Journal of Technology Innovations in Renewable Energy, 2014, 3, 21-30 21 Optimal Design of PID Controller for Doubly-Fed Induction Generator-Based Wave Energy Conversion System Using MultiObjective Particle Swarm Optimization Adel A.A. Elgammal* Utilities Engineering Department, The University of Trinidad & Tobago UTT, Point Lisas Campus, Esperanza Road, Brechin Castle, Couva, Trinidad and Tobago Abstract: This paper presents the complete modeling and simulation of Wave Energy Conversion System (WECS) driven doubly-fed induction generator with a closed-loop vector control system. Two Pulse Width Modulated voltage source (PWM) converters for both rotor- and stator-side converters have been connected back to back between the rotor terminals and utility grid via common dc link. The closed-loop vector control system is normally controlled by a set of PID controllers which have an important influence on the system dynamic performance. This paper presents a Multi-objective optimal PID controller design of a doubly-fed induction generator (DFIG) wave energy system connected to the electrical grid using Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). PSO and GA are used to optimize the controller parameters of both the rotor and grid-side converters to improve the transient operation of the DFIG wave energy system under a fault condition as compared with the conventional methods to design PID controllers. Keywords: Grid integration, Wave Energy Conversion systems, Doubly-Fed Induction Generator (DFIG), Vector control, Genetic Algorithm GA, Particle Swarm Optimization PSO. I. INTRODUCTION Producing energy from renewable energy resources such as solar, wind, ocean, micro-hydro, biomass, etc is becoming a necessity because of the the continuous increasing of world energy demand. Since the abundance of wave power potential and its pollutionfree nature, wave energy can be considered as one of the attractive and green alternative energy sources in the world today [1-7]. The Doubly Fed Induction Generator (DFIG) is widely used in the development of distributed renewable energy sources [8], [9]. The rotor windings of the DFIG are arranged via the Rotor Side Converter (RSC) to allow an AC current to be injected by field orientation control to optimize the energy conversion and keep the terminal voltage constant for variable speed. The field orientation control based on proportional, integral and differential controllers (PID controllers) controls the active and reactive powers that the DFIG exchanges with the electrical grid. The aim of the field orientation control is to maximize the extracted power from the wave [10-15]. Suitable controller parameters highly improve system stability and performance. However, the online tuning of these parameters is difficult due to the nonlinearity and the high complexity of the system [16]. “Differential evolution (DE) is a population-based method and generally considered as a parallel stochastic direct *Address correspondence to this author at the Utilities Engineering Department, The University of Trinidad & Tobago UTT, Point Lisas Campus, Esperanza Road, Brechin Castle, Couva, Trinidad and Tobago; Tel: (868) 6428888 Ext. 32334; Fax: (868) 636-3339; E-mail: adel_elgammal@ieee.org E-ISSN: 1929-6002/14 search optimizer which is very simple, precise, fast as well as robust algorithm” [17-19]. The DE can solve optimization problems with non-linear and multi-modal objective functions. Recently, intelligent optimization algorithms such as genetic algorithms (GAs), tabu search algorithm, simulated annealing (SA) and particle swarm optimization (PSO) have been successfully used as optimization tools in various applications, including the online tuning of the controller parameters [20-26]. “Particle Swarm Optimization (PSO) is an evolutionary computation optimization technique (a search method based on a natural system) developed by Kennedy and Eberhart” [27-30]. In this paper, number of fitness functions is defined to measure the performance of the proposed controllers. The proposed objective functions are designed to monomoze the over-current in the rotor circuit, to minimize losses as well as optimal power utilization. “Multi-objective optimization is used to find a Pareto front which is a set of acceptable solutions for conflected objective functions” [31-33]. MOPSO is used to determine the optimal gains for the PID controllers to both the stator-side converter and the rotor-side static converter of the DFIG. For the purpose of comparing the improvement obtained in the system dynamic performance with the application of the MOPSO procedures to design the