International Conference on Electrical Engineering Applications (ICEEA'2020), Department of Electrical Engineering,
Ahmadu Bello University, Zaria, Nigeria. 23rd-25th September, 2020
Loadability Analysis During Maximum Loading and
Contingency Condition with Unified Power Flow
Controller
Yusuf S. S1, Okorie P. U.2, Abubakar A. S.3, Alhasan, F.4, Momoh, I. O.5
1,2,3,4,5
, Nigeria Department of Electrical Engineering, Ahmadu Bello University, Zaria – Nigeria
1
yusufssamuel@gmail.com, 2puokorie@abu.edu.ng, 3abubaras@abu.edu.ng,
4
fahadalhassan1990@gmail.com, 5onimisiily@gmail.com.
of central important [3]. This essential task has led to the
introduction of advanced power electronics based converters
known as Flexible Alternating Current Transmission System
(FACTS).
Abstract: The application of grey wolf optimization technique is
presented in this paper for the minimization of line losses and
reduction of voltage deviation using Flexible Alternating Current
Transmission System (FACTS) device. Series-shunt FACTS
device; unified power flow controller (UPFC) is considered to
provide an alternative option for power improvement in the
network. Locating UPFC optimally in a congested network;
alleviates line congestion, increases power transfer capacity,
enhances system security and making power transfers fully
controllable. Grey wolf optimization technique is utilized to find
the optimal location and sizing of UPFC on the network. The
voltage stability and load margin of the line is evaluated with and
without UPFC under different loading variation using optimal
power flow technique. The effectiveness of this proposed technique
is carried out on 31-bus, 330kV Nigeria National Grid (NNG)
based on three scenarios: loadability analysis under normal
loading, maximum loading and single contingency. The results
show that power transmitted during normal and contingency
conditions could be improved without compromising system
stability at minimum power loss by using the proposed method in
this paper.
FACTS devices are used to alleviate line congestion, increase
power transfer capacity, enhance system security and making
power transfers fully controllable by controlling all the three
parameters of power flow, namely; line impedance, voltage
magnitude and phase angle between the sending end and
receiving end voltages [3]. These devices over the years have
brought to bear, the perceptions that network instability and
constraints can be solved successfully and promptly. Amongst
the various known FACTS devices, Unified Power Flow
Controller (UPFC) is the mostly commonly used, because of its
uniqueness to independently and/or simultaneously provides a
flexible control of the bus voltage magnitude and active and
reactive power flow through the line where it is placed [4, 5].
Due to the high cost of procuring and installing the FACTS
devices, adequate plan should be geared towards placing it at
an appropriate location, because the performance of FACTS
devices largely depend on the location on the network [3]. The
combination of FACTS devices along with optimization
technique is the prominent method used in the modern power
systems to efficiently curtail and alleviate line congestion. In
this paper, GWO is used for the optimal placement and sizing
of UPFC on 31-bus, 330kV NNG. It is deployed because of its
flexibility, scalability and its exceptional ability to strike the
balance between the exploration and exploitation in unknown
search spaces to give a favourable result and convergence.
UPFC is optimally placed on the network to alleviate
congestion, power loss reduction, and improved stability of the
network etc.
Keywords—Line Loadability, Grey Wolf Optimization, Nigeria
National Grid, UPFC, Maximum Loading
I. INTRODUCTION
The modern power systems are witnessing unprecedented
increase in the demand for electrical energy, due to the
population growth and recursive increase in technological
development under contingency and restructured market
environment. It is inevitable that voltage instability, line
congestion, power losses, frequency collapse and transient
instability will exist on the network [1]. Due to these
challenges, transmission lines are being operated closer or
beyond their stability limit along with emergence of other
associated limits that leads to power system instability[2].
Confronted with these challenges and constraints, power
system engineers have been struggling to develop a new and
robust device that can deal successfully and swiftly with these
constraints limiting network capacity and provides alternative
option for power improvement. The need to install this robust
device in an existing transmission asset to provide an effective,
economic, reliable, and environmental friendly way of
improving the power carrying capacity of a transmission line is
II.
