An approach to optimal allocation of SVC in power systems connected to DFIG wind farms based on maximization of voltage stability and system loadability

Abstract

This paper proposed an approach to determine optimal location of SVC (Static Var Compensator) to improve the voltage profile and maximize system loadability in power networks connected to a doubly-fed induction generator (DFIG)-based wind farm. A variable reactance model for SVC is presented in steady state studies and implemented in the load flow program with embedded Flexible AC Transmission Systems (FACTS) devices. The continuation power flow method is used to determine optimal location of SVC and steady state stability margin, based on closing to point of voltage collapse. As an important result in this paper, we obtained an optimal location of SVC devices on wind farm by calculating the new indices such as maximum loading point (MLP) and mega watt margin (MWM). A case study and simulation are done on modified IEEE14 bus test system.

Keywords

Continuation power flow DFIG voltage stability wind farm SVC

1 Introduction

Beyond any doubt, we may consider century 21st as the one devoted to renewable energy. According to the International Energy Agency (IEA) [1], Renewable Energy Sources shall provide about 35% of theEuropean Union’s (EU) electricity by 2020, and within this context, wind energy is set to contribute the most–nearly 35% –of all the power coming from renewable sources. This evolution is based on sustainability scenarios, like the BLUE one [2] related to the reduction of greenhouse emissions. However, the appropriate integration of such renewable energy into power networks still presents major challenges to Power Systems Operators (PSO) and planners. Under heavily stressed situations power network could become unstable and lead to voltage collapse. Voltage stability incidents in power networks with intermittent power generation have been experienced over the world. The majority of the voltage stability analysis or voltage collapse focuses on power systems with deterministic parameters. There are little pieces of work that address the voltage stability analysis of power networks with wind energy generation.

According to IEEE/CIGRE Power System Stability definitions [3], it could be said that voltage stability refers to the power system’s ability to maintain steady-state voltages at all buses of the system after being subjected to a disturbance in a given initial operating condition. Voltage instability is mainly associated with a reactive power imbalance. The loadability of a bus in the power system depends on the reactive power support that the bus can receive from the system, as the system approaches the Maximum Loading Point (MLP) or voltage collapse point, both real and reactive power losses increase rapidly. Therefore, the reactive power supports have to be local and adequate [4].

There are two types of voltage stability based on the time frame of the simulation: static voltage stability and dynamic voltage stability. Static analysis involves only the solution of algebraic equations and therefore is computationally less extensive than dynamic analysis. Static voltage stability is ideal for the bulk of studies in which voltage stability limit for many pre-contingency and post-contingency cases must be determined.

Based on bifurcation theory, two basic tools have been developed and applied to the computation of the collapse point; direct and continuation methods. Continuation power flow method is used for voltage analysis. These techniques involve the identification of the system equilibrium points or voltage collapse points where the related power flow Jacobian becomes singular. Voltage instability is the cause of system voltage collapse, which makes the system voltage decay to a level from which they are unable to recover. The voltage collapse occurs when a system is loaded beyond its maximum loadability point. The consequence of voltage collapse may lead to a partial or full power interruption in the system [5].

Static Var Compensators (SVCs) have been widely used to enhance voltage stability and power transfer. Location of SVC and other types of shunt compensation devices is important for the enhancement of the voltage stability for practical power systems.

In [5], the effects of four Flexible AC Transmission Systems (FACTS) controllers on voltage stability will be studied. The IEEE-14 bus system is simulated in order to test the increasing loadability. Based on the simulation, the test system requires the most reactive power at the weakest bus, which is located in the distribution level. It was found that these FACTS controllers significantly enhance the voltage profile and thus the loadability margin of power systems.

Reactive power planning by optimal allocation of static VAr compensator (SVC) and controlled series capacitor (TCSC) is presented in [6]. An optimization technique based on particle swarm optimization (PSO) algorithm is developed to determine the optimal locations of SVC and TCSC and their corresponding setting values. A case study with a modified IEEE 14-bus system is carried out to demonstrate the effectiveness of the proposed technique. It is found that the obtained optimal solutions meet the requirement of the objective functions while satisfying all the constraints. Numerical results for total real and reactive power losses, energy loss cost, installation cost, and total cost are also discussed.

