Tidal Power: Harnessing Energy from Water Currents

Preface

Water current power can be an important renewable energy source and is influenced by the sun, the moon or both at the same time. Their influence is shaped by the peculiarities of the earth - its motion and the presence of the atmosphere and hydrosphere. The feasibility of using renewable sources at a scale compared with major energy generators is essentially determined by:

1. Economics - The cost (material and labor) per kilowatt hour (or kilowatt)

2. Ecology – The environmental impacts resulting from the energy system

3. Power delivery in time and place

The economic and ecological limits vary with social, political and geographic conditions. Political will, regulations, and social compliance enables this technological advance. Site location and delivery of base load RE (renewable energy) is of critical importance.

In many parts of the world, environmental constraints on energy are lowered. That allows politicians to give a decisive role to energy development associated with petroleum and radioactive material risks. With the development of social activism and potential economic changes, the emphasis on cleaner sources is increasing.

Among renewable sources taking into account their economic efficiency and environmental performance, energy use of river and ocean currents is significantly growing. The energy capability of these currents is considerably greater than the needs of humanity, even in the distant future. The economic evaluation of technologies for converting this energy should be based on a direct measurement of received energy rather than the efficiency of the generator.

The author suggests specific modern technologies for the cost-effective use of tidal, and river power without creating a waterfront. In some regions, for example, in the Kola Peninsula, Kamchatca, Kuril Islands as well as in the other northern and eastern Russia, it is possible that the cost-effective use of tidal and rivers power in advanced grids, or in complexes with hydrogen production, can provide a universal source of energy.

We propose new technological methods of energy conversion, which create acceptable cost-effectiveness of systems and increase their investment attractiveness.

The following energy production methods are emphasized, with the appropriate use of new structural and technological solutions for each of them, to provide a low cost per installed kilowatt of power and a low cost of power production.

- Tidal current energy use without the creation of a waterfront and the cutting off the tidal basin from the sea such as with tidal barrages, but with the provision (if necessary) of guaranteed basic system components

- The use of river power without dams or a disruption to ship traffic, which introduces variability of current speeds as the regulating factor of river energy production

- Production and transportation of liquid hydrogen, with special piping in conjunction with superconducting channels of transmission.

The development of these areas can meet the energy needs of much of the world at a reasonable cost, without environmental damage, the unnecessary increase in global risk made by intensive nuclear power plant construction or the increased rate of hydrocarbon combustion.

Earlier results are covered in some Russian books by the author, Renewable power. Effective decisions., M.-Izewsk: 2011, 172 p., Technical and economic bases of the accelerated development of wind power, M: 1990, 67 p., Wind power stations of big power-M: 1987, 72 p. The same general calculation and testing problems are discussed in the author’s new book in English Wind Power. Turbine Design, Selection, and Optimization, 2013, p.311.

Chapter 1

Marine Hydro Kinetic- MHK

Traditional tidal power plants (TPP-tidal barrages) result in a complete separation of a sea from a gulf in order to create one or several power producing reservoirs [1]. Such systems have a number of fundamental flaws, which hamper the development of this energy industry.

All projects require the building of dams and other hydro-technical construction, which cut off the TPP basin from the sea. The existence of this kind of front noticeably changes the ecological situation in the basin.

The existence of a head front (dams and head construction) defines an often unfavorable system of finance where it is necessary to completely finish the building (and completely pay for all required work) and only after will the station begin to generate energy and return capital investments.

The heads at TPP are not large, the traditional hydropower equipment is expensive, and production is relatively small. The cost of TPP building and head front constructions designed for gale oceanic wave and heavy ice load is high. This establishes high capital investments per unit of the installed capacity and a relatively high primary cost of energy.

The power of TPP is changed in accordance with the tidal water regime with may be at zero many times per day.

A new MHK design approach has no such shortcomings and is based on the use of free tidal currents at maximum water speed areas. The tidal power plants proposed, consist of a floating or fixed hydraulic unit, on the surface (fixed to the bottom surface) or underwater (in areas with heavy ice), that converts the energy of tidal currents into electrical energy or into gaseous or liquid hydrogen in the event that direct delivery of electricity is not possible or is not economical. For the use of tidal energy, it is not necessary to completely block the mouth of the basin in order to create the structural works. The maximum possible power and maximum possible energy output is obtained under a specific hydraulic resistance introduced by turbines, and due to the economic feasibility, is also obtained by structures that funnel the water flow at the entrance to the MHK reservoir (at the narrowest part) [2].

