Tidal and Wave Energy Optimization

Module: Sustainable Tech | Difficulty: Premium

Tidal Power

where is the power coefficient (Betz limit = 0.593).

Wave Energy

where is significant wave height and is energy period.

Comparison

| Technology | Capacity Factor | LCOE ($/MWh) | Maturity | |-----------|----------------|--------------|----------| | Tidal stream | 25-35% | 150-300 | Commercial | | Tidal barrage | 25-30% | 100-200 | Proven | | Wave point absorber | 15-25% | 200-500 | Prototype | | Oscillating water column | 20-30% | 180-400 | Demonstration |

Python Implementation

import numpy as np
from scipy.optimize import minimize

class OceanEnergyOptimizer:
    def tidal_power(self, velocity, rotor_area, Cp=0.4):
        rho = 1025
        return 0.5 * rho * rotor_area * velocity**3 * Cp

    def wave_power(self, significant_height, energy_period):
        rho, g = 1025, 9.81
        return rho * g**2 / (64 * np.pi) * significant_height**2 * energy_period

    def turbine_array_layout(self, n_turbines, spacing_min=5):
        positions = np.random.uniform(0, 100, (n_turbines, 2))
        def objective(flat_pos):
            pos = flat_pos.reshape(-1, 2)
            distances = np.sqrt(((pos[:, None] - pos[None, :])**2).sum(axis=2))
            np.fill_diagonal(distances, np.inf)
            min_dist = distances.min()
            return -min_dist if min_dist > spacing_min else 1000 * (spacing_min - min_dist)
        result = minimize(objective, positions.flatten(), method='Nelder-Mead')
        return result.x.reshape(-1, 2)

    def resource_assessment(self, tidal_velocities, wave_heights, wave_periods):
        tidal_energy = np.mean([self.tidal_power(v, 100) for v in tidal_velocities])
        wave_energy = np.mean([self.wave_power(h, t) for h, t in zip(wave_heights, wave_periods)])
        return {'tidal': tidal_energy, 'wave': wave_energy, 'total': tidal_energy + wave_energy}

Research Insight: Tidal stream energy achieves capacity factors of 25-35%, higher than solar or wind in many locations.