Non-dispatchable renewable energy source node

Non-dispatchable renewable energy sources generate electricity from intermittent energy sources. Examples for intermittent energy sources are solar irradiation, the wind, or the flow within rivers. Although these energy sources have a constant nominal capacity, their production depends on intermittent energy sources. Although EnergyModelsX allows for capacities varying on the operational level, it is then not possible to include investments for a technology. As a consequence, the design of the RefSource is not satisfactory, when considering potential investments in capacities.=.

Hence, it is necessary to implement a source node representing intermittent renewable energy generation.

Introduced type and its field

The NonDisRES is implemented as equivalent to a RefSource. Hence, it utilizes the same functions declared in EnergyModelsBase.

Standard fields

The standard fields are given as:

• id:
  The field id is only used for providing a name to the node. This is similar to the approach utilized in EnergyModelsBase.
• cap::TimeProfile:
  The installed capacity corresponds to the nominal capacity 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.
• opex_var::TimeProfile:
  The variable operational expenses are based on the capacity utilization through the variable :cap_use. Hence, it is directly related to the specified output ratios. The variable operating expenses can be provided as OperationalProfile as well.
• opex_fixed::TimeProfile:
  The fixed operating expenses are relative to the installed capacity (through the field cap) and the chosen duration of a strategic period as outlined on Utilize TimeStruct.
  It is important to note that you can only use FixedProfile or StrategicProfile for the fixed OPEX, but not RepresentativeProfile or OperationalProfile. In addition, all values have to be non-negative.
• output::Dict{<:Resource, <:Real}:
  The field output includes Resources with their corresponding conversion factors as dictionaries. In the case of a non-dispatchable renewable energy source, output should always include your electricity resource.In practice, you should use a value of 1.
  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 only relevant for additional investment data when EnergyModelsInvestments is used.
  Note

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

Additional fields

NonDisRES nodes add a single additional field compared to a RefSource:

• profile::TimeProfile:
  The profile is used as a multiplier to the installed capacity to represent the maximum actual capacity in each operational period.
  The profile should be provided as OperationalProfile or at least as RepresentativeProfile. In addition, all values should be in the range $[0, 1]$.

This field is at the 3ʳᵈ position below the field cap as shown in NonDisRES.

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 non-dispatchable renewable energy source node types utilize all standard variables from the RefSource node type, as described on the page Optimization variables. The variables include:

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

Additional variables

NonDisRES nodes should keep track on the curtailment of the electricity, that is the unused capacity in each operational time period. Hence, a single additional variable is declared through dispatching on the method EnergyModelsBase.variables_node():

• $\texttt{curtailment}[n, t]$: Curtailed capacity of source $n$ in operational period $t$ with a typical unit of MW.
  The curtailed electricity specifies the unused generation capacity of the non-dispatchable energy source. It is currently only used in the calculation, but not with a cost. This can be added by the user, if desired.

Constraints

The following sections omit the direction inclusion of the vector of CO₂ source nodes. Instead, it is implicitly assumed that the constraints are valid $\forall n ∈ N^{\text{NonDisRES}\_source}$ for all NonDisRES 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 strategic periods).

Standard constraints

Non-dispatchable renewable energy source nodes utilize in general the standard constraints described on Constraint functions. In fact, they use the same create_node function as a RefSource node. 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_out:

  \[\texttt{flow\_out}[n, t, p] = outputs(n, p) \times \texttt{cap\_use}[n, t] \qquad \forall p \in outputs(n) \setminus \{\text{CO}_2\}\]

• constraints_opex_fixed:

  \[\texttt{opex\_fixed}[n, t_{inv}] = opex\_fixed(n, t_{inv}) \times \texttt{cap\_inst}[n, first(t_{inv})]\]

  Why do we use `first()`

  The variables $\texttt{cap\_inst}$ are declared over all operational periods (see the section on Capacity variables for further explanations). Hence, we use the function $first(t_{inv})$ to retrieve the installed capacities in the first operational period of a given strategic period $t_{inv}$ in the function constraints_opex_fixed.

• constraints_opex_var:

  \[\texttt{opex\_var}[n, t_{inv}] = \sum_{t \in t_{inv}} opex\_var(n, t) \times \texttt{cap\_use}[n, t] \times scale\_op\_sp(t_{inv}, t)\]

  The function `scale_op_sp`

  The function $scale\_op\_sp(t_{inv}, t)$ calculates the scaling factor between operational and strategic 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 data of the non-dispatchable renewable energy source, see above.

The function constraints_capacity is extended with a new method for non-dispatchable renewable energy source nodes to allow the inclusion of the production profile and the variable $\texttt{curtailment}[n, t]$. It now includes two individual constraints:

\[\texttt{cap\_use}[n, t] \leq \texttt{cap\_inst}[n, t]\]

and

\[\texttt{cap\_use}[n, t] + \texttt{curtailment}[n, t] = profile(n, t) \times \texttt{cap\_inst}[n, t]\]

This function still calls the subfunction constraints_capacity_installed to limit the variable $\texttt{cap\_inst}[n, t]$ or provide capacity investment options.

Additional constraints

NonDisRES nodes do not add additional constraints.