In recent years, the global energy infrastructure has been evolving toward low-carbon and renewable patterns because of rising environmental concerns. This transformation stimulates the development of the electric vehicle industry, and the electric vehicle is no longer only a transport tool but also a distributed mobile storage unit. The vehicle-to-grid concept enables the electric vehicle to exchange energy with the power grid, creating opportunities for peak shaving, valley filling, and demand response. However, the fast growth of electric vehicle penetration introduces significant uncertainties and challenges. Uncoordinated charging and discharging of numerous electric vehicles may lead to severe grid load fluctuation, larger peak-valley differences, and potential threats to the secure and stable operation of power systems.
Therefore, a scientifically designed charging and discharging scheduling strategy is essential for the coordinated operation of electric vehicles and power grids. Time-of-use pricing is one of the most effective demand-side management mechanisms. In a time-of-use tariff environment, electric vehicle owners respond to high and low electricity prices by changing their behaviour. A rational scheduling framework should guide electric vehicles to charge during valley periods and discharge during peak periods. Such a framework can simultaneously lower the operation cost for users and improve the reliability of the grid. In this article, I develop a price-driven scheduling approach in which a representative multi-objective evolutionary algorithm based on decomposition, named MOEA/D, is combined with a finite discrete action set strategy and a novel auction algorithm.
The central challenge in electric vehicle scheduling is that system operators and electric vehicle owners usually have conflicting objectives. The operator wants minimal load fluctuation, while the owner wants maximum arbitrage revenue from charging and discharging. These two objectives are intertwined and cannot be optimised individually. Multi-objective optimisation methods provide an appropriate mathematical framework for dealing with this kind of conflict. Unlike a single-objective approach, for example, one can obtain a set of non-dominated solutions that represent different trade-off preferences. I therefore choose MOEA/D because it can decompose the original multi-objective problem into a set of scalar sub-problems and assign an explicit weight vector to every solution. This property is particularly valuable in engineering practice because it makes the preference relationship among Pareto optimal solutions clear.
In the proposed scheduling mechanism, all electric vehicles participating in one optimisation horizon are evaluated as a population. A rolling horizon is used to obtain a forward-looking charging and discharging plan. For every time interval inside the horizon, the charging or discharging power of each electric vehicle is not treated as an arbitrary continuous variable. Instead, it is restricted to a finite discrete action set. This is important because a continuous random charging and discharging mode leads to enormous computational and communication cost, especially when there are hundreds or thousands of electric vehicles. The finite discrete action set expresses the power rate as several representative levels, for instance slow charging, standard charging, fast charging, slow discharging, standard discharging, and fast discharging. By using this discrete representation, the original high-dimensional continuous search problem is transformed into a search problem over a finite coordinate set, dramatically reducing complexity.
The second key technique is a new price-driven auction algorithm. Electric vehicle charging and discharging actions can be interpreted as bids in an auction. The grid or microgrid is the seller of peak-regulation tasks, while electric vehicles are the buyers. Based on the current battery state of charge and the current time-of-use electricity price, every electric vehicle bids for a corresponding action from its finite action set. The auctioneer adjusts these bids until the gap between the total bid amount and the required grid demand is minimised. This mechanism naturally enables the “buy low, sell high” strategy. Electric vehicles tend to charge when electricity is cheap and discharge when electricity is expensive, which maximises owners’ arbitrage income and simultaneously helps the grid to shave peaks and fill valleys.
The contribution of this work is threefold. First, I construct a multi-objective scheduling model for electric vehicle charging and discharging, in which the grid load variance is minimised and the electric vehicle arbitrage income is maximised under practical battery and power constraints. Second, I propose a finite discrete action selection policy based on the battery state of charge and the electricity price level, so that the scheduling plan is computationally tractable and realistic. Third, I design a novel auction method for coordinating the charging and discharging activity of electric vehicles. The auction method makes the scheduling solution responsive to dynamic price signals and can be embedded into the MOEA/D framework to search for optimal forward-looking plans.
