**A Comprehensive Review and Technical Guideline for Optimal Design and Operations of Fuel Cell-Based Cogeneration Systems**

#### **Farah Ramadhani 1, Mohd Azlan Hussain 1,\* and Hazlie Mokhlis <sup>2</sup>**


Received: 2 October 2019; Accepted: 10 December 2019; Published: 12 December 2019

**Abstract:** The need for energy is increasing from year to year and has to be fulfilled by developing innovations in energy generation systems. Cogeneration is one of the matured technologies in energy generation, which has been implemented since the last decade. Cogeneration is defined as energy generation unit that simultaneously produced electricity and heat from a single primary fuel source. Currently, the implementation of this system has been spread over the world for stationary and mobile power generation in residential, industrial and transportation uses. On the other hand, fuel cells as an emerging energy conversion device are potential prime movers for this cogeneration system due to its high heat production and flexibility in its fuel usage. Even though the fuel cell-based cogeneration system has been popularly implemented in research and commercialization sectors, the review regarding this technology is still limited. Focusing on the optimal design of the fuel cell-based cogeneration system, this study attempts to provide a comprehensive review, guideline and future prospects of this technology. With an up-to-date literature list, this review study becomes an important source for researchers who are interested in developing this system for future implementation.

**Keywords:** review; cogeneration; fuel cell; optimal design; guidelines

#### **1. Introduction**

The rapid increase of energy demand in conjunction with the depletion of oil and coal and the environmental threats to pollution over the world have led to an energy security issue. Researchers, scientists and engineers are making effort to find solutions by using more effective and efficient power generation systems or finding energy sources that are cleaner and renewable. The prospect in creating new technologies for energy generation purpose and utilizing cleaner energy sources have increased around the world by the commitment of countries to reduce their carbon emissions and to include the renewable energy sector into their energy plan [1,2].

In line with the development of energy generation systems, which are more efficient and reliable, the cogeneration system has played its role in power and heat production systems. The technology had been popular in 1977 using coal and oil as the fuels, but its prospect became more and more gloomy when the fuel price increased in 1980 [3]. However, this technology has gone back to be more popular in this last decade in line with the finding of new energy sources, which are renewable, cleaner and economically competitive. Currently, cogeneration systems can be derived not only using combustion engines or gas turbine but also employing fully renewable or semi-renewable energy sources such as photovoltaic thermal panels, Stirling engines and fuel cells.

Amongst the emerging technologies as the prime mover candidate for cogeneration systems, fuel cells are one of the most suitable devices that can generate electricity and heat continuously. Fuel cells act as an energy conversion device, which generates electricity from the thermodynamic and electrochemical reactions between hydrogen and oxygen. Along with the generated electricity from the fuel cells, they also generate heat, water and fewer carbon per kWh energy production compared to conventional combustion engines when using hydrocarbons as the fuel. The heat generated from the cell is potential to be used in the cogeneration system by producing hot water or converting it into cooling energy for room and water.

Based on its electrolyte technology and operating point, fuel cells have various types such as the proton exchange membrane fuel cell (PEMFC), direct methanol fuel cell (DMFC), alkaline fuel cell (AFC), phosphoric acid fuel cell (PAFC), molten carbonate fuel cell (MCFC), microbial fuel cell (MFC) and solid oxide fuel cell (SOFC) [4–6]. Amongst them, PEMFC being the low temperature fuel cell and SOFC as the high-temperature fuel cell are most popular to be employed as the prime mover in cogeneration systems. Application of these fuel cell types is not limited for residential use but also for industrial, public facilities and transportations [7].

Even though fuel cells are promising as a prime mover in cogeneration systems, the technology is expensive and has a long payback period, which is not economically competitive compared to other prime movers [8]. The research and development of new materials, which are cheaper and flexible with various fuels are needed to be done to reduce the investment cost of the fuel cells. Furthermore, the optimal design of the fuel cell-based cogeneration system has been proven to reduce the total cost and carbon emission generated by the system [9]. The optimal design of the fuel cell-based cogeneration system is also effective in tackling the size issue of the system capacity that leads to the energy-waste problem.

There has been a rise in the research, development and review of the fuel cell-based cogeneration system from year to year. Arsalis et al. [10] did a comprehensive review of fuel cell-based power and heat generation system which focused on the technology and configuration of the system. The study concerned two fuel cell types (PEMFC and SOFC) as the prime mover technology for the studied cogeneration system along with the thermal management for the system. Milcarek et al. [11] gave a review for the fuel cell-based cogeneration system covering the fundamental aspect on the future prospect of this system for commercialization. The study focused on the application of the cogeneration system for residential use only. Other reviews of the cogeneration systems not only focused on the fuel cell as the prime mover but also other technologies such as gas turbine, combustion engines, Stirling engine and renewable energy devices [3,12,13]. It can be concluded that reviews of fuel cell-based cogeneration systems are still limited. From our knowledge, there is no review that focused on the optimal design of fuel cell-based cogeneration system and guideline to design an optimal system based on its applications, energy requirements and various specific criteria.

Therefore, this study attempts to provide a comprehensive review of fuel cell-based cogeneration systems including its theoretical and working principle, research, development, commercialization, current state of the system and on the optimal design of the system. This study also provides guidelines for designing an optimal cogeneration system by using the fuel cell as the prime mover with its future prospects. An up-to-date summary of previous studies conducted in the past 5 years has also been included to give an insight for researchers who are interested in further studying the fuel cell-based cogeneration systems.

#### **2. Overview of Fuel Cells and Cogeneration Systems**

#### *2.1. Fuel Cells: Working Principle and Types*

All fuel cells have two porous electrodes called anode and cathode, which are separated by a dense electrolyte layer. They have similar characteristics to a battery in converting chemical primary sources into electrical energy through electrochemical reactions. The reactions occurring between hydrogen, oxygen and other oxidizing agents generate heat and water as the by-products and electricity as the primary product. In general, hydrogen as fuel moves through the porous anode while the oxygen as the oxidant transport through the porous cathode. In the interface between the anode and cathode, the hydrogen breaks up to H<sup>+</sup> ions and two electrons, which are absorbed to the electrode surface and pass through an external circuit to create direct current power as explained in the literature [11]. At the same time, the oxygen molecule at the porous anode combines with the two electrons from the electrode to form *O*2<sup>−</sup> ion, which diffuses to the electrolyte layer and reacts with H<sup>+</sup> ions to form water molecule.

The development of the electrolyte material enhances fuel cells to be fueled by other than pure hydrogen. Due to the high-cost of pure hydrogen, some fuel cells can be driven using hydrocarbon fuels. Hydrocarbons can be used via external reforming such as steam reforming or fuel combustion or via internal reforming on a catalyst layer with direct electro-oxidation [11]. Steam reforming is an endothermic reaction that reforms the hydrocarbon to hydrogen and syngas (CO). For several fuel cell types especially those that work at high temperature, the syngas can be used directly to form two electrons and carbon dioxide. Meanwhile, for low-temperature fuel cells, the gas must be processed into pure hydrogen through the water gas shift reaction where the syngas reacts to water to form pure hydrogen and carbon dioxide.

Fuel cells have also attracted much attention due to its environment friendly nature compared to the conventional generators, which generate harmful gases as by-products. According to Table 1, different types of fuel can be used to drive the fuel cells. Pure hydrogen is commonly used by low-temperature fuel cells such as alkaline fuel cell (AFC) and polymer electrolyte membrane fuel cell (PEMFC). The pure hydrogen itself can be produced from hydrocarbons, methanol or syngas. High-temperature types such as molten carbonate fuel cell (MCFC) and solid oxide fuel cell (SOFC) are more flexible in the use of the fuel. Furthermore, the fuel price can be competitive by using various types of hydrocarbon, biogas and natural gas.

Fuel cells can be categorized as pure renewable energy generation if pure hydrogen is used to drive the cells as they only produce water as the by-product [11]. However, the process of producing hydrogen, which mostly comes from the hydrocarbon reforming processes must be taken into consideration when calculating the life cycle assessment of the fuel cells. In several high-temperature fuel cells, the CO produced in the steam reforming process can be used directly and produces CO2 as by-products along with water. However, compared to combustion engines, fuel cells are more environmentally friendly even though some small emissions of carbon and NOx may be produced during the reforming processes as much as having higher operating efficiency.

#### *2.2. Cogeneration: System Components and Applications*

In several applications, especially for offices and residential homes, electricity is not the sole energy required. Other energies such as heating and cooling water are also needed continuously [14]. However, most office and residential buildings utilized the separated system (SP) in generating electricity, heating and cooling energies to meet those requirements, which caused inefficiency in energy usage and significantly raises the energy cost. Therefore, an integrated system that can cover more than one energy demand is desired to enhance the system efficiency, energy utilization and cost, using what is called the cogeneration system.



Cogeneration system can be defined as the system that generates simultaneous power and heat from the same primary energy source [3]. The power generated includes mechanical, electrical or even fuel conversion chemically. On the other hand, the system also generates useful heat, which can be used for heating, cooling, distiller purposes or converted to electricity. Furthermore, cogeneration processes can produce three or more types of energy, which are called trigeneration and polygeneration system with additional components.

Cogeneration system consists of a single or hybrid energy source called the prime mover that generates one or two types of primary power simultaneously and consists of auxiliary components to recover the primary energy from the prime mover as depicted in Figure 1. In several applications, a cogeneration system is also equipped with storage devices such as hot water tank or battery. The storages are used to store excess energies generated by the system. By using this configuration, cogeneration can reach an efficiency of up to 80% compared to the single-power generation system [19].

**Figure 1.** Cogeneration system layout.

Initially cogeneration system increased electricity generation by 58% in industrial plants [3] since the early century. However, due to economical, regulation and fuel availability issues, this system becomes less attractive for further development in the 1950s and accounted for only about 5% of the total electricity generation in the 1970s [3]. However, in the next few decades, implementation of cogeneration had been gaining attention again in line with the awareness of fuel depletion and environmental concern.

Combined heat and power (CHP) system is one of the most favorable types of cogeneration system, which generates electricity and heat. The CHP is efficient since it does not require additional fuels to produce heat power as in the separated system. The system was the first energy generation commercialized for residential applications, which had been successfully developed by several companies such as Hexis (Switzerland) and Ceres Power (UK), in partnership with British Gas and Ceramic Fuel Cells Ltd. (Australia) [20].

Currently, cogeneration systems have been designed and built for various other applications such as residential, industrial, public facilities and transportation. As the fuel cell is used as the prime mover, application for residential use as the stationary power system is more popular than others. In the industries, combinations of fuel cell fueled by biogas or syngas are also potential for waste-to-energy purposes in wastewater treatment (WWT) plant.

#### **3. Current Developments of the Fuel Cell-Based Cogeneration Systems**

The increased development of the fuel cell-based cogeneration system in the research and development sector as well as commercialization can be visualized by the rise of publications and commercial products in the last five years. Explanation of the current condition of the system development is discussed in these subsections below.

#### *3.1. Research and Development Sector*

Our review divides the research topics into three different types of fuel cell: polymer electrolyte membrane fuel cell (PEMFC), solid oxide fuel cell (SOFC) and other types of the fuel cell. The research and development of fuel cell-based cogenerations system as depicted in Figure 2 shows a positive trend in the past 10 years. It can be seen that both PEMFC and SOFC are the popular fuel cell implemented in cogeneration systems during that period.

**Figure 2.** The research trends of the fuel cell-based cogeneration systems within the past 10 years.

Comparing these two, the applications involving PEMFC as the prime mover show a sharper increase as compared to the SOFC and others. One of the reasons is due to its flexibility of operation without any reforming and burning systems. The stability and load following capability of the PEMFC add more benefits to this type for small and mobile power generation. Moreover, further studies have developed the high-temperature proton membrane exchange fuel cell (HT-PEMFC), which can be more suitable for power and heat applications. The HT-PEMFC is seen to be popular and extensively developed since the past 5 years with 90% of system employment for CHP systems [21].

On the other hand, the increase of publication regarding SOFC-based cogeneration system is consistent from year to year. Not only developing the HT version of PEMC, but other studies also paid attention to the low-temperature solid oxide fuel cell (LT-SOFC). The LT-SOFC has been reported in several studies [22,23]. One of the reasons for decreasing the temperature is to reduce the material cost of the SOFC. The high temperature SOFC generates more heat and power but with increased cost in the electrolyte material as compared to the PEMFC. The high-temperature also causes the material to get cracked and degraded thus reducing the life cycle of the SOFC [24].

