AbstractMultipleInputSinkStrat node

AbstractMultipleInputSinkStrat are Sink nodes that models flexible energy service demands that can be met by a combination of multiple input resources. Unlike MultipleInputSink nodes, we enforce that the ratio between the different input resources is the same in all operational periods of an investment period. The AbstractMultipleInputSinkStrat introduces strategic-period-based input fractions, used to proportionally allocate resource inflows across each operational period. This allows for continuous blending of energy carriers in a flexible and cost-optimal way.

Introduced types and their fields

We implement two types of AbstractMultipleInputSinkStrat nodes:

1. ContinuousMultipleInputSinkStrat and
2. BinaryMultipleInputSinkStrat.

ContinuousMultipleInputSinkStrat allows for a continuous blend between the different input resources while BinaryMultipleInputSinkStrat requires that either one or the other resource is utilized.

Both nodes have the same fields. These fields are:

• 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 AbstractMultipleInputSinkStrat 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.

Additional variables

AbstractMultipleInputSinkStrat nodes declare in addition several variables through dispatching on the method EnergyModelsBase.variables_element() for including constraints for deficits and surplus for individual resources as well as what the fraction satisfied by each resource. These variables are for an AbstractMultipleInputSinkStrat node $n$ in operational period $t$:

• $\texttt{input\_frac\_strat}[n, t_{inv}, p]$:
  Fraction of the demand satisfied by input resource $p$ in strategic period $t_{inv}$. The fraction is limited between 0 and 1 in the case of ContinuousMultipleInputSinkStrat and is binary in the case of BinaryMultipleInputSinkStrat.
• $\texttt{sink\_surplus\_p}[n, t, p]$:
  Surplus of input resource $p$ in node $n$ in operational period $t$.
• $\texttt{sink\_deficit\_p}[n, t, p]$:
  Deficit of input resource $p$ in node $n$ in operational period $t$.

Constraints

The following sections omit the direct inclusion of the vector of AbstractMultipleInputSinkStrat nodes. Instead, it is implicitly assumed that the constraints are valid $\forall n ∈ N$ for all AbstractMultipleInputSinkStrat 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

AbstractMultipleInputSinkStrat 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_installed:

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

• 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_capacity is extended with a new method as we moved the capacity constraint to the function constraints_flow_in as outlined below. As a consequence, it only calls the function constraints_capacity_installed.

The function constraints_flow_in is extended with a new method to account for the potential of supplying the demand with multiple resources. The inlet overall flow balance is given by

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

The inlet flow is linked to the binary choice and the capacity through the following function:

\[\begin{aligned} \frac{\texttt{flow\_in}[n, t, p]}{inputs(n, p)} + & \texttt{sink\_deficit\_p}[n, t, p] = \\ & capacity(n, {t_{inv}}) \times \texttt{input\_frac\_strat}[n, t_{inv}, p] + \texttt{sink\_surplus\_p}[n, t, p] \end{aligned}\]

The variable $\texttt{input\_frac\_strat}$ must sum up to one to avoid problems with the overall mass balance.

\[\sum_{p \in P^{in}} \texttt{input\_frac\_strat}[n, t_{inv}, p] = 1\]

The sum of the individual surplus and deficits of each resource represent then subsequently the complete surplus and deficit.

\[\begin{aligned} \sum_{p \in P^{in}} \texttt{sink\_surplus\_p}[n, t, p] = & \texttt{sink\_surplus}[n, t] \\ \sum_{p \in P^{in}} \texttt{sink\_deficit\_p}[n, t, p] = & \texttt{sink\_deficit}[n, t] \\ \end{aligned}\]