Aging Actually Creates An Opportunity for More Reliability Improvement

As a system becomes inherently less reliable due to aging, the effectiveness of many reliability improvement methods increases. In a system where SAIFI is expected to be .66, certain automated switching and fault location programs may not provide a benefit/cost ratio of 1.00 or more. There is not enough opportunity, in such a reliable system, for them to justify their expense. But if the SAIFI is 1.33, they are about twice as cost effective. Therefore, as a system ages and failure rates increase, the cost effectiveness of various reliability improvement methods gradually rises. And as more is spent to renew equipment, the cost effectiveness of reliability improvement methods drops.

What a utility wants is the lowest cost way to deliver satisfactory service reliability to its customers. To the customer, it does not matter if that reliability comes from an a network composed of worn out equipment that is controlled smartly by an advanced monitoring and control system, or from a network that is inherently reliable because equipment condition is maintained at a high level. What is important is that: a) service is reliable, and b) cost is as low as possible. The industrial power owner seeks the same cost “sweet spot.”

Not surprisingly, in every case, the lowest cost, lowest risk plan is always a combination of both approaches, something that basically picks the low hanging fruit from each method in order to provide just enough reliability to satisfy needs. Thus, reliability engineering – planning, specification, and implementation of measures to improve and control customer reliability – is an important aspect of planning for aging infrastructures. The other part is the planning of the best inspection, tracking, condition improvement, life extension, proactive replacement plan. The two interact, creating synergy if used together well and problems if not, so they must be planned in conjunction with one another.

Reliability Engineering of Power Delivery

This chapter summarizes power delivery reliability concepts and methods.

The goal of reliability-based planning, engineering, and operations is to cost effectively maximize reliability of service as seen by the customer, not necessarily to improve reliability of equipment or service time on the system. Customer-level results are what count.

While equipment availability and similar measures are important, the planning and engineering process should focus on customer-level measures of service reliability.

Why is Reliability More Important Today Than It Was Traditionally?

Distribution system reliability is driven by several factors including:

(1) The increasing sensitivity of customer loads to poor reliability, driven both by the increasing use of digital equipment, and changing lifestyles.

(2) The importance of distribution systems to customer reliability as the final link to the customer. They, more than anything else, shape service quality.

(3) The large costs associated with distribution systems. Distribution is gradually becoming an increasing share of overall power system cost.

(4) Regulatory implementation of performance based rates, and large-customer contracts that specify rebates for poor reliability, all give the utility a financial interest in improving service quality.

In the past, distribution system reliability was a by-product of standard design practices and reactive solutions to historical problems. In the future, distribution system reliability will be a competitive advantage for a distribution utility, in its competition with other forms of power and energy (DG, alternate fuels, and conservation). Reliability must be planned for, designed for, optimized, and treated with analytical rigor.

Optimal Reliability isn’t Necessarily Maximum Reliability

Planners must keep in mind that while reliability is important to all customers, so is cost, and that only a portion of the customer base is willing to pay a premium price for premium levels of reliability. The real challenge for a distribution utility is, within tight cost constraints, to:

• Provide a good basic level of reliability.

• Provide roughly equal levels of reliability throughout its system, with no areas falling far below the norm.

• Provide the ability to implement means to improve reliability at designated localities or individual customer sites where greater service quality is needed and justified.

In Section 14.2, this chapter will introduce an important concept: the engineering of reliability in a distribution system in the same way that other performance aspects such as voltage profile, loading, and power factor is engineered. Section

14.3 will summarize the analytical methods that can be used as the basis for such engineering and discuss their application. Section 14.4 gives an example of reliability-based engineering as applied to a medium-sized power system, designed for overall and site-specific targeted reliability performance. Financial risk, due to performance-based contracts and rates, is a big concern to a 21st century utility. Section 14.5 looks at the analytical methods needed to assess and optimize this, and shows an example analysis. Section 14.6 concludes with a summary of key points.

Results are dependable

The results from this process as dependable from an engineering standpoint as those obtained from a well-applied load flow application. Generally, the reliability assessment has a better base of customer data than a load flow. It uses customer count data at the “load end” of the model (information that can be accurately determined) not kW load data (which are most typically estimates based on kWh sales).

Table 14.1 Reliability of Typical Types of Distribution System Components

Using a Reliability Load Flow

Planning engineers use a reliability-assessment program in much the same manner that they use a load flow to design the feeder system. They begin with performance targets - voltages and loadings with certain limits- for load flow planning, reliability within a certain range for reliability engineering. They then enter into the program a candidate system model, a data representation of the system as it is, or as they propose to build it.

