J Control Autom Electr Syst (2016) 27:554–561 DOI 10.1007/s40313-016-0257-z Design of PSS and TCSC Damping Controller Using Particle Swarm Optimization Maxwell Martins de Menezes1 · Percival Bueno de Araujo2 · Danilo Basseto do Valle3 Received: 9 November 2015 / Revised: 6 June 2016 / Accepted: 20 June 2016 / Published online: 11 July 2016 © Brazilian Society for Automatics–SBA 2016 Abstract In this paper, we propose a methodology to tune power system stabilizers and thyristor-controlled series capacitor damping controllers simultaneously. The parti- cle swarm optimization algorithm is incorporated into a power systemmodel to tune the parameters of supplementary damping controllers. A test power system of 10 genera- tors, 39 buses and 46 transmission lines is simulated to validate the use of this optimization algorithm. The tuning of supplementary damping controllers using the proposed methodology increases their performance to provide addi- tional damping to low-frequency oscillation modes in the simulated power system. The controller position is deter- mined by the participation factors (power system stabilizers) and the distance between the interest pole and the zero of the open-loop transfer function of the power oscillation damping controller (thyristor-controlled series capacitor-power oscil- lation damping). The results show the operating efficiency of the power system after using the optimization technique to tune damping parameters, thereby improving power sys- tem integrity. The power sensitivity model is used for the simulations presented in this work focusing on the analysis small-signal stability. B Maxwell Martins de Menezes maxwell.menezes@unoesc.edu.br Percival Bueno de Araujo percival@dee.feis.unesp.br Danilo Basseto do Valle danilodovalle@gmail.com 1 Universidade do Oeste de Santa Catarina, Rua Getúlio Vargas, 2125, Joaçaba, SC, Brazil 2 Universidade Estadual Paulista, Av. Professor José Carlos Rossi, 1370, Ilha Solteira, SP, Brazil 3 Instituto Federal de São Paulo (IFSP), Avenida do Universitário, 145, Tupã, SP, Brazil Keywords Small-signal stability · TCSC · Damping controllers · PSO 1 Introduction Interconnections of power systems may result in insufficient damping of low-frequency oscillations. These variations trig- ger a series of events that can result in inadequate and even critical operating conditions. Generally, oscillations are classified as local, inter-area or intra-plant modes and are classified according to their natural undamped frequency (Milano 2010; Rogers 2000). Power system stabilizers (PSSs) (Milano 2010; Talaq 2012) are often used in the control loop of the excitation system of synchronous generators to guarantee damping to low-frequency oscillations, in particular of local oscillation modes. Their impact on inter-area oscillation modes can be ineffective in some power system structures, thus negatively contributing to the damping of other oscillation modes. This situation is even worse when long transmission lines are used for interconnections between areas. Flexible alternat- ing current system (FACTS) (Zhang et al. 2006; Sen and Sen 2009) is commonly used in the electrical energy mar- ket because it improves transmission and distribution. A thyristor-controlled series capacitor device (TCSC) was used in the design of this work (Sen and Sen 2009; Meikandasi- vam et al. 2010). It is suggested that the TCSC should be combinedwith a power oscillation damping (POD) controller (IEEE STANDARDS 2009;Morsali et al. 2013; Simoes et al. 2009), as this combination is able to introduce additional damping to oscillation modes, especially for inter-area oscil- lation modes. The performance of PSSs and TCSC-POD controllers in power systems can cause undesirable oscillations when the 123 http://crossmark.crossref.org/dialog/?doi=10.1007/s40313-016-0257-z&domain=pdf J Control Autom Electr Syst (2016) 27:554–561 555 supplementary controllers are adjusted incoherently or, as happens in some cases, if the controllers are adjusted indi- vidually (Jabr et al. 2010). Depending upon the number of supplementary damping controllers, algorithms based on classic techniques such as the decentralized modal control (Araujo and Zaneta 2001) have complicated computational responses in terms of programming and convergence. The ability to perform a systematic search independent of the number of supplementary controllers was decisive in the choice of the particle