Frequency and Duration

Two different aspects of reliability receive attention in any type of power supply reliability analysis, whether of interruptions or outages. These are the frequency (how often something occurs) and duration (how long it lasts). With respect to interruption, frequency refers to the number of times service is interrupted during a period of analysis – once a decade, two times a year, five times a month, or every afternoon. Duration refers to the length of interruptions - some last only a few cycles, others for hours, even days.

Extent

Frequency and duration are important factors in reliability analysis and design, but there is a third factor equally important to the electric service planner because it is the one over which the planner has considerable control, particularly in the design phase. The extent of an outage’s impact on service – how many customers or what portion of the plant’s loads are interrupted by the outage of a particular unit of equipment – is the key to the outage-interruption relationship. The design of the electric power supply system greatly influences just how much interruption occurs when an equipment outage occurs.

The Distribution Planner has control over extent to which outages lead to customer interruptions. Among other things it is a function of how the distribution system is laid out. In general, a system laid out to minimize extent of outages from any failure will be more expensive than one that is not, but for the planner this means that consideration of configuration and its influence on reliability is just one more alternative to be considered in planning. In many cases a higher-reliability layout may be less expensive than any other way of achieving the particular reliability goal.

Most distribution systems use some form of radial feeder and secondary layout, which means that a single failure anywhere in the electrical path between substation and customer will cause service interruptions to all customers downstream. One way to improve reliability in such systems is to lay out the feeder trunk and branches, and arrange the protection (fusing) so that outages have a low extent (i.e., so that the average feeder segment failure does not interrupt service to very large numbers of customers).

Types of Interruptions

Interruptions are classified by their duration. Table 4.2 lists typical interruption definitions (see IEEE Gold Book for more information), with the times given being averages obtained by the authors in a survey of definitions and usage throughout the power industry. Electric service planners should keep in mind that practice and interpretation of reliability definitions vary greatly from industry to industry, from utility to utility, and from engineer to engineer.

In the authors’ opinion, the definitions shown are all somewhat unsatisfactory. The names imply that they relate to interruption duration, yet they are defined by equipment and operating factors, such as whether an interruption is restored automatically or manually. This, along with differences in exactly how the definitions are interpreted, means that the application of a particular definition, for example “momentary interruption,” varies greatly both in definition and therefore in how it is used.

Table 4.2 Traditional Classification for Power Supply Interruptions

Table 4.3 Duration Limits Used to Define Instantaneous, Momentary, and Temporary Outages at Eight Utilities

Perhaps most importantly, since these distinctions mean nothing to electric consumers, they do little to help an electric service planner improve quality from the consumer’s perspective. A four-minute interruption is a four-minute interruption, whether classified as momentary or temporary or permanent. Beyond the distinctions shown in Table 4.2, interruptions are classified into scheduled interruptions (the utility scheduled the interruption for maintenance purposes) or forced interruptions (the interruption was not expected and not scheduled). Implicit in these definitions, and the most important factor in the authors’ minds, is whether customers are informed reasonably far in advance of the details of any “scheduled interruption.”

Every planner should pay close attention to the definitions used by his company and by utilities and other players in any planning situation of collaboration. What appear to be identical indices can vary because of differences in how interruptions are defined. Many utilities do not include scheduled outages, storms, and other “non-failure-related” interruptions in their reporting procedures.¹ Others leave momentary interruptions out of reported averages, or report them as a special category.

Every power system and DG Planner should bear in mind when working with reliability statistics that utilities that report a certain type of interruption statistic, such as number of momentary operations, vary widely in how they interpret that and other definitions. This is shown by Table 4.3, which lists interruption definitions from eight utilities in North America. They should also remember that utility customers and electric consumers do not really care about definitions and nomenclature. For them, an “outage” or “interruption” is anything that causes their equipment and facilities to stop working.

¹ Most utilities remove “storms” from their statistics, arguing that natural disasters should be removed from statistics that are meant to measure their performance. However this practice has been carried to extremes and abused by some utilities. As Samuel Clemens once said, “There are three kinds of lies: Lies, damned lies and statistics.”

Such differences in definitions, interpretations, and reporting practices can frustrate planners who try to find some real meaning in comparisons between the reliability figures reported by different electric utility companies or by different industrial facilities. Worse, these differences often cause confusion and frustration among customers, regulators, and standards organizations.

