Building reactors in series usually leads to a significant per-unit cost reduction. This is due to better construction work organisation, learning effect, larger volumes of orders for the plant equipment and other factors. However, the first-of-a-kind (FOAK) power plant is usually considerably more expensive than subsequent units.

Reference [6.4] suggests an algorithm, based on the French experience, (see Table 6.8) to calculate FOAK plant effects in the overnight capital cost and cost reductions from building more than one serial plant on a site:

The main parameters of this algorithm are:

-x: FOAK extra cost parameter

-y: parameter related to the gain in building a pair of units.

— z: parameter related to the gain in building two pairs of units on the same site.

-k: industrial productivity coefficient.

Productivity effect Cost of the last unit (multiplicative factor) (in a box)
Plant configuration	Total cost of the plant
	(1+x)To
FOAK
(1+x+y)T0 z
1+k 1
ЛШ
T
(1 + k)2

The industrial productivity coefficient k=0%-2%,

FOAK extra cost parameter x=15-55%,

Parameter related to the gain in building a pair of units y=74%-85%,

Parameter related to the gain in building two pairs of units on the same site z=82%-95% [49] [50]

Reference [6.4] suggests the following values of the parameters (based on the French experience):

x=15% to 55%, according to the nature and amount of changes in the design.

y=74%-85%

z=82%-95%

k=0%-2% (6.8)

According to (6.6) and (6.8), the FOAK plant could be 15% to 55% (35% on average) more expensive than the next ones (built at a site).

For the first and second pair of non-FOAK twin-units on the site, based on (6.6) and (6.8), the per-unit cost reduction factors would be:

1+y

Per unit cost reduction factor for twin units (first pair) = —^—=0.87 — 0.93 Per unit cost reduction factor for twin units (second pair)=1 x (Z — + ^ ) =0.76 — 0.9 (6.9)

(1+y+T+k+0+k)2)

If two pairs of non-FOAK twin-units are built on the site, the per unit overnight cost reduction may be as substantial as:

A reduction such as (6.10) is quite significant but it would not be sufficient to compensate the specific investment cost increase because of the scaling law (6.3).

Example: The cost of 4 non-FOAK 300 MWe versus 1 non-FOAK 1200 MWe

As an example, let us consider four non-FOAK 300 MWe PWRs (integral design or marine — type) built on the same site, and compare them to one large non-FOAK 1200 MWe PWR. In this case one should include the effects of economy from building subsequent units on the same site (equation [6.10]), simplification of the design (6.4) or (6.5), take into account the decrease of the cost of financing (due to reduction of the construction period from 6 to 3 years, see Figure 6.4), and multiply the result by the scaling factor (from 1 200 MWe to 300 MWe, see Table 6.7). The results are given in the Table 6.9.

From Table 6.9 it could be seen that, within the assumptions made, four integral type or marine derivative PWRs of 300 MWe class (and not FOAK) built on the same site may have the effective per unit specific overnight capital costs of about 10-40% higher (at n=0.5-0.6 and a 5% discount rate) compared to those of a NPP with a single large PWR of 1 200 MWe.

Similar results for almost identical case studies were obtained by the Westinghouse Electric Company [6.5]. In their case, the construction duration was assumed to be five years for the large plant and three years for each of the SMRs, the annual interest rate was 5%, and the scaling factor used (1.74) corresponds to n=0.6. They found that the specific capital cost of a 300 MWe PWR versus specific capital cost of a 1 200 MWe reactor of the same type would be increased by about 4% (compared to 10-22 % in our case, see Table 6.9 at n=0.6 and a 5% discount rate).

Table 6.9. Effective per unit specific (per kWe) overnight capital cost for the case of four 300 MWe marine derivative or integral design PWRs built on one site for different parameters of the scaling law Factors Scaling exponent and the corresponding factor n=0.4: n=0.5: X 2.30 x 2.00 n=0.6: n=0.7: X 1.74 x 1.52 Economy on cost of financing due to construction period reduction from 6 to 3 years Interest rate 5%: X 0.92 Interest rate 10%: X 0.86 Economy from building 4 subsequent units on the same site x (0.81-0.9 ) Design simplification factor x 0.85

Specific capital cost of a 300 MWe PWR versus specific capital cost of a 1 200 MWe reactor belonging to the same technology line Total factor between 4 SMRs of 300 MWE and one large reactor of 1 200 MWe (product of the above factors) n=0.4 n=0.5 n=0.6 n=0.7 Interest rate 5% 1.46-1.62 1.27-1.41 1.10-1.22 0.96-1.07 Interest rate 10% 1.36-1.51 1.18-1.32 1.03-1.14 0.90-1.00

The effects defined by the parametric equations (6.6), (6.7) and (6.8) include both, learning in construction (parameters x and z) and in factory fabrication (parameter k), and sharing of common facilities and systems on the site (parameters y and z). An important assumption regarding learning is that the costs of engineering and facilities for each site are identical, which means similarity of the sites. Otherwise, the learning effects may be not observed.

The international and national NPP build experience, specifically, that of the Russian Federation and Canada [6.5] indicates that learning will not apply:

• if NPPs are consequently built in different countries;

• if there are regulatory changes in a country during the next NPP build;

• if siting conditions for the consecutive plants are essentially different; and

• if the interval between building consecutive plants is too long.

The last effect of a “too long” interval between consecutive plants building is illustrated by Figure 6.5. It is based on the OKBM Afrikantov[51] experience in factory fabrication of the marine propulsion reactors in the Russian Federation [6.9]. As it can be seen from the figure, for the case of full factory fabricated nuclear plants the requirements of continuity are quite strict, with notable increase in labour intensity observed even for a one-year break in the production process (unit number 3 on Figure 6.5).

Table 6.10. Effective per module specific (per kWe) overnight capital cost for the case of a five — or a six — module NPP with 300 MWe marine derivative or integral design PWR modules Factors Scaling exponent and the corresponding factor n=0.5: X 2.24 n=0.6: X 1.904 Economy on cost of financing due to construction period reduction from 6 to 3 years Interest rate 5%: X 0.92 Interest rate 10%: X 0.86 Economy from building 5 subsequent units on the same site Factor (1 +y)/2 reduced by 15-17%: X (0.72-0.79) Design simplification factor x 0.85 Specific capital cost of a 300 MWe PWR versus specific capital cost of a 1 500 MWe reactor belonging to the same technology line Total factor between 5 SMRs of 300 MWE and one large reactor of 1 500 MWe (product of the above factors) n=0.5 n=0.6 Interest rate 5% 1.26 — 1.38 1.07 — 1.18 Interest rate 10% 1.17 — 1.29 1.00 — 1.10