Digital Implementation of Optimal Control of DCM LCC Resonant Converter

1 Introduction
The LCC resonant converter working in DCM has been widely used and studied because it can achieve soft switching well, has a wide output voltage range, and can work in the open-circuit and short-circuit state of the load. However, in DCM, the input voltage source of the circuit has not transmitted any energy to the load during the time when the current is intermittent, which leads to a decrease in energy transmission efficiency. In order to avoid this defect and ensure soft switching at the same time, the optimization control method of the LCC resonant converter in DCM is a good solution strategy, that is, the control method under the critical intermittent switching frequency.
Based on this, a digital implementation method of the optimized control of the LCC resonant converter is proposed, and an experimental prototype is built to verify the correctness of this control method.

2 Circuit working principle
Figure 1 shows a typical LCC resonant converter circuit topology with capacitive filtering output. VT1~VT4 are switch tubes; VD1~VD4 are anti-parallel diodes; Cr, Lr are series resonant capacitors and inductors; Cp is parallel resonant capacitor (Lr, Cp are parasitic parameters of transformer under high-frequency working state, representing winding leakage inductance and inter-turn capacitance of transformer converted to primary respectively); VDo1~VDo4 are output rectifier diodes; Co is output filter capacitor, and Co is much larger than Cr, Cp; Ro is output load: n is transformer ratio; Ue is equivalent output voltage converted to transformer primary; uCr, uCp are voltages across Cr, Cp respectively; ir is resonant current. All devices in the figure are assumed to be ideal devices.

According to whether uCp is clamped by Uo at the moment VT1, VT4 (or VT2, VT3) is turned on, the DCM of the circuit can be divided into two modes. When the circuit works in mode 2, since uCp has been clamped by Uo when VT1, VT4 (or VT2, VT3) is turned on, it no longer participates in the resonance at this time. Cr and Lr form LC series resonance, and ir lasts for half of the LC resonance cycle. In order to ensure that the switch tube works in the soft switching state when the circuit works, the driving pulse width of the switch tube meets certain conditions, which is more conducive to the circuit operation. Based on the above considerations, the appropriate resonance parameters are selected to make the circuit work mode 2, and its detailed working process can be divided into 8 working states. Due to the symmetry of the circuit, only 4 working modes of half a switching cycle need to be analyzed. Figure 2 shows the waveform of the circuit under working mode 2.

Mode 1 [t0~t1] At t0, VT1 and VT4 are turned on. Since uCp has been clamped by Uo, the resonance process is the forward resonance of Cr and Lr, ir increases from zero according to the sine wave, and VDo1 and VDo4 are turned on with zero current. Since ir rises from zero when VT1 and VT4 are turned on, VT1 and VT4 achieve zero current conduction. Mode 1 is exactly half the resonance cycle of Cr and Lr, and energy is transferred from the input source to the load. When ir returns to zero again, mode 1 ends.
[page] Mode 2 [t1~t2] At t1, ir increases from zero in the reverse direction, Cp and Cr discharge, causing VDo1~VDo4 to be reversely cut off. The resonance process changes from the forward resonance of Cr and Lr to the reverse resonance of Cr, Lr and Cp. The current is turned on from zero through VD1 and VD4, achieving the soft turn-on of VD1 and VD4. In this stage, VD1 and VD4 are turned on, resulting in the voltage at both ends of the switch tube being approximately zero. Therefore, turning off VT1 and VT4 can achieve zero voltage shutdown. In this stage, no energy is transferred from the input source to the load. When uCp increases in the reverse direction to uCp=-ue, mode 2 ends.
Mode 3 [t2~t3] At t2, VDo2 and VDo3 begin to conduct, uCp is clamped by Uo, and energy is transferred from the input source to the load. The resonance process changes from the reverse resonance of the three elements Cr, Lr, and Cp to the reverse resonance of the two elements Cr and Lr. VT1 and VT4 are turned off in this stage, and zero voltage shutdown can also be achieved. When ir returns to zero, mode 3 ends.
Mode 4 [t3~t4] ir returns to zero at t3. Since VT1 and VT4 have been turned off and VT2 and VT3 have not yet been turned on, the circuit maintains a discontinuous current state, and there is no energy transfer between the input source and the output source. When VT2 and VT3 are turned on, stage 4 ends. Due to the symmetry of the circuit operation, the working process of the other half cycle will not be repeated.

