Optimal Allocation of Flexible AC Transmission System Controllers in Electric Power Networks
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Abstract
Due to increasing power demand, incorporation of prosumers, continuous expansion, competitive market and inherent limitations of alternating current, the management and operation of power system has become very complex. For economical, reliable and secure operation, the use of emerging technologies is unavoidable. Flexible AC transmission system (FACTS) is one of the emerging technologies which does not only solve the problems but also gives new directions in existing high voltage AC (HVAC) and high voltage DC (HVDC) power systems. However, allocation of FACTS controllers i.e., determination of optimal location, size, number and type of these devices with minimized cost is a difficult problem. This paper, in broader sense, discusses FACTS allocation for the solution of issues of power system. The benefits and objectives of optimal allocation of FACTS have been reviewed from view point of objective functions, decision variables, constraints and recent optimization algorithms.
Keywords
FACTS Economic dispatch Stability analysis Power oscillation dampingIntroduction

Technical issues Active/reactive power control, power factor, loop flows, congestion, power loss, capacity, loadability, thermal limits, dielectric limits, line contingencies, overloads, stability, power oscillations, sub synchronous resonance, power quality, interfacing energy storage, distributed generation interconnection, etc.

Economic issues Economic dispatch, spinning reserve, investment cost, operation and maintenance cost, power loss, corona energy loss, etc.

Environmental and regulatory issues Effects of electric field, effects of magnetic field, radio interference, audible noise, step, touch and earth voltage, safety of human, beauty of nature, visual impacts, deregulated market, continuous expansion, amount of land used, right of way, corona glow, ground currents and corrosion effects.
Transmission of AC power over long distances (Molburg et al. 2008) can be enhanced by improving thermal limits, realtime monitoring, uprating lines and power equipment. However, these reinforcements are only cautionary measures, some may be very costly and others may not a permanent solution. On the other hand, conventional controllers like fixed/switched resistors, capacitors, inductors, phaseshifting and tap changing transformers (Rao 2009) are electromechanical in nature, very slow and subject to wear and tear. Hingorani et al. (1988) proposed power electronic based custom power devices to solve the issues of distribution system. Later on, he introduced the concept of FACTS as a complete power system control and solution philosophy (Hingorani et al. 2000). The electric power industry switched from conventional controllers to FACTScontrollers when researchers claimed about the superiority of power electronics controllers. These controllers received the support of electrical equipment manufacturers (Habur and O’Leary 2004), utilities (Renz et al. 1999; Fardanesh 2002; Acharya et al. 2005), researchers (Farkoush et al. 2016; Doerksen 2013; Tang 2010) and research organizations (Helbing and Karady 1994). The operating parameters (i.e., voltage, current, phase angle) of a power system depend on the network parameters (i.e., inductance, capacitance, impedance). FACTS controllers can control both types of parameters.
FACTS enhance power transfer capacity (Canizares et al. 1998), loadability (Kazemi and Badrzadeh 2004; Singh et al. 2006; Duan et al. 2016), loading margin (Chang 2012), voltage stability (Obadina and Berg 1990; Mohamed and Jasmon 1996), transient stability (Chatterjee and Ghosh 2007; Xia et al. 2014), power oscillation damping (Farsangi et al. 2004; Magaji and Mustafa 2009) and utilization of existing network assets (Pilotto et al. 1997). FACTS reduce losses (Phadke et al. 2009; Yuvaraj et al. 2017), manage congestion (Wibowo et al. 2011) and improve power quality (Sarker and Goswami 2016). Moreover, FACTS can control voltage profile (Faried et al. 2009), convert DC to AC, deliver power more efficiently and reliably (KaramiHorestani et al. 2014), prevent cascaded outages, voltage collapse (Yorino et al. 2003) and blackouts (Moazzami et al. 2013). FACTS increase flexibility (Hingorani et al. 2000), security (Verma and Srivastava 2005) of the electrical system and satisfaction of consumer (Farhangi 2010). FACTS can interface with distributed generation (Aziz et al. 2013; Mahdad et al. 2009) like photovoltaic/solar parks (Shadmand and Balog 2014), wind forms (Wang and Hsiung 2011; Zhao et al. 2010), small hydro/hydrothermal units (De Oliveira et al. 2000) and energy storage systems (BahmaniFirouzi and AzizipanahAbarghooee 2014).

What types of FACTS controllers installed for better performance of power system?

How to economically estimate the number or quantity of FACTS devices

How to optimize the size, rating and capacity of FACTS controllers to be installed in practical networks for better performance?

Where in the power grid, FACTS should be placed, located or installed for better performance of whole of the power system?

How to coordinate dynamically and interact multiple FACTS in the network to better exploit FACTS devices to improve power system performance?

