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A framework for optimal load-frequency control (LFC) in deregulated environments is proposed. The objective function of optimisation incorporates both the indices of economy and stability with their own physical meanings. Under this framework, the problem of market-based optimal LFC is formulated to be an optimisation problem of functional extremum. Since the structure-preserving model of power systems is adopted in order to consider the characteristics of loads, the optimisation problem is constrained by differential algebraic-equation systems (DAEs). Then a quasi-Newton algorithm is put forward to solve the formulated optimal DAEs-constrained optimisation problem. Simulation is carried out on the IEEE 30-bus system with different market structures. It is shown that the proposed framework and the corresponding algorithm are effective, and can achieve optimal operation of power systems in terms of both security and economy.