High penetration of renewable energy is transforming modern power systems into low-inertia and weak-grid networks, where frequency and voltage no longer respond independently to active and reactive power disturbances. Under such conditions, the conventional decoupled paradigm, which assigns active power mainly to frequency regulation and reactive power mainly to voltage control, may overlook cross-channel interactions and lead to inaccurate security assessment. To address this problem, this paper proposes an analytical framework for quantifying frequency-voltage coupling strength and assessing the corresponding joint security region in renewable-dominated power systems. First, a quasi-steady-state linearized coupling model is established by integrating source-side regulation, load response, and network impedance characteristics. Based on this model, a frequency-voltage coupling matrix is derived to explicitly map active-reactive power disturbances to coupled frequency and voltage deviations. Then, the relative gain array theory is introduced to construct a dimensionless interaction factor for evaluating coupling strength and identifying strongly coupled buses. Furthermore, the coupled response is reformulated as a linear mapping problem, through which equal-power disturbance boundaries are transformed into frequency-voltage response trajectories and regions. Finally, prescribed frequency and voltage security limits are inversely mapped to the active-reactive power input space to obtain a joint input power perturbation security region. Case studies show that frequency-voltage coupling is more pronounced at load and passive connection buses and in weak-grid areas. Stronger coupling rotates the response trajectory, deforms the coupled response region, and compresses the security input power disturbance region.

The generalized load refers to the sum of all electrical equipment within the power supply scope of a substation, including traditional loads, new type loads, distributed power sources, distributed energy storage, etc. Its flexible components can be divided into three categories, pure load type, pure power source type, and energy storage type. The generalized load is gradually becoming a research hotspot at home and abroad. Power modeling of it is an essential part of the research on the new power system. In view of the problem that most current reviews are oriented towards the electrical models of loads, the research status of the power models of typical flexible components of the generalized load is reviewed and prospected in this paper. Firstly, the modeling methods of the flexible components of the generalized load are summarized, and the similarities and differences among white box, black box, and grey box models are elaborated from the modeling principles. Then, in the order of pure load type, pure power source type, and energy storage type, the power models of the most typical, widely used and numerous flexible components in each category are classified and reviewed as white box, black box, and grey box models, and then the differences among various models are comprehensively compared. Finally, the future research directions of the modeling of the flexible components of the generalized load in the new power system are prospected.

The increasing penetration of renewable energy exacerbates source-load uncertainties, posing new challenges to system stability and renewable utilization. To overcome the limitations of conventional reserve scheduling in managing such uncertainties, this paper proposes a short-term demand response resource (DRR) reserving strategy that improves renewable integration while ensuring operational security. An R-vine Copula-based probabilistic model is developed to quantity the interdependence of wind, photovoltaic, and load forecasting errors, thereby generating scenario sets reflecting realistic uncertainty characteristics. Decision behavior models for distribution system operators (DSOs) and load aggregators (LAs) are formulated to capture their strategic rationality considering the bidirectional nature of power fluctuations. An interactive decision framework is proposed to establish deterministic and uncertainty optimization models that address short-term uncertainty, multi-dimensional source-load dependencies and interactions among LAs and DSO. Simulation results validate the effectiveness of the proposed approach in improving economic outcomes for both DSO and LAs, while significantly mitigating power fluctuations caused by renewable uncertainty.

The high penetration of renewable energy presents significant challenges for the secure and economical operation of power systems. To address the uncertainty in power system operations, this paper proposes a novel integrated probabilistic forecasting and robust optimization (PFRO) method to solve a robust optimal power flow (ROPF) problem driven by prediction intervals (PIs). In order to better balance robustness and cost-effectiveness in robust optimization, the proposed PFRO approach defines uncertainty sets based on prediction intervals with explicit probabilistic interpretations. Then the boundaries of uncertainty sets can be adaptively adjusted via optimizing predictor parameters according to the subsequent decision-making of ROPF. Furthermore, the proposed PFRO approach reduces the conservativeness of ROPF and bridges the gap between forecasting and decision-making. To accurately capture the statistical characteristics of renewable generation, a similar dataset is constructed for training the forecasting model. The nonconvex integrated optimization problem is then transformed into a form that can be solved directly using a difference of convex algorithm (DCA). Numerical simulations based on two test systems and renewable energy generation data demonstrate the overall superiority of the proposed approach in terms of forecasting accuracy and operational value.

