The 22nd Iranian Conference on Electrical Engineering (ICEE 2014), May 20-22, 2014, Shahid Beheshti University A Genetic Algorithm Optimized Fuzzy Logic Controller for UPFC in Order to Damp of Low Frequency Oscillations in Power Systems Roozbeh Torkzadeh Power System Planning Center Esfahan Regional Electric Company Esfahan, Iran Roozbeh.Torkzadeh.1988@ieee.org Hooman NasrAzadani Department of Electrical and Computer Engineering University of Kurdistan Sanandaj, Kurdistan, Iran Hooman.NasrAzadani@stu.uok.ac.ir Abstract—Due to the lack of damping torque, power system disturbances such as step changes in input mechanical power, may lead to Low Frequency Oscillations (LFO). Power System Stabilizer (PSS) is a solution that has been used for many years in order to mitigate these oscillations. Flexible AC Transmission Systems (FACTs) is another solution for this problem. Among the FACTs devices, Unified Power Flow Controller (UPFC) has an excellent ability to control power flow, reduce sub-synchronous resonance, and increase transient and dynamic stability and therefore, may be used instead of PSS. In this paper, a Genetic Algorithm Optimized Fuzzy Logic Controller (GA-FLC) is used to control UPFC for damping low frequency oscillations. This study is applied to a single-machine infinite-bus (SMIB) PhillipsHeffron model by using MATLAB®/ Simulink® software. Simulation results explicitly show that the performance of the proposed GA-FLC Based UPFC is better than using PSS and a PI controlled UPFC in terms of damping LFO. system damping of low frequency oscillations. PSSs have proved to be efficient in performing their assigned tasks. A wide spectrum of PSS tuning approaches has been proposed. These approaches have included pole placement [1], damping torque concepts [2], variable structure [3], and different optimization and artificial intelligence techniques [4, 5]. However, PSS may adversely affect voltage profile and may not be able to suppress oscillations resulting from severe disturbances, such as three-phase faults at generator terminals [6]. B. Flexible AC Transmission Systems Flexible AC Transmission Systems (FACTS) have shown very promising results when used to improve power system steady-state performance. Unified power flow controller (UPFC) is the most promising device in the FACTS concept. It has the ability to adjust three control parameters, i.e. bus voltage, transmission line reactance, and phase angle between two buses. A major function of UPFC is to redistribute power flow among transmission lines during steady state condition. Furthermore, it can be used to improve damping of low frequency oscillations during transients [7]. Gharedaghi et al. presented a new method to damping of LFO based on fuzzy logic controller [8]. Kadhim and Shrivastava investigated a neuro-fuzzy controller to command a UPFC for enhancing system stability by scaling down LFO [9]. Fig. 1 shows a single-machine infinite-bus power system with an installed UPFC which consists of an excitation transformer (ET), a boosting transformer (BT), two threephase GTO based voltage source converters (VSC) and a DC link capacitor. In Fig. 1, mE, mB, δE and δB are amplitude modulation ratio and phase angle of the control signal of each VSC respectively, which are the input control signals to the UPFC [10]. The rest of paper is organized as follows. An overview of dynamic model of system is presented in Section II. Section III introduces thedesign of optimized fuzzy logic controller (FLC) in brief. Simulation and resultsare presented in Section IV and finally conclusion is discussed in Section V. Keywords- Flexible AC Transmission Systems (FACTS); GAOptimized Fuzzy controller (GA-FLC); Low