Tidal Turbine Array Optimization Based on the Discrete Particle

China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364 DOI: https://doi.org/10.1007/s13344-018-0037-6, ISSN 0890-5487 http://www.chinaoceanengin.cn/ E-mail: [email protected]

Tidal Turbine Array Optimization Based on the Discrete Particle Swarm Algorithm WU Guo-weia, WU Hea, *, WANG Xiao-yonga, ZHOU Qing-weia, LIU Xiao-manb aNational Ocean Technology Center, Tianjin 300112, China bSatellite Environment Center, Ministry of Environmental Protection, Beijing 100094, China

Received May 18, 2017; revised February 11, 2018; accepted March 23, 2018

Abstract In consideration of the resource wasted by unreasonable layout scheme of tidal current turbines, which would influence the ratio of cost and power output, particle swarm optimization algorithm is introduced and improved in the paper. In order to solve the problem of optimal array of tidal turbines, the discrete particle swarm optimization (DPSO) algorithm has been performed by re-defining the updating strategies of particles’ velocity and position. This paper analyzes the optimization problem of micrositing of tidal current turbines by adjusting each turbine’s position, where the maximum value of total electric power is obtained at the maximum speed in the flood tide and ebb tide. Firstly, the best installed turbine number is generated by maximizing the output energy in the given tidal farm by the Farm/Flux and empirical method. Secondly, considering the wake effect, the reasonable distance between turbines, and the tidal velocities influencing factors in the tidal farm, Jensen wake model and elliptic distribution model are selected for the turbines’ total generating capacity calculation at the maximum speed in the flood tide and ebb tide. Finally, the total generating capacity, regarded as objective function, is calculated in the final simulation, thus the DPSO could guide the individuals to the feasible area and optimal position. The results have been concluded that the optimization algorithm, which increased 6.19% more recourse output than experience method, can be thought as a good tool for engineering design of tidal energy demonstration. Key words: tidal power, wake model, turbine layout, discrete particle swarm algorithm

Citation: Wu, G. W., Wu, H., Wang, X. Y., Zhou, Q. W., Liu, X. M., 2018. Tidal turbine array optimization based on the discrete particle swarm algorithm. China Ocean Eng., 32(3): 358–364, doi: https://doi.org/10.1007/s13344-018-0037-6

1 Introduction However, it is difficult to determine the optimal turbine ar- With the increasing issues of the environment degrada- ray due to the complicated flow interaction between the tur- tion, the countries in the world one after another adhere to bines. create the energy sustainable development system through Then, it is necessary to find out an effective method to the energy-structure adjustment. Because of high predictab- optimize and arrange the position of turbines, so that the ility in extracting power and little effect on environment, power generation efficiency will be improved. To increase tidal energy is one of most potential resources in ocean en- the tidal energy efficiency, many experimental studies have ergy (Bahaj, 2011). In order to improve the efficiency of the been conducted. Funke et al. (2014) applied the turbines tidal power generation, the array with hundreds of tidal tur- farm optimization software in the optimization of four ideal- bines should be arranged at a particular area (Macleod et al., ized scenarios, which is successful in increasing the power 2002), which leads to the question of how to place the tur- extracted by the farm. This software can predict the power bines within the area. When the space (between the rows extracted by using a two-dimensional nonlinear shallow wa- and turbines) is too small, the turbines located in the down- ter model. Lee et al. (2010) studied the reasonable distance stream will be influenced by the wake effect, which results between adjacent turbines in an array layout by applying a in the power reduction of the downstream turbines. When three-dimensional model. Myers and Bahaj (2005) investig- the space is too large, the tidal resource will be wasted and ated the energy losses within its layout and impacts because the economic benefits of the whole farm will be declined. of the interaction of many turbines by optimizing the struc-

