 Original research article
 Open Access
Sensitivity analysisbased performance and economic operation of windintegrated system with FACTS devices for optimum load dispatch
 Satish Kumar^{1, 2}Email author,
 Ashwani Kumar^{1} and
 Nikhlesh Kumar Sharma^{3}
https://doi.org/10.1186/s4080701700397
© The Author(s) 2017
 Received: 15 September 2016
 Accepted: 7 February 2017
 Published: 7 March 2017
Abstract
Supply of additional power generation by wind system to increase total power generation is increasing exponentially and globally to meet the challenge of surplus power demand. This total power generation should be at minimum cost and power loss, without violating stability limits. This paper presents modelling and tuning of flexible A.C. Transmission system (FACTS) devices with sensitivity analysis of buses for windintegrated system (WIS). When the conventional grid system is integrated with some renewable energy resources such as wind, the voltage of buses within the system tends to decrease. This dip in voltage profile of the system must be compensated by some suitable FACTS devices, which must be optimally placed so as to improve the voltage and current profile of the system. Particle swarm optimization algorithm is used here for suitable placement and precise tuning of FACTS devices to maintain the voltage profile of integrated system within stability limits. Optimal power flow (OPF) is also used in this paper to maintain steadystate operation of wind integrated system with mitigation of cost of generation and losses. OPF is computed and compared with and without placing FACTS devices for WIS. Total per unit generation cost and losses are also calculated and compared for FACTScontrolled WIS. Bus voltage and angle sensitivity have been calculated and presented to determine range of voltage stability and to prevent any possible voltage collapse or critical point within the system. Optimization of load between maxima and minima is solved using general algebraic modelling system software.
Keywords
 Wind integration
 FACTS
 Cost function
 Voltage stability
 Senstivity
 PF
 CPF
 OPF
 Voltage collapse
 PSO
Background
Exponential increase in power demand by variety of applications has compelled the power researchers to increase in power generation from conventional as well as from renewable energy resources. But due to increase in power generation, cost of power generation and losses also increases because of increase in cost of fuel consumed, installation cost and various losses incurred during the generation, transmission and distribution due to the distributed parameters present in the system. This increase in power generation may cause variations in voltage limits, thermal limits or possibility of voltage collapse at different stages of generation or transmission due to variable loading conditions at the consumers end. So it is highly desirable to synchronize this variation in load with the voltage profile of the integrated system. In recent years, renewable energy resources such as solar energy, wind energy, hydropower, geothermal energy and biomass energy have achieved significant contribution to support this surplus power in addition to the conventional power sources, so as to increase total power generation by the plant. WIS is most common and fastest growing application of power generation (Chi et al. 2006). Electricity produced from the wind systems differs from conventional methods only because of the power flow between wind energy system and transmission grid depends on fluctuating wind speed (Joslin Hurbert et al. 2007). Three types of commercial wind turbines systems have also been developed and integrated with conventional grid system to generate more costeffective power. It is also seen that sites can be more profitable for electrical and mechanical applications, i.e. water pumping and battery charging, if planned properly (Gaddada and Kodicherla 2016). Wind integration with conventional grid system can be made smooth and costeffective by incorporating adequate control strategies in the multimachine system. The implementation of optimal controllers is one of the ways which not only offer good dynamic performance, but ensure system dynamic stability also (Ehtesham et al. 2016).
Optimal power flow (OPF) is very useful tool to meet the challenge of variable wind speed, for windintegrated system especially if we consider the economic operation of power generating units (Segura et al. 2011; Momoh 1989). Main purpose of implementing OPF is to minimize the total cost of generation by power balance at each node using power flow equations with inequality constraints, i.e. network operating limits (line flows, voltages) and limits on control variables. So evaluation of OPF is very necessary and valuable specially when integration of wind energy system with conventional systems is incorporated to meet the variable load and increased power demand of consumer. It is also preferred to maintaining the voltage stability of the integrated system within the prescribed limit (Momoh et al. 1997). Another approach of power flow (PF), called continuation power flow (CPF), should also remain well conditioned at and around the critical point within the system (Ajjarapu and Christy 1998). So power flow solutions starting from some base load to full load should be carried out to maintain voltage stability limit for WIS. Previously various voltage problems on transmission networks subject to unusual power flow patterns have been identified which has compelled the power engineers to go for optimal power flow solutions to meet the challenges (Ilic and Stankovic 1991). Line stability indicesbased method is also valuable for calculating voltage stability limits and for monitoring voltage regulations in the multimachineintegrated systems for better planning and estimation (Lof et al. 1992). Earlier OPF was applied only with thermal energy power sources, but now due to increased demand and recent developments in renewable energy resources, inclusion of generating cost of wind energy system units has also become mandatory in classical OPF problem (Shi et al. 2012; Hetzer et al. 2008).
FACTS are power electronic devices which are frequently used to resolve and maintain various types of stability problems in power system planning and operation. Very common types of FACTS are shunt devices such as static VAR compensators (SVC) and series devices such as thyristorcontrolled series compensators (TCSC), which in combination with wind energy system can boost the generated power (Jovcic and Pillai 2005).
Estimation of power generation with integration of wind energy system by tuning power devices using optimization techniques is important but rigorous (Momoh 2001; Wood and Wollenberg 1996). But evolutionary programmingbased OPF algorithm is userfriendly and well suited for problem solving (Yuryevich and Wong 1999).
MATPOWER tool box is available in the MATLAB and can be used for the power flow and optimal power flow calculations for WIS because it gives direct results for power flow in terms of bus voltages and angles (Zimmerman et al. 2007). Various optimization techniques such as particle swarm optimization (PSO), genetic algorithm (GA) or artificial neural network (ANN) are available for optimizing cost function of system integrated with renewable energy resources. It is observed that finding solution using PSO is advantageous over GA, as it does not have evolution operators such as crossover and mutation (Mo et al. 2007). In PSO, particles update themselves with the internal velocity as they also have memory, which is important to the algorithm. PSO is also useful to integrate and locate FACTS devices when load on the system is uncertain and fluctuating in nature. Placement of FACTS devices within the system is mainly done to improve the voltage profile of the system, system loadability and minimization of losses. System performance analysis using GA and PSO (Shakib et al. 2009) shows that PSO gives better placement of FACTS devices to increase availability of power at users end. Variable speed wind turbines equipped with doubly fed induction generator (DFIG) are also widely used for advanced reactive power and voltage control strategies for windintegrated systems (Shi et al. 2012).
Organization of paper
The organization of paper is as follows: Background section explains the basic philosophy and motivation of work done in the area of voltage stability, optimization and power flow techniques. The importance of integrating wind energy systems with FACTS devices along with the need for optimal placement of FACTS devices is also presented. Optimal Power Flow with Wind Power Integration section explains the method to solve optimal power flow (OPF) for wind integrated system with necessary and governing equations. Particle Swarm Optimization Technique (PSO) explains the need of implementing PSO with its advantages over other intelligent techniques. Section Objective Function Formulation suggests formulation of objective function with and without integration of wind system with modelling of FACTS devices for optimal power flow to meet the variable load demand at the users end. Modelling of SVC and TCSC Using Firing Angle Control section presents NR power flow solution in terms of firing angle. In Bus Voltage and Angle Sensitivity Analysis section, branch and bus sensitivities of IEEE14 bus wind integrated system have been calculated to determine OPF. Similarly, procedure to find voltage stability index for maximum loading condition is presented in Determination of Voltage Stability Index (VSI). All concrete results and their detailed explanation with and without wind integrated system and performance of FACTS devices are presented in Results and Discussion section followed by Conclusion in which the usefulness of the software like GAMS and the work done is presented.
Optimal power flow with wind power integration
Particle swarm optimization technique (PSO)
Objective function formulation
To minimize active power generation cost of windintegrated system is to placing FACTS devices optimally, Considering the total load demand of 850 MW, this objective function is to be minimized for each PV Bus, except slack bus, such that \(150 < f(n) < 850\).

