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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 45, 2015 

A publication of 

 
The Italian Association 

of Chemical Engineering 

www.aidic.it/cet 
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Sharifah Rafidah Wan Alwi, Jun Yow Yong, Xia Liu  

Copyright © 2015, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-36-5; ISSN 2283-9216 DOI: 10.3303/CET1545185 

 

Please cite this article as: Ghosh P.C., Bandyopadhyay S., Krishnapriya G.S., Sharan P., 2015, Design space approach for 

storage sizing of hydrogen fuel cell systems through pinch analysis, Chemical Engineering Transactions, 45, 1105-1110  

DOI:10.3303/CET1545185 

1105 

Design Space Approach for Storage Sizing of Hydrogen 

Fuel Cell Systems through Pinch Analysis 

Prakash Chandra Ghosh*, Santanu Bandyopadhyay, Govindankutty Sreelatha 

Krishnapriya, Prashant Sharan 

Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India 

pcghosh@iitb.ac.in 

Fuel cell based systems can be used effectively to supply electricity to an isolated power system. With 

variations in electricity demand, fuel cell as well as the reformer operates in part load condition and a 

buffer storage tank is provided to cater to this fluctuating. Efficiency of a reformer deteriorates with part 

load operations. On the other hand, efficiency of a fuel cell improves during part load operations. It is 

important to size the buffer tank properly to improve overall system performance. The primary objective of 

this work is to optimize reformer size and storage volume for a given load profile. In this paper, a 

methodology, based on the principles of Pinch Analysis, is proposed by dividing the entire load cycle into 

several time intervals. The net energy balance in every interval is calculated and various design 

constraints, such as the turndown ratio of the reformer, electricity demand, and no wastage of hydrogen, 

are imposed. Set of all feasible configurations of the overall system, known as the design space, is 

identified on a graphical representation between reformer size and storage volume. In addition a sensitivity 

analysis is also carried to understand the variation of design space with variations in turn down ratio. 

1. Introduction 

Increasing fuel cost, depleting fossil fuel, and stringent environmental laws necessitate researchers to 

develop cleaner and efficient energy systems. Fuel cell based systems can be used effectively for 

transportation as well as for isolated energy systems. Among different types of fuel cells, Polymer 

Electrolyte fuel cell (PEFC) is considered to be the most promising candidate for such applications. 

Generation of hydrogen from the fossil fuel through reforming process is considered as short-term solution 

to meet the hydrogen demand for such applications. Hydrogen is produced mainly by steam reforming, 

partial oxidation, and auto-thermal reforming. The maximum reforming efficiency occurs at thermo-nuclear 

point (Ahmed and Krumpelt, 2001). Dutta (2013) carried out a review on various methods to produce and 

store hydrogen. Mori and Hirose (2009) talked about the various method how to store hydrogen for fuel 

cell vehicle and found an increase in 2.5 times in storage volume for metal hydride tank in comparison to 

high pressure tank. Oosthuizen et al., (2009) studied the performance of an autothermal reformer 

numerically for use in a fuel cell powered auxiliary power unit for transport applications. Ravey et al., 

(2015) developed a control strategy for fuel cell electric vehicle with hybrid tank. Ampelli et al. (2012) 

developed sensors for safety purpose for fuel cell transportation. Beside the cost efficiency another 

important field of research is sizing of the overall system. Several researchers have adopted different 

methodology for sizing the storage such as economic criteria which includes levelized cost of energy 

(LCE) (Paliwal et al., 2014),net present value (Ghosh, 2003), and annualized cost (Yang et al., 2008). 

Vosen and Keller (1999) found that the cost of storing energy is minimum for battery-hydrogen storage 

system in comparison to only battery storage and only hydrogen storage. Sopena et al. (2006) carried out 

a study to estimate the design parameter for feeding the fuel cell with 5 kW. Verhasselt et al. (2014) 

designed and tested 1.2 kW fuel cell vehicle.  

Pinch Analysis is another important optimisation method used in several system sizing problems. Kulkarni 

et al. (2007) applied the concept of Pinch Analysis for sizing solar thermal system and Arun et al. (2009), 



 

 

1106 

 
applied it for sizing photovoltaic-battery system. Pinch Analysis is also explored for wind – battery systems 

(Roy et al., 2009) and photovoltaic-thermal (PVT) systems by Krishna Priya et al. (2013).  

In present work, design space methodology, developed based on the principles of Pinch Analysis, is 

adopted for optimizing the reformer size and hydrogen storage for a known electrical load profile. The 

choice of reformer and storage sizes influence the overall system cost. 

2. System description 

For present study a reformer based fuel cell system is considered (Figure 1). The system consists of a 

reformer to produce hydrogen, a fuel cell to produce electricity to supply the load. A buffer storage tank is 

also incorporated in the system to cater a fluctuating hydrogen demand from fuel cell due to variable 

electrical load. It should be noted that the efficiency of a fuel cell varies with the load to be supplied. It has 

the unique characteristic of having higher efficiencies at part load than full load. Present study essentially 

aims in sizing of hydrogen generator (reformer) and storage tank for a given electrical load profile. 

