diff --git a/backend/services/planning_engine.py b/backend/services/planning_engine.py
index 350a7fc..eceb31e 100644
--- a/backend/services/planning_engine.py
+++ b/backend/services/planning_engine.py
@@ -71,9 +71,11 @@ NEG_BUY_CHARGE_SHORTFALL_PENALTY_CZK_KWH = 100.0
 PRE_NEG_CHARGE_PENALTY_CZK_KWH = 400.0
 PRE_NEG_BATT_EXPORT_SHORTFALL_PENALTY_CZK_KWH = 80.0
 PRE_NEG_BATT_EXPORT_MIN_SELL_CZK_KWH = 1.0
-PLANNER_BUILD_TAG = "2026-06-01-evening-push-keep-on-relaxed-import-v57"
+PLANNER_BUILD_TAG = "2026-06-01-fixed-pv-export-min-sell-charge-v58"
 # Ranní slabá FVE: neaplikovat pv_store ge_pv=0 (jinak curtail při sell < večerní peak).
 DAWN_LOW_PV_NO_CURTAIL_W = 1500
+# BA81/KV1: PV→bat jen v těsné blízkosti nejnižšího sell v horizontu (≈ poledne), ne při ~3 Kč ráno.
+FIXED_PV_CHARGE_ONLY_NEAR_MIN_SELL_CZK_KWH = 0.20
 # Mimo evening_push: preferovat bd pro dům místo gi, když buy >> acq (účinná cena importu).
 NIGHT_SELF_CONSUME_IMPORT_SURCHARGE_CZK_KWH = 4.0
 # Po t_detach v prep: necpát PV do bat (měkké; tvrdý hold přes soc_target z rampy).
@@ -2559,6 +2561,13 @@ def solve_dispatch(
         degrad_czk_kwh=float(degradation_cost_effective),
     )
     purchase_fixed_pre = _purchase_pricing_fixed(grid)
+    fixed_horizon_min_sell_pre: float | None = None
+    if purchase_fixed_pre:
+        _pos_sell_prices = [
+            float(s.sell_price) for s in slots if float(s.sell_price) >= 0.0
+        ]
+        if _pos_sell_prices:
+            fixed_horizon_min_sell_pre = min(_pos_sell_prices)
     block_export_neg_sell_pre = bool(
         getattr(grid, "block_export_on_negative_sell", False)
     )
@@ -2813,6 +2822,9 @@ def solve_dispatch(
             | set(pre_neg_buy_empty_ts)
             | set(neg_evening_push_ts)
         )
+        if purchase_fixed_pre:
+            # Fixní tarif: sell>buy v noci nesmí ge_bat=0 přes evening_early (BA81 úsvit).
+            evening_export_exempt_ts |= profitable_export_ts_pre
         evening_early_export_penalty_ts = _evening_early_export_penalty_indices(
             slots,
             discharge_export_slots=discharge_export_slots,
@@ -2951,8 +2963,17 @@ def solve_dispatch(
             if t in evening_push_ts:
                 continue
             if _in_night_battery_export_window(slots[t]):
-                # Večerní export jen v tvrdém push; jinak by shortfall rozplizňoval ge_bat.
-                continue
+                # Spot: večerní export jen v tvrdém push. Fixní: i profitable sell>buy v noci.
