diff --git a/tests/data/state_estimation/leaf-without-power-sensor/input.json b/tests/data/state_estimation/leaf-without-power-sensor/input.json
new file mode 100644
index 000000000..a6a823bcb
--- /dev/null
+++ b/tests/data/state_estimation/leaf-without-power-sensor/input.json
@@ -0,0 +1,27 @@
+{
+  "version": "1.0",
+  "type": "input",
+  "is_batch": false,
+  "attributes": {},
+  "data": {
+    "node": [
+      {"id": 0, "u_rated": 10},
+      {"id": 1, "u_rated": 10}
+    ],
+    "line": [
+      {"id": 2, "from_node": 0, "to_node": 1, "from_status": 1, "to_status": 1, "r1": 1.0, "x1": 0.0, "c1": 0.0, "tan1": 0.0, "i_n": 500}
+    ],
+    "source": [
+      {"id": 3, "node": 0, "status": 1, "u_ref": 1.0}
+    ],
+    "sym_load": [
+      {"id": 4, "node": 1, "status": 1, "type": 0, "p_specified": 9, "q_specified": 0}
+    ],
+    "sym_power_sensor": [
+      {"id": 5, "measured_object": 3, "measured_terminal_type": 2, "power_sigma": 1, "p_measured": 10, "q_measured": 0}
+    ],
+    "sym_voltage_sensor": [
+      {"id": 6, "measured_object": 0, "u_sigma": 1, "u_measured": 10}
+    ]
+  }
+}
\ No newline at end of file
diff --git a/tests/data/state_estimation/leaf-without-power-sensor/input.json.license b/tests/data/state_estimation/leaf-without-power-sensor/input.json.license
new file mode 100644
index 000000000..760105916
--- /dev/null
+++ b/tests/data/state_estimation/leaf-without-power-sensor/input.json.license
@@ -0,0 +1,3 @@
+SPDX-FileCopyrightText: Contributors to the Power Grid Model project <powergridmodel@lfenergy.org>
+
+SPDX-License-Identifier: MPL-2.0
diff --git a/tests/data/state_estimation/leaf-without-power-sensor/params.json b/tests/data/state_estimation/leaf-without-power-sensor/params.json
new file mode 100644
index 000000000..4167e1fbf
--- /dev/null
+++ b/tests/data/state_estimation/leaf-without-power-sensor/params.json
@@ -0,0 +1,12 @@
+{
+  "calculation_method": ["newton_raphson", "iterative_linear"],
+  "rtol": 1e-8,
+  "atol": {
+    "default": 1e-8,
+    ".+_residual": 5e-4
+  },
+  "fail": {
+    "raises": "SparseMatrixError",
+    "reason": "Bug in Sparse LU solver found in #853"
+  }
+}
\ No newline at end of file
diff --git a/tests/data/state_estimation/leaf-without-power-sensor/params.json.license b/tests/data/state_estimation/leaf-without-power-sensor/params.json.license
new file mode 100644
index 000000000..760105916
--- /dev/null
+++ b/tests/data/state_estimation/leaf-without-power-sensor/params.json.license
@@ -0,0 +1,3 @@
+SPDX-FileCopyrightText: Contributors to the Power Grid Model project <powergridmodel@lfenergy.org>
+
+SPDX-License-Identifier: MPL-2.0
diff --git a/tests/data/state_estimation/leaf-without-power-sensor/sym_output.json b/tests/data/state_estimation/leaf-without-power-sensor/sym_output.json
new file mode 100644
index 000000000..c0abb2f1c
--- /dev/null
+++ b/tests/data/state_estimation/leaf-without-power-sensor/sym_output.json
@@ -0,0 +1,27 @@
+{
+  "version": "1.0",
+  "type": "sym_output",
+  "is_batch": false,
+  "attributes": {},
+  "data": {
+    "node": [
