Pay-as-produced PPA energy source node

Pay-as-produced PPA energy sources generate electricity from intermittent energy sources with a specific constraint on the variable operating expenses (OPEX) such that curtailed energy is also included in the OPEX. This node models a Power Purchase Agreement (PPA) contract.

Introduced type and its fields

The PayAsProducedPPA is implemented as a subtype of AbstractNonDisRES extending the existing functionality defined in EnergyModelsRenewableProducers.

The fields of a PayAsProducedPPA are:

• id:
  The field id is 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.

• 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 $[0, 1]$.

• opex_var::TimeProfile:
  The variable operational expenses are based on the capacity utilization through the variable :cap_use. Hence, they are 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 pay-as-produced PPA energy source, output should include your electricity resource. In practice, you should use a value of 1.

• 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.

  Constructor for `PayAsProducedPPA`

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

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

The PayAsProducedPPA node types utilize all variables from the AbstractNonDisRES 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.
• $\texttt{curtailment}$

Constraints

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

PayAsProducedPPA utilize in general the standard constraints that are implemented for a AbstractNonDisRES node as described in the documentation of EnergyModelsRenewableProducers. These standard constraints are:

• constraints_capacity: This function utilizes the method introduced for AbstractNonDisRes nodes to include the variable $\texttt{curtailment}$:

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

  and

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

• 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 investments. Nodes with investments are then no longer constrained by the parameter capacity.

• constraints_flow_out:

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

• 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_data: This function is only called for specified data of the pay-as-produced PPA energy source, see above.

The function constraints_opex_var is extended with a new method to include the variable operating expenses also for the variable $\texttt{curtailment}$:

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

This change allows to model systems corresponding to the current regulation in which renewable power generation from solar PV or wind is paid, independently of the actual production.