def optimal_adapt_level(gross_damages, m, r):
if value(m.adapt_g1[r]) * value(m.adapt_g2[r]) == 0:
return 0
eps = 0.0005
return (soft_min(gross_damages, 0.01) / (m.adapt_g1[r] * m.adapt_g2[r]) + eps) ** (
1 / (m.adapt_g2[r] - 1)
)
def var_to_row(rows, m, var, is_regional):
# If var is a list, second element is the name
if isinstance(var, list):
name = var[1]
var = var[0]
else:
name = var.name
# Check if var is a function or a pyomo variable
if is_regional:
fct = lambda t, r: (var(m.year(t), r)
if callable(var) else value(var[t, r]))
for r in m.regions:
rows.append([name, r] + [fct(t, r) for t in m.t])
else:
fct = lambda t: (var(m.year(t)) if callable(var) else value(var[t]))
rows.append([name, "Global"] + [fct(t) for t in m.t])
def solve(
self,
verbose=True,
halt_on_ampl_error="no",
use_neos=False,
neos_email=None,
ipopt_output_file=None,
) -> None:
"""Sends the concrete model to a solver.
Args:
verbose (bool, optional): Prints intermediate IPOPT results. Defaults to True.
halt_on_ampl_error (str, optional): Lets IPOPT stop when invalid values are encountered. Defaults to "no".
use_neos (bool, optional): Uses the external NEOS server for solving. Defaults to False.
neos_email (str or None, optional): E-mail address for NEOS server. Defaults to None.
ipopt_output_file (str or None, optional): Filename for IPOPT intermediate output. Defaults to None.
Raises:
SolverException: raised if solver did not exit with status OK
"""
if use_neos:
# Send concrete model to external solver on NEOS server
# Requires authenticated email address
os.environ["NEOS_EMAIL"] = neos_email
solver_manager = SolverManagerFactory("neos")
solver = "ipopt" # or "conopt'
results = solver_manager.solve(self.concrete_model, opt=solver)
else:
# Solve locally using ipopt
opt: OptSolver = SolverFactory("ipopt")
opt.options["halt_on_ampl_error"] = halt_on_ampl_error
if ipopt_output_file is not None:
opt.options["output_file"] = ipopt_output_file
results = opt.solve(self.concrete_model,
tee=verbose,
symbolic_solver_labels=True)
if ipopt_output_file is not None:
visualise_ipopt_output(ipopt_output_file)
self.postprocessing()
logger.info("Status: {}".format(results.solver.status))
if results.solver.status != SolverStatus.ok:
logger.error("Status: {}, termination condition: {}".format(
results.solver.status, results.solver.termination_condition))
if results.solver.status != SolverStatus.warning:
raise SolverException("Solver did not exit with status OK")
logger.info("Final NPV: {}".format(
value(self.concrete_model.NPV[self.concrete_model.tf])))
def functional_form(x, m, r, is_slr=False):
if is_slr:
form = m.damage_slr_form[r]
b1, b2, b3 = m.damage_slr_b1[r], m.damage_slr_b2[r], m.damage_slr_b3[r]
a = m.damage_slr_a[r]
else:
form = m.damage_noslr_form[r]
b1, b2, b3 = m.damage_noslr_b1[r], m.damage_noslr_b2[
r], m.damage_noslr_b3[r]
a = m.damage_noslr_a[r]
# Linear functional form
if "Linear" in value(form):
return a * b1 * x / 100.0
# Quadratic functional form
if "Quadratic" in value(form):
return a * (b1 * x + b2 * x**2) / 100.0
# Logistic functional form
if "Logistic" in value(form):
return a * logistic(x, b1, b2, b3) / 100.0
raise NotImplementedError
def get_constraints(m: AbstractModel) -> Sequence[GeneralConstraint]:
"""Emissions and temperature equations and constraints
Necessary variables:
m.relative_abatement
m.cumulative_emissions
m.T0
m.temperature
Returns:
list of constraints (any of:
- GlobalConstraint
- GlobalInitConstraint
- RegionalConstraint
- RegionalInitConstraint
)
"""
constraints = []
m.regional_emissions = Var(m.t, m.regions)
m.baseline = Var(m.t, m.regions)
m.baseline_carbon_intensity = Param()
m.relative_abatement = Var(m.t, m.regions, initialize=0, bounds=(0, 2))
m.cumulative_emissions = Var(m.t)
m.global_emissions = Var(m.t)
constraints.extend([
# Baseline emissions based on emissions or carbon intensity
RegionalConstraint(
lambda m, t, r: (m.baseline[t, r] == m.carbon_intensity(
m.year(t), r) * m.GDP_net[t, r])
if value(m.baseline_carbon_intensity) else
(m.baseline[t, r] == m.baseline_emissions(m.year(t), r)),
name="baseline_emissions",
),
# Regional emissions from baseline and relative abatement
RegionalConstraint(
lambda m, t, r: m.regional_emissions[t, r] ==
(1 - m.relative_abatement[t, r]) * m.baseline_emissions(
m.year(t), r),
"regional_abatement",
),
RegionalInitConstraint(lambda m, r: m.regional_emissions[0, r] == m.
