Abstract:Grid-following voltage source converter (GFL-VSC) and grid-forming voltage source converter (GFM-VSC) have different dynamic characteristics for active power-frequency and reactive power-voltage supports of the power grid. This paper aims to clarify and recognize the difference between grid-following (GFL) and grid-forming (GFM) frequency-voltage support more intuitively and clearly. Firstly, the phasor model considering circuit constraints is established based on the port circuit equations of the converter. It is revealed that the voltage and active power linearly correspond to the horizontal and vertical axes in the phasor space referenced to the grid voltage phasor. Secondly, based on topological homology, GFL and GFM controls are transformed and mapped into different trajectories. The topological similarity of the characteristic curves for GFL and GFM controls is the essential cause of their uniformity. Based on the above model, it is indicated that GFL-VSC and GFM-VSC possess uniformity with regard to active power response, type of coupling, and phasor trajectory. They differ in synchronization, power coupling mechanisms, dynamics, and active power-voltage operation domain in the quasi-steady state. Case studies are undertaken on GFL-VSC and GFM-VSC integrated into a four-machine two-area system. Simulation results verify that the dynamic uniformity and difference of GFL-VSC and GFM-VSC are intuitively and comprehensively revealed.

Abstract:The increasing adoption of grid-forming converters (GFMCs) stems from their capacity to furnish voltage and frequency support for power grids. Nevertheless, GFMCs employing the current reference saturation limiting method often exhibit instability during various transient disturbances including grid voltage sags, frequency variations, and phase jumps. To address this problem, this paper proposes a virtual power angle synchronous (δ_v-SYN) control method. The fundamental of this method is to achieve synchronization with the grid using the virtual power angle δ_v instead of the active power. The transient stability characteristics of the proposed method are theoretically elucidated using a novel virtual power angle-power angle (δ_v-δ) model. The key benefit of the proposed method is its robustness to various grid strengths and diverse forms of transient disturbances, eliminating the requirement for fault identification or control switching. Moreover, it can offer grid-forming support to the grid during grid faults. Hardware-in-the-loop experimental results validate the theoretical analysis and the performance of the proposed method.

Abstract:Oscillations caused by small-signal instability have been widely observed in AC grids with grid-following (GFL) and grid-forming (GFM) converters. The generalized short-circuit ratio is commonly used to assess the strength of GFL converters when integrated with weak AC systems at risk of oscillation. This paper provides the grid strength assessment method to evaluate the small-signal synchronization stability of GFL and GFM converters integrated systems. First, the admittance and impedance matrices of the GFL and GFM converters are analyzed to identify the frequency bands associated with negative damping in oscillation modes dominated by heterogeneous synchronization control. Secondly, based on the interaction rules between the short-circuit ratio and the different oscillation modes, an equivalent circuit is proposed to simplify the grid strength assessment through the topological transformation of the AC grid. The risk of sub-synchronization and low-frequency oscillations, influenced by GFL and GFM converters, is then reformulated as a semi-definite programming (SDP) model, incorporating the node admittance matrix and grid-connected device capacities. The effectiveness of the proposed method is demonstrated through a case analysis.

Abstract:This study investigates a safe reinforcement learning algorithm for grid-forming (GFM) inverter based frequency regulation. To guarantee the stability of the inverter-based resource (IBR) system under the learned control policy, a model-based reinforcement learning (MBRL) algorithm is combined with Lyapunov approach, which determines the safe region of states and actions. To obtain near optimal control policy, the control performance is safely improved by approximate dynamic programming (ADP) using data sampled from the region of attraction (ROA). Moreover, to enhance the control robustness against parameter uncertainty in the inverter, a Gaussian process (GP) model is adopted by the proposed algorithm to effectively learn system dynamics from measurements. Numerical simulations validate the effectiveness of the proposed algorithm.

