Abstract:Grid-forming (GFM) converters are recognized for their stabilizing effects in renewable energy systems. Integrating GFM converters into high-voltage direct current (HVDC) systems requires DC voltage control. However, there can be a conflict between GFM converter and DC voltage control when they are used in combination. This paper presents a rigorous control design for a GFM converter that connects the DC-link voltage to the power angle of the converter, thereby integrating DC voltage control with GFM capability. The proposed control is validated through small-signal and transient-stability analyses on a modular multilevel converter (MMC)-based HVDC system with a point-to-point (P2P) GFM-GFM configuration. The results demonstrate that employing a GFM-GFM configuration with the proposed control enhances the stability of the AC system to which it is connected. The system exhibits low sensitivity to grid strength and can sustain islanding conditions. The high stability limit of the system with varying grid strength using the proposed control is validated using a system with four voltage source converters.

Abstract:This study analyzes the stability and reactive characteristics of the hybrid offshore wind farm that includes grid-forming (GFM) and grid-following (GFL) wind turbines (WTs) integrated with a diode rectifier unit (DRU) based high-voltage direct current (HVDC) system. The determination method for the proportion of GFM WTs is proposed while considering system stability and optimal offshore reactive power constraints. First, the small-signal stability is studied based on the developed linear model, and crucial factors that affect the stability are captured by eigenvalue analysis. The reactive power-frequency compensation control of GFM WTs is then proposed to improve the reactive power and frequency dynamics. Second, the relationship between offshore reactive power imbalance and the effectiveness of GFM capability is analyzed. Offshore reactive power optimization methods are next proposed to diminish offshore reactive load. These methods include the optimal design for the reactive capacity of the AC filter and the reactive power compensation control of GFL WTs. Third, in terms of stability and optimal offshore reactive power constraints, the principle and calculation method for determining the proportion of GFM WTs are proposed, and the critical proportion of GFM WTs is determined over the full active power range. Finally, case studies using a detailed model are conducted by time-domain simulations in PSCAD/EMTDC. The simulations verify the theoretical analysis results and the effectiveness of the proposed determination method for the proportion of GFM WTs and reactive power optimization methods.

Abstract:Diode-rectifier-based high-voltage direct current (DR-HVDC) systems are considered an attractive solution for integrating offshore wind farms (OWFs). Grid-forming (GFM) control with a rational reactive power allocation capability is crucial for the safe operation of numerous wind turbines (WTs). Most typical GFM controls aim to share surplus reactive power of the system equally among WTs, easily rendering capacity overloads for WTs that are outputting high levels of active power. In this paper, a novel GFM control for OWFs is proposed, allowing for adaptively allocating the reactive power according to the actual active power output of WTs. Firstly, the reactive power characteristics of the AC collection networks and WTs are analyzed across a wide wind power range. Then, combining the positive correlation of WT active power with the output AC voltage, a Q-θ type GFM control for WTs is presented. The adaptive reactive power allocation mechanism and the parameter design of the Q-θ based reactive power controller are elucidated, ensuring that WTs with lower active power output contribute more reactive power to the system than WTs with higher active power output. The AC impedance models of WTs under various GFM controls are established to evaluate the impact of different reactive power controllers. Finally, the feasibility of the proposed control is validated in PSCAD/EMTDC, accompanied by stability analysis.

Abstract:Conventional offshore wind farm (OWF) integration systems typically employ AC cables to gather power to a modular multilevel converter (MMC) platform, subsequently delivering it to onshore grids through high-voltage direct current (HVDC) transmission. However, scaling up the capacity of OWFs introduces significant challenges due to the high costs associated with AC collection cables and offshore MMC platforms. This paper proposes a diode rectifier (DR)-MMC hub based hybrid AC/DC collection and HVDC transmission system for large-scale offshore wind farms. The wind farms in proximity to the offshore converter platform utilize AC collection, while distant wind farms connect to the platform using DC collection. The combined AC/DC power is then transmitted to the offshore DR-MMC hub platform. The topology and operation principle of the DR-MMC hub as well as the integration system are presented. Based on the operational characteristics, the capacity design method for DR-MMC hub is proposed. And the control and startup strategies of the integration system are designed. Furthermore, an economic comparison with the conventional MMC-HVDC based offshore wind power integration system is conducted. Finally, the technical feasibility of the proposed integration scheme is verified through PSCAD/EMTDC simulation with the integration scale of 2 GW.