swarm optimization (PSO) algorithm for this study (Abido 2002; Bratton andKennedy 2007). PSO is an optimization algorithm used in various areas, and it can be adapted as a tool to adjust damping controlling parameters (Morsali et al. 2013; Shayeghi et al. 2010;Mahapatra and Jha 2012). Due to the recent expansion of the power system, research on operation and control alternatives using simulations to analyze small-signal stability is necessary to ensure safety. Hence, it is suggested that local and inter-area oscillation modes are studied after the installation of PSSs and TCSC- POD controllers in a power system. To validate the technique proposed by this work, simulations are presented using a test power system with 10 generators, 39 buses and 46 transmis- sion lines. This work differs from the others in the literature as the modeling of the devices uses the power sensitivity model, incorporating the PSO algorithm to simultaneously tune n damping controllers (PSS or POD). It is important to remem- ber that the PSO algorithm is completely independent of the number and type of controllers, thus providing a parameter tuning tool for other power systems. 2 Power System Model The models used to represent the power system, including linearized models of damping controllers, are described in this section. These supplementary controllers contribute by damping oscillationmodes. In thiswork, the damping to local oscillation modes is achieved using PSSs, while the TCSC- POD controller enhances damping of inter-area oscillation modes. A multi-machine system composed of n generators and n buses is considered to represent the power system in the power sensitivitymodel (PSM) as shown in Eq. (1)where�x is the vector of state variables,�z the algebraic variables and �u the input variables. [ �ẋ 0 ] = [ J1 J2 J3 J4 ] [ �x �z ] + [ B1 B2 ] [ �u ] (1) In Eq. (1), J1 is a matrix that associates state variables with state variables, and J2 is a matrix that correlates state sTw Kr K ω VS Vref Vk Efd + + - 1+sTw 1+sTr 1+sT1 1+sT3 1+sT2 1+sT4 Fig. 1 Representation with AVR and PSS VmVk __ Zkm XTCSC Fig. 2 Circuit equivalent of the TCSC device variables with algebraic variables. The matrix J3 correlates algebraic variables with state variables, and the relation- ships between algebraic variables with algebraic variables are defined by the matrix J4. The input matrices of the sys- tem are B1 and B2. On considering the elimination of the vector of algebraic variables �z, it is possible to represent the power system in the form of state space [Eq. (2)], where A is the matrix of states and B is the matrix of inputs. �ẋ = A�x + B�u (2) A = J1 − J2 J −1 4 J3 (3) B = B1 − J2 J −1 4 B2 (4) Themodel to represent PSSs is illustrated inFig. 1 (Hassan et al. 2013; Basler and Schaefer 2008). The voltage variation �Vs is defined as the resulting output signal, which is directly applied to the control loop of the automatic voltage regulator (AVR) (Basler and Schaefer 2008; Gurrala and Sen 2010). This controller has a gain K that regulates the amount of damping, a washout block defined by the time constant Tw and time constants T1, T2, T3 and T4 responsible for the required phase compensation (Basler and Schaefer 2008), with the input signal being the variations in the angular veloc- ity of the rotor �ω of the synchronous generator. TheTCSCcanbe represented by thyristor-controlled reac- tors in parallel with a variable capacitive reactance, XTCSC controlled by the firing angle of the thyristors (Zhang et al. 2006). Its model is shown in Fig. 2, with its use causing a decrease in the initial reactance, Xkm , of the transmission line. The POD controller is used in conjunction with the TCSC device (IEEE STANDARDS 2009) to damp low-frequency oscillations of the power system. Its structure is similar to the PSS, but differs in its operation and its input signal. The basic structure of theTCSC-PODcontroller is shown inFig. 3 (Simoes et al. 2009; Shayeghi et al. 2010) with a time con- 123 556 J Control Autom Electr Syst (2016) 27:554–561 sTw 1 K ΔPkm Δ Δ XPOD Xref ΔXTCSC - + 1+sTw 1+sTTCSC 1+sT1 1+sT3 1+sT2 1+sT4 Fig. 3 Block diagram for the TCSC-POD model stant TTCSC and the signal �Xref in respect of the reactance deviation of the TCSC in continuous operation. Additional damping to low-frequency oscillations in the power system is expected with the installation of PSSs and the TCSC-POD controller. For this, the parameters of the PSSs and TCSC-POD controller must be correctly adjusted. The next section describes the PSO algorithm, which is used to tune the parameters of the PSSs and TCSC-POD controller simultaneously. 