Emission mitigation policies

cap_reserve_margin!(EP::Model, inputs::Dict, setup::Dict)

Instead of modeling capacity reserve margin requirement (a.k.a. capacity market or resource adequacy requirement) using an annual constraint, we model each requirement with hourly constraint by simulating the activation of the capacity obligation. We define capacity reserve margin constraint for subsets of zones,$z \in \mathcal{Z}^{CRM}_{p}$, and each subset stands for a locational deliverability area (LDA) or a reserve sharing group. For thermal resources, the available capacity is the total capacity in the LDA derated by the outage rate, $\epsilon_{y,z,p}^{CRM}$. For storage ($y \in \mathcal{O}$), variable renewable energy ($y \in \mathcal{VRE}$), and flexibile demand resources ($y \in \mathcal{DF}$), the available capacity is the net injection into the transmission network in time step $t$ derated by the derating factor, also stored in the parameter, $\epsilon_{y,z,p}^{CRM}$. If the imported capacity is eligible to provide capacity to the CRM constraint, the inbound powerflow on all lines $\mathcal{L}_{p}^{in}$ in time step $t$ will be derated to form the available capacity from outside of the LDA. The reverse is true as well: the outbound derated powerflow on all lines $\mathcal{L}_{p}^{out}$ in time step $t$ is taken out from the total available capacity. The derating factor should be equal to the expected availability of the resource during periods when the capacity reserve constraint is binding (e.g. accounting for forced outages during supply constrained periods) and is similar to derating factors used in the capacity markets. On top of the flexible demand resources, load curtailment can also provide capacity (i.e., demand response or load management). We allow all segments of voluntary load curtailment, $s \geq 2 \in S$, to contribute to capacity requirements. The first segment $s = 1 \in S$ corresponds to involuntary demand curtailment or emergency load shedding at the price cap or value of lost load, and thus does not contribute to reserve requirements. Note that the time step-weighted sum of the shadow prices of this constraint corresponds to the capacity market payments reported by ISOs with mandate capacity market mechanism.

\[\begin{aligned} & \sum_{z \in \mathcal{Z}^{CRM}_{p}} \Big( \sum_{y \in \mathcal{H}} \epsilon_{y,z,p}^{CRM} \times \Delta^{\text{total}}_{y,z} + \sum_{y \in \mathcal{VRE}} \epsilon_{y,z,p}^{CRM} \times \Theta_{y,z,t} \\ + & \sum_{y \in \mathcal{O}} \epsilon_{y,z,p}^{CRM} \times \left(\Theta_{y,z,t} - \Pi_{y,z,t} \right) + \sum_{y \in \mathcal{DF}} \epsilon_{y,z,p}^{CRM} \times \left(\Pi_{y,z,t} - \Theta_{y,z,t} \right) \\ + & \sum_{l \in \mathcal{L}_{p}^{in}} \epsilon_{y,z,p}^{CRM} \times \Phi_{l,t} - \sum_{l \in \mathcal{L}_{p}^{out}} \epsilon_{y,z,p}^{CRM} \times \Phi_{l,t} + \sum_{s \geq 2} \Lambda_{s,t,z} \Big) \\ & \geq \sum_{z \in \mathcal{Z}^{CRM}_{p}} \left( \left(1 + RM_{z,p}^{CRM} \right) \times D_{z,t} \right) \hspace{1 cm} \forall t \in \mathcal{T}, \forall p\in \mathcal{P}^{CRM} \end{aligned}\]

Note that multiple capacity reserve margin requirements can be specified covering different individual zones or aggregations of zones, where the total number of constraints is specified by the GenX settings parameter CapacityReserveMargin (where this parameter should be an integer value > 0).

co2_cap!(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.

Mass-based emissions constraint

Mass-based emission limits are implemented in the following expression. For each constraint, $p \in \mathcal{P}^{CO_2}_{mass}$, we define a set of zones $z \in \mathcal{Z}^{CO_2}_{p,mass}$ that can trade CO$_2$ allowance. Input data for each constraint $p \in \mathcal{P}^{CO_2}_{mass}$ requires the CO$_2$ allowance/ budget for each model zone, $\epsilon^{CO_{2}}_{z,p, mass}$, to be provided in terms of million metric tonnes. For every generator $y$, the parameter $\epsilon_{y,z}^{CO_2}$ reflects the specific $CO_2$ emission intensity in tCO$_2$/MWh associated with its operation. The resulting constraint is given as:

\[\begin{aligned} \sum_{z \in \mathcal{Z}^{CO_2}_{p,mass}} \sum_{y \in \mathcal{G}} \sum_{t \in \mathcal{T}} \left(\epsilon_{y,z}^{CO_2} \times \omega_{t} \times \Theta_{y,z,t} \right) & \leq \sum_{z \in \mathcal{Z}^{CO_2}_{p,mass}} \epsilon^{CO_{2}}_{z,p, mass} \hspace{1 cm} \forall p \in \mathcal{P}^{CO_2}_{mass} \end{aligned}\]