Net load profiles have become more volatile and sensitive to meteorological conditions due to the rapid increase in distributed photovoltaic (PV) penetration and the ongoing change in electricity consumption behavior. However, system operators cannot directly observe key components embedded in net load measurements, such as behind-the-meter (BTM) PV generation and temperature-sensitive load (TSL). This lack of observability limits accurate attribution of load variations and the assessment of dispatchable potential. Therefore, this paper proposes an unsupervised disaggregation method that relies only on net load measurements and exogenous meteorological inputs to simultaneously decompose net load into BTM PV generation, TSL, and base load (BL). The method is further designed to explicitly address the practical identifiability issue inherent in unsupervised joint disaggregation of multiple components from net load. Prior constraints on the relative peak magnitudes of TSL and BL are first derived from a linear model built with net load and meteorological data. A three-branch neural network with a scale-and-sum aggregation structure is then developed to estimate the three components using component-specific features and to reconstruct net load. The network is trained end-to-end using a regression loss between the reconstructed and observed net load. Case studies demonstrate that the proposed method yields more accurate estimates of BTM PV generation and more physically consistent estimates of TSL than existing unsupervised methods. It also demonstrates favorable practical identifiability by producing stable and reliable disaggregation results across repeated runs, while enabling accurate short-term forecasting of net load and all three components.

The rapid growth of renewable energy generation challenges the secure operation of power systems. It becomes crucial to quantify the critical security boundaries and hosting capability of renewable generation at the system operation level. This paper proposes a novel point-hyperplane geometry (PHG) method to accurately obtain the geometric expression of the operational security region of renewable energy generation for power systems. Firstly, the geometric expression of the operational security region is defined as a polytope of boundary hyperplanes in the form of inequalities satisfying the system operation constraints. Then, an orthogonal basis generation method is proposed to solve a single boundary hyperplane of the polytope based on intersecting and orthogonal geometric principles. Next, a point-hyperplane iteration algorithm is developed to progressively obtain the overall geometric polytope of the operational security region of renewable energy generation in power systems. Besides, the flexible performance trade-off can be achieved by modifying the proposed maximum tolerated angle between adjacent hyperplanes. Finally, comprehensive case studies verify the effectiveness and superiority of the PHG method.

The growing integration of intermittent renewables aggravates power imbalances between supply and demand, increasing the uncertainty of system frequency variations. Traditional deterministic frequency control schemes of ten overlook the impact of stochastic frequency fluctuations on system stability. This paper proposes an innovative stochastic stability-oriented model predictive control approach for system frequency regulation in the face of uncertainty of renewable generation. Firstly, a generic nonlinear stochastic dynamic model is established to precisely quantify time-evolutionary impacts of non-Gaussian uncertainty on system frequency dynamics. Subsequently, a high-order stochastic Koopman operator (HSKO) approach is developed by integrating high-order probabilistic forecasts with the Koopman theorem, serving as a powerful tool for global linearization of nonlinear stochastic dynamic models. Therefore, an interpretable optimal control law can be seamlessly derived in line with existing conclusions on stochastic stability identification, which originally breaks through the technical bottleneck of frequency stabilization for power systems with nonlinear stochastic dynamics. Comparative experiments with several state-of-the-art dynamic models and frequency control approaches demonstrate the superiority of the proposed HSKO approach in terms of model fidelity, control optimality, and frequency stability.

High renewable penetration has increased the demand for flexible frequency regulation resources in power systems. As an energy-intensive upstream sector of the photovoltaic manufacturing chain, the polysilicon industry has considerable frequency regulation potential. However, its reliable assessment is challenged by weak observability of production states and the lack of a clear sequential response mechanism. This paper proposes a method to assess the sequential frequency regulation potential of polysilicon loads under weak observability based on inverse optimization. First, a state-task-network-based process model is developed to describe the coupling between production states and electricity consumption. Then, an inverse-optimization-based state estimation model is constructed, in which typical disturbance scenarios are incorporated to enhance robustness. Finally, the continuous regulation potential and economic performance over multiple time intervals are evaluated by considering temporal coupling and response aversion costs. Case studies show that the proposed method yields regulation capacity estimates close to the theoretical upper bound under full-information conditions while satisfying production constraints, thereby demonstrating its effectiveness and economic viability.

