INTRODUCTION

Due to capability of the DAB converter to auto-adjust the power flow in both directions, operate under wide voltage gain ratios and achieve zero-voltage-switching (ZVS), it has been widely used in many applications, including energy storage systems, micro-grids, solid state transformers, power electronic traction transformers and on-board chargers for electrical vehicles [1]. While DAB is a popular technology, there are many challenges to overcome. The high circulating current, which is analogous to reactive power in power system applications, does not participate in the power transfer of the converter. It is simply a heat source that affects the conduction and copper losses and eventually decreases the efficiency of the converter. Loss of ZVS is another issue that impacts the switching loss of the DAB [2]. Numerous modulation methods have been proposed in order to improve the performance of DAB converters. They can mainly be categorized into four techniques based on the degree of control freedom. The most common method is the single phase-shift (SPS), which uses only one control freedom to regulate the output power flow of the DAB [3]. In SPS control, the switch pairs in both full bridges are gated to obtain phase-shifted square waves with 50% duty cycle ratio. Only the phaseshift among the bridges is controlled. Adjusting the phase-shift between the primary and the secondary voltage results in the leakage inductor of the transformer changing to enable power flow direction and magnitude [4]. To increase the control flexibility of the DAB, extended phase-shift (EPS) [5] and dual phase-shift (DPS) [6] modulation schemes have been studied. In the EPS method, the switch pairs in one full bridge are switched with an inner phase-shift ratio. This enables the AC output voltage of one bridge to be a three-level wave while the other one is a two-level 50% square wave [5]. Both methods contain two control variables. In the EPS method, the duty ratio of one full bridge is considered in addition to the phase-shift, while in the DPS method, both full bridges use an inner equal phase-shift ratio in addition to the phase-shift. Comparatively, while both methods maintain the same operating conditions of the two bridges, even while the converter changes power flow direction, the implementation of the DPS is easier than the EPS method. The triple phase-shift (TPS) modulation strategy [7] regulates the duty ratios of the two full bridges and the phase-shift ratio independently. The SPS, EPS and DPS controls are all special cases of TPS. The same power flow can be obtained with different phase-shift and duty cycle values. Therefore, multiple optimization targets have been formed using the optimal TPS variables. In [8], the maximum fundamental active power was considered as the objective function. In [9], the current amplitude of the fundamental component was to be minimized. In [10], the minimum fundamental reactive power is used. In [11]- [13], the minimum current stress was taken into consideration and in [14] and [15] the RMS current was chosen as the objective function to be minimized. While these optimization targets are aimed at improving the overall performance and efficiency of the DAB, the maximum efficiency of the converter is not guaranteed. In order to obtain the maximum efficiency of the DAB, this paper is proposing the overall power loss of the converter as the target function to be minimized. Analyses and simulation studies using MATLAB /Simulink have been carried out to prove the effectiveness of the proposed methodology.

The paper is organized as follows. Section II presents a description of the DAB analysis and its operating power zones. In Section III, particular calculation and analysis of the DAB converter overall power losses are performed, and the manipulated variables to control the required power flow and minimize the DAB converter total power losses for each zones are obtained. The optimization methods and control structure are in Section IV. Section V presents a summary of the simulation results to validate the theoretical proposal.

II. DAB CONVERTER ANALYSIS

The DAB converter and the corresponding switching sequences, key voltages and current waveforms under TPS conditions are shown in Fig. 1, and Fig. 2, respectively. The DAB contains two full bridges, operating as a DC-AC and AC-DC converter connected via a high-frequency transformer. When the TPS control modulation scheme is used to regulate the DAB, the analyses can be divided into six regions. However, for the purpose of calculating the total power loss of the converter, three zones are retained and defined with their respective boundary conditions. In zone 1, which is analogous to the low power region, the power flow follows the following constraint 0≤ D2 ≤ φ ≤ D1 ≤1. Zone 2, which is the connotation for the medium power area, is defined by 0≤ D2 ≤ D1 ≤ φ ≤1. Zone 3 is the high power region with 0 ≤ D1 ≤ D2 ≤ φ ≤1 as the boundary condition. The different zones of operation are depicted in Fig. 3. D1 and D2 are the duty cycles of the first and second converters, respectively, and φ is the phase shift between V1 and V2. The DAB converter efficiency expression will be formulated in terms of the semiconductor and high frequency transformer losses in order to minimize the total power loss. Detailed and accurate analysis of each component of the total loss is presented for each of the three zones.

