# oemof.solph.constraints¶

Additional constraints to be used in an oemof energy model.

oemof.solph.constraints.equate_variables(model, var1, var2, factor1=1, name=None)[source]

Adds a constraint to the given model that set two variables to equal adaptable by a factor.

The following constraints are build:

$var\textit{1} \cdot factor\textit{1} = var\textit{2}$
Parameters: var1 (pyomo.environ.Var) – First variable, to be set to equal with Var2 and multiplied with factor1. var2 (pyomo.environ.Var) – Second variable, to be set equal to (Var1 * factor1). factor1 (float) – Factor to define the proportion between the variables. name (str) – Optional name for the equation e.g. in the LP file. By default the name is: equate + string representation of var1 and var2. model (oemof.solph.Model) – Model to which the constraint is added.

Examples

The following example shows how to define a transmission line in the investment mode by connecting both investment variables. Note that the equivalent periodical costs (epc) of the line are 40. You could also add them to one line and set them to 0 for the other line.

>>> import pandas as pd
>>> from oemof import solph
>>> date_time_index = pd.date_range('1/1/2012', periods=5, freq='H')
>>> energysystem = solph.EnergySystem(timeindex=date_time_index)
>>> bel1 = solph.buses.Bus(label='electricity1')
>>> bel2 = solph.buses.Bus(label='electricity2')
...    label='powerline_1_2',
...    inputs={bel1: solph.flows.Flow()},
...    outputs={bel2: solph.flows.Flow(
...        investment=solph.Investment(ep_costs=20))}))
...    label='powerline_2_1',
...    inputs={bel2: solph.flows.Flow()},
...   outputs={bel1: solph.flows.Flow(
...       investment=solph.Investment(ep_costs=20))}))
>>> om = solph.Model(energysystem)
>>> line12 = energysystem.groups['powerline_1_2']
>>> line21 = energysystem.groups['powerline_2_1']
>>> solph.constraints.equate_variables(
...    om,
...    om.InvestmentFlowBlock.invest[line12, bel2],
...    om.InvestmentFlowBlock.invest[line21, bel1])

oemof.solph.constraints.limit_active_flow_count(model, constraint_name, flows, lower_limit=0, upper_limit=None)[source]

Set limits (lower and/or upper) for the number of concurrently active NonConvex flows. The flows are given as a list.

Total actual counts after optimization can be retrieved calling the om.oemof.solph.Model.$(constraint_name)_count(). Parameters: model (oemof.solph.Model) – Model to which constraints are added constraint_name (string) – name for the constraint flows (list of flows) – flows (have to be NonConvex) in the format [(in, out)] lower_limit (integer) – minimum number of active flows in the list upper_limit (integer) – maximum number of active flows in the list the updated model Note SimpleFlowBlock objects required to be NonConvex Constraint: $N_{X,min} \le \sum_{n \in F} X_n(t) \le N_{X,max} \forall t \in T$ With F being the set of considered flows and T being the set of time steps. The symbols used are defined as follows (with Variables (V) and Parameters (P)): math. symbol type explanation $$X_n(t)$$ V status (0 or 1) of the flow $$n$$ at time step $$t$$ $$N_{X,min}$$ P lower_limit $$N_{X,max}$$ P lower_limit oemof.solph.constraints.limit_active_flow_count_by_keyword(model, keyword, lower_limit=0, upper_limit=None)[source] This wrapper for limit_active_flow_count allows to set limits to the count of concurrently active flows by using a keyword instead of a list. The constraint will be named$(keyword)_count.

Parameters: model (oemof.solph.Model) – Model to which constraints are added keyword (string) – keyword to consider (searches all NonConvexFlows) lower_limit (integer) – minimum number of active flows having the keyword upper_limit (integer) – maximum number of active flows having the keyword the updated model

limit_active_flow_count(), constraint_name(), flows()

oemof.solph.constraints.emission_limit(om, flows=None, limit=None)[source]

Short handle for generic_integral_limit() with keyword=”emission_factor”.

Note

Flow objects required an attribute “emission_factor”!

oemof.solph.constraints.generic_integral_limit(om, keyword, flows=None, limit=None)[source]

Set a global limit for flows weighted by attribute called keyword. The attribute named by keyword has to be added to every flow you want to take into account.