Foundation item: The work was financially supported by the Marine Renewable Energy Funding Project (Grant Nos. GHME2017ZC01 and GHME2016ZC04), the National Natural Science Foundation of China (Grant Nos. 5171101175 and 51679125), Tianjin Municipal Natural Science Foundation (Grant No. 16JCYBJC20600), and Technology Innovation Fund of National Ocean Technology Center (Grant No. F2180Z002). *Corresponding author. E-mail: [email protected] WU Guo-wei et al. China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364 359 ture of the array. Bilbao et al. solved the power maximiza- model is used to limit the minimum distances between the tion problem by using a gradient-based optimization al- adjacent rows of machines as shown in Fig. 2, which is bet- gorithm (Jensen, 1983). ter than the circular distribution model. However, the array optimization is formulated as a complex nonlinear problem which is restricted to multi-variable and multi-constraint. In this paper, a method has been presented to maximize the power extraction of the array configurations that combines the wake model, elliptic distribution model and Farm/Flux model with DPSO that takes the orders of magnitude iterations. The methodology could be taken as a scientific reference for the optimum arrangement of the tidal power generators.

2 Theoretical models Fig. 2. Elliptic distribution model. Jensen wake model is introduced to analyze the influence of the wake effect between the tidal turbines on the The elliptical distribution, reducing the influence of the flow distribution (Jensen, 1983; Kiranoudis and Maroulis, wake effect, can enlarge the longitudinal distance (parallel 1997). This model is based on the principle of the conserva- to the direction of tidal flow) between the adjacent rows of tion of the momentum which is considered as conserved in- the turbines and shorten the transverse turbine spacing (per- side the wake. The wake has a radius Dij which is the radius pendicular to the direction of tidal flow). Meanwhile, it can of the downstream wake, while D is the upstream turbine ra- avoid the turbine located in the downstream of the adjacent dius. X is considered as the distance between the upstream upstream turbines, and also obey the distribution of the of Turbine j and the downstream of Turbine i, while the re- wake effect using this distribution. Therefore, based on the lationship between D and Dij is described in the Jensen research conclusions in reference (Legrand, 2009), the dis- model as shown in Fig. 1. tances considered in the present cases are in the range from 2.5D (Diameter of turbine rotor) to 10D, where 2.5D is the space of the adjacent columns of generators, and 10D is the space of the adjacent rows of generators. Therefore, the following equations of calculating maximum number of turbines are defined in Eq. (1). ( ) ( ) x − x y − y N = int max min · int max min , (1) i 10D 2.5D

