Department of Electrical and Computer Engineering Bus Voltage Ranking and Voltage Stability Enhancement for Unbalanced Multiphase Networks Parachai Juanuwattanakul This thesis is presented for the Degree of Doctor of Philosophy of Curtin University February 2012
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Department of Electrical and Computer Engineering
Bus Voltage Ranking and Voltage Stability Enhancement
for Unbalanced Multiphase Networks
Parachai Juanuwattanakul
This thesis is presented for the Degree of
Doctor of Philosophy
of
Curtin University
February 2012
Declaration
To the best of my knowledge and belief this thesis contains no material previously
published by any other person except where due acknowledgment has been made.
This thesis contains no material which has been accepted for the award of any other
degree or diploma in any university.
Signature: ………………………………………….
Date: ………………………...
ABSTRACT
Voltage instabilities and subsequent system collapses are considered as growing
concerns in modern multiphase distribution networks as they are progressively
forced to operate closer to their stability limits due to many factors such as increasing
load level, lack of reactive power sources, high installation of single-phase shunt
capacitors and reverse action of voltage control devices. System operators must be
able to quickly identify trouble spots and take corrective steps to avoid critical
voltage collapses. To achieve this, suitable indices must be defined to assess system
security and take corrective control actions when predefined thresholds are reached.
In this regard, the identification and ranking of weak buses in a power system is an
important research area.
The existing conventional bus voltage ranking indices are only defined for single-
phase and balanced three-phase networks. This thesis proposes a new bus voltage
ranking index (VRI) to identify the weakest single-, two- and three-phase buses of
multiphase distribution networks. Then, applications of the proposed bus ranking
index will be tested for enhancing the voltage stability of unbalanced multiphase
distribution networks.
In the first part of this thesis, the definition of conventional voltage ranking indices
are modified and generalized to also include unbalanced and multiphase networks
using symmetrical components. For the first time, the method of symmetrical
components is applied to the three-phase voltages computed from three-phase power
flow. The new index is defined as the ratio of the (fundamental) positive-sequence
voltage at the point of voltage collapse to the positive-sequence voltage at the base-
load source. The former voltage level is determined by increasing the active power
of all loads while keeping power factor constant until the point of voltage collapse is
reached.
In the second part of this thesis, the new VRI is validated through the calculation of
grid losses and PV curves based on positive-sequence voltage. Extensive simulations
of the IEEE 13 and 34 node test feeders are performed using the DIgSILENT
PowerFactory to further validate and compare the performance of the new VRI with
three well-known conventional ranking indices.
In the third part of the thesis, the new VRI is used to identify the weakest three-phase
buses in unbalanced three-phase distribution networks. Then, the index is utilized to
place compensation devices at the weakest buses of the modified unbalanced three-
phase 13 node test feeder to improve voltage stability and increase the maximum
loading factor (MLF) under unbalanced three-phase operating conditions.
In the fourth part of the thesis, static analyses are carried out to demonstrate
applications of the proposed VRI in increasing MLF and improving voltage stability
of multiphase networks under unbalanced loading and/or network conditions. Then,
dynamic simulations are performed to further validate the accuracy of the proposed
VRI and improving voltage stability under dynamic operating conditions.
In the fifth part of the thesis, an online application of the proposed bus ranking is
introduced to identify the weakest buses in multiphase smart grids with plug-in
electric vehicle (PEV) charging stations.
Finally, the proposed voltage ranking and stability enhancement approach are
utilized to improve the performance of multiphase distribution networks by proper
placement and sizing of distributed generator (DG) units such as doubly-fed
induction generators (DFIGs) and single-phase capacitors. An iterative algorithm is
proposed for the placement and sizing of DG units and single-phase capacitors in
multiphase networks to reduce grid losses and increase MLF while keeping all bus
voltages within acceptable limits. The approach consists of utilizing the positive-
sequence voltage ratio Vcollapse/Vbase-load to identify the weakest three-phase and
single-phase buses for the installation of DG units and shunt capacitors, respectively.
DG penetration levels are increased (e.g., 40%) by evaluating their impacts on
voltage profile, grid losses, and voltage stability margin while considering the
voltage limits at all buses. The impacts of DIFG on voltage profile, active power
loss, MLF and voltage unbalance factor are highlighted.
DEDICATION
To my parents, Mamie and Papa, as well as my brother and sister for their endless
support and love.
ACKNOWLEDGMENT
I would like to express my special thanks to my supervisor, Associate Professor
Mohammad A.S. Masoum, for his invaluable advice, guidance and support all
throughout my PhD studies. I am also greatly thankful to my co-supervisor,
Professor Syed M. Islam for his assistance during the course of my study. Finally,
financial support from Sripatum University is gratefully acknowledged. Last but not
least, I wish to express my love and gratitude to my family and friends for their
endless support and love.
TABLE OF CONTENTS
Abstract ................................................................................................................... ii
Table of Contents ................................................................................................... vi
Weakest bus (single-phase)Weakest bus (three-phase) Weakest bus (two-phase)
Figure 3-5 Bus ranking for Case 6 (with one DG and one SVC at bus 675).
3.5.2 Validation of proposed VRI based on grid loss calculations for the
IEEE multiphase 13 node test feeder
Grid losses associated with the placement of DG units at each node (e.g., all possible
locations of DG) are computed and compared with the losses generated with the DG
unit connected at the weakest bus as identified by the proposed VRI.
3.5.2.1 Grid losses with one DG unit for the IEEE multiphase 13 node test feeder
A three-phase induction generator is placed at different buses of the IEEE multiphase
13 node feeder (Figure 3-1) and system active and reactive losses are plotted in
Figure 3-6. This figure confirms that bus 675 (resulting in the lowest grid losses) is
the most suitable bus for DG placement, as was previously identified by the proposed
VRI (2-14).
31
TABLE 3-4 BUS RANKING FOR CASE 6 BASED ON THE PROPOSED VRI.
Bus number Case 6
RG60 1.05177
632 0.96139
633 0.94595
634 0.77360***
645 0.94095
646 0.93346
671 0.98381
680 0.98381
684 0.89518**
611 0.77550*
652 1.00702
692 0.98381
675 1.00000
*) The weakest single-phase bus.
**) The weakest two-phase bus.
***) The weakest three-phase bus.
Bus Number
Re
acti
ve P
ow
er
Lo
ss (
MV
Ar)
Ac
tive
Po
wer
Lo
ss (
MW
)
0.285
0.295
0.305
0.315
0.325
0.335
0.345
0.355
RG60 632 633 671 680 692 675
0.090
0.095
0.100
0.105
0.110
0.115
Active power loss
Reactive power loss0.120
0.125
Figure 3-6 Reactive and active power losses associated with DG connections at different buses of Figure 3-1 (Case 2).
32
3.5.2.2 Grid losses with two DG units for the IEEE multiphase 13 node test feeder
According to (2-14), with the addition of one DG (at bus 675, Figure 3-4), the most
suitable location for the connection of a second DG unit is still at bus 675. This is in
agreement with the grid loss plots of Figure 3-7 generated by connecting the first DG
at bus 675 and placing a second DG at different buses of the IEEE 13 node feeder.
These results further confirm the accuracy of the proposed bus ranking index.
3.5.3 Validation of proposed VRI based on PV curves for the IEEE
multiphase 13 node test feeder
The PV curves based on positive-sequence voltages are plotted and compared with
the PV curve generated when DG and SVC units are connected at the weakest bus.
