A method for suppressing backflow power of a DAB converter based on Runge-Kutta method

Abstract

The application discloses a DAB converter backflow power suppression method based on the Runge-Kutta method. The method first selects an auxiliary inductance inductance value and an input capacitance value to construct a DAB converter. Secondly, through the volt-second balance and the inductance current symmetry, the relationship formula of the DAB converter backflow power and the bridge inner phase shift D1 and the bridge interphase shift D2 is calculated, and then the relationship formula of the backflow power and D1 is obtained, and the fourth-order Runge-Kutta equation about the backflow power and D1 is established. Then, according to the fourth-order Runge-Kutta equation of the backflow power and D1, the global optimal solution and the values of D1 and D2 are solved. Finally, the solved D1 and D2 values are used for the modulation of the PWM wave, and the backflow power is reduced under the condition of not changing the transmission power. The application realizes a faster dynamic response, reduces the backflow power on the basis of not changing the transmission power, thereby reducing the heat production and improving the efficiency of the converter.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power electronics, and particularly relates to a DAB converter backflow power suppression method based on the Runge-Kutta method. BACKGROUND

[0002] Energy storage power stations are developed vigorously because they can effectively deal with the need for renewable energy fluctuation and enhance the utilization rate of renewable energy. As a key link of energy conversion, a bidirectional DC-DC converter plays a crucial role in a battery management system (BMS) of an energy storage power station. A hybrid three-level dual active bridge converter (DAB) can realize bidirectional power flow and can be applied to the BMS to significantly improve the flexibility and reliability of the system. Compared with a traditional DC-DC converter, the DAB converter has a higher power density, is easier to realize soft switching, and can reduce costs due to lower voltage stress of the primary side. At present, one of the effective schemes to improve the efficiency of the DAB converter is to reduce backflow power; the simplest control method in the traditional DAB circuit is single phase shift control (SPS), but this method produces a large amount of backflow power and loses soft switching when the power is mismatched, thereby causing a serious reduction in efficiency. In order to solve the above problems, extended phase shift control (EPS) is proposed, which reduces backflow power and realizes full-range soft switching by controlling an additional degree of freedom of the primary side. However, when the Lagrange multiplier method is used for calculation, it is found that the expression of the inner phase shift ratio and the outer phase shift ratio is a first-order function when the voltage transfer ratio is constant, so reducing backflow power will greatly reduce the transmission power. SUMMARY

[0003] In view of the above problems, the application provides a DAB converter backflow power suppression method based on the Runge-Kutta method, which is solved by using a fourth-order Runge-Kutta formula, and backflow power is reduced without changing the transmission power by adding an additional degree of freedom to the secondary side full-bridge, which is of great significance to improve the operation efficiency and reliability of the battery management system of the energy storage power station.

[0004] The application is implemented by the following technical solutions:

[0005] Step 1: select the auxiliary inductance L1 inductance value, input capacitance C1, C2 capacitance value, and construct a hybrid three-level dual active bridge DAB converter.

[0006] Step 2: calculate the relationship between the backflow power of the DAB converter and the bridge inner phase shift ratio D1 and the bridge inter-phase shift ratio D2 through the volt-second balance and the inductance current symmetry, and obtain the relationship between the backflow power and D1.

[0007] Step 3: establish a fourth-order Runge-Kutta equation about the backflow power and D1 according to the relationship between the backflow power and D1.

[0008] Step 4: According to the fourth-order Runge-Kutta equation of the reflux power and D1, the global optimal solution and the values of D1 and D2 are solved.

[0009] Step 5: The values of D1 and D2 are used for modulation of the PWM wave, so as to reduce the reflux power without changing the transmission power.

[0010] Advantages or beneficial effects of the present application:

[0011] The present application adds one degree of freedom on the basis of the conventional extended phase-shift control, optimizes the performance, realizes faster dynamic response by more accurate adjustment of the parameters of the controller, realizes reduction of the reflux power without changing the transmission power, thereby reducing the heat production, reducing the burden of heat management, greatly improving the efficiency of the converter. At the same time, the reduction of the reflux power reduces the stress of the power device, thereby prolonging the service life and improving the stability and reliability of the entire system. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 is a line frame diagram of the present application;

[0013] Figure 2 is a topology diagram of a hybrid three-level dual active bridge converter;

[0014] Figure 3 is a PWM pulse sequence diagram;

[0015] Figure 4 is a reflux power and D1, D2 expression diagram of the hybrid three-level dual active bridge converter. DETAILED DESCRIPTION

[0016] To make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described below in combination with the drawings and embodiments.

