NaivePyDECOMP.TransmissionLine package

Module contents

EELT7030 — Operation and Expansion Planning of Electric Power Systems Federal University of Paraná (UFPR)

Package: TransmissionLine

Author

Augusto Mathias Adams <augusto.adams@ufpr.br>

Description

The TransmissionLine package defines the modular representation of transmission circuits for DC power flow formulations within Pyomo-based optimization frameworks. It encapsulates the data structures, variables, symbolic equations, constraints, and builder routines that describe the physical and operational behavior of power transmission networks.

Modules

TransmissionLineDataTypes

Defines the data classes (TransmissionLineUnit, TransmissionLineData) describing the physical and economic characteristics of each circuit, including susceptance, power limits, and endpoints.

TransmissionLineVars

Declares decision variables associated with transmission lines, such as active power flow for each line and time period.

TransmissionLineEquations

Provides symbolic equations that express DC power flow relations and nodal contributions of line flows to system balance.

TransmissionLineConstraints

Implements physical constraints for transmission lines: - DC flow definition: F_ij,t = b_ij (θ_i,t − θ_j,t) - For transport model power flow is just as is - Symmetric flow limits: −pmax_ij ≤ F_ij,t ≤ pmax_ij

TransmissionLineBuilder

High-level model constructor that integrates variables and constraints, assembling the complete transmission-line subsystem for DC power flow models.

Notes

  • The package is designed for hierarchical integration with ConnectionBar modules, forming the complete DC power flow network.

  • The formulation supports both operational (fixed network) and expansion (candidate lines) applications, consistent with the methodologies of DECOMP, DESSEM, and MDI.

  • Each module can be used independently or through the unified builder build_transmission_lines().

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.

Submodules

NaivePyDECOMP.TransmissionLine.TransmissionLineConstraints module

EELT7030 — Operation and Expansion Planning of Electric Power Systems Federal University of Paraná (UFPR)

Module: Transmission Line — Constraints

Author

Augusto Mathias Adams <augusto.adams@ufpr.br>

Description

Defines the physical and operational constraints for transmission lines in DC power flow formulations. These constraints link line flows to phase-angle differences through susceptance and limit the flow magnitude according to each line’s capacity.

Functions

add_transmission_line_flow_constraints(m)

Enforce the DC flow definition: F_ij,t = b_ij (θ_i,t − θ_j,t) for all lines and time periods.

add_transmission_line_flow_limits_constraints(m)

Apply the flow capacity limits: −pmax_ij ≤ F_ij,t ≤ pmax_ij for all lines and time periods.

Notes

  • Each line is characterized by: - b_ij : susceptance (1/x_ij) - pmax_ij : maximum active power flow (MW) - endpoints : list of two bars [i, j]

  • These constraints are suitable for both static (operational) and mixed-integer (expansion) formulations.

  • Phase angles θ_i,t and θ_j,t must exist in the model before these constraints are declared.

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.

NaivePyDECOMP.TransmissionLine.TransmissionLineDataTypes module

EELT7030 — Operation and Expansion Planning of Electric Power Systems Federal University of Paraná (UFPR)

Module: Transmission Line — Data Structures

Author

Augusto Mathias Adams <augusto.adams@ufpr.br>

Description

Defines lightweight data classes for representing transmission lines in DC power flow formulations. Each line connects two connection bars (endpoints), has a specified susceptance and maximum power limit.

These structures serve as standardized inputs for Pyomo-based optimization models, supporting both operational (DCOPF) and expansion (MDI) formulations.

Classes

TransmissionLineUnit

Encapsulates the physical andproperties of a single transmission line or circuit, including endpoints and flow limits.

TransmissionLineData

Aggregates multiple line units along with global configuration parameters such as planning horizon and reference data.

Notes

  • The line susceptance b is defined as the inverse of the series reactance x_ij in per-unit.

  • The endpoints are represented as a list [bar_i, bar_j].

  • The state attribute allows distinguishing between existing (1) and candidate (0) lines for expansion studies.

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.

NaivePyDECOMP.TransmissionLine.TransmissionLineEquations module

EELT7030 — Operation and Expansion Planning of Electric Power Systems Federal University of Paraná (UFPR)

Module: Transmission Line — Symbolic Equations

Author

Augusto Mathias Adams <augusto.adams@ufpr.br>

Description

Defines symbolic expressions for the active power flow on transmission lines under the DC power flow approximation. These expressions are used as intermediate components for nodal balance equations and other network-level constraints.

Functions

add_transmission_line_flow_expression(m, t, flow_dict)

Construct symbolic expressions for each line’s power flow at period t and append them to the supplied dictionary.

add_transmission_line_balance_expression(m, t, balance_dict)

Aggregate inflow and outflow terms for each bar at time t to be used in connection-bar power balance constraints.