Abstract:In this study, a novel parallel converter-based hybrid high-voltage direct current (HVDC) system is proposed for the integration and delivery of large-scale renewable energy. The rectifier uses the line commutated converter (LCC) and low-capacity modular multilevel converter (MMC) in parallel, while the inverter uses MMC. This configuration combines the economic advantages of LCC with the flexibility of MMC. Firstly, the steady-state control strategies are elaborated. The low-capacity MMC operates in the grid-forming mode to offer AC voltage support. It also provides active filtering for the LCC and maintains the reactive power balance of the sending-end system. The LCC efficiently transmits all active power at the rectifier side, fully exploiting its bulk-power transmission capability. Secondly, the fault ride-through strategies of both the AC faults at two terminals and the DC fault are proposed, in which the MMCs at both terminals can remain unblocked under various faults. Thus, the proposed system can mitigate the impact of the faults and ensure continuous voltage support for the sending-end system. Finally, simulations in PSCAD/EMTDC verify the effectiveness and performance of the proposed system.

Abstract:For doubly-fed induction generator (DFIG)-based wind farms connected to flexible DC transmission system, the oscillation suppression after fault clearance proves very difficult. Addressing this problem, this paper constructs the dynamic energy model of the interconnected system, reveals the mechanism of oscillation instability after fault clearance, and designs an oscillation suppression strategy. First, by considering the dynamic characteristics of the control links in grid-connected DFIG-based wind farms via voltage source converter based high-voltage direct current (VSC-HVDC) transmission system, the interconnected system is divided into several subsystems, and the energy model of each subsystem is constructed. Furthermore, the magnitudes and directions of different interaction energy items are quantitatively analyzed, so that the key control links that transmit and magnify the system energy can be identified. On this basis, the corresponding supplementary control links are designed to suppress the system oscillation. Finally, the accuracy and effectiveness of the proposed oscillation suppression strategy are verified by hardware-in-loop tests. The results prove that the d-axis subsystem of DFIG grid-side converter (GSC) current inner loop, phase-locked loop (PLL), and q-axis subsystem of VSC-HVDC voltage outer loop are the key links that induce the oscillation to occur, and the proposed strategy shows promising results in oscillation suppression.

Abstract:Innovative dynamic models for the DC modular multilevel converter (DC-MMC) in rotating dq frame are presented in this paper, which are specifically designed to enhance converter design and stability analysis. Open-loop and closed-loop models are developed using three dq frames, providing a detailed examination of the impact of 2 ^nd and 3 ^rd harmonic components on the model accuracy. A novel contribution of this paper is the integration of a 2 ^nd harmonic current suppression controller (SHCSC) within the closed-loop model, offering new insights into its effects on system stability. The DC-MMC model is further extended by coupling it with high-voltage direct current (HVDC) cables on each side, forming an interconnected system model that accurately represents a more authentic scenario for future DC grids. The proposed model is rigorously validated against PSCAD benchmark model, confirming their precision and reliability. The interconnected system model is then utilized to analyze the influence of cable length on system stability, demonstrating practical applications. The closed-loop model is subsequently employed for stability assessment of the interconnected system, showcasing its applicability in real-world scenarios. Additionally, a damping controller is designed using participation factor and residue approaches, offering a refined approach to oscillation damping and stability optimization. The effectiveness of the controller is evaluated through eigenvalue analysis, supported by simulation results, underscoring its potential for enhancing system stability.