[0017] The line frame diagram of the DAB converter reflux power suppression method based on the Runge-Kutta method provided by the present application is shown in Figure 1 The reflux power suppression method of the topology includes the following five steps:

[0018] Step 1: Select the values of key parameters such as the value of the auxiliary inductor L1, the values of input capacitors C1 and C2, etc. to construct a hybrid three-level dual active bridge DAB converter;

[0019] Step 2: Through the volt-second balance and the symmetry of inductor current, the relationship between the reflux power of the hybrid three-level dual active bridge converter and the bridge-in phase shift ratio D1 and the bridge-to-bridge phase shift ratio D2 is calculated, and then the relationship between the reflux power and D1 is further obtained through Lagrange multiplication;

[0020] Step 3: Based on the relationship between return power and bridge inward shift compared to D1, establish the fourth-order Runge-Kutta equation regarding return power and D1;

[0021] Step 4: Solve the fourth-order Runge-Kutta equations for the return power and D1 to obtain the global optimal solution and the values ​​of D1 and D2;

[0022] Step 5: Use the obtained D1 and D2 values ​​for PWM wave modulation. Compared with the original modulation method, this achieves the goal of reducing return power without changing the transmission power.

[0023] The hybrid three-level dual active full-bridge converter, such as Figure 2 As shown, it consists of a DC voltage source, a primary-side diode-clamped hybrid three-level full-bridge H1, a secondary-side two-level full-bridge H2, input capacitors C1 to C2, output capacitor C3, and a high-frequency isolation transformer;

[0024] The positive terminal of input capacitor C1 is connected to the positive terminal of the DC voltage source, the negative terminal of input capacitor C1 is connected to the positive terminal of input capacitor C2, and the negative terminal of the DC voltage source is connected to the negative terminal of input capacitor C2.

[0025] The primary-side diode-clamped hybrid three-level full-bridge circuit includes eight fully controlled transistors Q1 to Q8, clamping diodes D1 to D4, and an auxiliary inductor L1. The emitter of transistor Q1 is connected to the collector of transistor Q2, the emitter of transistor Q2 is connected to the collector of transistor Q3, the emitter of transistor Q3 is connected to the collector of transistor Q4, the emitter of transistor Q5 is connected to the collector of transistor Q6, the emitter of transistor Q6 is connected to the collector of transistor Q7, and the emitter of transistor Q7 is connected to the collector of transistor Q8. The collectors of transistors Q1 and Q5 are connected to the positive terminal of capacitor C1, and the emitters of transistors Q4 and Q8 are connected to the negative terminal of capacitor C2. One side of inductor L1 is connected to the connection line between transistors Q2 and Q3. The other end of inductor L1 is connected to one end of the primary winding of the high-frequency isolation transformer, and the other end of the primary winding of the high-frequency isolation transformer is connected to the connection line between switching transistors Q6 and Q7; the positive terminal of clamping diode D1 is connected to the negative terminal of clamping diode D2, the negative terminal of clamping diode D1 is connected to the connection line between switching transistors Q1 and Q2, and the positive terminal of clamping diode D2 is connected to the connection line between switching transistors Q3 and Q4; the positive terminal of clamping diode D3 is connected to the negative terminal of clamping diode D4, the negative terminal of clamping diode D3 is connected to the connection line between switching transistors Q5 and Q6, and the positive terminal of clamping diode D4 is connected to the connection line between switching transistors Q7 and Q8;

[0026] The auxiliary side full bridge comprises four full-controlled switching tubes S1-S4, the emitter of switching tube S1 is connected with the collector of switching tube S2, the emitter of switching tube S3 is connected with the collector of switching tube S4, the collectors of switching tube S1 and switching tube S3 are connected with the positive pole of capacitor C3, the emitters of switching tube S2 and switching tube S4 are connected with the negative pole of capacitor C3; the middle connecting line of switching tube S1 and switching tube S2 and the middle connecting line of switching tube S3 and switching tube S4 are respectively connected with the two ends of the high-frequency isolation transformer auxiliary side;

[0027] As described in step 2, because in one control period, the waveform of 0-T hs is completely symmetrical with the waveform of T hs -T s , the present application only analyzes the waveform of 0-T hs . When the DAB converter works in a steady state, the terminal voltage and current of the inductor have the following relationship:

[0028]

[0029] Wherein, Vab is the output voltage of the primary side bridge arm, Vcd is the output voltage of the auxiliary side bridge arm; i L (t) is the current flowing through the inductor L1 at time t, and the high-frequency isolation transformer ratio is n:1.