THE 31-BUS, 330KV NIGERIA NATIONAL GRID
The 31-bus, 330kV Nigeria National Grid used for this
analyses consists of seven (7) generator buses (PV), twenty four
(24) load buses (PQ), and thirty-seven (37) transmission lines.
It is made up of 6,000km of 132kV lines, 5,000km of 330kV
lines, 23km of 330/132kV sub-stations and 91km of 132/33kV.
106
International Conference on Electrical Engineering Applications (ICEEA'2020), Department of Electrical Engineering,
Ahmadu Bello University, Zaria, Nigeria. 23rd-25th September, 2020
These networks are characterized with the following
challenges; long transmission lines, radial and fragile grid
network, problems of dispatching generated energy from the
stations to the load centres, single circuit network, frequent
system collapse, poor network configuration, aging and
obsolete facilities, overloading, thermal limits violation, poor
voltage profile, and inability to control transmission line
parameters like; voltage and frequency [6]. Technically, these
challenges bedevilling NNG can be eliminated by constructing
additional generating units and transmission capacity to meet
the rising demand, so as to boost the system reliability and
stability, however, economic, political, environmental impacts
and construction time have made these measures not to be
anticipated. These problems have strongly demanded for the
optimization and upgrading of the existing network capacity to
enable more power transmission during both normal and
contingency conditions without violating network voltage
stability [7-10]. This paper presents the combination of FACTS
device (UPFC) along with GWO optimization technique to
solve the numerous challenges facing NNG.
III.
MODELLING OF UNIFIED POWER FLOW
CONTROLLER
The concept of unified power flow controller (UPFC) was first
proposed in 1991 by Gyugi [13]. It comprises of two switches
based on the voltage source converter valves; shunt (exciting
transformer) and series (boosting transformer) as shown in Fig.
1. Both the exciting and boosting transformers are connected by
a common DC voltage link which is signified by capacitor and
two-gate turn off (GTO) converters. Converter 1 (shunt) is
connected in parallel to a local bus to be improved through an
exciting transformer. This provides the active power needed by
Converter 2 at the terminal of the common DC voltage link
from the network alternating current power system of the local
bus. It also serves as both generator and absorber of reactive
power at its AC terminal, which is not dependent on the active
power emanating from or to its DC terminal. Converter 1
leverage on its ability to offers the role of independent advance
static VAR compensator by compensating the reactive power
of the transmission line and consequently providing voltage
regulation at the UPFC input terminal. Converter 2 is linked in
series to a bus via a boosting transformer. It generates voltage
source at the fundamental frequency with variable amplitude
(0 ≤ 𝑉 ≤ 𝑉
) and phase angle (0 ≤ ∅ ≤ 2𝜋). The
voltage source generated is coupled to a series connected
boosting transformer to the AC transmission line. Amongst the
various FACTS devices, UPFC has an exceptional ability to
simultaneously and/or independently control the three
parameters of power flow: voltage magnitude, phase angle and
line impedance. This has made UPFC more versatile and widely
used than other FACTS devices. Fig. 2 shows a typical
operating principle of UPFC. It depicts the steady-state model
of UPFC under different loading condition. Fig 2. shows a
typical operating principle of UPFC
A. The Effect of Line Loading on the Voltage Stability
Load characteristics are driving forces that causes voltage
instability; hence, voltage stability is sometimes refers to as
load stability [11]. When the load on the line increases voltage
stability margin decreases, thereby increasing the stress on the
network and also a rise in the reactive power consumption
which will further reduces the voltage level. Also, the larger the
load on the system, the more unstable the system will be. Since
this cause P-V curve nose to drift downward to a lower loading,
hence, reduce the load margin. Fig. 1 shows a progressive
voltage collapse event. As the power demand increases, the
system voltage decreases slowly until a critical point is attained.