Voltage Sags Often Look Like Interruptions

Many electric consumers report a momentary or “very short’ interruption when all that really occurred was a brief “voltage sag.” For example, during a fault (short circuit) on a distribution line, voltage on nearby circuits might drop to less than 70% of normal. Typically the fault would be cleared within less than a second, but this “blink” may be sufficient to halt the operation of computers, robotic equipment, and other digital systems. In that case, this short “voltage sag” is indistinguishable from a short, total cessation of voltage (an interruption). Either way, some critical equipment stops functioning.

The Computer and Business Equipment Manufacturers Association (CBEMA) has a recommended guideline on what voltage sags and surges should be tolerable to office and business equipment, as shown in Figure 4.1. The “CBEMA envelope” establishes a relationship between degree of voltage deviation and time.

The curve’s application is simple: if an event’s voltage deviation and duration characteristics are within the CBEMA envelope, then normal appliances should operate normally and satisfactorily despite it. But many appliances and devices in use are more sensitive than specified by the CBEMA curves and will not meet this criterion at all. Others may fail to meet it under the prevailing electrical conditions (i.e., line voltage, phase imbalance, power factor, and harmonics may be less than perfect).

The manner of usage of an appliance also affects its voltage sag sensitivity. The small circle in Figure 4.1 indicates an event that “crashed” a local net server (computer) at a hosiery plant. The event falls just within the CBEMA curve, and the computer’s manufacturer probably intended for it to withstand that particular deviation-time combination. However, the computer in question had been upgraded with three times the standard memory, a larger hard drive, and optional network cards, doubling its power usage and the load on its power supply. Such situations are common and mean that power systems that deliver voltage control within recommended CBEMA standards may still create problems for computers, robotic assembly tools, and other sensitive equipment.

Figure 4.1 Data from 67 disturbances which occurred over a two-year period at a clothing factory, plotted against the CBEMA curve (solid line) and the actual requirement envelope of a digitally-controlled hosiery loom (dotted line). In many systems, about 40% of all voltage sags and 10% of all voltage surges lie outside of the CBEMA envelope. Small circle refers to event mentioned in text.

Momentary Interruption Index

Momentary Average Interruption Frequency Index (MAIFI) is the average number of momentary (and sometimes instantaneous) interruptions per utility customer during the period of analysis.

MAIFI=number of customer momentary interruptionstotal customers in system(4.5)

Often, momentary interruptions are not included in the SAIFI value reported by an electric utility. In such cases, total interruptions (from the consumer standpoint) are best estimated by the sum: SAIFI + MAIFI.

Load Curtailment Indices

In addition, a number of indices try to relate reliability to the size of customer loads, in order to weight the interruption of a large load more than a small load,

Customer load curtailment = duration of outagé kVA unserved.         (4.6)

Customer Average Load Curtailment Index (CALCI) is the average kVA x duration interrupted per affected customer, per year.

CALCI=sum of all customer load curtailmentsnumber of customers who had at least one interruption(4.7)

Analysis Using Reliability Indices

Reliability indices are used to evaluate historical and recent data to reveal trends and patterns, expose problems, and reveal how and where reliability can be improved. Any of the reliability indices discussed above can be tracked over time to identify trends that indicate developing problems. Figure 4.2 shows frequency of customer interruption (SAIFI) for one suburban operating district of a metropolitan utility on an annual basis over a 35-year period. The operating district was open farmland (no tree-caused trouble) up to 1962. At that time suburban growth of a nearby metropolitan region first spilled into the area, with much construction and with it the typically high interruption rates characteristic of construction areas (trenchers digging into underground lines, early equipment failures of new distribution facilities, etc.).

Over the following ten years, as the area plotted in Figure 4.2 gradually filled in with housing and shopping centers and construction and system additions stabilized, frequency of interruption dropped. Twenty years after the area first began developing, the interruption rate again began to rise because of two factors:

1. Gradually increasing cable failure rates due to age.

2. The effects of trees, planted when the area first developed, reaching a height where they brushed against bare conductors on overhead lines.

Figure 4.2 Three-year moving average of the annual number of interruptions for a region of a utility in the central United States. This area grew from open farmland into a developed metropolitan suburb in the period from 1962 to 1970, during which time interruption rate rose due to the problems common to areas where new construction is present (digging into lines, initial above-average failure rates for newly installed equipment). Twenty years later, interruption rate began to rise again, a combination of the effects of aging cable (direct buried laterals in some residential areas) and trees, planted when the area was new, finally reaching a height where they brushed against overhead conductors. The anomaly centered on 1982 was due to a single, bad storm.

Figure 4.3 Average hours out of service per interruption on a monthly basis for a rural utility in the northern United States varies due to random fluctuations and changes in weather. It appears that duration of interruptions (dotted line) is slowly increasing over time, but further study is necessary before this conclusion can be confirmed.