where xmin, xmax, ymin, and ymax denote the range of research Fig. 1. Schematic of the Jensen wake model. region, Ni is an integer. A key issue of improving the extracted power and redu- The combined wake effect created by the turbines in tid- cing the cost of the power generation is to obtain the num- al field may cause a reduction in the energy power output, ber of the best installed turbines by the Farm/Flux and em- and also arise unsteady loads on the downstream machines. pirical method (staggered grid array) (Ammara et al., 2002), The short distances between the turbines will make the where Farm/Flux are reviewed as the analytical models of downstream generators suffer serious influence of wake ef- the resource assessment. The following equations of calcu- fect, which leads to low performance of the energy genera- lating number of the turbines are used: tion. Generally, in order to relief the loads of the down-   1 3  PAsite = ρV AcsSIF stream turbines, the minimum distances between the tur-  2  (2) bines are constant in the whole range which regarded as the  1 3  P = ρV A η circular distribution. But this layout which refers to the lay- Edevice 2 swept total out of the wind power generators easily makes the tidal re- where PAsite denotes the maximum extraction power, PEdevice sources to be wasted and the economic benefits of the whole is the extraction power of a single turbine, ρ is the sea water farm to be declined. The directionality of the tidal flow density, V is the flow velocity, Acs=H · ∆y is the cross-sec- throughout the tidal cycle has important implications for the 1 3 tional area of the channel, ρV A denotes the total tidal reserves, tidal energy capture. There has been a tendency to infer that 2 cs energetic sites possess near bi-directional flows or that there SIF denotes the ratio of PAsite to the total tidal reserves, Pm 2 are sufficient sites with near bi-directional flows such that is the power density, Aswept=π(D /4) is the area of the tur- = more omni-directional flow tidal currents can be neglected bine rotor swept, D is the turbine radius, ηtotal Cpηgearηgenerator (Lin et al., 2017). For this reason, an elliptic distribution ηtrans is the overall efficiency. Thus, the number of turbines 360 WU Guo-wei et al. China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364 is defined in Eq. (3). bad state, and it is not used as the critical target during = / . searching process. Nf PAsite PEdevice (3)   ∑Nt w The number of turbines is assumed to be Ni, which is  td  E(Z) = P[ui(zi,t)]dt calculated by the empirical method from Eq. (1). In this  t0 (5)  i=1 method, all the turbines are deployed in a staggered array,  E = E(Z) +E(Z) and the distance between adjacent rows are equal in the ar- total f e ray layout. The layout of the full array can be seen in Fig. 9. where E(Z) is the gross power generation, E(Z)f is the gross Then the best installed turbine number is defined in Eq. (4). power generation at the maximum speed in the flood tide, E(Z)e is the gross power generation at the maximum speed Nt = min{Ni, Nf}. (4) in the ebb tide, and P[ui(zi,t)] is the power generation effi- Particle swarm optimization algorithm (PSO) has cap- ciency related to the tidal velocity. tured great attention in recent years, which was proposed by Every particle is represented by two vectors, i.e., a posi- Kennedy (2010), and it has been successfully applied in t = t , t ,··· , t t = tion vector Xi (xi1 xi2 xin) and a velocity vector Vi many fields. A particle’s position is deemed as a potential t , t ,··· , t (vi1 vi2 vin), where n represents the number of raster. solution, and the flying trajectory of the particle is regarded t The vector Xi is regarded as a candidate particle while the as a continuous searching process. However, a number of vector Vt is treated as a searching direction and step size of studies demonstrated that the PSO easily falls into the pre- i the particle. Assuming that the present particle position is xt mature convergence when facing complicated conditions 1 and the previous particle position is xt at Iteration t, the new (Lin et al., 2017). And the principle of the PSO is described 2 speed of the particle from xt to xt can be calculated by Eq. in the previous study (Xia et al., 2017). 1 2 (5). Therefore, considering the serious resource wasted by t+1 t t unreasonable layout scheme of tidal current turbines, which v = x1 − x2 = (v1,v2,...,vn)  would influence the ratio of cost to output, the particle , ∈ , <  1 ri E1 ri E2  (6) swarm optimization algorithm is introduced and improved t+  ν 1 = −1, ri < E1, ri ∈ E2 in the paper. By re-defining the updating strategies of the   , particle’s velocity and position, the discrete particle swarm 0 other optimization algorithm (DPSO) has been executed to optim- where E denotes the collection of the optimum layout ri. ize the arrangement of tidal current turbines. Assuming the{ } Along with the optimization process, each particle ad- ∑n justs its trajectory relying on two vectors, namely as the per- collection Xn,m = (x1, x2,..., xn)|xi ∈ {0,1}, xi = m , i=1 sonal historical best position vector xt and the global where n represents the dimensionality of the space, k,best best position vector, xt respectively. Then, according to xi ∈ Xn,m is a random value generated in 0 and 1, and m de- gbest notes the number of particles. During the searching process the speed of the particle, a new particle position can be cal- in the rasterized tidal farm where the grids are regarded as culated by Eq. (6). Actually, the new speed is calculated by the present and previous position. the solution space, xi is defined as a candidate position that  { [ ]}  [ ] represented by 1 as illustrated in Fig. 3. T xk,best(t) − xk(t) + xgbest(t) − xk(t) vt+1 =  (7) The population (swarm) in the DPSO contains Nt can- k  didate solution (particles). The fitness function, defined in R[xk(t)] Eq. (4) is used to determine whether the particle positions of where [xk, best(t)–xk(t)]+[xgbest(t)–xk(t)]∈{–2, –1, 0, 1, 2}, and k is the number of population (swarms) in the DPSO. Nt are good. The fitness value is calculated on the basis of the tidal speed of the particle position. If the fitness value is In Eq. (6), T(x) is the convergence function and R(x) is very small, the particle position result will be assumed as a the probabilistic selection function, which are all related to p, a random number generated in the interval [0, 1]. If the function T(x) is selected to update the speed of the particle with the probability of p, the positions where the positive value of 1 or 2 is located in will be randomly selected and assigned to be 1. Similarly, the positions where the negat- ive value of –1 or –2 is located in will be randomly selected and assigned to be –1, and the other positions are assigned as the value of 0. For the complex functions T(x) with high probability of p, the DPSO has a slow speed on the convergence. Conversely, if the function R(x) is selected with the probability of 1–p, the positions where the positive value of Fig. 3. Conversion from vector dataset to raster. 1 is located in will be randomly selected and assigned to be WU Guo-wei et al. China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364 361

