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Real-time electricity price forecasting affects both the interests of power companies and the stability of power systems. Although deep learning models have achieved rich results in forecasting, due to the variable temporal characteristics and numerous influencing factors of real-time electricity prices, it is difficult for general deep learning models to extract electricity price features with obvious regularity, which affects forecasting accuracy. To solve this problem, this paper proposes an attention mechanism multi-size depthwise convolutional long short-term memory neural network (AM-MDC-LSTM) for predicting real-time electricity prices. The model improves prediction capability in the following aspects. 1) Using an attention mechanism to adaptively assign weights to electricity price time series and electricity price exogenous variables (production, consumption, electricity prices in neighboring regions) to improve electricity price feature extraction efficiency. 2) Using convolution kernels of different sizes to convolve individual electricity price exogenous variables one by one to extract local burst and global periodic electricity price features with obvious regularity. This is then combined with long short-term memory networks to extract temporal features reflected in electricity prices. Experimental results conducted in the Nordic and PJM electricity markets demonstrate that the proposed model outperforms other models discussed in the paper, exhibiting higher prediction accuracy.

The presence of multiple high voltage direct current (HVDC) systems in close proximity creates voltage-related cascading risks that are not adequately addressed by conventional grid-partitioning. This paper proposes an improved partitioning scheme to mitigate these new risks in addition to conventional objective of preventing parallel power flow from transferring adversely. Unlike classical partitioning approach, which relies solely on either optimization or clustering, our proposed bi-level architecture includes an additional HVDC clustering before optimization. However, this paper innovatively reveals that the distribution of correlation data to be used in clustering is non-Euclidean due to unusual equivalent reactance different from the normal operating condition, resulting from HVDC station's reactive power control. This non-Euclidean distribution makes heuristic clustering algorithms infeasible. To address this issue, an alternative solution is proposed to embed the correlation data into a dimension-reduced eigenspace spanned by selected eigenvectors, allowing clustering to be performed. The optimization implementing other objectives inherits the results of HVDC clustering as constraint, and the graphic betweenness weighted by power flows is presented to promote efficiency. Our proposed scheme is validated using cases studied in modified IEEE 118-bus benchmark system and practical regional grid, demonstrating its effectiveness in mitigating cascading risks in multi-infeed HVDC systems.

In a grid with PMSG-based wind farms, a lack of system strength can cause severe converter-driven instability issues, such as subsynchronous oscillation (SSO). Cyber adversaries can target the wind farm by maliciously changing the system strength observed from the power grid, triggering SSO, and further causing power outages and equipment damage. To understand the threat, this paper proposes a new model of cyber attacks targeting the system strength. Considering the common mitigations required by the operator's regulations, this paper demonstrates that the proposed attack model can trigger rapid SSO propagation by (i) simultaneously compromising the system strength provision for multiple wind farms or (ii) directly disrupting local system strength mitigation. Based on the developed attacks, this paper also presents an anomalous command verification (ACV) module incorporating a novel converter-driven stability assessment. The ACV module is designed to estimate the system strength buffer capacity in response to malicious tripping commands and indicate how close the system is to converter-driven instability. The impacts of attack-triggered SSOs are demonstrated by electromagnetic transient (EMT) simulations on the New England 39-bus system. The considered case studies validate the effectiveness of the proposed converter-driven stability assessment to detect malicious commands targeting the SSO in a timely manner.

A model predictive control (MPC) method for enhancing post-fault transient stability of grid-forming (GFM) inverter-based resources (IBRs) is developed in this paper. This proposed controller is activated as soon as the converter enters into the post-fault current-saturation mode. It aims at mitigating the instability arising from insufficient deceleration due to current saturation and thus improving the transient stability of a GFM-IBR. The MPC approach optimises the post-fault trajectory of GFM IBRs by introducing appropriate corrective phase angle jumps and active power references where the post-fault dynamics of GFM IBRs are addressed. These two signals provide controllability over GFM IBR's post-fault trajectory. This paper addresses the mitigation of oscillations between current-saturation mode and normal mode by forced saturation if conditions for remaining in the normal mode do not hold. The performance of the proposal is tested via dynamic simulations under various grid conditions and compared with other existing strategies. The results demonstrate significant improvement in transient stability.

False data injection (FDI) cyber-attacks on power systems can be prevented by strategically selecting and protecting a sufficiently large measurement subset, which, however, requires adequate cyber-defense resources for measurement protection. With any given cyber-defense resource, this paper proposes a preventive-corrective cyber-defense strategy, which minimizes the FDI attack-induced region in a preventive manner, followed by maximizing the cybersecurity margin in a corrective manner. First, this paper proposes a preventive cyber-defense strategy that minimizes the volume of the FDI attack-induced region via preventive allocation of any given measurement protection resource. Particularly, a sufficient condition for constructing the FDI unattackable lines is proposed, indicating that the FDI cyber-attack could be locally rather than globally prevented. Then, given a non-empty FDI attack-induced region, this paper proposes a corrective cyber-defense strategy that maximizes the cybersecurity margin, leading to a trade-off between the safest-but-expensive operation point (i.e., Euclidean Chebyshev center) and the cheapest-but-dangerous operation point. Simulation results on a modified IEEE 14 bus system verify the effectiveness and cost-effectiveness of the proposed preventive-corrective cyber-defense strategy.

Power utilities worldwide are facing a growing number of customers’ requests to authorize the interconnection of behind-the-meter distributed generation. This paper presents a new practical methodology for power utilities to estimate the amount of small-scale distributed generation they can accommodate in the low-voltage level of distribution feeders without potential harm to the latter. It considers both medium-voltage and low-voltage levels limiting criteria to determine the locational hosting capacities. The proposed method uses detailed models of distribution feeders extracted from the geographical information system of power utilities and the location of existing customers. A new tool based on the proposed methodology is also described in the paper to show how the methodology can be easily integrated into existing planning tools of power utilities. It reports the circuits’ total hosting capacity and provides hosting capacity maps with results per medium-voltage feeder section, distribution transformer, and low-voltage system. Results for real large-scale distribution feeder models demonstrate the practicality and potential of this methodology.

