 Open Access
 Authors : WenChih Yang, BoKai Zhuang
 Paper ID : IJERTV12IS123075
 Volume & Issue : Volume 12, Issue 12 (December 2023)
 Published (First Online): 23012024
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Fast Rule For Improving Threephase Voltage Imbalance in Distribution Feeders
WenChih Yang, BoKai Zhuang
Department of Electrical Engineering Taipei City University of Science and Technology
Taiwan, R.O.C.
AbstractThis paper proposes a fast rule to improve threephase voltage imbalance in distribution feeders. In practice, the three phase voltage of distribution feeders is unbalanced for a long time. Unbalanced threephase voltage will affect the efficiency and safety of electrical equipment. The fast rule proposed in this paper can be used to improve the threephase voltage imbalance on distribution feeders via the renewable energy generation systems connected to the distribution feeders. The fast rule is easy to use and can also increases the application benefits of renewable energy power generation systems.
KeywordsFast rule, distribution feeder, voltage imbalance.

INTRODUCTION
Distribution systems are downstream of the entire power system. They supply electricity to a wide range of medium voltage and lowvoltage customers. A distribution system is composed of transformers, distribution feeders, switches and protection equipment. The transformers are used to convert high voltage on the primary side to low voltage on the secondary side, and the distribution feeders are used to supply electric power to their loads. Distribution feeders have a three phase structure and supply threephase electric power to three phase loads. Unfortunately, singlephase loads also exist in
connected to the distribution systems [7,8]. Some small renewable energy power generation systems (REPGSs) are singlephase power generation equipment. If they can be properly arranged and connected to each phase of the distribution feeders, the threephase voltage imbalance of the distribution systems can be improved.
This paper proposes a quick rule for reducing threephase voltage imbalance in distribution feeders. This quick rule can help distribution system operators properly arrange the connecting phases of small REPGS to reduce the degree of threephase voltage imbalance on distribution feeders. There is no need to use reactive power compensation equipment or on load voltage regulation, which can reduce the operating cost of the power distribution system.

DESCRIPTION OF SYSTEM STRUCTURE
Fig. 1 shows the simplified structure of a distribution system, which is used as an example system in this paper. The example system includes a threephase transformer, a circuit breaker, a distribution feeder, 6 buses, 6 loads and a REPGS. The component parameters of the example system are shown in Table I, and the load parameters are shown in Table II.
distribution systems. Since distribution feeders supply power to singlephase and threephase loads simultaneously, the three phase currents are inconsistent, resulting in unbalanced three phase voltages.
Literature [13] has shown that threephase unbalanced voltage will reduce the torque of motors, increase the power loss of feeders, and interfere with the function of protection
Transmission system
Threephase transformer
Bus 1
Breaker
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6
REPGS
Distribution
feeder
equipment. Therefore, the threephase voltage imbalance
problem of distribution feeders must be improved, otherwise the economic losses will be huge.
Load 1
Load 2
Load 3
Load 4
Load 5
Load 6
At present, distribution system operators generally use reactive power compensation equipment or onload tapchangers to improve the threephase voltage imbalance problem of distribution feeders [46]. Although these devices can effectively reduce the threephase voltage imbalance of distribution feeders, they are expensive and have short service life, resulting in high operating costs of the distribution system. In the past 20 years, governments around the world have actively promoted renewable energy power generation policies and encouraged small wind power generation systems, solar power generation systems, hydroelectric power generation systems and biomass power generation systems to be
Fig. 1. The structure of the sample system employed in this paper.
The length of the distribution feeder is 1000 m, and the power supply structure is a threephase threewire scheme, so there are three phases A, B, and C. There are 6 buses on the distribution feeder, which are spaced 200 m apart from each other. The load of each bus is 150k W. The load of phase A is 40k W, the load of phase B is 50k W, and the load of phase C is 60k W.
The maximum power generation capacity of the REPGS is 100k W. Assuming that the connection position is at bus 6. The
connected phase of the REPGS depend on the research scenarios.
TABLE I. The Parameters of Each Component in the Example System
completely equal, so its threephase voltage is also completely balanced.
n n
2 2
Component Name
Parameters
Threephase transformer
Rating capacity : 25M VA
Winding connection : Delta Grounded wye Rating voltage : 69k/11.4k V
Winding impedance : 0.0196+j0.028 pu
Distribution feeder
Length : 1000 m
Crosssectional area : 477 MCM Impedance : 0.131+j0.405
Bus
Threephase structure (phase A, B, C)
REPGS
Power generation capacity: 100k W Output voltage: 11.4k V
STL,A = SLm,A
PLm,A QLm,A
(1)
m1 m1
n n
2 2
STL,B = SLm,B
PLm,B QLm,B
(2)
m1 m1
n n
2 2
STL,C = SLm,C
PLm,C QLm,C
(3)
m1 m1
n n
2 2
STG,A = SGm,A
PGm,A QGm,A
(4)
TABLE II. The Load Parameters of Each Bus in the Example System
m1 m1
n n
S = S
P2 Q2
(5)
TG,B
Bus No.
Load
Phase A (kW)
Phase B (kW)
Phase C (kW)
1
40
50
60
0
0
0
2
40
50
60
0
0
0
3
40
50
60
0
0
0
4
40
50
60
0
0
0
5
40
50
60
0
0
0
6
40
50
60
0
0
0
Gm,B
Gm,B Gm,B
m1 m1
n n
STG,C = SGm,C
P2m,C Q2 m,C
(6)
G G
m1 m1

