V2Sim: An Open-Source Microscopic V2G Simulation Platform in Urban Power and Transportation Network

A UTN is defined as a directed graph $G=<V,E>$, whose vertices $V$ are road junctions, and the edges $E$ are the roads. Since the graph is directed, any bi-directional road is treated as two uni-directional roads. Some bi-directional roads in the road network are dead-ended. When vehicles drive to a dead-end, they can only perform a U-turn. These dead-end points are also treated as junctions. Generally, the UTN will not change during simulation; thus, the directed graph is static. A vehicle always starts from an edge and ends at another. The optimal path algorithm is required to determine how an EV should move between an OD pair.

The parameters of a common vehicle include acceleration capability, deceleration capability, vehicle length, and maximum vehicle speed. In this study, to generate EVCL, additional EV specific parameters were defined: battery capacity, average discharge per unit distance, charging power, charging efficiency, discharge efficiency, and V2G power.

The battery capacity characterizes the capacity of the vehicle mounted battery, measured in kWh. There is a certain relationship between battery capacity and vehicle endurance.

The average discharge per unit distance represents the amount of electricity required by an EV per unit distance traveled, measured in kWh/m. For the convenience of calculating the range, this study simplified the characteristics of the EV motor and battery, assuming that the amount of electricity per unit distance traveled by the vehicle is the same in any situation.

Charging power represents the EVCL generated by a vehicle after connecting to a charging station, in kW. Each EV has different charging powers defined for both FCS and SCS. According to the actual situation, when the SoC of EV batteries is above 70% to 80%, the charging power will significantly decrease. Therefore, this study adopts a segmented charging power model. When the SoC is less than or equal to 80%, the charging power remains constant; When the SoC is greater than 80%, the charging power linearly decays. The charging power when the SoC is less than or equal to 80% is denoted as $P_{0}$, then the charging power $P$ subjects to

where $x^{i}$ denotes the SoC of the EV $i$. Since this approximation may not be able to satisfy all the situations, the platform also supports customized charging power model.

V2G power describes the maximum discharging power if the EV is required to send electricity back to the power grid, also in the unit of kW. EV $i$ also has a coefficient, $k_{v}^{i}$, to measure the EV user’s will to join V2G program. If the $SoC^{i}$ is lower than $k_{v}^{i}$, then the EV will not discharge V2G power. In the model employed, an EV shall never generate V2G power autonomously. The necessary conditions for an EV to generate V2G power are:

• •

  $SoC^{i}\geq k_{v}^{i}$;

• •

  Receive the central dispatcher’s command.

SUMO employs microscopic models to simulate the movement of every single vehicle on the street, mostly assuming that the behavior of the vehicle depends on the vehicle’s physical abilities to move and the driver’s controlling behavior[24]. The car-following and lane-change models are two important SUMO components used in this module.

The car-following mode[25] is constructed under the assumption of no crash. Each EV has a ideal maximum speed $v_{max}$ and a safe speed avoiding crash $v_{safe}$. The acceleration of the EV lies in a given range $[-b,a](a,b>0)$. The speed of an EV subjects to

where $v_{l}(t)$ denotes the speed of the former vehicle at time $t$, $g(t)$ denotes the distance between current EV and the former EV, $t_{r}$ denotes the reaction time of the driver, $v_{f}(t)$ denotes current vehicle speed, $b$ denotes the maximum deceleration of the vehicle and $\eta$ describes the random speed decrease caused by the not idealized driver operation.

The lane-change model is proposed in [26]. The basic idea of the lane-change model is that the vehicle only changes lanes when there is sufficient physical space in the target lane. The lane-change model consists of four steps:

1. 1.

   Determine the optimal lane that can be changed;

2. 2.

   Calculate the safe vehicle speed for the current lane based on the speed requirements related to the previous simulation and lane changing;

3. 3.

   Evaluate lane changing requirements;

4. 4.

   Execute the lane change action or calculate the speed of the next simulation step according to the urgency of the lane change request.

Two types of CS, the slow CS (SCS) and the FCS, are attached to the road network. An SCS is attached to each uni-directional road. Two SCSs are attached to a bi-directional road, since it is viewed as two uni-directional roads. A bi-directional dead-end road can be marked as an FCS, and no SCS will be attached to this road. From the description above, an EV trip can be seen as a trip from one SCS to another, possibly stopping temporarily at no more than one FCS.

Whatever the type of CS, it is always equipped with a given but runtime-changeable number of charging piles. The money an EV user purchases when buying a unit of electricity from the CS is defined as the user purchase price (UPP) of this CS. For various reasons, a CS may not be able to serve users all the time. When a CS can serve the users, it is online; otherwise, it is offline. UPP and online status of a CS can be defined in the configuration file or set dynamically at runtime.

