Research on the mechanical model and calculating design of an electrical generator for sea wave energy

MINISTRY OF EDUCATION AND TRAINING VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY ---------------------------- Nguyen Van Hai RESEARCH ON THE MECHANICAL MODEL AND CALCULATING DESIGN OF AN ELECTRICAL GENERATOR FOR SEA WAVE ENERGY Major: Engineering Mechanics Code: 9 52 01 01 SUMMARY OF MECHANICAL ENGINEERING AND ENGINEERING MECHANICS DOCTORAL THESIS HANOI – 2019 The thesis has been completed at: Graduate University of Science and Technology - Vietnam Academy of Science and Technology Supervisor: Prof. DrSc. Nguyen Dong Anh Reviewer 1: Reviewer 2: Reviewer 3: Thesis is defended at Graduate University of Science and Technology - Vietnam Academy of Science and Technology at, on datemonth2019. Hardcopy of the thesis be found at: - Library of Graduate University of Science and Technology - Vietnam National Library 1 INTRODUCTION 1. Reasons for choosing the topic According to calculations by scientists, the received energy from fossil fuels will become gradually exhausted, and now therefore looking for new energy sources is requisite. For Vietnam, the 2020 target is to become a country in which marine economics will constitute over 50% of GDP. Therefore, the energy demand supplying for general economics and particular marine economics is very important. The research and fabrication of electrical generators for sea wave energy are necessary. Moreover, the electrical energy received from sea wave energy conversion is friendly to environment, almost endless and is a clean energy source. The sea wave energy is an important energy source of the world as well as Vietnam in the future. In addition, Vietnam has the advantage of being a country with a coastline stretching over 3260 km, with more than 3000 islands and over one million km2 of sea surface, it indicates that the energy source from the sea is huge. In order to exploit the vast energy resources of the sea, the author proposes a research of thesis of building a device model to convert from sea wave energy to electricity. 2. Objective of the thesis For the purpose of building a model of electrical generator for sea wave energy, the device operates efficient and in suitable to Vietnam's sea condition; Determining the optimal damping coefficient of the generating motor, model parameters to received the 2 maximum output power; Design, fabrication of the electrical generator with the output voltages are 12 VDC, 220 VAC frequency 50 Hz and pure sine wave. 3. Research method The thesis uses analytical method, combining of the numerical simulation and experiment for calculation, being specifically described as follows: - Determining the optimal damping coefficient of the generating motor and model parameters by the analytical method. - Using fourth-order Runge-Kutta and Simpson methods in numerical simulation calculations, to determine the output power of the device received from the sea wave energy and survey the device's operation according to the sea wave conditions. - Calculation, design, fabrication and experiment of the electrical generator operates in sea. 4. Scientific and practical significance - The thesis brings the electrical generator model for sea wave energy, with the process of making the electrical generator device from research to fabrication, the device operates effectively and suitable to the actual conditions of Vietnam sea. - The electrical generator can be used for signal buoys of seaway and can supply the electrical power for lighthouses. 5. Structure of the thesis The contents of the thesis include the introduction, 4 chapters, the conclusion and proposition. 3 CHAPTER 1. OVERVIEW OF RESEARCHES ON THE ELECTRICAL GENERATOR FOR SEA WAVE ENERGY AND APPLICABILITY IN VIETNAM 1.1. Overview of researches on the electrical generator in the world In the world, the research and fabrication of the electrical generator devices for sea wave energy source have been considered for a long time. The received electrical energy source for wave energy conversion has met some demands of society. Up to now, the electrical generators from sea wave energy have been investigated and fabricated in many countries, for example, Britain, Canada, Denmark, France, Ireland, Japan, Norway, Spain, Sweden, South Korea, the United States, The models are researched in various forms such as the on-shore device, the device fixed on the bottom of the sea, and the floating device on the sea surface [1-19]. The analyses of models show that the electrical generator devices have been researched and fabricated in many ways. In device models, the generating motor is designed to operate in a rotational motion or in a vertical