As power systems transition toward Inverter-Based Resources (IBRs), grid dynamics are increasingly governed by the discrete control logic of Virtual Synchronous Generator (VSG) inverters rather than the continuous physics of synchronous machines. A critical observability gap exists during Fault Ride-Through (FRT) events, where VSG inverters instantaneously switch from voltage-regulating to current-limiting modes, introducing hybrid dynamical non-linearities that destabilize conventional estimators. While recent approaches have addressed mode identification, they often rely on sliding windows that introduce detection latencies incompatible with next-generation setting-less protection schemes. This paper proposes a recursive Interacting Multiple Model Unscented Kalman Filter (IMM-UKF) tailored for sub-cycle detection of VSG mode transitions. Unlike existing works, this framework explicitly incorporates negative-sequence dynamics to maintain observability during asymmetrical faults.

The significance of system inertia, especially its non-uniform spatial distribution, is becoming paramount in the power system. The scope of inertia estimation has traditionally been the estimation of overall or total system inertia. However, as frequency dynamics become increasingly localized with the increasing penetration level of inverter-based resources (IBRs), the need for higher spatial resolution (geographically localized estimation) and faster temporal resolution (online or continuous estimation) in inertia estimation becomes paramount. This paper proposes an analytical method to estimate the spatial inertia distribution down to the transmission bus level, i.e., nodal inertia. Depending on data availability, the proposed method is flexible and can be used in two ways: (1) to estimate nodal inertia under any given operating condition (or snapshot), or (2) to continuously estimate nodal inertia under both ambient and transient conditions using available measurements from local phasor measurement units (PMUs). The novelty of the proposed method lies in its analytical formulation, which does not require rate of change of frequency (ROCOF) measurements or rate of change of power injections, making it immune to the noise associated with the estimation of these derived quantities. Additionally, the proposed method does not require defining near-zero ROCOF thresholds, which is a system-specific and nontrivial problem. The proposed method is mode-agnostic, which makes it more general than the dominant mode-based linearized methods. The applicability of the proposed method is demonstrated through simulation studies performed on the IEEE 39-bus and IEEE 68-bus test systems with varying penetration levels of IBRs. The robustness of the proposed method is numerically assessed against modeling and measurement uncertainties.

Studying the dynamics and stability of inverter-driven power systems has become a top priority for grid operators in view of the massive renewable energy deployment. The simplest and most widely used model for stability analysis for such networks is the single-inverter single- bus (SISB) equivalent model. Although quite insightful, SISB models with an L-filter for the inverter suffer from implementation difficulties due to algebraic loops. This paper develops a closed-form SISB model for grid-following (GFL) and grid-forming (GFM) inverters and derives symbolic formulation for the linearized system, which resolves algebraic loops and obtains fast results with uncompromised precision. This model is then used in an N-Dimensional Stability Boundary Tracking (ND-SBT) algorithm, which identifies the stability boundary for GFL and GFM inverters. This is the first method to infer the stability region for an arbitrary number of dimensions in a computationally efficient and software-agnostic manner while preserving accuracy. A detailed sensitivity analysis yields useful findings on the stability impact of individual parameters, while the results are validated using the IEEE 14- bus system.

Traditional photovoltaic (PV) forecasting algorithms rely heavily on historical generation data or physical models, both of which are frequently unavailable or unreliable in practice. This paper addresses this challenge by proposing an online learning-based mutually-aided state estimation and forecasting (MASEF) algorithm, which integrates state estimation (SE) and PV forecasting into a coupled stochastic system and operates effectively without site-specific historical PV generation data or physical models. Inspired by the Kalman filter (KF), a mutually-aided online learning loop is established in the MASEF algorithm: a Bayesian neural network (BNN) approximates PV generation (prediction stage), which allows SE to refine the system state (update stage). These estimates are then fed back to the forecaster for online learning. The BNN further enhances reliability by providing probabilistic outputs and quantifying uncertainty. The forecasted values serve as pseudo measurements, which are critical in scenarios with limited observability or noisy data. Case studies demonstrate that the MASEF algorithm achieves performance competitive with state-of-the-art algorithms even in the complete absence of PV generation data or physical models. Furthermore, the results confirm the robustness of the MASEF algorithm to measurement noise and parameter inaccuracies, highlighting its adaptability and practical applicability in diverse power grid environments.