The FCS and the SCS follow different charging patterns. In an FCS, once an EV finishes charging, it will leave immediately and free the pile it occupied. If all the piles are occupied, then extra vehicles will queue and follow the principle of ‘first come, first served’. In an SCS, an EV occupying a pile shall never leave until all the piles are occupied; then, no more vehicles will be able to get charged here, even if they are willing to queue.

If an EV depletes its battery during driving, it will be removed from the simulation immediately and sent to the low battery set. After twice the time it needs normally driving to the nearest FCS, it will be teleported to the that FCS.

There are three algorithms for finding the optimal path inside SUMO: Dijkstra, A*, and Contract Hierarchy (CH) [24]. They produce the same results with different efficiency. There will be little difference among the three algorithms in a small road network with only several dozens of junctions. When a real-world road network is adopted, the CH algorithm will perform best, A* the second and Dijkstra the worst. Notably, the CH algorithm needs pre-processing, which may take some time. So, if only the optimal path is calculated just a few times, Dijkstra and A* will be better, even if in an extensive road network.

When an EV departs from one edge, its route should be determined. The route selected for the EV is the optimal path between the EV’s OD pair. Here, ‘optimal’ can be either shortest or fastest. The shortest paths are solved when the edge weight is the road length. Since the road length is unchanged, the shortest path between any OD pair needs to be solved no more than once. The fastest paths at a specific time are solved when the edge weight is the road’s average passing time (APT). As the APT of a road is dynamic, the fastest path of a particular OD pair must be re-calculated if it is used at different times.

When an EV departs from an SCS, there are two strategies available for the departure decision, namely ‘threshold strategy’ and ‘distance strategy’.

Under the threshold strategy, a threshold for SoC, $k_{f}^{i}$, is defined for each EV $i$ respectively. If the SoC is less than $k_{f}^{i}$, EV $i$ will first visit an FCS to get fully charged and then go to the destination. The selection of FCS will be introduced in the next section.

Before introduce the distance strategy, we define that a destination is reachable for EV $i$, if its user believes EV $i$ is able to arrive the CS. Formally, a place is reachable for EV$i$ if $k_{r}^{i}L\leq d^{i}$, where $k_{r}^{i}$ is a coefficient depicting the user preference, $L$ denotes the length of the fastest path between the OD pair, and $d^{i}$ denotes the range of EV $i$ with electricity remaining. Otherwise, if $k_{r}^{i}L>d^{i}$, then the place is unreachable for EV $i$.

Under the distance strategy, the length of the fastest path between the OD pair is measured. If the destination is unreachable for an EV, it will firstly visit an FCS to get fully charged, and then go for the destination. Otherwise, it will directly go to the destination.

Under both strategies, if the EV sets out without a halfway FCS given, it will go directly to the destination along the fastest path determined at the time of its departure. The route of the EV shall never change half-way. The strategy for departure decision can be altered runtime by a global switch.

When an EV finishes charging and departs from an FCS, its route will be set as the fastest path from the FCS to its destination.

We define a CS is nearby for an EV $i$ if the Euclid distance of the EV and the CS is smaller than a given threshold. In the case of FCS selection, the scores of nearby online and reachable CS are calculated. For a CS $j$ and a specific EV $i$, the score $f(j)$ is defined as

where $\omega^{i}$ is the coefficient of $EV$ i to describe the value of unit time of its user. $T_{d}^{i}(j)$ denotes the time needed to travel from the current position of EV $i$ to CS $j$. $n_{w}(j)$ denotes the number of waiting vehicles in CS $j$ and $T_{w}$ is a given constant describing the average time of fully charging an EV. $c^{i}$ represents the unit cost of electricity and $W^{i}$ denotes how much electricity will be charged into EV $i$.

The CS to be selected will be the CS with the minimum score. If no CS is reachable and online, the EV will be removed from the simulation and marked ‘low battery’.

A threshold for SoC, $k_{s}$, is defined for each EV respectively. On the arrival of an EV, the module will check whether its SoC is greater than or equal to $k_{s}$. If the SoC is less than $k_{s}$, the EV will try to join the SCS at the destination on condition that at least one free pile exists; otherwise, the EV will park at the destination without occupying any pile in the SCS.

The topology of 37-junction road network is shown in Fig 4. This network, containing 37 junctions and 65 bi-directional roads, is a simplification of a real-world UTN located in Nanjing, China. 10 FCSs, whose numbers are identify in Fig 4, are placed in the road network. Besides, 10 charging piles are placed in each CS, whatever FCS or SCS.

The IEEE 33-bus PDN[27] is adopted in this case, which contain 33 buses and 32 transmission lines. Four generators are placed at bus 2, 3, 6, 8 respectively. Bus 1 is connected to the external power grid, which is also treated as a generator. All the generators’ cost follow $f(x)=0.0001x^{2}+0.3x+10$ (unit of $x$ is kWh, and unit of $f(x)$ is dollar), while the money paid to user for purchasing V2G power is $1.0 per kWh.

