Current-sensorless model predictive control for DAB converter based on back-flow power optimization

To solve problems such as high back-flow power, low system efficiency and poor dynamic properties of dual-active-full-bridge DC-DC converters in energy routers under traditional single-phase-shift modulation, the present paper introduces a current-sensorless-based model predictive control method combining back-flow power optimization based on Extended-Phase-Shift (EPS) modulation strategy. The transmission power model of the DAB converter is analyzed, taking into account the extended phase shift and the optimal shift comparison combination is found by the Lagrange multiplier method with the return power as the objective function. Then, the cost function is constructed to track the output voltage to achieve model predictive control without a current sensor. Finally, the accuracy and efficiency of the proposed strategy are verified by simulation. The results demonstrate the efficacy of this approach in mitigating system back-flow power and enhancing dynamic performance.


Introduction
In recent years, to solve the environmental problems caused by carbon emissions, with the continuous development of green renewable energy technologies, many scholars both domestically and internationally have paid attention to the Electric Energy Router (EER), which plays a significant role in energy and information transmission [1] .As one of the core devices [2] , the Dual-Active-Bridge (DAB) DC-DC converter has a simple structure and is easy to control, which can realize soft switching and has characteristics such as bidirectional power flow [3] .The high-performance bidirectional DC-DC converter is of great significance in realizing the translation of energy structure and the effective utilization of clean energy.Since the DAB converter was proposed, the utilization of this technology has been extensively employed within the microgrid industry [4] , energy storage [5] and electric vehicles [6] .
The control methods of the DAB converter are mainly divided into phase shift control and pulse width modulation control.Among them, controlling the phase shift is the easiest and most practical way to get started.Nevertheless, the traditional Single-Phase-Shift (SPS) control has a large reflux power and current stress and only one variable degree of freedom, so it is not suitable for improving the transmission efficiency of the DAB converter [7] .To suppress the back-flow power of DAB converters, a Double-Phase-Shift (DPS) strategy is proposed, but it can only be achieved in the medium to low power range and is not optimal at full power [8] .A three-phase shift (TPS) strategy has been proposed for various operating conditions, but under this strategy, the DAB converter has three different degrees of freedom, multiple operating modes and a relatively complex model [9] .To reduce the power of the backflow, an Extended-Phase-Shift (EPS) control method is considered, which adds a degree of freedom in the primary bridge of the transformer for easy control [10] .Therefore, this paper considers only adding one degree of freedom and adopting the Extended-Phase-Shift expansion strategy.
In addition, the dynamic characteristics of the DAB converter are particularly important.A model control strategy for group optimization has been designed to reduce computational complexity, but the analysis only focuses on Single-Phase-Shift control, resulting in low system efficiency [11] .A direct power strategy combining current stress optimization has been designed, which can restore a stable state promptly when the system is disturbed and the number of sensors is not large [12] .Therefore, this paper considers the predictive control of output voltage without a current sensor to save cost.
To converter efficiency improvement, increase the sampling accuracy and comprehensively enhance the system's dynamic characteristics, the present paper introduces a current-sensorless model predictive control method for DAB converter based on Extended-Phase-Shift control combined with reflux power optimization.Firstly, the mathematical models of the power of the transmission and return power are analyzed comprehensively.The return power is taken as the objective function and the sampling Method of the Lagrange multiplier is used to find the optimal shift comparison combination.Secondly, the state space averaging equation is established and the dynamic performance of output voltage is optimized by the model prediction optimization algorithm in the absence of a current sensor.Finally, MATLAB/Simulink modeling simulation is used to compare with traditional SPS control to check the effectiveness of the suggested approach.

