The transition towards a low-carbon energy system has changed the way in which distribution networks are planned and operated. Among many low-carbon technologies, the electric car has become one of the most prominent contributors because of its ability to reduce transport-related emissions and to participate in demand-side management. The large-scale deployment of electric cars, however, introduces a new set of operational challenges to distribution networks. When a growing number of electric cars are connected through fast-charging stations, the resulting power demand can produce unacceptable voltage drops, increase line losses, and aggravate the peak-valley difference of load curves. Those issues become even more complex when the future distribution system operates in direct current form, because DC networks have different voltage control mechanisms and loss characteristics from conventional AC systems.
My research focuses on topology optimization of DC distribution networks under scaled electric car integration. The central idea is to exploit the inherent flexibility of electric car batteries through vehicle-to-grid discharge, and to couple this flexibility with the network reconfiguration capability provided by soft open points. This combination provides a coordinated method for improving voltage deviation and energy losses, not only in normal operation but also in fault restoration scenarios. In the remainder of this article, I summarize the detailed modelling framework, optimization methods, and representative numerical results of the work.
1. Background
DC distribution networks have attracted significant attention because of their simpler structure, higher efficiency, and more convenient integration of DC devices. Photovoltaic generation, storage batteries, modern electronic loads, and fast chargers of electric cars are natural DC resources. In contrast to AC distribution systems, DC systems avoid multiple AC/DC conversion stages for such resources, which reduces conversion losses and control complexity. Nevertheless, the operating flexibility of a DC network depends strongly on the power electronic interfaces and on the ability to reconfigure the network topology during emergency conditions.
From a load perspective, electric cars have a strong spatial and temporal randomness. Their arrival time, departure time, initial state of charge, and charging duration are difficult to predict. Large-scale clustered charging may make the voltage at the end of a DC feeder excessively low. From a resource perspective, electric cars can be viewed as distributed energy storage devices when they are connected to the network. If a sufficient number of electric cars are allowed to discharge during peak hours, they can supply part of the local load and reduce the amount of power drawn from the upstream grid. This capability is usually called vehicle-to-grid, and it makes the electric car not merely an uncontrollable load but a flexible resource that supports network operation.
Another important factor is the introduction of soft open points. A soft open point replaces a conventional tie switch with a fully controlled power electronic converter, allowing rapid and precise regulation of power flow between feeders. In a DC network, it can be realized by two DC-DC converters connected back-to-back. The soft open point can reshape the flow of active power, improve the voltage profile, and provide a fast path to connect islanded areas with the main grid after a fault. Therefore, by coordinating the discharge of electric cars with the placement and operation of soft open points, it is possible to achieve a multiple-resource topology optimization framework.
2. Dynamic Equivalent Modelling and Impact Analysis
To evaluate the influence of scaled electric car integration, I first established a dynamic equivalent model of the DC distribution system. This model includes the electric car battery charging/discharging behavior, distributed renewable generation, energy storage devices, DC-DC converters, and the DC network power flow.
The charging and discharging behaviour of an electric car is constrained by its rated converter power and by the fact that charging and discharging cannot occur simultaneously. I represented the operational status with binary variables and expressed the active power limits as:
$$
\begin{cases}
0 \le P_{j,t}^{c} \le \alpha_{j,t}^{c} P_{j,\max}^{c}, \quad \alpha_{j,t}^{c} \in \{0,1\}, \\[4pt]
0 \le P_{j,t}^{d} \le \alpha_{j,t}^{d} P_{j,\max}^{d}, \quad \alpha_{j,t}^{d} \in \{0,1\}, \\[4pt]
\alpha_{j,t}^{c} + \alpha_{j,t}^{d} \le 1,
\end{cases}
$$
where \(P_{j,t}^{c}\) and \(P_{j,t}^{d}\) denote the charging and discharging power of the \(j\)-th electric car at time step \(t\), respectively. The binary flags \(\alpha_{j,t}^{c}\) and \(\alpha_{j,t}^{d}\) indicate whether the car is charging or discharging.
The state of charge of the electric car battery is updated with respect to the initial value and the net energy transferred during a time interval:
$$
SOC_{j,t}^{EV} = SOC_{j,0}^{EV} + \frac{\Delta t}{Q_{j}^{EV}} \left( P_{j,t}^{c} – P_{j,t}^{d} \right),
$$
where \(Q_{j}^{EV}\) is the rated battery capacity, \(\Delta t\) is the control interval, and \(SOC_{j,t}^{EV}\) is the battery state of charge. I also considered the constraint that the state of charge must remain between the manufacturer-specified minimum and maximum values.
For a discharge station where many electric cars are aggregated, the total discharge power \(W_{d,t}\) is the sum of the active power contributions of the cars present at that station:
$$
W_{d,t} = \sum_{j \in \Omega_{d}} k_{j,t} P_{j,t}^{d},
$$
where \(k_{j,t}\) is a binary status variable showing whether the \(j\)-th electric car participates in discharge, and \(\Omega_{d}\) is the set of electric cars connected to discharge station \(d\).
The discharge capability is not only limited by converter power but also by battery state of charge. To prevent excessive discharge that would harm the battery and inconvenience the car owner, I used a minimum state-of-charge threshold of 0.2. The dispatchable energy from an electric car can then be expressed as:
$$
Q_{j,t}^{d} =
\begin{cases}
0, & SOC_{j,t}^{d} \le 0.2, \\[3pt]
\left( SOC_{j,t}^{d} – 0.2 \right) Q_{j}^{EV}, & SOC_{j,t}^{d} > 0.2.
\end{cases}
$$
In addition to electric cars, the DC distribution network contains renewable distributed generators and storage. For photovoltaic generation, I used a simplified maximum-power-point model in which the output power is a function of irradiance and cell temperature. The storage system is represented by charging/discharging power constraints and state-of-charge update equations that are similar in structure to those of the electric car, but with distinct limits because storage is a stationary asset.
DC-DC converters are included in every connection between distributed resources and the DC bus. Since isolated DC-DC converters are widely used on loads and renewable generators, I considered a full-bridge converter equivalent model. The converter model relates the input and output voltages through the duty cycle and the transformer turns ratio:
$$
n D U_{i} – U_{o} – n D U_{Q} – I_{o} R_{E} = 0,
$$
where \(U_i\) is the input voltage, \(U_o\) is the output voltage, \(D\) is the duty cycle, \(n\) is the transformer ratio, \(U_Q\) is the switch conduction voltage drop, \(R_E\) is the total equivalent resistance, and \(I_o\) is the output current. The total converter loss is then obtained as the difference between the input power and the output power.
For the DC network power flow, I used a Newton-Raphson formulation. In a DC network, the nodal power equation has no reactive power and no voltage angle; it depends only on voltage magnitudes and nodal conductance:
$$
P_{i} = U_{i} \sum_{j=1}^{n} G_{ij} U_{j},
$$
where \(G_{ij}\) is the conductance matrix entry, \(U_i\) and \(U_j\) are the node voltages, and \(n\) is the total number of nodes. The power mismatch at each node is written as:
$$
\Delta P_{i} = P_{i}^{sp} – U_{i} \sum_{j=1}^n G_{ij} U_{j},
$$
and the voltage correction equation is:
$$
\Delta \mathbf{P} = \mathbf{J} \Delta \mathbf{U},
$$
where \(\mathbf{J}\) is the Jacobian matrix of the DC power-flow equations. The iterative process updates all bus voltages until the active power mismatches are smaller than the convergence tolerance. With the power-flow solution, I can calculate the voltage of every node, the branch currents, branch losses, and the total network loss.
To investigate the impact of a scaled electric car load on a DC distribution network, I constructed a modified 33-node DC system. The system is supplied by an upstream AC/DC substation, integrated with several photovoltaic units and battery storage units, and has six possible electric car discharge stations. The base voltages were set according to a standard low-voltage DC distribution scheme. Table 1 summarizes how the system performance changes when the electric car charging demand is gradually increased.
| Electric car charging demand | Voltage deviation (p.u.) | Network loss (kW) |
|---|---|---|
| 0% of rated EV load | 0.6937 | 171.2 |
| 40% of rated EV load | 1.4030 | 236.7 |
| 70% of rated EV load | 1.9620 | 288.5 |
| 100% of rated EV load | 2.5475 | 368.1 |
The voltage deviation indicator in Table 1 is defined as the sum of per-unit deviations from the nominal voltage over all load nodes. It is clear that a higher electric car charging demand results in a more severe voltage drop and a larger network loss. This confirms that uncontrolled charging of many electric cars is a serious threat to DC network power quality.
I then examined the discharge side of electric cars. The same total load condition was used, while increasing the electric car discharge power from 50 kW to 150 kW. The resulting network performance is listed in Table 2.
| Electric car discharge power (kW) | Voltage deviation (p.u.) | Network loss (kW) |
|---|---|---|
| 0 | 2.5475 | 368.1 |
| 50 | 1.8258 | 273.8 |
| 100 | 1.1428 | 208.9 |
| 150 | 0.4934 | 87.2 |
Table 2 demonstrates that electric car discharge can dramatically improve the performance of a DC network. The discharge power injects active power at selected nodes, reduces the burden on upstream feeders, and restores node voltages to a healthier range. Therefore, electric cars should be treated not as passive loads but as mobile storage units that can be dispatched for system support.
3. Coordinated Topology Optimization with Electric Car Discharge and Soft Open Points
The results given above indicate that electric car discharge alone is useful, but a single type of resource may not be sufficient when the penetration level becomes very high. I therefore introduced a second control resource: soft open points. A DC soft open point is composed of two DC-DC converters connected by a dc link. It can be installed between two otherwise separated DC feeders. By controlling the power transfer of each converter, the soft open point can regulate the distribution of current and voltage across the network. In the model, a soft open point requires power balance between its two terminals while considering internal losses:
$$
P_{i,t}^{SOP} + P_{j,t}^{SOP} + A_{i} \left|P_{i,t}^{SOP}\right| + A_{j} \left|P_{j,t}^{SOP}\right| = 0,
$$
where \(P_{i,t}^{SOP}\) is the active power injected at terminal \(i\), and \(A_i\), \(A_j\) are loss coefficients. The capacity of a soft open point is limited by:
$$
\left|P_{i,t}^{SOP}\right| \le S_{ij}^{SOP}, \quad \left|P_{j,t}^{SOP}\right| \le S_{ij}^{SOP}.
$$
From a power-flow perspective, the soft open point behaves like a variable-ratio DC transformer. It can change the voltage relation between two nodes and therefore redistribute the branch currents. I used this equivalent model in the DC power flow to reduce the computational burden while retaining the key voltage regulation characteristics.
I first performed a sensitivity analysis of soft open point integration. The results show that installing one soft open point reduces the network loss from 368.1 kW to 276.5 kW in the studied scenario, while adding a second soft open point further reduces the loss to 261.1 kW. The additional benefit of adding more soft open points is relatively small compared with the benefit of installing the first one. More importantly, the location of the soft open point has a strong influence on the voltage profile. Different topology combinations yield different performance values. This finding illustrates the need to optimize the locations of soft open points rather than simply increasing their number.
Based on these observations, I proposed a bilevel multi-objective optimization model for a DC distribution network with scaled electric car penetration. The upper level optimizes the discharge power of electric cars at each discharge station. The lower level optimizes the locations and the number of soft open points used for network reconfiguration. The overall framework is shown in Table 3.
| Level | Decision variables | Objectives | Key constraints |
|---|---|---|---|
| Upper level | Total discharge power at each electric car discharge station | Minimize network loss; minimize voltage deviation; maximize electric car user income | Electric car discharge power limits; station capacity; battery state-of-charge limits |
| Lower level | Soft open point installation location and number | Minimize network loss | Radial topology feasibility; DC power-flow equations; nodal voltage limits; line capacity; DG output limits |
The upper-level voltage deviation is formulated as:
$$
f_{2} = \sum_{i \in \Omega_{node}} \frac{\left| U_{i,t} – U_{i,rated} \right|}{U_{i,rated}},
$$
and the network loss used in the objectives is decomposed into branch losses and soft open point losses:
$$
f_{1} = P_{t}^{loss} = \sum_{(i,j) \in \Omega_{line}} G_{ij} \left( U_{i,t} – U_{j,t} \right)^{2} + \sum_{(i,j) \in \Omega_{SOP}} \left( P_{i,t}^{SOP,L} + P_{j,t}^{SOP,L} \right).
$$
For the electric car user, the benefit is the difference between the income obtained from discharging and the cost paid for charging:
$$
f_{3} = \sum_{t} \left( N_{d,t} P_{d,t} \rho_{d,t} – N_{c,t} P_{c,t} \rho_{c,t} \right) \Delta t,
$$
where \(\rho_{d,t}\) and \(\rho_{c,t}\) are the discharge price and charging price, respectively.
Three objective functions are optimized simultaneously in the upper model. I used the multi-objective particle swarm optimization algorithm to find the Pareto solution set. The decision variables of the upper level are passed to the lower level. In the lower level, a simulated annealing algorithm searches among feasible network topology options to identify the best soft open point locations. The lower-level solution is then sent back to the upper level, and the two levels are iterated until convergence. The overall solution procedure can be summarized as follows:
First, each electric car discharge station is initialized with a set of candidate discharge powers. The power-flow is then solved, and the upper-level objectives are evaluated. After updating the Pareto archive, a non-dominated electric car dispatch is selected and sent to the lower level. The lower level enumerates feasible soft open point topologies using the radiality and connectivity constraints; for each topology, the network loss is computed. Simulated annealing refines the soft open point position until the best topology has been found. This final topology is then returned to the upper level as a fixed network configuration, and the process repeats.
I applied the coordinated optimization to a modified IEEE 33-node DC distribution network with six electric car discharge stations. The daily scheduling horizon was divided into 30-minute intervals. For each interval, the optimization produced a Pareto set containing trade-offs between network loss, voltage deviation, and electric car user income. In the peak-load intervals, I observed that the most frequent soft open point combination is located near the downstream and upstream feeder boundaries. I selected one representative Pareto solution to compare the proposed method with single-resource alternatives. Table 4 shows the comparison.
| Method | Voltage deviation (p.u.) | Network loss (kW) |
|---|---|---|
| 1: no EV discharge, no SOP | 2.5380 | 376.6 |
| 2: electric car discharge only | 0.5390 | 70.3 |
| 3: soft open point reconfiguration only | 1.6953 | 235.6 |
| 4: coordinated electric car discharge and soft open point reconfiguration | 0.2257 | 21.4 |
The results in Table 4 clearly show that the coordinated method is much better than both single-resource strategies. Compared with the strategy that only uses electric car discharge, the coordinated method reduces the representative network loss by about 69.6% and the voltage deviation by about 58.1%. This improvement is significant because the soft open point changes the network topology such that the electric car discharge power can be delivered more effectively to the nodes where it is most needed.
I also investigated the influence of discharging power deviations. When electric cars discharge at 150% or 50% of the optimal total power, the network loss and voltage deviation increase considerably. In addition, the optimal soft open point locations may shift. This observation suggests that a close coupling exists between electric car discharge scheduling and soft open point placement. Therefore, in real operation, the grid operator and the electric car aggregator should not be treated separately; a coordinated dispatch is necessary to achieve the best system-level performance.
4. Fault Recovery through EV Discharge and Soft Open Point Network Reconfiguration
Extreme weather events and equipment failures can cause permanent faults in distribution networks. Because the distribution network is close to customers, a fault may interrupt important loads such as hospitals, data centres, and emergency facilities. In my work, I extended the coordinated topology optimization concept to the fault restoration problem. The aim is not only to restore as many loads as possible, but also to restore important loads with a low network loss and a small voltage deviation.
Fault restoration generally relies on two actions. First, islanding divides the faulty network into small self-sufficient islands supplied by distributed generators and storage. Second, network reconfiguration changes the state of tie switches or soft open points to connect these islands to the main grid. I used conventional graph-analysis tools, including adjacency matrices and breadth-first search, to check connectivity. The main contribution is that I combined both islanding and soft open point reconfiguration with electric car discharge in a single framework.
In the proposed fault recovery model, the first objective is to restore important loads. The load at every node is classified into three priority levels. One-level loads receive the highest weight, followed by second-level loads and third-level loads. The restoration objective can be written as:
$$
\max \sum_{i \in \Omega_{node}} \omega_{i} P_{i,t} y_{i,t},
$$
where \(\omega_i\) is the priority weight, \(P_{i,t}\) is the active load at node \(i\), and \(y_{i,t}\) is a binary variable indicating whether the load is successfully restored. At the same time, the restoration process should minimize network loss and voltage deviation:
$$
\min \left( P_{t}^{loss}, \; f_{2} \right).
$$
Because the interests of the grid and the electric car owner may conflict, I again used a bilevel structure for fault recovery. The upper level optimizes the electric car discharge station outputs, while the lower level determines the locations of soft open points that connect islanded zones with the healthy main-network zone. The constraints include station capacity, battery energy limits, distributed generator power limits, line capacities, node voltage bounds, and radiality or connectivity constraints.
I simulated a two-fault scenario in the modified 33-node DC system. The fault locations divide the distribution system into one main-grid-connected region and two islanded regions. One islanded region can be fully supplied by the available photovoltaic and storage units in both fault periods, while the other islanded region may have an energy deficit. At 14:00, the deficit is 379.6 kW when only islanding is used; at 19:00, because there is no photovoltaic power, the deficit is much larger at 1336.5 kW. The important loads are always restored first, but third-level loads cannot always be supplied.
When soft open points are used to connect the islanded regions to the main grid, every load in the system can be restored without the need for load shedding. However, the resulting system loss and voltage deviation are relatively large. The proposed combination of soft open point reconfiguration and electric car discharge provides a much better solution. A representative comparison is shown in Table 5 for the 19:00 fault.
| Recovery strategy | Unserved load in the critical island (kW) | System network loss (kW) | Voltage deviation (p.u.) |
|---|---|---|---|
| Islanding only | 1336.5 | — | — |
| Soft open point reconfiguration only | 0 | 246.4 | 0.9587 |
| Coordinated electric car discharge and soft open point reconfiguration | 0 | 22.4 | 0.1002 |
The coordinated strategy reduces the network loss from 246.4 kW to 22.4 kW compared with the soft-open-point-only strategy in this illustrative scenario. At the same time, the voltage deviation is significantly reduced. These observations are repeated in the 14:00 fault scenario, where the Pareto solutions show system losses as low as 8 to 20 kW while all important loads are restored. This indicates that electric car discharge can act as a fast and flexible source that supports voltage and reduces the loading of feeders during the recovery horizon.
I further analyzed the influence of insufficient electric car discharge or excessive discharge during restoration. If only 90% of the required electric car power is available, the network loss and voltage deviation increase. Similarly, if electric cars discharge at 110% of the optimal value, the system performance also worsens because the excess power disturbs the power balance and leads to overvoltage at some nodes. The optimal soft open point position also changes as the electric car discharge power deviates. This result again emphasizes the need for accurate coordination between charging station dispatch and topology control.
Another practical issue is the uncertainty of photovoltaic output during fault restoration. In bad weather, the photovoltaic power may be much lower than its rated value. I tested the coordinated strategy with the photovoltaic output reduced to 60%, 30%, and 10% of the normal value. When the photovoltaic power decreases, the system loss increases and the voltage deviation becomes larger. Nevertheless, the coordinated strategy is still able to satisfy every load with an acceptable voltage range. Table 6 lists the performance as a function of photovoltaic output.
| Photovoltaic output percentage | Network loss (kW) | Voltage deviation (p.u.) |
|---|---|---|
| 100% | 20.0 | 0.0942 |
| 60% | 114.4 | 0.3906 |
| 30% | 190.1 | 0.5337 |
| 10% | 348.0 | 0.7568 |
Even with only 10% photovoltaic output, the proposed method can still restore all loads in the tested fault scenario. The network loss is noticeably larger than in clear-sky conditions, but the voltage deviation remains within the acceptable margin for emergency operation. Therefore, the combination of electric car discharge and soft open point network reconfiguration improves the resilience of the DC distribution network to adverse weather conditions.
5. Conclusions
This research investigated topology optimization methods for DC distribution networks with scaled electric car integration. The principal conclusions can be summarized as follows. First, the dynamic equivalent model indicates that an increase in electric car charging power causes a direct and significant increase in nodal voltage deviation and network losses. At the same time, the same electric cars, when properly discharged, act as mobile storage and improve both voltage quality and system efficiency. Hence, the bidirectional capability of electric cars is essential to the stable and efficient operation of future DC distribution networks.
Second, soft open points can be used to change the network topology and reallocate power flows. Their optimal number and location should be determined systemically. Adding too many soft open points has diminishing returns, while placing soft open points at the correct feeder boundaries provides the largest benefit.
Third, the proposed bilevel coordinated optimization framework is able to determine both the electric car discharge powers and the soft open point locations in a consistent manner. The Pareto results demonstrate that coordination yields lower network loss and lower voltage deviation than either electric car discharge alone or soft open point reconfiguration alone.
Finally, the fault recovery study shows that a hybrid strategy of islanding, electric car discharge, and soft open point network reconfiguration can restore all loads in a permanent fault scenario while providing a high-quality voltage profile. The strategy remains effective when electric car discharge power is altered and when photovoltaic generation is reduced by cloud cover or severe weather.
6. Future Work
The present work opens several promising paths for further research. One important direction is the establishment of an integrated traffic and power network model. The random mobility of electric cars means that their discharge availability is coupled with traffic flow. Future research should therefore include a travel-chain model to forecast the spatial distribution of electric car charging and discharging resources. Another direction is the study of hybrid AC/DC distribution networks, where soft open points are needed not only between DC feeders but also between AC and DC subsystems. The interaction between AC frequency control and DC voltage control under fault conditions is a challenging problem that has yet to be fully solved.
In summary, my research shows that scaled electric car integration should not be regarded only as a threat to DC distribution networks. With suitable models, optimization algorithms, and power electronic devices, electric cars can provide valuable discharge flexibility and contribute to both the economic and resilient operation of the future DC distribution system. The topology optimization method proposed in this work provides a useful framework for network operators and electric car aggregators to cooperate in a coordinated manner.