Abstract
The increasing integration of distributed household photovoltaics (PVs) and electric vehicles (EVs) may further aggravate voltage violations and unbalance of low-voltage distribution networks (LVDNs). DC distribution networks can increase the accommodation of PVs and EVs and mitigate mutilple power quality problems by the flexible power regulation capability of voltage source converters. This paper proposes schemes to establish hybrid AC/DC LVDNs considering the conversion of the existing three-phase four-wire low-voltage AC systems to DC operation. The characteristics and DC conversion constraints of typical LVDNs are analyzed. In addition, converter configurations for typical LVDNs are proposed based on the three-phase four-wire characteristics and quantitative analysis of various DC configurations. Moreover, an optimal planning method of hybrid AC/DC LVDNs is proposed, which is modeled as a bi-level programming model considering the annual investments and three-phase unbalance. Simulations are conducted to verify the effectiveness of the proposed optimal planning method. Simulation results show that the proposed optimal planning method can increase the integration of PVs while simultaneously reducing issues related to voltage violation and unbalance.
Upstream node set of node i
Downstream node set of node i
Phase difference between voltage and current
λ Fixed average annual cost coefficient
Three phases
CVSC Investment cost per apparent power of voltage source converter (VSC)
L Service life of VSC
Candidate location set of VSCs
, Node sets of AC and DC low-voltage distribution networks (LVDNs)
P, P The maximum transfer capacities of AC and DC LVDNs
r Discount rate
, Resistances of AC and DC lines
R Resistance of phase φ of AC branch ji
Rji Resistance of DC branch ji
S The maximum allowable installed capacity of VSC
The maximum apparent power capacity of AC lines
T Number of scheduling periods in a day
U, U Rated voltages of AC and DC LVDNs
Umin, Umax The minimum and maximum allowable voltages
Reactance of phase φ of AC branch ji
Line impedance matrix of AC lines
Convergence error
ΔUAC Voltage drop in AC network
ΔUDC Voltage drop in DC network
Annual investment of installed VSCs
, Objective functions of upper and lower models
Upper-level objective function values for and iterations
Three-phase voltage unbalanced factor (VUF)
VUF of node i
Current vector
, Current vectors of phase wires and neutral wires
Current of phase φ of AC branch ji
Current of DC branch ji
VUF of node i
Number of iterations of upper optimization
K The maximum iterations of upper optimization
Connection locations of the
NAC Node set of AC LVDN
NVSC Number of installed VSCs
P, P Active power outputs of VSC injected to AC and DC networks
P, P Power loss and rated power of VSC
Pji, Pik Line power of DC branches ji and ik
Pi Injected power of node i in DC LVDN
P, P Active power of AC branches ji and ik
P, Q Injected power of node i in AC LVDN
Q, Q Reactive power of AC branches ji and ik
Q Reactive power of VSC injected to AC system
S Line apparent power of AC branch ji
S Installed capacity of the
Ui Voltage of node i in DC network
U
, Allowable maximum and minimum voltages in LVDN
Three-phase average voltage of node i
LOW-VOLTAGE distribution networks (LVDNs) are required to achieve a high power quality standard to maintain the reliable power supply of end-users. However, the three-phase unbalanced issues caused by unbalanced loads and parameters of LVDNs may exacerbate the voltage quality and increase power losses [
The above problems can be relieved by building new distribution lines and transformers. However, the solution is considered as costly and infeasible as the unbalance may still exist and the land space in urban areas is limited [
The DC distribution network can effectively address the uncertainties from PVs and EVs [
One viable techno-economic solution to implementing a DC distribution network is to convert the operation mode of existing AC systems into DC [
Although there have been applications of hybrid AC/DC distribution networks, the DC conversion of LVDNs is still under study. Shortcomings of the existing DC conversion and planning solutions of LVDNs include:
1) The existing conversion methods rarely consider the widely used three-phase four-wire configuration in LVDNs. In addition, there are no quantitative evaluation methods for the improvement of DC upgrading on power supply capacities and voltage drops. The capacity of the existing LV wires is not fully utilized by the existing methods which focus on three-phase three-wire MVDNs.
2) The optimal planning of hybrid AC/DC LVDNs considering investments and comprehensive improvement of multiple power quality issues including three-phase unbalance and voltage violations, is still being studied. Moreover, a 24-hour optimal dispatch considering the coordination among multiple lines and phases in LVDNs needs to be achieved to calculate the benefits. However, the planning of DC distribution networks mainly focuses on MVDN, and the improvement of the unbalanced issues is not considered. Although the existing planning methods for AC LVDNs take the unbalance into account, the three-phase regulation of VSCs is still not considered.
This paper aims to convert parts of the three-phase four-wire AC lines into DC operation, thereby establishing hybrid AC/DC LVDNs to increase the power capacity and operation performance. An optimal planning method of hybrid AC/DC LVDNs is proposed, considering the DC conversion’s configuration, costs, and capability of mitigating the three-phase unbalanced degree. The main contributions of this paper are summarized as follows.
1) The characteristics and DC conversion constraints of typical LVDNs are analyzed. The converter configuration and DC connection mode for LVDNs are proposed considering the three-phase four-wire characteristics and quantitative analysis of various DC configurations.
2) An optimal planning method of hybrid AC/DC LVDNs converted from AC LVDNs is proposed considering three-phase power dispatch of VSCs, in which a bi-level model is built to minimize the three-phase unbalance and capital costs.
The rest of paper is organized as follows. Section II presents the problem statement. Section III analyzes converter configuration and connection mode for three-phase four-wire LVDNs. Section IV proposes the optimal planning method of hybrid AC/DC LVDNs. Section V presents the simulation and result analysis. Section VI concludes this paper.
An LVDN with two DTs (DT1 and DT2) and five LV lines (L1-L5) is shown in

