Cost curves for energy: Difference between revisions
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coefficients[j, 1:length(curves[[j]])] <- curves[[j]] | coefficients[j, 1:length(curves[[j]])] <- curves[[j]] | ||
} | } | ||
coefficients[nrow(coefficients) + 1, 1] <- x$deviation | |||
for(k in 1:ncol(coefficients)) { | for(k in 1:ncol(coefficients)) { | ||
coefficients[, k] <- ifelse(is.na(coefficients[, k]), 0, as.numeric(coefficients[, k])) | coefficients[, k] <- ifelse(is.na(coefficients[, k]), 0, as.numeric(coefficients[, k])) | ||
} | } | ||
x.new <- polyroot(as.vector(colSums(coefficients))) | x.new <- polyroot(as.vector(colSums(coefficients))) | ||
x.new <- | 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)) { | for(k in 1:ncol(coefficients)) { | ||
y.new <- y.new + coefficients[, k] * x.new^(k-1) | |||
} | } | ||
cat("Computed changes in energy production and consumption in a new situation.\n") | |||
return(y.new) | |||
return( | |||
} | } | ||
dependencies.Op_en5478 <- list( | dependencies.Op_en5478 <- list( | ||
curves = c("Op_en5478", "Cost curves for energy") | curves = c("Op_en5478", "Cost curves for energy"), | ||
bau = c("Op_en5469", "Energy balance in Kuopio"), | |||
deviation = -5 | |||
) | ) | ||
Revision as of 12:43, 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 | Parameters | 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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