| Summary: | 博士 === 國立交通大學 === 電機與控制工程系 === 90 === First of all, we present a modified parallel block scaled gradient method for solving block additive unconstrained optimization problems of large distributed systems. Our method makes two major modifications on the typical parallel block scaled gradient method: (1) we include a pre-processing step which will reduce the computation time; (2) we present a decentralized Armijo-type step-size rule. This rule will circumvent the difficulty of determining a step-size in a distributed computing environment and enable the proposed parallel algorighm to execute in a distributed computer network with limited amount of data transfer. We prove that method is globally convergent and demonstrate its efficiency comparted to a sparse matrix technique based method by several weighted least square problems of power system state estimation.
Secondly, with the decentralized step-size rule technique. We present a parallel dual-type algorithm for solving a class of quadratic programming problem. Our algorithm is suitable for implementation in a distributed computer network and can be used as a basic optimization tool for handling optimization problems of large distributed system.
Finally, we present two new techniques for solving optimal power flow (OPF) problem with large number of thermal-limit constraints. The first one is a graph method based decomposition technique which can decompose the large-dimension projection problem, caused by the large number of thermal-limit constraints, into several independent medium-dimension projection subproblems at the expense of slight increment of the dual problem’s dimension. The second technique is an active-set strategy based DT method, which can solve the medium-dimension projection subproblems efficiently. We have used the DT method embedded with these two new techniques in solving numerous OPFs with large number of thermal-limit constraints. The test results show that the proposed techniques are very efficient and effectively improve the DT method for handling large number of thermal-limit constraints.
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