+                if not (
+                    purchase_fixed_pre
+                    and _slot_profitable_battery_export(
+                        slots[t],
+                        charge_acquisition_czk_kwh=charge_acquisition_czk_kwh,
+                        min_spread=float(degradation_cost_effective),
+                        fixed_tariff=True,
+                    )
+                ):
+                    continue
             if _battery_export_push_defer_to_pv(slots[t]):
                 continue
             if not _slot_profitable_battery_export(
@@ -4008,6 +4029,23 @@ def solve_dispatch(
                 or fixed_pre_neg_pv_export
                 or fixed_block_pv_surplus_export
                 or fixed_mi_low_pv_surplus_export
+                or (
+                    purchase_fixed_pre
+                    and fixed_horizon_min_sell_pre is not None
+                    and sell_t >= 0.0
+                    and pv_surplus_w > NIGHT_EXPORT_PV_SUNRISE_SURPLUS_W
+                    and sell_t
+                    > fixed_horizon_min_sell_pre
+                    + FIXED_PV_CHARGE_ONLY_NEAR_MIN_SELL_CZK_KWH
+                )
+            )
+            fixed_high_sell_no_pv_charge = (
+                purchase_fixed_pre
+                and fixed_horizon_min_sell_pre is not None
+                and sell_t >= 0.0
+                and pv_surplus_w > NIGHT_EXPORT_PV_SUNRISE_SURPLUS_W
+                and sell_t
+                > fixed_horizon_min_sell_pre + FIXED_PV_CHARGE_ONLY_NEAR_MIN_SELL_CZK_KWH
             )
             fixed_pv_b_export_cap = (
                 purchase_fixed_pre
@@ -4017,6 +4055,9 @@ def solve_dispatch(
                 and not fixed_pre_neg_pv_export
                 and int(s.pv_a_forecast_w) >= DAWN_LOW_PV_NO_CURTAIL_W
             )
+            if fixed_high_sell_no_pv_charge:
+                prob += bc_pv[t] == 0
+                prob += bc_gi[t] == 0
             if fixed_pre_neg_pv_export:
                 prob += ge_pv[t] <= max(0.0, pv_surplus_w)
             elif fixed_pv_b_export_cap:
@@ -4594,6 +4635,10 @@ def solve_dispatch(
                 and bool(evening_push_ts)
                 and not push_override_eff
             ),
+            "fixed_horizon_min_sell_czk_kwh": fixed_horizon_min_sell_pre,
+            "fixed_pv_charge_near_min_sell_margin_czk_kwh": (
+                FIXED_PV_CHARGE_ONLY_NEAR_MIN_SELL_CZK_KWH if purchase_fixed_pre else None
+            ),
             "charge_commitment_ignored_on_relaxed": bool(
                 commitment_for_solve is None and charge_commitment_prev_w is not None
             ),
diff --git a/backend/tests/test_planning_dispatch_milp.py b/backend/tests/test_planning_dispatch_milp.py
index 6b148e6..1e6d0ca 100644
--- a/backend/tests/test_planning_dispatch_milp.py
+++ b/backend/tests/test_planning_dispatch_milp.py
@@ -1673,6 +1673,153 @@ class NegativeSellPvChargeTests(unittest.TestCase):
             "kladný sell>buy: alespoň částečný výdej (jednoslotový horizont — plný push až v integračním testu)",
         )
 
+    def test_fixed_high_sell_no_pv_charge_near_min_sell(self) -> None:
+        """v58: ráno sell~3 Kč → export FVE; poledne sell~1,45 Kč → nabíjení z PV."""
+        prague = ZoneInfo("Europe/Prague")
+        base = datetime(2026, 6, 2, 6, 0, tzinfo=prague)
+        slots: list[PlanningSlot] = []
+        for i in range(8):
+            sell = 3.15 if i < 4 else 1.45
+            slots.append(
+                PlanningSlot(
+                    interval_start=(base + timedelta(minutes=15 * i)).astimezone(
+                        timezone.utc
+                    ),
+                    buy_price=3.088,
+                    sell_price=sell,
+                    pv_a_forecast_w=8000,
+                    pv_b_forecast_w=200,
+                    load_baseline_w=400,
+                    ev1_connected=False,
+                    ev2_connected=False,
+                    allow_charge=True,
+                    allow_discharge_export=False,
+                    charge_acquisition_buy_czk_kwh=3.088,
+                    future_sell_opportunity_czk_kwh=3.2,
+                )
+            )
+        battery = _battery(uc_wh=12_500.0, min_pct=10.0, arb_pct=30.0)
+        battery.max_charge_power_w = 6250
+        hp = SimpleNamespace(
+            rated_heating_power_w=0,
+            tuv_min_temp_c=45.0,
+            tuv_target_temp_c=55.0,
+        )
+        grid = SimpleNamespace(
+            max_import_power_w=17_000,
+            max_export_power_w=8000,
+            block_export_on_negative_sell=False,
+            purchase_pricing_mode="fixed",
+        )
+        vehicles = [
+            SimpleNamespace(
+                max_charge_power_w=0,
+                battery_capacity_kwh=1.0,
+                default_target_soc_pct=80.0,
+            ),
+            SimpleNamespace(
+                max_charge_power_w=0,
+                battery_capacity_kwh=1.0,
+                default_target_soc_pct=80.0,
+            ),
+        ]
+        soc0 = 0.35 * battery.usable_capacity_wh
+        results, _, snap = solve_dispatch(
+            slots,
+            battery,
+            hp,
+            grid,
+            [None, None],
+            vehicles,
+            soc0,
+            50.0,
+            operating_mode="AUTO",
+        )
+        self.assertEqual(
+            snap["inputs"].get("fixed_horizon_min_sell_czk_kwh"),
+            1.45,
+        )
+        r_morning = results[0]
+        r_noon = results[5]
+        self.assertLess(
+            r_morning.grid_setpoint_w,
+            -2000,
+            "vysoký sell: přebytek FVE do sítě",
+        )
+        self.assertLessEqual(
+            r_morning.battery_setpoint_w,
+            200,
+            "vysoký sell: ne nabíjet z PV",
+        )
+        self.assertGreater(
+            r_noon.battery_setpoint_w,
+            800,
+            "min sell: nabíjení z PV",
+        )
+
+    def test_fixed_night_profitable_export_not_evening_early_banned(self) -> None:
+        """v58: v noci sell>buy nesmí evening_early držet ge_bat=0."""