Frequency Oscillations (LFO); Single Machine-Infinite Bus (SMIB); Unified Power Flow Controller (UPFC) I. INTRODUCTION Damping of Low Frequency Oscillations (LFO) has vital role in power systems because the un-damped LFOs may keep growing in magnitude until loss of synchronism happens. Today, power demand grows rapidly but on the other hand expansion in generation and transmission is restricted to the availability of resources and the strict environmental constraints; consequently, power systems are much more loaded today than before. In addition, interconnection between remotely located power systems is turned out to be a common practice. These give rise to low frequency oscillations in the range of 0.1-3.0 Hz. There are two major methods that used to damping LFO: A. Power System Stabilizer Power system stabilizers (PSSs) have been used in the recent decades to serve the purpose of enhancing power 978-1-4799-4409-5/14/$31.00 ©2014 IEEE Aliakbar Damaki Aliabad Department of Electrical and Computer Engineering Yazd University Yazd, Iran alidamaki@yazd.ac.ir 706 B. SMIB Dynamic Model A linearized Phillips-Heffron Model is used for dynamic modelling of Single Machine-Infinite Bus (SMIB). Equations (7), (8), (9) and (10) represent state equations of SMIB: δ$ = ωb (ω − 1) (7) ω$ = Fig. 1. Installed UPFC on Single-Machine Infinite-Bus (SMIB) power system II. A. UPFC Dynamic Model By applying Park’s transformation on three-phase dynamic differential equations of the UPFC and ignoring the resistance and transients of the transformers, the dynamic equations of the UPFC are demonstrated as below [10,11]. ⎡ mE cos(δ E )vdc ⎤ − xE ⎤ ⎡iEd ⎤ ⎢ ⎥ 2 ⎢ ⎥+ 0 ⎥⎦ ⎣iEq ⎦ ⎢⎢ mE sin(δ E )vdc ⎥⎥ 2 ⎦ ⎣ ⎡VBtd ⎤ ⎡ 0 ⎢V ⎥ = ⎢ ⎣ Btq ⎦ ⎣ xB ⎡ mB cos(δ B )vdc ⎤ − xB ⎤ ⎡iBd ⎤ ⎢ ⎥ 2 ⎢ ⎥+ 0 ⎥⎦ ⎣iBq ⎦ ⎢⎢ mB sin(δ B )vdc ⎥⎥ 2 ⎦ ⎣ iEd = m sin(δ B )vdc xBB + xd 5vb cos(δ ) Eq′ + xd 7 B xd 2 2 + xd 6 mE sin(δ E )vdc 2 iEq = xq 7 iBd = iEd mB cos(δ B )vdc + xq 5vb sin (δ ) 2 xE x m sin(δ B )vdc + xd 3vb cos(δ ) Eq′ − d 7 B xd 2 xd 2 2 x m cos(δ B )vdc = q1 B + xq 3vb cos(δ ) 2 xq 2 + xq 4 (8) E − ( xd − x′d )id − Eq′ E$ q′ = fd Tdo′ (9) K (V − v) − E fd E$ fd = A ref TA (10) Where Pe= vdid+vqiq, v= (vd2+ vq2)0.5,vd=xqiq,vq=E'q-x'd.id, id=iBd+iEd, iq=iBq+iEq also Pm and Pe are the input and output power, respectively; M and D are inertia constant and damping coefficient; ωb is synchronous speed; δ and ω are the rotor angle and speed; E'q, E'fd, and v are generator internal, field and terminal voltages; T'do is open circuit field time constant; xd, x'd, and xq are d-axis reactance, d-axis transient reactance, and qaxis reactance, respectively; KA and TA are exciter gain and time constant; Vref is reference voltage. SYSTEM DYNAMIC MODEL In order to determine a dynamic model for SMIB with UPFC, dynamic equations of each part are calculated separately. At first, the dynamic equations of UPFC are presented to determine UPFC dynamic model, and then dynamic equations of SMIB in absence and presence of UPFC are presented. ⎡VEtd ⎤ ⎡ 0 ⎢V ⎥ = ⎢ ⎣ Etq ⎦ ⎣ xE Pm − Pe − D(ω − 1) M In order to apply UPFC into Phillips-Heffron Model, another state equation is needed [10], which is (11). v$dc = ⎡i ⎤ ⎡i ⎤ 3mE [cos(δ E ) sin(δ E )]⎢ Ed ⎥ + 3mB [cos(δ B ) sin(δ B )]⎢ Bd ⎥ i 4 4Cdc C dc ⎣iBq ⎦ ⎣ Eq ⎦ (11) Where vEt, iE, vBt, and iB are the excitation voltage, the excitation current, the boosting voltage, and the boosting current. Also, Cdc and vdc are the capacitance and voltage of the DC link, respectively. (1) C. Linearizing Power System Dynamic Model In order to use linearized Phillips-Heffron Model non-linear dynamic equations should be linearized around the operating point. The linearized model is assumed by (12): (12) x$ = Ax + Bu (2) (3) Where the state vector x, the control vector u, and the matrices A and B are shown in (13), (14), (15) and (16): [ x = Δδ (4) u = [Δ m E (5) ⎡ 0 ⎢ k ⎢ − 1 ⎢ M ⎢ k A=⎢ − 4 Tdo′ ⎢ k ⎢− A k 5 ⎢ TA ⎢ k ⎣ 7 (6) mE cos(δ E )vdc 2 Where xE and xB are the Et and Bt reactances, respectively; the reactances xqE, xdE, xBB, xd1 to xd7, and xq1 to xq7 are as shown in [12]. 