This article proposes a taxonomy of power converter control schemes based on the recently proposed concept of complex frequency. This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus voltages and current injections. The paper derives the analytical expressions of the link between complex power variations and complex frequency of each converter controller as well as the identification of critical control parameters. The main contribution of this work is to provide a general framework that allows classifying converters synchronization mechanisms and controllers. This framework also allows comparing converters with synchronous machines. To validate the theoretical results, extensive simulations are performed using a modified version of the WSCC 9-bus system. Examples of how the theoretical formulations of the paper can be used to improve power converter control in power system applications are showcased.

This paper suggests a novel non-linear synergetic control for a unified power flow controller (UPFC). UPFC is a member of flexible AC transmission system devices, that controls power flow and regulates the voltage by enhancing the transient stability of the power system. UPFC comprises of two voltage source converters (VSCs). Equations of VSC are inherently non-linear. In this paper, we propose a non-linear approach to control the UPFC based on the synergetic control technique. It is simple to implement and valid for a variety of operations. It is also effective in suppressing inter-area oscillations. To verify the effectiveness of the proposed controller, various case studies are simulated and the results are compared with the traditional linear and non-linear controllers.

Increased penetration of renewable energy sources (RES) has brought challenges to load modelling techniques. This paper proposes a synthesis load model with RES (SLMR), and elaborates related industrial practice conducted by China Electric Power Research Institute. Several practical issues are addressed in designing and implementing SLMR, such as load survey and representation of different types of RESs. Besides, three new modelling concerns brought by RESs are novelly addressed in the paper, i.e., aggregation of various RES parameters, consideration of various RES terminal voltage, and additional line loss due to RES response. Parameterization of the SLMR calibrates widely varied node voltage in distribution grid, and aggregates them to one equivalent node. The proposed SLMR is practically applied in industrial works, which is demonstrated in the paper.

With the increasing deployment of distributed energy resources (DERs), dispatching DERs subject to operational constraints in distribution networks draws much attention. One challenge is the non-convexities in 1) system-wide AC power flow constraints and 2) the individual complementarity constraint of energy storage. To resolve this challenge, this paper studies an AC-feasible linear model in distribution networks with energy storage, including its formulation, analysis, and applications. First, an AC-feasible linear model is formulated as a set of linear constraints on controllable DERs and uncontrollable power demand by 1) converting the non-convex system-wide constraints into linear constraints based on the Brouwer's fixed-point theorem and the second-order Taylor expansion, and 2) replacing the non-convex individual complementarity constraint of energy storage with one properly designed linear constraint. Furthermore, to analyze the power demand level at which the proposed linear model can provide a solution, this paper proposes an examination-based projection method under the Monte Carlo framework to handle projections of thousands of dimensions from linear constraints over time periods. Finally, the potential applications of our AC-feasible linear model are discussed. Numerical experiments are conducted in the IEEE 33-bus and 136-bus test systems to demonstrate the effectiveness of the proposed methods.

Battery energy storage system (BESS) can effectively mitigate the uncertainty of variable renewable generation. Degradation is unpreventable and hard to model and predict for batteries such as the most popular Lithium-ion battery (LiB). In this paper, we propose a data driven method to predict the battery degradation per a given scheduled battery operational profile. Particularly, a neural network based battery degradation (NNBD) model is proposed to quantify the battery degradation with inputs of major battery degradation factors. When incorporating the proposed NNBD model into microgrid day-ahead scheduling (MDS), we can establish a battery degradation based MDS (BDMDS) model that can consider the equivalent battery degradation cost precisely with the proposed cycle based battery usage processing (CBUP) method for the NNBD model. Since the proposed NNBD model is highly non-linear and non-convex, BDMDS would be very hard to solve. To address this issue, a neural network and optimization decoupled heuristic (NNODH) algorithm is proposed in this paper to effectively solve this neural network embedded optimization problem. Simulation results demonstrate that the proposed NNODH algorithm is able to obtain the optimal solution with the lowest total cost including normal operation cost and battery degradation cost.

Carbon-capture-utilization-and-storage (CCUS) system plays a critical role in the process of decarbonization. This paper proposes a cooperative operation model for a CCUS-based thermal power plant and distributed energy resources. The critical purpose is to achieve a higher profit and flexibility together with a lower carbon emission for the CCUS system under the electricity, carbon, ancillary services, and synthesis fuel markets. First, to enhance the operational flexibility in various markets, a critical focus of this paper is on elaborating feasible operation domain of the CCUS system through identifying the physicochemical processes associated with carbon dioxide (CO2) treatment and multi-energy conversion. Second, a Nash-bargaining framework is developed to describe how the CCUS works with distributed energy resources cooperatively to consume cheap and clean renewables to treat CO2. Third, to solve the cooperative operation problem efficiently and accurately, an adaptive sequential cone programming (ASCP) method together with a progressive hedging variant of the Benders decomposition (PH-BD) algorithm are designed. Case studies indicate the total revenue of the thermal power plant under the cooperative mode is improved by up to 8.85% and 66.53% compared with the individual mode with and without the CCUS. Further, the solution quality and efficiency of proposed methods are verified.

The uncertainty of electricity prices poses a challenge to all market participants as their decisions highly depend on the accuracy of price forecasts. Prediction intervals become an efficient method to quantify the uncertainties that reside in electricity price forecasts. In this paper, we propose a probabilistic electricity price forecast with optimal prediction interval method that considers both reliability and sharpness requirements. Taking reliability and sharpness into account, we ensure the prediction interval has a narrow width without sacrificing reliability. In the proposed method, the quantile regression is utilized to estimate the upper and lower bounds of the prediction intervals to avoid electricity price distribution assumption. In addition, the extreme learning machine (ELM) method is embedded in the forecast method to capture the nonlinear relationship within price data, and its tuning parameters are optimized using the augmented Lagrangian relaxation method in this paper. The effectiveness of the proposed probabilistic forecast method is demonstrated using data from various electricity markets.

