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Introduction

Because of the intermittent nature of green technology power production, fossil-fired plants will be cycled more and more as wind and solar generation comprise an ever increasing percent of total power generation. This will give further impetus to this trend in conventional plant cycling, which began over a decade ago with the competitive dispatch introduced by market deregulation. The following discussion proposes a variation of the component-level depreciation method introduced in previous Energy Pulse articles that addresses the impact of cycling on component and plant depreciable life. In this regard, it can be characterized -- at least in part -- as a units-of-production depreciation method. This method, which draws on production-based maintenance programs, is the most accurate way to depreciate plants that are regularly cycled or only used periodically.

The discussion is organized into the following sections:

• Depreciation Accounting
• The Valuation of Useful Components Method
• Increased Cycling Trend
• The Impact of Cycling on Components
• The Units-of-Production Variation

Depreciation Accounting

Generally accepted accounting principles define depreciation as the systematic reduction in service value of property, plant, and equipment (PP&E) and other fixed assets over their respective service lives. The purpose is to recognize the expense of asset wear and tear or technological obsolescence as a function of time and operation. A depreciation expense is recorded each month and year to represent the portion of plant service value "consumed" in the process of producing revenue.

Financial accounting authorities have defined three general ways to depreciate assets:

• The straight-line method where annual depreciation is calculated by dividing PP&E original cost (the depreciable basis) by its estimated depreciable life (e.g., 10 years would equate to an annual depreciation expense of 10 percent of the original asset cost).
• The accelerated method where annual depreciation is calculated the same way as the straight-line method except that formulas are specified (declining balance or sum-of-year's digits) that yield higher levels of depreciation in early years and lower levels in later years.
• The units-of-production (UOP) method where annual depreciation is calculated by multiplying the depreciable basis by the ratio of the PP&E's annual production (e.g., 10,000 hours, units, or miles) to its estimated lifetime production capacity (e.g. 100,000 hours, units, or miles).

This article is only concerned with financial accounting, as opposed to tax accounting, which is governed by the Internal Revenue Service. Note, however, that these are two distinct ways to depreciate a plant and can (and often do) lead to different results. For example, it is possible to depreciate a plant in 15-to-20 years for federal tax accounting while using a 40-to-50 year depreciable life for financial accounting. This means an increase in book income resulting from a reduction in depreciable life, does not affect the plant's tax basis which determines cost recovery through tax deductions.

The Valuation of Useful Components Method

The Valuation of Useful Components (VUC) method was developed in 1997 to determine the depreciable life of unregulated plants in the emerging competitive market. It does this by first, projecting plant technological (i.e., physical) life; and second, determining if the plant can remain economically viable over this period.

Plant technological life is derived by completing the following steps:

• Develop a system-by-system component-level breakdown of original plant cost.
• Determine the service life of each component in this breakdown, where service life is defined as design life as extended by ongoing maintenance including component upgrades and replacements.
• Derive the cost-based weighted life of each system by adjusting the life of each component in the system by the ratio of its cost to total system cost and summing the weighted component lives.
• Determine the overall plant technological life by adding up the weighted system lives.

For most depreciable life studies, costs are broken down at the major component level, which typically results in from 5-to-7 components for each system. For example, the gas turbine facility would break down into the gas turbine, main power transformer, supporting structure (forms, rebar, concrete, and structural steel), system piping, and instrumentation and controls. A reference set of common component service life estimates have been developed by grouping components into the following operating environments:

• High energy components (e.g., power block components)
• Low energy components (e.g., pressure vessels, material handling, switchgear)
• Non-energy components (e.g., buildings, structural steel, concrete)
• Instrumentation and controls (e.g., instruments, computer-based controls)

Reference service life projections are based on factors common to all components including: design life and failure mechanisms; historic performance; and, the rate of technological change. They also consider plant and company-specific practices including: the mode of plant operation (i.e., baseload, cycling, or mid-merit); maintenance policies and the standard of care; and, how component repairs, replacements, and upgrades are accounted for (i.e., expensed or capitalized).

Economic viability is assessed by comparing the plant's cost of producing power over its projected technological life with long-term projections of market-clearing prices to determine if future earnings would be greater or equal to the plant's book value. Market clearing price projections are based on the introduction of newer and improved power generating technologies. Other external factors taken into account include trends in industry practices, fuel costs, and government and regulatory actions.

Once the technological life is determined to be economically viable, annual depreciation is calculated by dividing the original plant cost by the number of years depreciable life -- i.e., applying a straight-line depreciation method. This is the most accurate way to represent the reduction in plant service value of most plants that are not regularly cycled nor incur prolonged periods of inactivity.

Increased Cycling Trend

Over the past decade, various factors have contributed to the increased cycling of fossil-fired plants. When markets were deregulated, plants were cycled more because earnings could be optimized by increasing or decreasing production in response to power and fuel price fluctuations. Deregulation also created overly optimistic expectations regarding what new and more efficient combined-cycle plants could earn when competing against existing plants. Over building created power gluts in several markets and as new plants came on line, older and less efficient plants were displaced down the merit order into mid-merit or peaking operation.

More recently, the ever increasing penetration of wind and solar power has required conventional plants to be ramped up and down to balance the intermittency of these renewable energy sources. This trend will continue well into the future as both federal and state governments mandate that renewable technologies make up a greater percent of total generation.

The Impact of Cycling on Components

Cycling produces temperature and pressure transients that cause high energy components to wear out in a different way than continuous hours of operation. Figure 1 depicts this difference for a single-cycle peaking unit. As shown, the plant will meet its design life limit in different ways depending on how it is operated. If operated in a peaking mode (first arrow), the primary component failure mechanism is metal fatigue caused by the number of starts. If operated in a baseload mode (the second arrow), the primary failure mechanisms are oxidation, metal creep, and corrosion caused by continuous hours of service.

