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 ©2018 Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany, part of Springer Nature 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 com- plex 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 distri- bution 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 arrange- ment of the tidal power generators. 2 Theoretical models Fig. 2. Elliptic distribution model. Jensen wake model is introduced to analyze the influ- ence 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 fol- lowing equations of calculating maximum number of tur- bines 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- 8 > 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.