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Economy & Energy
No 22 October-November 2000    ISSN 1518-2932

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Economy & Energy

Energy Matrix:

Module for Converting Final Energy into Equivalent Energy

1 - Need of Expressing Energy in a Form Appropriate for Projections

The relations between economy and energy have been the basis for demand projections. The petroleum price crises in the seventies and the ecological concerns introduced important changes in the way energy is used. In particular, a sensitive reduction in the energy/product ratio was verified in the more developed countries.

This reduction was mainly due to improvements in the efficiency of energy utilization but also to changes in the production structure. For this reason, it is convenient to use sectorial energy/product coefficients.

Another important factor to be taken into account, specially when comparing countries of different development levels, is the efficiencies that are used and the possible ones for different fuels. Natural gas in modern furnaces and wood in primitive ones present a difference in efficiency due not only to the characteristics of the equipment but also to the peculiarities of the fuel itself, as can be shown by an analysis based on the exergy of this fuel.

Given the notable particularities of the Brazilian Energy Matrix, with a strong presence of hydroelectricity, alcohol fuels and charcoal competing in the last decades with energy forms that are considered “modern” and the still important participation of traditional fuels, we have expressed here the use of energy in a scale that considers these diversities in a time scale and among countries. The adopted form was the equivalent energy concept, which makes the energy/product ratio relatively independent of the development level of the different countries and, at least in the case of Brazil, has been reasonably stable along the three last decades.

2 – Primary, Final and Useful Energy –Revision of Concepts

Recently we have briefly described energy conversion to useful and equivalent energies and we have presented a quick way for evaluating equivalent energy using data from the Energy Balance in OCDE’s format (R1)[1]  and coefficients based on the Brazilian Useful Energy Balance (R2)[2].. In what follows we describe a summary of the concepts used.

The national energy balances used in different countries as a tool for planning and evaluation classify energy sources as primary, which are energy products provided by nature in their direct form, such as petroleum, natural gas, coal, uranium ore, firewood and others.

A first accounting could be made from the superior calorific power of these products since in most cases this energy is in chemical form. Other forms of primary energy such as hydraulic, wind, solar and nuclear are treated in a special way, generally taking into account their capacity of generating motion energy or heat

A good part of primary products such as petroleum undergo a transformation process that converts them to forms more appropriate for the different uses. The place where this process is applied is generically called transformation center.

In the case of petroleum, the transformation centers are the refineries where products of direct use such as gasoline, diesel oil, kerosene, liquefied gas and other products, classified as secondary energy, are obtained. In some cases, a secondary source as fuel oil, obtained from petroleum, goes through another transformation center where it is converted into electricity. In any transformation, part of the energy is lost in the process, generally dissipated under the form of heat.

Final energy designates the energy as it is received by the user in different sectors, both primary and secondary. The energy balances are structured in such a way that :

Primary Þ  Loses in transformation + Final; 

where final energy includes the fraction of primary energy of direct use and the secondary one.


Figure 1: Schematic representation of primary, secondary, final and useful energies fluxes with indication of loses in the transformation centers and in the final use. It should be noticed that final energy includes primary energy of direct use. In more complete schemes one should still consider other types of loses, imports and exports in the different steps as well as methodological or data adjustments.

Figure 1 shows the scheme of useful energy balance in a closed system (without imports or exports in the different forms of energy).

The so called final energy is final only from the point of view of the energy sector and it represents approximately the way in which energy is commercialized. In each productive unit, industrial or agricultural, or in other consuming sectors such as residential, commercial or public, energy has different uses as motion, illumination, heating, etc.

In order to convert energy, called final energy in the form it is used, it is necessary to consider a use efficiency or yield. In the case of motion energy part of the energy is transferred to the motor’s axis and part is dissipated in the form of heat. The ratio between this energy, in the form it is used and denominated useful energy and the final energy is called yield.  

3 – Equivalent Energy Concept

The equivalent energy concept was used by an inter-ministerial group coordinated by the Brazilian Ministry of Mines and Energy –MME, in the elaboration of the Brazilian Energy Matrix as an evolution of the useful energy concept [3]

It consists of taking an equivalent energy source for each use. In this case “equivalent fuel oil” was taken for process heat and direct heating and “equivalent diesel” for transport. This had been used in the analysis of PROALCOOL  - Brazilian Alcohol Program –in the eighties.

This concept has been recently developed for analyzing the energy X economical activity relationship in several countries (R3) [4] and a simplified methodology was developed for converting final energy balances into equivalent energy (R4) in the OCDE presentation (R4) [5]

Normally, the “energy content” of primary energy is obtained by calculating its capacity of dissipating heat in the environment. The “superior calorific power” is used for fuels. As we have seen, primary sources are less appropriate for direct use and they are converted into secondary sources by a transformation process. Several fuels, primary or secondary, are converted into electricity before final use.

