Monte Carlo simulation: Treatment of uncertainties in economic assessments

As discussed in Section 4, Monte Carlo simulations are an efficient way to take into account uncertainties in economic evaluations. In performing these simulations, a statistical distribution is provided for each input parameter. Each distribution provides random samples, representing the values of the input parameters. With uniform distributions, all that is needed is the maximum and minimum values for the input parameters. The input parameters for which a uniform distribution is given are electricity price, capacity factor, O&M cost, spent fuel removal, disposal and storage, decommissioning cost and refurbishment cost.

A sample of minimum and maximum values assigned for each parameter is given in Table 7.

Except for the electricity price, minimum and maximum values for each input parameter are set to be more severe than the value taken from Ref. [37] to reflect the ageing effect of the plant. All the cost input parameters are set to range from the reference value to 30% higher. The Monte Carlo based software can be set to calculate the NPV ranges. The NPV range for cost input parameters is shown separately and simultaneously, together with the standard deviations. The number of samples drawn from each distribution in the Monte Carlo simulation is 10 000.

The simulation is performed independently for each cost input parameter to show its effect on the NPV. As shown in Table 8, the effect of each parameter on the NPV is ranked in the following order: O&M cost; refurbishment cost; decommissioning cost; and spent fuel removal, disposal and storage cost. O&M cost has the greatest effect on NPV among the selected cost input parameters, while the effect from spent fuel removal, disposal and storage has the smallest. The effects of refurbishment and decommissioning costs lie between the two extremes.

When the cost input parameters are simultaneously applied in Monte Carlo simulations, the range of NPVs is 218~801, the mean value is 509 and the standard deviation is 109. This means that the effect on NPV of the cost input parameters becomes greater when they are considered simultaneously. The Monte Carlo simulation results for electricity price and capacity factors are shown in Table 9.

Table 9 shows that the effect on NVP is greater from the electricity price and the capacity factor than from the cost input parameters.

Considering all the input parameters simultaneously in Monte Carlo simulations, the distribution of NPV is shown in Fig. 6. When the uncertainties increase to certain values, negative NPVs occur in the simulation.

Figure 7 shows that NPV ranges between $498 and $1438 million, the mean value is +339 and the standard deviation is 389 (115%). The probability of negative NPVs is about 22% from this simulation. A number of Monte Carlo simulations, whose results are shown in Figs 7–10, were performed to see the effects of the discount rate on NPVs. Discount rates of 3%, 5%, 7% and 10% were selected.

Table 10 shows that the higher discount rates have a greater probability of producing negative NPVs. As expected, discount rates are lower for nuclear power operators in regulated electricity markets than in liberalized markets. The results support the general observation that the market structure in which an NPP operates makes a significant difference to the economic viability of LTO.

FIG. 6. Monte Carlo simulation results for NPVs with all input parameters.

FIG. 7. Monte Carlo simulation of NPVs at 3% discount rate.

FIG. 8. Monte Carlo simulation of NPVs at 5% discount rate.

TABLE 8. MONTE CARLO SIMULATION: NPV FOR EACH COST INPUT PARAMETER

Cost input parameter Range of NPV Mean Standard deviation

O&M cost 461~755 610 85 (14%)

Refurbishment cost 535~755 645 63 (9.8%)

Decommissioning cost 755~832 794 22 (2.8%)

Spent fuel removal, disposal and storage 704~755 730 15 (2.1%)

TABLE 9. MONTE CARLO SIMULATION: EFFECT OF COST INPUT PARAMETERS ON NPV

Cost input parameter Range of NPV Mean Standard deviation

Electricity price 19~1492 757 428 (56.5%)

Capacity factor 380~755 567 108 (19.0%)

TABLE 7. MONTE CARLO SIMULATION: MINIMUM AND MAXIMUM INPUT PARAMETERS

Parameter Reference value Minimum value Maximum value

Electricity price ($/MW⋅h) 40 30 50

Capacity factor (%) 85 60 85

O&M cost ($/MW⋅h) 13.33 13.33 17.33

(=13.33 × 1.30)

Spent fuel removal, disposal and storage ($/MW⋅h) 2.33 2.33 3.03

(=2.33 × 1.30) Ratio of decommissioning to overnight construction

cost (%) 15 15 20

Refurbishment investment (million $) 650 650 845

(=650 × 1.30)

TABLE 10. MONTE CARLO SIMULATIONS OF NPVs AT VARIOUS DISCOUNT RATES

Discount rate in real terms 3% 5% 7% 10%

Mean NPV ($ million) 411 339 264 130

Standard deviation of NPV ($ million) 423 (103%) 389 (115%) 355 (134%) 320 (246%)

Range of NPV ($ million) -500~1587 -498~1438 -519~1246 -624~1042

Probability of negative NPV 20% 22% 28% 38%

FIG. 6. Monte Carlo simulation results for NPVs with all input parameters.

