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: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: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: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: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: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: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 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: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: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: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:The continuous power supply system, which eliminates the neutral section and realizes safe and reliable operation, shows a development trend in suburban railways. However, the access of a power quality compensator (PQC) may alter the impedance characteristics of the system and introduce additional harmonics with a broader frequency band, potentially increasing the risk of resonance. Accordingly, in this paper, an analytical method is first adopted in conjunction with a field test to construct a simplified harmonic model for an actual continuous suburban line. A modal scanning algorithm is then used to analyze the effects of the controller and filter in the PQC on the harmonic resonance of the suburban railway continuous power supply system. Based on the improved particle swarm optimization algorithm, a multi-objective optimization design for PQC is proposed that can suppress harmonic resonance, filter the harmonics, and reduce the cost while preserving the stability of the control system. Finally, a real case study based on the field test demonstrates the effectiveness of the proposed design.

Abstract:The increasing penetration of renewable energy resources and reduced system inertia pose risks to frequency security of power systems, necessitating the development of fast frequency regulation (FFR) methods using flexible resources. However, developing effective FFR policies is challenging because different power system operating conditions require distinct regulation logics. Traditional fixed-coefficient linear droop-based control methods are suboptimal for managing the diverse conditions encountered. This paper proposes a dynamic nonlinear P-f droop-based FFR method using a newly established meta-reinforcement learning (meta-RL) approach to enhance control adaptability while ensuring grid stability. First, we model the optimal FFR problem under various operating conditions as a set of Markov decision processes and accordingly formulate the frequency stability-constrained meta-RL problem. To address this, we then construct a novel hierarchical neural network (HNN) structure that incorporates a theoretical frequency stability guarantee, thereby converting the constrained meta-RL problem into a more tractable form. Finally, we propose a two-stage algorithm that leverages the inherent characteristics of the problem, achieving enhanced optimality in solving the HNN-based meta-RL problem. Simulations validate that the proposed FFR method shows superior adaptability across different operating conditions, and achieves better trade-offs between regulation performance and cost than benchmarks.

Abstract:As the proportion of renewable energy sources continues to increase, the local damping contributions of sources in power system decrease, posing a challenge to the power system stability. Therefore, online tracking of the damping contributions of each source is crucial for the prevention of low-frequency oscillations. This paper proposes an online tracking method of local damping under ambient data. The proposed method is based on dissipation energy spectrum analysis (DESA) and the energy dissipation factor (EDF). First, the feasibility of using frequency-domain analysis for the dissipation energy of generator is analyzed. The frequency spectral function of dissipation energy of generator is then derived by integrating with Parseval’s theorem, and the EDF is defined. Second, the generator energy dissipation factor (GEDF) for the dominant oscillation mode frequency is established. The modal information of the dominant oscillation in the power system is obtained through DESA. The relationship between the frequency spectral function and eigenvalues is also established. Finally, an online tracking method of local damping is proposed based on DESA and GEDF. The effectiveness of the proposed method is validated through simulations on a four-machine 11-bus power system and an actual power system in Northwest China.

Abstract:This paper studies the problem of multi-stage robust unit commitment with discrete load shedding. In the day-ahead phase, the on-off status of thermal units is scheduled. During each period of real-time dispatch, the output of thermal units and the action of load shedding are determined, and the discrete choice of load shedding corresponds to the practice of tripping substation outlets. The entire decision-making process is formulated as a multi-stage adaptive robust optimization problem with mixed-integer recourse, whose solution takes three steps. First, we propose and apply partially affine policy, which is optimized ahead of the day and restricts intertemporal dispatch variables as affine functions of previous uncertainty realizations, leaving remaining continuous and binary dispatch variables to be optimized in real time. Second, we demonstrate that the resulting model with partially affine policy can be reformulated as a two-stage robust optimization problem with mixed-integer recourse. Third, we modify the standard nested column-and-constraint generation algorithm to accelerate the inner loops by warm start. The modified algorithm solves the two-stage problem more efficiently. Case studies on the IEEE 118-bus system verify that the proposed partially affine policy outperforms conventional affine policy in terms of optimality and robustness; the modified nested column-and-constraint generation algorithm significantly reduces the total computation time; and the proposed method balances well optimality and efficiency compared with state-of-the-art methods.

Abstract:External disturbances can induce torsional oscillation with weak damping in the shaft system of permanent magnet synchronous generators (PMSGs) based wind generation system, thereby inducing low-frequency oscillations. However, the influence of electromagnetic torque on the shaft system damping and corresponding parameter laws have been scarcely explored. We define the electrical damping coefficient as a quantitative measure for the influence of electromagnetic torque on the shaft system damping. The torsional oscillation damping characteristics of the shaft system under vector control are analyzed, and the transfer function for electromagnetic torque and speed is derived. Additionally, we elucidate the mechanism by which the electromagnetic torque influences the shaft system damping. Simultaneously, laws describing the influence of wind speed, system parameters, and control parameters on the torsional oscillation damping are analyzed. Accordingly, the optimal damping angle of the shaft system a torsional oscillation suppression strategy is proposed to compensate for with uncertainty in the parameters affecting damping. The studied system is modeled using MATLAB/Simulink, and the simulation results validate the effectiveness of the theoretical analysis and proposed torsional oscillation suppression strategy.

