Bapat–Beg theorem

Template:Sources All-electric range (AER) is the driving range of a vehicle using only power from its electric battery pack to traverse a given driving cycle. In the case of a battery electric vehicle, it means the total range per charge. For a plug-in hybrid (PHEV), it means the range of the vehicle in charge-depleting mode. PHEVs can travel considerably further in charge-sustaining mode which uses both on-board fuel and the battery pack.

Calculating AER is made more complicated because of variations in PHEV design. A vehicle like the Fisker Karma that utilizes a serial hybrid design has a clear AER. Similarly a vehicle like the Chevy Volt which disengages the internal combustion engine (ICE) from the drive train while in electric mode has a clear AER, however blended mode PHEVs which utilize the ICE and electric motor in conjunction do not have a clear AER because they utilize gasoline and grid provided electricity at the same time. Equivalent AER is a term used to denote the AER of vehicles following this architecture. One example of this calculation can be found in Argonne National Labs report titled "TEST PROCEDURES AND BENCHMARKING Blended-Type and EV-Capable Plug-In Hybrid Electric Vehicles."[1]

This procedure uses the formula below to calculate an equivalent AER for vehicles that operate in blended mode:

${\text{AER}}_{\text{Equivalent}}=(1-\frac{GP{M}_{CD}}{GP{M}_{CS}})d^{CD}$

Where GPM_CD designates efficiency in charge-depleting mode, and GPM_CS charge-sustaining mode as designated and d^CD is distance in charge depleting mode.

A plug-in hybrid's all-electric range is designated by PHEV-(miles) or PHEV(kilometers)km representing the distance the vehicle can travel on battery power alone. For example, a PHEV-20 can travel 20 miles without using its internal combustion engine, or about 32 kilometers, so it may also be designated as PHEV32km.