The computer analysis then determines the expected performance of the system as represented to it. In a load flow, computing the expected voltages, flows, and power delivery at every point in the system does this. In a reliability assessment, computing the expected frequency and duration of outages at every point in the system does this.

The results are displayed for the user, usually graphically in a way that quickly communicates problems (results that are unacceptably out-of-range).

The planning engineers review the results. If they are less than desirable, they make changes to the system model, using the results as a guide to where improvements or changes should be made. The model is re-run in this manner until a satisfactory result is obtained.

Root Cause and Sensitivity Analysis

Root-cause analysis determines the contribution of each component to poor reliability. For example, if reliability is measured using SAIDI, a root-cause analysis will identify if pole failures, breaker failures, and so forth contribute what impact to the original cause of the SAIDI.

The analysis is considerably more important when part of an aging infrastructure program as well as a reliability augmentation plan. In a way it unites the two endeavors and it definitely provides a starting point to coordinate them well. Both the root-cause analysis, and the analysis of equipment failure trends (whether and how much they are increasing, etc.) are dealing with much the same data. An important point is whether aging of various types of equipment is a root cause. When it is, trends found that show a gradually increasing failure rates should be applied predictively based on the root case analysis: their contribution to reliability issues will worsen in company with those trends, etc.

In addition to knowing the contribution each component makes to the overall poor reliability of the system, it is desirable to know the impact that improving component reliability or design would have on the system’s reliability: again, this links reliability engineering and aging equipment analysis. Will a change make a difference?

For example, what would be the impact of reducing overhead line failures, reducing transformer failures, or reducing cable repair-time? A sensitivity analysis can be used to answer such questions: this simple approach adjusts a component parameter (such as its failure rate) by a small amount and records the corresponding change in system reliability.

Engineering the Design Improvements

In determining how to improve system performance, planning engineers focus on equipment or areas of the system that score high in terms of both root cause (they create a lot of the problems) and sensitivity (changes will make a difference on reliability). After a system has been modeled, calibrated, and examined with root cause and sensitivity analyses, potential design improvements can be identified and modeled. The focus should be on critical components – those with both high root-cause scores and high sensitivity scores.

Methodologies for Distribution System Reliability Analysis

Reliability assessment models work from an arc-node type database, very similar to that used in a distribution load flow program. Unlike a load flow, which uses data on each element to compute the interconnected flow of power through the system to the customer locations, the reliability assessment program uses data on each element to compute the interconnected reliability of service to the customer locations.

There are four common methodologies used for distribution reliability assessment: network modeling, Markov modeling, analytical simulation, and Monte Carlo simulation. These differ in their bases – in what they use as the foundation for their analysis of reliability. Each uses a different approach to determining the reliability of the system. A brief description of each is provided below.

Modeling Each Contingency

A contingency occurring on a distribution system is followed by a complicated sequence of events. Each contingency may impact many different customers in many different ways. In general, the same fault will result in momentary interruptions for some customers and varying lengths of sustained interruptions for other customers, depending on how the system is switched and how long the fault takes to repair. The key to an analytical simulation is to accurately model the sequence of events after a contingency to capture the different consequences for different customers. A generalized sequence of events as modeled by analytical simulation is:

1. Contingency: A fault occurs on the system.

2. Reclosing: A reclosing device opens in an attempt to allow the fault to clear. If the fault clears, the reclosing device closes and the system is restored to normal.

3. Automatic Sectionalizing: Automatic sectionalizers that see fault current attempt to isolate the fault by opening when the system is de-energized by a reclosing device.

4. Lockout: If the fault persists, time over current protection clears the fault. Lockout could be the same device that performed the reclosing function, or could be a different device that is closer to the fault.

5. Automated Switching: Automated switches are used to quickly isolate the fault and restore power to as many customers as possible. This includes both upstream restoration and downstream restoration. In upstream restoration, a sectionalizing point upstream from the fault is opened. This allows the protection device to reset and for restoration of all customers upstream of the sectionalizing point. In downstream restoration, other sections that remain de-energized are isolated from the fault by opening switches. Customers downstream from these points are restored through alternate paths by closing normally-open tie switches.

6. Manual Switching: Manual switching restores power to customers that could not be restored by automated switching (certain customers will not be able to be restored by either automated or manual switching). As in automated switching, manual switching has both an upstream restoration component and a downstream restoration component.