The other types of fuel cell such as PAFC, MCFC and DMFC have been reported in some studies [25–28]. The development of PAFC in Japan reported in [28] showed slow progress but promising for CHP systems in residential applications. However, not much attention has been given to further developments of other fuel cell types and this lack of study affects the progress of commercialization and their competitiveness in real applications.

#### *3.2. Commercialization Sector*

As a leader in this technology, Japan is pioneer in the development of fuel cells and cogeneration systems. As reported in the literature, the world's first residential proton exchange membrane fuel cell (PEMFC) CHP system in the Japanese market was built in 2009 [29]. It is planned that 5.3 million units of residential FC-CHP systems would be installed by 2030 to achieve Japan's Intended Nationally Determined Contributions (INDC; a 26% reduction of total greenhouse gas (GHG) emissions by First Year (YF) 2030 compared with those in FY 2013) [30]. Furthermore, as Japan has succeeded to achieve GHG emission by 1270 MtCO2/a in FY 2019, it has attained about 50% of the target of INDC [31].

In some of the European countries, the project H2home decentralized energy supply using hydrogen fuel cells is part of the HYPOS initiative (Hydrogen Power Storage and Solutions) [32]. In the building sector, proof of function has been provided in practice by the completed national project CALLUX (field test fuel cell for home ownership, 500 units in Germany) and the ongoing European project "Ene.Field" (which will deploy up to 1000 residential fuel cell micro-CHP installations across eleven key European countries). The European Commission set the greenhouse gas emissions and energy sustainability targets to be achieved by 2020: reducing by 20% the greenhouse gas emissions compared to 1990, reaching a share of 20% of renewable resources in the energy production and reducing by 20% the overall primary energy consumption compared to the projections made in 2007 [33].

Therefore, commercialization activities such as reducing the cost of the fuel cell system, increasing the electrical efficiency, increasing the energy efficiency in generating hydrogen, demonstrating the large-scale competitiveness of fuel cell and hydrogen technologies produced from primary renewable energy [34] will ensure that performance of the system fulfill the low-carbon economy target during this period up to 2050.

#### *3.3. Governmental Support*

In Japan, the promotion of SOFC micro CHP units involves an investment-based support scheme in the form of a capital grant. It reduces by half the initial cost of the generator, which is currently in use [35]. In Europe countries, a Feed-in Tariff scheme (price-based) was instead launched in 2010 in the United Kingdom (UK) where eligible generators are the micro-CHP units with a power output below 2 kW. The latter value has been chosen according to the cap given by the Feed-in Tariff actually adopted in the UK for 2 kW capacity for residential usage. Pellegrino et al. [35] studied the possible support by the UK governments in the fuel cell-based cogeneration system such as Capital grants, purchase and resale supports, Net metering support and two scenarios of feed-in-tariffs.

The United Nations Environmental Program has supported the Fuel cell installation with a total investment of \$307.1 million in 2012, while the US Department of Energy (DOE) rolled out \$9 million in grants to speed up the technology in June 2013 [34]. In China, the Ministry of Science and Technology of China, the Ministry of Finance of China, the Ministry of Industry and Information Technology of China and the National Development and Reform Commission of China have collaborated to develop new energy strategies by rolling out national grants focusing on fuel cells development and commercialization starting from 2012 [36]. Following this, other countries in Asia such as Malaysia has supported the utilization of renewable energy and development of hydrogen fuel cell through national grants given to universities [37] and feed-in-tariffs (FiT) scheme for residential applications [38,39].

#### **4. Designing a Fuel Cell-Based Cogeneration System**

Development of a better cogeneration system needs optimization of the overall system. Even though the cogeneration system is theoretically better than a separated system, the high-cost issue in the fuel cell development must be tackled by the proper design of the system. In optimizing the design, there are several steps to be followed as guidelines: modeling of the components, choosing the criteria for evaluation, evaluation of the system design, system control and management and optimization of the overall design. As depicted in Figure 3, these guidelines can be applied for any applications and system components to provide an optimal cogeneration system. The details of these steps will be explained in the subsections below.

**Figure 3.** Guideline in designing an optimal cogeneration system with fuel cell as the prime mover.

#### *4.1. Modeling the Components*

In order to assess the performance of the cogeneration system, modeling the system components must be done first. The modeling part is always associated with the validation of the cogeneration component before going to be controlled and optimized. Most of the study focusing on the assessment of the cogeneration system built their system through mathematical modeling. With some assumptions and simplifications used, the model of components can validate the performance of the whole system. As a major prime mover of the cogeneration system, modeling of the fuel cell is vital to analyze the behavior of the component in generating power and heat for the cogeneration system.

In the modeling the cogeneration system, researchers have used several approaches such as 3D, 2D, 1D and even using 0D or black box predictions. Each approach is different in its complexity, accuracy and application. If the purpose is to achieve accuracy for detailed analysis, then the 3D approach is most suitable for the modeling approach. The mass, momentum and energy equations are presented in three dimensions with the heat transfer from the outer stack to surrounding surfaces [11]. This approach is mostly used for analyzing a single fuel cell where its geometry is appropriately discretized using the finite volume or finite difference method [11].

A 2D approach is simpler than the 3D approach because it neglects one dimension of fuel cell geometry and generates different models for different fuel cell geometries. However, the 1D approach is suitable for modeling of integrated fuel cells applications in a stack or combinations with other heating or cooling components in cogeneration systems. The 1D approach presents the fuel cell model in one direction for the variations of fuel cell temperature, pressure, concentration and other thermodynamic phenomena and material properties. In the literature, black box prediction models are also frequently used for analysis, control, management, evaluation and optimization studies in an integrated fuel cell-based system such as cogeneration.

Due to the complexity in integrating more than two components and applying adjusted operating strategies and sizes, the detailed fuel cell model must be simplified with a consequence in the reduction of accuracy. In order to enhance the accuracy of the model, most of the studies consider fuel cells as the prime mover in a cogeneration system and for more advanced systems, which include real experimental data from the literature to validate the cell model [39–42]. One example is that conducted by Asensio [43] that predicted the PEMFC system for optimal energy management using a black box model, and applied the adaptive neural network (ANN) combined with a 3D lookup table to predict the hydrogen consumed and output power of PEMFC in the cogeneration system.

#### *4.2. Choosing the Criteria for Evaluation*

While designing a cogeneration system, one, two or more criteria are used as the objective of the design. Based on the literature, criteria based on energy, economics and environmental are commonly used in the cogeneration design for evaluation of different configurations, parameter analysis, energy management and optimization of the system. In some studies, criteria used for the design is not limited to single criteria but also multi-criteria such as energy-environmental, exergoeconomic or eco-environmental parameters. The multi-criteria parameters are used to assess the system to deal with more than one criterion to be satisfied.

From the technical aspect, many studies in the literature commonly used efficiency of the system as the criterion [44,45]. Other studies use primary energy saving (PES) or primary energy consumption (PEC) as the energy criteria [25,46]. The values of the PES or PEC are obtained by subtracting the amount of primary energy or fuel used in the reference system (usually using a separated system) with the proposed cogeneration system. Besides using energy output and energy efficiency as the criteria, many studies in the literature focused on the second law of thermodynamics by using exergy as the criterion. Exergy is the available energy, which can be used from the consumption of primary energy including power and heat. The concept of exergy is more viable and practical in the cogeneration system since not only electric power is considered but also heating and cooling demands. Several studies in the literature also used exergy and efficiency as the criteria for the system performance achieved [45,47,48]. From the criteria, exergy destruction can also be used to indicate which part of the cogeneration components affects the system performance.

From the economical aspect, criteria such as energy cost, net present cost, payback period and total costs of the system are used in the cogeneration design. For the investment of the system and analysis of the system viability, the payback period is commonly used as the criterion. Some scenarios involving subsidiary from the government, tax reduction, net metering to feed-in-tariffs as incentives were studied to make the system more economically competitive compared to the conventional separated system (CSS) [35].

Environmental aspects have also been taken into account in achieving a cleaner environment and reducing the pollution caused by the energy sector. The older energy generation technologies using non-renewable sources have created negative impacts to the environment, thus the developments in the new emerging technologies are essential to achieve the sustainability of the energy. Reduction of carbon emission and other harmful gases are also other criteria, which are used in the cogeneration design. Furthermore, life cycle analysis (LCA) is also used to analyze the impact of the technology used in the cogeneration system to the environment, which is comprehensive since it covers all aspects from system production to system operation.

#### *4.3. Evaluation of the System Design*

Evaluations of the system consisting of system synthesis and assessment are important to analyze the actual performance of cogeneration systems. Evaluation and synthesis of the system include its configurations, prime mover types, heating/cooling devices, storages and other auxiliary components in the cogeneration system. Synthesis of the system defines the acceptability of each component in a cogeneration system in improving the performance of the system. System synthesis for cogeneration system has been made using the P-graph Fuzzy approach [49], TOPSIS [50] and MILP [51]. On the other hand, evaluation of the system can be performed by a parametric study to analyze the operating points of the components [27,40,45]. Furthermore, some modifications in the heat recovery system and system operation have also been done by [25,52]. Regarding the implementation of the cogeneration system, other studies compared the system for different climate conditions, places, and demand profiles [41,53,54].

Several works as reported in the literature, used a conventional separated system (CSS) and compared it with the proposed cogeneration [39,55,56]. The CSS uses different primary energy sources to provide electricity, cooling or heating for the users. Electric power is commonly provided from the national grid while heating or hot water is generated from a fuel driven boiler. Several studies found that the fuel cell-based cogeneration system is more promising to reduce primary energy consumption, energy cost and carbon emission generated by the system compared to the CSS [55,57,58].

#### *4.4. System Control and Management*

System operation in a cogeneration system plays an important role in reducing unused wasted energy that is generated by the prime mover and other components where, optimal energy management is able to reduce primary energy consumptions and operation costs. The operating strategies, which have been reported in the literature involve control and management for the prime mover, heating/cooling devices, storages and also dispatch mechanisms between cogeneration components in satisfying the load demands.

As the prime mover, a fuel cell can generate electricity and heat as long as the fuel is injected into the cell. However, the fluctuations in demand, fuel costs and other varying conditions affect the operation of the fuel cell. Therefore, fuel control is one of the options to optimize the utilization of the fuel depending on the power and heat required by the demands. Moreover, high-temperature fuel cells such as the SOFC and PAFC are very sensitive to the temperature shock caused by the high fluctuation of temperature during the operation. It needs thermal management to avoid material cracking and increase the life cycle of the cell.

Some energy management approaches related to energy storage control or demand control have also produced a better and efficient cogeneration system. The controls are also capable of reducing components capacity, thus reducing the investment and operational costs. The energy management approach in relation to storage control can also improve the reliability of the system, preventing system blackout and utilizing excess power generated from the supply side.

#### *4.5. Optimization of the Overall Design*

As the last step in designing the cogeneration systems, optimization approach can be conducted based on the fulfilled objectives. Optimization for the cogeneration system involves optimal operating strategy (OOS), optimal operating parameters (OOP) and optimal size of the cogeneration components (OS). These three design objectives are significant variables in increasing the overall performance of the cogeneration system.

In designing the operating strategies, several system operations need an optimization approach to find the best strategy in their cogeneration designs. Scheduling and dispatching the energy from the cogeneration components to the demand side involve many combinations that have to be examined. In order to fulfill one or more objectives, a combined operating strategy can be the better choice. Therefore, the role of optimization in this case is to find the best operating strategy to be applied with the specific objectives as the requirement.

In terms of the operating parameters, optimization of those parameters can improve the performance of the cogeneration components in reducing the fuel usage, decreasing its costs or generating less carbon emission. As the prime mover, fuel cell parameters such as temperature, hydrogen flow, steam to carbon ratio and pressure can be optimized to improve the flexibility in its operation and reducing its primary energy consumption. Meanwhile, other component parameters for generating hot water, cooling or hydrogen can also be used to reduce the costs of the components and increase the value of the cogeneration system.

Several studies in the literature have also focused on optimizing the size of the various components of the cogeneration system [38,59,60]. From these studies, comparisons of various configurations on the cogeneration performance is essential to avoid oversizing or under sizing of the system for the specific energy demand and applications.

