Scholarly article on topic 'Power system security enhancement with unified power flow controller under multi-event contingency conditions'

Power system security enhancement with unified power flow controller under multi-event contingency conditions Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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{"Power system security" / "Critical lines" / "Sensitive generators" / "System severity function" / "Unified power flow controller" / "Improved TLBO"}

Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — S. Ravindra, Chintalapudi V. Suresh, S. Sivanagaraju, V.C. Veera Reddy

Abstract Power system security analysis plays key role in enhancing the system security and to avoid the system collapse condition. In this paper, a novel severity function is formulated using transmission line loadings and bus voltage magnitude deviations. The proposed severity function and generation fuel cost objectives are analyzed under transmission line(s) and/or generator(s) contingency conditions. The system security under contingency conditions is analyzed using optimal power flow problem. An improved teaching learning based optimization (ITLBO) algorithm has been presented. To enhance the system security under contingency conditions in the presence of unified power flow controller (UPFC), it is necessary to identify an optimal location to install this device. Voltage source based power injection model of UPFC, incorporation procedure and optimal location identification strategy based on line overload sensitivity indexes are proposed. The entire proposed methodology is tested on standard IEEE-30 bus test system with supporting numerical and graphical results.

Academic research paper on topic "Power system security enhancement with unified power flow controller under multi-event contingency conditions"

Ain Shams Engineering Journal (2015) xxx, xxx-xxx

Ain Shams University Ain Shams Engineering Journal

www.elsevier.com/locate/asej www.sciencedirect.com

ELECTRICAL ENGINEERING

Power system security enhancement with unified power flow controller under multi-event contingency conditions

S. Ravindra a,% Chintalapudi V. Sureshd1, S. Sivanagaraju b2, V.C. Veera Reddy

a EEE Department, QIS College of Engineering & Technology, Prakasam, 523272, India b EEE Department, UCEK, JNTUK, Kakinada, E.G.Dt, A.P. 533003, India c EEE Department, AITS, Tirupati, A.P., India

d EEE Department, Vasireddy Venkatadri Institute of Technology, Nambur, Guntur, A.P, 522508, India

Received 27 March 2015; revised 3 June 2015; accepted 12 July 2015

KEYWORDS

Power system security; Critical lines; Sensitive generators; System severity function; Unified power flow controller;

Improved TLBO

Abstract Power system security analysis plays key role in enhancing the system security and to avoid the system collapse condition. In this paper, a novel severity function is formulated using transmission line loadings and bus voltage magnitude deviations. The proposed severity function and generation fuel cost objectives are analyzed under transmission line(s) and/or generator(s) contingency conditions. The system security under contingency conditions is analyzed using optimal power flow problem. An improved teaching learning based optimization (ITLBO) algorithm has been presented. To enhance the system security under contingency conditions in the presence of unified power flow controller (UPFC), it is necessary to identify an optimal location to install this device. Voltage source based power injection model of UPFC, incorporation procedure and optimal location identification strategy based on line overload sensitivity indexes are proposed. The entire proposed methodology is tested on standard IEEE-30 bus test system with supporting numerical and graphical results.

© 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

* Corresponding author. Tel.: +91 9440053880. E-mail addresses: sanguravindra11@gmail.com (S. Ravindra), venkatasuresh3@gmail.com (C.V. Suresh), sirigiri70@yahoo.co.in (S. Sivanagaraju), veerareddyj1@rediffmail.com (V.C. Veera Reddy).

1 Tel.: +91 9989254335.

2 Tel.: +91 8500961061.

Peer review under responsibility of Ain Shams University.

1. Introduction

Nowadays, power system operation, and control and management become one of the challenging tasks to maintain the continuity and reliability of the supply. The system security should be analyzed to avoid uncontrolled conditions such as line over-loadings, bus voltage violations, and system collapse conditions. Dynamic security analysis is necessary due to the continuous change in the system operating conditions [1]. Risk based security constrained optimal power flow (SCOPF)

http://dx.doi.org/10.1016/j.asej.2015.07.006

2090-4479 © 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

problem was implemented to investigate the stability of the system using QV-curves [2]. From this, the system security level has been enhanced because of SCOPF including risk modeling. Robust power system security (RPSS) method was presented to analyze the (n — 1) contingency conditions for PV penetration problem [3]. From this literature, it is identified that, power system security should be analyzed in terms of line loadings and bus voltage variations. In general, optimal power flow (OPF) problem with security constraints can solve this problem.

In [4], they proposed bacterial foraging algorithm for optimal power flow under the consideration of security constraints and non-smooth cost function. The proposed method is used to alleviate the congestion and voltage stability, improves the loadability and reduces the line losses and production cost by controlling the power flow in the network. In [5], they proposed Security-Constrained OPF (SCOPF) in electricity networks in which the transmission lines are potentially instrumented with Flexible AC Transmission Systems (FACTS). The single objective OPF problem was solved using some of the advanced optimization techniques reported in [6-11] while satisfying system constraints. Nowadays, hybrid algorithms reported in [12-14] are used to solve OPF problem. Because of this implementation, the convergence has been improved rapidly and global optimal solution is obtained in less time. In the same way, multi objective optimal power flow problem was solved in the presence of flexible AC transmission system (FACTS) controllers, using some of the latest optimization methodologies reported in [15-19]. Incorporation of FACTS controllers enhances the system parameters such as voltage magnitudes, power flow in transmission lines, and total system losses. Out of the various FACTS devices, unified power flow controller (UPFC) can control voltage magnitude at a bus and active and reactive power flow in line, in which, it is connected.

FACTS devices can play an important role for demand side management and thereby controlling transmission line congestion [20]; in this, they proposed two-step market clearing procedure for transmission lines congestion management in a restructured market environment using a combination of demand response (DR) and FACTS controllers. UPFC in overhead lines under line outage condition is used to increase the availability of the transmission network during peak loads effectively [21]. In [22], they proposed a dynamic model of UPFC for enhancing the active power flow in transmission line, improving the bus voltages and power losses reduction. In [22], they developed a steady state model of UPFC under the load variation condition. It has been used to improve the capability of power flow in power transmission lines and to enhance the transmission power flow in line, thereby reducing the active power losses as well as enhancing the bus voltages. A novel severity function was formulated in [15], to identify an optimal location to install one of the advanced multiline FACTS controllers, namely, generalized unified power flow controller. In this location, system security can be enhanced by minimizing the severity of the system.

From the careful review of the literature, it is identified that, the system can be operated under contingency conditions to analyze the system security. For this, critical transmission line(s) are identified using line collapse proximity indexes (LCPI) and sensitive generator(s) are identified using generator shift factors (GSF). The effect of optimal power flow (OPF) on

system severity with generation fuel cost and system severity functions is solved while satisfying system equality and in equality constraints. In this paper, a new improved teaching learning based optimization (ITLBO) algorithm is presented. To enhance the system security, under transmission line(s) and/or generator(s) contingency conditions, voltage source based power injection model of unified power flow controller (UPFC) is presented. The optimal location of UPFC is identified through line overload sensitivity index (LOSI) analysis. The various scenarios to analyze the system security under contingency conditions, using OPF and to enhance the system security using UPFC are tested on standard IEEE-30 bus test system with supporting numerical and graphical results.

