Modeling and Simulation of Energy Systems Thomas A. Adams II www.mdpi.com/journal/processes Edited by Printed Edition of the Special Issue Published in Processes Modeling and Simulation of Energy Systems Modeling and Simulation of Energy Systems Special Issue Editor Thomas A. Adams II MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor Thomas A. Adams II McMaster University Canada Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Processes (ISSN 2227-9717) from 2018 to 2019 (available at: https://www.mdpi.com/journal/processes/ special issues/simulation energy) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year , Article Number , Page Range. ISBN 978-3-03921-518-8 (Pbk) ISBN 978-3-03921-519-5 (PDF) Cover image courtesy of Jaffer Ghouse. c © 2019 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Thomas A. Adams II Special Issue: Modeling and Simulation of Energy Systems Reprinted from: Processes 2019 , 7 , 523, doi:10.3390/pr7080523 . . . . . . . . . . . . . . . . . . . . . 1 Avinash Shankar Rammohan Subramanian, Truls Gundersen and Thomas Alan Adams II Modeling and Simulation of Energy Systems: A Review Reprinted from: Processes 2018 , 6 , 238, doi:10.3390/pr6120238 . . . . . . . . . . . . . . . . . . . . . 7 Luca Riboldi and Lars O. Nord Offshore Power Plants Integrating a Wind Farm: Design Optimisation and Techno-Economic Assessment Based on Surrogate Modelling Reprinted from: Processes 2018 , 6 , 249, doi:10.3390/pr6120249 . . . . . . . . . . . . . . . . . . . . . 52 Mochamad Denny Surindra, Wahyu Caesarendra, Totok Prasetyo, Teuku Meurah Indra Mahlia and Taufik Comparison of the Utilization of 110 ◦ C and 120 ◦ C Heat Sources in a Geothermal Energy System Using Organic Rankine Cycle (ORC) with R245fa, R123, and Mixed-Ratio Fluids as Working Fluids Reprinted from: Processes 2019 , 7 , 113, doi:10.3390/pr7020113 . . . . . . . . . . . . . . . . . . . . . 82 Sergio F. Mussati, Seyed Soheil Mansouri, Krist V. Gernaey, Tatiana Morosuk and Miguel C. Mussati Model-Based Cost Optimization of Double-Effect Water-Lithium Bromide Absorption Refrigeration Systems Reprinted from: Processes 2019 , 7 , 50, doi:10.3390/pr7010050 . . . . . . . . . . . . . . . . . . . . . 110 Geetanjali Yadav, Leonard A. Fabiano, Lindsay Soh, Julie Zimmerman, Ramkrishna Sen and Warren D. Seider Supercritical CO 2 Transesterification of Triolein to Methyl-Oleate in a Batch Reactor: Experimental and Simulation Results Reprinted from: Processes 2019 , 7 , 16, doi:10.3390/pr7010016 . . . . . . . . . . . . . . . . . . . . . 126 Matias Vikse, Harry A. J. Watson, Truls Gundersen and Paul I. Barton Simulation of Dual Mixed Refrigerant Natural Gas Liquefaction Processes Using a Nonsmooth Framework Reprinted from: Processes 2018 , 6 , 193, doi:10.3390/pr6100193 . . . . . . . . . . . . . . . . . . . . . 135 Taufik Ridha, Yiru Li, Emre Gen ç er, Jeffrey J. Siirola, Jeffrey T. Miller, Fabio H. Ribeiro and Rakesh Agrawal Valorization of Shale Gas Condensate to Liquid Hydrocarbons through Catalytic Dehydrogenation and Oligomerization Reprinted from: Processes 2018 , 6 , 139, doi:10.3390/pr6090139 . . . . . . . . . . . . . . . . . . . . . 151 Matthew D. Stuber A Differentiable Model forOptimizing Hybridization of Industrial Process Heat Systems with Concentrating Solar Thermal Power Reprinted from: Processes 2018 , 6 , 76, doi:10.3390/pr6070076 . . . . . . . . . . . . . . . . . . . . . 172 v Fadhil Y. Al-Aboosi and Mahmoud M. El-Halwagi An Integrated Approach to Water-Energy Nexus in Shale-Gas Production Reprinted from: Processes 2018 , 6 , 52, doi:10.3390/pr6050052 . . . . . . . . . . . . . . . . . . . . . 197 Jianping Li, Salih Emre Demirel, M. M. Faruque Hasan Building Block-Based Synthesis and Intensification of Work-Heat Exchanger Networks (WHENS) Reprinted from: Processes 2019 , 7 , 23, doi:10.3390/pr7010023 . . . . . . . . . . . . . . . . . . . . . 223 Parikshit Sarda, Elijah Hedrick, Katherine Reynolds, Debangsu Bhattacharyya, Stephen E. Zitney and Benjamin Omell Development of a Dynamic Model and Control System for Load-Following Studies of Supercritical Pulverized Coal Power Plants Reprinted from: Processes 2018 , 6 , 226, doi:10.3390/pr6110226 . . . . . . . . . . . . . . . . . . . . . 251 Nathan Zimmerman, Konstantinos Kyprianidis and Carl-Fredrik Lindberg Waste Fuel Combustion: Dynamic Modeling and Control Reprinted from: Processes 2016 , 6 , 222, doi:10.3390/pr6110222 . . . . . . . . . . . . . . . . . . . . . 