#### **5. Summary of the Gathered Literature in the Past 5 Years**

As presented in Table 2, the publication summary shows an intense increase in research and development for fuel cell-based cogeneration system in the last 5 years. There are several important summaries to be extracted from the Table. Firstly, PEMFCs and SOFCs are still the popular fuel cells for cogeneration systems and will be further developed for use in cogeneration systems. In the future, steady-state and linear models are mostly used for the modeling process of the system. On the other hand, studies that concern in the model prediction are limited although the predicted models have some advantages in simplifying the mathematical equations used in the modeling process and closer to the real performance when using real experimental data as the reference. A few numbers of study that focused on the control and energy management strategy was reported from the literature.

Furthermore, the topics that studied the hybrid configurations between fuel cell and renewable energy devices are also limited. Most of the studies found in the literature used the fuel cell as the sole prime mover in the cogeneration system. Only several studies combined between two types of fuel cell [25,26,28,57,61,62] and the combinations between the fuel cell and other energy conversion devices such as photovoltaic, electrolyzer, thermoelectric and batteries as the storage were reported in [46,63–65].

In terms of its applications and designed scenario, most of the cogeneration systems were implemented for residential and building sectors while the use in the transportation sector and mobile power generation have not been found. Furthermore, the number of studies that implemented the cogeneration system for providing other than power and heat (example treated water, cooling, hydrogen, oxygen, etc.) is still limited. It can also be seen that very few of the studies consider the external support from the society or impacts of the cogeneration on the society as the feasibility study and only a few studies included government support as the assessment scenario [19,38] in the design of the cogeneration system.



#### *Processes* **2019** , *7*, 950




#### **Table 2.** *Cont.*


**Table 2.** *Cont.*

#### *Processes* **2019**, *7*, 950


**Table 2.** 

*Cont.*



19

#### *Processes* **2019**, *7*, 950


**Table 2.** *Cont.*

#### **6. Future Directions of Fuel Cells Application in Energy Generation Systems**

Based on the current status of fuel cell developments in cogeneration systems and the review done, several promising directions for future developments of the system can be obtained. In terms of the research topic regarding the optimum system, the study that involves monitoring and predictions aspects are potential in the design of optimal cogeneration system. The monitoring and predictions are not only conducted for the cogeneration components, but also for the demand profiles and the operation of the system. These topics could increase the value of the optimum system since the data collected is not based on the assumptions but real experimental data. Predicted system components and the demands also simplify the analysis of the system performance and lessen the complexity in the interactions between the cogeneration components since no mathematical model is used.

In line with the monitoring and prediction of the system, experimental studies involving the real fuel cell-based cogeneration system is valuable to analyze the durability of the system. A couple of studies that have implemented the cogeneration system for a real implementation can be used as references [109,110]. Since the PEMFC and SOFC are well known as the prime mover in cogeneration systems, the finding of its commercialized products is easier to obtain. However, finding the commercialized products for the other types of fuel cell is challenging, thus experimental studies regarding these other types of fuel cell is highly promising.

Moreover, the cost issue regarding fuel cell development can also be tackled by finding technologies for fuel reforming and using various types of fuel. Some studies have started to develop syngas and various hydrocarbons as fuels for driving the cogeneration system [75,90]. Other studies focused on the new materials of the electrolyte of the fuel cells to reduce the investment cost and increase the life cycle [111,112].

Besides using various types of fuel, the cogeneration performance can also be increased by finding technologies in optimizing electricity production from the fuel cells. Combination between fuel cells and other power generators as a hybrid prime mover is the key to doubling the electric power generation and reducing the size of the fuel cell. In terms of hybrid the cogeneration system with other energy conversion devices, several promising units such as solar rechargeable, thermoelectric, electrolyzer with solid oxide electrolysis cell and flow batteries can be coupled with the system to increase the fuel utilization and system capacity with valuable costs [27,63,113].

For system operations, energy management strategy combined with optimal operation parameters and system predictions seems important to be developed, which have shown good results in reducing primary energy consumption as well as its operating cost and carbon emission from the cogeneration system. The predictions in the demand can also tackle the energy loss issue and increase the reliability of the system.

Lastly, applications for waste-to-energy usage have huge potential for the further development of the fuel cell-based cogeneration system where these newly innovative systems can be economically competitive in the commercial and government sector.

#### **7. Conclusions**

Based on the scientific indicator that was presented in the research review, PEMFC and SOFC were the two well-known and most applied fuel cells among others. Current developments of those fuel cells show that they were more being widely used especially with further improvement of its material to increase its durability with higher temperature ranges. Furthermore, being one of the focuses of this study, a guideline to develop an optimal fuel cell cogeneration system was also presented. The guidelines start from the modeling of the components, assessment of the system design, designing the operating strategy and optimization of the overall design involving operating parameters and size of the components. Through the guidelines given, optimal design can be done comprehensively using different specific applications and criteria for the implementation of the cogeneration system. Numerous publications for the last five years can be a good point of reference to design an optimal cogeneration system with various approaches, objectives and applications. Those publications also

indicated the various ways to increase system performance, reduce system cost and emissions of the systems and give more insight for the researchers and developers who are interested to work in this area in the future.

For power generation, fuel cell-based cogeneration system has a better future compared to the conventional heat engine-based technology. From this study it also can be seen that various hydrocarbon fuels have been utilized to replace the utilization of pure hydrogen as to reduce the fuel cost with various materials chosen to increase the temperature range and durability of the fuel cells. Application of cogeneration system can be explored widely not only for stationary but also for mobile power generation uses in the future.

**Author Contributions:** All authors have contributed to this research article. M.A.H. has contributed in conceptualization and editing, while H.M. has revised technical terms in this article. As the main author, F.R. has contributed in conceptualization, writing and editing processes.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**/**Symbols**



#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Modeling, Management, and Control of an Autonomous Wind/Fuel Cell Micro-Grid System**

#### **Ibrahem E. Atawi 1, Ahmed M. Kassem <sup>2</sup> and Sherif A. Zaid 3,\***


**\*** Correspondence: shfaraj@ut.edu.sa or sherifzaid3@yahoo.com; Tel.: +2-023-567-8278

Received: 3 January 2019; Accepted: 4 February 2019; Published: 8 February 2019

**Abstract:** This paper proposes a microelectric power grid that includes wind and fuel cell power generation units, as well as a water electrolyzer for producing hydrogen gas. The grid is loaded by an induction motor (IM) as a dynamic load and constant impedance load. An optimal control algorithm using the Mine Blast Algorithm (MBA) is designed to improve the performance of the proposed renewable energy system. Normally, wind power is adapted to feed the loads at normal circumstances. Nevertheless, the fuel cell compensates extra load power demand. An optimal controller is applied to regulate the load voltage and frequency of the main power inverter. Also, optimal vector control is applied to the IM speed control. The response of the microgrid with the proposed optimal control is obtained under step variation in wind speed, load impedance, IM rotor speed, and motor mechanical load torque. The simulation results indicate that the proposed renewable generation system supplies the system loads perfectly and keeps up the desired load demand. Furthermore, the IM speed performance is acceptable under turbulent wind speed.

**Keywords:** wind energy; fuel cell; IM; induction generator; hybrid system; mine blast optimizer

#### **1. Introduction**

Modern industries, transportation means, and nearly all mankind's requirements mainly depend on electrical power. Traditionally, electrical power generation is essentially based on fossil fuel resources. Nevertheless, fossil fuels suffer from several drawbacks, such as depletion by 2050. However, the rapid growth of the world's population increases the world electrical power demand. The global energy demand estimated 2.1% in 2017 (more than twice the average increase over the previous five years) [1]. Also, it generates harmful emissions that form the essential cause of the phenomena of global warming and many environmental problems. Energy-related carbon dioxide (CO2) emissions rose—by an estimated 1.4% in 2017—for the first time in four years, at a time when climate scientists said that emissions needed to be in steep decline [1]. Several decades ago, renewable energy resources have gained more attention as a sustainable replacement for fossil fuels. Renewable energy resources have great advantages as they are clean, do not deplete, and are available everywhere. Many renewable energy resources [2–5] have been introduced recently, such as photovoltaic (PV), wind, ocean wave, ocean tides, and micro hydro. Thanks to technology advances and rapid growth, dramatic reductions in the costs of solar PV and wind energy systems have occurred [6]. In the same context, new energy alternative technologies like biomass, geothermal, microturbines, and fuel cells (FCs) have been investigated [7]. Now, electricity generation by renewable systems is less expensive than the newly installed fossil and nuclear power plants in many parts of the world. An assessment of different

renewable energy resources for electrical power production showed that wind energy is the first choice [8].

Renewable energy systems may be classified into grid-connected systems and standalone systems. The present capacities of the grid-connected renewable energy systems vary from several kilowatts of residential PV systems to large-scale wind farms. The grid-connected systems do not need any storage as the generated energy is injected directly to the grid. These systems are suitable for urban regions where the grid is available. However, standalone systems are suitable for rural areas, where grid extension is not feasible. In standalone renewable energy systems, the load is an individual house and not connected to a grid. The capacities of these systems are usually small. In some applications, several houses are connected to form a small power grid called microgrids (MGs) [9,10]. Microgrid technology has become popular in islands as it provides a cost-effective alternative where power grid extension is expensive and fuel transportation is difficult and costly [11,12].

The major obstacle for utilizing one technology of renewable energy sources is the intermittent nature of that source. That intermittent behavior of the renewable energy sources comes from the strong dependency on the environmental conditions, which are changing continuously. A suggestion to solve the intermittency problem of the renewable energy systems is the use of energy storage element. Energy storage units are classified as capacity-oriented storage systems and access-oriented storage systems. The capacity-oriented storage systems include pumped hydroelectric storage, compressed air energy storage, and hydrogen storage systems. It has a slow response and is considered long-term energy storage. Batteries, superconducting magnetic energy storage, supercapacitors, and flywheels are considered access-oriented storage systems. It has a fast time response that is useful for short duration disturbance applications [13–16]. In fact, the integration of energy storage systems with one technology of renewable energy sources has many disadvantages. One of them is the load power variations, which may harm the storage system and degrade its lifetime. On the other hand, the size and cost of the system increase [17]. Hybrid power generation systems are introduced essentially to alleviate these disadvantages. These systems contain two or more energy sources with a storage system. Hybrid renewable energy systems have benefits of high reliability, high efficiency, better power quality, and low energy storage requirements [18,19].

Usually, microgrids can operate in two modes: grid-connected mode and autonomous mode. So, the main benefit of a microgrid is that it is able to operate in both the above two modes [20]. The microgrid can then function autonomously. Both loads and generation in microgrids are usually interconnected at low levels of voltages. However, one issue regarding the microgrid is that the operator needs to be very vigilant because numbers of power system areas are connected to microgrid. Also, in microgrid generation resources can include wind, photovoltaic, fuel cells, energy storage, or other power generation sources [21].

In the literature, there are different types of standalone hybrid power sources have been reported [22–27]. They usually combine solar energy and/or wind energy with another green power source such as FC, biomass, etc. As the work in this paper is directed to hybrid wind/FC generation systems, we focus on the literature review of that subject. Khan et al. [28] investigates a hybrid wind/FC generation system and presented a detailed life cycle analysis of the system for application in Newfoundland and Labrador. It concludes that the system is highly nonlinear and difficult to model. Battista et al. [29] presents a wind/hydrogen power system with a novel power conditioning algorithm. It introduces a Maximum Power Point Tracking (MPPT) control strategy that was developed using concepts of the reference conditioning technique and of the sliding mode control theory. Gorgun et al. [30] presents a wind/hydrogen power system and developed the electrolyzer and hydrogen storage dynamic model. Bizon et al. [31] introduces a hybrid wind/FC generation system with a global extremum seeking a control algorithm for optimal operation of the wind turbine under the turbulent wind.

This paper presents a novel hybrid wind/FC energy system. In addition, it presents the system detailed dynamic model, the application of mine blast optimization, the controller design, the performance analyses, and the simulations of the developed system under the turbulent wind speed. In this study, the microelectrical power grid is managed and controlled based on an optimal controller using mine blast algorithm. The proposed microgrid system mainly consists of R-L static load, IM as a dynamic load, a wind generation system, FC generation system, water electrolyzer, uncontrolled rectifier, and controlled DC/AC converter.

The power system management is adapted to make the wind power generation is the master source for the loads. Also, hydrogen gas is produced using a water electrolyzer during wind power generation peaks. Hydrogen is fed back to the FC system adding to its energy storage.