2. Power system security

In general, the main aim of power system operation and control is to meet the demand continuously without any failures. While, in this operation, sometime, outage of generator due to failure of the auxiliary equipment or removal of a transmission line for maintenance purpose or due to storm and other effects may happen. Due to which, the system frequency may drop and lead to load shedding or uncontrolled operation and sometime lead to system collapse condition. This happens mainly due to the overloading of the transmission lines, voltage deviation and lack of reactive power support at the load buses.

From this discussion, while operating power system, it is necessary to consider a factor which relates to the system security and involves the design of the system to maintain the system security under various contingencies. In common practice, outage of a transmission line or a generator increases the loading on some of the transmission lines and voltage magnitudes at load buses may violate their minimum or maximum limits. It is necessary to minimize the system severity and analyze the system condition to enhance the system security. For this purpose, in this paper, two different parameters are defined to identify the most critical line(s) and generator(s) in a given system.

2.1. Line collapse proximity index

From the literature, it is identified that, there are variety of indices to identify the most severe lines in a given system. Due to the difficulties reported in the literature for the available indices, a new index based on the effect of power flow in transmission lines, line charging reactance and the direction of reactive power flow with respect to the direction of active power flow known as ''Line collapse proximity index" (LCPI) is proposed. The modeling of this index is based on the exact pi-model of the transmission lines using ABCD-parameters [23].

Conventionally, the relation between system parameters for a transmission line connected between buses's' and 'r' can be expressed as follows:

>s" A B >s"

A C D Js.

where A, B, C and D are the transmission line parameters related to two-port network and can be expressed as

a = (i + ZY)

C = Y(1 + ZYY) D = A

Open circuit reverse voltage transfer ratio Short circuit reverse transfer impedance Open circuit reverse transfer admittance Short circuit reverse current transfer ratio

Here, Z and Y are the transmission line impedance and line charging admittance respectively. Vs, Vr and Is, Ir are the voltage and current vectors at the respective buses.

The apparent power and the current at the receiving end of the transmission line can be calculated as

Sr = VrQr) *

(Sr) *

Pr - jQr Pr - jQr

VrL- Sr

where Pr and Qr are the active and reactive powers and Vr , dr are the voltage magnitude and voltage angles at the receiving end respectively.

From Eq. (1), the sending end voltage of the transmission line can be expressed as

VS\8S = A\aVr\8r + B\pIr\00 (4)

Here, A and B are magnitudes and a, b are the phase angles of the parameters A and B respectively.

After solving Eq. (4) using Eq. (3), the receiving end voltage can be derived as

-Vscosd±\J(VScosd)2 - 4Acosa(PrBcosb + QrBsinb) r 2A cos a

The real and non-zeros values of Eq. (5) can be obtained by equating determinant of this equation to greater than zero, i.e.

(Vs cos d)2 - 4A cos a(PrBcos b + QrB sin b) > 0 (6)

Based on this, the condition that should satisfy to operate power system securely to avoid voltage collapse condition can be expressed as

4A cos a(PrB cos b + QrB sin b)

(Vs cos d)2

From this, the line collapse proximity index for each of the transmission lines can be calculated using

4A cos a(PrB cos b + QrB sin b)

LCPI — -

(Vs cos S)2

For secured operation, the value of LCPI must be less than 1 (one). In Eq. (8), B sin b represents the resistance of a transmission lines and the first part of Eq. (8) resembles the voltage drop due to active power flow whereas the second part resembles the voltage drop due to reactive power flow in the transmission line. Pr and Qr are the values of the active and reactive powers at the receiving end of the line. If the direction of these powers is in the same direction, then, these two parts are additive whereas in opposite direction, then these parts are subtractive. From this, it can be identified that, the proposed

LCPI is prepared based on the magnitudes and directions of the active and reactive power flows in transmission lines. The value of LCPI is close to unity which means that, the line is ready to collapse condition. For a system, A, B, a and b values are predefined and P, Q and d at buses can be evaluated easily using load flow procedure, then the LCPI value for each of the transmission lines can be calculated easily. Thereby the security of a system can be predicted more precisely with less computational effort.

2.2. Generator shift factor

There are numerous methods in the literature to analyze security of a given power system in terms of power flows and bus voltage magnitudes when a contingency occurs. The recent studies concentrate in finding the effect of generators active power generation on power flow in interconnected transmission lines. There are some of the linear sensitivity factors which are formulated to show the approximate variation of power flow in lines for a change in generation. Based on this, the generation shift factor for a line T with the effect of generation at bus-i can be expressed as [24]

OSF„ =

where DPFl is the change of power flow in line-l for DPGi generation change at bus-i. In this study, the shift of generation of a generator compensated by the generation at slack bus, whereas other generators are fixed at constant values.

In general, the power flow in each of the transmission lines after generation shift (PFl) can be calculated as

PF, = PG0 + GSFiiDPGi; 81 = 1, 2,..., nl

Here, (PF°) is the power flow in each of the transmission lines before generation shift, and 'nl' is the total number of transmission lines.

From this analysis, it can be identified that, the shift of generation at a generator affects the governor action on other generating units in an interconnected system. The effect of generation change at each of the generators is calculated in each of the transmission lines using generator shift factors and power flows given in Eqs. (9) and (10) respectively. Finally, the generation shift of a generator which has highest impact on power flows can be identified as the most sensitive one.

3. Modeling of unified power flow controller

The UPFC is one of the most versatile FACTS devices. This device is a combination of the series and shunt static converters, which are connected through a common DC link provided by a dc storage capacitor. It allows bidirectional flow of real power between the shunt output terminals of STATCOM and series output terminals of SSSC. The series connected converter injects a voltage with controllable magnitude and phase angle in series with the transmission line, therefore providing real and reactive power to the transmission line. The shunt-connected converter provides the real power drawn by the series branch and the losses and can independently provide

reactive compensation to the system. The basic configuration with two voltage source converters in UPFC is shown in Fig. 1. [25-28].

The basic representation of UPFC with two controllable voltage sources can be shown in Fig. 2. The voltage magnitudes and phase angles of these two converters are controlled using the two converter coupling transformers. The series converter transformer has leakage reactance of Xse. To incorporate UPFC in a given system, one transmission line connected between two buses is required. For the sake of explanation, UPFC is connected in a line-l connected between buses i and j. For this, the voltage magnitude at UPFC connected buses can be expressed as Vi\èi and VjZdj.

