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.

PowerModels.run_obbt_opf — Function.

Iteratively tighten bounds on 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".

Example

The function can be invoked as follows:

data, stats = run_obbt_opf("matpower/case3.m", JuMP.with_optimizer(Ipopt.Optimizer, kwargs...)

data contains the parsed network data with tightened bounds. stats contains information output from the bounds-tightening algorithm. It looks roughly like

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

Keyword Arguments

model_constructor: relaxation to use for performing bound-tightening. Currently, it supports any relaxation that has explicit voltage magnitude and phase-angle difference variables.
max_iter: maximum number of bound-tightening iterations to perform.
time_limit: maximum amount of time (sec) for the bound-tightening algorithm.
upper_bound: can be used to specify a local feasible solution objective for the AC Optimal Power Flow problem.
upper_bound_constraint: boolean option that can be used to add an additional constraint to reduce the search space of each of the bound-tightening solves. This cannot be set to true without specifying an upper bound.
rel_gap_tol: tolerance used to terminate the algorithm when the objective value of the relaxation is close to the upper bound specified using the upper_bound keyword.
min_bound_width: domain beyond which bound-tightening is not performed.
termination: 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.
precision: number of decimal digits to round the tightened bounds to.

source