Operation-area-constrained Adaptive Primary Frequency Support Strategy for Electric Vehicle Clusters

Tianqi Liu; Pengyu Wang; Qiao Peng; Min Zhang; Tengxin Wang; Jinhao Meng

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Operation-area-constrained Adaptive Primary Frequency Support Strategy for Electric Vehicle Clusters PDF

- ORCID：
Tianqi Liu
✉
- ORCID：
Pengyu Wang
✉
- ORCID：
Qiao Peng
✉
- ORCID：
Min Zhang
✉
- ORCID：
Tengxin Wang
✉
- ORCID：
Jinhao Meng
✉

the College of Electrical Engineering, Sichuan University, Chengdu 610065, China； the Electric Power Research Institute, State Grid Shanxi Electric Power Company, Taiyuan 030001, China

Updated：2023-11-15

DOI：10.35833/MPCE.2023.000233

OUTLINE

Abstract

Due to their fast response and strong short-term power throughput capacity, electric vehicles (EVs) are promising for providing primary frequency support to power grids. However, due to the complicated charging demands of drivers, it is challenging to efficiently utilize the regulation capacity of EV clusters for providing stable primary frequency support to the power grid. Accordingly, this paper proposes an adaptive primary frequency support strategy for EV clusters constrained by the charging-behavior-defined operation area. First, the forced charging boundary of the EV is determined according to the driver’s charging behavior, and based on this, the operation area is defined. This ensures full utilization of the available frequency support capacity of the EV. An adaptive primary frequency support strategy of EV clusters is then proposed. The output power of EV is adaptively regulated according to the real-time distance from the EV operating point to the forced charging boundary. With the proposed strategy, when the EV approaches the forced charging boundary, its output power is gradually reduced to zero. Then, the rapid state-of-charge declines of EVs and sudden output power reductions in EV clusters caused by forced charging to meet the driver’s charging demands can be effectively avoided. EV clusters can then provide sustainable frequency support to the power grid without violating the driver’s charging demands. Simulation results validate the proposed operation-area-constrained adaptive primary frequency support strategy, which outperforms the average strategy in terms of stable output maintenance and the optimal utilization of regulation capacities of EV clusters.

Keywords

Primary frequency control; frequency support; electric vehicle; vehicle-to-grid (V2G); operation area; charging behavior

I. Introduction

WITH the ongoing energy revolution, electric vehicles (EVs) have played an increasingly significant role in transportation networks and power grids [

1]. The rapid development of EVs has promoted the development of vehicle-to-grid (V2G) technology [2]. Under the V2G framework, the power exchange between EVs and power grids becomes more flexible, and EVs can be treated as mobile energy storage units for power grids with bidirectional power control capabilities [3]. The large-scale distribution of EVs can provide significant active support for power grids [4], [5].

Common faults in power grids such as generator tripping or transmission line disconnection can lead to a reduction in grid frequency and even frequency collapse, as has been observed in Australia and the UK [

6], [7]. The research on frequency nadir estimation and under-frequency load shedding in modern power grids has increased significantly [8], [9]. Therefore, it is one of the most important scenarios for V2G to provide grid frequency support, especially when the frequency is reduced. When the power grid is disturbed, the power imbalance between power sources and demands leads to grid frequency oscillation. If the power imbalance cannot be adequately damped, the frequency deviates significantly from the rated value, which may threaten the stability and security of the power grid. When conventional synchronous generators (SGs) are replaced by power-electronic-based renewable energy systems, the governors, turbines, and rotors of the retained SGs may not be able to stabilize the grid frequency to an adequate degree [10]. Active frequency support from renewable energy systems and flexible loads is required [11]. Due to their rapid response and flexible control [12], EVs are promising participants in grid primary frequency regulation [13]. Despite the limited capacity of individual EVs, integrating them into EV clusters can provide substantial support to the power grid through centralized regulation [14].

In contrast to wind farms or large-capacity energy storage systems with unvaried installations [

15], [16], the primary purpose of EVs is to meet the driver’s transportation requirements, which should be prioritized when providing frequency regulation services to the power grid. In addition, the types of EVs, their charging/discharging characteristics, and the random charging behaviors of drivers all affect the performance of EVs in terms of grid frequency support [17], [18]. Thus, the critical factor in resolving the primary frequency support issues of EVs is how to fully utilize their regulation capacities to provide sufficient and sustainable support to the grid while meeting driver’s charging demands [19], [20].

To achieve this, we must first confirm the real-time operating boundary of the EV by considering the factors such as the EV’s real-time state of charge (SOC) and the remaining charging time [

21], [22]. The regulation capabilities of the EV and EV cluster can then be accurately assessed by providing frequency support to the power grid [23]. A distributed sorting-based control framework is proposed in [24] to realize primary frequency control of EVs. In [25], another attempt is made to involve EV clusters in the frequency regulation of virtual SGs. A charger controller is proposed in [26] to optimize the charging process of EVs while providing constant frequency support to the power grid. The controller considers the charging curve, charging status of the battery, and the number of EVs. Unfortunately, these studies have not fully addressed the effects of the travelling and charging behaviors of drivers on the operating boundary of EVs. This means that the operating boundary is conservative, further resulting in a waste of the regulation capacities of EVs.

As an improvement, an adaptive frequency control method is proposed in [

27] while considering the SOC and charging durations of EVs. In [28], an adaptive droop control is employed to regulate the charging of EVs to balance requirements of the frequency regulation provision and driver travelling. This has been subsequently improved in [29] by applying an advanced genetic algorithm optimization toolbox for parameter optimization. A hierarchical control framework consisting of a control center, EV aggregators, charging stations, and individual EVs is proposed in [30]. The framework balances the driver’s SOC expectations and the frequency support demand of the power grid. A similar idea is applied in [31] and [32] to develop a modeling method for the available power and capacity of an EV, where the model considers the driver’s charging demands. The operation area of the EV when frequency support is provided to the power grid is then obtained.

