# oemof.solph.components¶

## Sink¶

solph version of oemof.network.Sink

class oemof.solph.components._sink.Sink(*args, **kwargs)[source]

Bases: oemof.network.network.Sink

An object with one input flow.

constraint_group()[source]

## Source¶

solph version of oemof.network.Source

class oemof.solph.components._source.Source(*args, **kwargs)[source]

Bases: oemof.network.network.Source

An object with one output flow.

constraint_group()[source]

## Transformer¶

solph version of oemof.network.Transformer including sets, variables, constraints and parts of the objective function for TransformerBlock objects.

class oemof.solph.components._transformer.Transformer(*args, **kwargs)[source]

Bases: oemof.network.network.Transformer

A linear converter object with n inputs and n outputs.

Parameters: conversion_factors (dict) – Dictionary containing conversion factors for conversion of each flow. Keys are the connected bus objects. The dictionary values can either be a scalar or an iterable with length of time horizon for simulation.

Examples

Defining an linear transformer:

>>> from oemof import solph
>>> bgas = solph.buses.Bus(label='natural_gas')
>>> bcoal = solph.buses.Bus(label='hard_coal')
>>> bel = solph.buses.Bus(label='electricity')
>>> bheat = solph.buses.Bus(label='heat')
>>> trsf = solph.components.Transformer(
...    label='pp_gas_1',
...    inputs={bgas: solph.flows.Flow(), bcoal: solph.flows.Flow()},
...    outputs={bel: solph.flows.Flow(), bheat: solph.flows.Flow()},
...    conversion_factors={bel: 0.3, bheat: 0.5,
...                        bgas: 0.8, bcoal: 0.2})
>>> print(sorted([x[1][5] for x in trsf.conversion_factors.items()]))
[0.2, 0.3, 0.5, 0.8]
>>> type(trsf)
<class 'oemof.solph.components._transformer.Transformer'>
>>> sorted([str(i) for i in trsf.inputs])
['hard_coal', 'natural_gas']
>>> trsf_new = solph.components.Transformer(
...    label='pp_gas_2',
...    inputs={bgas: solph.flows.Flow()},
...    outputs={bel: solph.flows.Flow(), bheat: solph.flows.Flow()},
...    conversion_factors={bel: 0.3, bheat: 0.5})
>>> trsf_new.conversion_factors[bgas][3]
1

Notes

The following sets, variables, constraints and objective parts are created
constraint_group()[source]
class oemof.solph.components._transformer.TransformerBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for the linear relation of nodes with type Transformer

The following constraints are created:

Linear relation om.Transformer.relation[i,o,t]
$\begin{split}P_{i}(t) \cdot \eta_{o}(t) = P_{o}(t) \cdot \eta_{i}(t), \\ \forall t \in \textrm{TIMESTEPS}, \\ \forall i \in \textrm{INPUTS}, \\ \forall o \in \textrm{OUTPUTS}\end{split}$

While INPUTS is the set of Bus objects connected with the input of the Transformer and OUPUTS the set of Bus objects connected with the output of the Transformer. The constraint above will be created for all combinations of INPUTS and OUTPUTS for all TIMESTEPS. A Transformer with two inflows and two outflows for one day with an hourly resolution will lead to 96 constraints.

The index :math: n is the index for the Transformer node itself. Therefore, a flow[i, n, t] is a flow from the Bus i to the Transformer n at time step t.

symbol attribute explanation
$$P_{i}(t)$$ flow[i, n, t] Transformer, inflow
$$P_{o}(t)$$ flow[n, o, t] Transformer, outflow
$$\eta_{i}(t)$$ conversion_factor[i, n, t] Inflow, efficiency
$$\eta_{o}(t)$$ conversion_factor[n, o, t] Outflow, efficiency

## extractionTurbineCHP¶

ExtractionTurbineCHP and associated individual constraints (blocks) and groupings.

class oemof.solph.components._extraction_turbine_chp.ExtractionTurbineCHP(conversion_factor_full_condensation, *args, **kwargs)[source]

A CHP with an extraction turbine in a linear model. For more options see the GenericCHP class.

One main output flow has to be defined and is tapped by the remaining flow. The conversion factors have to be defined for the maximum tapped flow ( full CHP mode) and for no tapped flow (full condensing mode). Even though it is possible to limit the variability of the tapped flow, so that the full condensing mode will never be reached.

Parameters: conversion_factors (dict) – Dictionary containing conversion factors for conversion of inflow to specified outflow. Keys are output bus objects. The dictionary values can either be a scalar or a sequence with length of time horizon for simulation. conversion_factor_full_condensation (dict) – The efficiency of the main flow if there is no tapped flow. Only one key is allowed. Use one of the keys of the conversion factors. The key indicates the main flow. The other output flow is the tapped flow.

Notes

The following sets, variables, constraints and objective parts are created
• ExtractionTurbineCHPBlock

Examples

>>> from oemof import solph
>>> bel = solph.buses.Bus(label='electricityBus')
>>> bth = solph.buses.Bus(label='heatBus')
>>> bgas = solph.buses.Bus(label='commodityBus')
>>> et_chp = solph.components.ExtractionTurbineCHP(
...    label='variable_chp_gas',
...    inputs={bgas: solph.flows.Flow(nominal_value=10e10)},
...    outputs={bel: solph.flows.Flow(), bth: solph.flows.Flow()},
...    conversion_factors={bel: 0.3, bth: 0.5},
...    conversion_factor_full_condensation={bel: 0.5})
constraint_group()[source]
class oemof.solph.components._extraction_turbine_chp.ExtractionTurbineCHPBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for the linear relation of nodes with type ExtractionTurbineCHP

The following two constraints are created:

$\begin{split}& (1)\dot H_{Fuel}(t) = \frac{P_{el}(t) + \dot Q_{th}(t) \cdot \beta(t)} {\eta_{el,woExtr}(t)} \\ & (2)P_{el}(t) \geq \dot Q_{th}(t) \cdot C_b = \dot Q_{th}(t) \cdot \frac{\eta_{el,maxExtr}(t)} {\eta_{th,maxExtr}(t)}\end{split}$

where $$\beta$$ is defined as:

$\beta(t) = \frac{\eta_{el,woExtr}(t) - \eta_{el,maxExtr}(t)}{\eta_{th,maxExtr}(t)}$

where the first equation is the result of the relation between the input flow and the two output flows, the second equation stems from how the two output flows relate to each other, and the symbols used are defined as follows (with Variables (V) and Parameters (P)):

symbol attribute type explanation
$$\dot H_{Fuel}$$ flow[i, n, t] V fuel input flow
$$P_{el}$$ flow[n, main_output, t] V electric power
$$\dot Q_{th}$$ flow[n, tapped_output, t] V thermal output
$$\beta$$ main_flow_loss_index[n, t] P power loss index
$$\eta_{el,woExtr}$$ conversion_factor_full_condensation[n, t] P
electric efficiency
without heat extraction
$$\eta_{el,maxExtr}$$ conversion_factors[main_output][n, t] P
electric efficiency
with max heat extraction
$$\eta_{th,maxExtr}$$ conversion_factors[tapped_output][n, t] P
thermal efficiency with
maximal heat extraction
CONSTRAINT_GROUP = True

## GenericCHP¶

GenericCHP and associated individual constraints (blocks) and groupings.

class oemof.solph.components._generic_chp.GenericCHP(*args, **kwargs)[source]

Bases: oemof.network.network.Transformer

Component GenericCHP to model combined heat and power plants.

Can be used to model (combined cycle) extraction or back-pressure turbines and used a mixed-integer linear formulation. Thus, it induces more computational effort than the ExtractionTurbineCHP for the benefit of higher accuracy.

The full set of equations is described in: Mollenhauer, E., Christidis, A. & Tsatsaronis, G. Evaluation of an energy- and exergy-based generic modeling approach of combined heat and power plants Int J Energy Environ Eng (2016) 7: 167. https://doi.org/10.1007/s40095-016-0204-6

For a general understanding of (MI)LP CHP representation, see: Fabricio I. Salgado, P. Short - Term Operation Planning on Cogeneration Systems: A Survey Electric Power Systems Research (2007) Electric Power Systems Research Volume 78, Issue 5, May 2008, Pages 835-848 https://doi.org/10.1016/j.epsr.2007.06.001

Note

An adaption for the flow parameter H_L_FG_share_max has been made to set the flue gas losses at maximum heat extraction H_L_FG_max as share of the fuel flow H_F e.g. for combined cycle extraction turbines. The flow parameter H_L_FG_share_min can be used to set the flue gas losses at minimum heat extraction H_L_FG_min as share of the fuel flow H_F e.g. for motoric CHPs. The boolean component parameter back_pressure can be set to model back-pressure characteristics.

Also have a look at the examples on how to use it.

Parameters: fuel_input (dict) – Dictionary with key-value-pair of oemof.Bus and oemof.Flow object for the fuel input. electrical_output (dict) – Dictionary with key-value-pair of oemof.Bus and oemof.Flow object for the electrical output. Related parameters like P_max_woDH are passed as attributes of the oemof.Flow object. heat_output (dict) – Dictionary with key-value-pair of oemof.Bus and oemof.Flow object for the heat output. Related parameters like Q_CW_min are passed as attributes of the oemof.Flow object. Beta (list of numerical values) – Beta values in same dimension as all other parameters (length of optimization period). back_pressure (boolean) – Flag to use back-pressure characteristics. Set to True and Q_CW_min to zero for back-pressure turbines. See paper above for more information.

Note

The following sets, variables, constraints and objective parts are created

Examples

>>> from oemof import solph
>>> bel = solph.buses.Bus(label='electricityBus')
>>> bth = solph.buses.Bus(label='heatBus')
>>> bgas = solph.buses.Bus(label='commodityBus')
>>> ccet = solph.components.GenericCHP(
...    label='combined_cycle_extraction_turbine',
...    fuel_input={bgas: solph.flows.Flow(
...        H_L_FG_share_max=[0.183])},
...    electrical_output={bel: solph.flows.Flow(
...        P_max_woDH=[155.946],
...        P_min_woDH=[68.787],
...        Eta_el_max_woDH=[0.525],
...        Eta_el_min_woDH=[0.444])},
...    heat_output={bth: solph.flows.Flow(
...        Q_CW_min=[10.552])},
...    Beta=[0.122], back_pressure=False)
>>> type(ccet)
<class 'oemof.solph.components._generic_chp.GenericCHP'>
alphas

Compute or return the _alphas attribute.

constraint_group()[source]
class oemof.solph.components._generic_chp.GenericCHPBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for the relation of the $$n$$ nodes with type class:.GenericCHP.