 

 

Figure 1: Block diagram of hydrogen fuel cell system 

3. Methodology 

The proposed system is modelled considering the discretization of the entire cycle of operation into ‘n’ 

equal time intervals. The mismatch between the supply and demand mainly influences the stored energy 

(St) and it can be estimated for i
th 

interval as follows, 

   ( )
i i i

St g l i  (1) 

Here, gi is the generation from the reformer and li is the hydrogen demand by the fuel cell.  

The state of the stored energy level at the end of i
th
 interval is given by, 


   

( 1)i i i
St St St i  (2) 

It should be noted that the storage energy level must always be a positive quantity and can be expressed 

mathematically as follows: 

 0
i

St i  (3) 

Moreover, for the system to be at autonomous, the energy level of storage at the beginning and end of a 

cycle must be the equal, i.e., 

 


( 0) ( )i i n
St St  (4) 

In addition, the energy generated during each interval should be a non-negative quantity and maximum 

generation cannot exceed the rating of the reformer. 

 0
i

g i  (5) 

 
i ref

g g i  (6) 

The value of cumulative hydrogen generation must be equal to or greater than the cumulative hydrogen 

demand during entire cycle can be expressed mathematically as, 

 
0 0

i i

i i
g l  (7) 

FUEL RE-FORMER FUEL CELL LOAD 

STORAGE 



 

 

1107 

The point at which the cumulative hydrogen production touches the cumulative hydrogen demand, is 

referred as Pinch Point. The storage capacity is estimated as: 

 max( );0
i

St i n  (8) 

3.1 Limit imposed by load constraint. 

For a known load profile and reformer size, Eq(1), Eq(2), Eq(7) and Eq(8) facilitate estimating the storage 

size. The variation in the storage requirement is illustrated by the dotted line in Figure 2.It should be noted 

that for any reformer size less than the average load, the net energy generated in a cycle is less than the 

total energy required. This means that irrespective of the initial level of storage, the system can never 

ensure the autonomy in the system, as the final amount of energy in storage is always be less than the 

initial value. Thus, the constraint given by Eq(4) can never be satisfied and it is represented by the 

infeasible region-I in the Figure 2. For any reformer rating that is greater than the peak demand, storage is 

unnecessary as the reformer is capable of meeting the hydrogen demand. For any value of reformer size 

between these two limits, a minimum storage size is needed to ensure the autonomy of the system as 

illustrated by dotted curve in the Figure 2. It can be seen that as reformer size increases, storage needed 

decreases. This is very similar to the design space obtained for a PV battery system by Arun et al. (2009). 

As a PV battery system and a reformer–storage system are very similar in configuration, this trend is 

expected. In the region below the storage curve denoted by dotted line in the Figure 2, though enough 

energy is being generated by the reformer, the storage is not sufficient to store and meet the energy 

demand. This makes region-II also infeasible as far as the autonomy is concerned. Along the curve 

bordering regions-II and III, the size of reformer and storage are such that all the energy generated by the 

reformer is either used to meet the load directly or stored. No energy is wasted. In region-III, which lies 

above the curve, for any given storage volume, the reformer is oversized. This means that for any 

configuration in region-III, the storage size is overrated ensuring the autonomy of the system utilizing the 

entire hydrogen generated by the reformer. 

Figure 2: Design space for a hydrogen system 

3.2 Constraint due to reformer’s turndown ratio 
Often, in addition to the constraints mentioned in the last section, an additional constraint arising from the 

technical capabilities of the reformer known as turndown ratio, may be required to impose in the sizing of 

the system. Turndown ratio refers to the window of the operational range of the reformer, and is defined as 

the ratio of the minimum capacity to the maximum capacity. Hence, the inclusion of the turndown ratio in 

the system can be expressed mathematically as follows: 

 
mini

g g i  (9) 

Here, the minimum value, gmin refers to the minimum hydrogen generation capability considering the 

turndown ratio, ftd and is given by Eq(10), where Preformer refers to the rating of the reformer. 

 
min reformer td

g P f
 (10) 

Introduction of the turndown constrain in the estimation process, imposes limit in the minimum operating 

power of the reformer. In such a situation, the design space is altered accordingly as shown in Figure 2. 

The storage curve is altered in such a way providing local minima for a particular value of the reformer 

Feasible region – III(H2 wastage) 

 

 

In
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 I

 

(I
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g

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 (Insufficient storage) 

Feasible region - I 
(H2 wastage) 

 

Design space 

Reformer size 

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1108 

 
size. The value of the local minima depends on the turndown ratio. It can be seen that upto a certain value 

of reformer size, the value of minimum storage volume is the same as before. In these regions, since the 

reformer size in on the lower side, the reformer must already be operating at or above the minimum value 

constraint. Beyond the minimum storage point, however, the storage volume has to be increased so that 

the excess energy generated due to turndown ratio, can be stored to avoid the wastage of hydrogen. The 

region under design space offers a set of configurations capable of ensuring autonomous system without 

any excess generation of hydrogen. In feasible region-I, the reformer is forced to operate at the minimum 

power partly during operation when the demand is less and the storage capacity is insufficient to store the 

hydrogen casing some amount of hydrogen wastage to maintain the autonomous status of the system. In 

the feasible region-II, the minimum hydrogen generation capacity of the reformer due to turndown ratio 

becomes higher than the average hydrogen demand in the system. As a result of that a finite amount of 

hydrogen must be produced and wasted in every cycle of the operation so that the autonomy of the 

system is maintained following Eq(4). 

