International Journal of Power Electronics and Drive Systems (IJPEDS)

Vol. 12, No. 4, December 2021, pp. 2230~2242

ISSN: 2088-8694, DOI: 10.11591/ijpeds.v12.i4.pp2230-2242  2230

Fast detection technique for voltage unbalance in three-phase

power system

Ibrahim I. Al-Naimi1, Jasim A. Ghaeb2, Mohammed J. Baniyounis3, Mustafa Al-Khawaldeh4

1Electricaland Computer Engineering Department, Collage of Engineering, Sultan Qaboos University, Muscat, Oman
2ElectricalEngineering Department, Faculty of Engineering, Philadelphia University, Amman, Jordan
3,4Mechatronics Engineering Department, Faculty of Engineering, Philadelphia University, Amman, Jordan

Article Info ABSTRACT

Article history: In this paper, the problem of voltage unbalance in the three-phase power
systems is examined. A fast detection technique (FDT) is proposed to detect
Received May 17, 2021 the voltage unbalance precisely and speedily. The well-known detection
Revised Sep 3, 2021 methods require more than one cycle time to detect the unbalanced voltages,
Accepted Sep 13, 2021 whereas the proposed technique detects the unbalanced situations speedily in
a discrete manner. Reducing the time duration required to detect the
unbalanced voltages will enhance the dynamic response of the control system
Keywords: used to balance these voltages. The FDT acquires the instantaneous values of
the three load voltages, calculates the sum and the space vector for these
Power distribution voltages at each sample, and utilizes these parameters to detect the voltage
Power quality unbalance accurately within a quarter of the cycle time. A proof-of-concept
Space vector simulation model for a real power system has been built. The parameters of
Voltage unbalance the aqaba-qatrana-south amman (AQSA) Jordanian power system are
considered in the simulation model. Also, several test cases have been
conducted to test and validate the capabilities of the proposed technique.
This is an open access article under the CC BY-SA license.

Corresponding Author:
Ibrahim Izziddin Al-Naimi
Electrical and Computer Engineering Department
Sultan Qaboos University
Al Khod, Muscat OM, 123, Oman
Email: i.alnaimi@squ.edu.om

1. INTRODUCTION
The three-phase power systems suffer from different challenging problems, e.g., unbalanced
voltages at the load side [1]-[3]. The voltage unbalance usually degrades the power quality of the electrical
system [4], [5]. As a result, the U.S. economy loses between 15 to 24 billion dollars a year in power quality
problems [6]. In modern buildings, the frequent use of photovoltaics (PVs), battery storages, and charging
stations for electric vehicles (EV) intensify the voltage unbalance problem [4], [7]. Additionally, the
malfunctions of the electrical equipment in the power distribution systems normally lead to unbalanced
voltages [8]. In general, the voltage unbalance in electrical power systems is resulted from either unbalanced
loads or asymmetries in network topology [9]. In most practical cases, the unregulated distribution of loads is
the main factor that causes the unbalanced voltages [10]. Subsequently, the volt-amperes of the three lines
between the generator and the load become different, and thus generating unbalanced voltages at the load
side. Maintaining balanced voltages at the load side is not always possible. This is due to the frequent
connection and disconnection of the loads and the uneven load distribution between the three-phases [11].
Therefore, changing the system configuration through the feeder switching operations may balance the
electrical power distributions. This operation is based on allocating single-phase loads equally across the
three-phase system.

Journal homepage: http://ijpeds.iaescore.com

Int J Pow Elec & Dri Syst ISSN: 2088-8694  2231

Dissimilar inter-stage coupling of impedances and asymmetrical transformer windings normally

lead to network asymmetries [12], [13]. It is challenging to detect the sources that cause voltage unbalance,
especially in the power interconnected networks containing untransposed transmission lines and unbalanced
loads. Many problems are associated with the voltage unbalance, such as excessive energy losses, heating up
the system equipment, and the possibility of system instability [14]-[16]. The effect of the unbalanced
voltages appears clearly on three-phase motors [17], [18]. The inversely rotating magnetic field of the
negative-sequence system causes a negative braking torque. This torque has to be subtracted from the base
torque and thus weakening the machine torque. In addition, the excessive power losses and the heating due to
unbalance conditions will reduce the efficiency of the induction motor [19]. The voltage unbalance creates
adverse effects on electrical equipment. The efficiency of transformers, cables, or lines is reduced due to the
negative sequence components in which the equipment operating limits are determined by the RMS rating
current [20]. Additionally, the unbalanced conditions of power converters produce characteristic and
uncharacteristic harmonics [9], [21].
Employing the static volt-ampere-reactor compensation (SVC) in the electric power system provides
many advantages such as voltage regulation and load balancing, and also enhances the system stability [22]-
[24]. To balance three-phase load currents, the SVC needs to absorb a particular amount of positive or
negative reactive power to produce zero resultant reactive power at the SVC load common point [25].
However, the unbalance conditions of SVC will generate uncharacteristic harmonics. This will generate more
power losses in the power system transmission lines. To reduce the power outage duration, the restoration of
faulted lines or load changes should be achieved quickly. Additionally, the dynamic response of the
controller used to balance the three-phase voltages needs to be enhanced by reducing the time duration
required to detect the unbalanced voltages. In this work, the three load voltages are acquired intermittently to
determine the voltage unbalance speedily. The detection of voltage unbalance is based on calculating the sum
(Vsum) and the space vector (Vspace) of the three load voltages at each sample. The Vsum and Vspace parameters
are utilized by a novel algorithm to detect the voltage unbalance quickly and precisely.
The paper is organized as follows: Section 2 represents a literature review of similar work. Section 3
introduces the three-phase unbalance electric power system. The discrete data measurements are discussed in
sections 4 and 5. The proposed fast detection technique (FDT) is introduced in section 6. Section 7 represents
the effect of unbalanced load changes and unsymmetrical power system faults on the three load voltages,
together with the simulated results. Finally, conclusions are introduced in section 8.

