MEV Journal of Mechatronics, Electrical Power, an d Vehicular Technology 9 (2018) 29-35 Journal of Mechatronics, Electrical Power, and Vehicular Technology e-ISSN: 2088-6985 p-ISSN: 2087-3379 www.mevjournal.com doi: https://dx.doi.org/10.14203/j.mev.2019.v10.29-35 2088-6985 / 2087-3379 ©2019 Research Centre for Electrical Power an d Mechatronics - Indonesian Institute of Sciences (RCEPM LIPI). This is an open access article under the CC BY-NC-SA license (https://creativecommons.org/licenses/by-nc-sa/4.0/). Accreditation Number: (LIPI) 633/AU/P2MI-LIPI/03/2015 and (RISTEKDIKTI) 1/E/KPT/2015. Quasi-flat linear PM generator optimization using simulated annealing algorithm for WEC in Indonesia Budi Azhari a, *, Francisco Danang Wijaya b a Research Centre for Electrical Power an d Mechatronics, In donesian Institute of Sciences Jl. Cisitu No. 154D, Bandung, 40135, In donesia b Department of Electrical Engineering and Information Technology, Engineering Faculty, Universitas Gadjah Mada Jl. Grafika 2, Sleman, DI Yogyakarta, 55281 In donesia Received 29 A ugust 2019; accepted 5 December 2019; Published online 17 December 2019 Abstract Linear permanent magnet generator (LPMG) is an essential component in recent wave energy converter (WEC) which exploits wave’s heave motion. It could be classified into tubular-type, flat-tricore type, and quasi-flat type. In previous researches, these three models have been studied and designed for pico-scale WEC. Design optimization has further been conducted for flat-tricore LPMG, by using simulated annealing (SA) algorithm. It modified some parameters to minimize the resulted copper loss. This paper aims to optimize a quasi-flat LPMG design by applying SA algorithm. The algorithm would readjust the initial LPMG parts dimension. Then, the output of the optimized design would be analyzed and compared. The results showed that the optimization could reduce the copper loss by up to 73.64 % and increase the efficiency from 83.2 % to 95.57 %. For various load resistances, the optimized design also produces larger efficiency. However, the optimized design has a larger size and produces larger cogging force than the initial design. ©2019 Research Centre for Electrical Power and Mechatronics - Indonesian Institute of Sciences. This is an open access article under the CC BY-NC-SA license (https://creativecommons.org/licenses/by-nc-sa/4.0/). Keywords: Design optimization; copper loss; simulated annealing; quasi-flat LPMG. I. Introduction As the ocean wave provides relatively huge energy, several energy conversion methods have been developed. Considering the technique, one quite popular approach is by exploiting the heave motion of the ocean wave. Several models are utilizing this way, including Archimedes Wave Swing (AWS), SeaBeavl wave energy converter (WEC) and Aqua Buoy[1][2]. In recent WEC methods, the use of linear permanent magnet generators (LPMG) as mechanical to electrical converter is the key factor, hence it's design should be made as reliable and optimum as possible. Basically, the LPMG could be classified based on its stator core shape. The first one, tubular-type has tubular shape, higher maximum flux density, and is able to produce low detent force [3][4]. The second model, flat-type LPMG, forms prism shape. It could be further formed into different cross-section shape: quasi-flat with rectangular prism and flat-tricore with triangular prism. Compared to the first type of tubular LPMG, the flat-type LPMG could generate slightly higher output voltage and specific power for equal loads [5]. Furthermore, the previous investigation has found that the quasi-flat type produces slightly higher flux density as well as induced voltage than the flat-tricore LPMG [6]. The configurations of these types are shown in Figure 1 and Figure 2. According to the placement site, there are three options: offshore, shoreline, and nearshore. The offshore location provides the highest input power, thus the generated electrical energy of this placement model is also the highest. However, it is also exposed to greater risk from environment conditions, such as weather, water salinity, and possible natural disaster. These factors give challenges to its building and maintenance. The shoreline and nearshore WECs, on the other hand, experience different conditions. They might produce less output power, but cheaper and easier in maintenance [7]. * Correspon ding Author. Tel: +62-85729408875 E-mail address: budi.azhari19@gmail.com, budi030@lipi.go.id https://dx.doi.org/10.14203/j.mev.2019.v10.29-35 http://u.lipi.go.id/1436264155 http://u.lipi.go.id/1434164106 http://mevjournal.com/index.php/mev/index https://dx.doi.org/10.14203/j.mev.2019.v10.29-35 https://creativecommons.org/licenses/by-nc-sa/4.0/ https://crossmark.crossref.org/dialog/?doi=10.14203/j.mev.2019.v10.29-35&domain=pdf https://creativecommons.org/licenses/by-nc-sa/4.0/ B. A zhari and F.D. Wijaya et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 10 (2019) 29–35 30 As one of the countries with promising wave energy resources, Indonesia could benefit from this source for electrical power generation. Previous