diff --git a/src/core/auxiliary_variables.jl b/src/core/auxiliary_variables.jl
index c2baca4288..c4fc29faad 100644
--- a/src/core/auxiliary_variables.jl
+++ b/src/core/auxiliary_variables.jl
@@ -13,4 +13,18 @@ Auxiliary Variable for Thermal Generation Models that solve for power above min
 """
 struct PowerOutput <: AuxVariableType end
 
+"""
+Auxiliary Variable of DC Current Variables for DC Lines formulations
+
+Docs abbreviation: ``i_l^{dc}``
+"""
+struct DCLineCurrent <: AuxVariableType end
+
+"""
+Auxiliary Variable of DC Current Variables for DC Lines formulations
+
+Docs abbreviation: ``p_l^{loss}``
+"""
+struct DCLineLosses <: AuxVariableType end
+
 convert_result_to_natural_units(::Type{PowerOutput}) = true
diff --git a/src/core/formulations.jl b/src/core/formulations.jl
index 019b7f5b0f..2764fa0dc6 100644
--- a/src/core/formulations.jl
+++ b/src/core/formulations.jl
@@ -163,7 +163,7 @@ struct LossLessLine <: AbstractBranchFormulation end
 """
 DC Loss Line Abstract Model
 """
-struct DCLossLine <: AbstractBranchFormulation end
+struct DCLossyLine <: AbstractBranchFormulation end
 
 ############################## Network Model Formulations ##################################
 # These formulations are taken directly from PowerModels
diff --git a/src/core/variables.jl b/src/core/variables.jl
index 42d5bc0560..3ef58aa05b 100644
--- a/src/core/variables.jl
+++ b/src/core/variables.jl
@@ -168,6 +168,118 @@ Docs abbreviation: ``\\theta``
 """
 struct VoltageAngle <: VariableType end
 
+"""
+Struct to dispatch the creation of Voltage Variables for DC formulations
+
+Docs abbreviation: ``v^{dc}``
+"""
+struct DCVoltage <: VariableType end
+
+"""
+Struct to dispatch the creation of Squared Voltage Variables for DC formulations
+
+Docs abbreviation: ``v^{sq,dc}``
+"""
+struct SquaredDCVoltage <: VariableType end
+
+"""
+Struct to dispatch the creation of DC Converter Current Variables for DC formulations
+
+Docs abbreviation: ``i_c^{dc}``
+"""
+struct ConverterCurrent <: VariableType end
+
+"""
+Struct to dispatch the creation of Squared DC Converter Current Variables for DC formulations
+
+Docs abbreviation: ``i_c^{sq,dc}``
+"""
+struct SquaredConverterCurrent <: VariableType end
+
+"""
+Struct to dispatch the creation of DC Converter Positive Term Current Variables for DC formulations
+
+Docs abbreviation: ``i_c^{+,dc}``
+"""
+struct ConverterPositiveCurrent <: VariableType end
+
+"""
+Struct to dispatch the creation of DC Converter Negative Term Current Variables for DC formulations
+
+Docs abbreviation: ``i_c^{-,dc}``
+"""
+struct ConverterNegativeCurrent <: VariableType end
+
+"""
+Struct to dispatch the creation of DC Converter Binary for Absolute Value Current Variables for DC formulations
+
+Docs abbreviation: `\\nu_c``
+"""
+struct ConverterBinaryAbsoluteValueCurrent <: VariableType end
+
+"""
+Struct to dispatch the creation of Binary Variable for Converter Power Direction
+
+Docs abbreviation: ``\\kappa_c^{dc}``
+"""
+struct ConverterPowerDirection <: VariableType end
+
+"""
+Struct to dispatch the creation of Auxiliary Variable for Converter Bilinear term: v * i
+
+Docs abbreviation: ``\\gamma_c^{dc}``
+"""
+struct AuxBilinearConverterVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Auxiliary Variable for Squared Converter Bilinear term: v * i
+    
+Docs abbreviation: ``\\gamma_c^{sq,dc}``
+"""
+struct AuxBilinearSquaredConverterVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Continuous Interpolation Variable for Squared Converter Voltage
+    
+Docs abbreviation: ``\\delta_c^{v}``
+"""
+struct InterpolationSquaredVoltageVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Binary Interpolation Variable for Squared Converter Voltage
+    
+Docs abbreviation: ``z_c^{v}``
+"""
+struct InterpolationBinarySquaredVoltageVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Continuous Interpolation Variable for Squared Converter Current
+    
+Docs abbreviation: ``\\delta_c^{i}``
+"""
+struct InterpolationSquaredCurrentVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Binary Interpolation Variable for Squared Converter Current
+    
+Docs abbreviation: ``z_c^{i}``
+"""
+struct InterpolationBinarySquaredCurrentVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Continuous Interpolation Variable for Squared Converter AuxVar
+    
+Docs abbreviation: ``\\delta_c^{\\gamma}``
+"""
+struct InterpolationSquaredBilinearVariable <: VariableType end
+
+"""
+Struct to dispatch the creation of Binary Interpolation Variable for Squared Converter AuxVar
+    
+Docs abbreviation: ``z_c^{\\gamma}``
+"""
+struct InterpolationBinarySquaredBilinearVariable <: VariableType end
+
 """
 Struct to dispatch the creation of bidirectional Active Power Flow Variables
 
diff --git a/src/devices_models/device_constructors/hvdcsystems_constructor.jl b/src/devices_models/device_constructors/hvdcsystems_constructor.jl
index 668b41f70e..f95f088640 100644
--- a/src/devices_models/device_constructors/hvdcsystems_constructor.jl
+++ b/src/devices_models/device_constructors/hvdcsystems_constructor.jl
@@ -39,6 +39,112 @@ function construct_device!(
     return
 end
 