However, the aforementioned studies did not fully consider the small-timescale characteristics of EVs, such as their limited capacities and sustainable output power (i.e., discharging power) capabilities. Consequently, the primary frequency control performance of an EV cannot be guaranteed. Specifically, the primary frequency support may cause the EV to output excessive power, which can prevent the EV battery from charging according to the driver’s expectations during the remaining charging time. To meet the driver’s charging expectations, the EV is forced into the charging state once the remaining charging time is fully exhausted. This can cause the EV to switch suddenly to the discharging state during primary frequency support, leading to an unstable output power of EV clusters, which further disturbs the power grid. Therefore, the operation area of each EV must be accurately identified for stable and sustainable grid frequency support. In addition, the output power regulation of EV clusters should address the operation-area-constrained EV power characteristics. Otherwise, the primary frequency support performance deteriorates.

To address the aforementioned issues, this paper develops an adaptive primary frequency support strategy for EV clusters that more reasonably characterizes the operation area of the EV. The contributions of this paper are summarized as follows.

1) An operation area with a forced charging boundary is defined for EVs to consider the driver’s charging behaviors and the operating characteristics of EV batteries. The operation area ensures that the regulation capacities of EVs are fully utilized while stably supporting the grid on the premise of meeting the charging expectations of drivers.

2) Considering the operation-area-constrained output capabilities of EVs, an adaptive primary frequency support strategy is developed for EV clusters. This strategy methodically allocates frequency regulation tasks to the EVs in clusters, avoiding sudden output reductions of EV clusters due to unexpected forced charging of EVs, and thereby, improving the frequency support performance of power grid.

3) The proposed methodology can be applied to different types of EV clusters including private EVs, electric buses, and electric taxi clusters. With driver’s charging behaviors considered, the coordination of multiple EV clusters for primary frequency support can be achieved.

The remainder of this paper is organized as follows. An operation-area analytical method for EVs that considers driver’s charging behaviors is proposed in Section II. Section III describes the development of an adaptive primary frequency support strategy for EV clusters constrained by the operation area. In Section IV, case studies are presented to validate the proposed operation area and control strategy, and private EVs, electric taxi, and electric bus clusters are illustrated. Concluding remarks are provided in Section V.

II. Operation-area Analytical Method for EVs Considering Driver’s Charging Behaviors

As the primary purpose of EVs is to provide travel services to drivers, the daily behavior and travel demands of drivers significantly constrain the output power of EVs. To fully consider this effect, a forced charging boundary considering the charging expectations of drivers is proposed, which is a major constraint of EV output power. A charging behavior-defined operation area for the EV is then devised based on the forced charging boundary.

A. Charging Power Characteristics of EVs

To realize efficient primary frequency support, the power exchange characteristics of EVs and the power grid should be adequately considered. From a driver’s perspective, a reduced charging cost is desired. In this case, the EV is charged until the SOC reaches the driver’s charging expectation and then remains connected to the power system without power exchange. In other words, it is in an idle state. Accordingly, the EV charging law is expressed as follows.

1) The EV continues to be charged until the SOC reaches the expected value SOC_exp as set by the driver. Then, charging is terminated, and the EV is in an idle state. Since the sensitivities of drivers to charging costs are different, SOC_exp can be between the initial SOC and 1.

2) When SOC_exp is less than the battery overcharging boundary SOC_oc, constant power charging is applied.

3) When SOC_exp is greater than SOC_oc, the EV is initially charged at a constant power. When the SOC is greater than SOC_oc, trickle charging is triggered for battery protection, and the charging power gradually decreases with increasing SOC until the SOC reaches SOC_exp [

33].

According to the charging law, the charging power of an EV can be derived as:

P_{c h a r} = \{\begin{array}{l} P_{c o n} S O C < S O C_{o c} \\ P_{c o n} (e^{\frac{S O C - 1}{S O C_{o c} - 1} l n 2} - 1) S O C_{o c} \leq S O C \leq S O C_{e x p} \\ 0 S O C > S O C_{e x p} \end{array}

(1)

where P_char is the charging power considering the SOC state; and P_con is the charging power in the constant power charging state.

The charging power curve of an EV considering the SOC state is shown in Fig. 1, where SOC_exp1 and SOC_exp2 represent the expected SOCs that are less than and greater than SOC_oc, respectively. As Fig. 1 shows, when the expected SOC is less than SOC_oc, the EV is charged at a constant power P_con until the SOC reaches SOC_exp1. And then charging is stopped, and the EV enters an idle state. When the expected SOC is greater than SOC_oc, the EV is initially charged at a constant power P_con until the SOC reaches SOC_oc. It then switches to trickle charging mode until the SOC reaches SOC_exp2. Here, the charging ends and the EV enters an idle state.

Fig. 1 Charging power curve of an EV considering SOC state.

B. Discharging Power Characteristics of EV

The discharging power characteristics of an EV battery are also essential for primary frequency support performance. When the SOC of an EV battery is less than the overcharging boundary (defined as SOC_od), the battery is no longer allowed to discharge for lifespan considerations. When the SOC is between SOC_od and the expected value, the two-parabolic discharging mode is applied [

29]. Accordingly, the discharging power, when considering the SOC state, is given by:

\begin{array}{l} P_{d c h a r} = \\ \{\begin{array}{l} 0 S O C < S O C_{o d} \\ \frac{P_{d m a x}}{2} (1 - \sqrt[]{\frac{S O C - S O C_{m i d}}{S O C_{o d} - S O C_{m i d}}}) S O C_{o d} \leq S O C < S O C_{m i d} \\ \frac{P_{d m a x}}{2} (1 + \sqrt[]{\frac{S O C - S O C_{m i d}}{S O C_{e x p} - S O C_{m i d}}}) S O C_{m i d} \leq S O C \leq S O C_{e x p} \end{array} \end{array}

(2)

where P_dchar is the discharging power of the EV considering the SOC state; P_dmax is the maximum discharging power determined by the battery specification; and SOC_mid is the medium SOC between the overdischarging and expected values, i.e.,

S O C_{m i d} = \frac{S O C_{o d} + S O C_{e x p}}{2}

(3)

Figure 2 shows the discharging power curve of the EV considering the SOC state, where the discharging power curve is a parabola with an increasing slope before the SOC reaches SOC_mid. Thereafter, it continues to increase but with a reduced slope until the SOC reaches SOC_exp and the output power reaches P_dmax.