2. LITERATURE REVIEW
To study the unbalance voltage in a three-phase electrical power system, the so-called Fortescue
components or symmetrical components are employed [26]. In this method, the three-phase system is
decomposed into positive-sequence, negative-sequence, and zero-sequence subsystems. The voltage
unbalance is defined by National Electrical Manufacturers Association (NEMA) as maximum deviation from
the average of three-line voltages, referred to the average of three-line voltages [14], [27] Furthermore, it is
defined in IEEE Std.936-1987 as the difference between the highest and the lowest RMS voltages, referred to
the average RMS of the three voltages [28]. The IEEE Std.1159-1195 provides the confirmed true definition,
which is the ratio between the negative-sequence and the positive-sequence voltages [29]. It is recommended
that the voltage unbalance for AC motors do not exceed 1% [14]. If a motor with 94.4% efficiency, 1800
RPM, and 100 hp is operating at 2.5% unbalance conditions, the motor efficiency will reduce to 93% [14].
The space vector (SV) converts the effect of the three instantaneous values for the three-phase
quantities into a rotating two-axis complex plane [30], [31]. This property of the SV is employed in the three-
phase systems to convert the analysis into a stationary state of - axis. This will simplify the analysis of the
three-phase electric power system. A space vector modulation method is employed in three-phase inverters to
improve the inverter's output by generating fewer harmonics [24], [32], [33]. Furthermore, the space vector
was used in the author's prior work for voltage regulation [34].
Many research efforts have been directed toward detecting and solving the voltage unbalance
problems in the three-phase electrical network. Paranavithana and Perera [12] assigned the location of
individual lines causing voltage unbalance, by determining the line coupling impedance between the positive
and negative sequence networks. Sun et al. O’Rouke et.al, [35], [36] developed an algorithm for voltage
unbalance detection based on Clark transformation. In this algorithm, the three voltages are converted to 
stationary system. However, by using this method, the voltage unbalance can be detected after a complete
cycle time, which is 20 milliseconds in a 50 Hz power system. The unbalanced three-phase supply voltages
may exist in the power distribution system. The calculation of the voltage unbalance factor (VUF) was
obtained through the transformation of voltage phasors in a three-phase power system into simple
trigonometric equations [37]. This method reduced the number of parameters used in the calculation process,

Fast detection technique for voltage unbalance in three-phase power system (Ibrahim I. Al-Naimi)
2232  ISSN: 2088-8694

leading to fewer clock cycles for VUF calculation. Chen et al. [38], the VUF is defined as the ratio of
negative sequence to positive sequence voltages. The time needed to calculate the negative and positive
sequence voltages is one cycle time. Additional half-cycle time is needed to calculate the VUF.
Consequently, by using this method, voltage unbalance can be detected after one and a half cycle time which
is 30 milliseconds in a 50 Hz power system.
Shigenobu et al. [39] suggested a developed mathematical approach to detect the voltage unbalance
precisely in different conditions. In this approach, an additional VUF is calculated based on the zero-
sequence voltage in the symmetrical component method. Accordingly, by using this method, voltage
unbalance can be detected after one and a half cycle time. Girigoudar et al. [40] suggested using three metrics
to detect the unbalance voltages accurately in power systems, namely, VUF, phase-voltage unbalance rate
(PVUR), and line-voltage unbalance rate (LVUR). Although this method will minimize the effect of
unbalance voltages according to different metrics, it needs a relatively higher exciting time (i.e., more than
one and a half cycle time). Ghijselen et al. [41], the percentage of VUF is determined directly from the three
RMS line voltages. The triangle of three unequal voltages is divided into two equilateral triangles, in which
the triangle side lengths are the positive and negative sequence voltages. Therefore, a complete cycle is
needed to calculate the voltage unbalance using this definition. Sawitri et al. [42] Okelola et al. [43] applied
the support vector machine (SVM) and neural network (NN) respectively to detect the voltage unbalance in
induction motors. Additionally, Alkayyati et al. [44], [45] employed optimization with machine learning
techniques to solve the unbalance problem in electrical power systems.

3. THREE-PHASE UNBALANCE SYSTEM

The three-phase power systems are ideally balanced, and the related distribution systems are
designed carefully to guaranty the overall balance in the three phases. For any balanced electric power
system, the three voltages are equal in magnitude and out-of-phase by 2/3 rad. It is important to keep the
system voltage within specific limits at different points throughout the power system. Different kinds of large
disturbances (e.g., transmission line faults and sudden load changes) normally distort the performance of the
electrical power system, such as the voltage balance. In other words, unsymmetrical faults in the transmission
lines or unbalanced load changes will directly affect the balance of the three-phase system and produce
unbalanced currents and voltages. Consequently, three components will be generated, namely, zero-sequence,
positive-sequence, and negative-sequence components (𝑉 ⃗ 0, 𝑉
⃗ 1, 𝑉
⃗ 2 ). By considering the operator (a), each one
of the three unbalanced voltages (𝑉 ⃗𝑎 , 𝑉
⃗ 𝑏, 𝑉
⃗𝑐 ) can be written in terms of the three sequence components (𝑉 ⃗ 0,
⃗1,V
V ⃗ 2 ) as shown in (1) [46].