How to set or adjust the parameters of FACTS in the power system to assure stability, security limits and service continuity.
The problem of finding the best type of FACTS controllers with the best size and with best quantity installed at the best location(s) of the existing power system is referred as “optimal FACTS allocation problem”. This paper discusses, in a broader sense, the issues of national grid and reviews the literature of optimal allocation of FACTS controllers. Moreover, this paper reviews the literature from view point of objective functions in FACTS allocation problem, constraints, decision variables and recent optimization algorithms.
FACTS Controllers, Their Potential Benefits and Challenges
Static var compensator (SVC) can act as a source of reactive power as well as a sink of reactive power whose output is adjusted to exchange capacitive or inductive current (Hingorani et al. 2000; Song and Johns 1999). The primary purpose in a network is usually to control the voltage at weak points. Thyristor controlled series capacitor (TCSC) is a series type compensator and it is used to increase power transfer as well as to enhance system stability (Kazemi and Badrzadeh 2004). Thyristorcontrolled phase shifting transformer (TCPST) is a commonly used seriesshunt FACTS device (Kai and Kusic 1988). Through controlling the voltage phase angle, TCPST controls the power flow of the branch where it is located. It adds a quadrature component to the existing voltage in order to increase/decrease its phase angle.
Static synchronous compensator (statcom) is a solid state synchronous voltage source that is similar to a standard synchronous machine but without any rotating part (BarriosMartínez and ÁngelesCamacho 2017). Basically statcom consists of three main parts; voltage source converter (VSC), step down coupling power transformer and a control system. As compared to SVC, statcom produces a balanced set of sinusoidal voltage with very fast control over phase angle as well as amplitude (Song and Johns 1999). Static synchronous series compensator (SSSC) is also a VSC based converter that is serially connected to a transmission line through a transformer (Hingorani et al. 2000). As compared to TCSC, SSSC produces a balanced set of sinusoidal series voltage with faster control over phase angle as well as amplitude (Song and Johns 1999; Morsali et al. 2016). A unified power flow controller (UPFC) is capable of both supplying and absorbing real and reactive power. It consists of two voltage source converters (VSC). One of the two converters is connected in series with the transmission line through a series transformer and the other in parallel with the line through a shunt transformer. The dc side of the two converters is connected through a common capacitor, which provides dc voltage for the converter operation (Hingorani 2007; Edris 1997). As the series branch of the UPFC injects a voltage of variable magnitude and phase angle, it can exchange real power with the transmission line and thus improves the power flow capability of the line (RajabiGhahnavieh et al. 2015). The shunt converter exchanges a current of controllable magnitude and power factor angle with the power system.
Interline power flow controller (IPFC) is a combination of two or more separate SSSCs. The simplest one consists of two converters which are connected in series with two transmission lines via transformers. The DC terminals of the converters are connected together via a common DC link. IPFC is a unified series–series controller that significantly controls power flow in multiple lines (Hingorani 2007; Edris 1997) rather than control of power flow in a single line as by UPFC or SSSC. Due to high cost, quality issues and reliability concerns, deployment of FACTS in distribution system (DFACTS) is increasing as compared to transmission system (Sarker and Goswami 2016). Being light in weight, DFACTS devices can clamp onto lines rather than a separate building. Furthermore, DFACTS devices are very much faster, can communicate with other devices or a central control for distribution automation and SCADA and integrate DGs (Aziz et al. 2013), ESS (BahmaniFirouzi and AzizipanahAbarghooee 2014) and renewable power sources such as wind, solar (Shadmand and Balog 2014), small hydro (Chaudhry et al. 2016) with power system.
Potential Benefits of FACTS

Minimize the electrical length of transmission lines, power flow loops, losses, voltage violations, operations of tap changing transformer and shunt capacitors.

Manage congestion and reduce overloading.

Enhance capacity of lines to their thermal limits and increase loadability.

Can force current flow in cold weather conditions to prevent ice formation.

Provide dynamic reactive power support, voltage regulation and control power flow dynamically to reduce disturbances. Direction of power flow can be changed easily.

Can be switched in the line instantly to reduce fault current and short circuit levels.

Prevent the power system from large power swings, blackouts and cascading outages.

Can counter subsynchronous resonance problem and damp low frequency oscillations.

Withstand contingencies and load cannot cause voltage collapse.

Improve power quality by 3phase voltage balancing, mitigate flicker and work as active harmonic filters to control wave shape of voltage and current.

Control power dynamically and reduce operating margin or spinning reserve.

Provide greater flexibility and stability in interfacing energy storage systems and energy sources (solar, wind, small hydro).

Can be used as high power–frequency converters in megawatt range and synchronize power sources operating at different frequencies.

Required rating of FACTS is less than 100% of the transmission throughput rating.

Have cost five to seven times lower than HVDC for the same throughput.
Challenges for FACTS Devices

Power transmission systems are designed and constructed to use symmetrically and handle bidirectional power flow. The action of distancerelay depends upon the impedance of the line to be protected and tells the location of fault in zones. When a controller is installed on existing line, it significantly changes the effective impedance of the line/zones to be protected; this inturn leads malfunctioning and disrupts the performance of protective relays especially distance relays.

The distribution system is originally designed to handle unidirectional power flow (asymmetric) from utility to end users. The addition of DFACTS with ESS and renewable energy sources lead to flow bidirectional power. This feature also affects and disrupts the performance of protection system. Due to bidirectional power flow, FACTS normally increase short circuit currents.

If FACTS are not properly sized and located, they may lead to overvoltages, excessive power losses and may also cause stability issues.

Power oscillation damping controller can be attached to the reactive power control loop for overcoming the interference between active power modulation and shaft torsion modes oscillation (Pillai et al. 2002). However, they introduce oscillations to the terminal voltage for a while before it dies out (Padiyar and Prabhu 2006).

The steady state models cannot be used to study real time operations of power system. Moreover, uncoordinated design may deteriorate the power system performance. So, transient modeling and coordinated design of these devices is another requirement (Shayeghi et al. 2010a).

Transient over load capability of devices is not as much as generators or other transmission equipment.

Long term reliability and equipment life is not well established.

Technology is continuously changing and still under research.
Previous Reviews and Contribution of Present Review
Existing reviews/surveys related to FACTS allocation
References  Opt. type  OFS  OF  Application/objective  Con  Tool  Decision variable  FACTS type 

Germond (2002)  No  GA  Single  Load ability  No  No  Location  SVC and TCSC 
Singh et al. (2009)  No  No  No  Multi  No  Yes  Rating/size  Statcom 
Singh et al. (2010)  Yes  Multi  Multi  POD, stability  No  No  Placement  All 
Singh (2011)  No  No  No  Stability  No  No  Placement  All 
Eslami et al. (2012)  No  No  No  Multi  No  No  Placement  All 
Sautua (2013)  Yes  Multi  Multi  MOO  No  No  Location  Multi type 
Dixit (2014)  No  No  Conv. multi  Stability, min loss  No  No  Size and placement  TCSC 
Dubey et al. (2014)  No  Heuristic  Multi  Multi objective  No  No  Placement and sizing  SVC and statcom 
Jamhoria and Srivastava (2014)  No  No  Multi  Multi objective  No  No  Size and Location  TCSC 
Chindhi et al. (2013)  Yes  No  Multi  Multi objective  No  No  Location  (HPFC), (UPFC) 
Singh et al. (2015a)  Yes  Yes  Multi  Multi  Yes  No  All  
Jordehi (2015)  No  PSO  Single  Multi  Yes  No  Location  Multi type 
The work in Germond (2002) is very short and tutorial type and no classification of optimization algorithms has been provided. In Singh et al. (2009), the authors discussed component ratings, size and capacity of statcom in real world but focused on design, control issues, network architectures, their potential application areas and the future research avenues. In Singh et al. (2010), the authors focused on the problems of voltage profile, security, small signal stability, transientstability, power transfer capability and loadability and damping of power system oscillations with some methods of placements. In Singh (2011), author presented a comprehensive review on enhancement of power system stability. FACTS devices have been considered only for placement, there is no much information on optimization based methods and algorithms. In Eslami et al. (2012), the authors presented an extensive analysis on the research for power system stability using FACTS devices. However, a very little literature about location and feedback signals in designing of FACTS controllers was discussed.

