Combined heat and power economic dispatch by mesh adaptive direct search algorithm
Research highlights
► In this study, an optimization method, namely mesh adaptive direct search (MADS) is introduced to solve combined heat and power (CHP) economic dispatch problem. ► MADS is a recently developed algorithm that is supported by a thorough convergence analysis. The MADS method is illustrated using three test cases taken from the literature. ► Latin hypercube sampling (LHS), particle swarm optimization (PSO) and design and analysis of computer experiments (DACE) algorithms are employed as effective search strategies in MADS to solve the CHPED problems. The results clearly demonstrate that the MADS-based methods are practical and valid for CHPED applications. ► The MADS-DACE algorithm performs superior than or as well as the other recent methods in terms of solution quality, handling constraints and computation time.
Introduction
The conversion of primary fossil fuels to electricity is a relatively inefficient process. Even the most modern combined cycle plants can only obtain efficiencies of between 50% and 60% (Vasebi, Fesanghary, & Bathaee, 2007). Most of the energy wasted in this conversion process is released to the environment as waste heat. Cogeneration or CHP generation is a mature and established technology which has energy efficiency and environmental advantages over other forms of energy supply. Economic dispatch (ED) must be applied to obtain the optimal use of CHP units. The main objective of economic dispatch problem in a conventional power plant is to find the optimal solution for the power production such that the total demand matches the generation with minimum fuel cost. The mutual dependencies of heat and power generation propose a complication in the integration of cogeneration units into the power system economic dispatch. The best CHP schemes can obtain fuel conversion efficiencies of the order of 90% (Vasebi et al., 2007). Cogeneration systems have extensively been used by the industry, recently. Some industrial processes have large heat requirements, either as process steam or piped hot fluid, and large power demands. They can be built in urban areas and utilized as distributed electrical energy sources.
Several researches worked in the field of the CHPED problem. Non-linear optimization algorithms, such as dual and quadratic programming (Rooijers & van Amerongen, 1994), and gradient descent approaches, such as Lagrangian relaxation (Guo, Henwood, & van Ooijen, 1996), have been applied to it. However, these algorithms cannot deal with discontinuous and/or non-monotonic input–output models for generator fuel characteristics. Alternatives to the conventional mathematical approach: evolutionary computation techniques such as genetic algorithm (GA) (Song and Xuan, 1998, Su and Chiang, 2004), evolutionary programming (EP) (Wong & Algie, 2002), multi-objective particle swarm optimization (MPSO) (Wang & Singh, 2008), a hybrid of genetic algorithm with tabu search (GT) (Sudhakaran & Slochanal, 2003), harmony search (HS) (Vasebi et al., 2007), fuzzy decision making (FDM) (Chang & Fu, 1998), improved ant colony search algorithm (ACSA) (Song, Chou, & Stonham, 1999) and self adaptive real-coded genetic algorithm (SARGA) (Subbaraj, Rengaraj, & Salivahanan, 2009) have successfully been applied to the CHPED problem. In the optimization area, many interesting results come from the utilization of pattern search (PS) methods (Torczon, 1997). At this stage, mesh adaptive direct search (MADS) (Audet & Dennis, 2006) is one of the most powerful optimization algorithms that has recently emerged. The MADS method lends itself to optimization problems with discrete and continuous variables, such as the generator loads of the CHP problem. MADS does not depend on derivatives of the objective function of the problem to be solved, non-monotonic functions and accommodating discontinuous. Despite significant advantages of MADS over other optimization approaches, there have been some little scientific efforts directed at applying it to academic and practical problems (Audet et al., 2008, Nicosia and Stracquadanio, 2007).
The main objective of this study is to introduce the MADS algorithm to solve the CHPED problem. Three four-unit systems previously presented in the literature have been used as case studies. The Latin hypercube sampling (LHS), particle swarm optimization (PSO) and design and analysis of computer experiments (DACE) surrogate algorithms are used as search strategies in MADS to solve each of the CHPED problems. The results obtained by the MADS–LHS, MADS–PSO, MADS–DACE methods are further compared with those generated with other (evolutionary and mathematical programming) techniques reported in the literature. This paper is organized as follows: Section 2 describes the characteristics of a cogeneration unit and formulation of the CHPED problem, Section 3 deals with mesh adaptive direct search, Section 4 describes implementation of MADS to the CHPED problem, and Section 5 discusses the MADS performance on this specific problem.
Section snippets
Formulation of the CHPED problem
Combined heat and power generation is a mature and established technology. It has higher energy efficiency and less green house gas emission compared with the other forms of energy supply (Vasebi et al., 2007). The essential difference between combined heat and power units and conventional condensing plant is in the type of the power obtained and the overall efficiency of each plant. In conventional condensing plants, the energy from the fuel is utilized to produce electrical power only, while
Mesh adaptive direct search algorithm
The PS optimization algorithm is a class of direct search methods. This algorithm is suitable to solve different optimization problems that lie outside the scope of the standard optimization methods. In general, PS has the advantage of being very simple in concept, easy to implement and computationally efficient. A useful review of direct search methods for unconstrained optimization is introduced in Conn, Scheinberg, and Vicente, (2009), in which the authors give a modern perspective on the
Case studies
Three examples taken from the optimization literature are used to show the validity and effectiveness of the MADS algorithm. The MADS algorithm can handle the cases of multiple heat areas and power areas. For the demonstration, a single heat area and power area system is first considered (case study I). This case study was originally proposed by Guo, Henwood, and van Ooijen (1996). The system tested is comprised of a conventional power unit, two cogeneration units and a heat-only unit. The
Conclusion
This paper has introduced a recent optimization method, namely MADS to solve the CHP economic dispatch problem considering the feasible operating region. MADS is a recently developed algorithm that is supported by a thorough convergence analysis. The MADS method is illustrated using three test cases taken from the literature. The LHS, PSO and DACE algorithms are employed as effective search strategies in MADS to solve each of the CHPED problems. The performance of the utilized MADS–LHS,
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