Comparative Study of Controllers for an Isolated Full Bridge Boost Converter Topology in Fuel Cell Applications

Received Apr 16, 2018 Revised Jul 17, 2018 Accepted Jul 19, 2018 Now a day’s renewable energy sources became an interesting area of research of which fuel cells are emerged as an alternative source for producing electricity to meet the energy crisis. This led to a research on power conditioning systems through which fuel cell is interfaced to the utility. Of the different converter topologies Isolated full bridge boost converter (IFBC) topology is most suitable for fuel cell applications. In this paper a Predictive Switching Modulator (PSM) Control is proposed for the converter topology and its performance is compared with Linear Peak Current Mode control (LPCM), Non-Linear Carrier Control (NLC). Keyword:


INTRODUCTION
Now a day's renewable energy sources became an important area of research because of increase in energy demand, depletion of fossil fuel reserves, environmental pollution etc. Many alternative energy sources have been proposed in the literature of which fuel cells have emerged as a most efficient alternative energy source because of its advantages like refuel ability, producing very low emissions, portable in size, little maintenance etc. In spite of these benefits the price of fuel cell is its main constraint [1]- [2].
Fuel cell is an electro chemical device which gives electricity by combining hydrogen and oxygen without any combustion producing water and heat. These fuel cells show large change in output voltage under variable load conditions and also produce voltage very low in magnitude. To interface these fuel cells to utility loads or grid this low voltage must be raised to high value suitable for utility. Therefore high step up converters are required to interconnect fuel cells to utility loads.
Many models of DC-DC converters are mentioned in the previous survey papers which are acceptable for fuel cell applications. From the suggested topologies in the literature [3]- [5] Isolated Full Bridge Boost DC-DC converter topology is most efficient and acceptable for fuel cell applications. The main advantages of isolated full bridge topology are possibility of applying soft switching techniques, reasonable device voltage ratings, less transistor voltage and current stress, possibility of connecting devices in parallel to achieve desired power levels and high efficiency and galvanic isolation.
Under varying load and varying input voltage conditions DC-DC converters should provide regulated DC output voltage. Changes in time, temperature, pressure etc changes the values of the converter components. Applying of negative feedback in the form of a closed loop, regulation of DC voltage can be achieved. So the next task in designing a power conditioning system is developing a best controller meeting the requirements suitable for fuel cell applications.

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Basically there are two types of controllers, Voltage control and current control. Vast majority of DC-DC converters are implemented using current mode controllers because of its advantages [6]- [9]. Figure  1 shows the basic implementation diagram of current control.

Figure 1. Block Diagram of Current Mode Control
Here the output stage is fed by the inductor current and the error voltage output from the error amplifier (known as control voltage) controls it. This has an extreme effect on a dynamic behaviour of the negative feedback control loop. Peak current control, average current control, non-linear carrier control are some of the techniques using this approach [10], [11].
In the linear peak current control (LPCM) peak switching current has to be sensed and therefore the sensing devices needed are more. In non-linear carrier current control (NLC) three reset integrators are needed to generate the carrier waveform. The NLC controlled converter results in distorted input current waveform in discontinuous conduction mode of operation.
To overcome the problems in LPCM and NLC controllers another control known as Predictive switching modulator control (PSM) [12], [13] is proposed where only two reset integrators are used when compared to NLC. Also PSM control extends the range of continuous conduction mode as prediction of off state ripple current is possible which is added to on state actual current at the end of switching period.
In this paper an isolated full bridge boost dc-dc converter topology is taken and first open loop configuration simulation is done using simulink. Next three types of controllers linear peak current mode control (LPCM), Non Linear Carrier control (NLC) and Predictive switching mode control (PSM) are applied to the converter topology. Finally the simulated results of all the three controllers are analysed and the proposed PSM control is compared with existing LPCM and NLC controllers.

ISOLATED FULL BRIDGE BOOST CONVERTER TOPOLOGY (IFBC) 2.1. Basic Converter Operation
In this section complete working of the converter is presented. Figure 2 shows the circuit diagram of the chosen converter topology and Figure 3 shows the performance of the converter according to the modes of operation.