The voltage injected by the series connected controllable voltage source can be expressed as

VZ = Vse\0„ (11)

where ' Vse' and ' 6se' are per unit voltage magnitude and respective voltage angle of the series connected voltage source. These parameters are operating with the following controllable limits:

0 6 Vse

and 0 6 hse 6 hm

The final mathematical model of UPFC can be obtained by combining the developed series and shunt connected voltage source models. The final model of UPFC is shown in Fig. 3. The obtained power injections at UPFC connected buses can be expressed as

pUPFC = Q:Q1ViVeB

, Sin(hse - Si,

gUPFC ^-ViVseßse COs(Si - 6 Sl

1.02 VjVseBse

Sin(6se

Figure 1 Basic configuration of UPFC.

Figure 3 Combined mathematical model of UPFC.

= - VjVseBse Cos(Sj cos(Sj —

= VjVseBse

The developed UPFC mathematical model should be incorporated in a given system to analyze the effect of the same. For this, the conventional Newton-Raphson load flow method is modified by updating the Jacobian and power mismatch equations at the UPFC connected buses [27]. The network performance equation in the presence of UPFC can be expressed as

DP " pUPFC ' H N

AQ. + qUPFC , J L +

3.1. Optimal location

To enhance the security of power system in the presence of FACTS, it is necessary to place the UPFC in an optimal location. To identify an optimal location of UPFC, in this paper, a methodology based on line overload sensitivity index (LOSI) is developed. The proposed LOSI is evaluated for each of the transmission lines under contingencies. The LOSI value for a line ' i' is calculated by adding the power flow in a line-i under the considered ' Nc' number of contingencies. The expression used to calculate LOSI for a given based load condition is given as [29]

losiBl =

where SN, S]

are the power flows under contingency and maximum power flows in line-i.

The optimal location of UPFC is chosen in such a way that, it can sustain its controlled operation under variable load conditions. The system LOSI value is calculated using three different load conditions. Out of which, one is base load (BL), increased load (IL) and decreased load (DL) conditions. The increased/decreased load conditions are obtained by increasing both active and reactive demands by 5% from the based load condition. The overall LOSI value for line-i can be expressed as

LOSh =

losiBl + losiIl + losiDl

where LOSlf and LOSlfL are the LOSI values at increased and decreased load conditions.

After this, the transmission lines are ranked based on their LOSI values. UPFC is placed in top ranked lines and the sending end of the respective line considered being the common bus.

4. OPF problem formulation

Optimal power flow (OPF) gives the solution for a power flow problem by means of optimal settings of the system control parameters to meet the power demand either by minimizing or by maximizing a predefined objective function while satisfying system constraints. The simple form of this problem can be expressed as

minimize/maximize J(x, u)

Subjected to g(x, u) — 0; h(x, u) 6 0

Here, 'g' is the set of equality constraints and 'h' is the set of inequality constraints. These constraints are formulated using a set of dependent and independent variables. The brief details regarding these variables can be explained as follows:

i. All dependent variables such as active power generation at slack bus (Pg,slack), reactive power generation at generator buses (Qg), voltage magnitude at load buses (VL) and power flow in transmission lines (Si) constitute a state vector (x).

ii. All independent variables such as active power generation at generator buses other than slack (PG), voltage magnitude at generator buses (VG), tap settings of the tap-changing transformers (T) and reactive power injected by the shunt compensators (Qsh) constitute a control vector (w).

The consolidated expressions for these control and state vectors can be given as

uT — [PG2; • • • ; PGng ; VG1 ; ... ; VGng ; Qsh1 ; • • • ; QshNc; Tl; ••• ; TNT] xT — [PG1, VL1, ••• , VLnl , QG1 , ••• , QGNG , Sh , ••• , Slnl]

Here, 'NG', 'NC', 'NT', 'NL' and ' nl' are the total number of generators, shunt compensators, tap-changing transformers, load buses and transmission lines respectively.

4.1. Objectives formulation

To show the effectiveness of the proposed OPF problem, in this paper, two objectives such as generation fuel cost and system severity functions are formulated. The respective mathematical expressions for the considered objectives are given as follows.

4.1.1. Generation fuel cost

In power system operation and control, it is necessary to meet the power demand with lowest cost of generation. For this, in OPF, the generation fuel cost function should be minimized while satisfying system constraints. The generators in a given system are characterized by using a second order quadratic equation and this can be expressed as

Jcost — YJ(a'P2G, + b,PGi + c) $/h (21)

where ai, bi, and ci are the fuel cost coefficients, and PGi is the active power generation at bus-i.

4.1.2. System severity function

In today's ever increasing demand on large and complex power system, it has become a critical issue to operate the power system with enhanced security limits. Hence, it is necessary to operate the power system in such a way that, the power flow in transmission lines and voltage magnitude at buses should be within limits to increase the system security. A technical objective formulated using transmission line loadings and voltage violations in a given system can be expressed as

nl / S \ 2m Nbus I yref _ v \ 2n

Jseventy — W^ (Jm^ + Wv^—r (jf-) (22)

where Wl and Wv are the weight coefficients related to line loadings and voltage violations and the values of these coefficients must satisfy the condition Wl + Wv — 1 (hence, Wi — Wv — 0.5 is considered). St and S™ are the present and maximum limit values of apparent power flow in line-i, and Vj, Vjref are the present and the reference values of the voltage magnitudes at bus-j. 'm' and ' n' are the two coefficients used to penalize the overloadings and voltage violations and each is considered as ' 2'.

For the sake of explanation, the first part of this expression can be treated as over load index (OLI) and the second part can be treated as voltage violation index (VVI) (without weight coefficient).

4.1.3. Multi-objective function

To show the effectiveness of the proposed MO-OPF problem, in this paper, an objective function is formulated by combining generation fuel cost and system severity functions. The respective mathematical expression for the formulated objective is given as follows:

Jobjective X JCos t ^ W2 X Jseverity (23)

where Jcos t, and Jseverity are the generation fuel cost and system severity functions, and W1 and W2 are the weights assigned to the objective functions.

4.2. Constraints

The proposed OPF problem is solved while satisfying a set of equality and inequality constraints explained as follows.

4.2.1. Equality constraints

These constraints are simply load flow equations solved and satisfied in conventional load flow method. The active and reactive power balance expressions in load flow can be given as

Pgi - Pm — Yj Vj I V-| | Y| cos(0- + d- - di) (24)

QGl- Qdi — El Vj| V-II Y-I sinj d- - di) (25)

where PGi, QGi and PDi, QDi are the respective active and reactive power generations and loads at ith bus, Nbus is the total number of buses, and | Yj- |, dy are the bus admittance magnitude and its angle between ith and jth buses.