Abstract:The negative-sequence voltage is often caused by the asymmetrical fault in the AC system, as well as the harmonics after the symmetrical fault at the AC side of inverter in line commutated converter based high-voltage DC (LCC-HVDC). The negative-sequence voltage affects the phase-locked loop (PLL) and the inverter control, thus the inverter is vulnerable to the subsequent commutation failure (SCF). In this paper, the analytical expression of the negative-sequence voltage resulting from the symmetrical fault with the commutation voltage is derived using the switching function and Fourier decomposition. The analytical expressions of the outputs of the PLL and inverter control with respect to time are derived to quantify the contribution of the negative-sequence voltage to the SCF. To deal with the AC component of the input signals in the PLL and the inverter control due to the negative-sequence voltage, the existing proportional-integral controls of the PLL, constant current control, and constant extinction angle control are replaced by the linear active disturbance rejection control against the SCF. Simulation results verify the contributing factors to the SCF. The proposed control reduces the risk of SCF and improves the recovery speed of the system under different fault conditions.

Abstract:In a DC grid with dedicated metallic return (DMR), the coupling effects among the positive pole, negative pole, and DMR conductors must be considered, which makes fault identification particularly difficult. In addition, the identification of high-impedance faults remains a major challenge for DC grid protection. To address these issues, this study proposes an adaptive single-end protection method for DC grid based on the transient mean value of the current limiting reactor (CLR) modal voltage. First, a fault analysis model of the DC grid with DMR is established using the Clarke transformation. The characteristics of CLR modal voltage are then clarified. A fault pole-selection method based on a novel modulus phase plane is next proposed. A threshold scaling factor based on the differential of DC bus voltage is then constructed to enhance the sensitivity and rapidity of the protection, which can adaptively modify the threshold according to the fault severity. Finally, a simulation model of a four-terminal DC grid with DMR is developed in PSCAD/EMTDC. The speed and reliability of the proposed protection method are verified by simulations and experiments.

Abstract:The single-ended fault location based on travelling waves (TWs) is commonly used for long-distance high-voltage AC transmission lines. However, it relies on high sampling frequency and accurate capturing of the TW head arrival time. Accordingly, this study establishes a transient analytical method for fault location based on the similarity between the transient recorded waveform and output waveforms of analytical calculation model. In the proposed method, fuzzy constraints of fault features are constructed through time-distance and waveform-scaling correlations while considering the deviation factors of the frequency-dependent wave velocity and TW head arrival time. Accordingly, the high-dimensional space of the fitting problem is transformed into a one-dimensional implicit function fitting problem containing only the fault distance, thereby enabling the waveform comparison problem to be quickly solved based on fault TW features. Under the fuzzy constraints proposed in this study, the proposed method requires only a relatively vague identification of the TW head, and the requirements for sampling frequency are also more lenient. In addition, a sliding window scheme is adopted for enhancing the TW morphology characteristics. Finally, the proposed method is tested using PSCAD, and the simulations validate the fault location accuracy of the proposed method.

Abstract:Traditional protection methods are not suitable for hybrid (cable and overhead) transmission lines in voltage source converter based high-voltage direct current (VSC-HVDC) systems. Accordingly, this paper presents the robust fault detection, classification, and location based on the empirical wavelet transform-Teager energy operator (EWT-TEO) and artificial neural network (ANN) for hybrid transmission lines in VSC-HVDC systems. The operational scheme of the proposed protection method consists of two loops ① an EWT-TEO based feature extraction loop, ② and an ANN-based fault detection, classification, and location loop. Under the proposed protection method, the voltage and current signals are decomposed into several sub-passbands with low and high frequencies using the empirical wavelet transform (EWT) method. The energy content extracted by the EWT is fed into the ANN for fault detection, classification, and location. Various fault cases, including the high-impedance fault (HIF) as well as noises, are performed to train the ANN with two hidden layers. The test system and signal decomposition are conducted by PSCAD/EMTDC and MATLAB, respectively. The performance of the proposed protection method is compared with that of the traditional non-pilot traveling wave (TW) based protection method. The results confirm the high accuracy of the proposed protection method for hybrid transmission lines in VSC-HVDC systems, where a mean percentage error of approximately 0.1% is achieved.

