Parameters for Reliability Analysis

The application of the implemented Monte Carlo method requires the generation of random variables related to faults and switching and reconfiguration times. A fault is fully defined by specifying the faulted component (line, voltage regulator, or capacitor bank), the occurrence time, the duration, and the fault type.

Failed Elements

The system elements to be considered for failure are: distribution lines, voltage regulators, capacitor banks, distribution transformers, PV generator interconnection transformers, and PV plant modules.

Frequency of failures

The system is divided into zones, with different statistics for line sections. In all cases, it is assumed that the number of failures for each zone follows a normal probability density distribution (characterized by a mean and a standard deviation) while the location is assume to be uniformly distributed within the zone. These assumptions may not be fully correct; in fact, many works assume a constant failure rate, which is similar to assuming that failure rates follow a Poisson distribution. For other elements the failure rate will be assumed constant and the number of yearly faults will follow a Poisson distribution [5.4]. The failure of a distribution transformer or a voltage regulator is always sustained and interrupts the service to all customers located downstream, while the failure of a capacitor bank will not interrupt the service of any costumer, although it can affect some node voltages.

Duration

Line failures are classified as momentary and sustained, with a percentage for each type. Although a distinction is made between momentary and sustained, no duration is assigned to any type. By default sustained interruptions are assumed to be caused by permanent fault, while momentary interruptions are caused by temporary faults shorter than 5 minutes and that are isolated by the affected protective devices in less than 5 minutes. Failures of PV plant modules, transformers, voltage regulators and capacitor banks are assumed by default sustained. The design of distribution transformer protection is a relatively complex task since several technical choices may provide a correct protection [5.20]. In this work an internal distribution transformer failure forces the operation of an overcurrent protection located at the primary MV side of the transformer. In the case of voltage regulators, this operation will separate the component

Chapter 5: Reliability Assessment of Distribution Systems

123 from the upstream components; continue with a confirmation of the regulator failure and by its separation from the downstream components. Capacitor banks are protected by fuses. As for PV generation plants, the interconnection protection will detect abnormal voltage values caused by a fault in the proximities of the plant.

Type of fault

Faults causing failures may be one-phase (type 1), two-phase (type 2), and three-phase (type 3) [5.2]. This distinction is only used for overhead lines, because in case of fuse blowing the number of phases affected will depend on the type of fault. Failures of distribution transformers, voltage regulators and capacitor banks are three-phase.

Time of occurrence

Monthly and daily statistics will be used to determine the month, day and hour when a fault will occur on distribution lines. Time of occurrence for voltage regulators, capacitor banks, distribution transformers, PV generator interconnection transformers, and PV plant modules will be generated using a uniform distribution. No coincident faults will be considered.

Switching Times

The sequence of events, after a protective device has isolated the fault, may include fault location, isolation of the failed component, and some switching operations to reconfigure the system (e.g., load transfer between feeders). Depending on the system design, switching may be used for:

• Isolating only the faulted section after the protective device has operated. • System reconfiguration by using transfer switches.

• Restoring the original system configuration after the failed equipment has been repaired.

The times to be used for these operations may correspond to manually or remotely controlled switches. Switching times are defined as a constant average for every element and follow an exponential distribution [5.4]; time values are varied to reflect automation improvements, and will also depend on the failed component location. In this work, the switching time required for isolating the failed section or component includes also the time required for locating the fault.

Repair Times

Repair times are randomly generated using an exponential distribution and depend on the fault characteristics [5.4]; for line sections they depend on the system zone. The repair time values include several operations (protective device lockout, fault location, isolation of the faulted line section, reconfiguration of the system to restore service as quick as possible to as many customers as possible, equipment repair, and switching required to recover the original system configuration). Repair times are also used to fix

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the moment at which the normal operation of the whole system is restored, taking as a reference the moment at which the failure occurs.

Replacement Times

They must be considered when the fault causes a fuse operation. During calculations for sustained interruptions, this time is included in the time required for repairing the failed component. Fuse replacement depends on the number of faulted phases; a base time has been established and extra time is added for every phase to be replaced.

Load Transfer Times

The load transfer will depend on the time needed to disconnect the failed element and the time required to connect the back-up feeder. The latter will also be randomly generated and follow an exponential distribution. Two cases have been considered:

• Back-up feeder connection time is lower than time needed to disconnect the failed element and close the operated device: in this case the procedure will perform both actions simultaneously, using the greater time as the reference. • Back-up feeder connection time is greater than time needed to disconnect the

failed element and close the operated device: for this condition the procedure will perform both actions independently at their specified times.

PV Plant Availability Model

The reliability model of a PV plant is rather complex; see, for instance, [5.8], [5.21]- [5.23]. Implementing and applying an accurate model is out of the scope of this work; instead a simplified reliability model is used. All PV generators consist of one or more 100 kW modules characterized by the same failure rate and repair time. Therefore, the parameters of each generator to be defined for reliability assessment are the rated power (i.e. the number of 100 kW modules), the failure rate and the mean repair time. A PV plant can reduce partially or totally the power it injects into the distribution when either the interconnection transformer or a PV module fails. The reliability parameters for the interconnection transformer are those used for any other distribution transformer. The number of PV module failures in a year will be randomly generated using the failure rate and following a Poisson distribution; it is assumed that in average one module will fail in every event. The average repair time will be calculated multiplying the module’s mean repair time and the number of failed modules. The actual repair time will be randomly calculated using an exponential distribution.