+      {"id": 0, "energized": 1, "u_pu": 1, "u": 10, "u_angle": 0},
+      {"id": 1, "energized": 1, "u_pu": 0.9, "u": 9, "u_angle": 0}
+    ],
+    "line": [
+      {"id": 2, "energized": 1, "p_from": 10, "q_from": 0, "p_to": -9, "q_to": -0}
+    ],
+    "source": [
+      {"id": 3, "energized": 1, "p": 10, "q": 0}
+    ],
+    "sym_load": [
+      {"id": 4, "energized": 1, "p": 9, "q": 0}
+    ],
+    "sym_power_sensor": [
+      {"id": 5, "energized": 1, "p_residual": 0, "q_residual": 0}
+    ],
+    "sym_voltage_sensor": [
+      {"id": 6, "energized": 1, "u_residual": 0}
+    ]
+  }
+}
\ No newline at end of file
diff --git a/tests/data/state_estimation/leaf-without-power-sensor/sym_output.json.license b/tests/data/state_estimation/leaf-without-power-sensor/sym_output.json.license
new file mode 100644
index 000000000..760105916
--- /dev/null
+++ b/tests/data/state_estimation/leaf-without-power-sensor/sym_output.json.license
@@ -0,0 +1,3 @@
+SPDX-FileCopyrightText: Contributors to the Power Grid Model project <powergridmodel@lfenergy.org>
+
+SPDX-License-Identifier: MPL-2.0
diff --git a/tests/data/state_estimation/middle-without-power-sensor/input.json b/tests/data/state_estimation/middle-without-power-sensor/input.json
new file mode 100644
index 000000000..60c774719
--- /dev/null
+++ b/tests/data/state_estimation/middle-without-power-sensor/input.json
@@ -0,0 +1,29 @@
+{
+  "version": "1.0",
+  "type": "input",
+  "is_batch": false,
+  "attributes": {},
+  "data": {
+    "node": [
+      {"id": 0, "u_rated": 10},
+      {"id": 1, "u_rated": 10},
+      {"id": 7, "u_rated": 10}
+    ],
+    "line": [
+      {"id": 2, "from_node": 0, "to_node": 1, "from_status": 1, "to_status": 1, "r1": 1.0, "x1": 0.0, "c1": 0.0, "tan1": 0.0, "i_n": 500},
+      {"id": 8, "from_node": 1, "to_node": 7, "from_status": 1, "to_status": 1, "r1": 1.0, "x1": 0.0, "c1": 0.0, "tan1": 0.0, "i_n": 500}
+    ],
+    "source": [
+      {"id": 3, "node": 0, "status": 1, "u_ref": 1.0}
+    ],
+    "sym_load": [
+      {"id": 4, "node": 1, "status": 1, "type": 0, "p_specified": 9, "q_specified": 0}
+    ],
+    "sym_power_sensor": [
+      {"id": 5, "measured_object": 3, "measured_terminal_type": 2, "power_sigma": 1, "p_measured": 10, "q_measured": 0}
+    ],
+    "sym_voltage_sensor": [
+      {"id": 6, "measured_object": 0, "u_sigma": 1, "u_measured": 10}
+    ]
+  }
+}
\ No newline at end of file
diff --git a/tests/data/state_estimation/middle-without-power-sensor/input.json.license b/tests/data/state_estimation/middle-without-power-sensor/input.json.license
new file mode 100644
index 000000000..760105916
--- /dev/null
+++ b/tests/data/state_estimation/middle-without-power-sensor/input.json.license
@@ -0,0 +1,3 @@
+SPDX-FileCopyrightText: Contributors to the Power Grid Model project <powergridmodel@lfenergy.org>
+
+SPDX-License-Identifier: MPL-2.0
diff --git a/tests/data/state_estimation/middle-without-power-sensor/params.json b/tests/data/state_estimation/middle-without-power-sensor/params.json
new file mode 100644
index 000000000..4167e1fbf
--- /dev/null
+++ b/tests/data/state_estimation/middle-without-power-sensor/params.json
