diff --git a/oemof/solph/components.py b/oemof/solph/components.py
index b1ff77606..7bb3e444e 100644
--- a/oemof/solph/components.py
+++ b/oemof/solph/components.py
@@ -497,7 +497,7 @@ def _create(self, group=None):
         def _storage_investvar_bound_rule(block, n):
             """Rule definition to bound the invested storage capacity `invest`.
             """
-            return 0, n.investment.maximum
+            return n.investment.minimum, n.investment.maximum
         self.invest = Var(self.INVESTSTORAGES, within=NonNegativeReals,
                           bounds=_storage_investvar_bound_rule)
 
diff --git a/tests/constraint_tests.py b/tests/constraint_tests.py
index ad2f9358a..dc32ab74e 100644
--- a/tests/constraint_tests.py
+++ b/tests/constraint_tests.py
@@ -326,6 +326,21 @@ def test_storage_invest_6(self):
             investment=solph.Investment(ep_costs=145, existing=10000))
         self.compare_lp_files('storage_invest_6.lp')
 
+    def test_storage_minimum_invest(self):
+        """All invest variables are coupled. The invest variables of the Flows
+        will be created during the initialisation of the storage e.g. battery
+        """
+        bel = solph.Bus(label='electricityBus')
+
+        solph.components.GenericStorage(
+            label='storage1',
+            inputs={bel: solph.Flow()},
+            outputs={bel: solph.Flow()},
+            investment=solph.Investment(
+                ep_costs=145, minimum=100, maximum=200))
+
+        self.compare_lp_files('storage_invest_minimum.lp')
+
     def test_transformer(self):
         """Constraint test of a LinearN1Transformer without Investment.
         """
diff --git a/tests/lp_files/storage_invest_minimum.lp b/tests/lp_files/storage_invest_minimum.lp
new file mode 100644
index 000000000..98f558dba
--- /dev/null
+++ b/tests/lp_files/storage_invest_minimum.lp
@@ -0,0 +1,74 @@
+\* Source Pyomo model name=Model *\
+
+min 
+objective:
++145 GenericInvestmentStorageBlock_invest(storage1)
+
+s.t.
+
+c_e_Bus_balance(electricityBus_0)_:
+-1 flow(electricityBus_storage1_0)
++1 flow(storage1_electricityBus_0)
+= 0
+
+c_e_Bus_balance(electricityBus_1)_:
+-1 flow(electricityBus_storage1_1)
++1 flow(storage1_electricityBus_1)
+= 0
+
+c_e_Bus_balance(electricityBus_2)_:
+-1 flow(electricityBus_storage1_2)
++1 flow(storage1_electricityBus_2)
+= 0
+
+c_e_GenericInvestmentStorageBlock_balance(storage1_0)_:
++1 GenericInvestmentStorageBlock_capacity(storage1_0)
+-1 GenericInvestmentStorageBlock_capacity(storage1_2)
+-1 flow(electricityBus_storage1_0)
++1 flow(storage1_electricityBus_0)
+= 0
+
+c_e_GenericInvestmentStorageBlock_balance(storage1_1)_:
+-1 GenericInvestmentStorageBlock_capacity(storage1_0)
++1 GenericInvestmentStorageBlock_capacity(storage1_1)
+-1 flow(electricityBus_storage1_1)
++1 flow(storage1_electricityBus_1)
+= 0
+
+c_e_GenericInvestmentStorageBlock_balance(storage1_2)_:
+-1 GenericInvestmentStorageBlock_capacity(storage1_1)
++1 GenericInvestmentStorageBlock_capacity(storage1_2)
+-1 flow(electricityBus_storage1_2)
++1 flow(storage1_electricityBus_2)
+= 0
+
+c_u_GenericInvestmentStorageBlock_max_capacity(storage1_0)_:
++1 GenericInvestmentStorageBlock_capacity(storage1_0)
+-1 GenericInvestmentStorageBlock_invest(storage1)
+<= 0
+
+c_u_GenericInvestmentStorageBlock_max_capacity(storage1_1)_:
++1 GenericInvestmentStorageBlock_capacity(storage1_1)
+-1 GenericInvestmentStorageBlock_invest(storage1)
+<= 0
+
+c_u_GenericInvestmentStorageBlock_max_capacity(storage1_2)_:
++1 GenericInvestmentStorageBlock_capacity(storage1_2)
+-1 GenericInvestmentStorageBlock_invest(storage1)
+<= 0
+
+c_e_ONE_VAR_CONSTANT: 
+ONE_VAR_CONSTANT = 1.0
+
+bounds
+   0 <= flow(electricityBus_storage1_0) <= +inf
+   0 <= flow(electricityBus_storage1_1) <= +inf
+   0 <= flow(electricityBus_storage1_2) <= +inf
+   0 <= flow(storage1_electricityBus_0) <= +inf
+   0 <= flow(storage1_electricityBus_1) <= +inf
+   0 <= flow(storage1_electricityBus_2) <= +inf
+   0 <= GenericInvestmentStorageBlock_capacity(storage1_0) <= +inf
+   0 <= GenericInvestmentStorageBlock_capacity(storage1_1) <= +inf
+   0 <= GenericInvestmentStorageBlock_capacity(storage1_2) <= +inf
+   100 <= GenericInvestmentStorageBlock_invest(storage1) <= 200
+end