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Research ArticleA New Hybrid UPFC Controller for Power Flow
Control andVoltage Regulation Based on RBF Neurosliding Mode
Technique
Godpromesse Kenne,1 René Fochie Kuate,1,2 AndrewMuluh
Fombu,1,2
Jean de Dieu Nguimfack-Ndongmo,1 and Hilaire Bertrand
Fotsin2
1Unité de Recherche d’Automatique et d’Informatique Appliquée
(LAIA), Département de Génie Electrique,IUT FOTSO Victor
Bandjoun, Université de Dschang, BP 134, Bandjoun, Cameroon2Unité
de Recherche de Matière Condensée, d’Electronique et de
Traitement du Signal (LAMACETS), Département de Physique,Faculté
des Sciences, Université de Dschang, BP 69, Dschang, Cameroon
Correspondence should be addressed to Godpromesse Kenne;
[email protected]
Received 16 May 2017; Revised 17 July 2017; Accepted 17
September 2017; Published 22 October 2017
Academic Editor: George E. Tsekouras
Copyright © 2017 Godpromesse Kenne et al. This is an open access
article distributed under the Creative Commons AttributionLicense,
which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properlycited.
This paper presents a new technique to design a Unified Power
Flow Controller (UPFC) for power flow control and DC
voltageregulation of an electric power transmission system which is
based on a hybrid technique which combines a Radial Basis
Function(RBF) neural network (online training) with the sliding
mode technique to take advantage of their common features.The
proposedcontroller does not need the knowledge of the perturbation
bounds nor the full state of the nonlinear system. Hence, it is
robust andproduces an optimal response in the presence of system
parameter uncertainty and disturbances.The performance of the
proposedcontroller is evaluated through numerical simulations on a
Kundur power system and compared with a classical PI
controller.Simulation results confirm the effectiveness,
robustness, and superiority of the proposed controller.
1. Introduction
Presently, it is well established in the scientific
communitythat the UPFC has the ability to increase the power
flowcapacity and improve the stability of an electric power
trans-mission system through the proper design of its controller
[1].Over the past several decades, linear and nonlinear
controltechniques have been successfully proposed and applied inthe
literature for the control of UPFC based on modernand classical
control theories [2–10]. However, the maindrawback of such
techniques is that their application requiresthe development of
mathematical models which are difficultto obtain.Thus, only partial
and quite weak results have beenobtained in terms of online
implementation feasibility.
Faced with these difficulties, intelligent controls such asfuzzy
logic and artificial neural networks have emerged asbetter
alternatives to the conventional linear and nonlinearcontrol
methods. However, the complexities associated withthe adaption of
membership functions and computation
requirements for defuzzification have hindered the applica-tion
of fuzzy logic [11–15]. Hence, recent studies have turnedto
artificial neural networks (ANN) to achieve the desiredgoals
[16–18].
Artificial neural networks have an inherent capabilityto learn
and store information regarding the nonlineari-ties of the system
and to provide this information when-ever required. This renders
the neural networks suitablefor system identification and control
applications [19–21].Although intelligent and hybrid algorithms are
already beingimplemented in the domains of image processing,
robotics,financialmanagement, and so on, their application in the
fieldof FACTS devices for power flow control is fairly recent.
Somerecent results can be found in [12, 16, 17, 22, 23].
In [16], a radial basis function neural network hasbeen designed
to control the operation of the UPFC inorder to improve its dynamic
performance. Simulation andexperimental results were presented to
demonstrate therobustness of the proposed controller against
changes in
HindawiAdvances in Electrical EngineeringVolume 2017, Article ID
7873491, 11 pageshttps://doi.org/10.1155/2017/7873491
https://doi.org/10.1155/2017/7873491
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2 Advances in Electrical Engineering
Shunt converter
Series converter
Shunttransformer
Seriestransformer
DC-linkSsh = Psh + jQsh Sse = Pse + jQse
+
+ +
Vsh
VseVrVs
−
VdcC
(a)
+
+
VsepVsp VrpR L
Isep
Ishp
Lsh
Rsh
Vshp
(b)
Figure 1: UPFC in power system. (a) Schematic diagram of the
UPFC system. (b) Single-phase representation of the UPFC
system.