@@ -0,0 +1,12 @@
+{
+  "calculation_method": ["newton_raphson", "iterative_linear"],
+  "rtol": 1e-8,
+  "atol": {
+    "default": 1e-8,
+    ".+_residual": 5e-4
+  },
+  "fail": {
+    "raises": "SparseMatrixError",
+    "reason": "Bug in Sparse LU solver found in #853"
+  }
+}
\ No newline at end of file
diff --git a/tests/data/state_estimation/middle-without-power-sensor/params.json.license b/tests/data/state_estimation/middle-without-power-sensor/params.json.license
new file mode 100644
index 000000000..760105916
--- /dev/null
+++ b/tests/data/state_estimation/middle-without-power-sensor/params.json.license
@@ -0,0 +1,3 @@
+SPDX-FileCopyrightText: Contributors to the Power Grid Model project <powergridmodel@lfenergy.org>
+
+SPDX-License-Identifier: MPL-2.0
diff --git a/tests/data/state_estimation/middle-without-power-sensor/sym_output.json b/tests/data/state_estimation/middle-without-power-sensor/sym_output.json
new file mode 100644
index 000000000..9ea2249f5
--- /dev/null
+++ b/tests/data/state_estimation/middle-without-power-sensor/sym_output.json
@@ -0,0 +1,29 @@
+{
+  "version": "1.0",
+  "type": "sym_output",
+  "is_batch": false,
+  "attributes": {},
+  "data": {
+    "node": [
+      {"id": 0, "energized": 1, "u_pu": 1, "u": 10, "u_angle": 0},
+      {"id": 1, "energized": 1, "u_pu": 0.9, "u": 9, "u_angle": 0},
+      {"id": 7, "energized": 1, "u_pu": 0.9, "u": 9, "u_angle": 0}
+    ],
+    "line": [
+      {"id": 2, "energized": 1, "p_from": 10, "q_from": 0, "p_to": -9, "q_to": 0},
+      {"id": 8, "energized": 1, "p_from": 0, "q_from": 0, "p_to": 0, "q_to": 0}
+    ],
+    "source": [
+      {"id": 3, "energized": 1, "p": 10, "q": 0}
+    ],
+    "sym_load": [
+      {"id": 4, "energized": 1, "p": 9, "q": 0}
+    ],
+    "sym_power_sensor": [
+      {"id": 5, "energized": 1, "p_residual": 0, "q_residual": 0}
+    ],
+    "sym_voltage_sensor": [
+      {"id": 6, "energized": 1, "u_residual": 0}
+    ]
+  }
+}
\ No newline at end of file
diff --git a/tests/data/state_estimation/middle-without-power-sensor/sym_output.json.license b/tests/data/state_estimation/middle-without-power-sensor/sym_output.json.license
new file mode 100644
index 000000000..760105916
--- /dev/null
+++ b/tests/data/state_estimation/middle-without-power-sensor/sym_output.json.license
@@ -0,0 +1,3 @@
+SPDX-FileCopyrightText: Contributors to the Power Grid Model project <powergridmodel@lfenergy.org>
+
+SPDX-License-Identifier: MPL-2.0
diff --git a/tests/unit/utils.py b/tests/unit/utils.py
index 6de4a7429..7d246e3fd 100644
--- a/tests/unit/utils.py
+++ b/tests/unit/utils.py
@@ -29,6 +29,7 @@
     PowerGridBatchError,
     PowerGridError,
     PowerGridSerializationError,
+    SparseMatrixError,
 )
 from power_grid_model.utils import json_deserialize, json_deserialize_from_file, json_serialize_to_file
 
@@ -55,6 +56,7 @@
         AutomaticTapCalculationError,
         InvalidTransformerClock,
         NotObservableError,
+        SparseMatrixError,
         PowerGridSerializationError,
         AssertionError,
         OSError,