Figures 3-8, 3-9, and 3-10 show the PV curves of positive-sequence voltages at each
three-, two- and single-phase bus for Case 2, respectively. According to these
figures, buses 675, 684 and 611 are the weakest three-, two- and single-bus as
previously recognized by (2-14).
After connecting a combination of DG and SVC units at bus 675, PV curves for Case
6 are regenerated and plotted in Figure 3-11. As expected and previously recognized
by the proposed VRI, the lowest stability margins occur at bus 634.
Re
acti
ve P
ow
er
Lo
ss (
MV
Ar)
Acti
ve
Po
wer
Lo
ss (
MW
)
0.250
0.260
0.270
0.280
0.290
0.300
0.310
Bus NumberRG60 632 633 671 680 692 675
0.084
0.088
0.092
0.096
0.100
Active power loss
Reactive power loss0.104
0.108
Figure 3-7 Reactive and active power losses associated with the first DG installed at bus 675 and the second DG connected at different buses of Figure 3-1 (Case 3).
33
114669466746654663466
1.2
1.1
1.0
0.9
0.8
0.7
Total Load of Selected Loads (kW)
Bus 675; the weakest three-phase bus
632671
633 634675
RG60680 692
Po
sit
ive-S
eq
uen
ce V
olt
ag
e (
p.u
.)
Figure 3-8 PV curves of positive-sequence voltage at each three-phase bus for Case 2.
1146694667466
0.70
0.60
684645 646Total Load of S elected L oads (kW)
5466
Bus 684; the weakest two- phase bus
0.50
0.403466
Po
sit
ive
-Se
qu
en
ce
Vo
lta
ge
(p
.u.)
Figure 3-9 PV curves of positive-sequence voltage at each two-phase bus for Case 2.
34
11466946674665466
0.36
0.32
0.28
0.24
3466
0.20
0.16
611652Total Load of S elected L oads (kW)
Bus 611; the weakest single- phase bus
Po
sit
ive
-Se
qu
en
ce
Vo
lta
ge
(p
.u.)
Figure 3-10 PV curves of positive-sequence voltage at each single-phase bus for Case 2.
19466154661146674663466
1.2
1.1
1.0
0.9
0.8
0.7
Total Load of Selected Loads (kW)
Bus 634; the weakest three-phase bus
632671
633 634675
RG60680 692
Po
sit
ive-S
eq
uen
ce V
olt
ag
e (
p.u
.)
Figure 3-11 PV curves of positive-sequence voltage at each bus for Case 6.
3.5.4 Comparison of proposed VRI with other bus ranking approaches for
the IEEE multiphase 13 node test feeder
Table 3-5 compares the performance of the proposed VRI (2-14) with three well-
known bus ranking indices; 𝑉/𝑉0, 𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃 for the IEEE 13 node network
35
of Figure 3-1 under balanced three-phase, unbalanced three-phase and unbalanced
multiphase operating conditions.
Under balanced three-phase conditions (Table 3-5, column 2), all methods
identify the same weakest bus (e.g., node 634). However, the conventional
ranking approaches are not applicable to unbalanced three-phase and multiphase
systems and fail to identify the correct weakest buses.
Under unbalanced three-phase conditions (Table 3-5, column 3), the weakest bus
is node 675 as identified by the proposed VRI and confirmed by the calculated
PV curves (Figure 3-12) and grid losses (Table 3-6, columns 2-3). However,
based on the two voltage sensitivity methods (𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃), the weakest
bus is node 634 which is not correct. This is further confirmed by placing SVC
units at buses 634 and 675 and computing the corresponding maximum loading
factors as demonstrated in Table 3-7. Therefore, the magnitudes of the voltage
sensitivity methods do not provide a correct measure of voltage stability under
unbalanced three-phase networks.
For multiphase operation (Table 3-5, column 4), the weakest three-, two- and
single- phase buses are nodes 675, 684 and 611, respectively; as identified by the
proposed VRI (Figure 3-3) and confirmed by grid losses (Figure 3-6) and PV
curves PV curves (Figures 3-8 to 3-10). Therefore, the conventional indices
(𝑉/𝑉0, 𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃) cannot properly identify the weakest buses of
multiphase networks.
36
TABLE 3-5 BUS RANKING RESULTS FOR THE IEEE 13 NODE NETWORK WITH ONLY UNBALANCED THREE-PHASE NETWORKS/LOADS.
Bus ranking approach
The weakest buses of the unbalanced IEEE 13 node test feeder
(Figure 3-1)
Balanced
three-phase *
Unbalanced three-
phase **
Unbalanced
multiphase***
Grid losses 634 675 (Table 3-6) 675(3p), see Figure 3-7
*) Modified Figure 3-1 with only balanced networks/loads.
**) Modified Figure 3-1 with only unbalanced three-phase networks/loads.
***) 1p, 2p and 3p correspond to single-, two- and three-phase buses.
****) Calculated by positive sequence.
TABLE 3-6 BUS RANKING RESULTS FOR THE IEEE 13 NODE TEST FEEDER (FIG. 3-1) WITH ONLY UNBALANCED THREE-PHASE NETWORKS/LOADS.
Bus
number
Grid losses 𝜕𝑉/𝜕𝑃
[p.u./MW]
𝜕𝑉/𝜕𝑄
[p.u./MVAr]
Proposed VRI
(2-14) P
[MW]
Q
[MVAr]
634 0.13555 0.47702 -0.26223 0.36904 0.61776
675 0.13448 0.47281 -0.23591 0.30041 0.60153
37
TABLE 3-7 MAXIMUM LOADING FACTORS WITH SVC.
MLF
Base-case 2.687
SVC at bus 634 3.282
SVC at bus 675 5.095
971684667216596647163466
Total Load of S elected L oads (kW)
675634
1.00
0.90
0.80
0.70
0.60
0.50
Bus 675
Bus 634
Po
sit
ive-S
eq
uen
ce V
olt
ag
e (
p.u
.)
Figure 3-12 PV curves of positive-sequence voltages at buses 634 and 675 for the
modified IEEE 13 node network (Figure 3-1) with only unbalanced three-phase
networks/loads.
3.6 DETAILED SIMULATION OF IEEE MULTIPHASE 34 NODE
TEST FEEDER TO VALIDATE PROPOSED VRI
In this section, detailed simulations of the IEEE multiphase unbalanced 34 node test
feeder (Figure 3-13) is performed to: (1) find the weakest buses of the feeder
(without/with voltage regulators, induction generator and DFIG wind turbine) based
on the proposed VRI (2-14), (2) validate the identified weakest buses through grid
losses calculations, PV curves and voltage sensitivity indices (𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃).
38
The system data for the IEEE multiphase 34 node test feeder is presented in
Appendixes A3 and A4 [33]. This unbalanced multiphase feeder consists of three-
phase and single-phase sections with unbalanced spot loads (Y-PQ, D-PQ, Y-I, D-I,
Y-Z, and D-Z), distributed loads (Y-PQ, Y-I, Y-Z, D-I, D-Z, and D-PQ), three-phase
shunt capacitors (at buses 844 and 848), and an in-line transformer (between buses
832 and 888).
