Normas Oficiales Mexicanas u otras disposiciones que regulan las

Recognition of a defect in an insulation system alone is not sucient to decide upon the necessity and urgency of maintenance. Knowing its consequences would assist in eective decision making with regard to maintenance/replacement strategies. Risk analysis on the severity can be utilized for optimizing the remedial action. In this section the preliminary risk analysis is presented using the data obtained for each cluster during the defect identication process. In formation of clusters, several representative values are assigned for each cluster. These values, addressed from now on as preliminary risk factors, are provided as input for risk indexing. The preliminary risk factors are:

ˆ Total PD max./mean charge density per cluster per time block

ˆ Total PD max./mean charge occurrence rate per cluster per time block ˆ PD cluster width

5.3. RISK INDEXING 73 The most widely accepted approach for risk quantication is dened as: the mag- nitude of the risk is equal to probability of occurrence of an event multiplied by the severity of that event. So, obtaining the probability of the occurrence of an event is an important step in identifying its associated risk. Determining the rate of occurrence of an event is hampered because of lack of statistical information available on critical values for possible failures. In this thesis, the probability of defect occurrence (F ) for each cluster (potential defect), which will be referred as secondary risk factors, is calculated by applying the Logistic function [83] to the preliminary risk factors. Logistic regression is expressed by means of the logistic function:

F (z ) = 1

1 + e−z (5.5)

where, F (z) denotes the probability of a particular cluster quantity and varies from 0 to 1 according to parameter z.

Parameter z is dened by means of a variable x, having a turn-over value x0, and

a sensitivity factor r according

z = r · (xi− x0) (5.6)

The regression coecient r is calculated based on the Logistic curve slope. The secondary risk factors form the foundation for calculating the associated risk index for every potential defect, which consequently results in the decision of whether a discharging source considered to be a defect and if so, gives an indication on its severity.

Not always all chosen identiers result in consistent values presenting a defec- tive site. Sometimes, all identiers are actively representing defects, but in some cases, only one or two are providing positive identication. The risk index must be based on the combination of available identiers.

The dispersion of the measured data over the length of the cable is also infor- mative on defect severity. For instance, if discharge peaks appear repeatedly sharp above a certain location, the severity is considered higher than when discharges are spread over a larger region. Therefore, the width of the captured clusters (potential defect) is included in the risk calculation. Another important factor in risk identication is the underlying trend for a certain observed risk factor. Trend analysis reveals information on whether the levels of the indicators have increased or decreased over time and if they have, the rate these changes have occurred [84]. This would ideally provide information to estimate future activity. There- fore, apart from the risk factors that are being considered in the risk assessment, it is important to consider their associated time trends in the analysis as well.

In this research, a relation for risk indexing (RI), is adopted by combining the secondary risk factors:

where Fdensrepresents the probability of occurrence for certain PD charge density,

Focc.raterepresents probability of occurrence for certain PD occurrence rate, Fwidth

denotes the probability of occurrence of a PD cluster with certain width, and Ftrend −dens addresses the probability of occurrence for certain trend in charge

density per cluster.

Algorithm 5.6 illustrated the designated approach for identifying the risk level(s). Here, only the most inuential identiers are incorporated for risk approximation. This is not to say that the other identiers (i.e. the maximum values) are not important, but they are somehow already included by their inuence on the mean calculated parameters. This equation can be extended to include all PD represen- tators.

Relation 5.7 projects the potential risk on a scale between zero and one. Prob- abilities of occurrence are estimated through models that are created based on experimental data. A larger value of the risk index indicates a higher risk that the insulation is exposed to. Accordingly, the obtained quantity can be transferred to Low, Medium or High risk to qualitatively illustrate the condition of the insulat-

5.3. RISK INDEXING 75 0 200 400 600 800 1000 1200 1400 1600 1800 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probability

PD charge density [pC / power cycle] (a) 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probability

PD charge occurence rate [# / power cycle] (b) 0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probability

PD cluster width [0.1% of cable length] (c) 0 10 20 30 40 50 60 70 80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probability

PD Trend [pC / power cycle] (d)

Figure 5.17: General probability of occurrence (S-Curve) models: a) PD charge density, b)PD charge occurrence rate, c) PD cluster width, d) PD trend

ion, meaning that values close to 1 represent a high risk situation, while values close to zero can be tagged as low risks.

Figure 5.17, shows the general models developed for probability of occurrence for each set of preliminary risk factors. The scaling of the models are done based on experimental data. The critical values are specic for the insulation type. For instance, critical values for XLPE cable are dierent from those for PILC cable. The discharge level that can be disregarded for the PILC cable, might be harmful for XLPE cable. Low critical values may lead to unnecessarily activation of an alarm, and a high setting may result in missing a true warning. Therefore, the models for risk analysis must be provided based on the insulation type if available. Probability of occurrence for each preliminary risk factor is calculated based on the presented models, and the outcomes were provided for Risk index calculation

01−Sep−20070.98 11−Sep−2007 21−Sep−2007 0.985 0.99 0.995 1 1.005 1.01 Risk level (a)

01−Aug−20080 11−Aug−2008 21−Aug−2008 01−Sep−2008 0.2 0.4 0.6 0.8 1 Risk level (b)

Figure 5.18: Risk Index variation for the defect at the location a) 140 m - Circuit A, b) 500 m - Circuit C

by applying Equation 5.7. Figure 5.18 displays the RI variation for the two clusters formed at the location of about 140 m for Circuit A, and 500 m for Circuit C.

For both locations the clusters with high risk values are assigned. For Circuit A the risk is high as from the start of the diagnosis and for Circuit C a change from low to high risk occurred during the diagnosis. Both locations were indeed defective and suered from intense PD activity.

5.4. PERFORMANCE INDEX 77