IC is the optimal installation cost of FACTS devices in US$

C is the cost of installation of FACTS devices in US$/KVAR

S is the operating range of FACTS devices in MVAR
Initial conditions
To solve OPF, the initial conditions for all node voltage is assumed as 1.0 per unit, with phase angle of 10^{0} for all buses and starting firing angle of 10^{0} for both TCSC and SVC.
Modelling of SVC using firing angle control
Modelling of TCSC using firing angle control
Two power flow models are available to study the impact of TCSC. The easier one is called variable series reactance, which is automatically adjustable in nature to satisfy the demand of active power flow through it. The advance model called firing modal uses directly the firing angle characteristics, which is nonlinear in nature, so for power flow solutions α is chosen as static variable in N–R power flow solutions.
N–R solution converges to the point when Eqs. (4)–(8) are expressed in linear form up to the point \(P_{ij}^{\text{Linear}}\).
Bus voltage and angle sensitivity analysis
Voltage stability analysis in large complex power system is done to obtain the critical point in the system, but this critical point also gets affected when system conditions are changed. Identification of system stability index is done with the analysis of system sensitivity. The influence of voltage profile, angle profile, active power, reactive power and momentarily change in these parameters is calculated for better planning of the system and to prevent instability in the system. So bus sensitivity indicates how a particular bus is near the critical point and how much bus is close to bus voltage instability.
Determination of voltage stability index (VSI)
Results and discussion
Bus voltage angle and magnitudebased sensitivity analysis for WIS
No.  Bus no.  Tangent vector for voltage angle  Voltage angle sensitivity \(\frac{{\partial \delta_{i} }}{{{\text{d}}\lambda }}\)  Tangent vector for voltage magnitude (\(V_{i}\))  Voltage mag. sensitivity \(\frac{{\partial V_{i} }}{{{\text{d}}\lambda }}\) 

