6.12:
Thévenin Equivalent Circuits
The household power distribution system which includes distribution lines and transformers, can be considered the source network.
Inside the house, various electrical appliances can be represented as load impedances.
Thévenin's theorem simplifies this complex distribution system into a Thévenin equivalent circuit.
Finding the Thévenin equivalent circuit requires knowledge of two parameters: Thévenin voltage and Thévenin impedance.
To understand the process of determining them, consider a simplified RLC circuit connected to a voltage source.
To calculate the Thévenin impedance, replace the voltage source with a short circuit and determine the equivalent impedance of the circuit.
The Thévenin voltage is equal to the open circuit voltage, equivalent to the voltage drop across the parallel branch of the circuit.
Initially, the current flowing through the closed mesh of the circuit is calculated. Then using Ohm's law, the voltage drop across the parallel branch is determined, which gives the Thévenin voltage.
If the circuit has sources operating at different frequencies, the Thévenin equivalent circuit and capacitor and inductor impedances must be determined separately for each frequency.
6.12:
Thévenin 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 Voc , while Figure 4 indicates that the Thévenin impedance Zt is the equivalent impedance of circuit A*.
Figure 3:Thévenin equivalent circuit with Voc .
Figure 4:Thévenin equivalent circuit showing Zt. .
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 Zt can be determined by replacing series or parallel impedances with equivalent impedances repeatedly.