A new multi-objective scheduling framework is drawing attention for its ability to coordinate electric vehicle charging and discharging behavior while balancing two competing goals: reducing grid load fluctuation and increasing electric vehicle arbitrage income. The research focuses on a rolling, forward-looking scheduling mechanism that combines a multi-objective evolutionary algorithm based on decomposition, a finite discrete action set, and a price-driven auction method. The proposed approach is designed for vehicle-to-grid applications in which electric vehicle owners can respond to time-of-use tariffs by charging during low-price periods and discharging during high-price periods.
- Grid Pressure and the Electric Vehicle Challenge
The rapid growth of electric vehicle adoption has created new opportunities and new stresses for power systems. Electric vehicle batteries can act as distributed energy storage, and vehicle-to-grid technology allows electric vehicles to support peak shaving, valley filling, demand response, and price-driven scheduling. However, the same growth also introduces risk. Uncoordinated electric vehicle charging and discharging can increase load volatility, widen peak-valley differences, and create new load spikes when many electric vehicle users respond to the same price signal at the same time.
The research addresses this challenge by coordinating all potential electric vehicle charging and discharging actions within an optimization period. The aim is not to force electric vehicle owners into a single behavior pattern, but to produce a set of forward-looking scheduling plans that reveal clear trade-offs between grid-side stability and user-side economic benefit. This is important because electric vehicle owners are more likely to participate in scheduling when they can earn arbitrage income, while grid operators need smoother load curves and reliable operation.
The proposed framework is built around a decision center that collects forecast data, including basic load forecasts and electricity price forecasts, divides the optimization horizon into peak, flat, and valley periods, and sets charging prices and discharge subsidy prices for each period. On that basis, the decision center calculates the total remaining capacity available to support electric vehicle charging demand and the capacity gap between generation capability and expected load demand that could be filled by electric vehicle discharging.
A key concern is computational and communication cost. If every electric vehicle is treated as a continuous variable in every time interval, the decision space becomes extremely large. For a fleet of 50 electric vehicles over 24 hours, the charging and discharging power combination reaches 1,200 dimensions. Continuous optimization in such a space can become difficult to solve within a practical time frame. The research therefore introduces a finite discrete action set so that each electric vehicle chooses from a limited set of charging and discharging actions rather than an unlimited continuous range.
- Core Objectives: Load Smoothing and Electric Vehicle Arbitrage
The scheduling model is formulated as a multi-objective optimization problem with two main objectives. The first objective is to minimize grid load fluctuation over the optimization period. The second objective is to maximize electric vehicle arbitrage income. These objectives are related but not identical. A schedule that strongly favors load smoothing may reduce electric vehicle arbitrage opportunities, while a schedule that strongly favors arbitrage may allow larger load fluctuations.
The load fluctuation objective is expressed as the squared deviation of the net load after electric vehicle charging and discharging from the average load over the optimization period. Lower values indicate a smoother load curve. The arbitrage objective is based on the difference between charging and discharging behavior across time slices. Within each time slice, charging and discharging revenue are treated equally, so arbitrage mainly depends on price differences between different time slices rather than on differences within the same time slice.
For each time slice, if the sum of electric vehicle charging and discharging power is negative, the slice is treated as a charging slice. If the sum is positive, the slice is treated as a discharging slice. If the sum is zero, the slice has no arbitrage income because charging cost and discharge subsidy cancel out. The arbitrage objective is multiplied by minus one so that it can be handled as a minimization objective within the multi-objective optimization process.
The model also includes constraints. Charging and discharging power must remain within minimum and maximum limits. Battery state of charge must remain within a safe range. In the reported simulation, the state of charge upper and lower bounds are set to 0.9 and 0.2, respectively. The battery capacity is 43 kWh, and the maximum charging or discharging power is 7 kW. Private electric vehicle charging power is relatively small, so distribution line capacity limits are not considered in the reported model. The research also assumes that electric vehicles are available for scheduling for 24 hours, while idle states are still represented in the scheduling process.
