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feat(optimization): concave terminal value for the energy left in the battery

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The energy still stored when the horizon ends keeps its worth: it replaces
grid imports that are paid for afterwards. Crediting that with a single
price per kWh cannot describe it, because the value is not linear in the
amount stored. The first kWh replaces the most expensive hour that PV
cannot cover, the next one the second most expensive, and once every such
hour is served, further energy replaces nothing.

A scalar has to pick one slope for all of it. High enough for the first kWh
means hoarding a full battery; low enough for the last kWh means running it
empty by the end of the horizon - which is exactly what the previous default
of 0 EUR/kWh did.

terminal_value_mode = AUTO (the new default) builds the curve instead. There
is no forecast beyond the horizon, so its trailing window stands in for the
day that follows: residual load max(load - PV, 0) per slot, priced at its
import price, sorted and accumulated. LCOS is subtracted from every marginal
value so stored energy is not credited twice, and the tail beyond the
residual load is only credited when direct marketing allows an export. The
curve is built once per run; the search only interpolates on it.

The solution reports what a run used as terminal_value, curve included, so
the shape can be inspected instead of guessed. FIXED restores the previous
scalar behaviour.

In a 48 h scenario with two cheap slots at the end, AUTO keeps the battery
at 50 % and credits 3.85 EUR where FIXED with 0 EUR/kWh drains it to empty.
The stored optimization results move accordingly - the objective changed.
This commit is contained in:
Andreas
2026-09-04 10:37:48 +02:00
parent 2a9543e710
commit 1c10ab83ad
16 changed files with 1834 additions and 766 deletions
Download Patch File Download Diff File Expand all files Collapse all files
tests/test_geneticoptimize.py
+90
View File
@@ -379,3 +379,93 @@ def test_ev_deadline_charges_before_departure(config_eos: ConfigEOS):
# Slot 6 is the first slot at or after the deadline, so its start-of-slot SoC
# is what the target is checked against.
assert soc_per_hour[6] >= 60.0
def _terminal_value_run(config_eos: ConfigEOS, mode: str) -> GeneticSolution:
"""48 h with expensive energy and two dirt-cheap slots at the very end.
Charging in those last slots only pays off when the stored energy keeps a
value beyond the horizon.
"""
hours = 48
config_eos.merge_settings_from_dict(
{
"prediction": {"hours": hours},
"optimization": {
"horizon_hours": hours,
"interval": 3600,
"terminal_value_mode": mode,
"terminal_value_euro_per_kwh": 0.0,
"genetic": {"individuals": 80, "generations": 20},
},
}
)
ems_eos.set_start_datetime(to_datetime().set(hour=0, minute=0))
CacheEnergyManagementStore().clear()
prices = [0.0004] * (hours - 2) + [0.00002] * 2
parameters = GeneticOptimizationParameters(
ems={
"pv_prognose_wh": [0.0] * hours,
"strompreis_euro_pro_wh": prices,
"einspeiseverguetung_euro_pro_wh": [0.00007] * hours,
"preis_euro_pro_wh_akku": 0.0,
"gesamtlast": [200.0] * hours,
},
pv_akku={
"device_id": "battery1",
"capacity_wh": 10000,
"initial_soc_percentage": 20,
"min_soc_percentage": 0,
"max_soc_percentage": 100,
"charging_efficiency": 1.0,
"discharging_efficiency": 1.0,
"max_charge_power_w": 5000,
},
inverter={
"device_id": "inverter1",
"max_power_wh": 10000,
"battery_id": "battery1",
"ac_to_dc_efficiency": 1.0,
"dc_to_ac_efficiency": 1.0,
"max_ac_charge_power_w": 5000,
},
eauto=None,
)
return GeneticOptimization(fixed_seed=7).optimierung_ems(
