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 gastransfer 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

Hypothetical flow associated with node $n$ over the connection $conn$ in the direction $d$ for the stochastic scenario $s$ at timestep $t$ assuming all candidate connections are in place. See connection_investment_power_flow_impact_active

connections_decommissioned

Math symbol: $v^{connections\_decommissioned}$

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

Indices function: connections_invested_available_indices

Number of decommissioned 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 in at timestep $t$ 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 $conn$ available for the stochastic scenario $s$ at timestep $t$

min_capacity_margin_slack

Math symbol: $v^{min\_capacity\_margin\_slack}$

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

Indices function: min_capacity_margin_slack_indices

Shortfall of the capacity margin at node $n$ below capacity_margin_min for the stochastic scenario $s$ at timestep $t$. Penalised with capacity_margin_penalty

mp_min_res_gen_to_demand_ratio_slack

Math symbol: $v^{mp\_min\_res\_gen\_to\_demand\_ratio\_slack}$

Indices: (grid=g)

Indices function: mp_min_res_gen_to_demand_ratio_slack_indices

Shortfall of the renewable generation share of grid $g$ below mp_min_res_gen_to_demand_ratio in the Benders master problem. Penalised with mp_min_res_gen_to_demand_ratio_slack_penalty

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

Pressure at node $n$ for a specific stochastic scenario $s$ and timestep $t$. See: physics_type

node_slack_neg

Math symbol: $v^{node\_slack\_neg}$

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

Indices function: node_slack_indices

Slack variable that removes commodity from node $n$ (excess supply) for the stochastic scenario $s$ at timestep $t$. Penalised with balance_penalty

node_slack_pos

Math symbol: $v^{node\_slack\_pos}$

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

Indices function: node_slack_indices

Slack variable that adds commodity to node $n$ (supply shortfall e.g. unserved demand) for the stochastic scenario $s$ at timestep $t$. Penalised with balance_penalty

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_state_longterm

Math symbol: $v^{node\_state\_longterm}$

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

Indices function: node_state_longterm_indices

Long-term storage state at node $n$ for the stochastic scenario $s$ at timestep $t$ used for seasonal storage scheduling across representative periods

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 node $n$ for a specific stochastic scenario $s$ and timestep $t$. See: physics_type

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 $t$

sp_objective_upperbound

Math symbol: $v^{sp\_objective\_upperbound}$

Indices: (t=t)

Indices function: sp_objective_upperbound_indices

Estimate of the subproblem objective value in the Benders master problem for the current optimisation window $t$. Constrained by the Benders cuts

storages_decommissioned

Math symbol: $v^{storages\_decommissioned}$

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

Indices function: storages_invested_available_indices

Number of decommissioned 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 $n$ available for 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 associated with operating point $i$

unit_flow_op_active

Math symbol: $v^{unit\_flow\_op\_active}$

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

Indices function: unit_flow_op_indices

Control the activation of operating point $i$ of units

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 $u$ available for 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 $u$ mothballed at timestep $t$ for the stochastic scenario $s$

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_out_of_service

Math symbol: $v^{units\_out\_of\_service}$

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

Indices function: units_out_of_service_indices

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

units_returned_to_service

Math symbol: $v^{units\_returned\_to\_service}$

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

Indices function: units_out_of_service_indices

Number of units $u$ returned to service after an outage 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 $t$

units_taken_out_of_service

Math symbol: $v^{units\_taken\_out\_of\_service}$

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

Indices function: units_out_of_service_indices

Number of units $u$ taken out of service for an outage for the stochastic scenario $s$ at timestep $t$

user_constraint_slack_pos

Math symbol: $v^{user\_constraint\_slack\_pos}$

Indices: (userconstraint=uc, stochasticscenario=s, t=t)

Indices function: user_constraint_slack_indices

Slack variable penalizing positive deviations from the desired user constraint $uc$ for stochastic scenario $s$ and timestep $t$

user_constraint_slack_neg

Math symbol: $v^{user\_constraint\_slack\_neg}$

Indices: (userconstraint=uc, stochasticscenario=s, t=t)

Indices function: user_constraint_slack_indices

Slack variable penalizing negative deviations from the desired user constraint $uc$ for stochastic scenario $s$ and timestep $t$