272 Moksadur Rahman, Valentina Zaccaria and Konstantinos Kyprianidis Diagnostics-Oriented Modelling of Micro Gas Turbines for Fleet Monitoring and Maintenance Optimization Reprinted from: Processes 2018 , 6 , 216, doi:10.3390/pr6110216 . . . . . . . . . . . . . . . . . . . . . 291 Pravin P. S., Ravindra D. Gudi and Sharad Bhartiya Dynamic Modeling and Control of an Integrated Reformer-Membrane-Fuel Cell System Reprinted from: Processes 2018 , 6 , 169, doi:10.3390/pr6090169 . . . . . . . . . . . . . . . . . . . . . 311 Benjamin Decardi-Nelson, Su Liu and Jinfeng Liu Improving Flexibility and Energy Efficiency of Post-Combustion CO 2 Capture Plants Using Economic Model Predictive Control Reprinted from: Processes 2018 , 6 , 135, doi:10.3390/pr6090135 . . . . . . . . . . . . . . . . . . . . . 336 Chen Chen and George M. Bollas Dynamic Optimization of a Subcritical Steam Power Plant Under Time-Varying Power Load Reprinted from: Processes 2018 , 6 , 114, doi:10.3390/pr6080114 . . . . . . . . . . . . . . . . . . . . . 358 Mariana Corengia and Ana I. Torres Effect of Tariff Policy and Battery Degradation on Optimal Energy Storage Reprinted from: Processes 2018 , 6 , 204, doi:10.3390/pr6100204 . . . . . . . . . . . . . . . . . . . . . 377 Kody Kazda and Xiang Li Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks Reprinted from: Processes 2018 , 6 , 198, doi:10.3390/pr6100198 . . . . . . . . . . . . . . . . . . . . . 394 Jiawei Du and William R. Cluett Modelling of a Naphtha Recovery Unit (NRU) with Implications for Process Optimization Reprinted from: Processes 2018 , 6 , 74, doi:10.3390/pr6070074 . . . . . . . . . . . . . . . . . . . . . 425 Ian Miller, Emre Gen ̧ cer and Francis M. O’Sullivan A General Model for Estimating Emissions from Integrated Power Generation and Energy Storage. Case Study: Integration of Solar Photovoltaic Power and Wind Power with Batteries Reprinted from: Processes 2018 , 6 , 267, doi:10.3390/pr6120267 . . . . . . . . . . . . . . . . . . . . . 444 vi Muhammad Ehtisham Siddiqui, Aqeel Ahmad Taimoor and Khalid H. Almitani Energy and Exergy Analysis of the S-CO 2 Brayton Cycle Coupled with Bottoming Cycles Reprinted from: Processes 2018 , 6 , 153, doi:10.3390/pr6090153 . . . . . . . . . . . . . . . . . . . . . 468 vii About the Special Issue Editor Thomas A. Adams II , P.Eng, is Associate Professor and Associate Chair in Chemical Engineering at McMaster University. His research interests are in Process Systems Engineering, particularly with regards to the modeling, simulation, and the design of sustainable chemical and energy processes. This research encompasses different areas of application, including power generation, carbon capture, synthetic fuels, alternative fuels, advanced distillation technology, mobile and modular chemical plants, energy conversion, and eco-techno-economic analyses. Adams is Section Editor-in-Chief of the journal Processes , the chair of the Systems & Control Division of the Canadian Society for Chemical Engineering (CSChE) , and author of the popular textbook Learn Aspen Plus R © in 24 Hours. He has recently been recognized with awards such as the Canadian Journal of Chemical Engineering Lectureship Award, the CSChE Emerging Leader Award, and the Ontario Early Researcher Award, and received the title of University Scholar at McMaster in addition to being named by Industrial & Engineering Chemistry Research’s 2018 Class of Most Influential Researchers ix processes Editorial Special Issue: Modeling and Simulation of Energy Systems Thomas A. Adams II Department of Chemical Engineering, McMaster University, 1280 Main St W, Hamilton, ON L8S4L7, Canada; tadams@mcmaster.ca; Tel.: + 1-905-525-9140 Received: 1 August 2019; Accepted: 2 August 2019; Published: 8 August 2019 Abstract: This editorial provides a brief overview of the Special Issue “Modeling and Simulation of Energy Systems.” This Special Issue contains 21 research articles describing some of the latest advances in energy systems engineering that use modeling and simulation as a key part of the problem-solving methodology. Although the specific computer tools and software chosen for the job are quite variable, the overall objectives are the same—mathematical models of energy systems are used to describe real phenomena and answer important questions