- MOEA/D-EV: A Decomposition-Based Scheduling Algorithm
The proposed algorithm is named MOEA/D-EV. It is based on the multi-objective evolutionary algorithm based on decomposition, commonly known as MOEA/D. MOEA/D decomposes a multi-objective problem into a set of scalar subproblems and uses weight vectors to guide the search toward different regions of the Pareto front. This structure is useful for engineering decision-making because each solution in the population is associated with a clear trade-off preference.
The algorithm defines a decision vector that represents the charging and discharging power of each electric vehicle in each time slice. The full decision vector covers all electric vehicles across the optimization period. The algorithm initializes a population based on the battery state of charge range and the finite discrete action set. It then calls the auction algorithm to adjust each electric vehicle candidate’s charging and discharging action selection, generates a feasible scheduling plan, calculates fitness values for the population, and selects an ideal reference point according to the objective function set.
During each iteration, the algorithm performs crossover and mutation on a candidate to generate an offspring candidate. The auction algorithm is then called again to repair or adjust the offspring so that it remains feasible under the state of charge and action set constraints. The algorithm calculates the offspring fitness, updates the ideal point, and applies the Chebyshev function to update the current candidate. The process continues until the maximum number of iterations is reached. The output is a Pareto set and a Pareto front that provide different preference-based scheduling plans.
The reported control parameters include a population size of 200 and a maximum iteration count of 1,000. The algorithm returns a set of optimal forward-looking charging and discharging schedules under different weight preferences. This is important for decision-makers because it allows them to choose a plan that reflects either a stronger emphasis on grid load smoothing, a stronger emphasis on electric vehicle arbitrage income, or a balanced position between the two.
- Finite Discrete Action Set Strategy for Electric Vehicle Behavior
The finite discrete action set strategy is one of the central design choices in the proposed framework. Instead of allowing each electric vehicle to choose any continuous charging or discharging power value, the strategy maps electric vehicle behavior to a limited set of discrete actions. The reported action set uses three charging rates and three discharging rates: slow, normal, and fast. In unit terms, the charging actions are represented as 1c, 3c, and 7c, while the discharging actions are represented as 1d, 3d, and 7d. The minimum standardized charging power is 1 kW, represented by c with a value of -1 kW, and the minimum standardized discharging power is 1 kW, represented by d with a value of 1 kW.
The action set is linked to battery state of charge intervals. The reported intervals are [0.2, 0.3], (0.3, 0.5], (0.5, 0.6], (0.6, 0.8], and (0.8, 0.9]. At lower state of charge, discharging choices are limited to protect the battery. At higher state of charge, charging choices are limited to avoid overcharging. For example, when state of charge is in [0.2, 0.3], the available discharging action is {d}, while the available charging actions are {7c, 3c, c}. When state of charge is in (0.8, 0.9], the available discharging actions are {7d, 3d, d}, while the available charging action is {c}.
The action set is also linked to time-of-use price intervals. The research divides price levels into six intervals labeled D1, D2, D3, C1, C2, and C3. D1, D2, and D3 are discharge-side intervals, while C1, C2, and C3 are charge-side intervals. In the highest discharge interval D3, an electric vehicle is encouraged to choose the highest discharge rate, such as 7d, to respond quickly to a load demand gap and increase arbitrage income. In the lowest charge interval C3, an electric vehicle is encouraged to choose the highest charge rate, such as 7c, to absorb low-price electricity and support valley filling.
The finite discrete action set strategy has three reported advantages. First, it reduces the decision space from an infinite continuous space to a finite set of actions, which lowers computational complexity and supports real-time scheduling. Second, it protects battery life by preventing electric vehicle batteries from operating in extreme state of charge ranges and by defining clear state evolution paths. Third, it supports price-driven scheduling by matching charging and discharging actions to time-of-use price intervals, enabling a low-buy-high-sell strategy while helping to smooth the grid load curve.