⃗𝑎
𝑉 1 1 1 𝑉 ⃗0 ⃗0
𝑉
⃗ 𝑏 ] = [ 1 a 2 a ] [𝑉
[𝑉 ⃗ 1 ] = 𝐴 [𝑉
⃗ 1] (1)
2
⃗𝑐
𝑉 1 a a ⃗2
𝑉 ⃗2
𝑉
2π
Where the rotation operator a is given by: a= e 𝑗 3 , The inverse of the matrix (A) is given by:

1 1 1 12
𝐴-1 = [1 a a ]
3
1 a2 a

Multiplying (1) by (A-1) gives the three sequence components as shown in (2).

⃗0
𝑉 1 1 1 ⃗𝑎
𝑉
1
⃗ 1] =
[𝑉 2 ⃗ 𝑏]
[ 1 a a ] [𝑉 (2)
3
⃗2
𝑉 1 a2 a ⃗𝑐
𝑉

In this work, both the sum and the space vector of the three voltages are calculated at each sample
and utilized to detect the voltage unbalance quickly. The zero-sum of the three instantaneous voltages is not a
clear indication of voltage balance. Hence, the calculation of space vector is required to ensure precise
detection of unbalanced voltages. The space vector (𝑉 ⃗space ) depends on the three instantaneous voltages and
can be calculated as shown in (3) [46]. For balanced conditions, the magnitude of the space vector is fixed at
any instant of time.

Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2230 – 2242
Int J Pow Elec & Dri Syst ISSN: 2088-8694  2233

⃗space = a0 𝑣𝑎(𝑡) + a1 𝑣𝑏(𝑡) + a2 𝑣𝑐(𝑡)

𝑉 (3)

4. DISCRETE DATA MEASUREMENT

In this work, measurements of discrete data are employed to acquire different variables of the
AQSA Jordanian electrical power system at a discrete-time, i.e., samples f (kTs), where Ts is the sampling
period and k is an integer with the range 1 ≤ k ≤ 20. The three load voltages are measured at the sample.
Besides, the space vector value and the sum of these voltages should be calculated to detect the voltage
unbalance quickly and precisely. The number of samples per cycle (ns) is given by (4).
𝑇
𝑛𝑠 = (4)
𝑇𝑠

Where:
- T is the cycle time, which equals 0.02 sec in 50 Hz power system.
- Ts is the sampling period, which equals 1 ms for 20 samples/cycle in 50 Hz power system.
In general, the balanced three-phase variables va, vb, and vc produce zero-sum at any instant of time.
The space vector for each of the three voltages va, vb, and vc is the corresponding variable on its axis at the a-
axis of operator a0, b-axis of operator a1, and c-axis of operator a2. The total value of the space vector in a
balanced condition is fixed at all instants of time. The properties of the space vector and the sum of the three
voltages are used in this work to determine the voltage unbalance in a very short time.

5. THE SUM OF THE THREE INSTANTANEOUS LOAD VOLTAGES

The sum of any three balanced voltages is zero. For the three-phase power system shown in
Figure 1, the three-phase load voltages are given by (5).

⃗ AB - I𝑎 .ZTTa + I𝑏 .ZTTb
⃗ abL = V
𝑉
⃗ bcL = ⃗VBC - I𝑏 .ZTTb + I𝑐 .ZTTc
𝑉
(5)
⃗ CA - I𝑐 .ZTTc + I𝑎 .ZTTa
⃗ caL = V
𝑉

Where:
- ⃗𝑉abL , 𝑉
⃗ bcL , 𝑉
⃗ caL : Load voltages.
- ⃗𝑉AB , ⃗𝑉BC , ⃗𝑉CA : Balanced source voltages.
- 𝑍TTa , 𝑍TTb , 𝑍TTc : Transmission line and transformer impedances of phases a, b, and c

3- Phase
Transmissin Line - Connection
Source Ia Load
VA a
ZTTa
VAB Ib VabL
VB
ZTTb Zab
Ic VcaL
VC Zca
b
ZTTc
VbcL
Zbc

Figure 1. Three-phase power system

In this work, the sum of the three instantaneous load voltages (V sum) is calculated for different cases
of load changes (i.e., balanced and unbalanced load changes). The results are simulated for a signal frequency
of 50 Hz and 21 samples per cycle. The load changes are applied at the instant t = 0.05 sec (i.e., at the sample
number 50). Figure 2 (a) shows the response of the load currents caused by a balanced change in the three-
phase loads. This change caused a variation of 24.2% of the average inductive load current. The response of

