Capacitor voltage active balance control method of flying capacitor seven-level soft switching power amplifier

Abstract

The invention discloses a capacitor voltage active balance control method of a flying capacitor seven-level soft switching power amplifier, which is based on a topological mathematical model of the power amplifier, analyzes the working state of the power amplifier and the multi-level voltage and inductive current characteristics of the power amplifier, and researches the parameter characteristics of trapezoidal filter inductive current. According to a conversion mechanism of ten states of a soft switch, six key time domains of a trapezoidal filtering inductive current are dynamically allocated based on a current circulation conduction path and a constraint condition that a trapezoidal filtering equivalent average current error is minimum. The initial value condition of the flying capacitor is considered, the carrier phase shift modulation meets the initial voltage balance condition, and the stability of the voltage of the flying capacitor in multiple switching periods in the full operation range is realized by combining the dynamically reconstructed trapezoidal filtering current. A closed-loop simulation result shows that the control strategy provided by the invention can effectively control capacitor voltage balance and realize high-precision current output.

Description

Technical Field

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

[0002] Over the 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. Since the specifications of semiconductor switching devices have certain limitations, 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 situations. In order to enable the power amplifier to stably generate multiple levels and maintain the voltage stress at both ends of each switch tube, an additional method is required to achieve the balance of the flying capacitor voltage, which becomes the key to the stable operation of the flying capacitor multi-level power amplifier.

[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 states. Previous literature (Capacitor voltage balancing in a 5-L full-bridge flying capacitor inverte) proposed a method of using a controller to modify the switching time duty cycle to maintain flying capacitor voltage balance, such as Figure 1 This control scheme is based on the traditional multi-carrier control scheme. Although it solves the problem of flying capacitor balance, 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] The present invention combines the strict requirements of MRI and the characteristics of flying capacitor power topology to provide a method for active capacitor voltage balance control of a flying capacitor seven-level soft switching power amplifier. The method dynamically allocates the key time domain of the trapezoidal filter inductor current based on the constraints of the current circulation conduction path and the minimum error of the trapezoidal filter equivalent average current, realizes high-precision current output and flying capacitor voltage balance, and can be used to drive the gradient coil in the nuclear magnetic resonance imaging system to provide it with high-precision current.

[0005] The objective 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 ladder filter current:

[0008] In a single cycle, the trapezoidal filter current has 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 for optimal distribution to obtain the trapezoidal filter current i Lf The slope equation is:

[0009]

[0010] Among them, α is [t 0 , t 1 ]、[t 9 , t 10 ] Time period ladder filter current i Lf The slope of 4 , t 6 ] Time period ladder filter current i Lf The slope of 2 , t 3 ]、[t 7 , t 8 ] Time period ladder filter current i Lf For phase α and phase β, select the highest level V dc and minimum 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 and output voltage u out The closest electrical level; u p Represents the node voltage on the AC side; 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 iave >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 each 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, a time period [t 7 , t 8 ] is an adjustable parameter, which is determined by the average current i ave Make adjustments to ensure there is enough mid-level state:

[0016]

[0017] In the formula, Represents t 7 to 8 time; k 0 is a variable parameter; t min For the time period [t 7 , t 8 ]Minimum time length; 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, the time interval [t 5 , t 6 ] 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 half axis, and an upper limit needs to be set:

[0019] i Lfh =-i LfL +k 1 ·i ave

[0020] In the formula, k 1 is the variable coefficient;

[0021] Step 1.4: According to the charge equivalence principle, the following formula is obtained:

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

[0023] In the formula, Q p , Q N are respectively the positive and negative areas of the ladder filter current; t p Represents t 0 to 5 The time size, that is, the time size of the filter inductor current being positive; t N Represents t 5 to 10 The time size, that is, the time size of the filter inductor current being negative;

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

[0025] Step 2: The complete description of the reconstructed ladder filter current in a single cycle is obtained by calculation, so that the charge and discharge of the capacitor in a single cycle are balanced. 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 is:

[0027]

[0028] In the formula, i h Represents the highest point of the ladder filter current; i L Represents the lowest point of the ladder filter current; Represents t 2 to 3 time;

[0029] Step 2.2: In order to achieve the natural balance of the flying capacitor, the ladder filter current is reconstructed twice to maintain the charging and discharging charges of the flying capacitor equal in 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 xThe 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, [t 4 ,t 4’ ] is equal to t x In order to maintain voltage balance, set [t 4 ,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 p When , the dynamic time domain allocation is the most reasonable, and the trapezoidal filter equivalent average current error is the smallest at this time, 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, at this time, 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 needs to be reduced, assuming that the charging time is △t, 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, the discharge time of the flying capacitor needs to be increased by △t, and finally the charge amount △Q of the negative cycle is obtained. 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 is initially operated, the flying capacitor adopts a short phase shift modulation link, and when the voltage of the flying capacitor 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 realize the 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 The voltage change in one switching cycle:

[0054]