[0030] From the symmetry of the inductor current, we can get:

[0031] i(to)=—i(t4)

[0032] Combining the relationship between the inductor voltage and the current, the inductor current expression at each time can be obtained:

[0033]

[0034] Wherein, Vin is the input voltage, Vo is the output voltage; fs is the switching frequency, D1 is the internal phase shift ratio of the primary side full bridge H1 and the auxiliary side full bridge H2; D2 is the external phase shift ratio of the auxiliary side full bridge H1 relative to the primary side full bridge H1. The transmission power is calculated by the average power calculation formula, and the unit is taken:

[0035]

[0036] T s is a switching period, Th s is a half switching period, P n is the maximum transmission power of the converter under SPS control:

[0037]

[0038] Combining the above formula, the expression of the transmission power P* of the converter is:

[0039]

[0040] As Figure 3 shown, according to the pwm waveform diagram, it is obtained that there is backflow power during t1-t'1, and the normalized expression of the calculated backflow power is:

[0041]

[0042] As Figure 4 shown, the integral is obtained:

[0043]

[0044] To suppress the backflow power while keeping the transmission power unchanged, a common method is the Lagrange multiplier method, which is effective in solving extreme value problems under such constraints, therefore, the present application adopts this method for derivation, first, define the Lagrange multiplier equation relationship for solving the extreme value of backflow power under the transmission power constraint:

[0045]

[0046] In the formula, P is the target transmission power, and λ is the Lagrange multiplier; the partial derivatives of L in the formula with respect to D1 and D2 are obtained, and they are equal to 0, that is, the following formula is obtained:

[0047]

[0048] After eliminating the common term λ in the two formulas, the simplest expression of D1 and D2 is obtained:

[0049]

[0050] As described in step 3, let y be the backflow power P t * , and x be the full-bridge internal phase shift ratio D1, and the first-order derivative of the backflow power with respect to D1 is obtained, and the expression is substituted into:

[0051]

[0052] Substitute the expression to obtain the backflow power P t * Regarding the differential equation of the full-bridge internal phase shift ratio D1, let x0 and y0 represent the independent variable value and function value of the 0th iteration state classification, i.e. the initial value.

[0053] The solution is simplified to P * The optimization problem of the y function of the constraint condition is solved by using the fourth-order Runge-Kutta method, which is a single-step method for solving ordinary differential equations with high precision. By discretizing the solution domain of the differential equation, the value y nThe slope of the fourth-order Runge-Kutta method is calculated by a weighted average method of four evaluation points, and the value of the next moment is predicted by adding the time interval h and the calculated slope.

[0054]

[0055] Wherein, h is the step length after the state variable is discretized, K1, K2, K3, K4 respectively represent the slopes of the four evaluation points, x m is the independent variable value of the mth iteration state classification, y m is the function value of the mth iteration state classification.

[0056] As described in step 4, considering the actual accuracy range that can be taken, the present application sets the step length h to 0.01 to obtain a more accurate prediction result with lower calculation complexity. At this time, the simplest expression of D1 and D2 is D1=0.45, which is more consistent with the three-dimensional graph of the backflow power and D1, D2.

[0057] As shown in step 5, the present application verifies by using the commonly used parameters of the energy storage power station, and the parameters are as follows: V in =720v, V o =24v, n=15; through the simulation circuit verification, the backflow power at this time is which is basically consistent with the theoretical value calculated above, and the transmission power is unchanged, and the effect of suppressing the backflow power is achieved.

[0058] The present application combines the Lagrange number multiplication method with the fourth-order Runge-Kutta method, obtains the first four data through simulation for initial value parameter confirmation and model fitting, calculates the state variable y(x) by using the fourth-order Runge-Kutta method, sets x0=0, and the update step length is: x m+1 =x m +h, and iterates in this form to obtain the minimum value of the index function on the solution domain, thereby obtaining the global optimal solution.

