#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""This module contains constraints related to technology generation.
The power output of storage and each dispatchable (exclude hydropower)
technology (:math:`{\\rm{power}}_{h,m,y,z,e}`) is limited by the existing
installed capacity (:math:`{\\rm{cap}}_{y,z,e}^{\\rm{existingtech}}`)
and minimum technical output, as follows:
.. math::
{\\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
:math:`z` (:math:`{\\rm{power}}_{h,m,y,z,e={\\rm{hydro}}}`) is the sum of the
plant-level hydropower output
(:math:`{\\rm{power}}_{\\it{s,h,m,y}}^{\\rm{hydro}}`):
.. math::
{\\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 :math:`{\\rm{power}}^{\\rm{hydro}}_{s,h,m,y}` is obtained
by external net water head simulation procedure. In addition,
:math:`{\\rm{power}}^{\\rm{hydro}}_{s,h,m,y}` is bounded between the guaranteed
minimum output (:math:`{\\underline{{\\rm{POWER}}}}_s^{\\rm{hydro}}`) and the
nameplate capacity (:math:`{{\\rm{CAP}}}_s^{\\rm{hydro}}`), as follows:
Regardless of the technology type, actual power generation
(:math:`{\\rm{gen}}_{h,m,y,z,e}`) in a corresponding period :math:`\\Delta h`
can be calculated based on the power output (:math:`{\\rm{power}}_{h,m,y,z,e}`)
and the generation efficiency (:math:`\\eta_{y,e}^{\\rm{out}}`):
.. math::
{\\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 :math:`\\eta_{y,e}^{\\rm{out}}=1` when
:math:`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 (:math:`{\rm{power}}_{h,m,y,z,e}^{\rm{up}}`) and decrement
(:math:`{\rm{power}}_{h,m,y,z,e}^{\rm{down}}`) to describe changes in power
output in two successive periods (from :math:`h`-1 to :math:`h`) as follows:
.. math::
{\\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 :math:`h`-1 to :math:`h`,
the minimum of :math:`{\\rm{power}}_{h,m,y,z,e}^{\\rm{up}}` is obtained when
:math:`{\\rm{power}}_{h,m,y,z,e}^{\\rm{down}}` becomes zero. Similarly, when
the power plant ramps down from :math:`h`-1 to :math:`h`, the minimum of
:math:`{\\rm{power}}_{h,m,y,z,e}^{\\rm{down}}` is obtained when
:math:`{\\rm{power}}_{h,m,y,z,e}^{\\rm{up}}` becomes zero. Therefore,
we can constrain the maximum ramping up and down respectively, as follows:
.. math::
{\\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}}
.. math::
{\\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 :math:`{{R}}_e^{\\rm{up}}$/${{R}}_e^{\\rm{down}}` is the allowed
maximum/minimum ramping up/down capacity of technology :math:`e` in two
successive periods, expressed as a percentage of the existing capacity
of storage technology :math:`e`.
"""
import pyoptinterface as poi
[docs]class AddGenerationConstraints:
"""Add constraints for generation in the model.
"""
[docs] def __init__(self, model : object) -> None:
"""Initialize the class and add constraints.
Parameters
----------
model : object
Model object depending on the solver.
"""
self.model = model
model.gen_up_bound_cons = poi.make_tupledict(
model.hour, model.month, model.year, model.zone, model.tech,
rule=self.gen_up_bound_rule
)
model.ramping_up_cons = poi.make_tupledict(
model.hour, model.month, model.year, model.zone, model.tech,
rule=self.ramping_up_rule
)
model.ramping_down_cons = poi.make_tupledict(
model.hour, model.month, model.year, model.zone, model.tech,
rule=self.ramping_down_rule
)
[docs] def gen_up_bound_rule(
self, h : int, m : int, y : int, z : str, te : str
) -> poi.ConstraintIndex:
"""Generation is less than or equal to the existing capacity.
Parameters
----------
h : int
Hour.
m : int
Month.
y : int
Year.
z : str
Zone.
te : str
Technology.
Returns
-------
poi.ConstraintIndex
The constraint of the model.
"""
model = self.model
lhs = model.gen[h, m, y, z, te] \
- model.cap_existing[y, z, te] * model.params['dt']
return model.add_linear_constraint(lhs, poi.Leq, 0)
[docs] def ramping_up_rule(
self, h : int, m : int, y : int, z : str, te : str
) -> poi.ConstraintIndex:
"""Ramping up limits.
Parameters
----------
h : int
Hour.
m : int
Month.
y : int
Year.
z : str
Zone.
te : str
Technology.
Returns
-------
poi.ConstraintIndex
The constraint of the model.
"""
model = self.model
rp = model.params['ramp_up'][te] * model.params['dt']
if rp < 1 < h:
lhs = (
model.gen[h, m, y, z, te] - model.gen[h-1, m, y, z, te]
- rp * model.cap_existing[y, z, te]
)
return model.add_linear_constraint(lhs, poi.Leq, 0)
[docs] def ramping_down_rule(
self, h : int, m : int, y : int, z : str, te : str
) -> poi.ConstraintIndex:
"""Ramping down limits.
Parameters
----------
h : int
Hour.
m : int
Month.
y : int
Year.
z : str
Zone.
te : str
Technology.
Returns
-------
poi.ConstraintIndex
The constraint of the model.
"""
model = self.model
rd = model.params['ramp_down'][te] * model.params['dt']
if rd < 1 < h:
lhs = (
model.gen[h-1, m, y, z, te] - model.gen[h, m, y, z, te]
- rd * model.cap_existing[y, z, te]
)
return model.add_linear_constraint(lhs, poi.Leq, 0)