[0055] Among them, D n and D n+1 Respectively represent 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, in order to ensure the quality of the output current, after the initial voltage balancing is completed, the trapezoidal filter current control method is adopted to control the trapezoidal filter inductor current so that the flying capacitor can achieve charge and discharge balance in a single cycle. At the same time, the correct progress 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 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, the change value needs to be compensated 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 satisfies 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)t 0 <t<t 1 , (b)t 1 <t<t 2 , (c)t 2 <t<t 3 , (d)t 3 <t<t 4 , (e)t 4 <t<t 5 , (f)t 5 <t<t 6 , (g)t 6 <t<t 7 , (h)t 7 <t<t 8 , (i)t 8 <t<t 9 , (j)t 9 <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] Fig. 9 is the modulation wave i of a single switching cycle Lf 、u p and u cqx Waveform diagram;

[0071] Fig.10 It is the voltage balancing principle of flying capacitor under phase shift modulation;

[0072] Fig.11 is the output current i out ;

[0073] Fig.12 is the node voltage u p and partial magnified images;

[0074] Fig.13 is the filter inductor current i Lf and partial magnified images;

[0075] Fig.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 in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope 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 ladder filter current.

[0079] Power amplifier topology such as Figure 2 As shown, the specific structure can be found in CN202211254408.2. Through a single cycle of switching changes, 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 resonant mode and switching characteristics of the soft switch are combined for optimal allocation, and the trapezoidal filter current i is finally obtained. Lf The slope equation is:

[0080]

[0081] Among them, for phase α and phase β, the highest level V is selected dc and minimum 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 , Cr7 , 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. The size of the resonance time will affect the balance of the flying capacitor. Based on the balance of the flying capacitor, an accurate mathematical model of the trapezoidal filter current is established. The specific construction process of the mathematical model of the trapezoidal filter current in a single cycle is as follows:

[0083] Assuming the average 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 each 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 current. In order to ensure the stability of flying capacitor charging and discharging under different currents, the time period [t 7 , t 8 ] is an adjustable parameter, which is determined by the average current i ave Make adjustments to ensure there is enough mid-level state.

[0086]

[0087] In the formula, k 0 is a variable parameter, and the optimal result is determined according to the actual situation; t min For the time period [t 7 , t 8 ]Minimum time length; 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, the time interval [t 5 , t 6 ] and i L The size of the negative half-axis switching point of the filtered current and the complete description of the time interval are finally obtained in the controller.

[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 is iave is known. However, this is still not enough to describe the entire ladder filter current, because there is no specific limit on the current value and time interval of the positive half axis, so an upper boundary needs to be set. Here it is set as follows:

[0089] i Lfh =-i LfL +k 1 ·i ave

[0090] In the formula, the variable coefficient k 1 The size of 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] In the formula, 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 The 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 in a single or multiple cycles. According to 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 is:

[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 charge change curve is shown in Figure 1. It can be seen that the charge and discharge charge of the flying capacitor in a single cycle of the initially constructed ladder filter current varies greatly, and the flying capacitor voltage value will deviate. In addition, due to the complexity of the topological operation, it is difficult to find a periodic switching state with balanced capacitor charge and discharge in 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 amount 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 value of the current 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 at this time, 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, [t 4 ,t 4’ ] is equal to t x In order to maintain voltage balance, it is necessary to set [t 4 ,t 4’ ]Time is t y . The expression for charge balance 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, the expression is as follows:

[0100]

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

[0102]

[0103] Same reason ave <0, by Figure 6 It is known that the charging charge of the flying capacitor is less than the discharging charge at this time, so it is necessary 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 second reconstruction of the ladder filter current, the flying capacitor charge and discharge charge in a single cycle reaches stability, such as Figure 7 shown.

[0106] The output current of the power amplifier is determined by 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 the ladder filter current mode, due to the calculation error and to ensure the stability of the system, it is necessary to design a reasonable ripple range for the flying capacitor.

[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 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 discharge time of the flying capacitor needs to be increased by △t. The final amount of charge increased in 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 time △t, output current deviation and flying capacitor voltage ripple is obtained. This can not only limit the flying capacitor voltage ripple, but also compensate the output current in the controller.

[0114] Step 3: Design of 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 the voltage of the flying capacitor must be controlled during operation. To achieve this goal, the block diagram of the power amplifier based on the flying capacitor balance is as follows Figure 8As shown, it includes current closed loop, deviation current compensation link, flying capacitor voltage closed loop balance link, pre-charging link and trapezoidal filter calculation link. The working principle of the modulation switching module in the figure is that when the system starts to operate, the flying capacitor adopts a short phase shift modulation link. When the flying capacitor voltage completes pre-charging, it quickly switches to trapezoidal filter current control and enters the working state. Figure 8 The waveform diagram 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 realize the pre-charging of the flying capacitor by means of 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, thus achieving voltage balancing.

