My research journey began with a fundamental observation: China’s fossil-fuel-dominated energy structure faces the dual challenges of environmental pollution and resource depletion, and transportation energy consumption accounts for approximately 50% of the country’s total oil consumption. To accelerate the transition toward a green and low-carbon energy structure, China has been promoting the rapid deployment of renewable energy generation equipment and electric cars to gradually replace traditional fossil-fuel-based power generation and transportation means. However, the high penetration of renewable energy sources and electric cars brings about superimposed uncertainties that pose significant challenges to the reliable and economical operation of power grids. Therefore, developing effective scheduling strategies for electric cars to ensure grid reliability and economics while improving renewable energy accommodation has become an inevitable path for the deep development of both technologies.
The premise of scheduling electric cars is to precisely forecast their uncoordinated charging loads. In my work, I first conducted a comprehensive review of domestic and international research on electric car charging load forecasting and scheduling. Then I established the theoretical foundations by introducing the trip chain model, cumulative prospect theory, the dynamic adaptive sparrow-cuckoo algorithm, demand-side response mechanisms, and vehicle-to-grid (V2G) technology.
Theoretical Foundations: Trip Chain Model and Cumulative Prospect Theory
To predict the charging load distribution of electric cars accurately, I needed to capture the travel behaviour of electric car users. The trip chain model served as my primary tool. This model describes an individual’s travel behaviour as a temporal-spatial sequence of destinations. Suppose the traveller starts from an origin location O and arrives at destination nodes a₁,a₂,…,aₙ following a time sequence t₀,t₁,…,tₙ, finally returning to terminal D, its mathematical formulation can be expressed as:
$$C=(O,D,T,A,\Theta)$$
where Θ = {θᵢ | i = 1,2,…,n} contains attributes of each destination node, including stopping duration and destination type.
For the trip chain model, I classified travel destinations into three categories: residential areas (H), working areas (W), and other areas (O). Since the transfer probability of travel destinations changes dynamically across different time periods, I constructed a time-varying Markov chain model. The state space and time-varying transition matrix can be expressed as:
$$S=\{H,W,B\}$$
$$
P_t = \begin{bmatrix}
p_{HH}^t & p_{HW}^t & p_{HO}^t \\
p_{WH}^t & p_{WW}^t & p_{WO}^t \\
p_{OH}^t & p_{OW}^t & p_{OO}^t
\end{bmatrix}
$$
I divided one day into 24 time intervals and constructed 24 distinct Markov chains so that the destination transfer behaviour of electric car users at any given time follows the corresponding chain. For example, the transition probability matrix for weekdays from 8:00 to 9:00 was:
$$
P_{8\sim9} = \begin{bmatrix}
0.00701 & 0.41024 & 0.58276 \\
0.19009 & 0.53401 & 0.27590 \\
0.37760 & 0.24246 & 0.37994
\end{bmatrix}
$$
To address the issue that existing research mainly relied on foreign survey datasets such as the NHTS (National Household Travel Survey) from the United States, I incorporated the 2023 China New Energy Vehicle Big Data Annual Report to correct the probability density functions of characteristic quantities. This multi-source data fusion approach can more accurately reflect the actual travel behaviour patterns of electric car users in China.
Let f_d(t) denote the probability density function fitted from NHTS data. After the correction based on the domestic report’s interval statistics, the segmented probability density function becomes:
$$g(t)=C(t)\cdot f_d(t)$$
Here, C(t) is the correction factor established for each interval. For example, table 1 shows the correction factors for a single trip duration.
| Duration interval (h) | (0,0.5] | (0.5,1] | (1,1.5] | (1.5,2] | (2,2.5] |
|---|---|---|---|---|---|
| Type 1 trip | 0.8259 | 1.2508 | 1.8177 | 1.0327 | 0.3181 |
| Type 2 trip | 0.7161 | 1.6945 | 2.5946 | 1.4407 | 0.4023 |
| Type 3 trip | 0.7938 | 1.3514 | 1.9650 | 1.0939 | 0.3204 |
Charging Decision Model Based on Cumulative Prospect Theory
In traditional electric car charging load forecasting, users are often assumed to be fully rational economic agents. However, actual decision-making processes are influenced by various subjective psychological factors. To capture the “bounded rationality” of electric car users in their charging decisions, I employed cumulative prospect theory (CPT) to construct a charging decision model. The model components are as follows.
