A New Hybrid UPFC Controller for Power Flow Control and … · 2019. 7. 30. · the UPFC control...

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

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)

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)


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


0 0.1 0.2 0.3 0.4 0.5 0.6

(ii)

0 0.1 0.2 0.3 0.4 0.5 0.6

(iii)

(iv)

REFPINSC

0 0.1 0.2 0.3 0.4 0.5 0.6

(i)

1.8

2

2.2

PB3

(pu)

00.20.40.60.8

QB3

(pu)

0.970.980.99

11.01

VB2

(pu)

0.99

1

1.01

VDC

(pu)

0.1 0.2 0.3 0.4 0.5 0.60Time (s)

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6

(iii)

0 0.1 0.2 0.3 0.4 0.5 0.6

(iii)

(vi)

SNCPI

0 0.1 0.2 0.3 0.4 0.5 0.6

(i)

0.10.15

0.20.25

Id_S

H (p

u)

−0.4−0.2

00.20.4

Iq_S

H (p

u)1.6

1.8

2

2.2

Id_S

E (p

u)

−0.20

0.20.40.6

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,


0 0.1 0.2 0.3 0.4 0.5 0.60.8

1

Vd_S

H (p

u)(i)

0 0.1 0.2 0.3 0.4 0.5 0.6

(ii)

0 0.1 0.2 0.3 0.4 0.5 0.6

(iii)

(iv)

PISNC

−0.08−0.06−0.04−0.02

0

Vq_S

H (p

u)

−0.050

0.050.1

Vd_S

E (p

u)

0.150.2

0.250.3

Vq_S

E (p

u)

0.1 0.2 0.3 0.4 0.5 0.60Time (s)

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6

(i)

0 0.1 0.2 0.3 0.4 0.5 0.6

(ii)

0 0.1 0.2 0.3 0.4 0.5 0.6

(iii)

(iv)

PISNC

−240−220−200−180

PB2

(Mw

)

−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

]],


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,


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.


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;


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.

References

[1] I. Papic, P. Zunko, D. Povh, and M. Weinhold, “Basic controlof unified power flow controller,” IEEE Transactions on PowerSystems, vol. 12, no. 4, pp. 1734–1739, 1997.

[2] S. Kannan, S. Jayaram, andM. M. A. Salama, “Real and reactivepower coordination for a unified power flow controller,” IEEETransactions on Power Systems, vol. 19, no. 3, pp. 1454–1461,2004.

[3] B. Lu and B.-T. Ooi, “Nonlinear control of voltage-sourceconverter systems,” IEEE Transactions on Power Electronics, vol.22, no. 4, pp. 1186–1195, 2007.

[4] A. Zangeneh, A. Kazemi, M. Hajatipour, and S. Jadid, “A Lya-punov theory based UPFC controller for power flow control,”International Journal of Electrical Power & Energy Systems, vol.31, no. 7-8, pp. 302–308, 2009.

[5] B. Lei and S. Fei, “A brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theory,”Control Engineering Practice, vol. 29, pp. 147–157,2014.

[6] J. D. D. Nguimfack-Ndongmo, G. Kenné, R. Kuate-Fochie, A.Cheukem, H. B. Fotsin, and F. Lamnabhi-Lagarrigue, “A simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC device,” InternationalJournal of Electrical Power & Energy Systems, vol. 54, pp. 650–657, 2014.

[7] A. Ajami, S. H. Hosseini, S. Khanmohammadi, and G. B.Gharehpetian, “Modeling and control of C-UPFC for powersystem transient studies,” Simulation Modelling Practice andTheory, vol. 14, no. 5, pp. 564–576, 2006.

[8] A. Hamache, M. O. Bensidhoum, and H. Chekireb, “RoRobustsliding mode control of unified power flow controllerfor powerflow tracking,” in Proceedings of the 8th International Conferenceon Modelling, Identification and Control (ICMIC ’16), pp. 412–417, Algiers, Algeria, November 2016.

[9] A. Khodabakhshian, M. R. Esmaili, and M. Bornapour, “Opti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithm,” International Journal of Electrical Power & EnergySystems, vol. 83, pp. 124–133, 2016.

[10] S. K. Routray, R. K. Patnaik, and P. K. Dash, “Adaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farm,”Asian Journal of Control, vol. 19, no. 5, pp. 1–20, 2017.

[11] L. Saribulut, A. Teke, and M. Tümay, “Dynamic control ofunified power flow controller under unbalanced network con-ditions,” Simulation Modelling Practice and Theory, vol. 19, no.2, pp. 817–836, 2011.

[12] A. Mohanty, S. Patra, and P. K. Ray, “Robust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid system,” IET Generation,Transmission & Distribution, vol. 10, no. 5, pp. 1248–1257, 2016.