The main contribution of this study can be seen from the obtained results that the proposed renewable generation system can supply the system loads perfectly in addition to a better prediction of the electrical parameter waveforms. Also, the controller response follows up the desired load demand with a small maximum overshoot and little settling time. In addition to, the generated power is managed such that the load required power is supplied by the wind power and the more needed power is covered by the fuel cell generation unit.

This paper is arranged as follows. Section 2 includes the discussion of the system description. Section 3 presents the proposed system dynamic model. Details of the system controllers are found in Section 4. The simulation results and their discussion are presented in Section 5. Finally, Section 6 shows the conclusions.

#### **2. System Description**

The proposed system is a hybrid wind/FC microgrid supplies two loads, as shown in Figure 1. The wind turbine drives a 3-ϕ Induction Generator (IG) The output voltage of the IG is rectified via a diode rectifier producing the Direct Current (DC) bus voltage. That bus supplies a water electrolyzer that produces hydrogen gas to be saved in the FC generator. Then, the output voltage of the FC is connected to the system DC bus. In addition, the DC bus supplies the 3-ϕ inverter that converts DC power into Alternating Current (AC) power to feed the system loads. General R-L impedance represents the static load. In addition, the dynamic load is a speed controlled induction motor. That inverter is controlled in such a way to supply loads with a regulated AC voltage and frequency.

**Figure 1.** The proposed microgrid energy system and its controllers.

Usually, wind speed variations cause the IG output power to vary as well. Therefore, an FC unit supplies power to loads when the power of the wind generation unit drops. Hence, it acts as a slave to compensate for any decrease in the generated wind energy. In addition, it can supply additional power demanded by the loads.

Frequently, the load voltage of the system is not regulated due to the speed variations of the wind and load changes. Therefore, the voltage controller is used for the main inverter to regulate the load voltage and frequency. Also, the optimization algorithm is applied to control the speed of a vector controlled induction motor.

#### **3. The Dynamic Model of the System**

The detailed dynamic model of all proposed system components will be discussed in the following paragraphs.

#### *3.1. Wind Turbine Model*

The power output of the wind turbine can be represented as [32]

$$P\_m = 0.5 C\_p(\lambda, \beta) A \rho v\_w^3 \tag{1}$$

where, *A* = *πR*<sup>2</sup> is the swept area (m2) by the blades, *β* is the blade pitch angle (in degrees), *R* is the radius of the turbine blade, *vw* is the wind speed, *ρ* is the air density (kg/m3), *λ* is the tip–speed ratio as defined by Equation (2), *Cp* is the performance coefficient of the turbine that is given by Equation (3), and *ω<sup>m</sup>* is the turbine mechanical angular rotor speed.

$$
\lambda = R\omega\_m / \upsilon\_w \tag{2}
$$

$$\mathbb{C}\_{\mathbb{P}}(\lambda, \beta) = (0.44 - 0.0167\beta) \sin \pi \left(\frac{\lambda - 3}{15 - 0.3\beta}\right) - 0.00184(\lambda - 3)\beta \tag{3}$$

The wind turbine torque (*Tm*) is related to its power by the classical relation:

$$T\_m = P\_m / \omega\_m \tag{4}$$

The dynamic equation of the wind turbine and the electrical generator mechanical system can be written as

$$J\frac{d\omega\_m}{dt} = T\_m - T\_\varepsilon - B\omega\_m\tag{5}$$

where, *Te* is the electrical generator electromagnetic torque (N·m), *J* is the combined inertia of the generator rotor and the wind turbine (kg·m), and *B* is the mechanical viscous friction (N·m·s/rad).

#### *3.2. Dynamic Model of the Induction Machine*

In a synchronous reference frame, the induction motor dynamic model may be represented by [33]

$$\frac{di\_{ds}}{dt} = \frac{1}{\sigma L\_s} \left[ -\left( r\_s + \frac{r\_r L\_m^2}{L\_r^2} \right) i\_{ds} + \omega\_s \sigma L\_s i\_{qs} + \frac{r\_r L\_m}{L\_r} \lambda\_{dr} + \frac{L\_m}{L\_r} \omega\_r \lambda\_{qr} + \upsilon\_{ds} \right] \tag{6}$$

$$\frac{d\dot{\mathbf{u}}\_{qs}}{dt} = \frac{1}{\sigma L\_s} \left[ -\left( r\_s + \frac{r\_r L\_m^2}{L\_r^2} \right) \dot{\mathbf{u}}\_{qs} - \omega\_s \sigma L\_s \dot{\mathbf{u}}\_{ds} + \frac{r\_r L\_m}{L\_r} \lambda\_{qr} - \frac{L\_m}{L\_r} \omega\_r \lambda\_{dr} + \upsilon\_{qs} \right] \tag{7}$$

$$\frac{d\lambda\_{dr}}{dt} = (\omega\_s - \omega\_r)\lambda\_{qr} + \frac{r\_r L\_{ll}}{L\_r} i\_{ds} - \frac{r\_r}{L\_r}\lambda\_{dr} \tag{8}$$

$$\frac{d\lambda\_{qr}}{dt} = -(\omega\_s - \omega\_r)\lambda\_{dr} + \frac{r\_r L\_m}{L\_r} i\_{qs} - \frac{r\_r}{L\_r} \lambda\_{qr} \tag{9}$$

$$J\_m \frac{d\omega\_r}{dt} = T\_l - T\_{cm} - B\_m \omega\_r \tag{10}$$

where, *rr* is the rotor resistance; (*vds* and *vqs*) are the stator d- and q-axis voltage components, respectively; (*ids* and *iqs*) are the stator d- and q-axis current components, respectively; (*λdr* and *λqr*) are the rotor d- and q-axis flux linkage components, respectively; (*Ls, Lr,* and *Lm*) are the stator inductance, rotor, and mutual inductances, respectively; *ω<sup>r</sup>* is the motor speed; *ω<sup>s</sup>* is the motor synchronous speed; *Tem* is the motor electromagnetic torque (N·m); *Jm* is the inertia of the IM rotor (kg·m); and *Bm* is the viscous friction of the coupling (N·m·s/rad).

#### *3.3. Fuel Cell Model*

Typically, the Proton-Exchange Membrane Fuel Cell (PEM FC) has an electrical characteristic at normal environmental conditions as shown in Figure 2. Normally, FCs are subjected to internal voltage losses that cause a voltage drop beyond the nominal voltage values. Three kinds of voltage losses are presented: the ohmic polarization, the concentration polarization, and the activation polarization. The slowness of the chemical reactions is the cause behind the cell activation losses; it can be reduced by maximizing the catalyst contact area. However, the cause of the resistive losses is the resistance of all the FC electrical circuit and their connections. This part of losses can be alleviated by well hydrating the membrane. Finally, the concentration losses come from the changes in gas concentration at the electrodes surface.

**Figure 2.** The V–I characteristic of the Proton-Exchange Membrane (PEM) fuel cell at normal environmental conditions.

The model of the PEM FC is given by [34–36]

$$E = N \left[ E\_o + \frac{R'T}{nF} Ln \left( \frac{P\_{H2} \left( \frac{P\_{O2}}{P\_{std}} \right)}{P\_{H2Oc}} \right) - V\_{drop} \right] \tag{11}$$

$$V\_{drop} = \frac{R'T}{nF} \left[ Ln\left(\frac{i\_n + i}{i\_o}\right) + \frac{nFa}{R'T}(i\_n + i) - Ln\left(1 - \frac{i\_n + i}{i\_L}\right) \right] \tag{12}$$

where, *E* is the stack output voltage, *Eo* is the cell open circuit voltage at standard pressure, *N* is the number of cells in stack, *F* is Faraday's constant, *n* is the number of transferred electrons in the electrochemical reaction, *R'* is the universal gas constant, *T* is the operating temperature, *PH2* is the partial pressure of hydrogen, *PO*<sup>2</sup> is the partial pressure of oxygen, *PH2Oc* is the partial pressure of gas water, *Pstd* is the standard pressure, *Vdrop* is the voltage losses, *i* is the output current density, *in* is the internal current density related to internal current losses, *io* is the exchange current density related to activation losses, *iL* is the limiting current density related to concentration losses, and *α* is the area specific resistance related to resistive losses.

#### *3.4. Uncontrolled Rectifier Model*

The IG speed is directly related to the wind speed that changes usually with time. Hence, the IG output voltage is not regulated in terms of its magnitude or frequency. This issue is not suitable for many applications that require regulated sources. That problem can be alleviated by rectifying the IG output voltage to form the DC bus then converting it to an AC voltage via a power inverter. The rectifier is simply a diode bridge rectifier. Neglecting the source inductance, the average model of the rectifier is given by [37]

$$V\_d = 3\sqrt{3}/\pi V\_\mathcal{S} \quad , \quad I\_d = \pi/2\sqrt{3}I\_\mathcal{S} \tag{13}$$

where, (*Ig*, *Vg*) are the phase RMS current and voltage of the IG, respectively, and (*Id*, *Vd*) are the average rectifier output current and voltage, respectively.

#### *3.5. Boost Converter Model*

The classical circuit diagram of the boost converter is shown in Figure 3. The input of the boost converter is the DC bus voltage. However, its output feeds the water electrolyzer. Its function is to regulate the power transfer to the water electrolyzer in turn to the fuel cell. The average model of the boost converter is given by [38]

$$V\_d = V\_{fc} / (1 - d) \quad , \ I\_d = (1 - d)I\_{fc} \tag{14}$$

where, *d* is the duty ratio of the switch and (*Vfc, Ifc*) are the fuel cell output voltage and current, respectively.

**Figure 3.** The boost circuit diagram.

#### *3.6. Main Power Inverter Model*

The power circuit diagram of a 3-ϕ inverter connected to L-C filter is shown in Figure 4a. The output voltage *Vc*, the inverter voltage *Vi*, the output current *Io*, and the filter current *If* are expressed as space vectors by

$$\underline{F} = 2/3 \left( f\_a + a f\_b + a^2 f\_c \right) \tag{15}$$

where, (*fa*, *fb*, and *fc*) are the phase values, *F* is the space vector of the quantity, and *a=ej*(2*π/*3).

The switching states of the inverter are determined by its gate signals (Sa, Sb, and Sc). These states can also be expressed as space vector *S* using Equation (13). Considering the possible combinations of the gate signals, there are eight switching states. These states generate eight voltage vectors as shown in Figure 4b. There are two zero voltage vectors (*V0* = *V7*) and six active voltage vectors. The system dynamic behavior can be expressed by

$$L\frac{d\underline{I}\_f}{dt} = \underline{V}\_i - \underline{V}\_c \tag{16}$$

$$\mathbb{C}\frac{d\underline{V\_c}}{dt} = \underline{I}\_f - \underline{I}\_o \tag{17}$$

$$
\underline{V}\_i = V\_d \underline{S} \tag{18}
$$

where, (*L, C*) are the filter inductance and capacitance, respectively.

**Figure 4.** (**a**) The power circuit diagram of a 3-ϕ inverter. (**b**) The 3-ϕ inverter space vectors.

#### **4. System Controllers**

The control system of the proposed wind/FC system consists of three controllers. The first controller is the main inverter controller that regulates the load voltage and frequency. The second controller is the boost converter controller. However, the third controller is the induction motor controller that controls the speed of the induction motor. The three controllers will be discussed in the following paragraphs.

#### *4.1. Main Inverter Controller*

The proposed controller is shown in Figure 5, a current controlled voltage source inverter (VSI) is employed. The inverter output voltage is compared to the reference voltage generating an error signal. The error is sent to an optimized Proportional-Integral (PI) controller that generates the reference three-phase currents. These reference currents are compared to the actual three-phase currents producing error signals that are fed to hysteresis controllers to produce the inverter switches driving pulses.

**Figure 5.** Block diagram of the inverter controller.

#### *4.2. Mine Blast Optimization Algorithm*

The idea behind this algorithm is the exploration technique of landmines. An initial shot point (*zo*) is adapted using [39,40]

$$
\stackrel{\rightarrow}{z}\_o = SB + \{rand\} \times \left\{ \stackrel{\rightarrow}{LB} - \stackrel{\rightarrow}{SB} \right\}, \ 0 < rand < 1 \tag{19}
$$

where, *zo* is the first shot point and (*SB* and *LB*) are the problem upper and lower limits, respectively.

