The increasing integration of power electronic devices in modern power systems necessitates an accurate quantification of grid strength (GS). Conventional measures, such as short-circuit ratio (SCR)-based indices, fall short in capturing the nonlinear characteristics and voltage constraints inherent to power electronics. To overcome these limitations, we propose a novel GS measure to quantify the voltage support capability in multi-infeed systems with heterogeneous power electronic devices. Our approach begins with a quasi-equilibrium model to characterize the current injection behavior of power electronic devices. A grid characteristic function is then derived from the system's current balance equations. By leveraging Brouwer's fixed-point theorem, a sufficient condition for the existence of a quasi-equilibrium is established through the self-mapping property of the grid characteristic function. This condition yields a topology-independent critical value, effectively quantifying the voltage support capability of power electronics penetrated power systems. To compute the GS measure, we employ two complementary numerical methods: moment relaxation for rigorous bounds and interior-point optimization for computational efficiency, offering adaptable solutions for diverse scenarios. The effectiveness of the proposed method is validated through electromechanical transient simulations and comparative analysis on the modified IEEE 14-bus and 118-bus test systems, demonstrating improved accuracy and robustness over conventional SCR-based indices.

Power networks, while transmitting electromagnetic energy, also serve as channels for the propagation of both free and forced oscillations. To effectively understand and control these oscillations, it is crucial to model and analyze the dynamics of power networks, identifying potential oscillation risks. In this paper, we develop a matrix pencil-based dynamical model for general passive power networks, focusing on free and forced oscillation analysis. We discuss the underlying principles, model assumptions, and model formulation in detail. Specifically, the matrix pencil models for lumped-parameter transformers, distributed-parameter transmission lines, and the entire power network with arbitrary topology are comprehensively analyzed. The relationships between the dynamic model, the excitation source, network resonance, and the frequency-domain equivalent impedance are explored. Based on this model, an eigen-analysis method is developed to calculate critical modes, associated eigen-structures, and impedance. Comparative numerical results from the eigen-analysis method, analytical solutions, and EMT simulations are presented to validate the proposed approach.

With the rapid growth of renewable energy, new power systems are experiencing an increasing share of wind and solar generation. This shift reduces the system’s overall inertia and introduces greater variability, posing significant challenges for maintaining frequency stability. Traditional synchronous generators offer strong but sluggish frequency support, while renewables and energy storage systems respond more rapidly but often with constrained regulation capacity. These differences can lead to serious frequency fluctuations, especially under high renewable penetration. To address these challenges, this paper comprehensively reviews the frequency response characteristics of multiple energy resources, including thermal, hydro, wind, photovoltaic, load, and energy storage units. Moreover, the paper explores key control strategies such as deadband tuning and coordinated regulation, and discusses optimization approaches for system-level frequency support. The objective is to propose effective technical paths and parameter settings that support stable operation of power systems with high renewable integration. The findings aim to guide the development of frequency regulation frameworks for future renew-able-dominated power systems.

The dominant modes of the system can be described by the critical eigenvalues, which reflect the stability and stability margin. This paper proposes a dominant mode identification (DMI) method to assess the stability of the grey-box grid-tied converter. First, the analytical relationship between the eigenvalues and the transfer function is clarified based on the small-signal model. Furthermore, the critical eigenvalues are estimated by the system’s transfer function. On this basis, the discrete transfer function of the grey-box grid-tied converter is constructed utilizing the frequency sweeping technique. Finally, the critical eigenvalues are determined using the measured data based on the customized particle swarm optimization algorithm. The method can apply to different grid connection scenarios of converter-based components and is easy to implement. The DMI method can not only assess the stability margin of grey-box grid-tied converters in operation, but also predict the stability of black-box converters after being connected to the grid in the planning stage.