the transmission system operating conditions. However,large
memory and long computation time are required forits proper
functioning and, in addition, the controller isdesigned under the
assumption that the upper bound ofthe disturbance is known. A
comparative study of transientstability and reactive power
compensation issues in anautonomous wind-diesel-photovoltaic based
hybrid systemusing robust fuzzy-sliding mode based Unified Power
FlowController has been presented in [12], but it has the
limitationthat a linearized small-signal model of the hybrid
systemis considered for the transient stability analysis. Hence,
thesystem will suffer from performance degeneracy when theoperating
condition changes. In [22], the recently proposed𝐻∞-learning method
for updating the parameter of a singleneuron radial basis function
neural network has been usedas a control scheme for the UPFC to
improve the transientstability performance of amultimachine power
system. How-ever, the updating control parameters are optimized for
eachperturbation using a generic algorithm which increases
thecomputational burden and makes the control implementa-tion less
feasible. A neural network predictive controller forthe UPFC has
been designed in [23] to improve the transientstability performance
of the power system. Nevertheless,the neural network controller is
implemented only on theseries branch of the UPFC which limits the
performanceof the device. In [17], a neural network controller
basedon a feedback linearization autoregression average modelis
used to design an adaptive-supplementary unified powerflow control
for two interconnected areas of a power system.However, in this
paper andmany others, the bounds of systemuncertainty and
disturbances are assumed to be known. Butin practice, it is always
difficult to determine the exact upperlimit of system uncertainty
and disturbances. Hence, theabove controllers cannot provide
satisfactory results.
From the above drawbacks, in this paper, a new hybridapproach
which combines RBF neural network with thesliding mode technique to
design a UPFC controller forpower flow control and DC voltage
regulation of an electricpower transmission system with unknown
bounds of systemuncertainty and disturbances is proposed. The
advantagesof this design philosophy are that the controller is
suitablefor practical implementation and it makes the design
usefulfor the real world complex power system. The
remainingsections of this paper are organized as follows. In
Section 2,
the mathematical model of a UPFC in 𝑑𝑞 reference frameis
described. The design of the RBF neurosliding modecontroller is
developed in Section 3. In Section 4, simulationresults in a Kundur
two-area four-machine power system arepresented. Finally, in
Section 5, some concluding remarks endthe paper.
2. System Modeling
Figure 1(a) shows a schematic diagram of a UPFC system,while
Figure 1(b) shows a single-phase representation of thepower circuit
of the UPFC which consists of two back-to-back self-commutated
voltage source converters connectedthrough a common DC-link [24,
25]. The series converter iscoupled to the AC system through a
series transformer andthe shunt converter is coupled through a
shunt transformer.In Figure 1(b), the series and shunt converters
are representedby the voltage sources Vse and Vsh, respectively.The
subscripts“𝑠,” “𝑟,” and “𝑝” are used to represent the sending-end
bus,receiving end bus, and the three-phase quantities (phases𝑎, 𝑏,
𝑐), respectively. Also𝑅 and 𝐿 represent the resistance andleakage
inductance of series converter, respectively, 𝑖se is theline
current, 𝑅sh, 𝐿 sh, and 𝑖sh are the resistance, inductance,and
current of the shunt converter, respectively. The seriesand shunt
branch currents of the circuit in Figure 1(b) can beexpressed by
the following three-phase system of differentialequations
[24–26]:
𝑑𝑖se𝑝𝑑𝑡 =
1𝐿 (−𝑅𝑖se𝑝 + Vse𝑝 + V𝑠𝑝 − V𝑟𝑝) ,
𝑑𝑖sh𝑝𝑑𝑡 =
1𝐿 (−𝑅𝑖sh𝑝 + Vsh𝑝 − V𝑠𝑝) .
(1)
Using Park’s transformation and assuming that theinstantaneous
power is kept invariant and the sending-endvoltage vector V𝑠 is in
the 𝑑-axis (i.e., V𝑠 = (V𝑠𝑑 + 𝑗V𝑠𝑞) =(V𝑠𝑑 + 𝑗0)), the three-phase
system of differential equations(1) can be transformed into an
equivalent two-phase (𝑑, 𝑞)system of equations as follows:
𝑑𝑖se𝑑𝑑𝑡 = −𝑅𝐿 𝑖se𝑑 + 𝑤𝑖se𝑞 +
1𝐿 (Vse𝑑 + V𝑠𝑑 − V𝑟𝑑) , (2)
𝑑𝑖se𝑞𝑑𝑡 = −𝑤𝑖se𝑑 −
𝑅𝐿 𝑖se𝑞 +
1𝐿 (Vse𝑞 + V𝑠𝑞 − V𝑟𝑞) , (3)
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Advances in Electrical Engineering 3
𝑑𝑖sh𝑑𝑑𝑡 = −𝑅sh𝐿 sh 𝑖sh𝑑 + 𝑤𝑖sh𝑞 +
1𝐿 sh (Vsh𝑑 − V𝑠𝑑) , (4)
𝑑𝑖sh𝑞𝑑𝑡 = −𝑤𝑖sh𝑑 −
𝑅sh𝐿 sh 𝑖se𝑞 +1𝐿 sh (Vsh𝑞) , (5)
where 𝑤𝑏 = 2𝜋𝑓𝑏 is the fundamental angular frequency ofthe
supply voltage and 𝑤 = 2𝜋𝑓 is the angular frequency ofsynchronous
reference frame (rad/s).
