PowerModels Utility Functions

This section provides an overview of the some of the utility functions that are implemented as a part of the PowerModels julia package.

Optimization-Based Bound-Tightening for the AC Optimal Power Flow Problem

To improve the quality of the convex relaxations available in PowerModels and also to obtain tightened bounds on the voltage-magnitude and phase-angle difference variables, an optimization-based bound-tightening algorithm is made available as a function in PowerModels. The implementation of this function can be found in src/util/obbt.jl. The algorithm iteratively tightens the bounds on the voltage magnitude and phase-angle difference variables. The function can be invoked on any convex relaxation which explicitly has these variables. By default, the function uses the QC relaxation for performing bound-tightening. Interested readers are refered to the paper "Strengthening Convex Relaxations with Bound Tightening for Power Network Optimization" for an overview of the algorithm. The function can be invoked as follows:

data, stats = run_obbt_opf("case3.m", IpoptSolver());
# data is a dictionary that contains the parsed network data with tightened bounds
# stats is a dictionary that contains some useful information output by algorithm
Dict{String,Any} with 19 entries:
  "initial_relaxation_objective" => 5817.91
  "vm_range_init"                => 0.6
  "final_relaxation_objective"   => 5901.96
  "avg_vm_range_init"            => 0.2
  "final_rel_gap_from_ub"        => NaN
  "run_time"                     => 0.832232
  "model_constructor"            => PowerModels.GenericPowerModel{...}
  "avg_td_range_final"           => 0.436166
  "initial_rel_gap_from_ub"      => Inf
  "sim_parallel_run_time"        => 1.13342
  "upper_bound"                  => Inf
  "vm_range_final"               => 0.6
  "vad_sign_determined"          => 2
  "avg_td_range_init"            => 1.0472
  "avg_vm_range_final"           => 0.2
  "iteration_count"              => 5
  "td_range_init"                => 3.14159
  "td_range_final"               => 1.3085

The optional keyword arguments are self-explantory and can also be found in the function's implementation. The keyword arguments with their defaults are as follows:

model_constructor = QCWRTriPowerModel,
max_iter = 100, 
time_limit = 3600.0,
upper_bound = Inf,
upper_bound_constraint = false, 
rel_gap_tol = Inf,
min_bound_width = 1e-2,
improvement_tol = 1e-3, 
precision = 4,
termination = :avg,

1. The keyword model_constructor specifies the relaxation to use for performing bound-tightening. Currently, it supports any relaxation that has explicit voltage magnitude and phase-angle difference variables.
2. max_iter is the keyword that limits the number of bound-tightening iterations to perform.
3. time_limit is the limit on the computation time of the bound-tightening algorithm in seconds.
4. upper_bound is a keyword that can be used to specify a local feasible solution objective for the AC Optimal Power Flow problem.
5. upper_bound_constraint is a boolean option that can be used to add an additional constraint to reduce the search space of each of the bound-tightening solves. This option cannot be set to true without specifying an upper bound.
6. rel_gap_tol is a tolerance that is used to terminate the algorithm when the objective value of the relaxation is close to the upper bound specified using the upper_bound keyword.
7. min_bound_width, as the name suggests is the variable domain, beyond which point, bound-tightening is not performed for that variable.
8. The bound-tightening algorithm terminates if the improvement in the average or maximum bound improvement, specified using either the termination = :avg or the termination =:max option, is less than improvement_tol.
9. Finally, precision is used to round the tightened bounds to that many decimal digits.