Computational Management Science

, Volume 11, Issue 3, pp 237–266 | Cite as

Design optimization of an internal combustion engine powered CHP system for residential scale application

  • Nikolaos A. Diangelakis
  • Christos Panos
  • Efstratios N. Pistikopoulos
Original Paper


We present an analytical dynamic mathematical model and a design optimization of a residential scale combined heat and power system. The mathematical model features a detailed description of the internal combustion engine based on a mean value approach, and simplified sub-models for the throttle valve, the intake and exhaust manifolds, and the external circuit. The validated zero-dimensional dynamic mathematical model of the system is implemented in gPROMS\(^{\textregistered }\), and used for simulation and optimization studies. The objective of the design optimization is to estimate the optimum displacement volume of the internal combustion engine that minimizes the operational costs while satisfying the electrical and heating demand of a residential 10-house district. The simulation results show that the mathematical model can accurately predict the behavior of the actual system while the design optimization will later be the basis for advanced control studies.


Combined heat power Mathematical modeling  Design optimization 

List of symbols

Latin letters


Area \((\mathrm{m}^{2})\)


Cylinder bore (m)


Valve discharge coefficient


Mass specific heat capacity (J/kg K)


Pressure–flow coefficient


Engine compression ratio


Diameter (m)


Internal energy (J)


Flywheel inertia


Height (m)


Mass specific enthalpy (J/kg)


Lower heating value (J/kg)

\(\Delta H_{c}\)

Enthalpy change of combustion (J/kg)


Length (m)




Mass (kg)


Number of engine cylinders


Pressure (Pa)


Electric power (Watt)


Heat (J)

\(R_{\beta }\)

Ideal gas constant (J/kg K)


Stroke (m)


Stroke to bore ratio


Temperature (K)


Heat transfer rate coefficient


Torque (N m)


Control signal


Volume \((\mathrm{m}^{3})\)


Work (J)


Width (m)


Wetting surface (%)


Mass fraction (kg/kg)

Greek letters

\(\beta ,\gamma , \nu \)

Engine efficiency coefficients

\(\eta \)


\(\lambda \)

Excessive air to fuel ratio (kg/kg)

\(\rho \)

Mass density \((\mathrm{kg}/\mathrm{m}^{3})\)

\(\sigma _{0}\)

Stoichiometric air to fuel ratio (kg/kg)

\(\phi \)

Angle (rad)

\(\omega \)

Angular velocity (rad/s)

Subscripts and superscripts


Initial setting


Rate of size \(a\) [(units of \(a\))/s]


Ambient environment


Atmospheric air






Continuous value


Cylinder gasket






Cylinder or cylindrical


Cylinder walls




Engine block




Engine block


Exhaust gases




Mean effective break


Corresponding to engine friction losses


Corresponding to gas pump losses

\(me\varphi \)

Corresponding to fuel combustion losses


Intake manifold


External circuit


External circuit interaction




Steady state




Throttle valve




Utility water

\(\varphi \)