707 Δ E q′ Δω Δδ E ωb D − M 0 0 0 Δ E fd T T 0 0 1 Tdo′ 1 − TA 0 − ] Δδ B ] Δm B 0 k − 2 M k − 3 Tdo′ k k − A 6 TA k8 Δ v dc 0 ⎤ k pd ⎥ − ⎥ M ⎥ k qd ⎥ − Tdo′ ⎥ ⎥ k k − A vd ⎥ TA ⎥ − k 9 ⎥⎦ (13) (14) (15) ⎡ 0 ⎢ k pe ⎢ −M ⎢ k qe B=⎢ − ⎢ Tdo′ ⎢ k Akve ⎢− ⎢ TA ⎣⎢ kce − 0 k pδe M kqδe − Tdo′ k Akvδe − TA kcδe − 0 k pb M kqb − Tdo′ k Akvb − TA kcb 0 ⎤ k pδb ⎥ − M ⎥ kqδb ⎥ ⎥ − Tdo′ ⎥ k k ⎥ − A vδb ⎥ TA ⎥ kcδb ⎦⎥ For this purpose, four separate fuzzy logic controllers are used to control ∆mB, ∆mE, ∆δB, ∆δE. Each one has two inputs that are ∆δ and ∆ω and one output that controls ∆mB, ∆mE, ∆δB, ∆δE. Optimization fitness function is presented in (17). F = 12 f 1 + f 2 + f 3 + 100 f 4 (17) Where f1 is the maximum overshoot, f2 is the settling time, f3 is the zero crossing and f4 is the average of output signal. Weighting coefficients are selected by trial and error. Convergence characteristics of PSO and GA Optimizations are shown in Fig. 3. According to this figure, it is clear that the GA Optimization has a better performance to minimize fitness function in comparison to the PSO. Consequently, the GA optimized fuzzy logic controller is proposed in this paper. The procedure of the proposed genetic algorithm in this work is given below: a) Generate randomly a population of parameter strings to form primary population. The population number of each generation is assumed 40 and each individual in population has 48 gens. b) Calculate the fitness function as given in (17) for each individual in the population. c) Choose parents by applying selection function. Roulette wheel is used as selection function. d) Apply crossover function on parents in order to create next generation. 0.8 is assumed as crossover fraction. e) Apply mutation function on new population. A uniform function with the rate of 0.02 is assumed as mutation function. f) Compute the children and parents finesses. g) If the stopping criteria satisfied, optimization will stop, otherwise; return to step (c). Number of iterations is used as the stopping criteria and the maximum value of it is assumed as 150. (16) Where ∆δ and ∆ω are the linearized rotor angle and angular velocity; ∆E’q, ∆E'fd and ∆vdc are the linearized generator internal voltage, the linearized generator field voltage and the linearized DC link voltage, respectively. Also k-constants are linearization constants that are calculated as shown in Table I. Also the schematic diagram of dynamic model of the SMIB with UPFC is shown in Fig. 2 [10, 11]. III. DESIGN OF OPTIMIZED FUZZY LOGIC CONTROLLER In this section, the design procedure of GA Optimized fuzzy logic controller is presented. In this research, Genetic Algorithm (GA) and also Particle Swarm Optimization (PSO) are used to design an optimum fuzzy logic controller in order to reach the best dynamic performance of the power system. Table I - K-CONSTANTS OF LINEARIZING k5 = ∂Vt ∂δ k =∂V$ ∂V k6 = ∂Vt ∂Eq′ k3 = ∂Eq ∂Eq′ k7 = ∂V$dc ∂δ k 4 = ∂Eq ∂δ k8 = ∂V$dc ∂Eq′ dc kpd = ∂Pe ∂Vdc kqd =∂Eq ∂Vdc kpe = ∂Pe ∂mE kqe = ∂Eq ∂mE kve = ∂Vt ∂mE kpδe =∂Pe ∂δE kqδe = ∂Eq ∂δ E kvδe = ∂Vt ∂δ E kvd = ∂Vt ∂Vdc kce = ∂V$dc ∂mE k = ∂V$ ∂δ kpb =∂Pe ∂mB kqb =∂Eq ∂mB kvb = ∂Vt ∂mB kpδb = ∂Pe ∂δ B kqδb = ∂Eq ∂δ B kvδb = ∂Vt ∂δ B k1 = ∂Pe ∂δ k2 = ∂Pe ∂Eq′ 9 dc cδe dc E kcb =∂V$dc ∂mB k = ∂V$ ∂δ cδb dc B Fig. 2. Schematic of