The proposed method in [7] makes use of the nonlinear participation factors, in which the nonlinearity of power systems can be taken into consideration. As a result, the most suitable location where the SVC should be used in power system can be determined, even in the cases in which the system is characterized with strong nonlinearity. In order to show the effectiveness of the proposed method, the New England 39-bus power system with SVC is used as an example. Calculation results show that with the SVC being located at the place where the proposed method is determined, the voltage stability is considerably enhanced. The steady-state voltage stability index and the time domain simulation results verify the effectiveness of the proposed method.

Dynamic control of large SVCs is able to maintain a constant voltage, over a wide range of operation. Allocation and size of SVCs are normally determined by off-line model analysis. However, under various operating conditions, e.g. change of system topology, redispatch of generation, load variation, etc., the SVC has different effects on maximum loadability and voltage stability. This can lead to voltage collapse at normal operating voltage when maximum loadability has been reached. Under this circumstance, classical under voltage protection will fail to detect the problem. Reference [8] scrutinizes the impact of SVC capacity on voltage collapse and the mechanism behind. The analysis results in a method to identify the maximum loadability in real time, which can be used as an indicator for online voltage stability monitoring. Finally, the methodology is validated by dynamic simulations in PSS/E.

Reference [9] proposed a new approach to determine optimal location of SVC to improve the voltage profile and maximizing system loadability with and without generators’ Mvar limits. A variable reactance model for SVC at steady state studies is presented and implemented in the load flow program with embedded Flexible AC Transmission Systems (FACTS) Devices. A simultaneous genetic algorithm (GA) and continuation power flow (CPF) is used to determine the maximum number of SVC and steady state stability margin, based on closing to point of voltage collapse. As an important result in this paper, we obtained amaximum number of SVC beyond which system loadability can’t be increased and hence increasing the loading level leads to static voltage collapsephenomena.

In [10], the sensitivity coefficient is defined as a partial derivative of voltage/reactive power. The nodes that have a higher sensitivity coefficient are selected for installing capacitors or SVC to reduce the voltage to the largest extent. The stochastic primary solution of the problem is obtained by Tabu algorithm, and then an optimized solution is achieved by the iterative solving algorithm. At last the proposed method was tested in an actual wind farm in Inner Mongolia and computational results show that the proposed method is feasible and effective.

In [11] a detailed comparison between the effects of wind power penetration and SVC on the steady state voltage stability and transient stability of electrical power systems is presented. The voltage stability was studied on a 33-bus radial distribution system where the transient stability was studied on the IEEE 9-bus transmission system. The used Wind turbine (WT) is of DFIG, and the applied SVC is the standard IEEE model. For voltage stability studies, WT and SVC were adjusted to keep the voltage within ±5% for all buses. For transient stability studies, WT and SVC were connected at the faulted bus. Simulation results show that the wind power is preferred for both voltage stability and transient stability of the system.

Reference [12] intends to introduce a coordinated Reactive Power Planning strategy among DFIG variable speed wind turbines and FACTS devices. According to this strategy, the reactive power capability from DFIG wind turbines is obtained and the limitations on deliverable power are deduced for each operation point. Furthermore, instead of using the reactive power limit as it is traditionally done, the reactive power injection from SVC relates to the existing physical limits of the control variables. The optimization strategy is based on genetic algorithms and directly includes both the reactive power capability from wind turbines and the reactive power injection from SVC devices in its formulation.

In [13], new methods have been developed to increase wind penetration level by placing new wind generation at voltage stability with strong wind injection buses. Placing new generation at these buses has the least impact on voltages stability margins (VSMs) not only in the vicinity of new wind generation, but also throughout the power system. The new methods provide a comprehensive methodology for the identification of system weaknesses for each wind penetration level. The new methods incorporate modal analysis as well as traditional voltage stability methods (Q-V curves) in size and placing new wind farms. The study shows that the locations of SVCs are also key to increasing wind penetration. Wind penetration can be increased when placing SVCs at the weakest buses in the system instead of only locating them at the wind generation buses.

