Distributed Optimization Of OPF Using ADMM

For the future smart grid,one of the key aspect of future research trends is to devise a distributed algorithm that can solve global problems.This involves decentralized access to generation and storage resources.Optimal power flow is the main smart grid problem that has been taken into consideration for distributed optimization.OPF is the heart of power system and is difficult to solve due to its non-convex constraints.For this reason,widely used approach is to relax it into convex problem and then solve the problem by mean of distribution methods.Due to complex calculations involved in relaxation technique,lack of adherence to original problem and slow convergence arises.Also existing methods are generally iterative and require synchronization of all agents at each iteration which is hard to solve and poor utilization of computational sourcesThis thesis proposed an approach which is an alternative in the sense that we do not relax the non-convex problem,instead we work directly on non-convex problem.This thesis deals with solving non convex OPF problem through distributed optimization in a fully decentralized manner.By this way adherence of the problem is ensured and then distributed algorithm can be developed which can be solved in a decentralized manner.For this,we use,state of the art algorithm Alternating direction method of multiplier(ADMM),that can solve non convex AC OPF in a totally distributed manner.The problem of slow convergence is solved by careful selection of penalty parameter.To ensure fully distributed approach,local node based optimization approach is adopted.The main idea is to divide and decompose network in N nodes.Take the computation down to individual nodes by separating the variables responsible for coupling among the nodes.Auxiliary variables are introduced for real and imaginary voltages of neighbors as observed at working node.The problem is reformulated to be implemented by ADMM in distributed manner.By using the approach of message exchanges,locally voltages,powers,and primal and dual variables are computed and updated in alternate iteration.This shows the beauty of ADMM algorithm.After updating in first two steps,dual variables are getting updated in third iteration.Each iteration needs to solve a local optimization problem.The proposed solution is tested on different IEEE networks and results has been analyzed and discussed.IEEE networks 30.57 and 118 have been selected and after setting stopping criteria,algorithm become implemented.Convergence is being tested on active power,reactive power.Residual was analyzed and impact of penalty parameter is also observed on primal and dual residuals.The impact of choosing a penalty parameter on rate of convergence is also discussed.Finally,it has been showed that the ADMM for solving the OPF problem proves to be reliable,fast and robust and numerical results on IEEE networks show the promising performance as compared to the other techniques as well.