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Linear Sensitivity Factors
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==========================
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UnitCommitment.jl includes a number of functions to compute typical linear sensitivity
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factors, such as [Injection Shift Factors](@ref) and [Line Outage Distribution Factors](@ref). These sensitivity factors can be used to quickly compute DC power flows in both base and N-1 contigency scenarios.
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Injection Shift Factors
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-----------------------
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Given a network with `B` buses and `L` transmission lines, the Injection Shift Factors (ISF) matrix is an `L`-by-`B` matrix which indicates much power flows through a certain transmission line when 1 MW of power is injected at bus `b` and withdrawn from the slack bus. For example, `isf[:l7, :b5]` indicates the amount of power (in MW) that flows through line `l7` when 1 MW of power is injected at bus `b5` and withdrawn from the slack bus.
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This matrix is computed based on the DC linearization of power flow equations and does not include losses.
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To compute the ISF matrix, the function `injection_shift_factors` can be used. It is necessary to specify the set of lines, buses and the slack bus:
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```julia
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using UnitCommitment
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instance = UnitCommitment.load("ieee_rts/case14")
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isf = UnitCommitment.injection_shift_factors(lines = instance.lines,
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buses = instance.buses,
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slack = :b14)
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@show isf[:l7, :b5]
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```
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Benchmark Model
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===============
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UnitCommitment.jl includes a reference Mixed-Integer Linear Programming
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(MILP), built with [JuMP](https://github.com/JuliaOpt/JuMP.jl), which can
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either be used as-is to solve instances of the problem, or be extended to
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build more complex formulations.
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Building and Solving the Model
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-------------------------------
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Given an instance and a JuMP optimizer, the function `build_model` can be used to
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build the reference MILP model. For example:
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```julia
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using UnitCommitment, JuMP, Cbc
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instance = UnitCommitment.load("ieee_rts/case118")
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model = build_model(instance, with_optimizer(Cbc.Optimizer))
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```
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The model enforces all unit constraints described in [Unit Commitment
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Instances](@ref), including ramping, minimum-up and minimum-down times. Some
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system-wide constraints, such as spinning reserves, are also enforced. The
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model, however, does not enforce transmission or N-1 security constraints,
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since these are typically generated on-the-fly.
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A reference to the JuMP model is stored at `model.mip`. After constructed, the model can
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be optimized as follows:
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```julia
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optimize!(model.mip)
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```
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Decision Variables
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------------------
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References to all decision variables are stored at `model.vars`.
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A complete list of available decision variables is as follows:
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| Variable | Description
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| :---------------------------- | :---------------------------
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| `model.vars.production[gi,t]` | Amount of power (in MW) produced by unit with index `gi` at time `t`.
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| `model.vars.reserve[gi,t]` | Amount of spinning reserves (in MW) provided by unit with index `gi` at time `t`.
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| `model.vars.is_on[gi,t]` | Binary variable indicating if unit with index `gi` is operational at time `t`.
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| `model.vars.switch_on[gi,t]` | Binary variable indicating if unit with index `gi` was switched on at time `t`. That is, the unit was not operational at time `t-1`, but it is operational at time `t`.
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| `model.vars.switch_off[gi,t]` | Binary variable indicating if unit with index `gi` was switched off at time `t`. That is, the unit was operational at time `t-1`, but it is no longer operational at time `t`.
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| `model.vars.unit_cost[gi,t]` | The total cost to operate unit with index `gi` at time `t`. Includes start-up costs, no-load costs and any other production costs.
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| `model.vars.cost[t]` | Total cost at time `t`.
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| `model.vars.net_injection[bi,t]` | Total net injection (in MW) at bus with index `bi` and time `t`. Net injection is defined as the total power being produced by units located at the bus minus the bus load.
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Accessing the Solution
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----------------------
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To access the value of a particular decision variable after the
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optimization is completed, the function `JuMP.value(var)` can be used. The
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following example prints the amount of power (in MW) produced by each unit at time 5:
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```julia
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for g in instance.units
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@show value(model.vars.production[g.index, 5])
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end
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```
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Modifying the Model
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-------------------
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Prior to being solved, the reference model can be modified by using the variable references
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above and conventional JuMP macros. For example, the
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following code can be used to ensure that at most 10 units are operational at time 4:
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```julia
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using UnitCommitment, JuMP, Cbc
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instance = UnitCommitment.load("ieee_rts/case118")
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model = build_model(instance, with_optimizer(Cbc.Optimizer))
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@contraint(model.mip,
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sum(model.vars.is_on[g.index, 4]
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for g in instance.units) <= 10)
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optimize!(model.mip)
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```
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It is not currently possible to modify the constraints included in the
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reference model.
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Reference
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---------
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```@docs
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UnitCommitment.build_model
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```
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Reference in new issue