linearized Phillips-Heffron model with applying UPFC 708 Fig. 6. Fuzzy Logic Controller Structure IV. SIMULATION AND RESULTS In this research, a single machine infinite bus system is selected for/as a case study and simulated in MATLAB®/ Simulink®. The specification of the simulated system is presented in Appendix. Simulations have been done for four different cases and the rotor angel deviation (∆δ) is illustrated for each case as following. Fig. 3. Convergence characteristics of PSO and GA Fuzzy system rule’s consequents and input/output scale factors of FLC are optimized by GA. The fuzzy system membership functions for input and output are shown respectively in 4 and 5. A. Case A. SMIB in absence of PSS and UPFC In this case a SMIB is simulated with a 0.1 p.u step change disturbance in mechanical power at time = 2 sec that last for 0.5 sec. Neither PSS nor UPFC is connected to the system. The simulation result is presented in Fig. 11. As shown in this figure the LFO keep growing in magnitude and the system is not stable. B. Case B. SMIB with PSS In order to damping LFOs in case B a PSS is designed and connected to SMIB. For designing the stabilizer, the transformation function between PSS output and e'q state variable is obtained as (18). GE = k Ak3 (1 + sTA )(1 + sTd′0 k 3 ) + k A k 3 k 6 (18) By applying s=jωn the lagging property of GE which is considered as phase angle is calculated. In this condition, the lagging property of GE is achieved more than 45° and therefore, the PSS should contain two compensation blocks. Kpss and T1 could also be calculated according to (19), (20), (21) and (22) [13]. Fig. 4. Membership function for ∆δ and ∆ω Fig. 7. ∆δ deviations of SMIB without PSS and UPFC Fig. 5. Membership function of controller output signal 709 Table II - OPTIMAL VALUES OF KP AND KI FOR PI CONTROLLER Optimum Values ∆mE Controller ∆δE Controller ∆mB Controller ∆δB Controller KP KI -0.8574 -0.2306 -0.0074 -0.0530 0.1040 -0.0631 -0.3164 -0.1058 Fig. 8. PSS block structure ∠G E ( jω n ) = 2γ , γ < 0 1 + jω nT1 +γ = 0 1 + jω nT2 tan (tan −1 (ω n T2 ) − γ ) T1 = ωn ∠ (19) (20) (21) 2ξω n M k pss = k2 1 + jω nT1 G E ( jω n ) 1 + jω nT2 (22) Where kpss is the DC gain of PSS, ξ is the damping coefficient, T, T1 and T2 are the time constants of reset block and PSS block, respectively. T=3 sec, T2=0.2 sec are assumed in order to calculate T1 and kpss. The Calculated values are T1=0.7305 sec and kpss =7.408. Also, the PSS structure is shown in Fig. 12. By applying the designed PSS to the generator the deviation of the rotor angel is calculated again and shown in Fig 13. As shown in this figure the system has been stable in this condition. Fig. 10. ∆δ deviations of SMIB with PI Controlled UPFC D. Case D. SMIB with UPFC controlled by PSO-FLC and GA-FLC on ∆mB, ∆mE, ∆δB, ∆δE In this case, a separate fuzzy logic controller is used to control each UPFC inputs. Moreover, the fuzzy rules and fuzzy system inputs and output scale factors are optimized by GA and PSO. The GA-optimization parameters are calculated and shown in Table III. Using these parameters, the variation of ∆δ becomes as Fig. 15. In order to realize the applicability of the proposed method some comparisons have been made between four cases and presented in Fig 16, 17 and 18. Also, the Eigen values of system in each case are presented in Table IV. As seen from these results, the proposed method i.e. GA-FLC has the best performance among the other methods. The figures show that applying the proposed method leads to the lowest settling time and the lowest LFO amplitude in comparison with PSS, GA optimized PID and PSO-FLC. C. Case C. SMIB with UPFC controlled by a PI controller on ∆mB, ∆mE, ∆δB, ∆δE In