High Voltage Direct Current (HVDC) can quickly vary its power to damp power system angle oscillation. To handle the uncertainties of the faults and the system model, it is necessary to estimate the real-time linearized model of the AC/DC Hybrid system. This leads to two problems: Firstly, after the fault, the HVDC will quickly evolve to a steady state and, therefore, result in an unobservable control matrix. Secondly, the HVDC power should not exceed its stable range limited by the post-fault system. To address the above issues, the main novelties are as follows: First, this paper proposes a novel system identification method to handle that case when there is no control input excitation. Second, this paper presents a control strategy that fully considers the real-time stability constraints of the HVDC. More specifically, this paper estimates the system matrix and the control matrix separately. Based on the linearized model of the AC/DC hybrid system, the control matrix is calculated using the sensitivities of the active powers of the generators concerning those of the HVDC. Then, the system matrix is estimated using measures of the power angle and frequency. Finally, by processing the local voltage and current measurements, the system-side Thevenin equivalent parameters on the HVDC connecting point are estimated in real time and the regulating bound of the HVDC is determined. According to the linearized model and the HVDC power bound, a model predictive control strategy is used to damp the oscillation. Simulation results reveal the effectiveness of the proposed strategy.

This two-part paper develops a non-iterative coordinated optimal dispatch framework, i.e., free of iterative information exchange, via the innovation of the equivalent projection (EP) theory. The EP eliminates internal variables from technical and economic operation constraints of the subsystem and obtains an equivalent model with reduced scale, which is the key to the non-iterative coordinated optimization. In Part II of this paper, a novel projection algorithm with the explicit error guarantee measured by the Hausdorff distance is proposed, which characterizes the EP model by the convex hull of its vertices. This algorithm is proven to yield a conservative approximation within the prespecified error tolerance and can obtain the exact EP model if the error tolerance is set to zero, which provides flexibility to balance the computation accuracy and effort. Applications of the EP-based coordinated dispatch are demonstrated based on the multi-area coordination and transmission-distribution coordination. Case studies with a wide range of system scales verify the superiority of the proposed projection algorithm in terms of computational efficiency and scalability, and validate the effectiveness of the EP-based coordinated dispatch in comparison with the joint optimization.

Due to the increasing number of power electronics-based devices in modern power systems, there are concerns about the impact of higher-frequency interactions on system stability. The typically-used algebraic representation of networks fails to capture these newly emergent issues, but dynamically modelling the entire network with differential equations will lead to a prohibitively long simulation time. This paper proposes a computationally-efficient analysis framework to determine the system loadability in power electronics-rich, large networks with the consideration of multiple types of stabilities. The framework developed in this paper identifies the critical network elements based on the eigenvalue sensitivity in order to exploit a hybrid modelling approach. Within the hybrid model, only the critical network portion is modelled dynamically with the rest of the network represented by algebraic equations. Bifurcation theory is used to simultaneously analyze both small-disturbance rotor angle and small-disturbance voltage stability. The results obtained show that the high-frequency interactions are accurately captured with the proposed framework. Additionally, applying this methodology results in a small dimension for the system matrix and a reduction in the computational burden. Two test networks, a three-bus system and the IEEE 39-bus system, are used to illustrate and verify the analysis framework.

This paper proposes a novel estimation fusion approach for hybrid multi-stage power system state estimation. Hybrid estimation fusion architectures allow the incorporation of new classes of sensors without doing away with pre-existing estimators. The fusion module is responsible to produce final estimates based on the optimal merging of the individual estimators' outcomes. The proposed fusion formulation is based on the Maximum Correntropy Criterion (MCC), an optimization criterion borrowed from the information theoretic area that has been recently applied to conventional power system state estimation and enables the automatic suppression of bad data effects. In this paper, the correntropy-based formulation is used to replace the traditional minimum variance fusion methodology in the second stage of the hybrid estimation algorithm. To assess the applicability of the novel method, a three-sensor, MCC-based fusion architecture is evaluated through simulations conducted on the IEEE 14-bus, 30-bus, 57-bus, and 118-bus test systems. In the absence of bad data, the results confirm the expected compatibility between the proposed MCC-based fusion and the conventional minimum variance formulation. In addition, extensive experiments considering distinct bad data scenarios under several operational conditions have been performed. They illustrate a novel functionality imparted by the proposed approach to the fusion module, namely, the ability to automatically reject discrepant data. Therefore, MCC fusion provides an extra layer of protection against the harming effects of individual estimates contaminated with gross errors.

This paper proposes a tractable distributionally robust chance-constrained conservation voltage reduction (DRCC-CVR) method with enriched data-based ambiguity set in unbalanced three-phase distribution systems. The increasing penetration of distributed renewable generation not only brings clean power but also challenges the voltage regulation and energy-saving performance of CVR by introducing high uncertainties to distribution systems. In most cases, the conventional robust optimization methods for CVR only provide conservative solutions. To better consider the impacts of load and PV generation uncertainties on CVR implementation in distribution systems and provide less conservative solutions, this paper develops a data-based DRCC-CVR model with tractable reformulation and data enrichment method. Even though the uncertainties of load and photovoltaic (PV) can be captured by data, the availability of smart meters (SMs) and micro-phasor measurement units (PMUs) is restricted by cost budget. The limited data access may hinder the performance of the proposed DRCC-CVR. Thus, we further present a data enrichment method to statistically recover the high-resolution load and PV generation data from low-resolution data with Gaussian Process Regression (GPR) and Markov Chain (MC) models, which can be used to construct a data-based moment ambiguity set of uncertainty distributions for the proposed DRCC-CVR. Finally, the nonlinear power flow and voltage dependant load models and DRCC with moment-based ambiguity set are reformulated to be computationally tractable and tested on a real distribution feeder in Midwest U.S. to validate the effectiveness and robustness of the proposed method.