Abstract:Under weak grid conditions, grid impedance is coupled with a control system for voltage source converter based high-voltage direct current (VSC-HVDC) systems, resulting in decreased synchronization stability. Unfortunately, most studies are based on the assumption that impedance ratio (R/X) is sufficiently small to ignore the effects of grid impedance. In this study, we establish a dynamic coupling model that includes grid impedance and control loops, revealing the influence mechanism of R/X on synchronization stability from a physical perspective. We also quantify the stability range of R/X in the static analysis model and introduce a sensitivity factor to measure its effect on voltage stability. Additionally, we utilize a dynamic analysis model to evaluate power angle convergence, proposing a corresponding stability criterion. We then present a method of synchronous voltage reconstruction aimed at enhancing the grid strength. Theoretical analysis shows that this method can effectively mitigate the effects of coupling between grid impedance and the controller under weak grid conditions, ensuring stable operation even under extremely weak grid conditions. Experiments validate the accuracy and effectiveness of the analysis and method.

Abstract:The power loss minimization and DC voltage stability of the multi-terminal direct current (MTDC) system with large-scale wind farm (WF) cluster affect the stability and power quality of the interconnected power grid. This paper proposes a distributed optimal voltage control (DOVC) strategy, which aims to optimize voltage distribution in MTDC and WF systems, reduce system power losses, and track power dispatch commands. The proposed DOVC strategy employs a bi-level distributed control architecture. At the upper level, the MTDC controller coordinates power flow, DC-side voltage of grid-side voltage source converters (GSVSCs), and WF-side voltage source converters (WFVSCs) for power loss minimization and DC voltage stabilization of the MTDC system. At the lower level, the WF controller coordinates the controlled bus voltage of WFVSC and the active and reactive power of wind turbines (WTs) to maintain WT terminal voltages within feasible range. Then, the WF controller minimizes the power loss of the WF system, while tracking the optimal command from the upper-level control strategy. Considering the computational tasks of multi-objective optimization with large-scale WF cluster, the proposed DOVC strategy is executed in a distributed manner based on the alternating direction method of multipliers (ADMM). An MTDC system with large-scale WF cluster is established in MATLAB to validate the effectiveness of the proposed DOVC strategy.

Abstract:The introduction of fully controlled devices to build hybrid line commutated converter (H-LCC) has become a new idea to solve the commutation failure. However, existing H-LCC has not considered the implementation of a targeted firing angle control strategy during AC faults, with the objective of enhancing their power transmission and fault response performance. For this reason, this paper proposes an optimized control method for firing angle of H-LCC, designated as flexible virtual firing (FVF). This method first analyzes the influence of alterations in firing angle on reactive power, commutation process and associated action paths. By combining prediction and dynamic search, it optimizes the natural commutation process through the utilization of dynamic boundary and minimum commutation area difference. This can mitigate the impact of AC faults on H-LCC and DC system, thereby improving power transmission and defense to commutation failure, which is beneficial for improving the stability of AC/DC power grids. Finally, the simulation results in PSCAD/EMTDC verify the effectiveness of the proposed method.

Abstract:With the load growth and the power grid expansion, the problem of short-circuit current (SCC) exceeding the secure limit in large-scale power grids has become more serious, which poses great challenge to the optimal secure operation. Aiming at the SCC limitations, we use multiple back-to-back voltage source converter based (B2B VSC) systems to separate a large-scale AC power grid into two asynchronous power grids. A multi-objective robust optimal secure operation model of large-scale power grid with multiple B2B VSC systems considering the SCC limitation is established based on the AC power flow equations. The decision variables include the on/off states of synchronous generators, power output， terminal voltage, transmission switching, bus sectionalization, and modulation ratios of B2B VSC systems. The influence of inner current sources of renewable energy generators on the system SCC is also considered. To improve the computational efficiency, a mixed-integer convex programming (MICP) framework based on convex relaxation methods including the inscribed N-sided approximation for the nonlinear SCC limitation constraints is proposed. Moreover, combined with the column-and-constraint generation (C&CG) algorithm, a method to directly solve the compromise optimal solution (COS) of the multi-objective robust optimal secure operation model is proposed. Finally, the effectiveness and computational efficiency of the proposed solution method is demonstrated by an actual 4407-bus provincial power grid and the modified IEEE 39-bus power grid, which can reduce the consumed CPU time of solving the COS by more than 90% and obtain a better COS.

