1. Introduction

2. The Composition of a Power System

Figure 1. The power supply structure of semiconductor laser.

Figure 1. The power supply structure of semiconductor laser.

2.1. Mathematical Model Analysis of LCC Resonant Converter

The topology of the LCC resonant converter is illustrated in Figure 2. From a topological perspective, the LCC resonant converter exhibits not only the characteristics of a series resonant converter for DC component isolation and transformer protection but also possesses wide-range input/output regulation capabilities akin to those of a parallel resonant converter. Consequently, it demonstrates excellent constant current source characteristics and robust output short-circuit resistance [19,20]. In order to optimize the volume of resonant converter, reduce the circuit current and circuit equivalent capacitance, increase the characteristic impedance of resonant network, and reduce the current stress borne by the converter, the parallel resonant capacitor($C_P$) is designed on the secondary side of the transformer, so that the parallel resonant capacitor($C_P$) and series resonant inductor($L_r$) become parasitic parameters that cannot be ignored by the transformer under high frequency operation. It has good internal short-circuit protection function.

Figure 2. The Topology of LCC resonant converter.

Figure 2. The Topology of LCC resonant converter.

Because the mathematical model of LCC resonant converter is nonlinear, it is not conducive to the analysis of its working state, so it is necessary to linearize its nonlinear terms. When the frequency of the small-amplitude disturbed signal is much lower than the switching frequency of the system, the whole resonant converter can be considered as a quasi-steady-state system. In order to simplify the analysis, extended description function analysis [21,22] and linear differential equation theory are used to approximate the nonlinear terms, and the mathematical model of the steady-state system is obtained:

$$L_r(\frac{d{i}_{rs}}{dt}-{\omega }_s{i}_{rc})+v_{c_{s}s}+n{v}_{C_p^{’}s}=\frac{4v_g}{\pi }\sin (\frac{d}{2})$$

(1)

$$L_r(\frac{d{i}_{rc}}{dt}+{\omega }_s{i}_{rs})+v_{{\mathrm{c}}_{s}c}+n{v}_{C_p^{’}c}=0$$

(2)

$$i_{rs}=C_s(\frac{d{v}_{c_{s}s}}{dt}-{\omega }_s{v}_{{\mathrm{c}}_{s}c})$$

(3)

$$i_{rc}=C_s(\frac{d{v}_{{\mathrm{c}}_{s}c}}{dt}+{\omega }_s{v}_{c_{s}s})$$

(4)

$$C_{\mathrm{p}}^{’}(\frac{\mathrm{d}{v}_{C_{\mathrm{p}}^{’}s}}{\mathrm{d}t}-{\omega }_{\mathrm{s}}{v}_{C_{\mathrm{p}}^{’}c})+\frac{4i_{L_{\mathrm{f}}}}{\pi A_{\mathrm{p}}}{v}_{C_{\mathrm{p}}^{’}s}=n{i}_{\mathrm{rs}}$$

(5)

$$C_{\mathrm{p}}^{’}(\frac{\mathrm{d}{v}_{C_{\mathrm{p}}^{’}c}}{\mathrm{d}t}+{\omega }_{\mathrm{s}}{v}_{C_{\mathrm{p}}^{’}s})+\frac{4i_{L_{\mathrm{f}}}}{\pi A_{\mathrm{p}}}{v}_{C_{\mathrm{p}}^{’}c}=n{i}_{\mathrm{rc}}$$

(6)

$$L_{\mathrm{f}}\frac{\mathrm{d}{i}_{L_{\mathrm{f}}}}{\mathrm{d}t}+i_{L_{\mathrm{f}}}{r}_{\mathrm{c}}^{’}+(1-\frac{r_{\mathrm{c}}^{’}}{R_{\mathrm{L}}})v_{c_{\mathrm{f}}}=\frac{2}{\pi }\sqrt{v_{C_{\mathrm{p}}^{’}s}^2+v_{C_{\mathrm{p}}^{’}c}^2}$$

