Primary, Final, Useful and Equivalent
Energy and Economical Activity

Carlos Feu Alvim        
feu@ecen.com
Omar Campos Ferreira
omar@ecen.com
Frida Eidelman           
frida@ecen.com
José Goldemberg         

Introduction

Energy is the indispensable input for the activities of civilized society. The correlation between energy and production is a postulate of the industrial age where energy is one of the basic inputs.

The consumption increase after the petroleum crisis of the seventies checkmated this nearly linear correlation between the economic activity and the use of energy as the central countries were able to show economic growth for more than a decade without the corresponding increase of energy consumption.

The evolution of production methods made evident that considerable gains in efficiency could be attained through conservation measures (avoiding loses) or changes in the production process.

It became evident as well that the policy of conservation or reduction of energy amount per product would bring about better results in developed countries where financial resources were available. This is natural, since conservation, after an initial phase of use optimization, implies investments in machines, equipment and processes, besides management know-how.

Along the process of comparing Energy and Economical Activity, there was an important methodological improvement that made possible comparing the currency of different countries, not limited to their exchange rates, frequently distorted by governments or ruled by imperfect markets.

For example, if we use merely the exchange rate, the Brazilian GDP as well as its GDP per capita would be reduced in 40% a few months after the beginning of 1999. This inconvenience can be avoided using methodologies that calculate the purchase power of the local currency.

The energy area still lacks a convenient measurement to take into account the yield of different energy sources in their different uses. Some progress was attained when not only the primary but also the final consumable energy was measured.

Expressing the offered and consumed energy in terms of final energy, an equitable comparison could be made, for example, between hydraulic energy and natural gas for electricity generation.

Still in the form of final energy, the same natural gas is used to heat water, competing with electricity in domestic uses, without taking into account their relative efficiencies.

The final energy concept enhances the efficiency factor by taking into account for each use the efficiency of the different energy sources. In order to elaborate useful energy balances, it was necessary to organize the uses so that this concept could be applied in a practical manner.

Even though the concept of useful energy   permits comparing the different energy sources in each use, the energy sum expressed in this way presents generalization difficulties that are not smaller than those encountered in primary or final energy sum.

The optimal solution would be the elaboration of an exergetic analysis of the use of energy in a country or activity. The generalization of this methodology is possible and desirable but should be submitted to a methodological development - in part already done - and mainly to a didactic elaboration. This task could be successful since the concept of exergy is, in a strict sense, no less intuitive than that of energy.

We learn in school that energy is conserved in nature and only changes its form but we go on saying "spend energy" and even the specialists of the area, we say as we did above - conserve and consume energy ... Not to mention the conversion of mass into energy (in the nuclear area), what is "perfectly understood" by those who considered that the mass of wood that they watched being burned in their childhood was converted into energy under the most easily perceived form as such - heat.

Previous use of the 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 energy matrix of the country. This concept was presented in [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]). It consists of taking for each use an equivalent energy source. In that case it was used " fuel oil equivalent " for heat process and direct heating and "diesel equivalent" for the transportation area, as we have been doing in analyzing the Brazilian "Alcohol Program".

It should be mentioned that, considering the larger efficiency of hydraulic energy for generating electricity when compared to other sources - and satisfying a political desire to emphasize the participation of domestic energy in the Brazilian energy balance - hydraulic energy is valued in Brazil as primary energy, taking into account its capacity to generate electricity. Alcohol fuel received the same treatment in order to value it vis-à-vis gasoline.

In other words, the aim of the equivalent energy concept is to systematize, in a way easily understandable to the external analyst, energy "consumption" in terms of equivalent energy. In this work all energy sources, in all uses, are referred to natural gas equivalence.

Concepts

It is convenient to review some concepts. Normally, the "energy content" of primary sources is considered by calculating its heat dissipation capacity into the environment. For fuels it is normally used the "upper calorific power".

Primary sources can not be directly used so different transformation processes are used that converts petroleum into its products for several uses, coal into coke, wood into charcoal, etc. Several fuels, primary or secondary, are converted into electricity, in general, for more noble ends,.

In energy balances this is expressed by the formula

Primary Energy = Final Energy + Transformation Loses

In useful energy balances, for each use j, the fuel efficiency i is such that

Useful Energy (i,j) = Final Energy (i,j) * Efficiency (i,j)

or

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

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

Since the energy balances are not sub-divided according to use, in order to calculate the final energy used in each sector it is necessary to know the distribution D(i,j) of each energy source in each use.

Using the same technology, it is expected that this distribution is similar in all countries. Since actually there are different degrees of technological evolution, this distribution may diverge considerably in some sectors. We have

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

Considering the energy source efficiency i (always for a determined sector) in use j as E(i,j), we will have the useful energy defined as

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

For each specific use it makes sense, for example, to deal with useful energy by unit production. This rate is notably more stable than final energy/ product when different energy sources with different efficiencies are used. For this purpose, it makes sense to calculate the useful energy, for the same use, originating from various energy sources.