At this critical point, any small load demand increase will result
in enormous decrease in voltage level, until voltage collapse
occurs. To prevent this, engineers need to employ a good
voltage stability enhancement device to provide option for
power improvement. The combination of FACTS devices along
with optimization technique is the leading method used in the
modern power systems to efficiently curtail voltage collapse
and alleviate line congestion.
Vr/Vs
set margin
1.0
Fig. 2. The Operating principle of UPFC [5, 14]
The real power and reactive power injection at the bus-i with
the system loading (𝜆) is obtained using:
0.8
0.6
𝑃 = 𝑃 − 𝑃 (1 + 𝜆) =
0.4
Vs = fixed source voltage
Vr = variable load voltage
P = power delivered to load
Pm = maximum power
0.2
0.0
0.0
𝑃
(1)
∈
0.2
0.4
0.6
0.8
1.0
P/Pm
Fig. 1. Shows a progressive voltage collapse event [12]
107
𝑄 = 𝑄 − 𝑄 (1 + 𝜆) =
𝑄
(2)
∈
Where 𝑃 and 𝑄 are the initial real and reactive power
demand. 𝑃 and 𝑄 are the real and reactive power generations
at bus-i respectively. It is assumed that in equations (1) and (2),
International Conference on Electrical Engineering Applications (ICEEA'2020), Department of Electrical Engineering,
Ahmadu Bello University, Zaria, Nigeria. 23rd-25th September, 2020
that a uniform loading with the same increase in loading factor
of the power demand at all the P-Q buses have been considered
and is to be taken care of by the slack bus, whereas, sharing of
generation among the generators can easily be incorporated in
this model [5].
A.
Hunting in a pack is carried out by alpha, beta and delta. It is a
process of moving towards the prey using the shared
information obtained among the wolves in equation (3) and (4)
respective. The alpha, beta and delta positions are model in
equations (6), (7) and (8):
𝐻⃗ = 𝐴⃗ ∙ 𝐵⃗ − 𝐵⃗ , 𝐻⃗ = 𝐴⃗ ∙ 𝐵⃗ − 𝐵⃗ , 𝐻⃗ =
(6)
𝐴⃗ ∙ 𝐵⃗ − 𝐵⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
𝐵 = 𝐵 −𝑆 ∙ 𝐻
𝐵 = 𝐵 −𝑆 ∙ 𝐻 ,
𝐵⃗ = 𝐵⃗ − 𝑆⃗ ∙ 𝐻⃗
(7)
⃗
⃗
⃗
𝐵 +𝐵 +𝐵
𝐵( ) =
(8)
3
Grey wolf optimization technique
Based on the grey wolf (Canis lupus ) social hierarchy and
hunting characteristics, a metaheuristic algorithm called Grey
Wolf Optimization (GWO) technique was developed by [15] in
the year 2014. This animal belongs to the canidea family and
they live in a pack of 5-10 on average size. Wolves are
categorized into four divisions based on the hierarchical order
of alpha (α), beta (β), delta (δ), and omega (ω) [16]. Fig. 3
shows the social hierarchy of grey wolves. The leaders of the
pack are a male and a female known as alphas (α). The alphas
with the higher dominance are the decision maker of the pack.
They are endowed with the ability to manage pack properly by
commanding the other lower-level wolves. The three main
hunting phases are; tracking the prey, encircling the prey and
attack towards the prey. Hunting in the pack is carried out by
alpha, beta and delta. Alpha determines the fittest due to its best
knowledge for searching prey, while beta is the second best
solution and delta gives the third best solution, and gamma is
the other candidate solutions. GWO algorithm has proven to
strike balance between exploitation and exploration of the
unknown search spaces and yields a favourable result at a very
fast rate [15].
B. Optimal Power Flow Problem Formulation
The power flow problem is optimized to give the optimal
setting of the network control variables in order to meet the
rising power demand by minimizing a predefined objective
functions while satisfying power system equality and inequality
constraints:
Minimization of Real Power Loss
(9)
Minimize 𝐹 (𝑥, 𝑦)
Subject to: ℎ(𝑥, 𝑦) = 0, 𝑔(𝑥, 𝑦) ≤ 0
Where h is the active and reactive power balance equation and
g is the system operating constraint that includes generator
voltages, their real and reactive power outputs and shunt
compensation.