In the above constraint, we include both power discharge and charge term for each resource to account for the potential for CO$_2$ emissions (or removal when considering negative emissions technologies) associated with each step. Note that if a limit is applied to each zone separately, then the set $\mathcal{Z}^{CO_2}_{p,mass}$ will contain only one zone with no possibility of trading. If a system-wide emission limit constraint is applied, then $\mathcal{Z}^{CO_2}_{p,mass}$ will be equivalent to a set of all zones.

Load-side rate-based emissions constraint

We modify the right hand side of the above mass-based constraint, $p \in \mathcal{P}^{CO_2}_{load}$, to set emissions target based on a CO$_2$ emission rate limit in tCO$_2$/MWh $\times$ the total demand served in each zone. In the following constraint, total demand served takes into account non-served energy and storage related losses. Here, $\epsilon_{z,p,load}^{maxCO_2}$ denotes the emission limit in terms on tCO$_2$/MWh.

\[\begin{aligned} \sum_{z \in \mathcal{Z}^{CO_2}_{p,load}} \sum_{y \in \mathcal{G}} \sum_{t \in \mathcal{T}} \left(\epsilon_{y,z}^{CO_2} \times \omega_{t} \times \Theta_{y,t,z} \right) \leq & \sum_{z \in \mathcal{Z}^{CO_2}_{p,load}} \sum_{t \in \mathcal{T}} \left(\epsilon_{z,p,load}^{CO_2} \times \omega_{t} \times D_{z,t} \right) \\ + & \sum_{z \in \mathcal{Z}^{CO_2}_{p,load}} \sum_{y \in \mathcal{O}} \sum_{t \in \mathcal{T}} \left(\epsilon_{z,p,load}^{CO_2} \times \omega_{t} \times \left(\Pi_{y,t,z} - \Theta_{y,t,z} \right) \right) \\ - & \sum_{z \in \mathcal{Z}^{CO_2}_{p,load}} \sum_{s \in \mathcal{S} } \sum_{t \in \mathcal{T}} \left(\epsilon_{z,p,load}^{CO_2} \times \omega_{t} \times \Lambda_{s,z,t}\right) \hspace{1 cm} \forall p \in \mathcal{P}^{CO_2}_{load} \end{aligned}\]

Generator-side emissions rate-based constraint

Similarly, a generation based emission constraint is defined by setting the emission limit based on the total generation times the carbon emission rate limit in tCO$_2$/MWh of the region. The resulting constraint is given as:

\[\begin{aligned} \sum_{z \in \mathcal{Z}^{CO_2}_{p,gen}} \sum_{y \in \mathcal{G}} \sum_{t \in \mathcal{T}} & \left(\epsilon_{y,z}^{CO_2} \times \omega_{t} \times \Theta_{y,t,z} \right) \\ \leq \sum_{z \in \mathcal{Z}^{CO_2}_{p,gen}} \sum_{y \in \mathcal{G}} \sum_{t \in \mathcal{T}} & \left(\epsilon_{z,p,gen}^{CO_2} \times \omega_{t} \times \Theta_{y,t,z} \right) \hspace{1 cm} \forall p \in \mathcal{P}^{CO_2}_{gen} \end{aligned}\]

Note that the generator-side rate-based constraint can be used to represent a fee-rebate (``feebate'') system: the dirty generators that emit above the bar ($\epsilon_{z,p,gen}^{maxCO_2}$) have to buy emission allowances from the emission regulator in the region $z$ where they are located; in the same vein, the clean generators get rebates from the emission regulator at an emission allowance price being the dual variable of the emissions rate constraint.

write_co2_cap(path::AbstractString, inputs::Dict, setup::Dict, EP::Model)

Function for reporting carbon price associated with carbon cap constraints.

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!(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.

load_maximum_capacity_requirement!(path::AbstractString, inputs::Dict, setup::Dict)

Read input parameters related to maximum capacity requirement constraints (e.g. technology specific deployment mandates)

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.