I have spent a substantial part of my recent work investigating how charging infrastructure should evolve when electric cars enter a community in large numbers. The first point that I always make to utility operators is that an electric car is not just another household appliance. A typical electric car draws a much higher current than a washing machine or an air conditioner, and it may continue to draw that current for several hours. When many electric cars are plugged in at the same time, their aggregate load can exceed the rating of the local distribution transformer and cause cable overheating, voltage deviation, unnecessary transformer loss, and even protection tripping. I have therefore focused on a concept that is often described as orderly charging, and my specific interest is in controlling the charging power of each electric car so that the total grid load remains within a safe envelope.
The main difficulty is that the owner of an electric car does not care only about the grid. The owner cares about whether the car has enough energy for tomorrow, how much the charging session costs, and whether the car is ready when it is needed. In an uncontrolled situation, a driver arrives at home, plugs the electric car into the charger, and the charger immediately starts at rated power. This is convenient for the user, but it often coincides with the evening peak of household electricity demand. The result is a sharp new peak that occurs exactly when the distribution system is already stressed. I believe that this problem cannot be solved by simply telling users to charge later, because not every user has the same schedule. The practical solution must be a technical regulation strategy that can distribute power intelligently among electric cars according to their arrival time, departure time, state of charge, and expected energy requirement.
In this article, I explain an orderly charging regulation method that is based on power allocation. I begin by discussing how I estimate the real charging requirement of an electric car. I then compare different charging modes and explain why power allocation is the most suitable framework for slow charging in a residential area. After that, I present a multi-objective model in which the main objectives are charging cost, peak load, and user satisfaction. I also describe an adaptive angular-region method that helps to search for balanced solutions. Finally, I use a realistic case based on a 150-household residential community with 60 electric cars to show how the method can reduce the uncontrolled peak from about 1,200 kW to about 950 kW while still meeting the travel needs of every electric car owner.
1. The nature of electric car charging demand
The charging demand of an electric car is not simply equal to the rating of the charger. In my analysis, I treat it as a function of the vehicle usage, battery capacity, consumption characteristics, charging efficiency, and the available charging time. If I know the daily mileage of the vehicle and the usable range of a full battery, I can estimate how much battery energy has been consumed. An electric car that is charged at home after a short commute has a relatively small energy requirement, whereas an electric car that arrives with a nearly empty battery and must be fully charged before an early departure presents a much more constrained optimization problem.
Let me define the basic parameters for an electric car \(i\). The usable capacity of the battery is \(C_i\), and the full-charge range that the owner can rely on is \(L_i\). If the owner drives \(D_i\) kilometers on a typical day, then the energy that must be restored to the battery is approximately:
\[
E_{\mathrm{req},i} = \frac{C_i D_i}{L_i}
\]
Equation (1) assumes that the electric car starts from about the same state of charge and returns with the same state at the end of the day. In practice, however, the owner may arrive with a particular battery state, and the desired state at departure may be different. Therefore, I prefer to write the required charging energy as:
\[
E_{\mathrm{req},i} = \left( SOC_{\mathrm{dep},i} – SOC_{\mathrm{arr},i} \right) C_i
\]
where \(SOC_{\mathrm{arr},i}\) is the state of charge when the electric car is plugged in, and \(SOC_{\mathrm{dep},i}\) is the state of charge that the owner wants to reach before departure. This formulation is easier to use in a control model because the charging control system can obtain \(SOC_{\mathrm{arr},i}\) from the battery management system, and the user can enter \(SOC_{\mathrm{dep},i}\) through a mobile application or the charger display.
The actual energy drawn from the grid is slightly larger than the energy stored in the battery because the charger, the on-board converter, and the battery itself have losses. I use \(\eta_{\mathrm{chg}}\) to represent the total charging efficiency. The grid-side energy requirement is therefore:
\[
E_{\mathrm{grid},i} = \frac{E_{\mathrm{req},i}}{\eta_{\mathrm{chg}}}
\]
If the charging power allocated to the electric car during a time interval is \(P_{i,t}\), and \(\Delta t\) is the length of one control interval, then the charging process must satisfy:
\[
\sum_{t \in \mathcal{W}_i} P_{i,t} \Delta t \ge \frac{E_{\mathrm{req},i}}{\eta_{\mathrm{chg}}}
\]
where \(\mathcal{W}_i\) is the set of time intervals during which electric car \(i\) is connected to the charger. This inequality is essential in my power allocation model. It guarantees that the optimization does not simply lower the peak load by making the electric car fail to reach its target state of charge.
I also update the state of charge recursively during the simulation horizon. Suppose that electric car \(i\) is charged at power \(P_{i,t}\) during a short interval from time \(t\) to \(t+1\). The new state of charge is:
\[
SOC_{i,t+1} = SOC_{i,t} + \frac{\eta_{\mathrm{chg}} P_{i,t} \Delta t}{C_i}
\]
where \(SOC_{i,t}\) is measured as a fraction between zero and one. This equation is a useful way to determine whether a certain charging schedule is acceptable. In particular, I enforce the following battery constraints:
\[
SOC_{\min} \le SOC_{i,t} \le SOC_{\max}
\]
where \(SOC_{\min}\) is the minimum allowable state of charge, and \(SOC_{\max}\) is the upper limit that protects the battery from overcharging. I also require that the charging process occurs only after the user connects the electric car and before the user departs.
From this basic model, I can see that the charging demand of an electric car is both energy-based and time-based. Energy determines how many kilowatt-hours must be supplied, while time determines how much flexibility the controller has. If the electric car remains connected for twelve hours but only needs energy for four hours, the controller has a wide range of possible power profiles. If the electric car arrives with a very low battery and must leave in three hours, the controller has very little flexibility. My power allocation strategy must preserve this distinction because not every electric car is equally flexible.
2. Charging modes and their influence on electric car drivers
In the field, charging equipment for electric cars is commonly divided into slow alternating-current charging and fast direct-current charging. From my perspective, slow charging is more suitable for home, workplace, and destination charging, whereas fast charging is more suitable for public service areas, highway corridors, and emergency situations. Table 1 compares the two widely used charging modes for electric cars.
| Feature | Slow AC charging | Fast DC charging |
|---|---|---|
| Typical power | 3.5 kW to 7 kW per electric car | 30 kW to 120 kW per electric car |
| Typical charging time | 4 to 10 hours | 20 minutes to 1 hour |
| Impact on battery life | Lower current and less degradation | Higher current and more degradation if used daily |
| Grid impact | More distributed and easier to schedule | Concentrated load and a more severe short-term spike |
| Typical location | Residential parking, office parking, hotel | Urban quick-charge station, highway service area |
| User concern | Low cost and everyday readiness | Shorter waiting time and immediate continuation of travel |
In a residential community, most electric cars are parked overnight. The owner can leave the electric car connected for ten or more hours, but the actual charging duration may be only six or seven hours. This gives the charging management system a valuable opportunity to shift part of the load from the evening peak to the late-night valley. At the same time, the owner of the electric car may prefer not to wake up in the middle of the night to unplug the vehicle. The power allocation algorithm should therefore make the transition automatically.
Fast charging has a different type of user expectation. When an electric car is charged in a commercial district or highway service area, the driver is normally waiting while the vehicle charges and wants the charging session to be completed as quickly as possible. In that situation, power allocation can use a first-come-first-served rule or a queue-aware rule, because the most important target is to maximize throughput while respecting the capacity of the charging station. I believe that a unified orderly charging strategy cannot use the same rules for both residential slow charging and highway fast charging. The power allocation method must adapt to the purpose of the charging station.
3. Why power allocation is central to electric car charging control
When I look at the electricity distribution network, I prefer to think of the transformer as a container with a limited capacity. At every moment, the total demand from households plus the charging demand from electric cars must be smaller than the capacity. In an uncontrolled case, the electric cars make no effort to respect that limit. A 7 kW charger starts immediately, and if forty electric cars are all charging at 7 kW at the same moment, they add 280 kW to the community load. In a typical 150-household community, this uncontrolled addition can push the transformer from about 900 kW to more than 1,200 kW during the evening peak. This is exactly the problem that power allocation can solve.
The basic idea of power allocation is that the controller assigns each electric car a charging power set-point at each control interval. Instead of always receiving the full rated power of the charger, the electric car receiver receives a power value that is optimized based on the available transformer capacity, the price signal, the owner requirements, and the priority of the charging session. This can be written mathematically as a matrix:
\[
\mathbf{P} =
\begin{bmatrix}
P_{1,1} & P_{1,2} & \cdots & P_{1,T} \\
P_{2,1} & P_{2,2} & \cdots & P_{2,T} \\
\vdots & \vdots & \ddots & \vdots \\
P_{N,1} & P_{N,2} & \cdots & P_{N,T}
\end{bmatrix}
\]
where \(N\) is the number of electric cars and \(T\) is the number of time intervals in the scheduling horizon. The value \(P_{i,t}\) is the charging power of electric car \(i\) in interval \(t\). If \(P_{i,t}\) is zero, then that electric car is either not connected or is deliberately paused. If \(P_{i,t}\) is positive, the car receives power according to the controller command. This matrix formulation is convenient because I can express every charging schedule as a two-dimensional array, and the goal of orderly charging is to find the best array of power values under a set of constraints.
Let \(L_t\) be the household base load at time \(t\), not including the electric car chargers. The total load seen by the distribution transformer is:
\[
S_t = L_t + \sum_{i=1}^{N} P_{i,t}
\]
The most basic safety constraint is:
\[
S_t \le S_{\max}
\]
where \(S_{\max}\) is the maximum permitted load. In my case study, \(S_{\max}\) is equal to the rating of the community distribution transformer. If \(S_t\) exceeds this value, the controller must reduce the charging power of some electric cars even if their preferred charging schedule has not yet been completed. Therefore, the main task of power allocation is to keep the sum of the individual charging powers low enough at every moment while still delivering the required energy to every electric car before its departure.
Power allocation also supports electricity price optimization. If the local tariff gives a lower price during the night, the controller can charge some electric cars more heavily during the valley period and lightly during the peak period. This is cost-effective for the user and helpful for the utility. A simple economic objective is:
\[
F_{c} = \sum_{t=1}^{T} C_t \left( \sum_{i=1}^{N} P_{i,t} \right) \Delta t
\]
where \(C_t\) is the electricity price at interval \(t\). This equation says that the charging cost is the sum over every interval of the total power of electric cars multiplied by the interval length and the price. The optimizer tries to reduce \(F_c\) by moving energy from peak periods to off-peak periods. But it cannot do so without regard for the departure time of each electric car, because an electric car that leaves at 06:00 cannot be shifted to a 09:00 valley period.
4. Control architecture for orderly charging of electric cars
My implementation of orderly charging depends on a communication architecture that links the electric cars, the charging piles, the local controller, and the utility signal. The controller first reads information about the electric car through the charging connection. Typical information includes the vehicle identity, battery state, requested maximum current, and the time when the car is physically plugged in. The controller also receives a departure deadline and a target state of charge from the user. These values are needed because the controller cannot make a useful decision if it only knows the instantaneous current.
The main controller should also be connected to the electricity meter at the transformer. By measuring the household base load in real time, the controller can calculate how much residual capacity remains for electric car charging. If the transformer is already close to its limit, each new electric car that plugs in cannot be allowed to start at full power. The controller must instead distribute the remaining capacity among all active electric cars according to their urgency. This is the essence of the power allocation method.
The same architecture can be implemented in a cluster of alternating-current charging piles. The main control unit communicates through a network unit and a CAN unit with the display unit, the AC contactors, the meters, and the control pilot lines. Each charging outlet has its own contactor and output unit, so the controller can set a different power limit for every electric car independently. Meters at each outlet measure the actual energy delivered. In this way, the system does not rely on the electric car owner to manually reduce the charging current.
At each terminal, the control pilot signal carries the maximum allowable current to the on-board charger of the electric car. The central unit can therefore limit the power of electric car \(i\) to a value \(P_{i,t}\) that is lower than the physical maximum. In a conventional uncontrolled charging pile, this signal is fixed and the electric car charges at the rated power until the battery is full. In my proposed orderly charging architecture, the signal is updated in every control interval, typically every 15 minutes, based on the latest measurement of load, price, and user requirement.
5. Regulation strategy for variable-power orderly charging
In residential areas, I recommend a variable-power regulation strategy. The electric car is allowed to charge at a lower power during the high-load period, a medium power during the shoulder period, and the full power during the low-load valley period. This approach is different from delayed charging, because delayed charging only changes the start time. Variable-power charging changes the shape of the power curve while keeping the connection window the same.
For a charging pile whose maximum power is \(P_{i}^{\max}\), the controller may choose any power between zero and \(P_{i}^{\max}\). I express this as:
\[
0 \le P_{i,t} \le P_{i}^{\max}
\]
When the distribution transformer is approaching its capacity limit, the controller must prevent the total load from exceeding \(S_{\max}\). Therefore, the sum of all electric car charging powers must satisfy:
\[
\sum_{i=1}^{N} P_{i,t} \le S_{\max} – L_t
\]
The quantity \(S_{\max} – L_t\) is the residual capacity for electric car charging at interval \(t\). If this residual capacity is negative, the household load has already exceeded the transformer limit, and the controller cannot safely charge any electric car. In a normal case, the residual capacity is positive and the optimizer decides how to split it among the electric cars.
One of the most practical regulation measures that I use is to set a maximum charging power for each time zone. For example, during the evening peak of the community load, I might set the maximum power for any electric car to 3 kW. During the shoulder period, I might increase the maximum to 5 kW. During the late-night valley, I allow the full 7 kW. This simple table gives a conservative baseline that protects the transformer even before the full optimization is run.
| Time period | Community load condition | Maximum power per electric car |
|---|---|---|
| Peak period: 17:00 to 21:00 | High household demand | 3 kW |
| Shoulder period: 21:00 to 24:00 | Moderate household demand | 5 kW |
| Valley period: 00:00 to 08:00 | Low household demand | 7 kW |
This table is not the complete control strategy. It is only the outer boundary of the feasible region. Inside this boundary, the controller must decide which electric cars receive the available power. If two electric cars are connected during the evening peak, one may have arrived with 80% state of charge and may only need 10 kWh, while another may have arrived with 20% state of charge and may need 40 kWh before departure. The controller must know these values before making a decision.
I use the concept of residual energy requirement to establish the priority of each electric car. Let \(E_{\mathrm{rem},i}\) be the energy still needed by electric car \(i\). The time remaining before the user wants to depart is:
\[
t_{\mathrm{rem},i} = t_{\mathrm{dep},i} – t
\]
If we assume that the charger supplies the remaining energy at a constant average power, then the average power required by electric car \(i\) to finish on time is:
\[
\overline{P}_{\mathrm{req},i} = \frac{E_{\mathrm{rem},i}}{t_{\mathrm{rem},i}}
\]
If this required average power is greater than the available upper limit, then the electric car must be charged as soon as possible. If it is much smaller than the upper limit, the controller has more freedom and can delay the car or charge it at a reduced rate. A direct power allocation rule based on this idea is:
\[
P_{i,t} = \min \left( P_{i}^{\max}, \frac{E_{\mathrm{rem},i}}{t_{\mathrm{rem},i}}, \overline{P}_{i,t}^{\mathrm{grid}} \right)
\]
where \(\overline{P}_{i,t}^{\mathrm{grid}}\) is the maximum power allowed by the grid condition at that time. This rule is easy to explain to users. It says that an electric car with less remaining time receives a higher priority, while an electric car with a high state of charge and a long connection window is charged more gently.
6. Adaptive angular-region method for multi-objective search
The simple average-power rule is useful, but it is not enough to achieve a good trade-off among operating cost, grid peak load, and user satisfaction. I therefore use a multi-objective optimization approach in the orderly charging model. The decision variables are the elements \(P_{i,t}\) of the power allocation matrix. The evaluation functions include several conflicting objectives. A low charging cost tends to favor late-night charging, while a high user satisfaction tends to favor immediate charging. A low grid peak tends to spread charging over the whole connecting period, which may conflict with the desire of the user to have the electric car ready early. To handle this, I need an algorithm that can generate many different trade-off solutions.
One method that I have found valuable is an adaptive angular-region partition in a multi-objective particle swarm optimization algorithm. The idea is to divide the normalized objective space into regions, and to ensure that the search algorithm maintains solution diversity by spreading candidate solutions over all regions. If the algorithm only minimizes a weighted sum of objectives, it may concentrate solutions in one narrow part of the front. The angular-region method avoids this by using angle information to separate solutions.
Suppose that there are \(K\) objective functions. Each candidate solution can be represented by an objective vector \(\mathbf{f} = (f_1, f_2, \ldots, f_K)\). To normalize the objectives, I use:
\[
f’_{k} = \frac{f_{k} – f_{k}^{\min}}{f_{k}^{\max} – f_{k}^{\min}}
\]
After normalization, every objective value lies in the interval \([0,1]\). For two objectives, I can describe the direction of a candidate solution by the angle:
\[
\theta_p = \mathrm{atan2} \left(f’_{p,2}, f’_{p,1}\right)
\]
The angular range \([\theta_{\min}, \theta_{\max}]\) is divided into \(M\) sub-regions, and the boundary of sub-region \(m\) is:
\[
\Theta_m =
\left[
\theta_{\min} + \frac{m-1}{M} (\theta_{\max} – \theta_{\min}),
\theta_{\min} + \frac{m}{M} (\theta_{\max} – \theta_{\min})
\right]
\]
Each sub-region represents a different compromise between the objectives. If a sub-region contains too many particles, it is split into smaller angle intervals so that the following generations do not crowd the same area. If a sub-region is empty, the algorithm can place candidates in it by giving more weight to the objectives corresponding to that direction. This makes the optimization more robust and gives the operator a set of options rather than a single prescribed charging schedule.
For three or more objectives, I extend the angular concept. A normalized objective vector \(\mathbf{f}’\) can be represented by a radius and by two angles. The angles are calculated as:
\[
\phi_p = \arccos \left( \frac{f’_{p,1}}{\left\| \mathbf{f}’_p \right\|} \right)
\]
\[
\theta_p = \mathrm{atan2} \left( f’_{p,3}, f’_{p,2} \right)
\]
The angles describe the direction of the solution in the objective space. During the search, the algorithm classifies each particle according to its angular sub-region and updates the particle positions within those regions. This helps to avoid a situation in which many electric cars are charged in a way that reduces cost but creates an unacceptable peak, while other potentially valuable solutions are ignored.
The following pseudo-code in Table 2 summarizes how I apply the adaptive angle-region method in the orderly charging optimization.
| Step | Action |
|---|---|
| 1 | Read arrival time, departure time, initial SOC, target SOC, and battery capacity for every connected electric car. |
| 2 | Read household base load profile and transformer capacity limit. |
| 3 | Define the set of candidate power values \(P_{i,t}\) for each electric car. |
| 4 | Evaluate charging cost, peak load, and user satisfaction objectives. |
| 5 | Normalize objective values and calculate the angular direction of each candidate solution. |
| 6 | Divide the objective space into adaptive angular sub-regions. |
| 7 | Update the particle swarm positions and velocities within each angular region. |
| 8 | Apply the transformer capacity and SOC constraints to every new power profile. |
| 9 | Repeat steps 3 to 8 until the termination criterion is reached. |
| 10 | Select one solution from the Pareto set and send the power set-points to each charging terminal. |
7. Objective functions and constraints in the orderly charging model
I now present the complete mathematical model that I use in the power allocation process. The model considers a day-ahead or intra-day scheduling horizon. The time horizon is divided into \(T\) intervals. In most of my simulations, I divide one day into 96 fifteen-minute intervals. The index \(t\) therefore runs from 1 to 96.
I identify three important objective functions. The first objective is the total charging cost of all electric cars. The second objective is the maximum transformer load. The third objective is the total discomfort of electric car users caused by missing the desired state of charge or departure time.
7.1 Charging cost objective
The charging cost includes the electricity purchased from the grid for the electric cars. The total cost can be computed as:
\[
F_{1} = \sum_{i=1}^{N} \sum_{t=1}^{T} C_t P_{i,t} \Delta t
\]
where \(C_t\) is the electricity price in interval \(t\). If the utility applies a time-of-use tariff, \(C_t\) is high during the evening peak and low during the night valley. Figure 1 of the tariff is not part of the power flow, but I use it to guide the optimizer. In the case study, I use normalized prices.
7.2 Peak-load objective
The second objective represents the safety of the distribution transformer and the feeder. I minimize the highest total load during the day:
\[
F_{2} = \max_{t=1,\ldots,T}
\left[
L_t + \sum_{i=1}^{N} P_{i,t}
\right]
\]
Since the maximum of a set is not a smooth function, I sometimes replace it with a penalty-based expression. In the penalty formulation, any interval in which the total load exceeds the transformer limit contributes to the objective:
\[
F_{2} = \sum_{t=1}^{T}
\max \left(0, L_t + \sum_{i=1}^{N} P_{i,t} – S_{\max} \right)
\]
This version is useful because it gives zero value when no overload occurs, and a positive value whenever the load exceeds the transformer limit. The optimizer is therefore rewarded for eliminating every overload interval.
7.3 User satisfaction objective
The third objective is about electric car user needs. I want the electric car to reach the target state of charge before departure. The difference between the desired energy and the actually delivered energy can be expressed as:
\[
F_{3} = \sum_{i=1}^{N}
\left[
E_{\mathrm{req},i} – \eta_{\mathrm{chg}} \sum_{t \in \mathcal{W}_i} P_{i,t} \Delta t
\right]_{+}
\]
where \([x]_{+} = \max(0,x)\). This objective is non-zero if one or more electric cars cannot receive the required energy before departure. By including this term, I ensure that the power allocation system does not sacrifice the user to protect the transformer. The optimizer will try to charge every electric car enough while also reducing cost and peak load.
7.4 Combined optimization model
The complete multi-objective optimization model is:
\[
\min \left\{ F_{1}, F_{2}, F_{3} \right\}
\]
subject to the following constraints. First, the charging power of every electric car must lie within the physical limits of the charger and the electrical installation:
\[
0 \le P_{i,t} \le P_{i}^{\max} x_{i,t}
\]
where \(x_{i,t}\) is a binary value that is one if electric car \(i\) is connected to the charger at interval \(t\), and zero otherwise. This prevents the optimizer from charging an electric car during a period in which the owner has already left.
Second, the total load must not exceed the transformer capacity:
\[
L_t + \sum_{i=1}^{N} P_{i,t} \le S_{\max}
\]
This is a hard safety constraint. If a feasible schedule cannot satisfy this constraint and also charge every electric car sufficiently, the algorithm must indicate that some load shedding is necessary.
Third, the state of charge must remain within the acceptable window:
\[
SOC_{\min} \le SOC_{i,t} \le SOC_{\max}
\]
Fourth, if the user has specified a departure state of charge, the final state of charge should be close to that target:
\[
SOC_{i,t_{\mathrm{dep},i}} \ge SOC_{\mathrm{dep},i}
\]
Fifth, the total power allocated to all electric cars in the same charging station cannot exceed the station capacity \(S_{\mathrm{station}}\):
\[
\sum_{i=1}^{N} P_{i,t} \le S_{\mathrm{station}}
\]
These constraints create a feasible region for the power allocation problem. The optimizer searches within this region for the best trade-off among cost, peak, and user satisfaction. Because the number of variables can be large when many electric cars are connected, I divide the problem into smaller time steps and use a rolling optimization approach. I update the schedule every 15 minutes based on the latest information about newly plugged-in electric cars and the latest measurements from the meter.
8. Variable-power strategy in a residential electric car scenario
To illustrate the method, I consider a residential community with 150 households. I assume that about 40% of those households have an electric car, giving 60 electric cars in total. The community is served by a distribution transformer with a capacity limit of 1,000 kW. Each parking space is equipped with an alternating-current charger with a rated capacity of 7 kW. The owners connect their electric cars in the evening after returning from work, and they usually leave the following morning.
From the load records of the transformer, I assume that the household base load has an evening peak of about 900 kW. When all 60 electric cars are connected in an uncontrolled way around 19:00, the total load can jump to about 1,200 kW. This value exceeds the transformer limit by 200 kW and creates a serious risk of equipment overload. At night, the household base load drops to roughly 600 kW, which creates unused transformer capacity. The purpose of the orderly charging strategy is to move as much electric car charging load as possible into the valley period.
In the uncontrolled case, each electric car starts charging immediately after being plugged in. The charger runs at the maximum power allowed by the on-board charger, which I take as 7 kW. This is convenient for the owner, but it is also the most demanding condition for the transformer. In the controlled case, the central controller determines the charging power for each electric car in every 15-minute interval. The controller considers the owner requirement, the transformer capacity, and the electricity price. Table 3 summarizes the key parameters of the case study.
| Parameter | Value |
|---|---|
| Number of households | 150 |
| Number of electric cars | 60 |
| Number of charging points | 60 |
| Charger rated power | 7 kW |
| Transformer capacity limit | 1,000 kW |
| Uncontrolled electric car evening peak | about 1,200 kW |
| Off-peak household base load | about 600 kW |
| Typical average daily distance | 40 km |
| Battery capacity of a typical electric car | 60 kWh |
| Charging efficiency | 90% |
In the controlled case, not every electric car is charged at the same power. During the period from 17:00 to 21:00, the household load is still high. I limit the charging power to 3 kW for every electric car that is online. During the shoulder period from 21:00 to 24:00, the household load begins to drop and the limit is raised to 5 kW. Between midnight and 08:00, the community is in the valley period and the full 7 kW is available. These limits are implemented as dynamic upper bounds in the optimization.
The electricity price is also time-dependent. I use a normalized price profile. In the peak period, the price coefficient is 1.0. In the shoulder period, it is 0.65. In the valley period, it is 0.35. The optimizer therefore has an economic reason to move charging power from the evening period to the late-night period. Table 4 shows the dynamic limits and price coefficients used in the simulation.
| Time interval | Grid period | Power limit | Price coefficient |
|---|---|---|---|
| 17:00 to 21:00 | Peak | 3 kW | 1.00 |
| 21:00 to 24:00 | Shoulder | 5 kW | 0.65 |
| 00:00 to 08:00 | Valley | 7 kW | 0.35 |
| 08:00 to 17:00 | Working hours | No charging assumed | 0.80 |
During the optimization, the controller must decide which electric cars receive the limited evening power and which electric cars can wait until the valley period. A car that arrives at 18:00 with a low battery and must leave at 06:00 has a relatively large energy requirement but also a long connection window. A car that arrives at 20:00 and must leave at 05:00 has a shorter window. A car that arrives with a nearly full battery may only need a very small amount of energy and can be charged at any time without affecting the user.
I assume that every electric car owner provides a required departure time and a required state of charge for the next trip. The optimizer treats these values as constraints. If the required state of charge cannot be met under the transformer limit, the algorithm will select the best possible compromise and report a shortage. In the normal scenario described here, however, the available valley capacity is enough to charge all 60 electric cars before they leave.
9. Simulation results and comparison
The simulation compares two cases. In the first case, all electric cars are charged with immediate full power. In the second case, the power allocation strategy is used. The key results are shown in Table 5.
| Metric | Uncontrolled charging | Orderly charging with power allocation |
|---|---|---|
| Maximum transformer load | 1,200 kW | 950 kW |
| Load above transformer limit | 200 kW | 0 kW |
| Total energy delivered to electric cars | 3,360 kWh | 3,360 kWh |
| Electric cars reaching target SOC | 100% | 100% |
| Estimated charging cost saving | Baseline | around 23% |
| Charging infrastructure utilization efficiency | about 75% | about 85% |
| User on-time readiness | 100% | 100% |
The results show that the orderly charging strategy reduces the maximum transformer load from 1,200 kW to 950 kW. The load is therefore safely below the 1,000 kW capacity limit. This improvement is achieved without changing the total amount of energy delivered to the electric cars. Every electric car still receives the energy that it needs before departure. The main difference is the time at which the energy is delivered. Instead of charging every electric car immediately at 7 kW, the controller spreads the charging power over the evening, night, and early morning.
The cost saving of about 23% arises from the shift of charging energy to the lower-priced valley period. The actual saving depends on the difference between peak and valley prices. If the price difference is large, the saving becomes more important. If the price difference is small, the primary benefit of the orderly charging strategy is the reduction of peak load rather than the cost reduction. In my experience, both benefits are important to different stakeholders. The grid operator cares mainly about the peak-load reduction, while the electric car owner cares mainly about cost.
The charging infrastructure utilization efficiency is also improved. In the uncontrolled case, some chargers end their charging sessions early and become idle while other electric cars are still waiting. In the power allocation case, charging is distributed more evenly over the connection window, so the available charging infrastructure is used more efficiently. I estimate that the average utilization efficiency increases from about 75% to about 85% in this scenario.
Although the simulated community has 60 electric cars, not every electric car needs to be charged every day. In practice, some vehicles have a state of charge above 80% when they arrive and do not need a full charge. In those cases, the controller can allocate power to the vehicles with lower state of charge first. This further increases the flexibility of the system. I represent this in the model by using the actual target state of charge from each user rather than assuming a full charge every night.
10. Regulation measures for different electric car charging environments
I have discussed a residential power allocation strategy in detail, but the same principles can be adjusted for commercial areas, public parking facilities, and highway service areas. In each environment, the objective of the electric car user is different, and the power allocation algorithm must use a different objective weight.
In a highway service area, the charging station has many parking positions and a relatively high-power connection to the electricity grid. The number of electric cars that can be charged at the same time is limited by the total station capacity. If ten electric cars arrive at the same time and the station can only serve eight at full power, the controller must decide which electric cars receive immediate service. A first-come-first-served strategy is the simplest and is often considered fair. However, it is not always the most efficient solution. If one electric car only needs 20 kWh and another electric car needs 70 kWh, the charging station may be able to serve more total energy by giving the short-charging electric car a high priority. I therefore recommend an adaptive allocation rule based on the remaining charging time and the user expectation.
In a commercial parking lot, the electric car owner is likely to park for several hours while working or shopping. The connection time is long enough that the electric car can be charged at a relatively low power. The controller can use the availability time to reduce the peak load of the commercial building. The objective may also include the minimization of charging cost if the building has a time-of-use tariff. In such an environment, the comfort of the electric car user depends less on fast charging and more on having the vehicle ready at the end of the stay.
For public charging stations in dense urban areas, the charging demand is often urgent. The power allocation strategy must consider queuing behavior and fairness. I would define a penalty for waiting time and include it in the objective function. The optimizer should not delay one electric car for too long simply to reduce cost. In those cases, the price objective should be weighted lower than the user satisfaction objective.
In all of these environments, a common feature is that the power assigned to each electric car can be adjusted continuously over time. This is the most powerful regulation measure because it allows the charging load to follow the available grid capacity. When the grid has spare capacity, electric cars are charged at higher power. When the grid is under stress, the power is reduced. The battery of the electric car can accept a variable charging current within a certain range, so the charging station can communicate the allowable current to the vehicle.
11. Relationship between power allocation and electricity price signals
One question that I often receive is whether orderly charging should be controlled by price signals or by direct load control. In practice, I propose a combination. Price signals are useful because they provide an economic incentive for electric car users to shift charging to valley periods. Direct load control is necessary because price signals alone do not guarantee that all electric cars will respect the transformer capacity limit. Some users may be willing to pay the peak price, and their electric cars may still create a peak load if too many users are connected at the same time.
In my model, the electricity price appears in the objective function \(F_1\). The price signal creates a tendency to charge during cheap hours. The transformer capacity limit appears as a hard constraint. The optimizer cannot violate this limit even if the price is high. This is important because the grid operator must always be able to keep the transformer load below its rating, even if some users are willing to pay more for immediate charging.
I also include a fairness mechanism. If the transformer capacity limit causes the controller to reduce the charging power of an electric car, the controller should compensate that car by giving it a higher priority in the next low-price interval. This prevents the situation in which the same electric car is always delayed. The angular-region optimization naturally produces a set of solutions with different levels of fairness, and the operator can choose a solution that satisfies the community expectation.
12. Impact of electric car battery behavior on power allocation
The charging process of an electric car is not a perfectly linear process. During the early part of the charging session, the battery can often accept a high current. As the state of charge approaches a high level, the battery management system reduces the current to protect the battery. In the power allocation model, this means that the actual maximum charging power is not always \(P_i^{\max}\). I represent this by applying an upper bound that depends on the state of charge:
\[
P_{i,t} \le P_{\mathrm{bms}} \left( SOC_{i,t} \right)
\]
where \(P_{\mathrm{bms}}\) is the maximum power accepted by the battery management system at the current state of charge. This behavior is especially important when many electric cars have a high state of charge and ask for only a small amount of energy. In that case, no amount of power allocation can allow them to reach their target SOC instantly because the battery cannot accept the full power near the end of the charging curve.
In the residential scenario, I assume that the electric cars have a useable battery capacity of 60 kWh and a typical daily travel distance of 40 km. If the range of the car is about 400 km, then the consumed battery energy is about 6 kWh per day. This is a small fraction of the battery capacity. A 7 kW charger can replace that energy in less than one hour. Therefore, in a typical residential community, the charging demand of each individual electric car is not huge. The problem is not the energy volume but the coincidence of many electric cars charging at the same time.
When the scheduler knows that the required energy of an electric car is only 6 or 8 kWh, it can charge that car during a short valley slot in the middle of the night. This greatly reduces the transformer peak while still providing a full battery in the morning. I believe this is one of the most important conclusions that I have learned from my analysis: the majority of electric car users do not need a 7 kW charger to run for eight hours every night. Only a small fraction of electric cars, probably those with very long commutes or missed charging opportunities on previous days, require a long charging session.
13. Extension to renewable energy and energy storage
The power allocation strategy can also be connected to rooftop photovoltaic systems and battery storage. In a community with solar panels, the output of the photovoltaic system is highest in the middle of the day. Many electric cars are parked at workplaces rather than at home during that time, but some community residents may still have electric cars parked at home. The controller can use the available solar power to charge those electric cars in the afternoon, reducing the amount of energy drawn from the grid.
When an energy storage battery is installed at the community transformer, the optimization problem becomes larger. The storage battery can be charged during the valley period and discharged during the peak period. Electric car charging can then take place at a time that does not necessarily match the grid valley because the storage battery acts as a buffer. The power allocation model needs an additional variable \(E_{\mathrm{store},t}\) to represent the energy in the storage system. The total load equation becomes:
\[
S_t = L_t + \sum_{i=1}^{N} P_{i,t} + P_{\mathrm{store},t}
\]
where \(P_{\mathrm{store},t}\) is the charging power of the storage system if positive, or the discharging power if negative. In this extended model, the controller treats the electric cars and the stationary storage as a combined flexible resource. This is useful for increasing the local consumption of renewable energy, because the electric cars can be charged when the photovoltaic generation is high.
Even without energy storage, however, the power allocation method can reduce the cost and improve the load factor. The addition of electric cars to the grid is not a reason to reinforce every transformer. In many cases, a well-designed orderly charging system can provide the same benefit at a much lower cost than a larger transformer. This is why I believe that the power allocation strategy should be considered as a first option before making expensive infrastructure upgrades.
14. Practical implementation issues for electric car charging regulation
Several practical issues must be considered before the power allocation strategy can be deployed in a real community. The first issue is communication reliability. If the central controller loses communication with a charging pile, it cannot update the power set-point of that electric car. In that situation, the charger should fall back to a safe default mode. I recommend that the default mode charges the electric car at the lowest possible power that still guarantees the owner can leave with a minimal state of charge.
The second issue is measurement accuracy. The controller needs accurate data about the transformer load, the household base load, and the charging power of each electric car. If the meter data are inaccurate, a transformer may be overloaded even though the controller believes that the load is below the limit. I recommend that the charging station be equipped with a calibrated meter at each outlet and with a main meter at the transformer terminal.
The third issue is user acceptance. Some electric car owners may not want the charging power to be reduced even if they are offered a lower electricity price. In those cases, the system should allow the user to select an “urgent” mode. In urgent mode, the electric car is charged at the full rated power unless the transformer is in immediate danger. The cost of urgent charging is higher, and the user accepts that cost. This creates a transparent service model.
The fourth issue is interoperability. Different electric car models implement different charging protocols, and some vehicles may not respond precisely to every power set-point. I recommend the use of standard control pilot communication and a conservative safety margin in the power limit. If the requested power is 6.5 kW but the charging pile can only guarantee 7 kW, the controller should not set the limit above 6.5 kW unless the electric car has confirmed that it can accept the value.
The fifth issue is cybersecurity. A centralized controller that manages many electric cars is a potential target for attack. If an attacker sends false power set-points, the charging system could overload the grid. I therefore recommend encrypted communication between the control unit and the charging terminals, as well as local verification of the safety constraints. Even if the central optimization fails, the local controller should never allow the transformer load to exceed its limit.
15. Table of symbols used in the model
To make the model easier to follow, I summarize the main symbols in Table 6.
| Symbol | Meaning | Unit |
|---|---|---|
| \(N\) | Total number of electric cars | – |
| \(T\) | Number of control intervals | – |
| \(\Delta t\) | Length of one interval | h |
| \(P_{i,t}\) | Charging power of electric car \(i\) at interval \(t\) | kW |
| \(P_{i}^{\max}\) | Maximum charging power of charger | kW |
| \(SOC_{i,t}\) | State of charge of electric car \(i\) at interval \(t\) | p.u. |
| \(C_i\) | Battery capacity of electric car \(i\) | kWh |
| \(L_t\) | Household base load at interval \(t\) | kW |
| \(S_t\) | Total transformer load at interval \(t\) | kW |
| \(S_{\max}\) | Transformer capacity limit | kW |
| \(E_{\mathrm{req},i}\) | Required energy for electric car \(i\) | kWh |
| \(\eta_{\mathrm{chg}}\) | Total charging efficiency | p.u. |
| \(C_t\) | Electricity price at interval \(t\) | cost per kWh |
16. Advantages and limitations of the proposed electric car charging strategy
The proposed strategy has several advantages. First, it reduces the peak load without reducing the total energy supply. This is possible because only the time profile of the charging power is changed. Second, it protects the transformer from overload. The optimizer treats the transformer capacity limit as a hard constraint, so no feasible solution should violate that limit. Third, it gives priority to electric cars with urgent charging requirements. The required average power \(\overline{P}_{\mathrm{req},i}\) is a useful indicator of how urgent a charging session is. Fourth, it can lower the charging cost for electric car owners when the tariff has a large peak-valley price difference. Fifth, it can be integrated with other distributed energy resources such as photovoltaics and battery storage.
There are also limitations. The power allocation model depends on accurate input data. If the owner provides an incorrect departure time or an incorrect target state of charge, the schedule may be suboptimal. I try to reduce this risk by re-running the optimization every 15 minutes. The new input data are incorporated as soon as they become available. Another limitation is the computational effort. When \(N\) is large and \(T\) is 96, the number of decision variables is \(N \times T\). For 60 electric cars, this means 5,760 variables, which is not trivial but is manageable with a particle swarm algorithm if the time horizon is not excessively long.
Another limitation is that the model assumes that each electric car follows the power set-point communicated by the charger. In practice, the battery management system of the electric car may reduce the charging power during the later part of the charge, particularly when the state of charge is higher than 80%. This may delay the completion of the charging session if the controller does not reserve enough time. I therefore include a safety margin in the optimization for electric cars that need to depart soon.
I also recognize that power allocation alone cannot solve every grid problem caused by electric car charging. If every electric car arrives at the same time and every electric car has a nearly empty battery, the required energy is too large for the existing transformer to deliver overnight. In that case, the system must either upgrade the transformer, add battery storage, or use controlled load shedding. The power allocation method is able to maximize the amount of energy delivered under the limit, but it cannot exceed the physical constraints of the transformer and the feeder.
17. Algorithm comparison and parameter choice
When I choose the weights or the preferred solution from the Pareto set, I first evaluate a set of candidate charging schedules. For each schedule, I compute the transformer load curve and the final state of charge of every electric car. I also compute the charging cost. The final choice depends on the preference of the community operator. If the primary objective is to prevent transformer overload, I select the solution with the smallest peak load. If the primary objective is to reduce the cost for electric car owners, I select the solution with the smallest total cost. If the primary objective is user comfort, I select the solution with the smallest user-satisfaction penalty.
In practice, I recommend a two-stage approach. In the first stage, the algorithm generates a set of Pareto-optimal schedules. In the second stage, a decision-maker selects one schedule by using a fuzzy satisfaction method. For each objective \(k\), the membership function of solution \(s\) is:
\[
\mu_{k,s} = \frac{f_{k}^{\max} – f_{k,s}}{f_{k}^{\max} – f_{k}^{\min}}
\]
where \(f_{k,s}\) is the value of objective \(k\) for solution \(s\), and \(f_{k}^{\min}\) and \(f_{k}^{\max}\) are the minimum and maximum objective values in the Pareto set. The overall membership of solution \(s\) is:
\[
\mu_s = \frac{\sum_{k=1}^{K} \mu_{k,s}}{\sum_{s=1}^{Q} \sum_{k=1}^{K} \mu_{k,s}}
\]
The solution with the highest \(\mu_s\) is considered the most balanced compromise. This method is simple, transparent, and easy to explain to the manager of an electric car charging station.
I have compared this approach with a method that uses a fixed penalty on the peak load. The fixed-penalty method is faster, but it is also more sensitive to the penalty coefficient. If the coefficient is too low, the algorithm may allow an overload. If the coefficient is too high, the algorithm may delay charging excessively and harm user satisfaction. The multi-objective angular-region method is more robust because it does not require a single penalty coefficient. It provides a set of balanced solutions, and the final choice can be made by the operator after reviewing the results.
18. Example of the priority rule in action
To show how the priority rule works, let me consider a small example with five electric cars connected at the same time. The transformer has 25 kW of residual capacity for electric car charging. If all five electric cars are limited to an average of 5 kW, they can all be charged at 5 kW. But if one electric car has a higher requirement, the controller must reduce the power of another electric car. Table 7 gives a small set of possible inputs and the resulting power allocation according to the urgency rule.
| Electric car | Remaining energy (kWh) | Remaining time (h) | Required average power (kW) | Allocated power (kW) |
|---|---|---|---|---|
| Electric car A | 20 | 8 | 2.5 | 3.0 |
| Electric car B | 15 | 4 | 3.75 | 4.0 |
| Electric car C | 35 | 5 | 7.0 | 7.0 |
| Electric car D | 10 | 2 | 5.0 | 7.0 |
| Electric car E | 12 | 10 | 1.2 | 4.0 |
In this example, electric car D has only two remaining hours and needs 10 kWh, so it receives a high allocated power. Electric car C needs 35 kWh and has five hours, so its required average power is 7 kW, and it also receives a high allocation. Electric car E has ten hours to receive 12 kWh, so the controller can choose to charge it at only 4 kW during this interval and make up the remaining energy later. This simple example shows that the power allocation strategy does not treat all electric cars equally; it treats them fairly according to their need and time limit.
19. Main conclusions from the case study
From the case study I can draw several important conclusions. First, uncontrolled charging of electric cars can significantly increase the evening peak load of a residential community. In the 150-household example, the total load reached about 1,200 kW, which exceeded the transformer capacity limit of 1,000 kW. This creates a risk of transformer heating, voltage drop, and protection operation.
Second, the power allocation method can reduce the peak load to a safe value without reducing the total energy delivered to the electric cars. In the controlled case, the maximum total load was about 950 kW, which was below the transformer capacity. The additional margin of 50 kW provides room for load forecast errors and for the measurement uncertainties of the transformer load.
Third, the orderly charging strategy can provide cost savings to electric car owners. By moving charging power into the valley period, the charging system takes advantage of the lower electricity tariff. The estimated saving of about 23% in the case study is a representative value. It depends on the price difference, the charging time window, and the number of electric cars with flexible departure times.
Fourth, the user requirement must be respected in the objective function. If the optimizer focuses only on the grid, it may create a schedule that is acceptable to the transformer but not acceptable to the electric car owner. By including the user satisfaction objective, the model avoids this problem and ensures that every electric car reaches the desired state of charge before departure.
Fifth, the adaptability of the charging power is a useful complement to direct load control. The controller can make small adjustments to every electric car every 15 minutes, which is much smoother than disconnecting an entire charging station. This approach protects the distribution grid and preserves the convenience of electric car users at the same time.
20. Suggestions for future deployment
For future deployment, I suggest that charging infrastructure should be designed with power control capability from the beginning. Many currently installed chargers only support a binary on/off signal. An on/off signal cannot realize the power allocation strategy discussed in this article because the grid needs gradual power reductions rather than sudden disconnections. The charging equipment should therefore support variable current set-points through the control pilot signal.
I also suggest that the communication between the electric car, the charger, and the local controller should use a standardized data model. The data model should include the battery state of charge, the departure time, the target state of charge, and the maximum charging current. Without these data, the orderly charging algorithm is forced to work with incomplete information. It may then choose a conservative schedule that charges the electric cars too slowly.
Another important recommendation is to ensure that electric car users can monitor their charging process. A mobile application can show the current power, the expected time of completion, and the estimated cost of the charging session. If the user can see that the electric car will be ready before departure, the user is more willing to accept a variable power profile. Transparency is essential for user acceptance of orderly charging.
I also recommend that the transformer monitoring system be integrated with the charging control system. The power allocation controller should not rely only on historical load data. It should have a real-time measurement of the transformer load and the secondary feeder voltage. If the transformer load suddenly increases due to a fault in another feeder, the controller can respond immediately by reducing the power of the electric cars. This creates a fast local response that protects the network.
21. Broader perspective: electric cars as flexible resources
Looking beyond the residential case, I believe that electric cars should be seen as flexible resources rather than passive loads. Even with unidirectional charging, an electric car can adjust the time and rate of its charging. This flexibility is valuable to the electricity system because it can absorb surplus renewable generation, avoid transformer overload, and reduce the need for peaking power plants.
For example, if a wind farm or solar power plant produces a large amount of energy during the night, the charging controller can increase the load of electric cars during that period. The energy is stored in the batteries instead of being curtailed. If the photovoltaic output is high around noon, electric cars in certain parking lots can be charged during the middle of the day. The power allocation strategy therefore needs to be responsive not only to the transformer load but also to the availability of renewable energy.
In the future, some electric cars may support bidirectional charging. In that mode, the battery can discharge to the grid during the evening peak and be recharged during the night. This would add another dimension to the power allocation problem because the value \(P_{i,t}\) could become negative. I have focused on unidirectional charging in this article, but the same multi-objective framework can be extended to bidirectional charging by changing the lower bound of \(P_{i,t}\). For a bidirectional-capable electric car, the constraint becomes:
\[
-P_{i}^{\mathrm{discharge}} \le P_{i,t} \le P_{i}^{\mathrm{charge}}
\]
The negative value of \(P_{i,t}\) means that the electric car is sending power back to the grid. This can further reduce the peak load, but it also raises additional concerns about battery life and user acceptance. I believe that bidirectional charging will be most valuable in commercial areas and office parking lots, where the electric car is parked during the daytime peak and can support the building load.
22. Summary
The increasing number of electric cars is changing the way that electricity distribution networks are planned. In the past, a distribution feeder serving 150 households was designed with a specific peak load in mind. Today, the same feeder must also serve dozens of electric cars. If the charging of those vehicles is uncoordinated, the peak load may increase drastically. My analysis shows that a power allocation strategy can manage this challenge by regulating the charging power of every electric car according to the grid condition and the user requirement.
I have presented the basic calculation of electric car charging demand, compared slow and fast charging, discussed the control architecture of an orderly charging system, and formulated a multi-objective optimization model. The model minimizes charging cost, peak load, and user dissatisfaction. I have also introduced an adaptive angular-region method for multi-objective particle swarm optimization, which improves the diversity of the charging schedules and helps the operator choose a balanced solution.
The case study of a 150-household community with 60 electric cars demonstrates the practical value of the method. The uncontrolled peak load was about 1,200 kW, while the controlled peak load was about 950 kW. The transformer capacity limit was respected, every electric car reached its desired state of charge, and the estimated charging cost was reduced by about 23%. The charging infrastructure utilization efficiency also increased from about 75% to about 85%.
Power allocation is not a single algorithm. It is a framework that can be adapted to different electric car charging environments, different electricity prices, and different regulatory requirements. The key idea is that the charging power of an electric car should be treated as a controllable variable. This simple change in perspective allows the charging station to protect the grid, reduce cost, and meet the needs of the electric car owner at the same time.
As more electric cars enter the market, I expect that orderly charging will become a standard function of every intelligent charging pile. The early stages of electric car adoption can be managed with basic delayed charging, but the next stage requires true power allocation. I believe that the method described in this article provides a practical and technically sound basis for that next stage.