III. ANALYSIS OF THE DAB CONVERTER POWER LOSSES AND EFFICIENCY

In order to minimize the total power loss, the efficiency of the DAB converter will be formulated in terms of the four main losses: conduction, switching, winding and core losses based on the manipulated variables D1, D2 and φ. Therefore, detailed analyses are carried out for each component of the DAB and for each zone of operation.

A. Semiconductor Power Losses

In the semiconductors, two types of losses are considered for this analysis: conduction and switching. Conduction losses are formulated for each semiconductor device, transistor and diode, based on current and voltage waveforms for each interval, as demonstrated in Fig. 2. Von represents the transistor voltage during on state, Vd is the diode forward voltage drop and ͢ is the current during the conduction intervals. Switching losses are calculated for each switching event, based on Fig. 2. Vx and Vy are the voltages at turn-on and turn-off, respectively. iLpi is the peak current during each switching event, tf is the fall time and Cdev is the snubber capacitor of the transistor. Due to fact that the converter can operate in either hard-switching or soft-switching, the ZVS constraint is established when the il zero crossing is within the time interval where V1 and V2 have opposite polarities. When the converter is operating under soft-switching, only turn-off losses are calculated. When the converter is working under hard-switching, turn-on losses are also considered. Tables I -X summarize the derived expressions for obtaining the switching and conduction losses for each zone of operation.

TABLE IV. ZONE 3 CONDUCTION AND SWITCHING LOSSES

B. Transformer Power Losses

The transformer losses are the total sum of the core and winding losses. To obtain the winding loss, the RMS current is determined and both the skin and proximity effect are considered for calculating Reff. Due to the non-sinusoidal waveform characteristic for the given applications, the Improved Generalized Steinmetz Equation (IGSE) [16] is used to obtain the closed form expression for the core loss. Tables XI -XIV show the derived expressions for the transformer losses. Table XV summarizes the average power expressions for each zones, efficiency and the sum of the winding, core, switching and conduction losses to compute the total power loss for the converter.

IV. OPTIMIZATION METHOD AND CONTROL STRUCTURE

The goal of the optimization is to minimize the total power loss for a given average power. The variables are D1, D2, and φ. The objective function, f, is the total power loss which needs to be minimized and the constraint, g, is the average power the converter should be able to provide. Two optimization methods have been used, the LM and the PSO. Due to the nonlinearity of the system, in certain power regions it is extremely difficult to obtain a closed loop form for the optimal degree of freedom. In such a case, the PSO is utilized to obtain an optimal numerical value for the degree of freedom. This case is also referred to as LO. However, in other power regions it is possible to obtain a closed loop form for the optimal degree of freedom. In this case the LM method is used for the constraint optimization problem of the DAB. This case is also referred to as GO. Contrary to the LO method, the GO method covers multiple target functions, such as peak current stress, RMS current and total power loss. ( ,,,) = ( ,,) + ( ,, )

TABLE XV. TOTAL LOSSES, AVERAGE POWER AND EFFICIENCY OF THE DAB Average Power Transfer Efficiency

The optimal solution of the constraint optimization is described by a set of equations of the gradient of the LM as written in (2) for the DAB. Although ∂Λ/∂λ = 0 is part of ∇Λ = 0, it does not reveal any new information because it is simply the constraint function, g, itself.