4.2.2. Inequality constraints Generator constraints:

Voltage magnitude limit at vj?" 6 VGl 6 Viax 8i 2 NG generator buses:

Active power generation limit p™n 6 PGl 6 Pgax 8i 2 NG

at generator buses: i i

Reactive power generation Q™n 6 QG. 6 Qmax 8i 2 NG

limit at generator buses: i i

Other constraints:

Tap setting limit at tap- T™n 6 T 6 Tmax 8i e NT changing transformers:

Reactive power compensation Q™n 6 Qsh- 6 QSax 8i e NC limit by shunt compensators:

Security constraints:

Power flow limit in transmission Slt 6 S^ i 2 nl lines:

Voltage magnitude limit at load v™n 6 V 6 Vmax 8i 2 NL buses:

UPFC limits

The operating limits of control parameters related to UPFC can be given as follows:

0 6 Vse 6 VT; 0 6 dse 6 0T; 0 6 Xse 6 0 6 Qhi

Here, VT, 0™, XT and Qmax are considered to be 0.1 p.u., 360°, 0.1 p.u. and 0.1 p.u. respectively.

Here, PG, VG, T, Qsi inequality constraints are self restricted constraints and can be satisfied forcibly within the OPF problem, whereas the remaining three constraints and active power generation at slack bus are non-self restricted constraints and these can be handled using penalty approach. With this, the generalized form of the OPF problem can be defined as

Javg(x, U) = J(X, U) + Rp(PG, — P™ ") NL

+R^{Vm — Vmm ")2

+ RqYsiQGm — QZ") 2

m=1 nl

+ R^(Slm — S^0) 2 (26)

where Rp, Rv, Rq and Rs are the penalty factors related to the constraints. The limit values can be considered as

Jim . I x ; x > x

Xmin. x < xmin

Here 'x' is the value of PG1, Vm, and QGm.

5. Improved teaching learning based optimization (ITLBO) algorithm

The conventional Teaching Learning Based Optimization (TLBO) [30,31] algorithm is one of the nature inspired algorithms and developed based on the effect of influence of teacher on students in a class. In general teacher is rich in knowledge and tries to influence the students to learn the subject/concepts. In general, after completion of teachers lecture, students prepare the concepts through discussions among themselves. Due to this, the outcome of the students does not reflect the teacher knowledge completely. To overcome this difficulty, a new improved teaching learning based optimization (ITLBO) algorithm is proposed in this work. Before explaining the implementations of the proposed algorithm the important phases in the existing TLBO algorithm are explained as follows.

5.1. Teacher phase (Existing)

The teacher always tries to bring the knowledge of his/her students up to his/her knowledge. But in real time, this process may not yield good result; this is because of the different parameters such as learners knowledge, concentration, aptitude and commitment to learn the concepts, and also some times because of the improper lecture delivered by the teacher. From this, it can be consolidated that, a teacher can able to increase the mean level of the learners knowledge rather the individual learners knowledge.

5.2. Learner phase (Existing)

Each of the students always tries to improve his/her knowledge by participating in discussions with his/her friends. For example, a student wants to interact with one of his/her friends to share the knowledge. At this stage there are two possibilities. One is that, student gains the knowledge, provided his friend has more than his knowledge. Second is that, no knowledge is gained, provided his friend has less knowledge than his knowledge. Due to which, learners will take more time to gain full knowledge.

The proposed ITLBO algorithm overcomes the difficulties in teaching and learning phases of conventional TLBO algorithm. The details regarding the modified teaching and learning phases are explained as follows.

5.3. Teaching phase (Proposed)

The existing teaching phase consists one teacher for learners, but the proposed teaching phase consists more number of teachers for learners. Because of this, the student who has poor knowledge gets improvement rapidly than the student of the conventional teaching phase. In fact, the real time problem needs to evaluate many nonlinear functions, with the conventional teaching phase, getting an optimal solution in less number of iterations which is difficult and sometime leads to poor convergence. To overcome this, more number of teachers are defined and all students are divided into several groups based on their knowledge levels. After this, for each of these groups, a teacher is assigned to teach the students. With this implemen-

Figure 4 Flowchart of the proposed ITLBO algorithm.

Figure 5 Variation of LCPI values.

Table 1 Average GSF values for generators.

S. no Generator bus no Average GSF value

1 2 0.02876

2 5 0.0777

3 8 0.06684

4 11 0.05199

5 13 0.03166

tation, a teacher can concentrate more on their students to improve the knowledge by delivering the lecture according to the student understanding.

5.4. Learning phase (Proposed)

In existing learning phase, student gains the knowledge through discussions with his/her friends, but in the proposed learning phase, student participates in discussion not only with his/her friends but also with his/her teacher. Due to which, one can gain the knowledge in less time. In real time, the modification of control parameters in next stage reflects the best set of control parameters in earlier stage. With this, the convergence is enhanced with good optimum result.

Implementation procedure for the proposed ITLBO for power system optimization problem is summarized as follows.

The system control parameters such as active power generation (PG) and voltage magnitudes (VG) at generator buses, tap settings of tap-changing transformers (T) and shunt compensators (Qsh) are generated randomly between their limits for initial number of population (N).

P1 P1 V1 V1 T1 T1 Q1 Q1

PG1; ■ ■ ■ ; P Gng ; v G1 ; ■ ■ ■ ; V GnG ; T 1 ; ■■■ ; T NT; Qsh1 ; ■■■ Qs!

■ ;PGng;

■ ; VG ;

' gNG '

shNC s/Inc

QN ; Qshi ; ■

Each of the population is updated in line and bus data and the power flow problem is solved using Newton Raphson load flow solution. The formulated objective function values and the respective fitness values are evaluated for each of the populations using

fit, — —J-8i — 1,2, • • • , N

1 ^ Jobjective

The evaluated objective functions and respective fitness values given in the form of vectors can be expressed as

J1 fit1 ' J2 fit2

JN fitN

where J1, J2, • • • , JN and fitj, fit2, • • • , fitN are the respective objective function and fitness values of each of the population. Select the (T) population as the initial number of teachers randomly and treat the remaining population as the learners provided T < N.

Ji; Js-

; JT-1; JT; JL; JL+1; JL+s;

To assign the learners to each of the teachers, a criteria based on their fitness values is formulated and this can be expressed as

fiL P fitn > fitm+1 = 1; 2; •

, T & 8n = L; L + 1;

, N (30)

If this condition is satisfied then assign the learner to teacher ' m' else not assign this learner to teacher ' m + 1' and repeat the same process for all learners to form 'D' number of groups (i.e. Teachers group).

Figure 6 Variation of voltage magnitudes under contingency condition(s).

Figure 7 Variation of power flows under contingency condition(s).

After this, calculate the mean value of all control variables in each of the groups (MeanD) and using this, the teaching factor (TF) in ith iteration can be calculated as

Mbest,Di

where MbestDi is the position of the teacher in group 'D'.

Using this teaching factor, the updated control variables in iterative process are calculated as

Xnew,i Xi ^ rand. (Xteacher, Di — (TF x MeanDi)) (32)

In each group, learner interacts randomly with other learners and teacher to enhance his/her knowledge. Learner increases knowledge through discussions with other learners and teacher. The mathematical expressions used to update the knowledge of a learner can be given as

Table 2 SCOPF results of generation fuel cost under normal and contingency conditions.

