Storage State Rule: The constraint storage state rule is the main storage constraint and it defines the storage energy content of a storage s in a site v in support timeframe y at a timestep t. This constraint calculates the storage energy content at a timestep t by adding or subtracting differences, such as ingoing and outgoing energy, to/from a storage energy content at a previous timestep t − 1 multiplied by 1 minus the self-discharge rate dyvs (which is scaled exponentially with the timestep size δt). Here ingoing energy is given by the product of the variable storage input commodity flow ϵyvstin and the parameter storage efficiency during charge eyvsin. Outgoing energy is given by the variable storage output commodity flow ϵyvstout divided by the parameter storage efficiency during discharge eyvsout. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage state rule is defined and calculated by the following code fragment:
m.def_storage_state = pyomo.Constraint(
m.tm, m.sto_tuples,
rule=def_storage_state_rule,
doc='storage[t] = (1 - selfdischarge) * storage[t-1] + input * eff_in - output / eff_out')/../urbs/features/storage.py
Storage Power Rule: The constraint storage power rule defines the variable total storage power κyvsp. The variable total storage power is defined by the constraint as the sum of the parameter storage power installed Kyvsp and the variable new storage power κ̂yvsp. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage power rule is defined and calculated by the following code fragment: :
m.def_storage_power = pyomo.Constraint(
m.sto_tuples,
rule=def_storage_power_rule,
doc='storage power = inst-cap + new power')/../urbs/features/storage.py
Storage Capacity Rule: The constraint storage capacity rule defines the variable total storage size κyvsc. The variable total storage size is defined by the constraint as the sum of the parameter storage content installed Kyvsc and the variable new storage size κ̂yvsc. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage capacity rule is defined and calculated by the following code fragment: :
m.def_storage_capacity = pyomo.Constraint(
m.sto_tuples,
rule=def_storage_capacity_rule,
doc='storage capacity = inst-cap + new capacity')/../urbs/features/storage.py
Storage Input By Power Rule: The constraint storage input by power rule limits the variable storage input commodity flow ϵyvstin. This constraint restricts a storage s in a site v and support timeframe y at a timestep t from having more input power than the storage power capacity. The constraint states that the variable ϵyvstin must be less than or equal to the variable total storage power κyvsp, scaled by the size of the time steps :math: Delta t. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage input by power rule is defined and calculated by the following code fragment: :
m.res_storage_input_by_power = pyomo.Constraint(
m.tm, m.sto_tuples,
rule=res_storage_input_by_power_rule,
doc='storage input <= storage power')/../urbs/features/storage.py
Storage Output By Power Rule: The constraint storage output by power rule limits the variable storage output commodity flow ϵyvstout. This constraint restricts a storage s in a site v and support timeframe y at a timestep t from having more output power than the storage power capacity. The constraint states that the variable ϵvstout must be less than or equal to the variable total storage power κyvsp, scaled by the size of the time steps Δt. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage output by power rule is defined and calculated by the following code fragment: :
m.res_storage_output_by_power = pyomo.Constraint(
m.tm, m.sto_tuples,
rule=res_storage_output_by_power_rule,
doc='storage output <= storage power')/../urbs/features/storage.py
Storage State By Capacity Rule: The constraint storage state by capacity rule limits the variable storage energy content ϵyvstcon. This constraint restricts a storage s in a site v and support timeframe y at a timestep t from having more storage content than the storage content capacity. The constraint states that the variable ϵyvstcon must be less than or equal to the variable total storage size κyvsc. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage state by capacity rule is defined and calculated by the following code fragment. :
m.res_storage_state_by_capacity = pyomo.Constraint(
m.t, m.sto_tuples,
rule=res_storage_state_by_capacity_rule,
doc='storage content <= storage capacity')/../urbs/features/storage.py
Storage Power Limit Rule: The constraint storage power limit rule limits the variable total storage power κyvsp. This contraint restricts a storage s in a site v and support timeframe y 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 storage power κyvsp must be greater than or equal to the parameter storage power lower bound theory-storage.