There are also two automatic voltage regulators. Bus 800 is treated as a slack bus
with a voltage set point of 1.05 p.u. At a base-case load condition, the voltage at bus
890 is lower than the permissible voltage limit because the line between buses 888
and 890 is relatively long. However, other bus voltages are in the acceptable range of
0.95p.u. to 1.05p.u.
800
806 808 812 814
810
802 850818
824 826816
820
822
828 830 854 856
852
832888 890
838
862
840836860834
842
844
846
848
864
858
Single-phase (phase-a)
Single-phase (phase-b)
Single-phase (phase-b)
Figure 3-13 The IEEE multiphase 34 node test feeder.
Simulations are performed on the multiphase unbalanced IEEE 34 node test feeder
(Figure 3-13) for the following cases (Table 3-8):
Case 8: without a voltage regulator (fixed transformer tap ratio set to 1.0).
Case 9: with a voltage regulator (variable transformer tap ratio).
Case 10: Case 9 with a DG (three-phase induction generator) injecting 200 kW
active power (e.g., 10% of the total load) installed at the weakest three-phase node
(bus 890).
Case 11: Case 9 with one DG (200 kW DFIG wind turbine) installed at the weakest
three-phase node (bus 890).
39
Case 12: Case 9 with DGs (2.4 MW DFIG wind turbines) installed at the weakest
three-phase node (bus 890).
TABLE 3-8 SIMULATED CASE STUDIES FOR THE IEEE 34 NODE TEST FEEDER (FIG. 3-13).
Case
number
System operating condition of the IEEE 34 node
test feeder Simulation results
8 No voltage regulators, transformer tap ratio
set to 1.0
Fig. 3-14, Table 3-9
(column 1)
9 A voltage regulator, variable transformer tap
ratio
Figs. 3-15, 3-21 and 3-
22, Table 3-9
(column 2)
10 Case 9 with a DG (200 kW IG) at the
weakest three-phase node (bus 890)
Fig. 3-16, Table 3-10
11 Case 9 with a DG (200 kW DFIG wind
turbine) at the weakest three-phase node
(bus 890)
Fig. 3-17, Table 3-11
12 Case 9 with DGs (2.4 MW DFIG wind
turbines) at the weakest three-phase node
(bus 890)
Figs. 3-18 and 3-23,
Table 3-12
3.6.1 Identification of the weakest buses using the proposed VRI for the
IEEE multiphase unbalanced 34 node test feeder
In the following sections, the proposed VRI (2-14) will be utilized to locate the
weakest three-phase buses for the placement of three-phase induction generator and
DFIG wind turbine to enhance voltage stability. At each compensation level, the
proposed index (2-14) is calculated and the bus ranking is updated since the system
configuration is changed. To show the validity of the proposed bus ranking and the
effectiveness of the compensation devices (induction generator and DFIG wind
turbine), grid losses, PV curves (based on positive-sequence voltages) and voltage
stability margins are calculated and compared for the aforementioned cases.
40
3.6.1.1 Bus ranking without/with a voltage regulator (Cases 8 and 9)
Figures 3-14 (corresponding to columns 2 of Table 3-9) and 3-15 (corresponding to
column 3 of Table 3-9) show the bus rankings for Cases 8 and 9 based on (2-14)
without and with a voltage regulator, respectively. According to these figures, the
voltage regulator has no effect on the order of bus ranking.
0
0.2
0.4
0.6
0.8
1
1.2
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-14 Bus ranking for Case 8 (without any voltage regulators).
Note that the four nodes with the lowest positive-sequence voltage ratios (2-14) are
buses 890, 864, 822 and 888. Therefore, the most appropriate location for the
installation of a three-phase DG is bus 890 since nodes 864 and 822 are single-phase
buses and nodes 890 and 888 are three-phase buses.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-15 Bus ranking for Case 9 (with a voltage regulator).
3.6.1.2 Bus ranking with an induction generator DG unit at the most suitable bus (Case 10)
As mentioned before, installation of DG devices (e.g., induction generators) at the
most suitable three-phase buses (e.g., weakest buses with the lowest VRI values) can
improve the voltage stability. Simulation results of Figure 3-16 and Table 3-10
41
indicate that the application of one DG (an induction generator) at bus 890 does not
change the order of VRI values and therefore has no impact on the order of bus
ranking.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-16 Bus ranking for Case 10 (with a DG type induction generator at bus 890).
3.6.1.3 Bus ranking with a 200kW DFIG wind turbine DG unit at the most
suitable bus (Case 11)
One DFIG wind turbine DG unit is connected at bus 890 (e.g., the three-phase node
with the lowest VRI) and the proposed index (2-14) is recalculated. As a result, the
order of the weakest nodes are changed to buses 890, 864, 822, 888, and 620 as
shown in Figure 3-17 and Table 3-11. Simulation results indicate that the application
of one DG (200 kW DFIG wind turbine) at bus 890 does not change the order of VRI
values and therefore has no impact on the order of bus ranking.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-17 Bus ranking for Case 11 (with a DFIG wind turbine DG unit at bus 890).
42
TABLE 3-9 BUS RANKING FOR CASES 8 AND 9 BASED ON THE PROPOSED VRI.
Bus number Case 8 Case 9
800 1.00000 1.00000
802 0.99799 0.99573
806 0.99666 0.99290
808 0.97176 0.93948
810 (single-phase) 0.97495 0.94645
812 0.94172 0.87464
814 0.91684 0.82070
850 1.00154 0.83477
816 0.90944 0.83414
818 (single-phase) 0.88203 0.79616
820 (single-phase) 0.84634 0.71782
822 (single-phase) 0.84140 0.70916
824 0.89911 0.81571
826 (single-phase) 0.91036 0.84105
828 0.89828 0.81422
830 0.87777 0.77750
854 0.87725 0.77657
852 0.83959 0.70887
832 0.83322 0.74432
858 0.82963 0.73901
834 0.82548 0.73287
842 0.82538 0.73271
844 0.82488 0.73197
846 0.82442 0.73130
848 0.82437 0.73124
860 0.82491 0.73202
836 0.82455 0.73150
840 0.82452 0.73145
862 0.82454 0.73149
838 (single-phase) 0.83164 0.75167
864 (single-phase) 0.80473* 0.68868*
888 0.80342 0.69969
890 0.69640*** 0.54248 ***
856 (single-phase) 0.88758 0.80031
*) The weakest single-phase bus.
***) The weakest three-phase bus.
43
TABLE 3-10 BUS RANKING FOR CASE 10 BASED ON THE PROPOSED VRI.
Bus number Case 10
800 1.00000
802 0.99582
806 0.99305
808 0.94083
810 (single-phase) 0.94775
812 0.87803
814 0.82600
850 0.85138
816 0.85077
818 (single-phase) 0.79710
820 (single-phase) 0.73635
822 (single-phase) 0.72791
824 0.83300
826 (single-phase) 0.85770
828 0.83156
830 0.79632
854 0.79543
852 0.73097
832 0.77219
858 0.76691
834 0.76079
842 0.76063
844 0.75988
846 0.75920
848 0.75918
860 0.75996
836 0.75946
840 0.75941
862 0.75944
838 (single-phase) 0.77859
864 (single-phase) 0.71722*
888 0.73057
890 0.59503***
856 (single-phase) 0.81841
*) The weakest single-phase bus.
***) The weakest three-phase bus.
44
TABLE 3-11 BUS RANKING FOR CASE 11 BASED ON THE PROPOSED VRI.