As more renewable resources are integrated into the receiving-end AC grid through VSC-HVDC, the grid connected VSC-HVDC system is facing a critical dynamic stability issue involving multiple-frequency oscillatory behaviors, which mainly stems from the low-system-strength and the time-varying phase shift. This paper proposes a general stability analysis method to measure the dynamic stability of grid connected VSC-HVDC system from the point of view of input to state stability (ISS). A nonlinear time-varying discrete-time state space model (NTDS2M) of the grid connected VSC-HVDC system is built considering the impact of the time-varying phase shift. Then, the NTDS2M is decomposed into several interconnected subsystems. The general asymptotic gain matrix (GAGM), whose elements are derived from the proposed dissipative-form sum-type inequalities (DSIs), is constructed to quantify the interactions between multiple subsystems. Finally, a general dynamic stability analysis index, called dynamic short circuit ratio (DSCR), is proposed to effectively explain the critical dynamic instability point of the grid connected VSC-HVDC system, based on the spectral radius property of the GAGM. Moreover, the real-time simulations and multiple comparative studies are implemented in this paper to verify the effectiveness of the proposed NTDS2M and stability analysis method by using RT-LAB platform.

The use of the Weighted Least Absolute Value (WLAV) state estimator is especially advantageous in systems that utilize Phasor Measurement Units (PMUs). Although PMU measurements and the phasor state vector are complex-valued, traditional WLAV methods operate solely in the real domain. This paper introduces the Weighted Least Modulus (WLM) state estimator, which is the counterpart of the WLAV method in complex variables. The WLM state estimator exploits the coupling of real and imaginary measurement components for noise filtering and bad data elimination. The paper demonstrates that the WLM state estimator replaces the WLAV linear programs with conic programs. An efficient implementation in complex variables is also derived through the Iteratively Reweighted Least Squares (IRLS) technique within the Wirtinger calculus framework. The WLM state estimator is tested on networks with up to 6495 nodes in PMU-only and hybrid measurement scenarios. The results were compared to the IRLS solution using real variables and a traditional linear programming formulation. They show that the IRLS-based WLM state estimator achieves a significant speedup compared to WLAV implementations and, at the same time, gives overall better estimation results.

This paper investigates the large disturbance stability of single voltage source converter (VSC) connected to the infinite bus system through the transmission line. One conservative stable region is obtained via the direct method of Lyapunov. Based on the Poincaré Theorem, it is interesting to find there might exist limit cycle between the obtained stable boundary and the angle of unstable equilibrium point (UEP). Accordingly, the nonlinear damping effect on the system stability is defined, and one limit cycle exists when the positive and negative damping effect over one period is mutually balanced. A conservative existence condition of limit cycle is further derived by constructing a proper piece-wise curve to approximate one specified unstable system trajectory. The derived analytical existence condition can directly predict the limit cycle without numerical simulations. Finally, the paper also proves that the studied dynamic system has at most one limit cycle, and if it exists, it is unstable.

The traditional communication method will bring a heavy burden to the grid system in the distributed collaborative control of microgrids. In grid-connected ac microgrid, this paper adopts an event-triggered control method to resolve the power sharing problem and reduce the communication cost. To begin, the problem is stated as the control problem of a leader-follower multiagent system and uses a distributed hierarchical control strategy to solve it. The primary controller uses the internal model principle to control the voltage output. To optimize the secondary controller, this paper not only adopts an event-triggered control strategy for the microgrid based on the Lyapunov principle to control the output of the compensator state, but also carries out relevant theoretical verification and analysis to ensure that each agent can exclude Zeno behavior. Finally, simulation instances are used to verify the usefulness of the studied control algorithm.

This paper mainly focuses on the problem of non-fragile intermittent estimate tracking in microgrid systems with denial of service (DoS) attacks and gain fluctuation. Different from the common DC/AC microgrid system, the microgrid system studied in this paper involves large grid control and power line communication technology, which is more in line with the actual operating environment. Simultaneously, aiming at the occurrence of network-induced DoS attacks, an intermittent estimator based on partial measure information under cyber-attacks is designed. More importantly, instead of the existing single aperiodic or periodic DoS attacks, the DoS attacks scheme presented in this paper is semi-periodic DoS attacks whose the attack range is aperiodic and the attack width is certain. Furthermore, a variable obeying the Bernoulli distribution is proposed to characterize the randomly occurring gain fluctuation, in which the no-fragile observation is stochastic uncertain. Then, two sufficient conditions of stochastic stability of observation error system of microgrid are devised with the assistance of two different Lyapunov theories. Finally, the rationality of the developed theoretical method is verified by a numerical example.

It is well known that interdependence between electric power systems and other infrastructures can impact energy reliability and resilience, but it is less clear which particular interactions have the most impact. There is a need for methods that can rank the relative importance of these interdependencies. This paper describes a new tool for measuring resilience and ranking interactions. This tool, known as Computing Resilience of Infrastructure Simulation Platform (CRISP), samples from historical utility data to avoid many of the assumptions required for simulation-based approaches to resilience quantification. This paper applies CRISP to rank the relative importance of four types of interdependence (natural gas supply, communication systems, nuclear generation recovery, and a generic restoration delay) in two test cases: the IEEE 39-bus test case and a 6394-bus model of the New England/New York power grid. The results confirm industry studies suggesting that a loss of the natural gas system is the most severe specific interdependence faced by this region.

As a widely configured controller, the limiter is essential to ensure the security of the voltage source converter (VSC), which affects the stability characteristics of the grid-connected VSC system under severe faults. However, due to limiters' hard algebraic constraints, the existing methods have yet to reveal the stability mechanism related to the multi-limiters thoroughly. In this paper, the stability mechanism of the grid-connected VSC system with multi-limiters is investigated, and an improved Filippov Theorem is proposed to study the dynamic characteristics. Two kinds of points are essential to the stability, namely, the fixed switching point(FSP) and the fixed ending point(FEP). Expressly, transient stability can be guaranteed by the condition that FSP is in the region of attraction(ROA), even if other parts of the trajectory are outside the ROA. Moreover, the existence of FEP contributes to some control loop failure, which does not induce instability but may cause the power into the grid to be inconsistent with the reference value. This paper presents the analytical methods for these crucial points, which avoid time-domain simulation. What follows illustrates how to enhance the stability characteristics by configuring the FSP and FEP. Another advantage of the proposed method is easily extended to the VSC with multi-limiters and different control structures.