1. Problem Foundation
Before introducing the detailed algorithm, it is necessary to formulate the mathematical basis of multi-objective optimisation. A general multi-objective minimisation problem is defined as:
\[
\min \mathbf{F}(\mathbf{x}) = \bigl(f_1(\mathbf{x}), f_2(\mathbf{x}), \ldots, f_m(\mathbf{x})\bigr)^T
\]
subject to:
\[
g_k(\mathbf{x}) \le 0, \quad k=1,\ldots,K,
\]
\[
h_j(\mathbf{x}) = 0, \quad j=1,\ldots,M.
\]
Here \(\mathbf{x}\) is the decision vector in the feasible space \(\Omega\). The vector \(\mathbf{F}\) contains \(m\) conflicting objectives. In this study, \(m=2\). Since the two objectives are conflicting, no single feasible vector can simultaneously minimise both objectives. Instead, the solution is a set of Pareto optimal solutions.
For two different decision vectors \(\mathbf{x}^a\) and \(\mathbf{x}^b\), \(\mathbf{x}^a\) dominates \(\mathbf{x}^b\) if \(f_i(\mathbf{x}^a) \le f_i(\mathbf{x}^b)\) for all \(i \in \{1,\ldots,m\}\) and there exists at least one index \(i\) such that \(f_i(\mathbf{x}^a) < f_i(\mathbf{x}^b)\). A decision vector \(\mathbf{x}^*\) is Pareto optimal if there is no other feasible vector that dominates it. The set of all Pareto optimal decision vectors is denoted by:
\[
PS = \{\mathbf{x}^* \in \Omega \mid \nexists \mathbf{x}\in\Omega,\; \mathbf{x} \prec \mathbf{x}^*\}.
\]
The image of the Pareto solution set in the objective space is called the Pareto front:
\[
PF = \{\mathbf{F}(\mathbf{x}^*) \mid \mathbf{x}^* \in PS \}.
\]
Evolutionary algorithms are widely used to solve such problems because they do not require differentiability. In this work, I mainly consider MOEA/D because of its strong search capability and its natural connection with weight vectors.
Time-of-use electricity pricing is an important signal in the scheduling problem. A conventional TOU tariff divides one day into valley, flat, and peak periods. The prices in valley, flat, and peak periods are ordered as \(\lambda_v<\lambda_m<\lambda_p\). The price elasticity coefficient is a useful concept to describe the response of the electricity user:
\[
\eta = \frac{\Delta D / D}{\Delta \lambda / \lambda }.
\]
where \(D\) is the electricity demand and \(\lambda\) is the electricity price. For multiple periods, the relationship can be written in matrix form. Self-elasticity describes the impact of price at the same period on demand, whereas cross-elasticity describes the impact of price at one period on demand at another period. These elasticity relationships motivate the design of price-responsive electric vehicle charging and discharging strategies.
MOEA/D transforms a multi-objective problem into multiple scalar sub-problems. Each sub-problem is associated with a weight vector \(\mathbf{w}=(w_1,\ldots,w_m)\). In the minimisation case, the Tchebycheff scalarising function has the following form:
\[
g^{te}(\mathbf{x}|\mathbf{w}, \mathbf{z}^*) = \max_{1\le i\le m} \left\{ w_i \left| f_i(\mathbf{x}) – z_i^* \right| \right\},
\]
where \(\mathbf{z}^* = (z_1^*, \ldots, z_m^*)\) is the ideal point calculated from the best objective values found so far. A neighbourship relation is defined by Euclidean distances among weight vectors. During reproduction, parents are selected from the neighbourhood of a sub-problem. Offspring replace neighbours only if they improve the scalarised objective.