Small Signal Modelling of IFBC Using Average State Space
Many modelling techniques for the DC-DC converters are suggested in [14]- [18]. The converter can be modelled by state space averaging technique using following steps:  Obtain state equations for each state (switch closed/open).  Average the state equations in one switching period.  The average equations thus obtained are perturbed thereby the variables have a DC and AC component.  Next by applying Laplace Transform and excluding additional AC and DC terms (only the first order AC terms) the transfer functions needed can be achieved. The modelled equations are simplified by taking some presumptions  Ideal switches having no parasitic effect.  No resistance for inductor  Isolated transformer used is ideal and has no leakage, magnetizing inductance.  Filter capacitor in output having less equivalent series resistance is assumed and it can be disregarded.  Constant load  Starting conditions are taken as zero at the time of operation.

State Equations
As seen in previous section operation of IFBC has two main intervals and their identical circuit diagrams are as shown in Figure 4. (1) This interval continues for (d-0.5)T where T=1/f is the on period and d= is the effectual duty ratio and n is the turns ratio of the isolated transformer.
Interval 2: In this the switches M1 and M2 are on. The differential relations of state variables for this interval are written as follows Y= This interval continues for (1-d)T. The state equation for output in both the operations is same as (7). On averaging the state equations acquired during half of the switching cycle, a relation which has the features of both the modes is obtained The state equations are perturbed about their operating points. The resulted relations are used for getting the necessary transfer functions In matrix form the equations (14) and (15) are written as (16) [ For obtaining transfer functions auxiliary AC and DC terms are avoided. The Laplace transform to the relations (14) and (15) is applied and the following transfer functions are obtained Equation (18) is the control gain transfer function of IFBC and can be used for controlling of the converter.

OPEN LOOP SIMULATION AND RESULTS
The converter taken is constructed and simulated in MATLAB simulink in open loop configuration as in Figure 5. The design parameters of the topology are as given in Table 1. The output voltage of IFBC with and without load changes is as shown in Figure 6.   Figure 6. Output Voltage of IFBC with and without load change

IFBC WITH LPCM AND NLC CONTROLLERS 4.1. Operation of LPCM and NLC Control Topology
These types of controllers are based on current control mode theory. In this control mainly the inductor is transformed into a current source thereby removing the inductor performance in the loop. A set value for current is provided by the controller and the loop inside follows this value in each cycle and hence this control can also be called as one cycle control. Why this control is called as linear peak current control because, the peak value of the inductor current obeys the set value and the linear relation between the current and off duty cycle ratio. Generally this control has two loops. One is the voltage loop outside which has an error amplifier that counteracts the dynamic response of the output voltage and second is a current loop inside that gives compact control on peak inductor current. Sensing of output voltage in this technique can be from a feedback network and the two voltages (reference and output) are compared in a comparator for obtaining the control voltage. The feedback network impedance is much greater than that of the load. Then the inductor current sensed and the control voltage are compared in the modulator to calculate the duty ratio which is then changed to output voltage by the power stage. Inherent sub harmonic oscillations lead to stability problem when the duty ratio of the switches crosses 50% and noise susceptibility. This can soon reset the latch; interrupt the performance of the controller. Therefore the sensed switch current waveform is needed to be filtered by little amount so that the turn on current spike can be discarded which is effected by the diode stored charge. To overcome this adding an substitute ramp for the controller makes better the noise immunity of the circuit. So generally to keep away from the instability problem, the control scheme is altered by addition of an artificial ramp to the sensed inductor current waveform [19]- [21] but the result is it increases circuit complexity.
So to make the control scheme easy an approach known as quasi-steady-state is generally used. With this technique, a simple equation is solved in the modulator and thereby the duty ratio of switch is obtained. The equation consists of the sensed current (i.e. the switch current average for the NLC) on one side and opposite side is carrier wave obtained by computing the result of voltage regulator.
The main difference between NLC and LPCM controllers is by producing a proper carrier, the NLC controller executes average current control in contrast the peak current controller produces a distinct wave in order to apply the actual concept of peak current mode control. Figure 7 shows the Schematic form of representation of the LPCM and NLC controllers.
where is peak inductor current. This current in one switching period goes to its peak at when the switch reaches to the end of on time d .

