That you could do with a super capacitor, but not with a battery. I know of some railway train setup, which is deployed in Saudi Arabia by Siemens, that uses a

That you could do with a super capacitor, but not with a battery. I know of some railway train setup, which is deployed in Saudi Arabia by Siemens, that uses a combination of battery and super caps to power the train. While the train starts it takes the sparking current from the super caps. While riding it will take the energy slowly from the batteries. While deceleration it will recuperate and will charge up the super caps, because they can be charged easily with a high current. So the super caps are used as a high available energy buffer with very fast charge and discharge capabilities. While the battery is only used during the times of less energy consumption. Also at the stations the super caps are super charged very quickly. With that concept, they can run the train the whole day with only 40% discharge of the battery. The battery is actually way smaller then in a Tesla. This concept can be applied also locally. The problem: these super capacitors are way expansive so you need to design them to your specific requirements.