ENERGY SECURITY OF ELECTRIC POWER RECIPIENTS IN RURAL AREAS IN SOUTHERN POLAND

Małgorzata Trojanowska
Department of Power Engineering and Agricultural Processes Automation, Agricultural University of Cracow, Poland

ABSTRACT

Indices characterising unreliability of medium and low voltage power grids in rural areas of southern Poland, used by distribution companies in the analysis of electricity recipients’ energy security, were investigated. In particular they were compared with analogous values describing national networks, including networks in cities, and their changes in the years 2002–2011 were analysed. It was found that the condition of electric power security of rural consumers from southern Poland does not differ significantly from the average national value and it has improved some over the past ten years.

Key words: electric power networks, power supply reliability, failure rates.

INTRODUCTION

Energy security is defined, amongst other things, by the condition of the economy allowing for meeting recipients' demand for fuels and energy on an ongoing and future basis in a technically and economically justified manner, complying with the requirements of environmental protection [15, 16, 27] and the ensuring of energy security has been established as one of the basic objectives of countries' energy security. Partial security can be distinguished here, which is defined with reference to individual forms or energy carriers, in particular, electric power security.

The recipient's electric power security is closely connected with the security of electric power deliveries and it depends on its reliable and certain transmission and distribution. A lot of attention is paid to these issues in scientific publications [1–8, 11–13, 17, 22–25].

Locally, local government authorities and distribution companies are responsible for the consumer’s energy security [27]. Ensuring electric power security requires the construction of new energy sources, including local ones, extension and modernisation of electric power infrastructure, also on the part of the energy recipient, and mostly, intensification of the use of existing networks. To be able to plan such actions, also an analysis of the continuity of power supply to recipients, in particular, an analysis of the failure rate of grid elements. Various indices of power supply reliability are used for this purpose. An assessment of power supply reliability is also very important for proper settlements for electric power between its supplier and consumer.

The aim of this study was to analyse indices characterising unreliability of medium voltage (MV) and low voltage (LV) distribution grids over the past ten years. The analysis was presented using the example of rural grids in southern Poland. For the purpose of the analysis, the determined indices were compared with analogous values describing national networks, including networks in cities.

MATERIALS AND METHODS

The country's energy security is, to a large extent, a resultant of the individual regions’ energy security. The scope of the research conducted was limited to the region of southern Poland, which includes four provinces: Małopolska, Podkarpacie, Silesia and Świętokrzyskie. They are situated in regions served by nine distribution companies.

To the indices characterising unreliability of MV and LV networks, used in reliability analyses by distribution companies, belong [9, 10]:

• the frequency of failure of main grid components, i.e. overhead and cable lines as well as transformers, calculated from the following relationship:

(1)

(2)

where:
w_{u_L} – line fault rate [pcs./100 km lines],
w_{u_TR} – transformer fault rate [pcs./100 pcs.  transformers],
n_{u_L}, n_{u_TR} – number of failures for lines and transformers, respectively [pcs.],
L_L – length of lines [km],
L_TR – number of transformers [pcs.],

• average time of power interruption due to a failure of: lines – T_{p_L} [h], transformers – T_{p_TR} [h].

To ensure a comprehensive analysis of grid reliability, failure rates are often determined [10, 18]:

(3)

(4)

where:
q_L, q_TR – failure rate for lines and transformers, respectively.

Values of specified indices were determined in the study and the unreliability of overhead and cable lines was established separately, split into medium and low voltage categories. In addition, their usefulness for the identification of reliability of electric power supply to rural consumers was verified. For this purpose, the validity of the individual indices, treated as features, was assessed by determining the asymmetry distribution coefficient for the individual features [19]. Calculations were conducted on the basis of nine distribution companies’ data.

RESULTS AND DISCUSSION

Electric power characteristics of the area under investigation
Rural areas in southern Poland receive electric power using approx. 37.3 thousand km of MV lines, 67.8 thousand LV lines and nearly 31.8 thousand MV/LV transformer stations. Since 2001, the number of transformer stations increased annually by approx. 1.5%. The analogous increase in the length of MV and LV lines during this time was 1% and 0.6%, however, the increase in the cable lines was much greater than for overhead lines.

The density of lines per 1 km² of the area served is an interesting index for comparative purposes. Its values are determined separately for medium voltage and low voltage and for individual provinces are presented in Table 1. Higher line density is thought to guarantee higher reliability of power supply to recipients. In the area under analysis, the highest line density both for MV and LV is observed in rural areas of the Małopolska Province. It is comparable to the density of national grids (0.96 km of MV lines/km² and 1.37 km of LV lines/km²), which also include urban areas, which are characterised by higher density.

Such high density of lines in rural areas of Małopolska Province is due to high density of population in these areas. Its level is 124 inhabitants per km² of the area and is almost equal to the national density (123 inhabitants/km²). In cities of southern Poland the density of electric power lines is over four times higher than in rural areas.

