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By Anthony J. Carrino, Richard B. Jones, Ph.D., William E. Platt and Eric. D. Tiffany, Solomon Associates
Fossil-fired generation facility owners have always struggled to find the best balance between maintenance expenditures and plant availability. Few companies can determine this balance themselves because it requires years of unit-specific historical data. Even when many years of data are available, rapid changes in plants and the marketplace render data more than a few years old virtually irrelevant. Furthermore, operating data across all ranges of availability are needed to define an optimum point. Asset owners do not have the luxury of being able to “experiment” with a series of conditions to develop cost/availability relationships because they must meet short-term business demands.
To address this challenge, Solomon developed a methodology to determine a target optimum point where availability meets maintenance spending for Powder River Basin (PRB) coal-fired units. Using a database of sufficient size and composition across various operating ranges, Solomon generated an algorithm that predicts the relationship between maintenance spending and availability. Coupling this generalized algorithm with a unit-specific market-loss curve determines the optimum spending for a facility.
This article presents the results of our analysis, how this methodology can be applied to develop optimum operating and financial targets for specific units and markets and a process to achieve those targets. We also describe how this methodology can be used for other types of fossil-fired technologies and future enhancements to the analysis.
To optimize the total cost for a plant, it is crucial to understand the cost of achieving certain availability levels. Total costs are considered to include maintenance costs plus the opportunity cost of not being available when there is a positive spark spread. Evaluating the total cost of a generating unit at various degrees of unavailability provides insight into the plant’s optimum operating levels.
Consider first the elements of maintenance cost. For the purposes of this conceptual discussion, reactive maintenance is defined as actions or efforts taken as the result of unplanned outages or durations. Proactive maintenance is defined as preventive actions aimed at the source of potential failures to extend the life of the equipment and avoid failures. Figure 1 presents a conceptual illustration of both proactive and reactive costs versus varying levels of availability.
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Generally speaking, the cost of reactive maintenance decreases toward zero as the asset approaches 100 percent availability, whereas the cost of proactive maintenance increases exponentially with increasing availability. In other words, it is more difficult and costly to attain increasing levels of availability because of the amount of proactive maintenance that needs to be performed. The combination of the reactive and proactive costs produces the total maintenance cost curve, depicted as the blue line in Figure 1. Note that the curve’s inflection point is associated with the lowest maintenance costs. As availability increases past this point, so does total maintenance cost.
The point at which minimal spending occurs for maximum availability does not suggest an optimum operating point, because the asset is generating electricity for which the company is being compensated, which is a key component that must be considered when determining an optimum operating point. A commercial perspective provides the context for which the best balance of maintenance cost and availability is achieved. In other words, integrating a market dimension into the analysis establishes the value associated with a given level of maintenance cost and availability.
To quantify the market dimension, consider Solomon’s “lost revenue opportunity” (LRO), which is an opportunity cost for the amount of generation lost due to the unit being unavailable. For example, if the market is paying $60/MWh and the variable cost of generation is $25/MWh (fuel, auxiliaries, and so on), and if the unit is unable to produce, the LRO is $35/MWh (that is, $60/MWh minus $25/MWh). Including this economic factor into the analysis, the total cost describing the operations of the unit is the sum of the total O&M costs developed in Figure 1 plus the plot of LRO as shown in Figure 2. Such a conclusion assumes that bi-lateral contracts or the ability to cover market shortfalls through another means don’t exist.
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The inflection point of the total cost curve represents the optimum balance between maintenance spending and unavailability losses. As availability approaches 100 percent, total costs increase exponentially, possibly beyond market value. That is, the incremental cost to run the unit at higher availabilities is greater than the associated increase in incremental revenue.
Methodology
To bring the analysis from a conceptual discussion to an empirical application, Solomon considered a set of 30 generating units that burned PRB coal. Each of the units exhibited the following characteristics:
- Installed capacity: 360 to 750 MW
- Base load with net capacity factor: 61 to 89 percent
- Scrubbed and un-scrubbed
- 80 unit-years of data.
As this data set was homogeneous with regard to fuel and utilization, the results and conclusions cannot be generalized to other peer groups.
Maintenance costs and Solomon’s Maintenance Index from the CPA were used for this work. Maintenance Index is defined as a two-year average of non-overhaul expenditures plus the annualized portion of the most recent overhaul and major project expenditures for the major pieces of equipment, divided by the current and previous years’ average production in megawatthours per generating unit.
Note that the elements of maintenance cost (that is, proactive and reactive maintenance) depicted in Figure 1 were not used in favor of total maintenance cost simply because of the ease of data collection. Separating proactive and reactive components is addressed subsequently in this article.
Solomon’s Maintenance Index and the way overhauls and major projects are treated are crucial to this analysis. Regardless of whether a company classifies major projects as maintenance or capital, for the purposes of the CPA and this analysis any project significant in maintaining the plant in the same design, condition and operation—and that lasts longer than a year—is annualized over the life of the project. In this regard, only a portion of each major project is attributed to the operating costs of a unit. Without treating overhauls and major projects in this manner, cost data would exhibit so much variation it would hinder development of meaningful results.