S. no Control parameters Normal condition Outage condition

Existing TLBO Proposed ITLBO Lines Generator Both lines & generator

1 Real power generation (MW) Pg1 176.6828 178.2065 129.7393 191.209 128.9982

PG2 48.4953 47.6668 65.2268 51.5121 74

PG5 22.2098 21.237 25.3845 0 0

PG8 21.6529 21.9448 35 17.5482 32.113

PG11 11.6891 11.6916 21.1808 21.1356 24.9581

PG13 12 12 19.6162 14.4197 39.1755

2 Generator voltages (p.u.) VG1 1.07 1.07 1.07 1.0451 1.0664

Vg2 0.9952 1.0545 1.0589 1.0232 1.0321

Vg5 1.029 1.0215 1.0303 1.0083 1.0094

Vg8 1.0331 1.0361 1.0635 0.9777 0.9727

Vg11 1.07 0.9927 1.0679 1.0222 1.0316

VG13 1.0684 1.0548 1.0602 1.063 1.0523

3 Transformer tap setting (p.u.) T6-9 0.9928 0.9723 1.0132 1.0851 1.0791

T6-10 1.0483 1.0473 0.992 1.0073 0.9426

T4-12 0.9954 1.0217 1.0296 0.9988 1.0479

T28-27 0.9747 0.9856 1.017 0.9804 1.046

4 Shunt compensators (MVAr) QC, 10 25.4898 23.4276 21.0967 20.0176 17.9769

QC, 24 14.7325 15.0868 13.0522 20.3955 14.9654

5 Total generation (MW) 292.7299 292.7467 296.1475 295.8244 299.2448

6 Generation fuel cost ($/h) 801.8566 801.5371 844.0512 838.7347 905.0378

7 Severity index 0.93906 0.983441 2.648297 1.643743 3.322279

8 Total power losses (MW) 9.3299 9.3466 12.7475 12.4244 15.8448

9 OLI value 1.878027 1.966828 5.296475 3.28745 6.644328

10 VVI value 0.000109 5.42E-05 0.000119 3.49E-05 0.00023

11 Time (s) 27.3847 18.2839 36.9283 26.2119 43.2635

Xnew,i — X + rand1.(X, - Xj) + rand2.(X, - Xteacher)8if f(Xi)

< f(X) (33)

Xnew,i — X + rand1.(Xj - Xi) + rand2.(Xteacher - X,)8iff(Xi)

> f(X) (34)

At last, using these updated control parameters, evaluate the objective function and fitness values. Repeat this process for a predefined number of iteration or termination criteria is reached.

5.5. Flowchart of the proposed ITLBO algorithm

The flowchart of the proposed ITLBO algorithm is given in Fig. 4.

6. Results and analysis

To show the effectiveness of the proposed methodology, IEEE-30 bus system with forty-one transmission lines, six generators, four tap-changing transformers and two shunt compensators is considered [30]. The entire analysis is divided into the following three scenarios:

Scenario-1: Security analysis under contingency conditions. Scenario-2: Security analysis using optimal power flow. Scenario-3: Security enhancement with UPFC.

6.1. Scenario-1: Security analysis under contingency conditions

For this system, the LCPI value for each of the transmission lines is calculated using Section 2.1. Here, LCPI values are not calculated for seven lines i.e. lines 11, 12, 15 and 36 are transformer connected lines; lines 13, 16 and 34 isolate the generators and load from system. Hence, for this system, LCPI values for thirty-four transmission lines out of forty-one are calculated and the respective variation is shown in Fig. 5. To analyze the system security under transmission line outage condition, the top 15% LCPI value lines (i.e. lines 20, 14, 1, 6, 29) are removed from the system to create transmission line(s) contingency condition.

For this system, GSF value for each of the generators is calculated using Section 2.2. Here, GSF value for generator-1 is not calculated as it is slack generator. Hence, for this system average GSF values for five generators out of six are evaluated and are shown in Table 1. From this table, it is identified that, the average of GSF values is high for generator at bus-5, which implies, the generation shift at this bus affects the power flow in most of the transmission lines when compared to the power flow under normal condition. Here, the top 15% average GSF valued generator i.e. generator-5 is removed from the system to create generator(s) contingency condition.

Finally, to analyze the security under contingency conditions, transmission line(s) and/or generator(s) outage condi-

Figure 8 Convergence characteristics of generation fuel cost under normal and contingency conditions.

Figure 9 Variation of voltage magnitudes of generation fuel cost under normal and contingency conditions.

tions are simulated individually or simultaneously. Due to page restrictions, the graphical variation of voltage magnitude at buses and power flow in transmission lines are shown in Figs. 6 and 7 respectively.

From this Fig. 6, it is identified that, voltage magnitude at the buses near by the contingency lines is decreased due to the lack of reactive power support through transmission lines. Similarly, outage of generator affects the bus voltages and bus-5 is no longer a generator bus under generator contingency condition, and also, the voltage magnitude at this bus is decreased when compared to normal condition. At last, simultaneous outage affects more on bus voltages when compared to other conditions.

From Fig. 7, it is identified that, lines 2, 3, 4, 8, 18, 19, 21, 22 and 23 are overloaded under the outage of lines 1, 6, 14, 20 and 29; these are because of the nearer connections to the critical lines. Similarly from the numerical results, it is identified that, lack of generation at bus-5 compensated by the slack generator. Due to which, the power flow in line-1 and 2 is

Figure 10 Variation of power flows of generation fuel cost under normal and contingency conditions.

Table 3 SCOPF results of system severity function under normal and contingency conditions

S. No Control parameters Normal condition Outage condition

Lines Generator Both lines & generator

1 Real power generation (MW) PG1 74.8458 72.7798 163.5706 128.8717

PG2 80 80 49.9487 77.5815

PG5 50 50 0 0

PG8 35 35 31.7327 35

PG11 23.8402 30 18.7654 30

PG13 23.8501 21.3812 29.8113 29.2725

2 Generator voltages (p.u.) Vg1 1.0368 1.07 1.0512 1.0333

Vg2 1.0265 1.0601 1.0284 1.0423

Vg5 1.0138 1.0285 1.0452 0.9867

Vg8 1.0108 1.0313 0.9801 0.9517

Vg11 1.011 1.0343 1.0132 0.9883

VG13 1.0178 1.0586 1.0278 1.0453

3 Transformer tap setting (p.u.) T6—9 1.0074 0.9981 1.0524 0.9865

T6—10 1.0084 1.0022 1.0467 0.9996

T4—12 0.9943 0.9938 0.9734 0.9818

T28—27 0.9729 0.9624 0.9658 1.0568

4 Shunt compensators (MVAr) QC, 10 23.0615 28.7569 22.4963 26.4437

QC, 24 11.0729 10.9897 20.5813 23.0376

5 Total generation (MW) 287.5361 289.1609 293.8287 300.7257

6 Severity function value 0.3396 1.2223 1.1175 3.1234

7 Generation fuel cost ($/h) 924.4158 935.7118 846.8249 906.8274

8 Total power losses (MW) 4.1361 5.7609 10.4287 17.3257

9 OLI value 0.6793 2.4446 2.235 6.2464

10 VVI value 3.76E—06 0.0001 0 0.0003

11 Time (s) 14.5764 31.2837 23.7261 39.9481

Figure 11 Convergence characteristics of system severity function under normal and contingency conditions.