Fig. 1 Hybrid AC/DC LVDN considering DC conversion. (a) Five-feeder LVDN. (b) Possible topologies of hybrid AC/DC LVDN and VSC.
In this paper, two distribution areas are interconnected with DC links considering the DC conversion of the LV AC lines. The DC conversion will enhance the power capacities and realize comprehensive improvement of power quality in LVDNs using the flexible control capability of VSCs. An optimal planning method of the hybrid AC/DC LVDN is therefore needed and proposed in this paper.
LVDNs are typically with a three-phase four-wire configuration, distinguishing them from MVDNs that utilize a three-phase three-wire configuration. The characteristics of three typical LVDNs in urban, town, and rural areas are analyzed.

Fig. 2 Network structures and sectional views of wires for three typical LVDNs. (a) Urban areas. (b) Town areas. (c) Rural areas.
In urban LVDNs, the utilization of four-core cables is prevalent due to the limited corridor space, as shown in
Town LVDNs, as shown in
In some rural areas, the three-phase lines of LVDNs supply power separately. This structure is split into three circuits from the terminal of the DT for single-phase power supply, as shown in
1) Quantitative Analysis of DC Configurations Converted from AC LVDNs
The common VSC configurations include asymmetric monopole, symmetric monopole, and bipolar configurations [

Fig. 3 Possible DC configurations converted from AC LVDNs. (a) Asymmetric monopole configuration. (b) Symmetric monopole configuration. (c) Parallel operation monopole configuration. (d) Bipolar configuration. (e) Bipolar configuration with a dedicated metallic return. (f) Improved bipolar configuration.
By converting the AC LVDN into an asymmetric monopole configuration, the original four wires can be combined as the positive pole, as illustrated in
As shown in
As shown in
The bipolar configuration employs three of the original AC wires, serving as the positive pole, negative pole, and neutral wire, respectively, as illustrated in
To make full use of the four existing wires, the configuration shown in
After being converted into DC operation, the power transfer capacities and voltage drops of various DC configurations have changed in comparison to the original LVDNs, which can be calculated as follows.
According to [
(1) |
The maximum power transfer capacity of the AC LVDN is the maximum power under the three-phase balanced condition.
(2) |
for the configurations of
(3) |
for the configuration of
(4) |
for the configuration of
(5) |
The voltage drop of the three-phase four-wire LVDNs, for the given load power PL and QL, can be expressed as:
(6) |
(7) |
Assuming that the active load PL is evenly distributed on each DC line after the conversion. For the configurations of
(8) |
For the configuration of
(9) |
For the configuration of
(10) |
2) Converter Configuration and Connection Mode for LVDNs
Considering the characteristics and DC conversion constraints of typical LVDNs as well as quantitative analysis of various DC configurations, the converter configuration and DC connection mode for LVDNs are proposed in this part. The network structures for LVDNs after DC conversion are shown in