Abstract:In this paper, a dynamic equivalent method applicable to the direct-drive permanent magnet synchronous generator (PMSG) based wind farms under asymmetrical faults is proposed. Firstly, PMSGs are clustered based on their different active power characteristics under asymmetrical faults. Further, single-machine equivalent models (SMEMs) are constructed for different clusters of PMSGs. In particular, an SMEM with multi-segmented slope recovery is introduced for PMSGs with ramp recovery characteristics. Further, a collector network equivalent method for wind farms applicable to both symmetrical and asymmetrical faults is presented. Moreover, an iterative simulation method is used to gain the required clustering indicators before the fault actually occurs. Eventually, the effectiveness of the proposed dynamic equivalent method is verified on a modified IEEE 39-bus system.

Abstract:The flexible interconnection of microgrids (MGs) adopting back-to-back converters (BTBCs) has emerged as a new development trend in the field of MGs. This approach enables larger-scale integration and higher utilization of distributed renewable energy sources (RESs). However,their stability characteristics are very different from single MG due to the control characteristics of flexible interconnection. Meanwhile, the uncertainty and stochastic dependence structures of RESs and loads create challenges for stability analysis and cooperative control. In this paper, a probabilistic small-signal stability assessment and cooperative control framework is proposed for interconnected MGs via BTBCs. First, a cooperative control architecture for MGs is constructed. Then, a small-signal model of interconnected MGs via BTBCs containing primary control and secondary control is developed. This model facilitates the analysis of the impacts of BTBCs and various control strategies on the system stability. Subsequently, Copula functions and polynomial chaos expansion (PCE) are combined to achieve the probabilistic small-signal stability assessment. On this basis, the parameters of the cooperative control are optimized, enhancing the robustness of interconnected MGs via BTBCs. Finally, a case of interconnected MGs via BTBCs are built in MATLAB/Simulink to verify the accuracy and effectiveness of the proposed framework.

Abstract:Traditional virtual synchronous generator (VSG) suffers from frequency steady-state deviation in islanded microgrids, which negatively affects the frequency-sensitive loads. Moreover, similar to the synchronous generator, VSG introduces active power oscillation, especially under the condition of multiple parallel VSGs, which may cause overload or damage to the VSG because of its low overcurrent capability as a power electronic inverter. To address these issues, a decentralized frequency restoration and power oscillation damping control method is proposed in this paper, in which the global variable characteristic of the microgrid frequency is considered to restore it to the rated value while ensuring precise active power sharing. Moreover, the proposed control method can dampen the power oscillation during load disturbance without affecting the steady-state characteristics. In addition, the fully decentralized manner obviates the requirement for communication networks, thereby considerably reducing the communication burden and improving system reliability. Finally, simulations and experiments are conducted to validate the effectiveness of the proposed control method.

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:With the rapid integration of renewable energy, wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues. Existing methods are usually studied for local power systems with around one hundred nodes. However, for a large-scale power system with tens of thousands of nodes, the dimension of transfer function matrix or the order of characteristic equation is much higher. In this case, the existing methods such as eigenvalue analysis method and impedance-based method have difficulty in computation and are thus hard to utilize in practice. To fill this gap, this paper proposes a novel method named the smallest eigenvalues based logarithmic derivative (SELD) method. It obtains the dominant oscillation modes by the logarithmic derivative of the k-smallest eigenvalue curves of the sparse extended nodal admittance matrix (NAM). An oscillatory stability analysis tool is further developed based on this method. The effectiveness of the method and the tool is validated through a local power system as well as a large-scale power system.

Abstract:Realistic uncertainties of renewable energies and loads may possess complicated probability distributions and correlations, which are difficult to be characterized by standard probability density functions and hence challenge existing uncertainty propagation analysis (UPA) methods. Also, nonintrusive spectral representation (SR)-based UPA methods can only estimate system responses at each time point separately, which is time-consuming for analyzing power system dynamics. Thus, this paper proposes a generic multi-output SR (GMSR) method to effectively tackle the above limitations by developing the generic correlation transformation and multi-output structure. The effectiveness and superiority of GMSR in efficiency and accuracy are demonstrated by comparing it with existing SR methods.

Abstract:In DC power systems dominated by power electronic devices, constant power loads (CPLs) and saturation components significantly impact large-signal stability. During the large-signal stability analysis process, the presence of multiple state variables and high-order system poses substantial challenges. To address this, considering the complete control dynamics, this paper proposes an equivalent single-machine (ESM) model of the droop-based DC power systems to reduce the complexity of the large-signal analysis. Building on the proposed ESM model, considering the dynamics of CPL and saturation constraints, a region of attraction (ROA) estimation algorithm based on sum of squares (SOS) programming is proposed, which significantly reduces the conservativeness compared with other existing methods. Furthermore, a control parameter optimization algorithm based on SOS programming is proposed with the aim of expanding the ROA. Furthermgre, with the aim of expanding the ROA, controller sythesis is conducted with proposed control parameter optimization algorithm based on SOS programming. Ultimately, simulation experiments validate the accuracy of the proposed ESM model and the proposed ROA estimation algorithm, as well as the effectiveness of the control parameter optimization algorithm.

