Optimum Design Of Tall And Slender Wind Turbine Tower Considering Residual Vibration Constraints

As the competition in wind power market becomes fiercer and the demand for profit grows stronger,the need for tall wind turbine towers has grown dramatically.The wind load of tall towers is stronger and more stable,which improves power generating efficiency.Since the high cost of rigid tower design,slender tower is preferred,yet presents new challenges to strength,stability and fatigue design of these towers.However,the excessive vibration due to resonance during emergency shutdown operation is also an issue of great concern for tall and slender tower,which is considered as a residual vibration.Strong long-time residual vibration of the tower top is observed after emergency shutdown,which poses imminent threat to the safe operation,especially to tall and slender towers.To reduce the construction cost and ensure the safe operation of wind turbine towers,a frequency control based structural optimization,subject to residual vibration constraints,is presented in this work.For the sake of simplicity,a single tubular wind turbine tower is considered and modeled as a cantilever structure,and the platforms and ancillary structures neglected.The design variables are cross section parameters and subject to their upper and lower bound constraints based on manufacturing and logistic consideration.The objective function is minimum structural volume and the natural frequency is constrained to ensure the tower a slender design.A quadratic integral index which measures the residual vibration after emergency shutdown globally is constrained to control the effect of emergency shutdown.With the Lyapunov's second method,the quadratic integral index is simplified into matrix forms,which avoids the transit dynamic analysis for residual vibration and reduces computational time to a great extent.In order to calculate tower top displacement,the professional software Bladed is applied to obtain the wind load at emergency shutdown,which makes the study more relevant in industrial applications.For comparison with the constraint on integral residual vibration,the constraint on tower top displacement under the wind load at shutdown is examined to study its effect on optimum design.In the optimization process,the constraints and their sensitivities to the design variables are calculated.The sensitivities of the residual vibration constraints with respect to design variables are obtained by the adjoint method and solution of Lyapunov equation.The sensitivities of the tower top displacement constraints with respect to design variables are obtained by analytical method.Because the specific expression of the tower top displacement can be calculated by Mohr integration.The increments of the design variables are updated by the method of moving asymptotes(MMA).The results of the two examples indicate that the residual vibration constraint and the tower top displacement constraint have similar effect in optimum designs.But the optimal structure has different optimal shapes in accordance to different Rayleigh damping coefficients.Moreover,the topology of the damper distribution is optimized.It is also shown that the damper reduces the load,which makes the study more relevant for the tall and slender towers in industrial applications.