7. Repair: The fault is repaired and the system is returned to its pre-fault state.

The seven steps outlined above generate a set of system states for each contingency. Switches and protection devices being open or closed characterize these states. For each state occurring with frequency l and duration q, the accrued outage frequency of all de-energized components are incremented by l (if the component was energized in the preceding state) and the accrued outage duration of all de-energized components are incremented by l x q.

The simulation becomes more complicated if operational failures are considered. Operational failures occur when a device is supposed to operate, but fails to do so. The probability of such an event is termed probability of operational failure, POF. Operational failures cause the simulation sequence to split. One path assumes that the device fails to operate and has a weight of POF, the other path assumes that the device operates and has a weight of 1 – POF. This path splitting is illustrated in Figure 14.2, which shows the steps required when considering a fuse that is supposed to clear a fault.

The result of simulation path splitting is an enumerative consideration of all possible system responses to each contingency (in the context of operational failures). Enumerative consideration is important since some states may be rare, but have a major impact on the system when they do occur. During restoration, path splitting associated with the enumerative consideration of possible outcomes is important when intended switching fails and customers that would otherwise have been restored are not.

Figure 14.2 Simulation path splitting due to operational failures.

Incremental Studies of Improvement

An analytical simulation will produce identical results if an analysis is performed multiple times. In addition, small changes in input data will cause small changes in results (as opposed to some other methods). This allows the impact of small reliability improvements to be quantified for individual customers and reliability indices by running a series of studies of incremental changes in the system design. For example, the planning engineer can move the location of a sectionalizer or recloser up and down a feeder an eighth of a mile at a time, seeing the results in total reliability, and the distribution of reliability results up and down the feeder, with each change. This capability also allows input parameters to be perturbed and result sensitivities to be computed. However, analytical simulation does not allow the uncertainty of reliability to be quantified. For example, while expected that SAIDI might be 2.0 hours per year, there is some probability that next year will just be an “unlucky year.” To compute how often such unlucky years could occur, and how extreme SAIDI or other factors would be in those years, requires application of Monte Carlo techniques.

Example Application

An analytical simulation method was applied to the test system shown in Figure 14.1, which is based on an actual U.S. utility distribution system. The system model contains 3 voltage levels, 9 substations, more than 480 miles of feeder, and approximately 8,000 system components. The model was first calibrated to historical outage data, then used to analyze candidate designs as described above. In addition the authors used an optimization module that maximized reliability results versus cost. The diagram shown in Figure 14.1 was originally color coded (not shown here) based on computed outage hours, and shows the system plan that resulted from a combination of engineering study and use of optimization. Individual component reliability results can be easily used to generate a host of reliability indices. For this system, common indices include:

MAIFI (Momentary Average Interruption Frequency Index) = 2.03 /yr

SAIFI (System Average Interruption Frequency Index) = 1.66 /yr

SAIDI (System Average Interruption Duration Index) = 2.81 hr/yr

Targets for the area were 2.00, 1.75, and 2.9 hours (175 minutes) respectively, thus this system essentially meets its target reliability criteria.

Differentiated Reliability Design

Realistically, the expected reliability of service over an entire distribution system cannot be the same at all points. Distribution systems use transshipment of power through serial sets of equipment. Thus there are areas of the system that are more “downstream,” and being downstream of more devices and miles of line, have somewhat higher exposure to outage. Figure 14.1’s example demonstrates this. Although SAIDI is 2.81, expected performance for the best 5% of customers is

1.0 hours and 4.02 for the worst 5%.

However, planning engineers can engineer a system to keep the range of variation in what customers in one area receive versus customers in another, with within a reasonable range. This involves the selected use of protective equipment such as fuses and breakers, sectionalizers, reclosers, and contingency switching plans, and in some cases, distribution resources such as on-site generation and energy storage, and demand-side management. Artful use of these measures, combined with application of sound distribution layout and design principles, should result in a system that provides roughly equitable service quality to all customers.

However, there are situations where a utility may wish to promise higher than standard reliability to a specific customer, or to all customers in an area such as a special industrial park. These situations, too, can be engineered. In fact, generally it is far easier to engineer the reliability of service to a specific location than it is to engineer an entire system to a specific target.

Performance-Based Industrial Contracts

Generally, such situations arise in the negotiation for service to medium and large industrial customers. Many of these customers have special requirements that make continuity of service a special consideration. All of them pay enough to the utility to demand special attention – at least to the point of having the utility sit down with them to discuss what it can do in terms of performance and price.

Figure 14.3 Service to three industrial customers in the example system were designed to higher-than-normal reliability performance targets.