Fig. 2 Discharging power curve of an EV considering SOC state.

C. Charging-behavior-defined Operation Area of EVs

In addition to the charging and discharging power characteristics, the charging behavior of an EV also affects its grid-available frequency support capabilities. In this paper, the operation area of an EV is defined to consider the driver’s charging behavior, where the real-time SOC of the EV battery and remaining charging time are considered. When addressing the travel behaviors of drivers, we make the following assumptions [

34].

1) The charging behavior of each EV depends on the driver’s daily behavior and travel demands, which are independent of other EVs.

2) The charging duration and expected SOC of the EV are preset by the driver when the charging starts.

Figure 3 depicts the operation area of an EV, where FDP represents the frequency disturbance point; t₀ and SOC₀ are the frequency disturbance time and SOC at this time, respectively; SOC_start is the SOC when the charging starts; t_F is the forced charging time when the EV reaches SOC_od; t_mar is the margin of the forced charging time; and t_start and t_end are the charging start time and end time, respectively.

Fig. 3 Operation area of an EV defined by charging behavior of driver.

In Fig. 3, Point A represents the location at which charging starts. If the EV is charged under a constant charging power, the SOC will meet SOC_exp at Point B. The slope of Line AB represents the constant charging rate. If the EV does not provide support to the power grid, it becomes idle and reaches Point C at the end of the charging period. Line BC determines the upper boundary of the operation area, which is constrained by the SOC_exp.

Correspondingly, Point E represents the point at which the EV is discharged to the SOC_od with the maximum discharging power, and the slope of Line AE represents the maximum discharging rate. If the EV does not interact with the power grid, it reaches the forced charging boundary at Point D, where it must be charged to satisfy the driver’s travel demands. Line DE determines the lower boundary of the operation area, which is constrained by SOC_od.

As previously mentioned, the SOC of the EV battery should reach the expected value when charging ends. Thus a critical charging period remains, during which the battery can be opportunely charged to SOC_exp under constant charging power. In this context, the EV is forced into the charging state when the remaining charging time is critical. To alleviate the effects of the state monitoring error, charging loss, and unexpected travel demands, a margin is set for the critical remaining charging time. The forced charging boundary is indicated by Line CD in Fig. 3, and the forced charging time when the EV reaches SOC_od ( $i . e .$ , at Point D) is determined by [

32]:

t_{F} = t_{e n d} - (1 + t_{m a r}) (\frac{S O C_{e x p} - S O C_{o d}}{P_{c h a r} η_{c}}) Q_{d}

(4)

where $η_{c}$ is the charging efficiency; and Q_d is the battery capacity of the EV.

The forced charging boundary, i.e., Line CD in Fig. 3, is a linear function, the functional expression of which is given by:

S O C (t) = a t + b

(5)

where a and b are the constant coefficients calculated from the positions of C (t_end, SOC_exp) and D (t_F, SOC_od) as follows:

\{\begin{array}{l} a = \frac{S O C_{e x p} - S O C_{o d}}{t_{e n d} - t_{F}} \\ b = \frac{S O C_{o d} t_{e n d} - S O C_{e x p} t_{F}}{t_{e n d} - t_{F}} \end{array}

(6)

With the rated charging power of the EV, preset SOC_exp, charging end time, and forced charging time, a forced charging boundary can be drawn, as shown in Fig. 3. It is worth mentioning that the operation area of the EV can also be applied to EV dispatching in high-frequency events, where the EV should absorb power from the power grid to release power redundancy.

III. Adaptive Primary Frequency Support Strategy of EV Clusters Constrained by Operation Area

The output power characteristics of the EV can be obtained by constraining the operation area with a forced charging boundary. The most dominant feature of the EV output power is that once the operation point reaches the forced charging boundary, the EV output power becomes negative. The total output power of the EV clusters is then disturbed, and grid support becomes unstable. Therefore, we propose an adaptive primary frequency support strategy for EV clusters, which adequately considers the operating-area constraints of EVs when the output power of EV clusters is designed. This leads to stable primary frequency support for the power grid.

A. Operating and Control Framework of EV Clusters for Grid Frequency Support

Figure 4 shows the operating and control framework of EV clusters for grid frequency support, which is a three-layer system. The EV is controlled by a bidirectional converter in the V2G charging pile, where the operating data of the EV such as the charging start and end time, real-time SOC, and SOC_exp are collected. The EV cluster controller collects the data of all the EVs in the cluster and assesses their operation areas, based on which the real-time available frequency support capability of the EV cluster is obtained and provided to the EV control center. The EV control center is the connection between the power grid and EV clusters. It transfers the operating data of the EVs to the power grid and allocates grid-support commands to the EV clusters [

35].

Fig. 4 Operating and control framework of EV clusters for grid frequency support.

Once the power grid experiences a disturbance, a grid frequency support signal is sent from the grid operator to the EV control center. The EV control center sends a control signal to the EV cluster controllers according to available frequency support capacity distribution. The EV cluster controller then dispatches frequency support tasks to the EVs according to their operation areas.

This subsection illustrates the control of a single EV cluster. The subsequent subsection addresses the coordination among multiple types of EV clusters.

B. EV Output Power Constrained by Operation Area

To alleviate the effects of a sudden EV output power reversal on the output power of the EV cluster, the discharging power of the EV given by (2) should be modified. The primary purpose is to manipulate the discharging power of the EVs in an adaptive manner based on their operating points with respect to the forced charging boundaries. Specifically, the closer the EV operating point is to the forced charging boundary of the operation area, the smaller the output power is. When the operating point reaches the forced charging boundary, the discharging power is reduced to zero. This approach effectively prevents sudden output power losses from the EV cluster, leading to a more stable grid-support performance.