S 1.02

Ü 0.96

-S-Lines outage condition

-0~Both Outage condition

9 11 13 15 17 19 21 23 25 27 29 Bus number

Figure 12 Variation of voltage magnitudes of system severity function under normal and contingency conditions.

increased by 11.9087 MVA and 5.6108 MVA when compared to normal condition. Similarly, to meet the load at bus-5, the power flow in lines 5 and 8 is increased by 2.7868 MVA and 3.8061 MVA when compared to normal condition. Finally, under simultaneous transmission line(s) and generator(s) outage conditions lack of generation at bus-5 compensated by the slack generator. Due to which, the power flow in lines-2, 4 and 7 is increased by 183.6411 MVA, 167.6007 MVA and 71.6352 MVA when compared to normal condition. Similarly, to meet the load at bus-5, the power flow in lines 5 and 8 is increased by 4.2325 MW and 35.1326 MW when compared to normal condition.

From this analysis, it is concluded that, the outage of transmission lines affects more on power flows and outage of generator affects more on voltage magnitudes; similarly, simultaneous outage of transmission line(s) and generator(s) affects both power flows and voltage magnitudes. If this is the case, sometime, the system may reach the collapse condition. To avoid this, it is necessary to set the control parameters optimally rather than heuristically. For this, it is necessary to

perform optimal power flow rather than normal power flow. The complete discussion about the solution methodology is described in the next scenario.

6.2. Scenario-2: Security analysis using optimal power flow

The SCOPF results with the proposed ITLBO algorithm for the considered generation fuel cost under normal and contingency conditions such as individual or simultaneous outage of transmission line(s) or generator(s) are shown in Table 2.

From this table, under normal condition, it is identified that, with the proposed ITLBO algorithm, the generation fuel cost is decreased by 0.3195 $/h when compared with existing TLBO algorithm. Similarly, from the convergence characteristics under normal condition given in Fig. 8(a), with the proposed method, the iterative process starts with good initial value and reaches final best value in less number of iterations when compared to existing method. From Table 2, it is observed that, in lines outage condition, the total generation and thereby the total transmission power losses are increased, and at this condition, the total generation fuel cost value is increased by 42.5141 $/h when compared to normal condition. It is also observed that, in generator outage condition, the total active power generation and thereby the total transmission power losses, generation fuel cost values are increased when compared to normal conditions. It is also identified that, in simultaneous outage of lines and generator condition, total active power generation and thereby the losses are increased when compared to other conditions.

The convergence characteristics for the normal and contingency conditions are shown in Fig. 8(a)-(d). From these figures, it is identified that, the initial value of the iterative process and the number of iterations taken for final convergence are increasing from normal condition to simultaneous lines and generator outage condition.

The variation of voltage magnitude under normal and contingency conditions is shown in Fig. 9. From this figure, it is identified that, generator-5 outage and simultaneous outage affect more on voltage magnitudes, this is because of lack of reactive power support by generator-5. It is also observed that, the voltage magnitude at bus-5 is decreased under outage conditions, because of lack of generation at this bus.

The power flow variation in transmission lines under normal and contingency conditions is shown in Fig. 10. From this figure, it is identified that, no power flow violated the maximum limits. It is also observed that, simultaneous outage of lines and generator affects more on power flows than the remaining conditions.

The SCOPF results with the proposed ITLBO algorithm for the considered system severity function under normal and contingency conditions such as individual or simultaneous outage of transmission line(s) or generator(s) are shown in Table 3.

From this table, it is observed that, in outage of transmission lines condition, the total generation and thereby the total transmission power losses are increased, and at this condition, the severity function value and total generation fuel cost values are increased by 0.8827 and 11.296 $/h when compared to normal condition. It is also observed that, in generator outage condition, the total active power generation and thereby the total transmission power losses are increased when compared

Figure 13 Variation of power flows of system severity function under normal and contingency conditions.

35 m—I-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-r

0 _i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

Line number

Figure 14 Variation of LOSI values under different load conditions.

Bus voltage magnitude variation

1.1 -1-1-1-!-!-1-1-1-!-1-1-1-1-r

0.98 -1-1-1-1-1-1-'-'-1-1-1-1-1-*—

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Bus number

Figure 15 Variation of voltage magnitude with UPFC.

to normal and line outage conditions. In generator outage condition, the system severity function value is increased by 0.7779 and decreased by 0.1048 when compared to normal and line outage conditions. It is also identified that, in outage of lines and generator condition, total active power generation and thereby the losses are increased when compared to generator outage condition and these values are increased when compared to other conditions, whereas the generation fuel cost and system severity function values are increased when compared to generator outage condition.

The convergence characteristics for the normal and contingency conditions are shown in Fig. 11. From this figure, it is identified that, the initial value of the iterative process and

the number of iterations taken for final convergence are increasing from normal condition to simultaneous lines and generator outage condition.

The variation of voltage magnitude under normal and contingency conditions is shown in Fig. 12. From this figure, it is identified that, generator-5 outage affects more on voltage magnitudes, this is because of lack of reactive power support by generator-5. It is also observed that, the voltage magnitude at bus-5 is decreased in generator outage conditions, because of lack of generation at this bus.

The power flow variation in transmission lines under normal and contingency conditions is shown in Fig. 13 From this figure, it is identified that, simultaneous outage of lines and generator affects more on power flows than the remaining

Line power flow variation

140 -1-1-1-1-«-1-1-1-1-«-1-1-1-1-«-1-1-r

Q _I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_ T _I_I_I_

1 3 5 7 9 11 13 15 17 19 2123 25 27 29 3133 35 37 39 41 Line number

Figure 16 Variation of power flows with UPFC.

conditions. In line outage condition, most of the transmission lines are operating nearer to its MVA limit.

From this analysis, it is identified that, optimal power problem with generation fuel cost and system severity functions minimizes the line loadings and bus voltage violations. As the considered objectives are contradictory in nature, i.e. minimization of one of the objectives increases the value of the other objective and vice versa. From this, it is also concluded that, OLI value is less in severity function minimization rather than that of generation fuel cost minimization. So, the enhancement of security is obtained in the presence of UPFC described in next scenario. It is also concluded that, simultaneous outage of lines and generators is more severe than the individual outages. Hence, the further analysis is performed for normal and simultaneous outage conditions only.

