Current stress optimization control of isolated AC-DC matrix converter

The Isolated AC/DC matrix converter realizes bi-directional energy transmission through phase shift control. The existing control schemes do not coordinate the modulation coefficient and phase shift ratio well, which will cause large current stress to the converter, resulting in low efficiency. To solve this problem, this paper analyses the working mechanism of IAMC under dual phase shift control. It constructs a mathematical model under dual phase shift control to calculate the current stress. An optimal control method for the current stress of isolated AC/DC matrix converter is proposed. The current stress is suppressed by coordinating modulation coefficient and internal and external phase shift ratio. Finally, a simulation platform is built to verify the proposed method.


Introduction
The isolated three-phase AC/DC matrix converter (IAMC) has the advantages of the bidirectional flow of energy and adjustable input power factor [1].It has a good application value in wind power generation [2], electric vehicle V2G technology [3] and other fields.IAMC is mainly composed of a three-phase to single-phase matrix converter and an H-bridge converter, and the bidirectional energy transmission is realized by phase shift control technology [4].Currently, the current stress research is mainly focused on dual active bridge DC-DC converters, which is less in the field of isolated AC-DC matrix converters.Excessive current stress will also reduce the transmission efficiency of IAMC and even damage the power devices in severe cases [5][6].This paper focuses on addressing the current stress problem of IAMC in traditional phase shift control.[7].A current stress optimization control method for dual phase shift control is introduced [8], which is suitable for IAMC.Firstly, the working mechanism of IAMC under DPS control is analyzed.The dual phase shift control is utilized to perform calculations and determine the peak current and transmission power.[9].Due to the synthesis of two-stage line voltages in a switching cycle [10], calculating the current stress and transmitted power of the high-side voltage output by the 3-1MC becomes challenging.Therefore, in a switching cycle, the line voltages of the two stages on the high-voltage side are approximately replaced by the average value [11].The Lagrange conditional extremum method [12] is used to construct a mathematical model and solve the minimum current stress parameter combination.Finally, the simulation model of the control system is built.In addition, the obtained simulation results validate the effectiveness and feasibility of the proposed control method.

3-1MC modulation strategy
The topology of IAMC is presented in Figure 1.IAMC is comprised of a 3-1MC, H-bridge converter, high-frequency transformer and filter.Forming an integral part of the IAMC, the 3-1MC comprises six bidirectional switches (Sap-Scn), which are capable of conducting current in both directions.Each of these bidirectional switches is built with two unidirectional switches (Sxy1 and Sxy2).The H-bridge converter includes four switches (S 1 -S 4 ).and the L is defined as the total sum of the auxiliary inductor and the leakage inductor.In addition, we defined the as the current that flows through the transmission inductor.The 3-1MC plays a crucial role in the conversion process, transforming the three-phase utility grid voltage into a high-frequency single-phase voltage, which in turn enables the generation of DC voltage.This voltage is then rectified by the H-bridge.Since the 3-1MC is powered by a voltage source, it is imperative that the capacitor voltages are always prevented from being shorted.Furthermore, to prevent any open circuit on the transformer side caused by the leakage inductor of High-Frequency Transformer, it is crucial to avoid such situations.At the high-voltage side of the High-Frequency Transformer (HFT), it is imperative that the switching vectors produce both positive and negative voltages to generate high-frequency alternating voltage.Thus, for each vector, it is required to have two switching states to produce the same voltage amplitude in opposite directions.These switching states enable the balanced distribution of positive and negative voltages, allowing the desired voltage amplitude to be generated in both directions for each vector.Figure 2 shows the current spatial vector distribution of 3-1MC.It can be observed from Table 1, the switching states and output voltages are aligned for each vector.
Grid voltage and grid current are further defined, with their respective formulas as follows: cos( ) Where as the input phase voltage amplitude, φ as the power factor angle, ω is defined as the angular frequency.Finally, is defined as the input phase current amplitude.The two-stage line voltages in the sector I are shown in Equation (2).Where the θ is defined as the angular phase parameter between the axis and the reference current vector .The duty cycle action time of two-stage line voltages and in sector I are respectively represented by and , as shown in Equation (3).m is the modulation coefficient. (2) (3)

