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

## Abstract

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.

### Keywords

Combined heat power Mathematical modeling  Design optimization

### Latin letters

$$A$$

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

$$B$$

Cylinder bore (m)

$$c_{d}$$

Valve discharge coefficient

$$c_{p}$$

Mass specific heat capacity (J/kg K)

$$cpf$$

Pressure–flow coefficient

$$CR$$

Engine compression ratio

$$D$$

Diameter (m)

$$E$$

Internal energy (J)

$$FI$$

Flywheel inertia

$$H$$

Height (m)

$$h$$

Mass specific enthalpy (J/kg)

$$H_{l}$$

Lower heating value (J/kg)

$$\Delta H_{c}$$

Enthalpy change of combustion (J/kg)

$$L$$

Length (m)

$$l$$

Latency

$$m$$

Mass (kg)

$$NoC$$

Number of engine cylinders

$$P$$

Pressure (Pa)

$$Pec$$

Electric power (Watt)

$$Q$$

Heat (J)

$$R_{\beta }$$

Ideal gas constant (J/kg K)

$$S$$

Stroke (m)

$$SR$$

Stroke to bore ratio

$$T$$

Temperature (K)

$$TC$$

Heat transfer rate coefficient

$$To$$

Torque (N m)

$$u$$

Control signal

$$V$$

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

$$W$$

Work (J)

$$Wi$$

Width (m)

$$WS$$

Wetting surface (%)

$$x$$

Mass fraction (kg/kg)

### Greek letters

$$\beta ,\gamma , \nu$$

Engine efficiency coefficients

$$\eta$$

Efficiency

$$\lambda$$

Excessive air to fuel ratio (kg/kg)

$$\rho$$

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

$$\sigma _{0}$$

Stoichiometric air to fuel ratio (kg/kg)

$$\phi$$

$$\omega$$

### Subscripts and superscripts

0

Initial setting

$$\dot{a}$$

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

$$ab$$

Ambient environment

$$air$$

Atmospheric air

$$by$$

By-pass

$$c$$

Compression

$$cont$$

Continuous value

$$cg$$

$$cl$$

Flywheel

$$co$$

Coolant

$$cyl$$

Cylinder or cylindrical

$$cw$$

Cylinder walls

$$d$$

Displacement

$$eb$$

Engine block

$$ec$$

Electric

$$en$$

Engine block

$$ex$$

Exhaust gases

$$f$$

Friction

$$meb$$

Mean effective break

$$mef$$

Corresponding to engine friction losses

$$mepg$$

Corresponding to gas pump losses

$$me\varphi$$

Corresponding to fuel combustion losses

$$mn$$

Intake manifold

$$OTC$$

External circuit

$$pr$$

External circuit interaction

$$rec$$

Rectangular

$$ss$$

$$td$$

Thermodynamic

$$th$$

Throttle valve

$$vl$$

Volumetric

$$water$$

Utility water

$$\varphi$$

Fuel

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