diff --git a/custom_components/solar_optimizer/managed_device.py b/custom_components/solar_optimizer/managed_device.py
index ed007b8..5711e25 100644
--- a/custom_components/solar_optimizer/managed_device.py
+++ b/custom_components/solar_optimizer/managed_device.py
@@ -416,10 +416,17 @@ def is_usable(self) -> bool:
     @property
     def should_be_forced_offpeak(self) -> bool:
         """True is we are offpeak and the max_on_time is not exceeded"""
-        return (
-            self.now.time() >= self._offpeak_time
-            or self.now.time() < self._coordinator.raz_time
-        ) and self._on_time_sec < self._max_on_time_per_day_sec
+        if self._offpeak_time >= self._coordinator.raz_time:
+            return (
+                self.now.time() >= self._offpeak_time
+                or self.now.time() < self._coordinator.raz_time
+            ) and self._on_time_sec < self._max_on_time_per_day_sec
+        else:
+            return (
+                self.now.time() >= self._offpeak_time
+                and self.now.time() < self._coordinator.raz_time
+                and self._on_time_sec < self._max_on_time_per_day_sec
+            )
 
     @property
     def is_waiting(self):
diff --git a/custom_components/solar_optimizer/sensor.py b/custom_components/solar_optimizer/sensor.py
index 11d8079..0930dc8 100644
--- a/custom_components/solar_optimizer/sensor.py
+++ b/custom_components/solar_optimizer/sensor.py
@@ -324,6 +324,7 @@ def update_custom_attributes(self):
             "max_on_time_hms": seconds_to_hms(self._device.max_on_time_per_day_sec),
             "raz_time": self._coordinator.raz_time,
             "should_be_forced_offpeak": self._device.should_be_forced_offpeak,
+            "offpeak_time": self._device.offpeak_time,
         }
 
     @property
diff --git a/tests/conftest.py b/tests/conftest.py
index fa64825..c09d18a 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -240,3 +240,45 @@ async def init_solar_optimizer_with_2_devices_min_on_time_ok(
         hass, "solar_optimizer", config_2_devices_min_on_time_ok
     )
     return hass.data[DOMAIN]["coordinator"]
+
+
+@pytest.fixture(name="config_devices_offpeak_morning")
+def define_config_devices_offpeak_morning():
+    """Define a configuration with 1 devices which have its offpeak_time on morning"""
+
+    return {
+        "solar_optimizer": {
+            "algorithm": {
+                "initial_temp": 1000,
+                "min_temp": 0.1,
+                "cooling_factor": 0.95,
+                "max_iteration_number": 1000,
+            },
+            "devices": [
+                {
+                    "name": "Equipement A",
+                    "entity_id": "input_boolean.fake_device_a",
+                    "power_max": 1000,
+                    "check_usable_template": "{{ True }}",
+                    "duration_min": 2,
+                    "duration_stop_min": 1,
+                    "action_mode": "service_call",
+                    "activation_service": "input_boolean/turn_on",
+                    "deactivation_service": "input_boolean/turn_off",
+                    "battery_soc_threshold": 30,
+                    "max_on_time_per_day_min": 10,
+                    "min_on_time_per_day_min": 5,
+                    "offpeak_time": "01:00",
+                }
+            ],
+        }
+    }
+
+
+@pytest.fixture(name="init_solar_optimizer_with_devices_offpeak_morning")
+async def init_solar_optimizer_with_devices_offpeak_morning(
+    hass, config_devices_offpeak_morning
+) -> SolarOptimizerCoordinator:
+    """Initialization of Solar Optimizer with 2 managed device"""
+    await async_setup_component(hass, "solar_optimizer", config_devices_offpeak_morning)
+    return hass.data[DOMAIN]["coordinator"]
diff --git a/tests/test_config_flow.py b/tests/test_config_flow.py
index c6f3c5c..cfb8c90 100644
--- a/tests/test_config_flow.py
+++ b/tests/test_config_flow.py
@@ -34,13 +34,22 @@ async def test_empty_config(hass: HomeAssistant):
 
 @pytest.mark.parametrize(
     "power_consumption,power_production,sell_cost,buy_cost, raz_time",
-    itertools.product(
-        ["sensor.power_consumption", "input_number.power_consumption"],
-        ["sensor.power_production", "input_number.power_production"],
-        ["sensor.sell_cost", "input_number.sell_cost"],
-        ["sensor.buy_cost", "input_number.buy_cost"],
-        ["00:00", "04:00"],
-    ),
+    [
+        (
+            "sensor.power_consumption",
+            "sensor.power_production",
+            "sensor.sell_cost",
+            "sensor.buy_cost",
+            "00:00",
+        ),
+        (
+            "input_number.power_consumption",
+            "input_number.power_production",
+            "input_number.sell_cost",
+            "input_number.buy_cost",
+            "04:00",
+        ),
+    ],
 )
 async def test_config_inputs_wo_battery(
     hass: HomeAssistant,
diff --git a/tests/test_min_in_time.py b/tests/test_min_in_time.py
index 8bc7f17..f61b0b9 100644
--- a/tests/test_min_in_time.py
+++ b/tests/test_min_in_time.py
@@ -154,6 +154,38 @@ async def test_min_on_time_config_ko_2(
     assert coordinator is None
 
 
+@pytest.mark.parametrize(
+    "current_datetime, should_be_forced_offpeak",
+    [
+        (datetime(2024, 11, 10, 10, 00, 00), False),
+        (datetime(2024, 11, 10, 0, 59, 00), False),
+        (datetime(2024, 11, 10, 1, 0, 00), True),
+    ],
+)
+async def test_min_on_time_config_ko_3(
+    hass: HomeAssistant,
+    init_solar_optimizer_with_devices_offpeak_morning,
+    init_solar_optimizer_entry,
+    current_datetime,
+    should_be_forced_offpeak,
+):
+    """Testing min_in_time with min requires offpeak_time < raz_time"""
+
+    coordinator: SolarOptimizerCoordinator = (
+        init_solar_optimizer_with_devices_offpeak_morning
+    )
+
+    assert coordinator is not None
+
+    assert len(coordinator.devices) == 1
+    device = coordinator.devices[0]
+    assert device.offpeak_time == time(1, 0, 0)
+
+    device._set_now(current_datetime.replace(tzinfo=get_tz(hass)))
+
+    assert device.should_be_forced_offpeak is should_be_forced_offpeak
+
+
 async def test_nominal_use_min_on_time(
     hass: HomeAssistant,
     init_solar_optimizer_with_2_devices_min_on_time_ok,