A PROBABILISTIC ANALYSIS OF THE LOAD ON COUPLING ELEMENTS OF LONG-DISTANCE POWER TRANSMISSION LINES WITH INTERMEDIATE SYSTEMS

R. I. Borisov, A. G. Milyushkin

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

Questions of constructing power interconnections on the basis of system-forming ultra-high-voltage transmission lines, with intermediate systems of different structure and character connected to them, require comprehensive studies. In particular, studies are needed of the loading regimes of the elements coupling long-distance transmission lines with intermediate systems whose power is commensurate with the magnitude of the transmission capacity of the power line. Such studies are necessary in connection with the increasing requirements for the optimization of design decisions and operating regimes of power facilities, since the inaccuracy of calculation results and the consequent need to adopt nonoptimal decisions lead to large material losses even with a relatively small error in the calculations. By following only the path of improving calculation methods, it is difficult to achieve the desired results, because the mismatch between the deterministic methods used for solving problems and the stochastic nature of processes in power engineering leads to the fact that, despite the mathematical rigor of solution algorithms, the calculated estimates of parameters differ from the actual ones. Probably the main reason is the imposition on a process that is in fact probabilistic in character of qualities of a deterministic process that are not inherent in it [1].

The purpose of the present work is to determine integral characteristics that describe the loading regimes of power-transmission elements coupling a long-distance power transmission line with an intermediate power system, such as the distribution laws of load magnitudes and the parameters describing these distributions. An important task is to establish the dependence between the accompanying processes, its form and closeness to a functional one, and also to determine the minimum reliable statistical sample. Analysis of the dynamics of the parameters characterizing the processes under study is one of the basic aspects in problems of this kind.

Since the problem under consideration is by its very nature stochastic, owing to the randomness of a number of factors acting in the systems, it must also be solved using the methods of mathematical statistics and probability theory. The material used was hourly statistics of active and reactive loads for one of the intermediate connections to the strong tie of the Siberian power interconnection for the years 1969–1971.

The statistical material was processed according to the methodology of [2]. The distributions obtained, Fig. 1 and Fig. 2, fully reflect the nature of the power flow through the coupling elements and the load regime over the year. The histograms of the active-load distribution indicate the variable nature of the power flow through the coupling elements. For all the statistics studied, the distributions are bimodal and can be approximated by a curve \(f(p)\) representing the sum of two distribution densities:

Fig. 1.

Fig. 2.

\[ f(p)=f_1(p)+f_2(p), \tag{1} \]

where \(f_1(p)\) and \(f_2(p)\) are one-dimensional distribution densities averaged over the time interval under study, describing in this case the regimes of reduced and increased loads, respectively. The analysis showed that the distribution densities \(f_1(p)\) and \(f_2(p)\) are quite accurately fitted by curves of normal distribution density. The agreement of the adopted hypothesis is confirmed by a quantitative estimate using the Kolmogorov goodness-of-fit criterion \((\lambda=0.4\div0.8)\).

The distributions shown in Figs. 1, 2, and the estimates of the parameters describing the indicated distributions point to a tendency toward an increase in power flow toward the intermediate power system, as well as to a densification of the load schedule*.

The results of the correlation analysis indicate a weak dependence of the values of reactive-power flows on active power. The validity of this conclusion follows not only from the closeness of the correlation coefficient to zero \((R_{pq}=0.03)\), but also from the location of the regression lines \(Q=f(p)\) in the graph in Fig. 3. The straight lines obtained by approximating the empirical dependences as linear are almost parallel to the abscissa axis; i.e., the averaged values of reactive powers corresponding to fixed values of active power are approximately equal and lie on one horizontal straight line.

Fig. 3.

In the course of studying the statistical material on loads, it was established that the minimal statistical set in terms of volume, with a representation error not exceeding 5%, is a weekly random sample of hourly records of load values from the monthly aggregate; i.e., with a small difference in the estimate of mathematical expectations, the distribution law of the sample statistic repeats the distribution law of the general population (annual statistics).

Conclusions

1. The results obtained indicate the maneuvering nature of the connection, with a tendency toward an increase in power flow toward the intermediate pow—

* Note. The numbering of the curves in all figures corresponds to the years in increasing order.

power system, with simultaneous unbundling of the load schedule of the link.

1. The results of the correlation analysis indicate the absence of dependence between the values of active and reactive loads for this link.

2. Taking into account the monotonicity of the dynamics of the parameters characterizing the load schedules, it appears possible to carry out analogous studies for subsequent periods using small statistical samples.

REFERENCES

1. V. I. Kurdin, Yu. V. Kurdin. On the construction of statistical characteristics under operating conditions. Tashkent, Fan Publishing House, Uzbek SSR, 1971, No. 4.

2. R. I. Borisov, A. G. Milyushkin. Probabilistic analysis of power flows over intersystem links. In the present collection.

3. A. K. Mitropolsky. Technique of Statistical Computations. Moscow, Nauka, 1971.