up-down motion. Each device has different advantages and disadvantages, depending on the fabrication capabilities of each unit so that the research and fabrication devices operate effectively and suitable to the actual use. 1.2. Overview of researches on the electrical generator in Vietnam In Vietnam, several research institutions have fabricated electrical generators for sea wave energy. At National Research 4 Institute of Mechanical Engineering, the researchers have calculated device model with Pelamis type, the device has been experimented in Hon Dau - Haiphong sea and supplied the electrical power to the border guards on the island to use [24]; At Vietnam National University, the researchers have fabricated linear electrical generators that operate and float on the sea surface in vertical direction. The device has been tested in sea with the received output power still limited [26,27]; At Institute of Energy Science - VAST has fabricated an electrical generator device from sea wave energy, the device is fixed on the sea surface. The fabricated device used the vertical axis hydropower generator with 60 W power, the device has been tested in sea with the output power received 50.92 W [28]; At Institute of Mechanics - VAST has carried out researches on surveying the energy characteristics of floating wave energy converters, to propose the design, calculation and fabrication of energy conversion devices [30]. Moreover, since 2013, in the professional work, the author has calculated a numerical simulation of the electrical generator model from sea wave energy. The device model is calculated with the linear electrical generator, directly generating electricity and fixed on the seabed [31]. And more, the author has leaded the project "Study, design and fabrication of the electrical power system from the renewable energy sources, project’s code: VAST 02.04/11-12" [32]. The project has designed and fabricated a power generation system with input energy sources from solar panel, wind energy and sea wave energy. In which, the input source from sea wave energy has been calculated 5 and designed to be integrated with the electrical generator for sea wave energy will be studied and fabricated in the thesis. 1.3. Research on the ability to apply the electrical generator in Vietnam and research orientation of the thesis Vietnam is a country with a coastline stretching over 3260 km, a marine space of over 1 million km2, accounting for 29% of the area of the East Sea, with nearly 3000 large and small islands, it indicates that the energy source from the sea is huge. From the monitoring and survey data show that the average sea wave height at the near coast is about 0.5÷1.2 m with the wave period from 2÷8 seconds, offshore wave height is about 1.2÷2 m with a wave period from 6÷8 seconds. Especially, when the rough sea, the coastal wave height reaches about 3.5÷5 m, offshore reaches about 6÷9 m [34-37]. This is an abundant energy source, which is very suitable for the electrical generator devices from sea wave energy to be with small and medium power. Moreover, the demand for electricity to provide for the marine economics, electricity for national security in the protection of sea and island sovereignty is an urgent task, while Vietnam’s National electricity Network can not reach. Therefore, the research and fabrication of the electrical generator devices for sea wave energy to meet the actual needs is necessary. Research orientation of the thesis: The purpose of the thesis is research, calculate and design a device to generate electricity from sea wave energy. The device is 6 efficient operation, and suitable for processing ability in Vietnam. The power source of device generates at two voltage levels are 12 VDC and 220 VAC frequency 50 Hz, with voltage quality is pure sine wave and according to Vietnam’s National grid Standard. Especially, the electrical generator can be used for signal buoys of seaway and can supply the electrical power for lighthouses. Conclusions of chapter 1 Chapter 1 presents an overview of the electrical generators in the world, especially, the models mounted on the seabed and vertical direction operation. Having pointed out that domestic units have been realizing research and fabrication of the electrical generator with detailed analysises for each type of device model. The characteristics of sea wave energy have been collected and analyzed, with data on wave energy flux, wave height and wave period to along the Vietnam coast stretching over 3260 km. In which, the average sea wave height at the near coast is about 0.5÷1.2 m with the wave period from 2÷8 seconds, offshore wave height is about 1.2÷2 m with a wave period from 6 ÷ 8 seconds. Especially, when