Power flow management of triple active bridge for fuel cell applications

Received Nov 23, 2018 Revised Jan 22, 2019 Accepted Mar 3, 2019 The power conditioning circuits which are used in fuel cell systems should carefully be designed to prolong the life span of the system, for the reason of the dynamic nature, such that the unexpected and extreme changes in load decreases the life of the fuel cells. This paper presents the triple active bridge (TAB) and its average small signal modelling, which is used for design of the system controllers for stable operation. The extended symmetrical optimum method is used for realized the proportional integral (PI) controller, to control the output/Load voltage and power flow in the fuel cell/Source with a guaranteed minimum phase margin for the system with a variable process gain in addition to other accepted desired performances. This method ensures the maximum phase margin at a minimum required value at the desired gain crossover frequency with a compromise between system’s peak overshoot, rise time and settling time. This model and this approach helps in designing TAB suitable for healthy and uninterrupted fuel cell power generation systems as a part of a renewable /clean energy system. MATLAB/Simulink is used to simulate the proposed controllers with TAB.


INTRODUCTION
Recently, demand for the renewable or clean energy systems, due to the global warming and acid rains [1]. At present different types of electrical energy generation systems are available for both portable and residential applications. But one of the most favorable alternatives stays as the fuel cell, which provide energy with no pollution or environment degradation [2]. In addition, it's provide predictable amounts of instantaneous energy, which is not possible with other energy generation systems. When a fuel cell as an energy generation system for the load/grid it should connected to the storage system like battery or supercapacitors [3,4], which stores energy when in excess and delivers it on demand to sustain the load/grid stability to increase the fuel cell life span [5][6][7]. Therefore, power electronic interfaces are used to isolated the fuel cell with the load/grid, while an additional storage device is commonly adopted to supply power in transient conditions [8][9][10]. In such systems, when storing and retrieving the energy, the power conditioning circuits are involved as an integral part of the system [11,12].
Since the dual active bridge (DAB) topology [13,14], and proposed TAB employing a three winding transformer with high frequency [15][16][17], as shown in Figure 1. The transformer not simply merge and interchanges energy from/to all the ports, although also matches the different voltage levels and offers the full isolation between all the ports [18][19][20]. A power flow be able to accomplish bi-directionally by varying the phase shift of the AC voltages produced through full-bridge cell from respective ports. In this storage (Supercapacitors) system behave as a power filter to soft the flow of the power in source (Fuel Cell), and equal to average load power noticed, toward to select the limits of primary source for the whole system, no need to inspect the peak power [21,22]. In this paper proposes the modelling, controlling, and simulation of the power conditioning circuit, and an optimization technique for the topology illustrated in Figure 1 with the purpose of power flow management with the overall system losses should be minimized, where ensured circulating power within the DC-DC converter equals to zero. In addition, the average small signal model and the related controllers are developed for TAB. Hence the converter which is identified with Galvanic Isolation, Power Flow in Bidirectional, great Power Density, high Efficiency, and including Zero Voltage Switching (ZVS) capability is a suitable candidate for the DC-DC conversion of low voltage fuel cell power generation system. Furthermore, these systems can also be employed in vehicular technologies [23][24][25][26].