Assume that the population has *Ns* Shrapnel pieces. Mine blast algorithm has two phases named exploitation and exploration. The function of the exploitation phase is to encourage and to converge the solution. On the other hand, the exploration has the responsibility of exploring the search space. During the starting iterations of MBA, the exploration factor (*γ*) explores the search spaces then check the number of iterations (*i*). The exploration phase ends when (*γ* ) is greater than (*i*) which is given by [40]

$$\stackrel{\rightarrow}{\vec{z}}\_{\epsilon(i)} = \left\{ \stackrel{\rightarrow}{d}\_{i-1} \right\} \times (|randn|)^2 \times \cos\left(\frac{360}{N\_s}\right) \quad i = 1, 2, \dots, \gamma \tag{20}$$

Hence, the directions of the shrapnel pieces are given by

$$m\_{(i)} = \frac{F\_{(i)} - F\_{(i-1)}}{\stackrel{\rightarrow}{\mathbf{z}}\_{\mathbf{c}(i)} - \stackrel{\rightarrow}{\mathbf{z}}\_{\mathbf{c}(i-1)}} \qquad \qquad \qquad i = 1, 2, \dots, \gamma \tag{21}$$

The best locations of the shrapnel pieces are calculated by

$$\stackrel{\rightarrow}{\vec{z}}\_{(i)} = z\_{\epsilon(i)} + \exp\left(-\sqrt{\frac{\stackrel{\rightarrow}{m}\_{i}}{\stackrel{\rightarrow}{d}\_{i}}}\right) \times \stackrel{\rightarrow}{\vec{z}}\_{\epsilon(i)} \quad \quad i = 1, 2, \dots, \gamma \tag{22}$$

where <sup>→</sup> *<sup>d</sup> <sup>i</sup>*−<sup>1</sup> is the shrapnel distance of the exploded mines, *<sup>F</sup>* is the fitness function, and <sup>→</sup> *z <sup>e</sup>* is the best location.

Exploitation phase can be defined as

$$d\_i = \sqrt{\left(\stackrel{\rightarrow}{z}\_{\epsilon(i)} - \stackrel{\rightarrow}{z}\_{\epsilon(i-1)}\right)^2 + \left(F\_{(i)} - F\_{(i-1)}\right)^2}, \qquad i = \gamma + 1, \ldots, \text{Max\\_iteration} \tag{23}$$

$$\stackrel{\rightarrow}{z}\_{c(i)} = \left\{ \stackrel{\rightarrow}{d}\_{i-1} \right\} \times \{ \text{rand} \} \times \cos \alpha \quad \stackrel{\leftarrow}{i} = \gamma + 1, \dots, \text{Max\\_iteration} \tag{24}$$

The initial distances of the shrapnel pieces are gradually reduced in the exploitation phase. This can be achieved by reducing the user to converge constant (σ). The reduction in the initial distance is determined using

$$\stackrel{\rightarrow}{d}\_{i} = \frac{\stackrel{\rightarrow}{d}\_{i-1}}{e^{(\frac{i}{\delta})}} \quad i = 1, 2, \dots, Max\\_iteration\tag{25}$$

The mine blast algorithm may be summarized in the flowchart of Figure 6.

Usually, MBA uses an objective function check the optimality of the resulted parameters. There are several forms of the objective function [41], such as the Integral Time Absolute Error (ITAE), Integral Square Error (ISE), and Integral Time Square Error (ITSE). Nevertheless, ITAE is selected due to its better performance. Therefore, the suggested objective function in this paper is ITAE that is given by

$$ITAE = \int\_{0}^{t\_s} \left( (|\Delta e\_1| + |\Delta e\_2|) \times t \right) dt \tag{26}$$

$$
\Delta \mathfrak{e}\_1 = \Delta \omega\_{r(ref)} - \Delta \omega\_r \tag{27}
$$

$$
\Delta \mathcal{C}\_2 = \Delta V\_{Load(ref)} - \Delta V\_{Load} \tag{28}
$$

where, *ts* is the simulation time and [*Kp1*, *Ki1*, *Kp2*, and *Ki2*] are the parameters to be estimated, *x* =, and the constraints are assumed to be

$$0.45 \le \mathcal{K}\_{pz} < 15 \text{, } 0.45 \le \mathcal{K}\_{iz} < 15 \qquad z = 1 \text{, } 2 \tag{29}$$

**Figure 6.** Mine blast algorithm flowchart.

The proposed optimal controlling parameters of MBA are given in Table 1.


**Table 1.** Optimal mine blast algorithm controlling parameters.

#### *4.3. Boost Converter Controller*

The boost converter control circuit is shown in Figure 7. It is a simple voltage regulator. The reference voltage signal is generated based on the voltage error. Then the error is fed to the Proportional-Integral-Differentiator (PID) controller that generates the modulating signal to the Pulse Width Modulator (PWM) unit. In turn, the PWM unit generates the suitable duty cycle pulses for the converter switch.

**Figure 7.** Boost converter controller block diagram.

#### *4.4. Induction Motor Controller*

There are two techniques to control IM: vector and scalar control. The vector control technique is precise and has a high-performance operation. Hence, the speed of the induction motor is controlled using an optimal vector control technique as shown in Figure 8. The actual speed is measured and compared to the reference speed producing the error that is manipulated by an optimal PI controller. The controller generates the reference torque for the vector control. The rotor flux and torque of the IM are estimated using the IM model. The details of vector control and estimators are presented by Trzynadlowski et al. [42].

#### **5. Simulation Results**

Computer simulations have been carried out to prove the performance of the proposed system under loads and wind speed changes. The proposed system shown in Figure 2 is simulated using MATLAB software package (MATLAB 16, Math Works, Torrance, CA, USA) and tested under various values of wind velocity, IM speed changes, and static load changes. The management of the energy exchange algorithm of the proposed island microgrid is shown by the flowchart of Figure 9.

Figure 10 shows the obtained results for various system parameters like wind speed, FC power, IG (torque-stator-current-speed), the FC pressure of hydrogen and oxygen, the power required by the load, Dc bus voltage, static load (current–voltage), and IM (speed-torque-stator current). The system response is tested at step changes in wind velocity, load impedance, IM speed, and IM load torque. This figure shows that the wind speed varies between 11 and 14 m/s, as shown in Figure 10a. This figure shows also that as the wind speed increases the IG (speed-torque-stator current) increases as well, as indicated in Figure 10b–d, respectively. Enlarging of Figure 10d is shown in Figure 10e. The FC pressure of H2 and O2 are present in Figure 10f. Also, the wind power increases with the wind speed

increase as shown in Figure 10g. On the other hand, Figure 10g shows that the fuel cell compensates any reduction in wind power and the load power is the sum of the wind power plus FC power.

**Figure 8.** Block diagram of the IM controlled via vector control.

**Figure 9.** The flowchart of the power exchange strategy in the proposed autonomous microgrid.

Per unit DC-link actual and desired load voltage and its enlarging are shown in Figure 10h,i, respectively. These figures show that the applied controller tracks well the desired load voltage. It is clear that the response has little overshoot and settling time against all disturbances. This leads also to constant AC output voltage of the inverter as shown in Figure 10j,k.

The FC power increased at a time of 2 s, where the static load current is increased as shown in Figure 10g,l. Also, Figure 10g shows that the fuel cell generated power is more increased in time 2.25 s, where the wind power is decreased. However, the FC power is increased to recover the load power increase. Figure 10g shows also that the FC power decreased when the static load current decreased at time 4.5 s as shown in Figure 10l,m.

Figure 10n,o show the speed response of the induction motor and its enlarging respectively. From these figures it is seen that the vector controller tracks very well the reference speed of the induction motor. As indicated there is no overshoot and without settling time. Figure 10q shows the stator current of the IM at different speeds and torques. However, the IM load torque changes between 7 and 10 Nm and the IM speed varies between 120 and 200 rad/s, as shown in Figure 10p,n, respectively.

The obtained results are compared with the results obtained in [37], where sliding mode control (SMC) and NARMA-control are applied. The results show that both the proposed optimal control and the robust SMC are able to achieve good voltage and current waveforms parameters and to track the reference DC-link voltage and motor speed with very small overshoot and zero steady state error.

**Figure 10.** *Cont.*

**Figure 10.** *Cont.*

**Figure 10.** *Cont.*

**Figure 10.** *Cont.*

**Figure 10.** *Cont.*

**Figure 10.** Simulation results of the proposed system. (**a**) Wind velocity, (**b**) IG speed, (**c**) IG torque, (**d**) IG stator current, (**e**) enlarging of (**d**), (**f**) FC pressure of H2 and O2, (**g**) generated power, (**h**) DC-link voltage (pu), (**i**) enlarging of (**h**), (**j**) static load voltage, (**k**) enlarging of (**j**), (**l**) static load current, (**m**) enlarging of (**l**), (**n**) IM speed, (**o**) enlarging of (**n**), (**p**) IM torque, and (**q**) IM stator current.

#### **6. Conclusions**

This article proposed a microelectrical power grid system composed of an optimal controller design using an MBA algorithm. This studied controlled power system mainly includes hybrid wind/fuel cell generation unit which feeding both dynamic and static loads. These loads are fed by the fuel cell and the wind power generation system. At high values of wind speed wind power acts as the master source that supplies the loads and store hydrogen in the FC via the electrolyzer. Consequently, at low values of the wind speed, the FC acts as a slave that supplies the loads.

IM as a dynamic load, a series R-L load, and as a static load are considered in this paper. The main inverter controller has two nested control loops. The outer loop (voltage loop) uses an optimal PI controller, while the inner loop (current loop) uses hysteresis controller current. On the other hand, the rotor speed of the IM is controlled using optimal vector control.

The proposed microgrid system is simulated using Simulink/MATLAB software and is tested in step variations of wind speed, IM rotor speed, IM torque, and static load current. The results of the simulation show that the proposed generation system success to supply the loads perfectly under all disturbances. It is indicated that the performance of the main inverter controller is excellent, as the load power responses have low overshoot accompanied by small settling time. Also, the proposed optimal controller is able to maintain the DC-link voltage and hence the AC load voltage at its reference value for any variations in wind velocity and the current of the static load and/or dynamic load parameters variations. We also found that the speed of the IM follows its desired value without any settling time or any overshoot. The obtained results show that both the generated wind and fuel cell powers are generated so that the wind power feeds the load power demand, while the fuel cell power compensates for any extra needed power.

**Author Contributions:** I.E.A., A.M.K., and S.A.Z. conceived, designed the system model, analyzed the results, and wrote the paper.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclatures**



#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Design and Implementation of the O**ff**-Line Robust Model Predictive Control for Solid Oxide Fuel Cells** †

#### **Narissara Chatrattanawet 1, Soorathep Kheawhom 1, Yong-Song Chen <sup>2</sup> and Amornchai Arpornwichanop 1,\***


Received: 14 September 2019; Accepted: 23 November 2019; Published: 3 December 2019

**Abstract:** An off-line robust linear model predictive control (MPC) using an ellipsoidal invariant set is synthesized based on an uncertain polytopic approach and then implemented to control the temperature and fuel in a direct internal reforming solid oxide fuel cell (SOFC). The state feedback control is derived by minimizing an upper bound on the worst-case performance cost. The simulation results indicate that the synthesized robust MPC algorithm can control and guarantee the stability of the SOFC; although there are uncertainties in some model parameters, it can keep both the temperature and fuel at their setpoints.

**Keywords:** solid oxide fuel cell; robust model predictive control; off-line calculation; control synthesis

#### **1. Introduction**

A solid oxide fuel cell (SOFC) is a promising fuel cell technology that can be used in co-generation systems for widespread commercial applications [1]. No moving parts, quiet operation, low pollution, and high efficiency are the advantages of fuel cells. Many researchers have discussed the considerable environmental benefits of fuel cell technology [2]. Using SOFC technology also involves the depletion of greenhouse gas emissions when compared with traditional energy generation methods. Moreover, there is interest in the development of the fuel cell technology as a substitute for internal combustion [3]. In general, a SOFC is operated over a wide temperature range, from 873–1273 K, which leads to high energy conversion efficiency, fuel flexibility, and the possibility for combined heat and power systems [4].