–1, the positions where the value zero is located in will be randomly selected and assigned to be 1, and the other position is assigned to be 0. For the functions R(x) with high probability of p, the DPSO with good randomness is hard to converge and has low optimization precision. After the velocity is updated, the particle moves to a new position from the current position. The framework of the DPSO is shown in Fig. 4.

3 Implementation and discussion Fig. 5. Relationship between the output power and inflow speed. 3.1 Selection of turbine The MCT’s SeaGen turbines are selected. The rotor dia- Island (P–H) waterway, the technical exploitation amount is meter of the turbine is 16 m, rated flow velocity is 2.25 m/s, 1.98–3.23 MW based on the Flux method, and that is cut-in speed is 0.7 m/s, cut-out speed is 3.5 m/s, rated power between 5.33 MW and 6.08 MW based on the Garret meth- is 1.2 MW, and power coefficient is 0.45. The relationship od (Wu et al., 2017). As shown in Fig. 6, the research re- between the output power (P) and inflow speed (v) is shown gion located in the P–H water way has rich and stable tidal in Fig. 5. current resources, where is identified as the best develop- The output power and inflow speed are fitted by the ment environment for tidal current energy. The range of this least squares method with 28 points, and the relationship is region is 600 m×1000 m, the average depth of the seabed is given as follows. 37.03 m, and the grid resolution is 5 m. Ocean tide contains P(v) = − 73.819v5 + 664.97v4 − 2276.4v3 high tide process and low tide process. As shown in Table 1 and Fig. 7, the average annual flow velocity and flow direc- + 3882.3v2 − 3044.4v + 888.6. (8) tion at the maximum speed in the flood tide and ebb tide are 3.2 Experimental data used to facilitate the calculation. Statistically, the total tidal current energy of the import- 3.3 Algorithm simulation ant water course can be 1400 MW in Zhoushan sea area According to the Bryden’s study, SIF is selected as (Hou et al., 2014). Especially in the Putuo Mountain–Hulu 15%, ηtotal is 40%, and Aswept is 200.96. In the simulation experiment, the DPSO algorithm is applied to arranging the

turbines, the particle position range is xmin=442635.2662,

Fig. 6. Test area between the Putuo Mountain and Hulu Island in the city Fig. 4. Framework of the DPSO. of Zhoushan.

Table 1 Maximum, minimum and average of the average annual flow in Zhoushan Flow velocity (m/s) Flow direction (°) Depth (m) Tidal data Min. Max. Mean Min. Max. Mean Min. Max. Mean Maximum speed in the flood tide 1.10 1.79 1.40 324.86 339.91 332.35 27.06 45.19 37.03 Maximum speed in the ebb tide 1.27 1.61 1.44 157.24 165.20 160.63 362 WU Guo-wei et al. China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364

Fig. 7. Flow direction and flow velocity at the maximum speed. xmax=443635.2662, ymin=3320478.175, ymax=3321078.175, and H=50 m. The best number of the installed turbines is

