This paper presents a dynamic phasor-based state-space modelling framework for modular multilevel converters (MMCs) using multiple dq reference frames (DQsym). The main contribution is the development of a numerically stable state-space solver tailored to multi-dq dynamic phasor models. The solver employs integration and a systematic matrix update mechanism to consistently incorporate switching events within the unified state-space formulation, allowing harmonic interactions and topology changes to be captured without manual reconfiguration. The proposed framework is implemented as a standalone MATLAB/Simulink library to facilitate time-domain simulation and to provide a structured basis for future eigenvalue-based small-signal stability studies. The approach is validated on a point-to-point HVDC system and benchmarked against an EMT model. Results demonstrate that the DQsym-based implementation achieves EMT-level fidelity while maintaining state-space structure suitable for scalable, system-level analysis of converter-dominated grids.

Hybrid AC/voltage source converter-based multi-terminal DC (VSC-MTDC) power grids play a crucial role in enabling long-distance power transmission and flexible interconnection between AC grids. To fully leverage the functional advantages of such systems, it is essential that they operate in or close to optimal power flow (OPF) conditions. To address this, ACDC-OpFlow is developed as an open-source and cross-language framework for solving AC/DC OPF problems. Its core innovation lies in a unified modeling structure that supports MATLAB, Python, Julia, and C++, with Gurobi used as a consistent solver backend. This framework is beginner-friendly and allows users to work in their preferred programming languages. Both text-based and graph-topology results are provided to help users understand the system-wide power flow distribution and operational status. This work presents the design concept of ACDC-OpFlow, showcases representative example results, and discusses the performance differences observed in multiple programming language implementations.

The deployment of voltage source converters (VSC) to facilitate flexible interconnections between the AC grid, renewable energy system (RES) and Multi-terminal DC (MTDC) grid is on the rise. However, significant challenges exist in exploiting coordinated operations for such AC/VSC-MTDC hybrid power systems. One of the most critical issues is how to achieve the optimal operation of such wide-area systems involving several power entities with as minimal communication burden as possible. To address this issue, an enhanced AC/DC optimal power flow (OPF) is specifically proposed. Firstly, a mixed-integer convex AC/DC OPF model is explicitly formulated to describe the optimal operation of such hybrid power systems. Subsequently, a nested distributed optimization method with double iteration loops is developed to offer optimal system-wide decision-making through a more “thorough” distributed communication architecture. In the outer iteration, the original AC/DC OPF problem is decomposed into several slave problems (SPs) associated with systems (including the AC grid and RESs) and one master problem (MP) associated with the integrated VSC-MTDC grid. Generalized Benders decomposition (GBD) serves to solve the master and slave problems iteratively. Techniques such as multi-cut generation and asynchronous updating are utilized to upgrade the GBD performance of computation efficiency and address communication delays. In the inner iteration, the master problem is continuously decomposed into multiple sub-MPs associated with individual VSCs. The alternating direction method of multipliers (ADMM) is employed to solve these sub-MPs iteratively. Proximal terms and heuristic approaches are embedded to enable parallel computation and handling of integer variables. Numerical experiment results finally validate the effectiveness of the proposed enhanced AC/DC OPF. The constructed AC/DC OPF model exhibits acceptable accuracy in terms of power flow calculation, and the developed nested distributed optimization method showcases decent convergence rate and solution optimality performances.

The heterogeneous distribution of frequency support from dispersed renewable generation sources results in varying inertia within the system. The effects of disturbances exhibit non-uniform variations contingent upon the disturbance's location and the affected region's topology and inertia. A screening method for inertia-zone identification is proposed considering the combination of network structure and generator inertia distribution that will aid in comprehending the response of nodes to disturbances. The nodes' dynamic nodal weight (DNW) is defined using maximal entropy random walk that defines each node's spreading power dynamics. Further, a modified weighted kmeans++ clustering technique is proposed using DNW to obtain the equivalent spatial points of each zone and the system to parameterize the inertia status of each zone. The impact of the proposed scheme is justified by simulating a modified IEEE 39 bus system with doubly-fed induction generator (DFIG) integration in the real-time digital simulator.

The radial topology of the Multi-terminal High Voltage Direct Current (MTDC) power system is a preferred connection for the gigawatt- renewable power due to its scalability and reliability. However, a radial topology with a metallic return bipolar converter configuration MTDC network possesses technical challenges regarding DC fault current interruption and grid expansion. Furthermore, such HVDC networks are energized in a specific manner, usually involving a separate energizing controller. This paper proposes a design of DC Hubs with direct current circuit breakers (DCCBs) along with a network energization sequence without requiring a separate controller. Additionally, a PI-based controller for post-DC fault circulating current in MTDC's metallic return is proposed. This control operates after DCCB recloses, removing any offset in the metallic cable by regulating the power setpoint in the converters. The proposed control is investigated under a pole-to-ground fault occurrence in the DC Hub. The proposed solution is validated by RSCAD/RTDS^@ simulation by applying detailed and average equivalent models of turbines, DCCBs and converters. The results of this simulation show a successful suppression of the DC circulating current, which results in a balanced operation of the MMCs in the post fault steady state conditions.