The SOFC can use various fuel types, such as methane, methanol, ethanol, and other hydrocarbons, due to its high operating temperature range. Even though high-chain hydrocarbons, such as n-dodecane, can be used as a fuel for the SOFC system, methane is generally considered for SOFC operation, due to its availability, highest hydrogen to carbon ratio in hydrocarbon substances and low cost [5,6]. As the long-chain hydrocarbon fuel contains high carbon and it has a low hydrogen-to-carbon ratio, fuel processing is required for breaking this fuel down into small substances and increasing the hydrogen-to-carbon ratio for the avoidance of a carbon formation in SOFC [7]. In general, methane can be synthesized, as a major product or a by-product, from many chemical processes, or even formation process [8]. In addition, methane in biogas can be directly fed to SOFC under dry conditions; however, there is a risk that is associated with contaminants in biogas when it is introduced to commercial SOFCs

while using Ni-YSZ anode [9,10]. Therefore, either commercialized material development or fuel processing with cleaning technologies is required. There are many hydrogen production processes to convert methane into hydrogen-rich gas, such as steam reforming, partial oxidation, and autothermal reforming. However, the methane steam reforming process is perhaps the most well-established technology and it is widely used to produce hydrogen in the conventional SOFC system [11]. Internal reforming process can occur within the fuel cell to directly convert hydrocarbon fuel into hydrogen-rich gas since SOFC is operated at high temperatures [12]. The direct internal reforming (DIR) includes the reforming and water gas shift reaction rates and enthalpies, with these reactions occurring on the surface of the anode. The DIR of methane in an anode of the SOFC can possibly be due to the high temperatures that are present in the SOFC anode and it enables high energy conversion efficiency for the system [13]. However, the complete DIR-SOFC showed poorer performance when compared to the DIR-SOFC with partial external reforming, and thus using the pre-reformer with DIR-SOFC might be a suitable operational option [14]. Nevertheless, the internal reforming reaction that occurred at the anode leads to complicated dynamic behavior. Additionally, the steam reforming process is a highly endothermic reaction [15]. The endothermic cooling effect creates a temperature gradient inside the fuel cell stack. The thermal gradient in the cell stack is significantly managed to minimize, because this gradient results in thermal stresses that leads to cell degradation and failure [16,17]. Consequently, efficient control is needed for preventing thermal cracking and ensuring system stability for this process.

The model of SOFC in cell, stack, and system levels has been proposed, and each type of the SOFC model is employed for different purposes, i.e., design, improvement, control, and optimization [18]. Dynamic modeling is especially beneficial for dynamic system analysis, as well as in control design. SOFC operations are often subjected to transient conditions, and, as a result, the fuel cell dynamics have been increasingly considered in modeling activities [19]. Several published works have concentrated on the dynamic modeling and the control of solid oxide fuel cells [20,21]. Li and Choi [22] studied the control of the power output of an SOFC by applying proportional-integral (PI) controllers to maintaining fuel utilization and voltage as the current of the stack changed. To keep the voltage output under load changes, Chaisantikulwat et al. [19] developed an SOFC dynamic model and a feedback control scheme with a PI controller to control cell voltage by manipulating the concentration of H2. The low-order dynamic model that was derived from the step responses was used for designing feedback control. The results showed that the feedback PI controller was able to maintain a constant SOFC voltage for small step changes in the current load. Furthermore, a dynamic model was used to investigate the dynamics of the SOFC stack and design control strategies [23]. A proportional-integral-derivative (PID) controller was implemented to maintain the outlet fuel temperature and the fuel utilization of a planar anode-supported, direct internal reforming solid oxide fuel cell under intermediate-temperature operation. The feed air was used to maintain the outlet fuel temperature when a disturbance in the current density occurred. A control strategy must be more effective in avoiding oscillatory control action as well as in preventing potentially damaging temperature gradients under a higher magnitude of load changes. Stiller et al. [24] developed a dynamic model for the control of an SOFC and gas turbine hybrid system. The SOFC power, fuel utilization, air flow, and cell temperature were controlled while using a proportional–integral–derivative (PID) type controller. However, the conventional PID controller cannot guarantee stability and performance when large disturbances occur.

Model predictive control (MPC), which is a multivariable control algorithm, computes a controller action while using a process model to predict the processes output trajectory in the future [25]. The implementation of MPC requires the identification of an internal process model. Therefore, applying model-based controllers, such as MPC, is more challenging when compared to PI or PID controllers for which explicit controller equations exist [26]. Zhang et al. [25] developed the nonlinear MPC controller (NMPC) for a planar SOFC while using the moving horizon estimation (MHE) method. The current density and molar flow rates of fuel and air were manipulated variables to control the output power, fuel utilization, and cell temperature. The proposed NMPC controller

can drive the SOFC following the desired output trajectory when the power output was changed under constant fuel utilization and temperature. In addition, many real chemical processes involve a high degree of parameter uncertainty. Some studies have focused on the development of a robust MPC to handle nonlinear systems and guarantee system stability, as a traditional MPC algorithm is unable to address plant model uncertainties [27,28]. Kothare et al. [29] synthesized a robust MPC algorithm that explicitly incorporated plant model uncertainties. The state feedback control law was obtained by minimizing the worst-case performance cost. This worst-case scenario was used by the simultaneous design and control methodologies to evaluate the process cost function and constraints that were considered in the process [30]. Manthanwar et al. [31] studied the derivation of the explicit control strategy while using a min–max formulation to safeguard against the worst-case uncertainty problem. This guarantee process feasibility as well as process stability for efficient plant operation. A convex optimization problem with linear matrix inequalities (LMIs) constraints was formulated. Bumroongsri and Kheawhom [32] proposed a robust MPC for uncertain polytopic discrete-time systems. In addition, an ellipsoidal off-line MPC strategy for linear parameter varying (LPV) systems was studied. The smallest ellipsoid that contained the present measured state was determined in each sequence of ellipsoids and the scheduling parameter for LPV was measured on-line. Pannocchia [33] also developed a robust MPC algorithm to stabilize the system that was described while using a linear time-varying (LTV) model. Kouramas et al. [34] focused on the design of an MPC controller to control the cell voltage and cell temperature. The results showed that the controller was able to maintain the SOFC voltage and temperature at the desired values. A comprehensive model of SOFC behavior involves numerous complex phenomena, which include electrochemical reaction and the thermal and mechanical properties of the materials. Thus, the SOFC model involves a great deal of parameter uncertainty; the control design should take the model uncertainty into account. For an on-line synthesis approach, the optimization requirement leads to significant amounts of on-line MPC computational time. When MPC incorporates the model uncertainty, the resulting on-line computation will significantly grow with the number of vertices of the uncertainty set. As a result, an off-line synthesis approach is a focus for generating a robust MPC for an uncertain model. With the off-line approach, the computation of a robust MPC is significantly reduced, with only minor losses in its control performance. Wan and Kothare [35] implemented an off-line LMIs for robust MPC while using an asymptotically stable invariant ellipsoid. An off-line robust output feedback MPC approach can certify the robust stability of the closed-loop system in the presence of constraints and it can stabilize both polytopic uncertain systems and norm bound uncertain systems.

A model-based control system should be designed, while taking uncertain parameters into account, to avoid physical damage and achieve high energy efficiency, as the dynamics of SOFC, especially with a DIR operation, are complicated and its model consists of many key parameters. This study concentrates on control design for the DIR SOFC fed by methane-rich gas. The investigation of transient responses of an SOFC by changing the current density, the air and fuel inlet temperatures, and the air and fuel inlet molar flow rates in terms of velocity, is reported. A MIMO control approach using an off-line robust MPC algorithm with LTV system is implemented to control the SOFC with uncertainty in cell voltage. The paper is organized, as follows: Section 2 presents the mathematical model for the SOFC; Section 3 gives a brief review of the robust MPC algorithm; Sections 4 and 5 outline the application, and results and discussion of the proposed off-line robust MPC to the SOFC; and lastly, Section 6 presents the conclusions.

#### **2. SOFC Model**

The mathematical model of the solid oxide fuel cell (SOFC) consists of mass balances, energy balances, and the electrochemical model. The assumptions for the lumped model of the SOFC are as follows: (i) heat loss to the surroundings is negligible; (ii) all the gases are ideal gas; (iii) pressure gradients inside gas channels are negligible; (iv) the heat capacity of all gases is temperature independent; and, (v) the exit fuel and air temperatures and the cell temperature are the same.

Typically, the SOFC consists of a ceramic ion-conducting electrolyte and two porous electrodes with a sandwich structure (Figure 1). To generate electricity with an SOFC, methane-rich gas is directly fed into the anode side while air, which is the oxidant, is continuously delivered into the cathode side. At the cathode side, oxygen is reduced, which forms oxygen ions. The oxygen ions can diffuse through the ion-conducting electrolyte to the anode/electrolyte interface. At the anode side, the oxygen ions chemically react with hydrogen in the fuel, producing water and electrons. The electrons are transported via the external circuit and back to the cathode/electrolyte interface, thus producing electrical energy. Exhaust gases and heat are also produced by the SOFC as by-products. The reforming, electrochemical, and energetic models are simultaneously solved to obtain an exact solution [36].

**Figure 1.** Schematic diagram of solid oxide fuel cell operation.

#### *2.1. Mass and Energy Balances*

The internal methane steam reforming (MSR) reaction in porous-supported SOFC is the most important factor for determining the performance of the SOFC [37]. Furthermore, it is the main reaction for hydrogen production. Table 1 shows the reactions that occurred within the SOFC, which include steam reforming, water-gas shift (WGS), and overall redox reaction [38]. These reactions are used in mass and energy balances. In the fuel channel, it is assumed that methane can only be reformed to hydrogen, carbon monoxide, and carbon dioxide and, therefore, cannot be electrochemically oxidized [23]. In the endothermic steam reforming reaction, fuel in the presence of a catalyst produces hydrogen and carbon monoxide. Table 1 shows the rate expression of the steam reforming reaction *R*(i) [38], where *k*<sup>0</sup> is the pre-exponential constant, being equal to 4272 mol s−<sup>1</sup> m−<sup>2</sup> bar−1, and *E*<sup>a</sup> is the activation energy, equal to 82 kJ mol−1. Excess steam is used to prevent carbon formation on the catalyst and force the reaction to completion. An associated reaction to the reforming reaction is the water-gas shift reaction. Unlike the steam reforming reaction, the water gas-shift reaction is an exothermic reaction. The rate expression of the water gas shift reaction is written as *R*(ii). The overall redox reaction *R*(v) associates with the electric current density (*j*), according to Faraday's law.


**Table 1.** Reactions and reaction rates considered in a solid oxide fuel cell (SOFC) [38].

The lumped-parameter modeling, when only considering changes in time, is a simple approach for describing the dynamic modeling of the solid oxide fuel cell. Xi et al. [39] showed that lumped-parameter models are adequate for systems-level analysis and control through experimental validation. Moreover, the lumped model has been implemented for analysis and control of the planar SOFC systems [40]. Consequently, this work has used the lumped-parameter model for analysis, design, and control of the SOFC.

Equations (1) and (2), respectively, give the mass balances in the fuel and air channels, which provide the amount in moles of each species in the SOFC. The gas compositions in the fuel channel consist of CH4, H2O, CO, H2, and CO2, while O2 and N2 are the gas species in the air channel. The mass balances are:

$$\frac{dn\_{i,f}}{dt} = \dot{n}\_{i,f}^{in} - \dot{n}\_{i,f} + \sum\_{\mathbf{k} \in \{\mathbf{(i)}, (\mathbf{ii}), (\mathbf{v})\}} \upsilon\_{i,\mathbf{k}} R\_{\mathbf{k}} A \tag{1}$$

$$\frac{dn\_{i,\mathfrak{a}}}{dt} = \dot{n}\_{i,\mathfrak{a}}^{\dot{m}} - \dot{n}\_{i,\mathfrak{a}} + \upsilon\_{i,(\mathbf{v})} \mathcal{R}\_{(\mathbf{v})} A \tag{2}$$

where . *ni*, *<sup>f</sup>* and . *ni*,*<sup>a</sup>* are the molar flow rate of species *i* in the fuel and air channels, respectively; υ*i*,k is the stoichiometric coefficient of component *i* in reaction *k*; *R*<sup>k</sup> is the rate of reaction k; and, *A* is a reaction area.