Abstract:The oscillatory stability analysis of multi-converter-fed systems (MCFSs) with modest computational resources needs a precise parametric reduced-order impedance model (PROIM). However, the traditional Krylov subspace based parametric model order reduction (KS-PMOR) method has difficulty in building precise PROIM for MCFSs. This is because the factors related to the errors of PROIM are complicated and coupled. To fill this gap, the factors associated with the accuracy of the KS-PMOR method are estimated by defining three indicators: the convergence error, cumulative error, and rank of projection matrix. Using the three indicators, a frequency-domain adaptive parametric model order reduction (FDA-PMOR) method is developed to form the precise PROIM of MCFSs for the accurate and fast oscillatory stability analysis. The accuracy of the obtained PROIM using the proposed FDA-PMOR method and its efficiency in actual oscillatory stability analysis are validated by three MCFSs with different scales, i.e., a small-scale MCFS with four paralleled converter-based renewable energy generators (CREGs), a real-time simulation-based MCFS with eighteen paralleled CREGs, and a larger MCFS with ninety paralleled CREGs.

Abstract:Most permanent magnet synchronous generator (PMSG) based wind generation systems currently employ grid-following control, relying on a phase-locked loop (PLL) for grid connection. However, it leads to a lack of inertia support in the system. To address this, the virtual inertia control (VIC) is crucial for improvement, yet it introduces potential instability due to torsional oscillation interaction with PLL and low-frequency oscillations, which is an underexplored area. This paper presents a comprehensive analysis of the grid-connected PMSG-based wind generation system. It confirms the necessity of employing a full-order model for studying stability on the quasi-electromechanical timescale (QET) by a comparison with the reduced-order model. Then, a comprehensive modal analysis is conducted to analyze the effect of VIC parameters, shaft inertia time constant, PLL parameters, and torsional oscillation damping (TOD) controller gain on the interaction of QET oscillations under two typical control strategies. The occurrence of interaction and mode conversion is observed when the oscillation frequency and root loci of the torsional, PLL, and low-frequency oscillations are close. Finally, a theoretical analysis is validated via simulation verification in Simulink. These findings offer a valuable guidance for industrial PMSG applications considering VIC.

Abstract:In this paper, a set of distributed secondary controllers is introduced that provide active regulation for both steady-state and transient-state performances of an islanded DC microgrid (MG). The secondary control for distributed converter interfaced generation (DCIG) not only guarantees that the system converges to the desired operating states in the steady state but also regulates the state variations to a prescribed transient-state performance. Compared with state-of-the-art techniques of distributed secondary control, this paper achieves accurate steady-state secondary regulations with prescribed transient-state performance in an islanded DC MG. Moreover, the applicability of the proposed control does not rely on any explicit knowledge of the system topology or physical parameters. Detailed controller designs are provided, and the system under control is proved to be Lyapunov stable using large-signal stability analysis. The steady-state and transient-state performances of the system are analyzed. The paper proves that as the perturbed system converges, the proposed control achieves accurate proportional power sharing and average voltage regulation among the DCIGs, and the transient variations of the operating voltages and power outputs at each DCIG are regulated to the prescribed transient-state performance. The effectiveness of the proposed control is validated via a four-DCIG MG system.

Abstract:The virtual synchronous generator (VSG), utilized as a control strategy for grid-forming inverters, is an effective method of providing inertia and voltage support to the grid. However, the VSG exhibits limited capabilities in low-voltage ride-through (LVRT) mode. Specifically，the slow response of the power loop poses challenges for VSG in grid voltage support and increases the risk of overcurrent, potentially violating present grid codes. This paper reveals the mechanism behind the delayed response speed of VSG control during the grid faults. On this basis, a compound compensation control strategy is proposed for improving the LVRT capability of the VSG, which incorporates adaptive frequency feedforward compensation (AFFC), direct power angle compensation (DPAC), internal potential compensation (IPC), and transient virtual impedance (TVI), effectively expediting the response speed and reducing transient current. Furthermore, the proposed control strategy ensures that the VSG operates smoothly back to its normal control state following the restoration from the grid faults. Subsequently, a large-signal model is developed to facilitate parameter design and stability analysis, which incorporates grid codes and TVI. Finally, the small-signal stability analysis and simulation and experimental results prove the correctness of the theoretical analysis and the effectiveness of the proposed control strategy.