Since the series and shunt converters of the UPFC arecoupled
through a common DC-link, if the losses in theconverters are
neglected, then the dynamic of the DC-linkvoltage can be expressed
as [27]
𝑑Vdc𝑑𝑡 = −1
Vdc𝐶dc (𝑃se + 𝑃sh) , (6)where 𝑃se and 𝑃sh are the active power
supplied by the seriesand shunt converters, respectively, and Vdc
is the voltage of theDC capacitor of capacitance 𝐶dc.
It is clear from (6) that Vdc decreases when 𝑃se + 𝑃sh >0 and
it increases when 𝑃se + 𝑃sh < 0. Note that (6) is anonlinear
differential equation and has to be investigated atan operating
point. However, the derivative of V2dc can bewritten as
𝑑V2dc𝑑𝑡 = 2Vdc𝑑Vdc𝑑𝑡 . (7)
Using (6) and (7), the derivative of V2dc can be expressed
as
𝑑V2dc𝑑𝑡 = −2𝐶 (𝑃se + 𝑃sh) . (8)
Maintaining constant DC-link voltage is very important forthe
UPFC control system [1, 28, 29]. The DC-link voltagevaries when 𝑃se
+ 𝑃sh ̸= 0. Since (8) does not containa direct control signal like
(4), we will consider 𝑃sh as anauxiliary input that can be used to
maintain the DC-linkvoltage constant.
3. UPFC RBF Neurosliding ModeController Design
In this section, the method proposed in [30, 31] for
time-varying parameter estimation will be modified and appliedto
design a robust adaptive controller for the UPFC using theRBF
neural network.
Let us consider the SISO first-order nonlinear system inthe
following form:
�̇� = 𝑓 (𝑥, 𝑡) + 𝑔 (𝑥, 𝑡) 𝑢 + 𝑑 (𝑡) ,𝑦 = 𝑥, (9)
where 𝑥 ∈ 𝑅, 𝑢 ∈ 𝑅, and 𝑦 ∈ 𝑅 are state variables, systeminput,
and system output, respectively; 𝑓(𝑥, 𝑡) and 𝑔(𝑥, 𝑡) areunknown
smooth functions; 𝑓(𝑥, 𝑡) represents the nominalpart of the system
which does not depend upon the controlinput, while the
uncertainties and external disturbance are
concentrated in the term 𝑑(𝑡) assumed to be bounded by anunknown
constant 𝑑0 > 0. Since all physical plants operate inbounded
regions, we study the control problem of system (9)whose state 𝑥
belongs to a compact subsetΩ ⊂ 𝑅.
Let the desired smooth signal 𝑦∗ = 𝑥∗, the tracking error𝑒𝑥, and
augmented item 𝑆𝑥 be defined as𝑒𝑥 = 𝑥 − 𝑥∗,𝑆𝑥 = 𝑒𝑥 + 𝐶𝑥 ∫ 𝑒𝑥𝑑𝑡,
(10)
where 𝐶𝑥 > 0 is a design parameter. The integral term
isincluded in the sliding manifold 𝑆𝑥 so as to ensure that
thesystem trajectories start on the slidingmanifold from the
firstinstant of time. From (10), we have
̇𝑆𝑥 = ̇𝑒𝑥 + 𝐶𝑥𝑒𝑥 = �̇� + 𝐶𝑥𝑒𝑥 − �̇�∗= 𝑓 (𝑥, 𝑡) + 𝑔 (𝑥, 𝑡) 𝑢 + 𝜇𝑥
+ 𝑑 (𝑡) ,
with 𝜇𝑥 = 𝐶𝑥𝑒𝑥 − �̇�∗.(11)
From ̇𝑆𝑥, if the desired sliding mode controller is chosen
as[31]
𝑢∗𝑥 = − 1𝑔 (𝑥, 𝑡) (𝑓 (𝑥, 𝑡) + 𝜇𝑥 + 𝑑 (𝑡)) −𝑆𝑥𝜖𝑥 , (12)
where 0 < 𝜖𝑥 < 1 is a design parameter, then ̇𝑆𝑥 = 𝑆𝑥/𝜖𝑥
and𝑆𝑥 will converge exponentially to 0.The above desired controller
(12) is not implementable
in practice since the functions 𝑓(𝑥, 𝑡) and 𝑔(𝑥, 𝑡) and theterms
𝜇𝑥 and 𝑑(𝑡) are assumed to be unknown. Hence, inthis work, a RBF
neural network combined with the slidingmode technique will be
applied to approximate the unknowncontroller 𝑢∗𝑥 .