1  3  0.17206  1.0000  1.0000  1.0000 
2  1  0.17119  0.9952  −0.9981  −0.9981 
3  8  0.16209  0.9712  −0.9669  −0.9669 
4  6  0.16113  0.9253  −0.9571  −0.9571 
5  11  0.15792  0.8825  −0.9333  −0.9333 
6  2  0.15348  0.8695  −0.8997  −0.8997 
7  4  0.15111  0.8313  −0.8649  −0.8649 
8  5  0.14881  0.7976  −0.8412  −0.8412 
9  14  0.14628  0.7761  −0.8111  −0.8111 
10  9  0.13667  0.7123  −0.7939  −0.7939 
11  10  0.13419  0.6912  −0.7775  −0.7775 
12  7  0.13291  0.6777  −0.7558  −0.7558 
13  12  0.12825  0.6485  −0.7113  −0.7113 
14  13  0.12344  0.6117  −0.6999  −0.6999 
Bus voltage profile of different buses using OPF with wind integration
S. no.  Bus no.  Voltage (p.u.) at 334.6 MW  Voltage (p.u.) at 393.2 MW  Voltage (p.u.) at 122 MW 

1  1  1.029  1.026  1.129 
2  2  1.021  1.018  1.126 
3  3  0.929  0.911  1.119 
4  4  0.978  0.926  1.136 
5  5  1.018  1.006  0.998 
6  6  0.999  0.976  1.001 
7  7  0.952  0.949  0.936 
8  8  1.002  0.998  0.882 
9  9  1.039  1.027  1.019 
10  10  0.983  0.973  0.896 
11  11  0.958  0.951  0.889 
12  12  0.939  0.883  0.891 
13  13  0.926  0.913  0.875 
14  14  0.911  0.913  0.866 
Comparison of power loss with and without FACTS
S. no.  No of iterations  Load 400 (MW)  Load 300 (MW)  Load 150 (MW)  Total power loss (MW) WO FACT  Total power loss (MW) using SVC  Total power loss (MW) using TCSC 

1  0  400  300  150  15.16  14.69  15.55 
2  1  440.68  299.12  125.77  15.78  14.63  15.60 
3  2  433.94  300.11  131.74  15.84  14.60  15.46 
4  3  435.87  299.94  130.42  15.83  14.60  15.42 
5  4  434.13  299.99  130.71  15.83  14.32  15.44 
Voltage support by FACTS devices with firing controller for WIS
S. no.  Identified weak buses  Wind penetration level (%)  SVC firing angle control (°)  Voltage support by SVC (p.u.)  TCSC firing angle control (°)  Voltage support by TCSC (p.u.) 

1  1  20  138  0.5126  141.68  0.2865 
2  12  40  129.31  0.3020  132.02  0.2327 
3  11  50  131.59  0.2331  125.55  0.2119 
4  13  75  130.27  0.2110  124.87  0.1985 
5  14  100  130.60  0.2108  123.90  0.1888 
Comparison of cost of power generation ($) per/50 MW/h with and without FACTS controllers
S. no.  Power generation (MW)  Cost of generation ($/h) without FACTS  Cost of generation ($/h) with SVC  Cost of generation ($/h) with TCSC 

