A. M. Elaiw a, X. Xia a and A. M. Shehata b a Department of Electrical, Electronic and Computer Engineering, University of Pretoria, South Africa. b Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt.

The problem of allocating the customers' load demands among the available thermal power generating units in an economic, secure and reliable way has received considerable attention since 1920 or even earlier Static Economic Dispatch (SED) (i) Load-generation balance (ii) Generation capacity Significant cost savings A Small improvement in the SED

Drawbacks It may fail to deal with the large variations of the load demand due to the ramp rate limits of the generators It does not have the look-ahead capability

Dynamic Economic Dispatch (DED) Subject to (i) Load-generation balance (ii) Generation capacity (iii) Ramp rate limits P 1 P 2 P N 0 T 2T NT

Optimal Dynamic Dispatch Constraints Objective function Method of Solution Minimize Cost Minimize Emission Maximize Profit Math. Programming AI Techniques Hybrid Metheds Equality Inequality Dynamic

Smooth Non smooth The cost function

Periodic Implementation of DED Technical Deficiencies If the solutions are implemented repeatedly and periodically due to the cyclic consumption behavior and seasonal changes of the demand.

Subject to (i) Load-generation balance (ii) Generation capacity (iii) Ramp rate limits Problem DED-(P)

DED in control system framework (i) (ii) (iii) Problem DED-(P 1,U)

The solution of DED is an open-loop Modeling uncertainties External disturbances Unexpected reaction of some of the power system components A closed-loop solution is needed Model predictive control method

The idea of MPC

MPC Algorithm Input the initial status (1) Compute the open-loop optimal solution of DED-(P 1,U) (2) The (closed-loop) MPC controller is applied to the system in the sampling interval [m+1, m+2) to obtain the closed loop MPC solution over the period [m+1, m+2) and let m=0 (3) Let m:=m+1 and go to step (1) Model Predictive Control Approach to DED

Theorem 1. Suppose that problem DED-(P 1,U) is solvable, P * is the globally optimal solution of the DED-(P) problem, then MPC Algorithm converges to P* if Convergence

Theorem 2. Robustness Suppose that 1- problem DED-(P 1,U) is solvable, 2- P * is the globally optimal solution of DED-(P) the following is executed in step (2) of MPC Algorithm 5- the disturbance is bounded Then MPC Algorithm converges to the set

DED with emission limitations The emission of gaseous pollutants from fossil-fueled thermal generator plants including, Installation of pollutant cleaning Switching to low emission fuels Replacement of the aged fuel burners with cleaner ones; Emission/economic dispatch (I) Emission Constrained Dynamic Economic Dispatch (II) Dynamic Economic Emission Dispatch

Dynamic Economic Emission Dispatch (DEED) (i) (ii) (iii)

Simulation Results Ten units system

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