Revolutionizing photovoltaic consumption and electric vehicle charging: A novel approach for residential distribution systems

1 INTRODUCTION

Amidst the ongoing growth of global economies and cultures, the challenges of environmental degradation and energy deficits are becoming increasingly acute [1]. According to a forecast by the international energy agency (IEA), a potential shortfall in global oil supplies is anticipated by 2040, alongside a projected escalation in carbon dioxide emissions to 40 billion tons annually [2]. The advancement of electric vehicles (EVs) is heralded as a pivotal technological strategy to augment the efficiency of renewable energy utilization and mitigate carbon emissions [3]. To this end, several national governments have implemented policies to facilitate the proliferation of EV technology [4-7]. While EVs have demonstrated zero emissions in operational settings, the electricity powering these vehicles originates from primary energy sources at the generation stage, thus precluding true zero emissions. Despite rigorous regulations to curb emissions at the generation phase, the substantial demand for EV charging contributes to significant carbon emissions [8].

The adoption of distributed renewable energy generation represents a formidable measure to curtail carbon emissions from primary energy sources at their origin and has been actively endorsed in recent times [9-12]. In regions blessed with ample sunlight, the diminishing costs of components for photovoltaic (PV) power systems have facilitated the widespread deployment of small-capacity PV systems in residential settings [13, 14]. Nonetheless, PV output typically peaks at midday, which does not align with the peak demand periods in residential areas, and the unregulated reverse flow of power to the grid can precipitate stability concerns within the electrical system [13, 15]. As elucidated in the preceding analysis, employing EVs as a sink for distributed PV output not only addresses the consumption challenges of distributed PV but also enhances the proportion of EVs charged with ‘green electricity’ [16]. This approach is significantly important in advancing global initiatives for energy conservation and emission reduction.

Many scholars have conducted extensive research on the collaborative optimization problem between PV and EVs in the park. However, currently, the main focus is on optimizing the operation of PV charging stations [17-20]. The literature [21] evaluates the energy, economic, and environmental performance of a building in Canberra, Australia, that integrates an EV charging station and PV system. The results indicate that the building integrating EV charging stations and PV systems can not only meet the charging needs of EVs but also save costs for charging station operators and ensure their own economy. Study [22] optimized the ordered charging problem of commercial district optical storage charging stations from the perspective of charging stations, analysed the actual data of commercial district charging stations, and proposed a layered dynamic daily time pricing strategy. This strategy was optimized using an improved non-dominated sorting genetic algorithm 2 (NSGA2), and the results showed that it could improve the profit of charging stations and achieve grid load regulation and valley filling. In research [23, 24], they integrate different PV access scenarios and implement scheduling for EVs with the goal of minimizing daily operating costs in industrial parks. The above literature has done a lot of work in optimizing the operating costs, energy storage configuration and ensuring the safe operation of the power grid of PV charging stations. However, it lacks consideration for the carbon reduction effect reflected by EVs while consuming PVs. Therefore, further research is needed.

In addition, EV charging has great randomness. To guide users to charge in an orderly manner, current research mainly adopts demand response strategies [25]. In recent research [26, 27], the researchers have designed peak-to-valley time of use electricity prices to guide user charging behaviour, using price elasticity to characterize the degree of user response to electricity price fluctuations. The case results show that the proposed solution has a certain effect on grid stability and economy and also promotes the consumption of renewable energy. In [28], an optimization model was established based on the time-of-use pricing mechanism, with the goal of minimizing the variance of grid load and minimizing user charging costs. An improved hybrid algorithm is proposed by combining the particle swarm optimization (PSO) algorithm and gravitational search algorithm (GSA) for optimizing the allocation of charging and discharging power of EVs. The case results show that implementing an ordered charging and discharging strategy can significantly reduce the charging cost of users and the load changes of the power grid, thereby improving the operational stability of the power grid and the economic benefits of users. In [28], it comprehensively considers the overall charging demand, discharge potential, grid electricity prices, aggregators, and user interests of EVs. A dynamic electricity price based on a long short-term memory network (LSTM) was established, and an improved linear programming algorithm (ILP) was used to solve the optimization problem of EV charging and discharging, ultimately obtaining the optimal electricity price and EV charging and discharging schedule. The above research focuses on the analysis of collaborative scheduling problems between PV and EVs within the park and has achieved certain application effects. However, in the process of adopting demand response methods to guide user charging behaviour, there is no emphasis on the effective combination of EVs and PV power generation systems, resulting in suboptimal economic efficiency of the system.