+function construct_device!(
+    container::OptimizationContainer,
+    sys::PSY.System,
+    ::ArgumentConstructStage,
+    model::DeviceModel{PSY.InterconnectingConverter, QuadraticLossConverter},
+    network_model::NetworkModel{<:PM.AbstractActivePowerModel},
+)
+    devices = get_available_components(
+        model,
+        sys,
+    )
+    # Add Power Variable
+    add_variables!(container, ActivePowerVariable, devices, QuadraticLossConverter()) # p_c
+    add_variables!(container, ConverterPowerDirection, devices, QuadraticLossConverter()) #κ
+    # Add Current Variables: i, δ^i, z^i, i+, i-
+    add_variables!(container, ConverterCurrent, devices, QuadraticLossConverter()) # i
+    add_variables!(container, SquaredConverterCurrent, devices, QuadraticLossConverter()) # i^sq
+    add_variables!(
+        container,
+        InterpolationSquaredCurrentVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # δ^i
+    add_variables!(
+        container,
+        InterpolationBinarySquaredCurrentVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) #  z^i
+    add_variables!(container, ConverterPositiveCurrent, devices, QuadraticLossConverter()) # i^+
+    add_variables!(container, ConverterNegativeCurrent, devices, QuadraticLossConverter()) # i^- 
+    add_variables!(
+        container,
+        ConverterBinaryAbsoluteValueCurrent,
+        devices,
+        QuadraticLossConverter(),
+    ) # ν
+    # Add Voltage Variables: v^sq, δ^v, z^v
+    add_variables!(container, SquaredDCVoltage, devices, QuadraticLossConverter())
+    add_variables!(
+        container,
+        InterpolationSquaredVoltageVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # δ^v
+    add_variables!(
+        container,
+        InterpolationBinarySquaredVoltageVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # z^v
+    # Add Bilinear Variables: γ, γ^{sq}
+    add_variables!(
+        container,
+        AuxBilinearConverterVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # γ
+    add_variables!(
+        container,
+        AuxBilinearSquaredConverterVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # γ^{sq}
+    add_variables!(
+        container,
+        InterpolationSquaredBilinearVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # δ^γ
+    add_variables!(
+        container,
+        InterpolationBinarySquaredBilinearVariable,
+        devices,
+        QuadraticLossConverter(),
+    ) # z^γ
+    add_to_expression!(
+        container,
+        ActivePowerBalance,
+        ActivePowerVariable,
+        devices,
+        model,
+        network_model,
+    )
+    add_feedforward_arguments!(container, model, devices)
+    return
+end
+
+function construct_device!(
+    container::OptimizationContainer,
+    sys::PSY.System,
+    ::ModelConstructStage,
+    model::DeviceModel{PSY.InterconnectingConverter, QuadraticLossConverter},
+    network_model::NetworkModel{<:PM.AbstractActivePowerModel},
+)
+    devices = get_available_components(
+        model,
+        sys,
+    )
+    # TODO Constraints
+    add_feedforward_constraints!(container, model, devices)
+    objective_function!(container, devices, model, get_network_formulation(network_model))
+    add_constraint_dual!(container, sys, model)
+    return
+end
+
 function construct_device!(
     container::OptimizationContainer,
     sys::PSY.System,
@@ -71,3 +177,35 @@ function construct_device!(
     ::NetworkModel{<:PM.AbstractActivePowerModel},
 )
 end
+
+function construct_device!(
+    container::OptimizationContainer,
+    sys::PSY.System,
+    ::ArgumentConstructStage,
+    model::DeviceModel{PSY.TModelHVDCLine, DCLossyLine},
+    network_model::NetworkModel{<:PM.AbstractActivePowerModel},
+)
+    devices = get_available_components(
+        model,
+        sys,
+    )
+
+    dc_buses = PSY.get_components(
+        DCBus,
+        sys,
+    )
+    add_variables!(container, DCVoltage, dc_buses, DCLossyLine())
+    add_variables!(container, DCLineCurrent, devices, DCLossyLine())
+    add_variables!(container, DCLineLosses, devices, DCLossyLine())
+    add_feedforward_arguments!(container, model, devices)
+    return
+end
+
+function construct_device!(
+    ::OptimizationContainer,
+    sys::PSY.System,
+    ::ModelConstructStage,
+    model::DeviceModel{PSY.TModelHVDCLine, LossLessLine},
+    ::NetworkModel{<:PM.AbstractActivePowerModel},
+)
+end