StratPeriodDemandSink node

StratPeriodDemandSink nodes represent flexible demand sinks where the demand must be fulfilled on an annual level while individual demand periods can be specified to incorporate lower and upper bounds on the demand satisfaction per demand period. A demand period is a consecutive range of operational periods, that together will model, e.g., a day, a week or comparable.

Introduced type and its fields

The StratPeriodDemandSink node is a subtype of AbstractPeriodDemandSink which reutilizes the variables and some utility functions. It provides however new capacity and variable operating expenses constraints.

Standard fields

The standard fields are given as:

• id:
  The field id is only used for providing a name to the node.

• cap::TimeProfile:
  The maximum amount of demand that can be met in each operational period.
  A warning is printed if the sum of the scaled demand in a strategic period is lower than the strategic demand.

• 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 in each demand period is larger than 0 to avoid an unconstrained model.

  Chosen values

  The same value is chosen for violations of the lower and upper bounds for the individual demand periods and the strategic demand.

  The implementation for the demand period is relative to the chosen duration of a strategic period while the demand period deficit and surplus is scaled to a strategic period in the calculation.

• 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{<:ExtensionData}:
  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.

Additional fields

StratPeriodDemandSinks require additional fields to specify both the periods and their respective demands:

• strat_demand::TimeProfile:
  The total demand within a strategic period relative to a duration of 1 of a strategic period. If a duration of 1 corresponds to a year, this value will specify the annual demand that must be satisfied.
  It must be indexable by a strategic period, that is it can be specified as FixedProfile, StrategicProfile or StrategicStochasticProfile.

• period_duration::TimeProfile:
  Defines the total duration of the demand periods. For instance, if the duration of 1 of the operational time structure is 1 hour and period_duration = FixedProfile(24), then each demand period spans one day. Due to a constructor, it can either be specified as number (the same duration in all demand periods), as a vector (varying duration of each demand period), or as a time profile (e.g., varying period durations due to varying operational time structures).
  It cannot be specified as OperationalProfile.

• period_min::TimeProfile and period_max::TimeProfile:
  The fraction of annual demand that must be at least or can be at most satisfied within a demand period. The length of this time profile should match the number of demand periods (e.g., days) in the time structure.
  They cannot be specified as OperationalProfile. A warning is printed if either the sum of period_min is larger than 1 (guaranteeing a surplus penalty introduction) or if the sum of period_max is smaller than 1 (guaranteeing a deficit penalty introduction)

These fields are at the 3ʳᵈ and 4ᵗʰ position below the field cap as shown in StratPeriodDemandSink.

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 parantheses.

Variables

Standard variables

The StratPeriodDemandSink 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

Additional variables

StratPeriodDemandSink nodes declare in addition several variables through dispatching on the method EnergyModelsBase.variables_element() for including constraints for deficits and surplus for individual demand periods (as introduced by the method for AbstractPeriodDemandSink) and strategic periods (introduced through a dedicated method for StratPeriodDemandSink):

• $\texttt{demand\_sink\_surplus}[n, t_pd]$:
  Surplus of energy delivered beyond the required period_max fraction in demand period t_pd .
• $\texttt{demand\_sink\_deficit}[n, t_pd]$:
  Deficit of energy delivered relative to the required period_min fraction in demand period t_pd .
• $\texttt{demand\_sink\_strat\_surplus}[n, t_inv]$:
  Surplus of energy delivered beyond the required strat_demand in strategic period t_inv .
• $\texttt{demand\_sink\_strat\_deficit}[n, t_inv]$:
  Deficit of energy delivered relative to the required strat_demand in strategic period t_inv .

Constraints

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

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

• 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_flow_in:

  \[\texttt{flow\_in}[n, t, p] = inputs(n, p) \times \texttt{cap\_use}[n, t] \qquad \forall p \in inputs(n)\]

  Multiple inputs

  The constrained above allows for the utilization of multiple inputs with varying ratios. it is however necessary to deliver the fixed ratio of all inputs.

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

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

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

The function constraints_capacity is extended with a new method to account for the calculation of the period demand deficit and surplus.

The overall balance is modified as

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

while operational period surplus $\texttt{sink\_surplus}[n, t]$ is fixed to 0.

The deficit and surplus in a demand period can then be calculated as

\[\begin{aligned} \sum_{t \in t_{pd}} \texttt{​cap\_use}[n, t] \times duration(t) + {} & \texttt{demand\_sink\_deficit}[n, t_{pd}] \geq \\ & \frac{period\_demand\_min(n, t_{pd}) \times strategic\_demand(n, t_{inv})}{multiple(first(t_{pd})) / duration\_strat(t_{inv})} \\ \sum_{t \in t_{pd}} \texttt{​cap\_use}[n, t] \times duration(t) \leq {} & \texttt{demand\_sink\_surplus}[n, t_{pd}] + {} \\ & \frac{period\_demand\_max(n, t_{pd}) \times strategic\_demand(n, t_{inv})}{multiple(first(t_{pd})) / duration\_strat(t_{inv})} \end{aligned}\]

where $t_{pd}$ is the demand period consisting of a set of operational periods and $t_{inv}$ is the strategic period.

As a consequence, constraints_opex_var requires as well a new method as we consider the deficit within a strategic period and penalize violation of the period demand bounds:

\[\begin{aligned} \texttt{opex\_var}[n, t_{inv}] = {} & \texttt{demand\_sink\_strat\_surplus}[n, t_{inv}] \times \texttt{surplus\_penalty}(n, t_{inv}) + {}\\ & \texttt{demand\_sink\_strat\_deficit}[n, t_{inv}] \times \texttt{deficit\_penalty}(n, t_{inv}) + {}\\ & \sum_{t_{pd} ∈ periods(t_{inv})}(\texttt{demand\_sink\_surplus}[n, t_{pd}] \times \texttt{surplus\_penalty}(n, t_{pd}) + {}\\ &\phantom{\sum_{t_{pd} ∈ periods(t_{inv})}(} \texttt{demand\_sink\_deficit}[n, t_{pd}] \times \texttt{deficit\_penalty}(n, t_{pd})) \times {}\\ & scale\_op\_sp(t_{inv}, first(t_{pd})) / duration(first(t_{pd})) \end{aligned}\]