A State Space Modeling of Non-Isolated Bidirectional DC-DC Converter with Active Switch ()

J. Barsana Banu^{}, M. Balasingh Moses^{}

Department of Electrical and Electronics Engineering, Anna University, Trichirapalli, India.

**DOI: **10.4236/cs.2016.74018
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Department of Electrical and Electronics Engineering, Anna University, Trichirapalli, India.

In this paper, analysis, design and implementation of non-isolated soft-switching bidirectional DC-DC converter with an active switch are described. The proposed topology gives the output voltage as twice as the input voltage and enhances the efficiency up to 94.5% and 92.9% for boost and buck mode operation by proper selection of the duty cycle. Soft switching can be achieved at both steps up and step down operating modes. Small signal analysis based on state space averaging and transfer functions have been presented in detail for the proposed converter. Finally, the feasibility of the desired converter is confirmed to mat lab simulation and investigational results.

Keywords

Batteries, Bidirectional Power Flow, Mathematical Analysis, Zero Current Switching, Zero Voltage Switching

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Banu, J. and Moses, M. (2016) A State Space Modeling of Non-Isolated Bidirectional DC-DC Converter with Active Switch. *Circuits and Systems*, **7**, 187-197. doi: 10.4236/cs.2016.74018.

Received 9 March 2016; accepted 16 April 2016; published 19 April 2016

1. Introduction

With the advancement in various industrial applications such as battery charged/discharged converters, auxiliary power supplies, fuel cell-based DC-DC converters, the renewable energy system, hybrid electric vehicles and uninterruptible power supplies system bidirectional DC-DC converters have been widely used [1] - [4] . It should be able to provide both higher and lower output voltage than the input voltage. The bidirectional DC-DC converter is mainly divided into the Isolated and Non-Isolated topology. Among the various topologies of full bridge isolated bidirectional DC-DC converter (IBDC), the transformer-based DC-DC converter is a very familiar one which comprises of two bridges separated by an isolation transformer, and it produces conduction losses due to a number of power switches. Later IBDC with the fly back and RCD snubbers, active clamp, and some simple auxiliary circuits are developed to improve the power conversion ratio as well as reduces voltage and current stresses, but still they need a complex control circuit separately to achieve soft start-up capability [5] - [9] . Resonant based isolated DC-DC converter also proposed to regulate voltage gain in [10] [11] . Nowadays the focus of non-isolated bidirectional DC-DC converter (NIBDC) is getting increased because of simple structure, low cost, the less number of power switches and easy control than isolated bidirectional DC-DC converter topologies [12] - [14] to achieve high efficiency. Conventional NIBDC suffers from hard switching due to power losses and electromagnetic interference which decreases the efficiency. Therefore, the diode reverse recovery problem is analyzed [15] to improve the soft switching range of bidirectional converter by appropriate selection of snubber capacitor otherwise; it causes electromagnetic interference and probability of circuit damage due to heavy current spikes. Series resonance, parallel resonance, and quasi-resonance methods have also progressed to alleviate the reverse recovery problem in the conventional NIBDC.

PWM based zero voltage transition of the bidirectional buck-boost converter is implemented to achieve high efficiency and it requires coupled inductor and the minimum of four semiconductor switches [16] . Cascading the buck and boost converter through coupled inductor is introduced [17] [18] to minimize the ripple current, but it needs more than one input source. Non-isolated DC-DC converter with voltage multiplier cell is presented to achieve soft switching in [19] , but it is unsuitable for step-down operation. To overcome the above drawbacks, passive elements (inductance and Capacitance) LC series resonant tanks are connected in addition to the basic structure are proposed in [20] to achieve maximum efficiency at all load conditions. Soft-switching DC-DC converter with auxiliary switch control is proposed to improve the efficiency of the non-isolated bidirectional converter with lookup table reference [21] this method brings more efficient control in both step-up and step- down mode operation.

In this paper, non-dissipative LCD clamp with an active switch bidirectional DC-DC converter is introduced to achieve maximum efficiency, reduces switching losses by zero voltage turn on and turn off of all semiconductor switches and applicable to high power conversion. This non-dissipative LCD snubber recycles the energy absorbed from either input or output side, and it circulates throughout the switching period. The advantages of the proposed converter topology are high reliability, simple structure, low cost and high efficiency. With these characteristics, power can be exchanged from the input voltage source to the output DC battery and vice versa happens with maximum efficiency.