- Price-Driven Auction Algorithm for Immediate Coordination
The proposed auction algorithm is designed to coordinate electric vehicle charging and discharging behavior in response to time-of-use tariffs. In the auction model, peak-shaving and valley-filling tasks are treated as tasks on the seller side, while electric vehicle owners are treated as buyers. The goal is to assign these tasks to electric vehicles in a way that supports microgrid-side objectives such as reducing peak demand, improving energy efficiency, and maximizing grid stability, while also optimizing the arbitrage income of the active electric vehicle group.
The auction process has three main steps. First, the decision center collects peak-shaving and valley-filling tasks from the microgrid and collects electric vehicle bids based on the finite discrete action set. Peak-shaving tasks correspond to electric vehicle discharging, while valley-filling tasks correspond to electric vehicle charging. The bids reflect each electric vehicle’s willingness and capability to participate in charging or discharging at different price periods, based on the time-of-use tariff and the current battery state of charge.
Second, the algorithm allocates tasks according to time-of-use prices and grid demand. During high-price periods such as D3, the algorithm prioritizes discharging tasks for electric vehicles with higher bids so that the grid load gap can be addressed quickly. During low-price periods such as C3, the algorithm prioritizes charging tasks for electric vehicles with lower bids so that low-price electricity can be absorbed and user costs can be reduced. This dynamic allocation mechanism allows the algorithm to respond to grid needs while supporting electric vehicle arbitrage.
Third, the algorithm updates bids and iterates. After the initial allocation, the algorithm sums all electric vehicle bids to obtain total charging and discharging power, calculates the gap between that total and microgrid demand, and updates bids iteratively until the gap is minimized or a termination condition is met. The optimized bid vector becomes the charging and discharging power allocation plan for the next time slice. This process supports immediate coordination and allows the auction algorithm to work together with MOEA/D-EV during population initialization and offspring repair.
- Simulation Design and Reported Time-of-Use Tariffs
The reported simulation evaluates the proposed method under two time-of-use price schemes and two electric vehicle fleet sizes. The first scheme uses 10 electric vehicles, while the second scheme uses 50 electric vehicles. The optimization period is 24 hours. The battery capacity is 43 kWh, and the maximum charging or discharging power is 7 kW. Initial state of charge values are randomly generated between 20% and 90% to represent diverse electric vehicle conditions. The population size is 200, and the maximum number of iterations is 1,000.
The base commercial building load data has a reported daily peak-valley gap of 46 kW. The time-of-use price schemes are summarized in the following table.
Scheme Period type Time window Price (CNY/kWh) TOU 1 Peak 08:00-14:00, 18:00-23:00 1.070 TOU 1 Flat 07:00-08:00, 14:00-18:00 0.687 TOU 1 Valley 23:00-07:00 0.360 TOU 2 Peak 1 11:00-12:00, 19:00-23:00 1.210 TOU 2 Peak 2 08:00-11:00, 12:00-14:00, 18:00-19:00 1.120 TOU 2 Flat 07:00-08:00, 14:00-18:00 0.712 TOU 2 Valley 23:00-07:00 0.300 The simulation compares schedules under different weight combinations. A weight preference of [1,0] places priority on minimizing load fluctuation. A weight preference of [0,1] places priority on maximizing electric vehicle arbitrage income. A weight preference of [0.5,0.5] represents a balanced position. The reported results show that the proposed method can produce different scheduling plans along the Pareto front, allowing decision-makers to select a plan according to their operational priorities.
- Reported Trade-Off Results for Electric Vehicle Scheduling
The following table summarizes representative reported trade-off values from the two time-of-use price schemes. The load fluctuation objective is reported as F1 in kW squared. The arbitrage objective is reported as the absolute value of F2 in CNY because F2 is converted to a minimization objective by multiplying by minus one. Lower F1 indicates a smoother load curve. Higher absolute F2 indicates greater electric vehicle arbitrage income.
