Research on Bidirectional DC-DC Converters in Distributed Electric Propulsion Systems

This paper investigates bidirectional DC-DC converters in distributed electric propulsion systems, focusing on the dual active bridge (DAB) converter. To minimize voltage fluctuations in aircraft operating under complex conditions, a virtual voltage compensation control strategy based on active disturbance rejection (ADR-VVCC) is presented. The presented control strategy is grounded on the working characteristics under single-phase-shift (SPS) and introduces a virtual voltage to compensate for voltage fluctuations and degraded dynamic performance caused by the inherent uncertainty of converter parameters and power losses during the energy transfer process. The active disturbance rejection control is incorporated to replace traditional PI control, thereby enhancing the converter’s dynamic performance. Simulation outcomes demonstrate that the presented control strategy effectively improves the converter’s dynamic performance and maintains output voltage stability.


Introduction
With the rapid development of the aviation industry, the demands for sustainable development in the field are increasingly high, with particular attention being paid to the development of aviation power systems.Among numerous innovative concepts, Distributed Electric Propulsion (DEP) systems have demonstrated outstanding advantages [1].Due to the variable working environment, the DC bus power of DEP aircraft may fluctuate.Consequently, the bidirectional DC converter connected between the energy storage component and the DC bus needs to have excellent dynamic response performance [2].DAB converter has gradually become attracted attention in the aerospace power supply field, owing to higher power density, bidirectional power transfer capability, electrical isolation, and simple control [3].The dynamic characteristics of the DAB converter are preliminarily studied in [4].Later, various advanced control strategies were proposed successively.In [5], a direct power control (DPC) strategy rooted in SPS is introduced, which can maintain good dynamic performance during input voltage changes.However, this method has not analyzed the case of load transients.In [6], a feedforward control scheme is proposed for load current, which significantly improves the system's dynamic performance during load changes without relying on inductance parameters, but the load current needs to be collected by using sensors, increasing the design cost.
This article presents a virtual voltage compensation control scheme based on active disturbance rejection (ADR-VVCC).Firstly, the structure of the DAB converter and working principle and characteristics of SPS are introduced.To address issues such as power transmission loss and converter internal parameter uncertainties in the system, a virtual voltage compensation is introduced to achieve the goal of stabilizing the output voltage.Then, we combine active disturbance rejection control with virtual voltage compensation control to solve the issue with slow dynamic response and poor disturbance rejection capabilities inherent in PI control.Finally, through simulation comparisons with other control strategies, the consequences demonstrate that the suggested control scheme can productively strengthen the dynamic performance of the converter and keep output voltage stable.

DAB converter's single phase-shift principle and characteristics
As shown in Figure 1, the structure of the DAB converter, which is mainly composed of an isolation transformer T, an equivalent inductance L, the input-side and output-side capacitors C1 and C2, and two symmetrical H-bridges containing eight switching devices.Ui and Uo respectively represent the input voltage and the output voltage; VH1 and VH2 are the output square wave voltages on both sides of the isolation transformer's H-bridges; iL and io respectively represent the inductive current and the load current; n is the transformer ratio.
The SPS control of the DAB converter is changing the transmission power and magnitude of the converter by changing the phase angle between VH1 and VH2.For the sake of analysis, this article takes forward power transmission as an example.The waveform schematic diagram of the converter's steadystate operation is shown in Figure 2.
As seen in Figure 2, Ts represents the switching period, i.e., fs = 1/Ts.D is the phase shift ratio, and it is defined as φ/π, which represents the ratio of the phase difference φ between square wave voltage VH1 and VH2 to half of the period.Due to the symmetry of the iL waveform during the switching cycle, to simplify the analysis, the inductor current for the two time periods t0-t2 is represented as: where iL (t0) and iL (t1) represent the inductor current at moments t0 and t1, respectively.System losses are ignored, and the DAB converter's transmission power P can be obtained by combining Figure 2 and Equation (2): Under normal circumstances, the range of D is between -0.5 and 0.5.

Design of ADR-VVCC controller
In this paper, the ADR-VVCC strategy presented is shown in Figure 3. First, we use sensors to collect Ui, Uo, and io.Then, we subtract the sampled output voltage from the reference voltage Uo * and pass the difference through the active disturbance rejection controller to output the compensation voltage Uv.Next, we calculate the phase shift ratio d by using Equation (7).Finally, the single-phase-shift driving signal is generated to drive the 8 switching devices.

The design of virtual voltage compensation
Due to the uncertainty of the internal parameters of the converter system and the power losses generated during the energy transfer process, a virtual voltage is introduced to compensate for the possible voltage fluctuations caused by these issues.
The transmitted power after compensation by the DAB converter can be defined as: (2) where Uv represents the virtual compensation voltage, and io * is the desired value of the load current.Since the Uo is proportional to the io, io * can be defined as: Substituting Equation (4) into Equation (3) gives the transmission power after virtual voltage compensation: When the actual transmission power can track the compensated transmission power, the system will achieve good dynamic response performance.The actual transmission power expression of the DAB converter is shown in Equation ( 2).Combining Equations ( 5) and ( 2) with setting P =Pv, the calculated D is shown as follows: Due to the equivalent inductance, L has parameter uncertainty, and the introduced virtual voltage Uv can compensate for the effect of the converter parameter deviation on the system.Furthermore, Equation ( 6) can be simplified as:

The design of LADRC
The PI control suffers from a slow dynamic response and poor disturbance rejection capabilities.To address these issues, a fast response and robust linear active disturbance suppression control technique has been introduced.LADRC mainly consists of linear error feedback law (LESF), LESO, and disturbance compensation factor b0.The structure of LADRC control is shown in Figure 4. ̈=   +  (7) where b0 is the known part of the gain of the control variable u, and f is the unknown total disturbance.LESO is a crucial component of LADRC, which can expand the total disturbance f into a new state variable and perform real-time estimation and compensation for it, thus reducing the impact of interference.Therefore, the selection of state variables is x = [x1, x2, x3] and T = [y y  , f], so we rewrite Equation (8) as: The LESO state-space matrix equation is established according to Equation (9): In Equation (10), z1, z2, and z3 are the output state vectors of the LESO, and β1, β2, and β3 are the adjustable gain parameters of the observer.The dynamic performance of the observer is related to the choice of parameters.To simplify the controller design, the poles of Equation (10) are configured to the negative value of the observer bandwidth ωo.The gain parameters are represented as [7]: At this time, LESF can be represented as: We parameterize kp and kd in Equation ( 12), namely, kp=ωc 2 , kd=2ωc.The controller bandwidth is ωc, which becomes the only parameter in the LESF gain matrix.By compensating the observed values from LESO and the obtained total disturbance in real-time to the control value, u can be set as: where r is the given value, -z3/b0 is the compensation for disturbance, and kp and kd are the adjustable coefficients for the proportional and differential components.When the observer's gain parameters are well-tuned, the observer output can accurately estimate the selected state variables, the system reduces to a series connection of two integrator systems, and only proportional and differential control is needed to achieve good control performance.

Simulation results and analysis
We build the simulation circuit parameters of a DAB converter on the Matlab/Simulink platform, as shown in Table 1  3 seconds, the load impedance suddenly decreases from 30 Ω to 15 Ω, afterwards, it returns to its original state at 0.5 seconds.It can be observed that the dynamic performance is the worst when we use the TVLC scheme, with larger output voltage fluctuations and a longer recovery time.When the DPC strategy is used, voltage fluctuations can be effectively reduced.However, when the ADR-VVCC strategy is adopted, the output voltage drop is smaller, and the recovery time is faster.
In Figure 6, the voltage waveform for the three different control strategies when input voltage changes are displayed at 0.3 seconds, and the input voltage changes from 100 V to 80 V. Subsequently at 0.5 seconds, it returns to its initial value.It can be easily observed from the figure that when we use the TVLC strategy, the dynamic performance is poor, with the voltage dropping about 1 V at 0.3 seconds and increasing about 1.7 V at 0.5 seconds, which takes a longer time to recover to a stable state.However, when we use the DPC or ADR-VVCC schemes, there are virtually no voltage fluctuations.

Conclusion
This paper, set in the context of aircraft-distributed electric propulsion systems requiring good dynamic performance in bidirectional DC-DC converters, focuses on the DAB converter to enhance its dynamic response performance and maintain a stable output voltage.The paper provides a detailed introduction to the principles of the control strategy and conducts relevant simulations for validation.Principle analysis and simulation data demonstrate that the presented ADR-AACC can productively improve the converter's dynamic response performance under load resistance changes or input voltage variations, while a stable output voltage is maintained.

3 zFigure 4 .
Figure 4. LADRC block diagramThe controlled system can be represented as:̈=   +  (7) where b0 is the known part of the gain of the control variable u, and f is the unknown total disturbance.LESO is a crucial component of LADRC, which can expand the total disturbance f into a new state variable and perform real-time estimation and compensation for it, thus reducing the impact of interference.Therefore, the selection of state variables is x = [x1, x2, x3] and T = [y y  , f], so we rewrite Equation (8) as:̇=  +  + ℎ  =  (8)

Figure 5
Figure 5 displays the waveform of three different control strategies under load transient conditions, in which Figure (a) represents traditional voltage loop control (TVLC), Figure (b) represents DPC, and Figure (c) represents ADR-VVCC.At 0.3 seconds, the load impedance suddenly decreases from 30 Ω to 15 Ω, afterwards, it returns to its original state at 0.5 seconds.It can be observed that the dynamic performance is the worst when we use the TVLC scheme, with larger output voltage fluctuations and a longer recovery time.When the DPC strategy is used, voltage fluctuations can be effectively reduced.However, when the ADR-VVCC strategy is adopted, the output voltage drop is smaller, and the recovery time is faster.In Figure6, the voltage waveform for the three different control strategies when input voltage changes are displayed at 0.3 seconds, and the input voltage changes from 100 V to 80 V. Subsequently at 0.5 seconds, it returns to its initial value.It can be easily observed from the figure that when we use the TVLC strategy, the dynamic performance is poor, with the voltage dropping about 1 V at 0.3 seconds and increasing about 1.7 V at 0.5 seconds, which takes a longer time to recover to a stable state.However, when we use the DPC or ADR-VVCC schemes, there are virtually no voltage fluctuations.