from typing import Callable, NamedTuple, Union
from math import inf
from evrouting.T import SoC, Wh, ChargingCoefficient, Time, Node
class SoCProfile:
"""
The SoC Profile maps an initial SoC to the SoC after
traversing a path.
SoC profile of a path is fully described with two parameters:
- cost: Cost of going from u to v.
- out: Maximal SoC after passing the path from u to v.
"""
def __init__(self, path_cost: Wh, capacity: SoC):
"""
Calculates the maximum SoC after traversing the path, which is
(for non-negative path costs) U - cost.
:param path_cost: Cost of the path. The SoC Profile of
a single vertex has no cost.
:param capacity: The battery's capacity.
"""
self.capacity: SoC = capacity
self.path_cost: Wh = path_cost
self.out: SoC = capacity - self.path_cost
def __call__(self, initial_soc: SoC) -> SoC:
"""
:param initial_soc: The initial SoC.
:returns: The SoC after traversing the path.
"""
if initial_soc < self.path_cost:
return -inf
final_soc = initial_soc - self.path_cost
return final_soc if final_soc < self.capacity else self.capacity
def __add__(self, other: 'SoCProfile') -> 'SoCProfile':
"""
Combines to SoC Profiles.
The for the combined SoC Profile, given a SoC Profile for a path a
and a path b, holds:
cost = cost_a + cost_b
out = U - cost
:return: Combined SoC Profile.
"""
return SoCProfile(self.path_cost + other.path_cost, self.capacity)
class ChargingFunction:
"""
Charging functions map charging time to resulting SoCs. Since they are
monotonic, there exists also an inverse mapping SoC to charging time.
Dummy Charging Station
======================
Special case is a so called dummy charging station. This is the case
if the charging coefficient is 0. Then there is no actual charging and
the value of the charging station is always the same as the arrival SoC.
A dummy charging station is necessary for initialization of the problem
to trigger spawning of new labels.
"""
def __init__(self, c: ChargingCoefficient, capacity: SoC,
initial_soc: SoC = None):
"""
:param c: The stations charging coefficient. If c=0, the this becomes
a so called dummy charging station, that exists to trigger label
creation in the algorithm.
:param capacity: The battery's capacity, respectively the maximum of
the charging function.
:param initial_soc: The SoC at arriving at the charging station. This is
optional for dummy charging stations, that do not actually charge:
cf(b) = soc
"""
self.c: ChargingCoefficient = c
self.capacity: SoC = capacity
self.initial_soc: SoC = initial_soc
@property
def is_dummy(self) -> bool:
"""Tell if function is a dummy function."""
return self.c == 0
def __call__(self, t: Time, initial_soc: SoC = 0) -> SoC:
"""
:param t: Charging time
:param initial_soc: Initial SoC when starting to charge
:return: SoC after charging.
"""
if self.is_dummy:
if self.initial_soc is None:
raise ValueError(
'Charging coefficient is 0 but no initial SoC given.'
)
soc = self.initial_soc
else:
soc = initial_soc + self.c * t
return soc if soc < self.capacity else self.capacity
@property
def inverse(self) -> Callable[[SoC], Time]:
"""
:returns: Inverse charging function mapping SoC to charging
time (assuming initial SoC=0)
"""
if self.is_dummy:
raise ValueError('Dummy Carging function has no inverse.')
c = self.c
capacity = self.capacity
def cf_inverse(soc: SoC) -> Time:
if soc > capacity:
# Return max charge time
return capacity / c
elif soc < 0:
# Return min charge time
return 0
return soc / c
return cf_inverse
def __lt__(self, other) -> bool:
"""Comparison for dominance check."""
return self.c < other.c
def __gt__(self, other):
"""Comparison for dominance check."""
return self.c > other.c
class Label(NamedTuple):
"""
Label used for the Algorithm.
The (paleto optimal) label where u=t is the
contains the minimum trip time necessary to get to t.
The label of node v consists of a tuple:
(t_trip, soc_last_cs, last_cs, soc_profile_cs_v)
Where:
:t_trip: Trip time to node v without charging time at the last
charging station.
:soc_last_cs: Arrival SoC at the last charging station.
:last_cs: (Node ID of) The last charging station.
