Single Phase Power Generation System from Fuel Cell

Received Jun 25, 2018 Revised Sep 13, 2018 Accepted Sep 18, 2018 Power conditioning circuits are required for the fuel cell systems due to its nature in energetic state. This paper proposed the small signal average modelling of a duel active bridge (DAB) DC-DC converter with LC filter, to generate the single phase AC power by using the H1000 fuel cell system. The controller is designed for the stable operation of the system. Implemented the controller, which gives the constant output voltage to DCbus from the DAB DC-DC converter, this DC-bus voltage fed to the inverter, which inverts the DC-bus voltage to single Phase AC power with the LCfilter. The proposed system simulated in the MATLAB/Simulink. Keyword:

bidirectional power flow, and galvanic isolation which is fulfil the low voltage fuel cell power generation system requirements, the topology illustrate in Figure 1 to minimize the overall losses of system, where the futures of zero voltage switching (ZVS) capability, bidirectional power flow and high frequency transformer for galvanic isolation is adapted [9]- [11]. This feature provides the effective conversion of power, small volume and low weight construction. In addition, small signal model for the system, the related control design of the converter and open loop system with resistive and inductive load inverter are developed and also which reduce the cost of the system as well [12].

CIRCUIT DESCRIPTION
Fuel cell systems are generally rated with the power range of 10 W -5kW with the voltage ranges 7.8 V -72 V. Three phase of operational regions were in fuel cell which are activation, Ohmic, and concertation as shown in the polarization curve [13]. The operating point should choose in the Ohmic region from the data sheet of fuel cell to extend the life time. In critical applications such as a single phase AC power generation system with DC-DC converters.
Fuel cell system is connected with two full bridge isolated DC-DC converters as shown in Figure 1, which are connected with high frequency transformer (T f ) and extremal small leakage inductor (L lk ) , the electrolytic capacitor (C i ) as the energy buffer in the primary H-bridge (port-1), to reduce the low frequency current ripple in the input side connected to DC-bus voltage (Vdc) which is connected to a single phase voltage source inverter for the conversion of the DC-AC for the AC loads or Grid connection. In this circuit energy transfer occurs due to the phase shift between the two H-bridges, phase shift(ϕ) modulation is employed to proceed the power from input port-1 to output port-2 is determined by phase angle (ϕ) between the primary winding and secondary winding voltages of the transformer(Tf), that is given the power flow expression as [14].
where V FC -is the fuel cell DC output voltage d -is the voltage transfer ratio referred to primary, L lk -is the leakage inductance of the transformer, Φ -is the phase shift between the bridge gate signals. D voltage must be √2 times of the peak value A voltage required. So the voltage conversion ratio is very high for the medium and high power requirements where the need of isolated DC-DC converter is essential to meet the required voltage level and conventional boost converters cannot be used in such cases. The dual active bridge DC-DC converters which were originally proposed with soft switching is a better topology among others for fuel cell applications.

MODALING OF THE SYSTEM
In the literature so many PEM fuel cell models are reported based in the thermodynamic and electrochemical expressions. The fuel cell model considered with constant hydrogen pressure flow into the fuel cell stacks for dynamic operation. Fuel cell output voltage is expressed as [15].   (2) and based on the polarization cure has been observed that a fuel cell can operated with the linear region while changing the constant internal resistance with respective of output loads. So based on this observation it can be linearized by using the expression below (3), fc fc fc (3) where R fc -is linearized resistance I fc -is fuel cell current So its gives the dynamic operation region of the fuel cell between the lower and upper current limits. The DC voltage from the fuel cell is converted into a high frequency square wave AC voltage(nonsinusoidal) at the primary winding side of the transformer by the H-bridge of port-1. The converted AC voltage is stepped up to high voltage square wave(non-sinusoidal) at secondary winding of the transformer by the H-bridge of port-2 with a desired phase shift to meet the required load power. The output of the Hbridge of Port-2 is a high DC voltage.
As shown in Figure 2 waveforms of the voltage, currents in primary winding and secondary windings of the transformer. The instantaneous value of the primary current at any given instant of "θ" as follows the expressions are, The expression (4) can be deduced to get the values of the current (i p ) in the primary side of the transformer expressed as, Where the first zero crossing point (y) of form Figure 2 is given as The boundary conditions [16] of the H-bridge in the primary winding side voltage(LV) and Hbridge in the secondary winding side voltage(HV) for Zero voltage switching (ZVS) are found to be i p (0) < 0 and i p (ϕ) > respectively. This can be found by substituting i p (0) = 0 and i p (ϕ) , which will ensure a negative current in the LV H-bridge through the diodes clamping the voltage across the switches to be the negligible forward voltage drop across them enabling almost zero voltage at the time of turn ON. Similarly, a positive current in the HV H-bridge makes the diodes conduction ensuring almost zero voltage across the switches at the time of turn ON. During the turn OFF process, the capacitors across the switches store the ON state voltage and enables the ZVS at the time of turn OFF. Which will greatly reduce the switching losses and hence increase the efficiency.
Average power transferred to the load from the fuel cell is expressed below as, Ave Where w lk from the expressions of (1), (4) and (5).
Because of the half wave symmetry of the wave form shown in Figure 2. It gives the average power transfer expression as below Hence the average current can be used for modelling of the DAB, which is a non-linear function of the phase shift ϕ as given below