This investigation attempts to improve the previously mentioned researches in the field of FACTS devices allocation in power systems. This is done by considering static voltage stability enhancement, voltage profile improvement and maximizing system loadability simultaneously. The effect of SVC placement on system performances is evaluated by calculating the new indices. In this paper applying continuation power flow (CPF) that is based on a reformulation of load flow equations, calculating loading parameter and its corresponding mega watt margin in each location of SVC, we set to rank to the best locations based on the severity of their effects on improvement of static voltage stability. The objectives of this paper are twofold; Firstly, to analyse the voltage stability problem in power networks which are heavily stressed and secondly, to show that wind energy sources coupled to the network through power converters offer the ability to provide a very fast Var injection, and thus, their optimal allocation of SVC devices in the power network could alleviate the voltage instability or even prevent voltage collapse.

2 Analysis of voltage stability using CPF method

Nowadays, wind farms are being developed both in terms of size and number. One of the main characteristics of large wind farms is a high demand of reactive power, which causes the voltage problems in the power system. The largest wind farm has stronger effects and if the network is not able to meet the reactive power requirements of wind farm power, integration of wind farm into the system will be limited. The lack of reactive power due to the operation of the wind farm may lead to increased losses and negative effects on voltage stability of the whole network.

The voltage stability is the ability of a power system to maintain acceptable voltage at all system buses under normal operation and after the occurrence of a disturbance. Voltage instability characterized as a result of gradual decrease of voltage level in one or more buses of the power system [14]. Voltage instability is essentially a local phenomenon. However, its effects may be a universal influence. Voltage collapse is a more complex phenomenon than simple voltage instability, and the cascade effect of voltage instability leads usually to voltage drop in a huge part of a power system. Static and dynamic methods are used to study the voltage stability constraints. The dynamic method is recommended in severe collapse of voltage. However, dynamic analysis needs all accurate dynamic models of all effective components of power system on the voltage stability. In most cases, the voltage collapse is typically slow. Voltage stability analysis can be studied by a static method instead of the conventional dynamic methods. The steady state voltage analysis allows system designers that use the steady state models of load flow to study the voltage stability. Usually, voltage stability acts as a load driven and for that reason is often called load stability [15].

In this situation the load change scenarios, P_D and Q_D could be modified as: $P_{D} = P_{D 0} (1 + λ)$ (1) $Q_{D} = Q_{D 0} (1 + λ)$ (2) where P _D0, Q _D0 are original loads, base case and λ is loadalibility parameter.

Voltage stability is usually studied by a P–V diagram [15] as shown in Fig. 1. Loads in all buses are increased proportional to their initial load levels and the generator outputs are also increased proportional to their initial generations. The point where the load parameter becomes tangent to the network characteristic defines the Point of Collapse (PoC). At this point λ=λ _critical. In the same way, if a load increase beyond this critical value takes place, an unstable equilibrium will be produced, and consequently the system would be unable to operate any longer. For all the reasons mentioned above, in this paper the objective function tries to maximize the loadalibility parameter considering the minimum allowed voltage value according to the utility regulations.

In this discussion, in order to seek for transmission line (TL), the power flow equations on the buses associated with the loading increments were reformulated to contain a parameter λ. If the functional vector F (θ, V, Q _c, λ) is used to denote the whole set of equations, the problem can be expressed by: $F (θ, V, Q_{c}, λ) = 0, λ \geq 0$ (3) where vectors θ and V consist of system buses phase angles and load buses voltage magnitude; Q _c denotes the reactive powers provided by the installed compensator. If each PQ bus is installed with a compensator, the dimension of $\tilde{F} (θ)$ would be n_g + 3n_d + 1, with n_g and n_d being the numbers of the PV and PQ buses, and the number of total system buses N = n_g + n_d + 1. Given λ= 0, a base case state (θ _o, V_o) can be obtained first using a conventional power flow, and then λ will be sought along the loading increment path by applying the CPF process. During the process, when λ can no more be increased, namely λ reaches λ _critical, eventually the TL $(= λ_{critical} \sum_{i \in π_{L}} Δ P_{li})$ is derived.

The procedure of CPF uses a predictor-corrector scheme along the loading increment path to find subsequent values for λ. While the corrector is only a slightly modified Newton-Raphson power flow, predictor is quite unique from anything found in a conventional power flow and deserves detailed attention [16].

2.1 Predictor

After a base case state was obtained, a prediction of the next solution can be made by taking an appropriately sized step in a direction tangent to the solution path (loading increment path). Thus, the first task in the predictor process is to calculate the tangent vector. This tangent calculation is derived by first making derivative to both sides of Equation (1) as follows: $[\begin{matrix} F_{θ} & F_{V} & F_{λ} \end{matrix}] [\begin{matrix} d θ \\ dV \\ d λ \end{matrix}] = [\begin{matrix} 0_{V} \\ 0_{θ} \end{matrix}]$ (4)

On the left side of Equation (4) is a partial derivative matrix multiplied by a differential vector. The matrix is the conventional load flow Jacobian augmented by the column vector F _λ that is directly associated with the base loading increment. In order to find a unique solution, an important barrier must be overcome. This problem arises when variable λ was inserted into the power flow equations, but the number of equations remains unchanged.

Thus, one more equation is required. This problem can be solved by choosing a non-zero magnitude, say 1, from one of the components in the tangent vector. Since the equations in Equation (4) are linear, let d λ be equal to 1 to simply denote the tangent vector and suppose λ would increase in each step until λ _critical being reached. Equation (4) is then augmented and becomes: $[\begin{matrix} F_{θ} & F_{V} & F_{λ} \\ e_{k} \end{matrix}] [\begin{matrix} d θ \\ dV \\ d λ \end{matrix}] = [\begin{matrix} 0_{V} \\ 0_{θ} \\ \pm 1 \end{matrix}]$ (5) where e _λ is an appropriately dimensioned row vector with all elements equal to zero except the (n_g + 2n_d +1)th, which is equal to 1 associated with the unit change of λ. Once the tangent vector is obtained by solving Equation (5), the predication can be made by: $[\begin{matrix} θ^{*} \\ V^{*} \\ λ^{*} \end{matrix}] = [\begin{matrix} θ \\ V \\ λ \end{matrix}] \pm δ [\begin{matrix} d θ \\ dV \\ d λ \end{matrix}]$ (6) where “*” denotes the predicted solution for a subsequent value of λ and the scaling factor δ should be appropriately chosen during each predication so that the solution can be within the convergence radius of the corrector.

2.2 Corrector

The corrector process is used to modify the predicted solution onto the solution path with one of the state variables being ascertained into an additive equation, say. Then, the new set of equations would be: $[\begin{matrix} F (x, λ) \\ x_{k} - x_{k}^{*} \end{matrix}] = [0]$ (7)

One of the voltage magnitudes on the PQ buses will be denoted as $x_{k}^{*}$ , assuming on bus k, which has the most negative value in the prediction. With an additive equation and a variable λ, the augmented equations can be solved by a slightly modified Newton-Raphson power flow method [16].

For dealing with the saddle-node bifurcation point on the loading increment path, the PSAT program developed in [17, 18] is employed to execute the CPF process.

3 Modeling of power system components

In this section, modeling of the power system components such as DFIG wind generators and SVC will be discussed.

3.1 Modeling of DFIG

Wind turbines that are used in modern wind power plants consist of different parts such as rotor, gearbox, doubly fed induction generator (DFIG), brake mechanism, turbine deviation mechanism, vane and anemometer. In the next, modeling of the DFIG wind turbine is described.

DFIG is a wound rotor induction generator with a voltage source converter connected to the slip-rings of the rotor. The stator winding is coupled directly to the grid and the rotor winding is connected to the grid via a power electronic converter. The typical configuration of a wind turbine based on a DFIG is shown in Fig. 2.

The rotor winding is supplied using a back-to-back voltage source converter [19]. In high wind speeds the power extracted from the wind is limited by pitching the rotor blades. The reactive power exchanged between the machine and the network can be controlled up to certain limits. As DFIG units have reactive power capability, the wind farm is modeled in a way similar to the conventional generator for steady state analysis and is represented as either PV bus with appropriate VAR limits or PQ bus with constant power factor [20]. The studies carried out in this paper focused only on a variable speed unit, modelled as a PV bus.

3.2 Modeling of SVC

SVC consists of controllable thyristor switches, capacitor banks, and shunt reactors, which is able to compensate reactive power continuously. The thyristor controlled reactor with a fixed capacitor (TCR/FC) could be mentioned as a member of this family of compensators. The single line diagram of TCR/FC is shown in Fig. 3 [21].

The block diagram of the SVC regulator is shown in Fig. 4. The SVC regulator parameters on a 100 MVA base are: the regulator time constant, T_r = 10 s.; the regulator gain, K_r = 100; the reference voltage, V_ref = 1.0 pu. The model is completed by the algebraic equation expressing the reactive power injected at the SVC node [11]: $Q_{SVC} = - V^{2} B_{SVC}$ (8) Where:

Qsvc is the total reactive power of SVC,

V is the bus voltage magnitude,

Bsvc is the susceptance of SVC.

4 The proposed evaluation indices in SVC placement

The effect of SVC placement on system performances is evaluated by calculating the indices defined as following:

MWM (mega watt margin) is defined in Equation (9) to represent the additional load from the operating point to the point of voltage collapse, as shown in Fig. 1.

MWM = P_{max} - P_{base}

(9) where P _max is maximum load active power corresponding with MLP and P _base is base load active power.

System loadability improvement (SLI) is defined to calculate the effect of SVC on system loadability. To find out the maximum system loadability (λ _max) of the system, active and reactive power load is increased on all buses, till the voltage collapse is observed. SLI is given by Equation (10).

SLI % = \frac{λ_{max (w)} - λ_{max (wo)}}{λ_{max (wo)}} \times 100

(10) where, λ _max(wo) is maximum loadability of the system at base case (without SVC or DFIG) and λ _max(w) is maximum loadability of the system with SVC or DFIG.

Active line-loss reduction (ALLR), Reactive line-loss reduction (RLR) and mega watt margin improvement (MWMI) indices are defined asfollowing:

ALLR % = \frac{Re {losses}_{(w)} - Re {losses}_{(wo)}}{Re {losses}_{(wo)}} \times 100

(11)

RLR % = \frac{Im {losses}_{(w)} - Im {losses}_{(wo)}}{Im {losses}_{(wo)}} \times 100

(12)

MWMI % = \frac{{MWM}_{(w)} - {MWM}_{(wo)}}{{MWM}_{(wo)}} \times 100

(13)

5 Simulation results

In the test, a modified IEEE 14 bus system shown in Fig. 5 was used to validate the proposed method. The test system consists of five generators and eleven PQ buses (or load buses). The simulations use PSAT simulation software. The theoretical static load margin is computed in this paper by using PV curves. These curves are obtained in PSAT by means of the continuation power flows; this method uses predictor-corrector steps to ensure convergence of the nonlinear algebraic equations that describe the power system, avoiding the singularity of the Jacobian matrix near the maximum loading point.

Based on the CPF results which are shown in the Figs. 6 and 7, the buses 4, 5, 9 and 14 are the critical buses. Maximum loading point (MLP) or bifurcation point where the jacobian matrix becomes singular occurs at λ _max = 2 . 7116 p.u. Also load active powers are in the base and maximum cases are P _base = 3.626 p . u . and P _max = 9.7958 p . u . respectively.