The control signal (12) can be approximated by the
neuralcontroller proposed in [31] as
𝑢∗𝑥 (𝜒𝑥, 𝑡) = Ψ (𝜒𝑥, 𝑤∗) + 𝑒𝑓 (𝜒𝑥) + 𝛿𝑢𝑥 (𝑡) ,with Ψ (𝜒𝑥, 𝑤∗)
=
𝑁∑𝑗=1
𝑤∗𝑗 𝜙 (𝜒𝑥 − 𝐶𝑗 , ]𝑗) ,(13)
where 𝜙(⋅) denotes a nonlinear function; 𝐶𝑗 and ]𝑗, 𝑗 =1, . . .
, 𝑁, are the center and the width of the 𝑗th hidden
unit,respectively;𝑁 is the number of hidden nodes or Radial
BasisFunction (RBF) units; 𝑤∗ is the optimal weight vector
andsatisfies ‖𝑤∗‖ ≤ 𝑅𝜔; 𝜒𝑇𝑥 = (𝑥, 𝑆𝑥, 𝑆𝑥/𝜖𝑥) is the input vector
ofthe RBF network; 𝑒𝑓(𝜒𝑥) is the optimal approximation error,which
is unknown and bounded ∀𝜒𝑥 ∈ Ω𝑥.𝐶𝑗 and ]𝑗, 𝑗 = 1, . . . , 𝑁, are
chosen, respectively, using theClustering algorithm [32] as
follows:
]𝑗 = 𝜒𝑥max − 𝜒𝑥min𝑁 ,𝐶𝑗 = 𝜒𝑥min + 2𝑗 − 12 ]𝑗,
(14)
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4 Advances in Electrical Engineering
Phasors
Clockt
ABC
ABC
Area 1 B1 Area 2B4B5Line 1a Line 1b(110 km)
Line 2a(110 km)
Line 2B(110 km)
(110 km)
A B CFault
UPFC
Pref (pu)
Qref (pu)
[m]
[m]
TripBy passVdqrefPQrefUPFCA1
A2
B1
B2
C1C2
m
Bypass[PQref]
[PQref]
[Vdqref]
[Vdqref]Vdqref
P Pref (pu)Q Qref (pu)
Vdqref
UPFCmeasurements
measurementsV P Q
B2 B3Series 100MVA, 10% injection
Shunt 230 kv, 100 MVA
Vconv_phase (deg.)
Vpos. seq. B1 B2 B3 B4P B1 B2 B3 B4 (MW)
Q B1 B2 B3 B4 (MVar)
Vconv_mag (pu)
Scope
Scope 1
d_thetad_theta (deg)
Vt (pu)Machines
Machinesignals
Pa (pu)w (pu)w
Pa
VtStop
Stop
Stop simulationif there is loss of synchronism
++
+ +
Figure 2: Kundur power system test.
where 𝜒𝑥min and 𝜒𝑥max are the lower and upper bounds ofthe 𝑖th
element of the RBF input vector 𝜒𝑇𝑥 = (𝑥, 𝑆𝑥,
𝑆𝑥/𝜖𝑥),respectively.
Note that the term 𝛿𝑢𝑥(𝑡) is time-varying and cannot
beapproximated by a static neural network. In the
followinganalysis, sliding robust termswill be used in the
identificationscheme to compensate the effect of this uncertainty
time-varying term. The controller 𝑢∗𝑥(𝜒𝑥, 𝑡) will be
approximatedassuming that the terms 𝑒𝑓(𝜒𝑥) and 𝛿𝑢𝑥(𝑡) are bounded
byunknown positive constants.
For this purpose, the following neural controller is pro-posed
in order to approximate the control signal 𝑢∗𝑥(𝜒𝑥, 𝑡)
�̂�∗𝑥 (𝜒𝑥, 𝑡) = Ψ (𝜒𝑥, 𝑤) + 𝑏𝑥 (𝑡) , (15)where the term 𝑏𝑥(𝑡) is
introduced in order to improve theconvergence rate of the neural
network in the presence of theuncertainties terms.