A discharging coefficient k_dchar is proposed to modify the EV output power adaptively by considering the operation-area constraint. The discharging coefficient is calculated based on the distance from the operating point to the forced charging boundary:

k_{d c h a r} = \frac{S O C - b - a t}{a (t_{e n d} - t_{s t a r t})}

(7)

The derivation of (7) is provided in Appendix A. Notably, the SOC and t in (7) are real-time values, meaning that k_dchar varies during the discharging process. In addition, the EV output power changes in real time, and the primary frequency support from the EV becomes adaptive.

C. Output Power Coordination of EVs in Clusters

For EVs in the same cluster, their output power should be coordinated with others for optimal resource utilization. This is because the total output power of all EVs in the cluster should support the power grid as much as possible for optimal utilization of battery resources. Therefore, EV output power can be corrected based on the size of the disturbance.

The correction coefficient for the output power of the EVs in the cluster is defined as k_cl. When the discharging coefficient is considered, the discharging power of the EV is modified as:

P_{E V} = k_{c l} k_{d c h a r} P_{d c h a r}

(8)

where P_EV is the discharging power of the EV considering the constraint of the operation area and EV coordination in the cluster.

According to (8), the total output power of the EV cluster can be obtained as:

P_{c l} = k_{c l} \sum_{i = 1}^{n} k_{d c h a r, i} P_{d c h a r, i}

(9)

where n is the number of EVs in the cluster; and i is the i^th EV.

In (8), P_EV is the discharging power of an individual EV in the cluster; and P_cl in (9) is the discharging power of the entire EV cluster. The correction coefficient of the EV cluster is then derived as:

k_{c l} = \frac{P_{c l}}{\sum_{i = 1}^{n} k_{d c h a r, i} P_{d c h a r, i}}

(10)

When the maximum output power of the EV cluster (i.e., the available frequency support capacity) is defined as P_cl,max, P_cl in (10) can be determined by:

P_{c l} = \{\begin{array}{l} P_{s} P_{s} < P_{c l, m a x} \\ P_{c l, m a x} P_{s} \geq P_{c l, m a x} \end{array}

(11)

where P_s is the grid power shortage. When multiple EV clusters provide frequency support to the power grid, P_s in (11) should be allocated proportionally according to the available frequency support capacity of each cluster.

As (11) shows, P_cl,max is critical in determining k_cl, where P_cl,max is limited by the maximum primary frequency support capabilities of the EVs in the cluster. Specifically, for each EV in the cluster, a power exists that can enable the EV to reach the forced charging boundary at the charging end time from the FDP (defined as $P_{E V, m a x}$ ), which is constrained by $P_{d m a x}$ and is calculated as:

P_{E V, m a x} = \frac{Q_{d}}{η_{d}} (S O C_{0} - a t_{0} - a t_{f, d u r} - b)

(12)

where $t_{f, d u r}$ is the expected duration for the primary frequency support, which is preset and can be flexibly adjusted; and $η_{d}$ is the discharging efficiency.

A power correction coefficient of the EV $k_{E V, m a x}$ that reflects the relationship between P_EV and P_dchar can then be calculated as:

k_{E V, m a x} = \frac{P_{E V, m a x}}{k_{d c h a r 0} P_{d c h a r}}

(13)

where $k_{d c h a r 0}$ is the initial discharging coefficient calculated by substituting the initial state of the EV at the FDP into (7).

To maintain a stable output power of the EV cluster, the cluster output power correction coefficient should not exceed the output power correction coefficients of all the EVs, i.e.,

k_{c l, m a x} = m i n {k_{E V, m a x, 1}, k_{E V, m a x, 2}, \dots, k_{E V, m a x, n}}

(14)

where $k_{E V, m a x, n}$ is the power correction coefficient of the n^th EV.

The available frequency support capacity of the EV cluster can be obtained as:

P_{c l, m a x} = k_{c l, m a x} \sum_{i = 1}^{n} k_{d c h a r 0, i} P_{d c h a r, i}

(15)

When (15) is substituted into (11) and (10), the value of k_cl is obtained.

Figure 5 presents the principle of the proposed strategy for coordinating the EVs in a cluster, and the conventional average power allocation strategy proposed in [

26] is illustrated for comparison.

Fig. 5 Schematics of proposed strategy and conventional average power allocation strategy for coordinating EVs in cluster.

As Fig. 5 shows, under the conventional average power allocation strategy, the output power of the EVs in the cluster is assigned on average, and the difference in the available frequency support capacities is not considered. In these cases, the frequency support performance of the EV cluster is unstable. Specifically, in Stage 1, all the EVs are under the same and averaged frequency support command, which leads to the same SOC reduction rates. The EVs that are closer to their forced charging boundaries then switch to the charging mode more quickly than the others to ensure that batteries can be fully charged by the charging end time. The sudden change from the discharging to the charging state of these EVs leads to a shortfall in the EV cluster output power and generates an additional disturbance on the power grid. Similarly, in Stage 2, some EVs closer to their forced charging boundaries are switched to the charging state more quickly under the average power allocation strategy, leading to poorer grid-support performance of the EV cluster.

By contrast, under the proposed strategy, the EV output power is allocated according to the operating point of the EV in its operating area. An EV with a larger SOC, longer remaining charging time, or greater distance from the forced charging boundary will output more power than others. In this context, EVs with lower available frequency support capacities will have lower SOC reduction rates and will not suddenly switch to the charging state. This avoids sudden power loss in the EV cluster and allows for a more stable frequency support to the power grid. As Fig. 5 shows, under the proposed strategy, a few EVs reach the forced charging boundaries during the frequency event. In addition, EVs that reach the forced charging boundaries already have a very low output power, which leads to a negligible impact on the EV cluster output power.

