Transient Problem Specifications

Optimal Gas Flow

The transient optimal gas flow problem optimizes a linear combination of the total compressor power and the total load shed in the system subject to the time-varying pipeline dynamics modeled as ordinary-differential equations (ODEs), discretized using Backward Euler scheme. The readers are referred to this paper or its (arxiv version) for a derivation of the ODEs. Also, note that the Optimal Gas Flow problem currently can work with only time-periodic time-series data. If the data is not time-periodic, then GasModels will try to fit a time-periodic spline to the data and then run the transient optimal gas flow problem.

Model

GasModels.build_transient_ogf — Function

Builds the transient optimal gas flow Nonlinear problem

Variables

GasModels.variable_density — Function

variables associated with density (transient)

GasModels.variable_compressor_flow — Function

variables associated with compressor mass flow (transient)

GasModels.variable_pipe_flux — Function

variables associated with pipe flux (transient)

GasModels.variable_c_ratio — Function

variables associated with compression ratio (transient)

GasModels.variable_injection — Function

variables associated with injection in receipts (transient)

GasModels.variable_withdrawal — Function

variables associated with withdrawal in deliveries (transient)

GasModels.variable_transfer_flow — Function

variables associated with net withdrawal in transfers (transient)

Expressions

The following linear and non-linear expressions are created by the formulation for ease of formulating the constraints

GasModels.expression_density_derivative — Function

density derivative

GasModels.expression_net_nodal_injection — Function

net nodal injection

GasModels.expression_net_nodal_edge_out_flow — Function

net nodal edge flow out

GasModels.expression_non_slack_affine_derivative — Function

non slack affine derivative

GasModels.expression_compressor_power — Function

compression power

Constraints and Constraint Templates

GasModels.constraint_slack_junction_density — Function

Constraint: fixing slack node density value

Template: fixing slack node density value

GasModels.constraint_slack_junction_mass_balance — Function

Constraint: slack junction mass balance

Template: slack junction mass balance

GasModels.constraint_non_slack_junction_mass_balance — Function

Constraint: non-slack junction mass balance

Template: non-slack junction mass balance

GasModels.constraint_pipe_physics_ideal — Function

Constraint: pipe physics with an ideal gas assumption

Template: pipe physics with ideal gas assumption

GasModels.constraint_compressor_physics — Function

Constraint: compressor physics

Template: compressor physics

GasModels.constraint_compressor_power — Function

Constraint: compressor power

Template: compressor power

GasModels.constraint_transfer_separation — Function

Constraint: aggregate withdrawal at transfer points computation

Objective

Three types of objectives are supported by the transient OGF problem (i) a load shedding objective, (ii) a compressor power objective, and (iii) a linear combination of both controlled by the optional argument economic_weighting in the Matlab static file.

GasModels.objective_min_transient_load_shed — Function

minimum load shedding objective for transient OGF problem

GasModels.objective_min_transient_compressor_power — Function

minium compressor power objective for transient OGF problem

GasModels.objective_min_transient_economic_costs — Function

transient objective for minimizing a linear combination of compressor power and load shed