Another obvious comparison to look at is the average duration of an outage, which is simply the total duration of all interruptions divided by the total number of interruptions that occurred during a period. Average duration of interruption provides an indication of how the utility is managing the entire process from trouble call to service restoration, as shown in Figure 4.3. The increase in outage duration during winter for this utility in the northern United States is clearly visible (winter storms stress repair resources and make travel to repair sites lengthier). A trend upward is discernible. Without additional study, it is not possible to determine whether this is due to an increase in the number of outages, a change in type (perhaps “serious” outages are occurring more often as equipment ages), or a less effective (slower) repair process.

Indirect Reliability Engineering: Contingency and Margin Criteria

The vast majority of electric utilities engineer reliability of service into their system indirectly, through the use of contingency design criteria. The utility maintains reliability goals and still measures and reports SAIDI, SAIFI and similar indices, but these values are not used directly as goals in the design process. Rather, adequate performance is achieved by applying contingency margin criteria which have been interpreted from those SAIDI and SAIFI goals and which are hoped to be appropriate. For example, distribution system engineers will apply equipment loading standards, design and layout guidelines, and switching and fusing rules, which limit the extent of outages and afford extra capacity to pick up outaged load by alternative means.

Contingency margin standards are designed to allow sufficient leeway for any unit of equipment to pick up load interrupted due to the outage of a nearby unit, and to permit reasonably quick (e.g., 15 or 30 minutes to an hour) switching. For example, a utility may establish a policy saying that its substations will always have two transformers of equal size each loaded to no more than 80% of its rating. During the outage of either transformer, the other can pick up both loads with an overload of 60%, an amount it should be able to sustain for two to four hours, time enough, hopefully, for the utility to take steps to handle the problem over a longer period if necessary. Similarly, a utility may ensure that every feeder will have three switchable portions, or zones, each of which can be divided and transferred to other feeders if its primary feed is out of service.

Such a policy establishes a certain type of design (two transformers per substation), loading standard (a transformer cannot exceed 80% of its rating), and feeder layout (three switchable zones) in order to leave sufficient margin for equipment failure and switching. Similar and compatible criteria are established for conductor loading, switch placement, and other design practices, all rules and standards that imply certain reliability results.

Contingency-based Planning Methods Have Weaknesses for Aging Infrastructure Planning

This type of engineering, called contingency-based engineering, is heavily involved with the entire aging infrastructure issue. Contingency-based engineering has sensitivities to high utilization rates for system equipment, and other factors that make it not as dependable as it was traditionally with respect to use as a necessary and sufficient design criteria. Chapter 8 will discuss this in considerably more detail, with examples.

Direct Reliability Engineering

By contrast, reliability engineering achieves the targeted level for availability in the system by actually computing the expected reliability of the power system based on detailed analysis of its equipment and configuration. Areas of equipment that do not meet the criteria are re-engineered until they do. In this approach, frequency and duration of service interruption are computed for each potential alternative design and compared to planning reliability targets to assure compliance with all new designs, additions, and operating changes. Use of reliability values directly as design criteria is not a widely used practice at the time of this writing. Instead, most utilities still use indirect criteria based on contingency margin, switching zone counts, etc., as described above. However, it can be expected that in the future many will choose reliability directly as a criterion for three reasons:

1) It addresses reliability needs directly from the consumer standpoint, rather than indirectly from the utility (equipment criteria standpoint), leading to improved quality assurance.

2) It imposes no restrictions on design other than that the final result meet criteria. This can lead to lower costs.

3) Dependable, proven methods to accommodate reliability-based design are becoming widely available.

Duration Is the Most Popular Criterion

Regardless of whether an electric utility tries to ensure adequate customer service availability by using indirect or direct reliability engineering methods, almost all maintain specific reliability targets as their performance goal. In order of importance or popularity as a design rule, the most widely used are:

SAIDI = the expected total time in a year that the average customer in the area being studied will be without available power

MaxD = the maximum expected total time in a year that any customer in the area being studied will be without available power

SAIFI = the expected number of times in a year an average customer in the system or area being studied will have power availability interrupted

MaxF = the expected maximum number of times in a year that any customer in the area being studied will have power availability interrupted

These reliability targets are applied within any study or design area as general targets that must be satisfied, much like standards of voltage drop, power factor, etc. In the design of any feeder, substation layout, or other addition to the distribution system, the planners use these criteria as design constraints. Any acceptable plan must have an expected average frequency and duration of interruption equal to or better than the corporate goals. Otherwise, the plan would dilute the system’s overall reliability. In addition, the expected maximum frequency and duration for any customer covered in the planning case must be less than MaxF and MaxD.

