Surrogate-based optimization of tidal turbine arrays: a case study for the Faro-Olhão inlet

This paper presents a study for estimating the size of a tidal turbine array for the Faro-Olhão Inlet (Potugal) using a surrogate optimization approach. The method compromises problem formulation, hydro-morphodynamic modelling, surrogate construction and validation, and constraint optimization. A total of 26 surrogates were built using linear RBFs as a function of two design variables: number of rows in the array and Tidal Energy Converters (TECs) per row. Surrogates describe array performance and environmental effects associated with hydrodynamic and morphological aspects of the multi inlet lagoon. After validation, surrogate models were used to formulate a constraint optimization model. Results evidence that the largest array size that satisfies performance and environmental constraints is made of 3 rows and 10 TECs per row.Eduardo González-Gorbeña has received funding for the OpTiCA project (http://msca-optica.eu/) from the Marie Skłodowska-Curie Actions of the European Union's H2020-MSCA-IF-EF-RI-2016 / GA#: 748747. The paper is a contribution to the SCORE pro-ject, funded by the Portuguese Foundation for Science and Technology (FCT–PTDC/AAG-TEC/1710/2014). André Pacheco was supported by the Portuguese Foun-dation for Science and Technology under the Portuguese Researchers’ Programme 2014 entitled “Exploring new concepts for extracting energy from tides” (IF/00286/2014/CP1234).info:eu-repo/semantics/publishedVersio

Potential Hydrodynamic Impacts and Performances of Commercial-Scale Turbine Arrays in the Strait of Larantuka, Indonesia

The Strait of Larantuka, with highly energetic tidal stream currents reaching speeds of up to 3–4 m/s, is a promising site for renewable electricity production from the ocean. This paper presents the results of an assessment regarding the potential hydrodynamic impacts, wake characteristics, and the performances of large scale turbine arrays in the strait. A high-resolution, three-dimensional baroclinic model is developed using the FLOW module of the Delft3D modeling system to simulate tidal currents. The energy of currents is assumed to be extracted by horizontal-axis tidal turbines, which can harness strong bi-directional flow, positioned on sequential rows and alternating downstream arrangements. Enhanced momentum sinks are used to represent the influence of energy extraction by the tidal turbines. Four different array layouts with rated capacities of up to 35 MW are considered. We find that, in the Strait of Larantuka, array layout significantly affects the flow conditions and the power output, mainly due to the geometric blockage effect of the bounded channel. With respect to undisturbed flow conditions in the strait, decreases in current speeds of up to about 0.6 m/s, alongside increases in the order of 80% near-shore are observed. While operating efficiency rates of turbines reaching around 50%–60% resulted during the spring tide in the arrays with smaller rated capacities, the power output of the devices was negligible during the neap tide

A Study on Optimal Array Configuration of Tidal Stream Turbine Farm based on Actuator Disc Modeling