Scenario Weight preference F1 (kW squared) Absolute F2 (CNY) Peak-valley gap (kW) TOU 1, 10 electric vehicles [0,1] 242.000 196.278 16 TOU 1, 10 electric vehicles [0.5,0.5] 12.500 184.445 4 TOU 1, 10 electric vehicles [1,0] 0.950 177.665 1 TOU 2, 50 electric vehicles [0,1] 498.625 273.836 20 TOU 2, 50 electric vehicles [0.5,0.5] 59.958 245.898 6 TOU 2, 50 electric vehicles [1,0] 10.958 153.026 3 In the TOU 1 scheme with 10 electric vehicles, the load-fluctuation-oriented preference [1,0] produced an F1 value of 0.950 and a peak-valley gap of 1 kW. The balanced preference [0.5,0.5] produced an F1 value of 12.500 and a peak-valley gap of 4 kW. The arbitrage-oriented preference [0,1] produced an F1 value of 242.000 and a peak-valley gap of 16 kW. The reported absolute F2 values were 177.665 CNY, 184.445 CNY, and 196.278 CNY, respectively.
In the TOU 2 scheme with 50 electric vehicles, the load-fluctuation-oriented preference [1,0] produced an F1 value of 10.958 and a peak-valley gap of 3 kW. The balanced preference [0.5,0.5] produced an F1 value of 59.958 and a peak-valley gap of 6 kW. The arbitrage-oriented preference [0,1] produced an F1 value of 498.625 and a peak-valley gap of 20 kW. The reported absolute F2 values were 153.026 CNY, 245.898 CNY, and 273.836 CNY, respectively.
These results show a clear trade-off pattern. When the scheduling preference places more weight on load smoothing, the electric vehicle charging and discharging actions produce a flatter load curve and a smaller peak-valley gap. When the preference places more weight on arbitrage income, the electric vehicle group can achieve higher reported arbitrage income, but the load fluctuation and peak-valley gap increase. The balanced preference provides an intermediate position that may be attractive for practical electric vehicle scheduling because it supports both grid stability and owner participation.
- Dynamic Control of Electric Vehicle Charging and Discharging
The research also examines dynamic control capability under the balanced weight preference [0.5,0.5]. In both time-of-use schemes, electric vehicle charging and discharging behavior shows a visible price response. During peak price periods, the total discharging power of the electric vehicle group is generally higher, indicating that electric vehicles tend to discharge to earn arbitrage income and help balance the load. During valley price periods, the total charging power is generally higher, indicating that electric vehicles absorb low-price electricity and store energy for later use.
In the TOU 1 scheme with 10 electric vehicles, the reported hourly totals show that the electric vehicle group discharges more during high-price hours and charges more during low-price hours. Some hours show mixed charging and discharging activity because the auction algorithm adjusts bids and allocates tasks according to grid demand, state of charge, and price signals. The presence of idle states is also reported. An electric vehicle may remain idle when the marginal benefit of charging or discharging is insufficient under the current state of charge and price conditions.
In the TOU 2 scheme with 50 electric vehicles, the reported hourly totals show a similar pattern at a larger scale. The electric vehicle group provides larger total charging and discharging power because more vehicles participate. The auction algorithm and the finite discrete action set allow the system to coordinate these actions without treating every electric vehicle as a continuous variable. This is important for large-scale electric vehicle scheduling because the number of possible action combinations grows quickly as fleet size increases.
The state of charge trajectories further illustrate the dynamic control effect. In the TOU 1 scheme, five randomly selected electric vehicles show state of charge changes that are consistent with price periods. State of charge generally declines during peak price periods when electric vehicles discharge, and it generally rises during valley price periods when electric vehicles charge. Some time slices show an idle state, where the state of charge curve remains flat because the electric vehicle does not charge or discharge. In the TOU 2 scheme, five selected electric vehicles show similar behavior. When state of charge approaches the lower bound, the algorithm limits discharging and prioritizes charging. When state of charge is not near the lower bound but the price is high, the auction algorithm may still adjust bids so that the electric vehicle group supports grid peak shaving while considering battery health and arbitrage opportunities.
