Full power range DAB unified ZVS control strategy based on low current RMS

Inductive current RMS and soft switching are important performance indexes of dual active bridge DC-DC converter (DAB). This paper proposes a new optimal control strategy for the soft switching range based on the optimization of the effective value of the inductor current. This control strategy restricts the inductor current during switch action, ensuring a significant extension of the soft switching range across the entire power range, reducing switch losses, and achieving the accurate effective value of current, thereby further enhancing the efficiency of the DAB converter. Meanwhile, a new modulation method is proposed to achieve thermal balance between bridge arms. Finally, a simulation model is built and verified using Matlab.


Introduction
In response to the increasingly prominent global environmental problems and fossil energy crisis, new energy generation represented by photovoltaic power generation has been rapidly developing in distributed power distribution networks.Among them, an Isolated Bidirectional DC-DC Converter (IBDC) is used to connect high-voltage DC bus and energy storage devices, playing a role in bidirectional energy transfer.Dual-Active-Bridge (DAB) as a typical IBDC, has significant advantages such as high power density, bidirectional energy transfer, and easy implementation of soft switching [1].It has also been widely used in distributed photovoltaic power generation and DC microgrids.
Currently, DAB controllers mainly adopt phase-shift control, which first appeared in the form of single-phase shift (SPS) control.It has only one degree of freedom to control the magnitude and direction of power transmission, but under light load or mismatched input and output voltages, soft switching (ZVS) can be lost, resulting in a decrease in transmission efficiency.To solve these problems, modulation strategies with more degrees of freedom such as EPS, DPS, and TPS have been introduced.
In DAB systems, the main sources of power loss can be divided into conduction loss and switching loss.Switching loss is the dominant part of switching loss, and conduction loss is positively correlated with the effective value of the inductor current.Therefore, the most intuitive way to improve power efficiency is to expand the soft switching range of the switching device and optimize the effective value of the inductor current.
Currently, domestic and foreign scholars have researched optimizing DAB performance mainly in the following aspects: Expanding the ZVS range [2]; Reducing the reverse flow power [3]; Reducing current stress [4,5], and effective current value [6].Tong et al. [6] established a transmission power model under TPS control to solve the optimal control method for effective current value.Yan et al. [7] detailed the evolution process of operating modes when power magnitude changes.However, the above 2 works did not consider the soft switching range of the DAB converter during the optimization of effective current value to reduce conduction loss and ignored the impact of switching loss on efficiency.Yan et al. [8] and Shao et al. [9] analyzed the process of achieving soft switching in the operation of DAB, but did not consider the need for a sufficiently large inductor cut-off current to achieve soft switching of the switching device, nor do they obtain a direct and effective control method.
In response to the above issue, this paper proposes a global optimal control method for soft-switching based on the current RMS optimization control of the DAB converter, combined with the ZVS characteristics of the switching devices.
The remaining structure of this paper is as follows.Firstly, the topology structure and working principle of DAB are briefly introduced in Section 2. In Section 3, the principle of soft switching implementation is analyzed and the guaranteed soft switching expressions under each mode are derived.Then, in Section 4, a new modulation method is proposed to solve the problem of bridge arm thermal imbalance.The effectiveness of the proposed method is verified using MATLAB simulation software in Section 5. Finally, the conclusion is drawn in Section 6.

DAB topology model
The basic topology of the DAB converter is shown in Figure 1, where switches S1-S4 form the primary side inverter full bridge H1, and switches Q1-Q4 constitute the secondary side rectifier full bridge H2.TF represents the high-frequency transformer with a turns ratio of n, and Lr represents the resonant inductor.The input voltage is Vin, and the output voltage is Vout.The square waves Vab and nVcd generated by the two H-bridges jointly act on the inductor Lr to control the bidirectional flow of energy.Ts is the half-switching period, which is equal to 1/2f, where f represents the switching frequency.D1 represents the phase shift between the two arms of H1, and D2 represents the phase shift between the two arms of H2. d1 and d2 represent the duty cycle of the high level of the square waves Vab and nVcd, respectively, where d1=1-D1 and d2=1-D2.The auxiliary variable d2=D2+0.5(D3-D1)represents the centerline distance of the square wave voltage.The sign of d2 determines the direction of the output current, which can be classified into forward or reverse working modes based on the current direction.The voltage gain ratio K=nVcd/Vab, where K>1 and K<1 represent the boost and buck operation modes, respectively.This paper takes the forward buck type as an example for analysis.

Forward buck operating mode
The operation modes of the DAB converter in the forward buck scenario can be classified into 6 types [10].To achieve a wider ZVS range and optimal current RMS value, the proposed control scheme divides the system operation into four modes [6], as shown in Figure 3.The power reference value is shown in Equation ( 1): The power per unit value expressions of each mode are shown in Table 1.