5000 EVs are added into the road network for simulation. All the EVs are sampled from 6 prototypes, listed in Table I. The initial SoC assumes certain distribution, with an average about 0.60. The property $\omega^{i},k^{i}_{r},k_{s}^{i},k_{f}^{i},k^{i}_{v}$ of EV $i$ all assume certain distributions, specifically $\omega^{i}\sim U(5,10),k^{i}_{r}\sim U(1.0,1.2),k_{s}^{i}\sim U(0.4,0.6),k_{f}^{i}\sim U(0.2,0.25),k^{i}_{v}\sim U(0.65,0.75)$, where $U$ refers to uniform distribution.

In the case proposed, the simulation will last for 7 days. In the initial state, the road network is empty and the charging status is randomly generated instead of employing a real situation; therefore, an extra day of simulation is added before the formal simulation to make the state of EVs and road network more real. For each EV, 3 trips are generated for each day. Since the simulation will continue for 8 days, therefore, 24 trips are generated for each EV. On weekdays, the first trip departure time $T_{1}$ assumes: $T_{1}-114.54\sim\Gamma(6.63,65.76)$; on weekends, the first trip departure time $T_{1}$ assumes: $T_{1}-197.53\sim\Gamma(3.45,84.37)$. The interval between trips assumes certain distribution, determined by the type of origins. The probability of Markov transition among the places is also determined by the type of origins. The detailed data are shown in the appendix.

The following sections will demonstrate the results.

Figure 5 shows the simulation results of EVCL at FCS and SCS during a whole week. As the parameters for weekday and weekend are different, it can be found that the FCS PL at weekend is higher than that at weekdays, while the SCS PL at weekend is lower than that at weekdays. Data shown in Figure 5 does not enable V2G function.

Figure 6 displays the case results with and without V2G respectively. In this case, V2G is enabled at 8:00-10:00 and 13:00-16:00. It can be discovered that when V2G is enabled, a plunge appears in the accumulated slow charging load.

The first plunge happens around a quarter to ten when the cost of unit V2G output becomes lower than the cost of the unit output of a normal generator. Therefore, to minimize the cost (including the cost of V2G output and normal generator output), V2G power begins to be utilized, causing a sudden drop in slow charging load.

The second plunge happens at the beginning of the V2G period in the afternoon. At this time, the cost of unit V2G output is still lower than the cost of unit output of a normal generator. Therefore, the V2G power is used immediately. However, since the V2G power is quite large for each EV (about 20kW per EV), the SoC of EV declines quickly, and soon it will be lower than the threshold $k_{v}^{i}$. Thus, the V2G capacity is drained quickly. It is notable that the slow charging load does not resume to the level before V2G is enabled due to the charging limits of V2G. When V2G is disabled, an EV tries to get fully charged at an SCS; when V2G is enabled, an EV $i$ only tries to get charged when $SoC^{i}<k_{v}^{i}$.

Figure 7a and 7b display the parameters of SCS edge33_4. It can be discovered that the capacity of V2G is sufficient all the time, but not utilized effectively even in the V2G enabled period. This may be a result of the comparatively high cost of V2G power. If the cost of V2G power is set lower, the utilization rate of V2G capacity may increase.

To illustrate how the platform perceives CS fault dissemination, CS5 is forced offline at 11 am on the first day to represent a CS fault. The difference of FCS load are shown in Figure 8.

To discriminate the faulted CS5, its curve is drawn in dotted lines. It can be found that the load CS5 should have taken are transferred to nearby CSs, mainly CS8, CS6, CS4, and CS2. In contrast, the remote CSs are less affected. A interesting phenomenon is that the load of certain CSs declines for a comparatively long period, like CS1, CS2, and CS7. This may be attributed to the position change of the vehicles, which leads to different CS selection. Temporal alternation may also advance or postpone the time of load appearance, and therefore lead to a difference.

Since the selection of SCS is only related to the destination, only the influence of FCS charging price variation is considered in this section. Figure 9 shows the simulation results with different FCS charging price. FCS are divided into two groups, with Group A including CS1, CS3, CS5, CS7, and CS 9, Group B including CS2, CS4, CS6, CS8, CS10. Figure 9a displays the result when the FCS charging prices of both Group A and B are $1.5/kWh, while Figure 9b displays the result when charging price of Group A is $1.0/kWh and charging price of Group B is $1.5/kWh.

Average EVCL is employed for evaluation between Group A and B. In Figure 9a, the average EVCL of Group A is 274.7kW, while the average EVCL of Group B is 277.2kW. which displays no significant difference. In Figure 9b, the average EVCL of Group B is 13.8kW. Meanwhile, the average EVCL of Group A is 563.5kW, about 41 times of the average EVCL of Group B. It proves that the FCS charging price has a significant influence on the distribution of EVCL. Lower charging price will guide the users to gather in certain FCSs.