The temperature change within the cell is neglected for the energy balance. Equations (3) and (4) are used to compute the SOFC temperature (*TFC*).

$$\frac{dT\_{\rm FC}}{dt} = \frac{1}{\rho\_{\rm SOFC} \rm Cp\_{\rm SOFC} V\_{\rm SOFC}} \left( \dot{Q}\_{f,in} - \dot{Q}\_{f,out} + \dot{Q}\_{a,in} - \dot{Q}\_{a,out} + \sum\_{\mathbf{k} \in \{\rm(i), (ii), (v)\}} (-\Delta H)\_{\mathbf{k}} R\_{\mathbf{k}} A - jA V\_{\rm FC} \right) \tag{3}$$

$$\dot{Q}\_i = \sum\_j \dot{n}\_j \text{Cp}\_j (T\_i - T\_{ref}) \tag{4}$$

where . *Qi* is the enthalpy flow in/out each fuel cell channel.

#### *2.2. Electrochemical Model*

The Nernst equation explained the difference between the thermodynamic potentials of the electrode reactions is used (Equation (5)) to determine the reversible cell voltage or theoretical open-circuit voltage (*EOCV*).

$$E\_{\rm OCV} = E\_0 - \frac{RT\_{\rm FC}}{2F} \ln\left(\frac{p\_{\rm H\_2O}}{p\_{\rm H\_2}p\_{\rm O\_2}^{0.5}}\right) \tag{5}$$

where *E*<sup>0</sup> is the open-circuit potential at the standard pressure, which is related to the SOFC temperature, as shown in Equation (6) [41].

$$E\_0 = 1.253 - 2.4516 \times 10^{-4} T\_{\rm FC}(\rm K) \tag{6}$$

When an external load is combined, the actual voltage (*VFC*) is lower than the open-circuit voltage, owing to the voltage losses: ohmic losses (ηOhm), concentration overpotentials (ηconc), and activation overpotentials (ηact), which rely on the SOFC temperature, current density, and fuel compositions. Consequently, the cell voltage can be calculated by subtracting the open-circuit voltage with the voltage drops due to the various losses from the theoretical open circuit voltage, as reported by Aguiar et al. [23]:

$$V\_{\rm FC} = E\_{\rm CCV} - \left(\eta\_{\rm Chm} + \eta\_{\rm conc} + \eta\_{\rm act}\right) \tag{7}$$

$$\eta\_{\text{Chm}} = j \left( \frac{\tau\_{\text{anode}}}{\sigma\_{\text{anode}}} + \frac{\tau\_{\text{electrolyte}}}{\sigma\_{\text{electrolyte}}} + \frac{\tau\_{\text{cathode}}}{\sigma\_{\text{cathode}}} \right) \tag{8}$$

$$\eta\_{\rm conc} = \frac{RT\_{\rm FC}}{2F} \ln \left( \frac{p\_{\rm H\_2O,TPB} p\_{\rm H\_2}}{p\_{\rm H\_2O} p\_{\rm H\_2,TPB}} \right) + \frac{RT\_{\rm FC}}{4F} \ln \left( \frac{p\_{\rm O\_2}}{p\_{\rm O\_2,TPB}} \right) \tag{9}$$

$$p\_{\rm HI\_2,TPB} = p\_{\rm HI\_2,f} - \frac{RT\tau\_{\rm anode}}{2FD\_{\rm eff,anode}}j\tag{10}$$

$$p\_{\rm H\_2O,TPB} = p\_{\rm H\_2O,f} + \frac{RT\tau\_{\rm anode}}{2FD\_{\rm eff,anode}}j\tag{11}$$

$$p\_{\rm O2,TPB} = P - (P - p\_{\rm O2}) \exp\left(\frac{RT\tau\_{\rm cathode}}{4FD\_{\rm eff,cathode}P}j\right) \tag{12}$$

$$j = j\_{0, \text{anode}} \left[ \frac{p\_{\text{H}\_2, \text{TPB}}}{p\_{\text{H}\_2}} \exp \left( \frac{a n F}{R T\_{\text{FC}}} \eta\_{\text{act,anode}} \right) - \frac{p\_{\text{H}\_2\text{O}, \text{TPB}}}{p\_{\text{H}\_2\text{O}}} \exp \left( -\frac{(1 - a) n F}{R T\_{\text{FC}}} \eta\_{\text{act,anode}} \right) \right] \tag{13}$$

$$j = j\_{0, \text{anode}} \left[ \frac{p\_{\text{H}\_2, \text{TPB}}}{p\_{\text{H}\_2}} \exp \left( \frac{a n F}{R T\_{\text{FC}}} \eta\_{\text{act,anode}} \right) - \frac{p\_{\text{H}\_2\text{O}, \text{TPB}}}{p\_{\text{H}\_2\text{O}}} \exp \left( - \frac{(1 - a) n F}{R T\_{\text{FC}}} \eta\_{\text{act,anode}} \right) \right] \tag{14}$$

$$\text{j}\_{\text{0, \{\text{nano, cathode}\}}} = \frac{RT\_{\text{FC}}}{nF} k\_{\text{\{anode, cathode}\}} \exp\left(-\frac{E\_{\text{\{anode, cathode}\}}}{RT\_{\text{FC}}}\right) \tag{15}$$

where τanode, τelectrolyte, and τcathode are the thickness of the anode, electrolyte, and cathode layers, respectively; σanode and σcathode are the electronic conductivity of the anode and cathode, respectively; σelectrolyte is the ionic conductivity of the electrolyte; *pi*,TPB is the partial pressure of component *i* at three-phase boundaries (TPB); *D*eff,anode stands for the effective diffusivity coefficient in the anode, while considering a binary gas mixture of H2 and H2O with equi-molar, counter-current, one-dimensional diffusion due to a major difference in the concentration of these two key components at TPB and flow channel that are caused by the electrochemical reaction [23]; *D*eff,cathode stands for the oxygen effective diffusivity coefficient in the cathode (a binary gas mixture of O2 and N2) (the diffusion coefficient for the electrode is assumed to be constant [42]); α is the fraction of the applied potential that promotes the transfer coefficient, which is usually taken to be 0.5 [23]; and, *n* is the number of electrons that are transferred in the single elementary rate-limiting reaction step represented by the Butler–Volmer equation. The activation energies of the electrode exchange current densities (*E*{anode, cathode}) are 137 and 140 kJ mol−<sup>1</sup> for the cathode and anode, respectively [23]. The pre-exponential factors of the cathode and anode exchange current densities (*k*{anode, cathode}) are 2.35 <sup>×</sup> 1011 and 6.54 <sup>×</sup> 1011 <sup>Ω</sup>−<sup>1</sup> <sup>m</sup><sup>−</sup>1, respectively [23].

The power density (*P*) is the amount of power per unit area, which can be determined by multiplying the cell voltage by the current density, as expressed:

$$P = jV\_{FC} \tag{16}$$

The fuel utilization factor (*U*fuel) is the ratio between the total fuel consumption for electricity production and the total inlet fuel, as defined:

$$\mathcal{U}\_{\text{fuel}} = \frac{\bar{j}LW}{(8Fy\_{\text{CH}\_4}^0 + 2Fy\_{\text{H}\_2}^0 + 2Fy\_{\text{CO}}^0)F\_{\text{fuel}}^0} \tag{17}$$

The air ratio (λair) is the inverse of the air utilization factor, which is defined as:

$$
\lambda\_{\rm air} = \frac{y\_{\rm O\_2}^0 F\_{\rm air}^0}{\overline{j}LW/4F} \tag{18}
$$

where *L* is the cell length (cm2), *W* is the cell width (cm2), *j* is the average current density (A cm<sup>−</sup>2), *F* is the Faraday constant (C mol<sup>−</sup>1), *y*<sup>0</sup> *<sup>i</sup>* is the mole fraction (–), and *<sup>F</sup>*<sup>0</sup> *<sup>i</sup>* is the molar flow rate (mol s<sup>−</sup>1).

#### **3. Robust Model Predictive Control**

A linear time-varying (LTV) system is defined for a multi-model paradigm or polytopic uncertainty to synthesize a robust controller:

$$\begin{array}{c} \mathbf{x}(k+1) = \mathbf{A}(k)\mathbf{x}(k) + \mathbf{B}(k)\mathbf{u}(k) \\ \mathbf{y}(k) = \mathbf{C}\mathbf{x}(k) \\ \begin{bmatrix} \mathbf{A}(k) & \mathbf{B}(k) \end{bmatrix} \in \Omega \end{array} \tag{19}$$

where **x**(*k*) is the state of the plant, **u**(*k*) is the control input, and **y**(*k*) is the plant output. Furthermore, the set Ω to be the polytope for polytopic systems is defined as:

$$\Omega \Omega = \mathbb{C} \mathbf{o} \left\{ \begin{bmatrix} \mathbf{A}\_1 & \mathbf{B}\_1 \end{bmatrix} \Big| \begin{bmatrix} \mathbf{A}\_2 & \mathbf{B}\_2 \end{bmatrix} \Big| \dots \Big| \begin{bmatrix} \mathbf{A}\_L & \mathbf{B}\_L \end{bmatrix} \right\} \tag{20}$$

where Co represents the convex hull and **A***<sup>i</sup>* **B***<sup>i</sup>* are the vertices in the convex hull. If the system is the nominal linear time-invariant (LTI) model, it follows that *L* = 1. For other cases, **A**(*k*) **B**(*k*) ∈ Ω, being defined by *L* vertices as:

$$\begin{aligned} \left[\begin{array}{cc} \mathbf{A}(k) & \mathbf{B}(k) \end{array}\right] &= \sum\_{i=1}^{L} \lambda\_{i} \left[\begin{array}{cc} \mathbf{A}\_{i} & \mathbf{B}\_{i} \end{array}\right] \\ \sum\_{i=1}^{L} \lambda\_{i} &= 1, \quad 0 \le \lambda\_{i} \le 1 \end{aligned} \tag{21}$$

The nonlinear system can be represented by a polytopic uncertain linear time-varying system. Liu [43] has shown that every trajectory (**x**, **u**) of a nonlinear system is a trajectory of Equation (19) for some linear time-varying system in the polytope (Ω).

#### *3.1. Robust MPC Algorithm*

In this section, the explanation of the robust constrained MPC problem that is constituted of input and output constraints integrated with linear matrix inequality (LMI) constraints is presented. At each sampling time *k*, a robust performance objective is a min–max problem (minimization of worst-case performance cost) in terms of the quadratic objective for the LTV system, which is given by Equation (22):

$$\begin{array}{ll}\min\_{\mathbf{u}(k+i|k),i=0,1,\ldots,m} & \max\_{\mathbf{l}} & f\_{\text{so}}(k) \\ J\_{\text{os}}(k) = \sum\_{i=0}^{\infty} \left[ \mathbf{x}(k+i|k)^{T} \mathbf{Q}\_{1} \mathbf{x}(k+i|k) + \mathbf{u}(k+i|k)^{T} \mathbf{R} \mathbf{u}(k+i|k) \right] \end{array} \tag{22}$$

where **Q**<sup>1</sup> > 0 and **R** > 0 are the symmetric weighting matrices.

The optimization problem at each sample time step is formulated as a convex optimization problem that is related to linear matrix inequalities constraints [29]. The Lyapunov function *V*(*i*,*k*), which is defined as: *V*(*i*,*k*) = **x**(*k* + *i*/*k*) *<sup>T</sup>***P**(*i*,*k*)**x**(*<sup>k</sup>* <sup>+</sup> *<sup>i</sup>*/*k*), where ∀*k*, ∀*i* ≥ 0 and **P**(*i*,*k*) <sup>&</sup>gt; 0, is utilized to ensure stability for the MPC algorithm. It is noted that, for a vector **x**, **x**(*k*/*k*) represents the state measured at real time *k*, and **x**(*k* + *i*/*k*) represents the state at prediction time *k* + *i* predicted at real time *k*.