Value function: The value function captures the emotional asymmetry between perceived gains and losses.
$$v(c)=\begin{cases}
(c-c_0)^\alpha & c \ge c_0 \\
-\lambda(c_0-c)^\beta & c < c_0
\end{cases}$$
where c₀ is the reference point representing the cost of charging at home to the target SOC, α=0.88, β=0.92, and λ=2.25 is the loss aversion coefficient.
Weighting function: The probability weighting functions for gains and losses were:
$$w^{+}(p)=\frac{p^{\gamma}}{(p^{\gamma}+(1-p)^{\gamma})^{1/\gamma}}$$
$$w^{-}(p)=\frac{p^{\delta}}{(p^{\delta}+(1-p)^{\delta})^{1/\delta}}$$
with typical values γ=0.61 and δ=0.69. These functions capture the tendency to overweight small probabilities and underweight large probabilities.
Cumulative decision weights: To avoid violation of first-order stochastic dominance, cumulative rather than individual probability weighting was adopted:
$$\pi_i^{+}=w^{+}\left(\sum_{c=i}^{k}p_c\right)-w^{+}\left(\sum_{c=i+1}^{k}p_c\right)$$
$$\pi_j^{-}=w^{-}\left(\sum_{c=-m}^{j}p_c\right)-w^{-}\left(\sum_{c=-m}^{j-1}p_c\right)$$
Overall subjective value: Finally, the total subjective value of each decision option is given by:
$$V=\sum_{i=1}^{k}\pi_i^{+}v(x_i)+\sum_{j=-m}^{-1}\pi_j^{-}v(x_j)$$
In my charging decision model, I constructed a three-part cost function for electric car users: the cost of temporary charging, the psychological cost caused by range anxiety, and the travel cost of alternative transportation if the battery runs out. The psychological cost is particularly important — when the battery level falls below 20%, electric car users experience growing anxiety. I defined this cost as:
$$C_{psych}=p_{tow}\cdot\frac{r_{crit}-r_{rem}}{r_{crit}}$$
where r_rem is the remaining driving range after arriving at the next destination, r_crit is the critical range below which anxiety sets in, and p_tow represents the price of a towing service used to calibrate the maximum psychological cost.
The charging decision probability was computed using a Logit-type formula:
$$p_{ch}=\frac{1}{1+e^{-(V_{unch}-V_{ch})}}$$
I introduced a threshold probability that considers the incompleteness of the daily itinerary:
$$p_{ts}=\frac{1}{1+e^{r_{rem}/L_d}}$$
Only when p_ch ≥ p_ts did the electric car user decide to charge at the current location.
I validated this prediction model using Monte Carlo simulation for a fleet of 1000 electric cars. From the predicted temporal-spatial charging load, I found the residential area load peaked around 17:30 with 4194.35 kW, while the working area had three distinct peaks reflecting the typical commute. The other area load showed a single broader peak at 9:15 with 1496.51 kW. The overall load profile demonstrated a clear superposition of the three region loads, which validated that my prediction model accurately captures the travel patterns of electric car users during working days.
Dynamic Adaptive Sparrow-Cuckoo Algorithm
To solve the complex optimization models with high-dimensional decision variables and nonlinear constraints, I proposed a novel artificial intelligence algorithm named the dynamic adaptive sparrow-cuckoo algorithm, which integrates the advantages of the sparrow search algorithm and the cuckoo search algorithm. Traditional swarm intelligence algorithms often converge slowly or get trapped in local optima when faced with high-dimensional nonlinear optimization problems, so I designed several enhancements.
Initial population based on high-dimensional chaotic mapping: I employed the Sine-Tent-Cosine high-dimensional chaotic mapping to generate the initial population:
$$
x_{i+1}^{j}=
\begin{cases}
\cos\left(\pi(a x_i^{j} + (1-a)\sin(\pi x_i^{j}) – 0.5)\right) & x_i^{j} < 0.5 \\
\cos\left(\pi(a x_i^{j} + (1-a)\sin(\pi x_i^{j}) – 0.5) – 1\right) & x_i^{j} \ge 0.5
\end{cases}
$$
Dynamic variable-step Lévy flight strategy: Instead of using a fixed step factor, I made the step size dynamically adaptive to the fitness values of individual solutions:
$$x_i^{t+1}=x_i^{t}+\delta_i^{t}\otimes L(\phi)$$
$$
\delta_i^{t}=
\begin{cases}
\delta_{min}+(\delta_{max}-\delta_{min})\dfrac{f(x_i^{t})-f_{min}^{t}}{f_{ave}^{t}-f_{min}^{t}} & f(x_i^{t}) \neq f_{ave}^{t} \\
\delta_{max} & f(x_i^{t})=f_{ave}^{t}
\end{cases}
$$
Here, δ_max=0.9 and δ_min=0.4 represent the maximum and minimum inertia coefficients, and f_ave^t and f_min^t are the average and minimum fitness values at iteration t. This strategy allows the algorithm to explore the solution space more broadly in early iterations and fine-tune solutions in later iterations.