INVERTER WITH LC-FILTER
The DAB converse low DC-voltage to a high DC-voltage from the fuel cell in order to AC voltage as a part of multistage power converter topology. A switched mode DC-AC inverter is considered for grid or AC load connected fuel cell systems. The magnitude and the frequency of the sinusoidal AC output can be controlled in these inverters. The output of this inverter must be matched with the magnitude, frequency and phase of the specified AC load or grid voltage, which is achievable in this switched mode inverter. The high frequency switching of the pulse width modulation (PWM) inverter results from a nonsinusoidal voltage at the output with high frequency distortions. These non-sinusoidal voltages cause the current to be highly distorted when connected to the load or the grid. An LC-filter made up of inductor L f in series with the load and capacitor C f parallel to the load. t"s possess the advantages of the -filter and Cfilter. Aside from this ripple factor in LC-filter is lower value than that acquire by either one of the both filters (L or C) for the same values. Figure 4 shows the use of the LC-filter for minimizing the ripple from the voltage of a single-phase inverter output. The dominant harmonics are suppress by the filter inductor (L F ) and the Capacitor (C f ) provides a simple way to the harmonic ripple currents [17]- [19]. Where f ris cut-off frequency of LC-filter.

DESIGN OF THE PI-CONTROLLER
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 allows a double line frequency ripple in the voltage of the DC-bus. A low pass filter is introduced to limit the frequency of the ripple current extracted from fuel cell. The time constant T f of the low pass filter 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 voltage of the DC-bus under the desired set point and disturbance variations as shown in the Figure 5. In this design an extended symmetrical optimum method (ESOM) [20] is used in the tuning of the controller. The gain of the open loop system is given below as The cut off frequency w c is choose as 25Hz. The phase margin is 89 o at 32.9Hz of the closed loop system from the bode diagram as shown in the Figure 6(b). This ensures that stable operation of the system within the double line frequency of the inverter load with the safe range of ripple current in the fuel cell.

SIMULATION RESULT
Simulation of the model is done with MATLAB/Simulink by using the power system block sets connected to the two H-bridges with a high frequency transformer for different loads. The constant DC voltage source was chosen with 0.333ohm resistance, which is equal to the dynamic resistance of a 1kW Horizon fuel cell. The simulation was done in two parts, the first part without inverter only resistive loads. The simulation results are shown in Figure 7 for load voltage (V o ) and load current (I o ) with respect to the load changes, input voltage (Vi) and input current (Ii) as the load differs from 200W to 1000W and to 400W. The maximum ripple in the input current (Ii) is occurred 2A when it is connected to full load 1000W, it is safe range for fuel cell. Table 1 gives the simulation parameters.  The second part of the simulation result is shown in Figure 8

CONCLUSION
Dual active bridge DC-DC converter considered as single phase generation system for fuel cell applications and average small signal model has been developed for it. Simulations are done by using MATLAB/Simulink power system block sets. A PI controller has been proposed and developed for system stability under the desired output and varies loads using ESOM with DC load variations of 200W to 1000W and 400W as shown in Figure 7.
Implemented the LC-filter with the DAB to get the sinusoidal voltage as shown in Figures 8 (a) and (b) for different loads by choosing high resistance and low inductance in the AC load to get the maximum power output. This system design can be used for the implication of three port bidirectional dc-dc converter of fuel cell application and use it as single phase AC power generation.