controller gains, these results are compared with those obtained using the MultiObjective Genetic Algorithm (MOGA). A complete simulation model is developed for such machine under variable speed operation using MATLAB Simulink © 2014 Lifescience Global 22 Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 environment. Simulation results show that the proposed design approach is efficient to find the optimal parameters of the PID controllers and therefore improves the transient performance of the WECS over a wide range of operating conditions. II. MODELING OF THE STUDIED SYSTEM Figure 1 shows the proposed model for DFIG converting power from the wave to deliver power into the electric grid for a large range of wave variation. The stator of the DFIG is directly connected to the electric grid, whilst the rotor winding is fed through the back-toback PWM voltage-source inverters with a common DC link via slip rings to control the voltage applied to the rotor to allow DIFG to operate at a variety of speeds in response to wave changes. The rotor-side converter was implemented to provide an active and reactive power control by the field-oriented current control, as shown in Figure 2. The reactive power can be Adel A.A. Elgammal controlled by controlling the d-axis rotor current. The stator active power Ps can be independently controlled by controlling the q-axis rotor current. Figure 3 shows the overall control scheme of the grid-side converter. The grid-side converter is implemented to keep the dclink voltage constant regardless of the magnitude and direction of the rotor power. The control of the grid-side converter are organized in two loops; a DC-link current control loop, which controls the current through the grid filter, and DC-link voltage control loop that controls the dc-link voltage. III. DIGITAL SIMULATION RESULTS The proposed MOPSO strategy has been tested for validation using the DFIG whose ratings are given in the Appendix. The wave model of Figure 4 is adopted to generate a specific power reference and validate the good power tracking performances and therefore confirm the effectiveness of the proposed control Figure 1: Schematic representation of Wave energy converter with Doubly-Fed Full-Controlled Induction Generator. Figure 2: Rotor-side converter control. Optimal Design of PID Controller for Doubly-Fed Induction Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 23 Figure 3: Stator-side converter control. Figure 4: The wave model. strategy based on MOPSO. To compare the improvement obtained in the system dynamic performance with the application of the MOPSO procedure to design the controller gains, these results are compared with those obtained using the MOGA. For the same operation condition, the MOGA and MOPSO were used to obtain the optimal gains for the controllers of the stator-side and the rotor-side converters. In the GSC and the RSC control loops, there are four PID controllers and each of them has a proportional gain, an integral and differential gains. The behavior of the converter depends on the control system. If the controllers are tuned properly, it is possible to improve the GSC and RSC converter’s performance during the transient disturbances. The MOGA and the MOPSO algorithms are applied to find automatically the optimal parameters of the GSC and the RSC controllers. The objective of the MOGA and the MOPSO is to find the optimal parameters of the four PID controllers, namely, four proportional gains (KP1, KP2, KP3, and KP4) , four integral gains (KI1, KI2, KI3, and KI4) and four differential gains (KD1, KD2, KD3, and KD4) to optimize some fitness functions. The following objective functions were used to measure the quality of the gains tuning to improve the system performance during the transient disturbances. These functions are represented by the weighted sum of the Normalised Mean Square Error (NMSE) deviations between output plant variables and desired values. The NMSE deviations between output plant variables and desired values are defined as: 24 Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 J1 = NMSEVDC  (V
V =  (V DC DC
ref DC
ref J 2 = NMSE IDC ( I
I = ( I DC  (
  ( r r
ref r
ref J 4 = NMSEQs  (Q
Q =  (Q s ) ) ) ) 1 6. Check the Pareto optimality of the multi-objective fitness values of each particle. All non-dominated solutions are saved in the Pareto archive (external file) 7. The global gbest particle is randomly selected. 8. The velocity of each particle is updated using the following equation. 2 (3) 2 (4) 2 t  (