that, due to the hugeness or complexity of the systems of interest, cannot be answered experimentally on the lab bench. The topics explored relate to the conceptual process design of new energy systems and energy networks, the design and operation of controllers for improved energy systems performance or safety, and finding optimal operating strategies for complex systems given highly variable and dynamic environments. Application areas include electric power generation, natural gas liquefaction or transportation, energy conversion and management, energy storage, refinery applications, heat and refrigeration cycles, carbon dioxide capture, and many others. The case studies discussed within this issue mostly range from the large industrial (chemical plant) scale to the regional / global supply chain scale. Keywords: modeling; simulation; energy; energy systems; process systems engineering; optimization; process design; operations 1. Introduction Energy systems are currently a subject of rapidly growing interest within the engineering research community. Energy conversion and consumption impacts nearly all aspects of our lives, including the food we eat, the water we drink, the products we buy, how we battle the elements, how we communicate, how we move people and goods from place to place, how we work, and even how we are entertained. Although this has always been true throughout human history, the scale at which energy is consumed today is larger and expanding more quickly than ever before. The associated impacts of our energy consumption on our planet are now becoming so significant that the makeup of the atmosphere itself, particularly with regard to atmospheric CO 2 concentration, is being impacted. Since the possible consequences are so alarming, energy systems engineering has become an extremely important area of research since one key aspect of solving this problem relates to the development of energy systems with far lower environmental impacts. Although energy is used in very diverse ways at scales from large to very small, large-scale systems, such as electric power plants, chemical plants, refineries, and oil and gas supply chains, are the easiest targets for improvement and the likeliest places where meaningful environmental impact reductions can be achieved. This is why almost all of the systems discussed in this Special Issue are in these application areas and, at large scales, range from 100 MW to 1000 MW class plants to massive international supply chains. Moreover, about half of the studies in this issue concern electric power generation, in a large part because fossil-based combustion systems tend to be the largest single-point sources of CO 2 emissions in the Processes 2019 , 7 , 523; doi:10.3390 / pr7080523 www.mdpi.com / journal / processes 1 Processes 2019 , 7 , 523 world. To address these concerns, the articles in this Special Issue took a variety of approaches, including the design of new energy systems and networks, improved control strategies for existing systems, and improved daily or hourly operational strategies for very complex systems. As a consequence of the large scales involved, even relatively small percentage improvements to e ffi ciency or emissions can result in meaningful large-scale impacts. 2. Modeling Types This issue focuses on the modeling and simulation of energy systems, or more precisely, research which relies heavily on mathematical models in order to address critical issues within energy systems. The issue begins with an extensive review of how modeling and simulation is used in energy systems research by Subramanian et al. [ 1 ], which examined and categorized over 300 papers on the subject. They proposed the modeling taxonomy shown in Figure 1 and noted that the “Process Systems Engineering Approach” to modeling energy systems focuses on mathematical modeling using the bottom-up approach. This means that mathematical models of individual process units, pieces of equipment, or process sections are written in the form of equations that describe the thermo-physical phenomena associated with it. Figure 1. Taxonomy of energy systems modeling proposed by Subramanian et al. [ 1 ]. Reproduced with permission from MDPI. Most of the articles in this issue use mechanistic models via a “first principles” approach, in which the equations and constraints derive from fundamental