Bus number Case 11
800 1.00000
802 0.99498
806 0.99498
808 0.99165
810 (single-phase) 0.92914
812 0.93821
814 0.85398
850 0.79201
816 0.82070
818 (single-phase) 0.74986
820 (single-phase) 0.66849
822 (single-phase) 0.65709
824 0.79889
826 (single-phase) 0.83131
828 0.79720
830 0.75550
854 0.75444
852 0.67831
832 0.71712
858 0.71062
834 0.70310
842 0.70291
844 0.70201
846 0.70117
848 0.70109
860 0.70204
836 0.70150
840 0.70134
862 0.70138
838 (single-phase) 0.72512
864 (single-phase) 0.64766*
888 0.67604
890 0.53690***
856 (single-phase) 0.78413
*) The weakest single-phase bus.
***) The weakest three-phase bus.
45
3.6.1.4 Bus ranking with a 2.4 MW DFIG wind turbine DG unit (Case 12)
A 2.4 MW DFIG wind turbine (Case 12) is connected at bus 890 (e.g., the three-
phase node with the lowest VRI) and the proposed index (2-14) is recalculated. As a
result, the order of the weakest three-phase nodes are changed to buses 852, 890 and
814 as shown in Figure 3-18 and Table 3-12. This means the next suitable bus for
connecting a compensation device is bus 852.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
800
802
806
808
810
812
814
850
816
818
820
822
824
826
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
838
864
888
890
856
Weakest bus (three-phase)
Bus Number
VR
I
Weakest bus (single-phase)Single-phase Three-phase
Figure 3-18 Bus ranking for Case 12 (with DFIG wind turbines at bus 890).
3.6.2 Validation of proposed VRI based on grid loss calculations for the
IEEE multiphase 34 node test feeder
Grid losses associated with the placement of DG units at each node (e.g., all possible
locations of DG) are computed and compared with the losses generated with the DG
unit connected at the weakest bus as identified by the proposed VRI.
3.6.2.1 Grid losses with one DG unit for the IEEE multiphase 34 node test feeder
A three-phase DFIG wind turbine is placed at different buses of the unbalanced IEEE
34 node feeder (Figure 3-13) and the system active power losses are plotted in Figure
3-19. This figure confirms that bus 890 (resulting in the lowest grid losses) is the
most suitable bus for DG placement, as was previously identified by the proposed
VRI (2-14).
46
TABLE 3-12 BUS RANKING FOR CASE 12 BASED ON THE PROPOSED VRI.
Bus number Case 12
800 1.00000
802 0.99298
806 0.98835
808 0.90360
810 (single-phase) 0.92369
812 0.80679
814 0.73076
850 0.85460
816 0.85357
818 (single-phase) 0.71349
820 (single-phase) 0.54996
822 (single-phase) 0.52667*
824 0.82593
826 (single-phase) 0.89795
828 0.82374
830 0.77118
854 0.76989
852 0.68017***
832 0.76769
858 0.75772
834 0.74618
842 0.74588
844 0.74448
846 0.74326
848 0.74314
860 0.74459
836 0.74364
840 0.74355
862 0.74362
838 (single-phase) 0.79897
864 (single-phase) 0.63886
888 0.73966
890 0.68601
856 (single-phase) 0.83478
*) The weakest single-phase bus.
***) The weakest three-phase bus.
47
0
0.05
0.10
0.15
0.20
0.25
0.30
800
802
806
808
812
814
850
816
824
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
888
890
Acti
ve
Po
wer
Lo
ss (
MW
)
Bus Number
Figure 3-19 Active power loss associated with DG connections at different buses of Figure 3-13 (Case 9).
3.6.2.2 Grid losses with two DG units for the IEEE multiphase 34 node test
feeder
According to (2-14), with the addition of one DG (at bus 890, Figure 3-16), the most
suitable location for the connection of a second DG unit is still at bus 890. This is in
agreement with the grid loss plots of Figure 3-20 generated by connecting the first
DG at bus 890 and placing a second DG at different buses of the IEEE 34 node
feeder. These results further confirm the accuracy of the proposed bus ranking index.
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
800
802
806
808
812
814
850
816
824
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
888
890
Acti
ve
Po
wer
Lo
ss (
MW
)
Bus Number
Figure 3-20 Active power loss associated with the first DG installed at bus 890 and the second DG connected at different buses of Figure 3-13 (Case 10).
3.6.3 Validation of proposed VRI based on PV curves for the IEEE
multiphase 34 node test feeder
Figure 3-21 shows the PV curves of positive-sequence voltages at each three-phase
bus for Case 9. According to this figure, bus 890 has the lowest stability margin.
48
Therefore, this is the weakest three-phase bus as previously recognized by (2-14).
The PV curves based on positive-sequence voltages of single-phase bus are plotted
as shown in Figure 3-22. As expected and previously recognized by the proposed
VRI, the weakest single-phase bus is bus 864.
After connecting a 2.4 MW DFIG wind turbine at bus 890, PV curves for Case 12
are regenerated and plotted in Figure 3-23. As expected and previously recognized
by the proposed VRI, the lowest stability margins occur at bus 852.
3.6.4 Comparison of proposed VRI with other bus ranking approaches for
the IEEE multiphase 34 node test feeder
Table 3-13 compares the performance of the proposed VRI (2-14) with three well-
known bus ranking indices; 𝑉/𝑉0, 𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃 for the IEEE 34 node network
of Figure 3-13 under unbalanced multiphase operating conditions. For multiphase
operation (Table 3-13), the weakest three- and single- phase buses are nodes 890 and
864, respectively; as identified by the proposed VRI (Figure 3-15) and confirmed by
grid losses (Figure 3-19) and PV curves (Figures 3-21 and 3-22). Therefore, the
conventional indices (𝑉/𝑉0 , 𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃) cannot properly identify the
weakest buses of multiphase networks.
49
4769376927691769
1.125
1.000
0.875
0.750
0.625
0.500
0.375
Total Load of Selected Loads (kW)
Bus 890; the weakest three-phase bus
848840
852846858
888 890
808812 814
850
816 824832830828
854
800
834842 844
860
836
802
862
806
Po
sit
ive
-
Se
qu
en
ce
Vo
lta
ge
(p.u
.
Figure 3-21 PV curves of positive-sequence voltage at each three-phase bus for Case 9.
Total Load of Selected Loads (kW)
)
4769376927691769
0.39
0.36
0.33
0.30
0.27
0.24
0.21
810 818 820 822826 856 864 838
Bus 864; the weakest single-phase bus
Po
sit
ive
-
Se
qu
en
ce
Vo
lta
ge
(p.u
.
Figure 3-22 PV curves of positive-sequence voltage at each single-phase bus for Case 9.
50
801967695519426930191769
1.40
1.20
1.00
0.80
0.60
Total Load of Selected Loads (kW)
Po
sit
ive-
S
eq
uen
ce
Vo
lta
ge
(p.u
.)
Bus 852; the weakest three-phase bus
848840
852846858
888 890
808812 814
850
816 824832830828
854
800
834842 844
860
836
802
862
806
Figure 3-23 PV curves of positive-sequence voltage at each bus for Case 12.
TABLE 3-13 BUS RANKING RESULTS FOR THE MULTIPHASE IEEE 34 NODE NETWORK.