D. Adaptive Primary Frequency Support Strategy of EV Clusters

As (8) shows, the EV output power is corrected using two coefficients, k_cl and k_dchar. Based on the previous discussion, k_cl is a constant determined by the power disturbance, whereas k_dchar is a time-varying parameter determined by the real-time SOC and remaining charging time. The EV output power is then adaptively modified along with the change in k_dchar, and an adaptive primary frequency support strategy for the EV cluster is developed.

Step 1: determine the initial state settlement of the EV unit. Based on the battery specifications and charging behaviors, the three key parameters of k_dchar0, P_dchar, and k_EV,max are calculated for each EV unit.

Step 2: determine the initial state settlement of the EV cluster. Based on the initial states of the EVs, the available frequency support capacity of the EV cluster is obtained considering the constraints of the operation areas. The available frequency support capacity of the EV cluster is sent to the EV control center and compared with the grid power shortage caused by the disturbance to determine how the EV cluster provides frequency support, as shown in (11). If multiple EV clusters are controlled, the initial output power of each EV cluster is allocated according to its available frequency support capacity. And then k_cl is obtained, and the initial output power of each EV in the cluster is determined.

Step 3: involve adaptive output power regulation of EVs in the cluster. The discharging coefficients and EV output power are periodically updated according to the real-time EV operating points, where the time-step for the periodic control is denoted as m. In each control cycle, the system determines whether the i^th EV reaches the operation area boundary within the frequency support duration. If the EV reaches the operating-area boundary, it changes from the discharging state to the charging state. Otherwise, it continues to be discharged under the proposed control strategy. When t_f_,dur is reached, the discharging ends.

Figure 6 presents a flowchart of the primary frequency support strategy for an EV cluster. Figure 6 shows that most of the steps are processed by the EV cluster controller. In addition, the EV control center compares the grid power shortage and available frequency support capacity of the EV cluster.

Fig. 6 Flowchart of adaptive primary frequency support strategy of an EV cluster.

It should be noted that the primary frequency support strategy proposed in this paper is based on the premise that the grid power shortage is known. In other words, the EV control center is aware of the power that all EVs must provide. In cases in which the grid power shortage is unknown, additional algorithms are required to predict the disturbance size [

36], based on which the proposed strategy is still applicable. However, as the focus of this paper is on the evaluation of the operation area and coordinated control of EVs, disturbance prediction is not addressed here but will be explored in future work.

IV. Case Studies

A simulation using MATLAB/Simulink has been conducted as a case study. In the simulation system, the power grid is represented by an SG with an output power of 487.5 kW, inertial time constant of 5 s, and damping gain of 1 p.u.. The rated frequency of the system is 50 Hz. The turbine adopts the IEEE G1 model as a steam turbine, and the mechanical hydraulic control governor model is applied, as shown in [

37].

Private EVs, electric buses, and electric taxis clusters are used as examples to validate the proposed methodology under different charging behaviors and multiple clusters. In the following analysis and discussion, the superscripts “p”, “b”, and “t” represent private EVs, electric buses, and electric taxis, respectively. Note that the proposed strategy for multiple EV clusters is applicable to other types of EV clusters as long as their charging behaviors are explicitly or accurately predicted.

In this case study, the ratio of private EVs, electric buses, and electric taxis is 10:1:2. In practical scenarios, economic incentives are provided to EVs that provide frequency support to the grid based on the power they supply and real-time electricity prices, which encourages more EVs to provide frequency support to the power grid. In the simulation, three EV clusters are represented by three grid-connected battery packs, where the converter rated power of the battery systems is 100 kW, and the battery capacities are 35 kWh, 180 kWh, and 45 kWh, respectively. To minimize the loss of battery life, the battery overdischarging and overcharging boundaries are set to be 20% and 80%, respectively [

38]. The charging behaviors and operating parameters of the EVs are provided in Appendix B Table BI.

In Table AI, the charging start time and end time for private EVs and buses are given directly, whereas the charging start time and charging time for electric taxis are provided. In addition, as the daily routes of buses are relatively fixed, their initial SOC is relatively centralized, and the initial SOC distribution is given directly in Table AI as a normal distribution. However, the daily driving mileage of private EVs and electric taxis remains uncertain. Therefore, their daily mileage and battery power consumption rates are used to obtain their initial SOC.

A. Charging Behavior Modeling of Different EVs

The operation areas of all the EVs are first evaluated according to their charging and travel behaviors, which are demonstrated as follows.

1)　Private EV

Considering that drivers tend not to change their travel habits following a change in vehicle energy, the behavior data of the drivers of traditional cars can be utilized to investigate their associated travel laws. According to the National Household Travel Survey of the U.S. [

39], the normal distribution model of the traveling end time of private EVs can be obtained as a probability density function:

\begin{array}{l} N (t_{s t a r t}^{p}) = \\ \{\begin{array}{l} \frac{1}{σ_{s t a r t}^{p} \sqrt[]{2 π}} e x p (- \frac{(t_{s t a r t}^{p} + 24 - μ_{s t a r t}^{p})^{2}}{2 (σ_{s t a r t}^{p})^{2}}) 0 < t_{s t a r t}^{p} \leq μ_{s t a r t}^{p} - 12 \\ \frac{1}{σ_{s t a r t}^{p} \sqrt[]{2 π}} e x p (- \frac{(t_{s t a r t}^{p} - μ_{s t a r t}^{p})^{2}}{2 (σ_{s t a r t}^{p})^{2}}) μ_{s t a r t}^{p} - 12 < t_{s t a r t}^{p} \leq 24 \end{array} \end{array}

(16)

where t $_{s t a r t}^{p}$ is the time when the private EV arrives at the parking lot at the end of the trip (i.e., the charging start time); $μ_{s t a r t}^{p}$ is the mathematical expectation of the normal distribution function; and $σ_{s t a r t}^{p}$ is the standard deviation. According to the aforementioned survey, N(t $_{s t a r t}^{p}$ ) in (16) can be provided in segments to represent the distribution characteristics of different time intervals.

