Source code for prepshot._model.cost

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

"""This module contains objective functions for the model. The objective
function of the model is to minimize the net present value of the system's
cost. This includes capital cost, fixed O&M cost, variable cost and fuel cost
by cost type, technology cost, transmission line cost by the source of cost,
and operation cost and planning cost by the source of cost.

The cost equations are defined as follows:

.. image:: ../_static/cost_eq.png
    :width: 700
    :align: center
    :alt: Calculation of system-wide total cost

.. math::

    \\rm{cost}_{\\rm{tech}}^{\\rm{var}} &= \\frac{\\sum_{h,m,y,z,\\rm{e}}
    C_{y,z,\\rm{e}}^{\\rm{tech-var}}\\times \\rm{gen}_{h,m,y,z,\\rm{e}}}
    {\omega} \\times \\rm{factor}_{y}^{\\rm{var}} 
    
    \\rm{cost}_{\\rm{line}}^{\\rm{var}} &= \\frac{\\sum_{h,m,y,z_s,z_o}
    C_{y,z}^{\\rm{line-var}}\\times \\rm{export}_{h,m,y,z_s,z_o}}{\omega}
    \\times \\rm{factor}_{y}^{\\rm{var}}
    
    \\rm{cost}^{\\rm{fuel}} & = \\frac{\\sum_{h,m,y,z,\\rm{e}}
    C_{y,z,\\rm{e}}^{\\rm{fuel}}\\times \\rm{gen}_{h,m,y,z,\\rm{e}}}{\omega}
    \\times \\rm{factor}_{y}^{\\rm{var}} 

    \\rm{cost}_{\\rm{tech}}^{\\rm{fix}} &= \\sum_{y,z,\\rm{e}}
    C_{y,z,\\rm{e}}^{\\rm{tech-fix}}\\times 
    \\rm{cap}_{y,z,\\rm{e}}^{\\rm{existing-tech}}\\times 
    \\rm{factor}_{y}^{\\rm{fix}}

    \\rm{cost}_{\\rm{line}}^{\\rm{fix}} &= \\sum_{y,z_s,z_o}
    C_{y,z_s,z_o}^{\\rm{line-fix}}\\times 
    \\rm{cap}_{y,z_s,z_o}^{\\rm{existing-line}}\\times
    \\rm{factor}_{y}^{\\rm{fix}}

    \\rm{cost}_{\\rm{tech}}^{\\rm{inv}} &=  \\sum_{y,z,\\rm{e}}
    C_{y,z,\\rm{e}}^{\\rm{tech-inv}}\\times 
    \\rm{cap}_{y,z,\\rm{e}}^{\\rm{tech-inv}}\\times
    \\rm{factor}_{y}^{\\rm{inv}}

    \\rm{cost}_{\\rm{line}}^{\\rm{inv}} &= \\sum_{y,z_s,z_o}
    C_{y,z_s,z_o}^{\\rm{line-inv}}\\times
    \\rm{cap}_{y,z_s,z_o}^{\\rm{line-inv}}\\times
    \\rm{factor}_{y}^{\\rm{inv}} \\times 0.5

"""