Fast detection technique for voltage unbalance in three-phase power system (Ibrahim I. Al-Naimi)
2234  ISSN: 2088-8694

the three load voltages and the sum of their instantaneous values at different samples are shown in Figures 2
(b) and (c) respectively. Figure 3 (a) shows the response of the load currents caused by an unbalanced change
in the three-phase load. This change caused a variation of 38.6% of the average inductive load current. The
three load voltages and the sum of their instantaneous values at different samples are shown in Figures 3 (b)
and 3 (c) respectively. Zero-sum of the three load voltages is obtained for both balanced and unbalanced load
changes as shown in Figures 2 (c) and 3 (c). Figure 4 (a) shows the load currents caused by an unbalanced
fault in the power system impedance, causing an average variation of 14.3% in load current. The response of
the three load voltages is shown in Figure 4 (b). The instantaneous sum of three load voltages is not always
zero (i.e., varies with time) as shown in Figure 4 (c). It has a sinusoidal form.
According to the results shown in Figures 2 (c), 3 (c), and 4 (c), two different cases are discussed as
follows:
- Case (1): The balanced and unbalanced changes in the three-phase load produce three-line currents. By
substituting these currents in (5), the sum of the three instantaneous load voltages V sum is always equal to
zero as shown in (6). It is concluded that the balanced and unbalanced changes in the three-phase load,
without changing the impedance of the power system (ZTT), will always produce zero-sum of the three
load voltages, as shown in Figures 2 (c) and 3 (c)

𝑣𝑎𝑏𝐿(𝑡) + 𝑣𝑏𝑐𝐿(𝑡) + 𝑣𝑐𝑎𝐿(𝑡) = 0 (6)

- Case (2): If there is a change in the impedance (ZTT) of the power system, e.g., the impedance 𝑍TTa is
′ ′ ′
changed to 𝑍TTa , the instantaneous load voltage 𝑣𝑎𝑏𝐿(𝑡) is changed to 𝑣𝑎𝑏𝐿(𝑡) and 𝑣𝑐𝑎𝐿(𝑡) to 𝑣𝑐𝑎𝐿(𝑡) , leading to
(7). It is concluded that the sum of three instantaneous load voltages Vsum due to a fault in the power
system impedance is not necessarily equal to zero. In this case, V sum has a sinusoidal shape as shown in
Figure 4 (c).

′ ′
𝑣𝑎𝑏𝐿(𝑡) + 𝑣𝑏𝑐𝐿(𝑡) + 𝑣𝑐𝑎𝐿(𝑡) ≠ 𝑣𝑎𝑏𝐿(𝑡) + 𝑣𝑏𝑐𝐿(𝑡) + 𝑣𝑐𝑎𝐿(𝑡) (7)

(a) (b)

(c)

Figure 2. Results for a balanced change in the three-phase load, caused by injection of 24.2% of the average
inductive load current, (a) the p.u load currents, (b) the p.u load voltages, (c) the Sum of p.u instantaneous
load voltages

Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2230 – 2242
Int J Pow Elec & Dri Syst ISSN: 2088-8694  2235

(a)
(a)

(b) (b)

(c) (c)

Figure 3. Results for unbalanced change in the three- Figure 4. Results for unbalanced fault in power
phase load, caused by rejection of 38.6% of the system, causing an average variation of 14.3% in
average inductive load current, (a) the p.u load load current, (a) the p.u load currents, (b) the p.u
currents, (b) the p.u load voltages, (c) the sum of p.u load voltages, (c) the sum of p.u instantaneous load
instantaneous load voltage voltages

6. FAST DETECTION TECHNIQUE

A balanced power system produces a balanced voltage throughout the electrical system line. The
sum of the three instantaneous voltages is zero at any instant of time. Moreover, the space vector is fixed at
these instants of time. In this work, a FDT is developed to detect the voltage unbalance speedily. In the FDT,
the cycle time of the 50 Hz system is divided into 21 samples. The space vector (Vspace) and the sum (Vsum) of
the three load voltages are calculated at each sample. The proposed technique monitors the behavior of both
Vspace and Vsum for 5 consecutive samples and then applies predefined conditions to detect the unbalanced
voltages. Consequently, only a quarter of the cycle time is needed to detect the voltage unbalance precisely.
The AQSA Jordanian power system is considered and modeled in this paper as a real case study to
validate the proposed technique. Figure 5 shows the one-line diagram of the AQSA power System. South
Amman Station is connected to the Aqaba Station through a 328 km transmission line of 400 kV. The 373
MW Qatrana substation lies between South Amman and Aqaba stations. South Amman station distributes
about 800 MW through the 400 k V-11 kV multistage transformations to different loads [47]. To guarantee
accurate and real system response, the AQSA transmission line is represented in the simulation by three
nominal pi-sections. The Aqaba-Qatrana transmission line of 245 km is divided into two pi-sections, while
the Qatrana- South Amman transmission line of 83 km is represented by one pi-section. In this work, the
authors have developed the FDT to detect the voltage unbalance accurately and in short time. If there is a
change in the system, the FDT provides the three following conditions:

Fast detection technique for voltage unbalance in three-phase power system (Ibrahim I. Al-Naimi)
2236  ISSN: 2088-8694

- Condition (1): If the calculated sum of the three instantaneous load voltages (V sum) is zero and the
calculated space vector (Vspace) is fixed for the predefined samples, the change is balanced and occurred in
the load impedance.
- Condition (2): If the calculated sum of the three instantaneous load voltages (Vsum) is zeros and the
calculated space vector (Vspace) is varied in sinusoidal form for the predefined samples, the change is
unbalanced and occurred in the load impedance.
- Condition (3): If both the calculated sum of the three instantaneous load voltages (V sum) and the calculated
space vector (Vspace) are varied for the predefined samples, the fault is unbalanced and occurred in the
power system equipment. The three conditions are tested and validated using a simulation model in the
following section.

