# Emission mitigation policies

## Capacity Reserve Margin

## CO$_2$ Capacity

`Dolphyn.co2_cap_power_hsc`

— Method`co2_cap_power_hsc(EP::Model, inputs::Dict, setup::Dict)`

This policy constraints mimics the CO$_2$ emissions cap and permit trading systems, allowing for emissions trading across each zone for which the cap applies. The constraint $p \in \mathcal{P}^{CO_2}$ can be flexibly defined for mass-based or rate-based emission limits for one or more model zones, where zones can trade CO$_2$ emissions permits and earn revenue based on their CO$_2$ allowance. Note that if the model is fully linear (e.g. no unit commitment or linearized unit commitment), the dual variable of the emissions constraints can be interpreted as the marginal CO$_2$ price per tonne associated with the emissions target. Alternatively, for integer model formulations, the marginal CO$_2$ price can be obtained after solving the model with fixed integer/binary variables.

The CO$_2$ emissions limit can be defined in one of the following ways: a) a mass-based limit defined in terms of annual CO$_2$ emissions budget (in million tonnes of CO2), b) a load-side rate-based limit defined in terms of tonnes CO$_2$ per MWh of demand and c) a generation-side rate-based limit defined in terms of tonnes CO$_2$ per MWh of generation.

## Energy Share Requirement

`Dolphyn.energy_share_requirement!`

— Method`energy_share_requirement!(EP::Model, inputs::Dict, setup::Dict)`

This function establishes constraints that can be flexibily applied to define alternative forms of policies that require generation of a minimum quantity of megawatt-hours from a set of qualifying resources, such as renewable portfolio standard (RPS) or clean electricity standard (CES) policies prevalent in different jurisdictions. These policies usually require that the annual MWh generation from a subset of qualifying generators has to be higher than a pre-specified percentage of load from qualifying zones. The implementation allows for user to define one or multiple RPS/CES style minimum energy share constraints, where each constraint can cover different combination of model zones to mimic real-world policy implementation (e.g. multiple state policies, multiple RPS tiers or overlapping RPS and CES policies). The number of energy share requirement constraints is specified by the user by the value of the GenX settings parameter `EnergyShareRequirement`

(this value should be an integer >=0). For each constraint $p \in \mathcal{P}^{ESR}$, we define a subset of zones $z \in \mathcal{Z}^{ESR}_{p} \subset \mathcal{Z}$ that are eligible for trading renewable/clean energy credits to meet the corresponding renewable/clean energy requirement. For each energy share requirement constraint $p \in \mathcal{P}^{ESR}$, we specify the share of total demand in each eligible model zone, $z \in \mathcal{Z}^{ESR}_{p}$, that must be served by qualifying resources, $\mathcal{G}_{p}^{ESR} \subset \mathcal{G}$:

\[\begin{aligned} &\sum_{z \in \mathcal{Z}_{p}^{ESR}} \sum_{y \in \mathcal{G}_{p}^{ESR}} \sum_{t \in \mathcal{T}} (\omega_{t} \times \Theta_{y,z,t}) \geq \sum_{z \in \mathcal{Z}^{ESR}_{p}} \sum_{t \in \mathcal{T}} (\mu_{p,z}^{ESR} \times \omega_{t} \times D_{z,t}) + \\ &\sum_{y \in \mathcal{O}} \sum_{z \in \mathcal{Z}^{ESR}_{p}} \sum_{t \in \mathcal{T}} \left(\mu_{p,z}^{ESR} \times \omega_{t} \times (\Pi_{y,z,t} - \Theta_{y,z,t}) \right) \hspace{1 cm} \forall p \in \mathcal{P}^{ESR} \\ \end{aligned}\]

The final term in the summation above adds roundtrip storage losses to the total load to which the energy share obligation applies. This term is included in the constraint if the GenX setup parameter `StorageLosses=1`

. If `StorageLosses=0`

, this term is removed from the constraint. In practice, most existing renewable portfolio standard policies do not account for storage losses when determining energy share requirements. However, with 100% RPS or CES policies enacted in several jurisdictions, policy makers may wish to include storage losses in the minimum energy share, as otherwise there will be a difference between total generation and total load that will permit continued use of non-qualifying resources (e.g. emitting generators).

## Minimum Capacity Requirement

`Dolphyn.minimum_capacity_requirement!`

— Method`minimum_capacity_requirement!(EP::Model, inputs::Dict, setup::Dict)`

The minimum capacity requirement constraint allows for modeling minimum deployment of a certain technology or set of eligible technologies across the eligible model zones and can be used to mimic policies supporting specific technology build out (i.e. capacity deployment targets/mandates for storage, offshore wind, solar etc.). The default unit of the constraint is in MW. For each requirement $p \in \mathcal{P}^{MinCapReq}$, we model the policy with the following constraint.

\[\begin{aligned} \sum_{y \in \mathcal{G} } \sum_{z \in \mathcal{Z} } \left( \epsilon_{y,z,p}^{MinCapReq} \times \Delta^{\text{total}}_{y,z} \right) \geq REQ_{p}^{MinCapReq} \hspace{1 cm} \forall p \in \mathcal{P}^{MinCapReq} \end{aligned}\]

Note that $\epsilon_{y,z,p}^{MinCapReq}$ is the eligiblity of a generator of technology $y$ in zone $z$ of requirement $p$ and will be equal to $1$ for eligible generators and will be zero for ineligible resources. The dual value of each minimum capacity constraint can be interpreted as the required payment (e.g. subsidy) per MW per year required to ensure adequate revenue for the qualifying resources.

## Maximum Capacity Requirement

`Dolphyn.maximum_capacity_requirement!`

— Method`maximum_capacity_requirement!(EP::Model, inputs::Dict, setup::Dict)`

The maximum capacity requirement constraint allows for modeling maximum deployment of a certain technology or set of eligible technologies across the eligible model zones and can be used to mimic policies supporting specific technology build out (i.e. capacity deployment targets/mandates for storage, offshore wind, solar etc.). The default unit of the constraint is in MW. For each requirement $p \in \mathcal{P}^{MaxCapReq}$, we model the policy with the following constraint.

\[\begin{aligned} \sum_{y \in \mathcal{G} } \sum_{z \in \mathcal{Z} } \left( \epsilon_{y,z,p}^{MaxCapReq} \times \Delta^{\text{total}}_{y,z} \right) \leq REQ_{p}^{MaxCapReq} \hspace{1 cm} \forall p \in \mathcal{P}^{MaxCapReq} \end{aligned}\]

Note that $\epsilon_{y,z,p}^{MaxCapReq}$ is the eligiblity of a generator of technology $y$ in zone $z$ of requirement $p$ and will be equal to $1$ for eligible generators and will be zero for ineligible resources. The dual value of each maximum capacity constraint can be interpreted as the required payment (e.g. subsidy) per MW per year required to ensure adequate revenue for the qualifying resources.