  1. Afgan NH, Schluender EU (1974) Heat exchangers: design and theory sourcebook. Other information: ISBN 0-07-000460-9. Orig. Receipt Date: 31-DEC-75Google Scholar
  2. Aghdam EA, Kabir MM (2010) Validation of a blowby model using experimental results in motoring condition with the change of compression ratio and engine speed. Exp Therm Fluid Sci 34(2):197–209CrossRefGoogle Scholar
  3. Al-Hinti I, Akash B, Abu-Nada E, Al-Sarkhi A (2008) Performance analysis of air-standard Diesel cycle using an alternative irreversible heat transfer approach. Energy Convers Manag 49(11):3301–3304CrossRefGoogle Scholar
  4. Ambuhl D, Sundstrom O, Sciarretta A, Guzzella L (2010) Explicit optimal control policy and its practical application for hybrid electric powertrains. Control Eng Pract 18(12):1429–1439CrossRefGoogle Scholar
  5. Angulo-Brown F, Fernández-Betanzos J, Diaz-Pico CA (1994) Compression ratio of an optimized air standard Otto-cycle model. Eur J Phys 15(1):38–42Google Scholar
  6. Arisi O, Johnson JH, Kulkarni AJ (1999) Cooling system simulation; part 1—model development. SAE paper 1999–01-0240Google Scholar
  7. Arsie L, Pianese C, Rizzo G (1998) Models for the prediction of performance and emissions in a spark ignition engine. SAE paper 980779Google Scholar
  8. Aussant CD, Fung AS, Ugursal VI, Taherian H (2009) Residential application of internal combustion engine based cogeneration in cold climate–Canada. Energy Build 41(12):1288–1298CrossRefGoogle Scholar
  9. Bhattacharyya S (2000) Optimizing an irreversible diesel cycle—fine tuning of compression ratio and cut-off ratio. Energy Convers Manag 41(8):847–854CrossRefGoogle Scholar
  10. Chen C, Macchietto S (1989) SRQPD-version 1.1: users guide. Technical report, Centre for Process Systems Engineering, Imperial CollegeGoogle Scholar
  11. Cook JA, Powell BK (1988) Modeling of an internal combustion engine for control analysis. Control Syst Mag IEEE 8(4):20–26CrossRefGoogle Scholar
  12. Fazlollahi S, Mandel P, Becker G, Maréchal F (2012) Methods for multi-objective investment and operating optimization of complex energy systems. Energy 45(1):12–22. doi:10.1016/ CrossRefGoogle Scholar
  13. Guzzella L, Onder CH (2010) Introduction to modeling and control of internal combustion engine systems, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  14. Heywood JB (1989) Internal combustion engine fundamentals. McGraw-Hill Inc, USAGoogle Scholar
  15. IEA (2009) Combined heat and power: cogeneration and district energy. OECD/IEA, ParisGoogle Scholar
  16. Jarvis R, Pantelides C (1992) DASOLV: a differential–algebraic equation solver. Center for Process Systems Engineering, Imperial College of Science, Technology, and Medicine, London, Version 1 (2)Google Scholar
  17. Kong XQ, Wang RZ, Huang XH (2005) Energy optimization model for a CCHP system with available gas turbines. Appl Therm Eng 25(2–3):377–391CrossRefGoogle Scholar
  18. Konstantinidis D, Verbatov P, Klemes J (2010) Multi-parametric control and optimisation of a small scale CHP. PRES 210: 13th international conference on process integration, modelling and optimization for energy saving and pollution reduction, vol 21, pp 151–156Google Scholar
  19. Kortela J, Jämsä-Jounela S-L (2012) Model predictive control for biopower combined heat and power (CHP) plant. In: Iftekhar AK, Rajagopalan S (eds) Comput Aided Chem Eng, vol 31. Elsevier, London, pp 435–439Google Scholar
  20. Kuhn V, Klemes J, Bulatov I (2008) MicroCHP: overview of selected technologies, products and field test results. Appl Therm Eng 28(16):2039–2048CrossRefGoogle Scholar
  21. Mehleri ED, Sarimveis H, Markatos NC, Papageorgiou LG (2011) Optimal design and operation of distributed energy systems. In: Pistikopoulos MCG EN, Kokossis AC (eds) Computer aided chemical engineering, vol 29. Elsevier, London, pp 1713–1717. doi:10.1016/B978-0-444-54298-4.50121-5 Google Scholar
  22. Mehleri ED, Sarimveis H, Markatos NC, Papageorgiou LG (2012) A mathematical programming approach for optimal design of distributed energy systems at the neighbourhood level. Energy 44(1):96–104. doi:10.1016/ CrossRefGoogle Scholar
  23. Menon RP, Paolone M, Maréchal F (2013) Study of optimal design of polygeneration systems in optimal control strategies. Energy (0). doi:10.1016/
  24. Moran M, Shapiro HN (1992) Fundamentals of engineering thermodynamics. Wiley, New YorkGoogle Scholar
  25. North American Energy Standards Board (2005) Natural Gas Specs Sheet Accessed July 2012