4. Illustrative example 

In this section, the methodology of design space using Pinch Analysis is applied to meet the daily electrical 

demand with a profile as illustrated in Figure 3. The average daily electrical energy requirement is 5 kW 

with peak demand of 10 kW and base load of 2 kW. Since, the efficiency of the fuel cells depends on the 

load and it increases at partial load, the varying efficiency is considered for the estimation as shown in the 

Figure 3. The variation in daily hydrogen demand by the fuel cell from the reformer/storage is estimated 

based on the electrical load and the fuel cell efficiency as shown in Figure 3. The average energy 

requirement is around 10.2 kWh/d and the peak requirement is around 22.22 kWh. 

The optimum energy required for the system is estimated following the methodology explained in the 

previous section. The estimations of the storage size for three different sizes of reformer with two different 

turndown ratios are shown in Figure 4. In this figure, the cumulative plot of hydrogen generation by the 

reformer, hydrogen demand by the fuel cell and meeting point of these two curves refer to the Pinch Point, 

i.e. at this point the hydrogen generation is just sufficient to satisfy the hydrogen demand. So the storage 

requirement at this point is zero. Basically Pinch Point signifies a point at which driving force is minimum 

(zero in this case). The demand curve cannot go beyond this point, (as the storage cannot be negative).  

The cumulative mismatch between the hydrogen generation and the demand is referred as Grand 

Composite Curve (GCC), which falls to zero at a reformer size corresponding to the Pinch Point. The 

storage capacity is determined from GCC based on the Pinch Point on the plot. It is seen that when the 

reformer capacity is equal to the average load (10.17 kW in this example) a storage capacity of 36 % of 

the total daily hydrogen demand It should be noted that no turndown constrain of the reformer is imposed 

during the sizing of the storage as mentioned above. The variation in system behaviour with a turndown 

ratio of 0 % and 40 % is presented in Figure 4. Here, the reformer size is considered to be 16.67 kW (75 % 

of peak load). It is observed that the requirement of the storage size is increases with the introduction of 

the turndown ratio. 

It is observed that the storage size is increased from 10 % to 16 % in a system with minimum reformer size 

having a turndown ratio of 40 %.The variation in the storage requirement with reformer size is shown in 

Figure 5. It represents the variation in the storage size for different turndown ratio of the reformer. From 

the figure it is clear that the storage requirement decreases monotonously with the increase in the reformer 

size. However, with the inclusion of the turndown ratio constrain in the estimation of the storage size, a 

local minima is observed. In other words, for every reformer size there is a specific turndown ratio. 

 



 

 

1109 

 

Figure 3: Daily behaviour of the load profile, H2 demand and corresponding fuel cell efficiency 

Reformer turndown ratio=0% 

 

Reformer turndown ratio=40% 

 

Figure 4: System behaviour with a turndown ratio 

 

Figure 5: Design Space with variation in turndown ratio. 

0

10

20

30

40

50

60

70

0

4

8

12

16

20

24

1 3 5 7 9 11 13 15 17 19 21 23

F
u

e
l 
c
e

ll
 e

ff
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c
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 (

%
) 

P
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r 
(k

W
),

 E
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rg

y
 (

k
W

h
) 

Time (h) 

Electrical power H2 demand Efficiency

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S
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H
2
 d

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a
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d
) 

Reformer size (fraction of peak demand) 

30 % 

20 

40 

50 

60 
70 80 

90 % 

0 % 



 

 

1110 

 
5. Conclusion 

In this paper, a design space method based on Pinch Analysis is applied successfully to size a hydrogen 

storage supported reformer based fuel cell system. In order to do so, a hydrogen fuel cell system is 

studied and a mathematical formulation is done considering various constraints involved in sizing such a 

system. It is observed that for a given load profile, the size of the reformer must at least be equal to the 

average load. Also, the size of the storage decreases monotonously with the increase in the reformer size. 

This plot of reformer size vs. storage volume is found to deviate if the reformer turndown ratio of the 

reformer is introduced. If so, beyond a point, the storage volume increases to accommodate the increase 

in energy generation. This solution is also verified using GCC. This study can be further expanded to 

include a sensitivity analysis to the minimum reformer limit, load characteristics etc. The major benefit of 

the proposed methodology is that is does not needs any special optimisation tools or software for getting 

the optimal solution. As this work is the first adaptation of pinch analysis and design space for hydrogen 

system sizing, a comparison is not possible at the moment. It can however be seen that in addition to 

being a useful sizing technique, this method provides insights into the system behaviour, such as the 

relation of reformer size vs. storage volume plot to turn down ratio. Economic optimization can also be 

carried out to find the most cost effective solution. 

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