feat(optimization): model battery LCOS and probabilistic bypass

tests/test_interpolator.py

@@ -10,8 +10,8 @@ def test_quarter_hour_energy_is_converted_back_to_same_mean_power():
     hourly_pv_wh = 1200.0
     slot_duration_h = 0.25
 
-    hourly = interpolator.calculate_self_consumption(hourly_load_wh, hourly_pv_wh)
-    quarter_hour = interpolator.calculate_self_consumption(
+    hourly = interpolator.calculate_expected_direct_consumption(hourly_load_wh, hourly_pv_wh)
+    quarter_hour = interpolator.calculate_expected_direct_consumption(
         (hourly_load_wh / 4) / slot_duration_h,
         (hourly_pv_wh / 4) / slot_duration_h,
     )
@@ -28,3 +28,43 @@ def test_load_above_probability_grid_uses_highest_supported_distribution():
 
     assert above_boundary == pytest.approx(at_boundary)
     assert above_boundary > 0.99
+
+
+def test_expected_direct_consumption_accounts_for_subhourly_load_variation():
+    """Expected overlap must be below the optimistic overlap of interval means."""
+    interpolator = get_eos_load_interpolator()
+
+    direct_power_w = interpolator.calculate_expected_direct_consumption(800.0, 1200.0)
+
+    assert direct_power_w == pytest.approx(621.0, abs=2.0)
+    assert 0.0 < direct_power_w < 800.0
+
+
+@pytest.mark.parametrize(
+    ("mean_load_power_w", "pv_power_w"),
+    [(800.0, 1200.0), (1000.0, 500.0), (1500.0, 1500.0)],
+)
+def test_expected_direct_consumption_produces_conservative_energy_balance(
+    mean_load_power_w, pv_power_w
+):
+    """Direct use, residual load and surplus must conserve both mean powers."""
+    interpolator = get_eos_load_interpolator()
+
+    direct_power_w = interpolator.calculate_expected_direct_consumption(
+        mean_load_power_w, pv_power_w
+    )
+    residual_load_w = mean_load_power_w - direct_power_w
+    pv_surplus_w = pv_power_w - direct_power_w
+
+    assert 0.0 <= direct_power_w <= min(mean_load_power_w, pv_power_w)
+    assert direct_power_w + residual_load_w == pytest.approx(mean_load_power_w)
+    assert direct_power_w + pv_surplus_w == pytest.approx(pv_power_w)
+
+
+def test_expected_direct_consumption_preserves_forecast_mean_at_high_pv():
+    """A PV level above every normalized load bin covers the complete mean load."""
+    interpolator = get_eos_load_interpolator()
+
+    direct_power_w = interpolator.calculate_expected_direct_consumption(3000.0, 10000.0)
+
+    assert direct_power_w == pytest.approx(3000.0)