Abstract:The maximum power transfer capability (MPTC) of phase-locked loop (PLL)-based grid-following inverters is often limited under weak-grid conditions due to passivity violations caused by operating-point-dependent control loops. This paper reveals and compares the mechanisms of these violations across different control strategies. Using admittance decomposition and full-order state-space models for eigenvalue analysis, MPTC limitations from control loops and their interactions are identified. The small-signal stabilities of different control loops are compared under varying grid strength, and both static and dynamic MPTCs for each control mode are examined. This paper also explores how control loop interactions impact the MPTC, offering insights for tuning control loops to enhance stability in weak grids. For example, fast power control improves the MPTC when paired with a slow PLL, while power control has minimal effect when the PLL is sufficiently fast. The findings are validated through frequency scanning, eigenvalue analysis, simulations, and experiments.

Abstract:Fractional-order control (FOC) has gained significant attention in power system applications due to their ability to enhance performance and increase stability margins. In grid-connected converter (GCC) systems, the synchronous reference frame phase-locked loop (SRF-PLL) plays a critical role in grid synchronization for renewable power generation. However, there is a notable research gap regarding the application of FOC to the SRF-PLL. This paper proposes a fractional-order SRF-PLL (FO-SRF-PLL) that incorporates FOC to accurately track the phase angle of the terminal voltage, thereby improving the efficiency of grid-connected control. The dynamic performance of the proposed FO-SRF-PLL is evaluated under varying grid conditions. A comprehensive analysis of the small-signal stability of the GCC system employing the FO-SRF-PLL is also presented, including derived small-signal stability conditions. The results demonstrate that the FO-SRF-PLL significantly enhances robustness against disturbances compared with the conventional SRF-PLL. Furthermore, the GCC system with the FO-SRF-PLL maintains stability even under weak grid conditions, showing superior stability performance over the SRF-PLL. Finally, both simulation and experimental results are provided to validate the analysis and conclusions presented in this paper.

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:In a high-risk sector, such as power system, transparency and interpretability are key principles for effectively deploying artificial intelligence (AI) in control rooms. Therefore, this paper proposes a novel methodology, the evolving symbolic model (ESM), which is dedicated to generating highly interpretable data-driven models for dynamic security assessment (DSA), namely in system security classification (SC) and the definition of preventive control actions. The ESM uses simulated annealing for a data-driven evolution of a symbolic model template, enabling different cooperative learning schemes between humans and AI. The Madeira Island power system is used to validate the application of the ESM for DSA. The results show that the ESM has a classification accuracy comparable to pruned decision trees (DTs) while boasting higher global interpretability. Moreover, the ESM outperforms an operator-defined expert system and an artificial neural network in defining preventive control actions.

Abstract:Bulk power systems show increasingly significant frequency spatial distribution characteristics (FSDCs), leading to a huge difference in the frequency response between regions. Existing uniform-frequency models based on analytical methods are no longer applicable. This paper develops a reduced-order bus frequency response (BFR) model to preserve the FSDC and describe the frequency response of all buses. Its mathematical equation is proved to be isomorphic to the forced vibration of a mass-spring-damper system, and the closed-form solution (CFS) of the BFR model is derived by the modal analysis method and forced decoupling method in vibration mechanics. The correlation between its mathematical equation and the state equation for small-signal stability analysis is discussed, and related parameters in the CFS are defined by the eigen-analysis method without any additional devices or tools. Case studies show that the proposed reduced-order BFR model and its CFS can improve the solution accuracy while keeping the solution speed within milliseconds, which can preserve the significant FSDC of bulk power systems and represent a normalized mathematical description of distinct-frequency models.

Abstract:The significant increase in the proportion of renewable energy sources (RESs) has elevated risks of extreme ramp events and frequency instability in power systems. In recent years, frequency stability events have occurred in several countries/regions worldwide due to flexibility deficiencies. Generation flexibility has emerged as a critical factor influencing the frequency stability of power systems. This paper proposes a domain of attraction (DOA)-based quantitative method to assess the frequency stability region of power systems with a high proportion of RESs, considering generation flexibility constraints. First, ramp rate is adopted as the core indicator to characterize generation flexibility within automatic generation control (AGC) timescale, through which a nonlinear AGC model with rate saturation constraints is established. Second, the concept of DOA is introduced to define the stability region of the nonlinear AGC. Third, a quadratic Lyapunov-based estimation method is employed to quantitatively analyze the DOA of the nonlinear AGC at different generation flexibility levels. Simulation results demonstrate that increased generation flexibility expands the estimated DOA of the nonlinear AGC, whereas generation flexibility deficiency induces AGC instability. Moreover, state trajectory and time-domain simulation verify that the proposed estimation method accurately represents the stability region of the nonlinear AGC.

Abstract:The phenomenon of sub-synchronous oscillation (SSO) poses significant threats to the stability of power systems. The advent of artificial intelligence (AI) has revolutionized SSO research through data-driven methodologies, which necessitates a substantial collection of data for effective training, a requirement frequently unfulfilled in practical power systems due to limited data availability. To address the critical issue of data scarcity in training AI models, this paper proposes a novel transfer-learning-based (TL-based) Wasserstein generative adversarial network (WGAN) approach for synthetic data generation of SSO in wind farms. To improve the capability of WGAN to capture the bidirectional temporal features inherent in oscillation data, a bidirectional long short-term memory (BiLSTM) layer is introduced. Additionally, to address the training instability caused by few-shot learning scenarios, the discriminator is augmented with mini-batch discrimination (MBD) layers and gradient penalty (GP) terms. Finally, TL is leveraged to fine-tune the model, effectively bridging the gap between the training data and real-world system data. To evaluate the quality of the synthetic data, two indexes are proposed based on dynamic time warping (DTW) and frequency domain analysis, followed by a classification task. Case studies demonstrate the effectiveness of the proposed approach in swiftly generating a large volume of synthetic SSO data, thereby significantly mitigating the issue of data scarcity prevalent in SSO research.