The following constraints are created:

$\begin{split}& (1)\qquad \dot{H}_F(t) = fuel\ input \\ & (2)\qquad \dot{Q}(t) = heat\ output \\ & (3)\qquad P_{el}(t) = power\ output\\ & (4)\qquad \dot{H}_F(t) = \alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot P_{el,woDH}(t)\\ & (5)\qquad \dot{H}_F(t) = \alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot ( P_{el}(t) + \beta \cdot \dot{Q}(t) )\\ & (6)\qquad \dot{H}_F(t) \leq Y(t) \cdot \frac{P_{el, max, woDH}(t)}{\eta_{el,max,woDH}(t)}\\ & (7)\qquad \dot{H}_F(t) \geq Y(t) \cdot \frac{P_{el, min, woDH}(t)}{\eta_{el,min,woDH}(t)}\\ & (8)\qquad \dot{H}_{L,FG,max}(t) = \dot{H}_F(t) \cdot \dot{H}_{L,FG,sharemax}(t)\\ & (9)\qquad \dot{H}_{L,FG,min}(t) = \dot{H}_F(t) \cdot \dot{H}_{L,FG,sharemin}(t)\\ & (10)\qquad P_{el}(t) + \dot{Q}(t) + \dot{H}_{L,FG,max}(t) + \dot{Q}_{CW, min}(t) \cdot Y(t) = / \leq \dot{H}_F(t)\\\end{split}$

where $$= / \leq$$ depends on the CHP being back pressure or not.

The coefficients $$\alpha_0$$ and $$\alpha_1$$ can be determined given the efficiencies maximal/minimal load:

$\begin{split}& \eta_{el,max,woDH}(t) = \frac{P_{el,max,woDH}(t)}{\alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot P_{el,max,woDH}(t)}\\ & \eta_{el,min,woDH}(t) = \frac{P_{el,min,woDH}(t)}{\alpha_0(t) \cdot Y(t) + \alpha_1(t) \cdot P_{el,min,woDH}(t)}\\\end{split}$

For the attribute $$\dot{H}_{L,FG,min}$$ being not None, e.g. for a motoric CHP, the following is created:

Constraint:
$\begin{split}& (11)\qquad P_{el}(t) + \dot{Q}(t) + \dot{H}_{L,FG,min}(t) + \dot{Q}_{CW, min}(t) \cdot Y(t) \geq \dot{H}_F(t)\\[10pt]\end{split}$

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

math. symbol attribute type explanation
$$\dot{H}_{F}$$ H_F[n,t] V
input of enthalpy
through fuel input
$$P_{el}$$ P[n,t] V
provided
electric power
$$P_{el,woDH}$$ P_woDH[n,t] V
electric power without
district heating
$$P_{el,min,woDH}$$ P_min_woDH[n,t] P
min. electric power
without district heating
$$P_{el,max,woDH}$$ P_max_woDH[n,t] P
max. electric power
without district heating
$$\dot{Q}$$ Q[n,t] V provided heat
$$\dot{Q}_{CW, min}$$ Q_CW_min[n,t] P
minimal therm. condenser
$$\dot{H}_{L,FG,min}$$ H_L_FG_min[n,t] V
flue gas enthalpy loss
at min heat extraction
$$\dot{H}_{L,FG,max}$$ H_L_FG_max[n,t] V
flue gas enthalpy loss
at max heat extraction
$$\dot{H}_{L,FG,sharemin}$$ H_L_FG_share_min[n,t] P
share of flue gas loss
at min heat extraction
$$\dot{H}_{L,FG,sharemax}$$ H_L_FG_share_max[n,t] P
share of flue gas loss
at max heat extraction
$$Y$$ Y[n,t] V
status variable
on/off
$$\alpha_0$$ n.alphas[0][n,t] P
coefficient
describing efficiency
$$\alpha_1$$ n.alphas[1][n,t] P
coefficient
describing efficiency
$$\beta$$ Beta[n,t] P power loss index
$$\eta_{el,min,woDH}$$ Eta_el_min_woDH[n,t] P
el. eff. at min. fuel
flow w/o distr. heating
$$\eta_{el,max,woDH}$$ Eta_el_max_woDH[n,t] P
el. eff. at max. fuel
flow w/o distr. heating
CONSTRAINT_GROUP = True

## GenericStorage¶

GenericStorage and associated individual constraints (blocks) and groupings.

class oemof.solph.components._generic_storage.GenericInvestmentStorageBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for all storages with Investment being not None. See oemof.solph.options.Investment for all parameters of the Investment class.

Variables

All Storages are indexed by $$n$$, which is omitted in the following for the sake of convenience. The following variables are created as attributes of om.InvestmentStorage:

• $$P_i(t)$$

Inflow of the storage (created in oemof.solph.models.BaseModel).

• $$P_o(t)$$

Outflow of the storage (created in oemof.solph.models.BaseModel).

• $$E(t)$$

Current storage content (Absolute level of stored energy).

• $$E_{invest}$$

Invested (nominal) capacity of the storage.

• $$E(-1)$$

Initial storage content (before timestep 0).

• $$b_{invest}$$

Binary variable for the status of the investment, if nonconvex is True.

Constraints

The following constraints are created for all investment storages:

Storage balance (Same as for GenericStorageBlock)
$\begin{split}E(t) = &E(t-1) \cdot (1 - \beta(t)) ^{\tau(t)/(t_u)} \\ &- \gamma(t)\cdot (E_{exist} + E_{invest}) \cdot {\tau(t)/(t_u)}\\ &- \delta(t) \cdot {\tau(t)/(t_u)}\\ &- \frac{P_o(t)}{\eta_o(t)} \cdot \tau(t) + P_i(t) \cdot \eta_i(t) \cdot \tau(t)\end{split}$

Depending on the attribute nonconvex, the constraints for the bounds of the decision variable $$E_{invest}$$ are different:

• nonconvex = False
$E_{invest, min} \le E_{invest} \le E_{invest, max}$
• nonconvex = True
$\begin{split}& E_{invest, min} \cdot b_{invest} \le E_{invest}\\ & E_{invest} \le E_{invest, max} \cdot b_{invest}\\\end{split}$

The following constraints are created depending on the attributes of the components.GenericStorage:

• initial_storage_level is None

Constraint for a variable initial storage content:

$E(-1) \le E_{invest} + E_{exist}$
• initial_storage_level is not None

An initial value for the storage content is given:

$E(-1) = (E_{invest} + E_{exist}) \cdot c(-1)$
• balanced=True

The energy content of storage of the first and the last timestep are set equal:

$E(-1) = E(t_{last})$
• invest_relation_input_capacity is not None

Connect the invest variables of the storage and the input flow:

$P_{i,invest} + P_{i,exist} = (E_{invest} + E_{exist}) \cdot r_{cap,in}$
• invest_relation_output_capacity is not None

Connect the invest variables of the storage and the output flow:

$P_{o,invest} + P_{o,exist} = (E_{invest} + E_{exist}) \cdot r_{cap,out}$
• invest_relation_input_output is not None

Connect the invest variables of the input and the output flow:

$P_{i,invest} + P_{i,exist} = (P_{o,invest} + P_{o,exist}) \cdot r_{in,out}$
• max_storage_level

Rule for upper bound constraint for the storage content:

$E(t) \leq E_{invest} \cdot c_{max}(t)$
• min_storage_level

Rule for lower bound constraint for the storage content:

$E(t) \geq E_{invest} \cdot c_{min}(t)$

Objective function

The part of the objective function added by the investment storages also depends on whether a convex or nonconvex investment option is selected. The following parts of the objective function are created:

• nonconvex = False

$E_{invest} \cdot c_{invest,var}$
• nonconvex = True

$\begin{split}E_{invest} \cdot c_{invest,var} + c_{invest,fix} \cdot b_{invest}\\\end{split}$

The total value of all investment costs of all InvestmentStorages can be retrieved calling om.GenericInvestmentStorageBlock.investment_costs.expr().

List of Variables
symbol attribute explanation
$$P_i(t)$$ flow[i[n], n, t] Inflow of the storage
$$P_o(t)$$ flow[n, o[n], t] Outlfow of the storage
$$E(t)$$ storage_content[n, t] Current storage content (current absolute stored energy)
$$E_{invest}$$ invest[n, t] Invested (nominal) capacity of the storage
$$E(-1)$$ init_cap[n] Initial storage capacity (before timestep 0)
$$b_{invest}$$ invest_status[i, o] Binary variable for the status of investment
$$P_{i,invest}$$ InvestmentFlowBlock.invest[i[n], n]
Invested (nominal) inflow (Investmentflow)
$$P_{o,invest}$$ InvestmentFlowBlock.invest[n, o[n]]
Invested (nominal) outflow (Investmentflow)
List of Parameters
symbol attribute explanation
$$E_{exist}$$ flows[i, o].investment.existing Existing storage capacity
$$E_{invest,min}$$ flows[i, o].investment.minimum Minimum investment value
$$E_{invest,max}$$ flows[i, o].investment.maximum Maximum investment value
$$P_{i,exist}$$ flows[i[n], n].investment.existing Existing inflow capacity
$$P_{o,exist}$$ flows[n, o[n]].investment.existing Existing outlfow capacity
$$c_{invest,var}$$ flows[i, o].investment.ep_costs Variable investment costs
$$c_{invest,fix}$$ flows[i, o].investment.offset Fix investment costs
$$r_{cap,in}$$ invest_relation_input_capacity Relation of storage capacity and nominal inflow
$$r_{cap,out}$$ invest_relation_output_capacity Relation of storage capacity and nominal outflow
$$r_{in,out}$$ invest_relation_input_output Relation of nominal in- and outflow
$$\beta(t)$$ loss_rate[t] Fraction of lost energy as share of $$E(t)$$ per time unit
$$\gamma(t)$$ fixed_losses_relative[t] Fixed loss of energy relative to $$E_{invest} + E_{exist}$$ per time unit
$$\delta(t)$$ fixed_losses_absolute[t] Absolute fixed loss of energy per time unit
$$\eta_i(t)$$ inflow_conversion_factor[t] Conversion factor (i.e. efficiency) when storing energy
$$\eta_o(t)$$ outflow_conversion_factor[t] Conversion factor when (i.e. efficiency) taking stored energy
$$c(-1)$$ initial_storage_level Initial relativ storage content (before timestep 0)
$$c_{max}$$ flows[i, o].max[t] Normed maximum value of storage content
$$c_{min}$$ flows[i, o].min[t] Normed minimum value of storage content
$$\tau(t)$$   Duration of time step
$$t_u$$   Time unit of losses $$\beta(t)$$, $$\gamma(t)$$, $$\delta(t)$$ and timeincrement $$\tau(t)$$
CONSTRAINT_GROUP = True
class oemof.solph.components._generic_storage.GenericStorage(*args, max_storage_level=1, min_storage_level=0, **kwargs)[source]

Bases: oemof.network.network.Node

Component GenericStorage to model with basic characteristics of storages.