Bus ranking approach The weakest buses of the multiphase IEEE 34 node test
Figure 4-7 Reactive and active power losses associated with the first DG installed at bus 675 and the second DG connected at different buses of Figure 4-1 (Case 3).
4.2.3 Validation of proposed VRI based on PV curves
The PV curves based on positive-sequence voltages are plotted and compared with
the PV curve generated when DG and SVC units are connected at the weakest bus.
Figure 4-8 shows the PV curves of positive-sequence voltages at each bus for Case 2.
60
According to this figure, bus 675 has the lowest stability margin. Therefore, this is
the weakest bus as previously recognized by (2-14).
After connecting a combination of DG and SVC units at bus 675, PV curves for
Case 6 are regenerated and plotted in Figure 4-9. As expected and previously
recognized by the proposed VRI, the lowest stability margins occur at bus 634. This
will further reveal the validity of the proposed voltage ranking index for unbalanced
three-phase networks.
846674666466546644663466
1.04
1.00
0.96
0.92
0.88
0.84
0.80
Po
sit
ive-S
eq
uen
ce V
olt
ag
e [
p.u
.]
Total Load of Selected Loads (kW)
Bus 675
646 680 611 634 675 652
Figure 4-8 PV curves of positive-sequence voltage at each three-phase bus for Case 2.
61
184661546612466946664663466
1.10
1.00
0.90
0.80
0.70
Total Load of Selected Loads (kW)646 680 611 634 675 652
Bus 634
Po
sit
ive-S
eq
uen
ce V
olt
ag
e [
p.u
.]
Figure 4-9 PV curves of positive-sequence voltage at each bus for Case 4.
4.3 APPLICATION OF PROPOSED VRI IN IMPROVING MLF OF
THE MODIFIED UNBALANCED THREE-PHASE 13 NODE TEST FEEDER
Application of the proposed bus ranking index for the placement of DGs
without/with SVCs at the weakest three-phase buses will improve the maximum
loading factors as demonstrated in Table 4-5. According to the tabulated results:
A comparison of the maximum loading factors for Cases 1 and 2 indicates that the
voltage stability margin is higher with a voltage regulator. Therefore, voltage
regulators can help to improve the voltage stability margins of unbalanced
distribution systems.
After connecting DG at bus 675 (Case 3), the voltage stability margin has slightly
decreased from 2.375 to 2.343.
There is a significant improvement in MLF when a combination of DG and SVC
units is placed at the weakest three-phase bus. For example, after connecting DG
and SVC (358 kW and 0.36 MVar) at buses 680 (Case 5) and 675 (Case 4) the
maximum loading factor is improved (from 2.375 with no compensation) to 4.390
and 4.967, respectively.
62
TABLE 4-5 SIMULATION RESULTS OF THE MODIFIED UNBALANCED THREE-PHASE 13 NODE TEST FEEDER (FIG. 4-1, TABLE 4-1): COMPARISON OF MLF WITHOUT/WITH REGULATOR, DG
AND SVC.
Case
number Description Order of bus ranking
(2-14) MLF*
1 No regulation 675, 652, 611, 684, 680 2.199
2 With regulation 675, 652, 611, 684, 680 2.375
3 DG at bus 675 675, 652, 611, 684, 680 2.343
4 Combination of DG
and SVC at bus 675
634, 633, 646, 645, 632 4.967
5 Combination of DG
and SVC at bus 680
634, 633, 646, 645, 675 4.390
*) Computed by increasing the active power of all loads until the power flow solution
becomes unstable.
4.3.1 Enhancement of MLF by optimal sizing of one DG Unit
The maximum loading factors of Table 4-5 are computed for DG compensation
values of 358 kW. These factors can be improved by proper sizing of the
compensation devices as shown in Figure 4-10.
Figure 4-10 shows the impact of increasing the number of DG units on MLF. Each
DG unit injects 358 kW of active power. According to this figure, MLF can be
improved from 4.967 (Case 4) to 5.223 if the level of DG compensation at the
weakest three-phase node (bus 675) is increased from 358 kW to 5.012 MW.
63
4.80
4.85
4.90
4.95
5.00
5.05
5.10
5.15
5.20
5.25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
The number of DG units
Lo
ad
ing
Facto
r
Figure 4-10 MLF as a function of the number of DG units placed at the weakest node
(bus 675).
4.3.2 Improving MLF by placement and sizing of compensation devices
A relatively simple procedure is used to properly place and size the compensation
devices to further improve MLF of the unbalanced distribution system. The approach
is to place one compensation unit (e.g., a 358 kW DG with SVC) at the weakest bus
and compute the corresponding MLF. The procedure is then repeated by relocating
the weakest bus (based on Eq. 2-14 with all previous units in service) and placing
more compensation devices.
With the above-mentioned approach for placement of DG (with a 0.36 MVAr SVC
used for voltage regulation) are shown in Figure 4-11. The selected size of the unit
DG is 358 kW. Based on Figure 4-11, MLF can be further improved to 6.119 with a
total DG of 716 kW (consisting of 358 kW and 358 kW units at buses 675 and 634,
respectively).
0
1
2
3
4
5
6
7
No DG DG at bus
675
DG at bus
675, 634
DG at bus
675, 634, 646
Lo
ad
ing
Fa
cto
r
Figure 4-11 Simulation results for placement and sizing of DG units in the modified
Figure 5-17 Comparison of VRI values for dynamic operating conditions in the IEEE 34
node test feeder.
5.6 CONCLUSIONS
This chapter employed the new VRI of (2-14) to identify the weakest single-, two-
and three-phase buses of unbalanced and multiphase distribution networks for
voltage stability enhancement. Main conclusions are as follows:
Application of the proposed bus ranking index for the placement of shunt
capacitors and DGs without/with SVCs at the weakest single-phase and three-
phase buses will improve the maximum loading factors.
81
Installation of a single-phase shunt capacitor at the bus which is not the weakest
single-phase bus can reduced the overall loading factor.
The new index can be applied to both static and dynamic approaches. The
proposed index based on static approach can be used to determine which bus is
the weakest bus for the voltage stability enhancement whereas the proposed index
based on dynamic approach can be used as an indicator to identify the stability of
the system.
Time domain simulation is recommended in critical cases.
DG units with controllable reactive power such as a synchronous generator may
perform better than an induction generator in terms of voltage stability
enhancement.
The application of symmetrical components as employed in this thesis may
require values that are difficult to obtain without full three-phase measurements at
all levels of the system.
82
Chapter 6. Online bus voltage ranking in unbalanced
multiphase smart grids with plug-in electric vehicle
(PEV) charging stations
6.1 INTRODUCTION
Plug-in electric vehicles (PEVs) are expected to become popular in the near future as
alternatives to conventional fuel-based automobiles in order to reduce the emission to
the environment [35-40]. However with the random charging behaviors and
unpredictable penetration levels of PEVs in the residential feeders, voltage drop
issues and voltage stability problems are anticipated in the future smart grid
configurations [35-37, 41]. A possible solution will be to shift a portion of PEV
loading to the distribution networks by intelligently siting and sizing PEV charging
stations or PEV smart parks.
To promote and support the increasing penetration of PEVs entering into smart grid,
many counties are planning to increase the number of charging stations and/or smart
parks [39-40]. However, there are also important issues associated with increasing
the number of charging stations and smart parks in term of line overloading, bus
voltage regulations and stability problems. PEV charging stations can affect system
voltage profile, load flow and stability of the smart grid. Therefore, electric utilities
are very interested in investigating the possible impacts and drawbacks of PEV
charging demand on their distribution networks [38, 42].