Consider the systems described by (9), the sliding-neuralnetwork
controller (15), and Assumptions 1 and 2 given in[31]. If the bias
term 𝑏𝑥(𝑡), the learning rule of the weight 𝑤,and the adaptation
law for the unknown bound 𝜆𝑥 are chosenas
𝑏𝑥 (𝑡) = −�̂�𝑥 sgn (𝑆𝑥) ,
̇̂𝑤𝑗 = Proj[[−𝑆𝑥 𝜕Ψ𝜕𝑤𝑗
𝑤𝑗=𝑤𝑗]],
={{{{{{{−𝑆𝑥 𝜕Ψ𝜕𝑤𝑗
𝑤𝑗=𝑤𝑗, if 𝑤𝑗 < 𝑅𝑤,
0, otherwise,𝑗 = 1, . . . , 𝑁
̇̂𝜆𝑥 = {{{𝛼𝑥, if 𝑆𝑥 ̸= 0,0, if 𝑆𝑥 = 0,
(16)
with𝛼𝑥 > 0, �̂�𝑥(0) = 0, and Proj(⋅) the well-known
projectionfunction [33] on the compact set Ω𝜔 = {𝜔 : ‖𝜔‖ ≤ 𝑅𝜔},then
the neural network controller error 𝑆𝑥 will convergein finite time
to the origin. The proof of the convergenceof above neural network
controller to zero can be found in[31].
In order to apply the neurosliding controller describedabove to
power flow control, UPFC sending-end bus voltagecontrol and DC-link
voltage control, the dynamic equationsof the UPFC completely
described by (2) to (5) and (8) can berewritten as
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−0.20
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Iq_S
E (p
u)
0.1 0.2 0.3 0.4 0.5 0.60Time (s)
(b)
Figure 3: Control response to step changes in real and reactive
power flow references in the transmission line. (a) (i) Active
power at busB3. (ii) Reactive power at bus B3. (iii) Voltage
magnitude at bus B2. (iv) UPFC DC-link voltage. (b) (i)𝐷-axis
current of shunt converter. (ii)𝑄-axis current of shunt converter.
(iii)𝐷-axis current of series converter. (iv) 𝑄-axis current of
series converter.
�̇�1 = 𝑓1 (𝑥, 𝑡) + 𝑔1 (𝑥, 𝑡) 𝑢1 + 𝑑1 (𝑡) ,�̇�2 = 𝑓2 (𝑥, 𝑡) + 𝑔2
(𝑥, 𝑡) 𝑢2 + 𝑑2 (𝑡) ,�̇�3 = 𝑓3 (𝑥, 𝑡) + 𝑔3 (𝑥, 𝑡) 𝑢3 + 𝑑3 (𝑡) ,�̇�4
= 𝑓4 (𝑥, 𝑡) + 𝑔4 (𝑥, 𝑡) 𝑢4 + 𝑑4 (𝑡) ,�̇�5 = 𝑓5 (𝑥, 𝑡) + 𝑔5 (𝑥, 𝑡)
𝑢5 + 𝑑5 (𝑡) ,
(17)
with𝑥1 = 𝑖se𝑑;
𝑓1 (𝑥, 𝑡) = −𝑅𝐿 𝑖se𝑑 + 𝑤𝑖se𝑞;𝑔1 (𝑥, 𝑡) = 1𝐿 ;
𝑢1 = Vse𝑑 + V𝑠𝑑 − V𝑟𝑑,𝑥2 = 𝑖se𝑞;
𝑓2 (𝑥, 𝑡) = −𝑤𝑖se𝑑 − 𝑅𝐿 𝑖se𝑞;
𝑔2 (𝑥, 𝑡) = 1𝐿 ;𝑢2 = Vse𝑞 + V𝑠𝑞 − V𝑟𝑞,𝑥3 = 𝑖sh𝑑;
𝑓3 (𝑥, 𝑡) = −𝑅sh𝐿 sh 𝑖sh𝑑 + 𝑤𝑖sh𝑞;𝑔3 (𝑥, 𝑡) = 1𝐿 sh ;
𝑢3 = Vsh𝑑 − V𝑠𝑑,𝑥4 = 𝑖sh𝑞;
𝑓4 (𝑥, 𝑡) = −𝑤𝑖sh𝑑 − 𝑅sh𝐿 sh ;𝑔4 (𝑥, 𝑡) = 1𝐿 sh ;
𝑢4 = Vsh𝑞,
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6 Advances in Electrical Engineering
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−125−120−115−110−105
PB5
(Mw
)
0102030
QB2
(Mva
r)
121416182022
QB5
(Mva
r)
0.1 0.2 0.3 0.4 0.50 0.6Time (s)
(b)
Figure 4: Control response to step changes in real and reactive
power flow references in the transmission line. (a) (i)𝐷-axis
voltage of shuntconverter. (ii) 𝑄-axis voltage of shunt converter.
