Observability: enable error for meshed observability check

power_grid_model_c/power_grid_model/include/power_grid_model/math_solver/observability.hpp

@@ -505,9 +505,15 @@ sufficient_condition_meshed_without_voltage_phasor(std::vector<detail::BusNeighb
     prepare_starting_nodes(neighbour_list, n_bus, starting_candidates);
 
     // Try each starting candidate
-    return std::ranges::any_of(starting_candidates, [&](Idx const start_bus) {
+    bool const found_spanning_tree = std::ranges::any_of(starting_candidates, [&](Idx const start_bus) {
         return find_spanning_tree_from_node(start_bus, n_bus, neighbour_list);
     });
+
+    if (!found_spanning_tree) {
+        throw NotObservableError{"No full-spanning tree can be constructed from this meshed network. Unobservable.\n"};
+    }
+
+    return true;
 }
 
 } // namespace detail

tests/cpp_unit_tests/test_observability.cpp

@@ -1565,10 +1565,8 @@ TEST_CASE("Test Observability - sufficient_condition_meshed_without_voltage_phas
         // Expand bidirectional connections
         complete_bidirectional_neighbourhood_info(neighbour_list);
 
-        bool const result = sufficient_condition_meshed_without_voltage_phasor(neighbour_list);
-
         // Should fail due to insufficient measurements
-        CHECK(result == false);
+        CHECK_THROWS_AS(sufficient_condition_meshed_without_voltage_phasor(neighbour_list), NotObservableError);
     }
 
     SUBCASE("Single bus network - edge case") {

tests/data/state_estimation/meshed-network-observability/02-unobservable-with-branch-measurement/params.json

@@ -6,7 +6,7 @@
     ".+_residual": 5e-4
   },
   "raises": {
-    "raises": "SparseMatrixError",
+    "raises": "NotObservableError",
     "reason": "One nodal measurement can not be made use of."
   }
 }