An electrical current sensing system (140, 150, 160) comprising: a fuse housing and a fuse element in the fuse housing, the fuse element having a non-linear resistance when connected to an energized line side circuit and to a load side circuitry of an electrical power system; a compensation circuit connected in parallel with the fuse element and including a voltage source or a current source (122, 126, 128) that injects a current or a voltage across the fuse element when the fuse element is connected between the energized line side circuitry and the load side circuitry and while an electrical current is flowing through the fuse element from the energized line side circuit, wherein the voltage source or current source (122, 126, 128) is configured to inject the current or the voltage across the fuse element independently from the energized line side circuit; and a processor-based control device (112, 114) configured to: receive a first voltage sensed across the fuse element while the voltage source or the current source (122, 126, 128) injects the current or the voltage across the fuse element and while the electrical current is flowing through the fuse element from the energized line side circuit, determine a resistance of the fuse element in reference to the injected current or the injected voltage while the electrical current is flowing through the fuse element from the energized line side circuit and while the voltage source or the current source (122, 126, 128) injects the current or the voltage across the fuse element; calculate the electrical current flowing through the fuse element from the energized line side circuit based on the received first voltage and the determined resistance of the fuse element. a fuse housing and a fuse element in the fuse housing, the fuse element having a non-linear resistance when connected to an energized line side circuit and to a load side circuitry of an electrical power system; a compensation circuit connected in parallel with the fuse element and including a voltage source or a current source (122, 126, 128) that injects a current or a voltage across the fuse element when the fuse element is connected between the energized line side circuitry and the load side circuitry and while an electrical current is flowing through the fuse element from the energized line side circuit, wherein the voltage source or current source (122, 126, 128) is configured to inject the current or the voltage across the fuse element independently from the energized line side circuit; and a processor-based control device (112, 114) configured to: receive a first voltage sensed across the fuse element while the voltage source or the current source (122, 126, 128) injects the current or the voltage across the fuse element and while the electrical current is flowing through the fuse element from the energized line side circuit, determine a resistance of the fuse element in reference to the injected current or the injected voltage while the electrical current is flowing through the fuse element from the energized line side circuit and while the voltage source or the current source (122, 126, 128) injects the current or the voltage across the fuse element; calculate the electrical current flowing through the fuse element from the energized line side circuit based on the received first voltage and the determined resistance of the fuse element. receive a first voltage sensed across the fuse element while the voltage source or the current source (122, 126, 128) injects the current or the voltage across the fuse element and while the electrical current is flowing through the fuse element from the energized line side circuit, determine a resistance of the fuse element in reference to the injected current or the injected voltage while the electrical current is flowing through the fuse element from the energized line side circuit and while the voltage source or the current source (122, 126, 128) injects the current or the voltage across the fuse element; calculate the electrical current flowing through the fuse element from the energized line side circuit based on the received first voltage and the determined resistance of the fuse element.