Abstract:Oscillation accidents emerge in power systems integrated with increasing penetration of renewable energy sources. The impedance of electromagnetic dynamics is investigated in recent years, where the mechanical dynamics are neglected. So far, the low-frequency oscillations are not well addressed with the impedance analysis method. A novel analytical impedance is formulated and implemented for wind energy conversion system consisting of wind turbine generators (WTGs) and wind farm, which fills the gap in the mechanical dynamics of the impedance. Instead of assuming constant values, the electromechanical dynamics of the rotor speed and the pitch angle are involved in the WTG impedance. Besides, the impedance framework is generally and modularly designed and is adaptive to different operating regions. With the developed analytical impedance, the stability assessment can cover the low-frequency oscillations, providing an in-depth insight into the mechanical parameters influencing the small-signal stability performance. As an application, the impedance characteristic and stability performance of systems with active power reserve for grid supporting are analyzed and optimized. Furthermore, the shafting torsional vibrations of WTGs in wind farms are analyzed with modal decomposition and the low-frequency impedance model. The improved accuracy of the developed analytical impedance is illustrated by comparison with commonly used impedance, which ignores the coupling between the electrical and mechanical dynamics. It is proven that the mechanical dynamics have a significant influence on the impedance, particularly in the low-frequency range. Experimental validation is carried out to validate the low-frequency impedance model and the stability performance.

Abstract:The multi-voltage-level DC distribution network (MVL-DC-DN) is a promising network for efficiently integrating rapidly growing DC loads, and fast-growing load demand would bring a challenge to the MVL-DC-DN in terms of the maximum loadability. This paper considers the DC electric spring (DC-ES) as a novel candidate flexible resource for enhancing the maximum loadability of the MVL-DC-DN, and proposes an evaluation method for the maximum loadability. Firstly, with the consideration of device constraints, the impact that the DC-ES on the maximum loadability of the DC distribution network (DC-DN) is analyzed via a simplified equivalent circuit. Subsequently, the power flow (PF) model of an MVL-DC-DN with DC-ESs is established. Finally, a method based on continuation power flow (CPF) for evaluating the maximum loadability of an MVL-DC-DN with DC-ESs is proposed. During the evaluation, limitations of the DC-ES and the DC transformer (DCT) are considered. The consideration of the practical constraints avoids the overestimation of the maximum loadability. The case study verifies the effectiveness of the proposed method.

Abstract:In recent years, transmission system operators have started requesting converter-interfaced generators (CIGs) to participate in grid services such as power oscillation damping (POD). As power systems are prone to topology changes because of connection and disconnection of generators and lines, one of the most important requirements in the design of POD controller is to account for these changes. This can be done by either adjusting the controller structure during the operation or applying a fixed structure designed to address changes in the system. The fixed structure is usually preferred by transmission system operators since it is easier to determine its impact on the system. In this paper, a design procedure is proposed for network-reconfiguration-aware POD controller with fixed structure for CIG-based power plants that considers network configurations with any one line disconnected. The design procedure is based on frequency-response techniques, so it is suitable for application in CIG-based power plants, even in cases when a detailed small-signal model of the system is not available. Designs of a POD controller for the damping of critical system modes can be obtained by using active power, reactive power, or both power components simultaneously. The application to the design of a POD controller for a CIG-based power plant connected to the IEEE 39-bus system is presented as an example. Simulations performed in MATLAB and SimPowerSystems are used to validate the proposed design procedure. The validation includes an analysis of system performance with changes considered in the proposed designed procedure. Also, the system performance under unconsidered changes is examined, covering variations in load and inertia values, as well as disconnection of synchronous generators.

Abstract:Fault current limiting is a critical technology to ensure the safe operation of modular multilevel converter based multi-terminal direct current (MMC-MTDC) grids. This paper proposes a fault severity classification based coordination control strategy of fault current limiter (FCL) and MMC for adaptive fault current limiting. The proposed strategy reduces the investment in FCL, and keeps the bus voltages of non-faulty lines at reasonable values. Firstly, a rapid fault circuit parameter estimation (FCPE) method using initial fault current information is proposed. With this method, the fault distance and fault transition resistance can be quickly estimated, which are used for a quantitative indication of the fault severity. Subsequently, the coordination control strategy of FCL and MMC is proposed, in which the FCL action is prioritized, while the control of MMC is complementary for current limiting. Based on the proposed strategy, fault severity phase planes (FSPPs) are constructed to assess fault severity and calculate the activation time of FCL and voltage regulation factor of MMC. Therefore, the FCL activation and MMC control are matched to the fault severity. The effectiveness and advantages of the proposed strategy are validated by the simulations in PSCAD/EMTDC.

