A strategy for power transformer spares
With long lead times on power transformers, reliability impacts and cost implications make transformer spares a critical decision for utilities that own and maintain this equipment. For a given fleet of power transformers, there are a lot of elements that come into play when it comes to selecting the right quantity of spares. While most power transformer populations are a mixed bag (have a wide variety of loadings, criticality, ages, and asset condition), aging infrastructure and system reliability remains a critical concern for many utilities. The primary concern is multiple catastrophic failures combined with high replacement costs and long lead times for these critical components. So what is the right number, and how do we get to it?
Identifying and forecasting risk for utilities
Many utilities collect information and conduct diagnostics on an individual component basis. The key to a holistic sparing strategy is combining this information to look at the population as a whole. In order to identify the risk under various scenarios, we need to first identify the current state and possible outcomes:
- > Develop an adjusted age distribution for the population — This identifies the current state of the population as it is today. Adjusted age is the effective age of each component, taking the equipment condition into account.
- > Develop a failure probability curve associated with the population — This could be based on historical data if available; otherwise, assumptions regarding a typical expected life can be used to develop a practical proxy until failure data is available.
- > Identify risk levels associated with each failure scenario — These scenarios should define each type of failure and what the impact is in each scenario. There are operational impacts (e.g., reliability, loss of load), financial impacts (e.g., the cost of replacing the transformer with and without a spare), and safety impacts. For many utilities there may also be additional risks to take into account such as the relationship with regulators or companies served.
- > Define the time horizon(s) of interest — This time period needs to be clearly defined, since the benefits of spares may be realized over several years.
Power transformer population: a practical example
Figure 1 (below) is a hypothetical population of power transformers. This helps define the current state of the system. Also, assumptions can be made about what happens should a failure occur. In this example, it is assumed that if a failure happens, the unit is replaced with a new unit.
Adjusted age distribution (Figure 1)
For this example, we assume an average expected life of about 55 years. Using a Weibull distribution to represent the probability density function, we derive the probability of failure for a given asset at a specific age, as shown below in Figure 2 (e.g., if a unit has an effective age of 37 years, the probability that the unit will fail within the next year is 2 percent).
Probability density function (Figure 2)
Probability hazard function (Figure 3)
Using the information provided in Figures 2 and 3 (above), we can estimate the number of failures for the given year by taking the product of each probability of a failure times the quantity of components in each effective age category. With this, and an assumption about how assets are replaced, we can forecast this population through time as shown below in Figure 4 (e.g., on average we expect to require at least 3 spares for the 5 years).
Forecasted failure rate (Figure 4)
While such a forecast starts to make the average quantities clear, it does not identify the risk and probability of each quantity of spares. To better understand how these failures can be distributed in a given year we use a Monte Carlo analysis as shown below in Figure 5. This provides a probability of needing a given number of spares. For example, in 2012 the probability of 2 spares being adequate is the sum of 0 through 2 failures (56 percent), while the probability of that quantity being inadequate is easy to calculate (100 – 56 or 44 percent). Similarly, scenarios can be calculated for each spare quantity, providing probability of occurrence. This, in combination with the impacts identified in the event of a failure, provides a holistic approach to calculate risk under various spare quantities.
Range of forecasted failures (Figure 5)
Determining an acceptable risk level will vary by utility; however, the above approach establishes a framework to understand and identify that risk.
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This article is featured for DNV GL’s June 2012 issue of TECH Notes, a monthly publication that provides business and technical insights for secure transmission and distribution systems. Sign up to receive advance notification.