Abstract:With photovoltaic (PV) sources becoming more prevalent in the energy generation mix, transitioning grid-connected PV systems from grid-following (GFL) mode to grid-forming (GFM) mode becomes essential for offering self-synchronization and active support services. Although numerous GFM methods have been proposed, the potential of DC voltage control malfunction during the provision of the primary and inertia support in a GFM PV system remains insufficiently researched. To fill the gap, some main GFM methods have been integrated into PV systems featuring detailed DC source dynamics. We conduct a comparative analysis of their performance in active support and DC voltage regulation. AC GFM methods such as virtual synchronous machine (VSM) face a significant risk of DC voltage failure in situations like alterations in solar radiation, leading to PV system tripping and jeopardizing local system operation. In the case of DC GFM methods such as matching control (MC), the active support falls short due to the absence of an accurate and dispatchable droop response. To address the issue, a matching synchronous machine (MSM) control method is developed to provide dispatchable active support and enhance the DC voltage dynamics by integrating the MC and VSM control loops. The active support capability of the PV systems with the proposed method is quantified analytically and verified by numerical simulations and field tests.

Abstract:With the increased penetration of renewable energy sources, the grid-forming (GFM) energy storage (ES) has been considered to engage in primary frequency regulation (PFR), often necessitating the use of a frequency deadband (FDB) to prevent excessive battery charging cycling and mitigate frequency oscillations. Implementing the FDB is relatively straightforward in grid-following (GFL) control. However, implementing the FDB in GFM control presents a significant challenge since the inverter must abstain from providing active power at any frequency within the FDB. Therefore, in this paper, the performance of PFR control in the GFM-ES inverter is analyzed in detail first. Then, the FDB is implemented for GFM inverters with various types of synchronization methods, and the need for inertia response is also considered. Moreover, given the risk of oscillations near the FDB boundary, different FDB setting methods are proposed and examined, where an improved triangular hysteresis method is proposed to realize the fast response and enhanced stability. Finally, the simulation and experiment results are provided to verify the effectiveness of the above methods.

Abstract:The integration of converter-interfaced generators (CIGs) into power systems is rapidly replacing traditional synchronous machines. To ensure the security of power supply, modern power systems require the application of grid-forming technologies. This study presents a systematic small-signal analysis procedure to assess the synchronization stability of grid-forming virtual synchronous generators (VSGs) considering the power system characteristics. Specifically, this procedure offers guidance in tuning controller gains to enhance stability. It is applied to six different grid-forming VSGs and experimentally tested to validate the theoretical analysis. This study concludes with key findings and a discussion on the suitability of the analyzed grid-forming VSGs based on the power system characteristics.

Abstract:With the increase of the renewable energy generator capacity, the requirements of the power system for grid-connected converters are evolve, which leads to diverse control schemes and increased complexity of systematic stability analysis. Although various frequency-domain models are developed to identify oscillation causes, the discrepancies between them are rarely studied. This study aims to clarify these discrepancies and provide circuit insights for stability analysis by using different frequency-domain models. This study emphasizes the limitations of assuming that the transfer function of the self-stable converter does not have right half-plane (RHP) poles. To ensure that the self-stable converters are represented by a frequency-domain model without RHP poles, the applicability of this model of grid-following (GFL) and grid-forming (GFM) converters is discussed. This study recommends that the GFM converters with ideal sources should be represented in parallel with the P / Q - θ / V admittance model rather than the V - I impedance model. Two cases are conducted to illustrate the rationality of the P / Q - θ / V admittance model. Additionally, a hybrid frequency-domain modeling framework and stability criteria are proposed for the power system with several GFL and GFM converters. The stability criteria eliminates the need to check the RHP pole numbers in the non-passive subsystem when applying the Nyquist stability criterion, thereby reducing the complexity of stability analysis. Simulations are carried out to validate the correctness of the frequency-domain model and the stability criteria.