[13] M. Fadi, A. Shameem, M. Saad, A. Ibrahim, and A. H. MohdFairuz, “Power flow control using fuzzy based UPFC underdifferent operating conditions,” Journal of Electrical Systems, vol.13, no. 2, pp. 398–414, 2017.

[14] F. M. Albatsh, S. Mekhilef, S. Ahmad, and H. Mokhlis, “Fuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission lines,” IEEE Trans-actions on Industrial Electronics, 2017.

[15] M. Khaksar, A. Rezvani, and M. H. Moradi, “Simulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controller,” Neural Computing andApplications, 2016.

[16] M. E. A. Farrag and G. Putrus, “An on-line training radial basisfunction neural network for optimum operation of the UPFC,”European Transactions on Electrical Power, vol. 21, no. 1, pp. 27–39, 2011.

[17] N. Zeb, B. Khan, S. M. Ali et al., “Adaptive controller basedunified power flow control for low power oscillation damping,”Asian Journal of Control, vol. 20, no. 1, pp. 1–10, 2017.

[18] M. J. Rana, M. S. Shahriar, and M. Shafiullah, “Levenberg–Marquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stability,”Neural Comput-ing and Applications, 2017.

[19] Q. Zhu, S. Fei, T. Zhang, and T. Li, “Adaptive RBF neural-networks control for a class of time-delay nonlinear systems,”Neurocomputing, vol. 71, no. 16–18, pp. 3617–3624, 2008.

[20] J. Liu, Radial Basis Function (RBF) Neural Network Control forMechanical Systems, Design, Analysis and Matlab Simulation,Springer, Heidelberg, Germany, 2013.

[21] C. C. Hua, C. X. Yu, and X. P. Guan, “Neural network observer-based networked control for a class of nonlinear systems,”Neurocomputing, vol. 133, pp. 103–110, 2014.

[22] S. Mishra, “Neural-network-based adaptive UPFC for improv-ing transient stability performance of power system,” IEEETransactions on Neural Networks and Learning Systems, vol. 17,no. 2, pp. 461–470, 2006.

[23] S. Tiwari, R. Naresh, and R. Jha, “Neural network predictivecontrol of UPFC for improving transient stability performanceof power system,” Applied Soft Computing, vol. 11, no. 8, pp.4581–4590, 2011.

[24] C. M. Yam andM. H. Haque, “A SVD based controller of UPFCfor power flow control,” Electric Power Systems Research, vol. 70,no. 1, pp. 76–84, 2004.

[25] M. A. Sayed and T. Takeshita, “All nodes voltage regulationand line loss minimization in loop distribution systems usingUPFC,” IEEE Transactions on Power Electronics, vol. 26, no. 6,pp. 1694–1703, 2011.

[26] M. E. Elgamal, A. Lotfy, and G. E. M. Ali, “Voltage profileenhancement by fuzzy controlled MLI UPFC,” InternationalJournal of Electrical Power & Energy Systems, vol. 34, no. 1, pp.10–18, 2012.


[27] H. Chen, Y. Wang, and R. Zhou, “Transient stability enhance-ment via coordinated excitation and UPFC control,” Interna-tional Journal of Electrical Power & Energy Systems, vol. 24, no.1, pp. 19–29, 2002.

[28] H. Fujita, Y. Watanabe, and H. Akagi, “Transient analysis of aunified power flow controller and its application to design ofthe dc-link capacitor,” IEEE Transactions on Power Electronics,vol. 16, no. 5, pp. 735–740, 2001.

[29] I. Axente,M. Basu, andM. F. Conlon, “Dc link voltage control ofUPQC for better dynamic performance,” Electric Power SystemsResearch, vol. 81, no. 9, pp. 1815–1824, 2011.

[30] T. Ahmed-Ali, G. Kenné, and F. Lamnabhi-Lagarrigue, “Iden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observer,” Neurocomputing, vol.72, no. 7-9, pp. 1611–1620, 2009.

[31] G. Kenné, A. S. Fotso, and F. Lamnabhi-Lagarrigue, “A newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique: application to SEIG windturbine control system,” International Journal of Control, vol. 90,no. 4, pp. 855–872, 2017.

[32] A. K. Jain and R. C. Dubes, Algorithms for Clustering Data,Prentice Hall, 1988.

[33] D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Mass, USA, 1984.

[34] P. Kundur, Power System Stability and Control, McGraw-Hill,New York, NY, USA, 1994.

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal of

Volume 201

Submit your manuscripts athttps://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


Date post:	31-Jan-2021
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

A New Hybrid UPFC Controller for Power Flow Control and … · 2019. 7. 30. · the UPFC control...

Documents