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

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Notes

  1. 1.

    Assuming 4 occupants per residence and a daily need of water equal to 80 gallons per day per capita.

  2. 2.

    Refer to the Appendix for more information.

Abbreviations

\(A\) :

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)

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

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)

\(\phi \) :

Angle (rad)

\(\omega \) :

Angular velocity (rad/s)

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

\(cg\) :

Cylinder gasket

\(cl\) :

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

\(ss\) :

Steady state

\(td\) :

Thermodynamic

\(th\) :

Throttle valve

\(vl\) :

Volumetric

\(water\) :

Utility water

\(\varphi \) :

Fuel

References

  1. Afgan NH, Schluender EU (1974) Heat exchangers: design and theory sourcebook. Other information: ISBN 0-07-000460-9. Orig. Receipt Date: 31-DEC-75

  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):197–209

    Article  Google 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):3301–3304

    Article  Google 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):1429–1439

    Article  Google 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):38–42

  6. Arisi O, Johnson JH, Kulkarni AJ (1999) Cooling system simulation; part 1—model development. SAE paper 1999–01-0240

  7. Arsie L, Pianese C, Rizzo G (1998) Models for the prediction of performance and emissions in a spark ignition engine. SAE paper 980779

  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):1288–1298

    Article  Google Scholar 

  9. Bhattacharyya S (2000) Optimizing an irreversible diesel cycle—fine tuning of compression ratio and cut-off ratio. Energy Convers Manag 41(8):847–854

    Article  Google Scholar 

  10. Chen C, Macchietto S (1989) SRQPD-version 1.1: users guide. Technical report, Centre for Process Systems Engineering, Imperial College

  11. Cook JA, Powell BK (1988) Modeling of an internal combustion engine for control analysis. Control Syst Mag IEEE 8(4):20–26

    Article  Google 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/j.energy.2012.02.046

    Article  Google Scholar 

  13. Guzzella L, Onder CH (2010) Introduction to modeling and control of internal combustion engine systems, 2nd edn. Springer, New York

    Google Scholar 

  14. Heywood JB (1989) Internal combustion engine fundamentals. McGraw-Hill Inc, USA

    Google Scholar 

  15. IEA (2009) Combined heat and power: cogeneration and district energy. OECD/IEA, Paris

  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)

  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):377–391

    Article  Google 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 151–156

  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 435–439

    Google Scholar 

  20. Kuhn V, Klemes J, Bulatov I (2008) MicroCHP: overview of selected technologies, products and field test results. Appl Therm Eng 28(16):2039–2048

    Article  Google 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/j.energy.2012.02.009

    Article  Google 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/j.energy.2013.03.070

  24. Moran M, Shapiro HN (1992) Fundamentals of engineering thermodynamics. Wiley, New York

    Google Scholar 

  25. North American Energy Standards Board (2005) Natural Gas Specs Sheet NAESB.org. http://www.naesb.org/pdf2/wgq_bps100605w2.pdf. 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

    Article  Google 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):848–861

    Article  Google Scholar 

  28. Onovwiona HI, Ugursal VI (2006) Residential cogeneration systems: review of the current technology. Renew Sustain Energy Rev 10(5):389–431

    Article  Google Scholar 

  29. Paatero JV, Lund PD (2006) A model for generating household electricity load profiles. Int J Energy Res 30(5):273–290

    Article  Google 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 London

  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):4632–4641

    Article  Google Scholar 

  32. Pilatowsky I, Romero RJ, Isaza CA, Gamboa SA, Sebastian PJ, Rivera W (2011) Cogeneration fuel cell-sorption air conditioning systems. Springer, New York

    Google Scholar 

  33. Powell JD (1987) A review of IC engine models for control system design. In: Proceedings of the 10th IFAC world congress, San Francisco

  34. Process Systems Enterprise (1997–2014) gPROMS. http://www.psenterprise.com/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):111–126

  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 127:355–362

  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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google Scholar 

  42. Shah RK, Subbarao EC, Mashelkar RA (1988) Heat transfer equipment design. Taylor & Francis, London

    Google 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, Finland

  44. Videla J, Lie B (2007) State/parameter estimation of a small-scale CHP model. http://www.ep.liu.se/ecp/027/014/ecp072714.pdf. 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):687–697

    Article  Google Scholar 

  46. Williams FA (1985) Combustion theory, 2nd edn. The Benjamin Cummings Publishing Company Inc, Amsterdam

    Google Scholar 

  47. Wu DW, Wang RZ (2006) Combined cooling, heating and power: a review. Prog Energy Combus Sci 32(5–6):459–495

    Article  Google Scholar 

  48. Yokell S (1990) A working guide to shell and tube heat exchanges. McGraw-Hill Inc, USA

  49. Yun KT, Cho H, Luck R, Mago PJ (2013) Modeling of reciprocating internal combustion engines for power generation and heat recovery. Appl Energy 102:327–335

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Efstratios N. Pistikopoulos.