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:With good adaptability to weak power grids, the grid-forming inverter becomes the foundation of future power grids with high-proportion renewable energy. Moreover, the virtual synchronous generator (VSG) control is recognized as the mainstream control strategy for grid-forming inverters. For permanent magnet synchronous generator (PMSG) based wind generation systems connected to power grid via VSG-controlled grid-forming inverters, some novel impacts on the low-frequency oscillations (LFOs) emerge in power grids. The first impact involves the negative/positive damping effect on LFOs. In this paper, the small-signal torque model of VSG-controlled PMSG-based wind generation systems is established based on the damping torque analysis method, revealing the influence mechanism of machine-side dynamics on LFOs and proving the necessity of the double-mass model for accurate stability analysis. The second impact is the resonance effect between torsional oscillation and LFOs. Subsequently, this paper uses the open-loop resonance analysis method to study the resonance mechanism and to predict the root trajectory. Then, a damping enhancement strategy is proposed to weaken and eliminate the negative damping effect of machine-side dynamics on LFOs and the resonance effect between torsional oscillation and LFOs. Finally, the analysis result is validated through a case study involving the connection of the VSG-controlled PMSG-based wind generation system to the IEEE 39-bus AC grid, supporting the industrial application and stable operation of VSG-controlled PMSG-based wind generation systems.

Abstract:The transient synchronization characteristics and instability mechanism of the permanent magnet synchronous generator (PMSG)-based grid-forming wind energy conversion system (GFM-WECS) under symmetrical grid fault have received little attention to date. In this paper, considering the dynamics of DC-link voltage, the transient stability and an improved control strategy of PMSG-based GFM-WECS are studied in detail. Firstly, considering the dynamic interactions between the machine-side converter and the grid-side converter, the large-signal equivalent model of GFM-WECS is established. Furthermore, a novel Lyapunov function is derived to evaluate the transient stability margin and instability boundary of GFM-WECS during grid voltage sag. Additionally, the impacts of current-limitation control on the transient stability of GFM-WECS are revealed. Then, a stability evaluation index is proposed to evaluate the transient stability margin of GFM-WECS. Moreover, an improved control strategy is proposed to enhance the transient response characteristics and low voltage ride-through (LVRT) capability of GFM-WECS under symmetrical grid fault. Finally, simulations and experimental results are conducted to verify the effectiveness of the proposed control strategy.

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:Currently, the dominant trend in new energy power supply systems is the heterogeneous inverters-paralleled system (HIPS), which is a combination of grid-following (GFL) and grid-forming (GFM) inverters. The dynamic characteristics of different inverters in HIPS and the differences between GFL and GFM inverters undoubtedly increase the difficulty of the stability analysis and coordinated control. This paper establishes an interactive admittance matrix model of HIPS, fully considers the interactive effects among different inverters, and explores the multi-dimensional resonance characteristics of HIPS by utilizing the modal analysis method. To achieve the coordinated control and oscillation suppression among different inverters, a frequency-divided compensation strategy is proposed, which divides the operation modes of HIPS into three categories, i.e., GFM, GFL, and hybrid modes. Specifically, the frequency division boundary is determined based on the resonance characteristics of GFL and GFM inverters, with the operation modes of HIPS being dynamically adjusted according to the harmonic power ratio. Finally, the simulation and experimental results demonstrate that the HIPS can flexibly adjust the operation modes to adapt to the complex conditions after adopting the frequency-divided compensation strategy and suppressing the oscillation frequency ratio to less than 2%, ensuring the safe and reliable operation of HIPS.

Abstract:The gradual penetration of grid-forming (GFM) converters into new power systems with renewable energy sources may result in the emergence of small-signal instability issues. These issues can be elucidated using sequence impedance models, which offer a more tangible and meaningful interpretation than dq-domain impedance models and state-space models. However, existing research has primarily focused on the impact of power loops and inner control loops in GFM converters, which has not yet elucidated the precise physical interpretation of inner voltage and current loops of GFM converters in circuits. This paper derives series-parallel sequence impedance models of multi-loop GFM converters, demonstrating that the voltage loop can be regarded as a parallel impedance and the current loop as a series impedance. Consequently, the corresponding small-signal stability characteristics can be identified through Bode diagrams of sequence impedances or by examining the physical meanings of impedances in series and in parallel. The results indicate that the GFM converter with a single power loop is a candidate suitable for application in new power systems, given its reduced number of control parameters and enhanced low-frequency performance, particularly in weak grids. The results of PLECS simulations and corresponding prototype experiments verify the accuracy of the analytical analysis under diverse grid conditions.