3 Particle Swarm Optimization The purpose of this study is to adjust the parameters of the PSSs and the TCSC-POD controller simultaneously. In this work, we used the PSO algorithm (Shayeghi et al. 2010; Mahapatra and Jha 2012), which is based on the concept of the movement of several particles in a specific space, pro- vided that they do not approach each other, thereby avoiding collisions, and follow the remaining particles in an orderly manner (Kennedy and Eberhart 1995). As stated in Shayeghi et al. (2010), the location of the PSS controllers is defined by factors of participation. The damping controller parameters are calculated using the PSO algorithm. Thus, the significant difference is related to the number of controllers tuned simultaneously, the objective function used by the algorithm and the model used to rep- resent the power system. In this work, representations of the devices and controllers as well as the use of the PSO algorithm to tune the parameters that control the POD were incorporated in the power sensitivity model. A key point of this work is the association of a specific eigenvalue in rela- tion to a damping controller, which is routine when using the PSOalgorithm.Without this routine, the algorithmwould not identify the eigenvalues of interest to confirm the objective function of the algorithm. The movement of a particle in any space is determined by its speed [Eq. (5)], which varies at each change of position in the specific space. The velocity vi (t+1) and the new position of the particle xi (t + 1) from its current position xi (t) are defined in Eqs. (5) and (6), where i is the particle, t is the transition number and W is the search factor (weighted by the current velocity of the particle). The variables c1 and c2 are weights, and r1 and r2 are random distributions between 0 and 1. vi (t + 1) = Wvi (t) + c1r1coi (t) + c2r2soi (t) (5) xi (t + 1) = xi (t) + vi (t + 1) (6) The velocity of the movement of each particle depends on social (soi ) and cognitive factors (coi ) as defined in Eqs. (7) and (8), respectively. These factors are classified according to the positions travelled by the particles. The relationship of each of the particles with its respective best position (Pbesti ) is called its cognitive factor, and the relationship of each of the particles with the best position of all the particles (Gbest) is called its social factor. coi = Pbesti − xi (t) (7) soi = Gbest − xi (t) (8) For the displacement of a particle in any space, it is nec- essary to control the velocity and position. Restrictions for speed and position are defined, in Eqs. (9) and (10), respec- tively. The constants vmax (maximum speed of a particle of the algorithm), xmin (minimum allowable value for particles) and xmax (maximumallowable value for particles) are defined by the PSO algorithm. These constants limit the search area of the algorithm. ⎧⎨ ⎩ if −vmax ≤ vi (t + 1) ≤ vmax : vi (t + 1) if vi (t + 1) < −vmax : −vmax if vi (t + 1) > vmax : vmax (9) ⎧⎪⎪⎨ ⎪⎪⎩ if xmin ≤ xi (t) + vi (t + 1) ≤ xmax : xi (t) + vi (t + 1) if xi (t) + vi (t + 1) < xmin : xmin if xi (t) + vi (t + 1) > xmax : xmax (10) The restrictions imposed by Eqs. (9) and (10) guarantee that the particles do not extrapolate the boundaries of the search area as determined in the design. In the case of this work, the limits are defined by constants calculated by the residue method (Zhang et al. 2012). To set the damping constant of each controller in the power system, it is necessary to define an objective func- tion [Eq. (11)]. This equation tends to minimize the distance between the calculated oscillationmodes of interest (λck ) and desired oscillation modes of interest (λdk ). Np is the number of eigenvalues of interest related to the damping controllers. min Np∑ k=1 |λck − λdk | (11) Using Eq. (11), the equivalent value of the desired oscil- latory mode λdk is calculated for each oscillatory mode of interest from the definition of the desired damping coefficient ξdk (Kundur 1994). The calculated oscillatory modes λck are obtained from power system simulations with the parame- ters of the damping controllers (values of the constants T1, 123 J Control Autom Electr Syst (2016) 27:554–561 557 T2, T3, T4 and