2. Multi-Objective Scheduling Model for Electric Vehicle Charging and Discharging
In this section I present the proposed multi-objective scheduling model. Let \(T\) be the number of time intervals in one rolling optimisation horizon. Let \(n\) denote the number of electric vehicles participating in scheduling. For an electric vehicle \(i \in \{1,\dots,n\}\), its charging/discharging power at interval \(t\) is denoted by \(P_{i,t}\). By convention, \(P_{i,t}>0\) represents discharging, \(P_{i,t}<0\) represents charging, and \(P_{i,t}=0\) represents an idle state.
The first objective is to minimise the load fluctuation of the grid. The total load after electric vehicle charging and discharging is:
\[
P_{\text{total},t} = P_{L,t} – \sum_{i=1}^n P_{i,t},
\]
where \(P_{L,t}\) is the base load without electric vehicles at interval \(t\). In a lower-level context, the grid operator expects that the total load curve is as smooth as possible. Therefore, the first objective is defined as:
\[
\min F_1 = \sum_{t=1}^T \Bigl(P_{L,t} – \sum_{i=1}^n P_{i,t} – P_{\text{avr}}\Bigr)^2,
\]
with:
\[
P_{\text{avr}} = \frac{1}{T}\sum_{t=1}^T \Bigl(P_{L,t} – \sum_{i=1}^n P_{i,t}\Bigr).
\]
The second objective is to maximise the total arbitrage revenue of the electric vehicles. Electric vehicle owners buy electricity when charging and sell electricity when discharging. If the aggregate charging/discharging power in interval \(t\) is \(\sum_{i=1}^n P_{i,t}\), the revenue at interval \(t\) is:
\[
\left| \sum_{i=1}^n P_{i,t} \right| \lambda_t,
\]
where \(\lambda_t\) is the electricity price. However, if the aggregate power is negative, the electric vehicles are charging and the owner must pay for electricity. Such payment should be subtracted from revenue. I introduce a sign coefficient:
\[
\beta_t =
\begin{cases}
-1, & \text{if } \sum_{i=1}^n P_{i,t}<0,\\
0, & \text{if } \sum_{i=1}^n P_{i,t}=0,\\
1, & \text{if } \sum_{i=1}^n P_{i,t}>0.
\end{cases}
\]
The second objective is therefore:
\[
\max F_2 = \sum_{t=1}^T \beta_t\, \lambda_t\, \left|\sum_{i=1}^n P_{i,t}\right|.
\]
For numerical optimisation, I convert the maximisation problem into a minimisation one by considering \(-F_2\).
Charging and discharging powers of every electric vehicle are bounded by safe limits:
\[
P_{i,t}^{\min} \le P_{i,t} \le P_{i,t}^{\max},
\]
where \(P_{i,t}^{\min}<0\) is the maximum charging power and \(P_{i,t}^{\max}>0\) is the maximum discharging power. The battery state of charge of electric vehicle \(i\) evolves as:
\[
SOC_{i,t+1} = SOC_{i,t} – \frac{P_{i,t}\,\Delta t}{E_i},
\]
where \(E_i\) is the battery capacity and \(\Delta t\) is the duration of one time interval. In order to protect the electric vehicle battery from over-charge and over-discharge, the state of charge must remain in the healthy interval:
\[
\underline{SOC}_i \le SOC_{i,t} \le \overline{SOC}_i.
\]
In this study, I set \(\underline{SOC}_i=0.2\) and \(\overline{SOC}_i=0.9\), which is a common setting for lithium-ion electric vehicle batteries.
3. MOEA/D-EV Scheduling Algorithm
This section explains the MOEA/D-EV algorithm, which is designed for solving the electric vehicle charging/discharging scheduling model. The algorithm uses an explicit decision vector, a finite discrete action set, and an auction method for dynamic response to time-of-use price.
3.1 Decision vector and encoding
In the rolling horizon, the scheduling plan is represented as a matrix \(\mathbf{X}\), in which the entry at row \(t\) and column \(i\) denotes the electric vehicle charging/discharging power at that time interval. The complete decision vector can be written as:
\[
\mathbf{X} = (\mathbf{P}_1, \mathbf{P}_2, \ldots, \mathbf{P}_T),
\]
\[
\mathbf{P}_t = (P_{1,t}, P_{2,t}, \ldots, P_{n,t}).