[0059] On the basis of the traditional extended phase-shift control strategy, a degree of freedom D3 is added to the auxiliary full-bridge, and it is found in the calculation process that when D3=D1, the backflow power can be reduced, and the control precision of the system can be improved. Therefore, in the present application, D3 is directly set to D1, which improves the efficiency while minimizing the complexity of control. At the same time, since D1 can only be modified with an accuracy of 0.01 in practice, it is more suitable to use the fourth-order Runge-Kutta method, and a fixed step length is used to achieve high efficiency and high precision with the least calculation amount.

Claims

1. A method for suppressing backflow power in a DAB converter based on the Runge-Kutta method, characterized in that, Includes the following steps: Step 1: Select the inductance value of auxiliary inductor L1 and the capacitance values ​​of input capacitors C1 and C2 to construct a hybrid three-level dual active full-bridge DAB converter; Step 2: Calculate the relationship between the return power of the DAB converter and the bridge shift ratio D1 and the bridge shift ratio D2, and derive the relationship between the return power and D1; Step 3: Based on the relationship between return power and D1, establish a fourth-order Runge-Kutta equation regarding return power and D1, and modulate the PWM wave to achieve return power suppression. The specific implementation process is as follows: Let y be the return power P t * Let x be the full-bridge inward shift compared to D1. Taking the first derivative of the return power with respect to D1 and substituting the expression, we get: ； In the formula Input voltage, For the output voltage, the turns ratio of the high-frequency isolation transformer is n:1; Substituting the expression, we obtain the return power P. t * Regarding the differential equation for the full bridge inward shift compared to D1, let x0 and y0 represent the independent variable value and function value of the state classification in the 0th iteration, respectively, i.e., the initial value; The desired result is simplified to P. * For the optimization problem of the constrained y-function, the fourth-order Runge-Kutta method is used for solution. This is achieved by discretizing the solution domain of the differential equation, which is then obtained from the current value of y. n Adding the time interval h and the calculated slope to predict the next moment, the slope of the fourth-order Runge-Kutta method is calculated by a weighted average of four evaluation points; the calculation formula for the fourth-order Runge-Kutta method is as follows: ； ； Where h is the step size after discretization of the state variables, K1, K2, K3, and K4 represent the slopes of the four evaluation points, and x m Let y represent the value of the independent variable y for classifying the state in the m-th iteration. m The function value representing the state classification in the m-th iteration; Based on the fourth-order Runge-Kutta equation of the return power and D1, the global optimal solution and the values ​​of D1 and D2 are obtained. The obtained D1 and D2 values ​​are used for PWM wave modulation to reduce return power without changing the transmission power.

2. The method for suppressing backflow power in a DAB converter based on the Runge-Kutta method according to claim 1, characterized in that, The specific implementation process of step 2 is as follows: When the DAB converter is operating in a steady state, the inductor's terminal voltage and current have the following relationship: ； Among them, V ab V is the output voltage of the primary side bridge arm. cd For the secondary bridge arm output voltage; i L (t) represents the current flowing through inductor L1 at time t, and the turns ratio of the high-frequency isolation transformer is n:1; Due to the symmetry of the inductor current, we have: ； By combining the relationship between inductor voltage and current, the expression for the inductor current at each moment can be derived: ； ； ； ； In the formula Input voltage, The output voltage is given by fs; the switching frequency is given by fs; D1 is the ratio of the inward shift of the primary-side full-bridge H1 to the inward shift of the secondary-side full-bridge H2; D2 is the ratio of the outward shift of the secondary-side full-bridge H1 relative to the primary-side full-bridge H1; the transmitted power is calculated using the average power calculation formula and normalized to per unit. ； In the formula T hs For half a switching cycle, P n The maximum transmission power of the converter under SPS control: ； Combining the above formula, we can obtain the converter's transmission power P. * The expression is: ； Based on the PWM waveform diagram, the time from t1~ During this period, there is return power. The per-unit expression for the return power is calculated as follows: ； Integrating, we get: ； Define the Lagrange multiplier method equation for finding the extreme values ​​of return power under transmission power constraints: ； In the formula, P is the target transmission power. Let L be a Lagrange multiplier; taking the partial derivatives of L with respect to D1 and D2 respectively, and setting them equal to 0, we get: ； Find the common term in both equations After elimination, we obtain the simplest expressions for D1 and D2: 。

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