Th&#233venin Equivalent Circuits

The household power distribution system, encompassing distribution lines and transformers, serves as the primary network. Electrical appliances within a household can be represented as load impedance. To simplify this intricate distribution system, Thévenin's theorem can be applied to create a Thévenin equivalent circuit. If an AC circuit is partitioned into two parts (circuit A and circuit B), connected by a single pair of terminals as shown in Figure 1.

Figure 1: Circuit portioned into two parts

Figure 2:Circuit A replaced by its Thévenin equivalent circuit

Replacing circuit A with its Thévenin equivalent circuit (a voltage source in series with an impedance) does not alter the current or voltage of any element in circuit B (shown in Figure 2). The values of the currents and voltages of all the circuit elements in circuit B will be the same irrespective of whether circuit B is connected to circuit A or its Thévenin equivalent. Two parameters are required to find the Thévenin equivalent circuit: the Thévenin voltage and the Thévenin impedance. Figure 3 shows an open circuit connected across the terminals of circuit A to determine the open-circuit voltage V_oc , while Figure 4 indicates that the Thévenin impedance Z_t is the equivalent impedance of circuit A*.

Figure 3:Thévenin equivalent circuit with V_oc .

Figure 4:Thévenin equivalent circuit showing Z_t. .

Circuit A* is formed from circuit A by replacing all independent voltage sources with short circuits and all independent current sources with open circuits. Generally, the Thévenin impedance Z_t can be determined by replacing series or parallel impedances with equivalent impedances repeatedly.