3 Proposal of the critical intermittent frequency of the LCC resonant converter
The mathematical analysis of the working mode 2 of the LCC resonant converter in the literature points out that the switching frequency to keep the resonant circuit working in the intermittent mode is:

Where: t01~t34 are all functions of Go and K, t01 is the time of the circuit operation stage mode 1 [t0~t1], and the rest is analogous.
As shown in Figure 2, when there is no stage [t3~t4], [t7~t8], the circuit is in a critical intermittent state. Therefore, the switching frequency when t34=0 is defined as the critical intermittent switching frequency, that is:

For an actual LCC resonant converter device, K is a constant, so as long as the actual operating state of the circuit is detected and the Go value is calculated, the fs_cri at this time can be calculated by formula (2).

4 Program implementation of the optimization control strategy
Simple control refers to a control method that limits the switching frequency to a range less than or equal to the minimum critical intermittent frequency. As shown in Figure 2, there is no energy transfer between the input source and the load in the time periods [t3-t4] and [t7-t8] within one cycle, which reduces the energy transmission efficiency.
Here, the problem of how to achieve the optimal control method is studied. In the control of high-frequency and high-power circuit devices, the use of digital control is undoubtedly a better choice. From the perspective of digital control, it is a good method to use a digital control chip to control the operating frequency of the converter to achieve optimal control.

[page] This control strategy not only achieves the optimization control mode to maintain the critical discontinuity of IR and improve the transmission efficiency, but also can be combined with the adjustment of the input bus voltage to quickly achieve the critical discontinuity of IR during the voltage regulation process. The structure of the entire device is shown in Figure 4.

Figure 5b is the circuit operation waveform when the bus voltage is 40 V, Ro = 18.74 kΩ, Cr = 9.51 μF. At this time, the circuit operates in a critical intermittent state, fs_cri = 13.96 kHz. If simple control is used, the highest operating frequency is the minimum critical intermittent frequency of 9.11 kHz.
It can be seen from the experiment that this control method can stabilize Uo in the range of zero to maximum output voltage, and when the bus voltage is increased, if Uo has not reached the predetermined value, the circuit always operates under the critical intermittent condition of ir.
Since this control program dynamically calculates the fs_cri of the LCC resonant converter and adjusts this frequency during voltage regulation, the accuracy of the parameters is required to be high. Since the previous literature is a mathematical model established according to the ideal circuit model, it is necessary to make some corrections to the parameters actually sampled by the control circuit (such as Uin, Uo, etc.) during control to reduce the influence of the output silicon stack and IGBT voltage drop.
Compared with the simple control method, this optimized control program greatly improves the operating frequency of the inverter. It can be seen from the experimental waveform that the frequency is increased by about 25%. If Uo continues to increase and the appropriate parameter K is selected, the frequency increase will be more obvious. At the same time, the optimized control method also eliminates the time when ir is completely discontinuous in the simple control method, improves the system transmission efficiency and output power, and maintains the advantages of the simple control method such as soft switching.

6 Conclusion
Based on the mathematical model established by the LCC resonant converter in the discontinuous working mode, a digital implementation strategy for the optimized control of LCC in the discontinuous mode is proposed, and a practical control program is proposed, so that the original discontinuous resonant current reaches the critical discontinuous working mode. Compared with the simple control mode, the optimized control mode of the discontinuous mode LCC resonant converter has a higher output voltage and a higher operating frequency. Near the critical discontinuous frequency, the transmission efficiency of the converter reaches the maximum value of the discontinuous working mode, which makes up for the defects of the simple control.