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Optimal Design of Biomass Combined Heat and Power System Using Fuzzy Multi-Objective Optimisation: Considering System Flexibility, Reliability, and Cost

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Abstract

The increase in global energy demands has led to the need for efficient decarbonisation systems to produce renewable energy. One example of such system is the biomass combined heat and power (CHP) system. Biomass CHP systems have been gaining a lot of attention in the past few years. However, the variations of energy demand and biomass supply have created a challenge in synthesising flexible and reliable yet cost-effective biomass CHP systems. A system with high flexibility and reliability requires additional equipment that perform the same functions. The addition of equipment though, would increase the total cost of a biomass CHP system. In this respect, it is a challenge to synthesise a biomass CHP design with high flexibility, high reliability, and low cost. In this paper, a multi-objective fuzzy optimisation model was developed to synthesise the optimal design of the biomass CHP considering the system cost, flexibility, and reliability. Inspired by the reliability importance concept, this work expressed reliability linearly, unlike the complex and non-linear expressions developed in the past. Moreover, the changes of equipment performance under varying loads known as partial load performance is also considered. To demonstrate the proposed approach, a case study was conducted. The objective of the case study was to synthesise a CHP system using biomass from palm oil and wood mills as feed. Several scenarios with different power demand were solved to study the model performance. Additionally, the proposed linear model is compared with a model with non-linear expressions.

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Abbreviations

I :

Index for biomass fuel

j,j’,jj’ :

Index for technologies

p :

Index for product

e :

Index for energy

Fi :

Available flow of biomass fuel

Fj MIN :

Minimum capacity of technology j

Fj MAX :

Maximum capacity of technology j

\( {\upeta}_{ijp}^{\mathrm{FIX}} \) :

Fixed conversion of fuel i to product p through technology j

\( {\upeta}_{ijp}^{\mathrm{PARTIAL}\ \mathrm{LOAD}} \) :

Partial load conversion of fuel i to product p through technology j

PLj :

Partial load constant of technology j

Fj’ MIN :

Minimum capacity of technology j’

Fj’ MAX :

Maximum capacity of technology j’

\( {\upeta}_{pj\hbox{'}e}^{\mathrm{FIX}} \) :

Fixed conversion of product p to energy e through technology j’

\( {\upeta}_{pj\hbox{'}e}^{\mathrm{PARTIAL}\ \mathrm{LOAD}} \) :

Partial load conversion of product p to energy e through technology j’

PLj’ :

Partial load constant of technology j’

CFj VAR,CAPEX :

Variable cost conversion for the capital expenditure of technology j

CFj FIX,CAPEX :

Fixed cost constant for the capital expenditure of technology j

CFj’ VAR,CAPEX :

Variable cost conversion for the capital expenditure of technology j’

CFj’ FIX,CAPEX :

Fixed cost constant for the capital expenditure of technology j’

AF:

Annualising factor

R:

Rate of return for payment period

n:

Number of payment periods

CFj VAR, OPEX :

Variable cost conversion for the operationalexpenditure of technology j

CFj FIX, OPEX :

Fixed cost constant for the operational expenditureof technology j

CFj’ VAR, OPEX :

Variable cost conversion for the operationalexpenditure of technology j’

CFj’ FIX, OPEX :

Fixed cost constant for the operational expenditureof technology j’

Fe,BASE :

Baseline output of energy e

Fe,CHANGE :

Changes of energy e from baseline output

Rj :

Reliability of technology j

Rj’ :

Reliability of technology j’

RMIN,SYSTEM :

Minimum system reliability

RRj :

Relative reliability of technology j

RRj’ :

Relative reliability of technology j’

CUPPER :

Upper limit for cost

CLOWER :

Lower limit for cost

FIUPPER :

Upper limit for flexibility index

FILOWER :

Lower limit for flexibility index

RRUPPER :

Upper limit for relative reliability

RRLOWER :

Lower limit for relative reliability

F ij :

Flow of biomass fuel i to technology j

I j :

Binary variable of technology j

F jp :

Flow of output product p from technology j

F p :

Flow of product p

F pj’ :

Flow of output product p to technology j’

I j’ :

Binary variable of technology j’

F j’e :

Flow of energy e from technology j’

F e :

Flow of energy e

C j CAPEX :

Capital expenditure of technology j

C j’ CAPEX :

Capital expenditure of technology j’

C CAPEX :

Total capital expenditure of the system

C j OPEX :

Operational expenditure of technology j

C j’ OPEX :

Operational expenditure of technology j’

C OPEX :

Total operational expenditure of the system

C TOTAL :

Total cost of the system

FI :

Flexibility index

R jj :

Reliability of technology jj’

I jj :

Binary variable of technology jj’

R SYS :

Reliability of the system

RR TOTAL :

Total relative reliability

λ :

Trade-off degree of satisfaction

λ COST :

Degree of satisfaction for cost

λ FLEX :

Degree of satisfaction for flexibility

λ RELIABILITY :

Degree of satisfaction for reliability

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Acknowledgements

This author would like to acknowledge the support from the School of Engineering and Physical Sciences of Heriot-Watt University Malaysia. The technical support from LINDO SYSTEMS INC. for providing the LINGO v18.0 software is gratefully acknowledged, too.

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  1. School of Engineering and Physical Sciences, Heriot-Watt University Malaysia, 1, Jalan Venna P5/2, Precinct 5, 62200, Putrajaya, Wilayah Persekutuan, Malaysia

    Tommy Asni & Viknesh Andiappan

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Asni, T., Andiappan, V. Optimal Design of Biomass Combined Heat and Power System Using Fuzzy Multi-Objective Optimisation: Considering System Flexibility, Reliability, and Cost . Process Integr Optim Sustain 5, 207–229 (2021). https://doi.org/10.1007/s41660-020-00137-4

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