+        prague = ZoneInfo("Europe/Prague")
+        slot = PlanningSlot(
+            interval_start=datetime(2026, 6, 2, 5, 0, tzinfo=prague).astimezone(
+                timezone.utc
+            ),
+            buy_price=3.088,
+            sell_price=3.35,
+            pv_a_forecast_w=0,
+            pv_b_forecast_w=0,
+            load_baseline_w=400,
+            ev1_connected=False,
+            ev2_connected=False,
+            allow_charge=False,
+            allow_discharge_export=True,
+            charge_acquisition_buy_czk_kwh=3.088,
+        )
+        battery = _battery(uc_wh=12_500.0, terminal_soc_value_factor=0.0)
+        battery.max_discharge_power_w = 6250
+        battery.planner_daytime_charge_target_enabled = False
+        hp = SimpleNamespace(
+            rated_heating_power_w=0,
+            tuv_min_temp_c=45.0,
+            tuv_target_temp_c=55.0,
+        )
+        grid = SimpleNamespace(
+            max_import_power_w=17_000,
+            max_export_power_w=8000,
+            block_export_on_negative_sell=False,
+            purchase_pricing_mode="fixed",
+        )
+        vehicles = [
+            SimpleNamespace(
+                max_charge_power_w=0,
+                battery_capacity_kwh=1.0,
+                default_target_soc_pct=80.0,
+            ),
+            SimpleNamespace(
+                max_charge_power_w=0,
+                battery_capacity_kwh=1.0,
+                default_target_soc_pct=80.0,
+            ),
+        ]
+        soc0 = 0.28 * battery.usable_capacity_wh
+        results, _, _ = solve_dispatch(
+            [slot],
+            battery,
+            hp,
+            grid,
+            [None, None],
+            vehicles,
+            soc0,
+            50.0,
+            operating_mode="AUTO",
+        )
+        r0 = results[0]
+        self.assertLess(
+            r0.battery_setpoint_w,
+            -500,
+            "noci sell>buy: vývoz z baterie",
+        )
+
     def test_fixed_tariff_post_neg_pv_b_full_soc_feasible(self) -> None:
         """BA81: plná baterie + sell<0 + odpoledne pv_b — ge_pv==0 z pv_store dříve dělalo Infeasible."""
         slots = [
diff --git a/docs/04-modules/planning.md b/docs/04-modules/planning.md
index 544cc6d..ab2fe7e 100644
--- a/docs/04-modules/planning.md
+++ b/docs/04-modules/planning.md
@@ -19,6 +19,7 @@
   - **Tvrdé výkonové limity site/baterie:** `gi ≤ site_grid_connection.max_import_power_w` (breaker); **`bc_pv + bc_gi ≤ asset_battery.max_charge_power_w`**; **`ge ≤ max_export_power_w`** (proměnná `ge`, platí `ge = ge_pv + ge_bat`); **`bd + ge_bat ≤ asset_battery.max_discharge_power_w`** (vybíjení do domu + export z baterie nesmí současně překročit BMS). Dříve LP dovoloval import+nabíjení a dvojnásobné nabíjení; u prodeje hrozilo současné `bd` a `ge_bat` až 2× max discharge — viz `SitePowerCapTests`.