UE(j) =	S FE (i) * D(i,j) * E(i,j)
	i

It may be of interest to calculate, for each sector, the average efficiency of one energy source, namely

UE(i) = FE (i) *	S * D(i,j) * E(i,j)
	j

The addition at the right is the useful energy conversion factor into final energy for energy source i, given the distribution D(i,j) and efficiencies E(i,j).

The Equivalent Energy is defined as

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

where E(io,j) is the efficiency in the considered sector of the reference fuel io
or

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

By definition, we will have for an energy source io selected as reference,

EE(i) = FE (i) *	S D(i,j)*E(i,j)/E(io,j)
	j

For each sector and each energy source a conversion coefficient is generated which converts the final energy into equivalent energy resulting from the relative average efficiencies weighted by the final energy destination in the sector. In the expression for the useful energy it is obtained likewise a conversion coefficient for each energy source for each sector. A practical example will demonstrate the convenience of using preferably the equivalent energy.

Equivalence Coefficient – Useful Energy

For each sector specified in the energy balance, reference efficiencies were considered and the use of each energy source supplied by the Useful Energy Balance 1995 - MME/Brazil should tend to these reference values. These efficiencies are those used to evaluate the potential of a conservation policy in Brazil using present technologies. Since it is intended to use the average efficiencies for inter-comparison among different countries, these efficiencies were considered more significant than those presently adopted in Brazil where the efforts aiming at energy conservation are still very limited. The distribution of use of each energy source in each sector used was considered for Brazil in 1993. As the balance data used are more aggregated than those available in the Brazilian Energy Balance and the aim of this work is to obtain a first approximation, the average conversion coefficients were obtained for three aggregates, namely: industrial, transportation and others. For each energy source and the different sectors k of the economy comprised in each aggregate, the coefficients were obtained considering

UEa(i) =	S UE (i)
	k

Similarly, for the final energy of each energy source and each aggregate one obtains

UCa(i) = UEa(i)/FEa(i)

In the same manner, for equivalent energy one gets the coefficients

CEa(i) = EEa(i)/FEa(i)

Average Conversion Coefficients - Final Energy to Useful Energy

The present work aims at comparing in a first approximation the use of primary, final, useful and equivalent energy expressed as a function of the economic activity and of the power purchase parity. For this approximation, it was used the aggregated structure shown in the table and the energy source aggregate presented in the energy source balances disseminated by OECD for several countries. Considering the structure of Brazilian final energy use, the structure used yields the following equivalence table:

	Industry	Transportation	Others	Total
Coal	0,81			0,81
Petroleum Products	0,74	0,40	0,48	0,49
Gas	0,78	0,34	0,52	0,77
Renewable Fuels	0,65	0,40	0,20	0,48
Electricity	0,83	0,94	0,68	0,77

This table originates from the previous one where the different energy sources are grouped and weighted as a function of their use (addition of energy values/ addition of final energy values). In the two previous tables the inconvenience of using this type of equivalence when the total is considered becomes evident. The petroleum products in the last column that specifies the total have a relatively low efficiency when compared to coal and gas in this same column. The explanation is easy to understand when the column industry is examined - where the equivalencies are those expected - and compared to the column transportation, where the equivalencies are also those expected but the efficiencies are lower because in this case one is measuring the conversion of chemical energy into driving energy while in industry the predominance is the conversion of this energy into process heat or direct heating. Since the petroleum products are predominant in transportation, on the average, they evidently show low efficiency. Similar comments can be made concerning the primary sources in the first table, specially the low efficiencies of gasoline and alcohol when compared to fuel oil or mineral coal in their various forms. 

Coefficients for Equivalent Energy

In order to obtain the energy as equivalent energy it is necessary to choose a reference fuel for each kind of use. For driving force, gasoline was chosen and for process heat and direct heating, natural gas. For lighting, electrochemistry and others, electricity was chosen, which is exclusive or practically exclusive in these uses.

Subsequently, these values were unified to natural gas equivalent using equivalence 1 (ratio between efficiencies) between natural gas and gasoline, selected by the Brazilian Useful Energy Balance to be used for driving force. Finally, the equivalence between electricity and natural gas was fixed in 3.57, which is the efficiency of electricity generation using natural gas (28%). This procedure permitted to express all energy sources as a function of the equivalent energy in natural gas. The result is shown in the following table.

The relative values in the different columns are less discrepant among themselves what results in more compatible total values. The only surprise seems to be the efficiency of metallurgical coal, 6% higher than that of natural gas, used specifically in the steel industry, in direct contact with the material to which heat is supplied (part of the heat is incorporated into the material).

Average Conversion Coefficients - Final Energy to Equivalent Energy

For the aggregated structures of the OECD balance we used the following equivalencies

	Industry	Transportation	Others	Total
Coal	1,04			1,04
Petroleum Products	0,99	1,34	1,19	1,23
Gas	1,00	1,00	1,00	1,00
Renewable Fuel	0,83	1,38	0,37	0,81
Electricity	2,63	3,10	2,93	2,76

The results are intuitively expected except that of coal whose explanation was previously presented. This factor, to be used in other countries, should be closer to those in the previous table for vapor coal, since in the case of Brazil its use in industry is practically zero in what concerns heat generation.

