Marek KOTT, Bogumiła WNUKOWSKA

Wrocław University of Technology, Institute of Electrical Power Engineering

The computer simulation of energy-consuming factors in chosen industry branches

Abstract. The assurance for the delivery of energy is the basis of economic development. There are connections between the economic development of given country, the quality of life and energy consumption. To make an electric power system work properly, it is essential that a well developed industry produces energy-saving, competitive products. The dynamic transformations of economy in Poland and steels growing prices of energy supports in last decade caused major increase of interest of limitation of energy-consuming by business enterprises. One of the most important factors, which permits estimate the condition of industry is the energy-consuming factor and forecasting this index allow planning the strategy of national industry. In this paper was presented the way of forecasting the energy-consuming factor in chosen industry branches.

Keywords: energy, industry, analysis.

Introduction

Fast social-economical development can be observed in Poland in recent years and it has required the assertion for the delivery of energy in proper quantities and quality allows for more precise ecological norms. One of the most important problems is assurances of equilibrium for power industry policy. The effective activity of the social-economical should be based on gain information about economy. This information should be used to technological forecasting, simulation and finally to make the best decision of future power industry. If we know the most important factors which forming energy demand, specially in industry, we can foresee the development of this economy sector. The most interesting factor, which can valuate condition of industry, is energy-consuming factor. In Poland, in some branch of industry, this factor is higher (double, treble) then in Western Europe cantries.

Situation of power engineering in Poland

The Polish industry is characterized by energy consumption rise. It is caused by dynamic development of national economy. In spite of growth demand on electric energy in all sectors of economy, the industry is the largest energy consumer. Polish industry uses 55% electric energy which is produced in country (fig. 1).

Fig. 1. The electric energy consumption in Poland generally (red) and in industry (blue) in 1990 – 2005 [7]

The structure of consumption in particular energy supports is changing. In the last fifteen years, hard coal consumption was reduced by about 30% and is now 68 million tones per year (fig. 2). It increases however with natural gas consumption (fig. 3).

Fig. 2. The hard coal consumption in industry in 1990 – 2005 [7]

Fig. 3. The earth gas consumption in industry in yeras 1990 – 2005 [7]

This is connected with ecology, because natural gas emits less pollution than coal (tab. 1). The enlargement of gas consumption requires the logging of him from foreign supplier by steels growing prices of this support.

Tab. 1. The emission of natural gas air pollution in comparison with hard coal [3]

Name	Unit	Hard coal	Natural Gas
Carbon dioxide	%	100	55
Sulfur oxide	%	100	0
Nitric oxide	%	100	40

After 1989, the restructuring of industry was conducted. This influenced electric energy consumption in individual branches of industry. The characteristic factors are shown in figure 4. One can notice a increase electric energy consumption factor in industry per one worker. The perfect example is Metal industry for which this factor increased three times. There is many factors which can show condition of industry: the energy consumption factor, electric energy consumption factor in industry per one worker factor, but one of the most imported is energy-consuming factor. The forecasts of this factor permit to define the competitiveness of national industry and to compare it with Western Europe countries industry.

Fig. 4. The electric energy consumption factor in industry per 1 worker in 1992 – 2005 [7]

The forecasting with econometric models

One of the most popular simulation method is the cause-effect models building. It depends on searching dependence between variable which is explain (the energy-consuming factor in chosen branch of industry) and the explanatory variables ( the sold production, employment, number of companies, in chosen branch of industry). This models are called econometric or in special occasions energy-metric models. The linear model with many explanatory variables has figure:

(1)

where:

Y – variable which is explain,

X_k – k explanatory variables for k = 1, 2 …K,

a₀, a_k – structure model parameter for k = 1, 2 …K,

ε – random component.

To determinate the individual parameters of econometric model is the most comfortably to use classic method of the smallest square. To performance this method is introducing symbol matrix, where:

· the variable explain vector

· the explanatory variables matrix

· the structure parameters vector

· the remainder model vector

The structure parameters vector has calculate by formula:

(2)

and the variance and covariance structure parameters matrix is specified by formula:

(3)

where:

S_e – the variance random deviation matrix which is estimate by formula:

(4)

So that prepared model permits on undertaking next steps in analysis of energy-metric model which is introduce on figure 5.

Fig. 5. Econometric analysis diagram [2]

The next step is model verification. The estimators a_i should be effective and have to meet Gauss-Markov assumption:

· relation between variable which is explain and explanatory variables have linear character

· value of explanatory variables are steady (not random)

· random parameters ε for postvaccinal value of explanatory variables have normal distribution witch constant variance and the expectation value equal zero.

· random component are not correlated

The last step in analysis of econometric model is inference on this model. It is discriminate three kinds of forecasts:

· point forecast,

· interval forecast for value of explain variable y,

· interval forecast for expected value of explain variable y.