Aqaba 122.5km 122.5km Qatrana 83km Amman-South

Station 6.25 93.5mH 6.25 93.5mH Station  63.33mH Station

1.4F 1.4F 1.4F 1.4F 0.94F 0.94F

400kV 400kV
132kV

bus
15kV
C.B 33kV

G G G G G
11kV
STEAM GAS
603MW 373MW
15kV Ditribution Qatrana P.S Ditribution
Aqaba P.S
To Loads
Transmission Line parameters
R/km = 0.051 
L/km = 0.763 H
C.km = 0.0226 H

Figure 5. One line diagram of aqaba-qatrana- south amman power system

7. RESULTS AND DISCUSSIONS

In the proposed technique, the sinusoidal signal of the power system is sampled into a predefined
number of samples. The sum (Vsum) and space vector (Vspace) of the three load voltages are determined at each
sample. The FDT will calculate the Vsum and Vspace instantaneously. According to the three conditions
discussed in Section 6, the FDT will detect the voltage unbalance in the system.
Figure 6 shows the simulation model of the AQSA Jordanian electrical power system and the
proposed FDT. In this simulation, load changes are applied at the instant t = 0.1 sec (i.e., at the sample
number 100). Figure 7 (a) shows the response of the three load voltages due to a balanced change in the
three-phase load. This change is caused by injecting 21.4% of the average inductive load current. The Vsum
and Vspace for this case are shown in Figures 7 (b) and 7 (c) respectively. It can be observed from Figure 7
that when the balanced change occurred, the Vsum was zero at all instants of time and the Vspace settled at a
fixed value. The results in Figure 7 verified Condition (1) introduced in section 6.
Figure 8 (a) shows the three load voltages due to unbalanced change in the three-phase loads. This
change is caused by injecting 30% of the average inductive load current. The Vsum and Vspace for this case are
shown in Figures 8 (b) and 8 (c) respectively. It can be noted from Figure 8 that when the unbalanced change
occurred, Vsum was zero at all instants of time, but Vspace varied in sinusoidal form. The results in Figure 8
verified Condition (2) introduced in Section 6. Figures 9 (a) and 10 (a) show the three load voltages due to
unbalanced changes in the power system caused by one line-to-earth and two lines-to-earth faults,
respectively. As shown in Figures 9 (b), 9 (c), 10 (b) and 10 (c), both Vsum and Vspace values varied in
sinusoidal form. Thus, the results in Figures 9 and 10 verified Condition (3) given in Section 6. A short
circuit between the two windings of the 11kV-380V transformer is made and the results of the corresponding
three load voltages, Vsum, and Vspace are shown in Figures 11 (a), 11 (b), and 11 (c), respectively. It is also

Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2230 – 2242
Int J Pow Elec & Dri Syst ISSN: 2088-8694  2237

observed that when the change occurred, both Vsum and Vspace varied in sinusoidal form. The results in Figure
11 verified Condition (3) in the proposed FDT as introduced in section 6. According to the results shown in
Figures 7-11, it is reasonable to conclude that the proposed FDT can detect the voltage unbalance in the
three-phase power system quickly and accurately.

Figure 6. The simulation model of the AQSA electrical power system and the FDT

(a) (b)

(c)

Figure 7. Results for a balanced change in the three-phase, caused by injection of 21.4% of the average
inductive load current; (a) the p.u three load voltages, (b) the sum of the three p.u instantaneous load voltages
(c) the p.u space vector of the three instantaneous load voltages

Fast detection technique for voltage unbalance in three-phase power system (Ibrahim I. Al-Naimi)
2238  ISSN: 2088-8694

(a) (b)

(c)

Figure 8. Results for an unbalanced change in the three-phase, caused by injection of 30% of the average
inductive load current; (a) the p.u three load voltages, (b) the sum of the three p.u instantaneous load
voltages, (c) the p.u space vector of the three instantaneous load voltages

(a) (b)

(c)

Figure 9. Results for unbalanced fault in the power system, due to one line-to-earth fault; (a) the p.u three
load voltages, (b) the sum of the three p.u instantaneous load voltages, (c) the p.u space vector of the three
instantaneous load voltages

Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2230 – 2242
Int J Pow Elec & Dri Syst ISSN: 2088-8694  2239

(a)
(b)

(c)

Figure 10. Results for unbalanced fault in the power system, due to two lines-to-earth faults; (a) the p.u three
load voltages, (b) the sum of the three p.u instantaneous load voltages, (c) the p.u space vector of the three
instantaneous load voltages

(a) (b)

(c)

Figure 11. Results for unbalanced fault in the power system, due to the short circuit between two windings of
the 11kV-380V transformer; (a) the p.u three load voltages, (b) the sum of the three p.u instantaneous load
voltages, (c) the sum of the three p.u instantaneous load voltages

Fast detection technique for voltage unbalance in three-phase power system (Ibrahim I. Al-Naimi)
2240  ISSN: 2088-8694

8. CONTRIBUTION TO KNOWLEDGE
Table 1 introduces a brief comparison between the detection methods mentioned in the literature and
the proposed FDT. Accordingly, the contributions of knowledge in this paper are as follows: i) A novel
technique is proposed to detect the voltage unbalance by using the space vector and the sum of the three load
voltages. ii) The proposed technique has the superior ability among other techniques in detecting the voltage
unbalance quickly within a quarter of the cycle time (5 ms). In other words, the proposed technique
minimized the time duration required to detect the unbalanced voltages to 5 ms rather than 20 ms. iii) The
proposed technique has the ability to detect the all conditions of voltage unbalance accurately. iv) By
reducing the time duration required to detect the unbalanced voltages, the dynamic response of the controller
used to balance these voltages is enhanced noticeably.