Annualized Equivalent Availability Factor – As a measure of availability, Solomon initially used equivalent availability factor (EAF). This factor represents the maximum production a unit can generate, accounting for derates and full outages as defined by North American Electricity Reliability Corp. Generating Availability Data System (GADS). Later, we determined that a time-averaged EAF over a longer period was more appropriate.
Lost Revenue Opportunity – LRO was used to represent economic opportunity costs, as previously described. From Solomon’s CPA, LRO is determined by calculating the difference in market clearing price and plant variable cost at the time of the lost opportunity (that is, outage or derate) and applying any positive difference (for example, spark spread) to the megawatthours lost due to the incident. This effectively establishes a curve of lost market opportunity that is added to the maintenance cost to determine total cost of unavailability.
Analytical Method – Frontier analysis is a numerical technique used to estimate the boundary or limits of a data set. Using validated operating and financial data, the technique envelops rather than intersects the data, thus creating a “frontier” of performance that represents what is achievable as opposed to what is theoretical. In terms of this analysis, the frontier points are defined as the values that have the lowest Maintenance Index for a given average EAF interval. We used these points to develop an analytical curve that represents the “frontier” of Maintenance Index as a function of average EAF.
Results
We began the analysis considering Maintenance Index versus a one-year EAF as presented in Figure 3. However, a one-year EAF does not account for units that ran continuously, such as those that were not overhauled. A unit on which an overhaul is performed is going to have a reduced EAF in a given year. Therefore, in the context of determining a sustainable operating point, a time-averaged EAF over a longer period is more appropriate, which is more consistent with the manner in which Solomon’s Maintenance Index is used.
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To determine the average value, the EAF for each year was averaged over the period for each unit. An example is highlighted in Figure 3 with the dark-blue points. During the five years of operation, EAF for the unit ranged from 83 to 96.5 percent and the average Maintenance Index ranged from $1.5 to $3.0/MWh. The averaged EAF for this period is 92.5 percent and corresponds to an average Maintenance Index of $2.0/MWh, as represented with the large dark blue triangle.
Averaging each of the units in the data set, which ranged from three to seven years, produces a plot of average Maintenance Index versus averaged EAF, which is presented in Figure 4.
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The frontier of averaged EAF performance for the data set is shown as a curve in this figure. As one would expect, the Maintenance Index decreases as averaged EAF increases because less reactive costs are incurred and there is simply no opportunity to incur costs as the unit is operating more. Additionally, at approximately averaged EAF = 91 percent, the curve shifts upward, suggesting that more costs are incurred at higher availabilities; thus, an optimum point. Since EAF is an average value over a significant time frame, this optimum point is the target where units should strive to operate because it is sustainable over a multi-year period. To achieve an increase in availability beyond this point, additional maintenance will be needed that is going to cost incrementally more.
The curve illustrated in Figure 4 represents an algorithm for units that burn PRB coal. It describes the optimum point where maintenance costs meet availability. This curve, however, is a generalization and does not represent a specific unit’s cost structure and market conditions. The applicability of this curve to an individual unit is provided in the subsequent section.
Application
Consider, for example, a nominal 700 MW unit that burns PRB coal and has a net capacity factor (NCF) of 75 percent. The unit operates in the Western United States and participates in Solomon’s Power Generation Performance Analysis. Using the algorithm represented by the blue line in Figure 4 and superimposing the unit-specific LRO curve yields the total cost curve presented in Figure 5.
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Note that LRO results can vary significantly year-to-year depending on market conditions. To be consistent with other variables in the analysis, not only does the LRO value applied here have to be specific to the unit under analysis, it also has to be computed over a multi-year period.
Given the unit-specific curve, the target for this unit should be an averaged EAF of 93 percent, which is associated with a total cost of $6/MWh. This position represents the optimum balance between availability and maintenance spending considering the LRO when this unit moves to the frontier of best performance. At this point, the associated Maintenance Index would be approximately $2 to $3/MWh, a target that is slightly more than a minimized Maintenance Index. However, achieving this frontier may not be practical as a target within a short time frame. Intermediate goals may be needed to work programmatically toward reaching the frontier. Using this analysis will yield these targets regardless of whether the goal is to achieve best performance or an intermediate level of performance.
The results of this work are significant in that the conceptual relationship between maintenance spending and availability has been quantified such that an optimum point can be determined. Moreover, we have demonstrated a methodology to identify a long-term operational target for a specific generating unit.
Authors: Richard B. Jones, Ph.D. is director of Statistics and Risk Modeling-Power Generation, William E. “Ed” Platt, P.E. is senior consultant-Power Generation, Eric D. Tiffany, P.E. is senior vice president-Power Generation and Anthony Carrino is senior consultant-power generation for Solomon Associates. Carrino is also a Contributing Editor to Power Engineering magazine.