Save the multi-objective fitness value of each particle in vector form. These vectors store the values of each gain of the PID controller. These values are copied in the pbest vectors. (2) The SOPSO finds a single optimal solution of the following objective function (Jo) which combines several objective functions using specified or selected weighting factors: Jo = 5. 2 2 ) and the WECS-DFIG model is simulated to obtain the values of the objective functions. (1) 2 s
ref s
ref ) 2 2 DC
ref DC
ref J 3 = NMSE r = ) ) Adel A.A. Elgammal ) J1 +
2 J 2 +
3 J 3 +
4 J 4 dt (5) Vid =   Vid + C1  rand1  (P pd ) (
X id + C2  rand2  Prd
X id ) (7) Where Pid, Pad are randomly chosen from the Pareto archive,
is the inertia factor, Vi,d is the velocity of the particle i in the d_th dimension, c1 and c2 are weights. 0 Where
1 = 0.25,
2 = 0.25,
3 = 0.25,
4 = 0.25 are selected weighting factors. J1, J2, J3, J4 are the selected objective functions. The weighting factors in the objective function (Jo) are used to satisfy different design requirements. If a large value of
1 is used, then the objective is to minimize the error of the DC link voltage. 9. X id = X id + Vid Evaluate the quality of each particle. If the fitness value of the particle is non-dominated, save it into the Pareto archive. In the Pareto archive, if a particle is dominated by a new one, then discard it. 11. Then, the new gbest is randomly selected. Two Pareto solutions are chosen randomly for Pr,d , Pi,d from the Pareto archive. 12. Repeat the cycle, steps (8) to (11), until the predetermined maximum number of generations is reached or convergence is reached based on some desired single or multiple criteria. Initialize the population of the particle swarm with random values of gains which are restricted by the following minimum and maximum values: K P min
K P
K P max K Im in
K I
K Im ax (6) K D min
K D
K D max 2. The feasibility of each particle is checked to make sure the particle satisfies the constraints. 3. All particles are initialized with random velocities. 4. The objective functions are used to evaluate the fitness of each particle in the swarm. The PID controller gains are assigned for each individual (8) 10. The main steps of the the optimal PID controller gains design procedure using MOPSO is an iterative scheme involving the following steps: 1. The position Xi,d of each particle is also updated using the following equation to maintain the particles within the feasible solution region. In the calculation of the optimal gains by the GA and the PSO procedures, the objective is to improve the overall dynamic performance of the DFIG when it is subjected to severe electrical disturbances and faults in the electrical network. The dynamic simulations were carried out for a three phase short circuit next to the DFIG bus at time t = 0.2 s, lasting for 0.2 s. The gain values for the PSO and GA adjustment procedures are Optimal Design of PID Controller for Doubly-Fed Induction Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 25 Table 1: Gains Adjustments for the PID Controllers of GSC and RSC Converters Using PSO and GA SOGA SOPSO MOGA MOPSO KP1 14.1873 8.5814 11.0665 14.8185 KI1 1.0937 2.2297 1.6190 2.6380 KD1 0.5205 0.9560 1.0463 1.4554 KP2 13.5941 11.9220 12.7491 9.3607 KI2 1.1020 1.5187 1.1730 1.6929 KD2 0.2522 1.0467 1.6869 0.7970 KP3 12.3800 12.6762 15.8444 18.4986 KI3 0.9673 1.0840 0.9978 1.4495 KD3 0.1949 0.9218 0.5987 1.0303 KP4 6.8077 11.9575 13.0007 10.2206 KI4 1.7054 1.8599 2.3141 3.5095 KD4 0.4762 0.8695 1.1065 1.1325 presented in Table 1. The oscillations of the dc-link voltage, when applying the MOGA are slightly larger than when applying the MOPSO, as shown in Figure 5. However, the dc-link voltage oscillations in both designs do not affect the continuous operation of the WECS and consequently improving the DFIG dynamic performance. The grid-side converter current is shown in Figure 6-a, a reduction in the over-current can is easily be observed, when the gains are adjusted by the MOPSO as compared with those adjusted via MOGA, consequently contributes towards maintaining the converter in operation during the fault period. The gridside converter voltage dynamic behavior is shown in Figure 6-b. It is observed that with the use of gains obtained by MOGA the terminal voltage presents deeper sag as compared with those controllers with Figure 5: DC Link Voltage. gains adjusted by the proposed MOPSO procedure. Figure 6-c presents the grid side converter active power behavior. It is observed that in the case when controllers with gains adjusted by MOPSO are used, the active power presents smaller oscillations as compared with the MOGA. Figure 6-d shows a reduction in the reactive power injected into the electrical network by the grid-side