This paper is ordered as follows in Section 2, the proposed converter with configuration is presented, a small signal matrix model and its transfer function are obtained in Section 2.1, simulation results have appeared in Section 3, experimental results and its discussions have appeared in Section 4.

2. Proposed Topology

The proposed non-isolated bidirectional DC-DC converter with an active switch in addition with passive elements is shown in Figure 1. The proposed circuit consists of two main switches S_{1}, S_{2} and one active switch S_{a}, input side inductor L_{m}, Resonant inductor L_{r}, Snubber inductor L_{s}, Snubber Capacitor C_{s}, Resonant Capacitors C_{r}, and Output side Capacitor C_{0}, and the Diode D_{in} addition with a basic bidirectional DC-DC converter topology.

Figure 1. Proposed non-isolated topology with an active switch.

RCD snubber is a dissipative one which dissipates a large amount of energy stored in the capacitor through the resistance. Hence, it increases the component volume and generates heat transfer troubles. The proposed non- dissipative LCD clamp with passive components eliminates the above problems by storing the leakage energy into a capacitor even the power switches is in OFF condition. The active switch in the proposed topology reduces switching losses with the help of zero voltage turn on and turns off. The proposed technique is categorized into two kinds of conversion; boost mode conversion (step up) and buck mode conversion (step down) based on the current flowing through each component in a proposed circuit and voltage across the switches.

In boost mode, main switch S_{1}, The active switch S_{a} are controlled and the anti parallel diode of S_{2} operated to shift power from low voltage input side to the high voltage output side (batteries), whereas in buck mode vice versa operation takes place i.e. switches S_{2} and S_{a}, anti parallel diode of S_{1} tends to operate to exchange power from output high voltage side to the input low voltage side. Inductances L_{m} and L_{r} are generally used for filtering. The resonance of the proposed model is caused by the main inductor Lm and snubber capacitors C_{s}. The proposed LCD clamp to recycle the energy absorbed from either input or output side, and it circulates throughout the switching period and soft switching can be achieved. The proposed topology remains operated in continuous conduction mode during boost mode and buck mode conversion.

To intend the converter design, a theoretical investigation must be indomitable. The main aim of the steady state analysis is to obtain the transfer function of the proposed converter with the help of differential equations for various devices used in the circuit. The steady state modeling is an appropriate method that can be carried out to illustrate the relation between input and the output side of the proposed DC-DC converter with a matrix model.

The assumptions are

・ Input inductor L_{m} is considered as large;

・ All the devices are ideal and assumed to be negligible voltage drops.

Steady State Modeling

Consider the state variables,

・ Input voltage V_{L}

・ Magnetizing Inductor current iL_{m}

・ Resonant Inductor current iL_{r}

・ Snubber capacitor voltage V_{Cs}

・ Output voltage V_{C}_{0}

・ Duty cycles d

For simplicity, ideal assumptions are, V_{cs} = V_{c}_{r} and iL_{m} = iL_{s}

The state space equations at state 1 (Boost Mode) are given below.

When the switch S_{1} and S_{a} are ON,

(1)

(2)

(3)

(4)

When switch S_{1} is OFF,

(5)

(6)

(7)

(8)

Applying the state-space averaging method for the above Equations (1)-(8), state equations become over a switching cycle.

(9)

(10)

(11)

(12)

Next, Introducing perturbation in state variables such that

where is a small AC variation in duty ratio, And are small AC variations in magnetizing iductor

current and resonant Inductor current. Similarly, and are small AC variations in snubber capacitor

and output voltage.

(13)

(14)

(15)

(16)

Equate AC and DC quantities for Equations (13)-(16). Consider AC quantity only for small signal analysis, DC quantities in the above Equations (13)-(16) are neglected.

(17)

(18)

(19)

(20)

The output transfer function can be obtained either by building and simplified the linearized block diagram or by the matrix model. For constructing a matrix?Small signal model, the Equations (17)-(20) are arranged in symmetrical sequence after taking Laplace transformation. In matrix form, the equations can be written as,

(21)

(22)

From Equation (21) inverse matrix can be determined to obtain a control output converter transfer function. The Equation (22) represents the steady state control (duty cycle) to output transfer function of the proposed NIBDC converter boost mode. Similarly, control to output current transfer function derived for buck mode. Bode plot for the derived transfer function for boost and buck modes are shown in Figure 2 and Figure 3.