This paper tackles two pivotal challenges within Lyapunov-functional-based approaches to analyze and design power system damping control amidst communication time delays. The first challenge addresses the inadequacy of the reduced-order system model commonly employed in time-domain methods to accurately capture the stability of the original full-order system. By harnessing dissipativity theory, we introduce a model reduction technique coupled with a condition guaranteeing ϵ-exponential stability solely through the employment of the reduced closed-loop system model. This not only validates the use of model reduction strategies but also furnishes a theoretical underpinning for their application. The second challenge pertains to the computational complexity of nonlinear semidefinite programming problems encountered during the coordinated design of controllers. Rather than pursuing the global optimum, we advocate for a path-following methodology to systematically explore local solutions. This iterative algorithm enhances system damping and H2 performance by orchestrating automatic and coordinated adjustments to control parameters. Numerical experiments conducted on various benchmark systems underscore the efficacy of the proposed approach.

Electromagnetic transient (EMT) simulation is of fundamental importance for the design and operation of modern power systems. The solution of EMT models relies on numerical integration methods whose performance depends on the structure, scale, and stiffness of the system models. In this paper, we develop a synchronous generator model that maintains the underlying physical structure. In particular, a synchronous generator is represented as the interconnection of energy storage ports, dissipation ports, and external ports, leading to a canonical port-Hamiltonian system formulation. By exploiting the port-Hamiltonian structure, we introduce an energy-related invariant quantity for the developed model and construct a geometric numerical integrator based on the discrete gradient. This geometric numerical integrator can exactly maintain the energy-related invariant in the discrete-time solution. Numerical experiments verify the energy-preserving property of the proposed geometric. Comparative analysis with the Runge-Kutta method and the implicit trapezoidal method shows that, the energy-preserving geometric numerical integrator has better long-term numerical stability and accuracy especially at relatively large integration steps.

The calculation of the unstable eigenvalues without omission is vital in small signal stability analysis of power systems. In this letter, a quasi-exponential transform is proposed to compute all unstable eigenvalues with improved efficiency and accuracy. Numerical experiments on two public source systems, namely the Xingo6u and Juba5723 systems, show the effectiveness of the proposed method.

The detection and calculation of the rightmost modes are essential in the small signal stability assessment and control of power systems. This paper proposes an exponential transform based dual-layer Krylov subspace (DLKS) method for computing all unstable modes of power systems. Firstly, the exponential transform is introduced to map the unstable modes to the dominant modes outside the unit circle of the transformed spectrum. Then, based on the transformation, a Krylov decomposition is implemented to form the outer-layer Krylov subspace (OLKS) for solving the transformed dominant modes. In the process of forming the OLKS, the exponential matrix-vector multiplication (EMVM) needs to be solved. Next, combined with an accelerating convergence technique, the inner-layer Krylov subspace (ILKS) is formed to calculate the EMVM. Finally, four public source systems, namely the Xingo, Xingo6u, Juba5723 and Bauru5727 systems, are applied to verify the correctness and efficiency of the proposed method. Numerical experiments indicate that the proposed method can calculate all the unstable modes with high accuracy under the premise of ensuring calculation efficiency.

针对系统运行中临界短路比实际值伴随交流侧运行参数实时变化导致临界短路比经验值不够灵敏准确的问题,提出一种新能源临界短路比对电网运行参数灵敏度分析方法,以判断工程中常用临界短路比的准确性.首先,构建一种考虑静态负荷的交流侧戴维南电路数学模型和新能源临界短路比计算方法;然后,推导出新能源并网系统临界短路比对交流系统参数灵敏度分析方法;最后,通过算例分析表明负荷等参数变化对新能源并网系统临界短路比的计算值存在较大影响.所提方法弥补了临界短路比经验取值在系统实际运行中易因工况变化导致的指标不再灵敏准确的缺陷.

The loop impedance-based criterion (LIC) is a practical approach for studying the sub-synchronous oscillation (SSO) instability induced by converter-interfaced wind turbine generators (WTGs) via checking whether the resistance is positive or not. However, few existing works have discussed the background mathematical theory of such criterion. In this paper, a theoretical impedance solving method is raised based on a forced oscillation analysis method, which is efficient to obtain accurate impedance and can connects the state-space function, eigenvector and impedance inherently. Therefore, the applicability of LIC can be revealed in different stability regions from the viewpoint of the strict eigen-analysis based method (EBM). The general LIC stability criteria is then derived, and the conditions where LIC may cause misjudgment are discussed. Cases considering different operating scenarios are conducted to verify the proposed impedance calculation method and illustrate the connections and differences between LIC and EBM.

