The performance of existing protection methods for multi-terminal direct current systems depends on the availability and sizes of boundary components. To overcome the limitation, this paper proposes a non-unit DC line protection method based on the normalized backward traveling waves (BTWs) of the 1-mode voltage. Firstly, traveling wave propagation characteristics are analyzed, and a rationalization approach based on vector fitting is proposed. Next, the analytical expressions of normalized BTWs are derived, with the negative correlation between them and fault distance proved. Then, the derivative-free conjugate gradient algorithm is utilized for amplitude fitting and normalization calculation. Finally, a non-unit protection method using the normalized BTWs is developed. The performance is validated for both electromagnetic transient PSCAD/EMTDC and real-time digital RSCAD/RTDS simulation. The results demonstrate that the proposed method can accurately identify faults with various fault resistances and locations without requiring boundary components and high sampling frequencies, and it is robust against noise disturbances.

Unlike synchronous generators, the fault response of grid-forming (GFM) inverter-interfaced distributed generators (IIDGs) is notably governed by the selection of control and current limiting strategies rather than inherent physical traits. While recent research has focused on the sequence domain fault model of GFM IIDGs, a research gap exists in elucidating the influence of control and current limiting schemes on this model's characteristics. This article aims to fill this void by examining how different control and current limiting schemes influence the positive and negative sequence impedances in the phasor-domain fault model of GFM IIDGs. This investigation encompasses droop-based, virtual synchronous machine-based, and virtual oscillator-based reference generation controls alongside rotating and stationary reference-frame-based voltage controls. Furthermore, saturation-based, latching-based, circular and virtual impedance-based current limiting schemes are analyzed. To achieve this goal, a thorough numerical simulation study is conducted. Findings indicate that outer reference generation controls exhibit minimal impact. Conversely, the choice of voltage control and various current limiting schemes emerge as the predominant factors shaping the sequence models of GFM IIDGs. These analyses and results are instrumental in devising reliable protection strategies within inverter-based grids, as a comprehensive understanding of electrical elements in the sequence domain is imperative for effective protective measures.

There is a lack of knowledge on the development of a controller model into a black box dynamically-linked library (DLL) file which can be flexibly tested with a power system model through a real-time co-simulation platform. Developing a test bed to demonstrate the performance and compliance analysis enhances the approval of novel control and protection strategies. This paper presents the development of a controller DLL and a test bench that integrates this DLL with a real-time simulator. The DLL contains a previously developed grid-forming controller for the type‑3 wind turbine and works in co-simulation with the power system model on Real-Time Digital Simulator (RTDS) in real-time.

DC fault location technology is crucial for estimating the fault location and developing multi-terminal direct current (MTDC) systems. This article presents a novel fault location method using the parameter fitting approach. The propagation of traveling waves (TWs) in the decoupled line-mode fault network is first discussed, resulting in analytical expressions for the backward line-mode current TWs containing fault location information. Then, the adaptive multi-step Levenberg–Marquardt (AMLM) algorithm is applied for parameter fitting owing to its fast processing speed and precision. The exact fault location is estimated using the fitted coefficient. Different testing MTDC systems modeled in PSCAD/EMTDC and a real-time digital simulator (RTDS) validate the proposed fault location method. Based on numerous simulation tests, the AMLM-based parameter fitting and the proposed method are accurate, with errors smaller than 0.5%. Compared to the existing methods, the proposed method has desired performance under close-in faults, can withstand 35 dB noise interference, and obviates the need for an extremely high sampling frequency, estimation of tws velocity, and communication devices.

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.

