Multi-Mode Controller Development for Cross-Flow Hydrokinetic Turbines

Abstract

Cross-flow turbines, in which the axis of rotation is perpendicular to the direction of inflow, have particular advantages over axial-flow turbines in aquatic settings, but are not as well understood. The applicability of axial-flow controls research to cross-flow systems is limited because cross-flow turbines have unique dynamics and fewer means of control actuation. This work explores the unique dynamics of cross-flow turbines, proposes a methodology for performance characterization in non-uniform inflow appropriate for field-scale devices, and investigates potential torque control strategies through computer simulation, laboratory experiment, and field-scale testing. The objective is to develop and evaluate control algorithms that are broadly applicable to cross-flow turbines. An emphasis is placed on simplicity: required sensing, the complexity of any necessary turbine characterization, and actuation requirements are minimized to ensure that proposed controllers are broadly implementable on extant turbines. The potential costs and benefits of added system complexity can then be considered against this benchmark on a device-specific basis. Firstly, a method is suggested to define an effective inflow velocity for turbine performance characterization from a series of point velocity measurements in a spatially non-uniform but temporally consistent flow field. This characterization is necessary to appropriately anticipate device power outputs, to evaluate controller performance, and to allow accurate turbine simulation. When paired with time-average estimates of turbine power output, the developed performance characterization curve is found to be consistent for temporally-separated power measurements. Turbine performance is found to be highly sensitive to flow measurement location when subject to a hypothetical control law relying on an upstream point-measurement of velocity. This implies that multiple sensors or a spatially-resolved measurement of inflow would be necessary for good turbine performance, which contravenes the control objective of minimal sensing requirements. Secondly, three potential power-maximizing controllers were considered in simulation, experiment, and at field-scale. While the field-scale and laboratory turbines were not directly geometrically or hydrodynamically scaled, they were morphologically similar (i.e., both were four-bladed helical turbines) and had similar normalized time-average performance curves. The effect of neglecting phase variations in turbine performance in simulation is considered, but is found to be insignificant because the helically-bladed turbines have relatively consistent power output. In addition, the ability to apply torque in the direction of turbine rotation (i.e, ``motoring'' the turbine) is not presumed: only resistive control torques are allowed. Simulation was found to predict controller behavior in both a time-resolved and statistical sense, and trends in controller performance in the laboratory were also observed at field-scale. The largest sources of simulation error were related to un-modeled dynamics of the physical control implementations and simplifications to the flow interaction model. Accurately modeling dynamics of the physical implementation is found to be critical for simulation to be reflective of physical testing, particularly when the implementation is non-ideal (i.e., latency, sensor noise, etc.), and these non-ideal elements are likely to vary device-by-device. One evaluated controller required an upstream measurement of inflow and an advection model: this was not found to enhance performance of the laboratory turbine and significantly complicated implementation. Nonlinear ``K$\omega^2$'' control, which requires only a time-average turbine model and a measurement of angular velocity, showed the best performance of the evaluated controllers. Thirdly, the best-performing power-maximizing controller (a nonlinear controller) is incorporated with a nonlinear rated power-tracking controller and a strategy to transition between the objectives proposed. Power-tracking control is performed ``overspeed'' (i.e., the turbine accelerates to decrease power output) to provide superior stability properties to ``underspeed'' control. In keeping with controller objectives, each control law and the transition strategy requires only an angular velocity measurement and a time-average turbine characterization for implementation. The control law is examined in simulation and experiment for two cross-flow turbines: the helical turbine used in the previous study, and a turbine with two straight blades. Because the power output from the straight-bladed turbine is much more variable than for the helical turbine, these cases provide contrasting dynamics to evaluate controller effectiveness. Again, only resistive control torques were allowed, but because of the phase variation in power output, the simulation included phase-resolved turbine performance models. For both turbines, in all laboratory cases, constant power set points are closely tracked (less than 3\% mean absolute percentage error). The limited observed error has two contributing factors, both with a common cause. The combination of filtering, sensor sampling rate, and torque feedback loops present in experiment effectively delay control response. During relatively large flow accelerations, this delay results in a steady-state tracking error. Particularly for the straight-bladed turbine, the delay results in imperfect mitigation of the natural phase variation in power output. In simulation, steady-state error due to flow accelerations is negligible, but, as demonstrated via spectral analysis, unmitigated variations remain for the straight-bladed turbine. An analytical examination of phase-resolved turbine dynamics indicates that perfect mitigation is not generally possible under purely resistive torque, but scales favorably with turbine radius. Simulation suggests that this is not an issue for turbines with relatively constant power output, such as the helical turbine. These conclusions are extended to field-scale turbines and cross-flow wind applications. The presented controller can be broadly implemented on field-scale devices due to its minimal sensing and actuation requirements. However, it has yet to be demonstrated on a field-scale device. Additionally, the relationship between power-smoothing accomplished at the turbine (as investigated here) and that which can be performed by power electronics will vary by device. Thus, the presented algorithm is not expected to be generally optimal, but a useful benchmark against which the performance of more demanding implementations can be compared. Other areas suggested for future work include the exploration of optimal control trajectories for various cost-functions and actuation capabilities (e.g., the ability to motor the turbine) using phase-resolved turbine models. While these models are not expected to accurately predict physical turbine performance, the general form of the suggested optimal controller could serve as a starting point for the development of alternative control laws, specifically model-predictive control. The major contributions of this work are a method for performance characterization in non-uniform inflow, a demonstration of the extent to which simple simulation and laboratory-scale testing is predictive of field-scale response without explicit consideration of geometric or hydrodynamic scaling parameters, and a simple, general purpose turbine control law demonstrating good power-tracking performance and smooth, stable transitions between control objectives.