Total value of keyword attributes after optimization can be retrieved calling the om.oemof.solph.Model.integral_limit_${keyword}(). Parameters: om (oemof.solph.Model) – Model to which constraints are added. flows (dict) – Dictionary holding the flows that should be considered in constraint. Keys are (source, target) objects of the Flow. If no dictionary is given all flows containing the keyword attribute will be used. keyword (string) – attribute to consider limit (numeric) – Absolute limit of keyword attribute for the energy system. Note Flow objects required an attribute named like keyword! Constraint: $\sum_{i \in F_E} \sum_{t \in T} P_i(t) \cdot w_i(t) \cdot \tau(t) \leq M$ With F_I being the set of flows considered for the integral limit and T being the set of time steps. The symbols used are defined as follows (with Variables (V) and Parameters (P)): math. symbol type explanation $$P_n(t)$$ V power flow $$n$$ at time step $$t$$ $$w_N(t)$$ P weight given to Flow named according to keyword $$\tau(t)$$ P width of time step $$t$$ $$L$$ P global limit given by keyword limit Examples >>> import pandas as pd >>> from oemof import solph >>> date_time_index = pd.date_range('1/1/2012', periods=5, freq='H') >>> energysystem = solph.EnergySystem(timeindex=date_time_index) >>> bel = solph.buses.Bus(label='electricityBus') >>> flow1 = solph.flows.Flow(nominal_value=100, my_factor=0.8) >>> flow2 = solph.flows.Flow(nominal_value=50) >>> src1 = solph.components.Source(label='source1', outputs={bel: flow1}) >>> src2 = solph.components.Source(label='source2', outputs={bel: flow2}) >>> energysystem.add(bel, src1, src2) >>> model = solph.Model(energysystem) >>> flow_with_keyword = {(src1, bel): flow1, } >>> model = solph.constraints.generic_integral_limit( ... model, "my_factor", flow_with_keyword, limit=777)  oemof.solph.constraints.additional_investment_flow_limit(model, keyword, limit=None)[source] Global limit for investment flows weighted by an attribute keyword. This constraint is only valid for Flows not for components such as an investment storage. The attribute named by keyword has to be added to every Investment attribute of the flow you want to take into account. Total value of keyword attributes after optimization can be retrieved calling the oemof.solph.Model.invest_limit_${keyword}().

$\sum_{i \in IF} P_i \cdot w_i \leq limit$

With IF being the set of InvestmentFlows considered for the integral limit.

The symbols used are defined as follows (with Variables (V) and Parameters (P)):

symbol attribute type explanation
$$P_{i}$$ InvestmentFlowBlock.invest[i, o] V installed capacity of investment flow
$$w_i$$ keyword P weight given to investment flow named according to keyword
$$limit$$ limit P global limit given by keyword limit
Parameters: model (oemof.solph.Model) – Model to which constraints are added. keyword (attribute to consider) – All flows with Investment attribute containing the keyword will be used. limit (numeric) – Global limit of keyword attribute for the energy system.

Note

The Investment attribute of the considered (Investment-)flows requires an attribute named like keyword!

Examples

>>> import pandas as pd
>>> from oemof import solph
>>> date_time_index = pd.date_range('1/1/2020', periods=5, freq='H')
>>> es = solph.EnergySystem(timeindex=date_time_index)
>>> bus = solph.buses.Bus(label='bus_1')
>>> sink = solph.components.Sink(label="sink", inputs={bus:
...     solph.flows.Flow(nominal_value=10, fix=[10, 20, 30, 40, 50])})
>>> src1 = solph.components.Source(label='source_0', outputs={bus: solph.flows.Flow(
...     investment=solph.Investment(ep_costs=50, space=4))})
>>> src2 = solph.components.Source(label='source_1', outputs={bus: solph.flows.Flow(
...     investment=solph.Investment(ep_costs=100, space=1))})
>>> model = solph.Model(es)
...     model, "space", limit=1500)
>>> a = model.solve(solver="cbc")
>>> int(round(model.invest_limit_space()))
1500

oemof.solph.constraints.investment_limit(model, limit=None)[source]

Set an absolute limit for the total investment costs of an investment optimization problem:

$\sum_{investment\_costs} \leq limit$
Parameters: model (oemof.solph.Model) – Model to which the constraint is added limit (float) – Absolute limit of the investment (i.e. RHS of constraint)
oemof.solph.constraints.shared_limit(model, quantity, limit_name, components, weights, lower_limit=0, upper_limit=None)[source]

Adds a constraint to the given model that restricts the weighted sum of variables to a corridor.

The following constraints are build:

$l_\mathrm{low} \le \sum v_i(t) \times w_i(t) \le l_\mathrm{up} \forall t$
Parameters: model (oemof.solph.Model) – Model to which the constraint is added. limit_name (string) – Name of the constraint to create quantity (pyomo.core.base.var.IndexedVar) – Shared Pyomo variable for all components of a type. components (list of components) – list of components of the same type weights (list of numeric values) – has to have the same length as the list of components lower_limit (numeric) – the lower limit upper_limit (numeric) – the lower limit

Examples

The constraint can e.g. be used to define a common storage that is shared between parties but that do not exchange energy on balance sheet. Thus, every party has their own bus and storage, respectively, to model the energy flow. However, as the physical storage is shared, it has a common limit.

>>> import pandas as pd
>>> from oemof import solph
>>> date_time_index = pd.date_range('1/1/2012', periods=5, freq='H')
>>> energysystem = solph.EnergySystem(timeindex=date_time_index)
>>> b1 = solph.buses.Bus(label="Party1Bus")
>>> b2 = solph.buses.Bus(label="Party2Bus")
>>> storage1 = solph.components.GenericStorage(
...     label="Party1Storage",
...     nominal_storage_capacity=5,
...     inputs={b1: solph.flows.Flow()},
...     outputs={b1: solph.flows.Flow()})
>>> storage2 = solph.components.GenericStorage(
...     label="Party2Storage",
...     nominal_storage_capacity=5,
...     inputs={b1: solph.flows.Flow()},
...     outputs={b1: solph.flows.Flow()})