  26. Ong’iro A, Ugursal VI, Al Taweel AM, Lajeunesse G (1996) Thermodynamic simulation and evaluation of a steam CHP plant using ASPEN Plus. Appl Therm Eng 16(3):263–271. doi:10.1016/1359-4311(95)00071-2 CrossRefGoogle Scholar
  27. Onovwiona HI, Ismet Ugursal V, Fung AS (2007) Modeling of internal combustion engine based cogeneration systems for residential applications. Appl Therm Eng 27(5–6):848–861CrossRefGoogle Scholar
  28. Onovwiona HI, Ugursal VI (2006) Residential cogeneration systems: review of the current technology. Renew Sustain Energy Rev 10(5):389–431CrossRefGoogle Scholar
  29. Paatero JV, Lund PD (2006) A model for generating household electricity load profiles. Int J Energy Res 30(5):273–290CrossRefGoogle Scholar
  30. Pantelides CC (2003) The mathematical modeling of the dynamic behaviour of process systems. Lecture notes on “dynamic behaviour of process systems”. MSc Program of Advanced Chemical Engineering, Imperial College LondonGoogle Scholar
  31. Payri F, Olmeda P, Martin J, Garcia A (2011) A complete 0D thermodynamic predictive model for direct injection diesel engines. Appl Energy 88(12):4632–4641CrossRefGoogle Scholar
  32. Pilatowsky I, Romero RJ, Isaza CA, Gamboa SA, Sebastian PJ, Rivera W (2011) Cogeneration fuel cell-sorption air conditioning systems. Springer, New YorkCrossRefGoogle Scholar
  33. Powell JD (1987) A review of IC engine models for control system design. In: Proceedings of the 10th IFAC world congress, San FranciscoGoogle Scholar
  34. Process Systems Enterprise (1997–2014) gPROMS.
  35. Rakopoulos CD, Kosmadakis GM, Dimaratos AM, Pariotis EG (2011) Investigating the effect of crevice flow on Internal combustion engines using a new simple crevice model implemented in a CFD code. Appl Energy 88(1):111–126Google Scholar
  36. Rausen DJ, Stefanopoulou AG, Kang JM, Eng JA, Kuo TW (2005) A mean-value model for control of Homogeneous Charge Compression Ignition (HCCI) engines. J Dyn Sys Meas Control Trans ASME 127:355–362Google Scholar
  37. Riccio G, Chiaramonti D (2009) Design and simulation of a small polygeneration plant cofiring biomass and natural gas in a dual combustion micro gas turbine (BIO_MGT). Biomass Bioenergy 33(11):1520–1531. doi:10.1016/j.biombioe.2009.07.021 CrossRefGoogle Scholar
  38. Savola T, Fogelholm C-J (2006) Increased power to heat ratio of small scale CHP plants using biomass fuels and natural gas. Energy Convers Manag 47(18–19):3105–3118. doi:10.1016/j.enconman.2006.03.005 CrossRefGoogle Scholar
  39. Savola T, Fogelholm C-J (2007) MINLP optimisation model for increased power production in small-scale CHP plants. Appl Therm Eng 27(1):89–99. doi:10.1016/j.applthermaleng.2006.05.002 CrossRefGoogle Scholar
  40. Savola T, Keppo I (2005) Off-design simulation and mathematical modeling of small-scale CHP plants at part loads. Appl Therm Eng 25(8–9):1219–1232. doi:10.1016/j.applthermaleng.2004.08.009 CrossRefGoogle Scholar
  41. Savola T, Tveit T-M, Fogelholm C-J (2007) A MINLP model including the pressure levels and multiperiods for CHP process optimisation. Appl Therm Eng 27(11–12):1857–1867. doi:10.1016/j.applthermaleng.2007.01.002 CrossRefGoogle Scholar
  42. Shah RK, Subbarao EC, Mashelkar RA (1988) Heat transfer equipment design. Taylor & Francis, LondonGoogle Scholar
  43. Videla J, Lie B (2006) Simulation of a small scale SI ICE based cogeneration system in Modelica/Dymola. In: SIMS 2006—suomen automaatioseurary—47th conference on simulation and modelling, session B1 energy. Helsinki, FinlandGoogle Scholar
  44. Videla J, Lie B (2007) State/parameter estimation of a small-scale CHP model. Accessed July 2012
  45. Way RJB (1976) Methods for determination of composition and thermodynamic properties of combustion products for internal combustion engine calculations. Proc Inst Mech Eng 190(1):687–697CrossRefGoogle Scholar
  46. Williams FA (1985) Combustion theory, 2nd edn. The Benjamin Cummings Publishing Company Inc, AmsterdamGoogle Scholar
  47. Wu DW, Wang RZ (2006) Combined cooling, heating and power: a review. Prog Energy Combus Sci 32(5–6):459–495CrossRefGoogle Scholar
  48. Yokell S (1990) A working guide to shell and tube heat exchanges. McGraw-Hill Inc, USAGoogle Scholar
  49. Yun KT, Cho H, Luck R, Mago PJ (2013) Modeling of reciprocating internal combustion engines for power generation and heat recovery. Appl Energy 102:327–335Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Nikolaos A. Diangelakis
    • 1
  • Christos Panos
    • 1
  • Efstratios N. Pistikopoulos
    • 1
  1. 1.Department of Chemical Engineering, Centre for Process Systems Engineering (CPSE)Imperial College LondonLondonUK

Personalised recommendations