Improve singular matrix error (#301)

Improve error message when there is a NaN in the jacobian, by
identifying the problematic element

Closes #299

---------

Co-authored-by: Ali Hamdan <[email protected]>

Author: Saelyos

doc/Changelog.md

@@ -17,6 +17,11 @@ og:description: See what's new in the latest release of Roseau Load Flow !
 
 # Changelog
 
+## Unreleased
+
+- {gh-pr}`301` {gh-issue}`299` Improve the error message when the Jacobian matrix contains infinite
+  or NaN values.
+
 ## Version 0.11.0
 
 This release adds official support for Python 3.13 and adds a new experimental backward-forward solver.

roseau/load_flow/exceptions.py

@@ -105,6 +105,7 @@ class RoseauLoadFlowExceptionCode(StrEnum):
     LOAD_FLOW_NOT_RUN = auto()
     SEVERAL_NETWORKS = auto()
     BAD_JACOBIAN = auto()
+    NAN_VALUE = auto()
 
     # Solver
     BAD_SOLVER_NAME = auto()

roseau/load_flow/network.py

@@ -609,20 +609,31 @@ def _handle_error(self, e: RuntimeError) -> NoReturn:
         elif msg.startswith("1 "):
             msg = msg[2:]
             zero_elements_index, inf_elements_index = self._solver._cy_solver.analyse_jacobian()
-            if zero_elements_index:
+            if inf_elements_index:
+                inf_elements = [self._elements[i] for i in inf_elements_index]
+                printable_elements = ", ".join(f"{type(e).__name__}({e.id!r})" for e in inf_elements)
+                msg += (
+                    f"The problem seems to come from the elements [{printable_elements}] that induce infinite values."
+                )
+                power_load = False
+                flexible_load = False
+                for inf_element in inf_elements:
+                    if isinstance(inf_element, PowerLoad):
+                        power_load = True
+                        if inf_element.is_flexible:
+                            flexible_load = True
+                if power_load:
+                    msg += " This might be caused by a bad potential initialization of a power load"
+                if flexible_load:
+                    msg += ", or by flexible loads with very high alpha or incorrect flexible parameters voltages."
+                raise RoseauLoadFlowException(msg=msg, code=RoseauLoadFlowExceptionCode.NAN_VALUE)
+            elif zero_elements_index:
                 zero_elements = [self._elements[i] for i in zero_elements_index]
                 printable_elements = ", ".join(f"{type(e).__name__}({e.id!r})" for e in zero_elements)
                 msg += (
                     f"The problem seems to come from the elements [{printable_elements}] that have at least one "
                     f"disconnected phase. "
                 )
-            if inf_elements_index:
-                inf_elements = [self._elements[i] for i in inf_elements_index]
-                printable_elements = ", ".join(f"{type(e).__name__}({e.id!r})" for e in inf_elements)
-                msg += (
-                    f"The problem seems to come from the elements [{printable_elements}] that induce infinite "
-                    f"values. This might be caused by flexible loads with very high alpha."
-                )
             logger.error(msg)
             raise RoseauLoadFlowException(msg=msg, code=RoseauLoadFlowExceptionCode.BAD_JACOBIAN) from e
         else: