Development of an analytical model for real-time assessment of tidal barrage power generation

Abstract

The world is focusing on renewable energy especiallyonsolar, wind and tidal energy. However, research on tidal power, more specifically, tidal barrage power, has not yet received dueattention.Current approaches and practices for the assessment of tidal barrage power generation do not consider the continuous changes in the head differences between the sea and basin. Rather a static overall estimate using an arbitrary reduction in efficiency and head difference is used. Several equations or formulas based on this assumption are used to assess tidal power. Most of them use a static head rather dynamic head.This study considers the real-time changes in water levels inside and outside the basin to compute the actual power generation potential based on dynamic water head, with the specific objectives of developing an analytical model to assess real-time power and energy, and assessing an optimum basin configuration that generates the maximum tidal power. This study also assesses the tidal barrage power potential in the coastal area of Bangladesh. A hypothetical model for continuous generation is used as a base case to compute thedynamic head for a tidal barrage. This base model did not consider minimum head for turbine operation to avoid cavitation or provision of gates to increase the efficiency of operation and used a simplified sinusoidal tidal water level variation. However, in reality the observed tide is a superimposition of a series of tidal constituents having different tidal amplitudes, speeds and phase angles. Also, water level at the basin side at any particular time depends on the area of the basin, volume of the basin, basin configuration, water level of the basin, water passing through turbines, etc. In this study, a generalized polynomial equation is developed to calculate water surface area in terms of water level. The real-time analyticalmodel developed in this study, referred to as the‘RTA Model’, introduces a set of parameters that more closely represents the actual and real-time water level variations in the basin and the sea. A set of equations represents the discharge through the turbine and gate and computes power generation during different tidal phases. The analytical model has the flexibility to change the turbine capacity (size and number) and gate capacity (size and number).This model is implemented in Excel to test different realistic situations or scenarios of the base case, such as flood-ebb generation and ebb generation. In these cases, the thresholds for power generation and gate operation are considered. Results from the new RTA Model are compared with those from the hypothetical base model. The maximum peak power from the base modelis654.4 kW compared to 666.6 kW from the RTAModel. The RTA Model yields 1.86% higher power than that of base model. Similarly, the average peak power from the base model is 261.12 kW against 247.33 kW from the RTAModel. Energy from the RTA Model is 5.60% higher than that from the base model. The RTAModel is tested for three situations - flood-ebb generation with gates, ebb generation with gates and flood generation with gates. Resultsfor 24 hours show that ebb generation with gates gives more energy (9,280 kWh/day) than that for flood-ebb generation with gates (8,125 kWh/day) and flood generation with gates (5,190kWh/day). Generation time for ebb generation with gates, flood-ebb generation with gates and flood generation with gates are 66%, 48% and 37%, respectively, of the full duration. Ebb generation yields more energy than that of flood-ebb generation, but duration of ebb generation is slightly less than flood-ebb generation. The model is also validated using the data for the Severn tidal barrage, for which the annual energy output was initially 15.09 TWh and was later re-assessed to be 11.12 TWh. Using the present RTA Model (ebb generation), the annual energy output was foundto be 10.77 TWh which is only 3.15% less than the latestassessment, and about 28.62% less than the original assessment. Optimization of the plant capacity is conducted in this study. Generally,the higher the turbine capacity,the higher the extractable energy. However, the cost or investment increases with the capacity. Therefore, capacity optimization is required to make the energy generation cost-effective considering the turbine capacity and its cost. In this study, levelized tariff (cost/kWh) is considered as a basis for plant optimization. Levelized cost of energy (LCOE) is the cost for per unit energy production for the economic life of the plant. In this study, it is assumed that the water level remainshorizontal at the sea and the basin during the tides. However, in reality, the water level in the basin and sea varies non-linearly during each tidal cycle. This non-linearity depends on the aspect ratio (width/length ratio) of the basin and the openings of turbines and gates. To check the sensitivityof the basin aspect ratio, anarbitrarily basin of 10m depth and 90km2area having aspect ratios of 0.9, 0.625 and 0.4 m were considered with a tidal amplitude of 4 m. Using the two-dimensional NAO.99b model based on non-linear shallow water equations (Matsumoto et al., 2000)the actual non-liner water level variations for this hypothetical basin is determined. It is observed that the higher the aspect ratio the higher the annual energy output. The model was also run to assess the impact of the vertical cross section of the basin on energy generation. It is observed that a trapezoidal basin having a side slope s=0.5 yields more energy than a trapezoidal basin having a side slope s=2.0, or a rectangular basin or parabolic basin considering the same tide data (same tidal range) and same area of cross sections (within high tide and low tide) along the length of the basin irrespective of the shape. In Bangladesh, there are some potential sites for tidal powergeneration. Generally, at least a 5-meter tidal range is required to generate tidal range power or barrage power. This study reveals that some areas such as Sandwip, Khal No. 10, Mongla and Sadar Ghat (Chattogram) are promising sites for tidal barrage power development. This study applied the analytical RTA Model to a hypothetical case for the Sandwip channel (having a tidal range more than 7m) to assess the potential of the site. Using the past 20 years’ tidal data, 214 tidal constituents (each of which is considered as a simple harmonic motion with different amplitude, speed and phase) were developed using the‘GeoTide Analyzer (3.0.x, 2015)’software. GeoTide Analyzer converts observed tide gauge data directly into tidal harmonic constants which can then be used to make tidal predictions for any future or past date. Using the bathymetric data of Sandwip channel collected from BIWTA, CEGIS and Bangladesh Navy, an area-elevation curve is drawn which is used in the model to assess the incremental increase or decrease of water level as well as the water level change after a small interval to calculate the head for a given time step. Utilizing the flexibility of the RTA Model to change the number of turbines and gates, as well as their dimensions (diameter and size) and its suitability for flood-ebb generation, ebb generation or flood generation, it is observed that ebb generation yields more energy than that of flood-ebb generation, but duration of ebb generation is slightly shorter than flood-ebb generation. The optimum capacity of the plant is assessed by calculating the LCOE. Model results show that for a basin area of 500km2, the average plant capacity for Sandwip channel would be 854 MW and the plant will generate 2,203 GWh annually in ebb generation mode with 400 turbines (each 6 m in diameter) and 800 gates (each 12 m x 8 m in size). The maximum capacity will be 2,757 MW and will supply electricity 29% of the time in a year. The presentestimatedcost of the plant is BDT 14,763 crore USD 1,678million (at a conversion rate 1 USD = 88 BDT).