FIG. 7. Monte Carlo simulation of NPVs at 3% discount rate.

TABLE 8. MONTE CARLO SIMULATION: NPV FOR EACH COST INPUT PARAMETER

Cost input parameter Range of NPV Mean Standard deviation

O&M cost 461~755 610 85 (14%)

Refurbishment cost 535~755 645 63 (9.8%)

Decommissioning cost 755~832 794 22 (2.8%)

Spent fuel removal, disposal and storage 704~755 730 15 (2.1%)

TABLE 9. MONTE CARLO SIMULATION: EFFECT OF COST INPUT PARAMETERS ON NPV

Cost input parameter Range of NPV Mean Standard deviation

Electricity price 19~1492 757 428 (56.5%)

Capacity factor 380~755 567 108 (19.0%)

TABLE 7. MONTE CARLO SIMULATION: MINIMUM AND MAXIMUM INPUT PARAMETERS

Parameter Reference value Minimum value Maximum value

Electricity price ($/MW⋅h) 40 30 50

Capacity factor (%) 85 60 85

O&M cost ($/MW⋅h) 13.33 13.33 17.33

(=13.33 × 1.30)

Spent fuel removal, disposal and storage ($/MW⋅h) 2.33 2.33 3.03

(=2.33 × 1.30) Ratio of decommissioning to overnight construction

cost (%) 15 15 20

Refurbishment investment (million $) 650 650 845

(=650 × 1.30)

TABLE 10. MONTE CARLO SIMULATIONS OF NPVs AT VARIOUS DISCOUNT RATES

Discount rate in real terms 3% 5% 7% 10%

Mean NPV ($ million) 411 339 264 130

Standard deviation of NPV ($ million) 423 (103%) 389 (115%) 355 (134%) 320 (246%)

Range of NPV ($ million) -500~1587 -498~1438 -519~1246 -624~1042

Any decision on whether to pursue LTO should include externalities in the economic assessment of all options.

The difference to the electrical system cost due to externalities is more apparent, when diversifying the power mix.

As nuclear power usually provides baseload electricity, LTO may change the mix of baseload power generators, such as coal and nuclear power operating simultaneously. If there is a cost difference between the power produced by the NPP during LTO and the power produced by the other option, the cost difference should be shown as a cost saving. The total cost revised to reflect externalities due to the LTO option could be used for calculating the NPV.

Typical positive externalities from LTO include electricity price stabilization and carbon emission reductions.

Tools for planning electrical system expansion, such as MESSAGE and WASP⁸, can be used to show the cost effects of LTO on the system. This allows a comparison of electrical system costs with and without LTO.

The cost difference could then be considered in calculating the NPV. As the electrical system costs are a major component of the electricity price, a fall in electricity prices brings about positive externalities on the national economy. When LTO contributes to the stabilization of the electricity price, the contribution needs to be estimated

8 IAEA energy models:

MESSAGE: Model for Energy Supply Strategy Alternatives and their General Environmental Impacts;

WASP: Wien Automatic System Planning Package.

Out module

Cash flows Financial statements Indicators( Ra�os) Computa�on module

Reduced /adapted FINPLAN Input module NPP technical

descrip�on LTO cost es�ma�on Financial assump�ons

FIG. 11. Scheme of LTOFIN. FIG. 9. Monte Carlo simulation of NPVs at 7% discount rate.

FIG. 10. Monte Carlo simulation of NPVs at 10% discount rate.

and added to the benefit side in the economic assessment of extended operation. The value from mitigating GHG emissions with the LTO option should be added to its benefits list. Various approaches could be used to quantify the economic contribution. Sometimes it is convenient to use LCOE to compare economics between LTO and alternative power options. In comparing these LCOEs, the decommissioning cost difference with and without LTO should be considered.