The penetration of generalized energy storage re-sources (GESRs) in distribution systems is steadily increasing due to the ever-growing need for flexibility. Existing aggregate flexi-bility region (AFR) solution methods primarily employ a convex optimization-based paradigm, which cannot be applied to solve nonconvex regions. Hence, the charging-discharging mutual ex-clusivity of GESRs cannot be enforced. However, in high-pene-tration renewable energy (HPRE) power systems, state exclusiv-ity restrictions are often binding due to the occurrence of negative electricity prices. To effectively incorporate the state exclusivity of GESRs into the AFR, this paper proposes a novel region learn-ing method that can effectively calculate the projections of high-dimensional nonconvex polyhedrons. First, we propose a novel data generation method in which the label of each sample point can effectively perceive the margins of the AFR. Then, on the ba-sis of this dataset, we design and train a deep neural network (DNN) with a modified loss function to learn the mapping be-tween sampling points and the degree of margin deviation. Sub-sequently, we derive the AFR by analytically formulating the well-trained DNN, which consists of a union of disjoint convex polyhedrons. Finally, a novel simplification procedure is pro-posed to reduce the number of disjoint polyhedrons in the AFR. The case studies demonstrate that the proposed method can ef-fectively calculate the AFR while considering the state exclusivity of GESRs, thereby avoiding mismatched power and load shed-ding during disaggregation.

With the increasing proportion of power electronic devices (such as wind generators, photovoltaics, and HVDC systems) in modern power systems, the system dynamics are undergoing profound changes. A significant manifestation lies in the emergence of new oscillatory phenomena dominated by various power electronic devices. However, currently most studies on these oscillations are based on linearizing the nonlinear power system and applying linear system theory for analysis, with limited attention given to the influences of nonlinear components and stochastic fluctuations. In this paper, we show new oscillatory phenomena under the combined effects of power system nonlinearities and stochastic fluctuations, termed as multifrequency-band oscillations. System oscillations that exhibit linear system behavior and are traditionally analyzed via linearization approaches can be viewed as decoupled oscillations, while in contrast, we focus on multi-frequency-band coupled oscillations, where linear system theory loses efficacy. Furthermore, we explore how power system nonlinearities and stochastic properties influence multi-frequency-band coupled oscillations, and investigate the potential types of these oscillations and their respective triggering conditions. We demonstrate that system nonlinearities induce coupling among different frequency bands, and stochastic fluctuations significantly elevate the likelihood of these oscillatory phenomena. Finally, the validity of the analysis is verified through simulation.

Grid-connected power converters are ubiquitous in modern power systems, acting as grid interfaces of renewable energy sources, energy storage systems, electric vehicles, high-voltage DC systems, etc. Conventionally, power converters use multiple PID regulators to achieve different control objectives such as grid synchronization and voltage/power regulation, where the PID parameters are usually tuned based on a presumed (and often overly-simplified) power grid model. However, this may lead to inferior performance or even instabilities in practice, as the real power grid is highly complex, variable, and generally unknown. To tackle this problem, we employ a data-enabled predictive control (DeePC) to perform data-driven, optimal, robust, and adaptive control for power converters. We call the converters that are operated in this way DeePConverters. A DeePConverter can implicitly perceive the characteristics of the power grid from measured data and adjust its control strategy to achieve optimal, robust, and adaptive performance. We present the modular configurations, generalized structure, control behavior specification, inherent robustness, detailed implementation, computational aspects, and online adaptation of DeePConverters. High-fidelity simulations and hardware-in-the-loop (HIL) tests are provided to validate the effectiveness of DeePConverters.