baseline_emissions(m.year(0), r)),
# Global emissions (sum from regional emissions)
GlobalConstraint(
lambda m, t: m.global_emissions[t] == sum(
m.regional_emissions[t, r] for r in m.regions),
"global_emissions",
),
GlobalInitConstraint(
lambda m: m.global_emissions[0] == sum(
m.baseline_emissions(m.year(0), r) for r in m.regions),
"global_emissions_init",
),
# Cumulative global emissions
GlobalConstraint(
lambda m, t: m.cumulative_emissions[t] == m.cumulative_emissions[
t - 1] + m.dt * m.global_emissions[t]
if t > 0 else Constraint.Skip,
"cumulative_emissions",
),
GlobalInitConstraint(lambda m: m.cumulative_emissions[0] == 0),
])
m.T0 = Param()
m.temperature = Var(m.t, initialize=lambda m, t: m.T0)
m.TCRE = Param()
m.temperature_target = Param()
constraints.extend([
GlobalConstraint(
lambda m, t: m.temperature[t] == m.T0 + m.TCRE * m.
cumulative_emissions[t],
"temperature",
),
GlobalInitConstraint(lambda m: m.temperature[0] == m.T0),
GlobalConstraint(
lambda m, t: m.temperature[t] <= m.temperature_target
if (m.year(t) >= 2100 and value(m.temperature_target) is not False)
else Constraint.Skip,
name="temperature_target",
),
])
m.perc_reversible_damages = Param()
# m.overshoot = Var(m.t, initialize=0)
# m.overshootdot = DerivativeVar(m.overshoot, wrt=m.t)
# m.netnegative_emissions = Var(m.t)
# global_constraints.extend(
# [
# lambda m, t: m.netnegative_emissions[t]
# == m.global_emissions[t] * (1 - tanh(m.global_emissions[t] * 10)) / 2
# if value(m.perc_reversible_damages) < 1
# else Constraint.Skip,
# lambda m, t: m.overshootdot[t]
# == (m.netnegative_emissions[t] if t <= value(m.year2100) and t > 0 else 0)
# if value(m.perc_reversible_damages) < 1
# else Constraint.Skip,
# ]
# )
# global_constraints_init.extend([lambda m: m.overshoot[0] == 0])
# Emission constraints
m.budget = Param()
m.inertia_global = Param()
m.inertia_regional = Param()
m.global_min_level = Param()
m.regional_min_level = Param()
m.no_pos_emissions_after_budget_year = Param()
constraints.extend([
# Carbon budget constraints:
GlobalConstraint(
lambda m, t: m.cumulative_emissions[t] -
(m.budget + (m.overshoot[t] * (1 - m.perc_reversible_damages)
if value(m.perc_reversible_damages) < 1 else 0)) <= 0
if (m.year(t) >= 2100 and value(m.budget) is not False
) else Constraint.Skip,
name="carbon_budget",
),
GlobalConstraint(
lambda m, t: m.global_emissions[t] <= 0 if
(m.year(t) >= 2100 and value(m.no_pos_emissions_after_budget_year)
is True and value(m.budget) is not False) else Constraint.Skip,
name="net_zero_after_2100",
),
GlobalConstraint(lambda m, t: m.cumulative_emissions[t] >= 0),
# Global and regional inertia constraints:
GlobalConstraint(
lambda m, t: m.global_emissions[t] - m.global_emissions[t - 1] >= m
.dt * m.inertia_global * sum(
m.baseline_emissions(m.year(0), r) for r in m.regions)
if value(m.inertia_global
) is not False and t > 0 else Constraint.Skip,
name="global_inertia",
),
RegionalConstraint(
lambda m, t, r: m.regional_emissions[t, r] - m.regional_emissions[
t - 1, r] >= m.dt * m.inertia_regional * m.baseline_emissions(
m.year(0), r) if value(m.inertia_regional) is not False and
t > 0 else Constraint.Skip,
name="regional_inertia",
),
GlobalConstraint(
lambda m, t: m.global_emissions[t] >= m.global_min_level
if value(m.global_min_level) is not False else Constraint.Skip,
"global_min_level",
),
RegionalConstraint(
lambda m, t, r: m.regional_emissions[t, r] >= m.regional_min_level
if value(m.regional_min_level) is not False else Constraint.Skip,
"regional_min_level",
),
])
m.emission_relative_cumulative = Var(m.t, initialize=1)
constraints.extend([
GlobalConstraint(
lambda m, t:
(m.emission_relative_cumulative[t] == m.cumulative_emissions[t] / m
.baseline_cumulative_global(m, m.year(0), m.year(t)))
if t > 0 else Constraint.Skip,
name="relative_cumulative_emissions",
),
GlobalInitConstraint(lambda m: m.emission_relative_cumulative[0] == 1),
])
return constraints
def get_constraints(m: AbstractModel) -> Sequence[GeneralConstraint]:
"""Damage and adaptation costs equations and constraints
(RICE specification)
Necessary variables:
