Slice 45b: PV pitch dimension + real Appendix U3.3 S(orient, p) integral — replaces 45a 30°-pitch stub

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

packages/domain/src/domain/sap/rdsap/cert_to_inputs.py

@@ -107,6 +107,7 @@ from domain.sap.worksheet.solar_gains import (
     RoofWindowInput,
     SolarGainsResult,
     solar_gains_from_cert,
+    surface_solar_flux_w_per_m2,
 )
 from domain.sap.worksheet.heat_transmission import (
     DwellingExposure,
@@ -193,21 +194,49 @@ _INSTANTANEOUS_WATER_CODES: Final[frozenset[int]] = frozenset({907, 909})
 # the cert's tilt / orientation / shading data.
 _PV_MODULE_EFFICIENCY_FACTOR: Final[float] = 0.8
 
-# Appendix U3.3 annual solar radiation S (kWh/m²/yr) on a 30°-pitch
-# surface, by SAP orientation octant (1=N, 2=NE, 3=E, 4=SE, 5=S, 6=SW,
-# 7=W, 8=NW), UK-average climate (rating cascade per Appendix U). The
-# pitch dimension lands in a follow-on slice — for now 30° is the
-# RdSAP10 §11.1 default ("if not provided … facing South, pitch 30°").
-_PV_ANNUAL_S_KWH_PER_M2_BY_ORIENTATION_30_PITCH: Final[dict[int, float]] = {
-    1: 580.0,   # N
-    2: 720.0,   # NE
-    3: 880.0,   # E
-    4: 1010.0,  # SE
-    5: 1050.0,  # S
-    6: 1010.0,  # SW
-    7: 880.0,   # W
-    8: 720.0,   # NW
+# RdSAP10 §11.1 pitch enum → degrees from horizontal. RdSAP fixes the
+# tilt to one of five values; certs lodge the integer code while
+# Appendix U3.2 takes a continuous pitch.
+_PV_PITCH_DEG_BY_CODE: Final[dict[int, float]] = {
+    1: 0.0,    # horizontal
+    2: 30.0,
+    3: 45.0,
+    4: 60.0,
+    5: 90.0,   # vertical
 }
+_PV_PITCH_DEG_DEFAULT: Final[float] = 30.0  # RdSAP10 §11.1 default
+
+# SAP 10.2 Appendix U3.3 equation (U4) constant: converts (W/m² × days)
+# to (kWh/m²/yr) via 24 h/day ÷ 1000 W/kW = 0.024.
+_HOURS_PER_DAY_OVER_1000: Final[float] = 0.024
+_DAYS_PER_MONTH: Final[tuple[int, ...]] = (31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
+
+# SAP 10.2 Appendix U Table U4 row 0 = UK-average climate region. Rating
+# cascade uses UK average per Appendix U; demand cascade will switch to
+# postcode-specific climate in a follow-on slice.
+_PV_RATING_REGION: Final[int] = 0
+
+
+def _pv_annual_s_kwh_per_m2(orientation_code: int, pitch_code: int) -> float:
+    """SAP 10.2 Appendix U3.3 equation (U4): annual solar radiation
+    (kWh/m²/yr) on a surface of given orientation and tilt under UK-
+    average climate. Sums the monthly Appendix U3.2 surface flux over
+    the year. Returns 0.0 for unrecognised orientation codes (cert
+    octants outside 1..8) — these PV arrays contribute nothing."""
+    orientation = ORIENTATION_BY_SAP10_CODE.get(orientation_code)
+    if orientation is None:
+        return 0.0
+    pitch_deg = _PV_PITCH_DEG_BY_CODE.get(pitch_code, _PV_PITCH_DEG_DEFAULT)
+    total = 0.0
+    for month_idx, days in enumerate(_DAYS_PER_MONTH):
+        s_m = surface_solar_flux_w_per_m2(
+            orientation=orientation,
+            pitch_deg=pitch_deg,
+            region=_PV_RATING_REGION,
+            month=month_idx + 1,
+        )
+        total += days * s_m
+    return _HOURS_PER_DAY_OVER_1000 * total
 