This paper aims to present a general-purpose Surrogate Model for the probabilistic analysis of power distribution grids with a large number of input parameters. The distinctive feature of the novel technique is the employment of the partial derivatives of output variables versus input parameters to tame the “curse of dimensionality” problem exhibited by prior surrogate model calculation techniques. The second important feature of the proposed Surrogate Model method is that it does not require any a priori assumption about the nature or statistical distribution of the input parameters. In fact, it can be applied whenever design parameters are deterministic variables as well as when they are uncertain and represented by continuous and/or discrete random variables. Relevant applications presented in the paper refer to the probabilistic analysis of the distribution grid in the presence of a large number of photovoltaic sources and electric vehicle charging stations.

This paper investigates the load frequency control scheme for the large-scale networked power system with large delays, where the system states are unmeasurable. A matrix dimension transformation method is proposed to solve the problem of matrix dimension mismatch caused by the complex structure of the system in the controller design process. Two formal results are demonstrated. The first result studies the exponential stability using the backstepping-based partial differential equation (PDE) method in the continuous-time control framework. The second result examines the exponential stability based on the the reduction-based ordinary differential equation (ODE) method in the framework of sampled-data control. A two-sided mode-dependent loop-based Lyapunov-Krasovskii functional is constructed so that the information of sampled-data intervals can be utilized more sufficiently. Meanwhile, with the help of proposed method, the design algorithms of controllers are given base on two predictor methods, respectively. And $H_\infty $ performance indexes reflecting the system robustness under load-frequency control are given. The validity of the proposed methodology is verified in the simulation section using a three-area interconnected large-scale power system.

As Inverter-Based Resources (IBRs) gradually replace conventional synchronous generators (SGs), Dynamic State Estimation (DSE) techniques must be extended for the monitoring of IBRs. The key difference between IBRs and SGs is that the dynamics of IBRs comprise a heavy mix of physical processes and digital controller computations. This paper develops a generic framework of Control-Physics Dynamic State Estimation (CPDSE) for IBRs. First, a control-physics state-space representation of IBRs is presented. Noting the symmetry of the control and physical state spaces, it is proposed to use two dual estimators to track the states of the physical inverter subsystem and the digital controller subsystem, respectively. The CPDSE framework has the capability of suppressing errors in both measurement signals and control signals flowing between the two subsystems and the potential to distinguish between cyber and physical events. The advantages and versatility of the proposed CPDSE framework are validated on a variety of IBR systems (solar, wind, and storage), control strategies (grid-following and grid-forming), and both transmission and distribution systems.

Forced oscillation source location (FOSL) plays a significant role in mitigating forced oscillations (FOs), which threaten the power system stability. This paper proposes a data-driven approach for FOSL in power systems using synchrosqueezing wavelet transform (SWT). The proposed approach conducts SWT on the measured system responses to obtain the SWT matrix. Then, the SWT-based dissipating energy flow (DEF) model in time-frequency domain and dissipating energy spectrum (DES) model in frequency domain are derived from the traditional DEF model. Further, the characteristics of SWT-based DEF and DES are revealed by referring to the traditional DEF, and the FOSL criteria of the SWT-based DEF and DES can be hereby obtained. Using the obtained FOSL criteria, the FO source can be located from the measured responses. The performance of the proposed FOSL method is evaluated by simulation data of the WECC 179-bus test system and field-measurement PMU data of the ISO New England. The results confirm the accuracy and efficiency of the proposed method in the FOSL.

Optimally reconfiguring an active distribution network (ADN) during power outages has been regarded as a reasonable approach to facilitate system secure operation and reliability. Nevertheless, most existing studies for the reconfiguration virtually focus on taking actions from the generation- and network-side, in which the potential achievement from the demand-side is underestimated. Moreover, the phase-unbalance and voltage violation in ADNs should be restricted to avoid extreme conditions of distributed generators (DGs) that jeopardize system reliability. To bridge the gap, a new approach to reconfigure ADNs under multiple faults is proposed in this paper, incorporating a phase demand balancing (PDB) model to improve dispatch performance. The model regulates asymmetrical loads to mitigate the phase-unbalance issue from the demand-side, co-optimized with step voltage regulators (SVRs) and DG dispatching to enhance reliability and flexibility in reconfiguring ADNs. The derived optimization is a challenging mixed-integer non-convex programming (MINCP), which is reformulated as an efficiently solvable mixed-integer second-order cone programming (MISOCP) via exact equivalence and accurate approximation techniques. Case studies based on modified IEEE benchmark systems validate the effectiveness and advantages of the proposed method.

This paper proposes a novel unified nonlinear dynamic power network model in an arbitrary dimensional real vector space to study the quantitative interactions among the generalized current injections, the frequency oscillations, and the voltage variations. Further, an innovative dynamic current decoupling control (DCDC) approach is developed. The DCDC cancels the adverse influences of the nonlinear couplings between the active and the reactive control loops. Also, it increases the system damping of the changes of both frequency and voltage simultaneously. The closed-loop system with the proposed DCDC scheme is proved theoretically to be globally exponentially stable in the Lyapunov sense. Then, we apply the presented DCDC approach to the control syntheses of the voltage-sourced converter (VSC) based static synchronous compensator (STATCOM) and the doubly fed induction generator (DFIG). The superiority of the DCDC method is further evaluated comparatively by implementing the designed controllers of STATCOM and DFIG on WSCC 9-bus system, IEEE New England 39-bus system, and IEEE 14-bus system.

Wildfires can severely damage electricity grids leading to long periods of power interruption. Climate change will exacerbate this threat by increasing the frequency of dry weather conditions. Under these climate conditions, human-related actions that initiate wildfires should be avoided, including those induced by power systems operation. In this paper, we propose a novel optimization model that is capable of determining appropriate network topology changes (via switching actions) to alleviate the levels of power flows through vulnerable parts of the grid so as to decrease the probability of wildfire ignition. Within this framework, the proposed model captures the relationship between failure probabilities and line-flow decisions by explicitly considering the former as a function of the latter. The resulting formulation is a two-stage model with endogenous decision-dependent probabilities, where the first stage determines the optimal switching actions and the second stage evaluates the worst-case expected operation cost. We propose an exact iterative method to deal with this intricate problem and the methodology is illustrated with a 54-bus and a 138-bus distribution system.

