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This paper proposes a framework of optimal load frequency control in deregulated environment. The objective function of optimisation incorporates both the index of economy and stability with their own specific physical meaning. Under this framework, the problem of market-based optimal LFC is formulated to be an optimization problem of functional extremum. Since the structure-preserving model of power systems in order to consider the characteristics of loads, the optimization problem is constrained by differential equations as well as algebraic equations. Then a quasi-Newton algorithm is put forward to solve the formulated optimal DAE-constrained optimisation problem.