PART II: ECONOMIC MODELING AND IMPLICATIONS OF THE DECISION ON
12. EQUATIONS FOR CONTINUED OPERATION
12.4. Economic evaluation criterion for the decision on continued operation
At the point of transition from the nominal operations period to either an extended operation followed by delayed decommissioning, or a nominal decommissioning period, there exist five value/cost elements we need to consider in order to reach a decision on which path to follow.
Two of these value/cost elements we know at the point of decision, and three other elements, which will occur in the future, we need to estimate. These are:
(a) The discounted cumulative net cash flow at the end of the nominal operation period, CUMCF(t = N). This accumulates (discounted) and is computed t = N.
(b) The NPP refurbishment and up rate cost which occurs during the last year of nominal operation, CAPADD(t = N). This occurs at t = N.
(c) The extra revenues expected to accumulate during the extended operation period,
{
CUMCFLEX( k = NLEX) – CUMCFLEX(k = 1)}
. These will accumulate and be discounted over the period N + 1 to N + NLEX and will be computed at t = N + NLEX.(d) The total value of the decommissioning fund at the end of the nominal operation period, CDD available at t = N, or TDF(k = NLEX), available at the end of the extended operation period, t = N + NLEX.
(e) The total discounted cost of the decommissioning operation carried over a period of NDD years and computed either at the end of the nominal decommissioning operation t = N + NDD or at the end of the delayed decommissioning operation, t = N + NLEX + NDD. Items a, c, and d, represent positive values, such that a, is known and c and d could be estimated. Items b, and e represent negative values, or costs, such that b is known and e could be estimated. We can summarize the above value/cost elements notation in Table 2.
Table 2 Cost/Value elements during continued operation period of a plant in a restructured utility
Original design plant life Continued Plant Operation Value/Cost Elements
Element Designation
Time Point Computed
Element Designation
Time Point Computed
Nominal Operation Value a t = N a t = N
Refurbishment + Uprate Cost b t = N
Net Extended Operation Value c t= N + NLEX
Decommissioning Fund Value d t = N d’ t= N + NLEX
Net Decommissioning Cost e t= N + NDD e’ t= N + NLEX + NDD
12.4.2. Exact decision criterion
The economic evaluation criterion for the decision on whether to extend the plant operation period or not is the value of the discounted cumulative net cash flow at the end of the plant life span. The plant operations option which results in a higher discounted cumulative net cash flow available at the end of its decommissioning period is the more economic option to follow.
If we can estimate on a year-by-year basis the different cost components affecting the net cash flow, sum up over each time period taking care to use the right boundary conditions, and then discount back to the zero time point, we can compute the desired value. This capability in spreadsheet format is available to many economic analysis departments of electric utilities operating NPPs and other large plants.
Note that from equation (25) we can compute the discounted cumulative net cash flow at the end of the nominal decommissioning period, designated CUMCFDD(t = N + NDD). In similar fashion we can compute from equation (47) the discounted cumulative net cash flow at the end of an extended operation period followed by a delayed decommissioning period, designated as CUMCFLEXDD(t = N + NLEX + NDD). Based on the above discussion if we do these two projected lifetime cost estimations and find
CUMCFLEXDD(t = N + NLEX + NDD) ≥ CUMCFDD(t = N + NDD) (48)
Then the extended operation option is the more economic option for the plant to follow. The life span cumulative net cash flow is shown in the extreme right of Figure 6a for an original design plant life, and in Figure 7 for an extended operation plant.
If after computing the life span discounted cumulative net cash flows for the two options we find
CUMCFDD(t = N + NDD) ≥ CUMCFLEXDD(t = N + NLEX + NDD) (49) Then the original design plant life operation is the more economic option for the plant to follow and the extended operation period cannot be justified due to a combination of various factors which should be further investigated.
We should recall that the discussion here is limited to choosing between two nuclear plant related options – operating the plant for its original design life only, or proceeding to extended life operation. We did not discuss here the external options of building from the ground up and operating a new replacement generation plant, replacing the existing nuclear plant capacity after the end of nominal operation with increased generation from other plants the owner utility has, purchasing replacement power from within the region or from distant low cost generation plants, or expanding the transmission network and importing additional power into the region using the higher capacity transmission lines. These options are region, technology and utility specific and cannot be addressed within the contained scope of the economic analysis of Part II of this Publication.
12.4.3. Approximate decision criterion
If it is difficult to estimate year-by-year economic values and costs over the entire plant life span, it might be possible to devise an approximate decision criterion using Table 2 above.
Such simplifying procedure could serve as an initial screening process to be followed by a more detailed and exact computation as described in Sub-section 12.4.2. If we need a simplified, short methodology for a preliminary evaluation, then the procedure outlined below may be more appropriate.
Each of the value/cost elements designated at that table could be computed using a combination of simplifying assumptions inserted into the right equations of the above text. It is possible to assume that many of the annual cost elements included in these equations are constant over time, or could be merged with other elements. Depending on data availability, time and ingenuity, each of the value/cost elements in Table 2, designated a to e’, could be computed and discounted from the time point of computation, indicated in the Table to the start of the plant commercial operation.
Given the designations of Table 2 and assuming the right discounting performed, we can define:
Net Value (Original design life) = a + d – e
Likewise for the extended operation option we can define:
Net Value (Life extension) = a + c + d’ – b – e’
Comparing these values, if we find
a + c + d’ – b – e’ ≥ a + d – e (50)
Then the extended operation option is the more economic option for the plant, given all simplifying assumptions. If the converse is true, than the original design plant life operation (no extended operation) is the better economic choice for the particular conditions of that plant. The evolutions of the cumulative net cash flow over the nominal or extended operation of a plant operated by a non-regulated utility are shown graphically in Figures 6a, and 7, respectively. These two Figures and Table 2 above demonstrate the changes in the cumulative net cash flow of the plant, as it transitions from one life phase to the next.