6.3. Scenario-3: Security enhancement with UPFC

At first, an optimal location to install UPFC is identified using LOSI procedure described in Section 3.1. From this, the LOSI values under base load, increased load and decreased load

conditions are calculated. Due to page restrictions, the variation of overall system LOSI value for each of the transmission lines is shown in Fig. 14. From this figure, it is identified that, highest rank is given to the line-1 connected between buses 1 and 2. Hence, this line is considered as the most suitable location to install UPFC, here bus-1 is considered to be the common bus for UPFC shunt and series converters. From this, it is assumed that, the further analysis with UPFC is performed by placing in this location. Further, this scenario is divided into the following two cases:

Case-1: Effect of UPFC on system parameters.

Case-2: Severity analysis with UPFC under normal and

contingency conditions.

6.3.1. Case-1

In this case, the effect of UPFC on system parameters such as bus voltage magnitudes, line power flows and system losses is analyzed by varying device control parameters. The variation of bus voltage magnitudes is shown in Fig. 15. From this figure, it is identified that, voltage magnitude variation is high at bus-2, because, this bus is UPFC receiving end connected bus.

The variation of apparent power flow in transmission lines for the variation of UPFC control parameters is shown in Fig. 16. From this figure, it is identified that, power flow variation is high in device connected line i.e. line-1 when compared to the power flow variation in other lines.

The variation of active power losses in a system is shown in Fig. 17. From this figure, it is identified that, that losses are increasing as the Vse is increasing from 0 p.u to 0.1 p.u. It is also observed that, minimum losses are obtained when Vse is at 0.1 and hse is at 80 deg, similarly, maximum losses are obtained when Vse is at 0.1 and hse is at 120 deg.

From this analysis, it is concluded that, the system parameters can be controlled by controlling the device parameters. Finally, if these device control parameters are optimally controlled, then maximum benefit can be achieved. For this, the OPF problem in the presence of UPFC is solved while satisfying system constraints and device limits. The complete methodology is described in case-2.

6.3.2. Case-2

The SCOPF results for the generation fuel cost and the system severity objectives under normal and simultaneous outage condition for without and with UPFC are shown in Table 4. From this table, it is identified that, with UPFC, while minimizing severity function under normal condition, the OLI value is decreased by 0.017129 and consequently severity function is decreased by 0.008546 when compared to without device. It is also observed that, because of the redistribution of power generations with UPFC, the total power generation and thereby the total power losses are reduced. At this condition, the generation fuel cost is reduced by 40.4621 $/h. Further, the generation fuel cost with UPFC is validated with the existing literature [32]. In this, the generation fuel with UPFC is 804.0468 $/h, but with the proposed method, this cost is 801.2868 $/h. The effectiveness of UPFC under contingency conditions reflects the same type of analysis presented for normal condition. Here under contingency condition, the OLI

O 40 80 120 160 200 240 280 320

ese(deg)

Figure 17 Variation of active power losses with UPFC.

Table 4 SCOPF results of system severity function with UPFC under normal and contingency conditions.

S. Control parameters Generation fuel cost System severity function

no Normal condition Contingency condition Normal condition Contingency condition

Without With Without With Without With Without With

device UPFC device UPFC device UPFC device UPFC

1 Real power Pg1 178.2065 175.6312 128.9982 128.9587 74.8458 60.55224 128.8717 130.0781

generation (MW) PG2 47.6668 48.45219 74 78.52984 80 79.01612 77.5815 80

PG5 21.237 21.33432 0 0 50 50 0 0

PG8 21.9448 22.51908 32.113 32.61102 35 35 35 35

PG11 11.6916 12.57506 24.9581 27.21096 23.84023 24.37217 30 28.83878

PG13 12 12 39.1755 31.75134 23.85009 23.27694 29.2725 39.55849

2 Generator voltages VG1 1.07 1.07 1.0664 1.066585 1.0368 1.060364 1.0333 1.07

(p.u.) VG2 1.0545 1.058314 1.0321 1.028294 1.026501 1.051518 1.0423 1.055244

Vg5 1.0215 1.031152 1.0094 1.00038 1.013766 1.030585 0.9867 1.008182

VG8 1.0361 1.044296 0.9727 0.962906 1.010817 1.032608 0.9517 0.992254

Vg11 0.9927 1.062054 1.0316 1.058521 1.011002 1.017066 0.9883 1.051313

VG13 1.0548 1.066943 1.0523 1.054465 1.017849 1.023426 1.0453 1.053771

3 Transformer tap T6-9 0.9723 1.053216 1.0791 1.030927 1.007374 1.014235 0.9865 1.050841

Setting (p.u.) T6-10 1.0473 0.965538 0.9426 0.931889 1.00842 1.012596 0.9996 0.982444

T4-12 1.0217 1.021235 1.0479 1.044609 0.994309 1.00103 0.9818 1.000354

T28-27 0.9856 0.995016 1.046 0.9 0.972853 0.98452 1.0568 1.011129

4 Shunt compensators QC, 10 23.4276 19.06314 17.9769 19.6958 23.06153 26.04591 26.4437 29.73466

(MVAr) QC;24 15.0868 14.47542 14.9654 14.22137 11.07293 11.98987 23.0376 12.91414

5 UPFC control Vse, p.u — 0.09374 - 0.08293 - 0.09812 - 0.076285

parameters Xse, p.u - 0.02381 - 0.03272 - 0.014346 - 0.018903

h se, deg - 178.283 - 253.2839 - 288.6069 - 36.18119

Qse; p u - 0.03827 - 0.08372 - 0.071187 - 0.058338

6 Total generation (MW) 292.7467 292.5118 299.2448 299.0618 287.5361 272.2175 300.7257 313.4754

7 Severity function value 0.983441 0.941061 3.322279 3.010981 0.339634 0.331088 3.1234 2.625042

8 Generation fuel cost ($/h) 801.5371 801.2868 905.0378 901.0864 924.4158 883.9537 906.8274 964.6795

9 Total power losses (MW) 9.3466 9.111819 15.8448 15.66183 4.136124 3.965034 17.3257 13.32753

10 OLI value 1.966828 1.882016 6.644328 6.021898 0.679264 0.662135 6.2464 5.250019

11 VVI value 5.42E-05 0.000105 0.00023 6.35E-05 3.76E-06 2.03E-06 0.0003 6.41E-05

Figure 18 Convergence characteristics of system severity function with UPFC under normal condition.

Figure 19 Convergence characteristics of system severity function with UPFC under contingency condition.

Table 5 Multi-objective OPF results with UPFC under normal and contingency conditions.