Abstract:The self-synchronizing voltage source inverter (SSVSI) is widely studied because of its grid-forming capability. However, the slow response of the active power control loop (APCL) under the weak grid makes it difficult for the SSVSI to quickly support the frequency of a low-inertia grid. In this paper, a grid framework is established to analyze the frequency support service process of the SSVSI, and the shortcomings of the regulation of the damping coefficient and virtual inertia coefficient for frequency support are analyzed. Then, an adaptive additional damping control method is proposed to optimize the ability of SSVSI to support the grid frequency. The proposed control method adjusts the damping of the APCL without affecting the system steady-state characteristics, which improves the active power response speed of the SSVSI. Besides, the proposed control method adaptively adjusts the additional damping coefficient based on the active power response without measuring the grid parameters. Compared with other forms of control, the proposed control method excels in minimizing the rate of change of frequency (RoCoF) and the frequency deviation (FD) within the grid, without succumbing to the constraints posed by unknown grid parameters. Furthermore, the analysis of the system stability is also presented. Finally, the experimental hardware results obtained from a miniaturized grid prototype are presented, corroborating the effectiveness of the proposed control method.

Abstract:Power system optimal dispatch with transient security constraints is commonly represented as transient security-constrained optimal power flow (TSC-OPF). Deep reinforcement learning (DRL)-based TSC-OPF trains efficient decision-making agents that are adaptable to various scenarios and provide solution results quickly. However, due to the high dimensionality of the state space and action spaces, as well as the non-smoothness of dynamic constraints, existing DRL-based TSC-OPF solution methods face a significant challenge of the sparse reward problem. To address this issue, a fast-converging DRL method for optimal dispatch of large-scale power systems under transient security constraints is proposed in this paper. The Markov decision process (MDP) modeling of TSC-OPF is improved by reducing the observation space and smoothing the reward design, thus facilitating agent training. An improved deep deterministic policy gradient algorithm with curriculum learning, parallel exploration, and ensemble decision-making (DDPG-CL-PE-ED) is introduced to drastically enhance the efficiency of agent training and the accuracy of decision-making. The effectiveness, efficiency, and accuracy of the proposed method are demonstrated through experiments in the IEEE 39-bus system and a practical 710-bus regional power grid. The source code of the proposed method is made public on GitHub.

Abstract:Short-term voltage stability (STVS) assessment is a critical monitoring technology in modern power systems. During daily operations, transmission lines may switch on or off due to scheduled maintenance or unexpected faults, which poses challenges to the STVS assessment under varying topology change conditions. To adapt the STVS assessment to the system topology changes, we propose a deep-learning-based STVS assessment model with the topology-adaptive voltage dynamic feature and the fine-tuning domain transfer for power systems with changing system topologies. The topology-adaptive voltage dynamic feature, extracted from streaming time-series data of phasor measurement units (PMUs), is used to characterize transient voltage stability. The voltage dynamic features depend on the balance of reactive power flow and system topology, effectively revealing both spatio-temporal patterns of post-disturbance system dynamics. The simulation results based on large disturbances in the New England 39-bus power system demonstrate that the proposed model achieves superior STVS assessment performance, with an accuracy of 99.65% in predicting voltage stability compared with the existing deep learning methods. The proposed model also performs well when applied to the larger IEEE 145-bus power system. The fine-tuning domain transfer of the proposed model adapts very well to system topology changes in power systems. It achieves an accuracy of 99.50% in predicting the STVS for the New England 39-bus power system with the transmission line alternation. Furthermore, the proposed model demonstrates strong robustness to noisy and missing data.

Abstract:The widespread penetration of wind power has introduced challenges in managing the rotor angle stability characteristics of the power system, affecting both small- and large-disturbance rotor angle stabilities due to its uncertain steady-state power output and inverter-based grid interfacing. Traditionally, the two stability criteria are separately analyzed and improved via preventive control, e.g., generation rescheduling. However, they may have conflicting relationship during the preventive control optimization. Therefore, this paper firstly integrates both small- and large-disturbance rotor angle stabilities and proposes an optimization model for preventive generation rescheduling to simultaneously improve them while considering wind power uncertainty. The stability constraints are linearized using trajectory sensitivity analysis, while the wind power fluctuation is represented by employing a scenario-based Taguchi’s orthogonal array testing (TOAT) method. An iterative solution method is proposed to efficiently solve the optimization model. The proposed optimization model is established on the New England 10-machine 39-bus system and a large Nordic system, demonstrating its robustness and effectiveness in addressing wind power fluctuations.