In general, Distribution Planning studies focus on small portions of the system, at most a few substations at a time. If every such area of the system is planned so that its frequency and duration of interruption fall close to the corporate SAIDI and SAIFI targets, reliability will be as evenly distributed as is practical throughout the system. The utility might still compute CTAIDI and CAIFI in its assessment of actual operating experience, to make certain results match its goals, but planners do not need to apply more than these four criteria.

Duration Is Equivalent to “Probability of Unavailable Power”

Some utilities use a simple “probability of being without power” factor as a design target. This is equivalent, in practice, to planning with duration of interruption as the target. For example, a criterion that calls for the outage probability to be no more than .025%, means that the customer will be without power no more than

8,760 hours x .025% = 2.16 hours/year         (4.8)

Reliability Targets for DG Planning

Generally, distributed generation is not “distributed” over a large system like a distribution system, but is focused on one or a small number of customers. Thus, SAIDI and SAIFI are not really meaningful statistics to use in DG planning. Their equivalents in DG studies are the expected duration and frequency of unavailability. Again, often planners simply compute the expectation of total hours of outage, using this as the figure of merit in planning.

Tiered Reliability Areas

In a few cases, a utility will designate different frequency and duration targets for urban and rural areas. For example, its reliability criteria may specify part of the service territory as “urban” with SAIFI and SAIDI targets of 1.0 interruptions and 50 minutes/year for the system within that region. The rest of the system would be characterized as “rural” and designated with SAIFI and SAIDI rates of 2.2 and 150 minutes respectively. Such a tiered reliability design structure merely recognizes a common and long-standing characteristic of most utility systems – service reliability is lower in sparsely populated areas than in densely populated ones.

This disparity between urban and rural standards does not imply that rural customers are less important, nor is it due to inattention on the part of the utility or to poorer design practices applied to rural areas. The cost of reliability enhancement in rural areas is higher, because of the great distances involved, and the fact that the higher cost must be spread over fewer customers per mile of line. Most rate-design and regulatory processes do not consider it equitable to spread the cost of upgrading service in these rural areas to the same standards achievable in urban areas over the entire rate base (i.e., to those who live in the cities, too). Thus, a higher frequency of interruption and longer interruptions in electric service, are among the expected pleasures of rural life.

Predictive Reliability Analysis Methods

For planning purposes, reliability analysis normally focuses on comparing the expected reliability performance of different candidate designs. Plans are evaluated and compared to determine which is less likely to fall short of required capacity. Reliability is only one aspect of planning evaluation: cost and other factors enter into the final decision too, often with reliability vs. cost being the major design compromise the planner must consider.

Table 4.4 Reliability Evaluation Methods

Reliability Evaluation Methods

Literally hundreds of technical papers, and quite a few books, have been devoted to power system reliability analysis. Table 4.4 provides a summary of the methods along with references on each. But despite this diversity in the technical, numerical means of approach, reliability analysis for planning falls into two functional categories:

1. Historical Assessment Methods analyze historical operating results to determine the cause of past reliability performance problems and to infer the base equipment failure rates and reliability factors. For example, “Based on historical analysis overhead lines are likely to fail once every five years and require an average of five hours to repair.”

2. Predictive Reliability Methods estimate the reliability expected from a candidate design or system configuration. These are used by Planners to determine if a change in design, for example a “fix” to a reliability problem, will give sufficient availability of power.

Application of Probabilities

Almost all reliability prediction methods apply some form of analysis based on probabilities. A few rare methods based on adaptive pattern recognition do not. But the basis for what most methods apply as reliability, the way they apply it, and the detail and representations used in that application, vary greatly among methods. This makes it crucial to pick a method tailored to a situation’s particular needs. For instance, some methods analyze the probability or the expected amount of time that power is unavailable at a particular point in the power network. They estimate the total amount of time that power will be unavailable

(e.g., .03%, equal to 2.6 hours per year). Others predict the mean time between failures and expected time to repair or restore power in each case.

The best of these methods can estimate both the expected average frequency and duration of interruption for any particular candidate system /DG design (e.g., power is expected to fail on average twice a year and take an average of 1.3 hours to restore each time). Still more complicated methods predict the expected probability for both frequency and duration of interruptions. For example, power is expected to fail twice a year, but there is a 5% likelihood it could fail four times in a year - the average duration is expected to be 1.3 hours, but there is a 25% likelihood an interruption could last more than ten hours. But almost without exception, the more comprehensive methods require more data, involve more involved mathematical methods, and are more sensitive to details or implicit assumptions.

