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MATRIZ - Energy Matrix Projection Model

MATRIZ is a bottom-up model under development by CEPEL for long-term energy and environmental policy analysis. It is a linear programming based algorithm that produces the least-cost energy system which is able to satisfy the predicted energy demand for the next 20 to 30 years. In general, an energy system can be described by a set of energy resources and a set of technologies which are able to transform energy resources into energy services. Energy transformations usually occur in a sequential way, passing from energy resources to primary energy level, from primary to secondary levels, from secondary to final levels and from final to useful levels. Secondary energies are produced in energy transformation centers (e.g. refineries) and from there they flow to other transformation or consumption centers. Final energy is the energy such as it is delivered to the consumers (e.g. electricity, synthetic fuels etc) whereas the useful is what the consumers enjoy after the energy conversion at their own equipments (e.g. heating, lighting etc). Energy forms are defined for each energy level and technologies may consume one or more energy forms to produce one or more energy forms. The sequence of technologies required to transform a natural resource into useful energy defines an energy chain. In general, an energy system comprises oil, natural gas, coal, uranium, biomass and electricity chains.

The expansion planning studies of energy systems cannot be carried out separately for each energy chain. With the development of new technologies, an increasing interdependency among energy chains has been arisen. In Brazil, flex-fuel cars that can use either ethanol or gasoline coupled the biomass (products of sugar cane) and oil chains. Another important coupling is between the natural gas and electricity chains through the gas-fired power plants. In this context, an integrated analysis of the entire energy system is more adequate for a comprehensive assessment of the major energy and environmental challenges of the country.

MATRIZ model is based on a technical engineering approach to describe the energy system, from the resource extraction to the provision of energy services. Technologies are defined by linear relationships among their inputs and outputs, and they are usually classified into extraction, transformation, transport, distribution and conversion groups. The model can also consider the storage, export and import technologies, as well as the modeling of technologies with more than one operation mode, such as flex-fuel cars. Seasonal or intraday variability characteristic can be addressed through typical production curves. The Brazilian power sector is hydro dominated and the country still has a large hydro potential to be exploited. Hydro uncertainties are taken into account by analyzing the system operation for the critical and the average hydrological conditions. Usually, the planning horizon is divided in multi-year periods for operation analysis, and all years within a period are assumed to be identical. If seasonal and/or intraday demand or technology production variability are to be considered, a more detailed operation analysis can be done by dividing a year into seasons and each season into demand levels (e.g. peak and off-peak hours).

The energy system configuration as well as the intensity that technologies are operated should be adjusted along the planning horizon according to the predicted energy demand growth, the depletion of resources and/or the discovery of new ones, as well as the replacement of technologies by the end of their lifetimes or due to their obsolescence in face of the development of more efficient/less costly technologies. MATRIZ mathematical formulation allows describing, predicting and sizing the dynamic evolution of energy systems. Environmental concerns can be taken into account in MATRIZ model either by considering penalties for environmental impacts associated with the technology construction and/or operation or user-defined constraints such as greenhouse gas emission limits. The MATRIZ model is extremely flexible and can be very useful for energy and environmental policy analysis.

Key Data

The main input data required to run the MATRIZ model are:
planning horizon and length of each period for operation analysis;
time discount rate;
energy system configuration (subsystems and links for all energy chains);
demand projection for all forms of final energy;
techno-economical data for all technologies;
penalties for environmental impacts;
seasonal and intraday typical production/ demand curves;
imports and export costs.

Graphical Interface

MATRIZ model is part of ENCAD, a system for integrating the electrical energy models developed by CEPEL. Its graphical interface allows a set of procedures, such as:
• importation of input data from a pre-existing case;
• friendly data edition; 
• automatic execution of MATRIZ model;
• display of output plots and reports in text format.

Figure 1 shows ENCAD's graphical interface window displaying an energy chain configuration. Figure 2 shows the graphical display of results.

Figure 1 - Schematic diagram of a technology

Figure 2 - Plot of electricity chain evolution


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