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# PowerSystems Cost Functions | ||
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PowerSystems.jl provides an extensive type hierarchy to explicitly express relationships between power production and cost. This lets the modeler represent cost functions as linear, quadratic, or piecewise input-output curves, potentially piecewise marginal heat rates, average heat rates, and more, as best fits the input data. | ||
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To represent a cost for a particular [`Component`](@ref), the modeler first chooses one of the variable cost representations in the table below. Then, they wrap this [`ProductionVariableCost`](@ref) in either a [`CostCurve`](@ref) to indicate a cost in currency or in a [`FuelCurve`](@ref) to indicate a cost per unit of fuel plus a fuel cost. Finally, the user creates a domain-specific [`OperationalCost`](@ref) that contains this variable cost as well as other costs that may exist in that domain, such as a fixed cost that is always incurred when the unit is on. For instance, we may have `RenewableGenerationCost(CostCurve(TODO), 0.0)` to represent the cost of a renewable unit that produces at TODO, or `ThermalGenerationCost(; variable = FuelCurve(TODO), fixed = TODO, start_up = TODO, shut_down = TODO)` to represent the cost of a thermal unit that produces at TODO. Below, we give the options for `ProductionVariableCost`s. Information on what domain-specific cost must be provided for a given component type can be found in that component type's documentation. | ||
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## Variable Cost Representations | ||
For more details, see the documentation page for each type. | ||
| Type alias | Description | Constructor parameters | Example | | ||
| --- | --- | --- | --- | | ||
| `LinearCurve` | Linear input-output curve with zero no-load cost (constant average rate) | Average/marginal rate | `LinearCurve(3.0)` | | ||
| `LinearCurve` | Linear input-output curve with nonzero no-load cost (constant marginal rate) | Marginal rate, cost at zero production | `LinearCurve(3.0, 5.0)` | | ||
| `QuadraticCurve` | Quadratic input-output curve, may have nonzero no-load cost | Quadratic, proportional, and constant terms of input-output curve | `QuadraticCurve(1.0, 1.0, 18.0)` | | ||
| `PiecewisePointCurve` | Piecewise linear curve specified by cost values at production points | Vector of (production, cost) pairs | `PiecewisePointCurve([(1.0, 20.0), (2.0, 24.0), (3.0, 30.0)])` | | ||
| `PiecewiseIncrementalCurve` | Piecewise linear curve specified by marginal rates (slopes) between production points, may have nonzero initial value | Cost at minimum production point, vector of $n$ production points, vector of $n-1$ marginal rates/slopes of the curve segments between the points | `PiecewiseIncrementalCurve(20., [1.0, 2.0, 3.0], [4.0, 6.0])` | | ||
| `PiecewiseAverageCurve` | Piecewise linear curve specified by average rates between production points, may have nonzero initial value | Cost at minimum production point, vector of $n$ production points, vector of average rates at the $n-1$ latter points | `PiecewiseAverageCurve(20., [1.0, 2.0, 3.0], [12.0, 10.0])` | |
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