Power system state estimation (PSSE) is critical for accurately monitoring and managing electrical networks, especially with the increasing integration of renewable energy sources (RESs). This review aims to explicitly evaluate and compare state estimation techniques specifically adapted to handle RES-related uncertainties, providing both theoretical insights and clear practical guidance. It categorizes and analytically compares physical-model-based, forecasting-aided, and neural network-based approaches, summarizing their strengths, limitations, and ideal application scenarios. The paper concludes with recommendations for method selection under different practical conditions, highlighting opportunities for future research.

Virtual synchronous generators (VSGs) imitate traditional synchronous generators to provide virtual inertia and damping for inverter-based resources. The emulated damping relates to the power synchronization, therefore, has a major impact on system stability. Although various damping methods exist, phase-locked loop (PLL) integration is particularly concerning, as it is a key component in grid-following (GFL) control but now is being applied to grid-forming (GFM). This paper analyzes the typical VSG control and PLL damping unit by mapping stability boundaries and feasibility range. The boundaries are mapped in two dimensions to determine the relationship between the control parameters and the grid impedance. A comprehensive sensitivity analysis of controller parameters for VSG stability is conducted, drawing parallels with the equivalence of droop-based GFM stability. Finally, the boundary analysis is verified by time-domain simulation results and demonstrates the reliability of damping-switching method.

Power system state estimation (PSSE) is a critical tool for power system operation. Load/generation profiles are essential for performing accurate PSSE, and enable PSSE algorithms to handle errors in real and pseudo measurements. The classic approach of modelling the measurement error in PSSE is applying the mixture reduction algorithm to Gaussian mixture models (GMMs) fitted to existent load/generation profiles. However, this approach has inherent limitations in the mixing process. We propose a novel algorithm based on grey relational analysis (GRA) to derive a smaller load/generation profile from the original extensive profiles based on the forecast results of the next day. Our algorithm addresses the issues of mixture reduction and is applied before mixture reduction to improve PSSE accuracy. A case study is presented to evaluate the performance of the proposed algorithm in improving the accuracy of PSSE.

Nonlinear excitation controllers for power systems are considered as promising replacements for their linear counterparts, such as power system stabilizers (PSSs). However, Lyapunov based nonlinear controllers currently available in literature have been derived using simplified third order machine dynamics and have not been tested on realistic power system models, and the costs associated with these controllers have also not been studied. The paper aims to assess the performance of existing Lyapunov controllers for a detailed benchmark power system model. Two new Lyapunov based nonlinear controllers have been derived using IEEE recommended subtransient machine model, and their performance and costs have been compared with existing methods. The controllers have been evaluated using metrics for both small signal stability and transient stability. It has been proven theoretically (via stability analysis) and demonstrated via simulations that proposed Lyapunov controllers are more viable options for control of power system oscillatory dynamics. It has also been demonstrated that detailed subtransient model is required for accurate estimation of states via dynamic state estimation for use in the realization of Lyapunov controllers.

Electric vehicles (EVs) are a valuable means of reducing our reliance on traditional fossil fuel based transportation. In recent years, the market share of EVs is increasing, which raises some important questions: what is the impact of EVs on the electrical load of our electricity distribution systems, and how can we adequately model it? Some researches have been done to model the EV loads and influence, but they are limited in applications due to complexity and requirements of data. This paper proposes a model for EV loads which takes into account diversity of EV loads and difficulties in applications, and provides analysis of the EV loads in modern and future grids. Efficacy of the proposed model has been demonstrated using real EV-datasets, which provides valuable statistical analysis.

Electric vehicles are a new and upcoming technology in the transportation and power sector. The US Energy Information Administration states that the world has an adequate crude oil supply until about 2050. Basically, electric vehicles are expected to enter the world market such that by 2030, they will make up 10% of the vehicles being used. The most expensive part of an electric vehicle is the battery, and its charging and maintenance need to be taken care of. The major challenges while adopting EVs as an alternative to the fuel vehicles are the charging problems as it varies from one charger to another. Since the advent of electric vehicles, the need for electric chargers and new techniques for a sustainable solution has grown tremendously. The dead batteries are now getting replaced by the charging batteries. In this paper, we have attempted to improve the performance of the electric vehicle chargers by designing and simulating the same on the MATLAB. For this work, three converters, i.e. buck–boost converter, Cuk converter and Sepic converter, have been considered and designed using different methods such as PWM techniques, using PID and by implementing fuzzy logic techniques. The results have been compared, showing an improvement in their performance all of which has been reported in this paper.

Dynamic state estimation (DSE) accurately tracks the dynamics of a power system and provides the evolution of the system state in real-time. This paper focuses on the control and protection applications of DSE, comprehensively presenting different facets of control and protection challenges arising in modern power systems. It is demonstrated how these challenges are effectively addressed with DSE-enabled solutions. As precursors to these solutions, reformulation of DSE considering both synchrophasor and sampled value measurements and comprehensive comparisons of DSE and observers have been presented. The usefulness and necessity of DSE based solutions in ensuring system stability, reliable protection and security, and resilience by revamping of control and protection methods are shown through examples, practical applications, and suggestions for further development.

Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time-synchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving the way for developing the next generation of energy management systems and novel system monitoring, control and protection tools to achieve better reliability and resiliency.

This chapter presents an interpolated discrete-time Fourier transform-based method for estimating the parameters of analogue voltages and currents which are measured at a bus in a power system using a voltage transformer and current transformer, the parameters being the means and variances of the magnitude, phase, and frequency of the sinusoidal voltage or current signal. Estimating these parameters in real-time is used for monitoring, protecting, and estimating the power system. A detailed derivation of the mathematical expressions for these parameters is also presented. The estimation method has been demonstrated for one of the generating units of an example test system.

This paper presents a new method for estimating the rate of change of frequency (RoCoF) of voltage or current signals measured using instrument transformers. The method is demonstrably superior to currently available methods in the literature, in terms of estimation latency and estimation error. The estimation is performed in two steps. In the first step, the analog voltage or current signal obtained from an instrument transformer is statistically processed using interpolated discrete Fourier transform (IDFT) in order to obtain the means and variances of the signal parameters. These means and variances are then given as inputs to the second step, in which Kalman filtering (KF) is used to find the final RoCoF estimate. Accurate mathematical expressions for the means and variances of signal parameters have been derived and used in the second step, which is the main reason behind the superior performance of the method. The applicability of the method has been demonstrated on a benchmark power system model.

This paper summarizes the technical activities of the Task Force on Power System Dynamic State and Parameter Estimation. This Task Force was established by the IEEE Working Group on State Estimation Algorithms to investigate the added benefits of dynamic state and parameter estimation for the enhancement of the reliability, security, and resilience of electric power systems. The motivations and engineering values of dynamic state estimation (DSE) are discussed in detail. Then, a set of potential applications that will rely on DSE is presented and discussed. Furthermore, a unified framework is proposed to clarify the important concepts related to DSE, forecasting-aided state estimation, tracking state estimation, and static state estimation. An overview of the current progress in DSE and dynamic parameter estimation is provided. The paper also provides future research needs and directions for the power engineering community.

This chapter presents a control scheme for the decentralized control of power system dynamics. The scheme utilizes dynamic state estimation (DSE) using local measurements and machine parameters and employs the concept of pseudoinputs for decentralization. The method is based on the extended linear quadratic regulator (ELQR) and adapts in real-time to varying operating conditions of the system. The method is also computationally feasible and easily implementable. Using an example test system, it has been shown that the integrated scheme of DSE and ELQR can be utilized for dynamic estimation and control of small-signal dynamics of power systems in a decentralized manner, and it has several advantages over other linear control methods.

This chapter provides a basic conceptual guide to power system modeling, simulation, and control design, illustrating the ideas through application on an example test system. A power system is a large-scale complex network of components spread over a wide geographical region. Hence, building its physical prototype is prohibitive, and modeling and simulation have been the common practice for studying its operation and behavior. The chapter begins with a discussion of dynamics of power system components, which are primarily responsible for influencing the overall system dynamics and used to build their dynamic models. Next, the overall dynamic behavior of the power system is analyzed through simulations of the integrated model. The chapter concludes with a discussion about the basics of control design frameworks for designing an economic, practical, and efficient methodology for controlling the system's oscillatory dynamics.

In this chapter a nonlinear control scheme is presented for decentralized control of power system dynamics. The method uses an optimal control law, which has been derived in the general framework of nonlinear control using normal forms. This is done by first modeling the subtransient dynamics of power systems in a normal form and then deriving the optimal control law using the obtained normal form. Asymptotic stability of the whole system under the derived control has been proved. The control method utilizes dynamic state estimates as inputs. It is demonstrated using simulations on an example test system that the method can be used to ensure both transient stability and small signal stability of power systems.

This chapter presents various linear and nonlinear optimal control theories which can be used for power system control. A control scheme has been presented for the optimal control of a special case of linear time-invariant (LTI) systems in which both normal and exogenous inputs are present. The scheme is termed extended linear quadratic regulator (LQR), and it is shown to be significantly more cost-effective than other LQR schemes. The applicability of the scheme has been shown on a simple model LTI system. Nonlinear control theories which are used for power systems have also been briefly discussed, with the focus on normal form-based nonlinear control. Most important definitions and results of normal form-based control have been discussed.