1. Nomenclature
Indices and Sets
ancestor node of scenario tree node
renewable energy sources
descendant nodes of scenario tree node
power producers
transmission lines
power network nodes
scenario tree nodes
time periods
time period to which scenario tree node belongs
conventional generation units of producer at network node
Parametersavailability factor for renewable energy generation of type at node for scenario (-)
element of node susceptance matrix, where
generation cost of unit from producer at node (€/MWh)
ramp-up cost of unit from producer at node (€/MWh)
cost of discharge from storage (€/MWh)
intercept of linear inverse demand function at node in period (€/MWh)
slope of linear inverse demand function at node in period (€/)
storage input efficiency (-)
hourly rate of storage decay (MW/MWh)
maximum generation capacity of unit from producer at node (MW)
maximum generation capacity of producer for renewable energy type at node (MW)
element of network transfer matrix, where and
maximum capacity of power line (MW)
probability of scenario (-)
hourly rate at which storage can be charged (MW/MWh)
hourly rate at which storage can be discharged (MW/MWh)
dummy parameter for slack node, where (-)
maximum storage capacity of producer at node (MWh)
minimum storage capacity of producer at node (MWh)
duration of period (h)
Primal Variablesgeneration at node by producer using unit for scenario (MWh)
renewable energy generation of type at node by producer for scenario (MWh)
generation ramp-up at node by producer using unit for scenario (MWh)
sales at node by producer for scenario (MWh)
(end-of-period) stored energy by producer at node for scenario (MWh)
energy charged into storage at node by producer for scenario (MWh)
energy discharged from storage at node by producer for scenario (MWh)
voltage angle at node for scenario (rad)
Dual Variablesshadow price on generation capacity at node for conventional generation unit of producer and scenario (€/MWh)
shadow price on renewable energy generation capacity at node for energy source type , producer and scenario (€/MWh)
shadow price on ramp-up constraint at node for conventional generation unit of producer and scenario (€/MWh)
dual for slack node and scenario (-)
shadow price on energy balance for producer and scenario (€/MWh)
shadow price on stored energy balance at node for producer and scenario (€/MWh)
shadow price on maximum storage charging at node for producer and scenario (€/MWh)
shadow price on energy storage capacity at node for producer and scenario (€/MWh)
shadow price on maximum storage discharging at node for producer and scenario (€/MWh)
shadow price on transmission capacity for transmission line and scenario (€/MW)
congestion charge at node for scenario (€/MWh)