L Represents the lowest point of the ladder filter current; represents the time from t2 to t3;

[0029] Step 2.2: To achieve a natural balance of the flying capacitor, the ladder filter current is reconstructed twice to maintain the equal charge and discharge amounts of the flying capacitor within a single cycle.

[0030] Step 2.3, when i ave >0, the charging charge of the flying capacitor is greater than the discharging charge, and t x The charging time period, at the same time, in order to realize the calculation, the time period of the switch state with a slope of β is kept unchanged. According to the similarity principle, [t4,t 4’ ] is equal to t x In order to maintain voltage balance, set [t4,t 4’ ]Time is t y , from which the charge balance expression is obtained:

[0031]

[0032] Positive equivalent area Q p While increasing the negative equivalent area Q N Decrease, when Q N =Q pWhen , the dynamic time domain allocation is most reasonable, and the trapezoidal filter equivalent average current error is the smallest at this time, and the expression is as follows:

[0033]

[0034] t x and t y The mathematical expression is as follows:

[0035]

[0036] Step 2.4, when i ave <0, the charging charge of the flying capacitor is less than the discharging charge, then calculate t x and t y The system of equations is:

[0037]

[0038] The complete description of the reconstructed ladder filter current in a single cycle is obtained by calculation;

[0039] Step 2.5: Assume △U q is the voltage deviation of the flying capacitor. When the voltage upper limit of the flying capacitor exceeds U cq +△U q When the charging time of the flying capacitor is reduced, the amount of charge reduced in the positive cycle is △Q. p for:

[0040]

[0041] When the charging time of the flying capacitor is actively reduced, the cycle of the trapezoidal filter inductor current will be reduced synchronously. The change in cycle will increase the THD of the output current. Therefore, in order to ensure that the cycle remains unchanged, it is necessary to increase the discharge time of the flying capacitor by △t, and finally obtain the negative cycle increase in charge △Q N for:

[0042]

[0043] The deviation of the equivalent current △i is obtained from this bas for:

[0044]

[0045] Finally, a unified equation for adjusting the time △t, output current deviation and flying capacitor voltage ripple is obtained;

[0046] Step 3: Design of closed-loop control strategy based on flying capacitor voltage balance:

[0047] Step 3.1: When the system starts operating, the flying capacitor uses a short phase-shift modulation link. When the flying capacitor voltage is pre-charged, it quickly switches to ladder filter current control and enters the working state;

[0048] Step 3.2: The flying capacitor multi-level power amplifier relies on phase-shifted carrier pulse width modulation to achieve pre-charging of the flying capacitor. The switching function of the flying capacitor is:

[0049] i qx =(S n -S n+1 )i Lf

[0050] Among them, i qx Represents the current flowing through the flying capacitor C qx Current value; S n and S n+1 Represents two adjacent switch tubes; i Lf is the inductor current; in one modulation cycle, in order to maintain the voltage of the flying capacitor constant, the flying capacitor satisfies the ampere-second balance principle:

[0051]

[0052] in, Represents the current flowing through the flying capacitor C qx The average current value;

[0053] Perform switching cycle averaging on the above equation to obtain the flying capacitance C qx Voltage variation during one switching cycle:

[0054]

[0055] Among them, D n and D n+1 Represents the switch tube S n and S n+1 Duty cycle; T s represents the switching cycle; Represents the average value of the filter inductor current;

[0056] Step 3.3: To ensure the output current quality, after the initial voltage balancing is completed, a trapezoidal filter current control method is used. By controlling the trapezoidal filter inductor current, the flying capacitor achieves charge and discharge balance within a single cycle. At the same time, the correct operation of each working state and the continuity of the trapezoidal filter inductor current are reasonably guaranteed through the time allocation principle.