K ) obtained by means of iterations of the PSO algorithm. λdk = −ξdk |λdk | + j |λdk | √ 1 − ξ2dk (12) Equation (11) is subject to the set of constraints defined in Eq. (13), with λm being the eigenvalues of matrix A and k representing the oscillation mode related to the damping controllers. With these restrictions, infeasible solutions will not be allowed; examples of this are the saturation of the modes of damping controllers and eigenvalueswith a positive real part. Kmin ≤ K ≤ Kmax Tmin 1 ≤ T1 ≤ Tmax 1 Tmin 2 ≤ T2 ≤ Tmax 2 Tmin 3 ≤ T3 ≤ Tmax 3 Tmin 4 ≤ T4 ≤ Tmax 4 ξmin dk ≤ ξdk ≤ ξmax dk λm = Re(λm) ± j Im(λm), ∀Re(λm) < 0 (13) From Figs. 1 and 3, it can be seen that the dynamic mod- els relating to the PSSs and the POD controller are similar. They have a gain K , a washout block Tw and phase lead–lag constants (T1, T2, T3 and T4). The number of variables to be optimized increases the con- vergence time of the PSO algorithm. This is compounded with the increase in damping controllers installed in the power system, contributing to define that Tw = 10, T1 = T3 and T2 = T4. Each particle contains a configuration with the values of the constants T1, T2 and K of n damping controllers installed in the power system. Twenty-five particles are considered, which results in a set of 75 solutions to be controlled by the PSO algorithm for each damping controller inserted in the power system. With the parameters determined by the PSO algorithm, it is desired that the oscillation modes related to the PSSs and TCSC-POD controller are positioned in a particular region of the complex plane. Figure 4 shows the best regions for local and inter-area oscillation modes. In Fig. 4, the regions are defined by means of the damp- ing coefficients specified for each oscillation mode. The desired minimum is set as ξlocal = 5% for local modes and ξinter área = 10% for inter-area modes. The choice of a smaller damping coefficient for local modes is justified because they are not sensitive to changes in the power sys- tem operating conditions (Molina et al. 2013). 4 Results The simulated test power system has 10 generators, 39 buses and 46 transmission lines. Known in the literature as the i local i inter-area ξξ ξ ξ ξ ξ ξ ξ Fig. 4 Region of desired concentration for the eigenvalues “New England,” this system has local and inter-area oscilla- tion modes with low and even unstable damping using the loading data (Araujo and Zaneta 2001). The representative line diagram is shown in Fig. 5. Using simulations, the behavior of the power system was evaluated by the dominant eigenvalues, damping coefficients (ξ ) and the natural undamped frequencies (ωn). These results are given in Table 1. On analyzing the data given in Table 1, eight local oscil- lation modes and one inter-area oscillation mode, renowned for their natural undamped frequencies (ωn), are identified in the test system (Kundur 1994). Modes 1, 5 and 8 (local) and Mode 9 (inter-area) have negative damping, character- izing the instability of the power system with oscillations of increasing amplitudes. First, the locations where the control devices will be installed need to be defined, and then, the parameters of the damping controllers should be tuned using the PSO method. Participation factors are used to define the location of the PSS devices in the power system (Kundur 1994) and the dif- ference between the poles and zeros of the POD open-loop transfer function to define the position of the TCSC-POD controller (Moura et al. 2012). A control devicewill be installed for each oscillationmode of interest in order to obtain damping levels of at least 5% and at most 10% for local modes and between 10 and 20% for inter-area modes. Two case studies are considered: – Case study A: installation of PSSs and TCSC-POD con- troller for additional damping of unstable oscillation modes (Modes 1, 5, 8 and 9); – Case study B: installation of PSSs and TCSC-POD con- troller for additional damping of all oscillation modes. From additional simulations not shown in this work, the factors of interest were calculated, and it was found that 123 558 J Control Autom Electr Syst (2016) 27:554–561 01 01 31 30 08 08 25 32 18 26 28 29 09 09 17 27 16 24 06 06 2221 07 23 07 19 05 04 04 05 20 15 1433 02 0236 35 34 37 38 03 03 12 39 11 13 10 New England System area 2 10 Fig. 5 Test system Table 1 Dominant eigenvalues, damping coefficients and natural undamped frequencies (base