this case, a PI Controlled UPFC is added to the SMIB in order to damp LFO. The PI Controller is used to control ∆mB, ∆mE, ∆δB, ∆δE. The KP and KI coefficients of each controller is optimized with Genetic Algorithm and presented in Table II. In this condition, the deviation of ∆δ is calculated and shown in Fig. 14. This figure shows the good ability of UPFC for LFO damping. Fig. 11. Comparison between GA-FLC and PSO-FLC for UPFC Fig. 9. ∆δ deviations of SMIB with PSS 710 Table III - GA OPTIMIZATION RESULTS Fig. 12. Comparison between GA-FLC and SMIB without PSS and UPFC Optimum ∆mE ∆δE ∆mB ∆δB Values Controller Controller Controller Controller Rule#1 SP LP SP LP Rule#2 ZE ZE SN SN Rule#3 SP SN ZE ZE Rule#4 SP LN SP LP Rule#5 ZE ZE ZE ZE Rule#6 SN SP SN LN Rule#7 ZE ZE SP SP Rule#8 ZE SP ZE SN Rule#9 SP LP ZE SP ∆ω Scale Factor 2.2284 4.9985 9.9947 8.2858 ∆δ Scale Factor 7.3532 5.6136 7.5353 3.0665 U Scale Factor 4.7338 5.9043 9.1695 0.6036 Table IV- EIGEN VALUES OF CASE A, B, C AND D Eigen Values of Eigen Values each case Fig. 13. Comparison between GA-FLC and PSS SMIB SMIB with PSS SMIB with UPFC by GA-PI SMIB with UPFC by GA-FLC Fig. 14. Comparison between GA-FLC and GA-PI Controller 711 0.6020 + 5.7108i 0.6020 - 5.7108i -10.9470 + 0.6832i -10.9470 - 0.6832i -22.0021 -2.0813 +11.3023i -2.0813 -11.3023i -0.8463 + 3.3524i -0.8463 - 3.3524i -2.8297 -0.3363 -9.4145 + 9.0518i -9.4145 - 9.0518i -0.5655 + 6.0558i -0.5655 - 6.0558i -0.4531 -0.0588 -10.2324 + 9.2265i -10.2324 - 9.2265i -0.6304 + 6.9834i -0.6304 - 6.9834i -0.3163 V. [6] CONCLUSION In this paper, an Optimized GA-FLC controller is proposed for UPFC to mitigate low frequency oscillations. The controller was designed for a single machine infinite bus system. Then the simulation results for the system including SMIB, SMIB with PSS, SMIB with PI controlled UPFC and SMIB with GA-FLC controlled UPFC were presented. Simulations were performed for 0.1 p.u step change in mechanical power and 0.5 sec duration. The simulation results explicitly showed that the proposed GA-FLC has good performance to reduce settling time and reduce amplitude of LFO in comparison with PSS, GA optimized PID and PSO-FLC. [7] [8] [9] [10] [11] ACKNOWLEDGMENT R.Torkzadeh and H.NasrAzadani would like to express their gratitude to honourable faculties of Yazd University and University of Kurdistan especially to Dr A.R. Sedighi Anaraki and Dr A. Hesami Naghsh-Bandi and also would like to thank Dir. F.Eghtedarnia, Dr E.Karimi and their other colleagues in EREC's technical planning center due to their supports. [12] [13] APPENDIX Roozbeh Torkzadeh (S'14) was born in Esfahan, Iran, on 1988. He received his B.S. in electrical engineering from Islamic Azad University of Najaf Abad in 2011 and M.S. (Hon.) degree in electrical engineering from Yazd University in 2013. Currently he is with the Esfahan Regional Electric Company (EREC) as the protection and planning expert and he is a member of EREC Reliability Council's VoLL and RCM workgroups. He was also with Islamic Azad University of Naein as a part time lecturer. His major interests are protection, expansion planning and reliability of power systems, dynamics of power systems and application of computational intelligence to power system problems. The values for example SMIB system are: Poles=2; f=60 Hz; PFrated=0.85 pu; Vrated=26 kV; Prated=835 MW; rs=0.003, xd=1.8, xq=1.8, xls=0.19, r'fd=0.000929, x'lfd=0.1414, r'kd=0.01334, x'lkd=0.08125, r'kq1=0.00178, r'kq2=0.00841, x'lkq1=0.8125, x'lkq2=0.0939 pu; D=0, H=5.6, Rline=0.05, Xline=0.5, Glocal=0.25, Blocal=-0.25 pu. AVR parameters are: KA=50, TA=0.05 sec. UPFC and PSS parameters are: xtE=0.3, xE=0.5, xL=0.3, xB=0.01, xBv=0.3, Cdc=1 pu; Vdc0=2 pu, mE=0.4013, mB=0.0789, δE=-85.3478, δB=-78.21;T1=0. 