In smart parks, PEV charging operation can be performed in charging mode and
discharging mode. To increase the effectiveness of smart parks, PEVs should be
charged from the grid during off-peak load hours (charging modes) and discharged to
the grid during the peak load hours (discharging mode). The electric utilities may
require load shedding if there is a high demand charging during the peak load hours
[38, 40]. In [41, 43], smart parks are placed at the lowest voltage lines under normal
83
operating conditions as reactive power and voltage supports to enhance voltage
stability in discharging modes. However, in charging modes, the system is less
stable. In addition, the bus which has the lowest voltage may not be the most suitable
location for connecting smart parks as reactive and voltage supports.
Identification of weakest buses through the bus ranking indices will play an
important role for the analysis and voltage stability enhancement of smart grids. The
purpose of bus ranking in smart grid is to determine which nodes are the weakest
buses during 24 hours for connecting compensation devices [44]. Furthermore, it can
provide insights for properly placing and sizing future PEV charging stations and
smart parks. It has been shown that the best location for reactive power
compensation to improve voltage stability margin is the weakest bus [3, 10].
In this chapter, symmetrical components are applied to the conventional bus voltage
ranking index V/Vo to extend its application to online (for example every one hour)
identification of the weakest buses of unbalanced multiphase smart grids during the
24 hours considering the impacts of charging stations. Simulations are performed and
compared using DIgSILENT PowerFactory software to identify the weakest three-
phase buses of the modified unbalanced multiphase 13 node test feeder without/with
PEV charging stations.
6.2 THE MODIFIED IEEE 13 NODE TEST SYSTEM WITH PEV
CHARGING STATIONS
For the analysis of this chapter, the IEEE unbalanced multiphase 13 node test feeder
of Figure 6-1 [33] is considered with four PEV charging stations connected at bus
634 or bus 680. The network has been simulated using DIgSILENT PowerFactory
software [32]. The system is identical to Figure 3-1 with exception of the PEV
charging stations. System data is available in the Appendixes A1 and A2.
For the dynamic analysis of this chapter, the daily P and Q load curves of Figure 6-2
are assumed and utilized for the linear loads [45]. For the PEV charging stations (at
buses 634 and 680), the daily load curve of Figure 6-3 with two peaks at 7am and
6pm is employed [36].
84
646 645 632 633 634
650
692 675611 684
652
671
680
RG604.16 kV
0. 48 kV4. 16 kV
Switch
Two- phase
Single-phaseThree- phase
115 kV
CS1
CS4CS3CS2
CS8
CS5
CS6
CS7
Case 2
Case 3
Figure 6-1 The modified unbalanced multiphase 13 node test feeder with PEV charging
stations at bus 634 or bus 680.
6.3 SIMULATION RESULTS
Simulations are performed for the modified IEEE unbalanced multiphase 13 node
test feeder of Figure 6-1 without and with PEV charging stations to investigate their
impacts on voltage profiles and bus voltage ranking indices. Simulation results are
presented for four case studies.
Case 1: No PEV charging stations.
The VRI index for an online application (2-15) is calculated and ranked to locate the
weakest three-phase buses of Figure 6-1 without any PEV charging stations. Figure
6-4 shows the impact of the dynamic daily load curves of Figures 6-2 and 6-3 on the
voltage profiles of selected nodes (buses 634, 675 and 680). According to this figure,
bus 634 has the lowest voltage profile. However the three-phase buses over 24 hours
which have the lowest bus voltage ranking indices are buses 675, 634, and 680.
Therefore, the three-phase weakest bus for Case 1 is bus 675.
85
Case 2: Four PEV charging stations at bus 634.
In the multiphase unbalanced system of Figure 6-1 four 0.2MW PEV charging
stations with the total peak charge level of 0.8MW are included at bus 634. The peak
charging (0.8MW) is about 25% of total load (3.46MW). Figure 6-5 shows the
impact of placing the PEV charging stations at bus 634 on the voltage profiles of
buses 634, 675 and 680. With the pattern charging of PEVs (Figure 6-3) at buses
634, the voltage levels at bus 634 is lower than other buses as shown in Figure 6-5.
Table 6-1 shows bus voltage ranking indices with PEV charging stations at bus 634
over 24 hours. According to this Table, the weakest three-phase bus has changed
from bus 675 (Case 1) to bus 634 as a result of PEV charging activities at bus 634.
Case 3: Four PEV charging stations at bus 680.
Case 2 is repeated, except the four 0.2MW PEV charging stations with the daily load
curves of Figure 6-3 located at bus 680. Figure 6-6 shows the impact of the charging
stations on voltage profiles with PEV charging stations at bus 680. Compared to
Case 2, the voltage profile is improved during 11am to 17pm. Table 6-2 shows the
bus voltage ranking indices with PEV charging stations at bus 680 over 24 hours.
According to this Table, the three lowest bus voltage ranking indices are associated
with buses 675, 680, and 634.
Case 4: Four PEV charging stations at bus 680 and two PEV charging stations at bus
634.
Case 3 is repeated with the addition of two 0.2MW PEV charging stations with the
daily load curves of Figure 6-3 located at bus 634. Figure 6-7 shows the impact of
the charging stations on voltage profiles with four PEV charging stations at bus 680
and two PEV charging stations at bus 634. Table 6-3 shows the bus voltage ranking
indices over 24 hours with PEV charging stations at bus 680. According to this
Table, the locations of the weakest bus have changed between buses 675 and 680.
For example, the weakest three-phase bus has changed to bus 680 at 7-9 a.m. and 6-9
p.m.
86
24.019.214.49.64.80.0
100
80
60
40
20
0
Time [Hour]
Per
cent
age
of P
eak
Load
[%]
P daily load curve
Q daily load curve
Figure 6-2 Daily load curves associated with Figure 6-1 for linear loads [45].
24.019.214.49.64.80.0
100
80
60
40
20
0
Time [Hour]
Per
cent
age
of P
eak
Load
[%]
P load curve
Figure 6-3 Daily load curves associated with Figure 6-1 for PEV charging stations [36].
87
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Time [Hour]
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
Figure 6-4 Simulation results for Case 1: the 24 hour voltage profile of buses 634, 675
and 680.
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Time [Hour]
Figure 6-5 Simulation results for Case 2: the 24 hour voltage profile of buses 634, 675
and 680.
88
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Time [Hour]
Figure 6-6 Simulation results for Case 3: the 24 hour voltage profile of buses 634, 675
and 680.
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
Time [Hour]634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Figure 6-7 Simulation results for Case 4: the 24 hour voltage profile of buses 634, 675
and 680.
89
TABLE 6-1 CASE 2 - BUS VOLTAGE RANKING INDICES OVER 24 HOURS WITH FOUR PEV CHARGING STATIONS AT BUS 634.