:soc_profile_cs_v: The SoC Profile describing the costs going from
the charging station to current node v.
"""
t_trip: Time
soc_last_cs: SoC
last_cs: Node
soc_profile_cs_v: SoCProfile
class Breakpoint(NamedTuple):
t: Time
soc: SoC
class SoCFunction:
"""
SoC Function of a node's label maps trip time plus an additional charging
time at the last charging station to a SoC at the node.
"""
def __init__(self, label: Label, cf_cs: ChargingFunction):
"""
:param label: Label containing to a node. It has the fields:
:t_trip: Trip time. Includes time to reach v from the last
charging station in the path but excludes charging at u.
:soc_last_cs: The SoC at reaching the last charging station
before any charging.
:last_cs: The last charging station in the path to current node.
:soc_profile_cs_v: The SoC Profile of the path cs -> v.
:cf_cs: Charging function of cs.
:param cf_cs: The charging function of the last charging station.
"""
# Unpack label
self.t_trip: Time = label.t_trip
self.last_cs: Node = label.last_cs
self.soc_last_cs: SoC = label.soc_last_cs
self.soc_profile_cs_v: SoCProfile = label.soc_profile_cs_v
self.cf_cs: ChargingFunction = cf_cs
self.breakpoints = self.get_breakpoints()
def get_breakpoints(self):
breakpoints = [Breakpoint(self.minimum, 0)]
if not self.cf_cs.is_dummy:
breakpoints.append(
Breakpoint(
self.minimum + self.cf_cs.inverse(self.soc_profile_cs_v.out),
self.soc_profile_cs_v.out
)
)
return breakpoints
def __call__(self, t: Time) -> SoC:
"""
Maps a new trip time to a SoC at the current node. The new trip time
then includes and fixes charging time at the last charging station.
:param t: t = trip time + charging at the last charging station
:return: SoC at current node at time t after spending t - t_trip at
the last charging station to charge the battery.
"""
if t < self.t_trip:
# Impossible to reach the current node for times < trip time
return -inf
return self.soc_profile_cs_v(
self.cf_cs(t - self.t_trip, self.soc_last_cs)
)
def calc_optimal_t_charge(self, cs: ChargingFunction) -> Union[Time, None]:
capacity: SoC = self.soc_profile_cs_v.capacity
t_charge = None
if cs > self.cf_cs:
# Faster charging station -> charge as soon as possible
t_charge = self.breakpoints[0].t - self.t_trip
elif self.breakpoints[-1].soc < capacity:
# Slower charging station might still be dominating
# because the soc cannot be more than the full capacity
# decreased by the trip costs. This will be refilled at this station.
t_charge = self.breakpoints[-1].t - self.t_trip
return t_charge
def __lt__(self, other: 'SoCFunction') -> bool:
"""Comparison for dominance check."""
for t_i, soc_i in self.breakpoints:
if other(t_i) < soc_i:
return False
for t_i, soc_i in other.breakpoints:
if soc_i < self(t_i):
return False
return True
def __gt__(self, other: 'SoCFunction') -> bool:
"""Comparison for dominance check."""
for t_i, soc_i in self.breakpoints:
if other(t_i) > soc_i:
return False
for t_i, soc_i in other.breakpoints:
if soc_i > self(t_i):
return False
return True
@property
def minimum(self) -> Time:
"""
:returns: Least feasible trip time. That is, the minimum time when
the SoC functions yields a SoC value that is not -inf.
This is either the trip time, or if energy needs to be charged
at the previous charging station to traverse the path, trip time
plus charging time until the battery holds the minimum energy to
traverse the path to the current node (which is the cost of the
path). This time is:
t = t_trip + cf_cs^(-1)(cost_cs_v) - cf_cs^(-1)(soc_last_sc)
Thus, for t_min holds:
t_min = max(t_trip, t)
"""
cost_p = self.soc_profile_cs_v.path_cost
if cost_p > self.soc_last_cs:
if self.cf_cs.is_dummy:
# Not feasible. Dummy stations do not load.
return -inf
return self.t_trip + \
self.cf_cs.inverse(cost_p) - \
self.cf_cs.inverse(self.soc_last_cs)
return self.t_trip