The energy potential of sea tidal flows is usually estimated by the maximum potential energy of a body of water that rises in the gulf during high tide over the minimum low tide water level. The actual fact is that in order to obtain high tide energy, it is necessary to create an obstacle in the tidal flow path. The obstacle may be created by building power plants and dams that obstruct the strait between the reservoir and the sea, as is the case at the existing tidal barrages in France, Canada, Russia and China.

The obstacle may also be in the form of hydropower units of one sort or another, positioned in a strait without a dam or in the presence of embankments, which narrow the strait to the optimal size. Such design, proposed by the author in 1985, is implemented in the Myongyang Channel in Korea, and uses helicoidal orthogonal turbines. Other experts in different countries independently proposed this same solution for additional projects around this time.

In any case, a question arises about the maximum power and output, which can be obtained under given conditions. Obviously, for very large applied resistance (a tidal barrage), water expenditure will be minimal and, despite the maximum pressure, the power will be close to zero. With the absence of resistance, a pressure drop will be zero and, despite the maximum flow rate, power will be also zero. It was shown that there is an optimal resistance that corresponds to the maximum power and possibly another resistance that corresponds to the maximum energy output [3].

Let z0(t) and z(t) denote the water levels in the sea and the MHK reservoir, respectively, Ω – reservoir water surface area, Ωp – cross-sectional area of MHK water channel, A - height of tide with period T, and ξ - coefficient of resistance of the MHK water tract. Consider first the case when the reservoir connects with the sea only through one strait.

In this case, the flow through the strait (Q(t)) is determined by the movement of the water level in the pool:

(1.1) equation

The pressure loss in the strait is proportional to the current flow through the power tract:

(1.2)

The energy balance equation, in the zero-dimensional approximation for the periodic tide, takes the following form by the calculations below:

(1.3) equation

(1.4) equation

where

(1.5) equation

The water level z(t), in the reservoir and the sea, is measured in fractions of the initial amplitude equal to half the tide height (A). Time is measured in fractions of the period T. Thus, all the variables in (1.4) are dimensionless. Height of tide in the sea is the same.

Equation (1.4) can be written in explicit form with respect to the time derivative of the water level in the pool:

(1.6)

(1.7)

(1.8) equation

Equation (1.6) was solved numerically under conditions as α → 0 and t = 0.

(1.9) equation

The calculations were performed before the solution z(t) assumed periodic regime. Usually this has taken place, beginning no later than the fifth oscillation. Steady-state oscillations in the reservoir can be approximated as:

(1.10) equation

Traditional design tidal barrage power at a fixed water cross-sectional channel area is:

(1.11)

Here, η is the total efficiency of traditional design generators is usually:

(1.12) equation

Expression (1.11) reduces to:

(1.13)

(1.14)

(1.15)

(1.16)

Maximum power, within a tidal cycle, occurs when cos(4πt − β) = −1 and is expressed below:

(1.17)

where

(1.18) equation

MHK parameter calculations results (1.13, 1.17) are in table 1.1:

Table 1.1

Maximum MHK power, with fixed reservoir area, height, and tidal period, corresponding to the maximum coefficient C, takes place at α = 0.03 ÷ 0.04 and is approximately 7.27 (fig. 1.1).

Figure 1.1 A relative amplitude (zm) of fluctuating water levels in the MHK reservoir and relative maximum power of the MHK (C), depending on a.

A graph of MHK reservoir water level fluctuations is shown in fig. 1.2:

Figure 1.2 The reservoir water level z(t), for MHK at maximum power.

Relative height of inflow in the pool and phase angle are shown on fig.1.3:

Figure 1.3 Amplitude-phase characteristics of tides in the free-flow MHK reservoir.

Maximum power, which can be obtained from the tide in the fixed area reservoir, according to (1.17) is:

(1.19) equation

The moon and the sun determine the schedule of the tidal processes in which the semidiurnal, daily allowance or the mixed components (fig. 1.4) change. This depends on the geographical coordinates of a point of supervision relative to the influence of the moon and sun.

Figure 1.4 Forms of tidal water levels and flow.