The manuscript is structured methodically, beginning with Section 2, where we delve into the methodology, covering EV load modelling and the development of optimal ‘green’ charging strategies. Following this, Section 3 presents the model's structure, detailing the objective functions and constraints. The impact of the model is thoroughly examined in Section 4, through results and discussions. Finally, the paper concludes in Section 5, summarizing the key findings, contributions to the field, and outlining directions for future research.

2 MATHEMATICAL MODELLING AND ANALYSIS

2.1 Modelling of EV charging load

A statistical approach can be adopted to formulate the EV charging load model that aligns with users’ travel patterns. By randomly extracting specific charging data from EVs and designing a charging statistical model based on user travel behaviours, individual load curves for each EV can be generated. Summing up these individual load curves then yields the aggregated charging load curve for all EVs [29, 30]. The charging load experienced by EVs is a product of a multitude of intricate factors, including the initial state of charge (SOC) upon commencement of charging, the designated starting charging time, and the duration of the charging process. Notably, the SOC at the onset of EV charging is closely linked to the vehicle's prior energy consumption while driving. If we assume a proportional relationship between the driving energy consumption of EVs and their travel distance, the SOC at the initiation of charging can also be tied to their travel distance. Consequently, this paper employs the Monte Carlo method, which accounts for factors such as daily travel distance, initial charging timing, and charging duration of EVs. Through this methodology, the travel patterns of EVs are effectively modelled, culminating in the construction of an accurate EV charging load model.

2.1.1 Daily mileage of EVs

Considering how far EVs go each day, it becomes evident that users primarily utilize these vehicles to fulfil their weekday commuting requirements. This usage pattern is characterized by strong regularity in driving routines and a certain level of variability in daily mileage. Drawing insights from data provided by the United States Transportation Administration [31], the distribution of daily mileage for EVs conforms to the log-normal distribution function, which is mathematically represented as [32]:

$$f_l=\frac{1}{l·{\sigma }_l\sqrt{2\pi }}\exp \left[-\frac{{\left(\ln l-{\mu }_l\right)}^2}{2{\sigma }_l^2}\right]$$(1)

$${\mu }_l=3.2$$(2)

$${\sigma }_l=0.88$$(3)

where l is the EVs’ daily mileage, µ_l is the expected value of the logarithmic lnl of daily mileage l. σ_l is the standard deviation of the logarithmic lnl of daily mileage l.

2.1.2 Starting charging time of EVs

In a scenario where an EV owner initiates charging immediately upon reaching their destination, the time of arrival at the destination effectively becomes the starting charging time. The arrival time distribution for EVs adheres to a normal distribution pattern [33]. Consequently, the probability density function describing the distribution of the initial charging times for EVs also conforms to a normal distribution. This relationship is mathematically represented by (4):

$$f_{qs,t}=\{\begin{array}{c}{\displaystyle \frac{1}{{\sigma }_t\sqrt{2\pi }}}\exp \left[-{\displaystyle \frac{{\left(t+24-{\mu }_t\right)}^2}{2{\sigma }_t^2}}\right],0<t\le \left({\mu }_t-12\right)\\ {\displaystyle \frac{1}{{\sigma }_t\sqrt{2\pi }}}\exp \left[-{\displaystyle \frac{{\left(t-{\mu }_t\right)}^2}{2{\sigma }_t^2}}\right],\left({\mu }_t-12\right)<t\le 24\end{array}$$(4)

$${\mu }_t=17.6$$(5)

$${\sigma }_t=3.4$$(6)

where t represents the EV charging starting time, and µ_t is the expected value of t. σ_t is the standard deviation of t.