\]
This encoding allows the MOEA/D-EV algorithm to preserve the time-space characteristics of electric vehicle charging/discharging. Because the power values are chosen from the finite discrete action set instead of a continuum, each coordinate of \(\mathbf{P}_t\) takes only a small number of possible values.
3.2 Finite discrete action set strategy
The finite discrete action set has a strong practical motivation. In battery charging, the power level is usually classified as slow, moderate, and fast. Fast charging is represented by \(7c\), moderate charging by \(3c\), and slow charging by \(c\). Likewise, fast discharging is represented by \(7d\), moderate discharging by \(3d\), and slow discharging by \(d\). In the simulation, one unit \(c\) or \(d\) is set to 1 kW. The available actions for an electric vehicle are not fixed; instead, they depend on the battery state of charge. For instance, a battery with low SOC should not be allowed to discharge at a high rate, whereas a battery with high SOC should not be allowed to charge too quickly.
The following table summarises the finite discrete action sets under different SOC ranges.
| Battery SOC range | Discharging action set | Charging action set |
|---|---|---|
| \([0.2, 0.3]\) | \(\{d\}\) | \(\{7c, 3c, c\}\) |
| \((0.3, 0.5]\) | \(\{3d, d\}\) | \(\{7c, 3c, c\}\) |
| \((0.5, 0.6]\) | \(\{3d, d\}\) | \(\{3c, c\}\) |
| \((0.6, 0.8]\) | \(\{7d, 3d, d\}\) | \(\{3c, c\}\) |
| \((0.8, 0.9]\) | \(\{7d, 3d, d\}\) | \(\{c\}\) |
This strategy has three important benefits. First, it avoids exposing the electric vehicle battery to extreme SOC regions, thereby prolonging battery life. Second, it decreases the search dimension and communication overhead, which is crucial when a large number of electric vehicles are scheduled in real time. Third, it is compatible with TOU price signals because the action choice can be adjusted according to whether the current price is in a high, flat, or low region.
3.3 Price-driven auction algorithm
I map the finite-action electric vehicle scheduling problem to an auction process. In the auction, the microgrid presents regulation tasks that must be fulfilled. The electric vehicles act as bidders. Each electric vehicle places a bid corresponding to its desired charging or discharging action. The auction algorithm adjusts the bids according to the battery SOC and the TOU tariff. The process can be described as follows:
- Each electric vehicle receives the current price interval \(C_1,C_2,C_3,D_1,D_2,D_3\), which indicates whether charging or discharging is favourable.
- The electric vehicle selects the largest safe power level when the price is in a strongly favourable interval. For example, in a high-price discharging interval \(D_3\), the electric vehicle chooses the maximum possible discharging action from its finite action set.
- The auctioneer collects all bids, sums them into a total power value, and compares the total power with the demand required by the grid.
- The auctioneer updates the price signal or adjusts the bid allocation until the gap between total bid power and required power is as small as possible.
The auction rule is, in fact, a dynamic coordination process. It ensures that the electric vehicle charging/discharging plan does not violate battery constraints. At the same time, it responds sensitive to electricity price. Therefore, every scheduling candidate produced inside MOEA/D is modified by this auction algorithm before it is evaluated. The MOEA/D-EV algorithm combines auction-based local search with evolutionary global search, which improves both convergence and feasibility.
3.4 Overall algorithm flow
The overall algorithm can be summarized in the following pseudocode.
Input: maximum number of generations \(G_{\max}\), population size \(N_p\), finite action set \(\mathcal{A}\), TOU price tariffs, initial battery SOC \(\mathbf{SOC}^{(0)}\).
Output: Pareto solution set \(PS\) and corresponding Pareto front \(PF\).
