Extending Complex Conjugate Control to Nonlinear Wave Energy Converters

Abstract

This paper extends the concept of Complex Conjugate Control (CCC) of linear wave energy converters (WECs) to nonlinear WECs by designing optimal limit cycles with Hamiltonian Surface Shaping and Power Flow Control (HSSPFC). It will be shown that CCC for a regular wave is equivalent to a power factor of one in electrical power networks, equivalent to mechanical resonance in a mass-spring-damper (MSD) system, and equivalent to a linear limit cycle constrained to a Hamiltonian surface defined in HSSPFC. Specifically, the optimal linear limit cycle is defined as a second-order center in the phase plane projection of the constant energy orbit across the Hamiltonian surface. This concept of CCC described by a linear limit cycle constrained to a Hamiltonian surface will be extended to nonlinear limit cycles constrained to a Hamiltonian surface for maximum energy harvesting by the nonlinear WEC. The case studies presented confirm increased energy harvesting which utilizes nonlinear geometry realization for reactive power generation.

Recent advances in wave energy converters based on nonlinear stiffness mechanisms

“…[27], [31]- [66] [28], [67] [29], [68]- [71] [30], [72]- [73] the characteristics of the double-well potential, the system may have three motion patterns, i.e., low-energy local oscillations restricted in one potential well, chaotic mix-well oscillations, and periodic motion between two wells. Periodic oscillations with large amplitudes have been recognized to greatly enhance the energy harvesting performance of systems.…”

“…In contrast to the concrete nonlinear mechanisms discussed above, some scholars have also achieved nonlinear stiffness using a theoretical mathematical model. Zheng et al [30] employed a nonlinear hardening spring model, and Wilson et al [72] adopted cubic stiffness for a point absorber WEC. Fig.…”

Data-Driven Model Predictive Control for Wave Energy Converters Using Gaussian Process

“…When a random certain value is provided for one of these two unknown coefficients, the other coefficient can be computed according to Equation (21). When M pto = 0 in Equation ( 21), it is referred to as the complex-conjugate control [28]:…”

Dynamic performance of a point absorber WEC considering nonlinear hardening spring under irregular waves

“…Liu [10] developed the duffing type nonlinear oscillator dynamic differential equation of wave energy conversion and found the large displacement excitation amplitude and nonlinear stiffness will increase the nonlinearity, output voltage and harvesting frequency bandwidth. Wilson et al [11] demonstrated the performance of nonlinear WEC using the nonlinear cubic hardening spring and solved the dynamic response considering the nonlinear control. Sun et al [12] used the finite element analysis software COMSOL Multiphysics to obtain the nonlinear hardening spring characteristic of magnetic.…”

“…Sun et al [12] used the finite element analysis software COMSOL Multiphysics to obtain the nonlinear hardening spring characteristic of magnetic. Wilson et al [13] extended the concept of Complex Conjugate Control (CCC) to nonlinear WECs using Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) to design the optimal limit cycles. Wu et al [14] studied the nonlinear behavior of wave energy harvesting considering nonlinear stiffness in regular waves.…”