THE FAST RULE
In this research, it is assumed that the connecting bus of this
S=Max.( STL,A SGm,A , STL,B SGm,B , STL,C SGm,C )

Min.( STL,A SGm,A , STL,B SGm,B , STL,C SGm,C )


RESULTS
(7)
REPGS cannt be changed, but the connecting phase can be changed.
In order to make the threephase voltage of a distribution feeder as balanced as possible, the load distribution of the three phases of the distribution feeder should be as equal as possible to each other, that is, the difference between each other should be as close to zero as possible.
To achieve the above goal, this paper develops a fast rule and the algorithm is as shown in (1) to (7). The (1) to (3) are used to calculate the total load of each phase of a distribution feeder, the (4) to (6) are used to calculate the total power generation of REPGSs connected to each phase of the distribution feeder, the
(7) is used to calculate the load difference of the three phases of the distribution feeder, where n is the number of buses on the distribution feeder, m is the number of each bus, STL is the total load, and STG is the total power generation of REPGSs, SL is the load of each bus, and SG is the power generation of REPGS of each bus, S is the difference between the total load of the distribution feeder and the total power generation of REPGSs connected to the distribution feeder, and Max. and Min. represent obtaining the maximum and minimum values, respectively. When S is zero, it means that the load distribution of the three phases of the distribution feeder is
In order to verify the validity of the fast rule, 4 simulation
scenarios have been carried out by the research. The definitions of the 4 simulation scenarios are described as follows.
Scenario_0: No REPGS connected with the distribution feeder of the example system.
Scenario_A: A REPGS connected with the phase A of the bus 6 of the distribution feeder of the example system and output 100k W of active power.
Scenario_B: A REPGS connected with the phase B of the bus 6 of the distribution feeder of the example system and output 100k W of active power.
Scenario_C: A REPGS connected with the phase C of the bus 6 of the distribution feeder of the example system and output 100k W of active power.
Scenario_0 was used to demonstrate the original unbalanced situation of the threephase voltage of the distribution feeder of the example system. Scenario_A, Scenario_B and Scenario_C were used to demonstrate the impact on the threephase voltage imbalance of the distribution feeder when a REPGS outputs electric power to the phase A, B and C of the distribution feeder of the example system, respectively.
Simulation results include the voltage profiles and voltage unbalanced ratios (VURs) of the four scenarios have been
obtained by the research. The definition of the VUR is shown in (8). The simulation results are described in detail as follows
Max. VA , VB , VC Min. VA , VB , VC
B. Scenario_A
In this simulation scenario, a REPGS was connected to phase A of bus 6 of the distribution feeder and outputs 100k W of
VUR=
VA VB VC
3
(8)
active power. At this time, the load of feeder A was only 140k
W, which was less than the original 240k W, so the operation of the example system was inevitably become more unbalanced.
Where the VA, VB and VC are the phase voltages of a bus on
the distribution feeder of the example system.
A. Scenario_0
The voltage profiles of the distribution feeder of the example system in scenario_0 are shown in Fig. 2.
The distribution feeder of the example system has three feeders, namely phase A, B and C. The loads on the three feeders are not equal to each other, causing the example system to operate in an unbalanced state because the load of feeder A is the lightest, only 240k W, and the load of feeder C is the heaviest, reaching 360k W. Fig. 2 shows that the voltage profile of feeder A is the highest, feeder B is the second, and feeder C is the lowest.
The VURs of the distribution feeder of the example system in scenario_0 are shown in Fig. 3. The simulation results show that the VUR of the feeder is larger toward the end, which means that as the length of the feeder increases, the imbalance will become more serious.
Fig. 2. The voltage profiles of the distribution feeder of the example system in scenario_0.
Fig. 3. The VURs of the distribution feeder of the example system in scenario_0.
The simulation results of this scenario show that the voltage profile of feeder A becomes higher, and the difference with the voltage profile of feeders B and C becomes larger, as shown in Fig. 4. Because of this, the VURs of the distribution feeder become larger, as shown in Fig. 5.
Fig. 4. The voltage profiles of the distribution feeder of the example system in Scenario_A.
Fig. 5. The VURs of the distribution feeder of the example system in Scenario_A.

