Multi-phase unbalanced AC–DC distribution system state estimation with benders decomposition

State estimation for distribution system is an essential tool for monitoring and control operations such as energy management, Volt-VAR optimization, and load management. Therefore, the distribution system needs an effective monitoring system. However, the advancement in information and communication technology (ICT), such as advanced metering infrastructures and synchrophasors, has made the distribution system more observable and therefore, relatively convenient for state estimation. Moreover, monitoring the distribution system is challenging due to its unbalanced & multi-phase nature, limited measurements, and numerous nodes. The topological challenges for distribution systems include network configuration, such as weakly meshed and radial networks. The distribution system has a resistance-to-reactance ratio greater than one, which makes it prone to ill-conditioning. Further, imposing the additional challenge of Jacobian matrix inversion, which causes difficulty to apply the gradient-based optimization methods. On the other hand, the distribution networks accommodate the distributed energy resources, AC power flow and DC power flow forming an integrated network of AC–DC distribution. The AC–DC systems are coupled with power electronics converters. Therefore, a combined state estimation technique with an AC–DC system is necessary for effective monitoring and control decision-making. There is a challenge for combined AC–DC systems owing to topological characteristics and modelling of the power electronics converters for steady-state operation along with their control strategy. Thus, the simplified power electronics converter models are developed in this work for AC–DC distribution system state estimation (DSSE). However, DSSE is a mathematically intensive large-scale optimization problem and requires a substantial computational resource. Mathematical complexities include ill-condition Jacobian matrix inversion and time complexity challenges for large-scale optimization. The estimation problem formulated as a non-linear mathematical program adds the computational burden for the large-scale optimization problem. The other challenges, such as structural and mathematical complexity, have provided the pathway for decomposing larger problems into smaller sub-problems for improved efficiency in solving optimization problems. Hence, this work proposes the DSSE formulation as a linear optimization problem for the unbalanced multi-phase AC–DC distribution system. This work proposes a Benders decomposition-based AC–DC DSSE algorithm to address the above challenges and improve efficiency of solving the large-scale DSSE optimization problems. To demonstrate the effectiveness of the proposed DSSE algorithm, it is implemented on the distribution test system having the radial and meshed configurations with unbalanced network condition such as the IEEE 33-node system, modified IEEE 13-node, and IEEE 123-node unbalanced multi-phase AC–DC distribution systems. The accuracy of the proposed algorithm is compared with the existing literature, showing robustness to noise and ill-conditioned network. The developed method is implemented on large-scale network demonstrating the scalability and ease of implementation.