Controller Design of a Novel Interleaved Parallel Bi-Directional DC-DC Converter

To improve the dynamic performance of the output voltage of the new interleaved shunt bi-directional DC-DC converter, a double closed-loop control method of voltage and current based on fuzzy PI control is proposed. Firstly, based on the study of the operating principle and steady-state performance of the new interleaved parallel DC-DC converter, a small-signal mathematical model of the interleaved parallel bidirectional DC-DC converter with different modes is established, and based on the model, the transfer functions from duty cycle to output voltage and inductor current are derived, and accordingly, the double-closed-loop controller of the bidirectional DC-DC converter is designed. Then the design method of the fuzzy PI controller is described in detail, and the fuzzy control is applied to the voltage outer loop of the double closed-loop control so that the system can adjust the PI parameters in real time. Simulation experiments are carried out by Matlab/Simulink to compare the simulation experimental waveforms using fuzzy PI control and conventional PI control, and it is verified that the fuzzy PI control improves the output voltage response speed of the new interleaved shunt bi-directional DC-DC converter, reduces the voltage peak of the system, and reduces the overshoot.


Introduction
The interleaved parallel technique applied to the bidirectional DC converter can not only reduce the input and output current ripples, and improve the dynamic response capability of the converter and the power converter efficiency, but also effectively reduce the voltage and current stresses of the switching devices.Yangbo Zhang et al. [1][2][3] applied the fuzzy PID control method to different modes of the converter, which improved the stability and adaptive ability of the controller.Still, the response speed of the converter was slow.Renxi Gong et al. [4] have proposed a fuzzy PI control method for the conventional interleaved shunt bidirectional DC-DC converter with improved particle swarm algorithm optimisation to address the problem of poor dynamics of the fuzzy PI control of bidirectional DC-DC converter.However, although the traditional structure of the parallel interleaved bidirectional DC-DC is simple and reliable, there are some drawbacks.Aiming at the shortcomings of the traditional interleaved parallel DC-DC converter, Zhiguo Lu et al. [5] proposed a new type of interleaved parallel bi-directional DC-DC converter based on the traditional interleaved parallel DC-DC converter.Xiandong Chen [6][7] modelled and analysed this novel converter and verified experimentally that it can meet the requirements of an electric vehicle composite energy storage system.
On this basis, this paper designs a voltage-current double closed-loop control method based on fuzzy PI control for the optimal control problem of a new parallel interleaved bidirectional DC-DC converter.In Section II, the pair of converter operating modes is analysed and small-signal modelling is carried out.Then the basic principles of the fuzzy PI control system and the design process are described in Section III.Finally, simulation experiments are carried out by Matlab/Simulink to compare the experimental results of the conventional PI controller and the fuzzy PI controller: the output voltage of the converter under the control of the control method rises at a faster rate, reduces the voltage peak value of the system and the overshooting amount, and verifies the effectiveness of the proposed control method.

Novel Interleaved Parallel Bi-Directional DC-DC Topology
The conventional parallel interleaved bi-directional DC-DC converter is shown in figure 1, and [5] proposes a class of interleaved parallel bi-directional DC-DC converter as shown in figure 2, which adds a switched capacitor Cf, replaces one of the phase switching tubes, and connects the replaced switching tubes in series with the interleaved parallel structure to the conventional parallel interleaved bi-directional DC-DC converter.Thus, the new topology not only has the characteristics of the interleaved parallel converter, such as low input current ripple and easy electromagnetic interference (EMI) design, but also has the advantages of a large input-to-output ratio and low switching-tube voltage stress, and a switched capacitor is added to give it a self-averaging characteristic.
The control method adopts interleaved control so that the drive signals of the two converters differ by half a cycle.The modulation signals and current waveforms are shown in figure 3, in which d is the duty cycle; Ts is the switching period; iL1 and iLf are the inductor currents of the two branches, respectively; and iL is the sum of the inductor currents of the two circuits.Such a modulation method reduces the switching tubes' current stress and ripple compared to a single converter.The converter has two working modes: buck and boost.For example, when the bi-directional DC-DC converter is applied in the energy storage system, Ub is the battery side and the load is the DC bus side.When the converter works in Boost mode, its main function is to provide energy for the DC bus terminal on the right side of the energy storage system to maintain the stability of the DC bus voltage, at this time, the body diodes of the switching tubes S1, Sf1 and switching tubes S2, Sf2 are working.When it works in the Buck mode, its purpose is to feed the excess energy on the DC bus side back to the battery side for charging the battery, to achieve the purpose of a bidirectional energy flow.Currently, the body diodes of the switching tubes S2, Sf2, and switching tubes S1, and Sf1 are working.