Fig. 4 Network structures for LVDNs after DC conversion. (a) Urban areas. (b) Town areas. (c) Rural areas.
For urban LVDNs, high power transfer capacity and reliability are required to meet the growing load demands. A favorable method is to utilize the original four wires of the four-core cables, which have the same current-carrying capacities, as the positive and negative poles. Therefore, the parallel operation monopole configuration can be adopted in urban areas. In this configuration, any two of the original four wires are utilized as the negative pole, while the remaining two are utilized as the positive pole, as shown in
For town LVDNs, only three-phase wires of the overhead lines can be used to transmit DC power because the current carrying capacity of the neutral wire is smaller than that of other wires. Therefore, the bipolar configuration with a dedicated metallic return shown in
For rural LVDNs in single-phase power supply mode, the DC conversion scheme needs to ensure that there are three circuits. Therefore, the improved bipolar configuration with a dedicated metallic return, as shown in
The proposed converter configurations for three typical LVDNs consider the three-phase four-wire characteristics and quantitative analysis of various DC configurations, which can fully utilize the capacity of the existing LV wires.
Before the optimization process of the hybrid AC/DC LVDN, one of the three typical DC conversion structures can be selected according to the characteristics of the LVDN. Then, the topology of hybrid AC/DC LVDNs are optimized by the proposed optimal planning method. The proposed optimal planning method is formulated as a bi-level programming model. The VSC capacity and topologies of the hybrid AC/DC LVDNs are optimized at the upper level. Then, at the lower level, a 24-hour optimal dispatching is achieved considering the load level, power flow constraint, and VSC capacity constraints. The results of the lower level, including the three-phase power of the VSCs for 24 hours and three-phase unbalanced degree, will be returned to the upper level to update the overall objectives and generate a better configuration result for the hybrid AC/DC LVDNs. The optimal configuration results are finally obtained through iterations between the two levels.
Notice that the proposed optimal planning method includes three types of VSCs, i.e., VSCs at the terminal of the DC line (the VSC1 in

Fig. 5 Hybrid AC/DC LVDN.
The topologies of the hybrid AC/DC LVDNs can be achieved by installing VSCs and selecting the reasonable VSC control modes. In
The upper-level optimization model is established with the objective function of minimizing annual investments and three-phase unbalanced degree of the hybrid AC/DC LVDNs, as shown in (11), which is also the overall objective function of the optimization model. The installed capacities and locations of the VSCs are optimized at the upper level, which determines the topology of hybrid AC/DC LVDNs.
(11) |
The annual investments of the hybrid AC/DC LVDNs considering the DC conversion can be calculated as:
(12) |
(13) |
Minimizing the three-phase unbalanced degree of the hybrid AC/DC LVDNs is also the objective of the lower level, and a detailed calculation is described in the next subsection. In the process of solving this model, the lower-level results is returned to the upper level to calculate the overall objectives.
The installed capacity of each VSC should meet the maximum capacity constraint.
(14) |
The VSC locations are determined by which line is converted to DC operation and the candidate interconnection locations between the converted DC line and other AC lines. Therefore, the connection locations of VSCs should meet the following constraint.
(15) |
At the lower level, the three-phase power of the interconnection VSCs is optimized to minimize the three-phase unbalanced degree. The unbalanced degree of the LVDNs is expressed as the sum of the voltage unbalanced factors (VUFs) of all nodes, where the VUF of node i can be calculated according to the three-phase average voltage of the node [
(16) |
(17) |
Power flow constraints of the hybrid AC/DC LVDN are considered in the lower-level optimization.
(18) |
(19) |
It should be noted that (19) is the power flow equation for one DC circuit and the equation of each DC circuit in the selected DC structure needs to be considered. There are two DC circuits in the DC conversion structure of the urban and town LVDNs, and three circuits of the rural LVDNs.
The active power regulation of the VSCs needs to satisfy the power balance constraint, in which the converter losses are considered.
(20) |
Please note that the absolute value of the active power is used in (20), wherein if , the active power of VSC flows from the AC to DC network.
Generally, the power losses of VSCs are about 2% [
(21) |
The following inequality constraints are also considered, including voltage constraints, line transfer capacity constraints and VSC capacity constraints.
(22) |
(23) |
(24) |
(25) |
It should be noted that the maximum power transfer capacity of DC line is related to the converter configuration, which can be calculated by (8)-(10).
The optimization results of the lower-level model, including the three-phase power outputs of the VSCs and three-phase unbalanced degree, will be used to update the objectives and generate a better result for the hybrid AC/DC LVDNs.
The proposed optimal planning method only consider the external features of the VSC, i.e., the active and reactive power outputs of the VSC. The proposed optimal planning method can be applied to the configuration of various types of converters. It is needed to modify the unit capacity cost and power loss coefficient according to the converter type.
The power outputs of VSCs are optimized at the lower level, which is an optimal power flow problem of the hybrid AC/DC LVDN. The second-order cone relaxation method and CPLEX solver are used at the lower level. The optimality and convergence of the optimal power flow (OPF) based on the second-order cone programming model have been proven in [
Based on [
(26) |
(27) |
Consequently, the lower-level optimization model is transformed into the following SOCP problem.
(28) |
As the upper-level optimization is a multi-objective problem with discrete variables, the upper-level model is solved utilizing the non-dominated sorting genetic algorithm II (NSGA-II) [
The flowchart of the proposed optimal planning method is shown in

Fig. 6 Flowchart of proposed optimal planning method.
The LVDN with integration of PVs and EVs shown in

Fig. 7 Power curves of PV generations and loads. (a) PV power. (b) Load power.
The following five cases are designed and compared to verify the superiority of the proposed optimal planning method of the hybrid AC/DC LVDNs.
Case 1: AC LVDN.
Case 2: building new AC distribution lines.
Case 3: configuring SVGs in AC LVDN.
Case 4: configuring PCSs in AC LVDN.
Case 5: proposed optimal planning method of hybrid AC/DC LVDNs.
Case 1 is the base case without any configuration. To ensure a fair comparison, the configuration results of Cases 2-5 are obtained by solving the optimal planning model with the same objectives, i.e., the minimum annual investments and three-phase unbalanced degree. Moreover, the optimal operation is also considered in the planning process through the bi-level model. For the case of building new AC distribution lines, power flow calculation is conducted in the lower-level model, because there is no device to be dispatched. For the cases of configuring SVGs and PCSs, the optimal dispatchings of the SVG and PCS are separately considered in their optimal planning models, in which the optimal dispatching strategy in [
The maximum load level and PV accommodation capacity of LVDN are mainly determined by voltage limits and line transfer power limits. Under the assumption that load demand gradually increases, the AC network reaches its maximum load level at 325 kW, when the lowest voltage drops to 0.93 p.u.. The maximum PV accommodation capability of the AC network is about 117% of the system rated load, when the highest voltage reaches 1.07 p.u..
The five cases are compared from the following three aspects: the maximum load and PV capabilities, economic indices, voltage deviation and voltage unbalance.
1) Comparison of Maximum Load and PV Capabilities
Configuration results of Cases 2-5 are illustrated in

Fig. 8 Configuration results of Cases 2-5. (a) Case 2. (b) Case 3. (c) Case 4. (d) Case 5.
Case | The maximum load level (kW) | The maximum PV accommodation rate (%) |
---|---|---|
1 | 325 | 117 |
2 | 410 | 145 |
3 | 350 | 125 |
4 | 340 | 120 |
5 | 546 | 210 |
In Case 2, to eliminate the voltage violations of the AC LVDN, a new LV line is built (marked as L6), as shown in
In Case 3, two SVGs with capacities of 30 kvar and 50 kvar are configured at the terminal of DT1 and DT2, as shown in
In Case 5, the converted DC line L3 is interconnected with L4 and L5 by VSC2 and VSC3, as illustrated in
2) Comparison of Economic Indices
The cost of the configuration schemes is the investment of the installed devices. The annual profits of the configuration schemes include the power loss reduction Csave,loss and the increase of PV accommodation Csave,PV. Therefore, the payback time YPBT can be calculated in terms of the cost and the annual profit. The economic indices in different cases at the current load level are shown in
Case | ($) | ($) | ($) | (year) |
---|---|---|---|---|
2 | 17000 | 1413 | 1042 | 6.92 |
3 | 10880 | 404 | 428 | 13.07 |
4 | 1020 | 151 | 149 | 3.39 |
5 | 56103 | 4692 | 1547 | 8.99 |
Configuring PCSs needs the lowest investment and lowest profit, and the payback time is only 3.39 years, which is the most economical scheme. The investment of configuring SVGs is lower than building new AC lines and hybrid AC/DC LVDN, but the payback time is the longest. Building new AC lines can effectively increase the PV integration and reduce power losses, and the payback time is 6.92 years. The hybrid AC/DC LVDN has the highest investment and profit, and the investment can be returned in 8.99 years. With the growth of load and the further increase of PV integration, the payback time will be further reduced.
3) Comparison of Voltage Deviation and Voltage Unbalance
The maximum voltage deviation and VUF under different cases are shown in