DAB extended-phase-shift control principle
The typical DAB converter topology is displayed in Figure 1, which consists mainly of two symmetrical H-bridges (H1 and H2) and a medium-high frequency isolation transformer T.Among them, U1 and U2 are the converter input and output voltages, iin and i1 are the power supply current and input current of the primary side of the converter, i2 and iout are the output current and load current of the secondary side of the converter, C1 and C2 are the support capacitance of the input side and output side, Uab and Ucd are the H1 output voltage and H2 input voltage respectively.RL is the load resistance on the output side, L is the sum of the superimposed transformer leakage and auxiliary inductance, iL is the inductive current and the transformer turns ratio is n:1.In the following analysis, the operating mode 1(0 ≤ D1 ≤ D2 ≤ 1) is taken as an example.In one switching period, the inductor current has a half-period odd symmetry, that is, the current flowing through the inductor can be expressed at any given moment.( ) where the voltage conversion ratio is specified as The average transmitted power PE and the standard transmitted power PE * of the DAB converter using extended phase shift control can be expressed as: After the introduction of the inward-shift ratio D1, the converter control range under EPS control is wider and more flexible than the SPS control.The back-flow power Pbf and the standard back-flow power Pbf * of the DAB converter under extended phase shift control can be expressed as:  As shown in Figure 3, the reflux power increases with the increase of k value.When k is a constant value, selecting an appropriate combination of phase shift angles can effectively eliminate reflux power.

Back-flow power optimization
To reduce the switching loss of the converter and improve the transmission efficiency of the converter, it is also necessary to meet the ZVS condition of the switching tube.
In combination with Equation (1), the shift and comparison range under ZVS constraints can be obtained as: when the DAB converter works at a constant transmission power, there must be a set of shift ratio (D1, D2) combinations so that the converter's return power value is the minimum value under constrained conditions.Here, the objective function is the return power Pbf, the linear constraint function is the transmission power and the ZVS condition is the nonlinear constraint function.The Lagrange equation with constraints is established as: where λ is Lagrange's multiplicative factor, P * is the specified transmittance and μv is the constraint coefficient corresponding to Gv.Finally, constraints are given: As shown in Figure 4, in the traditional PI control mode, the outward shift ratio D2 is generated by the PI controller and the inward shift ratio D1 is output through the reflux power optimization algorithm to reduce the power of the back-flow in the primary side bridge of the system.

Current-sensorless model Model predictive control
In recent years, Model-Predictive Control (MPC) technology has been widely used in power electronic equipment with relatively stable control performance.For example, it was applied to the field of motor drive systems.In general, MPC technology can effectively improve DAB converter dynamic performance.Through the three steps of the prediction model, construction cost function and rolling optimization, the external shift ratio Df is generated to replace the original D2 and the internal shift ratio D1 is adjusted jointly with the optimized D1, which not only improves the working efficiency of the system, but also improves the ability of the current converter to protect against interference.
According to the topology of the DAB converter, the state space average model can be constructed on the output capacitance side according to KCL law as: The discretization is done by the forward Euler method.Combined with Equation (10) and Equation (11), predicting DAB converter output using EPS modulation is as follows.Since the DAB converter under EPS control minimizes the backflow power as much as possible while realizing the soft switch, the design cost function should ensure that the output voltage can quickly reach the desired value and stably without excessive overshoot and oscillation, so deviation between the expected value and the reference value should be reduced as much as possible.
Combined with reflux power optimization and model predictive control method, the cost function is established as: where ι is the constrained multiplier and oref U is the reference voltage.
To guarantee the stability of the output voltage and minimize the error as much as possible, for model prediction, the output current iout is generated by PI regulation, while the voltage sensor on the output side cannot be omitted.Therefore, the current sensor that samples the load current is omitted in this paper.No current sensor means that the variable iout is not directly involved in the converter control system.The output is adjusted to reference voltage quickly and accurately.
The hybrid modulation strategy of reflux power optimization and model predictive control is displayed in Figure 5 below.
Firstly, a state-space averaging model is established based on extended phase shift control (EPS).Secondly, the optimal combination of control variables (D1, D2) is solved by the Lagrange multiplier method with constraints, taking reflux power as the objective function.Furthermore, a model predictive control model is established and the final optimal phase shift control quantity is further solved by cost function and rolling optimization.The internal phase-shift D1 optimized by reflux power and the external phase-shift Df obtained by model predictive control are used in the drive controller of the converter.