2.1.3 Charging duration of EVs

Taking into account that the SOC of all EVs is presumed to be 100% upon the culmination of charging and recognizing the direct correlation between the energy consumed by EVs during driving and their daily mileage, it becomes possible to illustrate the charging duration for these vehicles using the subsequent equation:

$$T_j=\frac{l_j{\omega }_l}{P_{\mathrm{ev},j}}$$(7)

where T_j is the charging duration of the j-th EV. l_j is the daily mileage of the j-th EV. ω_l is the average energy consumption per kilometre of an EV. P_ev,j is the charging power of the j-th EV.

2.1.4 Analysis of EV charging demand

The study assumes a quantity of 1500 EVs and conducts a charging behaviour simulation. When EVs adopt a disordered charging mode, they start charging at constant power after the last return journey until their state of charge reaches 100%, during which time users are not affected by electricity price incentives.

EVs adopt a slow charging method, with a charging power of 7 kW. The average energy consumption per kilometre of EVs is 0.5 kWh/km. Due to individual independence, Monte Carlo simulation is used, as shown in Figure 1.

The daily grid load of a single EV is obtained from the starting charging time and charging duration, and then the charging load for each time period is accumulated according to (8) to obtain the daily load curve of the EV, as shown in Figure 2.

$$P_{\mathrm{ev},t}=\sum _{j=1}^J{\lambda }_{j,t}{P}_{\mathrm{ev},j}$$(8)

$${\lambda }_{j,t}=\{\begin{array}{c}0\begin{array}{cc}& t\notin \left[t_{\mathrm{qs},j},t_{qs,j}+T_j\right]\end{array}\\ 1\begin{array}{cc}& t\in \left[t_{qs,j},t_{qs,j}+T_j\right]\end{array}\end{array}$$(9)

where P_ev,t is the EV charging load at time t. J is the total number of EVs. λ_j,t is the correlation coefficient of whether the j-th EV charges at time t. If the j-th EV is charging at time t, its value is 1. Otherwise, its value is 0. t_qs,j is the starting charging time of the j-th EV.

2.2 Analysis of the optimal charging approach for EVs with a green electricity charging method

The traditional charging method for EVs is to define the charging electricity price for each time period based on the fluctuation of daily load, which is called the time of use electricity price, and add a certain amount on top of it to achieve the purpose of benefiting operators [34, 35]. However, with the continuous integration of renewable energy sources such as PVs and wind power into the grid, the drawbacks of such billing methods have gradually become apparent [36]. The pattern between PV output and residential electricity consumption is exactly opposite. The charging load of EVs reaches its peak in the evening, but at this time, PV output is in a low valley. At noon, the PV output reaches its peak, while the charging load of EVs is relatively average. Some studies have proposed dynamic time-of-use pricing strategies to guide the orderly charging of EVs in order to reduce the system load peak-to-valley difference. Although this strategy can effectively guide the charging and discharging behaviour of EVs, it fails to consider the arrival situation of EVs within the planning area, refine the charging model of EVs, and cannot fully utilize their potential for demand response, nor can it maximize the absorption of PV output. Therefore, in order to fully utilize renewable energy and reduce the use of primary energy, this article sets up a ‘green electricity’ billing method based on PV output to schedule the load of EVs. Through the ‘green electricity’ billing method, a real-time dynamic matching relationship between user EV charging and PV output is established, and an orderly charging model for EVs is constructed that takes into account the distribution of user arrival times, assisting in maximizing the consumption of renewable energy output.

The fundamental tenets of the ‘green electricity’ charging method encompass two key aspects. First, it establishes a symbiotic relationship between EVs and PVs, ensuring a harmonious alignment between EV charging loads and outputs. Second, the charging criterion for ‘green electricity’ must conform to the stipulated regulations of national electricity pricing. Assuming that the entire PV power generation system output is connected to the grid, the EV charging price curve is fitted based on the PV power generation system's output, as depicted in (10).

$$c_{\mathrm{ev},t}=-\frac{c_2-c_1}{P_{\mathrm{PV},\max }}{P}_{\mathrm{PV},t}+c_2$$(10)

where c_ev,t is the charging price of EVs. P_PV,t is the PV output status at time t. P_{PV_max} is the peak value of PV output in a day. c₁ is the valley time electricity price. c₂ is the peak time electricity price.