Similarly, the initial travel time (i.e., the time at which charging ends) and the average daily mileage of a private EV follow a normal distribution.

2)　Electric Bus

Compared with private EVs, the driving routes and charging durations of electric buses are more regular. This paper considers electric buses in providing grid-support services only at night, during which they are usually in a slow charging mode [

40]. It is assumed that the charging start time of an electric bus follows a normal distribution as given by:

N (t_{s t a r t}^{b}) = \frac{1}{σ_{s t a r t}^{b} \sqrt[]{2 π}} e x p (- \frac{(t_{s t a r t}^{b} - μ_{s t a r t}^{b})^{2}}{2 (σ_{s t a r t}^{b})^{2}})

(17)

where t $_{s t a r t}^{b}$ is the charging start time of the electric bus; and $μ_{s t a r t}^{b}$ and $σ_{s t a r t}^{b}$ are the mathematical expectation and standard deviation of its normal distribution function of the electric bus, respectively.

The charging end time t $_{e n d}^{b}$ and initial SOC of the electric bus also conform to a normal distribution, the distribution function of which is the same as in (17).

3)　Electric Taxi

An electric taxi is usually charged in the morning prior to lunchtime and in the evening prior to changing shifts, and it may continue to be charged several times during the day. Therefore, for a more accurate description of the charging behavior of electric taxis, the charging time distribution can be divided into four time intervals based on the actual operating data, which are 00:00-09:00, 09:00-14:00, 14:00-19:00, and 19:00-24:00 [

41]. However, charging anxiety is a common issue with electric taxis, which means that taxi drivers prefer a fast charging mode, and the charging duration is generally within 1 hour. The charging behaviors of electric taxis are represented by the charging start time t

_{s t a r t}^{t}

and charging duration t

_{d u r}^{t}

for the four charging time intervals. They conforms approximately to a normal distribution, the function of which is the same as in (17).

Based on the charging behavior models of various types of EVs and the EV operation-area model proposed in Section II, the operation areas of all EVs are obtained, where the forced charging time margin t_mar is set to be 5%.

B. Available Frequency Support Capacity of EV Clusters

The available frequency support capacities of the different EV clusters are then obtained, based on which the frequency support task is allocated to the EV clusters in proportion to their available frequency support capacities.

Specifically, when the system parameters are substituted into (9), the maximum power that the EV clusters can provide to the power grid within 24 hours of the day is obtained, as shown in Fig. 7, which provides the maximum power every 30 min.

Fig. 7 Daily available frequency support capacity of EV clusters under operation area constraint of EVs.

As the figure shows, the available frequency support capacity of the EV clusters is high during 00:00-05:00 and 20:00-24:00, as most private EVs, electric buses, and some electric taxis are connected to the power grid, charged to the expected levels, and thus prepared to provide frequency support to the power grid. Thus, the available frequency support capacity of the EV clusters remains high during this period. After 06:00, some EVs gradually disconnect from the power grid, which leads to a reduced available frequency support capacity of the EV clusters, with the lowest available frequency support capacity at 09:00. At this time, most electric buses and taxis operate in the city, and some private EVs remain connected to the power grid. Electric taxis are then gradually connected to the power grid at noon, causing the available frequency support capacity to increase again at approximately 12:00, which then continues to increase after a slight decline. At 17:00, private EVs begin to connect to the power grid one after another, and the available frequency support capacity of the EV clusters steadily increases and reaches a peak at 22:00.

C. Primary Frequency Support Strategy Validation

To verify the proposed primary frequency support strategy of the EV clusters, the system undergoes two random events, namely 25 kW generation power shortage at 13:00 and 40 kW generation power shortage at 21:00, respectively. The frequency dynamics without the support from the EV clusters (hereafter “without EV support”) and with the proposed strategy of EV clusters are analyzed, and the conventional average power allocation control strategy of the EV clusters as introduced in Section III-C (hereafter “average strategy”) is tested for comparison. Under the proposed strategy, the EV cluster controller updates the output power commands for the EVs every 1 s (i.e., $m = 1$ s in Fig. 6) and sustains the primary frequency support within 50 s (which can be set according to the specific grid operator requirements).

In this paper, a sustainability index is proposed to evaluate the stable primary frequency support performance of EV clusters within a specified primary frequency support duration, which is defined as:

S_{s u s} = [(P_{e n d} - P_{s t a r t}) / P_{s t a r t}] \times 100 %

(18)

where S_sus is the sustainability index; P_start is the total output power of the EV clusters at the beginning of primary frequency support; and P_end is the total output power of the EV clusters after primary frequency regulation.

With S_sus, the sustainability of the EV cluster power output when power support is provided to the power grid can be evaluated and compared.

1)　25 kW Generation Power Shortage at 13:00

A 25 kW generation power shortage at 13:00 is tested to validate the proposed strategy. The total output power of the EV clusters, grid frequency, and rate of change of frequency (RoCoF) dynamics are shown in Fig. 8, where the average and proposed strategies are compared.

Fig. 8 Simulation results when a 25 kW generation power shortage occurs at 13:00. (a) Total output power of EV clusters. (b) Grid frequency. (c) RoCoF dynamics.

As Fig. 8(a) shows, the proposed strategy exhibits almost negligible power output variation during the primary frequency support process. The sustainability index of the proposed strategy in this case is 1.87%. However, because the average strategy does not consider charging demands when assigning the output power of the EVs, all EVs output the same amount of power during the primary frequency support process. Subsequently, some EVs with smaller operating margins quickly reach their forced charging boundaries, resulting in a relatively unstable output power of EV clusters. As Fig. 8 shows, the output power of the EV clusters under the average strategy drops abruptly at 3 s, 8 s, 19 s, and 35 s during the primary frequency support process. The sustainability index is 6.31%, indicating that the output power of the EV clusters is considerably more unstable under the average strategy.

