Official Explanation
For an assumption, we can use the Negation Test. The credited answer is (A). Suppose (A) is false. Suppose an electrical substation is perfectly capable of handling currents well above its "maximum" capacity (it's unclear what "maximum" would mean in this instance, but we'll overlook that). If electrical substations can handle much more current, then even if current demands increase by a factor of three, that won't be a problem at all. Negating this statement devastates the argument, so this statement must be an assumption.
The argument is about current substations and whether they will fail. Facts about what new modern substations can handle are outside of the scope of this argument. Choice (B) is incorrect.
All we know is that the overall "demand from both industry and electronics in individual homes" will increase. Does this mean more demand from each house, or simply more houses with the same level of demand? And even if each house has more demand, does that mean they have more electronic devices, or simply a small number, each of which demands an intense amount of electrical power? There is too much we don't know, so choice (C) is incorrect.
Choice (D) could strengthen the argument if it were true, but if we negate it, this doesn't destroy argument. It's possible that the current substations are not that old, and would not break down at current levels, but still would fail at increased levels of demand. Since we can negate (D) and the argument could still work, this means (D) is not an assumption. Choice (D) is incorrect.
Choice (E) brings in irrelevant information about cost: how much it would or wouldn't cost to modernize the substations in operation now doesn't affect how likely it is that they will fail. Choice (E) is incorrect.
FAQ: Why is answer choice (B) incorrect? The conclusion says that there will be power failures if municipalities don't modernize their electrical substations. If we negate choice B, the power failures will occur - so (B) seems like a necessary assumption. Answer choice (B) can definitely be an attractive option. The passage does say that the amount of electric current in power grids might rise by a factor of three in ten years and does say that "a large percentage of municipalities throughout the country will experience power failures if they do not modernize their electrical substations." So it might look like the argument falls apart if modern substations can't handle three times as much power as existing substations.
However, it's important to pay very close attention to the exact phrasing of the argument. Note that the argument says that "currents are expected to rise, perhaps by as much as a factor of 3 in the next decade." So it's actually not completely certain that the amount of current in power grids will be that high in ten years. And as a result, it might not be necessary that modern substation be able to handle three times as much current as existing substations.
Also, note that the argument concludes that a large number of municipalities need to "modernize their electrical substations." This sounds like "build modern substations" but is actually slightly different. One could, for instance, "modernize" an existing substation by modifying it to handle twice as much power as it could previously and still see at least some sort of improvement. So we don't need to install completely new substations to successfully modernize substations.
Basically, then, there is a bit of "wiggle room" in the phrasing of the argument that makes B not an absolutely vital assumption. However, if A ("An electrical substation fails when the current it handles rises above its maximum capacity.") is false, the argument does fail to work. If electrical substation doesn't fail when it goes over capacity, then there's much less of a reason to improve substations to handle the increasing levels of electrical current. So this is by far the best option to pick for this question.