(7)

$$\frac{R_{\mathrm{L}}}{r_{\mathrm{c}}+R_{\mathrm{L}}}{C}_{\mathrm{f}}\frac{\mathrm{d}{v}_{C_{\mathrm{f}}}}{\mathrm{d}t}+\frac{1}{R_{\mathrm{L}}}{v}_{C_{\mathrm{f}}}=i_{L_{\mathrm{f}}}+i_{\mathrm{o}}$$

(8)

The output voltage $v_o$ is:

$$v_0=R_{\mathrm{L}}{i}_{\mathrm{o}}=i_{L_{\mathrm{f}}}{r}_{\mathrm{c}}^{’}+(1-\frac{r_{\mathrm{c}}^{’}}{R_{\mathrm{L}}})v_{c_{\mathrm{f}}}$$

(9)

i_o is the output current; v_o the output voltage; i_rs and i_rc are amplitude of sinusoidal component and cosine component of resonant current i_r respectively; $v_{c_{\mathrm{s}}\mathrm{s}},v_{{\mathrm{c}}_{\mathrm{s}}\mathrm{c}}$ are the amplitude of the sinusoidal and cosine components of the series resonant capacitor voltage $v_{c_s}$, respectively; $v_{C_{\mathrm{p}}^{’}\mathrm{s}},v_{C_{\mathrm{p}}^{’}\mathrm{c}}$ are the amplitude of the sinusoidal and cosine components of the series resonant capacitor voltage $v_{C_{\mathrm{p}}^{’}}$, respectively; ω_s is the operating angular frequency; n indicates the ratio of turns of the transformer; v_g indicates the input voltage; d represents duty cycle; i_Lf represents the current through the filtered inductor L_f; v_Cf represents the voltage of filter capacitor C_f. r_c represents the ESR of the filter capacitance; R_L indicates the resistance of the load.

Solve equations (1) through (9), The voltage gain of the open loop DC point of the LCC resonant converter is obtained:

$$G_V=\frac{V_{\mathrm{o}}}{V_{\mathrm{g}}}=\frac{{\omega }_{\mathrm{s}}{R}_{\mathrm{L}}{C}_{\mathrm{s}}\sin (\frac{d}{2})}{n\sqrt{{(1-{\omega }_{\mathrm{s}}^2{L}_{\mathrm{r}}{C}_{\mathrm{e}})}^2+{({\omega }_{\mathrm{s}}{R}_{\mathrm{e}}(C_{\mathrm{p}}+C_s)(1-{\omega }_{\mathrm{s}}^2{L}_{\mathrm{r}}{C}_{\mathrm{e}}))}^2}}$$

(10)

$C_{\mathrm{e}}=\raisebox{1ex}{$C_{\mathrm{s}}{C}_{\mathrm{p}}$}\!\left/ \!\raisebox{-1ex}{$(C_{\mathrm{p}}+C_{\mathrm{s}})$}\right.$ represents the equivalent capacitance of the resonant network.

According to the relationship between voltage gain and current gain, the current gain can be obtained by normalizing equation (10):

$$G_I=\frac{I_{\mathrm{o}}}{I_{\mathrm{i}}}=G_V{Q}_{\mathrm{L}}=\frac{Q_{\mathrm{L}}\sin (\frac{d}{2})}{n\sqrt{{(1+A)}^2{(1-\omega )}^2+Q_{\mathrm{L}}^2{(\omega -{\omega }^{-1}\frac{A}{1+A})}^2}}$$

(11)

ω=ωs/ωr, ωr is the angular frequency of the resonant network, ${\omega }_{\mathrm{r}}=\sqrt{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$L_{\mathrm{r}}{C}_{\mathrm{e}}$}\right.}$, $Q_L=\raisebox{1ex}{$Z_{\mathrm{r}}$}\!\left/ \!\raisebox{-1ex}{$R_{\mathrm{e}}$}\right.$, $Z_{\mathrm{r}}=\sqrt{\raisebox{1ex}{$L_{\mathrm{r}}$}\!\left/ \!\raisebox{-1ex}{$C_{\mathrm{e}}$}\right.}$, Z_r indicates the characteristic impedance.