Simulation verification
For verification purposes, the proposed hybrid control method of Lagrange reflux power EPS-based optimization algorithm and model predictive control based on current-free sensors were created to simulate the converting system on the MATLAB/Simulink simulation platform.The most important experimental parameters are listed in Table 1.DAB converter transmitting power under three modulation strategies is simulated, as shown in Figure 6.It can be seen that under the SPS modulation strategy, the system has a large return power value, which leads to a large on-off loss and low working efficiency of the system.When the EPS modulation strategy is implemented, the rebound performance improves, but it remains present.However, with the employment of the optimized EPS modulation strategy, the return power reduces considerably, and it can even reach zero back-flow power.7, shows the interference of a given input voltage surge of 0.10 s and an output load drop of 0.20 s respectively.It is evident that the conventional PI control strategy is in effect, the output voltage of the DAB converter will have a certain amplitude of overshoot phenomenon.When the input voltage surge or output load drop abnormal interference is added, although it can be restored to stability in time, it will still have a certain impact.After using the MPC control algorithm, the output voltage response time of the converter is fast.After experiencing a small oscillation, the output voltage remains stable and is not affected by any interference, which improves the dynamic properties of the system.

Conclusion
By analyzing the EPS-controlled DAB converter transmit, and back-flow power models and comprehensively improving the dynamic performance of the converter, this paper presents a proposal for a hybrid control strategy based on the EPS Lagrange reflux power optimization algorithm and current sensor-less model predictive control.Finally, according to theoretical analysis and experimental results, it can be concluded that closed-loop PI control using SPS is inferior.It is recommended to consider alternative control methods.
1) When the output load changes abruptly or the input voltage interferes, the output voltage under the strategy introduced in this paper is almost stable, and no overshoot and oscillation occur.
2) The proposed control strategy not only optimizes the return power of the converter well, but also minimizes the error caused by current sampling and effectively improves the working efficiency of the converter.

Figure 1 .
Figure 1.DAB converter topology.The working waveform of the DAB converter under extended phase-shift modulation is shown in Figure2, where D1 is the phase shift between S1 and S4 in comparison to the internal shift, D2 is the phase shift between S1 and S5 in comparison to the external shift and Ths is the half cycle of the switching tube.

Figure 2 .
Figure 2. Operating waveform of DAB converter controlled by EPS.In the following analysis, the operating mode 1(0 ≤ D1 ≤ D2 ≤ 1) is taken as an example.In one switching period, the inductor current has a half-period odd symmetry, that is, the current flowing through the inductor can be expressed at any given moment.

Figure 4 .
Figure 4. Back-flow power optimization PI control block diagram.As shown in Figure4, in the traditional PI control mode, the outward shift ratio D2 is generated by the PI controller and the inward shift ratio D1 is output through the reflux power optimization algorithm to reduce the power of the back-flow in the primary side bridge of the system.
tk) represents the output voltage sampled at the current time, U2(tk+1) represents the output voltage sampled at the next time and Ths represents half a cycle of the switch tube.
, d(tk) represents the control amount of the current time shift (D1, D2) combination.

Figure 5 .
Figure 5. Hybrid optimal control block diagram of DAB converter based on extended phase shift.

Figure 6 .
The simulation waveform of transmission power under different modulation strategies.a) SPS modulates transmission power; b) EPS modulates transmission power; c) Optimized transmission power of EPS modulation.

Figure 7 .
Output voltage dynamic characteristics simulation waveform diagram.a) Traditional PI control; b) MPC control.The simulation of DAB converters with two different output voltage control modes, as shown in Figure