(iii) 𝐷-axis voltage of series converter. (iv) 𝑄-axis voltage of
series converter. (b) (i) Activepower at bus B2. (ii) Active power
at bus B5. (iii) Reactive power at bus B2. (iv) Reactive power at
bus B5.
𝑥5 = V2dc;𝑓5 (𝑥, 𝑡) = − 2𝐶𝑃se;𝑔5 (𝑥, 𝑡) = − 2𝐶;
𝑢5 = 𝑃sh,(18)
where 𝑑1(𝑡) to 𝑑5(𝑡) represent system uncertainties.The
reference values of the state variables are obtained as
𝑥∗1 = 𝑖∗se𝑑 = 23𝑃∗𝑟 V𝑟𝑑 + 𝑄∗𝑟 V𝑟𝑞
V2𝑟𝑑+ V2𝑟𝑞 ,
𝑥∗2 = 𝑖∗se𝑞 = 23𝑃∗𝑟 V𝑟𝑞 − 𝑄∗𝑟 V𝑟𝑑
V2𝑟𝑑+ V2𝑟𝑞 ,
𝑥∗3 = 𝑖∗sh𝑑 = 23𝑃∗shV𝑠𝑑 + 𝑄∗shV𝑠𝑞
V2𝑠𝑑+ V2𝑠𝑞 ,
𝑥∗4 = 𝑖∗sh𝑞 = (𝑘𝑝𝑎𝑐 + 𝑘𝑖𝑎𝑐𝑠 ) (Vref − V𝑠𝑑) ,𝑥∗5 = V2∗dc ,
(19)
where 𝑃∗𝑟 and𝑄∗𝑟 are the active and reactive power referencesat
the receiving end bus of the transmission line, respectively.
We can design the neurosliding controller �̂�∗𝑘 using theUPFC
dynamics given in (17) as (for 𝑘 = 1, . . . , 5)
�̂�∗𝑘 (𝜒𝑥𝑘, 𝑡) = Ψ (𝜒𝑥𝑘, 𝑤𝑘) + 𝑏𝑥𝑘 (𝑡) ,𝜒𝑇𝑥𝑘 = (𝑥𝑘, 𝑆𝑥𝑘, 𝑆𝑥𝑘𝜖𝑥𝑘
) ,𝑆𝑥𝑘 = 𝑒𝑥𝑘 + 𝐶𝑥𝑘 ∫ 𝑒𝑥𝑘,
𝑏𝑥𝑘 (𝑡) = −�̂�𝑥𝑘 sgn (𝑆𝑥𝑘) ,̇̂𝑤𝑘𝑗 = Proj[[
−𝑆𝑥𝑘 𝜕Ψ𝜕𝑤𝑘𝑗𝑤𝑘𝑗=𝑤𝑘𝑗
]],
-
Advances in Electrical Engineering 7
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
(i)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
(ii)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
(iii)
(iv)
REFPISNC
1.98
2
2.02
PB3
(pu)
−0.05
0
0.05
QB3
(pu)
0.99
1
1.01
VB2
(pu)
0.98
1
1.02
VDC
(pu)
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180Time (s)
(a)
0 0.05 0.1 0.15 0.2 0.25 0.3
(i)
0 0.05 0.1 0.15 0.2 0.25 0.3
(ii)
0 0.05 0.1 0.15 0.2 0.25 0.3
(iii)
(iv)
PISNC
0.05 0.1 0.15 0.2 0.25 0.30Time (s)
05
1015
QB5
(Mva
r)
12141618202224
QB2
(Mva
r)
−206−204−202−200−198
PB2
(Mw
)
−120−118−116−114−112
PB5
(Mw
)
(b)
Figure 5: Control response to load variation. (a) (i) Active
power at bus B3. (ii) Reactive power at bus B3. (iii) Voltage
magnitude at bus B2.(iv) UPFC DC-link voltage. (b) (i) Active power
at bus B2. (ii) Active power at bus B5. (iii) Reactive power at bus
B2. (iv) Reactive power atbus B5.