theory related to the first and second laws of thermodynamics, such as mass, energy, and momentum balances. These are usually coupled with equations that represent the physical properties of various chemicals or mixtures under di ff erent conditions, as well as equations describing physical or mechanical behaviour of the process equipment. The model parameters for physical property and equipment models are usually empirically determined in prior studies and are readily available through physical property databases or other sources. As noted in the review by Subramanian et al. [ 1 ], statistical models are becoming increasingly more important in energy systems due to the increasing availability of data and computational capabilities in data analytics. Statistical models attempt to capture important characteristics of processes or process units without the use of fundamental first principles models. The benefits are usually improved computational speed at the risk of losing model rigor, extrapolative power, or 2 Processes 2019 , 7 , 523 certain nuances. For example, in this issue, Riboldi and Nord [ 2 ] use Kriging-type statistical models to create a surrogate of a much larger and more complex first principles model. The surrogate model is used for optimization purposes in place of the more rigorous one to help significantly reduce the computation time of optimization, which would be mostly intractable when using the fully-rigorous model. Similarly, Zimmerman et al. [ 3 ] create a statistical model from a more rigorous one, which is used for model predictive control (MPC). MPC requires very fast model solution times since it must re-solve the model frequently and repeatedly in order to determine ongoing control actions. 3. Implementation and Solution Frameworks Interestingly, the software and implementation frameworks on which the models were built and simulated in this Special Issue varied widely from article to article. The list of software and packages includes, but is not limited to, the following: Aspen Custom Modeler, Aspen Exchanger and Design Rating, Aspen HYSYS, Aspen Plus, Aspen Plus Dynamics, Aspen Properties, casADi, Dymola, EcoInvent, GAMS, JuliaPro, JuMP, LINGO, MATLAB, Minitab, Modellica, Plant Engineering And Construction Estimator, PVWatts, Thermoflex, and other software developed in-house specifically for the articles in this issue, such as SoLCAT and EVA. There were generally two approaches for construction of the models. Most rigorous models of chemical processes were constructed with flowsheeting software (most commonly with the Aspen suite), in which the software builds the overall flowsheet model from a convenient model library containing models of the individual unit operations and connections. Models with a lower resolution (often because the boundaries of the model are at a much larger scale, such as a supply chain), models not based on mass and energy balances, and models with less rigour intended for use in optimization, tended to be implemented in general equation solving software such as GAMS or MATLAB, in which all of the equations needed to be strictly written out by the user. However, the diversity of software packages and implementation methods indicates the wide variety of problem types that were considered throughout this Special Issue. 4. Issue Summary A summary of the articles in this Special Issue is provided in Table 1. It is an interesting snapshot of important research in energy systems and demonstrates both the breadth of problems considered and the depth of detail and understanding involved. Almost all articles use mathematical optimization to some degree, whether to find optimal designs, optimal controllers, or optimal operational strategies. Table 1. Summary of articles in this Special Issue, categorized by problem type. Authors / Ref Application Models and Software Comments Reviews Subramanian, Gundersen, and Adams [1] Field-wide survey of models in energy systems. Modelling taxonomy proposed Proposed connecting the PSE-style bottom-up approach with top-down approach used in energy economics. Energy System Design Riboldi and Nord [2] O ff shore power plants, integrated with renewables. 1st Principles + Kriging. Thermoflex, Plant Engineering, and Construction Estimator, MATLAB. Dynamic considerations with regard to wind and electricity demand. Surrogate models used for optimization purposes. Surindra, Caesarendra, Prasetyo, Mahlia, and Taufik [4] Organic Rankine cycles in geothermal energy systems. 