Vypanasenko S.I., Vypanasenko N.S.

National Mining University

Energy Efficiency Control of Coal Mining

The rating of energy efficiency at coal mines is carried out on the basis of regressive analysis. By means of regressive relation the average indexes of energy usage at the existing yield of coal mined are determined.

The control of energy efficiency by a coal mine on the basis of regressive analysis has some features which it is necessary to find out. The paper is devoted to the determination of these features for the conditions of coal mining in Ukraine.

Let us consider a known approach to analyse energy efficiency. Let us assume that such a regressive relation of energy usage is based on experimental data, obtained in a number of the previous experiments. Then actual energy consumption (parameter y) in all the next experiments must be compared with the average (planned) value a_y that refers to x (coal mining). If for х_n+1 actual energy usage у_n+1 exceeds the value а_у(n+1), it testifies about inefficient energy usage by a coal mine. If an index of actual energy consumption is below the average, it testifies about efficient energy usage. It is necessary to pay attention to the fact that forecasting indexes of energy usage must be obtained taking into consideration an accurate regressive relation a_y = φ (х). Actually, we have an approximate relation that allows to get an estimation (y) of true average value of a_y. Apparently, in this case it is necessary to build confidential intervals where the regressive relation a_y = φ (х) will exist with high confidential probability.Concerning the case of linear regression confidential intervals are shown on picture1.

Рic.1. Linear regression and its confidential intervals.

If the indexes of energy usage exceed confidential intervals (shaded area), then the value of у_n+1, for example, testifies about inefficient energy usage in structural division during on the controlled period (shift, day, week), and the value of у_n+2 testifies about efficient energy usage.

Thus, the feature of control is that functional relation between an average value of energy usage on an object and the accepted independent parameters, that characterize energy consumption, is the boundary that divides good results from unsatisfactory.

Coming from the principle of control of energy usage, obviously, it is possible to raise a question about the estimation of level of unsatisfactory or good work of a structural division. Therefore, sometimes the calculation of difference у_n+1 –у _(n+1)g = Δу_n+1 (in the theory of energy management Δу_n+1 is known as dispersion) is done and represented as the measure of difference of actual and forecasting energy usage. As in different experiments the levels of у_(n+1)g differ, it is necessary to present the level of waste (or saving) in relative units, given in percentage:

The calculation of δ - is an important moment of analysis as this index can determine that level of material encouragement (or losses) which will be applied to structural division as a result of its work.

Taking the value of dispersion Δу_n+1 on the level of wage incentives, apparently, it is necessary to put a task of enough accurate calculation of the most regressive correlation, so it is necessary to answer a question whether the type of regressive relation matches the data of an experiment, and how an approximate regression that we have got differs from a true one (a question of confidence intervals).

Answering the first question, it is necessary to pay attention to some features of relation between energy usage and the yield of coal mining. These features adjust us on the use of simple linear relation of the first order. It is connected with the following:

· It is necessary to apply linear regression in research where the law of “even accumulation” is just. It is known that y is connected with the change x, but does not depend on what “amount" of the parameter x is accumulated. It is this law that is acceptable to the existing at mines relation between energy consumption and coal mining.

· The limits of change of coal mining yield, which energy usage depends on, generally, is small. It is because of the rhythm of work of coal enterprise, which is permanent in motion of many years, where work is distinctly aimed at getting a result – coal mining. At the small limits of change of the argument linearity even of substantially nonlinear relation у = f (х) results in insignificant errors. So, linear relation is typical for the narrow range of change of argument x.

· Linear regressive relation has clear, simple interpreting indexes that characterize the degree of relation of one casual value from another. Mathematical equations that determine the coefficients of regressive line are simple. Linear relation allows to calculate the expected saving of energy usage, forecast the rates of energy consumption.

An answer to the second question (confidence intervals) is extremely important too. The forming of confidence intervals allows to highlight the area, in which it is possible to fix the acceptable results of energy usage (shaded area of lines, Pic.1). And only the overrun of results over the area is considered as an unsatisfactory (value y is located above) or good (below) result. In case if confidence intervals are wide, efficiency of control of energy usage goes down. Thus, greater part of experimental data will be in the shaded area and they will be examined as they match the forecasting indexes. Narrowing of the area will be observed at strengthening of correlation between dependent and independent variables, and also at the increase of amount of experiments. The narrower the area is, the more efficient control is carried out. Apparently, there is a reason to define the maximal width of this area, at which it is possible to consider the control as effective. So, it is suggested to define the value (у_ов – у_он)/у₀ ,and to give it in percentage (Pic. 1). It is obviously that these values of related variable y are obtained for the average value of independent variable х₀, which in its turn is obtained in a number of the previous experiments. Then there is a question, why are the values y which refer to an average value х₀ examined? This is justified taking into consideration a fact that dispersion of variable x takes place in the area of an average value of х₀, thus, it is worth expecting small dispersion of values of x. Therefore, the values of energy usage, characteristic for х₀, represent energy usage in other experiments too. Setting the level of parameter є [є = (у_ов – у_он) · 100% / у_о], we determine requirements for the confidence interval and, consequently, the accuracy of the control of level of energy usage. So, for example, if to require that the value does not exceed 10%, it means that in the area of values of x, close to х₀, the accuracy of control of energy usage, conditioned by the presence of confidence intervals, will approximately make the value ± 5%. It is clear that if the value є will be determined beforehand, then the formation of regressive relation with necessary confidence intervals (conditioned by the maximal value) є will be possible only by conducting a certain number of experiments. Let us remind that with the increase of a number of experiments the area, limited by the confidence intervals, narrows. Practical realisation of this requirement is that the amount of experiments, necessary for the regression construction, must be enough to provide the value is less, than is required. Therefore, the regressive relation construction will be connected with the previous estimation of necessary amount of experimental data.

The findings of energy usage and yield of coal mined should to be read daily and synchronously. Thus, in conditions of Ukrainian mines, the most appropriate period for fixing the resulted indexes is before the first shift, when there is a possibility to define the yield of coal mined and a relevant amount of energy consumed during a previous day.

The paper has been published with the support of Scientific and Education Center «Geotechnical systems stability: processes, phenomena, risks».