The actual engineering of the “solution” to an industrial customer’s needs is similar to that discussed above for systems as a whole. Planning engineers evaluate the expected reliability performance of the existing service to the customer, and to identify weaknesses in that system. Candidate improvement plans are tried in the model, and a plan evolves through this process until a satisfactory solution is obtained. The system design in Figure 14.1 includes three such customer locations, as shown in Figure 14.3. Special attention to configuration, fusing and protection coordination on other parts of the circuit, contingency (backup) paths and quick rollover switching, provided about 80% of the improvement in each case.

The other 20% came from extending the reliability assessment analysis to the customer’s site. In each case, the customer’s substation, all privately owned, was analyzed and suggested improvements in equipment or configuration were recommended to his plant engineer. In one case the analysis extended to primary (4 kV) circuits inside the plant. Table 14.3 gives the results for each. For site A, the target has been exceeded in practice to date because there have been no outages in three years of operation. However eventually performance will probably average slightly better than the target, no more.

In the case of site B, the customer’s main concern was that the length of any interruption be less than a quarter hour. Thus, the target is not aimed at total duration time, but on each event, something quite easy to engineer. Performance has greatly beaten this target – means to assure short outages such as automatic rollover and remote control restore power in much less time than required.

For customer C, any interruption of power resulted in loss of an entire shift’s (eight hours’) production. Thus, the major item of interest there was total count of events. Initial evaluation showed little likelihood of any interruption lasting that long. Reliability engineering focused on frequency only.

Table 14.3 Reliability Targets for Three Special Customers

In all three cases, the performance-based contracts call for a price to be paid that can be considered a premium service price. It is typical for industrial customers in this class to negotiate price and conditions with the utility, but in all three cases the price included an identified increment for the improvement in service. Unlike some performance-based rate schedules, there is no “reward” or extra payment for good service – the premium payment is payment for the good service.

But performance penalties are assessed, not on an annual basis depending on annual performance, but on an event basis. If reliability of service is perfect, the utility has earned all the premium monies paid. Any event (any, not just those exceeding the limits) garners a rebate according to a certain formula. For example, customer B receives a $30,000 rebate for any interruption of power, but the rebate rises to $300,000 if the interruption lasts more than 30 minutes. (Customer B’s average monthly bill is about $175,000.)

Analyzing the Risk from Performance-Based Rates

Deregulated utilities are reducing costs by deferring capital projects, reducing in-house expertise, and increasing maintenance intervals. As a direct consequence, the reliability on these systems is starting to deteriorate. Since these systems have been designed and maintained to high standards, this deterioration does not manifest itself immediately. System reliability will seem fine for several years, but will then begin to deteriorate rapidly. When reliability problems become evident, utilities often lack the necessary resources to address the problem.

Regulatory agencies are well aware that deregulation might have a negative impact on system reliability. In a perfect free market, this would not be a concern. Customers would simply select an electricity provider based on a balance between price and reliability. In reality, customers are connected to a unique distribution system that largely determines system reliability. These customers are captive, and cannot switch distribution systems if reliability becomes unacceptable. For this reason, more and more utilities are finding themselves subject to performance-based rates (PBRs).

A PBR is a contract that rewards a utility for providing good reliability and/or penalizes a utility for providing poor reliability. This can either be at a system level based on reliability indices, or can be with individual customers. Performance is usually based on average customer interruption information. This typically takes the form of the reliability indices SAIFI and SAIDI.

Figure 14.6 Performance based rate structure for the example in this section. There is no penalty or incentive payment for annual SAIDI performance that lies between 2 and 3 hours. Above that the utility pays a penalty of $1,666,666 per minute, up to 60 minutes. Similarly, it receives a reward of the same magnitude for each minute below the dead zone.

A common method of implementing a PBR is to have a “dead zone” where neither a penalty nor a bonus will be assessed. If reliability is worse than the dead zone boundary, a penalty is assessed. Penalties increase as performance worsens and are capped when a maximum penalty is reached. Rewards for good reliability can be implemented in a similar manner. If reliability is better than the dead zone boundary, a bonus is given. The bonus grows as reliability improves and is capped at a maximum value. All PBRs will have a penalty structure, and some will have both a penalty structure and a bonus structure. A graph of a PBR based on SAIDI is shown in Figure 14.6.

Most initial PBRs will be negotiated by the utility to be “easy to meet.” This means that business as usual will put the utility in the dead zone. This does not mean that a utility should do business as usual. It may want to spend less on reliability until marginal savings are equal to marginal penalties. Similarly, it may want to spend more money on reliability until marginal costs are equal to the marginal rewards. In either case, a utility needs a representative reliability assessment and risk model to determine the impact of reliability improvement and cost reduction strategies.

