diff --git a/ra-optimisation/search-tree-rao/src/main/java/com/powsybl/openrao/searchtreerao/result/impl/AbstractFlowRaoResult.java b/ra-optimisation/search-tree-rao/src/main/java/com/powsybl/openrao/searchtreerao/result/impl/AbstractFlowRaoResult.java
index 064fa64326..17cc203922 100644
--- a/ra-optimisation/search-tree-rao/src/main/java/com/powsybl/openrao/searchtreerao/result/impl/AbstractFlowRaoResult.java
+++ b/ra-optimisation/search-tree-rao/src/main/java/com/powsybl/openrao/searchtreerao/result/impl/AbstractFlowRaoResult.java
@@ -27,7 +27,7 @@ public boolean isSecure(Instant optimizedInstant, PhysicalParameter... u) {
         if (Arrays.stream(u).noneMatch(PhysicalParameter.FLOW::equals)) {
             throw new OpenRaoException("This is a flow RaoResult, isSecure is available for FLOW physical parameter");
         }
-        if (getFunctionalCost(optimizedInstant) >= 0) {
+        if (anyOverload(optimizedInstant)) {
             return false;
         }
         if (Arrays.stream(u).anyMatch(physicalParameter -> !PhysicalParameter.FLOW.equals(physicalParameter))) {
@@ -35,4 +35,11 @@ public boolean isSecure(Instant optimizedInstant, PhysicalParameter... u) {
         }
         return true;
     }
+
+    private boolean anyOverload(Instant optimizedInstant) {
+        if (getVirtualCostNames().contains("min-margin-violation-evaluator")) {
+            return getVirtualCost(optimizedInstant, "min-margin-violation-evaluator") > 0;
+        }
+        return getFunctionalCost(optimizedInstant) >= 0;
+    }
 }