Unlike previous reviews, in this review, a comprehensive classification of available research on problems of conventional grid and FACTS controllers will be done.

In this review, FACTS allocation with respect to power system objectives and constraints will be discussed.

Unlike most of previous reviews, in the current review, allocation problem with respect to applications, decision variables and tools will be discussed.

In most of previous reviews, a very limited number of optimization algorithms, applied to allocation problem, have been reviewed, however, in the current review, a very extensive and diverse set of recent optimization algorithms, applied to optimal FACTS allocation problem, will be reviewed.
Problems of HVAC Transmission
Comparison for HVAC and HVDC transmission systems
S. no.  Characteristic  HVAC transmission  HVDC transmission  System preferred 

1  Power transfer  Low and limited  High  HVDC 
2  Power control  Slow, difficult  Fast, accurate  HVDC 
3  Frequency disturbance  Can transfer  Reduced  HVDC 
4  System support  Oscillatory  Excellent pod  HVDC 
5  Transient performance  Poor  Excellent  HVDC 
6  Fault levels  Increased  Unchanged  HVDC 
7  Power swings  Long time  Quick damping  HVDC 
8  Submarine cables  Charge/discharge  No charge/discharge  HVDC 
9  Multiterminal  Economical  Costly  HVAC 
10  Reactive power flow  Occurs  Notpossible  HVDC 
11  Cascaded tripping  Likely  Avoided  HVDC 
12  Frequency conversion  Not possible  Possible  HVDC 
13  Backtoback  Not possible  Possible  HVDC 
14  Spinning reserve  Not reduced  Reduced  HVDC 
15  Transient stability  Less than half of thermal limit  Very high, upto thermal limit  HVDC 
16  Congestion and loop flows  Depend on path impedance  Do not occur  HVDC 
17  Protection  Difficult  Easy  HVDC 
18  Breakers  Simple  Special  HVAC 
19  Right of way  More  Less  HVDC 
20  No. of conductors  Six  Two  HVDC 
21  Skill and cost  Medium  High  HVAC 
Review from ViewPoint of Objectives in FACTS Allocation Problem
In this section, some literature on FACTS allocation problem is reviewed from the viewpoint of decision variables, constraints and objectives present in objective function.
Economic Dispatch/Minimize the Cost
Minimize cost (active power/economic dispatch)
Objective  Type of FACTS  Decision variable  Test system  Solution algorithm  Findings/application  References 

Minimize generation cost, investment cost, operation cost, etc.  Multi type  Location, rating, type  14 bus  GA  An effective and practical method in large power systems  Cai et al. (2004) 
TCSC  Locating and sizing  14 bus  HSA  HSA gives better size of TCSC that lead to more saving when compared with PSO and CRCM  Javaheri and GoldoostSoloot (2012)  
TCSC  Location  5, 14, 30bus  FFA  FFA produces better results and has fast computing than GA and DE  Bathina and Gundavarapu (2014)  
TCSC and others  Location and number  5 bus  DE  TCSC and DE gives better result than all types of FACTS with EP  Balamurugan et al. (2015)  
SVC, TCSC TCVR/TCPST  Location and type  39 bus  OPF and GA  Increased power and improved damping of electromechanical oscillations.  Alabduljabbar and Milanović (2010)  
Statcom and SSSC  Location and number  14, 30 and 118 bus  MINP, SQP and GA  Analysis with converter power loss, optimal operation by SQP and placement by GA  Rahimzadeh and Bina (2011)  
SVC, TCSC and UPFC  Location  4bus, 24bus  EP  Total overloads and total SOL were reduced. Real power contracts were established  Krishnan et al. (2016)  
SVC, DVR and statcom  Type, size, locations  10 bus  Niching GA  Larger the investment/mitigation measures, the bigger the reduction in costs  Milanovic and Zhang (2010)  
SVC and statcom  Size, rating and cost  57bus  (BFPSO) MINLP  For reactive power planning (RPP), bus facing minimum voltage is selected.  Hooshmand and Ezatabadi (2010)  
SVC and TCSC  Placement and location  30 bus  Fuzzy GA, EA and PSO  Weak node detection and simultaneous optimal parameter settings in a power system  Bhattacharyya and Gupta (2014)  
SVC and TCSC  Location  30 and 57 bus  GSA  GSA based approach is compared with GA, DE, PSO  Bhattacharyya and Kumar (2016)  
SVC  Location and size  NSGA II  System security, power flows and voltages in steady sate by nondominated sorting genetic algorithm  Yousefi et al. (2013) 
Minimize Loss and Voltage Deviations
Minimize loss and voltage deviations
Objective  Type of FACTS  Decision variable  Test system  Solution algorithm  Findings/application  References 

Minimize loss, voltage deviation and size/no of FACTS  Nil  Nil  30, 57, 118bus  ALCPSO  An effective and fast method for solving the ORPD problem in large power systems  Singh et al. (2015) 
TCSC, TCPS  Placement  30bus  Biography based  BBO approach is better than PSO, realcoded GA, and DE  Roy et al. (2011)  
TCSC  Location, no  30bus  GA  TCSCs sized, located and selected to improve performance and system stability  Abdelaziz et al. (2011)  
Dstatcom  Location, size  33, 69bus  Immune algorithm  Overall 10.9 and 18% power loss reductions in distribution systems  Taher and Afsari (2014)  
UPFC, IPFC, OUPFC  Location, placement  5, 14 bus  Sensitivity analysis  FACTS device are capable of controlling both active and reactive power  Rao and Rao (2015)  
UPFC, TCSC, IPFC  Location  30 bus  CS and GA  Cuckoo search (CS) and GA ensure good stability and better convergence  Akumalla et al. (2016) 
Maximize Capacity and LoadAbility of Lines to Thermal Limits
In Alabduljabbar and Milanović (2010), the placement of SVC, TCSC, TCVR and TCPST for increasing available transfer capability (ATC) was discussed. Jirapong and Ongsakul (2007) discussed the same objective to minimize the loss, voltage difference index and to maximize power index by utilizing FACTS controllers.
Maximizing available transfer capacity and loadability
Objective  Type of FACTS  Decision variable  Test system  Solution algorithm  Findings/application  References 

