💨Airborne Wind Energy Systems Unit 8 – Flight Trajectory Optimization & Energy Analysis

Key Concepts and Principles

• Airborne Wind Energy Systems (AWES) harness wind energy at higher altitudes using tethered flying devices (kites, gliders, or drones)
• AWES can access stronger and more consistent winds compared to traditional wind turbines
• Two main types of AWES:
  • Ground-gen systems generate electricity on the ground using a tether tension
  • Fly-gen systems generate electricity onboard the flying device and transmit it to the ground
• AWES operate in a periodic pumping cycle consisting of a power phase and a retraction phase
• The power phase generates energy by exploiting the high aerodynamic forces on the flying device
• The retraction phase consumes a fraction of the generated energy to bring the device back to its initial position
• AWES have the potential to reduce the cost of wind energy and expand the geographical range of wind power deployment

Fundamental Equations and Models

• The power output of an AWES depends on the wind speed, the aerodynamic properties of the flying device, and the tether tension
• The equation for the instantaneous power output is: $P = F_t \cdot v_t$, where $F_t$ is the tether tension and $v_t$ is the tether velocity
• The average power output over a complete pumping cycle is given by: $P_{avg} = \frac{1}{T} \int_0^T P(t) dt$, where $T$ is the cycle period
• The lift and drag forces on the flying device are modeled using aerodynamic coefficients ($C_L$ and $C_D$) and the apparent wind velocity
• The tether is modeled as a flexible cable with varying tension and aerodynamic drag
• The dynamics of the flying device are described by a set of nonlinear differential equations that account for the forces and moments acting on it
• Simplified models (point-mass, rigid-body) are often used to reduce computational complexity and enable real-time control

Flight Dynamics and Control

• The flight trajectory of the AWES is a critical factor in determining its power output and efficiency
• The flying device must follow a prescribed path (figure-of-eight, circular, or other patterns) to maximize the energy extraction from the wind
• The control system must ensure stable and robust operation in the presence of wind gusts, turbulence, and other disturbances
• Feedback control techniques (PID, LQR, MPC) are used to track the reference trajectory and regulate the tether tension
• The control inputs typically include the flying device's aerodynamic surfaces (elevator, rudder, ailerons) and the tether reel-out/reel-in speed
• Advanced control strategies (adaptive, robust, learning-based) are being developed to improve the performance and reliability of AWES
• The control system must also handle the transitions between the power and retraction phases and ensure safe landing in emergency situations

Energy Conversion and Efficiency

• The energy conversion process in AWES involves transforming the kinetic energy of the wind into electrical energy
• In ground-gen systems, the tether tension drives a generator on the ground, which converts the mechanical energy into electricity
• In fly-gen systems, the flying device carries a small wind turbine or a specialized generator that directly converts the wind energy into electricity
• The efficiency of the energy conversion depends on several factors:
  • The aerodynamic efficiency of the flying device (lift-to-drag ratio)
  • The efficiency of the generator and power electronics
  • The losses in the tether and the mechanical transmission
• The overall efficiency of an AWES is typically lower than that of conventional wind turbines due to the additional losses in the tether and the periodic pumping cycle
• However, the higher wind speeds and the reduced material costs can compensate for the lower efficiency and make AWES economically viable

Optimization Techniques

• The design and operation of AWES involve multiple optimization problems to maximize the power output, minimize the costs, and ensure safe and reliable operation
• The optimization variables include the flying device's geometry (wingspan, aspect ratio), the tether length and diameter, the flight trajectory, and the control parameters
• The objective function is typically the average power output or the levelized cost of energy (LCOE), which accounts for the capital and operational costs over the system's lifetime
• The optimization is subject to various constraints, such as the maximum tether tension, the minimum altitude, the maximum wind speed, and the regulatory requirements
• Gradient-based optimization methods (sequential quadratic programming, interior-point) are commonly used for smooth and differentiable problems
• Gradient-free methods (genetic algorithms, particle swarm optimization) are used for non-smooth or black-box problems
• Multidisciplinary design optimization (MDO) techniques are employed to handle the coupling between the aerodynamic, structural, and control aspects of the system

Simulation and Analysis Tools

• Simulation plays a crucial role in the design, optimization, and testing of AWES
• High-fidelity simulation tools are used to model the complex dynamics of the flying device, the tether, and the wind environment
• Computational fluid dynamics (CFD) is employed to analyze the aerodynamic performance of the flying device and the wake effects
• Finite element analysis (FEA) is used to assess the structural integrity and the dynamic behavior of the tether and the flying device
• Multibody dynamics simulation is used to model the coupled motion of the flying device and the tether
• Control system simulation is performed to test and validate the control algorithms and to assess the closed-loop performance
• Hardware-in-the-loop (HIL) simulation is used to test the real-time performance of the control system and to validate the simulation models
• Simulation results are compared with experimental data from wind tunnel tests, scaled prototypes, and full-scale demonstrators to improve the accuracy and reliability of the models

Real-World Applications

• AWES have the potential to unlock vast wind energy resources in areas where conventional wind turbines are not feasible or economical
• Off-shore AWES can harness the strong and steady winds over the oceans without the need for expensive foundations and underwater cables
• High-altitude AWES can reach winds at altitudes of several kilometers, where the wind power density is significantly higher than at ground level
• Mobile AWES can be deployed rapidly in remote or disaster-struck areas to provide emergency power supply
• AWES can be integrated with other renewable energy sources (solar, hydro) and energy storage systems to provide a stable and dispatchable power supply
• AWES can also be used for non-energy applications, such as cargo transportation, communication platforms, and weather monitoring

Challenges and Future Developments

• AWES are still an emerging technology with several technical, economic, and regulatory challenges to overcome
• The reliability and durability of the flying device and the tether are critical issues that require advanced materials, manufacturing techniques, and testing methods
• The control and automation of AWES are complex problems that require advanced sensors, actuators, and software algorithms to ensure safe and efficient operation
• The integration of AWES into the electrical grid requires suitable power electronics, energy storage, and grid control strategies
• The social acceptance and the environmental impact of AWES need to be carefully assessed and addressed through public engagement and sustainable design practices
• The regulatory framework for AWES is still evolving and requires close collaboration between the industry, academia, and policymakers
• Future developments in AWES include:
  • Advanced materials (composite, nanomaterials) for lighter and stronger flying devices and tethers
  • Improved aerodynamic designs (morphing wings, boundary layer control) for higher lift-to-drag ratios
  • Intelligent control strategies (reinforcement learning, swarm intelligence) for adaptive and cooperative control
  • Hybrid systems that combine AWES with other renewable energy sources and storage technologies
  • Standardized and modular designs for mass production and economies of scale