Small-signal Modelling of the Converter
When the converter satisfies the low-frequency assumption, the small ripple assumption and the smallsignal assumption, the state-space averaging method is used for modelling, which can simplify the nonlinear state equation of the system into a linear AC small-signal equation.The Boost mode is used as an example to establish the small-signal model of the system, and its small-signal equation can be expressed as: Where: L1, Lf are the inductance of the two branches, H; C0 is the capacitance of the output side, F; D' is the steady-state duty cycle of the switching device; V0 is the steady-state voltage of the output side, V; IL1, ILf is the steady-state inductance current of each branch, A; RESR is the load resistance, Ω.
To simplify the theoretical analysis, the influence of parasitic parameters of switching elements is ignored, and it is assumed that the voltage at the two ends of the switching capacitor is constant when the switching tube duty cycle phase adopts the independent voltage source, independent current source and ideal transformer equivalence, and the small-signal equivalent model of the converter in Boost mode d is established as shown in the figure.From the small-signal equivalent model of the converter, it is known that the output voltage to control variable transfer function under Boost operation Gvd(s) in equation ( 2).The equation ( 3) is the transfer function of the input current to the control variable Gid(s).

Structure of Fuzzy PI Controller
In this study, fuzzy control is applied to the voltage outer of double closed-loop control, and the PI parameters in the voltage outer loop PI controller are adjusted in real time by fuzzy control.The control block diagram of the fuzzy PI controller designed in the article is shown in figure 6, where e is the voltage error, ec is the rate of change of the voltage error, Ke, and Kec are the quantisation factors, and KUP, and KUI are the proportionality factors, the proportionality-integral gains of the adjusted PI controller are 0 0 Among them: KP 0 , KI 0 is the initial value of the PI parameter; ∆KP and ∆KI are the adjustment amount generated by the fuzzy control; KP and KI are the PI parameters adjusted by the fuzzy controller.

Fuzzification of Input Variables
Fuzzy PI control differs from conventional PID in that it fuzzifies the error and error variation into subsets, each with a degree of affiliation function describing the degree of affiliation.More subsets usually work better, but they also increase the complexity and difficulty of implementation, and the affiliation function needs to take into account the distribution of the variables.
In the designed fuzzy controller, the inputs and outputs of fuzzy inference use normalised theories.The theories are all set to [-3, 3].Its fuzzy variable language is {NB, NM, NS, ZE, PS, PM, PB}, which corresponds to the meanings of negative large, negative medium, negative small, zero, positive small, positive medium, and positive large.Since the range of the input deviation value and its rate of change, and the output PI parameter regulation amount is not [-3, 3], the input quantisation factor and output scaling factor need to be determined according to the actual range.

Design of Fuzzy Rule Base
Too large a value of e will lead to a slow response of the system, and the initial value of e will produce a large amount of overshooting; but too large a proportionality coefficient will make the system have a large overshooting, and produce oscillation, so that the stability of the deterioration of the integral action will also produce a large amount of overshooting, should take a smaller value of KI.When e begins to gradually reduce from the initial larger value, the KP value should be appropriately reduced, KI value should be appropriately increased.When e decreases to a certain value, the larger values of KP and KI should be taken to avoid the steady state error being too large and affecting the control effect.According to the above rules, the design ∆KP and ∆KI fuzzy control rule table are shown in table 1.