1  150  723  658.5  640.5 
2  200  964  878  854 
3  250  1205  1097.5  1067.5 
4  300  1446  1317  1281 
5  350  1687  1536.5  1494.5 
6  400  1928  1756  1708 
7  450  2169  1975.5  1921.5 
8  500  2410  2195  2135 
9  550  2651  2414.5  2348.5 
10  600  2892  2634  2562 
11  650  3133  2853.5  2775.5 
12  700  3374  3073  2989 
13  750  3615  3292.5  3202.5 
14  800  3856  3512  3416 
15  850  4097  3731.5  3629.5 
Conclusion
For windintegrated system, N–R method is used to calculate power flow, i.e. voltage magnitude and angle at each bus of windintegrated system by using power balance equations. Minimization of cost of generation including wind for economic operation of integrated system is solved using GAMS 23.4 software and is also explained and presented here. Simulations are performed on IEEE 14 bus windintegrated system. PSO as one of the best computer intelligence techniques for solving optimization problem is applied both for placement of FACTS devices at suitable locations and to improve the system loadability. Power loss comparison with and without FACTS devices is also presented for simulated system using optimal power flow. SVC gives lowest cost of power generation as compared to TCSC, but system loadability is much more improved with the help of TCSC. Sensitivity analysis of buses for windintegrated system is also performed which provides the possibility of voltage collapse within the system and for proximity of the fault for identified weak buses within the windintegrated system so as to place FACTS devices at the point of possible fault for necessary and corrective voltage support to increase available power.
Abbreviations
WIS: windintegrated system; PSO: particle swarm optimization; FACTS: flexible AC transmission; OPF: optimal power flow; PF: power flow; CPF: continuous power flow; SVC: static VAR compensator; TCSC: thyristorcontrolled series compensation; GA: genetic algorithm; ANN: artificial neural network; EP: evolutionary programming; DFIG: doubly fed induction generator; PSAT: power system analysis toolbox; VSI: voltage stability index; MW: megawatt; GAMS: general algebraic modelling system
List of symbols
 ρ :

air density (kg/m^{3})
 R :

wind turbine rotor radius (m)
 V _{w} :

equivalent wind speed (m/s)
 ϴ:

pitch angle of rotor
 C _{P} :

aerodynamics efficiency of rotor
 λ _{ w } :

tip speed ratio
 P _{gn} :

active power generation in the system by n no of units
 T _{g} :

total no of generators available in the system
 C _{gn} :

cost function of nth generator bus
 Q _{ k } :

reactive power of kth bus
 P _{ k } :

active power of kth bus
 X _{ C } :

capacitive reactance
 X _{ L } :

inductive reactance
 \(\alpha_{\text{SVC}}\) :

firing angle of static VAR compensator
 \(\Delta P_{k}\) :

change in reactive power of kth bus at ith iteration
 \(\Delta Q_{k}\) :

change in Active power of kth bus at ith iteration
 λ :

change in the loading (variable load) condition of the windintegrated system
 C _{w} :

operational wind power generation cost
 P _{gw} :

wind power generation cost
 C _{ n } :

operational conventional generation cost
 P _{gn} :

conventional generation output
 N _{w} :

number of weak buses in the system
 N _{ L } :

number of load buses in the system
 P _{gn} ^{Min} :

minimum active power limits of generators
 P _{gn} ^{Max} :

maximum active power limits of generators
 P _{di} :

active power demand at buses
 Q _{di} :

reactive power demand at buses
 Q _{gn} ^{Min} :

minimum reactive power limits of generators
 Q _{gn} ^{Max} :

maximum reactive power limits of generators
 Q _{ n } :

reactive power flow in the lines after placement of FACTS devices
 Q _{ n−1} :

reactive power flow in the lines before placement of FACTS devices
 V _{ n } :

node voltage of bus i
 \(V_{n}^{\text{Min}}\) :

minimum bus voltage
 V _{ n } ^{Max} :

maximum bus voltage
Declarations
Authors’ contributions
SK has simulated wind system with conventional IEEE 14 bus system with the use of PSAT and carried out preliminary sensitivity analysis for possibility of occurrence of fault. Modelling and optimization of FACTS devices are done by NKS. “Results and discussion” section was jointly drafted by SKC, AK and NKS. All the authors have read and approved the final manuscript.
Acknowledgements
The author would like to thank and acknowledge Federico Milano, Associate Professor, School of Electrical and Electronic Engineering, University College Dublin, Belfield, Dublin 4, Ireland, for developing and providing a multipurpose PSAT software which has reduced the computational time and has made simulation of multimachine system very easy and userfriendly. The author would also like to acknowledge the Management and Department of EIE, KIET Group of Institution, Ghaziabad, for providing licensed version of the software and all necessary facilities for preparing this manuscript.
Competing interests
The authors declare that they have no competing interests.
Authors’ information
SKC was born in Mathura, U.P., India, in 1979. He received the B.Sc. Engineering degree in Electrical and Electronics Engineering from the Faculty of Engineering Dayalbagh Educational Institute, Dayalbagh Agra, U.P., India, in 2001, and M. Tech. in Electrical Engineering (Instrumentation & Control Engineering) from Aligarh Muslim University, AMU Aligarh, U.P., India, in 2004. Presently he is Ph.D student at National Institute of Technology (NITKKR), Kurukshetra, Haryana, India. His research area includes voltage stability, FACTS devices, optimization of renewable energy resources, performence and operation of renewable energy systems specially wind energy systems with economic operation of power system.
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Authors’ Affiliations
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