1st Principles of thermodynamic cycles. Blends physical models (experimental apparatus) with mathematical ones. Mussati, Mansouri, Gernaey, Morosuk, and Mussati [5] Adsorption refrigeration cycles. 1st Principles. GAMS. Optimal design with a superstructure approach. 3 Processes 2019 , 7 , 523 Table 1. Cont. Authors / Ref Application Models and Software Comments Yadav, Fabiano, Soh, Zimmerman, Sen, and Seider [6] Transesterification of triolein to methyl-oleate (biofuels). 1st Principles. Aspen Plus with custom models. Experimental validation of models in some conditions. Models used to predict performance in other conditions. Vikse, Watson, Gundersen, and Barton [7] Multi-stream heat exchanger (MHEX) design for natural gas liquefaction. 1st Principles. Julia. Aspen Plus for comparison. Presents nonsmooth framework and algorithm for designing optimal MHEXs when standard methods fail. Ridha, Li, Gençer, Siirola, Miller, Ribeiro, and Agrawal [8] Shale gas condensate to oligomers and alkanes at the wellhead. 1st Principles. Aspen Plus, Aspen Economic Analyzer. Techno-economic analysis. Premise: Cheaper to transport oligomers than Natural Gas Liquids. Stuber [9] Concentrated solar power with thermal energy storage. 1st Principles with empirical elements. JuliaPro / JuMP. Equation oriented, di ff erentiable model for determination of optimal design params. Al-Aboosi and El-Halwagi [10] Integrated water and energy between systems. Mostly empirical models. LINGO. Optimal design of integrated multi-product, multi-source systems considering time-varying solar. Li, Demirel, and Hasan [11] Automatically generate work-heat exchanger networks (WHEN). 1st Principles. GAMS. Phenomena level models. Algorithm to create optimal WHENs from sources and sinks using building block superstructures. Control Systems Sarda, Hedrick, Reynolds, Bhattacharyya, Zitney, and Omell [12] Load-following Supercritical pulverized coal (SCPC). 1st Principles with reduced models. Aspen Plus Dynamics, Aspen Custom Modeler, Aspen Exchanger, and Design Rating. Plant-wide dynamic model for designing and simulating plant-wide control system. Zimmerman, Kyprianidis, and Lindberg [3] Combustion of fuel derived from waste (refuse). 1st Principles. Modellica. MPC with feedforward system developed. Soft sensors. Experimental validation. Rahman, Zaccaria, Zhao, and Kyprianidis [13] Micro gas turbine systems. 1st Principles with data-driven model tuning. EVA (in-house). Dynamic models. Fault detection and diagnostics. Pravin, Guidi, and Bhartiya [14] Integrated reformer-membrane fuel cell systems. 1st Principles ODEs with some empirical characteristics. MATLAB. Controllability analysis. Certain design considerations must be made for controllability purposes. Decardi-Nelson, Liu, and Liu [15] Flexible post-combustion CO 2 capture systems. 1st Principles. casADI, Python, Aspen Properties. Economic MPC for disturbances. Look-up table made from Aspen Properties for fast use. Flexible Operations and Operational Strategies Chen and Bollas [16] Flexible, load-following subcritical coal power plant. 1st Principles. Dymola. Modelon Thermal-Power Library, MATLAB. Dynamic optimization of transitions during load changes. Corengia and Torres [17] Optimal operating schedule of grid-scale battery energy storage. 1st Principles. GAMS. Considers degradation of the batteries, demand cycles, and local tari ff policies. Kazda and Li [18] Optimal operations of natural gas transport networks. 1st Principles. GAMS. Created piecewise linear models to capture nonlinearities with optimization problem tractability. Du and Cluett [19] Operational improvements to existing Naphtha recovery units. 1st Principles and statistical models (Principle Component Analysis). Aspen Plus, Minitab. Aspen Models released. Statistical models suggest unintuitive options, explained by Aspen model. 4 Processes 2019 , 7 , 523 Table 1. Cont. Authors / Ref Application Models and Software Comments Systems Analysis Miller, Gençer, and O’Sullivan [20] Life cycle analysis (LCA) of integrated solar PV, wind, and batteries. Empirical / data driven models. SoLCAT (in-house). Ecoinvent. PVWatts. LCA focused on emissions from use / manufacture of various power sources in several case studies. Siddiqui, Taimoor, and Almitan. [21] Supercritical CO 2 Brayton cycles coupled with bottoming cycles. 