Research on CLLLC Resonant Bidirectional DC-DC Converter

Based on the single-phase full-bridge LLC DC-DC converter, the LC series resonant network is introduced in the secondary side of the high frequency transformer to form the bidirectional CLLLC resonant DC-DC converter. Firstly, the bidirectional CLLLC resonant DC-DC converter was used for mathematical modeling. By extending the description function, the large-signal steady-state model of the converter was obtained, and the DC voltage gain when the DC-DC converter was running forward was deduced. The gain characteristics and frequency characteristics of the model are compared with those of the basic wave equivalent model. Secondly, the small-signal perturbation model of CLLLC DC-DC converter is modeled, and the small-signal perturbation is brought into the large-signal steady-state solution to obtain the transfer function when the CLLLC resonant converter is running forward. Finally, a 20kW CLLLC DC-DC converter is designed, and the simulation analysis is carried out to verify the correctness of the proposed scheme.


Introduction
With the increasing demand for natural resources in society, the active exploration of renewable energy is the most effective method to solve the energy crisis in view of the shortage of primary energy [1][2][3].New energy technology is becoming the main force to promote the development of renewable energy [4].In order to solve the energy problem, the bidirectional isolation DC-DC converter has a wide application prospect in the fields of distributed energy generation, micro-grid, DC distribution network, electric vehicle and uninterrupted power supply system [5]. Isolated bidirectional DC-DC converter can realize the bidirectional flow of energy. At present, a relatively mature (Dual Active Bridge, DAB) topology consists of two H-bridges and a high-frequency isolation transformer [6]. However, the voltage gain range of the dual active bridge structure is narrow, and when the voltage of the input end and the output end do not match, the ZVS characteristic will be lost and large back-flow power will be generated, which reduces the efficiency [7]. On this basis, a series of bidirectional full-bridge resonant DC-DC converters have evolved [8][9]. According to the number of resonant cavity components of the resonant converter, it is mainly divided into two components: series resonant SRC and parallel resonant PRC resonant converters; LCC and LLC Three-element Resonant Converter [10]; CLLC and LLCL Four-element Resonant Converter [11]; CLLLC five-element resonant converter [12].The two-element resonant and three-element resonant structures are asymmetrical, and when the energy flows in the opposite direction, the operating characteristics and soft switching characteristics are different, so the design of control strategy and resonance parameters is more  [13].A resonant inductor or capacitor is added to the secondary side of the three-element resonant cavity transformer to form the four-element resonant symmetric converter. The symmetric topology can ensure that the converter has the characteristics of LLC soft switching when it is running in both the forward and reverse directions [14]. In this paper, CLLLC resonant converter is taken as the research object. Based on the LLC converter, a series LC resonant slot is added on the secondary side of the high frequency transformer and its resonant parameters are designed and symmetrical with those on the primary side, forming a two-way LLC resonant topology [15]. Literature [16] introduces the working process of CLLLC resonant converter. Forward and reverse operation is similar to full-bridge LLC converter operation state.

Operating principle of CLLLC resonant converter
The topology of the CLLLC resonant converter is shown in Figure 1, which can be divided into two parts. The four IGBTs at the front stage constitute the inverter unit, and the four IGBTs at the rear stage constitute the rectification unit. When the resonance parameters design, will rank after the resonant inductor design for 2 = 1 / 2 , 2 = 2 1 ,where n variable than for transformer, make CLLLC converter topology is completely symmetrical. Figure 1. Topology of bi-directional CLLLC resonant converter When the CLLLC resonant converter is running forward, the primary side is the high voltage side, the switch tube 1~4 switch tube is supplemented with complementary drive signals, and the latter stage is rectified through the body diode of the switch tube. When the secondary side is the reverse operation of the low-voltage side, the switch tube 1~4 switch tube is supplemented with complementary drive signals, and the rectifier side is uncontrolled rectifier, which can realize the bidirectional transmission of energy [17]。Sf literature [18] in converter work frequency and the relationship between the size of the resonance frequency points will be resonant converter is divided into three kinds of working state and: < owe resonance state; = quasi resonant state; > harmonic state three work modes. Literature [19] points out that in order to obtain the maximum voltage gain, the converter generally operates in under resonant or quasi-resonant state by setting the resonant parameters of the multi-pass pair. At present, the main analysis method of resonant converter is the fundamental wave approximation FHA method, which is only used in the analysis near the resonant frequency. When the converter's working frequency is offset, FHA method has a large error [20]. Literature [21] analyzed the resonant converter in time domain by using the method of synchronous PWM fixed frequency and duty cycle adjustment, but the PWM modulation method has a small variable voltage gain and is not suitable for wide voltage gain. The Particle Swarm Optimization (PSO) algorithm in Literature [22] is used to model the LLC converter, but the PSO algorithm is too complex to be suitable for practical application.

