Superposition Theorem

Requirement:

Power System is a complex network having number of voltage and current sources and number of loads. Now to analyze the network we need to find voltage/current at particular branch or load.

In such cases calculations for thevenin's and norton's theorem becomes difficult. We can use superposition theorem to find voltage/current at any branch or load in complex network. In this theorem only one source considered at a time and total voltage/current is sum of voltage/current obtained by considering individual source.

Statement of Superposition Theorem:

In any multisource complex network consisting of linear bilateral elements, the voltage across or current through, any given element of the network is equal to the sum of the individual voltages or currents, produced independently across or in that element by each source acting independently, when all the remaining sources are replaced by their respective internal impedances.

In short, response in any element of linear circuit having more than one sources is equal to sum of the response produced by the sources, each acting independently.

Note:

Superposition Theorem is applicable for linear and bilateral networks only.
This theorem is not applicable to find power because power is non linear function. Power is proportional to square of current.
If the internal impedance of the sources are unknown, then

Independent voltage sources - replaced by short circuit
Independent current sources - replaced by an open circuit.

If dependent current and/or voltage sources are present in the circuit then such dependent sources should not be replaced by open and short circuit. They will remain as it is. Such sources have zero value only when voltage or current controlling them is zero.

Steps to solve questions of superposition theorem:

Questions of superposition theorem are important in examinations and they are useful in solving many other examples. In competitive exams like JEE, NEET, GATE, etc questions of superposition theorem are asked frequently.

To solve questions of other theories, superposition theorem is very useful.

Now to easily solve these questions we need to follow certain steps which are listed below.

Step 1:

Choose single independent source from circuit. Short other voltage sources and open other current sources present in circuit. If internal impedance of source is known then replace source by its internal impedance.

Step 2:

Find current/voltage at required branch or load due to source considered in step 1 with the help of any network simplification techniques such as KVL, KCL, source transformation, etc.

Step 3:

Now consider another independent source in circuit and repeat step 1 and step 2 for all sources present in a circuit.

Step 4:

Add all individual responses produced by individual sources to obtain total voltage/current at particular branch or load.