1. Initialise a population of \(N_p\) electric vehicle scheduling plans. Each element is sampled from \(\mathcal{A}\) and the battery SOC trajectories are computed.
2. For every candidate in the population, call the auction algorithm to adjust each time-interval action according to the current TOU price and SOC constraints.
3. Evaluate \(F_1\) and \(-F_2\) for all candidates and set the ideal point \(\mathbf{z}^*\).
4. Generate weight vectors uniformly and determine the neighbourhood of each weight vector.
5. While the termination criterion is not met, do:
- Select two parents from the neighbourhood of the current sub-problem.
- Apply crossover and mutation to produce an offspring plan.
- Use the auction algorithm to repair and adjust the offspring plan.
- Evaluate the two objective functions for the offspring.
- Update the ideal point and replace neighbouring solutions if the Tchebycheff value improves.
6. Return the final population as the Pareto optimal scheduling plans.
4. Complexity Advantages and Communication Cost
One major issue in large-scale electric vehicle scheduling is the curse of dimensionality. If we treat each electric vehicle’s power as a continuous variable, then every time interval involves an infinite number of possible states. In a rolling 24-h horizon with \(n\) electric vehicles and \(T\) intervals, the continuous decision space has dimension \(nT\). Continuous optimisation methods cannot quickly solve such a high-dimensional problem. In addition, many mathematical programming methods rely on convexity or differentiability. The discrete action set naturally avoids these difficulties.
For communication, the continuous formulation typically requires a 32-bit floating-point number for each power value. If one electric vehicle is scheduled over 24 intervals, the communication cost is at least \(24 \times 4 = 96\) bytes. With the finite discrete action set, one can encode each action with an integer index, for which one byte or less is sufficient. Let \(b\) denote the number of bits required to represent one action index. The total communication cost for all electric vehicles is \(O(nT b)\). This cost is significantly less than that of transmitting continuous real-valued vectors. Therefore, the finite discrete action set is a practical solution for massive electric vehicle coordination.
Let me define the computational complexity more formally. Suppose that each electric vehicle has only \(m_a\) available actions in the finite set. The total number of possible action combinations is \(m_a^{nT}\), which is still exponential but far smaller than an infinite continuous space. In practice, the MOEA/D-EV algorithm searches a population of size \(N_p\) for \(G_{\max}\) generations. The auction repair step runs in \(O(N_p T n)\). The overall complexity is therefore \(O(G_{\max} N_p T n)\), which is acceptable when the action set is compact.
5. Experimental Design and Analysis
5.1 Experimental settings
I design experiments under two different TOU tariffs and different numbers of electric vehicles. The first scenario uses a simple TOU tariff and ten electric vehicles. The second scenario uses a more complex TOU tariff with two peak sub-periods and fifty electric vehicles. The following table provides the basic load data of a commercial building in the local region, which is used as the base load without electric vehicle charging/discharging.
| Hour (h) | Base load (kW) | Hour (h) | Base load (kW) |
|---|---|---|---|
| 1 | 65 | 13 | 99 |
| 2 | 64 | 14 | 81 |
| 3 | 64 | 15 | 82 |
| 4 | 62 | 16 | 74 |
| 5 | 64 | 17 | 78 |
| 6 | 64 | 18 | 93 |
| 7 | 80 | 19 | 100 |
| 8 | 77 | 20 | 92 |
| 9 | 81 | 21 | 87 |
| 10 | 90 | 22 | 74 |
| 11 | 101 | 23 | 66 |
| 12 | 101 | 24 | 55 |
The peak-valley difference of the base load in this data is 46 kW. This clearly indicates the opportunity for electric vehicle charging and discharging to smooth the load curve.