[0057] Step 3.4: When reconstructing the ladder filter current, in order to maintain voltage balance, the current equivalent value changes. In order to ensure that the output current continues to track the given current signal, it is necessary to compensate the change value in the control loop. The compensation current i bas The size is:

[0058]

[0059] when i ave >0, i bas <0,i ave <0, i bas >0, it is necessary to use a negative feedback link in the control system to achieve current compensation.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] The present invention proposes a capacitor voltage balancing strategy based on trapezoidal filter inductor current and carrier phase shift reconstruction. The strategy is based on the mathematical model of the power amplifier topology, analyzes its working state, the multi-level voltage and inductor current characteristics of the power amplifier, and studies the parameter characteristics of the trapezoidal filter inductor current. According to the conversion mechanism of the ten states of the soft switch, the six key time domains of the trapezoidal filter inductor current are dynamically allocated based on the constraints of the current circulation conduction path and the minimum error of the trapezoidal filter equivalent average current. Considering the initial value of the flying capacitor, the carrier phase shift modulation meets the initial voltage balance condition, and combined with the dynamically reconstructed trapezoidal filter current, the stability of the flying capacitor voltage in multiple switching cycles within the full operating range is achieved. The closed-loop simulation results show that the control strategy proposed in the present invention can effectively control the capacitor voltage balance and achieve high-precision current output. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Flying capacitor voltage balance for duty cycle compensation;

[0063] Figure 2 It is a flying capacitor seven-level soft switching power amplifier;

[0064] Figure 3 is the ladder filter current in a single cycle (i ave >0 and γ>0);

[0065] Figure 4 is the equivalent circuit scheme of a single cycle in the power amplifier, (a) t0 <t<t1,(b)t1<t<t2,(c)t2<t<t3,(d)t3<t<t4,(e)t4<t<t5,(f)t5<t<t6,(g)t6<t<t7,(h)t7<t<t8,(i)t8<t<t9,(j)t9<t<t 10 ;

[0066] Figure 5 is the charge and discharge charge of the flying capacitor;

[0067] Figure 6 Reconstructed description of the ladder filter current (i ave >0);

[0068] Figure 7 is the charge and discharge charge of the adjusted flying capacitor;

[0069] Figure 8 The closed-loop control block diagram for flying capacitor balance;

[0070] Figure 9 The modulation wave i is a single switching cycle Lf 、u p and u cqx Waveform diagram;

[0071] Figure 10 The voltage balancing principle of flying capacitor under phase shift modulation;

[0072] Figure 11 is the output current i out ;

[0073] Figure 12 is the node voltage u p and a partial magnified view;

[0074] Figure 13 is the filter inductor current i Lf and a partial magnified view;

[0075] Figure 14 This is the voltage simulation result of the flying capacitor. DETAILED DESCRIPTION

[0076] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0077] The present invention provides a method for actively balancing capacitor voltage of a flying capacitor seven-level soft-switching power amplifier, the method comprising the following steps:

[0078] Step 1: Establish the mathematical model of the ladder filter current.

[0079] Power amplifier topology such as Figure 2 As shown, the specific structure can be found in CN202211254408.2. Through the switching change of a single cycle, a trapezoidal current signal is finally obtained on the filter inductor, such as Figure 3 As shown, the equivalent circuit scheme of a single cycle in the power amplifier is as follows Figure 4 As shown. In a single cycle of the trapezoidal filter current, there are two moments to choose to charge or discharge the flying capacitor. In order to ensure the feasibility of the trapezoidal filter shape, the optimal distribution is performed by combining the resonant mode and switching characteristics of the soft switch, and the final trapezoidal filter current i Lf The slope equation is:

[0080]

[0081] Among them, for phase α and phase β, the highest level V is selected dc and the lowest level -V dc As the required distribution level, for the level level corresponding to the intermediate stage part γ of the ladder filter current, the selected level uses the output voltage u out To determine, choose the output voltage u out The closest level.