55 in this research region from Eq. (4), because Ni is 90 from Eq. (1) and Nf is 55 from Eq. (3). The higher the probability of the function T(x) in the discrete particle swarm algorithm, the higher the accuracy of the optimization result, but the longer the calculation time. Therefore, in order to ensure the accuracy, the probability of this paper is set to 0.9, and the number of the particles is 20. This paper sets the maximum number of iterations to be 16000, and Etotal is calculated on the basis of the maximum speed in the flood tide and ebb tide. Since the DPSO algorithm will be probabilistic to select Fig. 8. Change process of total power generation under different itera- the particle velocity to update the function, the optimal lay- tions of the DPSO. out results with the same iteration times may be unstable. Fig. 8 shows the change in the power generation efficiency Owing to different layouts of the turbines, the power with the number of iterations. With the increase of the itera- output is different. In order to verify the validity and superi- tion number, the power generation efficiency of the turbine ority of the model and algorithm, the DPSO algorithm is keeps gradually increasing, indicating that the DPSO al- compared with the empirical method considering the same gorithm can optimize the turbine layout, and can effectively research region and turbines. In addition, the maximum iter- improve the power output and enhance the trend of energy ation number of the DPSO is 15000 which can be determ- utilization. And after 15000 of the DPSO algorithm itera- ined from Fig. 8. As shown in Fig. 9, the empirical layout is tions, the objective function values all have the indication of interlacedly placed according to the equal spacing between convergence. the row and column. The longitudinal spacing is 10 times

Fig. 9. Layout of the empirical method for 55 tidal turbines in Zhoushan. WU Guo-wei et al. China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364 363 the turbine diameter, and the horizontal spacing is 2.5 times ults, which are obtained by running 10 times with the max- the turbine diameter. imum number (15000 times) of iterations of the DPSO al- Table 2 shows the simulation results and empirical res- gorithm.

Table 2 Gross generation per unit time in different layouts DPSO (kW) Empirical method (kW) Iterations Min. Max. Mean StdDev Min. Max. Mean StdDev 0 – – – – 19052.21 19052.21 19052.21 0 10 19052.21 19052.21 19052.21 0 – – – – 50 19052.21 19199.21 19136.23 55.25 – – – – 100 19118.58 19287.4 19206.88 53.42 – – – – 500 19174.75 19354.71 19279.25 56.30 – – – – 1000 19263.61 19611.88 19385.83 82.78 – – – – 2000 19458.56 19747.94 14638.68 62.04 – – – – 3000 19474.10 19567.75 19527.65 72.50 – – – – 4000 19528.50 19714.86 19616.26 87.59 – – – – 5000 19510.40 20007.01 19702.89 168.63 – – – – 6000 19620.02 20062.67 19779.76 189.05 – – – – 7000 19771.21 19910.75 19826.32 174.25 – – – – 8000 19809.68 19878.20 19847.05 134.68 – – – – 9000 19845.19 19959.23 19898.96 148.33 – – – – 10000 19773.63 20242.26 19959.39 115.97 – – – – 11000 19873.12 20276.83 20022.04 76.45 – – – – 12000 20099.38 20199.59 20162.41 54.88 – – – – 13000 20166.12 20190.05 20175.97 12.51 – – – – 14000 20156.00 20195.72 20177.80 17.47 – – – – 15000 20150.39 20231.61 20179.78 13.35 – – – –

As shown in Table 2, the power generation is not ideal Table 2. The power generation efficiency with the DPSO al- with the empirical method, which is easy to perform. Com- gorithm increased 6.19% compared with the empirical pared with the DPSO algorithm, the empirical method could method. As shown in Fig. 10, according to the flow rate of not fully consider the flow field distribution and wake ef- the flood tide and ebb tide and safe running distance, the fect on the importance of micro-sitting, which results in the DPSO algorithm distributes more turbines in the area with low exploitation rate of tidal energy. the DPSO algorithm large power density, and less turbines in the area with low can achieve the optimal value of the power generation effi- power density. The optimized turbines layout by the DPSO ciency of 20231.61 kW, and the layout results are shown in is more reasonable than that by the empirical method.

Fig. 10. Layout of DPSO for 55 tidal turbines in Zhoushan.