异步互联系统调频资源和备用容量的分割使得频率稳定问题突出,利用高压直流输电系统的附加频率控制(AFC)可以实现异步互联系统调频备用共享,参与系统频率调控.文中以改善异步互联系统整体的调频性能和频率质量为目标,研究基于直流两侧电网频率差进行无差控制实现异步互联系统准同步运行的直流AFC对两侧电网频率稳定性的影响.利用换流站交直流系统的功率平衡关系建立较为精确的高压直流输电系统线性化模型,得到异步互联两区域系统的负荷频率控制模型,以此进行特征分析指导AFC参数设计.多场景仿真结果表明,准同步运行的直流AFC在使两侧电网趋于同频运行的同时,能够适应两侧电网的容量自动调节直流功率,有效改善全系统的频率稳定特性.

In this paper, a novel multi-Cayley transform is proposed to judge the small signal stability of large-scale power systems. Firstly, the relationships among the Cayley transform, exponential transform, and proposed multi-Cayley transform are given. As an improvement of the exponential transform, since the multi-Cayley transform has well spectral performance, the unstable eigenvalues are easy to coverage. Then, because the direct calculations of the exponential matrix and vector (EM-V) multiplications are avoided, the calculation accuracy of the proposed method is improved. Furthermore, the efficiency is also enhanced owing to the reduction of the forward and backward substitutions and the avoidance of the EM-V multiplications. Finally, case studies on the Xingo6u and Xingo3012 systems show that compared with the exponential transform method, the calculation accuracy is improved by about three orders of magnitude and the calculation time is shortened by more than 80% when calculating the unstable eigenvalues without omission.

风电的大规模并网给电力系统带来了惯量降低和一次调频能力不足等问题,可减载运行且具备调频功能的风电场可有效应对该问题.为此,提出了一种风电场减载方案以及相应的一次调频策略.首先,介绍了综合惯性控制和桨距角控制的原理,并分析了风电场减载运行的必要性.然后,研究了不同风速下风机减载能力的差异性并制定了风电场内减载功率分配方案,根据制定的减载方案,提出了相应的一次调频策略,以充分利用风电场的调频能力并避免频率的二次跌落.最后,基于Matlab/Simulink搭建了仿真系统模型,仿真结果表明所述减载方案和调频策略可以合理分配减载功率并提升风电场的调频效果.

风机通常采用惯量控制参与调频,而在退出调频时容易引发频率二次跌落问题.为此,提出了一种风机调频退出时刻的确定方法.首先由状态空间法,推导了研究所需的系统模型.然后以风机调频退出时刻为分界,得到了适用于频率动态分析的分段线性化模型;以提升频率二次跌落对应的频率最低值为目标,建立了优化模型,并给出了求解算法.基于Matlab/Simulink搭建了仿真系统模型,仿真结果验证了所建立分段线性化模型的准确性和退出时刻的合理性.

风电场基于下垂控制参与系统一次调频时,参数整定不当可能引发机组转速保护动作进而带来频率二次跌落问题.为此,提出了一种避免频率二次跌落的风电场一次调频功率分配方法.首先结合下垂控制的响应过程分析了转速保护动作带来频率二次跌落问题的物理机理,然后基于转速及功率约束条件提出了风电机组调频功率评估方法,进而得到风电场的调频功率评估方法和风电场一次调频功率分配方法.基于Matlab/Simulink搭建了含有风电场的仿真模型.仿真结果表明,所提方法可充分发挥风电机组的调频能力,并避免频率二次跌落问题.

