Wave Excitation Force Estimation Using an Electrical-Based Extended Kalman Filter for Point Absorber Wave Energy Converters

Accurate real-time knowledge of the wave excitation force affecting a wave energy converter (WEC) – either through measurement or by estimation – is crucial for implementing effective control strategies that ensure optimum power absorption, system reliability, and durability. The estimation of the excitation force using other readily available measurements is deemed a cost-effective solution given the technical difficulties associated with directly measuring the excitation force on the WEC’s floater hull. In this study, an electrical-based extended Kalman filter (E-EKF) estimator for estimating the wave excitation force, floater’s heave displacement, and velocity is proposed. The estimator is derived using a holistic nonlinear wave-to-wire model of a direct-drive heaving WEC. A continuous and differentiable approximation of the well-known Tustin friction model is utilized to incorporate the friction force model into the estimator. The proposed E-EKF estimator requires only the measurement of the three-phase permanent magnet linear generator stator currents using current transducers. A practical approach is provided to overcome the need for measuring the wave surface elevation and velocity. Simulations are conducted to assess the goodness of the proposed E-EKF under various sea-state conditions, modeling mismatches, and electric loading scenarios. For the sake of comparison, the performance of the E-EKF estimator is measured against mechanical-based extended Kalman filter and linearized mechanical Kalman filter estimators. The E-EKF estimator exhibits superior performance in terms of nearly all performance metrics, with an excitation energy percentage error score not exceeding 9 %, while being immune to measurement noise.