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PROBABILITY DENSITY FUNCTION AND HISTOGRAM APPLICATION IN REAL WORK OF AN ELECTRICAL POWER ENGINEER

FIGURE 1 IS THE STATISTICAL DATA FOR ANALYSIS
THESE NUMBERS ARE NOT BASED ON REAL DATA, SHOWN FOR EDUCATIONAL PURPOSES ONLY.

FIGURE 2 Data is Converted to Histogram

FIGURE 3 Histogram is Converted to Probability Distribution Function

FIGURE 4 Probability Distribution Function Shown in 3D Bubble Graph with Focus Bushing that has change of power factor from nameplate that is an outlier from the 128 bushing testing session history

Figure 4 above is using the visual display analysis looking only for an outlier bushing from the population.

If there is no outlier , it is hard to list all the bushings that are behaving differently from the rest of population. Central tendency method using mean and standard deviation will be the next logical method to find the list of bushing that need more attention.

Next step after having the list of bushing that needs more attention is using the trending analysis of power factor measurement, capacitance measurement, and watt measurement.

Finally additional tool such as Weibull Analysis of bushing failure will be helpful to prioritize the bushing overall strategy.

IMPORTANT: DON'T FORGET TO SEEK ADVICE FROM YOUR BUSHING VENDOR AND POWER FACTOR TEST INSTRUMENT VENDOR THEY ARE YOUR PARTNER.

FIGURE 5 Trending Analysis of Capacitance Reading Valid For OIP Bushing Only

FIGURE 6 Trending Analysis of Watt Reading Valid For OIP Bushing Only

By automating the data collection and statistical analysis, transformer engineer will have the necessary tool to monitor new Power Factor test measurement of transformer bushing for any outlier or listing of 2 or 3 standard deviation from their population of transformer bushing fleet to generate the list of bushing for more detailed analysis using trending method. This insight in turn will trigger maintenance strategy, operation strategy, replacement strategy, specification update, vendor management, purchasing strategy, and financial planning.

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