Mathematical modeling of CLLLC resonant converter
The state space averaging method is usually used to analyze the resonant converter with PWM control mode. In order to obtain wider voltage gain and further reduce switching loss, the CLLLC resonant converter adopts PFM pulse frequency modulation. The use of PFM frequency conversion control no longer meets the premise of PWM modulation small ripple hypothesis, and the state-space average method is no longer applicable to frequency conversion control [23]. Literature [24] proposes a control method of equivalent circuit model, but its working process for resonant converter is complicated, and the forward and reverse operation transfer function cannot be obtained. In Literature [25], the extended description function method was used to model and analyze the LLC converter. In this paper, the extended description function is used to analyze the large-signal steady-state model of the bidirectional CLLLC resonant converter, and on this basis, the small-signal model of the CLLLC resonant converter is established and the resonant cavity parameters are designed and calculated [26]. It is assumed that the waveform of the resonant cavity element is approximately sinusoidal and the IGBT switch tube is an ideal device. The influence of parasitic capacitance is very small and does not affect the normal state of the resonant frequency operating point.

Establishment of Stat
The input voltage in V can be equivalent to the high-frequency square-wave AC voltage at the output end of the full-bridge inverter circuit through the filter capacitor. The square wave voltage with the same amplitude as the input voltage is used to replace the input voltage of the resonator in the equivalent circuit. The rectifier side is replaced by a controlled voltage source. Its equivalent model is shown in Figure 2: controlled current source, output equivalent resistance as the eq R , output filter capacitor of series resistance. According to Kirchhoff's voltage and current law, the nonlinear state of the CLLLC resonant converter is as follows:

Extended Harmonic Approximation Analysis
When the CLLLC resonant converter works, the switching angular frequency is set as, and the current flowing through the resonant element and the voltage of the resonant element are approximately sine waves. According to the theory of frequency modulation signal, when the resonant converter is disturbed, the input square wave voltage of the resonant tank can be represented by the superposition of a timevarying amplitude sine signal and cosine signal during the adjustment of the system. According to the extension function theory, the resonant element voltage Derivation of nonlinear variables in (2) is taken and the harmonic approximate state expression of nonlinear variables is obtained by sorting out:

Establishment of Extended Description Functions
By the state of the (1)

Parameter design of CLLLC resonant converter
The resonant cavity parameters of the CLLLC resonant converter are designed by the fundamental equivalent circuit. The following steps are taken: (1) Determine the input and output indexes; (2) Select the resonant frequency at work; (3) Calculate the transformer ratio and resonant element values; (4) Analyze the voltage gain curve where, d V is the pressure drop of the switch tube. Calculation of equivalent load electric and reflection resistance at the output end: Minimum and maximum operating frequency range of the converter: The calculated resonant element parameters are as follows: represents no-load DC gain. In order to obtain greater voltage gain, the actual operating frequency of the converter should be less than the resonant frequency. On the premise of satisfying ZVS and ZCS, try to choose the quality factor with larger gain. Normalized frequency n f , namely, the ratio between series resonant inductor 1 L and excitation inductor m L , should not be too large, and n f generally takes a value of 2.5-6.

Small signal perturbation model analysis of CLLLC resonant converter
Assuming that CLLLC is in stable operation state, the transfer function of small signal model is deduced by adding small signal perturbation to large signal model. The small signal perturbation of CLLLC resonant converter can be expressed as 1 The small signal perturbation is brought into the steady-state solution of the large signal, and the influence of the infinite small amount is ignored, and the small signal model of the CLLLC resonant converter is obtained, namely: The small-signal model of the output voltage obtained by sorting out the above of state is: The frequency is taken as the input variable and the output variable as the voltage disturbance small signal. The design parameters of CLLLC are substituted into the small-signal model expression, and the above small-signal model is expanded to obtain the transfer function of the influence of switching frequency on voltage:

Simulation verification
The calculated resonant parameters were simulated under the PSIM simulation software when the CLLLC resonant converter was running forward. The resonant frequency was set as 10kHz, and the simulation results were shown in Figure 6  As can be seen from Figure 6, the output voltage of the inverter side 1 p V is 50% duty cycle, 1000V highfrequency square wave voltage, through the resonator and the output voltage of the high-frequency transformer, is a high-frequency sine wave. Figure 7 is a schematic diagram of the resonant current. The current is in phase with the output voltage of the resonator, which ensures the soft switching characteristics and reduces eddy current loss. When the CLLLC resonant converter is running forward, the rated output voltage is shown in Figure8, and the voltage can finally stabilize at 380V.The results are consistent with the above calculation results, which verifies the correctness of the design

Conclusion
In this paper, the extended description function method is used to establish the large-signal steady-state model of the forward operation of CLLLC, and the small-signal perturbation is added to the steady-state solution of the large-signal model to obtain the small-signal model of the CLLLC resonant converter. Mathcad software was used to compare the voltage gain and the gain of the equivalent model of fundamental wave, and the application of the extended description function method was verified. The resonant cavity design of 20kW/1000V/380VCLLLC resonant converter is completed, and the forward operation of CLLLC is simulated and verified by PSIM simulation software. The simulation results show that the model and the design parameters are correct, which provides a new idea for the practical application of CLLLC resonant converter and the design of feedback compensator.