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When to use I²R, V²/R or VI while calculating Electric Power?

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I came across a question that was asked to me quite a couple of time: When to use I²R, V²/R or VI while calculating power? At first, the question looks simple and as if it needs no formal explanation but that's not the case. Use of any of them will give the correct result provided that you apply it correctly. Correct application is possible only when you understand the type of circuit you are dealing with. Another important point is to use the one which is going to take less time and help you calculate easily. All of the three equations tell the same thing but their usage is subject to the type of problem you're trying to solve. Let us understand when, how an what to use while calculating power in an electrical circuit.
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Working & Application of a Variable Voltage Variable Frequency Drive (VVVfD)

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Variable Voltage Variable Frequency Drive (VVVfD) is one of the best and efficient methods of starting an Induction Motor Drive as well as it provides a smooth and wide range of Torque-Speed control. It saves electrical power and provides good motor starting and running characterstics. VVVfD controls the V/f (Volt/Hz) fraction to let the motor drive achieve good Torque-Speed characterstics as required. Hence it is also called, VSD - Variable Speed Drive or AFD - Adjustable Frequency Drive or Inverter based Drive as it uses Inverter to achieve the set points.  But how VVVfD works and why it is better than various other methods of Starting and Speed Control of Induction Motor based applications. Let's discuss the Theory, Working, Advantages and Applications of a VVVfD in detail.          
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