Visualization of available power transfer capability in a transmission system using morphological techniques

American Journal of Applied Sciences, Feb, 2009 by S.U. Prabha, B.S. Dayasagar, C. Venkataseshaiah

INTRODUCTION

The electrical power systems are very large and complicated networks. Power system operators need to interpret and integrate multiple measured parameters. Power availability and its utilization are the two significant parameters that are usually denoted by numerical values in MVA and MW units. Policy and decision makers consider these parameters to propose appropriate planning schedules to take care of the further power demands from the point of transferability from one zone to another. Analysis based on these numerically denoted parameters requires both expertise and understanding of statistics to properly summarize the power utilization and demands. If such statistical summaries can be represented as spatial phenomena over a geographic space, one can have a synoptic view of the total power availability and its utilization between the buses with significant contrast. This is a kind of visualization of the available maximum power capacity and the utilized capacity in terms of spatial maps.

This study addressed in this research with associated analysis is carried out based on certain map algebraic tools like mathematical morphology. In earlier studies, various methods for load flow tracing have been reported (1). A morphological image analysis technique was presented to visualize the strong sub networks in a power system (2). Different schemes of network representation using various aspects of transmission system were briefly discussed in (2). The purpose of the present work is to use the morphological decimation techniques to visualize the available power transfer capability in a transmission system. The special features of this proposed approach are multi-color visualization of the available power transfer capability in a transmission network and its application to optimal path finding for power transfer between any two buses.

MATERIALS AND METHODS

The IEEE 24 bus test system is considered as an example. Figure 1 shows a single-line diagram of the power network under consideration. The thickness of the line represents the rated megavolt-ampere (MVA) capacity. This is referred as input image. Using the results of power-flow analysis (4), another image is constructed for the megawatt (MW) flow in the lines and is shown in Fig. 2. These images were translated into eight-bit bitmap images. The image constructed with MW flow in the lines is decimated through a multiscale morphological opening transformation (3), such that the decimated image is represented as 9-category power flow network. This processed image is then superimposed on the input image. The comparison could be done between the used capacity and the maximum capacity to obtain the index of availability.

Image construction techniques: The logic in creating the input image in terms of pixels with varied ranges is based on the following steps.

Step 1: The largest capacity of the line is 500 MVA. The other input MVA capacities are 175 and 400. The later capacities are divided with the largest possible capacity to normalize all the MVAs. Accordingly the capacity values are respectively 0.35, 0.8 and 1.0.

Step 2: In order to make sure that the amount of MW that is flowing between the buses, which will always be the subset of the maximum allowable MVA capacity, the ratios obtained at step 1 are considered as the basis to decide the width of the input MVA in terms of pixels.

Step 3: Assigning pixels by taking the condition cited in step 2 yields the pixel width 14, 32 and 40 which clearly acts as sets of the subsets within the ranges of 2-8, 10-12 and 14-20.

The image created for the MW flow between the buses is also drawn to scale. The number of pixels corresponding to the thickness of each line is chosen after grouping the line flow values, i.e., 0 to 20 MW flow capacity is represented by the thickness of 2 pixels and henceforth the proportionality is maintained. The images that are constructed by the process explained above yield a bitmap image of the power grid as shown in Fig. 1 and 2. It would be appropriate if these spatially distributed diagrams are decimated according to their potentialities.

[FIGURE 1 OMITTED] [FIGURE 2 OMITTED]

Morphological transformations: The required basic transformations are briefly explained as follows. Let A, P and M denote sets representing total available power capacity, buses (open circles) and the power being utilized respectively over two-dimensional discrete space on black background. These sets depicting the important features in spatial form are created interactively with white pixels and black background. Figure 1 is obtained through logical union of sets A and P. It is also obvious from Fig. 1 and 2 that the set M, being the map denoting spatial distribution of the load being utilized, is a subset of set A. Morphologic transformations are explained with an image represented in discrete space (M) and a template (B) that would be used as a probing rule to make modifications in M. The basic binary morphologic transformations include erosion and dilation. Figure 3 shows the impact of the basic morphological transformations.