73 sec, T2=0.2 sec, T=3 sec, kpss =7.408. Hooman NasrAzadani was born in Esfahan, Iran, on September 18, 1988. He received his B.S. in electrical engineering from Islamic Azad University of Najaf Abad in 2011 and M.S. degree in electrical engineering from University of Kurdistan in 2013. Currently he is with the Esfahan Regional Electric Company (EREC) as a Consultant and also he is a member of EREC Reliability Council's VoLL and RCM workgroups. His research interests include power system stability/control and protection, power system dynamics and application of computational intelligence to power system problems. REFERENCES [1] [2] [3] [4] [5] A. R. Mahran, B. W. Hogg, and M. L. El-Sayed, "Co-ordinated control of synchronous generator excitation and static VAR compensator," IEEE Transactions on Energy Conversion, vol. 7, pp. 615-622, 1992. A. T. Al-Awami, M. A. Abido, and Y. L. Abdel-Magid, "Application of PSO to design UPFC-based stabilizers," in Swarm Intelligence, Focus on Ant and Particle Swarm Optimization, F. T. S. C. a. M. KumarTiwari, Ed., ed, 2007. F. Gharedaghi, M. Deysi, and H. Jamali, "A New Method to Damping of Low Frequency Oscillations," Australian Journal of Basic and Applied Sciences, vol. 5, pp. 1231-1238, 2011. K. H. Kadhim and J. Shrivastava, "Commanding UPFC with Neurofuzzy for Enhancing System Stability by Scaling down LFO," Global Journal of Advanced Engineering Technologies, vol. 1, p. 5, 2012 W. Haifeng, "A unified model for the analysis of FACTS devices in damping power system oscillations. III. Unified power flow controller," Power Delivery, IEEE Transactions on, vol. 15, pp. 978-983, 2000. S. Johri, S. S. Tanwar, and A. Khandelwal, "Analysis Of Upfc Based Damping Controller On A Single Machine Infinite Bus System (SMIB)," International Journal of Engineering Sciences & Research Technology, vol. 4, p. 9, 2012. M. A. Abido, A. T. Al-Awami, and Y. L. Abdel-Magid, "Analysis and Design of UPFC Damping Stabilizers for Power System Stability Enhancement," in Industrial Electronics, 2006 IEEE International Symposium on, pp. 2040-2045, 2006. Y. N. Yu, Electric Power System Dynamics: Academic Press, pp.85-86, 1983. C.L. Chen and Y.-Y. Hsu, "Coordinated Synthesis of Multimachine Power System Stabilizer Using an Efficient Decentralized Modal Control (DMC) Algorithm," IEEE Transactions on Power Systems, vol. 2, pp. 543-550, 1987. J M. J. Gibbard, "Co-ordinated design of multimachine power system stabilisers based on damping torque concepts," Generation, Transmission and Distribution, IEE Proceedings C, vol. 135, pp. 276284, 1988. V. G. D. C. Samarasinghe and N. C. Pahalawaththa, "Damping of multimodal oscillations in power systems using variable structure control techniques," IEE Proceedings - Generation, Transmission and Distribution, vol. 144, p. 323, 1997. Y. L. Abdel-Magid, M. A. Abido, S. Al-Baiyat, and A. H. Mantawy, "Simultaneous stabilization of multimachine power systems via genetic algorithms," IEEE Transactions on Power Systems, vol. 14, pp. 14281439, 1999. M. A. Abido, "Particle swarm optimization for multimachine power system stabilizer design," in Power Engineering Society Summer Meeting, 2001, pp. 1346-1351 vol.3. Aliakbar Damaki Aliabad was born in Yazd, Iran, on April 9, 1983. He received his B.S., M.S., and Ph.D. degrees in electrical engineering from Amirkabir University of Technology, Tehran, Iran in 2005, 2007, and 2012 respectively. He is currently Assistant Professor at Electrical and Computer Faculty of Yazd University, Yazd, Iran. His main interests are design, manufacturing, and fault detection of electrical machines, and also power system dynamics. 712