FlexibilityAnalysis.jl

A package for analyzing and quantifying the flexibility of complex systems.

Overview

FlexibilityAnalysis.jl (formerly FlexJuMP.jl) provides a computational framework to analyze and quantify system flexibility. It was originally developed as a JuMP extension to automate the setup and computation of the flexibility index problem with several different types of uncertainty sets. However, it is currently being expanded to compute a number of useful metrics and carry out helpful analyses. Currently, it capabilities include:

• Computing the flexibility index with ellipsoidal, hyperbox, or p-norm uncertainty sets
• Checking nominal point (mean) feasibility
• Computing the stochastic flexibility index via Monte Carlo sampling methods
• Using the flexibility index to expedite the solution to the stochastic flexibility index
• Computing the analytic and feasible centers of the feasible region to better nominal points
• Computing the confidence level which provides a lower bound on the stochastic flexibility index
• Ranking the most limiting system constraints via iterative solution of the flexibility index problem

These techniques are described in greater detail in Background.

Installation

FlexibilityAnalysis.jl is not yet a registered Julia package, but can still be installed by providing the package manager with the url of the repository instead of the name.

using Pkg
Pkg.add("git://github.com/pulsipher/FlexibilityAnalysis.jl.git")

The latest version of FlexibilityAnalysis.jl only supports Julia 1.0 and above. A version is still available for use with Julia 0.6 under the julia-0.6 branch in FlexJuMP.jl.

Quick Start

Below is a brief example of the high-level API, more explanation and examples are provided in User Guide and Examples.

using FlexibilityAnalysis, JuMP
using Gurobi

# Setup the uncertainty set parameters
means = [620; 388; 583; 313]
covar = [11.11 0 0 0; 0 11.11 0 0; 0 0 11.11 0; 0 0 0 11.11]

# Setup the model
m = FlexibilityModel(solver = GurobiSolver(OutputFlag = 0))

# Define variables
@randomvariable(m, T[i = 1:4], mean = means[i])
@recoursevariable(m, Qc)

# Define the constraints
@constraint(m, -0.67Qc + T[2] <= 350)
@constraint(m, 0.5Qc - 0.75T[1] - T[2] - T[3] <= -1388.5)
@constraint(m, -Qc + 1.5T[1] + 2T[2] + T[3] >= 2044)
@constraint(m, Qc - 1.5T[1] - 2T[2] - T[3] - 2T[4] <= -2830)
@constraint(m, -Qc + 1.5T[1] + 2T[2] + T[3] + 3T[4] <= 3153)

# Define the uncertainty set
setuncertaintyset(m, :Ellipsoid, covar)

# Solve
status = solve(m)

# Retrieve optimized data
flexibility_index = getflexibilityindex(m)
conf_lvl = getconfidencelevel(m)
critical_temperatures = getvalue(T)
critical_cooling = getvalue(Qc)
actives_constrs = getactiveconstraints(m)

# Print results
print(flexibility_index)

3.6003393030116135

Outline

• Background
• System Characterization
• Stochastic Flexibility Index Problem
• Flexibility Index Problem
• Uncertainty Set Characterization
• Analysis Techniques
• User Guide
• Model Definition and Setup
• Pre-Solution Methods
• Model Solution
• Post-Solution Methods
• Analysis Methods
• Examples
• Heat Exchanger Network
• IEEE-14 Bus Power Network
• Library
• Module
• Functions/Methods
• DataTypes
• Internals
• Index

Acknowledgements

We acknowledge our support from the Department of Energy under grant DE-SC0014114.