Max TTC, ATC and load ability  Multitype  Placement  30, 118bus  HEA  HEA integrates EP, TS and SA enhances more TTC than others and hence efficient  Jirapong and Ongsakul (2007) 
SSSC, UPFC statcom  Location  30, 57 bus  Firefly algorithm  Scheduling of generator is decided to decrease the system severity  Rao et al. (2016)  
TCSC, SVC TCPST, TCVR  Type, location  30bus, 345 kV  Ant and HSA  Improves steady state control and transfer capability of Taiwan power  Huang and Huang (2014)  
Multi type  Allocation type, no  GA  Simulation and testing FACTS in PSs using GUI, a user friendly tool  Ghahremani and Kamwa (2013)  
TCSC, SVC  Location  14 bus  OO  Loading capacity enhanced by OO is greater than PSO  Srikumar et al. (2014)  
TCSC  Location, size  6, 30 and 118 bus  Min cut, KCI  Maximizes load ability with reduced search space and clear formulation  Duong et al. (2014)  
Min losses and change in powers  PST, HFC, UPFC  Location setting  14bus  GAMS, econstraint  HFC gives best satisfaction based on technical and economical aspects  Ara et al. (2012) 
In Ara et al. (2012), the authors formulated objective function to minimize the total fuel cost, loadability and power loss with and without considering cost of installation of FACTS.
Minimize Overloads and Manage Congestion (N − 1 Contingency Analysis)
Minimize overloads and manage congestion (N − 1 contingency analysis)
Objective  Type of FACTS  Decision variable  Test system  Solution algorithm  Findings/application  References 

Minimize overloads, voltage deviations and losses  TCSC  Allocation  TLBO, LWS  TLBO is better than GSA, NLP, PS and FSO for N − 1 and N − 2 line contingencies  Jordehi (2015b)  
TCSC, SVC  location and setting  57 bus  BSOA  Better voltage profile and lower voltage deviations during contingencies  Jordehi (2015c)  
DTCSC  Allocation  14, 118bus  ELPSO  DTCSC’s are better for N − 1 and also for simultaneous outage of four branches  Jordehi et al. (2015)  
TCPST, TCSC  Allocation  39 bus  ICA  ICA is better than ABC, GSA, EP and bat swarm optimization  Jordehi (2016) 
Enhance Steady State and Voltage Stability
Enhance steady state Stability
Objective  Type of FACTS  Decision variable  Test system  Solution algorithm  Findings/application  References 

Min losses, voltage deviation and voltage stability index  SVC, TCSC  Location, setting  14 and 30 bus  NDSPSO, fuzzy  Scheduling and utilization of the power system  Sedighizadeh et al. (2013) 
UPFC  Location, size  14 and 30 bus  Hybrid of ABC,GSA  Maximum power loss bus is identified for fixing UPFC  Kumar and Srikanth (2015)  
UPFC  Location, capacity  14 and 30 bus  CS and MFA  Enhanced searching capability, degradation in complexity  Gopinath and Kumar (2016)  
SVC, statcom  Placement, size  14 and 57 bus  FuzzyGA  Min size of the shunt devices, max distance to saddlenode bifurcation,  Phadke et al. (2012)  
Statcoms  Location  30 and 57 bus  CRO  CRO is robust and suitable for sizing and locating statcom  Dutta et al. (2016a)  
SVC, TCSC  Allocation  14 and 30 bus  QOCRO  Higher quality solution in reasonable computational time with FACTS  Dutta et al. (2016b)  
Min VI, VAr and cost  SVC, TCSC statcom  Location, size  39 bus  APSO  Min vulnerability index (VI) and blackouts to improve stability  Moazzami et al. (2013) 
Sedighizadeh et al. (2013) proposed reactance model and injected power model of TCSC and SVC to enhance voltage stability and minimized active power loss, voltage stability index and voltage deviation. In Kumar and Srikanth (2015) and Gopinath and Kumar (2016), the optimal location and sizing of UPFC was proposed to enhance the dynamic stability. Phadke et al. (2012) proposed optimal placement and sizing of shunt FACTS to enhance stability in terms saddlenode bifurcation and minimized voltage deviation. Dutta et al. (2016a, b) investigated stability of power system by minimizing loss, voltage deviation and voltage stability index. In Dutta et al. (2016a), optimal location of statcom was suggested at IEEE 30bus and IEEE 57bus while in Dutta et al. (2016b), optimal allocation of SVC and TCSC was worked out at IEEE 14bus and 30bus systems. In Moazzami et al. (2013), the authors investigated stability improvement in terms of vulnerability of system, reactive power generation and cost of SVC, TCSC and statcom.
Transient Stability Improvement
Enhancing transient stability
Objective  Type of FACTS  Decision variable  Test system  Solution algorithm  Findings/application  References 