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 건설환경공학부, 2019. 2. 황진환.조류에너지는 지속가능한 대체에너지 중에서도 예측가능한 특성으로 인해 각광받고 있다. 조류발전단지는 목표 전력량 확보를 위해 백대 이상의 터빈으로 구성하기 때문에 배열의 최적화가 필수적이다. 비록 실제 조건에서의 최적 배열은 바닥지형 및 제한된 가용 구역 등에 큰 영향을 받으나, 조류에너지 부존량 산정과정에서 사용가능한 정형화된 최적 배열에 관한 연구가 필요한 실정이다. 또한 실제 배열을 설계할 때는 조류발전단지의 특성상 경사도 기반 최적화가 불가피한데, 경사도 기반 최적화의 해는 초기배열조건에 따라 국지 최적해로 수렴할 가능성이 높기 때문에 전역 최적해에 가까운 초기조건을 사용할 필요가 있다. 따라서 본 연구는 여러가지 제한조건에 대하여 2차원 조류발전단지 배열의 정형화된 최적해를 제시하고자 한다. 목적함수인 총 에너지 추출량을 구속하는 편미분 방정식은 2차원 정상상태 천수방정식을 사용하여 조류터빈에 의한 조류흐름의 비선형적인 변화를 반영할 수 있도록 하였다. 천수방정식 솔버와 최적화를 커플링하는 프로그램으로는 파이썬 기반 오픈소스 소프트웨어인 OpenTidalFarm을 사용하였다. 조류터빈은 액츄에이터 디스크로써 모델링 하였고, 다양한 선행연구에서 제시한 후류의 유속 변화를 가장 비슷하게 모의하는 미정계수들의 조합을 찾아 조류 모델링에 사용하였다. 다변수 함수의 경사도 기반 최적화는 전역 최댓값이 아닌 초기조건에 따라 다른 국지 극댓값으로 수렴하기 때문에 이상화 된 조류해협에 다양한 초기배열조건을 적용해 여러 국지 최적해 중 가장 출력량이 높은 배열의 형태를 찾았다. 수치모의 결과 가능하다면 가용영역의 폭 전체에 걸쳐 등간격으로 배치된 선형 보 형태의 배열이 최적형태로 나타났다. 하지만 터빈간 최소간격 조건과 가용영역 폭 등의 제한조건들에 의해 위와 같은 배열이 불가능하다면 곡률을 갖는 보 형태나, 더 나아가 V 형 보 형태의 배열이 최적형태로 나타났다. 이는 터빈 배열이 조류를 폭방향으로 가로막는 형태가 효율적이라는 것을 의미하며, 산출가능한 에너지를 계산한 결과 같은 개수의 터빈을 서로 영향을 주지 않도록 독립적으로 배치했을 때 얻을 수 있는 에너지보다 최대 30% 이상 효율적이다. 또한 같은 개수의 터빈의 최적배열이 조력발전단지 설계시 제한조건 (터빈간의 최소 간격, 가용 구역의 폭 제한 등)에 의해 에너지 출력량이 최대 50%까지 차이가 발생할 수 있음을 확인하였다. 이러한 결과는 효율적인 조력발전단지를 설계하기 위해서는 단순히 각 제한조건에서의 최적배열을 찾는 문제 뿐만 아니라 적절한 제한조건을 설계하는 문제의 중요성을 제시한다. 본 연구에서 제시한 방법론은 얕은 수역에서 최적해에 가까운 터빈배열을 찾기 위한 합리적인 접근방식이며, 터빈이 설치된 채널의 동역학적 특성에 관한 직관을 제공한다고 평가된다.Tidal current energy is a sustainable and predictable renewable energy resource. In tidal farm design, optimization of array configuration is essential as tidal farm is constituted of hundreds of turbines. This study aimed to suggest a generalized optimal array configuration for idealized tidal straits. Due to the strong nonlinear interaction between tidal device and tidal flow, optimizing two-dimensional array position should base on PDE-constrained gradient-based optimization algorithm. PDE is given as two-dimensional nonlinear steady shallow water equation in order to reflect the movement of tidal flow and reduce computational cost. Total power output is the target functional to be maximized, and OpenTidalFarm is used as a tool for coupling PDE solver and optimization algorithm. Turbine was parameterized as an actuator disc. Optimization was undertaken with various situations, such as varying number of deployed turbines N, minimum distance constraint , spanwise farm site constraint and initial conditions. It was found that optimization result is highly dependent on and , and also sensitive to initial condition. Thus, it is recommended to use proper initial condition which resembles optimal array configurations. Analysis on the various case of optimized result (over 100 cases) suggests that linear barrage with uniform spacing can be considered as acceptable optimal array. Furthermore, if linear barrage shape is impossible due to the optimization constraints (such as and ), it was observed that connecting all turbines as a curved or V shaped barrage performs better than splitting the array into two parts. This study highlights the necessity of designing proper site constraints and distance constraints, showing that the performance of optimal array for identical N can vary up to 50% with different constraints. It is expected that this optimal shape of array can be implemented for array design in tidal energy resource assessment or for recommended initial condition in gradient-based optimization.ABSTRACT i Table of Contents iii List of Figures vi List of Tables viii Nomenclature ix Chapter 1. Introduction 1 1.1 Tidal current energy and its assessment 1 1.2 Tidal farm optimization 4 1.3 Necessity of defining generalized configuration of decent tidal array 5 1.4 Aim of the thesis 6 1.4.1 Modeling tidal turbine in 2D Shallow Water using Actuator Disc modeling 7 1.4.2 Finding optimal array configuration via PDE-constrained gradient-based optimization 7 1.4.3 Analyzing the relationship between optimization constraints and optimization results. 8 Chapter 2. Theoretical background 9 2.1 Linear Momentum Actuator Disc Theory (LMADT) 9 2.1.3 Betzs unbounded flow 11 2.3.2 Garrett and Cumminss rigid lid flow 14 2.3.3 Houlsby et al.s free-surface flow 18 2.3.4 Limitations of LMADT 24 2.2 Shallow Water Equation (SWE) 25 2.3 PDE-constrained Gradient-based Optimization using Adjoint method 27 2.3.1 Gradient-based Optimization 28 Chapter 3. Methodology 30 3.1 Specifications of OpenTidalFarm 30 3.1.1 Design Parameters 30 3.1.2 PDE constraint 31 3.1.3 Turbine Parameterisation 31 3.1.4 Target functional 32 3.1.5 Box and inequality constraints 33 3.1.6 Gradient-based optimization with adjoint approach 34 3.2 Realistic Actuator Disc Modeling in 2D SWE 35 3.2.1 Actuator disc modeling in 2D SWE and 3D flow model 36 3.2.2 Wake properties behind tidal turbine 37 3.2.3 Simulation settings for tuning K and 38 3.2.4 Simulation results 44 3.3 Pilot Test 1: effect of initial condition and number of turbines on optimization result 46 3.3.1 Simulation settings 46 3.3.2 Simulation results 49 3.3.3 Conclusions of pilot test 1 49 3.4 Pilot Test 2: effect of minimum distance constraint and spanwise length of the farm site on optimization result 50 3.4.1 Simulation settings 50 3.4.2 Simulation results 52 3.4.3 Conclusions of pilot test 2 55 3.5 Main test: maximum number of turbines which can be considered as a barrage type configuration 56 3.5.1 Simulation settings 56 Chapter 4. Results and Discussions 60 4.1 Analysis on optimal array configuration and tidal farm output 60 4.2 Extracted Power and Nmax 64 4.3 Limitations of the Modeling 65 Chapter 5. Conclusions 68 APPENDIXS 71 Appendix A. 71 Appendix B. 73 Appendix C. 78 REFERENCES 86 국문초록 91Maste