The GenericStorage is designed for one input and one output.

Parameters: nominal_storage_capacity (numeric, $$E_{nom}$$) – Absolute nominal capacity of the storage invest_relation_input_capacity (numeric or None, $$r_{cap,in}$$) – Ratio between the investment variable of the input Flow and the investment variable of the storage: $$\dot{E}_{in,invest} = E_{invest} \cdot r_{cap,in}$$ invest_relation_output_capacity (numeric or None, $$r_{cap,out}$$) – Ratio between the investment variable of the output Flow and the investment variable of the storage: $$\dot{E}_{out,invest} = E_{invest} \cdot r_{cap,out}$$ invest_relation_input_output (numeric or None, $$r_{in,out}$$) – Ratio between the investment variable of the output Flow and the investment variable of the input flow. This ratio used to fix the flow investments to each other. Values < 1 set the input flow lower than the output and > 1 will set the input flow higher than the output flow. If None no relation will be set: $$\dot{E}_{in,invest} = \dot{E}_{out,invest} \cdot r_{in,out}$$ initial_storage_level (numeric, $$c(-1)$$) – The relative storage content in the timestep before the first time step of optimization (between 0 and 1). balanced (boolean) – Couple storage level of first and last time step. (Total inflow and total outflow are balanced.) loss_rate (numeric (iterable or scalar)) – The relative loss of the storage content per hour. fixed_losses_relative (numeric (iterable or scalar), $$\gamma(t)$$) – Losses per hour that are independent of the storage content but proportional to nominal storage capacity. fixed_losses_absolute (numeric (iterable or scalar), $$\delta(t)$$) – Losses per hour that are independent of storage content and independent of nominal storage capacity. inflow_conversion_factor (numeric (iterable or scalar), $$\eta_i(t)$$) – The relative conversion factor, i.e. efficiency associated with the inflow of the storage. outflow_conversion_factor (numeric (iterable or scalar), $$\eta_o(t)$$) – see: inflow_conversion_factor min_storage_level (numeric (iterable or scalar), $$c_{min}(t)$$) – The normed minimum storage content as fraction of the nominal storage capacity (between 0 and 1). To set different values in every time step use a sequence. max_storage_level (numeric (iterable or scalar), $$c_{max}(t)$$) – see: min_storage_level investment (oemof.solph.options.Investment object) – Object indicating if a nominal_value of the flow is determined by the optimization problem. Note: This will refer all attributes to an investment variable instead of to the nominal_storage_capacity. The nominal_storage_capacity should not be set (or set to None) if an investment object is used.

Notes

The following sets, variables, constraints and objective parts are created

Examples

Basic usage examples of the GenericStorage with a random selection of attributes. See the Flow class for all Flow attributes.

>>> from oemof import solph
>>> my_bus = solph.buses.Bus('my_bus')
>>> my_storage = solph.components.GenericStorage(
...     label='storage',
...     nominal_storage_capacity=1000,
...     inputs={my_bus: solph.flows.Flow(nominal_value=200, variable_costs=10)},
...     outputs={my_bus: solph.flows.Flow(nominal_value=200)},
...     loss_rate=0.01,
...     initial_storage_level=0,
...     max_storage_level = 0.9,
...     inflow_conversion_factor=0.9,
...     outflow_conversion_factor=0.93)
>>> my_investment_storage = solph.components.GenericStorage(
...     label='storage',
...     investment=solph.Investment(ep_costs=50),
...     inputs={my_bus: solph.flows.Flow()},
...     outputs={my_bus: solph.flows.Flow()},
...     loss_rate=0.02,
...     initial_storage_level=None,
...     invest_relation_input_capacity=1/6,
...     invest_relation_output_capacity=1/6,
...     inflow_conversion_factor=1,
...     outflow_conversion_factor=0.8)
constraint_group()[source]
class oemof.solph.components._generic_storage.GenericStorageBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Storage without an Investment object.

The following sets are created: (-> see basic sets at Model )

STORAGES
A set with all Storage objects, which do not have an
attr:investment of type Investment.
STORAGES_BALANCED
A set of all GenericStorage objects, with ‘balanced’ attribute set to True.
STORAGES_WITH_INVEST_FLOW_REL
A set with all Storage objects with two investment flows coupled with the ‘invest_relation_input_output’ attribute.

The following variables are created:

storage_content
Storage content for every storage and timestep. The value for the storage content at the beginning is set by the parameter initial_storage_level or not set if initial_storage_level is None. The variable of storage s and timestep t can be accessed by: om.Storage.storage_content[s, t]

The following constraints are created:

Set storage_content of last time step to one at t=0 if balanced == True
$E(t_{last}) = &E(-1)$
Storage balance om.Storage.balance[n, t]
$\begin{split}E(t) = &E(t-1) \cdot (1 - \beta(t)) ^{\tau(t)/(t_u)} \\ &- \gamma(t)\cdot E_{nom} \cdot {\tau(t)/(t_u)}\\ &- \delta(t) \cdot {\tau(t)/(t_u)}\\ &- \frac{\dot{E}_o(t)}{\eta_o(t)} \cdot \tau(t) + \dot{E}_i(t) \cdot \eta_i(t) \cdot \tau(t)\end{split}$
Connect the invest variables of the input and the output flow.
$\begin{split}InvestmentFlowBlock.invest(source(n), n) + existing = \\ (InvestmentFlowBlock.invest(n, target(n)) + existing) * \\ invest\_relation\_input\_output(n) \\ \forall n \in \textrm{INVEST\_REL\_IN\_OUT}\end{split}$
symbol explanation attribute
$$E(t)$$ energy currently stored storage_content
$$E_{nom}$$ nominal capacity of the energy storage nominal_storage_capacity
$$c(-1)$$ state before initial time step initial_storage_level
$$c_{min}(t)$$ minimum allowed storage min_storage_level[t]
$$c_{max}(t)$$ maximum allowed storage max_storage_level[t]
$$\beta(t)$$ fraction of lost energy as share of $$E(t)$$ per hour loss_rate[t]
$$\gamma(t)$$ fixed loss of energy relative to $$E_{nom}$$ per hour fixed_losses_relative[t]
$$\delta(t)$$ absolute fixed loss of energy per hour fixed_losses_absolute[t]
$$\dot{E}_i(t)$$ energy flowing in inputs
$$\dot{E}_o(t)$$ energy flowing out outputs
$$\eta_i(t)$$ conversion factor (i.e. efficiency) when storing energy inflow_conversion_factor[t]
$$\eta_o(t)$$ conversion factor when (i.e. efficiency) taking stored energy outflow_conversion_factor[t]
$$\tau(t)$$ duration of time step
$$t_u$$ time unit of losses $$\beta(t)$$, $$\gamma(t)$$ $$\delta(t)$$ and timeincrement $$\tau(t)$$

The following parts of the objective function are created:

Nothing added to the objective function.

CONSTRAINT_GROUP = True

## OffsetTransformer¶

OffsetTransformer and associated individual constraints (blocks) and groupings.

class oemof.solph.components._offset_transformer.OffsetTransformer(*args, **kwargs)[source]

Bases: oemof.network.network.Transformer

An object with one input and one output.

Parameters: coefficients (tuple) – Tuple containing the first two polynomial coefficients i.e. the y-intersection and slope of a linear equation. The tuple values can either be a scalar or a sequence with length of time horizon for simulation.

Notes

The sets, variables, constraints and objective parts are created

Examples

>>> from oemof import solph
>>> bel = solph.buses.Bus(label='bel')
>>> bth = solph.buses.Bus(label='bth')
>>> ostf = solph.components.OffsetTransformer(
...    label='ostf',
...    inputs={bel: solph.flows.Flow(
...        nominal_value=60, min=0.5, max=1.0,
...        nonconvex=solph.NonConvex())},
...    outputs={bth: solph.flows.Flow()},
...    coefficients=(20, 0.5))
>>> type(ostf)
<class 'oemof.solph.components._offset_transformer.OffsetTransformer'>
constraint_group()[source]
class oemof.solph.components._offset_transformer.OffsetTransformerBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for the relation of nodes with type OffsetTransformer

The following constraints are created:

$\begin{split}& P_{out}(t) = C_1(t) \cdot P_{in}(t) + C_0(t) \cdot Y(t) \\\end{split}$
Variables (V) and Parameters (P)
symbol attribute type explanation
$$P_{out}(t)$$ flow[n, o, t] V Power of output
$$P_{in}(t)$$ flow[i, n, t] V Power of input
$$Y(t)$$ status[i, n, t] V binary status variable of nonconvex input flow
$$C_1(t)$$ coefficients[1][n, t] P linear coefficient 1 (slope)
$$C_0(t)$$ coefficients[0][n, t] P linear coefficient 0 (y-intersection)
CONSTRAINT_GROUP = True

## experimental.ElectricalLine¶

In-development electrical line components.

class oemof.solph.flows.experimental._electrical_line.ElectricalLine(*args, **kwargs)[source]

An ElectricalLine to be used in linear optimal power flow calculations. based on angle formulation. Check out the Notes below before using this component!

Parameters: reactance (float or array of floats) – Reactance of the line to be modelled Note (This component is experimental. Use it with care.)

Notes

• To use this object the connected buses need to be of the type ElectricalBus.
• It does not work together with flows that have set the attr.nonconvex, i.e. unit commitment constraints are not possible
• Input and output of this component are set equal, therefore just use either only the input or the output to parameterize.
• Default attribute min of in/outflows is overwritten by -1 if not set differently by the user
The following sets, variables, constraints and objective parts are created
• ElectricalLineBlock
constraint_group()[source]
class oemof.solph.flows.experimental._electrical_line.ElectricalLineBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for the linear relation of nodes with type class:.ElectricalLine

Note: This component is experimental. Use it with care.

The following constraints are created:

Linear relation om.ElectricalLine.electrical_flow[n,t]
$\begin{split}flow(n, o, t) = 1 / reactance(n, t) \\cdot () voltage_angle(i(n), t) - volatage_angle(o(n), t), \\ \forall t \\in \\textrm{TIMESTEPS}, \\ \forall n \\in \\textrm{ELECTRICAL\_LINES}.\end{split}$

TODO: Add equate constraint of flows

The following variable are created:

TODO: Add fix slack bus voltage angle to zero constraint / bound

CONSTRAINT_GROUP = True

## experimental.GenericCAES¶

In-development generic compressed air energy storage.

class oemof.solph.components.experimental._generic_caes.GenericCAES(*args, **kwargs)[source]

Bases: oemof.network.network.Transformer

Component GenericCAES to model arbitrary compressed air energy storages.