4 Conclusion ation algorithm (DPSO) has been performed in order to In consideration of the wake effect, the reasonable dis- solve the problem of optimal deployment of tidal current tance between the turbines, and tidal velocities influencing turbines in rasterized tidal farm. In order to validate the sci- factors in the tidal farm, the discrete particle swarm optimiz- entificity and practicability of this algorithm, it is investig- 364 WU Guo-wei et al. China Ocean Eng., 2018, Vol. 32, No. 3, P. 358–364 ated in this paper by performing the simulation experiments al modeling, Acta Energiae Solaris Sinica, 35(1), 125–133. (in with the actual sea area data. Compared with the power gen- Chinese) erated by running experience method, the results show that Jensen, N.O., 1983. A Note on Wind Generator Interaction, Risø Na- tional Laboratory, Roskilde, Denmark. the DPSO algorithm can make the tidal turbine array self- Kennedy, J., 2010. Particle swarm optimization, in: Encyclopedia of optimization, thus maximize the production capacity. In Machine Learning, Sammut, C. and Webb, G.I. (eds.), Springer, Bo- summary, it is feasible to use an intelligent optimization al- ston, MA, pp. 760–766. gorithm under multi-constraint condition. However, due to Kiranoudis, C.T. and Maroulis, Z.B., 1997. Effective short-cut model- the immaturity of the method which determines the optimal ling of wind park efficiency, Renewable Energy, 11(4), 439–457. number of the turbines, we find that the number of 55 tur- Lee, S.H., Lee, S.H., Jang, K., Lee, J. and Hur, N., 2010. A numerical bines determined in this paper is not enough during the pro- study for the optimal arrangement of ocean current turbine generat- cess of the simulation experiments. In addition, the distribu- ors in the ocean current power parks, Current Applied Physics, tion of the power density in the test area is relatively un- 10(S2), S137–S141. Legrand, C., 2009. Assessment of Tidal Energy Resource: Marine Re- even, resulting that part of the study region is short of tur- newable Energy Guides, European Marine Energy Centre Ltd., Lon- bines. Therefore, the algorithm also needs to be further im- don. proved. The specific improvement of the DPSO algorithm Lin, T.Y., Yeh, J.T. and Kuo, W.S., 2017. Using particle swarm optim- will be comprehensively analyzed and verified according to ization algorithm to search for a power ascension path of boiling the actual power generation after the operation of the power water reactors, Annals of Nuclear Energy, 102, 37–46. station. Macleod, A., Barnes, S., Rados, K.G. and Bryden, I., 2002. Wake ef- fects in tidal current turbine farms, Proceedings of Conference on References Marine Renewable Energy (MAREC 2002), The Institute of Marine Ammara, I., Leclerc, C. and Masson, C., 2002. A viscous three-dimen- Engineering, Science and Technology, Newcastle, UK. sional differential/actuator-disk method for the aerodynamic analys- Myers, L. and Bahaj, A.S., 2005. Simulated electrical power potential is of wind farms, Journal of Solar Energy Engineering, 124(4), harnessed by marine current turbine arrays in the Alderney Race, 345–356. Renewable Energy, 30(11), 1713–1731. Bahaj, A.S., 2011. Generating electricity from the oceans, Renewable Wu, Y.N., Wu, H. and Feng, Z., 2017. Assessment of tidal current en- and Sustainable Energy Reviews, 15(7), 3399–3416. ergy resource at Putuo Mountain-Hulu Island waterway, Renewable Funke, S.W., Farrell, P.E. and Piggott, M.D., 2014. Tidal turbine array Energy Resources, 35(10), 1566–1573. (in Chinese) optimisation using the adjoint approach, Renewable Energy, 63, Xia, X.W., Xie, C.W., Wei, B., Hu, Z.B., Wang, B.J. and Jin, C., 2017. 658–673. Particle swarm optimization using multi-level adaptation and pur- Hou, F., Yu, H.M., Bao, X.W. and Wu, H., 2014. Analysis of tidal cur- poseful detection operators, Information Sciences, 385–386, rent energy in Zhoushan sea area based on high resolution numeric- 174–195.