the rough sea, the coastal wave height reaches about 3.5÷5 m, offshore reaches about 6÷9 m. Having indicated that the necessity and application capability of device model in Vietnam. Having shown out the structure of the electrical generator model for sea wave energy, and orient the research contents of the thesis, the device operates effectively and suitable to the actual conditions of Vietnam sea. 7 CHAPTER 2. RESEARCH ON THE MECHANICAL MODEL AND OPTIMIZATION OF THE ELECTRICAL GENERATOR FOR SEA WAVE ENERGY 2.1. Building a model of the electrical generator for sea wave energy The electrical generator device is fabricated for converting sea wave energy into electrical energy. This requires a system that can convert the vertical slow motion of buoy to a high speed rotating motion at the input of generating motor. The main structures of device include a circular cylinder-shaped buoy, a rope, a piston-rack, a gearbox, a generating motor, a block of 12 VDC voltage stabilizer, a DC-AC inverter and a protection system with the generating voltage being 220 VAC frequency 50 Hz and pure sine wave, as shown in Fig. 2.1. a. Illustration of device model [33] Figure 2.1. The schematic illustration of an electrical generator for sea wave energy z(t) zS(t) γ k m b. Mechanical model 8 The governing equation of buoy associated with piston-rack, as shown in Fig. 2.1, can be written as follows: ,)()()( 3002 2 zzkzzk dt dz mgzzgS dt zd m NLemsb   (2.7) where m is total mass of the buoy and the piston-rack, z= z(t) is the vertical coordinate describing the position of the buoy at time t; ρ is the water density, g is the acceleration of gravity, Sb is the bottom area of the buoy, zs is the vertical coordinate describing the height of sea wave from the seabed; the damping constant γ = γf +γem , in which the damping coefficient of fluid, γf, is assumed to be very small in comparison with the damping coefficient of generating motor γem [44,45], and can be neglected; kL is the linear spring coefficient, kN is the nonlinear spring coefficient, z0 is the rest position. The average of the power Pgm extracted from the wave by the converter taken over the time interval [0,τ] is given by [15,20,38-41]: .)( 1 0 2    dttzgmP em  (2.8) 2.2. Oscillating survey in nonlinear case From the motion equation (2.7), performing the variable transformation z – z0 = x, the equation (2.7) is rewritten as: .)( 3 02 2 xkxk dt dx mgxzzgS dt xd m NLems   b (2.22) The wave equation used here is .)cos( 0ztAzs  Use symbols c,,2  and B. In case of near resonance   22 , performing the calculation, the author gets equation: 9 ),,,( 2 2 2 txxfx dt xd   (2.25) with: .)cos(),,( 3 gtBxx dt dx ctxxf   Use transformation: .)cos( 0 xtax   (2.26) From the characteristics of the model, the thesis considers the case of weak nonlinear system. Applying the average method of nonlinear mechanics, to calculate at 0a and ,0 the author receives the relative formula between the amplitude and frequency as follows: .22 2 0 2 2 0 2 0 22 3 4 3  c a B xa  (2.39) Figure 2.2 shows the relationship between the amplitude function a0 versus frequency Ω2 with the coefficients taken as follows: m = 25 kg; a = 0.35 m; g = 9.81 m/s2; x0 = 0.4 m; kL = 1900 N/m and kN = 700 N/m3. The results showed that, in the case of the amplitude- frequency curve with the damping coefficient γem = 40, the oscillation of system is stable in the frequency range from point (1) to (2) and point (5 ) to (6). In the frequency range is increasing from point (2) to (3) and decreasing from point (5) to (4), the oscillation of system is unstable. On the other hand, if there is enough data of the actual sea wave conditions in sea areas with large wave amplitude, we can exploit the operating device in the the nonlinear region, and the received oscillating amplitude of device is the largest. 10 Figure 2.2. Graph of amplitude resonance curves versus frequency 2.3. Optimization of the electrical generator for sea wave energy With researching orientation for fabrication of the electrical generator to operate the near coast. From the assumption in sea wave height is below 1 m, the effect of nonlinear component in the model is negligible. The model parameters are determined according to a linear calculation, the equation (2.7) is considered with kN = 0 and changed the variable .0 xzz  Sea wave function acting on the model is considered by linear wave, and motion in the vertical direction z has the form: .)sin( 0ztAzs   (2.41) The motion equation of model received as follows: ).sin(2 2 t m AgS gx m kgS dt dx mdt xd bLbem      (2.42) Root of the equation (2.42) is found as follows: ),sin(      t gSk mg x bL (2.53) with χ is the oscillating amplitude of the system received as follows: 11   . 