Reliability index


Reliability index is an attempt to quantitatively assess the reliability of a system using a single numerical value. The set of reliability indices varies depending on the field of engineering, multiple different indices may be used to characterize a single system. In the simple case of an object that cannot be used or repaired once it fails, a useful index is the mean time to failure representing an expectation of the object's service lifetime. Another cross-disciplinary index is forced outage rate, a probability that a particular type of a device is out of order. Reliability indices are extensively used in the modern electricity regulation to assess the grid reliability.

Power distribution networks

For electric power distribution networks there exists a "bewildering range of reliability indices" that quantify either the duration or the frequency of the power interruptions, some trying to combine both in a single number, a "nearly impossible task". All indices are computed over a defined period, usually a year. Popular indices are typically customer-oriented, some come in pairs, where the "System" in the name indicates an average across all customers and "Customer" indicates an average across only the affected customers.

Interruption-based indices

The interruptions of the power supply affecting the customers can be either momentary or "sustained". Most indices in this group count the sustained interruptions.
Load-based indices are similar to their customer-based counterparts, but are calculated based on load. In a system with a lot of small customers, load-based indices will be equal to their customer-based counterparts, but if the system has few major customers, they might diverge.
  • Average system interruption frequency index is similar to SAIFI.
  • Average system interruption duration index is similar to SAIDI.

    History

Electric utilities came into existence in the late 19th century and since their inception had to respond to problems in their distribution systems. Primitive means were used at first: the utility operator would get phone calls from the customers that lost power, put pins into a wall map at their locations and would try to guess the fault location based on the clustering of the pins. The accounting for the outages was purely internal, and for years there was no attempt to standardize it. In 1947, a joint study by the Edison Electric Institute and IEEE included a section on fault rates for the overhead distribution lines, results were summarized by Westinghouse Electric in 1959 in the detailed Electric Utility Engineering Reference Book: Distribution Systems.
In the US, the interest in reliability assessments of generation, transmission, substations, and distribution picked up after the Northeast blackout of 1965. A work by Capra et al. in 1969 suggested designing systems to standardized levels of reliability and suggested a metric similar to the modern SAIFI. SAIFI, SAIDI, CAIDI, ASIFI, and AIDI came to widespread use in the 1970s and were originally computed based on the data from the paper outage tickets, the computerized outage management systems were used primarily to replace the "pushpin" method of tracking outages. IEEE started an effort for standardization of the indices through its Power Engineering Society. The working group, operating under different names, came up with reports that defined most of the modern indices in use. Notably, SAIDI, SAIFI, CAIDI, CAIFI, ASAI, and ALII were defined in a Guide For Reliability Measurement and Data Collection. In 1981 the electrical utilities had funded an effort to develop a computer program to predict the reliability indices at Electric Power Research Institute. In mid-1980, the electric utilities underwent workforce reductions, state regulatory bodies became concerned that the reliability can suffer as a result and started to request annual reliability reports. With personal computers becoming ubiquitous in 1990s, the OMS became cheaper and almost all utilities installed them. By 1998 64% of the utility companies were required by the state regulators to report the reliability.

Resource adequacy

For the electricity generation systems the indices typically reflect the balance between the system's ability to generate the electricity and its consumption and are sometimes referred to as adequacy indices; as NERC distinguishes adequacy and security aspects of reliability. It is assumed that if the cases of demand exceeding the generation capacity are sufficiently rare and short, the distribution network will be able to avoid a power outage by either obtaining energy via an external interconnection or by load shedding. It is further assumed that the distribution system is ideal and capable of distributing the load in any generation configuration.
Ibanez and Milligan postulate that the reliability metrics for generation in practice are linearly related. In particular, the capacity credit values calculated based on any of the factors were found to be "rather close".

Probabilistic vs. deterministic

The indices for the resource availability are broadly classified into deterministic and probabilistic groups:
  • deterministic indices are easier to use, historically popular, and are used when there is little uncertainty or in situations when the statistical calculations are infeasible;
  • probabilistic metrics assume that the calculation inputs have uncertainty and estimate resource adequacy by statistically combining their distributions. These indices take accommodate multiple possible situations and thus can be more accurate. EPRI further subdivides probabilistic indices into:
  • * average risk metrics that provide an average value of the index based on statistical distribution. This is the class of metrics that are typically used, and are further subdivided into frequency and duration indices that characterize the occurrence of adverse events and magnitude metrics that characterize the effects of the events. Both subtypes can be combined;
  • * full distribution metric produce a range of values in the distribution instead of a single average value. This is a relatively new class of metrics.

    Probabilistic metrics

Indices based on statistics include:
  • loss of load probability reflects the probability of the demand exceeding the capacity in a given interval of time before any emergency measures are taken. It is defined as a percentage of time during which the load on the system exceeds its capacity;
  • loss of load expectation is the total duration of the expected loss of load events in days, LOLH is its equivalent in hours;
  • expected unserved energy is an amount of the additional energy that would be required to fully satisfy the demand within some period. Also known as "expected energy not served", and as loss of energy expectation, LOEE. Normalized value "normalized expected unserved energy" NEUE allows comparison of across different system sizes. In the US, an acceptable value of this dimensionless index is not standardized, yet the US Department of Energy selected the threshold of 0.002%.
  • loss of load events is a number of situations in which the demand exceeded the capacity;
  • expected power not supplied ;
  • loss of energy probability ;
  • energy index of reliability ;
  • interruption duration index ;
  • energy curtailed.

    Deterministic metrics

The deterministic indices include:
  • the installed reserve margin was traditionally used by the utilities, with values in the US reaching 20%-25% until the economic pressures of 1970s. EPRI distinguishes between:
  • * planning reserve margin that uses the ratio calculated at the time of pealk demand and
  • * energy reserve margin that is similar to the PRM and is calculated for every hour, not just the peak one.
  • the largest unit index is based on the idea that the spare capacity needs to be related to the capacity of the largest generator in the system, that can be taken out by a single fault;
  • for the systems with significant role of the hydropower, the margin shall also be related to a power shortages in the "dry year" (a predefined condition of low water supply, usually a year or sequence of years.