Analysis of Dynamic Behaviour and Power Generation of a Wind-tidal System for Marine Environment

This work presents the analysis of dynamic behaviour and power generation of a wind-tidal hybrid system. Mathematical models and system design approach were used to investigate the feasibility, reliability and economic impact of the system. From the system design analysis carried out, by harnessing the tidal energy with wind energy in marine environment, the total power generated (approximately 180KW) by the hybrid power system showed a significant improvement over a wind turbine system which only generates a maximum power of 25KW at the rotor diameter as reported in literature. The effects of aerodynamics and hydrodynamics forces on the structure were investigated through the analysis of dynamic behaviour of the system under different loads and at various sites in the marine environment. The stability and the optimum turbine design were found to depend on the wind and tidal speed distribution of the specific site in the environment. The long term benefit of this work is aimed at meeting the energy needs of coastal dwellers by implementing the hybrid power system. Also, the gridless system could be used to generate power for both large and small scale industries in the marine environmen

Learning, future cost and role of offshore renewable energy technologies in the North Sea energy system

The pace of cost decline of offshore renewable energy technologies significantly impacts their role in the North Sea energy transition. However, a good understanding of their remains a critical knowledge gap in the literature. Therefore, this thesis aims to quantify the future role of offshore renewables in the North Sea energy transition and assess the impact of cost development on their optimal deployments. The following findings were observed in this thesis, 1) Fixed-bottom offshore wind is well established in the North Sea region and is already competitive with onshore renewables 2) Floating wind is emerging and their current costs are high, but it can reach about 40 EUR/MWh by early 2040 and would require 44 billion EUR of learning investment.3) Grid connection costs will become a major factor as wind farm moves further away. Policy actions and innovation is needed in this space to avoid increasing integration costs. 4) Offshore wind (fixed-bottom and floating) can play a significant role in the North Sea energy system, comprising 498 GW of deployments in 2050 (222 GW of fixed-bottom and 276 GW of floating wind) and contributing up to a maximum of 51% of total power generation in the North Sea power system. 5) The role of the investigated low-TRL offshore renewables, including the tidal stream, wave technology, and bioethanol, was limited in all scenarios considered, as they remain expensive compared to other mature technologies in the system

Modeling and Control of a Marine Current Turbine Driven Doubly-Fed Induction Generator

This paper deals with the modeling and the control of a variable speed DFIG-based marine current turbine with and without tidal current speed sensor. The proposed MPPT control strategy relies on the resource and the marine turbine models that were validated by experimental data. The sensitivity of the proposed control strategy is analyzed regarding the swell effect as it is considered as the most disturbing one for the resource model. Tidal current data from the Raz de Sein (Brittany, France) are used to run simulations of a 7.5-kW prototype over various flow regimes. Simulation results are presented and fully analyzedThis work has been funded by Brest Métropole Océan

Applying rotorcraft modelling technology to renewable energy research

The perceived need to reduce mankind's impact on the global climate motivates towards a future society in which a significant proportion of its energy needs will be extracted from the winds and the tides of the planet. This paper shows several examples of the application of Brown's Vorticity Transport Model, originally developed to perform simulations of helicopter aeromechanics and wake dynamics, to the analysis of the performance of renewable energy devices and their possible impact on the environment. Prediction of the loading on wind turbines introduces significant additional challenges to such a model, including the need to account fully for the effects of radial flow on blade stall. The wake-mediated aerodynamic interactions that occur within a wind farm can reduce its power output significantly, but this problem is very similar to that where the aerodynamic unsteadiness of the coupled wake of the main and tail rotors of a helicopter can result in significantly increased pilot workload. The helicopter-related problem of brownout, encountered during operations in desert conditions, has its analogue in the entrainment of sediment into the wakes of tidal turbines. In both cases it may be possible to ameliorate the influence of the rotor on its environment by careful and well-informed design. Finally, calculations of the distortion and dispersal of the exhaust plumes of a helicopter by the wake of its rotor allow insight into how wind turbines might interfere with the dispersal of pollutants from nearby industrial sites. These examples show how cross-disciplinary information transfer between the rotorcraft field and the renewable energy community is helping to develop the technologies that will be required by our future society, as well as helping to understand the environmental issues that might need to be faced as these technologies become more prevalent