Regarding the frequency support performance, Fig. 8(b) and (c) shows that without EV support, the grid frequency is reduced to the lowest point of 49.54 Hz at 2.67 s following the disturbance and reaches a new steady frequency of 49.85 Hz. The average strategy yields a frequency nadir of 49.74 Hz at 2.39 s following the disturbance, showing a 43.50% reduction in the maximum frequency deviation compared with the case without EV support. However, as some EVs are forced to discharge during the primary frequency regulation process, the grid frequency drops at 3 s, 8 s, 19 s, and 35 s following the disturbance, causing the RoCoF to decrease at these time, and it finally reaches 49.89 Hz at the end of the primary frequency regulation. In this case, the frequency support from the EVs is unstable, and the frequency quality is challenged. By contrast, the proposed strategy adequately considers the available frequency support capacities of EVs, resulting in stable output power during the primary frequency support process. Subsequently, the frequency does not suddenly drop once it reaches a new steady frequency, and reductions in RoCoF are effectively avoided. The proposed strategy behaves in a manner identical to that of the average strategy in terms of reductions in maximum frequency deviation (43.5% reduction as compared with the case without EV support). More importantly, it causes the frequency ultimately to reach 49.92 Hz in the new steady state, indicating frequency deviation reductions of 46.70% and 27.30% compared with the case without EV support and the average strategy, respectively.

The SOC changes in EVs for primary frequency support are analyzed to further validate the proposed strategy, where electric taxis are used as an example. The SOCs of the electric taxis before and after primary frequency regulation are shown in Fig. 9.

Fig. 9 SOCs of electric taxis before and after primary frequency regulation under 25 kW generation power shortage at 13:00 under different control strategies.

Figure 9 shows that the EVs output the same amount of power under the average strategy, whereas the proposed strategy varies the output power of the EVs based on the remaining charging time and SOC. For instance, for EVs with a short remaining charging time, like those in Region 1 of Fig. 9, the average strategy dictates that they output the same power, leading to a large SOC reduction and a higher possibility of reaching the forced charging boundary. By contrast, the proposed strategy minimizes the output power of the EVs in Region 1, and the SOC reduction is more reasonable in avoiding the sudden disconnection of EVs. For EVs with longer remaining charging time, such as those in Region 2, the proposed strategy allows the EVs to output more power as compared with the average strategy, and the available frequency support capacities of the EVs can be utilized more efficiently.

Based on this analysis, the proposed strategy adequately considers the charging behaviors of drivers and charging states of EVs. This ensures stable frequency support for the power grid while prioritizing EV charging demands.

2)　40 kW Generation Power Shortage at 21:00

A 40 kW power generation shortage at $21 : 00$ is tested to further validate the proposed strategy. The output power of the EV clusters, grid frequency, and RoCoF dynamics are shown in Fig. 10.

Fig. 10 Simulation results under a 40 kW generation power shortage at 21:00. (a) Total output power of EV clusters. (b) Grid frequency. (c) RoCoF dynamics.

As Fig. 10(a) shows, the proposed strategy facilitates a more stable output power of the EV clusters during the primary frequency regulation period. In this case, the sustainability index of the proposed strategy is 1.39%, and that of the average strategy is 5.45%. Thus, the proposed strategy behaves better in terms of stable primary frequency support in this case.

Figure 10(b) and (c) shows the frequency and RoCoF dynamics with and without frequency support from the EV clusters. Without EV support, the grid frequency drops to the lowest point of 49.20 Hz at 2.53 s following the disturbance and reaches a new steady state of 49.70 Hz at 17.64 s following the disturbance. The average strategy causes the frequency nadir to increase to 49.80 Hz, showing a 75% reduction in the maximum frequency deviation compared with the case without EV support. However, due to inadequate output power strategies, some EVs are forced to charge during the primary frequency regulation process. This results in sudden output power declines of EV clusters at 9 and 18 s, causing the corresponding frequency to drop before finally reaching 49.91 Hz at 28.59 s. By contrast, the proposed strategy assigns output power to EV clusters and EVs in a more reasonable manner. With the proposed strategy, the maximum frequency deviation is reduced by 75% compared with the case without EV support. In addition, this allows the grid frequency to reach a new steady state of 49.92 Hz at 13.68 s without any subsequent drops. Overall, the proposed strategy reduces the frequency deviation at the new steady state by 73.30% compared with the case without EV support and by 11.10% compared with the average strategy.

Figure 11 shows the SOC changes of EVs for primary frequency support, where electric taxis are analyzed as an example. As the figure shows, the EVs in Region 1, where the remaining charging time is limited, are assigned to provide less power for primary frequency support under the proposed strategy. The EVs in Region 2, where sufficient charging time occurs, output more power under the proposed strategy than they do under the average strategy. In addition, the EV output power under the proposed strategy adaptively varies depending on the SOC state and remaining charging time.

Fig. 11 SOCs of electric taxis before and after primary frequency regulation under a 40 kW generation power shortage of generator at 21:00 under different control strategies.

3)　Total Energy Provision of EV Clusters

Figure 12 shows the total energy provided by the EV clusters to the power grid in the aforementioned case studies. The figure shows that the total energy provided by the EV clusters under the first disturbance is 0.3130 kWh and 0.3462 kWh with the proposed and average strategies, respectively, representing a 10.61% energy output increase for the proposed strategy. Under the second disturbance, the total energy provision with the average strategy is 0.5363 kWh, whereas the proposed strategy realizes a 0.5546 kWh total energy provision, which is an increase of 3.41%. The analytical results indicate that the proposed strategy more efficiently uses the available frequency support capacities of EV clusters.

Fig. 12 Total energy provided by EV clusters to power grid under disturbances of 25 kW at 13:00 and 40 kW at 21:00 under different strategies.