Soft switch implementation conditions
In the DAB converter, the complete ZVS process of the switching devices is as follows.With the assistance of the initial energy of the inductor, the junction capacitance of the turned-on device is completely discharged, and the complementary switch junction capacitance is charged to the bus voltage.This must satisfy Equation (2). 12 Then the inductor current satisfying the primary side ZVS is quantized as in Equation (3).
Similarly, the condition for ensuring soft switching on the low-voltage side can be obtained as Equation (4).
In conclusion, iLr1(zvs) and iLr2(zvs) represent the inductor cutoff currents required for achieving ZVS when the primary-side and secondary-side switching devices are operated, respectively, ensuring the realization of soft switching on both sides.The constraints for achieving ZVS in each switching device are summarized in Table 2.
By solving Equation ( 5), the expressions for d1, d2, d3 and transmitted power in this mode are shown in Table 3.
As the power gradually increases, the duty cycle on the low-voltage side transitions to 50%.This corresponds to the critical state of transitioning from TPS to EPS, i.e., d3=1, as shown in Figure 3(b).The expressions for (d1, d2, d3) and the power at critical state 1 are shown in Table 3.
Mode 2: The DAB converter enters the EPS control mode.Due to the fixed iLr(t0)=iLr2(zvs), the current iLr(t1) gradually increases, causing the high-voltage side lagging bridge arm to lose the ZVS characteristic and transition to QZVS.Therefore, 6 switching devices can maintain the ZVS characteristic, as shown in Figure 3(c).In the same way as the analytical solution for Mode 1, the corresponding (d1, d2, d3) and P* for Mode 2 are solved, as shown in Table 3.
As the output power continues to increase, iLr(t1) gradually rises until it equals iLr(t0).At this point, the rising edges of the high-voltage and low-voltage side inverter bridge waveforms coincide, as shown in Figure 3(d).Due to the limitation on the current values of the low-voltage side switches, iLr(t0) is still fixed at iLr2(zvs).Therefore, the leading arm of the high-voltage side and the entire low-voltage side bridge maintain the ZVS characteristic, while the lagging arm of the high-voltage side loses the ZVS characteristic.This is defined as the second critical mode.The expressions for (d1, d2, d3) and P for critical Mode 2 are shown in Table 3.
Mode 3-1, Mode 3-2, and Mode 3-3: As the output power continues to increase, the rising edge of the high-voltage side square wave gradually advances the low-voltage side, and the phase shift increases with increasing power.Therefore, based on the fixed value of iLr(t1)=iLr2(zvs), iLr(t0) keeps decreasing.When iLr(t0) crosses zero and becomes negative, it corresponds to Mode 3-1, as shown in Figure 3(e).At this time, the lagging bridge arm on the high-voltage side re-implements QZVS.Until iLr(t0)=-iLr1(zvs), as shown in Figure 3(f), it corresponds to the critical Mode 3-2.At this point, the lagging bridge arm on the high-voltage side begins to achieve complete ZVS.As the power continues to increase, when iLr(t0)<-iLr1(zvs), as shown in Figure 3(g), it corresponds to Mode 3-3.In this process, the lagging bridge arm on the high-voltage side transitions from hard conduction to QZVS and then to ZVS, while all the switching devices on the low-voltage side maintain ZVS characteristics.The expressions for (d1, d2, d3) are the same and can be combined into one Mode 3, as shown in Table 3.
Critical Mode 3: As the output power continues to increase, d1 gradually increases until it reaches 1, and enters the SPS control, as shown in Figure 3(h).This power characteristic point is defined as the fourth critical mode.The corresponding (d1, d2, d3) and P* at this point are solved as shown in Table 3.
As shown in the above table, within the entire power range, under the constraint of the low-voltage side soft-switching control strategy, the duty cycles (d1, d2, d3) vary continuously as a function of K and P*.The controller design is simple, and the system has good responsiveness.The overall control block diagram is shown in Figure 4. Based on the optimization of the RMS current of the inductor, this paper extends the range of softswitching.Full ZVS can be achieved for all switching devices in Mode 1 and Mode 4.However, in Mode 2 and Mode 3, there are certain power ranges where global soft-switching cannot be achieved.The objective is to ensure ZVS for the low voltage side switching devices, while the leading bridge arm on the high voltage side can achieve ZVS, and the lagging bridge arm loses ZVS.The number of switching devices for achieving soft-switching is 6.If ZVS for the high voltage side switching devices needs to be ensured in this power range, the same method can be applied for analysis.

Thermal imbalance of the switch tube
The previous passage introduced an efficiency-optimized control strategy, which involves keeping the leading and lagging bridge arms fixed and unchanged based on the timing sequence of the driving pulses.A corresponding schematic diagram is provided in Figure 5.In the control strategy proposed earlier, during forward energy transfer, the leading bridge arm switch on the primary side can achieve ZVS within the entire power range.However, in some power ranges, the lagging bridge arm switch on the primary side loses ZVS, resulting in an imbalance in power loss in the primary side bridge arm within those power ranges.The lagging bridge arm switch exhibits significant heating, and the resulting "barrel effect" imposes a significant limitation on the overall power output capability.To optimize the efficiency of the converter and maximize its power output capability, the underlying modulation method also needs to be optimized synchronously.