   - **Hodnota FVE (PV store value):** tvrdé `ge_pv = 0` jen pokud `sell < future_sell_opportunity − degradation` **a** `sell < 0` (spot), nebo u fixního tarifu dle `fixed_pv_b_export_cap`. Při **`sell ≥ 0` (spot home-01, KV1):** `ge_pv` **neblokuje** pv_store — solver volí export vs. `bc_pv` podle `−ge_pv×sell` a degradace; **baterii** na večerní peak drží `ge_bat` (`evening_early` / push), ne curtail FVE. **v31:** při `sell ≥ 0` + PV přebytek **není** plný `ge_bat` push z `pre_neg_buy_discharge` / ranních shortfallů (export cap pro FVE). **Před prvním `sell < 0`:** `allow_pre_neg_pv_export`. Tag `2026-05-28-morning-pv-export-priority-v31`. Testy `Home01PvStoreValueTests`, `PreNegativeSellExportTests`.
   - **BA81 úsvit + MI (v51):** `fixed_pv_b_export_cap` (`ge_pv ≤ pv_b`) jen pokud **`pv_a_forecast ≥ 1500 W`** (`DAWN_LOW_PV_NO_CURTAIL_W`); při slabším A + přebytku → `fixed_mi_low_pv_surplus_export` (bez pv_store bloku). Exporter: při `forecast < 1500` a bez curtail A → **bez reg 340** (`setpoints.py`). Tag `2026-05-31-ba81-dawn-no-micro-curtail-v51`. Test `test_ba81_dawn_low_pv_no_full_curtail_for_mi_cap`.
+  - **Fixní tarif — PV export vs. nabíjení (v58):** `fixed_horizon_min_sell` z horizontu; při **`sell > min_sell + 0,20`** a PV přebytku → **`bc_pv = 0`**, **`bc_gi = 0`**, neblokovat `ge_pv` (ráno ~3 Kč export, poledne ~1,5 Kč nabíjení). Profitable `sell > buy` v noci: výjimka z `evening_early` + `peak_export_shortfall`. Tag `2026-06-01-fixed-pv-export-min-sell-charge-v58`. Testy `fixed_high_sell_no_pv_charge`.
   - **Drahý nákup → vlastní spotřeba z baterie:** mimo `allow_charge` platí `bd + pv_ld ≥ load_baseline + hp[t]` a `gi ≤ EV + hp[t]` (ne `hp_rated`). **Spot:** drahý slot = `buy > min(buy≥0) + degradace`. **Fixní nákup (DB `purchase_pricing_mode=fixed` nebo heuristika rozptylu buy &lt; 0,25):** navíc `buy > charge_acquisition + degradace`. Na spotu **nesmí** `charge_acquisition` (~0,9 Kč) označit všechny sloty jako drahé → Infeasible (home-01). Při **Infeasible** solver jednou opakuje s `relaxed_expensive_import` (síť smí krmit baseload v drahých slotech; v `solver_params.inputs.relaxed_expensive_import=true`). Testy `AutoPassiveSelfConsumptionTests`, `test_spot_low_acquisition_does_not_mark_all_slots_expensive`, `test_negative_buy_in_horizon_does_not_block_all_grid_import`.
   - **Záporný výkup (`sell < 0`) bez exportu:** `block_export_on_negative_sell` (KV1) **nebo** `purchase_pricing_mode=fixed` (BA81). **Spot (home-01):** `ge_pv=0` dokud není plná baterie; při plné jen ventil pole B (`ge_pv ≤ pv_b`, `w_pv_b_vent_neg`); výboj baterie při `sell<0` jen **12 slotů** před `buy ≤ planner_extreme_buy_threshold` (default −2), pokud spread do budoucna dává smysl — tag `2026-05-26-neg-sell-bat-dump-extreme-buy-v11`. Večerní discharge maska u spotu: denní peak ≥17:00 (ne `sell > ref_buy` v slotu). **v50:** u **KV1** při `sell≥0` a PV přebytku &gt;500 W i **po** 1. `sell<0` → `ge_pv` (PV_SURPLUS), ne tvrdý `ge_bat` z večerního peak/push.
   - **Pole B při sell&lt;0 (home-01):** pokud `block_export_on_negative_sell = false`, LP nesmí vynutit `ge_pv = 0` (přebytek neriťitelného PV B). KV1 s `block_export = true` jen curtail A / nabíjení.
@@ -133,7 +134,9 @@ flowchart TD
 
 12. **v57 — večerní push po rei:** `relaxed_expensive_import` **nesmí** vymazat `evening_push_ts`; tvrdý `ge_bat` push vypnut jen při `relaxed_neg_prep_window`. Tag **`2026-06-01-evening-push-keep-on-relaxed-import-v57`**.
 
-**Funkce:** … home-01 **v57**.