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.952573 0.976249 0.979515 634
1.00 0.903801 0.929840 0.933893 634
2.00 0.887627 0.913419 0.917316 634
3.00 0.877407 0.902948 0.906692 634
4.00 0.864649 0.889935 0.893688 634
5.00 0.859166 0.884163 0.887809 634
6.00 0.852665 0.878688 0.882301 634
7.00 0.830194 0.862575 0.866267 634
8.00 0.799218 0.841839 0.845514 634
9.00 0.766849 0.802819 0.807022 634
10.00 0.750888 0.775109 0.779623 634
11.00 0.735064 0.756605 0.761184 634
12.00 0.721301 0.741535 0.746147 634
13.00 0.716600 0.736621 0.741095 634
14.00 0.710610 0.730538 0.735009 634
15.00 0.708724 0.728681 0.733081 634
16.00 0.709924 0.730943 0.735222 634
17.00 0.705164 0.731868 0.736030 634
18.00 0.714965 0.748383 0.752134 634
19.00 0.718777 0.756636 0.76027 634
20.00 0.732496 0.766829 0.770428 634
21.00 0.755066 0.781949 0.785535 634
22.00 0.769885 0.794123 0.797730 634
23.00 0.781631 0.804035 0.807678 634
90
TABLE 6-2 CASE 3 - BUS VOLTAGE RANKING INDEX FOR THE MULTIPHASE SYSTEM OF FIGURE 6-1 WITH FOUR PEV CHARGING STATIONS AT BUS 680.
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.979404 0.972515 0.974186 675
1.00 0.933280 0.925467 0.927765 675
2.00 0.916540 0.909093 0.911267 675
3.00 0.905937 0.898683 0.900723 675
4.00 0.892817 0.885717 0.88779 675
5.00 0.887124 0.880024 0.882001 675
6.00 0.881562 0.874371 0.876254 675
7.00 0.865036 0.856942 0.858496 675
8.00 0.843357 0.833764 0.834641 675
9.00 0.804699 0.795358 0.797155 675
10.00 0.777989 0.769874 0.772719 675
11.00 0.760107 0.752256 0.755335 675
12.00 0.745374 0.737803 0.741009 675
13.00 0.740763 0.733249 0.736329 675
14.00 0.734825 0.727404 0.730494 675
15.00 0.733023 0.725723 0.728745 675
16.00 0.735255 0.727916 0.730753 675
17.00 0.735924 0.727764 0.730107 675
18.00 0.751547 0.742872 0.744385 675
19.00 0.758997 0.749838 0.750951 675
20.00 0.768964 0.760327 0.761631 675
21.00 0.784309 0.776794 0.778571 675
22.00 0.796762 0.789638 0.791612 675
23.00 0.807028 0.800091 0.802215 675
91
TABLE 6-3 CASE 4 - BUS VOLTAGE RANKING INDEX FOR THE MULTIPHASE SYSTEM OF FIGURE 6-1 WITH FOUR PEV CHARGING STATIONS AT BUS 680 AND TWO PEV CHARGING
STATIONS AT BUS 634.
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.980186 0.969367 0.969430 675
1.00 0.931868 0.919640 0.920164 675
2.00 0.915040 0.903259 0.903690 675
3.00 0.904979 0.893448 0.893767 675
4.00 0.892726 0.881386 0.881763 675
5.00 0.888124 0.876815 0.877107 675
6.00 0.882623 0.871067 0.871200 675
7.00 0.861427 0.847999 0.847394 680
8.00 0.830174 0.813725 0.811798 680
9.00 0.792331 0.777062 0.776437 680
10.00 0.774322 0.761940 0.763098 675
11.00 0.762916 0.751094 0.752668 675
12.00 0.753490 0.742078 0.743883 675
13.00 0.752773 0.741401 0.743099 675
14.00 0.749586 0.738288 0.740013 675
15.00 0.749811 0.738618 0.740282 675
16.00 0.752786 0.741394 0.742800 675
17.00 0.749838 0.736729 0.737238 675
18.00 0.759273 0.744732 0.743968 680
19.00 0.760036 0.744424 0.742983 680
20.00 0.768626 0.754182 0.753168 680
21.00 0.787815 0.775682 0.775632 680
22.00 0.803453 0.792100 0.792427 675
23.00 0.816681 0.805766 0.806365 675
92
6.4 ONLINE PLACEMENT OF SVC UNITS TO IMPROVE THE
PERFORMANCE OF THE MODIFIED IEEE 13 NODE TEST SYSTEM WITH
PEV CHARGING STATIONS
This section introduces a new online approach to improve the performances of the
emerging smart grids with renewable energy resources and smart appliances. For
these systems, prediction and forecasting of the daily load curves may not be feasible
as the location, time and duration of the smart loads (such as PEVs and smart
appliances) are randomly changing during the 24 hour period. Therefore, the
conventional approaches of locating and sizing of compensation devices based on the
forecasted daily load curves are not accurate.
The proposed approach is to place compensation devices at the weakest buses,
perform online VRI ranking, and then switch these devices in (and out of) service
according to the lowest VRI values. The approach will be demonstrated for the
modified unbalanced multiphase 13 node test feeder of Figure 6-1 through the
following case study.
Case 5: Online placement of SVC units for Case 4.
Online VRI ranking of the modified unbalanced multiphase 13 node test feeder with
four PEV charging stations at bus 680 and two PEV charging stations or bus 634
(Case 4) indicates that the weakest bus changed between nodes 675 and 680 over the
24 hour period (Table 6-3). Therefore, compensation devices which are installed at
buses 675 and 680 will be switched on and off according to the time in Table 6-3.
Figure 6-8 shows the impact of online placement of two SVC units on voltage
profiles with four PEV charging stations at bus 680 and two PEV charging stations at
bus 634.
Compared to Case 4 (Figure 6-7), the voltage profiles at all buses are improved,
especially at buses 675 and 680. Table 6-4 shows the bus voltage ranking indices
after the online placement of SVC units installed at bus 675 and 680. According to
this Table, the weakest node (after online SVC placement) is changed from buses
675 and 680 to bus 634.
93
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
Time [Hour]634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Figure 6-8 Simulation results for Case 5 with online placement of two SVC units: the
24 hour voltage profile of buses 634, 675 and 680.
94
TABLE 6-4 CASE 5 BUS VOLTAGE RANKING INDEX FOR THE MULTIPHASE SYSTEM OF FIGURE 6-1 WITH FOUR PEV CHARGING STATIONS AT BUS 680 AND TWO PEV CHARGING
STATIONS AT BUS 634 AFTER ONLINE PLACEMENT OF TWO SVC UNITS
%VUF Base-case%VUF with 30% DG penetration at bus 890%VUF with 30% DG penetration at buses 890 and 852%VUF with 30% DG penetration at buses 890 and 852and single-phase shunt capacitor at bus 822
Vo
ltag
e U
nb
ala
nce
Facto
r [%
]
Bus Number
Figure 7-12 Comparison of %VUF at different iterations of the proposed algorithm
(Figure 7-1).
7.5 CONCLUSIONS
This chapter has extended the definition of the conventional bus voltage ranking
index (VRI) of V/Vo defined for balanced three-phase systems to identify the
weakest buses of the multiphase systems. The new VRI is utilized through a
proposed iterative procedure to increase the penetration levels of DG and single-
phase capacitors in order to improve the performance of the multiphase networks.
The proposed algorithm is relatively simple and can effectively reduce total active
power loss, increase MLF and decrease VUF while keeping all bus voltages within
the allowable lower and higher limits. Main conclusions are:
The proposed bus ranking approach based on the positive-sequence voltage
ratio Vcollapse/Vno-load can effectively identify the weakest three-phase and
single-phase buses for DG and shunt capacitors placements, respectively.
