**3.1 Reliability assessment stages**

88 Electrical Generation and Distribution Systems and Power Quality Disturbances

According to the mathematical model adopted in the calculation of specific parameters of renewals non-periodic or periodic renewal, we can distinguish the following types of

deterministic character.


imposed by the failures occurring in the system.

{ *k Tk* Δ = , 1,2, ...} .

preventive renewals.

are the foundation of the RCM design.

imposed to the preventive maintenance actions.

successive renewals or after a fixed period of time;


type strategies.

the following sections:

techniques.

strategies:

based on a preventive maintenance program. In conclusion, that these strategies have a

It represents the simplest strategy of periodic renewal and consists of the renewal of the equipment either at the moment of its failure or at equal time intervals

A first criterion used to implement this strategy, i.e. the calculation of period ∆T or the number of *k* renewals, over the imposed period T, consists of imposing a certain minimum level of the reliability function over the interval between two successive renewals, or at the end of a period T. The strategies by BRP type have the disadvantage of inflexible schedules of renewals, by the fact that preventive renewals are performed at predetermined moments of time, without taking into account the failure renewals




These preventive strategies renewal operating at some predetermined time points and lead to total or partial elimination of accumulated wear, each time bringing equipment in operating condition characterized by lack of wear or with negligible wear. Establishing the renewal moment is made using the reliability model of equipment, based on the information referring to the behavior of the equipment in conditions of operating data, principles which

The option between the different RCM preventive renewal strategies must rely on uniform criteria leading to the best assessment. These criteria must be the result of technical and safety factors imposed to the system, as well as the result of economic considerations

We mention only some of these criteria which are valid for EDS, these criteria developed in


Different studies present additional evolutionary renewal strategies used in the renewal

Implementing the CRP type strategy by requires a continuous monitoring of equipment through measured quantities. Determining the moment of the next preventive renewal is made according to the evolution equipment parameters, established through diagnosis


equipment, which are part of the *CRP type (Continuous Replacement Policy)* strategies.

performed various technical criteria or economic criteria can be used.

Knowing the *availability* of EDS implies statistical processing of the database containing historical events, with the final purpose of determining the parameters and the analytical shape of the *reliability function R(t)*. This process is applied to each component of OEL, in accordance with corrective or preventive maintenance actions performed over time.

The analytical expression of the reliability function is a central issue of the reliability theory, in general and especially in RCM. The procedure for assessing the unknown parameters of a distribution function, is called an estimate and she performed in the selective treatment of data resulting from the analysis of reaction time in operation of the system with its components.

Estimating the reliability of OEL, based on statistical data processed during the operation, in this case from the (0 ÷ <sup>0</sup> T ), presented in Figure 1 is based on modeling the subsystems' behavior with random processes.

Estimation modeling involves the following steps, for a OEL:


To illustrate these steps, we study the case of OEL by 20 kV, has the following construction parameters:


### **3.2 Random variables**

The OEL operation time was selected as random variable form the database of the beneficiary of the 20 kV power line, which includes the sheets of incidents and interventions over a period of about five years. The OEL operation time is expressed according to:


Reliability Centered Maintenance Optimization of Electric Distribution Systems 91

There are several studies which present a lot of techniques and methods to evaluate the Weibull function parameters, depending on: the number of function parameters chosen, the

In (Dickey, 1991), (IEC 61649, 2008), are mentions statistical methods for assessing the parameters for Weibull distribution of failures type and constant repair time. The Statistics Toolbox MATLAB programming environment allows the evaluation of parameters of the

[parmhat,parmci]=wblfit (t)

parmhat (1); parmhat (2); A synthesis of the calculation methods and accuracy of the Weibull parameters is presented

In the paper (Baron et al.,1988), the authors presents a practical mathematical method of setting the *α* and *β* parameters with two parameters of Weibull law by the form of relationship (6), based on statistical data obtained from the analysis of operating

a. there are significant records concerning the concerning to the number of defects and

The value of the parameters 'α' and 'β' is derived from the relationship (6), which by

with notations: ( ) ( ) { ( ) } max R t 1 t / t ; a lg lg e lg ; b lg lg 1 /R t N fi =− = + α = fi fi <sup>i</sup> N fi (9)

is obtained from (8) equation of a straight line: ba l i f g <sup>i</sup> = + β t (10) for which using the method of least squares system is obtained the following equations

> n nn <sup>2</sup> i fi fi fi

b lg t alg t lg t

A na B C Ba D = ⋅+ β ⋅

= +β

n n

= ⋅ +β⋅

= =

which solved in relation with a and β unknown, result:

i fi i 1 i 1

b n a lg t

i 1 i 1 i 1

= ==

N fi ( ) fi lg R t t lg e <sup>β</sup> = −α ⋅ ⋅ or: N fi ( ) fi lg 1/R t t lg <sup>e</sup> <sup>β</sup> =α⋅ ⋅ (7)

{ N fi ( ) } ( ) fi lg lg 1 /R t lg lg e lg lg t = + α+β (8)

( )

= ⋅+ <sup>β</sup> <sup>⋅</sup> (12)

(11)

b. the average recovery times are negligible compared with the operating times.

**3.4 The parameters of Weibull distribution function** 

scope of the application, the available statistical data, etc.

Weibull function, with the instructions, (Blaga, 2002):

the operating times between them;

repeating the operation of logarithms, result:

logarithm application, results as:

system is obtained:Citiţi fonetic

or :

arrangements of the OEL, as well as in the following assumptions:

in (IEC 61649, 2008).




Table 1. Incidents database