Time delays are inevitable in load frequency control (LFC) of the power system, especially in a deregulated system where open communication networks are more favorable than the dedicated ones. However, extensive delays may affect the stability of a system. In this paper, an exact frequency-domain method for calculating the delay margin of LFC systems is presented, which is likely to be used to assess a system's stability caused by time-delays and guide the controller design. Firstly, a dynamic model of load frequency control systems is established, described by delay differential and algebraic equations (DDAEs). The Rekasius substitution is then employed to eliminate the transcendental terms in the characteristic equation without making any approximation. Afterward, an eigenvalue perturbation theory is introduced to transform the problem of calculating the delay margin into solving a series of one-dimensional nonlinear equations. Since only equivalent transforms are involved in the whole process, the delay margins obtained by the proposed method are exact. Finally, a two-area and a three-area deregulated LFC systems are applied to verify the correctness and efficiency of the proposed method.

This paper introduces a novel cascading frequency regulation scheme (CFRS) for VSC-HVDC to provide strong support for the connected weak AC grid without phase-locked loop and remote-communication considering the cost-effective property. The proposed CFRS utilises a DC voltage synchronisation control to enable the self-synchronisation of VSC-HVDC without phase-locked loop, while the corresponding inertia response can be exerted via utilising the stored HVDC capacitor energy. Meanwhile, the DC voltage acts as the reflection of system frequency, enabling the coordination between two-end VSC stations without communication. More importantly, to fully utilise the VSC-HVDC potentials, the CFRS that sequentially activates HVDC capacitor and primary frequency control is implemented so that the energy loss and the detrimental control impacts on the sending-end systems can be minimised while making sure the requirement of system frequency support. Analytical derivations have been done to evaluate the contribution of the proposed CFRS to system frequency regulation. Furthermore, the effectiveness of the proposed scheme has been well validated in PSCAD/EMTDC under several power system contingencies by fully comparing with existing control schemes. The proposed CFRS stands out by the reduced complexity of the control structure, the robustness for connecting the very weak AC grid and the fast frequency regulation ability with consideration of cost-effective property.

In this paper, the holomorphic embedding power flow method (HELM) is designed to solve the AC/DC hybrid power flow equations. According to the power flow model of the high voltage direct current systems (HVDC), an appropriate embedding technique with three recursive algorithms is developed for three different control modes, which is compatible with existing achievements of HELM for AC systems. In this method, the advantages of HELM, such as non-iterative, deterministic and non-ambiguous, are fully retained. In addition, a new calculation strategy based on Bauer's Eta algorithm is designed for the implementation of Pade approximations and the recursive process to avoid redundant calculations without reducing accuracy. In order to verify the reliability and effectiveness of the proposed extended HELM, several power flow cases with different scale are studied by HELM and traditional iterative method.

With the rapid development of DC asynchronous interconnection, in order to ensure the frequency quality, higher requirements are put forward for the primary frequency control of hydropower units. In the high proportion hydropower system, it is difficult for the governor parameters to meet the requirements of primary frequency control and dynamic stability simultaneously. In order to solve the problem, this paper proposes a recommended parameter switching method by referring to the Nordic system. The parameter optimization methods before and after switching are proposed, and the effectiveness of the method is verified by time domain simulation.

风电机组提供频率响应后,转子转速恢复过程可能导致的频率二次跌落是制约风机提供向上调节能力的关键问题.文章对云南电网风机转子动能控制展开研究,提出风机转子动能控制参数整定方法,在扰动初期利用综合惯量控制快速抑制频率变化率,减小最大频率偏差;在扰动中后期与水火等常规同步机组和直流频率限制器(frequency limit controller,FLC)协调配合,避免频率二次跌落问题,实现频率整体动态过程的优化.仿真研究表明,增加虚拟惯性控制系数Kdf,不利于改善频率最大偏差,会让频率在进入直流FLC死区后出现严重超调和反调现象;下垂控制系数Kpf是改善频率最大偏差和直流FLC动作量的关键,Kdf和Kpf取值相同时,运行在最大功率追踪区的风电机组改善频率最大偏差的能力几乎相同.