[0082] In the topology, C r1 、C r2 、C r3 、C r4 、C r5 、C r6 、C r7 、C r8 、C r9 、C r10 、C r11 and C r12 As a resonant element for the filter current, it enables the soft switching process of the switching transistor. The length of the resonance time affects the balance of the flying capacitor. Based on the balance of the flying capacitor, an accurate mathematical model of the ladder filter current is established. The specific construction process of the ladder filter current mathematical model within a single cycle is as follows:

[0083] Assume that the average value of equivalent current i ave >0 and γ>0, the commutation charge Q of the parallel resonant capacitor of a single MOSFET during the conversion process c Therefore, according to the area of ​​the cross section and the corresponding slope α, the minimum commutation current i can be obtained. LfL :

[0084]

[0085] In order to achieve ZVS at every switching point, the cross-sectional area of ​​the inductor current when it resonates must meet 2Q c , the resonant time interval is calculated according to the current. In order to ensure the stability of the flying capacitor charge and discharge under different currents, the time period [t7, t8] is given an adjustable parameter, which is the average current value i ave Make adjustments to ensure there is enough mid-level state.

[0086]

[0087] In the formula, k0 is a variable parameter, and the optimal result is determined according to the actual situation; t min is the minimum time length of the time period [t7, t8]; t rat The actual parameters are defined, and the specific parameters are determined according to the principle of reasonable time allocation. LfL , the slopes of each time period (α, β, γ) and the above formula can be derived to obtain the time interval [t5, t6] and i L The size of the negative half-axis filter current is finally fully described in the controller in terms of switching point value and time interval.

[0088] At the same time, since the purpose of the flying capacitor seven-level soft switching power amplifier is to obtain the desired ideal current, the filter inductor current i Lf The equivalent value after filtering i ave is known. However, this is still not enough to describe the entire ladder filter current, because the current value and time interval of the positive half axis have no specific limit, so an upper limit needs to be set. Here it is set as follows:

[0089] i Lfh =-i LfL +k1·i ave

[0090] In the formula, the variable coefficient k1 can be optimally adjusted according to the actual solution. In addition, according to the charge equivalence principle, the formula can be obtained as follows:

[0091] Q p -Q N =i ave (t p +t N )

[0092] Where Q p , Q N are the positive and negative areas of the ladder filter current respectively. Lfh , slope (α, β, γ) and the magnitude and time interval of the negative half-axis current, combined with the charge equivalent equation, the filter current i in a single switching cycle can be obtained. Lf A complete description of .

[0093] Step 2: The flying capacitor trapezoidal filter current constructed during the operation of the seven-level soft-switching power amplifier has two time periods for charging or discharging, so the flying capacitor voltage balance of the power amplifier must be maintained within a single or multiple cycles. Based on the mathematical model of the trapezoidal filter current, the charging charge Q of the flying capacitor in a single cycle can be obtained.h and discharge charge Q f The expression:

[0094]

[0095] According to the above formula, i h Represents the highest point of the ladder filter current; i L Represents the lowest point of the ladder filter current. set =18A, f=50Hz sinusoidal current, we can get Figure 5 The charge and discharge curves shown in Figure 2 show that the initially constructed ladder-shaped filter current exhibits significant variations in the charge and discharge of the flying capacitor within a single cycle, causing the flying capacitor voltage to deviate. Furthermore, due to the complexity of the topology, it is difficult to find a periodic switching state that achieves capacitor charge and discharge balance over multiple cycles.

[0096] Therefore, in order to achieve the natural balance of the flying capacitor, the ladder filter current is reconstructed twice, the core of which is to maintain the equal charge and discharge of the flying capacitor in a single cycle. ave The size of the reconstructed ladder filter current is as follows Figure 6 As shown, the red dotted line indicates that when i ave >0, the blue dotted line indicates that when i ave < 0. The average current value in the reconstructed trapezoid changes, which can be compensated in the control loop.