The full set of equations is described in: Kaldemeyer, C.; Boysen, C.; Tuschy, I. A Generic Formulation of Compressed Air Energy Storage as Mixed Integer Linear Program – Unit Commitment of Specific Technical Concepts in Arbitrary Market Environments Materials Today: Proceedings 00 (2018) 0000–0000 [currently in review]

Parameters: electrical_input (dict) – Dictionary with key-value-pair of oemof.Bus and oemof.Flow object for the electrical input. fuel_input (dict) – Dictionary with key-value-pair of oemof.Bus and oemof.Flow object for the fuel input. electrical_output (dict) – Dictionary with key-value-pair of oemof.Bus and oemof.Flow object for the electrical output. Note (This component is experimental. Use it with care.)

Notes

The following sets, variables, constraints and objective parts are created
• GenericCAES

TODO: Add description for constraints. See referenced paper until then!

Examples

>>> from oemof import solph
>>> bel = solph.buses.Bus(label='bel')
>>> bth = solph.buses.Bus(label='bth')
>>> bgas = solph.buses.Bus(label='bgas')
>>> # dictionary with parameters for a specific CAES plant
>>> concept = {
...    'cav_e_in_b': 0,
...    'cav_e_in_m': 0.6457267578,
...    'cav_e_out_b': 0,
...    'cav_e_out_m': 0.3739636077,
...    'cav_eta_temp': 1.0,
...    'cav_level_max': 211.11,
...    'cmp_p_max_b': 86.0918959849,
...    'cmp_p_max_m': 0.0679999932,
...    'cmp_p_min': 1,
...    'cmp_q_out_b': -19.3996965679,
...    'cmp_q_out_m': 1.1066036114,
...    'cmp_q_tes_share': 0,
...    'exp_p_max_b': 46.1294016678,
...    'exp_p_max_m': 0.2528340303,
...    'exp_p_min': 1,
...    'exp_q_in_b': -2.2073411014,
...    'exp_q_in_m': 1.129249765,
...    'exp_q_tes_share': 0,
...    'tes_eta_temp': 1.0,
...    'tes_level_max': 0.0}
>>> # generic compressed air energy storage (caes) plant
>>> caes = solph.components.experimental.GenericCAES(
...    label='caes',
...    electrical_input={bel: solph.flows.Flow()},
...    fuel_input={bgas: solph.flows.Flow()},
...    electrical_output={bel: solph.flows.Flow()},
...    params=concept, fixed_costs=0)
>>> type(caes)
<class 'oemof.solph.components.experimental._generic_caes.GenericCAES'>
constraint_group()[source]
class oemof.solph.components.experimental._generic_caes.GenericCAESBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for nodes of class:.GenericCAES.

Note: This component is experimental. Use it with care.

The following constraints are created:

$\begin{split}& (1) \qquad P_{cmp}(t) = electrical\_input (t) \quad \forall t \in T \\ & (2) \qquad P_{cmp\_max}(t) = m_{cmp\_max} \cdot CAS_{fil}(t-1) + b_{cmp\_max} \quad \forall t \in\left[1, t_{max}\right] \\ & (3) \qquad P_{cmp\_max}(t) = b_{cmp\_max} \quad \forall t \notin\left[1, t_{max}\right] \\ & (4) \qquad P_{cmp}(t) \leq P_{cmp\_max}(t) \quad \forall t \in T \\ & (5) \qquad P_{cmp}(t) \geq P_{cmp\_min} \cdot ST_{cmp}(t) \quad \forall t \in T \\ & (6) \qquad P_{cmp}(t) = m_{cmp\_max} \cdot CAS_{fil\_max} + b_{cmp\_max} \cdot ST_{cmp}(t) \quad \forall t \in T \\ & (7) \qquad \dot{Q}_{cmp}(t) = m_{cmp\_q} \cdot P_{cmp}(t) + b_{cmp\_q} \cdot ST_{cmp}(t) \quad \forall t \in T \\ & (8) \qquad \dot{Q}_{cmp}(t) = \dot{Q}_{cmp_out}(t) + \dot{Q}_{tes\_in}(t) \quad \forall t \in T \\ & (9) \qquad r_{cmp\_tes} \cdot\dot{Q}_{cmp\_out}(t) = \left(1-r_{cmp\_tes}\right) \dot{Q}_{tes\_in}(t) \quad \forall t \in T \\ & (10) \quad\; P_{exp}(t) = electrical\_output (t) \quad \forall t \in T \\ & (11) \quad\; P_{exp\_max}(t) = m_{exp\_max} CAS_{fil}(t-1) + b_{exp\_max} \quad \forall t \in\left[1, t_{\max }\right] \\ & (12) \quad\; P_{exp\_max}(t) = b_{exp\_max} \quad \forall t \notin\left[1, t_{\max }\right] \\ & (13) \quad\; P_{exp}(t) \leq P_{exp\_max}(t) \quad \forall t \in T \\ & (14) \quad\; P_{exp}(t) \geq P_{exp\_min}(t) \cdot ST_{exp}(t) \quad \forall t \in T \\ & (15) \quad\; P_{exp}(t) \leq m_{exp\_max} \cdot CAS_{fil\_max} + b_{exp\_max} \cdot ST_{exp}(t) \quad \forall t \in T \\ & (16) \quad\; \dot{Q}_{exp}(t) = m_{exp\_q} \cdot P_{exp}(t) + b_{cxp\_q} \cdot ST_{cxp}(t) \quad \forall t \in T \\ & (17) \quad\; \dot{Q}_{exp\_in}(t) = fuel\_input(t) \quad \forall t \in T \\ & (18) \quad\; \dot{Q}_{exp}(t) = \dot{Q}_{exp\_in}(t) + \dot{Q}_{tes\_out}(t)+\dot{Q}_{cxp\_add}(t) \quad \forall t \in T \\ & (19) \quad\; r_{exp\_tes} \cdot \dot{Q}_{exp\_in}(t) = (1 - r_{exp\_tes})(\dot{Q}_{tes\_out}(t) + \dot{Q}_{exp\_add}(t)) \quad \forall t \in T \\ & (20) \quad\; \dot{E}_{cas\_in}(t) = m_{cas\_in}\cdot P_{cmp}(t) + b_{cas\_in}\cdot ST_{cmp}(t) \quad \forall t \in T \\ & (21) \quad\; \dot{E}_{cas\_out}(t) = m_{cas\_out}\cdot P_{cmp}(t) + b_{cas\_out}\cdot ST_{cmp}(t) \quad \forall t \in T \\ & (22) \quad\; \eta_{cas\_tmp} \cdot CAS_{fil}(t) = CAS_{fil}(t-1) + \tau\left(\dot{E}_{cas\_in}(t) - \dot{E}_{cas\_out}(t)\right) \quad \forall t \in\left[1, t_{max}\right] \\ & (23) \quad\; \eta_{cas\_tmp} \cdot CAS_{fil}(t) = \tau\left(\dot{E}_{cas\_in}(t) - \dot{E}_{cas\_out}(t)\right) \quad \forall t \notin\left[1, t_{max}\right] \\ & (24) \quad\; CAS_{fil}(t) \leq CAS_{fil\_max} \quad \forall t \in T \\ & (25) \quad\; TES_{fil}(t) = TES_{fil}(t-1) + \tau\left(\dot{Q}_{tes\_in}(t) - \dot{Q}_{tes\_out}(t)\right) \quad \forall t \in\left[1, t_{max}\right] \\ & (26) \quad\; TES_{fil}(t) = \tau\left(\dot{Q}_{tes\_in}(t) - \dot{Q}_{tes\_out}(t)\right) \quad \forall t \notin\left[1, t_{max}\right] \\ & (27) \quad\; TES_{fil}(t) \leq TES_{fil\_max} \quad \forall t \in T \\ &\end{split}$

Table: Symbols and attribute names of variables and parameters

Variables (V) and Parameters (P)
symbol attribute type explanation
$$ST_{cmp}$$ cmp_st[n,t] V Status of compression
$${P}_{cmp}$$ cmp_p[n,t] V Compression power
$${P}_{cmp\_max}$$ cmp_p_max[n,t] V Max. compression power
$$\dot{Q}_{cmp}$$ cmp_q_out_sum[n,t] V
Summed
heat flow in compression
$$\dot{Q}_{cmp\_out}$$ cmp_q_waste[n,t] V Waste heat flow from compression
$$ST_{exp}(t)$$ exp_st[n,t] V Status of expansion (binary)
$$P_{exp}(t)$$ exp_p[n,t] V Expansion power
$$P_{exp\_max}(t)$$ exp_p_max[n,t] V Max. expansion power
$$\dot{Q}_{exp}(t)$$ exp_q_in_sum[n,t] V Summed heat flow in expansion
$$\dot{Q}_{exp\_in}(t)$$ exp_q_fuel_in[n,t] V Heat (external) flow into expansion
$$\dot{Q}_{exp\_add}(t)$$ exp_q_add_in[n,t] V Additional heat flow into expansion
$$CAV_{fil}(t)$$ cav_level[n,t] V
Filling level
if CAE
$$\dot{E}_{cas\_in}(t)$$ cav_e_in[n,t] V Exergy flow into CAS
$$\dot{E}_{cas\_out}(t)$$ cav_e_out[n,t] V Exergy flow from CAS
$$TES_{fil}(t)$$ tes_level[n,t] V Filling level of Thermal Energy Storage (TES)
$$\dot{Q}_{tes\_in}(t)$$ tes_e_in[n,t] V
Heat
flow into TES
$$\dot{Q}_{tes\_out}(t)$$ tes_e_out[n,t] V
Heat
flow from TES
$$b_{cmp\_max}$$ cmp_p_max_b[n,t] P
Specific
y-intersection
$$b_{cmp\_q}$$ cmp_q_out_b[n,t] P Specific y-intersection
$$b_{exp\_max}$$ exp_p_max_b[n,t] P Specific y-intersection
$$b_{exp\_q}$$ exp_q_in_b[n,t] P Specific y-intersection
$$b_{cas\_in}$$ cav_e_in_b[n,t] P Specific y-intersection
$$b_{cas\_out}$$ cav_e_out_b[n,t] P Specific y-intersection
$$m_{cmp\_max}$$ cmp_p_max_m[n,t] P
Specific
slope
$$m_{cmp\_q}$$ cmp_q_out_m[n,t] P
Specific
slope
$$m_{exp\_max}$$ exp_p_max_m[n,t] P
Specific
slope
$$m_{exp\_q}$$ exp_q_in_m[n,t] P
Specific
slope
$$m_{cas\_in}$$ cav_e_in_m[n,t] P
Specific
slope
$$m_{cas\_out}$$ cav_e_out_m[n,t] P
Specific
slope
$$P_{cmp\_min}$$ cmp_p_min[n,t] P Min. compression power
$$r_{cmp\_tes}$$ cmp_q_tes_share[n,t] P
Ratio
between waste heat flow and heat flow into TES
$$r_{exp\_tes}$$ exp_q_tes_share[n,t] P
Ratio
between external heat flow into expansion and heat flows from TES and
$$\tau$$ m.timeincrement[n,t] P
Time interval
length
$$TES_{fil\_max}$$ tes_level_max[n,t] P Max. filling level of TES
$$CAS_{fil\_max}$$ cav_level_max[n,t] P
Max.
filling level of TES
$$\tau$$ cav_eta_tmp[n,t] P
Temporal efficiency
(loss factor to take intertemporal losses into account)
$$electrical\_input$$ flow[list(n.electrical_input.keys())[0], n, t] P Electr. power input into compression
$$electrical\_output$$ flow[n, list(n.electrical_output.keys())[0], t] P Electr. power output of expansion
$$fuel\_input$$ flow[list(n.fuel_input.keys())[0], n, t] P
Heat input
(external) into Expansion
CONSTRAINT_GROUP = True

## experimental.PiecewiseLinearTransformer¶

In-development transfomer with piecewise linar efficiencies.

class oemof.solph.components.experimental._piecewise_linear_transformer.PiecewiseLinearTransformer(*args, **kwargs)[source]

Bases: oemof.network.network.Transformer

Component to model a transformer with one input and one output and an arbitrary piecewise linear conversion function.