D. Strategy Validation Under Different EV Operating Data

The charging behaviors and operating parameters of the EVs are altered to validate the adaptability and compatibility of the proposed strategy. The taxi charging duration conforms to the Laplace distribution:

L a p l a c e (t | μ_{L}, γ_{L}) = \frac{1}{2 γ_{L}} e^{- \frac{| t - μ_{L} |}{γ_{L}}}

(19)

where $μ_{L}$ is the position parameter, $μ_{L} = 56.28$ ; and $γ_{L} > 0$ is the scale parameter, $γ_{L} = 13.48$ .

Let us suppose that the charging start time of a private EV conforms to the normal distribution N(18.5, 3.4) and that 5% of the buses return to the charging station for recharging at 12:00 under an SOC distribution of N(0.4, 0.1) until 16:00. The remaining data are the same as those listed in Table AI.

A 25 kW generation power shortage is applied to the system at 13:00. Figure 13 shows the output power of the EV clusters and the grid frequency dynamics. As Fig. 13(a) shows, the proposed strategy facilitates a more stable output power of the EV clusters within the primary frequency regulation period, where the sustainability index is 1.69%. By contrast, the sustainability of the average strategy is 5.37%, generating instability in the output power of the EV clusters.

As Fig. 13(b) shows, without support from the EV clusters, the grid frequency drops to a nadir of 49.54 Hz at 2.67 s following the disturbance and then reaches a new frequency of 49.85 Hz. When the average strategy is applied, the grid frequency nadir becomes 49.74 Hz at 2.53 s following the disturbance. However, some EVs are forced into a discharge state during the primary frequency regulation process due to the inadequate output power strategy. The grid frequency suddenly drops at 9 s, 10 s, 21 s, and 26 s following the disturbance and finally stabilizes at 49.90 Hz, as shown in Fig. 13(b). By contrast, under the proposed strategy, the frequency does not decrease once it reaches a new steady frequency of 49.92 Hz at 10.5 s following the disturbance. Consequently, the proposed strategy reduces the frequency deviation at the new steady state by 46.70% and 20% compared with the case without EV support and the average strategy, respectively.

The simulation results indicate that the primary frequency support strategy proposed in this paper adequately considers the charging behaviors of drivers and battery states of EVs and can more efficiently utilize the available frequency support capacity of EV clusters. Compared with the average strategy, the proposed strategy facilitates a more stable output power of the EV clusters to the power grid during the primary frequency regulation process without violating the charging demands of drivers.

V. Conclusion

The primary frequency support performance of EV clusters is significantly affected by the charging behaviors of drivers and battery states, which has not been adequately addressed in the literature. To address this issue, this paper proposes an adaptive primary frequency support strategy for EV clusters constrained by operation areas. The forced charging boundary and operation area of the EV are defined according to driver charging behavior. A well-portrayed operation area can ensure full utilization of an EV’s available frequency support capacity while satisfying the driver’s charging demands. An adaptive primary frequency support strategy was then designed based on the operation area. The proposed strategy adjusts the EV output power based on the real-time distance from the EV operating point to the forced charging boundary. This avoids sudden output drops in EV clusters due to forced charging during the primary frequency regulation process. Finally, stable output power for the primary frequency support is realized while meeting the charging demands of drivers. Simulation results have validated the proposed strategy, particularly compared with the average strategy in terms of maintaining the stable output and efficiently utilizing the available frequency support capacities of EV clusters. In addition, this paper shows that the proposed strategy could be applied to multiple clusters of different types of EVs and could significantly improve the power grid frequency quality.

A future study will consider incentive measures for drivers in encouraging EVs to provide frequency support services. The proposed strategy will continue to be improved by considering grid disturbance prediction, charging behavior estimation, and battery life optimization.

Appendix

Appendix A

According to Fig. 3, the function for the forced charging boundary, i.e., Line CD, is given by:

S O C (t) = a t + b

(A1)

\{\begin{array}{l} a = \frac{S O C_{e x p} - S O C_{o d}}{t_{e n d} - t_{F}} \\ b = \frac{S O C_{o d} t_{e n d} - S O C_{e x p} t_{F}}{t_{e n d} - t_{F}} \end{array}

(A2)

The distance from the operating point to the forced charging boundary along the time axis is expressed by:

D (t) = \frac{S O C - b}{a} - t

(A3)

where D(t) is the distance.

The discharging coefficient k_dchar is determined by the charging time duration $t_{e n d} - t_{s t a r t}$ by:

k_{d c h a r} = \frac{S O C - b - a t}{a (t_{e n d} - t_{s t a r t})}

(A4)

Appendix B

TABLE bI Charging Behaviors and Operating Parameters of EVs in Simulation

Symbol	Quantity	EV type
Symbol	Quantity	Private EV	Bus	Taxi
n	Number	1000	100	200
Q_d	Battery capacity	35 kWh	180 kWh	45 kWh
t_start	Distribution of charging start time	N(17.5, 3.4) hour	N(20.56, 1.39) hour	N(3.86, 1.75), $N (11.98, 1.15)$ , $N (16.8, 1.17)$ , $N (21.37, 1.08)$ hour
t_end	Distribution of charging end time	N(8.9, 3.2) hour	N(6.61, 0.51) hour
t_dur	Distribution of charging time duration			N(56.28, 13.48) min
P_con	Constant charging power	7 kW	21 kW	45 kW
η_c	Charging efficiency	0.9	0.9	0.9
P_dmax	The maximum discharging power	7 kW	21 kW	45 kW
η_d	Discharging efficiency	0.9	0.9	0.9
R	Power consumption rate	0.195 kWh/km		0.195 kWh/km
M	Distribution of daily mileage	N(29.71, 3.41) km		N(50, 3.7), N(60,3.2), N(50, 3.4), N(60, 3.2) km
SOC_start	Distribution of initial SOC		N(0.4, 0.1)
SOC_exp	Expected SOC value	0.8	0.75	0.8
SOC_od	Over discharging boundary	0.2	0.2	0.2
SOC_oc	Over charging boundary	0.8	0.8	0.8

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