parameters=parameters, start_hour=0, ngen=20
)
def test_terminal_value_auto_keeps_energy_that_fixed_zero_throws_away(config_eos: ConfigEOS):
"""AUTO values the energy left in the battery, a fixed zero does not."""
auto = _terminal_value_run(config_eos, "AUTO")
fixed = _terminal_value_run(config_eos, "FIXED")
assert auto.terminal_value is not None
assert auto.terminal_value.mode == "AUTO"
assert auto.terminal_value.curve is not None
assert auto.terminal_value.credited_euro > 0.0
assert fixed.terminal_value is not None
assert fixed.terminal_value.mode == "FIXED"
assert fixed.terminal_value.credited_euro == 0.0
# The cheap slots at the end are only worth using with a terminal value.
assert auto.result.akku_soc_pro_stunde[-1] > fixed.result.akku_soc_pro_stunde[-1]
def test_terminal_value_curve_is_concave_and_reported(config_eos: ConfigEOS):
"""The reported curve is what the credit was read from."""
solution = _terminal_value_run(config_eos, "AUTO")
curve = solution.terminal_value.curve
assert curve.window_slots == 24
assert len(curve.energy_wh) == len(curve.value_euro)
assert len(curve.marginal_euro_per_kwh) == len(curve.energy_wh) - 1
marginals = curve.marginal_euro_per_kwh
assert all(a >= b for a, b in zip(marginals, marginals[1:]))
# The credit is the curve evaluated at the energy left in the battery.
expected = curve.value(solution.terminal_value.battery_energy_wh)
assert solution.terminal_value.credited_euro == pytest.approx(expected)
tests/test_terminalvalue.py
+114
View File
@@ -0,0 +1,114 @@
"""Tests for the concave terminal value of the energy left in the battery."""
import numpy as np
import pytest
from akkudoktoreos.optimization.genetic.terminalvalue import (
build_terminal_value_curve,
trailing_window,
)
def _curve(**overrides):
"""Two expensive slots, one cheap one, no PV, 10 kWh of usable battery."""
params = dict(
prices_euro_per_wh=np.array([0.0004, 0.0003, 0.0001]),
load_wh=np.array([1000.0, 1000.0, 1000.0]),
pv_wh=np.array([0.0, 0.0, 0.0]),
feed_in_euro_per_wh=np.array([0.00008, 0.00008, 0.00008]),
max_energy_wh=10000.0,
lcos_euro_per_kwh=0.0,
dc_to_ac_efficiency=1.0,
grid_export_allowed=False,
)
params.update(overrides)
return build_terminal_value_curve(**params)
def test_marginal_value_follows_the_most_expensive_hours_first():
"""The first stored kWh replaces the most expensive slot, then the next."""
curve = _curve()
# 0.40, 0.30 and 0.10 EUR/kWh, in that order.
assert curve.marginal_euro_per_kwh == pytest.approx([0.4, 0.3, 0.1])
assert curve.energy_wh == pytest.approx([0.0, 1000.0, 2000.0, 3000.0])
assert curve.value_euro == pytest.approx([0.0, 0.4, 0.7, 0.8])
def test_curve_is_concave_and_saturates():
"""Marginal values only decrease, and beyond the last breakpoint nothing is added."""
curve = _curve()
marginals = curve.marginal_euro_per_kwh
assert all(a >= b for a, b in zip(marginals, marginals[1:]))
# The residual load of the window is 3 kWh - more energy replaces nothing.
assert curve.value(3000.0) == pytest.approx(0.8)
assert curve.value(9000.0) == pytest.approx(0.8)
def test_value_interpolates_within_a_segment():
"""Half of the first slot is worth half of the first segment."""
curve = _curve()
assert curve.value(500.0) == pytest.approx(0.2)
def test_pv_reduces_the_residual_load():
"""Only load that PV cannot cover can be replaced by stored energy."""
curve = _curve(pv_wh=np.array([600.0, 1000.0, 0.0]))
# Slot 0 keeps 400 Wh, slot 1 is fully covered by PV, slot 2 keeps 1000 Wh.
assert curve.energy_wh == pytest.approx([0.0, 400.0, 1400.0])
assert curve.marginal_euro_per_kwh == pytest.approx([0.4, 0.1])
def test_lcos_is_subtracted_from_the_marginal_value():
"""Storage cost is already charged on discharge and must not be credited twice."""