from typing import Union

import pyoptinterface as poi

[docs]class AddCostObjective: """Objective function class to determine the total cost of the model. """
[docs] def __init__(self, model : object) -> None: """The constructor for objective functions class. Parameters ---------- model : object Model to be solved. """ self.model = model self.define_objective()
[docs] def define_objective(self) -> None: """Objective function of the model, to minimize total cost. """ model = self.model model.cost_var = self.var_cost_rule() model.cost_newtech = self.newtech_cost_rule() model.cost_fix = self.fix_cost_rule() model.cost_newline = self.newline_cost_rule() model.income = self.income_rule() model.cost = model.cost_var + model.cost_newtech \ + model.cost_fix + model.cost_newline - model.income model.set_objective(model.cost, sense=poi.ObjectiveSense.Minimize)
[docs] def fuel_cost_breakdown( self, y : int, z : str, te : str ) -> poi.ExprBuilder: """Fuel cost breakdown of technologies. Parameters ---------- y : int Year. z : str Zone. te : str Technology. Returns ------- poi.ExprBuilder Fuel cost at a given year, zone and technology. """ model = self.model fp = model.params['fuel_price'][te, y] vf = model.params['var_factor'][y] w = model.params['weight'] return (1 / w * fp * vf * poi.quicksum(model.gen.select('*', '*', y, z, te)))
[docs] def cost_var_line_breakdown( self, y : int, z : str, z1 : str ) -> poi.ExprBuilder: """Variable operation and maintenance cost breakdown of transmission lines. Parameters ---------- y : int Year. z : str Zone. z1 : str Zone. Returns ------- poi.ExprBuilder Variable operation and maintenance cost of transmission lines at a given year, source and destination zone. """ model = self.model lvc = model.params['transmission_line_variable_OM_cost'][z, z1] vf = model.params['var_factor'][y] w = model.params['weight'] return (0.5 / w * lvc * vf * poi.quicksum(model.trans_export.select('*', '*', y, z, z1)))
[docs] def cost_var_tech_breakdown( self, y : int, z : str, te : str ) -> poi.ExprBuilder: """Variable operation and maintenance cost breakdown. Parameters ---------- y : int Year. z : str Zone. te : str Technology. Returns ------- poi.ExprBuilder Variable operation and maintenance cost of technologies at a given year, zone and technology. """ model = self.model tvc = model.params['technology_variable_OM_cost'][te, y] vf = model.params['var_factor'][y] w = model.params['weight'] return (1 / w * tvc * vf * poi.quicksum(model.gen.select('*', '*', y, z, te)))
[docs] def cost_fix_line_breakdown( self, y : int, z : str, z1 : str ) -> poi.ExprBuilder: """Fixed operation and maintenance cost breakdown of transmission lines. Parameters ---------- y : int Year. z : str Zone. z1 : str Zone. Returns ------- poi.ExprBuilder Fixed operation and maintenance cost of transmission lines at a given year, source and destination zone. """ model = self.model lfc = model.params['transmission_line_fixed_OM_cost'] ff = model.params['fix_factor'] return lfc[z, z1] * model.cap_lines_existing[y, z, z1] * ff[y] * 0.5
[docs] def cost_fix_tech_breakdown( self, y : int, z : str, te : str ) -> poi.ExprBuilder: """Fixed operation and maintenance cost breakdown. Parameters ---------- y : int Year. z : str Zone. te : str Technology. Returns ------- poi.ExprBuilder Fixed operation and maintenance cost of technologies at a given year, zone and technology. """ model = self.model tfc = model.params['technology_fixed_OM_cost'][te, y] ff = model.params['fix_factor'][y] return tfc * model.cap_existing[y, z, te] * ff
[docs] def cost_newtech_breakdown( self, y : int, z : str, te : str ) -> poi.ExprBuilder: """New technology investment cost breakdown. Parameters ---------- y : int Year. z : str Zone. te : str Technology. Returns ------- poi.ExprBuilder Investment cost of new technologies at a given year, zone and technology. """ model = self.model tic = model.params['technology_investment_cost'][te, y] ivf = model.params['inv_factor'][te, y] return tic * model.cap_newtech[y, z, te] * ivf
[docs] def cost_newline_breakdown( self, y : int, z : str, z1 : str ) -> poi.ExprBuilder: """New transmission line investment cost breakdown. Parameters ---------- y : int Year. z : str Zone. z1 : str Zone. Returns ------- poi.ExprBuilder Investment cost of new transmission lines at a given year, source and destination zone. """ model = self.model lic = model.params['transmission_line_investment_cost'][z, z1] d = model.params['distance'][z, z1] ivf = model.params['trans_inv_factor'][y] capacity_invested_line = model.cap_newline[y, z, z1] return lic * capacity_invested_line * d * ivf * 0.5
[docs] def income_rule(self) -> poi.ExprBuilder: """Income from water withdrawal. Reference: https://www.nature.com/articles/s44221-023-00126-0 Returns ------- poi.ExprBuilder Income from water withdrawal. """ model = self.model if model.params['isinflow']: coef = 3600 * model.params['dt'] * model.params['price'] vf = model.params['var_factor'] w = model.params['weight'] income = sum( model.withdraw[s, h, m, y] * coef * vf[y] for s in model.station for h in model.hour for m in model.month for y in model.year ) / w return income return poi.ExprBuilder(0)
[docs] def var_cost_rule(self) -> poi.ExprBuilder: """Calculate total variable cost, which is sum of the fuel cost of technologies and variable Operation and maintenance (O&M) cost of technologies and transmission lines. Returns ------- poi.ExprBuilder Total variable cost across all years, zones and technologies. """ model = self.model model.cost_var_tech_breakdown = poi.make_tupledict( model.year, model.zone, model.tech, rule=self.cost_var_tech_breakdown ) model.cost_fuel_breakdown = poi.make_tupledict( model.year, model.zone, model.tech, rule=self.fuel_cost_breakdown ) model.cost_var_line_breakdown = poi.make_tupledict( model.year, model.zone, model.zone, rule=self.cost_var_line_breakdown ) cost_var = poi.ExprBuilder() cost_var += poi.quicksum(model.cost_var_tech_breakdown) cost_var += poi.quicksum(model.cost_fuel_breakdown) cost_var += poi.quicksum(model.cost_var_line_breakdown) return cost_var
[docs] def newtech_cost_rule(self) -> poi.ExprBuilder: """Total investment cost of new technologies. Returns ------- poi.ExprBuilder Total investment cost of new technologies over all years, zones and technologies. """ model = self.model model.cost_newtech_breakdown = poi.make_tupledict( model.year, model.zone, model.tech, rule=self.cost_newtech_breakdown ) return poi.quicksum(model.cost_newtech_breakdown)
[docs] def newline_cost_rule(self) -> poi.ExprBuilder: """Total investment cost of new transmission lines. Returns ------- poi.ExprBuilder Total investment cost of new transmission lines over all years, zones. """ model = self.model model.cost_newline_breakdown = poi.make_tupledict( model.year, model.zone, model.zone, rule=self.cost_newline_breakdown ) return poi.quicksum(model.cost_newline_breakdown)
[docs] def fix_cost_rule(self) -> poi.ExprBuilder: """Fixed O&M cost of technologies and transmission lines. Returns ------- poi.ExprBuilder Total fixed O&M cost of technologies and transmission lines over all years, zones and technologies. """ model = self.model model.cost_fix_tech_breakdown = poi.make_tupledict( model.year, model.zone, model.tech, rule=self.cost_fix_tech_breakdown ) model.cost_fix_line_breakdown = poi.make_tupledict( model.year, model.zone, model.zone, rule=self.cost_fix_line_breakdown ) return poi.quicksum(model.cost_fix_tech_breakdown) + \ poi.quicksum(model.cost_fix_line_breakdown)