Simulation Verification
To verify the correctness and effectiveness of the control strategy proposed above, the interleaved parallel bi-directional DC-DC converter is controlled using the control method proposed in this paper, and the simulation analysis is carried out in Matlab/Simulink.In Boost mode, the DC input voltage of the low-voltage side is 100 V, the rated power of the converter is 2 kW, the rated current is 5 A, the inductor current ripple is within 20%, the capacitor voltage ripple is within 1%, and the switching frequency is 160 kHz.The two-phase inductance value of the converter is calculated to be 0.6 mH, the output-side capacitance value is 180 uF, and the switching capacitance Cf is 180 uF.Duty cycle D = 0.75, then the DC output voltage of the highvoltage side is 400 V.The simulation results obtained are shown in figure 7.  When using conventional PI control, the rise time for the output voltage to reach 400 V for the first time is about 9.12ms, the peak value of the voltage waveform is about 430.8 V, the peak time is about 18ms, and the steady state time to reach ±3 V is about 70ms; while using fuzzy PI control, the rise time of the output voltage is about 8.83ms, the peak value is 420.1 V, the peak time is 16ms, and the steady state time is 65ms.The output voltage rise time of the system under fuzzy PI control is reduced by 3.2%, the overshoot is reduced by 2.6%, and the steady state time is reduced by 7.1%, the rise is faster, the overshoot is smaller, and the steady state is reached faster.
In Buck mode, the DC input voltage at the high voltage side is 400 V, the output voltage at the low voltage side is 100 V, and the rest of the parameters are the same as in Boost mode.The simulation results are shown in figure 8.By comparison, it can be seen that: when the conventional PI control is used, the rise time for the output voltage to reach 100 V for the first time is about 1.13 ms, the peak value of the voltage waveform is about 111.0 V, the peak time is about 1.86 ms, and the time to reach the steady state is about 4.87 ms; whereas, when the fuzzy PI control is used, the rise time for the output voltage is about 1.11 ms, the peak value is about 100.7 V, the peak time is about 1.41ms, and the steady state time is 3.19ms.The output voltage rise time of the system under fuzzy PI control is reduced by 1.8%, the overshoot is reduced by 10.3%, and the steady state time is reduced by 34.7%.

Conclusion
There is a poor dynamic effect of the bidirectional DC-DC converter in the conventional double closed-loop PI control.In order to achieve accurate control of this new two-phase interleaved parallel bidirectional DC-DC converter, a control strategy based on voltage-current double closed-loop fuzzy control is proposed, the small-signal model of the converter is analysed and established, the structural model of the fuzzy PI control is determined, and a detailed and effective rule-base structure is established.It is verified through simulation that, compared with the output voltage waveforms of conventional PI control, the proposed fuzzy control strategy accelerates the rising speed of the voltage in the buck and boost modes of the converter, reduces the peak value of the system voltage, decreases the amount of overshooting, and improves the comprehensive control performance of the system to achieve the optimal control of the system.The experimental results show that the control strategy improves the voltage dynamic performance of the converter, but in the future, other optimization algorithms can be added on the basis of fuzzy PI control, such as combining the fuzzy control with the particle swarm algorithm and self-resistant perturbation control, to improve the system's anti-jamming ability, and to further optimize the control effect of the system, and the response speed of the control system is faster so that the converter shows strong stability and robustness.The system can be used in applications requiring bidirectional transmission and conversion of electric energy.

Figure 4 .
Figure 4. Frequency domain small signal model of the converter in Boost mode.

3 .
Design of PI ControllerAccording to the above mathematical model of the parallel interleaved bidirectional DC-DC converter, the voltage-current double closed-loop controller of the converter is designed.The basic control strategy of the controller is the voltage outer loop, two current inner loops control, in which each branch has a current loop.The control system frame is shown in the figure.5.The reference current of the controller's current loop is obtained from the voltage loop after PI control, and the reference value is the sum of the two-phase inductor current reference values; each phase inductor current reference value is half of this reference value.

Figure 6 .
Figure 6.Block diagram of fuzzy PI control.

Figure 7 .
Figure 7.Comparison of output voltage in Boost mode.

Figure 8 .
Figure 8.Comparison of output voltage in Buck mode.