𝑚𝑖𝑛 𝑃
=
[𝐺
𝑉 + 𝑉 − 2𝑉 𝑉 𝑐𝑜𝑠𝜃
(10)
𝑃
is the active power loss, 𝐺 is the conductance of branch
k, 𝑉 and 𝑉 are the magnitude of voltage at sending end and
receiving end buses respectively and 𝜃 is the phase angle
difference between 𝑖 and 𝑗 bus.
C. Voltage Deviation (VD)
Fig. 3. Social hierarchy of grey wolves [17]
(a)
Encircling prey
The distance between wolf and prey is mathematically model
in equations (3) and (4):
(𝑡) − 𝐵⃗ (𝑡)
𝐻⃗ = 𝐴⃗ ∙ 𝐵⃗
(3)
(𝑡) − 𝑆⃗ ∙ 𝐻⃗
𝐵⃗(𝑡 + 1) = 𝐵⃗
(4)
This objective function is aimed at improving the voltage
profile by minimizing the voltage deviation at all load buses.
This is mathematically expressed in (11):
𝐹
= min(𝑉𝐷) = min(
Voltage at bus i and 𝑉
Where; t indicates the current iteration
𝑉
−𝑉
. )
(11)
reference voltage limit at bus j.
Equality Constraints
The Active and reactive power equality constraint is given by:
S⃗ and A⃗ are coefficient vectors,
⃗
B is the position vector of the prey,
B⃗ the grey wolf vector position
The vectors 𝑆⃗ and 𝐴⃗ are calculated as shown in equations (5):
𝑆⃗ = 2𝑎⃗ ∙ 𝑟⃗ − 𝑎⃗, and 𝐴⃗ = 2 ∙ 𝑟⃗
(5)
𝑎⃗ are linearly decrease from 2 to 0, r1 and r2 =[0, 1]
(b)
Hunting
0=𝑃 −𝑃 −𝑉
𝑉 𝐺 𝑐𝑜𝑠𝜃 + 𝐵 𝑠𝑖𝑛𝜃
𝑓𝑜𝑟 𝑖
∈
∈𝑁
108
(12)
International Conference on Electrical Engineering Applications (ICEEA'2020), Department of Electrical Engineering,
Ahmadu Bello University, Zaria, Nigeria. 23rd-25th September, 2020
0=𝑄 −𝑄
−𝑉
𝑉 𝐺 𝑠𝑖𝑛𝜃 + 𝐵 𝑐𝑜𝑠𝜃
Normal
loading
𝑖
158.9220
-89.1600
120.4123
28
24.2318
∈
∈𝑁
(13)
Where 𝑁 is the total number of buses, 𝑃 is the total real
power generation, 𝑃 is the total power demand, 𝑄 is the
generation of reactive power, 𝑄 is the reactive power demand,
𝐺 and 𝐵 denote conductance and susceptance between 𝑖
and 𝑗 bus respectively.
Operational Inequality Constraints
The inequality constraints for both generator and network limits
are expressed in terms of lower and upper limits as follows:
𝑉
≤𝑉 ≤𝑉
𝑖∈𝑁
𝑄
≤𝑄
≤𝑄
𝑖∈𝑁
𝑇
≤𝑇 ≤𝑇
𝑘 = 1 … … , 𝑁𝑇
𝑃
≤𝑃
≤𝑃
𝑘 = 1 … … , 𝑁𝑇
𝑄
≤𝑄 ≤𝑄
𝑘 = 1 … … , 𝑁𝑇
Fig.4, shows a voltage profile result under normal loading
condition with and without UPFC device. It is observed that bus
28 violated the permissible voltage tolerance of 0.95pu
(313.5kV) and 1.05pu (346.5kV) as prescribed by NERC which
is the ±5% tolerance. The result also reveals that the network
may have a very small loadability capacity due to poor voltage
profile and may be susceptible to possible voltage collapse if
loading is not properly monitored. It is also observed that with
the optimal placement of UPFC using GWO at Bus 28 an
overall improvement of voltage magnitude is achieved on the
entire network.
