Using Lagrangian Relaxation to Include Operating Limits of VSC-MTDC System for State Estimation

This paper proposes an improved state estimation (SE) method by combining Lagrangian relaxation and WLS (weighted least square) such that the operating limits of voltage sourced converter based multi-terminal direct current (VSC-MTDC) system are considered. Taking advantage of the fast-regulating ability of pulse-width modulation (PWM), the operating range of the converter is strictly restricted within limits. In addition, when the limits violate, the new control strategy can be executed in a very short time to ensure safe operation. However, the conventional SE approaches, which rely on global optimization, may fail to tackle the operating limits due to the different measurement errors of AC and DC grids. To improve the accuracy of SE for VSC-MTDC system, an improved SE method is proposed with three main contributions. First, the operating limits, together with the regulations, are analyzed in detail. Then, a violation-checking procedure is implemented inside the Sequential Method. Finally, once the violated estimations are detected, the corresponding equality constraints which represent the precise operating points are added in WLS and solved by Lagrangian relaxation. The accuracy and efficiency of the proposed method are tested on two typical systems with different control parameters.