case) Modes Eigenvalues ξ ωn (rad/s) 1 0.0580 ± j 6.8626 −0.0084 6.8628 2 −0.2079 ± j 7.2578 0.0286 7.2608 3 −0.1139 ± j 6.4738 0.0176 6.4748 4 −0.1956 ± j 8.2569 0.0237 8.2592 5 0.1693 ± j 5.9126 −0.0286 5.9151 6 −0.2694 ± j 8.0989 0.0332 8.1033 7 −0.2432 ± j 8.3145 0.0292 8.3181 8 0.0901 ± j 6.3175 −0.0143 6.3182 9 0.0015 ± j 3.5348 −0.0004 3.5348 Generators 1, 5 and 9 (G1, G5 and G9) are more influential in local Modes 1, 5 and 8. Analyzing the open-loop transfer function of the PODcontroller, the transmission line between Buses 30 and 31 (transmission line 30–31) has a greater dis- tance between the pole of interest and its respective zero, which implies a better performance range for the POD con- troller (Moura et al. 2012). Considering case study A, PSSs are installed at Gener- ators G1, G5 and G9, while the TCSC-POD controller is installed between Buses 30 and 31. A 10% compensation of the reactance of the transmission line where the TCSC-POD controller is installed is also imposed. The configuration given in Table 2 was obtained after run- ning of the PSO algorithm (the results were processed in about 30 seconds with eight iterations of the algorithm). Table 2 Configuration of the PSO with the inclusion of the PSSs (G1, G5 and G9) and the TCSC-POD in LT 30–31 Device T1 = T3 T2 = T4 K PSS G1 1.2363 0.0346 4.6534 PSS G5 0.2915 0.0611 3.8878 PSS G9 0.1669 0.0548 6.7013 TCSC-POD 0.0765 0.3704 0.2532 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0 1 2 3 4 5 6 7 8 9 10 Real Axis A yraniga mI xi s 10% 5% Case Study A Case Base Fig. 6 Case study A On adjusting the parameters of the PSSs and TCSC-POD controller with the data presented in Table 2, it is possible to compare the behavior of the power system with and without the supplementary damping controllers. Figure 6 shows the displacement of poles caused by the inclusion of PSSs and the TCSC-POD controller using the parameters obtained by the PSO algorithm. 123 J Control Autom Electr Syst (2016) 27:554–561 559 Table 3 Configuration of PSO with the performance of the PSSs (G1, G2, G3, G4, G5, G7, G8 and G9) and TCSC-POD in LT 30-31 Device T1 = T3 T2 = T4 K PSS G1 1.1321 0.0639 2.2108 PSS G2 1.2010 0.0912 0.6431 PSS G3 1.3963 0.0276 0.6103 PSS G4 1.4185 0.0517 0.5700 PSS G5 0.2861 0.0243 3.3749 PSS G7 0.3940 0.0743 0.5633 PSS G8 1.4707 0.0436 0.7482 PSS G9 0.2501 0.0567 4.6833 TCSC-POD 0.0877 0.3011 0.1321 Figure 6 shows that the oscillation modes of the base case (in red) are displaced compared to those of case study A (in blue). The unstable local modes are shifted to the area with damping between 5 and 10%, whereas the unstable inter- area mode is shifted to the area with damping between 10 and 20%. These values are considered for the safety margin in the operation of the power system. Moreover, this figure shows that five other local modes continuewith dampingbelow5%and the installation of other PSSs is considered for additional damping to these modes. The factors of participation were again verified in order to define the best locations to install the other PSSs. Besides the PSSs and TCSC-POD controller installed in the case study, another five PSSs were installed at Generators 2, 3, 4, 7 and 8 (G2, G3, G4, G7 and G8). Therefore, the system will operate with eight PSSs (installed in G1, G2, G3, G4, G5, G7, G8 and G9) and the TCSC-POD controller installed on transmission line 30–31 with this situation being treated as case study B. The val- ues obtained for gain and the time constants using the PSO algorithm (processing approximately 88 secondswith 26 iter- ations) for the PSSs and TCSC-POD controller are given in Table 3. Figure 7 shows the displacement of oscillation modes in the base case (in red) compared to case study B (in black) after reconfiguring the systemwith the PSSs and TCSC-POD controller using the parameters tuned according to Table 3. The configuration calculated by the PSO algorithm provided the desired damping (minimumof 5%for local andminimum of 10% for inter-area modes) to all oscillation modes of the power system. Figure 8 compares the damping coefficients of the oscil- lation modes between the base case, case study A and case study B. The lack of damping to oscillation modes is evident in the base case, in particular in respect of the oscilla- tion modes that have negative damping coefficients. The algorithm calculated configurations to provide damping as -0.6 -0.5 -0.4 -0.3-0.7-0.8-0.9 -0.2 -0.1 0 0.1 0.2 0 1 2 3 4 5 6 7 8 9 10 Real Axis six A yraniga mI 10% 5% Case Study B Case Base Fig. 7 Case study B 1 2 3 4 5 6 7 8 9 -0.05 0 0.05 0.1 0.15 Modes of Oscillations gnip ma D Case Base Case Study A Case Study B Fig. 8 Comparison of damping coefficients for the case studies defined by the project 0.05 ≤ ξwi ≤ 0.1 for local modes and 0.1 ≤ ξwi ≤ 0.2 for inter-area modes in both case study A and case study B. The oscillation Modes 1, 5 and 9 of case study A have higher damping coefficients compared to case studyB.This is due to the independence of one case with the other where the settings were independently found by the PSO algorithm. In contrast, the overall damping of the system has an operating safety margin in case study B, which is not necessarily the situation in case study A. Two distinct situations are considered to check the behav- ior of the power system with load variations on the buses: increases and decreases of 5% in the active and reactive powers. Figure 9 shows the damping coefficients of each oscillation mode in case study B. It can be seen that no oscil- lation mode was damped below the desired level (5% for local modes and 10% for inter-area modes). This situation was repeated in several loading situations; however, not all loading situations were tested by this algorithm, and so an optimal response cannot be guaranteed in all power system operating ranges. On considering the power system without changes in the loads and a disturbance rejection of 0.05 pu. in Generator G2 (system reference generator), changes in the internal angle of Generator G5 (�δ5−�δ2) and its dynamic behavior were 123 560 J Control Autom Electr Syst (2016) 27:554–561 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 Modes of Oscillations gnip ma D Decreases by 5% Case Study B Increases by 5% Fig. 9 Comparison of damping coefficients for case studies B 0 1 2 3 4 5 6 7 8 9 10 -0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 Time (s) )dar( elgn A lanretnI 5ro tarene G Case Study A Case Study B Fig. 10 Internal angle of Generator G5 with the parameters of case studies B calculated as shown in Fig. 10. One can see that in case study B, the system tends toward the permanent regime value before case study A, which gives the power system a better performance when subjected to small perturbations. 5 Conclusions The work presents discussions related to small-signal sta- bility, considering the performance and simultaneous tuning of controllers, in order to increase damping levels of low- frequency oscillation modes in power systems. The efficiency of the proposed optimization algorithmwill depend on the complexity of the power system. In a less complex power system, the solution using the PSO algorithm is faster compared with other published studies (Menezes et al. 2014). The same objective function was used in the work cited with just the coordinated solution search structure being different. The PSO algorithm was used to adjust the parameters of the supplementary damping controllers. The objective func- tion of the algorithm is to position the oscillation mode of interest in a defined region using the desired damping coef- ficients (5% for local modes and 10% for inter-area modes). Nine oscillation modes were detected in a test power sys- tem subjected to unstable operation conditions characterized by oscillations of increasing amplitude; three local modes and one inter-area mode were responsible for this instability. Three PSSs and one TCSC-POD controller with locations and parameter settings defined by the techniques discussed in this paper were added to make the power system stable. With this configuration, the power system became stable, though there was the need to install other supplementary PSSs at five other synchronous generators to increase the power system damping levels. 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Berlin, Heidelberg: Springer. 123 http://dx.doi.org/10.1109/ICPCES.2012.6508094 http://dx.doi.org/10.1109/ICPCES.2012.6508094 http://dx.doi.org/10.1109/INDUSCON.2014.7059408 http://dx.doi.org/10.1109/INDUSCON.2014.7059408 http://dx.doi.org/10.1109/TSG.2012.2233224 http://dx.doi.org/10.1109/TPWRS.2008.2006999 http://dx.doi.org/10.1109/TPWRS.2012.2188820 Design of PSS and TCSC Damping Controller Using Particle Swarm Optimization Abstract 1 Introduction 2 Power System Model 3 Particle Swarm Optimization 4 Results 5 Conclusions References