*3.3. Analysis of EV Paths*

When performing SUE-ED traffic assignment, the GVs can choose any route because of no range limit. However, the selection of feasible path sets is required before the distribution of EV flow. To describe the three types of EV paths more clearly, the concept of sub-path is described as follows.

Suppose that the origin is *r* and the destination is *s* in a pair OD *w*, and there are two charging stations *i*, *j*, which are also regarded as nodes, located in the arc of the path *k* (Figure 1). When *kri*, *kij*, *kjs* no longer includes other charging facilities except *i*, *j*, they are called sub-paths [41].

**Figure 1.** Description of the sub-path.

Based on the relationship between the travel mileage limit *Re* and the sub-path distance, the three travel paths of EVs are discussed, as shown in Table 1:

Scenario 1. A travel path that can be completed without charging. When *l w <sup>k</sup>* ≤ *R <sup>e</sup>*, the EV drivers can reach the destination without charging. The generalized travel cost is *c w ke* = *cw <sup>k</sup>* (no charging stations) or *c w ke* = *cw <sup>k</sup>* − *U* (with charging stations).

Scenario 2. A travel path that cannot be completed after charging. When *l ri <sup>k</sup>* ≥ *Re* or *l ij <sup>k</sup>* ≥ *Re* or *l js <sup>k</sup>* ≥ *Re*, the path *k* is an infeasible path. And the generalized path travel cost becomes infinite *(c w ke* = ∞) and the probability that the drivers select the path is zero.

Scenario 3. A travel path that can be completed after charging. The path *k* is defined as a feasible path, if *l w <sup>k</sup>* ≥ *Re* and *l ri <sup>k</sup>* ≤ *Re* and *l ij <sup>k</sup>* ≤ *Re* and *l js <sup>k</sup>* ≤ *Re*. The drivers can complete the trip by charging at least once and the minimum charging time is *t w ck* = ε... (*l w <sup>k</sup>* − *Re)*. The generalized travel cost is expressed as *c w ke* = *<sup>c</sup><sup>w</sup> <sup>k</sup>* + *<sup>t</sup> w ck* <sup>−</sup> *<sup>U</sup>* <sup>+</sup> *<sup>K</sup>*·*<sup>U</sup>* <sup>=</sup> *<sup>c</sup><sup>w</sup> <sup>k</sup>* + *t w ck* + (*K* − 1)*U*, consisting of four parts: travel time, charging time, charging facilities utility, and charging stations' waiting cost.

For GVs, the general path travel cost is *c w kg* <sup>=</sup> *<sup>c</sup><sup>w</sup> k* .

**Table 1.** Three travel paths of electric vehicles (EVs).