Abstract:Battery energy storage systems (BESSs) are an important asset for power systems with high integration levels of renewable energy, and they can be controlled to provide various critical services to the power grid. This paper presents the real-world experience of using a megawatt-scale BESS with grid-following (GFL) and grid-forming (GFM) controls and a run-of-river (ROR) hydropower plant to restore a regional power system. To demonstrate this, we carry out power-hardware-in-the-loop experiments integrating an actual GFL- or GFM-controlled BESS and a load bank. Both the simulation and experimental results presented in this paper show the different roles of GFL- or GFM-controlled BESS in power system black starts. The results provide further insight for system operators on how GFL- or GFM-controlled BESS can enhance grid stability and how an ROR hydropower plant can be converted into a black-start-capable unit with the support of a small-capacity BESS. The results show that an ROR hydropower plant combined with a BESS has the potential of becoming one of enabling elements to perform bottom-up black-start schemes as opposed to conventional bottom-down method, thus enhancing the system resiliency and robustness.

Abstract:With the rapid increase in the installed capacity of renewable energy in modern power systems, the stable operation of power systems with considerable power electronic equipment requires further investigation. In converter-based islanded microgrid (CIM) systems equipped with grid-following (GFL) and grid-forming (GFM) voltage-source converters (VSCs), it is challenging to maintain stability due to the mutual coupling effects between different VSCs and the loss of voltage and frequency support from the power system. In previous studies, quantitative transient stability analysis was primarily used to assess the active power loop of GFM-VSCs. However, frequency and voltage dynamics are found to be strongly coupled, which strongly affects the estimation result of stability boundary. In addition, the varying damping terms have not been fully captured. To bridge these gaps, this paper investigates the transient stability of CIM considering reactive power loop dynamics and varying damping. First, an accuracy-enhanced nonlinear model of the CIM is derived based on the effects of reactive power loop and post-disturbance frequency jump phenomena. Considering these effects will eliminates the risk of misjudgment. The reactive power loop dynamics make the model coefficients be no longer constant and thus vary with the power angle. To evaluate quantitatively the effects of reactive power loop and varying damping on the transient stability of CIM, an iterative criterion based on the equal area criterion theory is proposed. In addition, the effects of parameters on the stable boundary of power system are analyzed, and the dynamic interaction mechanisms are revealed. Simulation and experiment results verify the merits of the proposed method.

Abstract:Stability in unbalanced power systems has deserved little attention in the literature. Given the importance of this scenario in distribution systems with distributed generation, this paper revisits modal analysis techniques for stability studies in power systems, and explains how to tackle unbalanced power systems with voltage-dependent loads. The procedure is described in detail and applied to a low-voltage (LV) simple case study with two grid-forming electronic power converters and unbalanced loads. Results are then compared with those obtained with the popular impedance-based method. While the latter is easier to implement using simulation or field data, the former requires complete information of the system, but gives a better insight into the problem. Since both methods are based on a small-signal approximation of the system, they provide similar results, but they discern different information. A larger second case study based on an LV CIGRE distribution system is also analysed. Results are obtained using a detailed Simulink model of the microgrids with electronic power converters.

Abstract:Grid-forming (GFM) control based high-voltage DC (HVDC) systems and renewable energy sources (RESs) provide support for enhancing the stability of power systems. However, the interaction and coordination of frequency support between the GFM-based modular multilevel converter based HVDC (MMC-HVDC) and grid-following (GFL) based RESs or GFM-based RESs have not been fully investigated, which are examined in this study. First, the detailed AC- and DC-side impedances of GFM-based MMC-HVDC are analyzed. The impedance characteristics of GFL- and GFM-based wind turbines are next analyzed. Then, the influences of GFL- and GFM-based wind farms (WFs) on the DC- and AC-side stabilities of WF-integrated MMC-HVDC systems are compared and evaluated. The results show that the GFM-based wind turbine performs better than the GFL-based wind turbine. Accordingly, to support a receiving-end AC system, the corresponding frequency supporting strategies are proposed based on the GFM control for WF-integrated MMC-HVDC systems. The GFM-based WF outperforms the GFL-based WF in terms of stability and response time. Simulations in PSCAD/EMTDC demonstrate the DC- and AC-side stability issues and seamless grid support from the RESs, i.e., WFs, to the receiving-end AC system.