researches have designed tubular and flat LPMGs for WEC in Indonesia [8][9]. The designs were built based on the offshore condition in south Java Ocean, Indonesia. Further research was also conducted to optimize the design of flat-tricore LPMG. The optimization was aimed to minimize resulted copper losses, by modifying the dimension of the generator parts. For this purpose, simulated annealing (SA) algorithm had been used [10]. The results showed that the utilization of the algorithm could reduce the copper loss and increase the electrical efficiency of the LPMG [10]. In this paper, the copper loss optimization by using the simulated annealing algorithm would be applied to a quasi-flat LPMG. This LPMG would also be used as a component of a pico-scale WEC in south Java Ocean. Prior to the optimization, an initial unoptimized 1 kW quasi-flat LPMG design would be provided. After the optimization process, the output parameters of the optimized design would be analyzed and compared to the initial one. II. Materials and Methods A. Proposed quasi-flat LPMG For comparison purposes, an initial unoptimized design would be presented first. In this case, a quasi- flat LPMG had been designed before, considering wave characteristics in south Java Ocean during certain periods [9]. The design has rectangular prism- shaped surface, as shown in Figure 3. The process and technique of designing this generator were based on [11]. The generator would be used for WEC with a floating buoy, where the scheme is shown in Figure 4. The quasi-flat LPMG was composed of two main parts: translator and stator. The stator core was made of US steel type 2 core. To reduce power loss from eddy current, the stator was composed of stacks of lamination, with each lamination width of about 0.6 mm. Moreover, electrical output could be extracted from stator winding terminal, which used AWG 11 wire. In translator, permanent magnets were placed in radial array. The magnets used NdFeB 35/N35, with residual flux density of 1.17 T and coercivity of 868,000 A/m. Meanwhile, the translator core was made of ferromagnetic carpenter silicon iron 1066 C. The use of ferromagnetic material in the translator core was meant to maximize the magnetic flux flowing to the stator. The path of the flowing magnetic flux in the radial array is shown in Figure 5. The dimension of the generator parts were being calculated considering the expected output and wave characteristics in its location. The wave characteristics were previously analyzed based on the monthly average wave height data on that location from 2000 to 2010. However, only the wave height in July and August which were considered because the wave height in these periods was maximum. According to the data, the average wave height used as the reference was 0.845 m, with wave period Figure 1. Flat-tricore type (left) and quasi-flat type (right) of LPMG Figure 2. Tubular type LPMG Figure 3. Upper view of proposed quasi-flat LPMG Figure 4. Placement scheme of LPMG in wave energy power plant: (A) floating buoy, (B) connector, (C) tran slator, (D) stator, (E) supporting part [10] B. A zhari and F.D. Wijaya et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 10 (2019) 29–35 31 was 5.61 s. The potential power which could be provided was then about 34.57 kW/mcl. Given these conditions, the size of the quasi-flat LPMG parts was then specified. The length of the stator (Ls, in meter) could be calculated using the equation below, 𝐿𝑠 = P√2 MsBmJWsv . (1) Parameter P is expected output power (W), Ms is number of armature, Bm is air-gap flux density under magnets (T), J is current density (A/m), Ws is stator width (m), and v is rated translation speed (m/s). The Ls then determines the dimension of pole pitch (τp, in meter) and tooth pitch (τt, in meter). However, they are also determined by number of slot (s), pole (p), and phase (m). 𝜏𝑝 = Ls p , (2) 𝜏𝑡 = τp mq . (3) q is slot/pole/phase. The size of the tooth pitch (τt) is then partitioned for slot width (bs) and tooth width (bt) –both are in meter by a certain proportion, 𝜏𝑡 = bt + bs. (4) Meanwhile, the length of the permanent magnet (τm, in meter) is affected by magnetic flux comparison of Cm, 𝜏𝑚 = Cmτp, (5) 𝐶𝑚 = Bg Bm . (6) Bg is average flux density in air gap (T). The pole pitch (p, in meter) then determines the thickness of stator yoke (Ys) and translator yoke (Yr) –both in meter, as follow, 𝑌𝑠 = τpBg 2Bys , (7) 𝑌𝑟 = τpBg 2Byr . (8) Bys and Byr are the permissible flux density in stator core and rotor core (T) respectively. The equivalent air gap width (geq, in meter) is based on initial air gap (g, in meter). It could be calculated by using the equation below, 𝑔𝑒𝑞 = τt(5g+bs) τt(5g+bs)−bs 2 g. (9) The value geq and Br (PM remanence, in tesla) then determine the thickness of the permanent magnet (hm, in meter), ℎ𝑚 = geq(BrBg) μ0|Hc|(Br−Bg) . (10) Finally, the number of stator coil turn is decided based on the expected induced voltage (Eph, in volt), 𝐸𝑝ℎ = MsNphBmWsv √2 , (11) 𝑁𝑐 = Nph pq . (12) Nc and Nph are winding turn/slot and winding turn/phase successively. For Rw is typical wire resistance (Ω/m) and Lc is