Optimal design of residential cogeneration systems under uncertainty
Introduction
The economic and environmental benefits yielded through the proper use of resources in the industrial sector have motivated the extension to residential complexes (Cucek et al., 2011, Terrazas-Moreno and Grossmann, 2011, Martin and Grossmann, 2012, Ahmetovic et al., 2014, Ibric et al., 2014, Abdelhady et al., 2015). This way, combined heat and power (CHP) systems have become an efficient alternative for supplying the needed power and heat in residential complexes. This is because CHP systems offer several advantages in terms of efficiency (Maghanki et al., 2013), environmental impact (Peacock and Newborough, 2005) and economic cost (De Paepe et al., 2006, Cravioto et al., 2014) compared with conventional systems. The design of cogeneration systems is determined by several factors, as the availability of natural resources that can feed the system (Tchanche et al., 2014), weather conditions (Lazos et al., 2014), energy demands (Alanne and Saari, 2004), available technologies (González et al., 2015) and the conditions and policies of the local energy market (Streimikiene and Baležentis, 2013). In this context, Collazos et al. (2009) proposed a method for management polygeneration systems. Zhou et al. (2013a) presented an economic assessment for distributing energy in a new residential area in China, and Zhou et al. (2013b) incorporated the impacts of the equipment size in designing cogeneration systems. Fazlollahi et al. (2014) presented a multi-objective optimization approach for designing district energy systems. Recently, Fuentes-Cortés et al., 2015a, Fuentes-Cortés et al., 2015b reported an optimization formulation for designing CHP systems for the residential sector; however, this approach did not account for the involved uncertainty in the system. It should be noticed that there are several uncertain factors involved in the design of CHP systems (Jradi and Riffat, 2014, Li and Ierapetritou, 2008). But, usually designing CHP systems is based on overage values of the parameters that represent significant uncertainty (Gamarra and Guerrero, 2015). Nevertheless, this approach is not the best way to account for the involved uncertainty, since the ambient temperature, the energy market prices and the energy demands are factors that have involved significant uncertainty in designing residential CHP systems (Houwing et al., 2008). These variables have been addressed separately for analyzing CHP systems in the residential sector. In this context, Barbieri et al. (2012) proposed a model to adjust the design of CHP systems to variable energy demands in dwellings. Fubara et al. (2014) studied the seasonal changes in energy demands. Rezvan et al. (2013) used Monte Carlo-based models for determining uncertain energy demands, and Al-Mansour and Kozuh (2007) analyzed the uncertain energy prices in the market. Ren and Gao (2010) presented an analysis for the variations of electricity price through a year. Rysanek and Choudhary (2013) accounted for the installation costs and annual electricity demand. Arnold and Yildiz (2015) incorporated Monte Carlo models for the prediction of energy prices in distributed generation systems. Carvalho et al. (2011) proposed a model to take into account the influence of climatic conditions on energy demands, and Kitapbayev et al. (2015) analyzed the losses in the thermal storage systems resulting from changes in ambient temperature. On the other hand, recently there have been reported proper optimization formulations to take into account the involved uncertainty in designing chemical processes. In this context, Steimel and Engel (2015) reported an optimization approach for designing chemical processes under uncertainty. Nemet et al. (2015) incorporated fluctuating utility prices for designing total site energy systems. Ricardez-Sandoval et al. (2011) accounted for parametric uncertainty in design and control of large-scale systems. Nápoles-Rivera et al. (2015) incorporated parametric uncertainty in designing macroscopic water networks. Guillén-Gosálbez and Grossmann (2010) presented a model for designing supply chains under uncertainty, whereas Longinidis and Georgiadis (2013) accounted for the trade-offs between financial performance and credit solvency in designing supply chains under uncertainty. Betancourt-Torcat et al. (2012) presented a study about the environmental and operational factors that affect the production of synthetic crude oil. The importance of financial analysis in the optimization of energy systems has been addressed by Pintaric and Kravanja (2015a). Similar models for the optimal design of processes under uncertainty have been presented by Wendt et al. (2002) for nonlinear modelling of distillation columns and reactors, Ricardez-Sandoval (2012) for the simultaneous design and control of a continuous stirred tank reactor, Gomes et al. (2014) and Bahakim et al. (2014) used uncertainty models for the operation of a reactor–heat exchanger system, Rooney and Biegler (2003) presented an approach for solving the multi-period problem in chemical processes, Sánchez-Sánchez and Ricardez-Sandoval (2013) presented a multi-scenario approach for determining the best operation of some chemical processes, Ostrovsky et al. (2012) presented an analysis for reactor networks involving uncertain data, and Ostrovsky et al. (2013) developed an approach for solving optimization problems with normally distributed uncertain parameters transforming chance constraints into deterministic ones.
