Debugging infeasible models
Getting infeasible solutions to models is a common occurrence in operations simulations, there are multiple reasons why this can happen. PowerSimulations.jl has several tools to help debug this situation.
Adding slacks to the model
One of the most common infeasibility issues observed is due to not enough generation to supply demand, or conversely, excessive fixed (non-curtailable) generation in a low demand scenario.
The recommended solution for any of these cases is adding slack variables to the network model, for example:
template_uc = ProblemTemplate(
NetworkModel(
CopperPlatePowerModel;
use_slacks = true,
),
)will add slack variables to the ActivePowerBalance expression.
In this case, if the problem is now feasible, the user can check the solution of the variables SystemBalanceSlackUp and SystemBalanceSlackDown, and if one value is greater than zero, it represents that not enough generation (for Slack Up) or not enough demand (for Slack Down) in the optimization problem.
Services cases
In many scenarios, certain units are also required to provide reserve requirements, e.g. thermal units mandated to provide up-regulation. In such scenarios, it is also possible to add slack variables, by specifying the service model (RangeReserve) for the specific service type (VariableReserve{ReserveUp}) as:
set_service_model!(
template_uc,
ServiceModel(
VariableReserve{ReserveUp},
RangeReserve;
use_slacks = true,
),
)Again, if the problem is now feasible, check the solution of ReserveRequirementSlack variable, and if it is larger than zero in a specific time-step, then it is evidence that there is not enough reserve available to satisfy the requirement.
Getting the infeasibility conflict
Some solvers allows to identify which constraints and variables are producing the infeasibility, by finding the irreducible infeasible set (IIS), that is the subset of constraints and variable bounds that will become feasible if any single constraint or variable bound is removed.
To enable this feature in PowerSimulations the keyword argument calculate_conflict must be set to true, when creating the DecisionModel. Note that not all solvers allow the computation of the IIS, but most commercial solvers have this capability. It is also recommended to enable the keyword argument store_variable_names=true to help understanding which variables are with infeasibility issues.
The following code creates a decision model with the Xpress optimizer, and enabling the calculate_conflict=true keyword argument.
DecisionModel(
template_ed,
sys_rts_rt;
name = "ED",
optimizer = optimizer_with_attributes(Xpress.Optimizer, "MIPRELSTOP" => 1e-2),
optimizer_solve_log_print = true,
calculate_conflict = true,
store_variable_names = true,
)Here is an example on how the IIS will be displayed as:
Error: Constraints participating in conflict basis (IIS)
│
│ ┌──────────────────────────────────────┐
│ │ CopperPlateBalanceConstraint__System │
│ ├──────────────────────────────────────┤
│ │ (113, 26) │
│ └──────────────────────────────────────┘
│ ┌──────────────────────────────────┐
│ │ EnergyAssetBalance__HybridSystem │
│ ├──────────────────────────────────┤
│ │ ("317_Hybrid", 26) │
│ └──────────────────────────────────┘
│ ┌─────────────────────────────────────────────┐
│ │ PieceWiseLinearCostConstraint__HybridSystem │
│ ├─────────────────────────────────────────────┤
│ │ ("317_Hybrid", 26) │
│ └─────────────────────────────────────────────┘
│ ┌────────────────────────────────────────────────┐
