150 watt room light or rechargeable 3AA batts in a torch.?

Let's go back to basics.

You want a light source to perform a function, and the function defines the minimum amount of light that will meet your needs. Regardless of the option you choose, the amount of light you need to create is the samel.

So the problem is providing a source of electrical energy that can be converted to provide that amount of light. You appear to recognize that LEDs are the most efficient source of lights that we have available today, so LEDs are the obvious choice. But the question is should the LED light source be supplied from the grid via a power converter, or should they be supplied from energy stored in rechargeable batteries. Because the amount of light is fixed, its reasonable so assume that the LEDs would be the same in either case, which then means that the amount of energy that must be sourced is also the same.

Now, LEDs operate on DC, and the grid in AC. So to provide power from the grid, you would need an AC to DC power converter. But if you use rechargeable batteries, they will require a charger. While the power converter for an AC-powered LED is a different device from a battery charger, it's a reasonably close approximation to assume that they will cost about the same. So you eliminate the electronics from the evaluation.

So then there is the question of the source of energy. In both cases, energy will come from the grid, and the rate that you will have to pay for the energy will be the same. So there is no difference between the two choices when it comes to the cost of electrical energy.

The only thing that is left is the relative efficiency of delivering the electrical energy to the LED. There are losses in both the power converter for AC-powered LEDs and in the charger for rechargeable batteries. Again, I would imagine that while these losses could be different, because they are electronic circuits, I would not expect an especially remarkable difference.

So what is left? Well, the process of storing energy in a battery, and then recovering that energy at a later time also incurs losses. So the battery option includes a block of losses for which there comparable quantity in the arrangement in which grid power is used directly. And the cost of those losses will make the battery option relatively more expensive than the direct supply option.

Also, batteries have a fixed life cycle - the number of times that a batter can be charged and then discharged is a fixed by the design of the battery, and at the end of that period of time. So if you are doing a total life cycle cost comparison, you also must take into account that the cost of replacement batteries over the period of time for which you are comparing the battery option with the grid supply option.

Therefore, even without applying numbers, it is clear that the battery option carries two inherent penalty components compared with the grid supply option:

- the cost of losses associated with storing energy, and then recovering that stored energy

- the replacement cost of batteries

Therefore, the battery storage option is inexorably more expensive.

Rechargeable batteries are very inefficient, perhaps 50% overall at best, perhaps lower, plus you have the cost of the batteries, the charger, and the nuisance of swapping them and recharging.

However, an incandescent light is about 5% effieciency as opposed to 20-30% for a LED, so that could push the balance the other way.

Better than both of these is either use of LED bulbs made for 120 VAC, or a low voltage DC system powered from the mains. Of these two, the first is more efficient and makes use of your existing wiring.

It is economical to run LED. Use SMPS unit to run LED.It is more efficient than transformer or rechargeable battery.