The first TOU tariff is defined as follows:
| Period type | Time | Price (CNY/kWh) |
|---|---|---|
| Peak | 8:00-14:00 and 18:00-23:00 | 1.070 |
| Flat | 7:00-8:00 and 14:00-18:00 | 0.687 |
| Valley | 23:00-7:00 | 0.360 |
The second TOU tariff has two peak levels and is listed below:
| Period type | Time | Price (CNY/kWh) |
|---|---|---|
| Peak 1 | 11:00-12:00 and 19:00-23:00 | 1.210 |
| Peak 2 | 8:00-11:00, 12:00-14:00 and 18:00-19:00 | 1.120 |
| Flat | 7:00-8:00 and 14:00-18:00 | 0.712 |
| Valley | 23:00-7:00 | 0.300 |
Every electric vehicle has a battery capacity of 43 kWh and a maximum charging/discharging power of 7 kW. The initial SOC is randomly generated between 20% and 90%. In MOEA/D-EV, the population size is 200 and the maximum number of generations is 1000.
5.2 Multi-objective trade-off analysis
The proposed algorithm provides a Pareto front with solutions corresponding to different user preferences. To demonstrate the trade-off, I select three representative preference weights: \([1,0]\), \([0.5,0.5]\), and \([0,1]\). The weight \([1,0]\) strongly minimises the grid load variance, while \([0,1]\) strongly maximises the electric vehicle arbitrage revenue. The middle weight \([0.5,0.5]\) balances both objectives.
The following table reports the objective values, peak-valley differences, and total energy quantities for several representative solutions in the first TOU scenario with 10 electric vehicles.
| \([w_1,w_2]\) | \(F_1\) (kW²) | \(\lvert F_2 \rvert\) (CNY) | Peak-valley difference (kW) | Charging energy (kWh) | Discharging energy (kWh) |
|---|---|---|---|---|---|
| \([0,1]\) | 242.000 | 196.278 | 16 | 113 | 255 |
| \([0.1,0.9]\) | 48.000 | 191.248 | 6 | 119 | 249 |
| \([0.3,0.7]\) | 22.958 | 187.318 | 4 | 124 | 249 |
| \([0.5,0.5]\) | 12.500 | 184.445 | 4 | 123 | 247 |
| \([0.7,0.3]\) | 5.958 | 182.665 | 2 | 124 | 247 |
| \([0.9,0.1]\) | 2.000 | 178.735 | 1 | 128 | 246 |
| \([1,0]\) | 0.950 | 177.665 | 1 | 128 | 245 |
From the table, one can see that when the weight moves toward \(F_1\), the load variance dramatically decreases. When the weight moves toward \(F_2\), the arbitrage revenue improves, but the load variance increases. This is exactly the expected conflict between grid-side and user-side objectives. In the case of the trade-off weight \([0.5,0.5]\), the electric vehicle charging/discharging plan achieves a good compromise.
For the second TOU scenario with 50 electric vehicles, the corresponding results are listed below.
| \([w_1,w_2]\) | \(F_1\) (kW²) | \(\lvert F_2 \rvert\) (CNY) | Peak-valley difference (kW) | Charging energy (kWh) | Discharging energy (kWh) |
|---|---|---|---|---|---|
| \([0,1]\) | 498.625 | 273.836 | 20 | 1249 | 1418 |
| \([0.1,0.9]\) | 254.500 | 269.118 | 14 | 1259 | 1431 |
| \([0.3,0.7]\) | 92.958 | 260.188 | 7 | 1119 | 1421 |
| \([0.5,0.5]\) | 59.958 | 245.898 | 6 | 1251 | 1406 |
| \([0.7,0.3]\) | 34.500 | 239.114 | 5 | 1254 | 1404 |
| \([0.9,0.1]\) | 17.625 | 219.986 | 3 | 1256 | 1389 |
| \([1,0]\) | 10.958 | 153.026 | 3 | 1199 | 1246 |
In the second scenario, the original peak-valley difference of the commercial building is 46 kW. When the scheduling weight is \([1,0]\), the peak-valley difference is reduced to 3 kW, which represents a reduction of 93.5%. Even when the weight gives great importance to the electric vehicle arbitrage revenue, the peak-valley difference is still kept below 20 kW. The experiment confirms that the scheduling of electric vehicles can substantially improve the load profile.
