Mathematical relationships or equations: the mathematical models can be classified as equalities, inequalities and logical conditions. The model equalities are usually composed of mass balances, energy balances, equilibrium relations and engineering relations which describe the physical phenomena of the system. The model inequalities often consists of allowable operating limits, specification on qualities, performance requirement and bounds on availability's and demand. The logical conditions provide the connection between the continuous and integer variables.
Linear programming is a method for finding the arrangement of activities that will maximizes or minimizes a defined criterion, subject to the operative constraints . All relationships are expressed in fully linearized terms as the technique can deal only with situations where activities can be expressed in the form of linear equalities or inequalities, and where the criterion is also linear. Linear programming is a relatively simple technique which gives quick results and demands little mathematical complexity. Disadvantages are that all coefficients must be constant and that LP results in choosing the cheapest resource up to its limits before any other alternative is used at the same time for the same item. Also, LP models can be very sensitive to input parameter variations. This technique is used for almost all optimization models, and applied in national energy planning as well as technology related long-term energy research.
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Mixed Integer Programming (MIP)
Mixed Integer programming (MIP) is actually an extension of Linear Programming which allow for greater detail in formulating technical properties and relations in modeling. Decisions such as yes/no (1/0) are admitted as well as nonconvex relations to discrete decision problems. MIP can be used when addressing questions such as whether or not to include a particular energy plant into a system.
Dynamic programming is a method used to find optimal growth path. The solution of the original problem is obtained by splitting the original problem into sub problems for which optimal solutions are calculated. The original problem then can be solved using the calculated solutions of the sub problems. Dynamic programming overcomes many of the restrictions in linear programming, as follows :
The capacity constraints on individual technologies actually make it easier, in contrast to most optimisation procedures where constraints increase computation times.
Load duration curves can be of any form, especially without the requirement of linear approximation.
There are fewer mathematical restrictions in dynamic programming, unlike the linearity and convexity requirements of linear programming.
This approach can also incorporate uncertainties in demand and in fixed and variable costs.
There are a number of energy analysis tools that are available for the analysis of the integration of carbon mitigation technologies into the energy system. A review focusing on the various computer tools for analyzing the integration of renewable energy into various energy systems can be found in .
Dynamic energy optimization models are technology oriented models that minimizes the total cost of the energy system.
The WASP (Wien Automatic System Planning Package) tool permits the user to find an optimal expansion plan for a power generating system over a long period, within the constraints defined by the planner. It is maintained by the IAEA (International Atomic Energy Agency), who have developed four versions of the program and distributed it to several hundred users. WASP is freely available to IAEA member states and requires 4-6 weeks of training. In WASP the optimum expansion plan is defined in terms of minimum discounted total costs. The entire simulation is carried out using 12 load duration curves to represent each year, for up to a maximum duration of 30 years. Conventional fossil-fuel, nuclear, and biomass power-plants can be simulated along with wind, wave, tidal, hydro power, and pumped-hydroelectric energy storage. Using the electricity demand for the future year, WASP explores all possible sequences of capacity additions that could be added to the system within the required constraints. These constraints can be based on achieving a certain level of system reliability, availability of certain fuels, build-up of various technologies, or environmental emissions. The different alternatives are then compared with one another using a cost function which is composed of capital investment costs, fuel costs, operation and maintenance costs, fuel inventory costs, salvage value of investments, and cost of energy demand not served. WASP has previously been used to evaluate the impact of CO2 taxation and introduction of biomass power generation in Thailand , to examine the future role of nuclear power in Korea , and to evaluate Thailand's dependence on natural gas and imported fuels .
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