Ydinvoimalan kustannus-hyötyanalyysi

Tämä sivu on tietokide alatyypiltään metodi. Sivutunniste: Op_fi4686
Moderaattori:Jouni (katso kaikki) Sivun edistymistä ei ole arvioitu. Arvostuksen määrää ei ole arvioitu (ks. peer review).
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Kysymys

Miten lasketaan suunniteltavan ydinvoimalan kannattavuus käyttöiän aikana?

Perustelut

Data

All data comes from the original Excel file.

Yearly data(€,MW)

Obs	Variable	Uncertainty	Year	Result	Description
1	Oil_price	Oil price 20 % higher		96
2	Oil_price	Oil price same		80
3	Oil_price	Oil price 20 % lower		64
4	New_capacity	2 %/a growth	2015	1860.730594
5	New_capacity	2 %/a growth	2020	5481.175799
6	New_capacity	2 %/a growth	2025	9222.751142
7	New_capacity	2 %/a growth	2030	10084.121
8	New_capacity	2 %/a growth	2035	8859.360731
9	New_capacity	2 %/a growth	2040	8859.360731
10	New_capacity	2 %/a growth	2045	8859.360731
11	New_capacity	2 %/a growth	2050	8859.360731
12	New_capacity	TEM scenario (1.7%/a growth)	2015	1860.730594
13	New_capacity	TEM scenario (1.7%/a growth)	2020	4931.506849
14	New_capacity	TEM scenario (1.7%/a growth)	2025	8105.022831
15	New_capacity	TEM scenario (1.7%/a growth)	2030	8835.616438
16	New_capacity	TEM scenario (1.7%/a growth)	2035	7796.803653
17	New_capacity	TEM scenario (1.7%/a growth)	2040	7796.803653
18	New_capacity	TEM scenario (1.7%/a growth)	2045	7796.803653
19	New_capacity	TEM scenario (1.7%/a growth)	2050	7796.803653
20	New_capacity	1 %/a growth	2015	1860.730594
21	New_capacity	1 %/a growth	2020	3549.657534
22	New_capacity	1 %/a growth	2025	5295.091324
23	New_capacity	1 %/a growth	2030	5696.917808
24	New_capacity	1 %/a growth	2035	5125.570776
25	New_capacity	1 %/a growth	2040	5125.570776
26	New_capacity	1 %/a growth	2045	5125.570776
27	New_capacity	1 %/a growth	2050	5125.570776
28	Demand_change	Demand 1 %/a growth	2015	0
29	Demand_change	Demand 1 %/a growth	2020	4200.913242
30	Demand_change	Demand 1 %/a growth	2025	6563.926941
31	Demand_change	Demand 1 %/a growth	2030	8716.894977
32	Demand_change	Demand 1 %/a growth	2035	9950.913242
33	Demand_change	Demand 1 %/a growth	2040	9950.913242
34	Demand_change	Demand 1 %/a growth	2045	9950.913242
35	Demand_change	Demand 1 %/a growth	2050	9950.913242
36	Demand_change	Demand 0.5 %/a growth TEM scenario	2015	0
37	Demand_change	Demand 0.5 %/a growth TEM scenario	2020	1826.484018
38	Demand_change	Demand 0.5 %/a growth TEM scenario	2025	2853.881279
39	Demand_change	Demand 0.5 %/a growth TEM scenario	2030	3789.954338
40	Demand_change	Demand 0.5 %/a growth TEM scenario	2035	4326.484018
41	Demand_change	Demand 0.5 %/a growth TEM scenario	2040	4326.484018
42	Demand_change	Demand 0.5 %/a growth TEM scenario	2045	4326.484018
43	Demand_change	Demand 0.5 %/a growth TEM scenario	2050	4326.484018
44	Demand_change	Demand 0 %/a growth	2015	0
45	Demand_change	Demand 0 %/a growth	2020	0
46	Demand_change	Demand 0 %/a growth	2025	0
47	Demand_change	Demand 0 %/a growth	2030	0
48	Demand_change	Demand 0 %/a growth	2035	0
49	Demand_change	Demand 0 %/a growth	2040	0
50	Demand_change	Demand 0 %/a growth	2045	0
51	Demand_change	Demand 0 %/a growth	2050	0
52	Fixed_costs_of_new_capacity		2015	6144
53	Fixed_costs_of_new_capacity		2020	0
54	Fixed_costs_of_new_capacity		2025	0
55	Fixed_costs_of_new_capacity		2030	0
56	Fixed_costs_of_new_capacity		2035	0
57	Fixed_costs_of_new_capacity		2040	0
58	Fixed_costs_of_new_capacity		2045	0
59	Fixed_costs_of_new_capacity		2050	0
60	New_capacity_of_interest		2015	0
61	New_capacity_of_interest		2020	440
62	New_capacity_of_interest		2025	1100
63	New_capacity_of_interest		2030	1100
64	New_capacity_of_interest		2035	1100
65	New_capacity_of_interest		2040	1100
66	New_capacity_of_interest		2045	1100
67	New_capacity_of_interest		2050	1100

