A wireless communication device and method therein for handling connection state changes in a wireless communication system are disclosed. The wireless communication device comprises at least two SIMs, in which a first SIM is in a first original connection state towards a first network node, a second SIM is in a second original connection state towards a second network node. The wireless communication device first determines whether a battery power in the wireless communication device is below a first threshold. When the battery power is below the first threshold, the wireless communication device selects a SIM out of the at least two SIMs for which to change its original connection state to a third connection state based on a parameter. The third connection state is a connection state implying lower power consumption for the wireless communication device compared to its original connection state. Then the wireless communication device performs a connection state change for the selected SIM from its original connection state to the third connection state.