Transmission Constraints

Transmission Capacity Rule: The constraint transmission capacity rule defines the variable total transmission capacity \(\kappa_{af}\). The variable total transmission capacity is defined by the constraint as the sum of the variable transmission capacity installed \(K_{af}\) and the variable new transmission capacity \(\hat{\kappa}_{af}\). In mathematical notation this is expressed as:

\[\forall a\in A, f\in F\colon\ \kappa_{af} = K_{af} + \hat{\kappa}_{af}\]

In script urbs.py the constraint transmission capacity rule is defined and calculated by the following code fragment:

m.def_transmission_capacity = pyomo.Constraint(
    m.tra_tuples,
    rule=def_transmission_capacity_rule,
    doc='total transmission capacity = inst-cap + new capacity')

Transmission Output Rule: The constraint transmission output rule defines the variable transmission power flow (output) \(\pi_{aft}^\text{out}\). The variable transmission power flow (output) is defined by the constraint as the product of the variable transmission power flow (input) \(\pi_{aft}^\text{in}\) and the parameter transmission efficiency \(e_{af}\). In mathematical notation this is expressed as:

\[\forall a\in A, f\in F, t\in T_m\colon\ \pi^\text{out}_{aft} = \pi^\text{in}_{aft} e_{af}\]

In script urbs.py the constraint transmission output rule is defined and calculated by the following code fragment:

m.def_transmission_output = pyomo.Constraint(
    m.tm, m.tra_tuples,
    rule=def_transmission_output_rule,
    doc='transmission output = transmission input * efficiency')

Transmission Input By Capacity Rule: The constraint transmission input by capacity rule limits the variable transmission power flow (input) \(\pi_{aft}^\text{in}\). This constraint prevents transmissions from exceeding their possible power input capacity. The constraint states that the variable transmission power flow (input) \(\pi_{aft}^\text{in}\) must be less than or equal to the variable total transmission capacity \(\kappa_{af}\). In mathematical notation this is expressed as:

\[\forall a\in A, f\in F, t\in T_m\colon\ \pi^\text{in}_{aft} \leq \kappa_{af}\]

In script urbs.py the constraint transmission input by capacity rule is defined and calculated by the following code fragment:

m.res_transmission_input_by_capacity = pyomo.Constraint(
    m.tm, m.tra_tuples,
    rule=res_transmission_input_by_capacity_rule,
    doc='transmission input <= total transmission capacity')

Transmission Capacity Limit Rule: The constraint transmission capacity limit rule limits the variable total transmission capacity \(\kappa_{af}\). This constraint restricts a transmission \(f\) through an arc \(a\) from having more total power output capacity than an upper bound and having less than a lower bound. The constraint states that the variable total transmission capacity \(\kappa_{af}\) must be greater than or equal to the parameter transmission capacity lower bound \(\underline{K}_{af}\) and less than or equal to the parameter transmission capacity upper bound \(\overline{K}_{af}\). In mathematical notation this is expressed as:

\[\forall a\in A, f\in F\colon\ \underline{K}_{af} \leq \kappa_{af} \leq \overline{K}_{af}\]

In script urbs.py the constraint transmission capacity limit rule is defined and calculated by the following code fragment:

m.res_transmission_capacity = pyomo.Constraint(
    m.tra_tuples,
    rule=res_transmission_capacity_rule,
    doc='transmission.cap-lo <= total transmission capacity <= '
        'transmission.cap-up')

Transmission Symmetry Rule: The constraint transmission symmetry rule defines the power output capacities of incoming and outgoing arcs \(a , a'\) of a transmission \(f\). The constraint states that the power output capacities \(\kappa_{af}\) of the incoming arc \(a\) and the complementary outgoing arc \(a'\) between two sites must be equal. In mathematical notation this is expressed as:

\[\forall a\in A, f\in F\colon\ \kappa_{af} = \kappa_{a'f}\]

In script urbs.py the constraint transmission symmetry rule is defined and calculated by the following code fragment:

m.res_transmission_symmetry = pyomo.Constraint(
    m.tra_tuples,
    rule=res_transmission_symmetry_rule,
    doc='total transmission capacity must be symmetric in both directions')