The Mega Watt Margin (MWM) of the system is the distance measured in MW from the initial operating point, the nose of the P-V curve. MWM is calculated 6.1698 p.u. By using CPF analysis, bus 14 is recognized as the weak bus from voltage analysis and the wind farm is connected to this bus.

The corresponding collector system is shown in Fig. 8; one transformation stage is modeled: one from 69 V to 13.8 kV. Detailed data for the DFIG-based wind turbine, wind model and collector system can be found in the Tables 5–8 in the Appendix.

The wind farm includes 43 wind turbine generators equipped with DFIGs with total capacity of 43 MW. The wind farm under study is connected to bus 14 through a transmission line with a line impedance of 5.25×10-7+j1×10-6 p.u. and a transformer with a capacity of 100 MVA.

The DFIG-based wind turbine with terminal voltage control operation delivers the reactive power required to keep the voltage at terminals constant at 1 p.u. The loading parameter and MWM for this case is calculated 2.8381 and 6.665 p.u. respectively. This margin is 666.5 MW, which is 8.02% higher than the static load margin in pervious case. The optimum value of the wind farm is 0.46707 p.u, and λ _max is equal to 2.66562 p.u. at this point, after which λ _max starts to decrease. It meant that a higher wind penetration might weaken the system’s voltage stability (Fig. 9).

It is shown that the optimal management of FACTs devices in distribution networks with high wind energy enhances the voltage profile and increases the maximum loading of the system. Most specifically, if SVC device is added to the power network, the maximum loading of the system for operational voltage limit will increase.

Table 1 shows the impact of the SVC location on maximum loading. As can be seen SVC injection increases the maximum loading level. According to table SVC power injection at bus 9 has more positive effects on voltage stability. This bus is the best location for installation of SVC. This bus with λ _max = 2.92315 p.u. and MWM 6.9734 p.u. is identified as the optimal location among other buses. The SVC is also installed at other buses to increase the maximum loading level. The location of buses 9, 10 and 7 are at higher ranks in this table. Also Figs. 10 and 11 show the impact of the SVC location on maximum loading and MWM of test power system. Table 2 shows comparison of the proposed method with other methods. As can be seen bus 14 was selected in previous methods. While using the proposed method bus 9 has been selected for installation of SVC. It is because of wind farms installed in the test system and thus the network topology is modified by placing a wind farm.

By applying the CPF for this test system, both voltage profiles in each bus and power flow in each line will change. In this system total generation, total power and total losses in MLP are shown in Table 3. According to this table, it can be seen that the capacity of CPF is more than that of power flow (PF) analysis. According to the table, total losses in MLP with DFIG are less than other cases and the reactive power generation in MLP with DFIG and SVC is more than that of other cases.

The values of λ _max and Mega Watt Margin (MWM) and other evaluation indices with all cases are compared in Table 4. Also Fig. 12 shows comparison of evaluation indices for modified IEEE 14-bus. From the Table 4 and Fig. 12, it is obvious that installation of SVC and DFIG together gives more maximum loading margin compared to other cases. It could be observed that the loadability and the distance to the point ofcollapse of the system increased. Also Fig. 13 shows the comparison of P-V curves for IEEE 14-bus test system at all cases. So, as a conclusion, it could be stated that the incorporation of wind farms and SVC in power systems improves voltage stability and maximum loading point.

6 Conclusion

The loading margin to the point of voltage collapse is a fundamental index of relative voltage stability and system security. This paper has demonstrated that computing the MW margin sensitivities from the nose of the P-V curve can do effective analysis of voltage collapse studies. In this paper, optimal location of SVC devices is carried out by using continuation power flow method to cover the problem associated with wind penetration in power systems. This device is modeled for steady-state studies. The system loadability and improving the bus voltage profile were employed as a measure of power system performance in an optimization algorithm. Simulations are done without and with the wind farm. The method in this paper is examined in a modified IEEE 14 bus system. Moreover Results have shown that the use of CPF is an efficient solution to find the maximum system loadability and optimal placement of SVC. Besides, SVC devices are located at buses that are weak from reactive power requirements.