curve = _curve(lcos_euro_per_kwh=0.05, dc_to_ac_efficiency=1.0)
assert curve.marginal_euro_per_kwh == pytest.approx([0.35, 0.25, 0.05])
def test_negative_prices_do_not_create_value():
"""Storing energy for an hour that pays nothing is not worth anything."""
curve = _curve(prices_euro_per_wh=np.array([0.0004, -0.0001, 0.0]))
assert curve.marginal_euro_per_kwh == pytest.approx([0.4])
assert curve.value(5000.0) == pytest.approx(0.4)
def test_export_tail_only_with_direct_marketing():
"""Surplus beyond the residual load is worth an export - if export is allowed."""
without = _curve(grid_export_allowed=False)
with_export = _curve(grid_export_allowed=True)
assert without.value(10000.0) == pytest.approx(0.8)
# 7 kWh beyond the residual load at the median feed-in tariff of 0.08 EUR/kWh.
assert with_export.value(10000.0) == pytest.approx(0.8 + 7.0 * 0.08)
assert with_export.marginal_euro_per_kwh[-1] == pytest.approx(0.08)
def test_curve_is_capped_by_the_usable_battery_energy():
"""A battery smaller than the residual load ends the curve early."""
curve = _curve(max_energy_wh=1500.0)
assert curve.energy_wh[-1] == pytest.approx(1500.0)
assert curve.value(5000.0) == pytest.approx(0.4 + 0.5 * 0.3)
def test_empty_window_yields_an_empty_curve():
"""Without data there is no curve, and no credit."""
curve = build_terminal_value_curve(
prices_euro_per_wh=np.zeros(0),
load_wh=np.zeros(0),
pv_wh=np.zeros(0),
feed_in_euro_per_wh=np.zeros(0),
max_energy_wh=10000.0,
)
assert curve.energy_wh == []
assert curve.value(5000.0) == 0.0
def test_trailing_window_takes_the_end_of_the_horizon():
values = np.arange(10, dtype=float)
assert list(trailing_window(values, end_slot=8, window_slots=3)) == [5.0, 6.0, 7.0]
# A window longer than the horizon yields what there is.
assert list(trailing_window(values, end_slot=2, window_slots=5)) == [0.0, 1.0]
assert list(trailing_window(None, end_slot=8, window_slots=3)) == []
tests/testdata/optimize_result_1.json
Vendored
+161 -98
View File
@@ -116,13 +116,14 @@
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@@ -144,12 +143,75 @@
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],
"battery_grid_export_allowed": [],
"terminal_value": {
"mode": "AUTO",
"battery_energy_wh": 17857.05093527103,
"credited_euro": 2.9274511210000003,
"curve": {
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],
"window_slots": 24
}
},
"battery_grid_export_factor": [],
"eautocharge_hours_float": null,
"result": {
"Last_Wh_pro_Stunde": [
@@ -239,9 +301,9 @@
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"Gesamt_Verluste": 3807.1176630027076,
"Gesamtbilanz_Euro": 0.22702041221600888,
"Gesamteinnahmen_Euro": 1.0402628835513343,
"Gesamtkosten_Euro": 1.2672832957673432,
"Gesamt_Verluste": 3596.923518513394,
"Gesamtbilanz_Euro": 0.4923980569215065,
"Gesamteinnahmen_Euro": 1.0754450157888547,
"Gesamtkosten_Euro": 1.5678430727103612,
"Home_appliance_wh_per_hour": [
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@@ -324,6 +386,14 @@
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"Netzbezug_Wh_pro_Stunde": [
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tests/testdata/optimize_result_1_be.json
Vendored
+64 -1
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@@ -150,6 +150,68 @@
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@@ -759,5 +821,6 @@
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tests/testdata/optimize_result_2.json
Vendored
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tests/testdata/optimize_result_2_be.json
Vendored
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View File
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