The procedure of selecting the set of decision variables that maximizes/minimizes the objective function subject to the system constraints is called the optimization procedure (Simonovic, 2009). Until now, there has not been a single method that could be applicable for solving all types of optimization problem in an effective way. Therefore, various methods of optimization have been developed based on the characteristic of the problem. Rao (1996) mentioned that the foundations of the calculus of variations, which deals with the minimization of functionals, were laid by Bernoulli, Euler, Lagrange, and Weirstrass. The optimum seeking methods are also known as mathematical programming techniques and are generally studied as a part of operations research, a branch of mathematics dealing with the application of scientific methods and techniques to establish the best or optimal solutions (Rao, 1996). Operations research actually started during World War II, when the British military was having problem in allocating their limited resources (fighter planes, submarines, etc.).
2.3.1
Applications of Optimization
Optimization methodologies are being widely used in formulating energy system models. An energy system optimization model can describe a large number of technical components and can be used to find the best possible way to design and operate.
Linear programming has long been used as an optimization tool for energy system modelling. In 1975, Singpurwalla used a LP model to minimize the system cost subject to each energy source and air quality policy constraints (Jebaraj and Iniyan, 2006). MARKAL is a linear programming model used to analyze minimum discounted cost configurations for the Australian energy system during the period 1980–2020. Another linear optimized model was used by Zhen (1993) to study long-term changes of the system to a village level in the North China Plain. A linear programming model of an integrated energy system for industrial estates (IESIE) was also developed around the same time as a prefeasibility tool (Jebaraj and Iniyan, 2006). Macchiato et al. (1994) developed a LP model for the planning of emissions abatement with a cost minimization objective. Because of China‘s massive energy production from coal, Xie and Kuby (1997) developed a strategic-level network based investment-planning optimization model for a coal and electricity delivery system.
Taking the advantages of multidimensional optimization problems, Kaboudan (1989) built up a non-linear dynamics econometric forecasting model to predict the electricity consumption in Zimbabwe. Lai and Chen (1996) developed a MILP based model for planning coal import strategies in Taiwan. Rozakis et al. (2001) also developed an integrated micro-economic, multi-level mixed integer linear programming (MILP) staircase model to estimate the aggregate energy supply at the national level.
Hoog and Hobbs (1993) proposed a multi-objective linear programming (MLP) model to discuss issues including utility costs, emissions, regional economic effects, and net values to customers. Another MLP model for energy capacity expansion was developed by Climaco et al. (1995) where three conflicting objectives were considered, including net present cost of expansion plans, reliability of the supply system, and environmental impacts. Chedid et al. (1999) built up a fuzzy MLP model to deal with energy resources allocation issues.
Bowe et al. (1990) introduced the use of a stochastic programming Markov model for engineering-economic planning. Groscurth (1995) developed a model that describes regional and municipal energy systems in terms of data-flow networks. A stochastic version of the dynamics linear programming model was presented by Messner et al. (1996). Davide et al. (2004) employed a stochastic method to establish a decision support system for regional energy planning. In the following year Floros and Vlachou (2005) developed a theoretical TSP model for analyzing energy demand and the effects of carbon taxes on energy-related CO2 emissions.
2.3.2
Most Used Optimization Energy-Economy Models
There are many available optimization models that deal with the energy-economy sector. A few of these are used in various long term projections undertaken in the international community. These include the Model for Analysis of Energy Demand (MAED), PRIMES energy system model, the Market Allocation (MARKAL) family of models, the Model of Energy Supply Strategy Alternatives and their General Environmental Impacts (MESSAGE), the World Energy Model (WEM), Modelling to Generate Alternatives (MGA) and so on.
PRIMES energy system model was developed by the National Technical University of Athens, Greece. It focuses on the market-related mechanisms that influence the evolution of energy demand and supply, as well as the context for technology penetration in the market. The PRIMES model is now used for projections, scenario construction and policy impact analysis, with a forecasting horizon up to 2030 (Capros et al., 1998).
The Model for Analysis of Energy Demand (MAED) was originally developed by Chateau and Lapillonne at the University of Grenoble, France. MAED provides a
methodical accounting framework for evaluating the effect on energy demand as a result of changes in the technological and socio-economic system under analysis (IAEA, 2006).
The Market Allocation (MARKAL) family of models has contributed to energy- environment planning since the 1980‘s. MARKAL is a widely used modelling tool and its recognition relies on the fact that there are more than 150 teams in more than 50 countries using it (Mundaca et al., 2009).
The Model of Energy Supply Strategy Alternatives and their General Environmental Impacts (MESSAGE) was developed at the International Institute for Applied Systems Analysis (IIASA) in connection with its Environmentally Compatible Strategies (ECS) programme (Mundaca et al., 2009). The model calculates an optimal and feasible energy supply technology mix that requires the least total costs and meets a given useful or final energy demand. In other words, MESSAGE determines the optimal solution (Schrattenholzer, 2004).
Modelling to generate alternatives (MGA) can work as a way to flex energy models and systematically explore the feasible, near-optimal solution space in order to develop alternatives that are maximally different in decision space but perform well with regard to the modelled objectives (DeCarolis, 2011). The MGA method allows modelers and decision-makers to probe the decision space quickly and efficiently in order to identify plausible alternative options.
The World Energy Model (WEM) has been utilized since 1993 by IEA for long-term energy projections, mostly through the World Energy Outlook publication. The WEM model has been coupled with a top-down General Equilibrium Model (GEM) called IMACLIM-R to develop a hybrid modelling framework (Roques and Sassi, 2008). To
support the development of alternative policy scenarios, the IEA has built a database containing more than 3,000 policies in OECD and non-OECD countries.