Abstract:Existing sub-/super-synchronous oscillation stability control methods are primarily focused on specific operating conditions at discrete frequencies, limiting their adaptation to varying oscillation ​scenarios in the power system connected with direct-drive permanent magnet synchronous generator (PMSG)-based wind farms. Based on supplementary dissipation compensation, this paper proposes an oscillation stability control method incorporating equipment-level and farm-level cooperative optimization ​to enhance the system-level stability. First, the effects of dynamic self-dissipation and dynamic coupled dissipation on system stability are analyzed, ​establishing the foundational principle of supplementary dissipation compensation. Subsequently, the optimal locations for supplementary dissipation compensation are identified based on critical control designed to enhance the dynamic self-dissipation effect and suppress the dynamic coupled dissipation effect. Furthermore, by considering energy requirements under the combined wind farm-grid interaction and inter-PMSG interactions and balancing the wind farm-grid interaction dissipation energy with inter-PMSG interaction dissipation energy distribution, an equipment-level control parameter optimization algorithm and a farm-level power cooperative optimization algorithm are established. Finally, the simulation results demonstrate that dynamic coupled dissipation constitutes the ​root cause of oscillation inception and progression. Through equipment-level and farm-level cooperative optimization, the proposed method can reliably compensate dynamic dissipation energy, while adapting to the variation of oscillation frequency and the oscillation scenario. It can maximize the energy dissipation effect of the interconnected system, achieving rapid suppression of sub-/super-synchronous oscillations.

Abstract:The mutual impedance between doubly-fed induction generator (DFIG) system and weak grid may cause a resonance, which yields to undesirable distortions and harmonics. The equivalent impedance of DFIG systems is high, which creates high-frequency resonance (HFR) in interaction with weak grids. Although several studies are conducted to mitigate HFRs, more improvements are needed in terms of damping and phase-margin. Accordingly, an active damping control strategy based on virtual admittance is proposed, which properly mitigates the disturbances. The proposed strategy is accurate as it considers the dynamic high-frequency model of DFIG system to effectively reduce the HFR. The performance of the proposed strategy is verified by using different case studies on a 2 MW DFIG system with time-domain simulations in MATLAB/Simulink environment.

Abstract:This paper demonstrates a new type of sub-synchronous oscillation of the grid-forming (GFM) converter, which occurs at low rather than high power levels. To reveal the intrinsic mechanism, a simplified analytical small-signal impedance model of the GFM converter is derived. It is found that the reactive power control loop (RPCL) can have a significant impact on the system stability. In particular, the voltage matrix introduced by the RPCL is the key factor causing instability in the GFM grid-connected system at low operating points. Therefore, this paper proposes a control strategy that reshapes the RPCL to counteract the negative effect of the voltage matrix by introducing a q-axis current feedforward, ensuring stable operation at any operating point. Finally, experimental results validate the correctness and effectiveness of the proposed control strategy.

Abstract:Wide-area damping controllers (WADCs) help in damping poorly damped inter-area oscillations (IAOs) using wide-area measurements. However, the vulnerability of the communication network makes the WADC susceptible to malicious dynamic attacks. Existing cyber-resilient WADC solutions rely on accurate power system models or extensive simulation data for training the machine learning (ML) model, which are difficult to obtain for large-scale power system. This paper proposes a novel non-intrusive hybrid two-stage detection framework that mitigates these limitations by eliminating the need for real-time access to large system data or attack samples for training the ML model. In the first stage, an autoencoder is deployed at the actuator location to detect dynamic attacks with sharp gradient variations, e.g., triangular, saw-tooth, pulse, ramp, and random attack signals. In the second stage, an unscented Kalman filter with unknown input estimation at the control center identifies smoothly varying dynamic attacks by estimating the control signal received by the actuator using synchrophasor measurements. A modified cosine similarity (MCS) metric is proposed to compare and quantify the similarity between the estimated control signal and the control signal sent by the WADC placed at the control center to detect any dynamic attacks. The MCS is designed to differentiate between events and dynamic attacks. The performance of the proposed framework has been validated on a hardware-in-the-loop (HIL) cyber-physical testbed built by using the OPAL-RT simulator and industry-grade hardware.

Abstract:Variable renewable energy (VRE) integrated via non-synchronous inverters exhibits low inertia and fluctuating output, posing substantial frequency security challenges for future power systems. When frequency security constraints are omitted from generation planning, the resulting low-inertia generation portfolios often fail to meet critical frequency requirements. To address this issue, this paper proposes a novel frequency security constrained generation planning (FSCGP) model that leverages the frequency support potential of diverse power sources, including conventional thermal generators (CTGs), VRE units, concentrating solar power (CSP) units, and energy storage systems (ESSs). A physics-data hybrid-driven method is introduced to formulate frequency security constraints, enabling accurate representation of diverse frequency regulation characteristics, particularly the fast frequency support capabilities of inverter-based generators (IBGs). To further enhance the computational efficiency, several acceleration techniques are incorporated into the proposed FSCGP model. Case studies based on a modified IEEE RTS-79 system validate the effectiveness of the proposed FSCGP model. The numerical results identify the primary contributors to frequency security under different renewable energy penetration (REP) levels and demonstrate the cost-effectiveness of coordinating various frequency support sources, especially CSP units and IBGs, in mitigating challenges in low-inertia grids.

