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Within the framework of a successive quadratic programming method for problems involving discrete variables on power systems, this work formulates the distributed optimal power flow with continuous and discrete variables problems (Distributed OPFCDP) and distributed state estimation with continuous and discrete variables problems (Distributed SECDP) as categories of the distributed quadratic programming with continuous and discrete variables problems (Distributed QCDP). A three-level algorithm combined with the ordinal optimization (OO) theory and the distributed asynchronous dual-type (DADT) method is also developed to solve the Distributed QCDP of power systems. Additionally, the efficiency of the proposed three-level algorithm is demonstrated, along with a comparison made with four competing methods (i.e., Tabu search, genetic algorithm, ant colony system, and simulated annealing) for solving the Distributed SECDP and Distributed OPFCDP on the IEEE 118-bus and 244-bus systems in a deregulated environment. Test results further demonstrate that the proposed algorithm is highly promising for the Distributed QCDP.