Dynamic discovery probability: The fixed probability of host birds discovering cuckoo eggs was improved into a time-varying parameter:
$$P_a=P_{a,min}+(P_{a,max}-P_{a,min})\cdot r\cdot\mu\cdot\tau(1,2)$$
Enhanced host nest update: The abandoned host nests were updated by integrating the discoverer position update strategy from the sparrow algorithm with the original cuckoo search mechanism:
$$
x_{i,j}^{t+1}=
\begin{cases}
x_{rand}^{t} \cdot e^{\left(\frac{f(x_i^t)-f_{ave}^t}{x_{rand}^{t}-x_{i,j}^{t}}\right)} + Q \cdot f(x_i^t) & f(x_i^t) \ge f_{mid}^t \\
x_{i,j}^{t} + Q & f(x_i^t) < f_{mid}^t
\end{cases}
$$
The convergence speed comparison results of these algorithms are shown in table 2.
| Algorithm | Dynamic Adaptive Sparrow-Cuckoo | Traditional Sparrow Algorithm | Traditional Cuckoo Algorithm |
|---|---|---|---|
| Solving time (s) | 1286 | 1875 | 1832 |
Two-Stage Optimal Scheduling Model for Electric Cars
I developed a two-stage electric car scheduling model to take full advantage of the scheduling flexibility of electric cars at different time scales.
Day-Ahead Scheduling Model
In the day-ahead stage, I designed a dynamic time-of-use charging tariff for electric cars, based on the predicted uncoordinated charging load curves. The tariff was updated every 15 minutes:
$$p_{ch,t}=p_{ch,base}+\alpha\left(p_{ch,dy}-\frac{P_{EV,t}}{\sum_{t=1}^{96}P_{EV,t}}\right)$$
where p_ch,base is the benchmark electricity price, p_ch,dy is the dynamic adjustment price constant (50 yuan/kWh), and α is the dynamic adjustment weight (0.5). Since the EV load is higher during peak hours, the dynamic tariff approach assigns higher charging prices accordingly, guiding electric car users to shift their charging demands to lower-load periods.
Intraday Scheduling Model with V2G Response
In the intraday stage, I further constructed a dynamic real-time charging/discharging price model updated every 15 minutes:
$$p_{ch,t+1}^{inday}=p_{ch,base}^{inday}+\lambda\left(p_{ch,dy}^{inday}-\frac{P_{EV,t}^{inday}}{P_{EV,t}}\right)$$
$$p_{dis,t+1}^{inday}=p_{dis,base}^{inday}+\mu\left(p_{dis,dy}^{inday}-\frac{P_{EV,t}^{inday}}{P_{EV,t}}\right)$$
A crucial innovation was my accounting for the V2G response rate of electric car users. Many economic-oriented scheduling strategies over-exploit batteries, increasing degradation and causing users to opt out of V2G. I evaluated the response rate through:
Economic benefits of V2G for electric car users:
$$U_i=\frac{C_i^{dis}-C_i^{ch}-C_i^{wastage}}{C_i^{dis}}$$
Battery degradation cost:
$$C_i^{wastage}=\sum_{t} K_{unit}\cdot x_{i,t}\cdot S_{i,t}^{dis}$$
$$K_{unit}=\frac{C_{bat}}{E_{cap}}\cdot\frac{\varphi_1}{2^{\varphi_2+1}\cdot DoD_{i,t}}$$
Probability of a residential electric car participating in V2G:
$$P_i^{V2G}=\frac{e^{U_i}}{e^{U_i}+e^{p_{i,park}}}$$
where the state-of-charge effect factor is:
$$
p_{i,park}=
\begin{cases}
0 & E_{i,t}-E_i^{dis} \leq E_i^{need} \\
\dfrac{E_{i,t}-E_i^{dis}-E_i^{need}}{E_i^{need}-E_i^{need}} & E_{i,t}-E_i^{dis} > E_i^{need}
\end{cases}
$$
The intraday real-time scheduling strategy had two distinguishing features: short-period state updates by refreshing EV information every 15 minutes while maintaining a long-horizon optimization covering the maximum remaining schedulable time, and closed-loop error correction that used the actual power outputs of grid components sampled from the previous period to correct accumulated forecast errors in the next scheduling period.