Parameters: in_breakpoints (list) – List containing the domain breakpoints, i.e. the breakpoints for the incoming flow. conversion_function (func) – The function describing the relation between incoming flow and outgoing flow which is to be approximated. pw_repn (string) – Choice of piecewise representation that is passed to pyomo.environ.Piecewise

Examples

>>> import oemof.solph as solph
>>> b_gas = solph.buses.Bus(label='biogas')
>>> b_el = solph.buses.Bus(label='electricity')
>>> pwltf = solph.components.experimental.PiecewiseLinearTransformer(
...    label='pwltf',
...    inputs={b_gas: solph.flows.Flow(
...    nominal_value=100,
...    variable_costs=1)},
...    outputs={b_el: solph.flows.Flow()},
...    in_breakpoints=[0,25,50,75,100],
...    conversion_function=lambda x: x**2,
...    pw_repn='CC')
>>> type(pwltf)
<class 'oemof.solph.components.experimental._piecewise_linear_transformer.PiecewiseLinearTransformer'>
constraint_group()[source]
class oemof.solph.components.experimental._piecewise_linear_transformer.PiecewiseLinearTransformerBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Block for the relation of nodes with type PiecewiseLinearTransformer

The following constraints are created:

CONSTRAINT_GROUP = True

## experimental.SinkDSM¶

In-development functionality for demand-side management.

class oemof.solph.components.experimental._sink_dsm.SinkDSM(demand, capacity_up, capacity_down, approach, shift_interval=None, delay_time=None, shift_time=None, shed_time=None, max_demand=None, max_capacity_down=None, max_capacity_up=None, flex_share_down=None, flex_share_up=None, cost_dsm_up=0, cost_dsm_down_shift=0, cost_dsm_down_shed=0, efficiency=1, recovery_time_shift=None, recovery_time_shed=None, ActivateYearLimit=False, ActivateDayLimit=False, n_yearLimit_shift=None, n_yearLimit_shed=None, t_dayLimit=None, addition=True, fixes=True, shed_eligibility=True, shift_eligibility=True, **kwargs)[source]

Demand Side Management implemented as Sink with flexibility potential.

There are several approaches possible which can be selected: - DIW: Based on the paper by Zerrahn, Alexander and Schill, Wolf-Peter (2015): On the representation of demand-side management in power system models, in: Energy (84), pp. 840-845, 10.1016/j.energy.2015.03.037, accessed 08.01.2021, pp. 842-843. - DLR: Based on the PhD thesis of Gils, Hans Christian (2015): Balancing of Intermittent Renewable Power Generation by Demand Response and Thermal Energy Storage, Stuttgart, <http://dx.doi.org/10.18419/opus-6888>, accessed 08.01.2021, pp. 67-70. - oemof: Created by Julian Endres. A fairly simple DSM representation which demands the energy balance to be levelled out in fixed cycles

An evaluation of different modeling approaches has been carried out and presented at the INREC 2020. Some of the results are as follows: - DIW: A solid implementation with the tendency of slight overestimization of potentials since a shift_time is not accounted for. It may get computationally expensive due to a high time-interlinkage in constraint formulations. - DLR: An extensive modeling approach for demand response which neither leads to an over- nor underestimization of potentials and balances modeling detail and computation intensity. fixes and addition should both be set to True which is the default value. - oemof: A very computationally efficient approach which only requires the energy balance to be levelled out in certain intervals. If demand response is not at the center of the research and/or parameter availability is limited, this approach should be chosen. Note that approach oemof does allow for load shedding, but does not impose a limit on maximum amount of shedded energy.

SinkDSM adds additional constraints that allow to shift energy in certain time window constrained by capacity_up and capacity_down.

Parameters: demand (numeric) – original electrical demand (normalized) For investment modeling, it is advised to use the maximum of the demand timeseries and the cumulated (fixed) infeed time series for normalization, because the balancing potential may be determined by both. Elsewhise, underinvestments may occur. capacity_up (int or array) – maximum DSM capacity that may be increased (normalized) capacity_down (int or array) – maximum DSM capacity that may be reduced (normalized) approach (‘oemof’, ‘DIW’, ‘DLR’) – Choose one of the DSM modeling approaches. Read notes about which parameters to be applied for which approach. oemof : Simple model in which the load shift must be compensated in a predefined fixed interval (shift_interval is mandatory). Within time windows of the length shift_interval DSM up and down shifts are balanced. See SinkDSMOemofBlock for details. DIW : Sophisticated model based on the formulation by Zerrahn & Schill (2015a). The load shift of the component must be compensated in a predefined delay time (delay_time is mandatory). For details see SinkDSMDIWBlock. DLR : Sophisticated model based on the formulation by Gils (2015). The load shift of the component must be compensated in a predefined delay time (delay_time is mandatory). For details see SinkDSMDLRBlock. shift_interval (int) – Only used when approach is set to ‘oemof’. Otherwise, can be None. It’s the interval in which between $$DSM_{t}^{up}$$ and $$DSM_{t}^{down}$$ have to be compensated. delay_time (int) – Only used when approach is set to ‘DIW’ or ‘DLR’. Otherwise, can be None. Length of symmetrical time windows around $$t$$ in which $$DSM_{t}^{up}$$ and $$DSM_{t,tt}^{down}$$ have to be compensated. Note: For approach ‘DLR’, an iterable is constructed in order to model flexible delay times shift_time (int) – Only used when approach is set to ‘DLR’. Duration of a single upwards or downwards shift (half a shifting cycle if there is immediate compensation) shed_time (int) – Only used when shed_eligibility is set to True. Maximum length of a load shedding process at full capacity (used within energy limit constraint) max_demand (numeric) – Maximum demand prior to demand response max_capacity_down (numeric) – Maximum capacity eligible for downshifts prior to demand response (used for dispatch mode) max_capacity_up (numeric) – Maximum capacity eligible for upshifts prior to demand response (used for dispatch mode) flex_share_down (float) – Flexible share of installed capacity eligible for downshifts (used for invest mode) flex_share_up (float) – Flexible share of installed capacity eligible for upshifts (used for invest mode) cost_dsm_up (int) – Cost per unit of DSM activity that increases the demand cost_dsm_down_shift (int) – Cost per unit of DSM activity that decreases the demand for load shifting cost_dsm_down_shed (int) – Cost per unit of DSM activity that decreases the demand for load shedding efficiency (float) – Efficiency factor for load shifts (between 0 and 1) recovery_time_shift (int) – Only used when approach is set to ‘DIW’. Minimum time between the end of one load shifting process and the start of another for load shifting processes recovery_time_shed (int) – Only used when approach is set to ‘DIW’. Minimum time between the end of one load shifting process and the start of another for load shedding processes ActivateYearLimit (boolean) – Only used when approach is set to ‘DLR’. Control parameter; activates constraints for year limit if set to True ActivateDayLimit (boolean) – Only used when approach is set to ‘DLR’. Control parameter; activates constraints for day limit if set to True n_yearLimit_shift (int) – Only used when approach is set to ‘DLR’. Maximum number of load shifts at full capacity per year, used to limit the amount of energy shifted per year. Optional parameter that is only needed when ActivateYearLimit is True n_yearLimit_shed (int) – Only used when approach is set to ‘DLR’. Maximum number of load sheds at full capacity per year, used to limit the amount of energy shedded per year. Mandatory parameter if load shedding is allowed by setting shed_eligibility to True t_dayLimit (int) – Only used when approach is set to ‘DLR’. Maximum duration of load shifts at full capacity per day, used to limit the amount of energy shifted per day. Optional parameter that is only needed when ActivateDayLimit is True addition (boolean) – Only used when approach is set to ‘DLR’. Boolean parameter indicating whether or not to include additional constraint (which corresponds to Eq. 10 from Zerrahn and Schill (2015a) fixes (boolean) – Only used when approach is set to ‘DLR’. Boolean parameter indicating whether or not to include additional fixes. These comprise prohibiting shifts which cannot be balanced within the optimization timeframe shed_eligibility (boolean) – Boolean parameter indicating whether unit is eligible for load shedding shift_eligibility (boolean) – Boolean parameter indicating whether unit is eligible for load shifting

Note

• method has been renamed to approach.
• As many constraints and dependencies are created in approach ‘DIW’, computational cost might be high with a large ‘delay_time’ and with model of high temporal resolution
• The approach ‘DLR’ preforms better in terms of calculation time, compared to the approach ‘DIW’
• Using approach ‘DIW’ or ‘DLR’ might result in demand shifts that exceed the specified delay time by activating up and down simultaneously in the time steps between to DSM events. Thus, the purpose of this component is to model demand response portfolios rather than individual demand units.
• It’s not recommended to assign cost to the flow that connects SinkDSM with a bus. Instead, use cost_dsm_up or cost_dsm_down_shift
• Variable costs may be attributed to upshifts, downshifts or both. Costs for shedding may deviate from that for shifting (usually costs for shedding are much larger and equal to the value of lost load).
constraint_group()[source]
class oemof.solph.components.experimental._sink_dsm.SinkDSMDIWBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Constraints for SinkDSM with “DIW” approach

The following constraints are created for approach = ‘DIW’:

$\begin{split}& (1) \quad DSM_{t}^{up} = 0 \quad \forall t \quad if \space eligibility_{shift} = False \\ & (2) \quad DSM_{t}^{do, shed} = 0 \quad \forall t \quad if \space eligibility_{shed} = False \\ & (3) \quad \dot{E}_{t} = demand_{t} \cdot demand_{max} + DSM_{t}^{up} - \sum_{tt=t-L}^{t+L} DSM_{tt,t}^{do, shift} - DSM_{t}^{do, shed} \quad \forall t \in \mathbb{T} \\ & (4) \quad DSM_{t}^{up} \cdot \eta = \sum_{tt=t-L}^{t+L} DSM_{t,tt}^{do, shift} \quad \forall t \in \mathbb{T} \\ & (5) \quad DSM_{t}^{up} \leq E_{t}^{up} \cdot E_{up, max} \quad \forall t \in \mathbb{T} \\ & (6) \quad \sum_{t=tt-L}^{tt+L} DSM_{t,tt}^{do, shift} + DSM_{tt}^{do, shed} \leq E_{tt}^{do} \cdot E_{do, max} \quad \forall tt \in \mathbb{T} \\ & (7) \quad DSM_{tt}^{up} + \sum_{t=tt-L}^{tt+L} DSM_{t,tt}^{do, shift} + DSM_{tt}^{do, shed} \leq max \{ E_{tt}^{up} \cdot E_{up, max}, E_{tt}^{do} \cdot E_{do, max} \} \quad \forall tt \in \mathbb{T} \\ & (8) \quad \sum_{tt=t}^{t+R-1} DSM_{tt}^{up} \leq E_{t}^{up} \cdot E_{up, max} \cdot L \cdot \Delta t \quad \forall t \in \mathbb{T} \\ & (9) \quad \sum_{tt=t}^{t+R-1} DSM_{tt}^{do, shed} \leq E_{t}^{do} \cdot E_{do, max} \cdot t_{shed} \cdot \Delta t \quad \forall t \in \mathbb{T} \\ &\end{split}$

Note: For the sake of readability, the handling of indices is not displayed here. E.g. evaluating a variable for t-L may lead to a negative and therefore infeasible index. This is addressed by limiting the sums to non-negative indices within the model index bounds. Please refer to the constraints implementation themselves.

The following parts of the objective function are created:

$\begin{split}DSM_{t}^{up} \cdot cost_{t}^{dsm, up} + \sum_{tt=0}^{|T|} DSM_{t, tt}^{do, shift} \cdot cost_{t}^{dsm, do, shift} + DSM_{t}^{do, shed} \cdot cost_{t}^{dsm, do, shed} \quad \forall t \in \mathbb{T} \\\end{split}$

Table: Symbols and attribute names of variables and parameters

Variables (V) and Parameters (P)
symbol attribute type explanation
$$DSM_{t}^{up}$$ dsm_up[g,t]
$$DSM_{t,tt}^{do, shift}$$
dsm_do_shift[g,t,tt]
V DSM down shift (less load) in hour tt to compensate for upwards shifts in hour t
$$DSM_{t}^{do, shed}$$ dsm_do_shed[g,t]
V DSM shedded (capacity shedded, i.e. not compensated for)
$$\dot{E}_{t}$$ flow[g,t] V Energy flowing in from (electrical) inflow bus
$$L$$ delay_time P
Maximum delay time for load shift (time until the energy balance has to be levelled out again; roundtrip time of one load shifting cycle, i.e. time window for upshift and compensating downshift)
$$t_{she}$$ shed_time P
Maximum time for one load shedding process
$$demand_{t}$$ demand[t] P
(Electrical) demand series (normalized)
$$demand_{max}$$ max_demand P
Maximum demand value
$$E_{t}^{do}$$ capacity_down[t] P
Capacity allowed for a load adjustment downwards (normalized) (DSM down shift + DSM shedded)
$$E_{t}^{up}$$ capacity_up[t] P
Capacity allowed for a shift upwards (normalized) (DSM up shift)
$$E_{do, max}$$ max_capacity_down P
Maximum capacity allowed for a load adjustment downwards (DSM down shift + DSM shedded)
$$E_{up, max}$$ max_capacity_up P
Capacity allowed for a shift upwards (normalized) (DSM up shift)
$$\eta$$ efficiency P Efficiency loss for load shifting processes
$$\mathbb{T}$$   P Time steps
$$eligibility_{shift}$$
shift_eligibility P
Boolean parameter indicating if unit can be used for load shifting
$$eligibility_{shed}$$
shed_eligibility P
Boolean parameter indicating if unit can be used for load shedding
$$cost_{t}^{dsm, up}$$ cost_dsm_up[t]
P Variable costs for an upwards shift
$$cost_{t}^{dsm, do, shift}$$
cost_dsm_down_shift[t] P
Variable costs for a downwards shift (load shifting)
$$cost_{t}^{dsm, do, shed}$$
cost_dsm_down_shed[t] P
$$\mathbb{R}$$ recovery_time_shift P
Minimum time between the end of one load shifting process and the start of another
$$\Delta t$$ timeincrement P
The time increment of the model
CONSTRAINT_GROUP = True
class oemof.solph.components.experimental._sink_dsm.SinkDSMDIWInvestmentBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Constraints for SinkDSM with “DIW” approach and investment

The following constraints are created for approach = ‘DIW’ with an investment object defined:

$\begin{split}& (1) \quad invest_{min} \leq invest \leq invest_{max} \\ & (2) \quad DSM_{t}^{up} = 0 \quad \forall t \quad if \space eligibility_{shift} = False \\ & (3) \quad DSM_{t}^{do, shed} = 0 \quad \forall t \quad if \space eligibility_{shed} = False \\ & (4) \quad \dot{E}_{t} = demand_{t} \cdot (invest + E_{exist}) + DSM_{t}^{up} - \sum_{tt=t-L}^{t+L} DSM_{tt,t}^{do, shift} - DSM_{t}^{do, shed} \quad \forall t \in \mathbb{T} \\ & (5) \quad DSM_{t}^{up} \cdot \eta = \sum_{tt=t-L}^{t+L} DSM_{t,tt}^{do, shift} \quad \forall t \in \mathbb{T} \\ & (6) \quad DSM_{t}^{up} \leq E_{t}^{up} \cdot (invest + E_{exist}) \ s_{flex, up} \quad \forall t \in \mathbb{T} \\ & (7) \quad \sum_{t=tt-L}^{tt+L} DSM_{t,tt}^{do, shift} + DSM_{tt}^{do, shed} \leq E_{tt}^{do} \cdot (invest + E_{exist}) \cdot s_{flex, do} \quad \forall tt \in \mathbb{T} \\ & (8) \quad DSM_{tt}^{up} + \sum_{t=tt-L}^{tt+L} DSM_{t,tt}^{do, shift} + DSM_{tt}^{do, shed} \leq max \{ E_{tt}^{up} \cdot s_{flex, up}, E_{tt}^{do} \cdot s_{flex, do} \} \cdot (invest + E_{exist}) \quad \forall tt \in \mathbb{T} \\ & (9) \quad \sum_{tt=t}^{t+R-1} DSM_{tt}^{up} \leq E_{t}^{up} \cdot (invest + E_{exist}) \cdot s_{flex, up} \cdot L \cdot \Delta t \quad \forall t \in \mathbb{T} \\ & (10) \quad \sum_{tt=t}^{t+R-1} DSM_{tt}^{do, shed} \leq E_{t}^{do} \cdot (invest + E_{exist}) \cdot s_{flex, do} \cdot t_{shed} \cdot \Delta t \quad \forall t \in \mathbb{T} \\\end{split}$

Note: For the sake of readability, the handling of indices is not displayed here. E.g. evaluating a variable for t-L may lead to a negative and therefore infeasible index. This is addressed by limiting the sums to non-negative indices within the model index bounds. Please refer to the constraints implementation themselves.

The following parts of the objective function are created:

• Investment annuity:
$\begin{split}invest \cdot costs_{invest} \\\end{split}$
• Variable costs:
$DSM_{t}^{up} \cdot cost_{t}^{dsm, up} + \sum_{tt=0}^{T} DSM_{t, tt}^{do, shift} \cdot cost_{t}^{dsm, do, shift} + DSM_{t}^{do, shed} \cdot cost_{t}^{dsm, do, shed} \quad \forall t \in \mathbb{T}$

Table: Symbols and attribute names of variables and parameters

The following variables and parameters are exclusively used for investment modeling:

Variables (V) and Parameters (P)
symbol attribute type explanation
$$invest$$ invest V DSM capacity invested in. Equals to the additionally installed capacity. The capacity share eligible for a shift is determined by flex share(s).
$$invest_{min}$$ minimum
P minimum investment
$$invest_{max}$$ maximum
P maximum investment
$$E_{exist}$$ existing
P existing DSM capacity
$$s_{flex, up}$$ flex_share_up
P Share of invested capacity that may be shift upwards at maximum
$$s_{flex, do}$$ flex_share_do
P Share of invested capacity that may be shift downwards at maximum
$$costs_{invest}$$ ep_costs
P specific investment annuity
$$T$$   P Overall amount of time steps (cardinality)
CONSTRAINT_GROUP = True
class oemof.solph.components.experimental._sink_dsm.SinkDSMDLRBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Constraints for SinkDSM with “DLR” approach

The following constraints are created for approach = ‘DLR’:

$\begin{split}& (1) \quad DSM_{h, t}^{up} = 0 \quad \forall h \in H_{DR} \forall t \in \mathbb{T} \quad if \space eligibility_{shift} = False \\ & (2) \quad DSM_{t}^{do, shed} = 0 \quad \forall t \in \mathbb{T} \quad if \space eligibility_{shed} = False \\ & (3) \quad \dot{E}_{t} = demand_{t} \cdot demand_{max} + \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo} - DSM_{h, t}^{do, shift} - DSM_{h, t}^{balanceUp}) - DSM_{t}^{do, shed} \quad \forall t \in \mathbb{T} \\ & (4) \quad DSM_{h, t}^{balanceDo} = \frac{DSM_{h, t - h}^{do, shift}}{\eta} \quad \forall h \in H_{DR} \forall t \in [h..T] \\ & (5) \quad DSM_{h, t}^{balanceUp} = DSM_{h, t-h}^{up} \cdot \eta \quad \forall h \in H_{DR} \forall t \in [h..T] \\ & (6) \quad DSM_{h, t}^{do, shift} = 0 \quad \forall h \in H_{DR} \forall t \in [T - h..T] \\ & (7) \quad DSM_{h, t}^{up} = 0 \quad \forall h \in H_{DR} \forall t \in [T - h..T] \\ & (8) \quad \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{do, shift} + DSM_{h, t}^{balanceUp}) + DSM_{t}^{do, shed} \leq E_{t}^{do} \cdot E_{max, do} \quad \forall t \in \mathbb{T} \\ & (9) \quad \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo}) \leq E_{t}^{up} \cdot E_{max, up} \quad \forall t \in \mathbb{T} \\ & (10) \quad \Delta t \cdot \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{do, shift} - DSM_{h, t}^{balanceDo} \cdot \eta) = W_{t}^{levelDo} - W_{t-1}^{levelDo} \quad \forall t \in [1..T] \\ & (11) \quad \Delta t \cdot \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} \cdot \eta - DSM_{h, t}^{balanceUp}) = W_{t}^{levelUp} - W_{t-1}^{levelUp} \quad \forall t \in [1..T] \\ & (12) \quad W_{t}^{levelDo} \leq \overline{E}_{t}^{do} \cdot E_{max, do} \cdot t_{shift} \quad \forall t \in \mathbb{T} \\ & (13) \quad W_{t}^{levelUp} \leq \overline{E}_{t}^{up} \cdot E_{max, up} \cdot t_{shift} \quad \forall t \in \mathbb{T} \\ & (14) \quad \displaystyle\sum_{t=0}^{T} DSM_{t}^{do, shed} \leq E_{max, do} \cdot \overline{E}_{t}^{do} \cdot t_{shed} \cdot n^{yearLimitShed} \\ & (15) \quad \displaystyle\sum_{t=0}^{T} \sum_{h=1}^{H_{DR}} DSM_{h, t}^{do, shift} \leq E_{max, do} \cdot \overline{E}_{t}^{do} \cdot t_{shift} \cdot n^{yearLimitShift} \\ (optional \space constraint) \\ & (16) \quad \displaystyle\sum_{t=0}^{T} \sum_{h=1}^{H_{DR}} DSM_{h, t}^{up} \leq E_{max, up} \cdot \overline{E}_{t}^{up} \cdot t_{shift} \cdot n^{yearLimitShift} \\ (optional \space constraint) \\ & (17) \quad \displaystyle\sum_{h=1}^{H_{DR}} DSM_{h, t}^{do, shift} \leq E_{max, do} \cdot \overline{E}_{t}^{do} \cdot t_{shift} - \displaystyle\sum_{t'=1}^{t_{dayLimit}} \sum_{h=1}^{H_{DR}} DSM_{h, t - t'}^{do, shift} \quad \forall t \in [t-t_{dayLimit}..T] \\ (optional \space constraint) \\ & (18) \quad \displaystyle\sum_{h=1}^{H_{DR}} DSM_{h, t}^{up} \leq E_{max, up} \cdot \overline{E}_{t}^{up} \cdot t_{shift} - \displaystyle\sum_{t'=1}^{t_{dayLimit}} \sum_{h=1}^{H_{DR}} DSM_{h, t - t'}^{up} \quad \forall t \in [t-t_{dayLimit}..T] \\ (optional \space constraint) \\ & (19) \quad \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo} + DSM_{h, t}^{do, shift} + DSM_{h, t}^{balanceUp}) + DSM_{t}^{do, shed} \leq \max \{E_{t}^{up} \cdot E_{max, up}, E_{t}^{do} \cdot E_{max, do} \} \quad \forall t \in \mathbb{T} \\ (optional \space constraint) \\ &\end{split}$

Note: For the sake of readability, the handling of indices is not displayed here. E.g. evaluating a variable for t-L may lead to a negative and therefore infeasible index. This is addressed by limiting the sums to non-negative indices within the model index bounds. Please refer to the constraints implementation themselves.

The following parts of the objective function are created:

$\begin{split}\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo}) \cdot cost_{t}^{dsm, up} + \sum_{h=1}^{H_{DR}} (DSM_{h, t}^{do, shift} + DSM_{h, t}^{balanceUp}) \cdot cost_{t}^{dsm, do, shift} + DSM_{t}^{do, shed} \cdot cost_{t}^{dsm, do, shed} \quad \forall t \in \mathbb{T} \\\end{split}$

Table: Symbols and attribute names of variables and parameters

Variables (V) and Parameters (P)
symbol attribute type explanation
$$DSM_{h, t}^{up}$$ dsm_up[g,h,t]
V DSM up shift (additional load) in hour t with delay time h
$$DSM_{h, t}^{do, shift}$$
dsm_do_shift[g,h, t]
V DSM down shift (less load) in hour t with delay time h
$$DSM_{h, t}^{balanceUp}$$
balance_dsm_up[g,h,t]
V DSM down shift (less load) in hour t with delay time h to balance previous upshift
$$DSM_{h, t}^{balanceDo}$$
balance_dsm_do[g,h,t]
V DSM up shift (additional load) in hour t with delay time h to balance previous downshift
$$DSM_{t}^{do, shed}$$
dsm_do_shed[g, t]
V DSM shedded (capacity shedded, i.e. not compensated for)
$$\dot{E}_{t}$$ flow[g,t] V Energy flowing in from (electrical) inflow bus
$$h$$ element of delay_time P
delay time for load shift (integer value from set of feasible delay times per DSM portfolio) (time until the energy balance has to be levelled out again; roundtrip time of one load shifting cycle, i.e. time window for upshift and compensating downshift)
$$H_{DR}$$
range(length(:attr:~SinkDSM.delay_time) + 1)
P Set of feasible delay times for load shift of a certain DSM portfolio (time until the energy balance has to be levelled out again; roundtrip time of one load shifting cycle, i.e. time window for upshift and compensating downshift)
$$t_{shift}$$ shift_time P
Maximum time for a shift in one direction, i. e. maximum time for an upshift or a downshift in a load shifting cycle
$$t_{she}$$ shed_time P
Maximum time for one load shedding process
$$demand_{t}$$ demand[t] P
(Electrical) demand series (normalized)
$$demand_{max}$$ max_demand P
Maximum demand value
$$E_{t}^{do}$$ capacity_down[t] P
Capacity allowed for a load adjustment downwards (normalized) (DSM down shift + DSM shedded)
$$E_{t}^{up}$$ capacity_up[t] P
Capacity allowed for a shift upwards (normalized) (DSM up shift)
$$E_{do, max}$$ max_capacity_down P
Maximum capacity allowed for a load adjustment downwards (DSM down shift + DSM shedded)
$$E_{up, max}$$ max_capacity_up P
Capacity allowed for a shift upwards (normalized) (DSM up shift)
$$\eta$$ efficiency P Efficiency loss for load shifting processes
$$\mathbb{T}$$   P Set of time steps
$$T$$   P Overall amount of time steps (cardinality)
$$eligibility_{shift}$$
shift_eligibility P
Boolean parameter indicating if unit can be used for load shifting
$$eligibility_{shed}$$
shed_eligibility P
Boolean parameter indicating if unit can be used for load shedding
$$cost_{t}^{dsm, up}$$ cost_dsm_up[t]
P Variable costs for an upwards shift
$$cost_{t}^{dsm, do, shift}$$
cost_dsm_down_shift[t] P
Variable costs for a downwards shift (load shifting)
$$cost_{t}^{dsm, do, shed}$$
cost_dsm_down_shed[t] P
$$\Delta t$$ timeincrement P
The time increment of the model
$$n_{yearLimitshift}$$ n_yearLimitShift
P Maximum allowed number of load shifts (at full capacity) in the optimization timeframe
$$n_{yearLimitshed}$$ n_yearLimitShed
P Maximum allowed number of load sheds (at full capacity) in the optimization timeframe
$$t_{dayLimit}$$ t_dayLimit
P Maximum duration of load shifts at full capacity per day resp. in the last hours before the current
CONSTRAINT_GROUP = True
class oemof.solph.components.experimental._sink_dsm.SinkDSMDLRInvestmentBlock(*args, **kwargs)[source]

Constraints for SinkDSM with “DLR” approach and investment

The following constraints are created for approach = ‘DLR’ with an investment object defined:

$\begin{split}& (1) \quad invest_{min} \leq invest \leq invest_{max} \\ & (2) \quad DSM_{h, t}^{up} = 0 \quad \forall h \in H_{DR} \forall t \in \mathbb{T} \quad if \space eligibility_{shift} = False \\ & (3) \quad DSM_{t}^{do, shed} = 0 \quad \forall t \in \mathbb{T} \quad if \space eligibility_{shed} = False \\ & (4) \quad \dot{E}_{t} = demand_{t} \cdot (invest + E_{exist}) + \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo} - DSM_{h, t}^{do, shift} - DSM_{h, t}^{balanceUp}) - DSM_{t}^{do, shed} \quad \forall t \in \mathbb{T} \\ & (5) \quad DSM_{h, t}^{balanceDo} = \frac{DSM_{h, t - h}^{do, shift}}{\eta} \quad \forall h \in H_{DR} \forall t \in [h..T] \\ & (6) \quad DSM_{h, t}^{balanceUp} = DSM_{h, t-h}^{up} \cdot \eta \quad \forall h \in H_{DR} \forall t \in [h..T] \\ & (7) \quad DSM_{h, t}^{do, shift} = 0 \quad \forall h \in H_{DR} \forall t \in [T - h..T] \\ & (8) \quad DSM_{h, t}^{up} = 0 \quad \forall h \in H_{DR} \forall t \in [T - h..T] \\ & (9) \quad \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{do, shift} + DSM_{h, t}^{balanceUp}) + DSM_{t}^{do, shed} \leq E_{t}^{do} \cdot (invest + E_{exist}) \cdot s_{flex, do} \quad \forall t \in \mathbb{T} \\ & (10) \quad \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo}) \leq E_{t}^{up} \cdot (invest + E_{exist}) \cdot s_{flex, up} \quad \forall t \in \mathbb{T} \\ & (11) \quad \Delta t \cdot \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{do, shift} - DSM_{h, t}^{balanceDo} \cdot \eta) = W_{t}^{levelDo} - W_{t-1}^{levelDo} \quad \forall t \in [1..T] \\ & (12) \quad \Delta t \cdot \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} \cdot \eta - DSM_{h, t}^{balanceUp}) = W_{t}^{levelUp} - W_{t-1}^{levelUp} \quad \forall t \in [1..T] \\ & (13) \quad W_{t}^{levelDo} \leq \overline{E}_{t}^{do} \cdot (invest + E_{exist}) \cdot s_{flex, do} \cdot t_{shift} \quad \forall t \in \mathbb{T} \\ & (14) \quad W_{t}^{levelUp} \leq \overline{E}_{t}^{up} \cdot (invest + E_{exist}) \cdot s_{flex, up} \cdot t_{shift} \quad \forall t \in \mathbb{T} \\ & (15) \quad \displaystyle\sum_{t=0}^{T} DSM_{t}^{do, shed} \leq (invest + E_{exist}) \cdot s_{flex, do} \cdot \overline{E}_{t}^{do} \cdot t_{shed} \cdot n^{yearLimitShed} \\ & (16) \quad \displaystyle\sum_{t=0}^{T} \sum_{h=1}^{H_{DR}} DSM_{h, t}^{do, shift} \leq (invest + E_{exist}) \cdot s_{flex, do} \cdot \overline{E}_{t}^{do} \cdot t_{shift} \cdot n^{yearLimitShift} \\ (optional \space constraint) \\ & (17) \quad \displaystyle\sum_{t=0}^{T} \sum_{h=1}^{H_{DR}} DSM_{h, t}^{up} \leq (invest + E_{exist}) \cdot s_{flex, up} \cdot \overline{E}_{t}^{up} \cdot t_{shift} \cdot n^{yearLimitShift} \\ (optional \space constraint) \\ & (18) \quad \displaystyle\sum_{h=1}^{H_{DR}} DSM_{h, t}^{do, shift} \leq (invest + E_{exist}) \cdot s_{flex, do} \cdot \overline{E}_{t}^{do} \cdot t_{shift} - \displaystyle\sum_{t'=1}^{t_{dayLimit}} \sum_{h=1}^{H_{DR}} DSM_{h, t - t'}^{do, shift} \quad \forall t \in [t-t_{dayLimit}..T] \\ (optional \space constraint) \\ & (19) \quad \displaystyle\sum_{h=1}^{H_{DR}} DSM_{h, t}^{up} \leq (invest + E_{exist}) \cdot s_{flex, up} \cdot \overline{E}_{t}^{up} \cdot t_{shift} - \displaystyle\sum_{t'=1}^{t_{dayLimit}} \sum_{h=1}^{H_{DR}} DSM_{h, t - t'}^{up} \quad \forall t \in [t-t_{dayLimit}..T] \\ (optional \space constraint) \\ & (20) \quad \displaystyle\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo} + DSM_{h, t}^{do, shift} + DSM_{h, t}^{balanceUp}) + DSM_{t}^{shed} \leq \max \{E_{t}^{up} \cdot s_{flex, up}, E_{t}^{do} \cdot s_{flex, do} \} \cdot (invest + E_{exist}) \quad \forall t \in \mathbb{T} \\ (optional \space constraint) \\ &\end{split}$