Table 1. A comparison between different detection methods and the proposed FDT
Research The method used for The time needed The time needed to detect Comments
work detection for data collection the voltage unbalance (50
(50 Hz Ac power Hz Ac power system)
system)
[36] Convert the three 1 complete cycle >10 ms The total time needed for data collection
voltages to a-b (20 ms) and detecting the voltage unbalance is
stationary system more than 30 ms
using Clark-
transformation
[37] Transform the 1 complete cycle ≤10 ms The total time needed for data collection
voltage phasors into (20 ms) and detecting the voltage unbalance is
simple less than 30 ms
trigonometric
equations
[38] Calculate the 1 complete cycle 10 ms The total time needed for data collection
positive and (20 ms) and detecting the voltage unbalance is
negative sequence 30 ms
components
[39] Use modified 1 complete cycle 10 ms The total time needed for data collection
mathematical (20 ms) and detecting the voltage unbalance is
approach to 30 ms
calculate modified
VUF based on zero
sequence
component
[40] Calculate the VUF, 1 complete cycle >10 ms The total time needed for data collection
PVUR, and LVUR (20 ms) and detecting the voltage unbalance is
to detect the voltage more than 30 ms
unbalance
The Calculate the space 4 ms (The time The time needed for collecting data and
proposed vector and the sum interval between 5 1ms detecting the voltage unbalance is 5 ms
technique of three voltages in consecutive (a quarter of the cycle time)
a discrete manner samples)

9. CONCLUSIONS
A novel technique has been proposed to detect the voltage unbalance in the three-phase power
system. The proposed FDT depends on measuring the three load voltages in a discrete manner. The FDT
utilizes the Vsum and Vspace to detect the unbalanced voltages at the load quickly and precisely. A simulation
model for aqaba-qatrana-south amman (AQSA) Jordanian power system has been built and several test cases
have been conducted to test and validate the capability of the proposed technique. The results have revealed a
high performance of the proposed FDT in detecting the unbalanced voltages quickly within 5 ms.

REFERENCES
[1] Y. Kim, “Development and Analysis of a Sensitivity Matrix of a Three-Phase Voltage Unbalance Factor,” IEEE
Transactions on Power Systems, vol. 33, no. 3, pp. 3192-3195, May 2018, doi: 10.1109/TPWRS.2018.2807980.
[2] P. T. Ogunboyo, R. Tiako and I. E. Davidson, “Effectiveness of Dynamic Voltage Restorer for Unbalance Voltage
Mitigation and Voltage Profile Improvement in Secondary Distribution System,” Canadian Journal of Electrical
and Computer Engineering, vol. 41, no. 2, pp. 105-115, Spring 2018, doi: 10.1109/CJECE.2018.2858841.
[3] J. Saroha, “Harmonic and voltage unbalance compensation in an islanded microgrids using parallel neural digital
filter,” International Journal of Electronics Engineering, IET, vol. 10, issue 1, pp. 384-391, 2018.

Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2230 – 2242
Int J Pow Elec & Dri Syst ISSN: 2088-8694  2241