[0097] when i ave >0, by Figure 6 It can be seen that the charging charge of the flying capacitor is greater than the discharging charge at this time, so it is necessary to reduce t x At the same time, in order to realize the calculation, the time period of the switch state with a slope of β is kept unchanged. According to the similarity principle, [t4,t 4’ ] is equal to t x In order to maintain voltage balance, it is necessary to set [t4,t 4’ ]Time is t y . The charge balance expression is obtained as follows:

[0098]

[0099] Figure 6 Indicates the positive equivalent area Q p While increasing the negative equivalent area Q N Decrease, when Q N =Q p When , the dynamic time domain allocation is most reasonable, and the trapezoidal filter equivalent average current error is the smallest at this time, and the expression is as follows:

[0100]

[0101] According to the above formula, we can solve the simultaneous equations to get t x and t y The mathematical expression is as follows:

[0102]

[0103] Similarly ave <0, by Figure 6 As we know, the charging charge of the flying capacitor is less than the discharging charge, so we need to reduce t x The discharge time period is constructed in the same way as i ave >0 is similar. We can get the calculation of t at this time x and t y The system of equations:

[0104]

[0105] Through calculation, we can get a complete description of the reconstructed ladder filter current in a single cycle. After the secondary reconstruction of the ladder filter current, the flying capacitor charge and discharge charge in a single cycle reaches a stable state, such as Figure 7 shown.

[0106] The output current of a power amplifier is determined by both the DC power supply voltage and the flying capacitor voltage. The quality of the output current is affected by the flying capacitor voltage ripple. When the power amplifier operates in a ladder-type current filter mode, a reasonable ripple range must be designed for the flying capacitor to ensure system stability and avoid calculation errors.

[0107] Assume △U q is the voltage deviation of the flying capacitor. When the voltage upper limit of the flying capacitor exceeds U cq +△U q When , it is necessary to actively reduce the charging time of the flying capacitor. Assuming the charging time is △t, the amount of charge reduced in the positive cycle is:

[0108]

[0109] When the flying capacitor charging time is actively reduced, the cycle of the trapezoidal filter inductor current will also decrease. This change in cycle will increase the THD of the output current. Therefore, to ensure that the cycle remains unchanged, the flying capacitor discharge time needs to be increased by Δt. The resulting increase in charge during the negative cycle is:

[0110]

[0111] From this we can get the deviation of the equivalent current:

[0112]

[0113] Finally, a unified equation for adjusting the time Δt, output current deviation, and flying capacitor voltage ripple is obtained. This not only limits the flying capacitor voltage ripple, but also allows the output current to be compensated in the controller.

[0114] Step 3: Design a closed-loop control strategy based on flying capacitor voltage balance.

[0115] The ultimate goal of the power amplifier is to output a high-precision output current, and at the same time, the voltage of the flying capacitor must be controlled during operation. To achieve this goal, the power amplifier block diagram based on the flying capacitor balance is as follows Figure 8 As shown, it includes a current closed loop, deviation current compensation, flying capacitor voltage closed loop balancing, pre-charging, and trapezoidal filter calculation. The modulation switching module in the figure works by briefly phase-shifting the flying capacitor at the beginning of the system operation. Once the flying capacitor voltage is pre-charged, it quickly switches to trapezoidal filter current control and enters the working state. Figure 8 Waveforms of the switching signal, filter current, and node voltage for the trapezoidal filter current and carrier phase-shift reconstruction control.

[0116] The flying capacitor multi-level power amplifier can achieve pre-charging of the flying capacitor by relying on phase-shifted carrier pulse width modulation. The basic principle is that since each carrier is modulated in sequence during the switching cycle, the average current flowing through the flying capacitor is 0, achieving voltage balancing.