IFBC WITH PREDICTIVE SWITCHING MODULATOR CONTROL (PSM) 5.1. Operation Of Psm Control Topology
This control topology is mentioned in [22]. Inductor current evaluated is made proportional to the input voltage at the end of the switching period (T) by controlling the switch duty ratio. Over a period of switching the inductor current evaluation is feasible as the input voltage is nearly sustained. Therefore estimation of ripple current in the subsequent off period throughout the switch on time is possible. Now to control to the current the estimated off state ripple current is added with the on state actual current at the end of the switching period. Figure 12 shows schematic form of operation of PSM control. The first objective i.e. attaining the control gain transfer function of the IFBC was done in section 2.2 and is given by equation (18).

Low Frequency Small Signal Model of the Converter for PSM
Here to derive the model, variables are indicated by capital letters (nominal as well as DC) and small-signal variations are shown by (^) above the symbol. The control formation of the current mode controller is as shown in Figure 13. First the converter model is derived in normal forms with reference to perturbations of duty ratio. The modulator small signal model is acquired eventually in and substitute ̂ by the perturbations in error amplifier output voltage ̂ and other state variables ̂ and ̂. The relations of state space average model of the IFBC are given by (16).
The duty ratio of the period is produced by using the inductor current and the output voltage in the modulator according to (22) where is the resistance from which the inductor current is sensed. The steady state duty ratio can be derived (is the positive real root and less than 1) by solving equation (13).It can be developed by using equation (12) and the equations = (1-d) and 〈 〉 * + * + * + * + Perturbing equation (23) and linearizing the quantities subsequently i.e. D=D+ ̂, ̂, ̂ and ̂ to derive small signal model of PSM as shown below Let us define a constant N as follows Rewriting (16) The systematic model which is acquired is justifiable only at input -output and load condition when the IFBC continues to operate in continuous conduction mode. At last a closed loop controller can now be constructed for the outer voltage loop depending on the control transfer function given by equation (27) by using the normal method mentioned in linear control theory. Now the frequency response of the voltage error amplifier can be drawn by using this.

Boost Compensator Design in PSM Control
Now in this section a closed loop boost compensator can be constructed depending on the model given by equation (27). The schematic form is shown in Figure 14. The transfer function of the boost compensator is given by equation (18)   (28) where where A is positive and < . As there is a pole at the origin, the phase of starts with -90º. The existence of the zero yields a "boost" to be something greater than -90º. Finally he pole at causes the phase angle of to come back down to -90º.

Designing of Boost Compensator
The specifications in equation (18) can be designed using K-factor approach [23]- [25]. The step by step design process of the suggested closed loop boost compensator PSM controller is described as below.
STEP 1: Find out the cross over frequency . The K-factor is utilised such that (29) K can be defined as

SIMULATION RESULTS WITH CONTROLLERS
The open loop IFBC constructed is simulated in MATLAB simulink applying three controllers. Figure 17 shows the output voltage of the converter with the controllers for step change of load.  Table 2 shows the performance analysis of the IFBC converter topology with LPCM, NLC and PSM controllers. It shows that PSM controller gives better transient response and steady state stability.

CONCLUSION
In this paper an Isolated Full Bridge Boost Converter used for fuel cell applications was presented and implemented in closed loop configuration. The detailed modelling of the converter topology was also presented. The IFBC topology was constructed for three types of controllers i.e. LPCM, NLC and PSM and comparison of the three controllers was observed and presented. The obtained results show that the proposed PSM controller gives good transient and steady state stability performance compared to LPCM and NLC controllers as the peak overshoot, rise time and settling time of PSM are reduced during load changes. Further the PSM controller extends the continuous conduction mode of converter which will reduce the size of EMI and the problem of using three integrators in NLC is also eliminated by using only two in PSM.