IV RESULTS AND DISCUSSION
This section presents three scenarios: loadability analysis under
normal loading, maximum loading and single contingency
conditions on 31-bus, 330kV Nigeria National Grid. This is aim
at verifying the viability of this technique at delivering power
during both maximum loading and contingency conditions
without interruption of supply to consumers. All simulations
analyses are done in MATLAB R2017a software using Intel(R)
Pentium (R) CPU 2020M with Dual Core processor speed of
2.40GHz. The maximum loading occurs at a point where
Newton-Raphson has no value (diverged). The network voltage
stability is enhanced by optimal placement of UPFC on the
network using Grey wolf optimization technique.
Fig. 4. Voltage profile results under normal loading condition
2) B. Loadability Analysis at Critical Loading Condition
Table 2 shows the power flow results of 31-bus, 330kV NNG
under increasing percentage load demand index of 39.72% with
and without UPFC at 56th iterations. It is observed that the load
growth results in huge power losses in line 33 (7-28) by
11.56MW, followed by line 35(17-19) with 6.89MW loss and
line 36(8-29) increased by 4.89MW respectively when
compared to the power flow under normal condition. This is as
a result of the long distance from the generating unit and the
cascading effects of the nearer critical lines. An overall power
loss of 210.7861MW is obtained and after optimal placement
and sizing of UPFC device using GWO, the power loss reduces
to 145.4235MW representing 40.6661% power loss reduction
with the installation of UPFC device with reactive power setting
of -103.3200MVar at bus 19, the UPFC considerably reduced
the total power loss on the network.
1) A. Loadability Analysis at Normal Loading Condition
The power flow result of 31-Bus, 330kV Nigeria National Grid
is presented in Table 1. It is observed that the highest power
loss of 33.73MW occurs on the line 33(7-28) due to the long
transmission line (about 310km apart) from the generating unit,
but in the presence of UPFC with reactive power setting of 89.1600MVar at bus 28, it yields a power loss reduction of
26.09MW representing 22.65% loss reduction. An overall
power loss of 158.9220MW is obtained and after optimal
placement and sizing of UPFC device using GWO, the power
loss reduces to 120.4123MW representing 24.2318% power
loss reduction on the entire network, the UPFC considerably
reduced the total power loss on the network.
Table II: Power flow result of 31-bus, 330kV Nigeria National
Grid at critical loading.
Table I: Power flow result of 31-bus, 330kV Nigeria National
Grid at Normal loading
Loading
Factor
Losses
without
UPFC
(MW)
Rating of UPFC
(MVAr)
Losses
with
UPFC
(MW)
UPFC
Location
Percentage
Loading
Value
% Power
Loss
Reduction
39.72
109
Loss
without
UPFC
(MW)
210.7861
UPFC
Rating
(MVAr)
Loss with
UPFC (MW)
UPFC
Location
Percentage
Power Loss
Reduction
-103.3200
145.4235
19
31.0090
International Conference on Electrical Engineering Applications (ICEEA'2020), Department of Electrical Engineering,
Ahmadu Bello University, Zaria, Nigeria. 23rd-25th September, 2020
Fig. 5 shows the voltage profile with and without placing UPFC
device under critical loading of the network. It is observed that,
bus 28 has the minimum base voltage of 0.9031p.u due to the
large distance of the bus from the generating unit. When UPFC
was optimal placed on the network it increases the voltage
magnitude to 0.9540p.u. Many of the load buses especially
buses 11, 16, 18, 20, 21, 22, 25, and 29 are the overloaded buses
and as such very close to their specified lower limit of 0.95p.u,
which means any slight increase in the load demand will result
in voltage collapse. But with an optimal placement of UPFC
using GWO at Bus 19, it is observed that the magnitude of the
voltage profile increased significantly thereby enhanced the
voltage stability margin of the system to enable more power to
be transmitted over the existing network.