It should be noticed that none of previous studies has presented a suitable methodology for selecting and sizing CHP technologies accounting for the involved uncertainty. Therefore, this paper presents an optimization approach for designing domestic CHP systems, accounting for the involved uncertainty in the ambient temperature, energy market conditions, demand for electricity and demand for hot water, based on stochastic forecasting methods. The proposed model is based on a superstructure that allows determining the optimal structure for the CHP system, and the optimal selection for the central CHP units, which can be internal combustion engine (ICE), fuel cell (FC), Stirling engine (SE) and microturbine (MT), coupled to a thermal storage tank and interacting with the grid of the electric company to smooth the gaps between the demand for electricity and hot water. The proposed scheme also accounts for the hourly variability in temperature throughout the day. Weather conditions (especially temperature) modify the energy demand of domestic users. In this work, a case study for a residential complex from the State of Michoacan in Mexico was considered, where the uncertainty for the energy demands and ambient temperatures were accounted for during the optimal design of a CHP system. In this case, the uncertainty was taken into account through normal distributions based on historical behavior of ambient temperature, floating population and changes in energy market prices are used for creating different scenarios. The objective functions are used to measure the financial risk, which is associated with the total annual cost and the environmental risk, which in turn is associated with CO2 emissions.
Section snippets
Problem statement
The problem addressed in this paper is schematically described in Fig. 1, and it can be stated as follows. Given are the hourly seasonal thermal consumptions associated to hot water for sanitary use (HWS), as well as the power demands of a housing complex, the average hourly seasonal temperature and the prices for fuel and hourly electrical rates. The energy demands are subject to the ambient temperature and demographic changes; especially for the floating population (Wei et al., 2014). It is
Model formulation
The proposed model formulation is based on the superstructure shown in Fig. 2, which is a mixed-integer nonlinear programming problem (MINLP) and is described as follows.
Case Study
As case study is presented a residential zone from Mexico located in the central part of the country, which consists of 1,440 homes (the average demands are shown in Fig. S4 (available in the electronic supplementary material)); it presents a stable behavior of temperature during the year (INEGI, 2013). The profiles for the energy demands have been obtained by applying a survey in the zone and through direct measurements. The survey was administered directly into the homes and the direct
Results and discussion
The uncertain scenarios were generated using the normal random distribution in the software MATLAB (MATLAB, 2010). For each analysis, there were generated twenty random scenarios because the complexity to find a solution increases exponentially with the number of scenarios. The behavior of the uncertain parameters has been taken as normal because it may be used when the designer is not able to access to the exact behavior. The multi-objective optimization formulation was coded in the software
Conclusions
This paper has presented a superstructure for the optimal design of domestic CHP systems involving the optimal selection of multiple technologies to satisfy electricity and hot water demands under the uncertainty associated to the ambient temperature, energy market conditions and energy demands considering demographic factors. Based on this superstructure, a mathematical programming formulation has been developed for the simultaneous minimization of the total annual cost and the associated
Acknowledgement
The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) and the Scientific Research Council of the Universidad Michoacana de San Nicolás de Hidalgo in Mexico.
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