For each of the modes and power regions where GO is feasible, as summarized in Table XVI, the corresponding average power transferred and the objective function can be used to obtain the closed form expressions according to (1) and ( 2). This paper covers the case of V1>V2 for all three power regions. Similarly, the case for V1<V2 and V1=V2 can be derived. In zone 2, GO exists; therefore, the closed form expressions for minimizing the power loss can be obtained. For the sake of simplicity, the peak current stress (ilp1) from Tables II, V and VIII is chosen as the objective function and the corresponding average power for zone 2 in Table XV is used. Substituting the per unit expressions as formulated in ( 3) into ( 1) and ( 2) yields the following closed form expressions for D1 and D2 as formulated in (4). The rated values of the power and the peak current are computed as follows:

B. Particle Swarm Optimization Method

The flowchart of the offline PSO technique is presented in Fig. 4. This method is used for obtaining the optimal control variables for zones 1 and 3. The PSO formulation comprises two principal equations, as seen in ( 5) and ( 6), where X is defined as particle positions (TPS variables) and V is the particle velocity that is used to modify the particle position X for every iteration. Pbest is the best remembered individual particle position and Gbest is the best remembered swarm position. k is the iteration index, c1 and c2 are positive constants and r1 and r2 are two randomly generated numbers, such that 0≤ r1, r2≤1 [17].

C. Control Structure

The optimal closed loop control is shown in Fig. 5. This figure depicts the case V1>V2. Similarly, for the other modes of operation the corresponding data can be added based on table XVI. The phase-shift φ1 is generated by a PI controller and is fed into the optimal control variables generation block to estimate the average power transferred from the first bridge to the second bridge. Based on the estimated average power, the operating zone is then determined. The optimal D1opt and D2opt are calculated either from (4) or are chosen from the PSO look up table (LUT). Fig. 6 shows the optimization trajectories for obtaining the optimal degree of freedom: (a) -(d) for zone 3, -(h) for zone 2, (i) -(l) for zone 1.

V. SIMULATION RESULTS

Utilizing the total power loss equation from Table XV, two optimization algorithms can be used. PSO is used when the optimal values that minimize the power loss are different from the optimal values that minimize the RMS or the peak current. The LM is used for obtaining a closed form expression for the optimal degree of freedom when there is an optimal value that minimizes the power loss, the RMS and the peak current simultaneously. The simulation of the DAB was carried out based on Fig. 3. Table XVII summarizes the effectiveness of the control strategy. The simulation results for all three zones are presented in Fig. 7. -9.

Additionally, the SPS is compared to the proposed TPS method in order to validate the effectiveness of the proposed technique. As seen in Table XVII, for the high power zone the efficiency is increased by 0.4% while the RMS current is decreased by 0.5 A. This case can be predicted from Table XVI where it shows for zone 3 only one objective function can be minimized. For the medium power range, the LM method is used to minimized multiple objective functions at the same time. It can be seen that the efficiency is increased by 1.25% and the RMS current is decreased by 16.3 A.

The most significant improvement of the efficiency happens for the low power zone: it is increased by 14.1%. In this zone of operation, the optimal control variables for the maximum efficiency also minimize the RMS current by 36.8 A. While it is expected that RMS current will be lower for the optimum variables for power loss minimization in the low power zone, these are not necessarily the optimum variables for the RMS current.

RMS current can be achieved while compromising the efficiency. Such a case was evaluated in the simulation and the RMS current was further decreased by 40.7 A while the efficiency was increased by 12.7%. As summarized in Table XVII, utilizing the TPS control strategy based on the formulated equations results in an increased efficiency of the converter. The switches parameters were extracted from the C3M0060065J Silicon Carbide Power MOSFET C3M TM MOSFET Technology from CREE.

VI. CONCLUSIONS

This paper presents detailed analyses of obtaining the total power loss utilizing the TPS method resulting in the optimal control and maximum efficiency of the DAB converter. The methodology to calculate the DAB losses (including conduction, switching, winding and core losses) and efficiency was developed for three zones and modes of operation. The buck mode analysis and simulation results are presented for each zone. The analysis and summary of the simulation results from Table XVII demonstrate the effectiveness of the study. It is seen from the results that the efficiency of the converter is greatly improved for zone 1 and 2 by using the proposed method.