Monthly variables(MWh/week)

Obs	Variable	Month	Result	Description
1	Dthermal	Weeks 1 to 4	4328000
2	Dthermal	Weeks 5 to 8	4304750
3	Dthermal	Weeks 9 to 12	4246750
4	Dthermal	Weeks 13 to 16	3881000
5	Dthermal	Weeks 17 to 20	3226250
6	Dthermal	Weeks 21 to 24	2822750
7	Dthermal	Weeks 25 to 28	2661500
8	Dthermal	Weeks 29 to 32	2585250
9	Dthermal	Weeks 33 to 36	2904500
10	Dthermal	Weeks 37 to 40	3255750
11	Dthermal	Weeks 41 to 44	3757250
12	Dthermal	Weeks 45 to 48	4120000
13	Dthermal	Weeks 49 to 52	4220750
14	Dthermal_sd	Weeks 1 to 4	448471.90225
15	Dthermal_sd	Weeks 5 to 8	372222.83725
16	Dthermal_sd	Weeks 9 to 12	431200.65775
17	Dthermal_sd	Weeks 13 to 16	530007.6645
18	Dthermal_sd	Weeks 17 to 20	539874.6175
19	Dthermal_sd	Weeks 21 to 24	514974.322
20	Dthermal_sd	Weeks 25 to 28	515219.12525
21	Dthermal_sd	Weeks 29 to 32	543795.49475
22	Dthermal_sd	Weeks 33 to 36	446860.6225
23	Dthermal_sd	Weeks 37 to 40	316494.73225
24	Dthermal_sd	Weeks 41 to 44	420111.4905
25	Dthermal_sd	Weeks 45 to 48	487450.071
26	Dthermal_sd	Weeks 49 to 52	490019.918
27	dummies	Weeks 1 to 4	490300
28	dummies	Weeks 5 to 8	589230
29	dummies	Weeks 9 to 12	571340
30	dummies	Weeks 13 to 16	198190
31	dummies	Weeks 17 to 20	-317120
32	dummies	Weeks 21 to 24	-684420
33	dummies	Weeks 25 to 28	-849080
34	dummies	Weeks 29 to 32	-851290
35	dummies	Weeks 33 to 36	-664640
36	dummies	Weeks 37 to 40	-371490
37	dummies	Weeks 41 to 44	0
38	dummies	Weeks 45 to 48	218750
39	dummies	Weeks 49 to 52	288840

Other parameters(-)

Obs	Parameter	Unit	Value	Description
1	discount_rate	1 /a	0.04
2	new_capacity_marginal_cost		12
3	beta.0		589000
4	beta.oil		-23987
5	beta.eua		0
6	beta.p		1185400
7	price.eua		0
8	price.feed		0
9	price.ceiling		2000
10	noise_step		0.1
11	grid_points	#	101

Laskenta

Nuclear investment calculator. Copyright James Corbishley and Matti Liski 2014 Original calculator in Excel [1].

