Economic Model Predictive Control And Its Application In Power System

The goal of a control system is to steer the system to the set-point quickly and reliably.Model Predictive Control(MPC)is widely used due to its excellent ability to handle the com-plex systems with constraints.In system optimization and control,MPC in the lower layer is usually used to track the set--point given by the upper layer.Although the hierarchical control strategy has been successful,with the increasing demand for dynamic market--driven operations,efficiency and flexibility of the control strategy,the traditional hierarchical control is not suit-able for the current control requirements.In order to combine the system economic optimization and process control to realize the real--time optimization,improve the control performance and economic benefits of the system,an economic model predictive control(EMPC)algorithm has been proposed recently.Unlike tracking the set--point in tracking MPC,in EMPC,the controller directly optimizes the economic objective function.Therefore,the dynamic economic benefit of the system has been significantly improved.Modern power systems are large,geographically dispersed and interconnected distributed systems.The centralized EMPC method can not solve the optimization problem with such a large number of variables in time.And the centralized approach has poor scalability and security for the distributed system.Therefore,the distributed EMPC algorithm is proposed in this paper.By using the global objective function,each subsystem--based controller cooperates with each other,rather than compete.Through multiple iterations between subsystems,the optimal solution of subsystem’s controller gradually approaches to the global optimal solution of centralized method.At the same time,the computation time of the distributed algorithm is greatly reduced compared with the centralized way.The main work of this paper is as follows:(1).A two--mode EMPC algorithm based on continuous nonlinear system is studied.The proposed algorithm can optimize and control the nonlinear system with external disturbance.By using the two--mode EMPC algorithm,the system states are operating within the safe range,and finally approach to the steady--state point.For the distributed system,the real--time economic optimization and process control are realized through the distributed iterative algorithm.By using the Lyapunov function,the stability of the system under disturbance is guaranteed by selecting the appropriate sampling time.A distributed EMPC method for a nonlinear wind-photovoltaic--battery microgrid power system(WPB--MPS)is studied.The communications between each subsystem are taken into consideration and the economic objectives which are established based on the aspects that: a)satisfy the total demand? b)make full use of the power generated by the WPB--MPS? c)optimize the battery’s state of charge(SOC)? d)reduce the fluctuation of power exchange with the grid.The subsystem--based EMPCs work iteratively and cooperatively to solve the economic objective functions which reflect economies of the system and not necessary to drive the system to a certain steady state as hierarchical control.A dual-mode Lyapunov--based EMPC has been formulated to guarantee the stability of the system with disturbance,and under certain conditions,the closed--loop system state can be driven and hold in a safe region.Simulations demonstrate the advantages and efficiency of the proposed method.(2).An EMPC algorithm for the discrete--time system is proposed.The proposed algo-rithm can be divided into terminal equality constraints based on EMPC and terminal region constraints based on EMPC algorithm.In EMPC,the controller directly optimizes the general-ized economic objective function.Different from the tracking cost function used in MPC,the economic objective function can be written in a more generalized form,even with non--convex form.By using the auxiliary objective function and the auxiliary optimization problem,the auxiliary objective function of the system is defined as Lyapunov function,and the asymptotic stability of the system under the proposed method can be proved.(3).A distributed EMPC algorithm is proposed to realize the overall economic optimiza-tion and process control of the distributed system.For distributed control,the system cen-tralized model is decomposed into several distributed models,and each subsystem designs the distributed EMPC algorithm according to its own distributed model.During each sampling period,the subsystems work iteratively and cooperatively,to achieve the system--wide control performance.In addition,by using the convexity property of the objective function and select-ing the appropriate objective function coefficients,the local optimal solution of the subsystem gradually approaches the global optimal solution of the centralized control strategy during the iterative process,and the asymptotic stability of the system is achieved.(4).An EMPC strategy for the constrained optimization problem of the wave energy con-verter system is proposed.Unlike the standard MPC using the tracking cost function,in EMPC,a general economic cost function,which directly reflects the economic objective of the system,is established.The terminal equality constraint in the optimization problem is used to steer the system state to the steady--state at the end of the optimization horizon,as well as the controller solves the non--convex optimization problem in real--time.The auxiliary optimization prob-lem is used for the stability analysis,and the convergence of the system can be proved via the Lyapunov technique.Several simulation results are presented to demonstrate the effectiveness of the proposed strategy.In addition,for multi--terminal high voltage direct current(MTDC)transmission systems,a distributed EMPC algorithm is proposed.In the system,the economic optimization(economic load dispatch,ELD)and process control(load frequency control,LFC)can be realized by one layer.The generation power of each subsystem and the power flow be-tween each subsystem are regulated by the voltage of the converter,and finally the optimal ELD and frequency stability of the system are obtained.By using the terminal equality constraint,the system state is steered to approach the steady--state gradually.Finally,simulation results show the effectiveness and economic benefits of the proposed algorithm.Compared with hierarchical control,the economic benefits of the system is improved greatly.