={{{{{{{−𝑆𝑥𝑘 𝜕Ψ𝜕𝑤𝑘𝑗
𝑤𝑘𝑗=𝑤𝑘𝑗, if 𝑤𝑘𝑗 < 𝑅𝑤,
0, otherwise,𝑗 = 1, . . . , 𝑁
̇̂𝜆𝑥𝑘 = {{{𝛼𝑥𝑘, if 𝑆𝑥𝑘 ̸= 0,0, if 𝑆𝑥𝑘 = 0.
(20)
4. Simulation Results
The performance of the proposed nonlinear controlleris evaluated
through digital simulations using MATLAB/SIMULINK software. The
power system used is a Kundurtwo-area four-machine power system
shown in Figure 2. Thedetails of system data and initial operating
point are givenin [34]. The proposed controller can be applied to a
UPFCconnected between any two buses of the power system (with𝑛 bus)
regardless of the interaction between these two busesand other
buses. Only local measurements information is
required for the implementation of the proposed algorithm.The
simulation results of the proposed controller (SNC)are compared
with conventional Proportional Integral (PI)controllers used for
power flow control, UPFC sending-endbus voltage control, and
DC-link voltage control. These clas-sical controllers are tuned
using optimal control techniquesand the parameters obtained are
given in the Appendix. Toevaluate the performance of the proposed
controller, four setsof simulations have been performed. In all
simulations, theuncertainty factor is set at +10%. That is the
parameters ofthe system under simulation are set at 110% compared
to thesame parameters introduced in the controller.
4.1. Step Changes in Transmission Line Real and ReactivePower
Flow References. In this case study, the initial complexpower flow
(𝑃B3 + 𝑗𝑄B3) at the receiving end of the trans-mission line is
found as (1.8 + 𝑗0.0) pu. A step change inactive power reference
from 1.8 to 2.2 pu and reactive powerreference from0.0 to 0.5 pu of
the transmission line take placeat 𝑡 = 0.02 s and 0.32 s,
respectively. The simulation resultsfor this case study are
depicted in Figures 3 and 4. It can beseen from these figures that
the active and reactive power flowthrough the transmission line,
the UPFC DC-link voltage,
-
8 Advances in Electrical Engineering
0 0.05 0.1 0.15 0.2 0.25 0.3
(i)
0 0.05 0.1 0.15 0.2 0.25 0.3
(ii)
0 0.05 0.1 0.15 0.2 0.25 0.30.95
1
VB2
(pu)
(iii)
0.9
1
1.1
VDC
(pu)
(iv)
REFSNC
1.8
2
2.2
PB3
(pu)
00.20.40.6
QB3
(pu)
0.05 0.1 0.15 0.2 0.25 0.30Time (s)
(a)
0 0.05 0.1 0.15 0.2 0.25 0.3
(i)
0 0.05 0.1 0.15 0.2 0.25 0.3−0.1
−0.05
0
Vq_S
H (p
u)
(ii)
0 0.05 0.1 0.15 0.2 0.25 0.30
0.1
Vd_S
E (p
u)
(iii)
(iv)
0.2
0.25
Vq_S
E (p
u)
0.5
1
1.5
Vd_S
H (p
u)0.05 0.1 0.15 0.2 0.25 0.30
Time (s)
(b)
Figure 6: Control response to measurement noise. (a) (i) Active
power at bus B3. (ii) Reactive power at bus B3. (iii) Voltage
magnitude at busB2. (iv) UPFC DC-link voltage. (a) (i) 𝐷-axis
voltage of shunt converter. (ii) 𝑄-axis voltage of shunt converter.
(iii) 𝐷-axis voltage of seriesconverter. (iv) 𝑄-axis voltage of
series converter.
and the voltagemagnitude at bus B2 are controlled
effectively.The results also clearly show that the response speed
andtransient conditions are further improved with the
proposedcontroller as compared to the conventional PI
controllers.Figure 4 clearly shows the excellent performance of
theUPFCin power flow control under the influence of the
proposedcontroller.
4.2. Load Variation. In practice, the references values of
thecontrol power system remain constant and the quantitiesbeing
controlled vary under the effect of load variation,disturbance, and
other perturbations. In this case study,the load increases by 20%
of its nominal value from 𝑡 =0.02 s. The simulation results are
depicted in Figure 5. Itcan be noticed in these figures that the
active and reac-tive power flow through the transmission line, the
DC-link voltage, and the voltage magnitude at bus B2 areall
regulated to their respective reference values. Figure 5shows that
the excess active and reactive power requestedby the load is
supplied only by generator G2. The figurealso demonstrates once
more the excellent performance ofthe proposed controller in terms
of overshot and settlingtime.