Abstract:Multiterminal low-frequency transmission system (LFTS) has promising potential for large-scale offshore wind power integration. Nevertheless, the existing protection suffers from low sensitivity, and even operates incorrectly because the converters connected to both ends of cables change fault characteristics substantially. To address this problem, this paper firstly inspects the adaptability of current differential protection, revealing the manner in which control strategies after fault impact the sensitivity of the existing protection. Then, based on the characteristics of armored three-core cable, phase-mode transformation is utilized to decouple the fault information and the specific moduli are selected to reflect all kinds of fault types. The expression of backward traveling-wave (BTW) voltage based on interpolation is derived under the condition of low sampling frequency. Finally, a pilot protection based on BTW voltage difference for submarine cables of LFTS with integrated offshore wind power is proposed, which has higher sensitivity because the difference between BTW calculated from local information and the one from remote information is considerable during fault transient period. Simulation tests compare the performance of the existing protection with that of the proposed protection. Extensive simulations corroborate that the proposed protection reliably identifies the fault cable in various fault scenarios.

Abstract:The development of low-carbon energy systems and renewable energy sources (RESs) are critical to solving the energy crisis around the world. However, renewable energy generation control strategies lead to fault characteristics such as fault current amplitude limitation and phase angle distortion. Focusing on large-scale renewable energy transmission lines, the sensitivity of traditional current differential protection and distance protection may be reduced, and there is even the risk of maloperation. Therefore, a suitable transmission line model is established, which considers the distributed capacitance. Afterward, a novel dynamic state estimation based protection (DSEBP) for large-scale renewable energy transmission lines is proposed. The proposed DSEBP adopts instantaneous measurements and additional protection criteria to ensure the quick action and reliability. Finally, faults are identified by checking the matching degree between the actual measurements and the established transmission line model. The performance of the proposed DSEBP is verified through PSCAD/EMTDC and real-time digital simulator (RTDS) hardware-in-loop tests. The results demonstrate that the proposed DSEBP can identify various types of faults quickly and reliably. Meanwhile, the proposed DSEBP has a better capability to withstand fault resistance and disturbance.

Abstract:This paper proposes a continuous control set model predictive control (CCS-MPC) algorithm of a modular multilevel matrix converter (M3C) for low-frequency AC transmission (LFAC), via which the offshore wind farm (OWF) is integrated. The M3C is operated with a 16.7 Hz frequency at the OWF side and a 50 Hz frequency at the onshore grid side. The balance of the capacitor voltages and the regulation of circulating currents in the M3C are performed using the proposed CCS-MPC algorithm, which is based on the online solution of a cost function with constraints. Simulation and experimental work (with a 5 kW M3C prototype) are provided, showing the performance of the LFAC system to operate with symmetrical and asymmetrical voltage dips, active and reactive power steps, and optimal limitation of currents and voltages using constraints. Unlike previous publications, the predictive control system in this paper allows seamless operation under balanced and unbalanced conditions, for instance, during asymmetrical voltage dips.

Abstract:Transmission expansion planning (TEP) addresses the intricate task of optimizing new transmission infrastructure within an existing grid to meet system objectives. As a critical strategy in power system development, TEP significantly influences the long-term efficiency, reliability, and scalability of the network, with enduring effects on overall system performance. This paper explores the application of unconventional high surge impedance loading (HSIL) lines as a cost-effective alternative to conventional extra high-voltage (EHV) transmission lines. By optimizing the geometry of subconductors, HSIL designs could achieve higher power delivery capacities while operating at reduced voltage levels, addressing the increased demand for sustainable energy infrastructure. Two 500 kV HSIL line configurations are analyzed for their feasibility in replacing the conventional 765 kV transmission lines for the TEP to integrate the large-scale wind energy sources located in far remote areas. The analysis is carried out within the 23-bus EHV test system. This study reveals that both HSIL line configurations successfully meet the technical constraints of the TEP problem, ensuring reliable system operation even under contingency conditions. Therefore, the HSIL lines offer significant cost savings due to infrastructure and accessories at reduced voltage levels with much smaller right of way (ROW) than conventional counterparts. This underscores the potential of unconventional HSIL lines to contribute to more sustainable and cost-effective grid planning strategies for integrating large-scale renewable energy sources.