In script storage.py the constraint storage power limit rule is defined and calculated by the following code fragment: :
m.res_storage_power = pyomo.Constraint(
m.sto_tuples,
rule=res_storage_power_rule,
doc='storage.cap-lo-p <= storage power <= storage.cap-up-p')/../urbs/features/storage.py
Storage Capacity Limit Rule: The constraint storage capacity limit rule limits the variable total storage size κyvsc. This constraint restricts a storage s in a site v and support timeframe y from having more total storage content capacity than an upper bound and having less than a lower bound. The constraint states that the variable total storage size κyvsc must be greater than or equal to the parameter storage content lower bound theory-storage.
In script storage.py the constraint storage capacity limit rule is defined and calculated by the following code fragment: :
m.res_storage_capacity = pyomo.Constraint(
m.sto_tuples,
rule=res_storage_capacity_rule,
doc='storage.cap-lo-c <= storage capacity <= storage.cap-up-c')/../urbs/features/storage.py
Initial And Final Storage State Rule: The constraint initial and final storage state rule defines and restricts the variable storage energy content ϵyvstcon of a storage s in a site v and support timeframe y at the initial timestep t1 and at the final timestep tN. There are two distinct cases:
1. The initial and final storage states are specified by a value of the parameter Iyvs between 0 and 1. 2. Iyvs is not specified (e.g. by setting it '#NV' in the input sheet). In this case the initial and final storage state are still equal but variable.
In case 1 the constraints are written in the following way:
Initial storage state: Initial storage represents the storage state in a storage at the beginning of the simulation. The variable storage energy content ϵyvstcon at the initial timestep t1 is defined by this constraint. The constraint states that the variable ϵvst1con must be equal to the product of the parameters storage content installed Kyvsc and initial and final state of charge Iyvs.
Final storage state: Final storage represents the storage state in a storage at the end of the simulation. The variable storage energy content ϵyvstcon at the final timestep tN is restricted by this constraint. The constraint states that the variable ϵyvstNcon must be greater than or equal to the product of the parameters storage content installed Kyvsc and initial and final state of charge Iyvs. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint initial and final storage state rule is then defined and calculated by the following code fragment: :
m.res_initial_and_final_storage_state = pyomo.Constraint(
m.t, m.sto_init_bound_tuples,
rule=res_initial_and_final_storage_state_rule,
doc='storage content initial == and final >= storage.init * capacity')/../urbs/features/storage.py
In case 2 the constraint becomes a lot easier, since the initial and final state are simply compared to each other by the following inequality:
∀v ∈ V, s ∈ S: ϵvst1con ≤ ϵvstNcon
In script storage.py the constraint initial and final storage state rule is then defined and calculated by the following code fragment: :
m.res_initial_and_final_storage_state_var = pyomo.Constraint(
m.t, m.sto_tuples - m.sto_init_bound_tuples,
rule=res_initial_and_final_storage_state_var_rule,
doc='storage content initial <= final, both variable')/../urbs/features/storage.py
Storage Energy to Power Ratio Rule: For certain type of storage technologies, the power and energy capacities cannot be independently sized but are dependent to each other. Hence, the constraint storage energy to power ratio rule sets a linear dependence between the capacities through a user-defined "energy to power ratio" kyvsE/P. It has to be noted that this constraint is only active for the storages with a positive value under the column "ep-ratio" in the input file, and when this value is not given, the power and energy capacities can be sized independently. The mathematical explanation of this rule is given in theory-storage.
In script storage.py the constraint storage energy to power rule is then defined and calculated by the following code fragment: :
m.def_storage_energy_power_ratio = pyomo.Constraint(
m.sto_en_to_pow_tuples,
rule=def_storage_energy_power_ratio_rule,
doc='storage capacity = storage power * storage E2P ratio')/../urbs/features/storage.py