+13. **v58 — fixní tarif PV vs. nabíjení (BA81/KV1):** `fixed_horizon_min_sell`; při **`sell > min + 0,20`** → **`bc_pv = 0`**, **`bc_gi = 0`**, export FVE; profitable noc **`sell > buy`** mimo `evening_early` + shortfall. Tag **`2026-06-01-fixed-pv-export-min-sell-charge-v58`**.
+
+**Funkce:** … home-01 **v57**; BA81/KV1 fixed **v58**.
 
 ### Arbitráž baterie — účtování mezi sloty (povinné čtení)
 
diff --git a/docs/planning-changelog.md b/docs/planning-changelog.md
index 903a1b7..68065b4 100644
--- a/docs/planning-changelog.md
+++ b/docs/planning-changelog.md
@@ -5,6 +5,37 @@ Formát: **datum (ISO)** · stručný důvod · soubory · chování / ověřen
 
 ---
 
+## 2026-06-01 — BA81/KV1: FVE export při vysokém sell, nabíjení u min sell (v58)
+
+**Problém:** U **`purchase_pricing_mode=fixed`** (BA81 buy ~3,09 Kč, KV1 ~6,35 Kč) oproti home-01 (spot):
+- půlnoc→ráno baterie **~24–30 %** bez vývozu i tam, kde `sell > buy + degrad` (BA81 úsvit ~3,35 Kč);
+- **~06:00** nabíjení z FVE při výkupní **~3 Kč/kWh**, místo exportu přebytku a nabíjení až u **nejnižšího sell** v horizontu (**~1,5 Kč**, poledne);
+- KV1 večer jen malý vývoz ve špičce, ráno zbytečně vysoká rezerva.
+
+Příčiny v LP: chybějící **`bc_pv == 0`** při sell výrazně nad denním minimem; `pv_store` / `ge_pv == 0` u fixního tarifu mimo úzké `fixed_pre_neg_*`; **`evening_early_export_ban`** (`ge_bat = 0`) i pro profitable `sell > buy` v noci; `peak_export_shortfall` noční okno přeskakoval (pravidlo pro spot / `evening_push`).
+
+**Změna (v58)** — `backend/services/planning_engine.py`:
+- Konstanta **`FIXED_PV_CHARGE_ONLY_NEAR_MIN_SELL_CZK_KWH = 0.20`**; **`fixed_horizon_min_sell_pre`** = `min(sell_price)` pro `sell ≥ 0` v horizontu.
+- **`fixed_high_sell_no_pv_charge`:** `sell > min_sell + 0,20` a PV přebytek > `NIGHT_EXPORT_PV_SUNRISE_SURPLUS_W` → **`bc_pv = 0`**, **`bc_gi = 0`**; rozšířen **`skip_pv_store_block`** (FVE do sítě, ne do baterie).
+- Fixní tarif: **`evening_export_exempt_ts |= profitable_export_ts_pre`** (`_slot_profitable_battery_export`: `sell > buy + degrad`).
+- **`peak_export_shortfall`:** v nočním okně pokračovat i pro fixní profitable sloty (ne jen tvrdý `evening_push`).
+- Snap: `fixed_horizon_min_sell_czk_kwh`, `fixed_pv_charge_near_min_sell_margin_czk_kwh`.
+
+**Soubory:** `backend/services/planning_engine.py`, `backend/tests/test_planning_dispatch_milp.py`, `docs/04-modules/planning.md`, `docs/planning-changelog.md`.
+
+Tag **`2026-06-01-fixed-pv-export-min-sell-charge-v58`**.
+
+**Ověření:**
+
+```bash
+cd backend && pytest tests/test_planning_dispatch_milp.py \
+  -k "fixed_high_sell_no_pv_charge or fixed_night_profitable" -q
+```
+
+MCP po replanu BA81/KV1: `planning_run.solver_params->>'planner_build_tag'` obsahuje `v58`; ráno export (`grid_setpoint_w < 0`, `battery_setpoint_w` malé), poledne nabíjení (`battery_setpoint_w` vysoké u min sell).
+
+---
+
 ## 2026-06-01 — home-01: večerní vývoz po relaxed_expensive_import (v57)
 
 **Problém:** v55 při **jakékoli** relaxed větvi vynulovalo `evening_push_ts` → `evening_early_export_ban` zakázal `ge_bat` i při sell **~9,6 Kč/kWh**; baterie jen samospotřeba, zítra export FVE za **~2 Kč**.