Fig. 9 Voltage profiles under different cases. (a) The maximum voltage deviation. (b) VUF.
In Case 1, over-voltage issues occur at midday and under-voltage issues occur at night, which are caused by the high PV output at midday and high EV charging load at night. Meanwhile, more than 65% of the sampling data of the VUF are larger than 2% in Case 1, and the maximum VUF is 12%.
Voltage violations and unbalanced issues still happen in Case 2 with a newly built AC line. This is because the new line is not interconnected with DT2, and the improvement of power quality is limited to the area of DT1 station.
Configuring SVGs and PCSs can effectively alleviate the unbalanced problem. The maximum VUF decreases to 4.5% and 3.3% in Case 3 and Case 4, respectively. However, the voltage violation problem has not been completely eliminated.
Power quality issues in hybrid AC/DC LVDN are completely eliminated. Voltage violations are eliminated by power coordination between the interconnected lines. Moreover, the three-phase power control of VSCs helps to improve the unbalanced issues and the maximum VUF is 0.73%.

Fig. 10 Comparison of different cases.
Assuming that the LVDN is fully loaded with the increase of the load, the LVDN can only be expanded or converted, and the configurations of SVGs and PCSs are no longer applicable. In order to verify the feasibility of the proposed optimal planning method, two schemes of hybrid AC/DC LVDN and building new AC lines are comparatively analyzed, considering the total amount of new loads and the proportion of DC loads in new loads. The investment situations with different load ratio are shown in

Fig. 11 Investment situations with different load ratio.
The following conclusions can be drawn from
When the ratio of the new load is in interval 2 ([32.5%, 44%]), the optimal scheme is mainly affected by the proportion of DC load. In this interval, as the amount of new load increases, the minimum threshold of the DC load ratio that determines the economics of the hybrid AC/DC LVDN is reduced from 100% to 0%. This is because that the investment of converter related to the DC load is the main factor affecting the investment in this interval.
When the ratio of the new load is in interval 3 ([44%, 50%]), hybrid AC/DC LVDN is the better scheme. This result shows that, in this interval, the investment related to the new-built AC lines dominates all the factors that affect the investment in this interval.
With the development of DC technologies, the cost of converter stations would be gradually reduced. However, the cost of building new lines will be more expensive, due to the limited land in urban areas. Based on the above reasons, the economic advantages of the DC conversion scheme will be more prominent in the future.
A large-scale LV system modified by a real system in Anhui Province, China, as shown in

Fig. 12 Configuration of hybrid AC/DC LVDN. (a) A modified real system. (b) Configuration result.
Economic index | Value |
---|---|
Total investment ($) | 67154.00 |
Annual Power losses reduction ($) | 1687.00 |
Annual increase of PV accommodation ($) | 5066.00 |
Payback time (year) | 9.94 |
In this case, L3 is converted to DC and interconnected with L6 by VSC, and coordinated power control between two lines is also achieved through optimal dispatching of VSCs. The maximum PV accommodation rate is increased by 7.25%, because of the large power transfer capacity and LV drop of DC operation and flexible power transfer between L3 and L6. The maximum load level is also increased by 25.5% because load power and PV outputs are complementary between the two lines. The economic indices of this configuration are shown in
The simulation program of this paper is conducted on the MATLAB R2016a-YALMIP platform, utilizing the CPLEX solver. The hardware device used for the simulation is a computer with a 2.2 GHz Intel Core i5-5200 processor and 12 GB of RAM. The computation time is about 20 min for the five-line system in Section V-B, and 23 min for the real system in this subsection.
An optimal planning method of hybrid AC/DC LVDNs considering the DC conversion from AC lines is proposed. DC configurations for three typical LVDNs in urban areas, town areas, and rural areas are analyzed. A bi-level optimal configuration model for hybrid AC/DC LVDNs is further proposed based on the selected DC configuration.
With the proposed optimal planning method considering DC conversion, the maximum PV accommodation rate and load level in the hybrid AC/DC LVDN are increased to 1.79 times and 1.68 times of the conventional AC LVDN, respectively. At the same time, the unbalanced issues are completely eliminated by power regulation of VSCs. The investment of the hybrid AC/DC LVDN can be returned in 9 years. With the growth of loads and the increase of PV integration, the payback time will be further reduced.
Simulation results show that in case the ratio of the new load is higher than 32.5%, the investment of the DC conversion is sensitive to the DC load ratio. If the ratio of the new load is higher than 44%, DC conversion is always the optimal investment scheme.
The optimal planning of hybrid AC/DC LVDNs considering the uncertainty of PVs can be further studied in the future.
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