CIRCUIT DESCRIPTION
The TAB topology as shown in Figure 1 have a fuel cell as source for the system with full bridge (BFC) cell, which converts an alternating voltage v1 from the DC voltage Vfc, this voltage v1 is given to three winding high frequency transformer (TTW), this is connected to another two full bridge cells with Load (BLOAD) port, and storage (BSC) port, here storage as supercapacitors, this full bridges are functioning with DC feeding voltages to load port and from/to the supercapacitors port. The voltages and are rectified by full-bridges of BLOAD and BSC, respectively. TAB is the heart of the system, it provides the interface between the source to inverter load, and storage device. It should match the specific requirements of the overall system, for instant, galvanic isolation, bi-directional power flow, ability to equivalent dissimilar voltages, and quick response to fulfill the fleeting demand from the load. Figure 1, shown the recommended the TAB, with the voltage levels of port 1, and 3 are low voltage buses 50V and 48V respectively, and port 2 is high voltage bus 400V. Here, representation of voltages from full bridge cells are , , and along 50% duty cycle, to govern the power flow. All the parameters and variables are taken from equivalent circuits shown in figure 2, variables of port-2 and port-3 are referred to the primary side bridge (BFC), and as follows L2 = /n2, V2 = /n2 , u2 = /n2, i2 = .n2 for port 2 and L3 = /n3, V3 = /n3 , u3 = /n3, i3 = .n3 for port 3. Where and are the DC voltage levels of the port 2, and 3, and currents i1, , and are belongs to the leakage inductance. Here, transformer magnetizing inductance (Lm) is not conceder for this modeling. And transformer has two important functions, such as it is provide electrical isolation between all three buses and its can be harmonized the dissimilar voltage levels by selecting suitable turns ratios in the respective winding. The converter power flow is not depending on the port voltages but it is dependent on phase displacement between the any of the two bridges, here the control signal phase shifts are symbolized as ϕ12 which is the square wave voltage sources u1 and u2 generated by two full-bridge cells at Port-1 and 2, and ϕ13 symbolized the phase displacement between u1 and u3 as shown in figure 3. And ϕ12 and ϕ13 are denoted positive value when u1 is leading to u2 and/or leading to u3. Equivalent circuit of the transformer, which make things easier for the power flow analysis with help of Y and Δ-type circuit was projected in [27] . In this equivalent circuit, the voltages u1, u2, and u3 signifies the voltages produced through bridges BFC, BLOAD, and BSC respectively, and the leakage inductances are expressed in terms of inductances L12, L13, L23. To define the converter power flow, the fundamental system becomes three square-wave voltage sources with help of equivalent model, and a grid of inductors are exchange the sources energy throughout the system. The phase shifted by ∅ and ∅ in voltages and with respect to the v1, respectively. The phase displacement is negative, when the output voltage leads the reference (source) voltage and or else it is positive. The inductors in figure 3 is based on a Δ-model illustration and inductors network is extracted from the transformer of the system [27].  A TAB, as extension of the dual active bridge (DAB) circuit [28], so it shows the patterns of three two port circuits, the inductive network with voltage and current waves at transformer windings with respect to the bridge phase displacement and power transferred in the whole system to be express in [28][29][30]. With the delta-model, the power delivered by each port equivalent to integration of the power flows over any of the two related branches (inductors). For lossless converter system, they are Where P1 = PFC power delivered by port 1, P 2 = -PLoad power supplied by port 2, (negative sign means the load consumes energy) P 3 = PSC power taken from port 3 Therefore, from the above expressions the two phase shifts are chosen for control the total system power flow. In the view of above equations, the maximum power flow through every indictor is at and the absolute value of the phase displacement shall be |∅ | and |∅ | , note it in this case ∅ should be positive for the all instants because we are using the source as fuel cell.

MODELLING OF THE SYSTEM
In this section, firstly shows the modelling of fuel cell, Dual Active Bridge (DAB), by using DAB model resolve the Triple Active Bridge (TAB).

Fuel cell
In the literature so many PEM fuel cell models are described based on the thermodynamic and electrochemical expressions. This model considered with constant hydrogen pressure flow into stack of the fuel cell for dynamic operation. Fuel cell output voltage is expressed as [31] where E -is open circuit fuel cell voltage (Voc) Vact -is activation voltage losses at zero current density (Io) Vconc -is voltage drop due to concentration losses in fuel input Vohm -is voltage drop of Ohmic losses

Dual active bridge (DAB)
The voltage (DC) from the fuel cell is transformed into a square wave voltage with high frequency (non-sinusoidal-AC) at primary winding of the transformer by bridge BFC in port-1. After, converted AC voltage is stepped up to high voltage square wave (non-sinusoidal) at secondary winding (n2) of the transformer by the bridge BLoad at port-2 and stepped down to low voltage square wave (non-sinusoidal) at secondary winding (n3) of the transformer by the bridge BSC at port-3 with a desired phase shift to meet the required load power. The output of the BLoad of Port-2 is a high DC voltage and the BSC port-3 is low voltage.
Thanks to the ∆-model representation as shown in Figure 3, the system evaluation is significantly easy. The TAB system model is fragment to three DAB system models. So from [32][33][34] the averaged model of the DAB is shown in Figure 4