[0117] Figure 9 The most basic unit of the flying capacitor is given, which can be divided into three states. The direction of the current arrow indicates the direction of current flow. The switching function is:

[0118] i qx =(S n -S n+1 )i Lf

[0119] Among them, i Lf is the inductor current, the inductor current ripple can be ignored, i Lf In order to maintain the voltage of the flying capacitor constant within a modulation cycle, the flying capacitor must meet the ampere-second balance principle:

[0120]

[0121] By averaging the switching cycles of the above equation, we can get the flying capacitance C qx Voltage variation during one switching cycle:

[0122]

[0123] Among them, D n and D n+1 Represents the switch tube S n and S n+1 Duty cycle, T s The flying capacitor voltage change formula shows that the duty cycle directly affects the flying capacitor voltage balance, such as Figure 10 As shown, the duty cycle of each switch during phase-shift modulation is symmetrical, so the flying capacitor voltage exhibits a periodic rise-and-fall pattern within a range, achieving initial voltage equalization across the flying capacitor. Furthermore, phase-shift modulation outputs a trapezoidal pattern to approximate the output voltage. However, with fewer levels or low-frequency modulation, the output harmonics are significant, so it is only used for voltage pre-charging during startup.

[0124] In order to ensure the output current quality, after the initial voltage equalization is completed, the following Figure 10 The trapezoidal filter current control method shown in FIG. By controlling the trapezoidal filter inductor current, the flying capacitor achieves charge and discharge balance within a single cycle. At the same time, the correct operation of each working state and the continuity of the trapezoidal filter inductor current are reasonably guaranteed through the time allocation principle. It should be noted that when reconstructing the trapezoidal filter current, in order to maintain voltage balance, the current equivalent value changes. In order to ensure that the output current continues to track the given current signal, it is necessary to compensate the change value in the control loop. The compensation current i bas The size is:

[0125]

[0126] From this we can see that when i ave >0, i bas <0,i ave <0, i bas >0. Negative feedback is required in the control system to achieve current compensation. The above analysis shows that the capacitor voltage balancing strategy based on trapezoidal filtering of the inductor current and carrier phase-shift reconstruction not only achieves voltage balance across the flying capacitor, but also ensures that the output equivalent current continuously tracks the given reference current, significantly improving output accuracy and demonstrating excellent practicality.

[0127] Step 4: A simulation model was established based on Simulink, parameters were configured, and the correctness of the control method was verified.

[0128] In order to verify the flying capacitor voltage active balancing control algorithm proposed in this invention, a simulation model was established based on Simulink. The main parameters in the simulation are: DC bus voltage V dc =250V, switching frequency range is 5~10KHz, load resistance is 5Ω, load inductance is 20mH, flying capacitor value is 220μF. setA sinusoidal setpoint current with an amplitude of 18 A and a frequency of 50 Hz was simulated.

[0129] Figure 11 is the output current i out and output voltage u out The waveform of the output current is exactly the given sinusoidal set point, and the voltage and current have a phase difference. p , filter inductor current i Lf The result waveform and the local magnified image are as follows Figure 12 and Figure 13 The filter inductor current i obtained by the control scheme proposed in the present invention is Lf The peaks are clearly visible, and their shapes match those described in theory. The node voltage graph shows the transition between two intermediate levels due to the output voltage change. The slope of the ladder filter current and the node voltage also correspond to each other, validating the correctness of the control strategy proposed in this paper.

[0130] Flying capacitor balance Figure 14 As shown, it can be seen from the figure that the flying capacitor voltage can realize the pre-charging of the flying capacitor in about 0.5s and complete the initial voltage equalization of the flying capacitor. When the startup process is completely completed at 1s, it is switched to the trapezoidal filter current modulation. Although the voltage of the flying capacitor fluctuates up and down, due to the flying capacitor voltage deviation compensation, the flying capacitor voltage will always fluctuate up and down within a range, and the system is in long-term stable operation. At the same time, in order to verify the output performance of the power amplifier control scheme proposed in the present invention, a 50Hz sinusoidal set point current is used for excitation. The gradient coil drive depends on the linearity of the output current generated by the power amplifier. The flying capacitor voltage balance control scheme proposed in the present invention shows performance with high-precision applications.