1st Principles. Aspen HYSYS. Energy and exergy cycle analysis for working fluid screening. Funding: This research received no external funding. Conflicts of Interest: The author declares no conflict of interest. References 1. Subramanian, A.S.R.; Gundersen, T.; Adams, T.A., II. Modeling and simulation of energy systems: A review. Processes 2018 , 6 , 238. [CrossRef] 2. Riboldi, L.; Nord, L.O. O ff shore power plants integrating a wind farm: Design optimization and techno-economic assessment based on surrogate modeling. Processes 2018 , 6 , 249. [CrossRef] 3. Zimmerman, N.; Kyprianidis, L.; Lindberg, C.-F. Waste fuel combustion: Dynamic modeling and control. Processes 2018 , 6 , 222. [CrossRef] 4. Surindra, M.D.; Caesarendra, W.; Prasetyo, T.; Mahlia, T.M.I. Comparison of the utilization of 110 ◦ C and 120 ◦ C heat sources in a geothermal energy system using organic Rankine cycle (ORC) with R235fa, R123, and mixed-ratio fluids as working fluids. Processes 2019 , 7 , 113. [CrossRef] 5. Mussati, S.F.; Mansouri, S.S.; Gernaey, K.V.; Morosuk, T.; Mussati, M.C. Model-based cost optimization of double-e ff ect water-lithium bromide absorption refrigeration systems. Processes 2019 , 7 , 50. [CrossRef] 6. Yadav, G.; Fabiano, L.A.; Soh, L.; Zimmerman, J.; Sen, R.; Seider, W.D. Supercritical CO 2 transesterification of triolein to methyl-oleate in a batch reactor: Experimental and simulation results. Processes 2019 , 7 , 16. [CrossRef] 7. Vikse, M.; Watson, H.A.J.; Gundersen, T.; Barton, P.I. Simulation of dual mixed refrigerant natural gas liquefaction processes using a nonsmooth framework. Processes 2018 , 6 , 193. [CrossRef] 8. Ridha, T.; Li, Y.; Gençer, E.; Siirola, J.J.; Miller, J.T.; Ribeiro, F.H.; Agrawal, R. Valorization of shale gas condensate to liquid hydrocabons through catalytic dehydrogenation and oligomerization. Processes 2018 , 6 , 139. [CrossRef] 9. Stuber, M.D. A di ff erentiable model for optimizing hybridization of industrial process heat systems with concentrating solar thermal power. Processes 2018 , 6 , 76. [CrossRef] 10. Al-Aboosi, F.Y.; El-Halwagi, M.M. An integrated approach to water-energy nexus in shale-gas production. Processes 2018 , 6 , 52. [CrossRef] 11. Li, J.; Demirel, S.E.; Hasan, M.M.F. Building block-based synthesis and intensification of work-heat exchanger networks (WHENS). Processes 2019 , 7 , 23. [CrossRef] 12. Sarda, P.; Hedrick, E.; Reynolds, K.; Bhattacharyya, D.; Zitney, S.E.; Omell, B. Development of a dynamic model and control system for load-following studies of supercritical pulverized coal power plants. Processes 2018 , 6 , 226. [CrossRef] 13. Rahman, M.; Zaccaria, V.; Zhao, X.; Kyprianidis, K. Diagnostics-oriented modelling of micro gas turbines for fleet monitoring and maintenance operation. Processes 2018 , 6 , 216. [CrossRef] 14. Pravin, P.S.; Gudi, R.D.; Bhartiya, S. Dynamic modeling and control of an integrated reformer-membrane-fuel cell system. Processes 2018 , 6 , 169. 15. Decardi-Nelson, B.; Liu, S.; Liu, J. Improving flexibility and energy e ffi ciency of post-combustion CO 2 capture plants using economic model predictive control. Processes 2018 , 6 , 135. [CrossRef] 16. Chen, C.; Bollas, G.M. Dynamic optimization of a subcritical steam power plant under time-varying power load. Processes 2018 , 6 , 114. [CrossRef] 5 Processes 2019 , 7 , 523 17. Corengia, M.; Torres, A.I. E ff ect of tari ff policy and battery degradation on optimal energy storage. Processes 2018 , 6 , 204. [CrossRef] 18. Kazda, K.; Li, X. Approximating nonlinear relationships for optimal operation of natural gas transport networks. Processes 2018 , 6 , 198. [CrossRef] 19. Du, J.; Cluett, W.R. Modelling of a naphtha recovery unit (NRU) with implications for process optimization. Processes 2018 , 6 , 74. [CrossRef] 20. Miller, I.; Gençer, E.; O’Sullivan, F.M. A general model for estimating emissions from integrated power generation and energy storage. Case study: Integration of solar photovoltaic power and wind power with batteries. Processes 2018 , 6 , 267. [CrossRef] 21. Siddiqui, M.E.; Taimoor, A.A.; Almitani, K.H. Energy and exergy analysis of the S-CO 2 Brayton cycle coupled with bottoming cycles. Processes 2018 , 6 , 153. [CrossRef] © 2019 by the author. 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 / ). 