Triple active bridge (TAB)
Thanks to the ∆-model illustration of TAB as shown in figure 3, its make the much easier analysis of the system. The TAB system is split to three DAB. The perfect operating waveform of the converter are demonstrated. Note that according to the operating point waveforms are differ. The state of ZVS for every bridge cell influenced by the current magnitudes of every switching moment. The summarized waveforms of selected operating point is positive currents at the output voltages of bridge cells , , and falling edge and negative currents for the rising edge. For the instant currents in three arms are expressed depending on the above illustration for the reference power, ; ; 6 Based on the modeling of DAB, the linearized small signal average model can be resolved for the TAB. The converter is patterned as three current sources (DC) whose amplitudes are ordered by phase displacement of any of the two bridge cells is shown in Figure 5. Each port current is averaged for one cycle of switching, now represent of the average values iP1, iP2, and iP3 by IP1, IP2, and IP3, correspondingly. Here, the three-port system model only two independent variables are considered for modeling. Therefore, IP3 is redundant. The voltages at each port is considered as stable. Since, by using the power flow expressions (1) and (2), we obtain The current source behaves as nonlinear, so to be linearized at the preferred state for a control oriented model, The dynamics of linearization can be resultant with partial differentiation of the current source functions where ∅ , ∅ is the operating point. The resulting small signal representations are

DESIGN OF THE DUAL-PI
From the Figure 6, output to control model for TAB converter is offered, the cross-coupling technique is used here. The DAB transfer function is represented with H2(s) and H1(s) is the transfer function of the LPF with the gain block "V1" is required since the power is average current times of the voltage at the respective port. The system is considered with two-output and two-input. The Load (output) voltage V2 is controlled by ϕ12, while the power of fuel cell to be regulated by ϕ13. And power P1 is computed from quantities of the voltage (VFC) and the average current (IFC) sensed through a Low Pass Filter (LPF). Now single phase inverter is considered to be as the load, it should be chosen so as to limit the bandwidth below the double line frequency of the load, which permits a same frequency ripple in the DC-bus voltage. A LPF is presented to regulate the frequency of the ripple current extracted from fuel cell. The time constant Tf1 of the LPF is chosen to limit in only a DC current extract from the fuel cell, which is good for the fuel cell membrane.
PI-controller is considered in the system for the stability in the DC-bus voltage under the desired set point. In this design an extended symmetrical optimum method (ESOM) [35] is used in the tuning of the controller.   (15) For the TAB controlled power flow by using the controller variables are ∅ and ∅ . In additional verses, two degrees of freedom are obtainable to control the overall power transitions in the whole system. In this case considered the two PI controllers are linked and impact each other as shown in figure 6. Interaction should be minimized between the control loops in order to assurance of a fast response to variations in load. So, the bandwidth of the control loops should obey the, fuel cell power control loop GPϕ13(s) remains agreed lower than that of the load voltage in output control loop GVϕ12(s). In other words, the control of the power in fuel cell need not to be as fast as the regulation of the output voltage.
Where β-is a parameter chosen between 4 and 16 based on required system performance such as rise time, peak overshoot, and settling time.  The TAB is modeled under small signal modeled, and simulation results are shows in figure 9. There are three major parts in the case of TAB configuration. They are the input bridge, the high frequency transformer and the two output bridges. These bridges are full bridge configuration and are controlled by Phase Shift Modulation with 50% duty cycle. The control signals are generated and applied to the bridges to make the input bridge as the leading bridge and the output bridges are as the lagging bridge to ensure the power from the input to the output. The switching frequency has been selected as 20 kHz keeping the limitations on the magnetic core materials in mind. The waveform ensures the operation of TAB and the input power transfer to the output and depicts the primary voltage, phase and level shifted secondary voltages with their respective currents. The various values assumed in the modeling are shown in table 1. Figure 9. Input and output voltage and currents for load 600 W to 800 W and to 1000 W

CONCLUSION
TAB considered as interface power electronic circuit system for fuel cell applications and average small signal model has been developed for it with help of DAB model. Simulations are done by using MATLAB/Simulink power system block sets. A dual PI controller has been proposed and developed for system stability under the desired output and varies loads using ESOM with DC load variations of 600W to 1000W and 800W as shown in Figure 9, and the maximum ripple in the fuel cell current (Ifc) is found to be nearly 2A, which is within the safe range for fuel cell operation.