A more general parallel dual-type method and application to state estimation

In our previous work, a parallel dual-type (PDt) method was presented for solving a class of weighted-least-squares (WLS) with equality constraints problems and obtained some successful results. In this work, we propose a more general parallel dual-type (MPDt) method using the framework of the PDt method to solve more extensive WLS problems (with equality and inequality constraints). The MPDt method embedded with a successive gradient and projection (SGP) technique is used to solve the dual problem with constrained set induced by the inequality constraints. The MPDt method associated with a successive quadratic programming (SQP) method is used to solve more extensive WLS problems with equality and inequality constraints. We have tested our method in the IEEE 118-bus system of distributed state estimation problems with equality and inequality constraints. We demonstrated the computational efficiency through numerical simulations and compared our method with the conventional approach of Karush–Kuhn–Tucker (KKT) and the original PDt methods. Test results showed that the performance of our method is significant for solving distributed state estimation problems with equality and inequality constraints in the distributed computing environment.

Research highlights
► Presented a parallel dual-type (PDt) method.
► Solving a class of weighted-least-squares with equality constraints problems.
► Embedded with a successive gradient and projection (SGP) technique.
► Associated with a successive quadratic programming (SQP) method.