coil length (m), the phase resistance is, 𝑅𝑝ℎ = RwLcNph. (13) The output real power of the generator (Pout, in watt) could be calculated based on the load resistance, 𝑃𝑜𝑢𝑡 = iph 2RL. (14) Meanwhile, the copper power loss of the generator (Ploss, in watt) is, 𝑃𝑙𝑜𝑠𝑠 = iph 2Rph. (15) iph is phase current (A), RL and Rph are the load winding resistance (Ω) and phase winding resistance (Ω) successively. The complete design and its parameters’ symbol is shown in Figure 6. B. Simulated annealing (SA) algorithm In an optimization process, there are basically several ways to solve a problem. One of them is by using stochastic approach. In this way, optimal solution is searched by trials and error in several iterations. Furthermore, this approach could be divided into heuristic and metaheuristic. The latter approach includes tradeoff and randomization during trial and error process. The randomization is useful so that the search is for global optimal rather than local optimal, thus the result would be more accurate. Many nature events inspire the building of metaheuristic optimization algorithms. Among them, there is simulated annealing (SA), composed by Kickpatrick et al. in 1983. This method uses a single agent or solution which goes along a search space in a piecewise style [12][13]. The algorithm has a similar concept with annealing process of solid material. It is a physical process where a solid material is heated up to its melting state. After that, the material would be chilled down slowly until reaching a certain low temperature, with sometimes crystallization occurs to the material. In optimization problem, probable solution is represented by the solid material’s state. Meanwhile, the values of the objective function are represented by the energy of states. In this case, the optimal solution corresponds to the lowest energy state. Figure 5. The flow of magnetic flux in radial permanent magnets array (red arrows show PMs’ orientation) B. A zhari and F.D. Wijaya et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 10 (2019) 29–35 32 In finding the optimum solution, the SA algorithm exploits iterations. In each iteration, current solution is randomly updated to a new solution. The algorithm would compare the updated solution in each iteration to the previous one. If a new solution is better according to the objective, it would replace the old one and would become the new solution for the next iterations. Nevertheless, the probability of random uniform number that is generated from the iteration process might be smaller than predetermined function value. In this case, the new solutions would be treated as a better solution to replace the prior solution. This repeated process would run until the last iteration. This algorithm has had wide applications in power system. It helps to solve economic load dispatch problems in power generation by minimizing generation cost function, even penalty terms are included [14]. It could also guide to optimum distribution network reconfiguration with power loss considerations. The mechanism of this algorithm could avoid the search process being fell into local optimal, and thus the solution of this method is most likely the global optimal. On the other hand, this algorithm requires quite longer computation time than some other metaheuristic algorithms. In this research, the SA algorithm would be used to find the optimum dimension of the quasi-flat LPMG design which produce minimum copper loss, as stressed in the objective function below, 𝐹𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 = min⁡(𝑃𝑙𝑜𝑠𝑠) (16) To achieve this objective, the dimension of stator width (Ws), slot height (hs), and slot width (bs) were modified. However, the dimension of the remaining LPMG parts would be affected and would be readjusted later based on those three. Among the three variables, the first is affecting the induced voltage. Meanwhile, the other two affect the coil length, which corresponds to its resistance. Combination of these components would determine the resulted copper loss, and the algorithm is expected to adjust these variables in order to minimize the copper loss. After setting those variables, the resulted copper loss would be calculated. At the end of this process, the minimum copper loss would be obtained, and other parts’ dimensions were re-calculated based on the optimized parameters. Finally, the output values of the resulted generator would be presented and compared. The optimization flowchart is presented in Figure 7, while the optimization settings are shown in Table 1. (a) (b) Figure 6. Design of the LPMG; (a) 3-dimen sion, (b) front view Start i = 0 Determine initial Ws, bs, bh Calc ulate initial P loss i ++ Ploss(i)>Ploss(i-1)? Use Ws(i), bs(i), bh(i) Use Ws(i-1), bs(i-1), bh(i-1) i = m ax _iter? Calc ulate other LPMG parameters End Yes Yes No No Figure 7. Flow chart of the optimization using SA algorithm Table 1. LPMG optimization setting using SA algorithm Parameters Symbol Value Initial temperature T0 324 (oC) Reduction rate alpha 0.99 Maximum iteration i 100 Number of sub-iteration 20 Variables stator width (m) Ws 30