The diagram is based on an original equipment manufacturers' (OEM) technical guide, which explains how both the number of starts and hours of service should be considered when scheduling major and minor maintenance. This can be done by putting unit starts on an equivalent operating hours (EOH) basis (e.g., 20 hours of service per start) and adding this to the number of service hours.

As combined-cycle plants have been increasingly cycled, owners have also developed ways to include the number of plant starts when scheduling maintenance. Approaches can range from an OEM simply providing an EOH for each start to using sophisticated production-based maintenance planning models that monitor hours and start-related factors (e.g., hot starts, cold starts, fuel factors, PH factors) to determine optimum maintenance intervals.

Figure 2 provides an example of how the latter approach applies guidelines established by the gas turbine OEM to schedule maintenance based on both starts and operating hours. The sample curve depicts a 24,000-hour inspection limit based on a design life of 210,000 hours. This represents 80 percent of original gas turbine's 300,000 hour design life. Points on the curve mark the various combinations of starts and hours factors that equate to the 24,000-hour inspection limit for continuous duty -- at point "b". Moving up the curve, gives the EOH impact of cyclic duty, which introduces non-optimal service conditions and a shorter interval in terms of total operating hours. Point "a" marks the combination of starts (1,050) and operating hours (12,000) that represents an equivalent impact on GT components in terms of maintenance requirements as well as total design life hours.

The Units-of-Production Variation

The units-of-production (UOP) variation to the VUC method was developed to determine the depreciation of single-cycle peaking units and combined-cycle plants that were cycled beyond design parameters. In initially assessing these plants, we found that all the elements of the VUC Method, including the economic viability assessment and service life projections for most components were applicable, but with one notable exception. Reference service life projections of power block components, which account for the large majority of construction and maintenance costs, did not take into account the impact of cycling.

The approach taken to address this shortcoming is based on the same four steps outlined above for determining a plant's technological life. In completing the first step, the system-by-system component-level breakdown of original plant cost is expanded to include high energy components. Table 1 provides an example of this for a combined-cycle plant's gas turbine (GT) facility. The italicized entries in the first column represent high energy components. The second column provides the percent of total system cost represented by each component.

The data is presented at a summary level to maintain the confidentiality of the source. It is assumed that gas turbine high energy components represent about 66 percent of total system costs. Gas turbine piping is the other high energy component representing about 1 percent of system costs.

The second step, determining the service life of each component, relies on reference component service life projections for low energy, non-energy, and I&C components, which are not affected by cycling. The impact of cycling on high energy component service life is addressed by developing a "cycling factor" based on the ratio of annual design life hours to actual annual equivalent operating hours. OEM technical guides provide the design life of gas turbine and other power block components. Using the same example as Figure 2, the design life of the GT is 300,000 hours. Assuming a 30 year design life equates to a 10,000 EOH annual design life. Actual EOH would be derived from the approach used to determine maintenance intervals -- e.g., based on a production-based maintenance planning model or an OEM's expert opinion of the EOH per plant start.

Deriving the cost-based weighed system life, the third step, is completed by multiplying each component's service life by its percent of system cost and summing the results. To show the impact of cycling on system life, Table 1 provides examples of three cycling factors based on operating hours of 10,000, 13,000, and 8,000, respectively -- i.e., equal to, greater than, and less than design life hours.

• When the cycling factor is 1.00 (10,000/10,000), all component service lives (column 3) are based on reference service life estimates. This includes high energy components because cycling is within plant design parameters. The cost-based weighted component life (column 4) yields a GT facility life of 45.0 years.
• When the cycling factor is .77 (10,000/13,000), the service life of high energy components declines to 34.6 years (.77 times the reference service life of 45.0 years). The weighted lives of GT high energy components and system piping decline to 22.8 and 00.4 years, respectively, which reduces the GT facility life to 38.1 years.
• When the cycling factor is 1.25 (10,000/8,000), the service life of high energy components increases to 56.3 years (1.25 times 45.0 years). The weighted lives of GT high energy components and system piping increases to 37.0 and 00.6 years, respectively, which increase the GT facility life to 52.5 years.

The fourth and final step is completed by adding the weighted service lives of each system to determine the plant's technological life. Table 2 provides this calculation using the alternative service lives from Table 1. The impact of cycling on the steam turbine facility's and heat recovery system generator's components affected by cycling is not included in this example.

The cost-based weighted service life corresponding to each of the three cycling factors is derived by multiplying each GT facility service life by the 43.0 percent of total plant cost represented this system. The results are 19.4, 16.4, and 22.6 years, respectively. The corresponding plant technological life is provided in the last row. The change in service life would be more dramatic if the high energy components for other systems were included as would be the case in a depreciable life study.

There are a number of ways to apply the above approach. The example is based on a year-end adjustment using annual plant operating data. In practice, the plant's monthly depreciation would be derived by dividing its original cost by a 50.3 year depreciable life -- the plant life if cycled within design parameters. However, end-of-month adjustments could be made when the actual equivalent operating hours are greater or less than the design basis. This would be particularly appropriate for single-cycle peaking plants which vary production substantially from month-to-month due to seasonal demand fluctuations.

The discussion has only considered gas-turbine based plants because these plants are cycled much more than coal, oil, or natural gas fired steam generating plants. Depending on the circumstances, it may also be appropriate to apply this approach to these plants as well.