Thermal No Commit

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

This function defines the operating constraints for thermal power plants NOT subject to unit commitment constraints on power plant start-ups and shut-down decisions ($y \in H \setminus UC$).

Ramping limits

Thermal resources not subject to unit commitment ($y \in H \setminus UC$) adhere instead to the following ramping limits on hourly changes in power output:

\[\begin{aligned} \Theta_{y,z,t-1} - \Theta_{y,z,t} \leq \kappa_{y,z}^{down} \Delta^{\text{total}}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

\[\begin{aligned} \Theta_{y,z,t} - \Theta_{y,z,t-1} \leq \kappa_{y,z}^{up} \Delta^{\text{total}}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

(See Constraints 1-2 in the code)

This set of time-coupling constraints wrap around to ensure the power output in the first time step of each year (or each representative period), $t \in \mathcal{T}^{start}$, is within the eligible ramp of the power output in the final time step of the year (or each representative period), $t+\tau^{period}-1$.

Minimum and maximum power output

When not modeling regulation and reserves, thermal units not subject to unit commitment decisions are bound by the following limits on maximum and minimum power output:

\[\begin{aligned} \Theta_{y,z,t} \geq \rho^{min}_{y,z} \times \Delta^{total}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

\[\begin{aligned} \Theta_{y,z,t} \leq \rho^{max}_{y,z,t} \times \Delta^{total}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

(See Constraints 3-4 in the code)

thermal_no_commit_reserves!(EP::Model, inputs::Dict)

This function is called by the thermal_no_commit() function when regulation and reserves constraints are active and defines reserve related constraints for thermal power plants not subject to unit commitment constraints on power plant start-ups and shut-down decisions.

Maximum contributions to frequency regulation and reserves

Thermal units not subject to unit commitment adhere instead to the following constraints on maximum reserve and regulation contributions:

\[\begin{aligned} f_{y,z,t} \leq \upsilon^{reg}_{y,z} \times \rho^{max}_{y,z,t} \Delta^{\text{total}}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

\[\begin{aligned} r_{y,z,t} \leq \upsilon^{rsv}_{y,z} \times \rho^{max}_{y,z,t} \Delta^{\text{total}}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

where $f_{y,z,t}$ is the frequency regulation contribution limited by the maximum regulation contribution $\upsilon^{reg}_{y,z}$, and $r_{y,z,t}$ is the reserves contribution limited by the maximum reserves contribution $\upsilon^{rsv}_{y,z}$. Limits on reserve contributions reflect the maximum ramp rate for the thermal resource in whatever time interval defines the requisite response time for the regulation or reserve products (e.g., 5 mins or 15 mins or 30 mins). These response times differ by system operator and reserve product, and so the user should define these parameters in a self-consistent way for whatever system context they are modeling.

Minimum and maximum power output

When modeling regulation and spinning reserves, thermal units not subject to unit commitment are bound by the following limits on maximum and minimum power output:

\[\begin{aligned} \Theta_{y,z,t} - f_{y,z,t} \geq \rho^{min}_{y,z} \times \Delta^{\text{total}}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

\[\begin{aligned} \Theta_{y,z,t} + f_{y,z,t} + r_{y,z,t} \leq \rho^{max}_{y,z,t} \times \Delta^{\text{total}}_{y,z} \hspace{1cm} \forall y \in \mathcal{H \setminus UC}, \forall z \in \mathcal{Z}, \forall t \in \mathcal{T} \end{aligned}\]

Note there are multiple versions of these constraints in the code in order to avoid creation of unecessary constraints and decision variables for thermal units unable to provide regulation and/or reserves contributions due to input parameters (e.g. Reg_Max=0 and/or RSV_Max=0).