19^th International CODATA Conference
Category: Poster

Spatial Electrical Loads Modelling by Geostatistical Methods

Prof. dr hab. Barbara Namyslowska-Wilczynska (B.Namyslowska-Wilczynska@pwr.wroc.pl), Prof. dr hab. eng. Artur Wilczynski (artur.wilczynski@pwr.wroc.pl)
Wroclaw University of Technology, Poland

Spatial modelling and prediction of electrical loads are key elements in planning the development and operation of power transmission and distribution networks. The effectiveness, economy and reliability of operation of the electric power system depend on the choice of electrical equipment and its location in the areas where there is demand for electricity. The role of spatial modelling of electrical loads is particularly important now when a competitive energy market is being developed.

Estimation kriging techniques were applied to process and analyse data on electrical loads measured at high voltage (220 and 400 kV) nodes and in a meshed 110 kV network for the area of Poland. The load data were for characteristic moments in time, i.e. 3:00 a.m. and 11:00 am in the summer season and 3:00 a.m., 11:00 a.m. and 5:00 p.m. in the winter season of 2001. Two kinds of databases were created: one containing the values of geographic coordinates X and Y, specifying measurement taking locations, and the other containing the power values and the successive numbers of the measurements. The variogram function was used for the spatial modelling of the electric loads and then different kriging estimators, such as ordinary kriging, simple kriging with a global mean, simple kriging with a local mean and lognormal kriging (in their point and block modifications), were applied to estimate the areas of average loads.

The paper will present the load variability in the above mentioned power networks at selected moments in time, i.e. 11:00 a.m. in summer and winter, estimated by the different kriging techniques. Isotropic variograms, fitted by spherical or exponential models, show the variability of the loads. In the roses of the directional variogram roses, calculated for 11:00 am on the basis of 220 and 400 kV network data, certain periodicity in the NE-SW and N-S as well as W-E and NW-SW directions is noticeable. Similarity between the graphs of variogram function (h) for pairs of directions, i.e. NE-SW and N-S as well as W-E and NW-SW, becomes apparent. The tendency to periodic differentiation, mainly along the NE-SW line, but also along the N-S line, is confirmed by directional variograms calculated using the data for the 110 kV network nodes. The average electrical loads were estimated using a grid of 10 km 10 km elementary blocks and nodes, covering the area of Poland. 5625 coordinates X and Y, estimated averages Z* and standard deviations of estimation k were calculated for the block centres and then for the elementary nodes. As results new data bases were created. The databases were used in estimation by the different kriging techniques whereby a set of raster maps of the estimation areas for the values of the two main geostatistical parameters, i.e. estimated averages Z* and standard deviations of estimation k, was obtained. The transmission network's lines were plotted on the maps. This extensive documentation can be useful in managing the electric power system whereby the risk of blackouts can be reduced. It was found that irrespective of the analysed power network variant, the season and the time, simple kriging with a local mean yielded both the highest and lowest estimated averages Z*, but with higher standard deviations S than the average (from the estimated averages Z*) in comparison with the results obtained by the other techniques. While standard deviation S of the value of standard deviation of estimation k for the 220 and 400 kV variants of the nodes grid was on the whole lower for simple kriging with a local mean. As regards the other basic statistics, the differences for deviation k (the average, the minimum and the maximum) were statistically insignificant for all the tested techniques. As regards the nodes of the 110 kV network, the lowest standard deviation S for deviation k, its maximum and minimum (zero) were obtained when ordinary (point) kriging was used. The results of calculating the statistics by simple (block) kriging with a local mean did not differ from those yielded by ordinary (block) kriging.