With the domination of modular multilevel converters (MMCs) interfaced power grids, especially for transmission of the wind generated energy, the control of such power electronic interfaced grids is of an utmost important for the proper operation and grid stability. This control is very complex due to multivariable intercoupling and plausible nonlinearity. To enhance the grid stability and reduce the total harmonic distortion (THD) of the converter, the paper proposes development of an optimal voltage level-model predictive control (OVL-MPC) for a fast dynamic response, integrated with classical proportional–integral (PI) outer-loop control for robust steady-state performance. This control eliminates the problems of poor steady-state performance of MPC while achieving faster transient response in comparison to the classical proportional integral (PI) dual-loop control. The work proposes OVL-MPC for lower computational burden in comparison to switching state-based MPC, for the inner loop replacing the classical PI inner loop. With the inherent advantages of lower computational burden and superior transient performance, AC current deadbeat controller is used for the modulation in OVL-MPC. To improve the robustness of the control method, the Moore–Penrose pseudo-inversion is applied to address control parameter mismatches, while the Smith predictor compensates for time delays. The designed control algorithm is tested with two real-time simulation platforms, i.e., OPAL-RT and RTDS for thorough power system validation.

The potential of advanced neural networks (NNs) has yet to be explored in the field of HVDC transmission. Implementing such intelligent computational techniques on a real-time digital simulator (RTDS) is challenging due to the need for rapid computation and the risk of overfitting with extensive data generated at tiny time steps. To overcome these limitations, different NN techniques are studied using a supervised and reinforced imitation learning method to mimic the suggested controller with labeled data for real-time applications. Furthermore, the NN component does not necessarily just take a label, and therefore, the authors propose a more advanced approach by incorporating reinforced learning through an error-tracking mechanism into the NN, apart from its loss function. The initial offline processing identifies the best-suited NN technique for online computational feasibility. Both online and offline training methods as well as online adjustments are showcased to provide a robust control solution that is easy to implement. This work deals with developing an intuitive and versatile Toolbox installed on a real-time simulator platform that can integrate complex NN-based control strategies. Extensive simulations on the RTDS platform and experimental investigations of the four terminal HVDC systems validate the interest and viability of the proposed design methodology.

The widespread use of modular multilevel converters (MMCs) in the evolution of complex power grids presents new challenges for grid stability. MMCs have highly nonlinear impedance characteristics due to their complex internal dynamics and intricate control architectures. Due to practical constraints, physics-based models cannot accurately compute these impedances, and the use of closed-box measurement techniques is time-consuming, resulting in a limited amount of data available for impedance characterization. Thus, using current methods to estimate impedances over a wide range of operating points can be unreliable. This paper presents a transfer learning-based framework for MMC impedance characterization using system-level parameters as operating point variables. The proposed approach predicts both AC and DC side impedances simultaneously by extrapolating impedances derived using state-space modeling approaches to real-time electromagnetic transient (EMT) simulations. Finally, the method is evaluated on a practical converter from the CIGRE B4 DC grid test system for various types of controllers and scenarios involving unknown parameters.

An economical approach for incorporating Battery Energy Storage Systems (BESS) onto DP-2 vessels is presented in this research. The paper deals with developing a Battery Optimization for Optimal Sizing and Throughput Energy Regulation (BOOSTER) framework for putting research findings into practice by optimizing battery size, technology choice and power generation scheduling while considering battery degradation. Twelve battery sizes are analyzed based on three key performance metrics: return on investment, payback period, and years of profitability. A Mixed Integer Linear Programming (MILP) is developed to operate the energy and power management system of the vessel in a fuel and economically efficient manner. The study considers two load profiles of a DP-2 vessel operating near Taiwan and the North Sea. Our findings emphasize the significance of taking battery ownership costs in the form of energy throughput cost and fuel price into account, resulting in a longer battery lifetime and higher return on investment. The research also proposes a BESS operation matrix that provides vessel operators with valuable information on BESS usage for economic benefits. This matrix translates analytics and decision-making into tangible actions that can be implemented in real-time operations. Based on the findings, energy systems may be optimized for a sustainable future, which benefits vessel operators and industry stakeholders.

The extensive integration of distributed renewable energy resources (DRES) can lead to several issues in power grids, particularly in distribution grids, due to their inherent intermittency. This paper presents a stochastic simulation-based approach to estimate the maximum permissible penetration level of DRES and to determine the optimal capacity of centralized battery energy storage systems (BESS) in distribution networks while adhering to technical constraints. The stochastic method creates a wide range of scenarios under various conditions. For each scenario, our proposed approach calculates the maximum allowable penetration level of DRES and the required BESS capacity with different DRES control logics. The maximum allowable penetration level of DRES and the requirements of the BESS capacity are determined by an analysis of various simulation results. This paper's unique contribution lies in equipping distribution system operators (DSOs) with the ability to compare results and select the most appropriate voltage control and power smoothing methods. This aids in mitigating challenges associated with overvoltage and intermittency issues arising from DRES-generated power, thereby enhancing the overall resilience and reliability of the power grid. Case studies that include four voltage control algorithms and three power smoothing methods demonstrate the universality and effectiveness of the proposed approach.