Figure 2. Proposed control to output bode plot-boost mode.

Figure 3. Proposed control to output bode plot-buck mode.

3. Simulation Results

The whole circuit is simulated using MATLAB software and following the results is obtained for the proposed non isolated bidirectional DC-DC converter with active switch during boost and buck modes. Then the results obtain from the proposed topology is compared with the conventional simple non isolated bidirectional DC-DC converter without any additional switch and auxiliary circuits to verify its feasibility.

Figure 4 shows the input (50 V) and output voltage for the boost conversion. It is evident that the output voltage obtained is twice than the given input. Gate pulse, current flow through and voltages across the main switch S_{1} are shown in Figure 5. It is clearly noticed that switch S_{1} are turned on and off at zero voltage. Input and output voltage for buck mode is illustrated in Figure 6.

Similarly, the voltage across S_{2} and the current through it in buck mode is observed in Figure 7. So switching losses in the conventional NIBDC is eliminated. Therefore, the proposed NIBDC improves the efficiency by >5% from the conventional converter in boost and buck modes.

Figure 4. Input and output voltage for boost mode.

Figure 5. Triggering pulse, current through and voltage across switch S_{1}.

Figure 6. Input and output voltage for buck mode.

Figure 7. Triggering pulse, current through and voltage across switch S_{2}.

Comparative Results

Figure 8 and Figure 9 illustrate the efficiency comparison of the boost and buck mode with a conventional converter that is a simple non isolated bidirectional DC-DC converter for various input voltages. Which implies the proposed topology achieves high efficiency nearly from 86.2% to 94.4% for boost conversion and for buck mode it improves from 86.6% to 92.9% successfully. Similarly, the output power comparison of boost and buck mode is done in Figure 10 and Figure 11, which shows that proposed topology gives more output power than conventional NIBDC for the same input voltages given.

Figure 8. Efficiency comparison of boost mode.

Figure 9. Efficiency comparison of buck mode.

Figure 10. Output power comparison of boost mode.

Figure 11. Output power comparison of buck mode.

4. Hardware Results and Discussion

In order to confirms the feasibility of the proposed topology. A 0.5 KW converter model was built and implemented with PIC Microcontroller and driver circuits to obtain the same results as discussed in Section 3. The experimental setup is depicted in Figure 12.

The input voltage of the given prototype for boost mode is 50 V and obtains 100 V as output it is twice than the given input voltage and vice versa for buck mode is observed. The operating power of the converter is 500 W and its switching frequency is considered as 100 kHz. For all the three power switches S_{1}, S_{2} and S_{a} IRF840 are employed and IN 4007 diode is used. L_{r} and C_{r} are designed as 40 mH and 80 nF. L_{m} and L_{s} values are 450 mH and 4 mH respectively. The values of C_{s} and C_{0} are 18 nF and 47 µF. The switching pulse and voltage waveforms for both the buck and boost modes are measured. The gate pulse and voltage across the switches are also observed to verify its effectiveness.

The triggering pulses for the boost mode switch S_{1} and active switch S_{a} is observed in Figure 13. During boost conversion S_{2} remains OFF state. The switching pulse and zero crossing voltage across the switches S_{1} and S_{2} are indicated in Figure 14 and Figure 16. It is noted that switches are turned ON and OFF at zero voltage. The triggering pulses for the buck mode switch S_{2} and active switch S_{a} is measured in Figure 15.

Figure 12. Experimental set up.

Figure 13. Triggering pulses for S_{1} and S_{a} during boost mode.

Figure 14. Experimental results of the switching pulse and voltage across S_{1} of the proposed boost mode.

Figure 15. Triggering pulses for S_{2} and S_{a} during buck mode.

Figure 16. Experimental results of the switching pulse and voltage across S_{2} of the proposed buck mode.

5. Conclusion

In this paper, non-isolated bidirectional DC-DC converter with active switch suitable for battery charging/dis- charging application is proposed with high efficiency up to 94.5% and 92.9% for boost and buck mode operation as compared to conventional topologies. The proposed topology is analyzed by state-space averaging technique and its transfer function is derived. The zero voltage turns on and turns off, and the switches are obtained in simulation and experimental waveforms. From the above results, the performance of the proposed converter with active switch achieves higher efficiency than the conventional NIBDC is verified.

Conflicts of Interest

The authors declare no conflicts of interest.

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