[0117] Fig. 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 a constant voltage on the flying capacitor within a modulation cycle, the flying capacitor must satisfy the ampere-second balance principle:

[0120]

[0121] By averaging the switching cycle, the flying capacitance C can be obtained. qx The voltage change in one switching cycle:

[0122]

[0123] Among them, D n and D n+1 Respectively represent the switch tube S n and S n+1 The duty cycle, T s represents the switching period. The flying capacitor voltage change formula shows that the duty cycle directly affects the flying capacitor voltage balance, such as Fig.10As shown in the figure, the duty cycle of a single switch tube is symmetrical during the phase-shift modulation process, so the flying capacitor voltage will show a periodic change of rising and then falling within a range, realizing the initial voltage equalization of the flying capacitor. In addition, the phase-shift modulation output approaches the output voltage in a trapezoidal manner, and the output harmonics are large under a small number of levels or low-frequency modulation, so it is only used for the voltage pre-charging link during the startup process.

[0124] In order to ensure the quality of output current, after the initial voltage equalization is completed, the following Fig.10 The trapezoidal filter current control method shown in the figure. By controlling the trapezoidal filter inductor current, the flying capacitor achieves charge and discharge balance in 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. It is necessary to use the negative feedback link in the control system to realize current compensation. According to the above analysis, the capacitor voltage balancing strategy based on the ladder filter inductor current and carrier phase shift reconstruction not only realizes the flying capacitor voltage balance, but also makes the output equivalent current continuously track the given reference current, greatly improving the output accuracy and having good 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 the present invention, a simulation model was established based on Simulink. The main parameters in the simulation are: DC bus voltage V dc =250V, the switching frequency range is 5~10KHz, the load resistance is 5Ω, the load inductance is 20mH, and the flying capacitor value is 220μF. set A sinusoidal set point current with an amplitude of 18 A and a frequency of 50 Hz was simulated.

[0129] Fig.11 is the output current i out And the output voltage u outThe 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 Fig.12 and Fig.13 The control scheme proposed in the present invention obtains the filter inductor current i Lf The peak is clearly visible and its shape is the same as the theoretical description. The curve of the node voltage shows the conversion process of the two intermediate levels due to the change of the output voltage. At the same time, the slope of the ladder filter current and the node voltage also correspond to each other, which verifies the correctness of the control strategy proposed by the present invention.

[0130] The flying capacitor is balanced as Fig.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 balancing of the flying capacitor. When 1s, the startup process is completely completed, and the current modulation of the trapezoidal filter is switched to. 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 by the present invention, a 50Hz sinusoidal set point current is used for excitation, and the gradient coil drive depends on the linearity of the output current generated by the power amplifier. The control scheme of the flying capacitor voltage balance proposed by the present invention shows the performance of high-precision applications.

Claims

1. A method for actively balancing capacitor voltage 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 ladder filter current: In a single cycle, the trapezoidal filter current has 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 for optimal distribution to 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 the filter current i in the time period [t4, t6] is 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 minimum 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 node voltage on the AC side; 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 the 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: Obtain a complete description of the reconstructed ladder filter current in a single cycle by calculation, so that the charge and discharge of the capacitor in a single cycle are balanced; Step 3: Design of closed-loop control strategy based on flying capacitor voltage balance: Step 3.1, when the system is initially operated, the flying capacitor adopts a short phase shift modulation link, and when the voltage of the flying capacitor 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 realize the 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 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: 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 The voltage change in one switching cycle: Among them, D n and D n+1 Respectively represent 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, in order to ensure the quality of the output current, after the initial voltage balancing is completed, the trapezoidal filter current control method is adopted to control the trapezoidal filter inductor current so that the flying capacitor can achieve charge and discharge balance in a single cycle. At the same time, the correct progress 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 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, the change value needs to be compensated in the control loop. The compensation current i bas The size is: 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.

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 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 and the corresponding slope α when the inductor current resonates. LfL : In order to achieve ZVS at each 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 current average value i ave Make adjustments to ensure there is enough mid-level state: In the formula, 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 α, β, γ of each time period and the above formula, the time interval [t5, t6] and i are derived 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 half axis, and an upper limit needs to be set: and Lfh =-i LfL +k1 i ave In the formula, k1 is the variable coefficient; Step 1.4: According to the charge equivalence principle, the following formula is obtained: Q p -Q N =i ave (t p +t N ) In the formula, 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, that is, the time size of the filter inductor current being negative; Step 1.5: The current i at the known transition point Lfh , slopes α, β, γ and the magnitude and time interval of the negative half-axis current, combined with the charge equivalent equation, the final result is the filter current i within a single switching cycle 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 1, 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 is: In the formula, 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: In order to achieve the natural balance of the flying capacitor, the ladder filter current is reconstructed twice to maintain the charging and discharging charges of the flying capacitor equal in 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, [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: 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 the most reasonable, and the trapezoidal filter equivalent average current error is the smallest at this time, 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, at this time, 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 needs to be reduced, assuming that the charging time is △t, 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 discharge time of the flying capacitor needs to be increased by △t, and finally the charge amount △Q of the negative cycle is obtained. N for: The deviation of the equivalent current △i is obtained from this bas for: Finally, a unified equation for adjusting time △t, output current deviation and flying capacitor voltage ripple is obtained.

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