G.2 Detector η of the three leading jets for data and MC after pre-selection, electron
4.1 Summary of the MET35 trigger logic used in collecting the data
Distribution reliability analysis is based on two major methodologies, namely the analytical and simulation methods. The analytical method rep-resents the power distribution system with a mathematical equation derived for solving or evaluating the reliability indices. It is transparent among results, model, and data simulation methods that simulate the random behavior of the system, addressing the actual failure repair and restoration of the system under disturbance. The simulation method provides records in the form of a distribution function indicating that the reliability is expected to vary. It can also handle complexity in data, procedures, and processes.
ENS= a
∑
i R∈ P Ui iAENS ENS
=
∑
i R∈ NiACCI ENS
=
∑
i=R1 MiApago PDF Enhancer
Distribution System Reliability and Maintenance 123
The proposed analytical methods to be discussed are used to evaluate transmission reliability as well as distribution system reliability. We are concerned more with determining the reliability based on systemwide meas-ures of performance than on reliability based on specific supply loads.
In general, the variants of theoretical methods are equivalent. However, the selection of a particular method may be based on the practical applica-tion. This chapter provides an overview of the analytical methods in use. To start with, we consider distribution system component models to be normal operating states, faulted, opened/closed, or undergoing repair.
4.5.1 Analytical Methods
A distribution system can be modeled as a set of interconnected components.
Various reliability indices can be defined to capture the effects of failure of each component on the system. The analytical methods used for reliability assessment provide the average performance of the system. The commonly used tools to evaluate distribution system reliability include state space diagrams, failure modes and effects analysis (FMEA), state enumeration, event trees, minimal cut sets, and fault trees. These are discussed in the following sections.
4.5.2 State Space Diagrams
A state space diagram represents a system by defining all possible states of interest that the system can adopt. The method uses transition between failed states of components to repaired normal states or partial states of restoration during an abnormal or adverse weather condition. Transitions between states are modeled as Markov processes. The state space diagram is referred to as the Markov diagram.
Two state transitions resulting from the failure and repair of typical power system components (buses, transformers, and circuit breakers) can be rep-resented as follows:
λ = failure rate, μ = repair rate
For the case when power is available to a customer at time t = 0, λ and μ do not vary with time, and the probability that power is available at time t is given as follows:
(4.12)
As t→∞, the steady state of available power is Pr
( )
ob P t
e t
( ) ( )
=μ λ+μ +λλ μ− ++λ μApago PDF Enhancer
124 Electric Power Distribution, Automation, Protection, and Control
(4.13)
, unavailability for μ > λ
i.e., when the repair rate μ is greater than the failure rate λ. From the foregoing, the failure rate λ is based on the interruption frequency experi-enced by the customer.
4.5.2.1 Case A, Series Components For the series-connected components,
Ti for N = 3 (4.14)
where ΣλiTi is the long-term unavailability, and Ti is the interruption or repair time.
4.5.2.2 Case B, Parallel Systems
In parallel systems, the frequency of a failure in a parallel network, where one interruption of power can cause loss failure in a second bus but not the second line, is deduced. The frequency of such a failure is computed as
l = λ2(λ1T1) + λ1(λ2T2)
= λ1λ2(T1 + T2) (4.15) This is defined as the product of the failure rate of both components with summation of the repair times for both. Whereas the unavailability of both parallel paths when they both fail is defined as unavailability of power as determined by the product of the failure rate of components and the product of the times to repair both paths (given as λ1λ2T1T2), for distribution systems arranged in a parallel structure rather than services connected in a radial network.
4.5.2.3 Case C, Series and Parallel System
Most components in distribution can be connected in series or in parallel.
Depending on the type of connection, reliability analysis will be different.
For example, for a series network, a loss of one component such as a trans-former or a circuit breaker can cause total loss of the feeder connecting them,
μ μ λ
λ μ λ
+ +
⎧
⎨⎪⎪
⎩
, ,
availability unavailability
⎪⎪⎪
≅ λμ
λ= λ
∑
i 1=3 iApago PDF Enhancer
whereas in a parallel system, the interruption of one of the components may not cause a total failure of the system, as shown in Figure 4.1
4.6 Failure Modes and Effects Analysis (FMEA) Method This method is one of the simplest ways of estimating reliability. It is based on an inductive (what if?) analysis that can be used to identify the failure mode of components in a distribution system affected by changes in power or loss of power to a specified load caused by the states of breakers, circuit breakers, loads, and subsequent control actions to restore the system.
FMEA identifies single-component failure states that occur independently and are repaired before another occurs. It can be used as a repetitive survey of failure behavior or as a precursor to other analysis techniques, such as cut-set and fault-tree analyses. The failure states are recorded as the number of customers affected and duration of the event. To facilitate minimum cut set (first-order cut set, etc.) or a fault-tree approach for distribution reliability, a probability approach is used to weigh categories or put limits on them to be selected prior to determination of reliability. The principal advantage of FMEA is that it provides a detailed description of the failure behavior of the distribution system while evaluating the consequences of all failure modes of all components. The drawback of FMEA is that it is repetitive, and it is difficult to examine multiple failures in an efficient manner.