Fault ride-through capability studies of MMC-HVDC connected wind power plants have focused primarily on the DC link and onshore AC grid faults. Offshore AC faults, mainly asymmetrical faults have not gained much attention in the literature despite being included in the future development at national levels in the ENTSO-E HVDC code. The proposed work gives an event-triggered control to stabilize the system once the offshore AC fault has occurred, identified, and isolated. Different types of control actions such as proportional-integral (PI) controller and super-twisted sliding mode control (STSMC) are used to smoothly transition the post-fault system to a new steady state operating point by suppressing the negative sequence control. Initially, the effect of a negative sequence current control scheme on the transient behavior of the power system with a PI controller is discussed in this paper. Further, a non-linear control strategy (STSMC) is proposed which gives quicker convergence of the system post-fault in comparison to PI control action. These post-fault control operations are only triggered in the presence of a fault in the system, i.e., they are event-triggered. The validity of the proposed strategy is demonstrated by simulation on a ±525 kV, three-terminal meshed MMC-HVDC system model in Real Time Digital Simulator (RTDS).

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.

In this paper, a Reinforcement Learning controller (RLC) is designed and implemented on a 5-level Packed U-Cell (PUC5) grid-connected inverter to control the injected current flowing into the electric network.The RL agent is trained using a Proportional-Integral (PI) reward function to optimize its control strategy. Moreover, the voltage balancing of the auxiliary capacitor in PUC5 is separated from the RL controller and integrated into the switching algorithm to reduce the training burden. This modification reduces the observation inputs required for RL training, significantly shorten the training time. Simulation studies conducted in Matlab/Simulink evaluate the performance of the proposed RL controller, demonstrating robust dynamic response and accurate tracking of reference signals across different operational conditions.

In this paper, a distributed optimal power flow (OPF) for the AC/DC hybrid grid, composed of the AC grid, renewable energy system (RES), and voltage source converter (VSC)-based multi-terminal DC (MTDC) grid, is presented. Firstly, we apply a series of linear approximations/convex relaxations to construct a mixed-integer convex AC/DC OPF model. To address the uncertainties from RESs, we then illustrate scenario-oriented decision making for the constructed AC/DC OPF model. Additionally, we verify that considering all possible scenarios can be replaced by a small set of extreme scenarios if the OPF model is (mixed-integer) convex. Furthermore, we develop a scenario-oriented multi-cut generalized Benders decomposition to achieve more efficient distributed problem solving for the constructed AC/DC OPF model. Finally, numerical results are provided to validate the effectiveness of our constructed AC/DC OPF model and our developed distributed problem-solving approach.

Optimizing operational set points for modular multilevel converters (MMCs) in Multi-Terminal Direct Current (MTDC) transmission systems is crucial for ensuring efficient power distribution and control. This paper presents an enhanced Optimal Power Flow (OPF) model for MMC-MTDC systems, integrating a novel adaptive voltage droop control strategy. The strategy aims to minimize generation costs and DC voltage deviations while ensuring the stable operation of the MTDC grid by dynamically adjusting the system operation points. The modified Nordic 32 test system with an embedded 4-terminal DC grid is modeled in Julia and the proposed control strategy is applied to the power model. The results demonstrate the feasibility and effectiveness of the proposed droop control strategy, affirming its potential value in enhancing the performance and reliability of hybrid AC-DC power systems.

