Research On Nonlinear Stochastic Model Predictive Control And Its Application In Wind Power Generation System

As is well known,energy and electricity play a vital role in national economic development.In order to realize the green energy transformation,it is necessary to promote clean energy generation vigorously.Wind power generation has become an important part of power generation systems because of its renewability,cleanness,low cost,and high environmental benefits.Consequently,the control system design plays a key role in the operational security and generation efficiency of wind farms.A wind power generation system(WPGS)is a complex,multi-variable,multi-constrained,and multi-objective nonlinear system,while the wind speed is intermitted,stochastic,and fluctuating.Under the stochastic wind speed disturbance,the fatigue loads on equipment may be increased,resulting in a huge challenge to WPGS control on economics and security.Stochastic model predictive control(SMPC)is such an effective method to realize the high-accuracy tracking of stochastic uncertain systems.In SMPC implementation,the stochastic optimal control problem(OCP)considering probabilistic constraints and expected performance indicators is transformed into a deterministic one by incorporating the stochastic characteristics(such as probability density function,mean,variance,and higher-order moments)into the controller design,through the mathematical concepts and tools such as probability theory,mathematical statistics,and stochastic processes.Therefore,to enhance the capability of overcoming stochastic wind speed disturbance in WPGS,there exist great practical significance and theoretical value in designing an effective SMPC strategy for WPGS.In order to satisfy the comprehensive requirements of WPGS on system security,economy,and production efficiency in different wind speed regions,this paper constructs various effective SMPC strategies considering output power probabilistic constraints for coping with the control difficulties caused by strong nonlinear and wind speed uncertainty:(1)For tacking the intractability of nonlinear stochastic OCP of WPGS,this paper designs a robust-probabilistic tube-based SMPC strategy.The nonlinear stochastic model of WPGS is transformed into a linearized stochastic model with bounded model mismatch through Jacobian linearization.A probabilistic tube and a robust tube are designed for the linearized model and the model mismatch respectively to drive the actual WPGS state towards the steady point.The advantage of the proposed SMPC strategy in suppressing stochastic wind speed disturbance and its practicality is verified by comparing it with the classical RMPC method in simulations including the FAST module under different wind speed regions(2)For coping with the conservativeness of the robust and probabilistic tube solving,this paper proposes an SMPC method incorporating the multi-step control strategy(M-SMPC).The multi-step control strategy is introduced in both the robust and probabilistic tube design to enlarge the feasible region of the controller,thereby guaranteeing the feasibility and convergence of the wind power generation system.The advantage of the M-SMPC algorithm in terms of capability to suppress wind speed disturbance with a lower conservativeness is verified in simulations considering the WPGS mechanistic model and the FAST module under various wind speed regions.(3)In order to realize the real-time control of WPGS,this paper designs a simple and efficient SMPC strategy based on deterministic equivalents(D-SMPC)to reduce the computational burden of robust and probabilistic tube calculation.The probabilistic constraints of output power are directly transformed into the linear deterministic inequalities by utilizing the Chebyshev-Cantelli inequality.By optimizing the min-max objective function,the D-SMPC achieves the reference point tracking and coping with the model mismatch caused by the Jacobian linearization.The advantage of the proposed D-SMPC in suppressing stochastic wind speed disturbance is verified by comparing it with the classical RMPC method in simulations.(4)Aiming at the problem that the modern power grid requires the wind power system to operate more and more economically,this paper proposes a stochastic economic model predictive control incorporating a multi-step control strategy(M-SEMPC).The multi-step control strategy is incorporated in the stochastic economic model predictive control(SEMPC)design to reduce the conservativeness caused by constraint tightening.Maximizing power generation and minimizing fatigue loads are achieved by optimizing the min-max objective function,provided that the transformed deterministic constraints transformed by Chebyshev-Cantelli inequality are satisfied.The advantages of the M-SEMPC in improving the WPGS dynamic economy and suppressing stochastic wind speed disturbance are illustrated by comparing it with the classical economic model predictive control(EMPC)and stochastic economic model predictive control incorporating fixed-step control strategy(F-SEMPC)in simulations under different wind speed regions.