Notes

  • The DC power flow model assumes:

    F_ij,t = b_ij (θ_i,t − θ_j,t)

    where:

    • F_ij,t : active power flow (MW)

    • b_ij : susceptance (1/x_ij)

    • θ_i,t : voltage phase angle at bar i (radians)

  • Line flows are positive from the first to the second endpoint in the endpoints list, and negative in the opposite direction.

  • This module produces expressions only; the corresponding constraints are enforced in TransmissionLineConstraints.

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.

NaivePyDECOMP.TransmissionLine.TransmissionLineBuilder module

EELT7030 — Operation and Expansion Planning of Electric Power Systems Federal University of Paraná (UFPR)

Module: Transmission Line — Builder

Author

Augusto Mathias Adams <augusto.adams@ufpr.br>

Description

Provides the high-level construction routine for assembling the transmission line subsystem within DC power flow formulations. This module integrates sets, variables, and constraints that represent line flows, capacity limits, and their relationship with nodal phase angles.

Functions

build_transmission_lines(m)

Create and attach all components of the transmission line subsystem to the given Pyomo model, including variables and constraints.

Notes

  • This module orchestrates the routines from:

    • TransmissionLineVars

    • TransmissionLineConstraints

  • The formulation is consistent with the DC power flow approximation:

    F_ij,t = b_ij (θ_i,t − θ_j,t)

  • The resulting subsystem is compatible with both fixed-network (operational) and mixed-integer (expansion) models.

  • Phase angles θ[b,t] must be declared before calling this builder.

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.

NaivePyDECOMP.TransmissionLine.TransmissionLineBuilder.add_transmission_line_subproblem(m: ConcreteModel, data: TransmissionLineData, stage: bool = False) → ConcreteModel[source]

Attach the transmission-line subsystem to an existing Pyomo model.

This function populates a given ConcreteModel with all sets, parameters, variables, and constraints related to transmission lines under the DC power flow approximation. It forms the network component of the system model, complementing the connection-bar formulation.

Parameters:

  • m (pyomo.environ.ConcreteModel) –

    Pyomo model to which the transmission-line subsystem will be added. The model must contain or be prepared to receive:

    • m.LT : set of transmission lines

    • m.T : set of time periods

    • m.lines_b[l] : susceptance (1/x_ij)

    • m.lines_pmax[l] : flow capacity limit (MW)

    • m.lines_endpoints[l] : list of connected bars [i, j]

    • m.theta[b,t] : phase angle variable (radians)

  • data (TransmissionLineData) – Structured input containing the system horizon and the physical and operational parameters of each transmission line, including endpoints, susceptance, and capacity.

  • stage (int) – the stage subproblem, informed for data copying

Returns:

The same model, augmented with transmission-line sets, variables, and constraints.

Return type:

pyomo.environ.ConcreteModel

Notes

  • Steps performed:

    1. Initialize sets and parameters from TransmissionLineData.

    2. Declare line flow decision variables (lines_flow[l,t]).

    3. Add DC flow definition constraints: F_ij,t = b_ij (θ_i,t − θ_j,t)

    4. Add flow capacity limit constraints: −pmax_ij ≤ F_ij,t ≤ pmax_ij.

  • The order of addition ensures that variables are defined before constraints that depend on them.

  • The formulation is compatible with both pure DC models and hybrid DC/transport formulations (lines marked with model: "transport" are automatically excluded from the DC flow constraint).

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.

NaivePyDECOMP.TransmissionLine.TransmissionLineVars module

EELT7030 — Operation and Expansion Planning of Electric Power Systems Federal University of Paraná (UFPR)

Module: Transmission Line — Sets, Parameters, and Variables

Author

Augusto Mathias Adams <augusto.adams@ufpr.br>

Description

This module defines initialization routines for transmission lines within DC power flow formulations in Pyomo. It provides the sets, parameters, and decision variables associated with transmission circuits, including susceptance, flow limits, and endpoint connectivity between connection bars.

Functions

transmission_line_add_sets_and_params(m, data)

Initialize sets and parameters for transmission lines, including susceptance, flow capacity, and bar-to-bar connectivity.

transmission_line_add_variables(m)

Declare line-level decision variables representing active power flows for each line and time period.

Notes

  • Designed for integration with connection-bar models and other subsystems (hydro, thermal, renewable, storage).

  • The time set m.T is assumed global and will only be created if not already defined.

  • Each line connects two bars defined by its endpoints attribute.

  • The parameters b, pmax and endpoints are initialized directly from the data structure TransmissionLineData.

References

[1] CEPEL, DECOMP / DESSEM. Manuais de Metodologia, 2023. [2] Unsihuay Vila, C. Introdução aos Sistemas de Energia Elétrica,

Lecture Notes, EELT7030/UFPR, 2023.