Note: For the sake of readability, the handling of indices is not displayed here. E.g. evaluating a variable for t-L may lead to a negative and therefore infeasible index. This is addressed by limiting the sums to non-negative indices within the model index bounds. Please refer to the constraints implementation themselves.

The following parts of the objective function are created:

• Investment annuity:
$\begin{split}invest \cdot costs_{invest} \\\end{split}$
• Variable costs:
$\begin{split}\sum_{h=1}^{H_{DR}} (DSM_{h, t}^{up} + DSM_{h, t}^{balanceDo}) \cdot cost_{t}^{dsm, up} + \sum_{h=1}^{H_{DR}} (DSM_{h, t}^{do, shift} + DSM_{h, t}^{balanceUp}) \cdot cost_{t}^{dsm, do, shift} + DSM_{t}^{do, shed} \cdot cost_{t}^{dsm, do, shed} \quad \forall t \in \mathbb{T} \\\end{split}$

Table: Symbols and attribute names of variables and parameters

The following variables and parameters are exclusively used for investment modeling:

Variables (V) and Parameters (P)
symbol attribute type explanation
$$invest$$ invest V DSM capacity invested in. Equals to the additionally installed capacity. The capacity share eligible for a shift is determined by flex share(s).
$$invest_{min}$$ minimum
P minimum investment
$$invest_{max}$$ maximum
P maximum investment
$$E_{exist}$$ existing
P existing DSM capacity
$$s_{flex, up}$$ flex_share_up
P Share of invested capacity that may be shift upwards at maximum
$$s_{flex, do}$$ flex_share_do
P Share of invested capacity that may be shift downwards at maximum
$$costs_{invest}$$ ep_costs
P specific investment annuity
CONSTRAINT_GROUP = True
class oemof.solph.components.experimental._sink_dsm.SinkDSMOemofBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Constraints for SinkDSM with “oemof” approach

The following constraints are created for approach = ‘oemof’:

$\begin{split}& (1) \quad DSM_{t}^{up} = 0 \quad \forall t \quad if \space eligibility_{shift} = False \\ & (2) \quad DSM_{t}^{do, shed} = 0 \quad \forall t \quad if \space eligibility_{shed} = False \\ & (3) \quad \dot{E}_{t} = demand_{t} \cdot demand_{max} + DSM_{t}^{up} - DSM_{t}^{do, shift} - DSM_{t}^{do, shed} \quad \forall t \in \mathbb{T} \\ & (4) \quad DSM_{t}^{up} \leq E_{t}^{up} \cdot E_{up, max} \quad \forall t \in \mathbb{T} \\ & (5) \quad DSM_{t}^{do, shift} + DSM_{t}^{do, shed} \leq E_{t}^{do} \cdot E_{do, max} \quad \forall t \in \mathbb{T} \\ & (6) \quad \sum_{t=t_s}^{t_s+\tau} DSM_{t}^{up} \cdot \eta = \sum_{t=t_s}^{t_s+\tau} DSM_{t}^{do, shift} \quad \forall t_s \in \{k \in \mathbb{T} \mid k \mod \tau = 0\} \\ &\end{split}$

The following parts of the objective function are created:

$\begin{split}DSM_{t}^{up} \cdot cost_{t}^{dsm, up} + DSM_{t}^{do, shift} \cdot cost_{t}^{dsm, do, shift} + DSM_{t}^{do, shed} \cdot cost_{t}^{dsm, do, shed} \quad \forall t \in \mathbb{T} \\\end{split}$

Table: Symbols and attribute names of variables and parameters

Variables (V) and Parameters (P)
symbol attribute type explanation
$$DSM_{t}^{up}$$
dsm_up[g, t] V DSM up shift (capacity shifted upwards)
$$DSM_{t}^{do, shift}$$
dsm_do_shift[g, t]
V DSM down shift (capacity shifted downwards)
$$DSM_{t}^{do, shed}$$
dsm_do_shed[g, t]
V DSM shedded (capacity shedded, i.e. not compensated for)
$$\dot{E}_{t}$$ inputs V Energy flowing in from (electrical) inflow bus
$$demand_{t}$$ demand[t] P
(Electrical) demand series (normalized)
$$demand_{max}$$ max_demand P
Maximum demand value
$$E_{t}^{do}$$ capacity_down[t] P
Capacity allowed for a load adjustment downwards (normalized) (DSM down shift + DSM shedded)
$$E_{t}^{up}$$ capacity_up[t] P
Capacity allowed for a shift upwards (normalized) (DSM up shift)
$$E_{do, max}$$ max_capacity_down P
Maximum capacity allowed for a load adjustment downwards (DSM down shift + DSM shedded)
$$E_{up, max}$$ max_capacity_up P
Capacity allowed for a shift upwards (normalized) (DSM up shift)
$$\tau$$ shift_interval P Shift interval (time within which the energy balance must be levelled out
$$\eta$$ efficiency P Efficiency loss forload shifting processes
$$\mathbb{T}$$   P Time steps
$$eligibility_{shift}$$
shift_eligibility P
Boolean parameter indicating if unit can be used for load shifting
$$eligibility_{shed}$$
shed_eligibility P
Boolean parameter indicating if unit can be used for load shedding
$$cost_{t}^{dsm, up}$$ cost_dsm_up[t]
P Variable costs for an upwards shift
$$cost_{t}^{dsm, do, shift}$$
cost_dsm_down_shift[t] P
Variable costs for a downwards shift (load shifting)
$$cost_{t}^{dsm, do, shed}$$
cost_dsm_down_shed[t] P
CONSTRAINT_GROUP = True
class oemof.solph.components.experimental._sink_dsm.SinkDSMOemofInvestmentBlock(*args, **kwargs)[source]

Bases: pyomo.core.base.block.ScalarBlock

Constraints for SinkDSM with “oemof” approach and investment

The following constraints are created for approach = ‘oemof’ with an investment object defined:

$\begin{split}& (1) \quad invest_{min} \leq invest \leq invest_{max} \\ & (2) \quad DSM_{t}^{up} = 0 \quad \forall t \quad if \space eligibility_{shift} = False \\ & (3) \quad DSM_{t}^{do, shed} = 0 \quad \forall t \quad if \space eligibility_{shed} = False \\ & (4) \quad \dot{E}_{t} = demand_{t} \cdot (invest + E_{exist}) + DSM_{t}^{up} - DSM_{t}^{do, shift} - DSM_{t}^{do, shed} \quad \forall t \in \mathbb{T} \\ & (5) \quad DSM_{t}^{up} \leq E_{t}^{up} \cdot (invest + E_{exist}) \cdot s_{flex, up} \quad \forall t \in \mathbb{T} \\ & (6) \quad DSM_{t}^{do, shift} + DSM_{t}^{do, shed} \leq E_{t}^{do} \cdot (invest + E_{exist}) \cdot s_{flex, do} \quad \forall t \in \mathbb{T} \\ & (7) \quad \sum_{t=t_s}^{t_s+\tau} DSM_{t}^{up} \cdot \eta = \sum_{t=t_s}^{t_s+\tau} DSM_{t}^{do, shift} \quad \forall t_s \in \{k \in \mathbb{T} \mid k \mod \tau = 0\} \\ &\end{split}$

The following parts of the objective function are created:

• Investment annuity:
$\begin{split}invest \cdot costs_{invest} \\\end{split}$
• Variable costs:
$\begin{split}DSM_{t}^{up} \cdot cost_{t}^{dsm, up} + DSM_{t}^{do, shift} \cdot cost_{t}^{dsm, do, shift} + DSM_{t}^{do, shed} \cdot cost_{t}^{dsm, do, shed} \quad \forall t \in \mathbb{T} \\\end{split}$

Symbols and attribute names of variables and parameters

The following variables and parameters are exclusively used for investment modeling:

Variables (V) and Parameters (P)
symbol attribute type explanation
$$invest$$ invest V DSM capacity invested in. Equals to the additionally installed capacity. The capacity share eligible for a shift is determined by flex share(s).
$$invest_{min}$$ minimum
P minimum investment
$$invest_{max}$$ maximum
P maximum investment
$$E_{exist}$$ existing
P existing DSM capacity
$$s_{flex, up}$$ flex_share_up
P Share of invested capacity that may be shift upwards at maximum
$$s_{flex, do}$$ flex_share_do
P Share of invested capacity that may be shift downwards at maximum
$$costs_{invest}$$ epcosts
P specific investment annuity
CONSTRAINT_GROUP = True