**2. RCM – Evolutive process of renewal**

In the analysis presented in section 1, aimed to observe the natural process of degradation of the system performance, without taking into account the capacity of external interventions, to oppose this degradation through the partial or total reconditioning system, in a word's through its renewal. Starting from these considerations, in this section we will try to present the specific models of external interventions, defined as a renewal strategy, performed to restore systems performance and to modelling the reliability function of systems in study, (Catuneanu & Mihalache, 1983).

#### **2.1 Renewal process**

We define the action of *renewal*, as: *the external intervention performed on a system that restores the system operating status and/or changes the level of its wear, respectively of the system reliability*. From the definition we can distinguish two types of renewal actions that can be performed on systems:


their strategies. Thus, the random or deterministic strategy of preventive renewals is added to a random process of failure renewals.

The classification of renewal actions can be performed on several criteria, of which we remind a few: the purpose, timing and costs of their occurrence, distribution and frequency and last but not least, the effects on the system safety, (Anders et al., 2007).

In this work, we analyze and study only preventive renewal processes, through their modelling influence on the system in the following cases:


The evolution of an equipment will thus be represented by the succession of renewal moments 1 2 , , ... , *<sup>n</sup> tt t* , and the intervals between them: 1 2 , , ... , ... *<sup>n</sup> xx x* presented in the Figure 2.

$$\begin{array}{c} \mathrel{\times\_1} \qquad \times\_2 \qquad \times\_3 \qquad \cdots \qquad \times\_{\mathfrak{t}\_{\mathbf{n}}} \qquad \times\_{\mathfrak{t}\_{\mathbf{n}-1}} \qquad \cdots \end{array}$$

Fig. 2. The evolution of an equipment with renewal

If it is considered a certain time interval (0, t), the number of PR denoted by *Nt* , performed during this time, is a discrete deterministic process, called preventive renewal process, as the basic component of preventive maintenance, which in turn determine planning, development and the effects of RCM on system. This, requires the development of PR strategies, enabling knowledge of behaviour of renewal equipment, used in the development of PM programs.

#### **2.2 Renewal strategies**

86 Electrical Generation and Distribution Systems and Power Quality Disturbances

A particular problem consist of identifying the type of wear that characterizes an equipment/system, which can be obtained from reliability tests or from the analysis of the moments of failure in operation, which mathematically modelled, give the wear function,


According to system reliability T fFt <sup>S</sup> = ( ) ( ) , the graph function of the wear inscribed in a

Thus, the literature allow for the study maintenance of OEL, the following assumptions:


We mention that all models specific to these assumptions/behaviours of the OEL are dependent on the reliability function of the system in study and their effects model this

In the analysis presented in section 1, aimed to observe the natural process of degradation of the system performance, without taking into account the capacity of external interventions, to oppose this degradation through the partial or total reconditioning system, in a word's through its renewal. Starting from these considerations, in this section we will try to present the specific models of external interventions, defined as a renewal strategy, performed to restore systems performance and to modelling the reliability function of systems in study,

We define the action of *renewal*, as: *the external intervention performed on a system that restores the system operating status and/or changes the level of its wear, respectively of the system reliability*. From the definition we can distinguish two types of renewal actions that can be performed




square with l side, can indicate the type of equipment wear by its form:




(Catuneanu & Mihalache, 1983).

failure of the system;

**2.1 Renewal process** 

on systems:

**2. RCM – Evolutive process of renewal** 

performances.

function.

Ft 1 Rt () () = − (5)

denoted by Ts (F) .

function *R(t):*

With:

Studies classify and model the renewal strategies according to technical and economic parameters, which determine these strategies, in two distinct categories: non-periodic and periodic, (Catuneanu & Mihalache, 1983), (Andres et al., 2007).


Reliability Centered Maintenance Optimization of Electric Distribution Systems 89

This type of evolutionary strategy of renewal is underlying the maintenance actions

In this section, we try to exemplify an algorithm for the RCM planning, through the optimizing the PM strategies for OEL 20kV, through his components, as a subsystem of the

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

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

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'

a. the selection and processing of data resulting from the network operation until ( <sup>0</sup> T ), i.e.

b. establish the type of the theoretical distribution function which model the best random

d. verifying the correspondence between the adopted theoretical law and the database, with regard to the behavior of the system in operation. The regression method is given

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

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:

corrective actions in installation to bring the facility into operation of OEL;

accordance with corrective or preventive maintenance actions performed over time.

planning by *CBM (Condition Based Maintenance) type*.

**3.1 Reliability assessment stages** 

behavior with random processes.

by the statistical information;


e. reliability indices of OEL at the time <sup>0</sup> T ; f. availability estimation function of OEL.

EDS.

components.

variables;

parameters:

**3.2 Random variables** 

**3. Electric Distribution Systems reliability assessment** 

Estimation modeling involves the following steps, for a OEL:

c. calculation of distribution function parameters;

of random variables given by the behaviour of the system;


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

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 strategies:


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 { *k Tk* Δ = , 1,2, ...} .

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 imposed by the failures occurring in the system.


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 are the foundation of the RCM design.

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 imposed to the preventive maintenance actions.

We mention only some of these criteria which are valid for EDS, these criteria developed in the following sections:


Different studies present additional evolutionary renewal strategies used in the renewal equipment, which are part of the *CRP type (Continuous Replacement Policy)* strategies.

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 techniques.

This type of evolutionary strategy of renewal is underlying the maintenance actions planning by *CBM (Condition Based Maintenance) type*.
