PROCEEDINGS

of the Tomsk Polytechnic Institute named after S. M. Kirov, awarded the Order of the October Revolution and the Order of the Red Banner of Labor

Volume 295　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1976

PROBABILISTIC ANALYSIS OF FLOWS OVER INTERSYSTEM TIES

R. I. BORISOV, A. G. MILYUSHKIN

(Presented by the scientific seminar of the Department of Electrical Systems and Networks)

Optimization of design decisions and operating modes of electric power transmissions imposes increased requirements on calculation methods, requiring them to obtain reliable estimates of operating-mode parameters, to take more accurate account of the regularities in the variation of loads and of the connections between them. Since the magnitudes of flows over intersystem ties are conjunctural in character and, by their nature, random, calculations should be carried out using probabilistic-statistical methods and, on the basis of the results obtained, means and parameters of additional devices should be selected that increase the economy of operation of electric power transmissions. Probabilistic-statistical methods in power engineering are relatively new, and in solving many problems an axiomatic approach has become established toward the distribution of quantities as being obviously normal, which does not always correspond to reality and requires additional investigations in order to establish reliable estimates of particular parameters that are not deterministic by their nature. However, confidence in the correctness of the chosen solutions is possible only when probabilistic-statistical methods are used to study a real, objectively existing process with all its features, and when the actual regularities in the variation of flow magnitudes and the stochastic relationships between them are taken into account. The statistical material in the present work consisted of hourly records of the load magnitudes of intersystem lines of electric power transmissions of the Central Siberia interconnection for the period 1968–1972. The possibility of obtaining regularities and parameters characterizing the normal mode from the full body of statistical material proceeds from the assumption that, for overhead transmission lines, as for networks [1], it is possible to conditionally divide the information into two arrays. One characterizes short-term transient modes and is used for operational control; the other determines the most prolonged normal mode (97–98.5%) and is intended for technical-economic justification of measures that bring the mode indices and the parameters of electric power transmissions into optimal correspondence.

Flows were investigated along line (I), connecting systems with different structures, and along line (II), connecting power systems with approximately the same structure. The investigations were carried out according to the methodology set forth in [2], with division of the flows according to the scheme of Fig. 1 in accordance with the sign before the quantities $P$ and $Q$, which denotes coord—

lability (+) or nonconformity (−) with the adopted direction.* The empirical distributions obtained in Figs. 2 and 3 fully determine the load regimes of the interconnections. According to the definition [3], the LEP-I regime is of a maneuvering character; the LEP-II regime is defined as

Fig. 1.

reversible; the load distributions can be described by Pearson curves [4], i.e., a theoretical distribution function can be established with the parameters characterizing it. The dynamics of the parameters

Fig. 2.

* Note. The adopted direction is from East to West.

of the load distributions for LEP-I indicates increased utilization of the line’s transmission capacity; at the same time, for LEP-II no such regularity is observed. In the fluctuations of the parameters characterizing the load distributions of both LEPs for individual months, no

Fig. 3.

systematic pattern is traceable; an illustration of this may be the change in the mathematical expectations \(T_p\) of the active load of LEP-I for 1970–1971 (Fig. 4).

Fig. 4.

Of particular interest in studying normal load regimes of intersystem ties is determining whether there is a dependence between the quantities \(Q\) and \(P\), and, if such a dependence exists, determining its character, i.e., establishing the regression of \(Q\) on \(P\). For each value \(P = P_i\), the reactive power remains a random variable, admitting

greater scattering of their values, whereas the dependence of \(Q\) on \(P\) is manifested in the change of the mean values \(Q_i\) from \(P_i\) when the quantity \(P\) passes from one value to another. Thus, from the form and arrangement of the graphical representations of the existing dependences, one can judge the presence or absence of a correlation between \(Q\) and \(P\), and also draw a preliminary conclusion about the nature of these dependences.

The results obtained indicate the presence of a correlation between the quantities \(Q\) and \(P\) for power transmissions, which agrees well with a linear approximation of the dependences obtained by the method of least squares. It should be noted that failure to take into account the directions of power flows leads to significant distortions in the results of estimating the relation between active and reactive powers.

In the course of the study it was established that, for LEP-1, a sufficient statistical sample with a minimal error of representativeness is a weekly random sample from the monthly aggregate.

References

1. V. V. Kernogo. Analysis of the Development and Improvement of Electrical Networks. Minsk, “Science and Technology,” 1971.

2. R. I. Borisov, A. G. Milyushkin. Statistical analysis of load regimes of the power systems of Siberia. Present collection.

3. V. V. Bolotov et al. Questions of the Theory and Methods of Designing Power Systems. L., “Nauka,” 1970.

4. A. K. Mitropolsky. Techniques of Statistical Computations. M., “Nauka,” 1971.

5. E. S. Venttsel. Probability Theory. M., “Nauka,” 1969.