generation¶

This module contains constraints related to technology generation. The power output of storage and each dispatchable (exclude hydropower) technology (${\rm{power}}_{h,m,y,z,e}$) is limited by the existing installed capacity (${\rm{cap}}_{y,z,e}^{\rm{existingtech}}$) and minimum technical output, as follows:

\[{\underline{{\rm{POWER}}}}_{h,m,y,z,e}\times {\rm{cap}}_{y,z,e}^{\rm{existingtech}}\le{\rm{power}}_{h,m,y,z,e}\le {\rm{cap}}_{y,z,e}^{\rm{existingtech}}\quad\forall h,m,y,z,e\in {\mathcal{STOR}}\ \&\ {\mathcal{DISP}}\]

Since hydropower processes are explicitly modelled at the plant level in PREP-SHOT, total hydropower output in zone $z$ (${\rm{power}}_{h,m,y,z,e={\rm{hydro}}}$) is the sum of the plant-level hydropower output (${\rm{power}}_{\it{s,h,m,y}}^{\rm{hydro}}$):

\[{\rm{power}}_{h,m,y,z,e={\rm{hydro}}}=\sum_{s\in{\mathcal{SZ}}_z} {\rm{power}}_{s,h,m,y}^{\rm{hydro}}\quad\forall h,m,y,z\]

Here, calculation of ${\rm{power}}^{\rm{hydro}}_{s,h,m,y}$ is obtained by external net water head simulation procedure. In addition, ${\rm{power}}^{\rm{hydro}}_{s,h,m,y}$ is bounded between the guaranteed minimum output (${\underline{{\rm{POWER}}}}_s^{\rm{hydro}}$) and the nameplate capacity (${{\rm{CAP}}}_s^{\rm{hydro}}$), as follows:

Regardless of the technology type, actual power generation (${\rm{gen}}_{h,m,y,z,e}$) in a corresponding period $\Delta h$ can be calculated based on the power output (${\rm{power}}_{h,m,y,z,e}$) and the generation efficiency ($\eta_{y,e}^{\rm{out}}$):

\[{\rm{gen}}_{h,m,y,z,e} = {\rm{power}}_{h,m,y,z,e}\times\Delta h \times\eta_{y,e}^{\rm{out}}\quad \forall h,m,y,z,e\in {\mathcal{E}}\]

Note that $\eta_{y,e}^{\rm{out}}=1$ when $e\in {\mathcal{E}}\backslash {\mathcal{STOR}}$.

All technologies apart from dispatchable technology are limited by the so-called ramping capability, meaning that the variation of their power output in two successive periods is limited. We introduce two non-negative auxiliary variables: increment (${ m{power}}_{h,m,y,z,e}^{ m{up}}$) and decrement (${ m{power}}_{h,m,y,z,e}^{ m{down}}$) to describe changes in power output in two successive periods (from $h$-1 to $h$) as follows:

\[{\rm{power}}_{h,m,y,z,e}^{\rm{up}}-{\rm{power}}_{h,m,y,z,e}^{\rm{down}} ={\rm{power}}_{h,m,y,z,e}-{\rm{power}}_{h-1,m,y,z,e} \quad\forall h,m,y,z,e\ \in {\mathcal{E}}\backslash {\mathcal{NDISP}}\]

When the power plant ramps up from $h$-1 to $h$, the minimum of ${\rm{power}}_{h,m,y,z,e}^{\rm{up}}$ is obtained when ${\rm{power}}_{h,m,y,z,e}^{\rm{down}}$ becomes zero. Similarly, when the power plant ramps down from $h$-1 to $h$, the minimum of ${\rm{power}}_{h,m,y,z,e}^{\rm{down}}$ is obtained when ${\rm{power}}_{h,m,y,z,e}^{\rm{up}}$ becomes zero. Therefore, we can constrain the maximum ramping up and down respectively, as follows:

\[{\rm{power}}_{h,m,y,z,e}^{\rm{up}}\le{{R}}_e^{\rm{up}}\times \Delta h\times {\rm{cap}}_{y,z,e}^{\rm{existingtech}}\quad \forall h,m,y,z,e\in {\mathcal{E}}\backslash {\mathcal{NDISP}}\]

\[{\rm{power}}_{h,m,y,z,e}^{\rm{down}}\le{{R}}_e^{\rm{down}}\times \Delta h\times {\rm{cap}}_{y,z,e}^{\rm{existingtech}} \quad\forall h,m,y,z,e\in {\mathcal{E}}\backslash {\mathcal{NDISP}}\]

where ${{R}}_e^{\rm{up}}$/${{R}}_e^{\rm{down}}$ is the allowed maximum/minimum ramping up/down capacity of technology $e$ in two successive periods, expressed as a percentage of the existing capacity of storage technology $e$.

class prepshot._model.generation.AddGenerationConstraints(model)[source]¶

Bases: object

Add constraints for generation in the model.

Parameters: model (object) --

__init__(model)[source]¶

Initialize the class and add constraints.

Parameters: model (object) -- Model object depending on the solver.
Return type: None

gen_low_bound_rule(h, m, y, z, te)[source]¶

gen[h,m,y,z,te] >= cap_existing × p_min_pu × dt.

Defaults to p_min_pu = 0 (no minimum) when the tech has no entry in tech_min_gen_profile.csv. Set p_min_pu > 0 for must-run plants with a minimum stable load.

Parameters

h (int) --
m (int) --
y (int) --
z (str) --
te (str) --

Return type

ConstraintIndex

gen_up_bound_rule(h, m, y, z, te)[source]¶

gen[h,m,y,z,te] <= cap_existing × p_max_pu × dt.

Defaults to p_max_pu = 1 (full capacity) when the tech has no entry in tech_max_gen_profile.csv. Variable renewables specify a time-varying p_max_pu < 1 to cap by capacity factor; must-run techs set p_max_pu = p_min_pu to lock generation to a profile.

Parameters

h (int) --
m (int) --
y (int) --
z (str) --
te (str) --

Return type

ConstraintIndex

ramping_down_rule(h, m, y, z, te)[source]¶

Ramping down limits.

Parameters

h (int) -- Hour.
m (int) -- Month.
y (int) -- Year.
z (str) -- Zone.
te (str) -- Technology.

Returns

The constraint of the model.

Return type

poi.ConstraintIndex

ramping_up_rule(h, m, y, z, te)[source]¶

Ramping up limits.

Parameters

h (int) -- Hour.
m (int) -- Month.
y (int) -- Year.
z (str) -- Zone.
te (str) -- Technology.

Returns

The constraint of the model.

Return type

poi.ConstraintIndex