[4] T. Antic, T. Capuder, and M. Bolfek, “A Comprehensive Analysis of the Voltage Unbalance Factor in PV and EV
Rich Non-Synthetic Low Voltage Distribution Networks,” Energies, MPDI, vol. 14, no. 1, pp. 1-30, 2021, doi:
10.3390/en14010117.
[5] J. Huang and Z. Jiang, “Power Quality Assessment of Different Load Categories,” Energy Procedia, vol. 141, pp.
345-351, 2017, doi: 10.1016/j.egypro.2017.11.041.
[6] D. Lineweber and S. McNulty, “The Cost of Power Disturbances to Industrial and Digital Economy Companies,”
Primen, EPRI’s Consortium for Electric Infrastructure for a Digital Society CEIDS, 2001.
[7] H. K. M. Paredes, D. T. Rodrigues, J. C. Cebrian and J. P. Bonaldo, “CPT-Based Multi-Objective Strategy for
Power Quality Enhancement in Three-Phase Three-Wire Systems Under Distorted and Unbalanced Voltage
Conditions,” IEEE Access, vol. 9, pp. 53078-53095, 2021, doi: 10.1109/ACCESS.2021.3069832.
[8] C. Okoli, B. Anyaka, C. Nwokedi, and V. Anya, “Application of Composite Method for Determining Fault
Location on Electrical Power Distribution Lines,” Journal of Electrical and Computer Engineering, Hindawi, vol.
2020, ID. 2836940, pp. 1-9, 2020, doi: 10.1155/2020/2836940.
[9] G. Wang, F. Gao, J. Liu, Q. Li and Y. Zhao, “Design consideration and performance analysis of a hybrid islanding
detection method combining voltage unbalance/total harmonic distortion and bilateral reactive power variation,”
CPSS Transactions on Power Electronics and Applications, vol. 5, no. 1, pp. 86-100, March 2020, doi:
10.24295/CPSSTPEA.2020.00008.
[10] M. H. Albadi, A. S. Al Hinai, A. H. Al-Badi, M. S. Al Riyami, S. M. Al Hinai and R. S. Al Abri, “Unbalance in
power systems: Case study,” IEEE International Conference on Industrial Technology (ICIT), 2015, pp. 1407-
1411, doi: 10.1109/ICIT.2015.7125294.
[11] G. Bao and S. Ke, “Load Transfer Device for Solving a Three-Phase Unbalance Problem Under a Low-Voltage
Distribution Network,” Energies, vol. 12, no. 15, pp. 1-18, 2019, doi: 10.3390/en12152842.
[12] P. Paranavithana and S. Perera, “Location of sources of voltage unbalance in an interconnected network,” IEEE
Power & Energy Society General Meeting, pp. 1-6, 2009, doi: 10.1109/PES.2009.5275641.
[13] S. Omran, R. Broadwater, J. Hambrick, M. Dilek, C. Thomas, and F. Kreikebaum, “Load growth and power flow
control with DSRs: Balanced vs unbalanced transmission networks,” Electric Power Systems Research, Elsevier,
vol. 145, pp. 207-213, 2017, doi: 10.1016/j.epsr.2017.01.012.
[14] Energy Tips: Motor System, “Eliminate Voltage Unbalance,” U. S. Department of Energy: Washington, 2012.
[15] B. Tomoiaga, M. Chindris, A. Sumper, R. V. Robles, and A. S. Andreu, “Distribution system reconfiguration using
genetic algorithm based on connected graphs,” Electric Power Systems Research, Elsiever, vol. 104, pp. 216-225,
2013, doi: 10.1016/j.epsr.2013.06.021.
[16] J. Ghaeb and J. Chebil, “Prediction of Voltage Unbalance Employing Space Vector Property,” International
Journal of Engineering Research and Development, vol. 12, no. 12, pp. 65-70, 2017.
[17] W. H. Kersting and W. H. Phillips, “Phase frame analysis of the effects of voltage unbalance on induction
machines,” IEEE Transactions on Industry Applications, vol. 33, no. 2, pp. 415-420, March-April 1997, doi:
10.1109/28.568004
[18] D. Zhang, R. An and T. Wu, “Effect of Voltage Unbalance and Distortion on the Loss Characteristics of Three-
Phase Cage Induction Motor,” IET Electric Power Applications, vol. 12, no. 2, pp. 264-270, 2018, doi: 10.1049/iet-
epa.2017.0464.
[19] Ching-Yin Lee, “Effects of unbalanced voltage on the operation performance of a three-phase induction motor,”
IEEE Transactions on Energy Conversion, vol. 14, no. 2, pp. 202-208, June 1999, doi: 10.1109/60.766984.
[20] J. Driesen and T. Craenenbroeck, “Voltage Disturbances: Introduction to Unbalance,” Copper Development
Association, Katholieke Universiteit Leuven: Brussels, 2002.
[21] J. Thomas, P. S. Revuelta, A. P. Valles, and S. P. Litran, “Practical evaluation of unbalance and harmonic distortion
in power conditioning,” Electric Power Systems Research, Elsevier, vol. 141, pp. 487-499, 2016, doi:
10.1016/j.epsr.2016.08.012.
[22] J. Ghaeb and O. Aloquili, “High performance reactive control for unbalanced three-phase load,” Europian
Transaction in Electrical Power, vol. 20, no. 6, pp. 710-722, 2009, doi: 10.1002/etep.349.
[23] J. Martinez and G. Ramos, “Reactive power and harmonic distortion control in electric traction systems,”
IEEE/PES Transmission and Distribution Conference and Exposition: Latin America (T&D-LA), 2010, pp. 190-
195, doi: 10.1109/TDC-LA.2010.5762881.
[24] J.H. Chen, W.-J. Lee and M.S. Chen, “Using a static VAr compensator to balance a distribution system IAS '96,”
Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting, 1996, pp.
2321-2326 vol.4, doi: 10.1109/IAS.1996.563896.
[25] F. R. Quintela, J. M. G. Arevalo, R. C. Redondo, and N. R. Melchor, “Four-wire three-phase load balancing with
Static VAr Compensators,” International Journal of Electrical Power and Energy Systems, vol. 33, no. 3, pp. 562-
568, 2011, doi: 10.1016/j.ijepes.2010.11.010.
[26] S. Marx, D. Bender, “An Introduction to Symmetrical Components, System Modelling and Fault Calculation,” 33th
Annual HANDS-ON Relay School March 16-20, Washington State University Pullman, Washington, 2016.
[27] NEMA Standards, “Motors and Generators,” 1993.
[28] IEEE Standard Dictionary of Electrical and Electronics Terms, in IEEE Std. 1996.
[29] “Definitions of Voltage Unbalance,” IEEE Power Engineering Review, vol. 22, no. 11, pp. 49-50, Nov. 2002, doi:
10.1109/MPER.2002.4311797.
[30] J. Hu, K. Chen, T. Shen and C. Tang, “Analytical Solutions of Multilevel Space-Vector PWM for Multiphase
Voltage Source Inverters,” IEEE Transactions on Power Electronics, vol. 26, no. 5, pp. 1489-1502, May 2011, doi:
10.1109/TPEL.2010.2084107.