Scenario_B
In this simulation scenario, the REPGS's connection phase was changed from A to B, and it outputs 100k W of active power to the feeder B, so the load on the feeder B dropped from 300k W to 200k W. At this time, the load of feeder B was smaller than feeder A, so its voltage profile was higher than feeder A, as shown in Fig. 6. Even so, the example system was still operating in an unbalanced state, but the degree of imbalance was smaller than that of scenario_A, but larger than scenario_0, as shown in Fig. 7. In addition, the simulation results show that different connection phase of a REPGS have different effect on the imbalance of a distribution system.
Fig. 6. The voltage profiles of the distribution feeder of the example system in Scenario_B.
Fig. 7. The VURs of the distribution feeder of the example system in Scenario_B.

Scenario_C
In this simulation scenario, the REPGS's connection phase was changed from B to C, and it outputs 100k W of active power to the feeder B, so the load on the feeder C dropped from 360k W to 260k W. Although the load of feeder C was still greater than that of feeders A and B, the difference between them had become smaller, so the imbalance of the example system had also become lighter. Fig. 8 shows the voltage profiles of the distribution feeder of the example system, where the voltage profile of feeder C is clearly improved. Fig. 9 shows the VURs of the distribution feeders of the example system, which are significantly smaller than the VURs of the other three scenarios. The simulation results of the scenario_C show that if the connection phase of a REPGS can be appropriately selected, it will improve the imbalance of a distribution system. On the contrary, if the connection phase is inappropriately selected, it will aggravate the imbalance of a distribution system.


DISCUSSION
How to select the connection phases of REPGS is a challenge for distribution system operators. The fast rule proposed in Section II of this paper can assist distribution system operators. According to (1) to (3), the values of STL,A, STL,B and STL,C can be obtained as follows.
STL,A =40+40+40+40+40+40=240k W STL,B =50+50+50+50+50+50=300k W STL,C =60+60+60+60+60+60=360k W
Fig. 8. The voltage profiles of the distribution feeder of the example system in Scenario_C.
Fig. 9. The VURs of the distribution feeder of the example system in Scenario_C.
Assuming that the REPGS is connected to phase A of the bus 6 of the distribution feeder, according to (4) to (6), the values of STG,A, STG,B and STG,C can be obtained as follows.
STG,A =0+0+0+0+0+100=100kW STG,B =0+0+0+0+0+0=0kW STG,C =0+0+0+0+0+0=0kW
At this time, the load difference value can be obtained according to (7) as follows.
SA =Max.(240100,3000,3600)Min.(240100,3000,3600)
=360140=220k W
Assuming that the REPGS is connected to phases B or C of the bus 6 of the distribution feeder, the load difference values can be obtained according to (7) as follows.
SB =Max.(2400,300100,3600)Min.(2400,300100,3600)
=360200=160k W
SC =Max.(2400,3000,360100)Min.(2400,3000,360100)
=300240=60k W
Comparing SA SB and SC, it can be found that SC has the smallest value, so this solution shows that connecting the REPGS to the phase C of bus 6 of the distribution feeder will be the most beneficial to the operation of the example system.

CONCLUSIONS
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