Footnotes

Appendix

References

Organization for Economic Cooperation & Devel, Energy technology perspectives: Scenarios and strategies to 2050:2010. Organization for economic cooperation & Devel, Paris, France, 2010.

International Energy Agency, Ensuring green growth in a time of economic crisis – the role of energy technology. International Energy Agency, Siracusa, Italy, 2009.

Kundur

Paserba

Ajjarapu

Andersson

Bose

Canizares

Hatziargyriou

Hill

Stankovic

Taylor

Van Cutsem

Vittal

2004

Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions

IEEE Trans Power Syst 19 3 1387 1401

Ahmadi Kamarposhti

Lesani

2011

Effects of STATCOM, TCSC, SSSC and UPFC on static voltage stability

Electrical Engineering 93 1 33 42

Ahmadi Kamarposhti

Alinezhad

Lesani

Talebi

2008

Comparison of SVC, STATCOM, TCSC, and UPFC Controllers for Static Voltage Stability Evaluated by Continuation Power Flow Method

The IEEE 8th Annual Electrical Power & Energy Conference 1 8

Auchariyamet

Sirisumrannukul

2009

Optimal reactive power planning with facts devices by particle swarm technique

8th International Conference on Advances in Power System Control, Operation and Management (APSCOM 2009) 1 6

Jing Zhang

Wen Cheng

2007

A novel SVC allocation method for power system voltage stability enhancement by normal forms of diffeomorphism

IEEE Transactions on Power Systems 22 4 1819 1825

Duong Thuc

Dinh

Uhlen Kjeti

2014

Analysis of impacts of SVC on voltage collapse mechanism and maximum loadability

International Conference and Utility Exhibition on Green Energy for Sustainable Development (ICUE) 1 6

Najafi

Abedi

Hosseinian

2006

A Novel Approach to Optimal Allocation of SVC using Genetic Algorithms and Continuation Power Flow

IEEE International Power and Energy Conference, PECon ’06 202 206

10.

Ping

Zhang

Xiang Jun

Zeng

Ling

2008

Optimal Allocation of Reactive Power Source in Wind Farms Using Sensitivity Analysis and Tabu Algorithm

International Conference on Intelligent Computation Technology and Automation (ICICTA) 1 1230 1234

11.

Mohamed

Aly Sayed

Said Abdel-Akher

Mamdouh

2012

Comprsion Between Wind Turbine and Static Var Compensator for Power System Stability

Proceedings of the 15th International Middle East Power Systems Conference (MEPCON’12) Alexandria University

Egypt

12.

Amaris

Hortensia

Alonso

Monica

2011

Coordinated reactive power management in power networks with wind turbines and FACTS devices

Energy Conversion and Management 52 7 2575 2586

13.

Tamimi

Pahwa

Starrett

2012

Effective wind farm sizing method for weak power systems using critical modes of voltage instability

IEEE Transactions on Power Systems 27 3 1610 1617

14.

Kundur

1994

Power System Stability and Control

McGraw-Hill

New York

15.

Ajjarapu

2006

Power Electronics and Power Systems

Computational techniques for voltage stability assessment and control Springer

United State of America

16.

Ajjarapu

Christy

1992

The continuation power flow: A tool for steady state voltages stability analysis

IEEE Trans On Power Systems 7 1 416 423

17.

Milano

2013

Version 2.1.8, Software and Documentation

Power System Analysis Toolbox

18.

Milano

2005

An open source power system analysis toolbox

IEEE Transactions on Power Systems 20 3 1199 1206

19.

Hansen

Michalke

2007

Fault ride-through capability of DFIG wind turbines

Renewable Energy 32 1594 1610

20.

Feijóo

2009

On PQ models for asynchronous wind turbines

IEEE Trans Power Syst 24 4 1890 1891

21.

Ebadian

Mahmoud

Edrisian

Ashakn

Goudarzi

Arman

2014

Investigating the effect of high level of wind penetration on voltage stability by quasi-static time-domain simulation (QSTDS)

International Journal of Renewable Energy Research 4 2