+ Näytä koodi- Piilota koodi library(OpasnetUtils) library(ggplot2) #rm(Dthermal_noisegrid, k.new, ElPrice, average_monthly_price, marginal_costs_for_the_new_capacity, nominal_costs) ##### RESULTS SHEET #### Locations in the Excel sheet # average_monthly_price (€/MWh) # discount_rate # noisedens calculations.2015!E5:DA5 # expected_price calculations.2015!B68:B80 # ElPrice calculations.2015 E68:DA80 # k.new calculations.2015!E53:DA65 and parameters!D50:K62 (MWh per week) # Dthermal_noisegrid calculations.2015!E38:DA50 # dummies parameters!D78:D90 # beta.0 parameters!D72 # beta.oil parameters!D73 # beta.eua parameters!D74 # beta.p parameters!D75 # price.ceiling parameters!D66 # price.oil results!C5:J5 and scenarios!C25:J25 # new_capacity_of_interest (MW) # new_capacity_marginal_cost (€/MWh) # noisedens calculations.2015!E5:DA5 # noisegridbase calculation.2015!E3:DA3 # Dthermal_sd calculations.2015!E23:DA35 # noise_step parameters!D65 # grid_points parameters!D66 # Dthermal parameters!A5:A17 # estimated demand data: weekly average thermal demands in GWh # Dthermal_sd parameters!A20:A32 # standard deviations of demand shock for each week (GWh/month) ###### INDICES AND FUNCTIONS year <- seq(2015, 2050, 5) month = c( "Weeks 1 to 4", "Weeks 5 to 8", "Weeks 9 to 12", "Weeks 13 to 16", "Weeks 17 to 20", "Weeks 21 to 24", "Weeks 25 to 28", "Weeks 29 to 32", "Weeks 33 to 36", "Weeks 37 to 40", "Weeks 41 to 44", "Weeks 45 to 48", "Weeks 49 to 52" ) tim <- Ovariable("time", data = data.frame( Year = year, Result = year )) tim0 <- 2015 ERF <- function(x) { result(x) <- 2 * pnorm(result(x) * sqrt(2)) - 1 # Use pnorm to produce the error function (ERF in Excel) functionality. return(x) } cumfun <- function(x, cols) { # integrates an ovariable over a numerical index. ind <- as.numeric(as.character(unique(x@output[[cols[1]]]))) intmatrix <- (Ovariable(output = data.frame(temp = ind, Result = ind), marginal = c(TRUE, FALSE)) <= Ovariable(output = data.frame(temp2 = ind, Result = ind), marginal = c(TRUE, FALSE))) * 1 colnames(intmatrix@output)[colnames(intmatrix@output) == "temp"] <- cols[1] out <- oapply(x * intmatrix, cols = cols, FUN = sum) # You can sum over several indices but integrate only over the first in cols. colnames(out@output)[colnames(out@output) == "temp2"] <- cols[1] # out <- unkeep(out, cols = c("tempResult", "tempSource", "temp2Result", "temp2Source")) return(out) } ##### USER INPUTS yearly <- opbase.data("Op_fi4686.yearly_data") monthly <- opbase.data("Op_fi4686.monthly_variables") parameters <- opbase.data("Op_fi4686.other_parameters") oil <- yearly[yearly$Variable == "Oil_price" , ! colnames(yearly) %in% c("Variable", "Year", "Obs")] colnames(oil)[colnames(oil) == "Uncertainty"] <- "Oil_price" price.oil <- Ovariable("price.oil", data = oil) capacity <- yearly[yearly$Variable == "New_capacity" , ! colnames(yearly) %in% c("Variable", "Obs") ] colnames(capacity)[colnames(capacity) == "Uncertainty"] <- "New_capacity" new_capacity_other <- Ovariable("new_capacity_other", data = capacity) demand <- yearly[yearly$Variable == "Demand_change" , ! colnames(yearly) %in% c("Variable", "Obs") ] colnames(demand)[colnames(demand) == "Uncertainty"] <- "Demand_change" change_in_demand <- Ovariable("change_in_demand", data = demand) costs <- yearly[yearly$Variable == "Fixed_costs_of_new_capacity" , ! colnames(yearly) %in% c("Variable", "Uncertainty", "Obs") ] fixed_costs_of_new_capacity <- Ovariable("fixed_costs_of_new_capacity", data = costs) interest <- yearly[yearly$Variable == "New_capacity_of_interest" , ! colnames(yearly) %in% c("Variable", "Uncertainty", "Obs") ] new_capacity_of_interest <- Ovariable("new_capacity_of_interest", data = interest) ##### CONSTANTS discount_rate <- parameters$Result[parameters$Parameter == "discount_rate"] new_capacity_marginal_cost <- parameters$Result[parameters$Parameter == "new_capacity_marginal_cost"] #(e€/MWh) constant beta.0 <- parameters$Result[parameters$Parameter == "beta.0"] beta.oil <- parameters$Result[parameters$Parameter == "beta.oil"] beta.eua <- parameters$Result[parameters$Parameter == "beta.eua"] beta.p <- parameters$Result[parameters$Parameter == "beta.p"] price.eua <- parameters$Result[parameters$Parameter == "price.eua"] # Price - EU emission permits price.feed <- parameters$Result[parameters$Parameter == "price.feed"] # Feed in tariff price floor price.ceiling <- parameters$Result[parameters$Parameter == "price.ceiling"] noise_step <- parameters$Result[parameters$Parameter == "noise_step"] grid_points <- parameters$Result[parameters$Parameter == "grid_points"] dummies <- Ovariable("dummies", data = monthly[monthly$Variable == "dummies" , ! colnames(monthly) %in% c("Variable", "Obs") ] ) Dthermal <- Ovariable("Dthermal", data = monthly[monthly$Variable == "Dthermal" , ! colnames(monthly) %in% c("Variable", "Obs") ] ) Dthermal_sd <- Ovariable("Dthermal_sd", data = monthly[monthly$Variable == "Dthermal_sd" , ! colnames(monthly) %in% c("Variable", "Obs") ] ) ###### ACTUAL MODEL discount_factor <- 1 / (1 + discount_rate) ^ (tim - tim0) d <- (grid_points - 1) / 2 * noise_step noisegridbase <- Ovariable("noisegridbase", data = data.frame( Grid = seq(-d, d, noise_step), Result = seq(-d, d, noise_step) )) Dthermal_noisegrid <- Dthermal + noisegridbase * Dthermal_sd result(Dthermal_noisegrid)[result(Dthermal_noisegrid) < 0] <- 0 k.additional <- (new_capacity_of_interest + new_capacity_other - change_in_demand) * 24 * 7 k.new <- new_capacity_of_interest * 24 * 7 ElPrice <- exp((1 / beta.p) * (Dthermal_noisegrid - k.additional - beta.0 - beta.oil * price.oil - beta.eua * price.eua - dummies)) result(ElPrice)[result(ElPrice) < 0] <- 0 result(ElPrice)[result(ElPrice) > price.ceiling] <- price.ceiling noisedens <- 1/2 * (ERF((noisegridbase + noise_step / 2)/sqrt(2)) - ERF((noisegridbase - noise_step / 2)/sqrt(2))) average_monthly_price <- oapply(ElPrice * noisedens, cols = "Grid", FUN = sum) # (€/MWh) marginal_costs_for_the_new_capacity <- new_capacity_marginal_cost * k.new / 10^6 * 4 * 13 # There are 13 28-day months revenue_for_the_new_capacity <- average_monthly_price * k.new / 10^6 * 4 revenue_for_the_new_capacity <- oapply(unkeep(revenue_for_the_new_capacity, prevresults = TRUE, sources = TRUE), cols = "Month", FUN = sum) ###nominal analysis (euros millions) nominal_costs <- -1 * fixed_costs_of_new_capacity - marginal_costs_for_the_new_capacity * 5 # (M€ per 5 a) nominal_revenues <- revenue_for_the_new_capacity * 5 # (M€ per 5 a) nominal_net_revenues <- nominal_revenues + nominal_costs cumulative_net_revenues <- cumfun(nominal_net_revenues, cols = "Year") ###integrated over time ###present value analysis (euros millions) present_costs <- nominal_costs * discount_factor present_revenues <- nominal_revenues * discount_factor present_net_revenues <- nominal_net_revenues * discount_factor present_cumulative_net_revenues <- cumfun(present_net_revenues, cols = "Year") ###integrated over time. ggplot(present_cumulative_net_revenues@output, aes(x = Year, weight = Result, fill = Oil_price)) + geom_bar(position = "dodge") + facet_grid(New_capacity ~ Demand_change)

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