Distributed rooftop photovoltaic (PV) generators prospered distributed generation (DG) in recent years. Certain randomness of rooftop PV connection may lead to significant PV power imbalance across three phases, especially in lowvoltage distribution systems. Due to interphase line coupling, traditional Var compensation methods which typically have competent voltage regulation performance may become less effective in such PV imbalance scenarios. In this paper, the limitation of traditional Var compensation methods in voltage regulation with unbalanced PV power integration is demonstrated and comprehensively analyzed. After describing the voltage regulation challenge, based on the voltage sensitivity analysis, it is revealed that PV power unbalanced level together with equivalent mutual impedance among phase conductors has a significant impact on the effectiveness of traditional Var compensation methods on voltage regulation. On this basis, to improve the performance of voltage regulation methods, some suggestions are proposed for both current system operation and future distribution system planning. Numerical studies demonstrate the effectiveness of the proposed suggestions. Future rooftop PV integration in LV systems can benefit from this research.
In recent years, various distributed generation and storage systems including photovoltaic, wind power, electric vehicles, etc., have been developed vigorously [
To avoid the potential overvoltage problem, the maximum PV penetration of a distribution system should be carefully assessed. In early research, singlephase equivalent systems are used to estimate possible voltage problems with high PV penetration levels [
In order to accommodate more rooftop PV generators, Var compensation devices are required to actively participate in voltage regulation [
On the other hand, Var compensation methods that only rely on local measurements (e.g., PV generation and local linetoground voltage) also have already been widely implemented in centralized PV plants for the point of common coupling (PCC) voltage regulation [
However, since singlephase rooftop PV generators are integrated into lowvoltage distribution systems randomly, PV power penetration across three phases tends to be unbalanced. In such situations, widely implemented locally dependent Var compensation methods that can successfully control the PCC voltage of largescale PV plants may become less effective in voltage regulation with distributed rooftop PV generators. In this paper, the limitation of locally dependent Var compensation methods in voltage regulation with unbalanced PV power integration is comprehensively analyzed.
The remainder of this paper is organized as follows: Section
Rooftop PV generators are becoming more and more popular in recent days, not only due to its clean and renewable characteristics, but these PV systems can sell excessive power back to the utility after providing power supply for customers’ household appliances.
PV panels generate active power only in the daytime, with a peak value during noon as shown in Figure
PV power and load demand in one day: (a) normalized PV power profile; (b) load profile without PV power integration; (c) load profile with PV power integration.
Schematic diagram of a PV system with corresponding control loops is displayed in Figure
PV system schematic diagram.
A PLL component is adopted to synchronize PWM and control schemes to the PCC voltage. In this way, the AC signals are converted into dqframe correspondence signals, and the controllers can deal with their DC equivalent values instead of the original sinusoidal signals.
The error between the square of the DC voltage
The current commands are transmitted to a currentcontrol scheme, which is established in a dqframe drive
Reverse power flow caused by a large amount of PV power integration will significantly increase system voltage at the end of distribution feeders, which might induce overvoltage issues. In order to mitigate the voltage rise, PV inverters are required to provide Var compensation.
Due to the effectiveness and easy implementation, Var compensation methods that only rely on local measurements have already been widely applied on voltage regulation for largescale PV plants so far. Two typical locally dependent Var compensation methods are shown in Figure
Traditional Var compensation methods: (a) constant power factor curve; (b) power factor droop curve [
Residential customers are almost directly connected to 415 V lowvoltage systems which are fed by 11 kV/415 V distribution transformers. Since the 11 kV/415 V transformer cannot participate in system voltage regulation due to its fixed tap position, voltage fluctuations in the 11 kV side have a significant impact on 415 V systems. A monthlong voltage profile recorded from the secondary side of an 11 kV/415 V distribution transformer is displayed in Figure
Recorded onemonth voltage profile at the secondary side of an 11 kV/415 V transformer.
In traditional distribution systems, residential loads are approximately balanced across three phases. However, rooftop PV generators are usually installed randomly. Therefore, PV power integration tends to be unbalanced especially in lowvoltage systems with limited customers. A possible scenario (PV penetration is 25%, 30%, and 45% in Phases A to C, respectively) is assumed in Case 1. Detailed load and PV capacity are shown in Table
Load and PV installation capacity.
Phase A  Phase B  Phase C  

Peak load  58 kW, 11.6kVar  60 kW, 12kVar  62 kW, 12.4kVar 
PV capacity (Case 1)  14.5 kW (25%)  18 kW (30%)  28 kW (45%) 
PV capacity (Case 2)  29 kW (50%)  30 kW (50%)  31 kW (50%) 
Voltage regulation performance with different cases.
Voltage regulation method  Phase A  Phase B  Phase C 



Constant power factor (0.9)  1.038  1.069  1.036 
Power factor droop curve  1.041  1.065  1.043 