This article rethinks the meaning, analysis, evaluation, and enhancement of system strength in power electronics (PE)-dominated power systems. It highlights why existing metrics intended for conventional power systems may fail to fully capture the voltage and frequency performance in PE-dominated power systems, underscoring the need for novel multidimensional strength metrics. We explore how emerging technologies [e.g., grid-forming (GFM) converters] contribute to enhancing system strength, and we highlight ongoing engineering practices worldwide aimed at strengthening power systems.

Power converters serve as grid interfaces of renewable energy generators, electric vehicles, etc., which have become one of the most crucial components in modern power systems. However, it has been frequently observed that converters may become unstable in practice, leading to sustained oscillations that could endanger power system operations. In this paper, we demonstrate that the converters' stability is largely affected by the so-called waterbed effects existing in dynamical systems. To be specific, there is a paradox between the system stability margin and its response speed (reference tracking performance) if the system satisfies certain conditions. We particularly investigate and compare the water bed effects of grid-following (GFL) and grid-forming (GFM) converters, which are the two prevailing types of converters now a days. One important finding is that the synchronization dynamics of converters are strongly affected by the waterbed effects, especially for GFL converters, where a high response speed can easily cause instabilities. Inspired by the mechanism and conditions of waterbed effects, we propose control design guidelines to alleviate the waterbed effects of power converters and therefore improve their stability.

High penetration of renewable energy generation (REG) presents severe uncertainties for power system operation. It is critical to quantify the accommodation level of REG in the nonlinear system operation model by calculating the geometry of the security region projection. This paper proposes a novel simplex rotating hyperpyramid (SRH) method to effectively obtain the geometric operational security region of REG based on the AC optimal power flow model. As a generalized convex geometry projection method, affine subspaces-based matrix operations are defined to simplify complex cross-dimensional geometric operations. Then, a rotating hyperpyramid is established as the basis tool of convex projection, which is conveniently constructed from a standard simplex. Based on the generated rotating hyperpyramid, a localized geometry construction method is proposed to achieve basic approximation components of the convex nonlinear region. Next, a dynamic global approximation iteration algorithm is developed to rapidly obtain the global geometric operational security region of REG. Comprehensive case studies demonstrate the effectiveness and superiority of the SRH method.

With massive integration of photovoltaic (PV) generation in power systems, multivariate probabilistic forecasting (MPF) is essential for analysis and decision-making of power systems, which provides comprehensive information about uncertainty of future PV generation. Traditional MPF methods separate probabilistic forecasting and dependency structure estimation, limiting their ability to generate multivariate distributions in an analytical form. This paper innovatively proposes a hybrid score-driven MPF method to directly generate semi-parametric joint predictive density of correlated PV generation using deep mixture density network. Firstly, an integrated framework of MPF based on multivariate Gaussian mixture models is established to unify the training of probabilistic forecasting and the optimization of conditional correlation modeling. Then, a novel hybrid score-based network loss function with the closed-form expression is meticulously devised for the robust training of MPF. In addition, graph structure learning is incorporated to adaptively capture spatial dependency among correlated PV generation. To address overwhelming parameters of joint distributions, a parameter-reduced structure of covariance matrices using incomplete Cholesky decomposition is formulated, which enhances the tractability of MPF in high-dimensional settings. Comprehensive case studies on three realistic PV power datasets are conducted to validate the superior performance of the proposed method for day-ahead multivariate probabilistic forecasting.

The large-scale integration of inverter-based resources (IBRs) has deteriorated the frequency/voltage (F/V) responses of power systems, leading to a higher risk of instability. Consequently, evaluating the F/V strength has become an important task in power electronics (PE)-dominated power systems. Existing methods typically examine F/V strength separately, employing fundamentally different metrics, such as inertia (focusing on device dynamics) and short-circuit ratio (SCR, addressing network characteristics). These fragmented approaches have resulted in a lack of comprehensive understanding of the overall system strength, potentially overlooking critical aspects. To address this problem, this paper proposes a unified framework for analyzing F/V strength. First, a unified modeling of F/V regulations is introduced. Then, based on modal decoupling, the power systems are decomposed into several eigen-subsystems, where the F/V responses are both decomposed into common-mode (CM) and differential-mode (DM) components, namely, CM-F, DM-F, CM-V, and DM-V. The CM-F and CM-V represent the collective response of all devices to external active or reactive power disturbances, independent of the power network characteristics. In contrast, the DM-F and DM-V capture the redistribution of disturbance power within the system, which is strongly influenced by the network topology and the locations of devices. Notably, traditional strength analysis generally ignores the CM-V (global voltage response), which, as discovered in this paper, may also become unstable in PE-dominated power systems. Based on the proposed framework, new metrics are proposed to evaluate the strength of each modal component. Finally, the effectiveness of the proposed approach is validated through simulations.