This paper presents a novel unified peer-to-peer (P2P) framework for both kilowatt (kW) and negawatt (nW) trading. The aim is to coordinate these two transaction types and maximize customer benefits, by reducing customers’ electricity bills and helping customers trade energy with their neighbors while also adhering to the physical limits of the electricity networks. An auction-based joint kW and nW P2P trading approach is proposed to enable prosumers to conduct the optimal strategy in switching their market roles between kW and nW trading and scheduling their demand. As such, in the virtual layer, the household energy management system (HEMS) models are formulated to determine the optimal market bidding strategy during each trading period. For the agent equipped with a battery energy storage system (BESS), the battery cycling degradation issue is also considered through the embedded battery cycle life model. A double-sided auction method with an average pricing market (APM) mechanism is performed in P2P kW and nW trading for market clearing. In the physical layer, voltage issues and line congestion management are considered through the distribution network models. The proposed formulation is tested on the modified IEEE 33-bus distribution system and simulation results demonstrate that the proposed framework outperforms the single trading mode.

Aiming at the transient instability and overcurrent issues of the virtual synchronous generator (VSG) under severe grid voltage sag, the accurate and simultaneous control for the phase angle and current of VSG is hard to be achieved without using the fault information. And the requirement of the grid code for the reactive current should be also considered. To address the issues, this paper proposes a non-fault information based dual-loop adaptive feedback control to take transient angle stability, current limitation and the demand of the reactive current of VSG into account. First the large-signal model of VSG with a dual-loop control is built. To design the feedback coefficients, the feasible coefficient region under different fault degrees and cases is analyzed subsequently. It provides reference for the curve fitting, which is further applied in the self-adaptive regulation of the feedback coefficients. Thereby, a dual-loop adaptive feedback control is realized based on an additional reactive power feedback loop. With the proposed control scheme, all of the three control objectives can be achieved without the fault information, since the feedback coefficients are within the feasible coefficient region by the self-adaptive regulation. Finally, the effectiveness and robustness of the proposed control scheme for both VSG and a paralleled system of VSG and grid-following (GFL) converter are validated by the simulation results and the experimental results.

In pursuit of achieving carbon neutrality goals, modern power systems are increasingly characterized by low-carbon and low-inertia properties, leading to significant concerns regarding the security of system frequency. These ancillary services for providing frequency regulation (FR) can contribute to the system inertia, FR reserve capacity, and the response rate of FR reserves. However, it could be challenging to motivate low-carbon resources, like carbon-capture-utilization-and-storage (CCUS) systems and grid-forming inverter-based renewable energy systems (RESs), to participate in FR ancillary service markets. A critical focus of this paper lies in assessing the marginal value of diverse FR ancillary services for improving the performance of frequency-secured systems in under-frequency and over-frequency cases. Given the tight relations among energy and FR ancillary services, the frequency-secured performance criteria are introduced, including maximum rate of change of frequency (RoCoF), maximum frequency deviation, and quasi-steady-state (Q-S-S) frequency which are devised in a joint energy, carbon, and FR ancillary service market. To solve this nonconvex and nonlinear market problem, while minimizing the uplift payment, a tractable shrunken convex hull pricing method is presented. Multiple case studies confirm the proposed method's effectiveness in enhancing the system frequency stability, reducing total costs, and curtailing carbon emissions.

This paper proposes a machine learning-based method for predicting generator rotor angle responses (trajectories) following large disturbance in power system. A Long Short-Term Memory (LSTM)-based Recurrent Neural Network (RNN) is used to predict responses at any time instant after the fault inception by designing the input and output of the network with predefined sliding time windows. The numbers of neurons in the LSTM and Fully-Connected (FC) layers are optimised with the Particle Swarm Optimisation (PSO) algorithm, which was proved to be effective in similar tasks in past research. A wide range of realistic constraints associated with the use of the Phasor Measurement Unit (PMU) data has been considered, to demonstrate the feasibility of the proposed method when applied in real systems. Results obtained using modified IEEE 68 bus test system show that the proposed method can predict the future rotor angle responses accurately, and that is highly robust towards the imperfections of the realistic PMU data.

High renewable penetration brings diversified operation states and complex dynamic behaviors to power systems and challenges the dynamic security assessment calculation. Data-driven methods have become increasingly important to address this challenge. However, the performance of data-driven DSA is heavily driven by the quality of the database generated for training the model, i.e., how well the database represents the operation states which need to be evaluated by the data-driven DSA. This paper proposes a database generation method that can generate samples following the probability distribution of operation states which need to be evaluated by the data-driven DSA in high renewable penetrated power system. In the method, the probability distribution of operation states which need to be evaluated by data-driven DSA in high renewable penetrated power system is modeled as probabilistic feasible region, which is a probability distribution of unnormalized PDF on convex polytope. An efficient sampling method is designed to generate operation state samples from the probability distribution of unnormalized PDF on polytope. The effectiveness of the proposed method and the improvement compared to OPF-based method, Gapsplit method, and optimization-based exploration method are demonstrated by case study on the transient angular stability problem of a 170-bus dynamic test system.

Probabilistic power flow (PPF) is the fundamental to reveal the influence of stochastic sources on the AC-DC hybrid grids. In the operational PPF analysis, the accurate probability density functions (PDFs) of PPF responses must be obtained in a very short period, which is quite challenging for existing methods. In this paper, a fractional moments based adaptive scaled unscented transformation (ASUT) is proposed to overcome the operational PPF challenge. The ASUT creates a new path to fully catch the probability information, which adaptively selects the sample point sets from each random input variable through the fractional moment assessment. A handful of fractional moments can contain the information identical to the one generated from a great many integer moments (e.g., central or raw moments). This feature is beneficial to present and propagate the abundant probability information using only a few sample points, which enables the reconstruction the PDFs of PPF results accurately by the maximum entropy, leading to the great enhancement in the execution accuracy and efficiency of PPF calculations. Test results on the IEEE 118 bus system integrated with DC systems and a provincial AC-DC hybrid grid in South China validate the effectiveness and advantages of proposed method herein.