As can be seen in Figure 1, final energy includes a fraction of primary energy that reached the consumer, i. e.:

Final Energy = Secondary Energy + Primary Energy of direct use.

In useful energy balances, for each use j, efficiency or yield is considered so that:

Useful Energy (i,j) = Final Energy (i) * Yield (i,j).


UE (i,j) = FE (i) * Y (i,j)

The uses considered in the Brazilian Useful Energy Balance are: motion force, direct heating, process heat, illumination, electrochemistry and others. 

From the final energy distribution D(i,j) of each energy source by use type, one has:

FE (i,j) = FE (i) * D(i,j)

Considering the efficiency a determined sector of the energy source i in the use j as Y(i,j), one has the useful energy defined as:

UE(i,j) = FE(i,j) * Y(i,j)

The useful energy for the same use from different energy sources will be given by:

UE(j) =

S FE (i) * D(i,j) * Y(i,j)


The average efficiency with which an energy source will be used will be obtained from:

UE(i) = FE (i) *

S * D(i,j) * Y(i,j)


The sum at the right is the conversion factor from useful energy into final energy for energy source j with distributions D(i,j) and yields Y(i,j).

The Equivalent Energy is defined as:

Equivalent Energy (i,j) = UE(i,j) / Y(io,j)

Where Y(io,j) is the yield in the considered sector of the reference fuel, or still:

EE(i,j) = UE(i,j) / Y(io,j) = FE(i,j) * Y(i,j) / Y(io,j)

Once a reference energy source is chosen, we have by definition:  

EE(i) = EF (i) *

S D(i,j)*R(i,j)/R(io,j) = EF(i)*C(i)


Naturally this is valid for each economical sector (k) considered and we could write:

EE(i,k) = FE(i,k)*C(i,k)

  4 – Why Equivalent Energy ?

In the elaboration of a useful energy balance it is necessary to have for each sector, as seen in the previous item, the final energy used by each energy source. For each of these energy sources it is necessary the distribution in the different uses and the yields in each one of these uses. In this way, the sum of the useful energy values has the advantage of taking into account the different yields for the same use of the different energy sources.

Using the useful energy sum of the elements representing the different uses has however the inconvenient of a valuation that depends on the type of use. For example, fuel as firewood is used for generating process heat in an industry with efficiency of say 75%. Diesel oil is used in the same industry for generating motion force with 30% efficiency. When both fuels are added in the form of useful energy they present a merit factor that does not corresponds to their potentialities. Actually diesel oil could be used for generating process heat with efficiency greater than that of firewood and when used for motion power it would also present much larger efficiency than that obtained from firewood in a steam machine. In other words, in spite of its larger potentialities or because of them, diesel’s final energy appears multiplied by 0.30 and that of firewood by 0.75.

To take into account these differences we use the equivalent energy concept as well as that of useful energy. In this concept, the efficiency of each energy source is compared with the efficiency of a reference source for the same use.

In most cases natural gas was used as reference. In the mentioned example, firewood, mineral coal, fuel oil – and eventually diesel oil itself – would be compared with natural gas for heat generation in this use. For motion power, diesel would also be compared with natural gas used for the same end.

In the mentioned case, natural gas would be considered as having efficiency of 85% for heat generation and 25% for motion power. The equivalence obtained would be more independent of the use form:

1 toe of firewood -> 0.88 toe of NG (heat generation)

1 toe of diesel -> 1.2 toe of NG (motion power)

In other words, yield for any energy source is always compared with the yield of the reference energy source for the same use.

The choice if natural gas as the reference energy source is due to its large use flexibility in the industrial, residential, commercial and, when available, in the agricultural sectors for all applications as thermal source. For the transport sector (motion use) it would be more logical to use liquid fuel of large use (diesel or gasoline). It should be emphasized that gasoline presents in the Brazilian Useful Energy Balance the same yield as that of natural gas (NG) in transport use. We have then chosen gasoline as reference fuel, expressing the result as “equivalent to NG”. In the specific uses of electricity, we have used for expressing equivalent energy a procedure analogous to that used in the National Energy Balance BEN(R5)[6] for calculating hydraulic energy that is valued based on the thermal energy necessary for generating one kWh of electrical energy. In this work, all energy values are expressed in tone equivalent petroleum (1tep = 10.800 Mcal). This unit is used in practically all energy balances, therefore we prefer to maintain it instead of creating a tone equivalent NG or cubic meter equivalent NG. 

5 –Coefficients for Conversion into Equivalent Energy

The coefficients for final and equivalent energies for each energy source were obtained by applying for each energy source and for the different economical sectors the coefficient described in 3. For each sector specified in the energy balance, the reference efficiencies considered were those to which each energy source of the Useful Energy Balance 1993 MME/Brazil should have a trend. These efficiencies are used to evaluate the Brazilian potential for conservation using the existing technologies. Since we intend to use average efficiencies for inter-comparison  among different countries, this second set of parameters was considered as more significant than those presently used in Brazil. Furthermore, energy conservation efforts tend to contemplate not only a determined fuel but all of them, affecting less the absolute values than the relative ones.

The use distribution of each energy source in a determined sector was that considered for Brazil in 1993. The coefficients so obtained permitted the creation of an equivalent factor table for each energy source relative to NG.

6 –  Balance in Equivalent Energy 

Even though the word balance is not at all adequate to treat equivalent energy – it is not conserved in transformation – one could talk about equivalent energy balance. In this type of “balance”, transformation of natural gas into electricity would not generate loses and in some cases occasional gain could even occur. Incidentally, the Brazilian Energy Balance - BEB published by the Brazilian Mines and Energy Ministry - MME copes with this problem because it values electricity by the fuel necessary to generate it.

The advantage of using equivalent energy is that it permits to treat with more transparency fuel substitutions. On the other hand, this seems to be the best way to approach the economic activity and energy use relationship, as shown by the results already obtained.

In order to carry it out, we have developed a program that uses conversion coefficients that allows calculating the corresponding values in equivalent energy from Final Energy values in BEB/MME. This is done by simply multiplying the coefficients for each sector and energy source by the corresponding values in equivalent energy. The advantage of the program is that it permits to quickly obtain spreadsheets by year, by account (economic sector in most cases) or by energy  source. The following figures illustrate the calculation process.

Figure 2: Brazilian Energy Balance Annex BEB/MME  showing final energy values for 1993 (partial view)

Figure 3: Conversion coefficients that allows calculating values in equivalent energy  from the corresponding Final Energy values from BEB/MME data .

Figure 4: Values in equivalent energy obtained by multiplying data from Figure 2 (final energy) by the coefficients shown in Figure 3.

Clicking the “Data Updating” button the program saves data from the energy balance converted to equivalent energy in a tri-dimensional matrix by year, energy source and account (sector). Figures 5 and 6 present (partial) views of the generated spreadsheets by account and by fuel

Figure 5: Choose from the energy source that contains data of the sector or set of sectors energy use in equivalent energy values. 

Figure 6; Choose from the “account” that contains data of the sector or set of sectors. Values are in equivalent energy. The “Data Updating” button permits to introduce in the computer balance data of all years, making fast the generation of spreadsheets. 

[1] (R1) - Energy balances of OECD Countries 1995-1996 - International Energy Agency - OECD - 1998 Edition 349 pag. and Energy Statistics and Balances non-OCDE Countries 1995-1996 - IEA - OCDE

[2] (R2) - Balanço de Energia Útil - Ministério de Minas e Energia MME - Versão Eletrônica 1984

[3] (R3)Metodologia de Projeção de Demanda de energia a partir da Energia Equivalente de Substituição Carlos Feu Alvim et al. – Reunião Brasil/EUA de Planejamento Energético – Washington 4 a 6/12/1990]

[4] (R4) Energy Final and Equivalent - Simplified Procedure for Conversion; Carlos Feu Alvim, Omar Campos Ferreira, Frida Eidelman e José Goldemberg .

[5] (R5)Energia, Primária, Final, Útil e Equivalente – Processo Simplificado; Carlos Feu Alvim, Omar Campos Ferreira, Frida Eidelman e José Goldemberg

[6] (R6) - Balanço energético Nacional - BEB - MME - Versão Eletrônica 1999

[1] (R1) - Energy balances of  OECD Countries 1995-1996 - International Energy Agency - OECD - 1998 Edition 349 pag. e Energy Statistics and Balances non-OCDE Countries 1995-1996 - IEA - OCDE

[2] (R2) - Balanço de Energia Útil - Ministério de Minas e Energia MME - Versão Eletrônica 1984

[3] (R3)Metodologia de Projeção de Demanda de energia a partir da Energia Equivalente de Substituição Carlos Feu Alvim et al. – Reunião Brasil/EUA de Planejamento energético – Washington 4 a 6/12/1990]

[4] (R4) Energia, Primária, Final, Útil e Equivalente e Atividade Econômica – Procedimento  Simplificado; Carlos Feu Alvim, Omar Campos Ferreira, Frida Eidelman e José Goldemberg .

[5] (R5)Energia, Primária, Final, Útil e Equivalente – Processo Simplificado; Carlos Feu Alvim, Omar Campos Ferreira, Frida Eidelman e José Goldemberg

[6] (R6) - Balanço energético Nacional - BEB - MME - Versão Eletrônica 1999