Fast detection technique for voltage unbalance in three-phase power system (Ibrahim I. Al-Naimi)
2242  ISSN: 2088-8694

[31] S. Das, G. Narayanan and M. Pandey, “Space-Vector-Based Hybrid Pulsewidth Modulation Techniques for a
Three-Level Inverter,” IEEE Transactions on Power Electronics, vol. 29, no. 9, pp. 4580-4591, Sept. 2014, doi:
10.1109/TPEL.2013.2287095.
[32] T.-P. Chen, Y.-S. Lai and C.-H. Liu, “A new space vector modulation technique for inverter control,” 30th Annual
IEEE Power Electronics Specialists Conference. Record. (Cat. No.99CH36321), 1999, pp. 777-782 vol.2, doi:
10.1109/PESC.1999.785598.
[33] Y. Tadano, H. Shizunori, U. Shota, N. Masakatsu, S. Yukihiko, and I. Muneaki, “Direct Space Vector PWM
Strategy for Matrix Converters with Reduced Number of Switching,” IEEJ Transactions on Industry Applications,
vol. 128, no. 4, pp. 550-559, 2008, doi: 10.1541/ieejias.128.550.
[34] J. A. Ghaeb, “Sampled data and space vector technique for static VAR compensation,” 13th International Multi-
Conference on Systems, Signals & Devices (SSD), 2016, pp. 30-35, doi: 10.1109/SSD.2016.7473654.
[35] M. Sun, S. Demirtas and Z. Sahinoglu, “Joint Voltage and Phase Unbalance Detector for Three Phase Power
Systems,” IEEE Signal Processing Letters, vol. 20, no. 1, pp. 11-14, Jan. 2013, doi: 10.1109/LSP.2012.2226717.
[36] C. J. O’Rourke, M. M. Qasim, M. R. Overlin and J. L. Kirtley, “A Geometric Interpretation of Reference Frames
and Transformations: dq0, Clarke, and Park,” IEEE Transactions on Energy Conversion, vol. 34, no. 4, pp. 2070-
2083, Dec. 2019, doi: 10.1109/TEC.2019.2941175.
[37] H. Wen, D. Cheng, Z. Teng, S. Guo and F. Li, “Approximate Algorithm for Fast Calculating Voltage Unbalance
Factor of Three-Phase Power System,” IEEE Transactions on Industrial Informatics, vol. 10, no. 3, pp. 1799-1805,
2014, doi: 10.1109/TII.2014.2327485.
[38] T. Chen. C. Yang, and N. Yang, “Examination of the definitions of voltage unbalance,” International Journal of
Electrical Power and Energy Systems, vol. 49, pp. 380-385, 2013, doi: 10.1016/j.ijepes.2013.02.006.
[39] A. Nakadomari, Y. Y. Hong, P. Mandal, H. Takahashi, and T. Senjyu, “Optimization of Voltage Unbalance
Compensation by Smart Inverter,” Energies, vol. 13, no. 8, pp. 1-22, 2020, doi: 10.3390/en13184623.
[40] K. Girigoudar and L. Roald, “On the impact of different voltage unbalance metrics in distribution system
Optimization,” Electric Power System Research, Elsevier, vol. 189, no. 106656, 2020, doi:
10.1016/j.epsr.2020.106656.
[41] J. A. L. Ghijselen and A. P. M. V. Bossche, “Exact voltage unbalance assessment without phase measurements,”
IEEE Transactions on Power Systems, vol. 20, no. 1, pp. 519-520, 2005, doi: 10.1109/TPWRS.2004.841145.
[42] D. R. Sawitri, D. A. Asfani, M. H. Purnomo, I. K. E. Purnama and M. Ashari, “Early detection of unbalance
voltage in three phase induction motor based on SVM,” 9th IEEE International Symposium on Diagnostics for
Electric Machines, Power Electronics and Drives (SDEMPED), 2013, pp. 573-578, doi:
10.1109/DEMPED.2013.6645772.
[43] M. Okelola and O. Olabode, “Detection of Voltage Unbalance on Three Phase Induction Motor Using Artificial
Neural Network,” International Journal of Emerging Trends in Engineering and Development, vol. 4,no. 8, pp. 18-
25, 2018, doi: 10.26808/rs.ed.i8v4.03.
[44] M. Alkayyati, and J. Ghaeb, “Hybrid PSO–ANN algorithm to control TCR for voltage balancing,” IET Generation,
Transmission & Distribution, vol. 14, no. 5, pp. 863-872, 2020, doi: 10.1049/iet-gtd.2019.1246 .
[45] D. M. R.agab, J. A. Ghaeb, and I. A. Naimi, “Enhancing the response of thyristor-controlled reactor using neural
network,” International Transactions on Electrical Energy Systems, Wiley, vol. 29, no. 12, pp. 1-16, 2019, doi:
10.1002/2050-7038.12137.
[46] J. Grainger and W. Stevenson, “Power system analysis,” 1994, New York: McGraw- Hill.
[47] Report of National Control Centre, Operation Department, National Electric Power Company, Jordan, 2017.

Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2230 – 2242