6 processes Review Modeling and Simulation of Energy Systems: A Review Avinash Shankar Rammohan Subramanian 1 , Truls Gundersen 1 and Thomas Alan Adams II 2, * 1 Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Kolbjørn Hejes vei 1B, NO-7491 Trondheim, Norway; avinash.subramanian@ntnu.no (A.S.R.S.); truls.gundersen@ntnu.no (T.G.) 2 Department of Chemical Engineering, McMaster University, 1280 Main St. W, Hamilton, ON L8S 4L7, Canada * Correspondence: tadams@mcmaster.ca; Tel.: +1-905-525-9140 (ext. 24782) Received: 12 October 2018; Accepted: 18 November 2018; Published: 23 November 2018 Abstract: Energy is a key driver of the modern economy, therefore modeling and simulation of energy systems has received significant research attention. We review the major developments in this area and propose two ways to categorize the diverse contributions. The first categorization is according to the modeling approach, namely into computational, mathematical, and physical models. With this categorization, we highlight certain novel hybrid approaches that combine aspects of the different groups proposed. The second categorization is according to field namely Process Systems Engineering (PSE) and Energy Economics (EE). We use the following criteria to illustrate the differences: the nature of variables, theoretical underpinnings, level of technological aggregation, spatial and temporal scales, and model purposes. Traditionally, the Process Systems Engineering approach models the technological characteristics of the energy system endogenously. However, the energy system is situated in a broader economic context that includes several stakeholders both within the energy sector and in other economic sectors. Complex relationships and feedback effects exist between these stakeholders, which may have a significant impact on strategic, tactical, and operational decision-making. Leveraging the expertise built in the Energy Economics field on modeling these complexities may be valuable to process systems engineers. With this categorization, we present the interactions between the two fields, and make the case for combining the two approaches. We point out three application areas: (1) optimal design and operation of flexible processes using demand and price forecasts, (2) sustainability analysis and process design using hybrid methods, and (3) accounting for the feedback effects of breakthrough technologies. These three examples highlight the value of combining Process Systems Engineering and Energy Economics models to get a holistic picture of the energy system in a wider economic and policy context. Keywords: energy systems; modeling and simulation; multi-scale systems engineering; sustainable process design; energy economics; top-down models; hybrid Life Cycle Assessment 1. Introduction Energy is one primary driver of the modern economy that involves several stakeholders such as energy production and distribution firms, energy investors, end users, as well as government regulators. Population growth and improving standards of living, especially in developing countries, are expected to significantly increase energy consumption. The IEA predicts an increase in total primary energy demand (TPED) from 13.8 billion tonnes of oil equivalent (toe) in 2016 to 19.3 billion toe under its “current policies” scenario in 2040 [ 1 ]. Alternatively, in the “sustainable development” scenario where policies are enacted in order to achieve the objectives of the COP 21 Paris agreement (2015) together with universal access to energy services and a large reduction in energy-related Processes 2018 , 6 , 238; doi:10.3390/pr6120238 www.mdpi.com/journal/processes 7 Processes 2018 , 6 , 238 pollution, TPED grows to 14.1 billion toe in 2040. In this period, CO 2 emissions would increase from 32.1 billion tonnes to 42.7 billion tonnes under the current policies scenario or would have to decrease to 18.3 billion tonnes in the sustainable development scenario. Transitioning to a sustainable energy future through the accelerated adoption of clean energy technologies and energy efficiency practices requires the engagement of various decision makers from the scientific, financial, industrial, and public-policy communities with an interdisciplinary approach that combines engineering, economics, and environmental perspectives [2]. An energy system is defined by the