Variables

binary_gas_connection_flow

Math symbol: $v_{binary\_gas\_connection\_flow}$

Indices: (connection=conn, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: binary_gas_connection_flow_indices

Binary variable with the indices node $n$ over the connection $conn$ in the direction $to\_node$ for the stochastic scenario $s$ at timestep $t$ describing if the direction of gas flow for a pressure drive gas transfer is in the indicated direction.

connection_flow

Math symbol: $v_{connection\_flow }$

Indices: (connection=conn, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: connection_flow_indices

Commodity flow associated with node $n$ over the connection $conn$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

connection_intact_flow

Math symbol: $v_{connection\_intact\_flow}$

Indices: (connection=conn, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: connection_intact_flow_indices

Represents the ptdf-based flow on connections where all investment candidate connections are present in the network.

connections_decommissioned

Math symbol: $v_{connections\_decommissioned}$

Indices: (connection=conn, stochastic_scenario=s, t=t)

Indices function: connections_invested_available_indices

Number of decomissioned connections $conn$ for the stochastic scenario $s$ at timestep $t$

connections_invested

Math symbol: $v_{connections\_invested}$

Indices: (connection=conn, stochastic_scenario=s, t=t)

Indices function: connections_invested_available_indices

Number of connections $conn$ invested at timestep $t$ in for the stochastic scenario $s$

connections_invested_available

Math symbol: $v_{connections\_invested\_available}$

Indices: (connection=conn, stochastic_scenario=s, t=t)

Indices function: connections_invested_available_indices

Number of invested connections $conn$ that are available still the stochastic scenario $s$ at timestep $t$

mp_objective_lowerbound_indices

Math symbol: $v_{mp\_objective\_lowerbound\_indices}$

Indices: (t=t)

Indices function: mp_objective_lowerbound_indices

Updating lowerbound for master problem of Benders decomposition

node_injection

Math symbol: $v_{node\_injection}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: node_injection_indices

Commodity injections at node $n$ for the stochastic scenario $s$ at timestep $t$

node_pressure

Math symbol: $v_{node\_pressure}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: node_pressure_indices

Pressue at a node $n$ for a specific stochastic scenario $s$ and timestep $t$. See also: has_pressure

node_slack_neg

Math symbol: $v_{node\_slack\_neg}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: node_slack_indices

Negative slack variable at node $n$ for the stochastic scenario $s$ at timestep $t$

node_slack_pos

Math symbol: $v_{node\_slack\_pos}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: node_slack_indices

Positive slack variable at node $n$ for the stochastic scenario $s$ at timestep $t$

node_state

Math symbol: $v_{node\_state}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: node_state_indices

Storage state at node $n$ for the stochastic scenario $s$ at timestep $t$

node_voltage_angle

Math symbol: $v_{node\_voltage\_angle}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: node_voltage_angle_indices

Voltage angle at a node $n$ for a specific stochastic scenario $s$ and timestep $t$. See also: has_voltage_angle

nonspin_ramp_down_unit_flow

Math symbol: $v_{nonspin\_ramp\_down\_unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: nonspin_ramp_down_unit_flow_indices

Non-spinning downward reserve commodity flows of unit $u$ at node $n$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

nonspin_ramp_up_unit_flow

Math symbol: $v_{nonspin\_ramp\_up\_unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: nonspin_ramp_up_unit_flow_indices

Non-spinning upward reserve commodity flows of unit $u$ at node $n$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

nonspin_units_shut_down

Math symbol: $v_{nonspin\_units\_shut\_down}$

Indices: (unit=u, node=n, stochastic_scenario=s, t=t)

Indices function: nonspin_units_shut_down_indices

Number of units $u$ held available for non-spinning downward reserve provision via shutdown to node $n$ for the stochastic scenario $s$ at timestep $t$

nonspin_units_started_up

Math symbol: $v_{nonspin\_units\_started\_up}$

Indices: (unit=u, node=n, stochastic_scenario=s, t=t)

Indices function: nonspin_units_started_up_indices

Number of units $u$ held available for non-spinning upward reserve provision via startup to node $n$ for the stochastic scenario $s$ at timestep $t$

ramp_down_unit_flow

Math symbol: $v_{ramp\_down\_unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: ramp_down_unit_flow_indices

Spinning downward ramp commodity flow associated with node $n$ of unit $u$ with node $n$ over the connection $conn$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

ramp_up_unit_flow

Math symbol: $v_{ramp\_up\_unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: ramp_up_unit_flow_indices

Spinning upward ramp commodity flow associated with node $n$ of unit $u$ with node $n$ over the connection $conn$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

shut_down_unit_flow

Math symbol: $v_{shut\_down\_unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: shut_down_unit_flow_indices

Downward ramp commodity flow during shutdown associated with node $n$ of unit $u$ with node $n$ over the connection $conn$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

start_up_unit_flow

Math symbol: $v_{start\_up\_unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: start_up_unit_flow_indices

Upward ramp commodity flow during start-up associated with node $n$ of unit $u$ with node $n$ over the connection $conn$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

storages_decommissioned

Math symbol: $v_{storages\_decommissioned}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: storages_invested_available_indices

Number of decomissioned storage nodes $n$ for the stochastic scenario $s$ at timestep $t$

storages_invested

Math symbol: $v_{storages\_invested}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: storages_invested_available_indices

Number of storage nodes $n$ invested in at timestep $t$ for the stochastic scenario $s$

storages_invested_available

Math symbol: $v_{storages\_invested\_available}$

Indices: (node=n, stochastic_scenario=s, t=t)

Indices function: storages_invested_available_indices

Number of invested storage nodes $n$ that are available still the stochastic scenario $s$ at timestep $t$

unit_flow

Math symbol: $v_{unit\_flow}$

Indices: (unit=u, node=n, direction=d, stochastic_scenario=s, t=t)

Indices function: unit_flow_indices

Commodity flow associated with node $n$ over the unit $u$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$

unit_flow_op

Math symbol: $v_{unit\_flow\_op}$

Indices: (unit=u, node=n, direction=d, i=i, stochastic_scenario=s, t=t)

Indices function: unit_flow_op_indices

Contribution of the unit flow assocaited with operating point i

units_available

Math symbol: $v_{units\_available}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_on_indices

Number of available units $u$ for the stochastic scenario $s$ at timestep $t$

units_invested

Math symbol: $v_{units\_invested}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_invested_available_indices

Number of units $u$ for the stochastic scenario $s$ invested in at timestep $t$

units_invested_available

Math symbol: $v_{units\_invested\_available}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_invested_available_indices

Number of invested units $u$ that are available still the stochastic scenario $s$ at timestep $t$

units_mothballed

Math symbol: $v_{units\_mothballed}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_invested_available_indices

Number of units $u$ for the stochastic scenariocenario $s$ mothballed at timestep $t$

units_on

Math symbol: $v_{units\_on}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_on_indices

Number of online units $u$ for the stochastic scenario $s$ at timestep $t$

units_shut_down

Math symbol: $v_{units\_shut\_down}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_on_indices

Number of units $u$ for the stochastic scenario $s$ that switched to offline status at timestep $t$

units_started_up

Math symbol: $v_{units\_started\_up}$

Indices: (unit=u, stochastic_scenario=s, t=t)

Indices function: units_on_indices

Number of units $u$ for the stochastic scenario $s$ that switched to online status at timestep $t$