#### *3.2. O*ff*-Line Robust MPC Algorithm Using Ellipsoidal Invariant Sets*

The state-feedback control law can be defined as:

$$\mathbf{u}(k+i|k) = F\mathbf{x}(k+i|k), \quad i \ge 0 \tag{23}$$

The state feedback gains *F* in the control law are defined as *F* = *YiQ*<sup>−</sup><sup>1</sup> *<sup>i</sup>* to stabilize the closed-loop system within the ellipsoidal invariant set ε = **<sup>x</sup>**|**x***T***Q**−1**<sup>x</sup>** <sup>≤</sup> <sup>1</sup> . The matrix variables *Qi* > 0 and *Yi* are achieved from the result of the linear objective minimization problem *J*∞(*k*), with the upper bound γ on the worst-case MPC. The symbol ∗ represents the corresponding transpose of the lower block part of the symmetric matrices. Therefore, it is determined that:

$$\min\_{\mathcal{V}\mathcal{Q}\mathcal{Y}\_i\mathcal{Y}\_i} \mathcal{V} \tag{24}$$

subject to

$$
\begin{bmatrix} 1 & \* \\ x\_i & Q\_i \end{bmatrix} \ge 0 \tag{25}
$$

$$
\begin{bmatrix} Q\_i & \* & \* & \* \\ A\_j Q\_i + B\_j Y\_i & Q\_i & \* & \* \\ Q\_1^{1/2} Q\_i & 0 & \gamma I & \* \\ R^{1/2} Y\_i & 0 & 0 & \gamma I \end{bmatrix} \ge 0, \quad j = 1, 2, \ldots, L \tag{26}
$$

Input constraints that are limited by the process equipment impose hard constraints on the manipulated variable **u**(*k*). Boyd et al. [44] proposed the basic idea to handle these constraints for continuous-time systems. However, the discrete-time robust MPC is presented here, as follows:

$$
\begin{bmatrix} X & \* \\ \ Y\_i^T & Q\_i \end{bmatrix} \succeq 0,\tag{27}
$$

with

$$X\_{\rm hlu} \le u\_{\rm h,max}^2 \quad h = 1, 2, \ldots, n\_{\rm u} \tag{28}$$

For output constraints, performance terms impose constraints on the process output y(*k*), as:

$$\left\{ \begin{array}{ccc} & \mathbf{S} & & \\ & \mathbf{C}\_{j} \mathbf{Q}\_{i} + \mathbf{B}\_{j} \mathbf{Y}\_{i} \end{array} \right\} \geq \mathbf{0},$$
 
$$\left\{ \begin{array}{ccc} \mathbf{S} & & \mathbf{0} \\ \end{array} \right\} \geq \mathbf{0},$$

with

$$S\_{\mathcal{T}} \le y\_{r,\text{max}}^2, \quad r = 1, 2, \dots, n\_y \tag{30}$$

It is noted that Equation (27) is used to guarantee input constraint satisfaction, whereas Equation (29) is used to guarantee output constraint satisfaction.

#### **4. SOFC Operation**

In this work, the SOFC models that are mentioned above are implemented and simulated while using Matlab for analysis, design, and controls study of the SOFC. The lumped parameter model of SOFC is created by the relation between mass and energy balances and is used to investigate steady state and dynamic behavior. Table 2 shows the model parameters and operating conditions for the

SOFC. Regarding the steady-state analysis of the cell voltage, power density, and cell temperature related to the current density, the SOFC is designed to be operated at a current density (*j*) of 0.45 A cm<sup>−</sup>2, at which the SOFC efficiency is optimized [45]. Under this operating condition, the cell voltage (*VFC*) is 0.72 V, the power density (*P*) is 0.32 W cm<sup>−</sup>2, and the cell temperature (*TFC*) is 1058 K.


**Table 2.** Model parameters and operating conditions used in SOFC simulation.

#### **5. Results and Discussion**

#### *5.1. Dynamics of SOFC*

In this part, the dynamic behavior and performance of the SOFC simulated by using nonlinear mass and energy balance equations (Section 2), coupled with initial operating conditions (Section 4), are given. By varying the current density, the inlet air and fuel temperatures, and the inlet air and fuel molar flow rates, the responses of the cell temperature and cell voltage are investigated. Figure 2 shows the open-loop response of the cell temperature and voltage that result from step changes of ±10% in the current density, the inlet air and fuel temperatures, and the inlet air and fuel molar flow rates, given in terms of velocity. It can be seen that, in the initial period between 0 and 3000 s, the cell voltage and cell temperature move to 0.72 V and 1058 K, respectively, which are the nominal operating points in the dynamic model. Step changes of +10% in each input are present during the second period. For the third period, which occurs between 6000 and 9000 s, the responses are a result of step changes of −10% in each input. The last period shows a return to the initial conditions.

As seen in Figure 2a, cell voltage depends on the cell operating temperature, which relies on the gas inlet temperatures and current density. The transient response of the cell voltage and temperature is considered by a step change in current density, with the gas inlet temperatures and molar flow rates maintaining the nominal values. The result provides that the increase of cell operating temperature is caused by an instantaneous increase in hydrogen consumption within the cell when the SOFC is operated at high current densities. In addition, the cell voltage suddenly drops, which is associating with ohmic losses, although the increase in cell temperature will ultimately decrease the activation overpotentials and the internal resistance in ohmic losses. The cell voltage is dependent on the magnitude of ohmic losses [40]. The step changes of ±10% in the inlet air and fuel temperatures are also investigated with the other inputs being kept at their nominal values (Figure 2b,c). The results show that the dynamic response of fuel cell voltage and cell temperature depend on the inlet temperatures of the fuel and air. The increase in fuel and air inlet temperatures causes an increase in the cell temperature and voltage. However, it can be seen that the air inlet temperature significantly affects the fuel cell voltage and temperature. High air feed increases the heat input to the fuel cell, which promotes the reforming reaction rate; more H2 generated leads to high power generation. The inlet flow rates of both air and fuel can be expressed in terms of air and fuel velocity, being calculated from air ratio and fuel utilization factor, respectively. Figure 2d,e show the transient responses of fuel cell voltage and cell temperature for step changes of ±10% in the inlet flow rate of air and fuel. All other inputs, such as the current density and the inlet temperatures of air and fuel, are kept constant. Changes in the fuel cell voltage and cell temperature are observed when the molar flow rates are changed. The increase in inlet molar flow rate of fuel causes an increase in the hydrogen production rate, which is associated with an increase in the reforming reaction rate. Heat for the reformer, which is provided by heat produced in the fuel cell, results in a decrease of the cell temperature, because of the endothermic steam reforming reaction. However, the fuel cell voltage increases due to an increase in the partial pressure of hydrogen and the partial pressure of water decreases as a result of an increase in the fuel flow rate. It is noted that the overshoots in fuel cell voltage that occurred after step changes could be attributed to numerical errors, which are generated by the discontinuity in time [19].

**Figure 2.** Voltage and cell temperature responses due to step changes in: (**a**) the current density (*j*); (**b**) the inlet temperature of air (*T*air,in); (**c**) the inlet temperature of fuel (*T*fuel,in); (**d**) the molar flow rate of air in terms of velocity (*ua*); and, (**e**) the molar flow rate of fuel in terms of velocity (*uf*).

#### *5.2. Control of SOFC*

In this part, the implementation of the ellipsoidal off-line robust MPC algorithm for LTV systems is presented and performed while using SeDuMi [46] and YALMIP [47]. The cell voltage (*VFC*) is considered as the uncertainty parameter and it is assumed to be arbitrarily, varying in time within the indicated range. The lumped-parameter model of the SOFC that is represented by the nonlinear mass and energy balance ODEs is linearized, as follows:

$$\begin{aligned} \dot{\mathbf{x}} &= \mathbf{A}\mathbf{x} + \mathbf{B}\mathbf{u} \\ \mathbf{y} &= c\mathbf{x} \end{aligned} \tag{31}$$

where **x** is the state variables of the SOFC, i.e., the moles of each species in the fuel and air channels and the cell temperature, **u** is the inputs, such as the inlet molar flow rates of air and fuel, **A** and **B** are the matrices obtained from linearization, and **y** is the output variables.

Next, the linearized model is discretized while using an Euler first-order approximation in the discrete-time model expressed in Equation (32), with a sampling period of 5 s. Let **¯ <sup>x</sup>**(*k*) = **<sup>x</sup>** <sup>−</sup> **<sup>x</sup>***SS* and **¯ u**(*k*) = **u** − **u***SS*, where the subscript *ss* denotes the corresponding variable at the steady-state condition, which results in the following:

$$\begin{aligned} \dot{\mathbf{x}}(k+1) &= \mathbf{A}(k)\mathbf{\bar{x}}(k) + \mathbf{B}(k)\mathbf{\bar{u}}(k) \\ \dot{\mathbf{y}}(k) &= \mathbf{c}\mathbf{x}(k) \end{aligned} \tag{32}$$

An increase in cell temperature causes the material stresses, which is a potential problem, resulting in the anode and electrolyte material cracking. Additionally, the voltage must be controlled to make a high-efficiency SOFC. The objective is to control the cell temperature and the moles of methane at their desired values by manipulating the inlet molar flow rate of air and fuel with weighting matrices **Q**1= *I* and **R**= 0.1 *I*. In this study, the polytopic uncertainty model includes two vertices due to the existence of one uncertain parameter, *VFC*. This parameter is randomly varied between 0.6 and 0.8 V in time.

Figure 3 shows the schematic diagram of the MIMO control system for the SOFC. The dashed line shows the off-line robust MPC algorithm in which the optimization problem is solved to obtain the corresponding state feedback gain, F. The solid line represents the measured on-line states at each sampling time and the corresponding state feedback control law, **u**. The SOFC non-linear model is linearized (the state, input, and output variables are expressed in the deviation variables) and then discretized while using an Euler first-order approximation, which results in a discrete-time model. The uncertain parameters are implemented with the discrete-time model to generate the vertices sets. After the LTV system is obtained, it is implemented with the robust MPC algorithm. To obtain the gain *F*, the values of *Qi* and *Yi* are determined after optimization. Lastly, the state feedback control, **u**, can be calculated and implemented in the control of the SOFC.

Figure 4 shows the closed-loop responses of the SOFC for the robust MPC based on the LTV systems. Figure 4a shows the closed-loop response of the cell temperature of the SOFC, whereas Figure 4b shows the closed-loop response of the moles of methane in the fuel channel. Figure 5a,b, respectively, show the control inputs of the SOFC, i.e., the inlet molar flow rates of air and fuel in velocity terms. Figure 6 shows the response of the cell voltage; the proposed MPC controller can indirectly drive the cell voltage to its desired value. The results show that when fuel cell temperature shifts from its steady-state value (1058 K), the mole fraction of methane has a slight change from the control action. The controller raises a small flow rate of fuel to reduce the temperature by enhancing the endothermic reforming reaction, which results in a slight increase in methane. In addition, the air flow is initially reduced to decrease the heat input. The robust MPC reduces the fuel flow while increasing the air flow to minimize its impact on controlled variables due to the increased methane. As a change in inputs could affect both of the controlled variables due to the inputs-outputs interaction, the MPC controller had to adjust both of the control inputs, which results in fluctuations in the initial control input profiles. The simulation results show that the proposed control algorithm obtains good

results. The MPC controller for the LTV system can maintain the cell temperature and the moles of methane at their setpoints by manipulating the inlet molar flow rates of air and fuel, respectively.

**Figure 4.** Closed-loop responses of SOFC: (**a**) the cell temperature of SOFC; and, (**b**) the moles of methane in fuel channel (*TFC* and *n*CH4,f are in a deviation form).

**Figure 5.** Control inputs of SOFC: (**a**) the inlet molar flow rate of air in terms of velocity; and, (**b**) the inlet molar flow rate of fuel in terms of velocity (velocities of air and fuel are in a deviation form).

**Figure 6.** Closed-loop response of the cell voltage.

#### **6. Conclusions**

In this paper, an off-line robust MPC algorithm for a discrete-time LTV system with polytopic uncertainty while using the ellipsoidal invariant set was synthesized and designed for controlling a solid oxide fuel cell. The state feedback control law minimizing an upper bound on the worst-case objective function was implemented. The lumped-parameter model was employed to explain the SOFC's dynamic behavior and design the MPC controller. In the open-loop dynamic simulations, the inlet fuel and air temperature, and the current density are related to the fuel cell temperature and voltage. Regarding the performance of the SOFC control, the off-line robust MPC algorithm can guarantee the stability of the SOFC under the model uncertainty. The controller can keep the operating temperature and the moles of methane at their setpoints by manipulating the inlet molar flow rate of air and fuel. Consequently, the cell voltage also moves to its desired value.

**Author Contributions:** Conceptualization, N.C. and A.A.; methodology, N.C. and A.A.; validation, N.C.; formal analysis, N.C. and A.A.; investigation, N.C.; S.K.; Y.-S.C. and A.A.; writing—original draft preparation, N.C. and A.A.; writing—review and editing, S.K.; Y.-S.C. and A.A.; supervision, S.K.; Y.-S.C. and A.A.; project administration, A.A.; funding acquisition, A.A.

**Funding:** This research was funded by Chulalongkorn Academic Advancement into Its 2nd Century Project, Chulalongkorn University.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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