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Overheat Problem: I need lower power because my system is running too hot.
Cost of use problem: I need lower power because my electricity bill is too high
Supply Problem: I need lower power because I can't supply so much power to my system
Or a combination of above three issues.

Each case is different and it becomes very important to understand the problem before we can jump on solving the problem. Each problem have a different solution and the solution for the same problem varies by end customers use case.  Nearly in all the cases some level of customization is required to properly address the problem.

Lets look at some of the common problems. If the part is overheating or if a given part is unable to meet the thermal targets, there is very little that can be done at the silicon level. Any changes that will brought about in the silicon will most likely hurt the performance. In such cases the best approach would be to design the thermal solution adequately. Several times, a simple design tweak and an innovative system layout solves the problem. Whereas a few times it is not possible to cool a part economically. If this issue occurs very infrequently, then the thermal throttling feature in the silicon ensures that the part is not damaged. It is however recommended to fix the thermal solution if these thermal throttling instances are frequently observed.
Cost of ownership:  Lower power can mean a lot of savings in terms of utility bill to the end user. In order to reduce the cost of ownership several power management features are available in Intel processors. When the processor is not doing any useful work it can shut off a few components and lower its voltage and do a bunch of things  to reduce power. Each use case is different hence some customization might  be required.
Supply problem: This is the most challenging problem out of all. Power supply should be able to handle occasional spikes in the power. Sometimes these spikes that range for a millisecond or so can be as high as one and half times to twice the nominal value. Often designers complain that if the max possible power in all rails are added the power becomes very high. It is a tricky call for the designer who has to design the system without being overly conservative.  Have you ever wondered if you plug in something in every socket of your home and turn on every light bulb, will the power supply of your house be able to withstand the load? Probably not.  So its all boils down to how much risk one is willing to take and how many failures per million is acceptable.

Each power related problem is different. Even if the requirement is "lower power" . The solution for each case is different.

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