It can be seen from equation (11) that when ω=1, the LCC resonant converter exhibits constant current characteristics, and the output current is independent of the load, but only related to the input voltage and resonance parameters. When the LCC resonant converter works in this mode, the output current can remain unchanged even if the semiconductor laser load changes. In order to study the influence of current gain G_I on Q_L, A, d and n, assuming A=n=1 and d=π, the change curve of current gain with different values of Q_L and A is drawn, as shown in Figure 3.

Figure 3. Parameter influence curve of current gain.

Figure 3. Parameter influence curve of current gain.

As can be seen from Figure 3(a), when the QF value increases continuously, the value of the current gain also increases. When the load is open (limQ_L→∞), the voltage gain G_I will change sharply and tend to infinity, which will damage the power system in serious cases. When ω=1, the current gain is independent of the load, showing constant current characteristics; As can be seen from Figure 3(b), when the capacitance ratio (A value) increases, the current gain will change in the same direction as the A value, that is, with the increase of the A value, and when ω > 1, the smaller the A, the more gentle the current gain change.

The values of duty cycle (d) and coil turns (n) of the transformer also affect the LCC resonant converter, and the gain influence curve of its output current and voltage is shown in Figure 4.

Figure 4. Effect curve of d and n values on current-voltage gain.

Figure 4. Effect curve of d and n values on current-voltage gain.

According to the influence curve of d value and n value on current-voltage gain, it can be seen that voltage gain and current gain change dramatically near ω=1. With the increase of d value, voltage gain and current gain increase, and decrease with the increase of n value, and when ω > 1, the smaller n or the larger d value, the more gradual the change of voltage and current gain.

2.2. Design of LCC Resonator Parameters

Ignoring the loss in the power transmission of the LCC resonant converter, the resonant current peak I_r is obtained from the power conservation, which is expressed as:

$$I_{\mathrm{r}}=\frac{2\pi V_{\mathrm{i}}{G}_I^2}{Q_{\mathrm{L}}^2{R}_{\mathrm{L}}\cos \phi }$$

(12)

Where, φ represents the impedance Angle.

The characteristic curve of resonant current peak I_r affected by capacitance ratio A, quality factor Q_L, impedance Angle φ and input voltage V_i is shown in Figure 5. It can be seen from the characteristic curve that when the converter current gain, load and input voltage are constant, the smaller the φ is, the smaller the value of Ir is, and the smaller the current stress of the switching tube is. Only by ensuring φ > 0 can the ZVS conduction of the MOS tube be ensured, and sufficient margin is often left in the actual selection, generally within the range of 15° < φ < 30°. At the same time, too small quality factor and capacitance ratio will cause the resonant current peak to be too large, and the increase of input voltage will also cause the resonant current to increase.

Figure 5. Resonant current peak characteristics.

Figure 5. Resonant current peak characteristics.

In order to obtain more accurate parameters of the resonant network, reduce the current stress of the resonant components, and ensure that the resonant converter can achieve ZVS conduction, the following parameter design steps are given:

(1) The peak range of resonant current is determined according to input voltage, output power and output current;

(2) Select the appropriate resonant frequency and operating frequency range;

(3) The quality factor and capacitance ratio are determined according to the resonant current peak range;

(4) The transformer ratio n is calculated according to formula (13).

$$n=\frac{G_v{\sin }^2(\frac{\theta }{2})}{2\cos \phi }$$

(13)

In formula (13), θ represents the conduction Angle of the rectifier tube.

(5) Finally, the LCC resonator parameters are calculated by formulas (14)-(16).