Considering the strong real-time nature of the charging pricing described in (10), which is not suitable as a charging standard, this article takes (10) as a reference and sets up a three-layer pricing model based on the pricing structure/guidelines of public utilities. This model establishes a real-time dynamic matching relationship between EV users and PVs and then constructs an orderly charging model for EVs. The pricing model is shown in (11).

$$\{\begin{array}{cc}{c}_x=\max \{c_{\mathrm{ev},t}\}\hfill & t\in x\hfill \\ c_y=\max \{c_{\mathrm{ev},t}\}\hfill & t\in y\hfill \\ c_z=\max \left\{c_{\mathrm{ev},t}\right\}\hfill & t\in z\hfill \end{array}$$(11)

In (11), c_x, c_y, and c_z represent the high, mid-range, and low-range electricity prices when charging EVs, respectively. In this context, the variables x, y, and z distinctly signify the charging intervals associated with the three distinct tiers of electricity pricing. These tiers encompass high-end periods, mid-range intervals, and low-range spans.

Through the ‘green electricity’ charging method, EV users establish a dynamic real-time alignment with PV systems. This method facilitates a systematic and orderly charging approach, aided by the three-tiered charging price framework. When configuring an orderly EV charging model, this study concentrates on situations contingent upon the presence of PV output, demarcating based on this criterion. When PV output is available during a specific time of day, the EV charging method pivots around segmented electricity prices. Conversely, when PV output is absent at a certain point, the EV charging protocol primarily adheres to time-of-use electricity prices. Consequently, an organized EV charging model is delineated as follows:

1. If there is no PV output upon EV arrival, the system must first ascertain the current time-of-use electricity price period. Otherwise, proceed to step (4).

2. When there's no PV output upon the EV's arrival and the electricity price is at its lowest, immediate charging of the EV should commence.

3. In the absence of PV output at the time of EV arrival, and if the time aligns with the standard or peak electricity price period, the system should ascertain the existence of a subsequent low-price charging period. If such a period exists, users must wait until the low-price interval to initiate charging. If not, they should delay charging until the low-price period of the following day, as also stated in [37].

4. If there is PV output upon EV arrival, it should be assessed within which segmented electricity price period the arrival time falls.

5. If PV output coincides with the EV's arrival and the time falls within a low-range charging period, the EV should be immediately charged.

6. If PV output aligns with the EV's arrival and the time corresponds to a mid-range charging period, the system must assess whether a subsequent low-range charging period follows this interval. If a low-range period exists, users should wait until that interval for charging. If not, they should defer charging to the low-range period of the ensuing day.

7. If the PV output matches the EV's arrival time and corresponds to a high-range charging period, the system should continue analysing whether a mid-range charging period follows the high-range interval. If such a mid-range period exists, users should delay charging until that time. Otherwise, they should plan to charge for the low-range period on the following day.

Based on the charging steps outlined above, a sequential charging framework for EVs is devised using the ‘green electricity’ charging approach, as depicted in Figure 3.

3 METHODOLOGY AND DESIGNING

This article primarily addresses an energy trading system encompassing PV power generation, public power networks, energy storage setups, EV charging users, and residential energy management platforms. Following PV power generation and grid integration, electricity is distributed to users via the public power system. The PV and energy storage systems are overseen by the load aggregator, with the energy storage unit operating during instances of excess solar energy or when PV output is fully utilized. EV charging users serve as the ultimate beneficiaries of the load aggregator's services. These users are focused on minimizing their charging expenses and adjusting their charging schedules in response to the pricing strategies set by load aggregators. This approach not only reduces individual charging costs but also encourages the consumption of PV-generated electricity.