Thermal balance wave method
According to Figure 5, Vab and Vcd can be expressed using switch functions as shown in Equation ( 6).
From Equation ( 7), the full-bridge output voltages for any combination of switch states on the primary and secondary sides are shown in Table 4: It can be seen from Table 4 that the interchange of the driving signals of the corresponding switching devices does not affect the output voltage of the full bridge.
Based on the above theory, for the loss imbalance due to the fixation of the over-hysteresis bridge arm, this section proposes a wave generation method to equalize the loss by adjusting the driving signal of the over-hysteresis bridge arm without changing the output square wave voltage.
The proposed waveform generation method in this paper involves detecting the edge of the PWM signal from the switch device with the earliest timing within one switching period and counting it, as shown in Figure 6.Theoretically, an interchange can be performed every integer number of switching periods.Considering the actual model's heat dissipation conditions, the driving signal of the corresponding switch device is interchanged every 10 switching periods when the count reaches 10.
In conclusion, the converter swaps the driving signals of the corresponding switches every ten switching cycles, exchanging the leading and lagging bridge arms of the H-bridge.This is done to balance the device losses and overcome the power output bottleneck caused by the thermal imbalance between the bridge arms.

5.1.Simulation model building
Build a simulation model of the DAB converter to validate the aforementioned control strategy.The specific parameters are shown in Table 5.According to the switch device parameters, the inductor cutoff currents to ensure ZVS for the primary and secondary-side switch devices are calculated as 2.59 A and 3.65 A, respectively.Several different power points are selected for verification, and the corresponding control strategies (D1, D2, D3) calculated are shown in Table 6.The simulation waveform is shown in Figure 7.The above simulation results show that at P*=0.1 (Figure 7(a)), the system operates in Mode 1, and both the primary and secondary-side switch devices achieve ZVS.At P*=0.2, P*=0.5, and P*=0.6, the system operates in the EPS mode, corresponding to Mode 2 and Mode 3, as shown in Figures 8(b), 8(c), and 8(d).The rising edges of the primary and secondary-side voltages approach and then diverge, inevitably leading to the interval of soft-switching loss, where the ZVS characteristic of the lagging switch device on the high-voltage side of the primary side is lost and then recovered.Figure 7(e) corresponds to the high-power interval, where the system operates in Mode 4, and both the primary and secondary-side switch devices achieve ZVS.

Comparison of RMS current, soft-switching range, and efficiency
Figure 8 compares the RMS current values of the proposed strategy (PCS), SPS control, and the current RMS optimization strategy (GOC) proposed in Tong et al.'s work [6].As shown in the figure, the RMS current values of the proposed strategy in this paper are slightly higher than the GOC algorithm in the low-power range.As the output power increases, the RMS current values of the PCS algorithm gradually converge with the GOC algorithm.There is no significant increase in conduction losses, and they are much lower than the RMS current values under SPS control.The number of switches that can achieve soft switching with two strategies in the entire power range can be compared in Figure 10.In the GOC control strategy, in the larger power range, only two switching devices can achieve soft switching.The control strategy in this paper greatly expands the soft switching range of the DAB controller.Six switching devices can achieve soft switching in the worst power range, and all other ranges can achieve soft switching for all switching devices.It effectively reduces the switching loss during operation and improves the efficiency of the DAB converter.The efficiency curve is shown in Figure 9.

Conclusion
Based on the optimization of the current RMS value, this paper proposes an optimal control strategy to expand the soft-switching range.Firstly, all operating modes of the DAB converter in the full power range are listed.Combined with the proposed ZVS constraint, the phase-shift angles and corresponding power ranges for each mode are derived for this control strategy.The obtained global optimum solution achieves a smaller current RMS value and greatly expands the soft-switching range, effectively improving the efficiency of the DAB converter within the full power range.Additionally, a new modulation method is proposed to balance the thermal imbalance between the leading and lagging bridge arms, addressing the limitation of output power caused by thermal imbalance in practical applications.

Figure 4 .
Figure 4. Soft switch optimization control block diagram.

Figure 6 .
Figure 6.Schematic diagram of driver signal exchange.

Figure 8 .
Figure 8.Comparison of RMS current.Figure 9. Comparison of efficiency.Figure 10 compares the soft-switching ranges of the proposed strategy (PCS) with that of the RMS optimization strategy (GOC) proposed in Tong et al.'s work [6] under different ratios.

Figure 9 .Figure 10 .
Figure 8.Comparison of RMS current.Figure 9. Comparison of efficiency.Figure 10 compares the soft-switching ranges of the proposed strategy (PCS) with that of the RMS optimization strategy (GOC) proposed in Tong et al.'s work [6] under different ratios.

Table 1 .
The transmission power expression of each mode.
(5)on the high-voltage side always operate at the current stress point, which enables automatic zerovoltage switching (ZVS).To achieve zero-voltage operation and maintain low effective current under light load, the constraints are given by Equation(5).

Table 3 .
Control strategy of soft-switching on the low voltage side.

Table 5 .
DAB converter simulation model parameter setting.

Table 6 .
Phase shift corresponding to different power levels.