5.3 Electric vehicle charging/discharging behaviour under dynamic price signals
I further select the balanced weight \([0.5,0.5]\) and analyse the charging/discharging behaviour of electric vehicles in different TOU scenarios. The table below lists the total discharging and charging power of 10 electric vehicles in each hour under the first TOU tariff.
| Hour | Discharging power (kW) | Charging power (kW) | Hour | Discharging power (kW) | Charging power (kW) |
|---|---|---|---|---|---|
| 1 | 2 | -11 | 13 | 25 | 0 |
| 2 | 3 | -13 | 14 | 10 | -2 |
| 3 | 3 | -13 | 15 | 10 | -2 |
| 4 | 1 | -13 | 16 | 6 | -6 |
| 5 | 1 | -11 | 17 | 7 | -3 |
| 6 | 0 | -10 | 18 | 20 | 0 |
| 7 | 8 | -2 | 19 | 26 | 0 |
| 8 | 6 | -3 | 20 | 18 | 0 |
| 9 | 11 | -3 | 21 | 13 | 0 |
| 10 | 18 | -2 | 22 | 5 | -2 |
| 11 | 28 | -1 | 23 | 0 | -8 |
| 12 | 26 | 0 | 24 | 0 | -18 |
One can observe that the electric vehicles mainly charge during valley-price hours from 23:00 to 6:00 and discharge during peak-price hours from 9:00 to 14:00 and from 18:00 to 21:00. This pattern exactly follows the “low-price charging and high-price discharging” principle. The dynamic adjustment of the electric vehicle battery SOC also remains within the safe interval due to the finite discrete action set and the auction process.
5.4 Peak shaving and valley filling performance
The load curves before and after electric vehicle scheduling are clearly smoother after introducing the proposed scheduling algorithm. In the first TOU tariff, the charging action in deep valley hours lifts the valley load, while the discharging action in peak hours suppresses the peak load. In the second TOU tariff, the electric vehicles in the system similarly shift the energy consumption from high-price periods to low-price periods. The action of the auction algorithm acts like a price-driven negative feedback loop. If the grid load is still too high during a peak interval, the auctioneer increases the incentive for electric vehicles to discharge. If the grid load is too low during a valley interval, the auctioneer encourages electric vehicles to charge at the attractive low electricity tariff.
From a statistical perspective, the load variance \(F_1\) drops significantly after scheduling. In the first TOU scenario, \(F_1\) reaches only 0.95 kW² when the scheduling plan strongly favours grid load flattening. In the second TOU scenario, \(F_1\) can be as low as 10.96 kW². These results confirm that the method supports effective peak shaving and valley filling. The scheduling plan also increases the daily average load inside the valley period, which improves asset utilisation.
5.5 Example of a day-ahead electric vehicle charging/discharging plan
To provide more insight into the solution, I present a particular day-ahead electric vehicle charging/discharging plan from the first TOU scenario with 10 electric vehicles. Each row corresponds to one electric vehicle and each column corresponds to one hour. Positive integers denote discharging action levels, zero denotes idle, and negative integers denote charging action levels. The power levels are multiples of 1 kW chosen from the finite action set.