In the next point are presented energy-metric models for three chosen of branch of industry. All necessary data to construction models are from The Statistic yearbook published by Central Statistical Office of Poland.

Simulation of energy-consuming factors in chosen industry branches

The energy-consuming factor means amount of electric energy which is use to produce 100 PLN sold production. Three industry branches was chosen to present: metals producing industry, coal industry and food industry. The metals producing industry is a part of economy which include: cast iron, steel, iron alloy, noble and base metals production, cast iron founding and cast iron or steel pretreatment. The coal industry include output material and preparation to enrichment for other industry branches. The last industry is food industry which produce and prepare foodstuffs. This three branches used 29% electric energy which was produced in Poland in 2006:

· metals producing industry 13%,

· coal industry 10%,

· food industry 6%.

The most important date are introduce on table 2.

Tab. 2. The staple chosen industry in 2006 [7]

	food industry	coal industry	metals producing industry
Number of company	1544	117	166
Sold production [mln PLN]	91 260,7	33 647,8	27 549,6
Investment expenditure [mln PLN]	6 720,7	3 650,2	2 516,3
Employment [thousand workers]	292,0	181,0	61,5
Energy consumption [GWh]	4 359	6 170	9 687
energy-consuming factor [ kWh/100PLN*]	5,3	27,8	31,1

* Energy consumption per 100 PLN sold production

After deeply date analysis was proposed linear energy-metric models for chosen industries, where variable which is explain is energy-consuming factor and explanatory variables are number of company, sold production, employment and energy consumption.

To prepare this models was used digital-circuit engineering. On market is a lot of computer programs which used classic smallest square method. This method use programs for specialist (Gretl, Forecast PRO Unlimited, STAT-EK) or common programs (MS Excel, STATISTICA). At professional literature you can find a lot of information who prepare model correctly and who check it. The final effect are models which are presented below:

· for metals producing industry

(6)

· for coal industry

(7)

· for food industry

(8)

where:

Y - energy-consuming factor [ kWh/100PLN*],

PS - Sold production [mln PLN],

PZ – Employment [thousand workers].,

PG - Number of company,

NI – Investment expenditure [mln PLN]

This energy-metric models are base to prepare medium-range forecast for energy-consuming factor until year 2015. Determination factor for all presented models is higher then 83%, relative forecasting error is 4,6% and maximal relative error 9,8%. Small forecasting errors means that all models are correctly prepare and it is possible to build forecasts for this branches of industry.

a)

b)

c)

Fig. 6. The energy-consuming factor forecasts for a) metals producing industry, b) coal industry, c) food industry in 1990 -2015

* Energy consumption per 100 PLN sold production

Summary

The presented energy-metric models show that energy-consuming factor decrease but it is possible to see decrease rate will be lower in the future. To change this fact the industry should:

· exchange energy-consuming and material-consuming technologies to modern and energy-saving technologies, especially in heavy industry,

· magnify work productivity with a better organization of production and exploitation,

· introduce a suitable legal-economic settlement, which will promote energy-saving and ecology technologies,

· allow the Polish government to promote, by suitable legal means, saving energy.

LITERATURE

[1] Gładysz B., Mercik J.: Modelowanie ekonometryczne. Studium przypadku, Oficyna Wydawnicza PWr, Wrocław, 2007.

[2] Guzik B.: Podstawy ekonometrii, Wydawnictwo Akademii Ekonomicznej w Poznaniu, Poznań, 2008.

[3] Ney R.: Ocena zasobów energetycznych Polski, Elektroenergetyka nr 1, (2002).

[4] Luszniewicz A.: Statystyka z pakietem komputerowym STATISTICA PL, Wydawnictwo C.H. Beck, Warszawa, 2003.

[5] Pyk J.: Szanse i zagrożenia rozwoju rynku energetycznego w Europie i Polsce, Wydawnictwo Akademii Ekonomicznej w Katowicach, Katowice, 2007.

[6] Radzikowska B.: Metody prognozowania – Zbiór zadań, Wydawnictwo Akademii Ekonomicznej we Wrocławiu, Wrocław, 2004.

[7] Rocznik statystyczny przemysłu, GUS, Warszawa 1990-2007

[8] Snarska A.: Statystyka Ekonometria Prognozowanie, Wydawnictwo Placet, Warszawa, 2005.

[9] Winston W. L.: Microsoft Excel. Analiza i modelowanie, ZP-Poligrafia, Warszawa 2005.

_____________

Autors: mgr inż. Marek Kott, E-mail: marek.kott@pwr.wroc.pl.;dr hab. inż. Bogumiła Wnukowska, E-mail: bogumila.wnukowska@pwr.wroc.pl, Wroclaw University of Technology, Institute of Electrical Power Engineering, 27 Wybrzeze Wyspianskiego Street , 50-370 Wroclaw.