Public API

Ancillary service fraction assigned to Storage Discharging to product p

Docs abbreviation: $sb^{std}_{p,t}$

Ancillary service fraction assigned to Storage Charging to product p

Docs abbreviation: $sb^{stc}_{p,t}$

Slack variable for energy storage levels < target storage levels

Docs abbreviation: $e^{st-}$

Slack variable for energy storage levels > target storage levels

Docs abbreviation: $e^{st+}$

Slack variable for the cycling limits to allow for more charging usage than the allowed limited

Docs nomenclature: $c^{ch-}$

Slack variable for the cycling limits to allow for more discharging usage than the allowed limited

Docs nomenclature: $c^{ds-}$

Slack variable for energy storage levels > target storage levels

Docs nomenclature: $z^{st, ch}$

Slack variable for energy storage levels > target storage levels

Docs abbreviation: $z^{st, ds}$

Auxiliary Variable for Storage Models that solve for total energy output

Struct to create the state of charge constraint limits.

The specified constraint is formulated as:

\[E_{st}^{min} \le e^{st}_{t} \le E_{st}^{max}, \quad \forall t \in \{1,\dots, T\}\]

Struct to create the storage cycling limits for the charge variable. Used when cycling_limits = true.

The specified constraint is formulated as:

\[\sum_{t \in \mathcal{T}} \left(\sum_{p \in \mathcal{P}^{\text{as}_\text{dn}}} R^*_{p,t} sb_{stc,p,t} + p^{st,ch}_{t} \right)\eta^{ch}_{st} \Delta t - c^{ch-} \leq C_{st} E^{max}_{st}\]

Struct to create the storage cycling limits for the discharge variable. Used when cycling_limits = true.

The specified constraint is formulated as:

\[\sum_{t \in \mathcal{T}} \left(\sum_{p \in \mathcal{P}^{\text{as}_\text{up}}} R^*_{p,t} sb_{std,p,t} + p^{st,ds}_{t}\right)\frac{1}{\eta^{ds}_{st}} \Delta t - c^{ds-} \leq C_{st} E^{max}_{st}\]

Struct to specify the individual product ancillary service coverage at the beginning of the period for charge and discharge variables.

The specified constraints are formulated as:

\[\begin{align*} & sb_{stc,p,1} \eta^{ch}_{st} N_{p} \Delta t \le E_{st}^{max} - e^{st}_0, \quad \forall p \in \mathcal{P}^{as_{dn}} \\ & sb_{stc,p,t} \eta^{ch}_{st} N_{p} \Delta t \le E_{st}^{max} - e^{st}_{t-1}, \quad \forall p \in \mathcal{P}^{as_{dn}}, \forall t \in \{2,\dots, T\} \\ & sb_{std,p,1} \frac{1}{\eta^{ds}_{st}} N_{p} \Delta t \leq e^{st}_0 - E^{min}_{st}, \quad \forall p \in \mathcal{P}^{as_{up}} \\ & sb_{std,p,t} \frac{1}{\eta^{ds}_{st}} N_{p} \Delta t \leq e^{st}_{t-1} - E^{min}_{st}, \quad \forall p \in \mathcal{P}^{as_{up}}, \forall t \in \{2,\dots, T\} \end{align*}\]

Struct to specify the individual product ancillary service coverage at the end of the period for charge and discharge variables.

The specified constraints are formulated as:

\[\begin{align*} & sb_{stc,p,t} \eta^{ch}_{st} N_{p} \Delta t \le E_{st}^{max} - e^{st}_{t}, \quad \forall p \in \mathcal{P}^{as_{dn}}, \forall t \in \{1,\dots, T\} \\ & sb_{std,p,t} \frac{1}{\eta^{ds}_{st}} N_{p} \Delta t \leq e^{st}_{t}- E^{min}_{st}, \quad \forall p \in \mathcal{P}^{as_{up}}, \forall t \in \{1,\dots, T\} \end{align*}\]

Struct to specify all products ancillary service coverage at the beginning of the period for charge and discharge variables. Used when the attribute complete_coverage = true.

The specified constraints are formulated as:

\[\begin{align*} & \sum_{p \in \mathcal{P}^{\text{as}_\text{dn}}} sb_{stc,p,1} \eta^{ch}_{st} N_{p} \Delta t \le E_{st}^{max} - e^{st}_0 \\ & \sum_{p \in \mathcal{P}^{\text{as}_\text{dn}}} sb_{stc,p,t} \eta^{ch}_{st} N_{p} \Delta t \le E_{st}^{max} - e^{st}_{t-1}, \quad \forall t \in \{2,\dots, T\} \\ & \sum_{p \in \mathcal{P}^{\text{as}_\text{up}}} sb_{std,p,1} \frac{1}{\eta^{ds}_{st}} N_{p} \Delta t \leq e^{st}_0 - E^{min}_{st} \\ & \sum_{p \in \mathcal{P}^{\text{as}_\text{up}}} sb_{std,p,t} \frac{1}{\eta^{ds}_{st}} N_{p} \Delta t \leq e^{st}_{t-1}- E^{min}_{st}, \quad \forall t \in \{2,\dots, T\} \end{align*}\]

Struct to specify all products ancillary service coverage at the end of the period for charge and discharge variables. Used when the attribute complete_coverage = true.

The specified constraints are formulated as:

\[\begin{align*} & \sum_{p \in \mathcal{P}^{\text{as}_\text{dn}}} sb_{stc,p,t} \eta^{ch}_{st} N_{p} \Delta t \le E_{st}^{max} - e^{st}_{t}, \quad \forall t \in \{1,\dots, T\} \\ & \sum_{p \in \mathcal{P}^{\text{as}_\text{up}}} sb_{std,p,t} \frac{1}{\eta^{ds}_{st}} N_{p} \Delta t \leq e^{st}_{t}- E^{min}_{st}, \quad \forall t \in \{1,\dots, T\} \end{align*}\]

Struct to specify an auxiliary constraint for adding charge and discharge into a single active power reserve variable.

The specified constraint is formulated as:

\[sb_{stc, p, t} + sb_{std, p, t} = r_{p,t}, \quad \forall p \in \mathcal{P}, \forall t \in \{1,\dots, T\}\]

Struct to specify the lower and upper bounds of the discharge variable considering reserves.

The specified constraints are formulated as:

\[\begin{align*} & p^{st, ds}_{t} + \sum_{p \in \mathcal{P}^{\text{as}_\text{up}}} sb_{std,p,t} \leq \text{ss}^{st}_{t}P^{max,ds}_{st} \quad \forall t \in \{1,\dots, T\} \\ & p^{st, ds}_{t} - \sum_{p \in \mathcal{P}^{ ext{as}_\text{dn}}} sb_{std,p,t} \geq 0, \quad \forall t \in \{1,\dots, T\} \end{align*}\]

Struct to specify the lower and upper bounds of the charge variable considering reserves.

The specified constraints are formulated as:

\[\begin{align*} &p^{st, ch}_{t} + \sum_{p \in \mathcal{P}^{\text{as}_\text{dn}}} sb_{stc,p,t} \leq (1 - \text{ss}^{st}_{t})P^{max,ch}_{st}, \quad \forall t \in \{1,\dots, T\} \\ & p^{st, ch}_{t} - \sum_{p \in \mathcal{P}^{\text{as}_\text{up}}} sb_{stc,p,t} \geq 0, \quad \forall t \in \{1,\dots, T\} \end{align*}\]

Parameter to define energy limit

Adds a constraint to enforce a minimum energy level target with a slack variable associated witha penalty term.

Adds a constraint to limit the sum of a variable over the number of periods to the source value