PART II: ECONOMIC MODELING AND IMPLICATIONS OF THE DECISION ON
10. EQUATIONS FOR ORIGINAL DESIGN PLANT LIFE OPERATION
10.3. Decommissioning period
The equations derived above for the operating period, which were general in nature until we got into the components breakdown of the fuel and decommissioning costs, need now be further modified to account for changes occurring during the decommissioning period. We continue here, as before, our basic practice of discounting all future expenses to the plant initial commercial operations date, thus keeping in mind that we now address a NPP specific case. It is convenient at this point to define new running time indices. The complete decommissioning period over which all activities occur, and at the end of which the former NPP site is released to new industrial or general use is NDD years, starting at the plant shutdown date. We thus have k = 0, 1, 2, 3, …………..,NDD, and
j = N + k = N + 1, N + 2, N + 3, …………,N + NDD
as our running time indices during the decommissioning period. The time index j is the extension of the time index t, employed during the operations period.
To be consistent with our decision to employ separate summation over each time period we will use the decommissioning period time specific index k though it is possible to use the joint operations-decommissioning time index j. The value of keeping separate summation for each
phase of the plant’s life span will become apparent during the discussion on extended life operation in section 12.
Based on the end of discussion in the previous Section, we can now define
CUMCFDD (k = 0) = CUMCF(t = N) + CDD × (1 + r) -N – CAPADD(t = N) × (1 + r) –N (20) Where
CUMCFDD(k = 0) – The discounted cumulative net cash flow at the beginning of the decommissioning period [M$]
Equation (20) and Equation (19) above represent the boundary conditions for the transition from the operations period to the decommissioning period. Equation (20) implies that the net total cash flow available to fund decommissioning activities is the sum of the net cumulative cash flow generated by the end of the operations period, as computed by equation (14) above, and the decommissioning fund CDD released at that point to the NPP, minus the capital additions costs incurred during the last operations year – all discounted to the zero time point.
The value of CUMCFDD(k = 0) represents the largest value of the discounted cumulative net cash flow over the entire life span of the plant (in this case the NPP), and is the initial cash flow value at the start of the decommissioning period. From now on there will be no more in-flows of annual incoming revenues, as discussed below, and the NPP will only experience annual cash outflows to pay for decommissioning expenses.
The necessary financial condition for initiating the decommissioning process is that the total net cash flow available at the start of this phase is equal to or exceeds the expected cost of the decommissioning operations. In more exact definition,
CUMCFDD(k = 0) ≥
{
Expected discounted cumulative decommissioning cost}
.To anticipate the discussion that follows we can state that CUMCFDD(k = 0) should be equal to, or exceed, the summation term in the right hand side of Equation (25) below, when carried out from k = 1 to k = NDD.
Since during the decommissioning period the NPP does not generate electricity any more, no revenues from the sale of electricity are available during this period. Thus
REVDD(k) = 0 (21) For all k values from K = 1 to k = NDD, which correspond to j values from j = N + 1 to j = N +
NDD
It is possible that some revenues could be obtained during the decommissioning period from the salvage value of some equipment or commodities left over from the operations period.
Additional credits might apply from the use of balance of plant equipment or facilities with a replacement power plant or other industrial facility installed on site, or transferred to other plants operated by the owner utility. Given the uncertain nature of these possible revenue sources (if they materialize), we prefer to treat them here as negative capital addition costs in the year they accrue, rather than treating them explicitly as distinct revenue items.
Capital addition costs CAPADDDD(k) might be incurred during the decommissioning period, e.g. for new facilities related to spent fuel storage on site, however the distinction made between small capital items expensed in the year they accrue or large capital items added to investment and then depreciated, is no longer necessary. All capital expenditures are now
expensed as they accrue. Very limited interim replacement costs are incurred during the decommissioning period, to account for replacement parts for some NPP systems kept operational such as the decay heat removal system from the spent fuel pool.
Another change that occurs in the cost equations is that the fuel cost component and the variable O&M cost component are now zeroed out. No nuclear fuel is burned in the reactor any more and all O&M expenses related to generation do not accrue. Thus
FLDD(k) = VOMDD(k) = 0 (22) For all k values from k = 1 to k= NDD
We can now define the net annual cash flow equation applicable during the decommissioning period as
NCFDD(k) = -
{
CAPADDDD(k) + OMDD(k)}
(23) For all k values from k = 1 to k= NDDEquation (23) implies that all new cash flows that occur during the decommissioning period represent expenditures on decommissioning activities without offsetting new revenue sources (save for possible salvage values), hence the negative sign in front of the right hand side of equation (23). These expenditures are recovered from funds becoming available at the end of the operations period, or the start of the decommissioning period, as specified in equation (20). We now need to define O&M costs during the decommissioning period.
OMDD(k) = NSTAFDD(k) × SALAVDD(k) × 10-3 + FOMDD(k) × CAP × 10-3 + FSCDD(k) × CAP × 10-3 (24)
For all k values from k = 1 to k= NDD Where
OMDD(k) – Annual O&M costs in year j during the decommissioning period [M$/year]
NSTAFDD(k) – Number of NPP remaining staff in year j, during the decommissioning period [persons]
SALAVDD(k) – Average loaded salary for the mix of plant employees defined by NSTAF(j), remaining in the plant in year j during the decommissioning period [K$/year]
FOMDD(k) – Annual fixed O&M costs in year j, during the decommissioning period, excluding personnel costs [$/KWe – year]
FSCDD(k) – Spent fuel storage costs in year j during the decommissioning period [$/KWe – year]
As seen in equation (24) we break the decommissioning period O&M costs into three distinct components –distinct from each other and from parallel activities during the operations period. These are the remaining staff salaries and benefits, other fixed O&M costs and spent fuel storage costs. The staff size and mix during the decommissioning period NSTAFDD(k) are different than those during the operations period NSTAF (t) since the NPP does not need plant operators and as much operations department personnel. The sizes of the training staff security staff, and most other plant departments are reduced and different mix of talents are required. This results in a different average salary value for the remaining plant personnel, as compared with the operations period. We have decided to break spent fuel storage costs into a
distinct cost category since spent fuel might have to be stored on site long after all other O&M costs have stopped.
We can now define the discounted cumulative cash flow equation during the decommissioning period as follows
k
CUMCFDD(k) = CUMCFDD(k = 0) –
Σ {
CAPADDDD(k) + OMDD(k)} ×
(1+r) -(N+k) (25)k = 1
Equation (25) is the main equation governing the discounted cumulative cash flow during the decommissioning period. This equation though general is applicable mostly to NPP situations and represents the evaluation of the economics of a NPP decommissioning process. The final numerical value computed from equation (25) for k = NDD is the final numerical result of the entire computational procedure developed here, and covering expenses and revenues –all cash flows attributed to the NPP — during its construction, operations and decommissioning life phases. The annual and the cumulative net cash flows over the nominal life span of a non-regulated NPP are shown graphically in Figure 5a, and Figure 6a, respectively.
If CUMCFDD(k = NDD) = CUMCFDD(j = N +NDD) ≥0
The NPP represented a positive profit centre for its parent utility over its entire life span – starting with a clean power plant site and ending up with (hopefully) a clean plant site again.
If CUMCFDD(k = NDD) = CUMCFDD(j = N +NDD) ≤ 0
The NPP has ended its total life span with a loss that should be covered by its parent utility or by an external source of public funding.
11. PLANT OPERATION IN RESTRUCTURED VERSUS REGULATED UTILITY