Another index characterising the electric power infrastructure includes average lengths of MV and LV lines for one MV/LV transformer station (Tab. 2). These lengths have not changed significantly over the past ten years.

During the period under analysis, also stabilization of the average number of customers and the amount of electric power sold was also observed as calculated per one MV/LV transformer station. In 2011, the number of rural households in southern Poland was approx. 1.5 million and they used 3340 GWh of electric power. These values calculated per one MV/LV transformer stations are presented in Table 3.

In rural areas of southern Poland, the values of indices specified in Table 3 are on average nearly four times lower than in the cities, which confirms much lower profitability of electric power sales through rural grids as compared to urban grids.

Especially low profitability is observed in rural areas of the Podkarpacie and Świętokrzyskie provinces, where the annual electricity sales per transformer station is at the level of 70–80 MWh.

Unreliability of MV and LV grids
The values of indices characterising the unreliability of network components in rural areas of southern Poland in the year 2011 and their percentage changes in the years 2002–2011 are presented in Table 4. Table 5 presents analogous values referring to failure rates.

For the assessment of unreliability of rural grid components in southern Poland, the values of individual indices were compared with their values for national grids [9, 20]. Similar, and in some cases even lower, values were obtained than those for national grids which include also urban grids, which are characterised by lower unreliability of network components.

Analogous comparisons of failure rates rendered similar results. The knowledge of failure rates allows for determining the quantity of electric power which is not supplied as a result of failures during a year, which is taken into account in economic analyses.

In rural areas of analysed provinces the yearly quantity of electricity which is not supplied as a result of failures during didn’t exceed the 0.4% energy sold to customers during tested period. Both the electric energy suppliers and the customers suffer a loss caused by power interruptions, but customers are the ones who lose more. In many countries intensive researches for the purpose to determine costs of power interruptions are managed. In Poland extensive researches in this field haven’t been carried out so far, on account of lack of distribution companies’ interest.

It should be noticed that over the past ten years, all of failure rates under analysis reduced and some of them, such as, e.g. failure rates for cable lines decreased considerably. Among grid components included in the analysis, transformers are characterised by the lowest failure frequency, despite the fact that their average age is quite height.

And although it all evidences on improvement of energy security in rural areas of southern Poland, but the increase of power interruption times due to a failure of MV grids and the increase of frequency of LV overhead lines’ power failures cause some anxiety. It raises doubts about technical conditions of these elements. Some influence on the obtained results, especially about middle voltage lines, could have adverse weather conditions, which occurred in recent years.

Assessment of validity of indices characterising power supply unreliability
All indices characterising unreliability of power supply analysed in this study are universal characteristics. Not all of them must be equally useful for identification of unreliability of network components. For the purposes of the analysis of their usefulness, distributions of individual indices were analysed, determining asymmetry coefficients. All coefficients were positive, which indicates right-sided asymmetry of features. Strong right-sided asymmetry is characteristic of important features [19].

On the basis of the analysis conducted, it was found that such features characterising unreliability of networks may, first of all, include average times of power interruptions due to a failure of overhead low voltage and medium voltage lines. Amongst the indices tested in the study, they are not only the best at identification of the continuity of power supply but also provide the most information to its recipients. A sample diagram of empirical distribution of average times of power interruptions due to LV overhead line failures T_{p_Ln(LV)} is presented in Figure 1.

Finally, the relationship between the state of electric power infrastructure, which is characterised by indices presented in Tables 1 and 2, as well the number of customers supplied from one transformer station (Tab. 3) and the average time of supply interruption due to a failure of overhead MV (T_{p_Ln(MV)}) and LV (T_{p_Ln(LV)}) lines has been examined, using correlation analysis.

Statistical analysis showed that between the state of electric power grids MV, as well the number of customers supplied from one transformer station and the average time of supply interruption T_{p_Ln(MV)} occurs a significant correlation, in the case of MV lines density – a high correlation (Spearman correlation coefficient r_S = -0.67).

Similarly, the analysis in relation to the low voltage grids revealed a significant correlation only between the values T_{p_Ln(LV)} and the length of LV lines supplied from one transformer station MV/LV (r_S = 0.43).

CONCLUSIONS

The reliability indices presented in the study are among the most often used in the analysis of local and regional electric power security. Their main advantages include the simplicity of calculations and mutual complementation of information about system operation. However, they do not say anything about the resultant annual value of failure intensity, time distribution of failures and they do not include mutual relationships between failures.

The assessment of the values of indices under analysis is possible using analogies, in particular by comparison with the values of indices for grids considered to be reliable as well as by analysing their changes in time. It was found that the condition of electric power security of rural consumers from southern Poland does not differ significantly from the average national value and it has improved some over the past ten years.

On the basis of the analysis conducted, it was found that, amongst the indices tested, average time of power interruptions due to a failure of overhead low voltage and medium voltage lines are the most useful for the assessment of electric power security. The values of these indices depend significantly on the electricity infrastructure state, in particular the density of lines, the length of power circuits and the number of customers supplied from one transformer station.

Accepted for print: 15.10.2014

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