Computational Management Science

, Volume 11, Issue 3, pp 237–266

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

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

DOI: 10.1007/s10287-014-0212-z

Cite this article as:
Diangelakis, N.A., Panos, C. & Pistikopoulos, E.N. Comput Manag Sci (2014) 11: 237. doi:10.1007/s10287-014-0212-z


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

\(\varphi \)


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

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