Min rotor angle deviation  SVC, statcom  Location, size  2 area machine  GA  Improved stability of two hydraulic generating units of 1400 and 700 MVA  Panda and Patel (2007) 
Min invest. cost, settling time and overshoots  SVC  Size, site, no and setting  39 bus, 10 machine  MOPSO  SVC can improve greatly the transient stability of the multimachine system  Gitizadeh et al. (2014) 
Min function of capacity and phase angle  SSSC  Allocation  6 and 57 bus  SA and GA  Dezaki et al. (2013)  
Min CTEM, CTKE and CCT  SVC, TCSC, UPFC  Type  3, 39 and 145 bus  Simulation, Lyapunov  Results of energy functions for direct and simulation methods are almost equal  Aghaei et al. (2016) 
preserve energy function  Statcom, UPFC  Placement  39 and 246 bus  SA  Potential energy, contributed by facts influenced the transient stability  Jain et al. (2009) 
Dezaki et al. (2013) proposed objective function of the transient stability in terms of capacity and phase angle with optimal allocation of SSSC at 6bus and 57bus system. Aghaei et al. (2016) analyzed an appropriate criterion for the transientstability evaluation in term of CTEM that has a linear performance over a wide range of the system changes. Jain et al. (2009) analyzed the structure to preserve energy function by placement of statcom and UPFC at 39bus and 246bus system.
Power Oscillations Damping (POD)
Enhancing power oscillation damping
Objective  Type of FACTS  Decision variable  Solution algorithm  Findings/application  References 

Max damping of small signal oscillations  SVC, TCSC UPFC  Location  Loss sensitivity  UPFC settles down oscillations in 9 s, TCSC or SVC in 13 s at 39 and 68 bus  Kumar et al. (2007) 
Maximize the damping ratio  SVC, TCSC  Location, setting  PSO  TCSC is better than SVC for higher loading and mitigating small signal stability problem  Mondal et al. (2012) 
Max voltage stability and damping oscillations  SVC at 14 bus  Placement size, setting  GA,MA  Best stabilizing signal, controllability and observeability using 2× SVCs  Farsangi et al. (2007) 
Max damping of power oscillations  SVC, TCSC, statcom UPFC  Rating, type  PSO, Eign. Ana  The rating of SVC is found between − 50 and + 50 MVAR by using load flow study  Kumar (2010) 
Min square of error between P_{ref} and P_{act} power  TCSC  Location  STFPIC  greater penalty on large errors and STFPIC quite effective in POD  Hameed et al. (2008) 
Min angle, frequency and voltage deviations  IPFC and UPFC  Location, size  ANFIS MsPSO  Iranian power grid and New England power system selected to install CSC (200 MVA)  Isazadeh et al. (2016) 
Minimize a function of settling time and overshoot  TCSC  Optimal tuning  PSO  TCSC has excellent capability in damping interarea oscillations and enhances stability  Shayeghi et al. (2010a) 
Minimize a function of settling time and overshoot  TCSC  Optimal tuning  PSO, GA  PSO is superior to the genetic algorithm based damping controller  Shayeghi et al. (2010b) 
Minimize a function of settling time and overshoot  UPFC  Optimal tuning  QPSO  QPSO based UPFC has excellent capability in damping low frequency oscillations  Shayeghi et al. (2010c) 
The damping of oscillations was improved significantly through the fast control of UPFC and IPFC (Isazadeh et al. 2016). Shayeghi et al. suggested optimal tuning of PSS, TCSC (Shayeghi et al. 2010a, b) and UPFC (Shayeghi et al. 2010c) for improving the objective of POD in terms of settling time and overshoots.
Power Quality and Interfacing PS with ESS, DGs and DFIGs
Power quality and capacity enhancement with FACTS, DG, DFIG and ESS
Objective  FACTS/DG/ESS  Decision variable  Solution algorithm  Findings/application  References 