Appendix: Optimization in gPROMS with gOPT

Appendix: Optimization in gPROMS with gOPT

In general, the CVP approach assumes that the time-varying control variables are piecewise-constant (or piecewise-linear) functions of time over a specified number of control intervals. The precise values of the controls over each interval, as well as the duration of the latter, are generally determined by the optimization algorithm. As the number of control variables is usually a small fraction of the total number of variables in the problem, the optimization algorithm has to deal only with a relatively small number of decisions, which makes the CVP approach applicable to large problems.

Specifically for this design optimization, two control variables need to be determined over 864 intervals. The first control variable is the engine size. The displacement volume of the engine is a piecewise-constant design variable that remains steady for the entire optimization horizon. The second control variable is the amount of power that needs to be obtained from the grid to cover any power production deficit. The power that needs to be obtained is treated as a piecewise-constant function of time. The objective of the optimization is the minimization of the daily cost of the CHP operation while the demand in both electrical and thermal output is covered.

The solver DASOLV (Jarvis and Pantelides 1992) was implemented for integrations of the model equations at each iteration of the optimization. DASOLV is based on backward differentiation formulae methods for integrating the DAEs.

The SRQPD nonlinear programming code (Chen and Macchietto 1989) implements a reduced sequential quadratic programming algorithm. The NLP algorithm requires the gradients of the constraints and the objective function with respect to the optimization decision variables. The solution of the optimization problem is a two-stage iterative procedure:

  • Integration of the model differential–algebraic equations to determine the objective function and constraints, given initial estimates for the control variables and

  • Implementation of SRQPD to determine new estimates for the control variables.

The optimization ends when the objective function has converged to the minimum. The optimization tolerance was set to 0.0010. More specifically, the criterion for convergence was set as follows:

$$\begin{aligned} a+\frac{b}{\left| f \right| +1}\le \varepsilon _0 \end{aligned}$$

where

$$\begin{aligned} a&= \mathop \sum \limits _{i=1}^{meq} \left| {c_i } \right| +\mathop \sum \limits _{i=meq+1}^m max\left( {0,-c_i } \right) +\mathop \sum \limits _{j=1}^n max\left( {0,\left( {x_j^L -x_j } \right) \left( {x_j -x_j^U } \right) } \right) \\ b&= \left| {\nabla _x f^{T}d} \right| +\mathop \sum \limits _{i=1}^m \left| {\lambda _i c_i } \right| +\mathop \sum \limits _{j=1}^n \left| {\mu _i } \right| max\left( {0,\left( {x_j^L -x_j } \right) \left( {x_j -x_j^U } \right) } \right) \end{aligned}$$

\(\varepsilon _{0}\) :

optimization tolerance

\(f\) :

objective function

\(c\) :

constraint vector

meq :

number of equality constraints

\(n\) :

size of the variable vector \(x\)

\(x_{j}^{L}\) and \(x_{j}^{U}\) :

lower and upper bound of the variable \(x\), respectively

\(d\) :

vector of corrections to \(x\)

\(\lambda _{i}\) :

Lagrange multipliers corresponding to the equality constraints

\(\mu _{i}\) :

Lagrange multipliers corresponding to the inequality constraints.

The control variables, the length of the optimization horizon and the length of individual control intervals may vary significantly resulting into deteriorating the performance of the optimizer. Scaling had to be considered. The scaling follows the general mathematical form:

$$\begin{aligned} \widetilde{q}_j =\frac{q_j -c_j }{d_j } \end{aligned}$$

where \(q_{j}\) is the jth optimisation variable and \(\widetilde{q}_j \) the corresponding scaled variable. \(c_{j}\) and \(d_{j}\) vary according to the scaling procedure. The latter can be based on the range of the optimisation variables, the values of their initial guesses or the value of the gradient of the objective function at the initial guess.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Diangelakis, N.A., Panos, C. & Pistikopoulos, E.N. Design optimization of an internal combustion engine powered CHP system for residential scale application. Comput Manag Sci 11, 237–266 (2014). https://doi.org/10.1007/s10287-014-0212-z

Download citation

Keywords

  • Combined heat power
  • Mathematical modeling
  • Design optimization