m.damage_costs (sum of residual damages and adaptation costs, as % of GDP)
Returns:
list of constraints (any of:
- GlobalConstraint
- GlobalInitConstraint
- RegionalConstraint
- RegionalInitConstraint
)
"""
constraints = []
m.damage_costs = Var(m.t, m.regions)
m.smoothed_factor = Var(m.t, bounds=(0, 1))
m.gross_damages = Var(m.t, m.regions)
m.resid_damages = Var(m.t, m.regions)
m.adapt_costs = Var(m.t, m.regions)
m.adapt_level = Var(m.t, m.regions, bounds=(0, 1))
m.damage_a1 = Param(m.regions)
m.damage_a2 = Param(m.regions)
m.damage_a3 = Param(m.regions)
m.damage_scale_factor = Param()
m.adapt_g1 = Param(m.regions)
m.adapt_g2 = Param(m.regions)
m.adapt_curr_level = Param()
m.fixed_adaptation = Param()
constraints.extend(
[
# Smoothing factor for partially reversible damages
GlobalConstraint(
lambda m, t: m.smoothed_factor[t]
== smoothed_factor(t, m.temperature, m.dt, m.perc_reversible_damages),
name="smoothed_factor",
),
# Gross damages
RegionalConstraint(
lambda m, t, r: m.gross_damages[t, r]
== calc_gross_damages(m, t, r, m.perc_reversible_damages),
name="gross_damages",
),
RegionalConstraint(lambda m, t, r: m.gross_damages[t, r] >= 0),
RegionalInitConstraint(lambda m, r: m.gross_damages[0, r] == 0),
]
)
# Adaptation
constraints.extend(
[
RegionalConstraint(
lambda m, t, r: m.adapt_level[t, r]
== (
m.adapt_curr_level
if value(m.fixed_adaptation)
else optimal_adapt_level(m.gross_damages[t, r], m, r)
),
name="adapt_level",
),
RegionalConstraint(
lambda m, t, r: m.resid_damages[t, r]
== m.gross_damages[t, r] * (1 - m.adapt_level[t, r]),
"resid_damages",
),
RegionalConstraint(
lambda m, t, r: m.adapt_costs[t, r]
== adaptation_costs(m.adapt_level[t, r], m, r),
"adapt_costs",
),
RegionalConstraint(
lambda m, t, r: m.damage_costs[t, r]
== m.resid_damages[t, r] + m.adapt_costs[t, r],
"damage_costs",
),
]
)
return constraints
def get_constraints(m: AbstractModel) -> Sequence[GeneralConstraint]:
"""Abatement cost equations and constraints
Necessary variables:
m.abatement_costs
Returns:
list of constraints (any of:
- GlobalConstraint
- GlobalInitConstraint
- RegionalConstraint
- RegionalInitConstraint
)
"""
constraints = []
### Technological learning
# Learning by doing
m.LBD_rate = Param()
m.log_LBD_rate = Param(initialize=log(m.LBD_rate) / log(2))
m.LBD_scaling = Param()
m.LBD_factor = Var(m.t) # , bounds=(0,1), initialize=1)
constraints.append(
GlobalConstraint(
lambda m, t: m.LBD_factor[t]
== soft_min(
(
m.baseline_cumulative_global(m, m.year(0), m.year(t))
- m.cumulative_emissions[t]
)
/ m.LBD_scaling
+ 1.0
)
** m.log_LBD_rate,
name="LBD",
)
)
# Learning over time and total learning factor
m.LOT_rate = Param()
m.LOT_factor = Var(m.t)
m.learning_factor = Var(m.t)
constraints.extend(
[
GlobalConstraint(
lambda m, t: m.LOT_factor[t] == 1 / (1 + m.LOT_rate) ** t, "LOT"
),
GlobalConstraint(
lambda m, t: m.learning_factor[t]
== (m.LBD_factor[t] * m.LOT_factor[t]),
"learning",
),
]
)
# Abatement costs and MAC
m.abatement_costs = Var(m.t, m.regions, within=NonNegativeReals, initialize=0)
m.area_under_MAC = Var(m.t, m.regions, within=NonNegativeReals, initialize=0)
m.rel_abatement_costs = Var(m.t, m.regions, bounds=(0, 0.3))
m.MAC_gamma = Param()
m.MAC_beta = Param()
m.MAC_scaling_factor = Param(m.regions) # Regional scaling of the MAC
m.carbonprice = Var(m.t, m.regions, bounds=lambda m: (0, 1.5 * m.MAC_gamma))
constraints.extend(
[
RegionalConstraint(
lambda m, t, r: (
m.area_under_MAC[t, r]
if value(m.allow_trade)
else m.abatement_costs[t, r]
)
== AC(
m.relative_abatement[t, r],
m.learning_factor[t],
m.MAC_gamma,
m.MAC_beta,
m.MAC_scaling_factor[r],
)
* m.baseline[t, r],
"abatement_costs",
),
RegionalConstraint(
lambda m, t, r: m.rel_abatement_costs[t, r]
== m.abatement_costs[t, r] / m.GDP_gross[t, r],
"rel_abatement_costs",
),
RegionalConstraint(
lambda m, t, r: m.carbonprice[t, r]
== MAC(
m.relative_abatement[t, r],
m.learning_factor[t],
m.MAC_gamma,
m.MAC_beta,
m.MAC_scaling_factor[r],
),
"carbonprice",
),
RegionalInitConstraint(
lambda m, r: m.carbonprice[0, r] == 0, "init_carbon_price"
),
]
)