Max loadability within allowed voltage  SVC  Number at 14 and 140 bus  GA  An existing 140bus improve the voltage stability and the voltage profile of the power network according to the utility regulations  Amaris and Alonso (2011) 
Increase loadability and voltage stability  UPQC and DG  Allocation  SPAC model  Tested at 33 node and 69 node, efficient in under voltage mitigation, beneficial for DG units  Taher and Afsari (2012) 
Improve voltage and current profiles, reduce power loss and cost  UPQC  Location and size  DE  DE is a nearer to global optimal in minimizing the OF than GA and I in radial distribution  Ganguly (2014) 
Max voltage stability, min power loss and VAr investment cost  SVC and DGs  Location, 140 bus  GA  Improves the voltage stability, reduces active power losses as well as the cost of SVC in wind forms  Alonso et al. (2012) 
Min cost of generation  TCSC  Location capacity  Monte Carlo, DE  A high penetration of renewable generation  Galloway et al. (2010) 
Min cost of power loss, cost of UPQC and cost of interruption  UPQC  Location, number  CSO  UPQC with Cuckoo Optimization algorithm gives better results in distribution network  Sarker and Goswami (2016) 
Min oscillations of PCC voltage and Rotor angle deviations  Statcom, SVC and DFIGs  Transient ratings  SQP  Statcom is cost effective for stabilizing rotor oscillations of induction generator in wind form  Kumar and Gokulakrishnan (2011) 
Improve rotor speed stability and angle stability  FACTS, DFIGs  Transient ratings  Enhancement of rotor speed stability of induction generators and angle stability of synchronous generators  Kumar and Khan (2008) 
The role of FACTS devices for the dynamic stability of power system is investigated in Kumar and Khan (2008) using a variable speed doublyfed induction generator model. The impact of FACTS parameters and short circuit faults on wind turbine induction generators were discussed in Grainger et al. (2014).
Methods and Techniques Used in FACTS Allocation Problem
FACTS allocation problem is a nonlinear, highly constrained, multiobjective, mixedinteger, multimodal problem and finding global solution is very difficult. The solution approaches applied to FACTS allocation problem are discussed in this section.
Analytical and Numerical Techniques
Sensitivity based, loss sensitivity, index based, Eigenvalues based, econstraint and modal analysis are analytical and numerical based methods. In Krishnan et al. (2016), the authors proposed severity index to indicate most sensitive line in case of single contingency. In Rao and Rao (2015), authors proposed sensitivity index for optimal placement of UPFC, IPFC and OUPFC. The objective function is differentiated with respect to angle of injected voltage and verified on 5 bus and 14 bus system. The authors proposed sensitivity based method in Preedavichit and Srivastava (1997) for finding the optimal location of FACTS devices. Song et al. (2004) have applied an analytical method in order to minimize the security indices. In Rao et al. (2016), the authors proposed SA for the evaluation of ATC using statcom, SSSC and UPFC. The powertransferdistribution factors based and novel current based model was developed and tested on 30bus and 57bus systems. In Aghaei et al. (2016), the authors also proposed SA for allocation of SSSCs to enhance the stability and capacity. The proposed method does not require exact modeling and limit on number of SSSCs. The method was tested on 6bus and 57bus system.
Kumar et al. (2007) proposed a set of loss sensitivity and controllability indices for optimal placement of UPFC, TCSC and SVC. The optimal placement based on proposed indices is also effective in critical contingency situations. The proposed method was tested for power oscillations damping at 68bus and 39bus. Farsangi et al. (2007) proposed modal analysis and GA to damp out the inter area oscillations using SVC. The MA is best in finding location while GA is best in finding the optimal size of SVC. In Kumar (2010), the authors proposed Eigen Analysis to calculate the dynamic ratings of TCSC, UPFC, SVC and statcom. In Ara et al. (2012), the authors proposed econstraint approach using GAMS in Matlab. The proposed method is tested on IEEE 14 bus system with PST, HFC and UPFC.
Classical Optimization Based Techniques
NLP, MINLP, ordinal optimization (OO), Newton–Raphson method, OPF based, quadratic programming (QP) and sequential QP are classical methods. In Kumar and Gokulakrishnan (2011), the authors proposed SQP for stability assessment using SVC and statcom in the area of wind power. The proposed method was tested for a 3phase short circuit without and with FACTS controllers in the power network. In Rahimzadeh and Bina (2011), authors proposed GA and SQP to solve a MINP related optimization problem for optimal allocation of FACTS devices in power systems. In GA, the location of FACTS devices are represented by chromosomes having integer numbers while the length of each chromosome represents the number of FACTS device. In Krishnan et al. (2016), authors suggested NR method for contingency analysis and transient stability study. In Duong et al. (2014), the authors proposed minimum cut methodology to determine best location and applied Kirchhoff’s current law to determine the best setting of TCSC. Ara et al. (2012) used NLP and MINLP for finding the optimal location and best setting of FACTS.
Artificial Intelligence Based Techniques
Heuristic Approaches
GA, PSO, EA, harmony search algorithm (HSA), TLBA, GSA, CRO, QOCRO and BSOA are heuristic approaches. In Cai et al. (2004), authors proposed GA to determine the optimal location and suitable type of FACTS device from TCSC, SVC, UPFC and TCPST. In Amaris and Alonso (2011), authors proposed GA using SVC for maximizing power generation from wind turbines. An existing 140bus power system is used to validate the performance and effectiveness. In Alonso et al. (2012), GA was validated at 140 bus power system with wind farms using FACTS units due to its effective speed and simplicity. Alabduljabbar and Milanović (2010) proposed GA and OPF to allocate SVC, TCSC, TCVR, and TCPST. The placement methods not only considered different costs simultaneously but also increased power transfer in the lines and damping of electromechanical oscillations. The authors studied GA for minimizing the total loss and improving the loadability of the lines using TCSC (Abdelaziz et al. 2011). The approach was tested on 30bus system for optimal number and optimal compensation level of TCSC. The authors proposed GA (Ghahremani and Kamwa 2013) to search the suitable location and determine the best sizes of SVC, TCSC, TCVR, TCPST and UPFC. A GUI was presented with the FACTS toolbox up to 300bus system to maximize the loadability. In Amaris and Alonso (2011), authors proposed GA using SVC for maximizing power generation from wind turbines. An existing 140bus power system is used to validate the performance and effectiveness. In Alonso et al. (2012), GA was validated at 140 bus power system with wind farms using FACTS units due to its effective speed and simplicity. In Panda and Patel (2007), the authors proposed GA for placing statcom in order to improve transient stability. The proposed method was tested at twoarea test system for determining the optimal allocation.
In Kumar (2010), PSO was proposed to solve the optimization problem and EA analysis to perform calculations in time domain. The dynamic ratings of TCSC, UPFC, SVC and statcom were determined in a multi machine power system. Mondal et al. (2012) proposed PSO to tune the parameters of TCSC for damping power oscillation. The performance of the PSO based controller is evaluated in a fourmachine power system and compared with GA in terms of robustness subjected to the different types of disturbances. Shayeghi et al. (2010a) also proposed PSO for coordinated control of PSS and TCSC as an efficient damping controller. The proposed optimization problem with time domainbased multiobjective function is tested under different operating conditions. It has good robust performance for damping low frequency interarea oscillations. Javaheri and GoldoostSoloot (2012) proposed HSA with sensitivity factors for to mitigate congestion using TCSC. The concept of HSA is derived from musical practice for searching an ideal state of harmony (Lee and Geem 2004). Line outage sensitivity factors can reduce the solution space and point out suitable lines for placement of TCSC. The simulation results on 14bus system show the effectiveness of HSA over PSO. In Balamurugan et al. (2015), authors proposed EP and DE algorithms for optimal placement of multitype FACTS. The proposed approaches were compared for minimizing the costs, overloads, excess power flow and maximizing the benefit.