Claims

1. A method for active capacitor voltage balancing control of a flying capacitor seven-level soft-switching power amplifier, characterized in that The method comprises the following steps: Step 1: Establishment of the mathematical model of the ladder filter current: In a single cycle of the trapezoidal filter current, there are two moments to choose to charge or discharge the flying capacitor. In order to ensure the feasibility of the trapezoidal filter shape, the resonant mode and switching characteristics of the soft switch are combined to optimize the distribution and obtain the trapezoidal filter current i Lf The slope equation is: Where α is [t0, t1], [t9, t 10 ] Time period ladder filter current i Lf The slope of β is the trapezoidal filter current i in the [t4, t6] period. Lf The slope of γ is the trapezoidal filter current i in the time period [t2, t3] and [t7, t8] Lf For phase α and phase β, select the highest level V dc and the lowest level -V dc As the required distribution level, for the level level corresponding to the intermediate stage part γ of the ladder filter current, the selected level uses the output voltage u out To determine, choose the output voltage u out The closest electrical level; u p Represents the AC side node voltage; L f Represents the inductance value of the filter inductor; In the flying capacitor seven-level soft switching power amplifier topology, C r1 、C r2 、C r3 、C r4 、C r5 、C r6 、C r7 、C r8 、C r9 、C r10 、C r11 and C r12 As a resonant element of the filter current, it realizes the soft switching process of the switch tube; based on the balance of the flying capacitor, an accurate mathematical model of the ladder filter current is established; Step 2: Calculate and reconstruct a complete description of the ladder filter current in a single cycle so that the charge and discharge of the capacitor are balanced in a single cycle. Step 3: Design of closed-loop control strategy based on flying capacitor voltage balance: Step 3.1: When the system starts operating, the flying capacitor uses a short phase-shift modulation link. When the flying capacitor voltage is pre-charged, it quickly switches to ladder filter current control and enters the working state; Step 3.2: The flying capacitor multi-level power amplifier relies on phase-shifted carrier pulse width modulation to achieve pre-charging of the flying capacitor. The switching function of the flying capacitor is: i qx =(S n -S n+1 )i Lf Among them, i qx Represents the current flowing through the flying capacitor C qx Current value; S n and S n+1 Represents two adjacent switching tubes; in one modulation cycle, in order to maintain a constant voltage across the flying capacitor, the flying capacitor satisfies the ampere-second balance principle: in, Represents the current flowing through the flying capacitor C qx The average current value; Perform switching cycle averaging on the above equation to obtain the flying capacitance C qx Voltage variation during one switching cycle: Among them, D n and D n+1 Represents the switch tube S n and S n+1 Duty cycle; T s represents the switching cycle; Represents the average value of the filter inductor current; Step 3.3: To ensure the output current quality, after the initial voltage balancing is completed, a trapezoidal filter current control method is used. By controlling the trapezoidal filter inductor current, the flying capacitor achieves charge and discharge balance within a single cycle. At the same time, the correct operation of each working state and the continuity of the trapezoidal filter inductor current are reasonably guaranteed through the time allocation principle. Step 3.4: When reconstructing the ladder filter current, in order to maintain voltage balance, the current equivalent value changes. In order to ensure that the output current continues to track the given current signal, it is necessary to compensate the change value in the control loop. The compensation current i bas The size is: When the average value of the equivalent current i ave >0, i bas <0,i ave <0, i bas >0, it is necessary to use a negative feedback link in the control system to achieve current compensation.