Analysis of simulation results indicates that the penetration level of DG is
limited by considering the bus voltage limits rather than grid losses and/or
MLF. Therefore, at high penetration levels of DG units, it is necessary to take
voltage limits into account.
Placements of shunt capacitors at the weakest single-phase buses will not only
increase MLF, but also further improve the unbalanced voltage factor.
108
TABLE 7-1 DETAILED SOLUTION FOR DFIG AND CAPACITOR PLACEMENT AND SIZING IN THE IEEE MULTIPHASE 34 NODE TEST FEEDER (FIGURE 3-13) USING THE PROPOSED
ALGORITHM OF FIGURE 7-1.
Stage one: Placement and sizing of DFIGs
Itera
tion
Weakest
three-
phase bus
Penetration
of DFIG [%]
Total
loss
[MW]
MLF VUF at
bus 890
[%]
Simulation
results
0 - - 0.2641 2.518 2.985199 Fig. 7-12
1 890 30 0.1053 3.150 0.492043 Figs. 7-2, 7-3,
7-12
2 852 30 0.0610 3.519 0.361299 Figs. 7-6, 7-7,
7-12
3 814 - - - - Fig. 7-9
Stage two: Placement and sizing of single-phase shunt capacitors
Itera
tion
Weakest
single-
phase bus
Capacitor
size [kVAr]
Total
loss
[MW]
MLF VUF at
bus 890
[%]
Simulation
results
0 - - 0.0610 3.519 0.361299 Fig. 7-12
1 822 273 0.0778 3.575 0.356531 Figs. 7-10 and
7-12
2 820 - - - - Fig. 7-11
Final Solution: 30% DFIG penetration at bus 890, 30% DFIG penetration at bus 852
and 273kVAr capacitor at bus 822.
109
Chapter 8. Conclusions
This thesis proposes a new bus voltage ranking index (VRI) and applies it to improve
the voltage stability of unbalanced three-phase and multiphase networks. After a
literature review conducted in Chapter 1, Chapter 2 proposed a new bus ranking
approach based on positive-sequence voltage of Vcollapse/Vbase-load for unbalanced and
multiphase networks (2-14) to identify the weakest single-phase, two-phase, and
three-phase buses. Another bus ranking approach is also introduced for online
applications such as the emerging smart grids.
Chapter 3 compares the performance and accuracy of the conventional and the
proposed VRI for multiphase networks. The new index is validated using the well-
known voltage sensitivity approaches 𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃 for balanced and
unbalanced three-phase distribution networks. Further validations are performed
through grid loss calculations and generation of PV curves based on positive-
sequence voltage and voltage sensitivity methods. Detailed simulation results for the
modified IEEE multiphase 13 node and 34 node test feeders show the validity and
accuracy of the new bus ranking approach. The main outcomes of this chapter are as
follows: (1) the proposed ranking index can accurately identify the weakest single-,
two- and three-phase buses under different operating conditions without and with
voltage regulators, capacitor banks and DG units (without/with SVCs); (2) the
conventional bus voltage ranking index and the two voltage sensitivity methods
(𝜕𝑉/𝜕𝑄 and 𝜕𝑉/𝜕𝑃) are able to accurately identify the weakest buses of balanced
networks. However, in unbalanced networks, the conventional VRI and the two
voltage sensitivity methods failed to detect the weakest bus.
Chapter 4 presents the application of the proposed VRI in improving the voltage
stability and increasing the MLF of unbalanced three-phase networks. Detailed
simulation results including five case studies are presented for the modified IEEE
unbalanced three-phase 13 node test feeder. Main conclusions are: (1) the proposed
ranking index can be properly utilized to identify the weakest bus under unbalanced
110
three-phase operating conditions; (2) the proposed VRI can be used as an index to
place compensation devices at the weakest buses of unbalanced three-phase networks
to enhance the voltage stability and improve MLF; (3) placement of compensation
devices at the weakest bus may change the location of the weakest bus.
In Chapter 5, the proposed VRI in utilized to improve the voltage stability margins
and MLF of multiphase distribution networks. Extensive simulation results are
carried on for the IEEE multiphase 13 and 34 node test feeders. It is revealed that the
proposed VRI can fulfill both the static and dynamic voltage stability criteria. Static
voltage stability improvements are achieved by using the proposed VRI to identify
the weakest single-, two- and three-phase buses of multiphase distribution networks,
while the proposed index based on dynamic approach at the critical time can be used
as an indicator to identify the stability of the system.
In Chapter 6, an online bus ranking approach is proposed to identify the weakest
buses over the 24 hour period considering active and reactive daily loads curves. The
approach is used to study and compensate the detrimental impacts of PEV charging
stations on voltage profiles and voltage stability of the distribution network.
Simulations results indicate that the location of the weakest buses can be changed
over 24 hours with PEV charging stations. Then, the switching strategy of
compensation devices connected at the weakest buses according to the lowest hourly
VRI values can perform better than the conventional installations of the
compensation devices in terms of voltage profiles.
In Chapter 7, the proposed VRI is utilized to improve the performance of multiphase
distribution networks by properly increasing the penetration levels and ratings of DG
units such as DFIGs and single-phase capacitors. Simulation results show that high
penetration levels of DG units can cause overvoltage problems. Consequently, at
high penetration levels of DGs, it is necessary to also take voltage limits into
account. Therefore, an iterative algorithm for the placement and sizing of DG units
and single-phase capacitors is introduced to reduced grid losses and increase MLF in
multiphase networks while keeping all bus voltages within acceptable limits. It is
shown that the new algorithm for the placement and sizing of three-phase DG units
and single-phase capacitors can effectively reduce total active power loss, increase
111
MLF and decrease VUF of multiphase distribution networks while keeping all bus
voltages levels within the permissible limits.
8.1 CONTRIBUTIONS
The main results of this thesis have been released in five conference papers and three
journal articles (two under review) as listed in Section 1.5. The primary contributions
are as follow.
1. The proposed bus voltage ranking index can be used to identify the weakest
single-, two- and three-phase buses in multiphase networks for voltage stability
enhancement.
2. The proposed index can be applied to both static and dynamic approaches. Static
voltage stability can be improved by using the proposed VRI to identify the
weakest single-, two- and three-phase buses of multiphase distribution networks,
while the proposed index based on dynamic approach at the critical time can be
used as an indicator to identify the stability of the system.
3. The proposed index is modified for online bus voltage ranking and voltage
stability improvement in distribution systems with dynamic loads to identify the
weakest buses over the 24 hour period considering active and reactive daily loads
curves.
4. A new iterative algorithm is proposed and tested for properly placing and
increasing the penetration levels of three-phase DG units and single-phase
capacitor banks in multiphase networks to reduced grid losses, increase MLF and
decrease VUF while keeping all bus voltages within acceptable limits.
8.2 FUTURE WORKS
The following areas are suggested for future research in continuation of this work.
1. Online bus voltage ranking and control of compensation devices for voltage
stability enhancement in the emerging smart grid configurations with renewable
energy resources and dynamic loads such as PEVs and smart appliances.
112
2. Online application of the proposed iterative algorithm for the placement and
sizing of DG units and single-phase capacitors in smart grids for dynamically
increasing the penetration levels of compensation devices.
113
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Every reasonable effort has been made to acknowledge the owners of copyright
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