Augmented ε-Constraint Algorithm Applied to Multi-objective Optimization Programs of Residential Micro-CHP Systems

Process Integration and Optimization for Sustainability https://doi.org/10.1007/s41660-022-00254-2 ORIGINAL RESEARCH PAPER Augmented ε‑Constraint Algorithm Applied to Multi‑objective Optimization Programs of Residential Micro‑CHP Systems Fatemeh Teymoori H.1 · Amir Safari2 · Mostafa Kamalinasab3 Received: 13 November 2021 / Revised: 17 April 2022 / Accepted: 18 April 2022 © The Author(s) 2022 Abstract Micro-combined heat and power systems (Micro-CHP) are expected to play a major role in reducing carbon dioxide emission, increasing the primary energy and economic saving in the future. In this paper, the optimal planning of a residential MicroCHP system for a single-family house situated in Iran is investigated. In order to achieve this target, a new mixed-integer linear programming model is developed. Mathematical modeling and optimization were carried out for the Micro-CHP system using natural gas, at the residential building level and for three different operating strategies, cost-driven, primary energy driven, and carbon emission driven. Three competing objective functions are simultaneously minimized using an augmented ε-constraint optimization algorithm. This work has multiple novelties, containing the consideration of some economic and technical constraints previously neglected, such as the energy, economic, and environmental effects of replacing conventional energy systems with a residential Micro-CHP system and the effects of integrating an electrical heating element for storing thermal energy (electrical heating element can act as a power sink when required). A detailed case study on a residential building situated in Tabriz city, Iran, was carried out by applying the developed model and the optimum strategies and optimal sizes for Micro-CHP, axillary boiler, and other equipment are obtained. Results have shown that the optimal values of CSR, PESR, and ERR, in the augmented ε-constraint method, were 12.46%, 1.19%, and 88.38%, respectively. In this case, the obtained result for a nominal capacity of Micro-CHP and boiler was 3.6 kW and 1.05 kW, respectively. Finally, the payback period was obtained for 2 years. Furthermore, to understand the influence of key parameters on the planning of the MicroCHP system, the sensitivity analysis has been performed on energy prices. Sensitivity analysis of electricity price indicated that, by increasing the electricity price, the overall annual cost-saving value clearly increases, while increasing gas prices significantly reduces the profitability index. Keywords Micro-CHP · Techno-economic evaluation · Energy and environmental assessment · Electrical heating element Nomenclature υTCHP Total cost of residential Micro-CHP system ($) υTCON Total energy costs of a separate system ($) υCON Investment cost of the separate system ($) υCHP Investment cost of Micro-CHP unit ($) υBoiler Investment cost of the boiler ($) υTank Investment cost of the storage tank ($) * Amir Safari 1 Regional Water Company of Mazandaran, Ministry of Energy, Sari, Iran 2 University of South-Eastern Norway (USN), Kongsberg, Norway 3 Ferdowsi University of Mashhad, Mashhad, Iran υOPCHP Operation cost of Micro-CHP ($) υOPBoiler Operation cost of boiler ($) υGasCON Cost of purchasing gas for separate system ($) υG Cost of buying electricity from the grid ($) υS Benefit of selling electricity to the grid ($) υMCHP Maintenance cost of Micro-CHP ($) υSave Annual energy cost saving ($) υMCON Annual maintenance cost of a separate system ($) υECON Electricity purchasing cost for separate system ($) δCHP Investment cost coefficient of Micro CHP ($/ kw) Boiler δ Investment cost coefficient of boiler ($/kw) δBCON Investment cost coefficient of boiler in a separate system ($/kw) 13 Vol.:(0123456789) Process Integration and Optimization for Sustainability δTank Investment cost coefficient of storage tank ($/ kw) ξRCHP Maintenance cost coefficient of Micro-CHP ($/kWh) ξRBoiler Maintenance cost coefficient of boiler ($/ kWh) RCHP N Nominal capacity of Micro-CHP (kW) NRBoiler Nominal capacity of auxiliary boiler (kW) NRTank Nominal capacity of the storage tank (kW) NRBoilerCON Nominal capacity of auxiliary boiler in a separate system (kW)  Electricity generated by Micro-CHP (kWh) GECHP d,h  Heat produced by Micro-CHP (kWh) GH CHP d,h s  Electrical energy consumed by the electrical GERe d,h heating element (kWh)  Total electrical energy purchased from the GG d,h grid (kWh) GSd,h Total electrical energy sold to the grid (kWh) Boiler Generated heat of boiler (kWh) Td,h STCHP Heat generated by Micro-CHP, stored in the Td,h storage tank (kWh) Sto Heat stored in the storage tank (kWh ( Td,h Binary variable for charging the storage tank bIn d,h Binary variable for discharging the storage bOut d,h tank C Specific heat of water (kJ/kg °C) ETCHP Energy consumption of Micro-CHP (kWh) ECON Energy consumption of separate systems (kWh) CECON Emission of a separate system (kg) CECHP Emission of Micro-CHP (kg) υGC Cost of buying electricity from the grid in the conventional system ($) Out Heat discharged from the storage tank (kWh) Td,h In Heat input to the storage tank (kWh) Td,h BCHP Heat generated by Micro-CHP for using in Td,h building Boiler Heat generated by boiler (kWh) Td,h Re s Heat produced by electrical heating element Td,h (kWh ( E Electrical load (kWh) 𝜅d,h S Space heating load (kWh) 𝜅d,h W Hot water load (kWh) 𝜅d,h ele Power consumption tariff ($/kWh) 𝜛d,h Gas Gas price ($/m3) 𝜛d,h S Selling price of electricity to the grid ($/ 𝜛d,h kWh) Bele  Monthly base fee for electricity price ($) m m Number of months (12) d Number of days (365) h Number hours (24) I Interest rate T lifetime of each system (year) 13 HR Heating ratio (kWh/m3) V Tank Volume of storage tanks (m3) ηb Efficiency of boiler (%) ηt Efficiency of building heating equipment (%) ηe Average efficiency of power plants (%) ηgrid Transmission and distribution efficiency (%) ηeCHP Electrical efficiency of Micro-CHP (%) ηtCHP Thermal efficiency of Micro-CHP (%) ηRes Electricity to heat converting efficiency in electrical heating element (%) k Steps of consumption T Upper bound of water storage temperature (°C) T Lower bound of water storage temperature (°C) Re s GE Maximum electric power of electrical heating element (kW) σ Heat loss coefficient (h−1( NLimCHP Minimal commercial capacity of Micro-CHP (kW) MHbig Big enough parameter γgas Carbon intensity of the natural gas (kg/m3) γele Carbon intensity of the grid (kg/kwh) CSR Cost-saving ratio (%) PESR Primary energy saving ratio (%) ERR Emissions reduction ratio (%) Payback Payback period (year) ρ Density of water (kg/m3) Introduction At the present time, many countries are developing sustainable energy policies to increase the overall energy conversion efficiencies and reduce emissions. So, technologies such as Micro-CHP, which has been promoted (...truncated)