2. The method for active capacitor voltage balancing control of a flying capacitor seven-level soft-switching power amplifier according to claim 1, characterized in that The specific steps of step 1 are as follows: Step 1.1: Assume that the average value of equivalent current i ave >0 and γ>0, the commutation charge Q of the parallel resonant capacitor of a single MOSFET during the conversion process c It needs to be fully released, and the minimum commutation current i is obtained according to the cross-sectional area when the inductor current resonates and the corresponding slope α LfL : In order to achieve ZVS at every switching point, the cross-sectional area of ​​the inductor current when it resonates must meet 2Q c , the resonance time interval is calculated according to the magnitude of the current; Step 1.2: In order to ensure the stability of flying capacitor charging and discharging under different currents, an adjustable parameter is given to the time period [t7, t8], which is determined by the average value of the equivalent current i ave Make adjustments to ensure there is enough mid-level state: Where, represents the time from t7 to t8; k0 is a variable parameter; t min is the minimum time length of the time period [t7, t8]; t rat is the actual parameter defined; the minimum commutation current i is known LfL , the slopes α, β, γ of each time period and the above formula are used to derive the time interval [t5, t6] and the lowest point i of the trapezoidal filter current L The size of the negative half axis of the filter current is finally obtained in the controller. The complete description of the switching point value and time interval of the negative half axis of the filter current is obtained; Step 1.3: There is no specific limit for the current value and time interval of the positive axis. An upper limit needs to be set: and Lfh =-i LfL +k1 i ave Where k1 is the variable coefficient; Step 1.4: According to the charge equivalence principle, we get the following formula: Q p -Q N =i ave (t p +t N ) Where Q p , Q N are respectively the positive and negative areas of the ladder filter current; t p Represents the time from t0 to t5, that is, the time when the filter inductor current is positive; t N Represents t5 to t 10 The time size of the filter inductor current is negative; Step 1.5: The current i at the transition point is known. Lfh , slopes α, β, γ and the magnitude and time interval of the negative half-axis current, combined with the charge equivalent equation, the trapezoidal filter current i in a single switching cycle is finally obtained. Lf A complete description of .

3. The method for active capacitor voltage balancing control of a flying capacitor seven-level soft-switching power amplifier according to claim 2, characterized in that The specific steps of step 2 are as follows: Step 2.1: Based on the ladder filter current mathematical model, the charging charge Q of the flying capacitor in a single cycle is obtained. h and discharge charge Q f The expression: Where i h Represents the highest point of the ladder filter current; i L Represents the lowest point of the ladder filter current; represents the time from t2 to t3; Step 2.2: To achieve a natural balance of the flying capacitor, the ladder filter current is reconstructed twice to maintain the equal charge and discharge amounts of the flying capacitor within a single cycle. Step 2.3, when i ave >0, the charging charge of the flying capacitor is greater than the discharging charge, and t x The charging time period, at the same time, in order to realize the calculation, the time period of the switch state with a slope of β is kept unchanged. According to the similarity principle, the time [t4, t4'] is equal to t x In order to maintain voltage balance, set the time [t5, t5'] to t y , from which the charge balance expression is obtained: Positive equivalent area Q p While increasing the negative equivalent area Q N Decrease, when Q N =Q p When , the dynamic time domain allocation is most reasonable, and the trapezoidal filter equivalent average current error is the smallest at this time, and the expression is as follows: t x and t y The mathematical expression is as follows: Step 2.4, when i ave <0, the charging charge of the flying capacitor is less than the discharging charge, then calculate t x and t y The system of equations is: The complete description of the reconstructed ladder filter current in a single cycle is obtained by calculation; Step 2.5: Assume △U q is the voltage deviation of the flying capacitor. When the voltage upper limit of the flying capacitor exceeds U cq +△U q When the charging time of the flying capacitor is reduced, the amount of charge reduced in the positive cycle is △Q. p for: When the charging time of the flying capacitor is actively reduced, the cycle of the trapezoidal filter inductor current will be reduced synchronously. The change in cycle will increase the THD of the output current. Therefore, in order to ensure that the cycle remains unchanged, the flying capacitor discharge time needs to be increased by △t, and the charge amount △Q is finally obtained in the negative cycle. N for: The deviation of the equivalent current △i is obtained from this bas for: Finally, a unified equation for adjusting the time △t, output current deviation and flying capacitor voltage ripple is obtained.

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