In order to make intelligent decisions about PBRs based on average system reliability, a probability distribution of financial outcomes is needed. This requires a PBR structure (such as the one shown in Figure 14.6) and a distribution of relevant reliability outcomes (like the histogram shown in Figure 14.5). It is also desirable to describe the reliability histogram with a continuous mathematical function. A good function to use for reliability index histograms is the log-normal distribution, represented by f(x):

f(x)=1xσ2πexp[−(Inx⁢−μ)22σ2];x≥0(14.2)

The parameters in this equation can be determined by a host of curve-fitting methods, but a reasonably good fit can be derived directly from the mean and variance. If a mean value, x, and a variance are computed, log-normal parameters are:

σ=In(variance+e21Inx¯)−2 Inx¯(14.3)

μ=In x¯−12σ2(14.4)

The log-normal curve corresponding to the test system is shown along with the histogram in Figure 14.5. The curve accurately captures the features of the histogram including the mean, median, mode, standard deviation, and shape.

Assume that a system analyzed earlier, characterized by the reliability shown in Figure 14.5, is subject to the PBR formula shown in Figure 14.6. Using these two functions, a financial risk analysis can be easily determined. For example, the expected penalty will be equal to:

Penalty=∫0∞PBR(SAIDI)⋅f(SAIDI)dSAIDI(14.5)

The probability of certain financial outcomes can also be computed. For example, the probability of landing in the dead zone will be equal to the probability of have a SAIDI between 2 hours and 3 hours. This is mathematically represented by:

%in⁢Dead⁢Zone=100%⋅∫23f(SAIDI)dSAIDI(14.6)

The expected outcome of the test system is $14 million in penalties per year. Thus, despite the fact that the expected annual SAIDI (2.81 hours) lies in the dead zone (no penalty – no reward) the utility will on average have to pay a fine amounting to about 8.4 minutes per year. Penalties will occur 32% of the time, bonuses will occur 12% of the time, and the utility will be in the Dead Zone 57% of the time. The distribution of all possible outcomes and their associated probabilities is shown in Figure 14.7.

For a cash-strapped utility, Figure 14.7 represents an unwelcome situation. And it is risky, because even though the average penalty of $14 million may be acceptable, that outcome will rarely happen. The $14 million average occurs because a penalty of $50 million or more will occur once every 7 years and the maximum penalty of $100 million will occur once every 12 years. Faced with this situation, a utility would be wise to negotiate a less risky PBR. Possibilities for adjusting the PBR to mitigate risk include:

1. Make the reward and penalty slopes less steep,

2. Widen the dead zone boundaries,

3. Move the dead zone to the right, and

4. Reduce bonus and penalty caps. Each of these options can be used alone, or a combination can be negotiated.

Figure 14.7 Distribution of financial outcomes for the example PBR problem. Although it is most likely the penalty/reward is zero (performance lies in the dead zone) the utility has a significant probability of getting hit with the maximum penalty (about once in every 12 years), while no chance of getting the maximum reward.

A suggested change to the PBR rules to mitigate the risk for this utility system is shown in Figure 14.8. This change stretches out the bonus and penalty transition zones from one hour to two hours. The impact of this changed PBR on the utility’s expected financial exposure is shown in Figure 14.9. On the surface, it may seem like not much has changed. Penalties will still occur 32% of the time, bonuses will still occur 12%, but total risk is reduced greatly, by $5 million. Utility companies can use predictive reliability assessment tools when planning and designing their systems and their responses to regulatory rules. This will allow the reliability of existing systems to be assessed, the reliability impact of projects to be quantified, and the most cost-effective strategies to be implemented. In most cases, an analytical model (Chapter 14) will be sufficient. This will allow utilities to compare the expected performance of various systems and various design options. Analytical/Monte Carlo hybrid techniques become necessary when technical and financial risk needs to be examined. This chapter has shown methodologies to serve both of these need categories.

Figure 14.8 Changed PBR schedule that reduces risk. The schedule has a milder rise in both penalty and reward sides and is a “fair” proposal for the utility to make to regulators because it treats both penalty and reward sides equally.

Figure 14.9 Financial outcome with the revised PBR formula. The utility’s expected average is still a penalty, but only $9 million, an improvement of $5 million. More important, the possibility of it being hit with a large (over $50 million) penalty has decreased greatly.