S. no W1 W2 Normal condition Contingency condition

Without device With UPFC Without device With UPFC

Cost ($/h) Severity Cost ($/h) Severity Cost ($/h) Severity Cost ($/h) Severity

1 0.9 0.1 809.8275 0.9867 808.0169 1.095 915.2738 4.7183 914.1723 4.8877

2 0.8 0.2 810.7332 0.9188 809.9701 0.9786 918.3845 4.6928 917.9283 4.7182

3 0.7 0.3 812.1652 0.8461 811.2832 0.8986 921.8394 4.6428 919.2837 4.6884

4 0.6 0.4 815.1772 0.796 814.5321 0.8254 924.7475 4.5827 921.8293 4.6173

5 0.5 0.5 820.2884 0.7442 822.2983 0.7754 926.9384 4.5482 925.8127 4.5629

6 0.4 0.6 833.2124 0.6646 834.7786 0.6824 929.3485 4.5103 931.9464 4.5056

7 0.3 0.7 840.8991 0.6407 844.7786 0.6102 931.8762 4.4998 933.3984 4.4898

8 0.2 0.8 851.466 0.6172 854.1042 0.5658 934.2737 4.4896 935.7284 4.4724

9 0.1 0.9 855.562 0.6017 867.1958 0.5075 936.8474 4.4674 938.7383 4.4627

Figure 20 Pareto solutions obtained for multi objective function with UPFC under normal condition.

Figure 21 Pareto solutions obtained for multi objective function with UPFC under contingency condition.

value is decreased by 0.996381 and consequently the severity function value is reduced by 0.498358.

The convergence characteristics for without and with UPFC under normal and contingency conditions are shown in Figs. 18 and 19. From these figures, it is identified that, with UPFC, the iterative process starts with good initial value. Similarly, the final best value is obtained with increased number of iterations; this is because of solving NR load flow in the presence of UPFC.

To solve the proposed multi-objective function, the weights assigned to the objectives (W1, W2) in Eq. (23) are increased from 0.1 to 0.9 in steps of 0.1 in such a way that W1 + W2 = 1. For the proposed problem, there are nine different possibilities based on the weights distribution between the objectives. The obtained multi-objective OPF results with UPFC under normal and contingency conditions are shown in Table 5. From this table, it is identified that, based on the weights distributions between objectives, the respective solutions are obtained using the proposed ITLBO algorithm. It is also observed that, obtained results are further enhanced in the presence of UPFC.

To explain this briefly, under normal condition, If, W1 is 0.9 and W2 is 0.1 for generation fuel cost and severity functions, the obtained solution is 809.8275 $/h and 0.9867 similarly, for W1 is 0.1 and W2 is 0.9 for generation fuel cost and severity functions is 855.562 $/h and 0.6017. This clearly shows that, there is an increment of generation fuel cost by 45.7345 $/h and decrement of severity value by 0.385. Similar observations can be obtained for the remaining cases. From this, it is also observed that, best compromised solution is obtained when W1 is 0.5 and W2 is 0.5. From the results under contingency condition, it is observed that, the values of generation fuel cost and system severity functions are further increased when compared to the values obtained under normal condition. The similar observations as in the normal condition can be observed for contingency condition also.

The Pareto front solutions obtained for the considered nine cases under normal and contingency conditions are shown in Figs. 20 and 21. From these figures it is observed that, with UPFC the obtained Pareto confines the entire solution region when compared to without device. Finally, the system security

and economic benefits can be obtained using the proposed methodology.

- 0.02V,VseBse sin(0se - S,)

7. Conclusions

In this paper, a new methodology to analyze the system security under transmission line(s) and/or generator(s) outage conditions has been presented. To identify the system severity, a novel objective function based on transmission line loadings and bus voltage magnitude deviations has been presented. To optimize the generation fuel cost and the formulated system severity functions, a new optimization algorithm ITLBO has been proposed. The formulated OPF problem has been solved while satisfying system equality and in equality constraints. The proposed method has proven its effectiveness by starting iterative process with good initial value and reaches final best value in less number of iterations when compared to existing method. In voltage source based power injection model of UPFC, NR load flow incorporation procedures have been presented to enhance the system security with this device in optimal location through proposed LOSI analysis. Finally, it has been concluded that, the system security has been analyzed under contingency conditions, using optimal power flow and security has been enhanced in the presence of UPFC. The proposed methodology has been tested on standard IEEE-30 bus test system with supporting numerical as well as graphical results.

Appendix A.

NUPFC - \Vj

■=-1.02VjV„B„ sin(0se - Sj)

gpUPFC

NUPFC=\V¡\ = 0

■ = PU

NUPFC = \V\\ Njj V dV

The diagonal and off-diagonal elements of ' JUPFC' are

- V, VseBse sin(S, - dse)

Similarly, the diagonal and off-diagonal elements of ' Lu

A.l. Modifications in power mismatch equations

The power mismatch equations at the UPFC connected buses are modified as follows (here, superscript '0' represents the equations without UPFC):

- dp0 + PU

DQUpfc - DQ0 + QU

lUpfc = i Fi ^_= 0

Lji |V| dV, 0

- DP0 + Pu

- DQ,0 + QU

A.2. Modifications in Jacobian elements

The diagonal and off-diagonal elements of ' HUPFC' are

QpUPFC

UPFC _ i

HUPFC _

UPFC _ dl i

HUPFC _

dpUPFC

UPFC _ j

H^PFC _

UPFC _ j

HUPFC _

dpUPFC

- -0.02QU

= 1.02QU

■ = -QU

Similarly, the diagonal and off-diagonal elements of

'NUPFC' are

-wf-QU-

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S. Ravindra received his B.Tech. in Electrical Engineering from JNT University, Hyderabad & M.E. in Power Electronics & Indstrial Drives from Satyabhama University, Chen-nai. He is currently pursuing Ph.D. at JNT University, Kakinada. His research interest areas are FACTS controllers, power system security, and Power quality.

Chintalapudi V. Suresh is currently working in the Department of Electrical and Electronics Engineering, Vasireddy Venkatadri Institute of Technology, Guntur and is pursuing Ph.D. in the department of Electrical and Electronics Engineering, University College of Engineering Kakinada, Jawaharlal Nehru Technological University Kakinada, Kakinada, AP, India. His interests include, Computer Applications in Power Systems, Optimization Techniques, FACTS, Power System Analysis including FACTS devices and Power System Operation and Control.

Dr. S. Sivanagaraju is Professor in the department of Electrical and Electronics Engineering, University College of Engineering Kakinada, Jawaharlal Nehru Technological University Kakinada, Kakinada, AP, India. He completed his master's degree from Indian Institute of Technology, Khargpur, India, in electrical power systems. He completed his doctoral program in Jawaharlal Nehru Technological University Hyderabad, Andhra Pradesh, India. His interests include FACTS Controllers, Electrical Distribution System Automation, Optimization Techniques, Voltage Stability, Power System Analysis, and Power System Operation and Control.

Dr. V.C. Veera Reddy received his B.Tech. in Electrical Engineering from JNT University, Anantapur in 1979 & M.Tech. in Power System Operation & Control from S.V University Tirupati, in 1981. He received Ph.D. degree in Modeling & Control of Load Frequency using new optimal control strategy from S.V. University Tirutati, in 1999.