Modal analysis of IAMC under DPS
The implementation of double phase shift control is illustrated in Figure 3.
is the switching period.and are the two-stage line voltages output by the high-voltage side of High-Frequency Transformer, and the is voltage value, and this voltage value calculated from the output DC voltage of the low-voltage side of High-Frequency Transformer to the high-voltage side.In addition, is phase shift ratio between the low-voltage side and the high-voltage side of High-Frequency Transformer, which is called external phase shift ratio.The internal phase shift ratio, referred to as , represents the phase shift ratio between the high-voltage side of the High-Frequency Transformer.According to Figure 3, the operation of IAMC can be divided into 12 switching modes.Considering the mechanisms of zero average current within a single switching period and the current symmetry, only the first 6 operating modes are given due to space limitations.As shown in Figure 4, the specific functional characteristics are as follows: The operating mode 1 ( ): It can be observed from Figure 4(a).The switches on the highvoltage side of High-Frequency Transformer ( , ) and the low-voltage sides of High-Frequency Transformer ( , ) are activated respectively.The inductor current is negative, and the inductor L voltage is .The current expression at this stage is (4) The operating mode 2 ( ): It can be observed from Figure 4(b) that the switches on the highvoltage side of High-Frequency Transformer ( , ) and the low-voltage sides of High-Frequency Transformer ( , ) are activated respectively.In addition, the inductor current is still negative, and the inductor current is zero at time t1.Inductor L voltage is .The current expression at this stage is (5) The operating mode 3 ( ): It can be observed from Figure 4(c) that the switches on the highvoltage side of High-Frequency Transformer ( , ) and the low-voltage sides of High-Frequency Transformer ( , )are activated respectively.In addition, the inductor current changes from negative to positive and rises gradually.Inductor L voltage is .The current expression in this stage is the same as that in switching mode 2.
The operating mode 4 ( ): The active state is presented in Figure 4(d) that the switches on the high-voltage side of High-Frequency Transformer ( , ) and the low-voltage sides of High-Frequency Transformer ( , ) are activated respectively.In addition, the inductor current continues to rise.Inductor L voltage is .The current expression at this stage is  The operating mode 5 ( ): It can be observed from Figure 4(e) that the switches on the highvoltage side of High-Frequency Transformer ( , ) and the low-voltage sides of High-Frequency Transformer ( , ) are activated respectively.In addition, the inductor current decreases gradually, and the voltage of inductor L is .The current expression at this stage is  The operating mode 6 ( ): It can be observed from Figure 4(f) that the switches on the highvoltage side of High-Frequency Transformer ( , ) and the low-voltage sides of High-Frequency Transformer ( , ) are activated respectively.In addition, the inductor current continues to decrease, and the voltage of inductor L is .The current expression at this stage is

K-order structural entropy model
The sampling period is .According to the forward Euler formula: the peak current of the primary inductor is focused on.The high voltage output of the 3-1MC is formed by combining two stage line voltages during a single switching cycle.Calculating the transmission power and current stress of IAMC under DPS control can be a complex task.To solve this problem, the two stage line voltages of the highvoltage side are equivalent to the average voltage in one switching cycle.As shown in Equation ( 9).
(9) In Equation ( 9), is the line voltage amplitude, and the power factor 1, so the average voltage is approximately equal to 1.5 .For the convenience of analysis, 1.5 is replaced by , and k is the voltage regulation ratio, as shown in Equation (10).The turns ratio n is equal to 1.  Since the waveform of inductor current has symmetry, it is easy to obtain .According to Equations ( 1)-( 11), the expressions of , , , and can be obtained as shown in Equation ( 12). ( According to Figure 5 and Equations ( 4) to (12).For both > and < , the peak current is equal to , and is similar in both cases.without considering the converter transmission loss, the transmission power of IAMC under the control of DPS at > and < is (13)  The Lagrangian conditional extreme value equation is established using the peak current and transmission power.It is expressed in Equation ( 14). ( 14) Take partial derivatives of variables in Equation ( 14) and set them equal to zero.
(15) According to Equation (15), the relationship between the modulation coefficient and the internal and external phase shift ratio is calculated, as shown in Equation ( 16). (16) According to Equation ( 16), multiple parameter combinations of voltage regulation ratio k, external phase shift ratio and modulation coefficient m and internal can be derived.