Intergovernmental Panel on Climate Change (IPCC) in its fifth Assessment Report as a “system [that] comprises all components related to the production, conversion, delivery, and use of energy” [ 3 ]. Figure 1 shows the different components of an energy system. First, primary energy stored in natural resources (such as fossil fuels, uranium, renewable resources) is harvested and transported to the conversion site(s) in which a wide range of processes (such as combustion, refining, bioconversion, etc.) may take place to transform energy to more usable forms such as electricity and liquid fuels. This conversion process may integrate with local utilities such as the water distribution network. The usable energy is then transported and distributed through a potentially large number of infrastructure components to the final user. Final energy demand can be disaggregated into homogeneous categories of users such as transportation, residential, industrial, and commercial users. However, the energy production, conversion, transportation, and distribution steps combined typically also consume the largest amount of energy as a result of generally low efficiencies [4]. Figure 1. Energy system showing the flow of energy from primary energy supply to final energy consumption. 8 Processes 2018 , 6 , 238 Trade between suppliers and consumers occurs in energy markets with the primary energy price depending on a large number of factors such as supply and demand quantities, geopolitics and international trade policies, interaction with other economic sectors, technological changes, and even natural disasters. Figure 2 presents a comparison of the normalized prices (in $/GJ) of natural gas, oil, and coal fuels in the United States in order to illustrate the complex interdependencies between the energy sector and other sectors. For example, historically speaking, gas and oil have followed approximately the same price trends when expressed on a normalized per-energy basis up until the shale gas boom, which caused an unprecedented and sustained decoupling of oil and gas prices that has persisted for the past decade. Other recognizable events within the past generation include the gulf war of 1990, and the energy crisis and subsequent Great Recession during 2008–2009 that had major impacts on prices, although often temporary. Coal, on the other hand, has followed a relatively stable and consistent trend independent of world events, and has consistently been the lowest cost form of energy. However, it is possible that if gas continues its steady decline further below what are now the lowest prices in a generation, gas could even overtake coal as the cheapest form of energy within about 6–10 years at current rates. Figure 2. The variation of the normalized prices of natural gas, oil, and coal fuels with a variety of factors such as supply and demand quantities, geopolitics and international trade policies, interaction with other economic sectors, technological changes, and even natural disasters. Coal, gas, and oil prices were collected from various publications from the US Energy Information Administration (see inset) depending on fuel type and year (See inset). Note that a small change in the standard indexing procedure for coal explains a slight jump in coal price at the beginning of 2012. Gas prices are for natural gas located at the city gates (i.e., prior to “last mile” transportation). Oil prices are the refiner’s composite cost of oil, which includes transportation and storage of oil, factoring in both domestic and imported crudes. Coal prices are free-on-board prices and do not include shipping or insurance. Prices are normalized by the consumer price index and converted to an energy basis using the following assumed energy densities: 32 GJ per tonne of coal (using medium-volatility bituminous), 6.118 GJ per barrel of oil, and 1037 BTU per standard ft 3 of natural gas. The need to understand and predict the functioning and performance of individual components of the energy system or the overall system behavior motivates the development of models. Several modeling approaches have been proposed in the literature for different purposes. In Section 2, we propose a classification of these approaches into computational, mathematical, and physical models, and outline the capabilities of the different formalisms in describing different phenomena. 9