Abstract:This two-part paper presents a generic methodology for measuring the short-term voltage stability (STVS) of power systems dominated by inverter-based resources (IBRs), which introduces the concept of generalized voltage damping (GVD) for quantifying STVS from both global and local perspectives. It leads to a model-independent approach to assessing the voltage stability, the system strength, and the capability of dynamic devices to support voltage during transient process. Part I of this paper focuses on deriving the system-wise generalized voltage damping (sGVD) index and its applications. The sGVD index is defined as the decay rate of voltage-related transient energy (VTE) dissipated on the (aggregated) buses of the power system, which can be obtained using the maximum Lyapunov exponent (MLE) technique. The proposed sGVD index is theoretically demonstrated to capture the actual voltage damping of devices and to be strongly linked with STVS. These unique properties enable a model-independent approach to measuring STVS and system strength, even in the presence of heterogeneous and strongly nonlinear dynamics of IBRs. We verify the theoretical results by conducting simulations on the modified IEEE 39-bus system and two large-scale practical power systems with integration of massive renewable resources, demonstrating the effectiveness and practicality of the methodology.

Abstract:Future power systems will be characterized by low levels of inertia and limited frequency regulation capacity due to the widespread use of renewable energy sources. Furthermore, the response of different types of loads to system disturbances significantly affects the frequency dynamics. To address these issues, this paper proposes an aggregated system frequency response model considering load dynamics. Initially, a dynamic model of different loads is established, followed by the derivation of a small-signal load model that affects the active power imbalance of the system. The active power variations of loads are categorized into three components: load voltage dynamics, load frequency dynamics, and load inertia contribution. These components are incorporated into the system frequency response model, which accounts for load active power dynamics. The final output is an aggregated reduced-order system frequency response model, where the aggregation is primarily weighted by the primary frequency regulation capability of the load, load capacity, and rotor kinetic energy. Finally, the accuracy and effectiveness of the proposed model are validated using the WECC 9-bus test system with power electronic sources, and the influence of load parameters on the frequency stability indicators is analyzed.

Abstract:The large-scale integration of renewable energy sources, such as wind power and solar power, into the power system has significantly transformed its characteristics. The issue of sub-synchronous oscillation (SSO) becomes increasingly prominent, severely impacting the system stability. As the wind turbines vary in structures and parameters, existing model-based SSO suppression approaches do not fully consider wind turbine differences and multi-mode oscillation frequencies. To address these issues, this paper proposes a decentralized SSO suppression controller for doubly-fed induction generator (DFIG)-based wind farms using periodic updating data-enabled predictive control (PUDeePC) approach. Firstly, to better adapt to the time-varying system and external disturbance, a periodic updating algorithm is proposed incorporating anomaly detection. The stability of the PUDeePC approach is theoretically validated, and its robustness to variations and disturbances is qualitatively analyzed. Finally, the effectiveness of the PUDeePC approach is revealed through numerical simulations under various conditions, including compensation level variation, wind power output variation, number of online DFIG variations, multi-mode SSOs, and asynchronous PUDeePC approach.

Abstract:Grid-connected systems with multiple self-synchronizing voltage source inverters (SSVSIs) (referred to as multi-SSVSI grid-connected systems for simplicity) are exposed to low-frequency oscillations (LFOs) and synchronous frequency resonance (SFR). However, the synergistic suppression of these two oscillation modes has not been achieved to date. Considering the dynamic characteristics of transmission circuits and power coupling characteristics, an improved power-frequency (P/ω) admittance model for multi-SSVSI grid-connected systems is established, reflecting the mechanism of LFOs and SFR, as well as the positive and negative effects of corresponding control parameters. In addition, an oscillation suppression method is proposed to enhance the system damping by adding virtual resistance control and transient virtual power feedback control, simultaneously suppressing LFOs and SFR. Unlike existing methods, the proposed method introduces virtual active power instead of real active power as the power feedback into the control loop, thus suppressing LFOs with a smaller transmission resistance and avoiding severe power coupling. Experimental results verify the effectiveness and superiority of the proposed method.

Abstract:The dynamics of diverse synchronization control, such as grid-following (GFL) and grid-forming (GFM) control, are complicating the oscillatory behaviors in multi-converter systems. In this context, the impedance network (IN) based frequency-domain modal analysis (FMA) method is useful for diagnosing oscillations. However, since the conventional impedance model retains only electric nodes, the FMA primarily reflects the circuit-related information, e.g., node participation factor, making it less intuitive for probing the synchronous dynamics. To address this issue, this paper proposes an augmented impedance network (AIN) modeling method by explicitly characterizing synchronous control loops for stability assessment. First, a four-port augmented impedance model (AIM) with an additional synchronization port is proposed for a generic AC/DC converter, and the corresponding AIN model of a generic AC/DC multi-converter system is formulated in a scalable approach. Then, the FMA method is generalized by simultaneously incorporating the electric nodes (including AC and DC nodes) and synchronous nodes. Finally, the AIN model and its associated FMA method are comprehensively validated in a typical point-to-point high-voltage direct current (HVDC) system and a modified IEEE 9-bus system, both with GFM and GFL converters.