Control strategy
Figure 6 demonstrates the control block diagram of IAMC.The control block diagram of IAMC is demonstrates in Figure 6, which enables the synchronized adjustment of modulation control coefficients as well as internal and external phase shift ratios.The control block diagram includes three parts, power factor loop, DC voltage loop and phase shift loop.The power factor loop controls the AC to ensure the system operates at a unit power factor.In addition, the * is the difference between the given value of DC side voltage and the actual value through PI adjustment [13].The deviation of * from the actual value of is fed into the PI regulator to get the modulation coefficient m required by the phase shift loop.In addition, the parameter of internal and external phase shift ratios and are calculated, which can be derived by utilizing the voltage regulation ratio k and modulation coefficient m.

Simulation
The MATLAB simulation model is conducted to prove the combination of control variables proposed in Equation ( 16).Table 2 shows the parameters of simulation.
Table 3 presents a comparison of current stress and transmission efficiency between the two different methods, with the value of k set to 0.8.Method I is based on current stress control method proposed in this paper.According to Equation ( 16), the coordinated control of modulation coefficient and internal and external phase shift ratio is achieved.Method II refers to the conventional phase shift control approach.As is well known, most conventional phase shift control method controls the converter by changing the phase shift angle while keeping the modulation coefficient unchanged.The external phase shift ratio set for 0.5 (equivalent to the external phase shift Angle set for 90°, and the forward transmission power is maximum), and the internal phase shift ratio is half of the external phase shift ratio.
According to Equation (10), when the voltage ratio and load are the same, the output power of DC voltage is the same.The two methods' current stress and transmission efficiency were compared under the same load with k=0.8. Figure 7 illustrates the grid side voltage and current waveform of method I at k=0.8. Figure 8 shows the output power waveform of method I at k=0.8.  Figure 9 shows the two methods' waveforms when k=0.8. Figure 9 demonstrates that the high-side voltage and low-side voltage amplitudes of the two methods are the same, while the peak values of the high-side currents are different.Figure 10 demonstrates the comparison waveforms of the high-side currents of the two methods at k=0.8.From Table 3 and Figure 10, it is evident that the peak value of the high-side currents of method I is the smallest, so the converter experiences minimal current stress and achieves maximum transmission efficiency.In comparison to the conventional phase shift control method, it can be observed that the proposed current stress optimization control method effectively reduces the current stress on switching devices in IAMC.

Conclusions
The traditional phase shift control method in the isolated AC-DC matrix converter fails to effectively coordinate the modulation coefficient and the shift ratio, resulting in significant current stress on the converter.Aiming at the problem of the high current pressure of IAMC, this paper proposed a current stress optimization method suitable for IAMC double-phase shift control.The mathematical model for determining transmission power and current stress is established using the principle of Lagrangian extremum.The minimum current stress parameter combination of voltage regulation ratio, modulation coefficient, and internal and external phase shift ratio is deduced.The current stress control method employed in this paper proves to be effective in reducing the peak current of the transmission inductor and improving the converter's efficiency.

Figure 4 .
Figure 4. Working modes of IAMC under DPS control.

Figure 5
Figure5shows the waveform of the equivalent DPS control.When IAMC is in steady state, In Figure5(a), when > , the phase shift in period is taken as the research object., , , as shown in Equation (11(a)).And < is presented in Equation(11(b)).

Figure 6 .
Figure 6.Implementation of improved control variables for isolated AC-DC matrix converter.

Figure 7 .
Figure 7. Grid side voltage and current waveform.Figure 8. Output power waveform.

Figure 8 .
Figure 7. Grid side voltage and current waveform.Figure 8. Output power waveform.

Figure 9 .
Figure 9. Two methods' waveforms of high-side voltage, low-side voltage, and high-side currents when k=0.8.

Figure 10 .
Figure 10.Comparison of primary current waveforms between the two methods when k=0.8.

Table 2 .
Parameters of simulation.

Table 3 .
Comparison of current stress and transmission efficiency of the two methods with k=0.8.