The growing uncertainty associated with renewable energy generation necessitates effective solutions addressing stochastic optimization of power system operations. Traditional stochastic optimization methods typically take scenario reduction as a preliminary step to alleviate computational burdens, which overlooks the connections between scenario reduction and stochastic optimization. This paper proposes a novel cost-oriented scenario reduction approach for stochastic optimal power flow (SOPF) to enhance the cost-effectiveness of operational decisions while maintaining system reliability. Firstly, an integrated scenario reduction and stochastic optimization (ISRSO) framework is established for SOPF, in which the reduced scenarios serve as a bridge between uncertainty quantification and uncertainty-aware optimization. Subsequently, a coordinated optimization model of scenario reduction and stochastic optimal power flow is formulated to jointly optimize the reduced scenarios and generation schedules, which preserves the probabilistic characteristics of the original scenarios and minimizes the operational cost of SOPF. Then, an alternating optimization algorithm is developed to convert the original nonconvex model into iterative convex problems with enhanced tractability. Simulation results on IEEE 14- bus and 118- bus test systems with realistic renewable energy generation data illustrate the statistical accuracy and cost-effectiveness of the proposed method.

The increasing proportion of renewable energy sources has promoted the widespread adoption of power electronic converters, which may elevate instability risks and pose new challenges to modern power systems. Traditional stability analysis methods (such as eigenvalue and impedance-based approaches) typically rely on linearized system models, and rarely account for the influence of nonlinear components, potentially leading to incomplete results. In this paper, we investigate the influence of the controller limiter on the stability of grid-following (GFL) converters. By employing the describing function (DF) method, we model the system’s nonlinear and linear components separately and analyze stability via the DF-based Nyquist criterion. On the basis, we further explore two potential oscillatory phenomena: sustained constant-amplitude oscillations and forced oscillations. We demonstrate that the presence of nonlinear components can lead to sustained oscillations in GFL converters, a phenomenon absent in linear systems. Furthermore, we explore the possibility of forced oscillations triggered by external sinusoidal disturbances during such sustained oscillations. In addition, a loop-shaping method accounting for system nonlinearity is proposed to suppress these sustained oscillations. Finally, the above analysis is validated through time-domain simulations.

With the increasing penetration of renewable energy, the secure and stable operation of power systems faces the challenge brought by renewable generation uncertainties. This paper proposes a truncated Gaussian mixture model (TGMM)-based analytical method to quantify the impact of renewable generation uncertainty on power system small-signal stability. The renewable generation uncertainty based on probabilistic forecasting is accurately modelled as a Gaussian mixture model. Then a piecewise affine transformation is developed to obtain the analytical piecewise mapping relationship between renewable generation injection and small-signal stability index output. Besides, a discrete integral method is proposed to derive the conditional distributions of renewable generation with regard to each subregion in the analytical form of TGMM. It is proved that one-dimensional TGMM exhibits truncated invariance. Thus, the probability mapping from renewable generation to stability index in each subregion is obtained by the truncated invariance of TGMM. Finally, the overall probability distribution of stability index is constructed analytically based on the probability distribution weighted fusion from different dimensional projections. The superior performance of the proposed method is verified by comprehensive case studies in the modified IEEE 39-bus system.

In recent years, an increasing number of electrical devices have been connected to the power grid through power electronic devices. As the scale of such devices continues to expand, their impact on overall load characteristics has gradually deepened, and the dynamic characteristics of the power system are also affected to a certain extent. To this end, based on the dynamic and static integrated model and simulation examples of power electronic interface loads, the impact of power electronic interface loads, model parameters, and the proportion of constant impedance and constant power loads on the dynamic characteristics of the system under two types of disturbances is analyzed.