The entire scheduling model aimed to maximize microgrid operational net revenue:
$$F=\sum_{s=1}^{n_s}p_s\sum_{t=1}^{T}\left(B_{S,t,s}^{sell}-C_{MT,t,s}-C_{buy,t,s}-C_{M,t,s}-C_{cut,t,s}\right)$$
Simulation Results
I constructed a simulation case study based on data from a demonstration microgrid project. The day-ahead dispatch results comparing the two strategies are shown in table 3.
| Strategy | Operating Cost (yuan) | Revenue (yuan) | Net Revenue (yuan) | Curtailment Rate |
|---|---|---|---|---|
| Strategy 1 (traditional TOU) | 3482.16 | 15876.05 | 12393.88 | 10.83% |
| Strategy 2 (dynamic TOU) | 2396.27 | 15609.39 | 13213.12 | 0.00% |
For the islanded operation state, similar improvements in economic performance and reliability were observed. Under strategy 2, the total curtailed load was 309.42 kW compared to 4988.89 kW under strategy 1, demonstrating the effectiveness of the proposed method in enhancing microgrid reliability under islanding scenarios.
For the intraday scheduling, four strategies were compared. Strategy 3 (considering V2G response rate) achieved a V2G response rate of 92.94%, much higher than strategy 2’s 82.71%. Strategy 4, which increased the EV number to 500 under islanded operation, still maintained a response rate of 90.14% and avoided load shedding entirely. This demonstrated that my proposed scheduling model could effectively enhance the hosting capacity of the microgrid for electric cars and improve power supply reliability. The intraday scheduling results for different strategies are summarized in table 4.
| Strategy | V2G Response Rate | Purchased Power from Grid (kW) | Net Revenue Improvement | Load Curtailment |
|---|---|---|---|---|
| Strategy 1 (no V2G) | — | high | baseline | present |
| Strategy 2 (unconstrained V2G) | 82.71% | 82.22 | moderate | none |
| Strategy 3 (response-constrained V2G) | 92.94% | 31.27 | higher | none |
| Strategy 4 (islanded, 500 EVs) | 90.14% | N/A | sustainable | none |
These findings collectively validate the feasibility and superiority of the proposed electric cars scheduling model.
In conclusion, my research established a complete chain from accurate spatiotemporal charging load forecasting to effective two-stage scheduling. Key contributions of this work are as follows. First, I developed a charging load forecasting model that integrates time-varying Markov chains and multi-source data fitting with cumulative prospect theory to capture the bounded rationality of electric car drivers. By considering the psychological cost of range anxiety and non-linear probability weighting, the model produces more realistic spatiotemporal charging load predictions. Second, I addressed the shortcomings of static electricity pricing by proposing dynamic tariffs in both day-ahead and intraday time frames, guiding electric car users to participate in demand-side response and V2G services more effectively. Third, I constructed a comprehensive V2G response evaluation model that quantifies user willingness based on economic benefits and battery degradation, and integrated this evaluation into the scheduling process. Finally, I introduced a dynamic adaptive sparrow-cuckoo search algorithm for efficient global optimization, which demonstrated substantially faster convergence compared with conventional algorithms in the simulation study. The proposed framework enables microgrids to achieve greater economic performance, reduce wind and solar curtailment, and enhance the ability to host large-scale electric cars while keeping user participation rates at sustainable levels.
There are several directions for future research. The behaviour patterns of electric car users should be further refined using Chinese user travel big data based on artificial intelligence methods. Integrating the trip chain model with an actual road network model would produce even more accurate predictions of electric car driving trajectories. Additionally, extending the scheduling framework to consider uncertainty in user responses to real-time pricing signals and multi-microgrid coordination could unlock further value from both demand-side resources and electric car batteries. By advancing these areas, China can better realize the vision of simultaneously transporting people and storing clean energy through the same connected set of electric cars.
All the above findings and strategies were fully verified by numerical case studies based on a realistic microgrid architecture. The two-stage scheduling model was also validated under both grid-connected and islanded operation modes, highlighting the robustness of my approach. It is my sincere hope that the achievements of this thesis can serve as a meaningful reference for the future development of electric car forecasting and scheduling methods.