Large-scale integration of renewable generation has changed the way that distribution networks are operated, posing significant challenges to voltage control. To address this challenge, system operators need to exploit the potential of inverter-based renewable generation for reactive power regulation. However, the distribution network parameters are usually inaccurate or incomplete, making conventional centralized or model-dependent distributed control methods difficult for fast voltage tracking and optimal reactive power distribution. This paper proposes a model-free distributed Newton method for voltage control based on data-driven lift-dimension linear power flow which does not reply on accurate and complete network parameters. By using matrix splitting to calculate Hessian matrix, the proposed method possesses a super-linear convergence and exhibits superiority in fast response over existing linear methods. Furthermore, a Koopman-based state space mapping method is proposed to obtain global sensitivity and tune the iteration direction in an off-line manner, which can realize model-free voltage control. The convergence and optimality of the proposed method are validated by case studies. Especially, the parameter independence feature of the model-free scheme provides decided superiority in scenarios of incomplete model. Even under communication failures, the proposed method still can maintain voltage stability at a suboptimal point.

Increasing renewable energy resources introduces uncertainties into utility grids, calling for more frequent use of alternative current optimal power flow (AC-OPF) than before. Conventional AC-OPF solvers are too slow for real-time applications; to speed up the computation, deep neural network (DNN) based solvers are introduced. However, their results typically cannot enforce the security constraints of the utility grid. To overcome this difficulty, FRMNet is proposed in this paper, which combines DNN with feasibility restoration mapping (FRM). The DNN receives the load as input and outputs a partial solution. The following FRM maps the infeasible solution to the feasibility region to satisfy the AC-OPF constraints. The proposed FRMNet has four advantages compared to conventional and DNN-based solvers. First, the feasibility of overall solutions is guaranteed via FRM. Second, FRMNet is a self-supervised training method so that it avoids the laborious preparation of the optimal solutions for a training dataset using conventional solvers. Third, FRM is differentiable so that AC-OPF information encoded in gradients is transferred to DNN, which leads to a DNN with high feasibility rate. Fourth, the overall computation time of FRMNet is fast due to its DNN's high feasibility rate. Comprehensive experiments are conducted on IEEE standard cases. Results show that FRMNet's outcomes satisfy all constraints at a significantly faster average speed than conventional solvers. When FRM participates in training, the performance of DNN is stably improved and achieves better results than other DNN-based models. Even DNN alone achieves a high feasibility rate, a negligible degree of constraint violations and a small optimality gap, compared to the state-of-the-art DNN based solvers.

The high penetration of distributed generators (DGs) deteriorates the uncertainty of active distribution networks (ADNs). Soft open points (SOPs) can effectively improve flexibility and deal with operational issues in ADNs. However, the formulation of SOP control strategies depends on the accurate mechanism model. Data-driven method can utilize only measuring data to conduct operation and becomes a promising way. In practical conditions, the measuring data may suffer from bad data and measuring errors, which poses a challenge to meet the diverse operational requirements. This paper proposes a data-driven multi-mode adaptive control method for SOP with measuring bad data. First, considering the inaccurate network parameters and quality of measuring data, a robust data-driven framework for SOP operation is proposed based on robust hierarchical-optimization recursive least squares (HO-RLS). Then, a multi-mode control strategy for SOP is proposed to adapt to the diverse operational requirements. A dynamic triggering mechanism is designed to achieve adaptive mode switching. The case studies on practical distribution networks show that the proposed method can fully explore the benefits of SOP to improve the operational performance of ADNs. The potential limitations are discussed to enhance practicality.

To achieve long-distance transmission of onshore wind power, different high-voltage direct-current (HVDC) technologies have been proposed, including the line-commutated converter (LCC), the modular multilevel converter (MMC), and the cascaded LCC-MMC converter. However, there is still room for improvement in existing topologies. This paper proposes a cascaded LCC-DR HVDC transmission system and the corresponding communication-less reactive power control (CLRPC) for the grid-forming wind turbines, ensuring operational reliability with good economic efficiency. Firstly, the topology and control strategies of the cascaded LCC-DR HVDC transmission system are introduced. Then, the operation principle and threshold design of CLRPC are analyzed. Finally, the feasibility of the proposed structure and control strategies under various operation scenarios are verified in PSCAD/EMTDC.

The effects of fast frequency response (FFR) on rotor angle stability have predominately been established by examining the oscillatory behavior of synchronous generators (SGs). What remains largely unexamined, however, is the effect that FFR has on the angle separation and power transfer between SGs. This paper systematically examines the evolution of the angle separation and power transfer between SGs during FFR provision in the context of frequency containment events. Droop based FFR schemes, which are popular and effective in practical systems, are analyzed. This research investigates how the location of the initiating system wide active power deficit, the location of resources providing FFR, and the delays associated with FFR provision all impact rotor angle stability. The key results are obtained using a modified IEEE 39-bus system and further verified using a reduced-order dynamic Great Britain system model. The results show that the angle separation and power transfer between SGs decrease when power deficits occur in areas with extensive generation sources which, conversely, implies that angle stability deteriorates if power deficits occur near load centers. A key finding is that providing the FFR at locations closest to the source of the initial power deficit does not always enhance angle stability, and sometimes has a significant adverse effect. The effect that FFR delays have on rotor angle stability is explained, highlighting the necessity to carefully consider and design FFR provision timing, particularly in areas with diminishing levels of inertia.