Nevertheless, as the coal used in Brazil is of poor quality, the coefficient value should be higher than 0.87. Furthermore, it would be necessary to consider the use in the steel industry in other countries, which would also present relative high efficiency.

The preliminary results that will be presented use the coefficients calculated for Brazil. In future works, less aggregated sectors and energy sources will be considered, which would avoid the inconveniences of the aggregated analysis now presented.

Energy and Economical Activity

In what follows, the results of the comparison made regarding the energy source consumption in countries presenting a large range of development and their respective economical activities measured by the purchase power (PPP methodology) are presented. The values were also obtained from the OCED energy source balances. All values are relative to 1996. The countries are listed according to the GDP per capita and the GDP was measured in purchase power parity (PPP methodology) expressed in 1990 dollar.

Countries, population, Equivalent Energy and Primary Energy (PE), Final FE), Useful (UE) and Equivalent (EE) intensity use per product measured in purchase power parity (GDP PPP – Gross Domestic Product, Purchase Power Parity)

 In Figure 1 the countries are presented according to GDP/inhab, per capita product value, and the Final Energy coefficients /GDP. It can be noticed that the poorer countries present a larger final energy index by product than the richer countries. When this rate is observed in terms of useful energy and equivalent energy this difference practically disappears as can be observed in figures 2 and 3.

Figure 1: Final Energy / GNP and per Capita Product for countries classified as a function of this parameter whose values are represented in graphic in the secondary axis.

Figure 2: Equivalent Energy by dollar of product by country classified by GDP/inhab.

Figure 3: Useful Energy by dollar of product by country classified by GDP/inhab

A preliminary analysis of the graphics makes it noticeable that those countries with low revenue present a high consumption of final energy relative to the product. This is fundamentally due to the low efficiency of the type of energy source used (efficiencies for each country were not considered). Except for Haiti, whose relative consumption is high by any criterion adopted, the poorer countries do not stand out against the average regarding both the useful and equivalent energy coefficients. The Final Energy/ Equivalent Energy rate shown in Figure 4 demonstrates that explicitly.

Figure 4: The poorer countries present high Final Energy/ Equivalent Energy rate pointing up the low efficiency of the energy sources used.

Another interesting fact is that the small dispersion of the Final Energy/ Equivalent Energy values makes it clear that the advantages of considering equivalent energy - and not final energy - are greater for countries with low or average income. In the case of rich countries, if the change brings no improvement, it does not generate distortions as well rendering it convenient for general use.

Even in countries with high GDP per capita it can be noticed a trend to a more efficient use of energy sources when the income rises, as shown in Figure 5.

Figure 5: Values of the previous figure for countries with GDP per capita higher than 10 000 dollars annually

 Energy x Product

The positive relation between product and energy still exists no matter the way energy is computed, as shown in Figure 6 where the primary, final, equivalent and useful energy are represented as a function of the GDP.

Figure 6: Energy X GNP values for the different studied countries (logarithmic graphic)

In terms of Energy/Product coefficients to be used it is easy to notice in Figure 7 that the primary and final energies present very different values for rich and poor countries.

Figure 7: Energy/Product Coefficients for different countries for primary, final, useful and secondary energy

By fitting lines to the points in Figure 7, it can be seen the negative slopes for curves referring to primary and final energy, a smaller slope for useful energy and a practically zero slope for equivalent energy.

	PE/GDP	FE/GDP	UE/GDP	EE/GDP
Line slope	-0,00909	-0,01011	-0,00251	-0,00004

In terms of dispersion, the results of the table below show that, even though the useful energy coefficient may be used in different energy ranges, it introduces a larger relative dispersion for all countries. A smaller dispersion is found in the equivalent energy coefficient

	Unit	PE/GDP	FE/GDP	UE/GDP	EE/GDP
Coefficient	koe/US$	0,34	0,26	0,12	0,27
Standard Deviation	koe/US$	0,18	0,19	0,10	0,13
Standard Deviation	%	53%	71%	82%	46%

In Figure 8 it is shown Equivalent Energy per capita as a function of the GDP PPP per capita for the different studied countries.

Figure 8: Equivalent Energy per inhabitant relative to consumption per inhabitant.

Conclusion

Just like the economical activity indexes need to be corrected so that the exchange rate effects can be minimized, likewise the energy data need to be corrected in order to take into account the different efficiencies in the different uses.

For the same type of use (driving force, heat process, direct heating, lighting, etc.) the useful energy concept seems to be satisfactory to handle the different types of energy. The Equivalent Energy concept, suggested here, seems adequate to study the relation energy /product. It is advisable that in further studies a better determination of the coefficients should be made through the improvement of the efficiencies used and of the distribution of the energy by use in each country.

The preliminary results show that the poorer countries utilize the normally used

energy sources with lower efficiency. It should be noted that there is no technology suitable to improve this efficiency in spite of the fact that some laboratories have indicated the possibility of substantially increasing this efficiency with low cost.

As an example, we could mention the work developed in 1984/85 by Fundação Christiano Ottoni for the Fuel Contingency Plan of the Brazilian Energy Commission where gains of 300 and 200% were obtained, respectively, for the use of firewood and charcoal in domestic ovens with better design.