2222   embL b gSkm AgS   The mechanical power of the device received from the sea wave energy in a period is determined:   . )( 2 1 2222 2   embL bem gm mgSk AgS P   (2.56) The maximum spring force is determined: FL_max = kLHmax. (2.57) The maximum Acsimet force of buoy: FAcs_max = ρgπa2h. (2.58) The device model is researched and fabricated with the selection of Hon Dau - Hai Phong sea to test and exploit in the actual operation. At Hon Dau sea, the sea wave conditions have a period to change in the range of 3.5÷4.5 seconds and the wave height of 0.5÷1.4 m [36], so the moving velocity in the vertical direction reaches from 0.29÷0.62 m/s. In the thesis, the model is determined with the smallest mechanical power level of device to reach 270 W, the oscillating range of the model is 0.45 m. From the expressions (2.57), (2.58) combining the wave data in Hon Dau sea, the model parameters are determined kL = 2100 N/m, the buoy is circular cylinder-shaped with a height of 0.42 m and radius of 0.4 m. Figure 2.4 shows the graph of the mechanical power levels of the device according to the damping coefficient γem at the wave wave periods 3.5 seconds, 4.0 seconds, 4.26 seconds, 4.5 seconds in a wave amplitude of 0.5 m. In the thesis, the selected generating motor has a damping coefficient of 3400 Ns/m, corresponding to the mechanical power of the device is obtained maximum. 12 Survey of the mechanical power according to the buoy size: In survey calculation, the buoy radius varies from 0.35÷0.55 m. Calculation results given a comprehensive picture of the mechanical power levels of device received from sea wave energy. In figure 2.8 is a graph of the mechanical power of the device received from sea wave energy according to the buoy radii at sea wave periods. 2.4. Building a numerical simulation program and survey the operation of device to converte from sea wave energy to mechanical energy Building a numerical simulation program: The motion equation (2.7) is solved by the fourth-order Runge - Kutta method, applying the Simpson method to calculate the numerical integral and determine the mechanical power level of the device. The numerical simulation program is programmed on Matlab software, to investigate the operation of the device with the effect of the nonlinear spring when the device operates at 1 m wave height or higher. Figure 2.8. The power versus radius of buoy Figure 2.4. The power versus damping coefficient 13 Algorithm flowchart of numerical simulation program: Figure 2.9. Flowchart of the numerical simulation program In the survey calculation, the author has performed in two cases that is the first-order wave (linear wave) in the expression (2.41) and Stockes's second-order wave is given by [38,51,52]: .00 0 3 0 2 )2sin()]2cosh(2[ )(sinh4 )cosh( )sin( ztkz kz kzkA tAsz   (2.59) End Integral (2.8) by Simpson method:    1 ,...3,1 )( 2 ),(41 n j s j pZQkq    2 ,...4,2 )( 2 ),(22 n j s j pZQkq 321 ),)(2(), )0( 2( t kqkq sp nZQspZQ gm P             Yes Output results 2 )( 2;1 )( 1 Z j ZZ j Z  ti:= ti+1 ti+1:= ti + Δt 6/)432221( )()1( tkkkkiZiZ  No ti+1≥ tmax k4 = f(ti+Δt, Z(i) + Δtk3, ps) k3 = f(ti+ 2 t , Z(i) + 2 t k2, ps) Calculation: k1 = f(ti, Zi, ps) k2 = f(ti+ 2 t , Z(i) + 2 t k1, ps) Inputs t0, Z0, Δt, tmax, ps Bigin 14 Numerical simulation calculation of the device's operation: From the calculating results are shown that the operation of the device depends on both the amplitude and frequency of the sea waves. In the case, with the first-order wave, the oscillating buoy is delayed in phase compared with the sea wave about 33.60 (Fig. 2.11). The Figure 2.16 illustrates the relationship between velocity and displacement of the buoy motion in the case of the second-order wave. It shows that the phase orbit of buoy motion is stable and varies in the frequency and amplitude components of the second- order sea wave. 0 2 4 6 8 10 12 5 5.2 5.4 5.6 5.8 6 6.2 Am pl itu de (m ) Time (s) Buoy displacement Sea wave displacement 5.2 5.3 5.4 5.5 5.6 5.7 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Ve lo ci ty (m /s ) Displacement (m) Figure 2.20 shows the characteristic curves of mechanical power according to the sea wave amplitudes, at the wave frequency appears continuous when testing the device in sea that received 1.47 rad/s. Figure 2.21 is the motion of the buoy according to the sea wave amplitude with Stockes's second-order wave function. The results are calculated at wave amplitude A = 0.5 m, the difference of power between the two cases when considering linear system (kN = 0) and nonlinear (with kN = 1680 N/m3) is 4.4%. For wave amplitude A = 1.5 m, the difference is 17.1%, respectively. Figure 2.11. The displacement of buoy and t