In Bhattacharyya and Kumar (2016), GSA was proposed to maximize power transfer capacity using FACTS devices. The proposed approach is compared with GA, DE, and PSO at 30bus and 57bus system. The authors outlined BBO in Simon (2008) and implemented in Roy et al. (2009, 2010, 2011), and for optimal reactive power dispatch using multiple TCSC and TCPS devices. This approach studies optimal setting of control variables for minimizing power loss and voltage deviations. The approach was tested at 30 bus and compared to PSO, GA and DE. In Taher and Afsari (2014), authors proposed biologically inspired Immune Algorithm (IA) to search the best location and determine the best size of Dstatcom. The proposed approach minimizes the cost of installation and power loss within the constraints of the objective function. The proposed approach was tested on 33bus and 69bus distribution systems.
The authors proposed TLBO using TCSC (Jordehi 2015b) to decrease overload, power loss and voltage deviations. Optimal settings of TCSC contingencies show that TLBO is more efficient than GSA, FSO, PS and NLP in solving these problems. The authors proposed BSOA (Jordehi 2015c) to find optimal setting and location of TCSC and SVC for the objectives of voltage profile, losses and overloads. The results of proposed method at IEEE 57bus system shows that BSOA is better than PSO, GA, DE, SA, hybrid of GA and PS, backtracking search algorithm and GSA. In Dutta et al. (2016a), CRO was proposed to find the optimal location of statcom at IEEE 30 bus and IEEE 57 bus systems. The results show effectiveness of the proposed method and better performance when compared with PSO, DE, etc. Dutta et al. (2016b) proposed QOCRO to find optimal location of FACTS device. The proposed concept successfully speeds up the convergence of conventional CRO to decrease power loss, improve the voltage stability and voltage profile.
MetaHeuristic Approaches
Fuzzy logic (FL), GA and variants, PSO and variants, FFA, ANN, ABC, EP and DE are metaheuristic approaches. In Bathina and Gundavarapu (2014), the authors proposed FFA to solve the problem of optimal placement of a TCSC. The proposed method was tested at 5 bus system, IEEE 14 bus system and the modified IEEE 30 bus test systems. Milanovic and Zhang (2010) proposed Niching GA (NGA) for optimal placement and sizing of SVC, statcom and Dynamic Voltage Restorer (DVR). The purpose of the scheme is to reduce losses and the overall cost. The method was tested on 295bus and 278branch system. In Hooshmand and Ezatabadi (2010), the authors proposed FACTS with BF oriented by PSO (BFPSO). The simulation were carried out at IEEE 57 bus test system and compared with PSO and GA. In Ghahremani and Kamwa (2013) and Srikumar et al. (2014), authors proposed NSGA II for solving multiobjective problem of optimal location and ratings of SVC.
In Chen et al. (2013), the authors developed ALCPSO that tunes the lifetime of the leader adaptively as per leader’s leading authority. Singh et al. (2015b) proposed ALCPSO for the solving ORPD problem in electric system and minimized power loss and absolute value of total voltage deviations. The proposed method was tested on IEEE standard 30 bus, 57 bus and 118 bus system. Jordehi et al. (2015) proposed enhanced leader PSO (ELPSO) to minimize power loss, power flow violations and voltage deviations using DTCSCs. ELPSO and eight other optimization approaches tested at IEEE 14bus and 118bus systems with N – 1 contingency conditions for outage of 4 × branches simultaneously. The results are batter in terms of lower power flow violations, voltage variations and power loss. Jordehi (2016) proposed ICA using TCPSTs and TCSCs to minimize overloads and voltage deviations during line outage contingencies and demand growth. In Moazzami et al. (2013), the authors proposed APSO to determine the most economic and cost effective bus for load shedding. The proposed method also prevents the system instability and blackout situation in power systems. In Gitizadeh et al. (2014), authors proposed MOPSO for finding optimal rating, placement and parameter setting of SVC to enhance power system stability. In Phadke et al. (2012), authors proposed a FuzzyGA framework to address the problem of optimal location of shunt FACTS devices. The method minimizes the bus voltage variation and maximize loading margin simultaneously and was tested at 14bus and 57bus system. The authors proposed ANFIS and MsPSO (Isazadeh et al. 2016) to avoid shutdown scenarios. The different configurations of UPFC and IPFC were investigated for damping of power oscillations.
Hybrid Approaches
GA and DE along with FL was proposed for the optimal placement and setting of TCSC and SVC (Bhattacharyya and Gupta 2014). The fuzzy membership functions with Eigen value analysis are utilized for the selection of weak buses for the placement of SVCs while the locations of TCSCs are determined by the power flow in lines. A combination of CS and GA is proposed in Akumalla et al. (2016) to find optimum placement of UPFC, TCSC and IPFC in a multimachine power system. The purposed hybrid approach speeds up the convergence and improves the quality of solution through expanded search space. The simulation results of proposed method on IEEE 30 bus network show good stability, better convergence, simultaneous and efficient use of several kinds of FACTS controllers. In Huang and Huang (2014), authors proposed a hybrid approach that combines HSA and an ant system for the optimal solution of FACTS allocation problem. The proposed approach is verified on 30bus and 345 kV Taiwan power system. The results show better steadystate control of power systems and improvement in the total power transfer capacity.
A new hybrid evolutionary algorithm combining EP, TS, and SA methods (Jirapong and Ongsakul 2007) was proposed for improving power transfer capacity. In Sedighizadeh et al. (2013), the authors also proposed a hybrid approach which combines FL with NSPSO algorithm for the solution of multiobjective FACTS allocation problem. The active power loss and voltage stability index were minimized by using reactance model of TCSC and power injection model of SVC. In Kumar and Srikanth (2015), authors proposed a hybrid approach integrating ABC and GSA for optimal placement and sizing of UPFC to improve the dynamic stability. The optimal location is searched out by using ABC algorithm and the required optimal number of the UPFC by using GSA. The highest power loss bus is recognized as favorable location for placement of the UPFC, because the generator failure affects the constraints regarding voltage, real/reactive power flow and power loss. The performance has been verified by comparing with ABC and GSA. In Galloway et al. (2010), the authors proposed DE algorithm and Monte Carlo simulation technique for minimizing cost in DG and finding the optimal location, respectively. These techniques together are called renewable uncertaintybased optimal allocation techniques. The operation with FACTS devices gives highest benefit in terms of reducing cost of generation. In Chaudhry et al. (2017), authors have proposed a novel hybrid technique for energy mix cost reduction and proved that chaotic DE hybridized with SQP works efficiently. It can also be implemented on FACTS allocation effectively.
Case Study: IEEE14 Bus System
Buses data IEEE14bus system
Bus no.  Bus code  Voltage magnitude  Angle (°)  Load  Generator  Injected MVAR  