- Peak Shaving, Valley Filling, and Load Curve Smoothing
The reported comparison between the base load and the optimized load shows that electric vehicle scheduling can significantly reduce load volatility. Without electric vehicle scheduling, the base load curve shows clear peak and valley differences. With electric vehicle charging and discharging coordination, the load curve becomes flatter. During low-price periods, electric vehicle charging raises the valley load and supports valley filling. During high-price periods, electric vehicle discharging reduces the peak load and supports peak shaving.
In the TOU 1 scheme, the reported peak-valley gap after scheduling falls to 1 kW under the load-fluctuation-oriented preference and to 4 kW under the balanced preference. In the TOU 2 scheme, the reported peak-valley gap falls to 3 kW under the load-fluctuation-oriented preference and to 6 kW under the balanced preference. These values are reported against a base load peak-valley gap of 46 kW. The results indicate that the proposed method can use electric vehicle charging and discharging to smooth the load curve while still offering arbitrage-oriented plans for users who prioritize economic return.
The peak shaving and valley filling effect depends on the time-of-use price design and the electric vehicle fleet size. A larger electric vehicle fleet provides more flexible capacity, but it also increases the number of decisions that must be coordinated. The finite discrete action set and the auction algorithm are intended to manage this complexity. The decision center can evaluate the capacity gap and the remaining charging capacity, map these values to discrete electric vehicle actions, and use MOEA/D-EV to evolve a set of feasible scheduling plans.
- Computational and Communication Complexity
The research highlights computational and communication complexity as a practical barrier for large-scale electric vehicle scheduling. Under a continuous formulation, each electric vehicle in each hour would require a continuous power value. For 50 electric vehicles over 24 hours, the decision space reaches 1,200 dimensions. Continuous optimization in such a high-dimensional space can be difficult to solve within a reasonable time, especially when many scenarios and uncertainties are considered.
The finite discrete action set reduces the decision space by mapping continuous power values to a limited set of discrete actions. The reported action set uses three charging rates and three discharging rates, so each electric vehicle chooses from a finite set of actions rather than an unlimited continuous range. The number of possible combinations remains large, but the search space becomes finite and more manageable for evolutionary optimization. This design supports the practical use of MOEA/D-EV for electric vehicle scheduling.
The communication complexity is also reduced. In a conventional continuous scheme, a single electric vehicle may require 4 bytes per hour for a floating-point value, resulting in 96 bytes per day for 24 hours. With a discrete action index, 1 byte per hour can represent the action, reducing the daily communication requirement to 24 bytes. With further compression or encoding, the reported daily communication requirement can be reduced to 6 bytes, corresponding to a compression rate of 93.75%. These reported figures show how discrete action representation can lower communication overhead for electric vehicle coordination in a connected grid environment.
- Dispatch Plan Analysis and Practical Implications
The reported dispatch plan for the TOU 1 scheme with 10 electric vehicles provides a detailed view of how individual electric vehicles are scheduled across the day. During peak price periods, most electric vehicles are in discharging states or idle states. During valley price periods, electric vehicles mainly charge to store low-price electricity. During flat price periods, charging and discharging behavior is more diverse. Some electric vehicles charge, some discharge, and some remain idle. Idle states appear when the auction algorithm adjusts bids and allocates tasks while respecting state of charge constraints and battery safety limits.
This dispatch pattern is consistent with practical electric vehicle operation. Electric vehicle batteries must remain within safe state of charge limits, and electric vehicle owners may not always be willing or able to charge or discharge at maximum power. The finite discrete action set provides a clear set of choices, and the auction algorithm provides a dynamic coordination mechanism. The MOEA/D-EV algorithm then evaluates the resulting schedules against both grid load fluctuation and electric vehicle arbitrage income.