Due to coupling and correlation between nodes and buses in the power system, Power Grid Partitioning (PGP) is a promising approach to analyze large power systems and provide timely actions during disturbances. From this perspective, this paper proposes an efficient framework for fast and optimal PGP, based on singular value decomposition analysis of the graph's Laplacian. An Affinity Propagation clustering algorithm-based PGP is tailored for automatically forming highly interconnected clusters based on pairwise similarities without requiring a predefined number of partitions. The core objective is to quantify the clustering performance based on internal clustering validity indices, such as the Silhouette Index, Calinski-Harabasz Index, and Davies-Bouldin Index. The adopted methodology aims to enhance partitioning efficiency substantially while preserving a high level of partitioning quality. The proposed framework is verified on IEEE 14, 39, 118, and 2000-bus systems and compared to nine other well-known and widely used clustering techniques, including K-Means and Gaussian Mixture models. The simulation results demonstrate the scalability of the proposed approach and its high-quality partitioning output with a Silhouette index of 0.6162, 0.6597, 0.6664, and 0.6555 for the IEEE 14, 39, 118, and 2000-bus systems, respectively.

Most existing studies on probabilistic frequency stability analysis ignore the dynamics of wind power generations (WPGs) and thus result in inaccurate analysis results especially when the fast frequency response of WPGs is expected. This paper proposes a method of probabilistic frequency stability analysis that considers the dynamics of WPGs with different control strategies. Firstly, a multi-interval sensitivity (MIS) method is proposed to simulate the frequency response, thereby significantly saving the simulation time. Then, a multi-element low-rank approximation (MELRA) uncertainty propagation analysis method suitable for large-scale uncertainty analysis is proposed. And the introduction of multi-element effectively improves the accuracy. In addition, by applying the Gaussian mixture model (GMM), the limitations of moment-based uncertainty propagation analysis methods are discussed, demonstrating the comparative superiority of the proposed method. Also, the necessity of considering the dynamics of WPGs in frequency stability analysis is revealed by analyzing the differences of frequency response with and without dynamics of WPGs using different control strategies. The performance of the proposed method is verified on the IEEE 68-bus system and the provincial large-scale power system.

Natural wildfire becomes increasingly frequent as climate change evolves, posing a growing threat to power systems, while grid failures simultaneously fuel the most destructive wildfires. Preemptive de-energization of grid equipment is effective in mitigating grid-induced wildfires but may cause significant power outages during natural wildfires. This paper proposes a novel two-stage stochastic program for planning preemptive de-energization and solves it via an enhanced Lagrangian cut decomposition algorithm. We model wildfire events as stochastic disruptions with random magnitude and timing. The stochastic program maximizes the electricity delivered while proactively de-energizing components over multiple time periods to reduce wildfire risks. We use a cellular automaton process to sample grid failure and wildfire scenarios driven by realistic risk and environmental factors. We test our method on an augmented version of the RTS-GLMC test case in Southern California and compare it with four benchmark cases, including deterministic, wait-and-see, and robust optimization formulations as well as a comparison with prior wildfire risk optimization. Our method reduces wildfire damage costs and load-shedding losses, and our nominal plan is robust against uncertainty perturbation.

The linearization of the optimal power flow (OPF) model is widely-used to meet the computational demands of power system dispatch. To improve the accuracy of the OPF solution, existing studies are devoted to reducing the linearization error of nonlinear power flow constraints. However, the linearization accuracy of model fractions does not necessarily represent the linearization error of the OPF result. In this paper, an improved linear OPF formulation is derived from the optimality condition of the OPF solution. Based on the Karush–Kuhn–Tucker (KKT) condition, we transform the OPF optimization into solving a set of nonlinear equations, which consists of non-gradient and gradient terms. The traditional approach to linearize OPF constraints is regarded as deriving the first-order and zero-order Taylor expansions of non-gradient and gradient terms, respectively. The missing first-order component of gradient terms causes considerable linearization error. We formulate it as a bias factor in the OPF objective to improve the accuracy and maintain linearity of the OPF model. By considering the bias factor, the performance of linear OPF optimization is notably improved, which is illustrated in theory and verified in numerous IEEE and Polish test systems.

By combining the advantages of line commutated converter (LCC) and voltage source converter (VSC), the hybrid AC and LCC-VSC-based DC system (HALVDS) has broad application prospects to deliver remote wind power to the load center. Faced with the increasing uncertainties, the reliability issues of HALVDS with remote wind farms can be significantly serious, especially in the operational phase. In previous studies, the traditional reliability models are usually developed based on Markov stochastic process (MSP) where the duration times of different states are supposed to follow exponential distributions. However, in intricate operational environments, several components may not obey the above assumptions, e.g., the state duration times of wind turbines and electronic components following arbitrary distributions. Hence, the traditional method cannot be suitable for evaluating the operational reliability of HALVDS with complicated structures of various components whose state duration times follow different distributions. To address this, a semi-Markov stochastic process (SMSP) model is innovatively proposed in this paper for evaluating the operational reliability of HALVDS. By solving the integral equations of the SMSP, the operational reliability of components following arbitrary distributions can be determined. On this basis, the Lz-transform technique is applied to develop the generalized reliability models of different components, whose time-varying characteristics can be described in a unified way. The optimal AC/DC power flow (OADPF) operator is then defined to aggregate the reliability models of components to determine the operational reliability of HALVDS with complex structures. Furthermore, time-varying reliability indices of nodes and systems are defined to evaluate the spatial-temporal reliability of HALVDS. Case studies validate the effectiveness of the proposed technique.

This paper proposes an area inertia estimator based on an iterative equation error (EE) system identification (SI) approach. The inertia value can be accurately extracted for areas of different compositions with different penetrations of converter-interfaced generators. Firstly, the internal frequency variation of the generator units is computed by means of a frequency divider-based estimator. Subsequently, these internal frequency variations are used to carry out a generator clustering, which provides groups of coherent generators to the proposed inertia estimator. Finally, the iterative EE SI approach provides a joint inertia estimation for each of these coherent groups. Numerical results on a properly modified version of both the IEEE 39-bus and the IEEE 118-bus test systems highlight the accuracy of the proposed method using both ambient measurements and ringdown signal measurements (power imbalance events). Furthermore, the proposed method presents a low computational burden that allows fast estimation updating times.