It does not require flow to have power, It requires flow to have Electricity.

 1. If i pinch off the hose for the sprinkler the water is still in the hose. Yes, but not running water. you cut off its flow.

 2. If i cut off the track behind the coaster the people are still in the car.  Yes, but they are still going , you did not cut off their flow. There is track ahead of them and momentum or gravity forceing them on.

 3. If i unplug the wire at the battery no electricity is in the wire. Correct no "electricity" you cut off the flow of electrons, but there are still electrons in the copper atoms of the wire. You see electrons are electrons just like water drops are water drops.  If you have a 1 drop open container and you add just 1 more drop, you now have running water.  Your sprinkler hose can hold only so many drops of water if you add 1 more drop 1 has to come out the other end. Each copper atom in wire can only hold so many electrons. If you try to add 1 more electron one has to leave the wire. But since none can leave the wire none can enter either.  So the extra electron is still at its source, the battery.

Electricity   I fell the best way to explain it is that it is an event.  You don’t have electricity until something is happening.  Picture a ring made of copper.  This ring is made up of copper atoms; they are evenly spaced throughout the ring.  Now cut the ring and straighten it out.  The atoms are still evenly spaced throughout the copper.  Now about the copper atom, it has 29 total electrons orbiting the nucleus in 4 different shells with only one electron in the outer shell.  This electron can not enter any of the inner shells as each shell has a maximum number allowed, so it’s just happy to orbit the nucleus in it own little shell. 

UNTIL something happens, in this case an electron, from a battery or power plant, is pushed into its shell and since there can only be one electron in that outer shell of the copper atom it gets pushed into the next copper atom.  Knocking its outer electron out of  its shell into another and on and on it goes until the force that started all this finds its way back to the opposite side of the battery or power plant that started all this.  So none of this can happen unless there is somewhere for the extra electron to go.   You see the battery or power plant has two sides.  Pos and Neg with one side having more electrons stored in it.  And that side is just ready to push electrons to the other side but it CAN NOT because there is no pathway or complete circuit.  So when you connect the two sides together BAM.  The battery explodes.  Unless you slow the flow of electrons by a light, a motor or some sort of resistance.