For grid operators, the proposed framework offers a way to coordinate electric vehicle charging and discharging without treating every electric vehicle as an independent continuous control variable. For electric vehicle owners, the framework offers a way to earn arbitrage income by responding to time-of-use prices. For decision-makers, the Pareto front provides a set of plans with different trade-off preferences, allowing them to choose a schedule that matches local grid conditions, market rules, and user participation goals.
The research also notes that the proposed method is not a complete solution for all electric vehicle scheduling scenarios. The reported model assumes that electric vehicles are available for scheduling for 24 hours and does not consider distribution line capacity limits because private electric vehicle charging power is relatively small. Future work can extend the model to include user behavior, renewable energy integration, traffic conditions, and trusted transaction mechanisms.
- Future Directions for Electric Vehicle Scheduling
The research outlines several directions for future work. These directions are relevant for improving the practical value of electric vehicle scheduling in complex power systems.
- User behavior modeling and uncertainty analysis: Future work can use historical travel data and machine learning methods to predict electric vehicle user behavior. It can also analyze how incentives and subsidies affect user willingness to participate in charging and discharging scheduling.
- Dynamic coordination with renewable energy: Future research can build multi-energy scheduling models that coordinate electric vehicle charging and discharging with photovoltaic generation, wind power, and energy storage systems. This can help absorb surplus renewable energy during high-generation periods and fill power gaps during low-generation periods.
- Traffic flow and road conditions: Electric vehicle mobility is closely related to traffic flow and road conditions. Future work can combine intelligent transportation systems and connected vehicle data to adjust electric vehicle charging and discharging plans in real time and coordinate route planning with charging station scheduling.
- Blockchain-based trusted transactions: Future work can explore decentralized transaction networks based on blockchain technology, smart contracts for automatic settlement, and peer-to-peer electricity trading among electric vehicle users. These mechanisms may reduce transaction costs and support new energy-sharing models.
These future directions suggest that electric vehicle scheduling will continue to evolve from a grid-side coordination problem into a broader energy system problem that includes user behavior, renewable generation, transportation, and market design. The reported MOEA/D-EV framework provides a foundation for such development because it combines multi-objective optimization, discrete action representation, and price-driven auction coordination.
- Conclusion: Balancing Grid Stability and Electric Vehicle Owner Benefits
The reported research presents a multi-objective scheduling framework for electric vehicle charging and discharging based on MOEA/D. The framework coordinates electric vehicle behavior within an optimization period and produces forward-looking scheduling plans under different weight preferences. The two objectives are minimizing grid load fluctuation and maximizing electric vehicle arbitrage income. The proposed MOEA/D-EV algorithm combines the decomposition-based search strength of MOEA/D with a finite discrete action set and a price-driven auction algorithm.
The finite discrete action set reduces the decision space and communication overhead while protecting battery state of charge limits and supporting price-responsive behavior. The auction algorithm maps peak-shaving and valley-filling tasks to electric vehicle actions, responds to time-of-use tariffs, and iterates toward a smaller demand gap. The MOEA/D-EV algorithm evaluates and evolves candidate schedules to generate a Pareto set and Pareto front for decision-makers.
The simulation results under two time-of-use price schemes and two electric vehicle fleet sizes show that the proposed method can reduce the peak-valley gap, smooth the load curve, and provide different trade-off plans between grid load fluctuation and electric vehicle arbitrage income. The reported comparison between the load-fluctuation-oriented preference and the arbitrage-oriented preference demonstrates that the framework can support both grid-side and user-side objectives. The balanced preference offers an intermediate plan that may be suitable for practical electric vehicle scheduling.
Overall, the research shows that coordinated electric vehicle charging and discharging can be managed as a multi-objective scheduling problem with clear trade-off information. The proposed framework supports decision-makers in selecting a plan that reflects local priorities, helps electric vehicle owners participate through price-driven arbitrage, and provides a scalable approach for integrating electric vehicle flexibility into future power systems.