Abstract:The utilization of high-voltage direct current (HVDC) lines for the segmentation of the European power grid has been demonstrated to be a highly effective strategy for the mitigation of the risk of cascading blackouts. In this study, an accurate and efficient method for determining the optimal power flow through HVDC lines is presented, with the objective of minimizing load shedding. The proposed method is applied to two distinct scenarios: first, the segmentation of the power grid along the Pyrenees, with the objective of segmenting the Iberian Peninsula from the rest of Europe; and second, the segmentation of the power grid into Eastern and Western Europe, approximately in half. In both scenarios, the method effectively reduces the size of blackouts impacting both sides of the HVDC lines, resulting in a 46% and 67% reduction in total blackout risk, respectively. Furthermore, we have estimated the cost savings from risk reduction and the expenses associated with converting conventional lines to HVDC lines. Our findings indicate that segmenting the European power grid with HVDC lines is economically viable, particularly for segmenting the Iberian Peninsula, due to its favorable cost-risk reduction ratio.

Abstract:This paper constructs a synthetic framework for the operational reliability evaluation and risk mitigation of asynchronous grids coupled through flexible high-voltage DC (HVDC) systems (AGs-FDCSs). First of all, an analytical model for the unavailability of DC units is reformulated to refine and facilitate the reliability modeling of such flexible HVDC systems considering their time-dependent features as well as the impacts of converter station configurations. Subsequently, the operational risk associated with the redispatch procedure is extended to the reliability evaluation of composite power system, and the risk is mitigated through an optimal power flow (OPF) based short-term state assessment model. In addition, some new reliability indices like expected DC transmission power (EDCTP) and DC terminal outage probability (DCTOP) are defined to quantify the impact of the reliability of flexible HVDC systems on the entire grid. The effectiveness of the proposed framework on a modified IEEE RTS-79 system is validated with the elaborate discussions on the time-dependent reliability of AGs-FDCSs as well as the impacts of the converter station configurations.

Abstract:This paper presents a comprehensive control of modular multilevel converter-based high-voltage direct current (MMC-HVDC) integrated offshore wind farm (OWF) system, which is aimed at enhancing the fast frequency support capability. The comprehensive control consists of the active energy control (AEC), the optimized energy control (OEC), and the OWF control. The proposed OEC decouples the voltage of MMC submodule (SM) capacitor and the DC-link voltage of the MMC-HVDC. A mathematical model of the energy release process in an MMC and onshore frequency dynamics is developed, and a sinusoidal-function-based energy utilization preset curve is derived to theoretically achieve optimized frequency support, while ensuring the constrained energy usage. Upon the occurrence of a frequency event, MMC SMs may adjust their responses according to the energy utilization preset curve. The MMC then provides onshore frequency support by releasing energy. The coordination process with the OWF is also explored to further enhance the frequency support performance. Finally, case studies are conducted on the PSCAD/EMTDC platform through employing actual engineering parameters. The frequency support performance of various controls under both load increase and load decrease conditions are compared, demonstrating the effectiveness of the proposed OEC.

Abstract:Sending-end multi-terminal high-voltage direct current (MT-HVDC) systems are well-suited for large-scale renewable energy collection and transmission. However, the capacity planning for converter stations (CSs), which is directly correlated with their ability to convert renewable energy, remains a critical issue. In this paper, an optimal capacity planning method for CSs is proposed to maximize the converted energy (CE). The proposed method considers the uncertainties of photovoltaic (PV) generation and derives analytical formulas for stochastic CEs. The equal incremental rate (EIR) principle is employed to calculate the optimal capacity planning scheme, and then a general guideline for the capacity planning in stochastic scenarios is presented. Case studies are conducted to validate the effectiveness of the proposed method and the proposed guideline. The results demonstrate that the proposed method converts more renewable energy than the deterministic method.