The parameters of tidal inflow outflow observed ashore, keeping cyclic character, significantly change under the influence of coastal topography. The form of function a water level – time depends on local conditions and can be defined for a coastal zone or for the ocean as a whole (fig. 1.5).

Figure 1.5 Tidal forms in world oceans.

From the image it is visible that almost all the coasts of the Russian and American seas have the characteristic period of tidal phenomena about 12 hours and a small amount are the mixed form. For any supervision point data or calculations for 369 days though the greatest period of changes is equal to about 18.6 years. The main features of local inflow can be perceived within one month of supervision or calculations. Data on inflow near the USA, Canada and the Pacific Islands can be found on the internet at http://tidesandcurrents.noaa.gov/tide_pred.html and http://tidesandcurrents.noaa.gov/currents06. The example is shown in fig. 1.6.

Figure 1.6 The level of water (meters) in Saint John, New Brunswick by hour in January.

Complete data on inflow in the seas of Russia are limited.

If the tidal period T = 12.4h = 4.46 10⁴ sec, and the reservoir area is in km², the formula (1.19) becomes:

(1.20)

Where A is the maximum height of tide (m).

The MHK power graph can be described by the following:

P = 2πzm|−sin φ + Bsin4πt|ΩA²/T, where zm = 0.775, sinφ = 0.744, B = 0.751 or approximately

(1.21) equation

The average value of power for an ebb-tide cycle in optimum conditions is half of maximum power. When calculating development after one year, it is necessary to consider the variability of inflow height from the year before. Thus, average capacity in a year in optimum conditions can be represented by:

(1.22)

< > is the symbol of averaging.

The real schedule of delivery of power and development of a tidal power plant depends on the design of applied turbines and the structure of their use. If, for example, you use a tidal power plant without dams with orthogonal units and the frequency of rotation changes in proportion to the speed of a stream of U = Umax Sin (2πt − φ), providing the highest efficiency of turbines, the average capacity of that power plant is defined by the expression:

Where the integral undertakes range from 0 to 1/4. Thus, in this case:

(1.22a)

If the design and the scheme of management at the station is arranged so that its capacity changes periodically with the period of inflow and shifts in some phases, its average capacity will appear more than in both previous estimates:

(1.22b)

Tidal flow isn’t a strict sinusoidal process, however its main lines are established by the sum of two components defined by lunar and solar influence. The amplitudes of these two harmonicas differ by 2.17 times. Therefore, as a first approximation the maximum and minimum heights of inflow can be estimated by the following ratios:

(1.23)

(1.24)

Here A0 = 0,685 Amax is the height of the inflow caused by the moon.

The mean square height of inflow defining the possible development of a tidal power plant, has to be defined with the actual mode of inflow:

(1.25)

(1.26) equation

If the average or maximum height of inflow are defined by the yearly average or separately for high and low inflow, ratios can differ. In fig. 1.7 the maximum heights of inflow for the gulfs in the Kola Peninsula for the periods of the maximum inflow are shown as functions of the average heights (line 1, formula 1.26) and the yearly average (line 2, formula 1.27).

Figure 1.7 Data showing the natural supervision on gulfs of the Kola Peninsula during high inflow (line 1) and on the yearly average (line 2).

(1.27)

Rating (1.21, 1.22) gives a substantially lower maximum energy potential than the known estimates that are based on the potential energy of water that rises in a closed reservoir of a tidal sea.

The choice of rated capacity of MHK is a technical and economic task. The power of MHK can be set according to the corresponding financial opportunities of the investor, but smaller than the limit value set by the hydrological and topographical conditions. TPP in our proposal (Marine Hydro Kinetic- MHK) consist of the hydro units transforming energy of an ebb-tide current. Such hydro units are installing in the passage connecting the pool to the sea where current speeds are high. Units can be equipped with the orthogonal turbines. Optimum speeds of currents for the free flow orthogonal turbines are from 2 to 4 m/s. If such speeds aren’t reached naturally, there will probably need to be a preliminary or subsequent narrowing of the passage by coastal dams or ground dumping. The turbine capacity P depends on the running stream speed U and the linear speed of blades.

V = πDn/60 can be given in two forms:

(1.28) equation

(1.29)

Where S = D H − area of axial cross-section of the body swept around by the blades, (S σ) - area of the median (chord) surface of working blades, σ - solidity, i - number of blades, b - length of the blade chord, D - diameter