Constant power factor (0.9)  1.053 pu  1.054 pu  1.046 pu 
Power factor droop curve  1.054 pu  1.054 pu  1.050 pu 
Nevertheless, there exists an interesting phenomenon that with the PV penetration of all three phases increased to 50% as in Case 2, the overvoltage problem on Phase B could be successfully eliminated by either of those two locally dependent Var compensation methods. Detailed case data and voltage regulation performance are, respectively, listed in Tables
Generally, since a large amount of PV power integration might cause overvoltage problem, the maximum allowable PV penetration level should be estimated by utilities. However, based on voltage regulation performance in Case 1 and Case 2, if a higher but balanced PV penetration is regarded as the most severe case, the potential overvoltage issue might be under estimated. An overvoltage problem might occur before the estimated PV integration level with a lower but unbalanced PV penetration.
Besides, it is worth mentioning that the phase with highest PV penetration does not necessarily have the highest voltage. As in Table
The limitation of locally dependent Var compensation methods in voltage regulation with unbalanced PV power integration is revealed above. In this section, the reason for this voltage regulation problem is analyzed.
For distribution systems with 3phase 4wire overhead lines, the voltage drop along a feeder can be expressed as [
Due to the existence of equivalent mutual impedance (
To investigate the voltage regulation performance with unbalanced PV power integration, the threephase voltage sensitivity with respect to singlephase active power injection is demonstrated in this section. Without loss of generality, a certain amount of active power is assumed to be injected into Phase C, which results in line current
The voltagecurrent relationship given in (
Threephase voltage sensitivity with respect to singlephase power flow: (a) only active power injection at Phase C; (b) only reactive power absorption from Phase C.
As shown in Figure
To figure out the impact of reactive power absorption on phase voltage, similar analysis is given. In Figure
Threephase voltage variations caused by singlephase active power injection or reactive power absorption are summarized as in Table
Summary of threephase voltage sensitivity.
Threephase voltage variation  

P injection at phase A 



P injection at phase B 



P injection at phase C 



Q absorption at phase A 



Q absorption at phase B 



Q absorption at phase C 



To summarize, due to equivalent mutual impedance among phase conductors, active and reactive power flows in one phase can have significant impact on voltage rise or drop in other two phases. Furthermore, unbalanced PV power integration also makes locally dependent Var compensation methods less effective, which significantly challenges the effectiveness of voltage regulation methods. In order to improve the effectiveness, some suggestions are proposed.
Most previous researches highlight that high PV penetration may cause voltage regulation issues in distribution systems. However, based on Section
Since the end of a distribution feeder is most vulnerable to severe overvoltage problems caused by excessive PV power injection, all PV power installation capacities at different buses are first converted to the end of a feeder as
Although the limitation in voltage regulation is inevitable to all locally dependent Var compensation methods, different methods have different voltage regulation performance. For example, when PV penetration is unbalanced, the power factor droop curve scheme results in lower overvoltage in comparison to that of the constant power factor scheme as in Case 1 of Table
According to the threephase voltage sensitivity summarized in Table
In order to further mitigate the overvoltage issue of Phase B, the dead band (distance between
Power factor droop curve with wider dead band.
Voltage regulation performance with different power factor droop curves.
Parameters of power factor droop curve  Phase A  Phase B  Phase C 


1.041 pu  1.065 pu  1.043 pu 

1.050 pu  1.059 pu  1.053 pu 
As the dead band of a power factor droop curve becomes wider, less reactive power will be absorbed with the same local voltage before voltage violation. Therefore, the reactive power absorption from Phases A and C can be further reduced, which will lead to a voltage rise at both Phases A and C as in Table
As revealed in Section
According to (
A 415 V lowvoltage distribution system with 64 customers shown in Figure
A typical 415 V lowvoltage distribution system with 64 customers.
415 V distribution systems were designed to operate with all possible load levels and upstream (11 kV side) voltage fluctuations. Assuming that the secondary side voltage of an 11 kV/415 V transformer varies between 1.0 pu and 1.05 pu, the corresponding threephase voltage profiles of Bus 9 in one day with highest and lowest upstream voltages are shown in Figures
Threephase voltage at Bus 9 before PV power integration with different upstream voltages: (a) highest upstream voltage (1.05 pu); (b) lowest upstream voltage (1.0 pu).
As analyzed in this paper, besides PV power penetration, PV power imbalance index also has a significant impact on distribution system voltage regulation. If PV installation capacity has an approximately balanced distribution across three phases (24 kW, 25 kW, and 26 kW in Phase s A to C, with a total capacity of 75 kW), the imbalance index of PV power is 0.023 according to the definition in Section
Figures
Voltage regulation performance with approximately balanced PV power integration: (a) constant power factor; (b) power factor droop curve.
However, since rooftop PV generators are randomly distributed across three phases, it is inevitable to face unbalanced PV power integration in distribution systems. With the same total installation capacity (75 kW), if PV installation capacity in each phase is 17 kW, 24 kW, and 34 kW, respectively, the limitation of locally dependent Var compensation methods arises. In this situation, the PV power imbalance index is 0.2.
Corresponding timeseries simulation results with the constant power factor scheme and the power factor droop curve scheme are shown in Figures
Threephase voltage profiles with different locally dependent Var compensation methods: (a) constant power factor; (b) power factor droop curve.
Overvoltage problem can be mitigated in a certain extent if locally dependent Var compensation follows a power factor droop curve with a wide dead band. Figures
Voltage regulation performance of power factor droop curves with different parameters: (a)
With random connection of rooftop PV generators, PV penetration tends to be unbalanced across three phases especially in lowvoltage distribution systems. In such situations, locally dependent Var compensation methods may become less effective in overvoltage mitigation.
The voltage regulation problem is analyzed in this paper. The analysis result indicates that the equivalent mutual impedance among phase conductors together with unbalanced PV power integration make locally dependent Var compensation methods less effective.
On this basis, some suggestions are proposed for utilities in both current system operation and future planning. Specifically, (1) utilities are suggested to use both PV penetration and the PV imbalance index to describe the integration of rooftop PV generators; (2) the power factor droop curve with a wider dead band is suggested to be applied on rooftop PV generators due to its better voltage regulation performance with unbalanced PV integration; (3) for future distribution system planning, utilities are suggested to design future distribution feeders with less equivalent mutual impedance among phase conductors in order to accommodate more randomly connected rooftop PV generators.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.