fix(water-heating): count electric showers in Noutlets for mixer demand (App J)

The mixer-shower hot-water demand (worksheet 42a) divided N_shower by the
count of MIXER outlets only. But SAP 10.2 Appendix J step 1a is explicit:
"Establish how many shower outlets are present in the dwelling, Noutlets
(including in the count any instantaneous electric showers)" — and the
electric-shower step (64a) uses that same Noutlets from step 1a. So a
dwelling with both a mixer and an electric shower assigned the FULL N_shower
to the mixer system AND billed the electric shower on top of it, double-
counting shower demand → over-counted main HW → under-rated the dwelling.

Fix: thread the electric-shower count into the mixer demand so the
denominator is the total outlet count (mixer + electric), iterating the
warm-water draw over the mixer outlets only (per step 1e).

shower_types=1,2 cohort: -0.37 median -> +0.28 (crossed zero); API gauge
68.4% -> 69.0% within-0.5. Golden cert 0300-2747 (1 mixer + 1 electric)
re-pinned: PE +0.93 -> -0.10, CO2 +0.25 -> +0.15 (both toward zero,
confirming the double-count). Worksheet harness 47/47, 0 divergers (the
Elmhurst fixtures have no electric showers).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

domain/sap10_calculator/worksheet/water_heating.py

@@ -132,6 +132,7 @@ def hot_water_mixer_showers_monthly_l_per_day(
     has_bath: bool,
     mixer_shower_flow_rates_l_per_min: tuple[float, ...],
     cold_water_temps_c: tuple[float, ...],
+    n_electric_showers: int = 0,
 ) -> tuple[float, ...]:
     """SAP 10.2 §4 line (42a)m via Appendix J equations J1, J2, J3.
 
@@ -145,14 +146,23 @@ def hot_water_mixer_showers_monthly_l_per_day(
     Each outlet's warm-water draw for a month is the flow rate × 6 min ×
     Table J5 fbeh. The hot fraction is (41 − Tcold[m])/(52 − Tcold[m]).
     Per-outlet daily warm water is scaled by N_shower / N_outlets, then
-    summed across outlets to give (42a)m.
+    summed across the MIXER outlets to give (42a)m.
 
-    Instantaneous electric showers belong to worksheet (64a)m, not (42a)m
-    — those should be excluded from `mixer_shower_flow_rates_l_per_min`.
+    N_outlets is the dwelling's TOTAL shower-outlet count: SAP 10.2
+    Appendix J step 1a is explicit that the count INCLUDES "any
+    instantaneous electric showers" (which then bill their own energy via
+    (64a)m). So `mixer_shower_flow_rates_l_per_min` lists only the mixer
+    outlets (iterated for the warm-water draw), but `n_electric_showers`
+    must be added to the denominator — otherwise a dwelling with both a
+    mixer and an electric shower assigns the FULL N_shower to the mixer
+    system AND bills the electric shower on top, double-counting shower
+    demand (over-counts main HW → under-rates the dwelling).
     """
-    n_outlets = len(mixer_shower_flow_rates_l_per_min)
-    if n_outlets == 0:
+    n_mixer_outlets = len(mixer_shower_flow_rates_l_per_min)
+    if n_mixer_outlets == 0:
         return tuple(0.0 for _ in range(12))
+    # Appendix J step 1a: Noutlets includes instantaneous electric showers.
+    n_outlets = n_mixer_outlets + n_electric_showers
     if has_bath:
         n_shower = 0.45 * n_occupants + 0.65
     else:
@@ -894,6 +904,8 @@ def water_heating_from_cert(
         has_bath=has_bath,
         mixer_shower_flow_rates_l_per_min=mixer_shower_flow_rates_l_per_min,
         cold_water_temps_c=cold_water_temps_c,
+        # SAP 10.2 Appendix J step 1a — Noutlets includes electric showers.
+        n_electric_showers=electric_shower_count if has_electric_shower else 0,
     )
     has_shower = (
         len(mixer_shower_flow_rates_l_per_min) > 0

tests/domain/sap10_calculator/rdsap/test_golden_fixtures.py

@@ -224,8 +224,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
         cert_number="0300-2747-7640-2526-2135",
         actual_sap=78,
         expected_sap_resid=+0,
-        expected_pe_resid_kwh_per_m2=+0.9264,
-        expected_co2_resid_tonnes_per_yr=+0.2495,
+        expected_pe_resid_kwh_per_m2=-0.1033,
+        expected_co2_resid_tonnes_per_yr=+0.1488,
         notes=(
             "Large semi-detached, TFA 526, age D, gas boiler PCDB-listed "
             "(no Table 4b code). Cert lodges open_flues_count=1 + "
@@ -245,7 +245,11 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
             "CO2 / PE factors through the cert's mains-gas "
             "`secondary_fuel_type` (mirroring the cost-side Slice 58 "
             "fix), closing PE +8.28 → +0.93 and CO2 −0.25 → +0.25 — "
-            "second-biggest cohort PE closure to date."
+            "second-biggest cohort PE closure to date. Slice S0380.xx "
+            "(SAP 10.2 Appendix J step 1a — Noutlets includes electric "
+            "showers) halved this cert's mixer-shower HW (1 mixer + 1 "
+            "electric → /2 not /1), removing the double-counted shower "
+            "demand: PE +0.93 → -0.10, CO2 +0.25 → +0.15 (both toward 0)."
         ),
     ),
     _GoldenExpectation(

tests/domain/sap10_calculator/worksheet/test_water_heating.py

@@ -344,6 +344,34 @@ def test_hot_water_mixer_showers_two_outlets_distributes_shower_count_evenly() -
         assert t == pytest.approx(s, abs=1e-9), f"month {m+1}"
 
 
+def test_hot_water_mixer_showers_counts_electric_showers_in_noutlets() -> None:
+    # Arrange — SAP 10.2 Appendix J step 1a (PDF p.~): "Establish how many
+    # shower outlets are present in the dwelling, Noutlets (INCLUDING in the
+    # count any instantaneous electric showers)". The mixer (42a) demand
+    # divides N_shower by this TOTAL outlet count, so a coexisting electric
+    # shower reduces each mixer outlet's share. Adding one electric shower to
+    # a single-mixer dwelling makes Noutlets=2 → the mixer demand halves
+    # (vs. counting only the mixer outlet, which over-counts main HW and
+    # under-rates the dwelling).
+    mixer_only = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=2.0, has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(8.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+
+    # Act — same single mixer outlet, but one electric shower also present.
+    with_electric = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=2.0, has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(8.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+        n_electric_showers=1,
+    )
+
+    # Assert — N_shower / 2 instead of / 1 → exactly half the mixer demand.
+    for m, (only, both) in enumerate(zip(mixer_only, with_electric)):
+        assert abs(both - only / 2.0) <= 1e-9, f"month {m+1}"
+
+
 @pytest.mark.parametrize("fixture", ALL_FIXTURES, ids=[fixture_id(f) for f in ALL_FIXTURES])
 def test_total_hot_water_monthly_matches_elmhurst_line_44(fixture: ModuleType) -> None:
     """SAP10.2 §4 line (44)m via Appendix J equation J13: