MultipleInputSink node

MultipleInputSink nodes are Sink nodes that allow the use of multiple energy carriers (resources) to satisfy a single demand. Each input resource has a conversion factor, and their combined contribution must meet the demand.

Introduced type and its fields

The MultipleInputSink node extends the Sink functionality to support multiple simultaneous energy inputs with equivalent service delivery. This is useful for modeling technologies such as hybrid heating systems or multi-fuel industrial boilers.

The fields of a MultipleInputSink node are given as:

• id:
  The field id is only used for providing a name to the node.
• cap::TimeProfile:
  The installed capacity corresponds to the nominal demand of the node.
  If the node should contain investments through the application of EnergyModelsInvestments, it is important to note that you can only use FixedProfile or StrategicProfile for the capacity, but not RepresentativeProfile or OperationalProfile. In addition, all values have to be non-negative.
• penalty::Dict{Symbol,<:TimeProfile}:
  The penalty dictionary is used for providing penalties for soft constraints to allow for both over and under delivering the demand.
  It must include the fields :surplus and :deficit. In addition, it is crucial that the sum of both values is larger than 0 to avoid an unconstrained model.
• input::Dict{<:Resource,<:Real}:
  The field input includes Resources with their corresponding conversion factors as dictionaries.
  All values have to be non-negative.
• data::Vector{Data}:
  An entry for providing additional data to the model. In the current version, it is used for both providing EmissionsData and additional investment data when EnergyModelsInvestments is used.
  Included constructor

  The field data is not required as we include a constructor when the value is excluded.

  Using `CaptureData`

  As a Sink node does not have any output, it is not possible to utilize CaptureData. If you still plan to specify it, you will receive an error in the model building.

Mathematical description

In the following mathematical equations, we use the name for variables and functions used in the model. Variables are in general represented as

$\texttt{var\_example}[index_1, index_2]$

with square brackets, while functions are represented as

$func\_example(index_1, index_2)$

with paranthesis.

Variables

Standard variables

The MultipleInputSink nodes utilize all standard variables from a Sink node, as described on the page Optimization variables. The variables include:

• $\texttt{opex\_var}$
• $\texttt{opex\_fixed}$
• $\texttt{cap\_use}$
• $\texttt{cap\_inst}$
• $\texttt{flow\_out}$
• $\texttt{sink\_surplus}$
• $\texttt{sink\_deficit}$
• $\texttt{emissions\_node}$ if EmissionsData is added to the field data

It does not add any additional variables.

Constraints

The following sections omit the direct inclusion of the vector of MultipleInputSink nodes. Instead, it is implicitly assumed that the constraints are valid $\forall n ∈ N$ for all MultipleInputSink types if not stated differently. In addition, all constraints are valid $\forall t \in T$ (that is in all operational periods) or $\forall t_{inv} \in T^{Inv}$ (that is in all investment periods).

Standard constraints

MultipleInputSink utilize in general the standard constraints that are implemented for a Sink node as described in the documentation of EnergyModelsBase. These standard constraints are:

• constraints_capacity:

  \[\texttt{cap\_use}[n, t] + \texttt{sink\_deficit}[n, t] = \texttt{cap\_inst}[n, t] + \texttt{sink\_surplus}[n, t]\]

• constraints_capacity_installed:

  \[\texttt{cap\_inst}[n, t] = capacity(n, t)\]

  Using investments

  The function constraints_capacity_installed is also used in EnergyModelsInvestments to incorporate the potential for investment. Nodes with investments are then no longer constrained by the parameter capacity.

• constraints_opex_fixed:
  The current implementation fixes the fixed operating expenses of a sink to 0.

  \[\texttt{opex\_fixed}[n, t_{inv}] = 0\]

• constraints_opex_var:

  \[\begin{aligned} \texttt{opex\_var}[n, t_{inv}] = & \\ \sum_{t \in t_{inv}} & surplus\_penalty(n, t) \times \texttt{sink\_surplus}[n, t] + \\ & deficit\_penalty(n, t) \times \texttt{sink\_deficit}[n, t] \times \\ & scale\_op\_sp(t_{inv}, t) \end{aligned}\]

  The function `scale_op_sp`

  The function $scale\_op\_sp(t_{inv}, t)$ calculates the scaling factor between operational and investment periods. It also takes into account potential operational scenarios and their probability as well as representative periods.

• constraints_data:
  This function is only called for specified additional data, see above.

The function constraints_flow_in receives a new method to account for that the individual resources can be used interchangeably adjusted by their specific conversion factor:

\[\sum_{p \in P} \frac{\texttt{inflow}[n,t,p]}{inputs(n,p)}=\texttt{cap\_use}[n,t]\]

The total effective input from all resources (accounting for their conversion factors) must equal the capacity used to meet demand.