MW  MVAR  MW  MVAR  Q _{min}  Q _{max}  
1  1  1.06  0  30.38  17.78  40  − 40  0  0  0 
2  2  1.045  0  0  0  232  0  − 40  50  0 
3  2  1.01  0  131.88  26.6  0  0  0  40  0 
4  0  1  0  66.92  10  0  0  0  0  0 
5  0  1  0  10.64  2.24  0  0  0  0  0 
6  2  1.07  0  15.68  10.5  0  0  − 6  24  0 
7  0  1  0  0  0  0  0  0  0  0 
8  2  1.09  0  0  0  0  0  − 6  24  0 
9  0  1  0  41.3  23.24  0  0  0  0  0.19 
10  0  1  0  12.6  8.12  0  0  0  0  0 
11  0  1  0  4.9  2.52  0  0  0  0  0 
12  0  1  0  8.54  2.24  0  0  0  0  0 
13  0  1  0  18.9  8.12  0  0  0  0  0 
14  0  1  0  20.86  7  0  0  0  0  0 
Lines data for IEEE14bus system
Line no.  Sending end bus  Receiving end bus  Resistance (p.u)  Reactance (p.u)  Half susceptance (p.u)  Transformer tap  MW limit (p.u) 

1  1  2  0.01938  0.05917  0.0264  1  0.6 
2  2  3  0.04699  0.19797  0.0219  1  0.7 
3  2  4  0.05811  0.17632  0.0187  1  0.8 
4  1  5  0.05403  0.22304  0.0264  1  0.5 
5  2  5  0.05695  0.17388  0.017  1  0.4 
6  3  4  0.06701  0.17103  0.0173  1  0.3 
7  4  5  0.01335  0.04211  0.064  1  0.2 
8  5  6  0  0.25202  0  0.932  0.5 
9  4  7  0  0.20912  0  0.978  0.4 
10  7  8  0  0.17615  0  1  0.2 
11  4  9  0  0.55618  0  0.969  0.2 
12  7  9  0  0.11001  0  1  0.2 
13  9  10  0.03181  0.0845  0  1  0.2 
14  6  11  0.09498  0.1989  0  1  0.3 
15  6  12  0.12291  0.25581  0  1  0.2 
16  6  13  0.06615  0.13027  0  1  0.2 
17  9  14  0.12711  0.27038  0  1  0.2 
18  10  11  0.08205  0.19207  0  1  0.2 
19  12  13  0.22092  0.19988  0  1  0.2 
20  13  14  0.17093  0.34802  0  1  0.2 
In the case study results we have observed that the recursive technique Sequential Quadratic Programming is better than classical Newton’s method. While the evolutionary techniques Partial Swarm Optimization and Differential Evolution outperform the SQP. But the most optimal results are provided by the hybrid technique of DE and SQP.
Weakness of the Existing Research Work and Guidelines for Future

Almost all the existing works, attempt to find optimal placement or location of FACTS and some find size of FACTS but do not find optimal number and type of FACTS. Development of efficient approaches capable of finding optimal type, size and number of FACTS is recommended.

The utilities as well suppliers mostly employ experience based conventional approaches rather than modern approaches for allocation of FACTS. Even in many countries, particularly in developing countries like Pakistan, the power generation, transmission and distribution is totally without any FACTS. Transmission system operators and sub station operators switch on conventional fixed capacitors and inductors for compensation which is time consuming along many other drawbacks. Convincing the utilities and suppliers in different countries about the advantages of FACTS and encouraging them to use modern FACTS allocation approaches is highly recommended.

Almost all existing research works, attempt to optimize simple steady state characteristics of transmission and distribution systems, while dynamic, transient and coordinated control issues of the system should be considered in multiFACTS allocation.

Shunt compensators are a source of reactive power and can be considered as Qtype FACTs. In order to reduce costs, a minimum number and size of fixed capacitors and fixed inductors in concert with FACTS devices is recommended in transmission and distribution systems in FACTS allocation approaches.

The addition of energy storage systems along with FACTS can provide smooth output and quality power and relieve intermittency of renewable energybased FACTS, however, a very small portion of existing works have investigated FACTS allocation problem with energy storage systems. Using energy storage systems integrated with FACTS and thorough study of their effects on solution of FACTS allocation problem is highly recommended.

A lot of the existing works analyze the optimization approaches for FACTS allocation problem on very small scale power systems. A geographically and countrywise power system bus data and transmission lines data should be collected, in which analysis of optimal size and optimal placement of different types and number of FACTS devices is recommended. This will make implementations and improvements very simple and fast.

Full investigation of the effects of different models of FACTS is recommended with power system modeling, while load models such as constant impedance model, constant current model, etc., is recommended for future research in distribution system.

Although a lot of research effort has already been put to develop efficient and powerful metaheuristic optimization algorithms for solving allocation problem, there is still room for improvement. Developing more efficient metaheuristic optimization algorithms with strong capability in discovery of global optimum is recommended for future research.

In hybrids of sensitivity analysis and classic/heuristic/metaheuristic optimization approaches, optimal size, location and type of FACTS are not found simultaneously. No doubt, the computational time of such approaches is less, however, the obtained solutions cannot be considered optimal. Therefore, more concise study on other optimization algorithms that simultaneously optimize size, type and location of FACTS is recommended.

To provide a practical reasonable solution for FACTS allocation problem, all the associated economical, technical, geographical and environmental constraints must be included into study, whereas a large number of existing research works have neglected some of constraints. As an example, about in all the cases, the cost of power transformers, inductors and capacitors is not taken into account but cost of power electronic component is taken into consideration. Similarly right of way problems may not allow the installation of FACTS at certain buses of system, while in most of research such a constraint has been simply ignored. As another example, in most of the research works, design of power electronic components has been considered but ratings and size of electrical equipment i.e., power transformers, inductors and capacitors has not been considered.

This review shows that different existing research works have used a number of different constraints, different decision variable and different objective functions. So comparison of the concert of different optimization approaches is unworkable. Comparison of different optimization approaches with same constraints, same decision variables and same objectives in FACTS allocation problem is recommended for research in future. A comparison can be prepared in terms of computational time, robustness, convergence speed and accuracy.
Conclusion
FACTS allocation is a hot topic for research in electric power systems and represents a challenging problem in power resources optimization. In this paper, the existing works on FACTS allocation have been studied from the viewpoint of applied optimization approaches, objectives, constraints, design variables and FACTS types. Based on the review of research works, the research shortcoming has been identified and some useful recommendations and suggestions for future study on FACTS allocation problem have been provided. As a major judgment of this review, it was searched out that although a lot of research attempt has already been put to extend powerful and efficient metaheuristicoptimization approaches for solving FACTS allocation problem, there is still an opportunity for more efficient metaheuristic optimization approaches. Another effort of using hybrid of sensitivity analysis with classical/heuristic/metaheuristic approach with strong capability and improvement in discovery of global optimum is recommended.
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