| EV | 1h | 2h | 3h | 4h | 5h | 6h | 7h | 8h | 9h | 10h | 11h | 12h |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 0 | 3 | 3 | 3 | 3 |
| 2 | -1 | 1 | -1 | 0 | -1 | -1 | 1 | 1 | 3 | 3 | 7 | 3 |
| 3 | -1 | 0 | -3 | -1 | -3 | -1 | 1 | 1 | -1 | 3 | 3 | 7 |
| 4 | -1 | -3 | -1 | 0 | -1 | -1 | -1 | -1 | -1 | 1 | 0 | 3 |
| 5 | 0 | 0 | 1 | -3 | 0 | -1 | 1 | 1 | -1 | 1 | 3 | 1 |
| 6 | 1 | 1 | 1 | -1 | 0 | -1 | 3 | 1 | 1 | 3 | -1 | 3 |
| 7 | -3 | -1 | -3 | -3 | -1 | -1 | 1 | -1 | 1 | 3 | 3 | 1 |
| 8 | -1 | -7 | -3 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | 3 | 1 |
| 9 | -3 | -1 | 1 | -3 | -1 | -1 | 0 | 1 | 1 | -1 | 3 | 3 |
| 10 | -1 | -1 | -1 | -1 | -3 | -1 | 0 | 1 | 1 | 1 | 3 | 1 |
During the low-price valley period, most electric vehicles are in charging mode. During the peak-price period, the same electric vehicles switch to discharging mode. It is worth mentioning that some electric vehicles remain idle in some hours because their battery SOC is close to the upper or lower boundary. This behaviour is generated by the auction algorithm, which limits the bid of an electric vehicle when the action would violate battery safety constraints.
6. Discussion and Future Extensions
The experimental results demonstrate that the proposed MOEA/D-EV method is effective in coordinating electric vehicle charging and discharging under different TOU tariffs. However, there are still several limitations. First, the model assumes that electric vehicles are always available for grid scheduling. In reality, driving patterns and travel demand significantly influence availability. Future studies should incorporate data-driven prediction of electric vehicle travel behaviour. Second, the current method focuses on charging and discharging power scheduling, but it does not explicitly model the interaction between electric vehicles and renewable energy sources. Future work can extend the model to include photovoltaic and wind power with an even larger number of electric vehicles.
Another promising direction is to include route planning and transport networks. Electric vehicles are mobile energy storage units, and their charging demands are strongly coupled with the traffic state. If the geographic information and traffic flow are available, the scheduling centre can send price signals not only in the time dimension but also in the space dimension. The finite discrete action set can be further enriched with location-aware charging and discharging choices. This would be a valuable step toward city-scale vehicle-grid integration.
In addition, the auction algorithm introduced in this article can be improved by using game-theoretic incentive mechanisms. Electric vehicle owners may behave strategically and bid strategically to increase their individual incomes. A truthful auction mechanism would make it more difficult for participants to manipulate the market. This is an interesting topic for future research. It would also be useful to combine the proposed multi-objective scheduling framework with blockchain-based peer-to-peer energy trading, in which electric vehicle users can trade energy directly with each other under the supervision of the grid operator.
7. Conclusion
In this article, I have presented a comprehensive multi-objective scheduling framework for electric vehicle charging and discharging based on MOEA/D. The framework combines three important ingredients: a multi-objective scheduling model, a finite discrete action set, and a price-driven auction algorithm. The finite discrete action set transforms the continuous charging/discharging decision space into a finite coordinate system, thereby significantly reducing computational and communication burden. The auction algorithm dynamically coordinates the actions of electric vehicles according to the battery SOC and the time-of-use electricity price. MOEA/D provides an efficient global search engine that produces a set of Pareto optimal scheduling plans with diverse trade-off preferences.
Simulation studies have been conducted under two TOU tariff structures with different numbers of electric vehicles. The results confirm that the proposed algorithm can smooth the load curve and lower the peak-valley difference effectively. The electric vehicle arbitrage revenue is also maintained at a satisfactory level. With a balanced preference weight, the load fluctuation is small and the electric vehicle users receive reasonable financial benefits. The finite discrete action set not only ensures the feasibility of the charging and discharging solution but also protects the electric vehicle battery from aggressive charging or discharging. The MOEA/D-EV algorithm therefore provides a valuable and feasible solution for the smart grid environment.
The work can be extended in several directions. In the future, I will explore the integration of electric vehicle scheduling with renewable energy production, traffic-aware mobility models, and more advanced market mechanisms. The ultimate goal is to build an intelligent and user-friendly scheduling ecosystem that can support massive electric vehicle integration in modern cities while maintaining grid stability and user satisfaction.