converter in case the controllers’ gains are adjusted by the MOGA and MOPSO procedures. This implies that the transient performance of the WECS is improved using MOGA and MOPSO. Figure 7-a shows the rotor side converter voltage, where it can be observed that the over-voltage in the rotor circuit is reduced when the controllers’ gains are those obtained with the MOGA and MOPSO procedures. Figure 7-b presents a reduction on the 26 Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 Adel A.A. Elgammal Figure 6: Grid Side Converter transient performance during the fault period. (a) Grid Side Converter Current. (b) Grid Side Converter Voltage. (c) Grid Side Converter Active Power. (d) Grid Side Converter Reactive Power. Optimal Design of PID Controller for Doubly-Fed Induction Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 27 Figure 7: Rotor Side Converter transient performance during the fault period. (a) Rotor Side Converter Current. (b) Rotor Side Converter Voltage. (c) Rotor Side Converter Active Power. (d) Rotor Side Converter Reactive Power. 28 Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 Adel A.A. Elgammal Table 2: System Dynamic Behavior Comparison SOGA SOPSO MOGA MOPSO RMS Stator Voltage (PU) 0.9906 0.9943 0.9955 0.9987 RMS Rotor Voltage (PU) 0.1838 0.1901 0.1969 0.1974 RMS Stator Current (PU) 0.7213 0.7555 0.7229 0.7355 RMS Rotor Current (PU) 0.1707 0.1706 0.1775 0.1748 Maximum Transient Stator Voltage Over/Under Shoot (PU) 0.0689 0.0609 0.0622 0.0507 Maximum Transient Stator Current – Over/Under Shoot (PU) 0.0924 0.0980 0.0967 0.0862 Maximum Transient Rotor Voltage Over/Under Shoot (PU) 0.0721 0.0779 0.0681 0.0620 Maximum Transient rotor Current – Over/Under Shoot (PU) 0.0980 0.0868 0.0986 0.0807 NMSEVDC 0.0847 0.0671 0.0614 0.0519 NMSE
r 0.0912 0.0949 0. 0899 0.0845 NMSEIDC 0.0612 0.0669 0.0675 0.0504 NMSEQs 0.0669 0.0863 0.0961 0. 0789 THDGSV (%) 0. 0625 0.0518 0.0971 0.0602 THDGSI (%) 0.0966 0.0847 0.0845 0.0778 THD RSV (%) 0.0725 0.0799 0.0834 0.0689 THD RSI (%) 0.0868 0.0825 0.0764 0.0739 Generator Efficiency (PU) 0.8557 0.8577 0.8772 0.8842 Generator Power Factor 0.9859 0.9814 0.9997 0.9985 rotor side converter current oscillation when the gain adjustments are accomplished by the MOPSO as compared to the result with the MOPSO technique. Figures 7-c and 7-d illustrate the dynamic response of both rotor side converter active and reactive powers, for the cases of gains adjusted by MOPSO and by the MOGA procedures. It could be easily concluded that the proposed control strategies based on MOGA and MOPSO achieve satisfactory dynamic performances. Table 2 shows the system behavior comparison using the SOGA, SOPSO, MOGA and MOPSO based Self tuned controllers. The table illustrates the total harmonic distortion measurement in the three phase grid voltage waveforms, three phase grid current waveforms, three phase rotor voltage waveforms and three phase rotor current wave forms. The system produces less than 10% voltage and current THD which is compliant to IEC 6100-3-2. IV. CONCLUSION This paper has presented the modeling and simulation of wave energy driven doubly-fed induction generator which is connected to the utility grid. The stator of the DFIG is directly connected to the AC mains, whilst the rotor winding is fed through the backto-back PWM voltage-source inverters with a common DC link via slip rings to control the voltage applied to the rotor to allow DIFG to operate at a variety of speeds in response to wave changes. The PID controllers are used to control both GSC and RSC converters and their parameters are optimally designed using the particle swarm optimization (PSO) algorithm and Genetic Algorithm (GA). Simulation studies are carried out and compared the results obtained with the proposed optimal PID controller parameters design using MOPSO with those using controllers adjusted by the MOPSO. Results show that the proposed design approach is efficient to find the optimal parameters of the PID controllers and improves the transient performance of the wave energy system over a wide range of operating conditions. THD levels of the converter output voltage has been estimated using fast Fourier transform which satisfies the IEEE 519-1992 standard. Optimal Design of PID Controller for Doubly-Fed Induction Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1 V. APPENDIX [9] Hu J, He Y, Xu L, Williams BW. Improved control of DFIG systems during network unbalance using PI–R current regulators. IEEE Trans Ind Electron 2009; 56(2): 439-51. http://dx.doi.org/10.1109/TIE.2008.2006952 [10] Yamamoto M, Motoyoshi O. 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