# How are mitigation costs distributed over regions?
m.allow_trade = Param()
constraints.extend(
[
GlobalConstraint(
lambda m, t: sum(m.abatement_costs[t, r] for r in m.regions)
== sum(m.area_under_MAC[t, r] for r in m.regions)
if m.allow_trade
else Constraint.Skip
),
RegionalConstraint(
lambda m, t, r: m.abatement_costs[t, r] <= 1.5 * m.area_under_MAC[t, r]
if m.allow_trade
else Constraint.Skip
),
# RegionalConstraint(
# lambda m, t, r: m.abatement_costs[t, r] >= 0.5 * m.area_under_MAC[t, r]
# if m.allow_trade
# else Constraint.Skip
# ),
]
)
# Keep track of relative global costs
m.global_rel_abatement_costs = Var(m.t)
constraints.extend(
[
GlobalConstraint(
lambda m, t: m.global_rel_abatement_costs[t]
== sum(m.abatement_costs[t, r] for r in m.regions)
/ sum(m.GDP_gross[t, r] for r in m.regions),
"global_rel_abatement_costs",
)
]
)
return constraints
def get_constraints(m: AbstractModel) -> Sequence[GeneralConstraint]:
"""Economics and Cobb-Douglas equations and constraints
Necessary variables:
m.L (equal to m.population)
m.dk
Returns:
list of constraints (any of:
- GlobalConstraint
- GlobalInitConstraint
- RegionalConstraint
- RegionalInitConstraint
)
"""
constraints = []
m.init_capitalstock_factor = Param(m.regions)
m.capital_stock = Var(
m.t,
m.regions,
initialize=lambda m, t, r: m.init_capitalstock_factor[r] * m.GDP(
m.year(t), r),
)
# Parameters
m.alpha = Param()
m.dk = Param()
m.sr = Param()
m.GDP_gross = Var(m.t,
m.regions,
initialize=lambda m, t, r: m.GDP(m.year(0), r))
m.GDP_net = Var(m.t, m.regions)
m.investments = Var(m.t, m.regions)
m.consumption = Var(m.t, m.regions)
m.ignore_damages = Param()
# Cobb-Douglas, GDP, investments, capital and consumption
constraints.extend([
RegionalConstraint(
lambda m, t, r: m.GDP_gross[t, r] == economics.calc_GDP(
m.TFP(m.year(t), r),
m.L(m.year(t), r),
soft_min(m.capital_stock[t, r], scale=10),
m.alpha,
),
"GDP_gross",
),
RegionalConstraint(
lambda m, t, r: m.GDP_net[t, r] == m.GDP_gross[t, r] *
(1 - (m.damage_costs[t, r] if not value(m.ignore_damages) else 0)
) - m.abatement_costs[t, r],
"GDP_net",
),
RegionalConstraint(
lambda m, t, r: m.investments[t, r] == m.sr * m.GDP_net[t, r],
"investments",
),
RegionalConstraint(
lambda m, t, r: m.consumption[t, r] ==
(1 - m.sr) * m.GDP_net[t, r],
"consumption",
),
RegionalConstraint(
lambda m, t, r: (m.capital_stock[t, r] == m.capital_stock[
t - 1, r] + m.dt * economics.calc_dKdt(m.capital_stock[
t, r], m.dk, m.investments[t, r], m.dt))
if t > 0 else Constraint.Skip,
"capital_stock",
),
RegionalInitConstraint(lambda m, r: m.capital_stock[
0, r] == m.init_capitalstock_factor[r] * m.GDP(m.year(0), r)),
])
return constraints