 # SAP 10.2 Table M1 — PV overshading factor ZPV. RdSAP10 omits SAP10.2's
 # 5th "Severe" bucket; the four RdSAP codes map directly:
@@ -719,11 +748,12 @@ def _secondary_fuel_cost_gbp_per_kwh(
 
 def _pv_array_generation_kwh_per_yr(array: PhotovoltaicArray) -> float:
     """SAP 10.2 Appendix M (M1) for a single array: EPV = 0.8 × kWp × S × ZPV.
-    S comes from Appendix U3.3 by orientation (30°-pitch column for now);
-    ZPV from Table M1. Arrays with missing peak power contribute zero."""
+    S is the Appendix U3.3 annual solar radiation for the array's
+    orientation and tilt under UK-average climate; ZPV is the Table M1
+    overshading factor. Arrays with missing peak power contribute zero."""
     if array.peak_power is None:
         return 0.0
-    s = _PV_ANNUAL_S_KWH_PER_M2_BY_ORIENTATION_30_PITCH.get(array.orientation, 0.0)
+    s = _pv_annual_s_kwh_per_m2(array.orientation, array.pitch)
     z = _PV_OVERSHADING_FACTOR.get(array.overshading, 1.0)
     return _PV_MODULE_EFFICIENCY_FACTOR * array.peak_power * s * z
 

packages/domain/src/domain/sap/rdsap/tests/test_cert_to_inputs.py

@@ -436,6 +436,32 @@ def test_pv_generation_differentiates_arrays_by_orientation() -> None:
     assert south_kwh > north_kwh
 
 
+def test_pv_generation_differentiates_arrays_by_pitch() -> None:
+    # Arrange — two south-facing arrays, identical kWp / orientation /
+    # overshading, but differing pitch codes: 2 (30° tilt) vs 5 (vertical).
+    # Per SAP 10.2 Appendix U3.3 the annual solar radiation S(orient, p)
+    # depends on the tilt via the Rh-inc polynomial in U2/U3; a 30°-pitched
+    # array intercepts far more annual radiation than a vertical wall-
+    # mounted one at the same orientation. The Slice-45a stub fixed pitch
+    # at 30° and so produced identical numbers for both — this test
+    # forces the cascade to consume `PhotovoltaicArray.pitch`.
+    tilted = _typical_semi_detached_epc()
+    tilted.sap_energy_source.photovoltaic_arrays = [
+        PhotovoltaicArray(peak_power=2.0, pitch=2, orientation=5, overshading=1),
+    ]
+    vertical = _typical_semi_detached_epc()
+    vertical.sap_energy_source.photovoltaic_arrays = [
+        PhotovoltaicArray(peak_power=2.0, pitch=5, orientation=5, overshading=1),
+    ]
+
+    # Act
+    tilted_kwh = cert_to_inputs(tilted).pv_generation_kwh_per_yr
+    vertical_kwh = cert_to_inputs(vertical).pv_generation_kwh_per_yr
+
+    # Assert
+    assert tilted_kwh > vertical_kwh
+
+
 def test_open_chimneys_raise_infiltration_ach() -> None:
     # Arrange — Direction check: chimneys add Table 2.1 volume to the
     # infiltration calc, so an otherwise identical dwelling with 2 open

packages/domain/src/domain/sap/rdsap/tests/test_golden_fixtures.py

@@ -138,19 +138,19 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
     _GoldenExpectation(
         cert_number="2130-1033-4050-5007-8395",
         actual_sap=82,
-        expected_sap_resid=+2,
-        expected_pe_resid_kwh_per_m2=-48.8108,
+        expected_sap_resid=+3,
+        expected_pe_resid_kwh_per_m2=-51.0719,
         expected_co2_resid_tonnes_per_yr=+0.1422,
         notes=(
             "End-terrace + 1 extension, TFA 64, gas combi PCDB index 17505, "
             "postcode DE22 (PCDB Table 172 match), PV: 2× 2.04 kWp arrays "
-            "(SE + NW, overshading 1 + 2). Slice 45a applied SAP10.2 "
-            "Appendix M per-array yield (orientation S-table at 30° pitch "
-            "+ Table M1 ZPV) — pulled SAP residual +9 → +2 and PE residual "
-            "−69.57 → −48.81 vs the prior lump-sum 850 × total_kWp. "
-            "Remaining drift: pitch dimension and full Appendix U3.3 "
-            "monthly integral (currently approximated by the 30°-pitch "
-            "S-table) will land in follow-on slices."
+            "(SE + NW, overshading 1 + 2). Slice 45a/b applied SAP10.2 "
+            "Appendix M per-array yield with the real Appendix U3.3 "
+            "S(orient, p) integral + Table M1 ZPV — pulled SAP residual "
+            "+9 → +3 and PE residual −69.57 → −51.07 vs the prior lump-"
+            "sum 850 × total_kWp. Remaining drift: demand cascade still "
+            "uses UK-average climate for S; switching to postcode-specific "
+            "climate (PCDB Table 172) lands in a follow-on slice."
         ),
     ),
     _GoldenExpectation(