Percentage
Load
Increase
Losses
without
UPFC
(MVar)
Rating of UPFC
(MVAr)
42.30
250.5430
-189.98MVar
Losses with
UPFC
(MW)
164.6500
UPFC
Location
24
Percentage
Power Loss
Reduction
34.28
In order to analyse the steady-state stability condition of the
network under a heavily loaded reactive power and a single
generator outage, bus 17 is loaded to a maximum load level of
42.30% and generator-7 is made out of service to create
contingency. High severity is witnessed when the outage of
generator at bus-7 occurred. Fig. 6 shows the voltage profile of
a heavy reactive loading of bus 17 at 42.30% with and without
UPFC installation. The highest voltage dip occurred at bus 28
(0.9092) due to the lack of reactive power that should come
from generator bus 7 that was made out of service. From this
Fig. 4, it is identified that, simultaneous heavy loading and
generator-7 outage have more effects on the voltage
magnitudes, this is as a result of lack of reactive power that
generator-7 ought to have provided to support the network.
With an optimal installation of UPFC device of reactive power
setting -189.98MVar at Bus 24, all voltage at the buses are
augmented and normalized to the tolerable limit.
Figure 5: Voltage profile results under critical loading
condition
C. Heavy Reactive Loading with Single Generator Outage
Table 3 shows the performance of GWO during a heavy
reactive loading under single generator outage condition. The
power flow result revealed that, lack of generation at Bus-7,
increases the losses at line 6 to 85.54MVAr from the initial base
case with subsequent cascading effects on lines 7 (4-21) and
31(6-27) due to their nearer connections to the critical lines.
Also, at line 36(8-29) a loss of 155MVar, the highest reactive
power loss occurs due to the network topology and distance
from the source. Bus 28 is the weakest and most vulnerable
node, due to its lowest permissible reactive load of
0.4154MVAr in the presence of contingency. It is also evident
from the result that the generator outage condition increases the
total power losses of the network when compared to normal
condition. It can also be revealed that with the installation of
UPFC on the network, apparent power loss at 6th line reduces
from 105.54MVAr to 32.22MVAr representing 69.47% loss
reduction and at branch 36 a loss of 155MVAr reduces to
28.95MVAr representing 81.32%. This improvement witnessed
on the entire network has demonstrated the capability of UPFC
device at controlling voltage magnitude at a bus reactive and
active power flow in a line where it is installed.
Fig. 6. Voltage profile under heavily reactive loading at Bus
17 with Single Generator Outage
V.
CONCLUSION
This paper proposes nature-inspired metaheuristic grey wolf
optimization technique for optimal location and sizing of UPFC
on 31-bus, 330kV Nigeria National Grid with the aim of
minimizing power losses, while improving voltage profile of
the network. Optimal power flows at steady-state analyses are
performed to determine the performance of the proposed GWO
algorithm on the test system under different loading variations
and contingency for a voltage range of 0.95p.u. to 1.05p.u. The
analyses used power loss as objective function for optimal
location and sizing of the FACTS device. The simulation of the
proposed system is performed in MATLAB environment. The
results are evaluated based on three scenarios: loadability
analysis under normal loading, maximum loading, and single
contingency. The simulation results have corroborated the
Table III: Power flow result for 31-bus, 330kV Nigeria
Network at generator outage
110
International Conference on Electrical Engineering Applications (ICEEA'2020), Department of Electrical Engineering,
Ahmadu Bello University, Zaria, Nigeria. 23rd-25th September, 2020
effectiveness of UPFC at an optimal location in power loss
reduction and improvement of voltage profile compared to the
base case without FACTS device. Furthermore, it is also
evident that finding out the optimal location and sizing of
UPFC, more power can be wheeled and delivered to meet the
ever-growing demand over an existing transmission asset under
both normal operation and contingency conditions without
compromising the system stability at minimum power loss by
using the proposed method presented in this paper.
[10]
[11]
[12]
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