Fast, sensitive, and selective protection principles are one of the major challenges in the feasibility of modular multi-terminal (MMC) high voltage direct current (HVDC) grids. Rate of change of voltage (ROCOV) and transient-based solutions are the traditional and widely accepted protection principles. Despite the speed and practicality of these solutions, they generally suffer from sensitivity and selectivity issues, particularly when dealing with high-resistance faults and low-size current limiting inductors (CLIs). To improve upon these methods, this paper proposes a new primary protection method that utilizes a selective drop rate of fault-generated voltage traveling waves (TW) to detect internal DC line faults. This is achieved by a comprehensive analysis of the line-mode fault-generated voltage (LFGV) under various internal and external fault scenarios. As the key fault characteristics, the proposed method exploits the minimum points of initial LFGV and the corresponding time to form the basis of the proposed protection method. The effectiveness of this approach is evaluated using a four-terminal MMC-HVDC grid in PSCAD/EMTDC. Compared to ROCOV and transient-based solutions, the proposed method identifies internal faults up to 1250 Ω with fast response, while maintaining its practicality and independence to CLI size.

AC/multi-terminal DC (MTDC) hybrid power systems have emerged as a solution for the large-scale and long-distance accommodation of power produced by renewable energy systems (RESs). To ensure the optimal operation of such hybrid power systems, this paper addresses three key issues: system operational flexibility, centralized communication limitations, and RES uncertainties. Accordingly, a specific AC/DC optimal power flow (OPF) model and a distributed robust optimization method are proposed. Firstly, we apply a set of linear approximation and convex relaxation techniques to formulate the mixed-integer convex AC/DC OPF model. This model incorporates the DC network-cognizant constraint, enabling DC topology reconfiguration. Next, generalized Benders decomposition (GBD) is employed to provide distributed optimization. Enhanced approaches are incorporated into GBD to achieve parallel computation and asynchronous updating. Additionally, the extreme scenario method (ESM) is embedded into the constructed AC/DC OPF model to provide robust decisions to hedge against RES uncertainties. ESM is further extended to align the GBD procedure. Numerical results are finally presented to validate the effectiveness of our proposed optimization method.

Identifying faulty lines and their accurate location is key for rapidly restoring distribution systems. This will become a greater challenge as the penetration of power electronics increases, and contingencies are seen across larger areas. This paper proposes a single terminal methodology (i.e., no communication involved) that is robust to variations of key parameters (e.g., sampling frequency, system parameters, etc.) and performs particularly well for low resistance faults that constitute the majority of faults in low voltage DC systems. The proposed method uses local measurements to estimate the current caused by the other terminals affected by the contingency. This mimics the strategy followed by double terminal methods that require communications and decouples the accuracy of the methodology from the fault resistance. The algorithm takes consecutive voltage and current samples, including the estimated current of the other terminal, into the analysis. This mathematical methodology results in a better accuracy than other single-terminal approaches found in the literature. The robustness of the proposed strategy against different fault resistances and locations is demonstrated using MATLAB simulations.

The stability of an HVDC transmission network is very important for the reliable transfer of power from renewable energy resources. Therefore, this paper proposes a region of attraction stability analysis method for grid-forming-based modular multilevel converters. The grid forming control uses a model predictive control-based controller for the inner current loop. The stability analysis is carried out using the direct Lyapunov method. For the model predictive control, the modified version of the cost function is used; the same function is also used as the cost function for the direct Lyapunov method. Furthermore, the boundaries formed by the limiters and Lyapunov function entirely explain transient event behavior.

It is challenging to determine the active filter control factors in wind power plants (WPP) to obtain effective harmonic voltage mitigation and avoid over-modulation or system instability problems caused by overlarge feedforward or feedback gains. To address this issue, an active filter tuning (AFT) method is proposed in this paper to offer a common parameter tuning and stability assessment strategy for both current-controlled and voltage-controlled harmonic impedance reshaping (HIR) methods by introducing a coordination factor including different weight coefficients for system stability margin, wind turbine (WT) harmonic suppression, and grid harmonic mitigation. The superiority of the proposed method is verified in a 20 MW WPP with four cases considering both WT harmonic voltage amplification and grid voltage amplification. Compared to previous methods, the AFT-based HIR method achieves a more flexible balance between system stability and harmonic voltage mitigation, obtaining better performance in WT harmonic suppression, grid harmonic suppression, system robustness, and transient response.