These various reliability prediction methods differ in the degree of approximation; the type of system they can analyze; and the type of reliability evaluation they provide; their complexity of analysis; and data requirements. In addition many methods are most appropriate for application to one type of system design (e.g., network, radial) or under certain conditions (only one source of supply but many available power transmission paths). The choice of reliability assessment method depends on all these factors, as well as the degree of detail sought by the planner.

In most places throughout this book, the authors will use a simple reliability assessment method that computes only the expected time power is unavailable, not the frequency and duration. This method is general enough for our examples and much simpler. In many cases, merely adding together the probabilities of rare occurrences, rather than considering that they could overlap further approximates reliability analysis.

Electricity Pricing Has Traditionally Been Based Only On Quantity

Traditionally, the price of power in the electric utility industry was based solely upon the quantity used. A consumer would pay more if he or she used more power and less if their use was less. Except in rare and specially treated cases, an electric utility would offer a “one size fits all” level of quality. Customers got what was available, whether or not they needed and would have paid for higher quality, or whether they would have preferred a discount even if it meant somewhat lower quality.

The Market Comb

Numerous surveys and customer focus meetings conducted by utilities, consultants, and research firms (including the authors’ firm) indicate that electric consumers differ widely in their need for, and their willingness to pay for, reliability of service. Consumers also differ in exactly what “reliability,” and in a broader sense, “quality,” means to them, although availability of service, quick and knowledgeable response on the part of their supplier, and power of a usable nature are always key factors in their evaluation.

Figure 4.5 The electric marketplace can be likened to a comb: composed of many small niches, each made up of customers who have a different need for and cost sensitivity to reliability of service. Even those who put a high value on reliability may differ greatly in how they define “good reliability,” one reason why there are no broad market segments, only dozens of somewhat similar but different niches.

As a result, the electric power demand marketplace can be likened to a comb as shown in Figure 4.5 with a series of small niches, that vary from the few customers who need very high levels of reliability, to those who do not need reliability, only power, and are motivated purely by lowest cost.

Offering Variable Levels of Reliability

Traditionally, electric utilities have not offered reliability as a price-able commodity. They selected equipment, and designed and engineered their systems based on engineering standards that were aimed at maintaining high levels of power system equipment reliability. These standards and methods, and the logic behind them, were actually aimed at minimizing utility equipment outages. The prevailing dogma maintained that this led to sufficiently high levels of reliable service for all customers and that reliable service was good. This cost of the reliability level mandated by the engineering standards was carried into the utility rate base. A utility’s customers basically had no option but to purchase this level of reliability (Figure 4.6). Only large industrial customers, who could negotiate special arrangements, had any ability to make changes bypassing this “one-size-fits-all” approach to reliability that utilities provided.

The traditional way of engineering the system and pricing power has two incompatibilities with a competitive electric power marketplace. First, its price is cost-based; a central tenet of regulated operation, but contrary to the market-driven paradigm of deregulated competition.

Figure 4.6 Generally, the cost of providing reliability in a power system is a non-linear function of reliability level: providing higher levels carries a premium cost, as shown by the line above. While reliability varies as a function of location, due to inevitable differences in configuration and equipment throughout the system, the concept utilities used was to design to a single level of reliability for all their customers.

Figure 4.7 A competitive market in power will recognize the demand for various levels of reliability and providers will have to broaden the offerings they provide (left) until the range of options available to the customer covers the entire spectrum of capabilities, as shown at the right. Actual options offered will be even more complicated because they will vary in the type of reliability (e.g., perhaps frequency or duration is more important to a specific customer; seven days a week or only normal business hours).

Secondly, any “one-size-fits-all” reliability price structure will quickly evaporate in the face of competitive suppliers. Someone among the various suppliers will realize there is a profit to be made and a competitive advantage to be gained by providing high-reliability service to consumers willing to pay for it. While others will realize that there are a substantial number of customers who will buy low reliability power, as long as it has a suitably low price. The concept that will undoubtedly emerge (in fact, is already evolving at the time this book is being written) in a deregulated market will be a range of reliability and cost options. The electric utility market will broaden its offerings, as shown in Figure 4.7.

For example, distributed generation (DG) interacts with the opportunities that the need for differentiated reliability creates in a deregulated marketplace in two ways. First, this new marketplace will create an opportunity for DG, which can be tailored to variable reliability needs by virtue of various design tricks (such as installing more/redundant units). Secondly, DG is a “threat” that may force utilities to compete on the basis of reliability, because it offers an alternative, which can easily be engineered (tailored), to different reliability-cost combinations. Utilities may have no choice but to compete in pricing reliability.