Series resonant capacitance:

$$C_{\mathrm{s}}=\frac{\sqrt{1+A}}{2\pi n^2{f}_{\mathrm{r}}{Q}_{\mathrm{L}}{\mathrm{R}}_{\mathrm{e}}}$$

(14)

Parallel resonant capacitance:

$$C_{\mathrm{p}}^{’}=n^2{C}_{\mathrm{s}}/\mathrm{A}$$

(15)

Resonant inductance:

$$L_{\mathrm{r}}=\frac{1}{{(2\pi f_{\mathrm{r}})}^2}\frac{A+1}{C_{\mathrm{p}}}$$

(16)

3. Power System Control Strategy and Algorithm Analysis

Figure 6. Variable frequency phase shifting compound control strategy structure.

Figure 6. Variable frequency phase shifting compound control strategy structure.

Figure 7. Linear active disturbance rejection current loop control algorithm.

Figure 7. Linear active disturbance rejection current loop control algorithm.

4. Simulation and Test Results

Figure 8. Prototype test platform.

Figure 8. Prototype test platform.

4.1. Constant Current Characteristic Test of Semiconductor Laser Power Supply

The simulation and test results of the constant current (40A) characteristics of the semiconductor laser power supply are shown in Figure 9, where V_gs and V_ds are respectively the drive voltage and the drain-source voltage of the MOS tube, V_ab is the input voltage of the resonant network, I_r is the resonant current, and V_cp is the shunt capacitor voltage. It can be seen from the simulation and test results that the variable frequency phase-shift composite control method extends the input voltage/output power range of the LCC resonant converter by synchronously adjusting the switching frequency and duty ratio, narifies the switching frequency range, and effectively reduces the current and voltage stress of the switching tube. The output current ripple coefficient is < 0.8%, and the output voltage ripple coefficient is < 0.45%. It can realize ZVS conduction under any power input voltage, effectively reduce the loss of power tube, and improve the performance of LCC resonant converter.

Figure 9. Simulation and experimental results of constant current characteristics of semiconductor laser power supply.

Figure 9. Simulation and experimental results of constant current characteristics of semiconductor laser power supply.

4.2. Experiment on Anti-Interference Characteristics of Semiconductor Laser Power Supply

The simulation and test results of anti-interference characteristics of semiconductor laser power supply are shown in Figure 10. When t=0.02~0.03s, the input voltage V_in=60V changes to V_in=80V, and when t=0.04~ 0.05s, the load switches from full load to light load. According to the simulation and test results, the output current of the PID algorithm has a fast response speed, a large overjump, a large error and a large current ripple. When the input voltage or load is transformed, the ripple of the current and voltage increase and the current and voltage remain at the set value. Therefore, the LADRC algorithm has a good performance in anti-interference.

Figure 10. Simulation and experimental results of anti-jamming characteristics of semiconductor laser power supply.

Figure 10. Simulation and experimental results of anti-jamming characteristics of semiconductor laser power supply.

4.3. Power Efficiency Characteristic Test of Semiconductor Laser

The simulation and test outcomes of the semiconductor laser power supply efficiency, as illustrated in Figure 11, reveal that the conventional frequency conversion control exhibits limited output adjustment capability and stability, leading to an overall low power supply efficiency. Consequently, only traditional phase shift control and composite control with frequency conversion phase shift are subjected to testing and analysis. Based on the simulation and test results, various control strategies yield differing power efficiencies; specifically, the phase-shifting control strategy induces hard switching states in the converter switch, thereby increasing switching losses and reactive power losses of the resonant converter. By implementing inverter phase-shifting compound control under full load conditions, a maximum power supply efficiency of 92% can be achieved concurrently with superior constant current characteristics.

Figure 11. Simulation and experimental results of power efficiency of semiconductor laser.

Figure 11. Simulation and experimental results of power efficiency of semiconductor laser.

5. Conclusions

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