Cost curves for energy: Difference between revisions
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== Answer == | == Answer == | ||
<t2b index="Actor | <t2b index="Row,Actor,Fuel,Use,Reference,Unit,Observation" locations="Result,Description" unit="-"> | ||
1|Kuopion energia|Coal and peat|Demand|Current|€,ton|0, -0.06| | |||
2|Kuopio market|Coal and peat|Supply|Current|€,ton|0, 0.5| | |||
</t2b> | </t2b> | ||
Parameter c<sub>i</sub> are estimated from data: it is the current supply or demand given the current price (used as the point where p = 0). | |||
<rcode | |||
name="answer" | |||
label="Run code" | |||
include=" | |||
page:Object-oriented_programming_in_Opasnet|name:answer| | |||
page:OpasnetBaseUtils|name:generic| | |||
page:Cost_curves_for_energy|name:formula | |||
" | |||
> | |||
out <- formula.Op_en5478(dependencies.Op_en5478) | |||
cat("Computed changes in energy production and consumption in a new situation.\n") | |||
print(out) | |||
</rcode> | |||
== Rationale == | == Rationale == | ||
For detailed rationale, see [[Energy balance]]. | |||
<math>\Sigma f_i(p) = \Sigma (a_i p^2 + b_i p + c_i) = 0</math> | |||
<math>p = \frac{-\Sigma b_i \pm \sqrt{(\Sigma b_i)^2 - 4 \Sigma a_i \Sigma c_i}} {2 \Sigma a_i}</math> | |||
Cost curves are parameterised in the way that the current price p = 0 and therefore the current supply or demand is c<sub>i</sub>. | |||
When a demand or supply changes, a new price p must be calculated based on f<sub>i</sub>, and then the supplies and demands of other actors can be calculated, resulting in a new balance. | |||
{{comment|# |There is an alternative way to describe the functions: | |||
* Zero price is considered as 0 €/product unit. The true market price must be known. This function's parameters are more difficult to estimate.|--[[User:Jouni|Jouni]] 06:16, 28 January 2012 (EET)}} | |||
{{comment|# |There is also alternative possibilities for functional forms (p is the price of the product): | |||
* Exponential: P0 + P1 * exp(P2*p - P3) | |||
|--[[User:Jouni|Jouni]] 17:04, 28 January 2012 (EET)}} | |||
=== Dependencies === | === Dependencies === | ||
=== Formula === | === Formula === | ||
<rcode | |||
name="formula" | |||
label="Initiate functions" | |||
include=" | |||
page:Object-oriented_programming_in_Opasnet|name:answer| | |||
page:OpasnetBaseUtils|name:generic | |||
" | |||
> | |||
formula.Op_en5478 <- function(x) { | |||
data <- tidy(op_baseGetData("opasnet_base", x$curves[1]), direction = "wide") | |||
curves <- strsplit(as.character(data$Parameters), split = ",") | |||
coefficients <- data.frame(array(NA, dim = c(length(curves), 10))) | |||
for(j in 1:length(curves)) { | |||
coefficients[j, 1:length(curves[[j]])] <- curves[[j]] | |||
} | |||
coefficients[nrow(coefficients) + 1, 1] <- x$deviation | |||
for(k in 1:ncol(coefficients)) { | |||
coefficients[, k] <- ifelse(is.na(coefficients[, k]), 0, as.numeric(coefficients[, k])) | |||
} | |||
x.new <- polyroot(as.vector(colSums(coefficients))) | |||
x.new <- ifelse(abs(Im(x.new)) < 1e-6, Re(x.new), 1e+30) # Take only the real roots. | |||
x.new <- x.new[abs(x.new) == min(abs(x.new))] # Pick the root that is closest to zero (=BAU). | |||
y.new <- 0 | |||
for(k in 1:ncol(coefficients)) { | |||
y.new <- y.new + coefficients[, k] * x.new^(k-1) | |||
} | |||
temp <- data[1, ] | |||
temp[1, ] <- "Deviation" | |||
data <- rbind(data, temp) | |||
data <- cbind(data, data.frame(Result = y.new)) | |||
return(data) | |||
} | |||
dependencies.Op_en5478 <- list( | |||
curves = c("Op_en5478", "Cost curves for energy"), | |||
bau = c("Op_en5469", "Energy balance in Kuopio"), | |||
deviation = -5 | |||
) | |||
</rcode> | |||
==See also== | ==See also== | ||
Latest revision as of 14:44, 5 May 2012
| Moderator:Jouni (see all) |
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Question
What costs curves should be used for different energy products?
Answer
| Obs | Row | Actor | Fuel | Use | Reference | Unit | Result | Description |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | Kuopion energia | Coal and peat | Demand | Current | €,ton | 0, -0.06 | |
| 2 | 2 | Kuopio market | Coal and peat | Supply | Current | €,ton | 0, 0.5 |
Parameter ci are estimated from data: it is the current supply or demand given the current price (used as the point where p = 0).
Rationale
For detailed rationale, see Energy balance.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Sigma f_i(p) = \Sigma (a_i p^2 + b_i p + c_i) = 0}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p = \frac{-\Sigma b_i \pm \sqrt{(\Sigma b_i)^2 - 4 \Sigma a_i \Sigma c_i}} {2 \Sigma a_i}}
Cost curves are parameterised in the way that the current price p = 0 and therefore the current supply or demand is ci.
When a demand or supply changes, a new price p must be calculated based on fi, and then the supplies and demands of other actors can be calculated, resulting in a new balance.
----#: . There is an alternative way to describe the functions:
- Zero price is considered as 0 €/product unit. The true market price must be known. This function's parameters are more difficult to estimate. --Jouni 06:16, 28 January 2012 (EET) (type: truth; paradigms: science: comment)
----#: . There is also alternative possibilities for functional forms (p is the price of the product):
- Exponential: P0 + P1 * exp(P2*p - P3) --Jouni 17:04, 28 January 2012 (EET) (type: truth; paradigms: science: comment)
Dependencies
Formula
See also
Keywords
References
Related files
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