4.3. Robustness to Measurement Noise. In practice, it is
notpossible to measure a signal accurately due to the presence
of noise. For this reason, the third case study investigatesthe
robustness of the proposed nonlinear controller withrespect to
measurement noise (uncertainties). In this casestudy, all
simulations are conducted under noise condi-tions in the measured
line currents with the magnitudeof the noise reaching about 4% of
the maximum valueof the measurable line currents. A step change in
reac-tive power under the same conditions as in the first casestudy
is used to evaluate the robustness of the system.The simulation
results for this case study are depicted inFigure 6. From these
results, it can be seen that the activeand reactive power flow
through the transmission line, theUPFC DC-link voltage, and the
voltage magnitude at busB2 are all regulated to their respective
reference valuesdespite the presence of measurement noise. Hence,
it canbe concluded that the controller exhibits an excellent
noiseresistance.
4.4. Three-Phase-to-Ground Fault Test. In this case study,
athree-phase-to-ground fault is applied on bus-5 and the faultis
cleared after 100ms. Simulation results for this case studyare
shown in Figure 7. From these results, it can be seenthat the
proposed controller rapidly steers the system to itsprefault steady
state and satisfactorily improves the transientstability of the
power system as compared to the conventionalPI controllers.
-
Advances in Electrical Engineering 9
Table 1
Shunt converter Parameters 𝑆 (MVA) 𝑉rms𝐿-𝐿 (kV) 𝑓 (Hz) 𝑅sh (pu)
𝐿 sh (pu)Values 100 255 60 0.22/30 0.22
Series converter Parameters 𝑆 (MVA) 𝑉rms-max (kV) 𝑓 (Hz) 𝑅 (pu)
𝐿 (pu)Values 100 255 ∗ 10% 60 0.16/30 0.16
DC-link Parameters 𝑉dc-mon (kV) 𝑉dc-ref (pu) 𝐶 (𝜇F) — —Values 40
1.0 750 — —
0 1 2 3 4 5 6 7
(i)
0 1 2 3 4 5 68
10
12
Delt
a 2 (d
eg)
(ii)
0 1 2 3 4 5 6
−14
−12
−10
Delt
a 3 (d
eg) (iii)
(iv)
PISNC
16182022
Delt
a 1 (d
eg)
−22−20−18−16
Delt
a 4 (d
eg)
1 2 3 4 5 60Time (s)
(a)
0 0.5 1 1.5
(i)
0 0.5 1 1.5
(ii)
0 0.5 1 1.5
(iii)
(iv)
PISNC
0.5 1 1.50Time (s)
0.9
1
1.1
Vt4
(pu)
0.951
1.051.1
Vt3
(pu)
0.9
1
1.1
Vt2
(pu)
1
1.05
1.1
Vt1
(pu)
(b)
Figure 7: Control response to three-phase fault. (a) All
generator rotor angle in COI. (b) All terminal generator
voltage.
5. Conclusion
In this paper, a new hybrid approach which combines RadialBasis
Function (RBF) neural network with the sliding modetechnique has
been used to design a Unified Power FlowController (UPFC) for power
flow control, UPFC sending-end voltage control, and DC voltage
regulation of an electricpower transmission system. The RBF
neurosliding modecontrol technique uses online training to get its
optimalparameter values.The proposed technique is robust and
doesnot need the knowledge of the perturbation bounds nor thefull
state of the nonlinear system. The performance of theproposed
controller has been evaluated through simulationson a Kundur power
system and compared with a classicalPI controller. Simulation
results have shown the effectivenessand satisfactory performance of
the proposed controller indealing with the perturbations
considered. Future worksshould be targeted towards the extension of
the proposed
hybrid approach to a wide area interconnected power systemfor
power oscillation damping.
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1.(ii) PI
controllers parameters are as follows:
Series converter:𝐾𝑝 = 0.16; 𝐾𝑖 = 8.33.Shunt converter:𝐾𝑝 =
0.2;𝐾𝑖 = 20.DC-link:𝐾𝑝 = 10−3; 𝐾𝑖 = 15 ∗ 10−3.
(iii) RBF controller parameters are as follows:
𝐶𝑥1 = 0.15;
-
10 Advances in Electrical Engineering
𝐶𝑥2 = 0.05;𝐶𝑥3 = 10−3;𝐶𝑥4 = 3 ∗ 10−3;𝐶𝑥5 = 3 ∗ 10−4;𝑁 = 5.
(A.1)
The values of 𝑤𝑗 are randomly initialized.Conflicts of
Interest
The authors declare that they have no conflicts of interest.
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