│ │ PieceWiseLinearCostConstraint__ThermalStandard │
│ ├────────────────────────────────────────────────┤
│ │ ("202_STEAM_3", 26) │
│ │ ("101_STEAM_3", 26) │
│ │ ("118_CC_1", 26) │
│ │ ("202_STEAM_4", 26) │
│ │ ("315_CT_6", 26) │
│ │ ("201_STEAM_3", 26) │
│ │ ("102_STEAM_4", 26) │
│ └────────────────────────────────────────────────┘
│ ┌──────────────────────────────────────────────────────────────────────┐
│ │ ActivePowerVariableTimeSeriesLimitsConstraint__RenewableDispatch__ub │
│ ├──────────────────────────────────────────────────────────────────────┤
│ │ ("122_WIND_1", 26) │
│ │ ("324_PV_3", 26) │
│ │ ("312_PV_1", 26) │
│ │ ("102_PV_1", 26) │
│ │ ("101_PV_1", 26) │
│ │ ("324_PV_2", 26) │
│ │ ("313_PV_2", 26) │
│ │ ("104_PV_1", 26) │
│ │ ("101_PV_2", 26) │
│ │ ("309_WIND_1", 26) │
│ │ ("310_PV_2", 26) │
│ │ ("113_PV_1", 26) │
│ │ ("314_PV_1", 26) │
│ │ ("324_PV_1", 26) │
│ │ ("103_PV_1", 26) │
│ │ ("303_WIND_1", 26) │
│ │ ("314_PV_2", 26) │
│ │ ("102_PV_2", 26) │
│ │ ("314_PV_3", 26) │
│ │ ("320_PV_1", 26) │
│ │ ("101_PV_3", 26) │
│ │ ("319_PV_1", 26) │
│ │ ("314_PV_4", 26) │
│ │ ("310_PV_1", 26) │
│ │ ("215_PV_1", 26) │
│ │ ("313_PV_1", 26) │
│ │ ("101_PV_4", 26) │
│ │ ("119_PV_1", 26) │
│ └──────────────────────────────────────────────────────────────────────┘
│ ┌─────────────────────────────────────────────────────────────────────────────┐
│ │ FeedforwardSemiContinuousConstraint__ThermalStandard__ActivePowerVariable_ub │
│ ├─────────────────────────────────────────────────────────────────────────────┤
│ │ ("322_CT_6", 26) │
│ │ ("321_CC_1", 26) │
│ │ ("223_CT_4", 26) │
│ │ ("213_CT_1", 26) │
│ │ ("223_CT_6", 26) │
│ │ ("123_CT_1", 26) │
│ │ ("113_CT_3", 26) │
│ │ ("302_CT_3", 26) │
│ │ ("215_CT_4", 26) │
│ │ ("301_CT_4", 26) │
│ │ ("113_CT_2", 26) │
│ │ ("221_CC_1", 26) │
│ │ ("223_CT_5", 26) │
│ │ ("315_CT_7", 26) │
│ │ ("215_CT_5", 26) │
│ │ ("113_CT_1", 26) │
│ │ ("307_CT_2", 26) │
│ │ ("213_CT_2", 26) │
│ │ ("113_CT_4", 26) │
│ │ ("218_CC_1", 26) │
│ │ ("213_CC_3", 26) │
│ │ ("323_CC_2", 26) │
│ │ ("322_CT_5", 26) │
│ │ ("207_CT_2", 26) │
│ │ ("123_CT_5", 26) │
│ │ ("123_CT_4", 26) │
│ │ ("207_CT_1", 26) │
│ │ ("301_CT_3", 26) │
│ │ ("302_CT_4", 26) │
│ │ ("307_CT_1", 26) │
│ └─────────────────────────────────────────────────────────────────────────────┘
│ ┌───────────────────────────────────────────────────────┐
│ │ RenewableActivePowerLimitConstraint__HybridSystem__ub │
│ ├───────────────────────────────────────────────────────┤
│ │ ("317_Hybrid", 26) │
│ └───────────────────────────────────────────────────────┘
│ ┌───────────────────────────────────────┐
│ │ ThermalOnVariableUb__HybridSystem__ub │
│ ├───────────────────────────────────────┤
│ │ ("317_Hybrid", 26) │
│ └───────────────────────────────────────┘
Error: Serializing Infeasible Problem at /var/folders/1v/t69qyl0n5059n6c1nn7sp8zm7g8s6z/T/jl_jNSREb/compact_sim/problems/ED/infeasible_ED_2020-10-06T15:00:00.jsonNote that the IIS clearly identify that the issue is happening at time step 26, and constraints are related with the CopperPlateBalanceConstraint__System, with multiple upper bound constraints, for the hybrid system, renewable units and thermal units. This highlights that there may not be enough generation in the system. Indeed, by enabling system slacks, the problem become feasible.
Finally, the infeasible model is exported in a json file that can be loaded directly in JuMP to be explored. More information about this is available here.