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As synchronous generators (SGs) are extensively replaced by converter-based generators (CBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration CBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for a CBG-integrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters, which dramatically reduces the complexity of frequency analysis. On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system's frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system. [ABSTRACT FROM AUTHOR]

This paper proposes a novel repair rule set (RRS) for scheduling the power system infrastructure repair after the occurrence of extreme events. RRS is made up of multiple repair rules, each of them can be applied in arbitrary post-disaster failure scenarios to rank the repair actions by priority. A learning-to-rank technique called AdaRank is used to train the repair rules by combining the weak learners derived from the dynamic repair scheduling model. Then, RRS is constructed by iteratively clustering the training cases and retraining the repair rule for each cluster. Increasing the number of repair rules within RRS allows it to differentiate various types of failure scenarios, thereby improving its performance. Further combined with multi-label K nearest neighbor (ML-KNN) technique, RRS is able to schedule the repair without the full knowledge of real-time failure information, such as the estimated repair time. The results of case studies on IEEE-118 test systems show that the proposed method has a desirable performance compared to the exact mathematical optimization model. Moreover, it reduces the requirement for failure information while significantly improving the computational efficiency. [ABSTRACT FROM AUTHOR]

Smart distribution grid with multiple renewable energy sources can experience random voltage fluctuations due to variable generation, which may result in voltage violations. Traditional voltage control algorithms are inadequate to handle fast voltage variations. Therefore, new dynamic control methods are being developed that can significantly benefit from the knowledge of dominant voltage influencer (DVI) nodes. DVI nodes for a particular node of interest refer to nodes that have a relatively high impact on the voltage fluctuations at that node. Conventional power flow-based algorithms to identify DVI nodes are computationally complex, which limits their use in real-time applications. This paper proposes a novel information theoretic voltage influencing score (VIS) that quantifies the voltage influencing capacity of nodes with DERs/active loads in a three phase unbalanced distribution system. VIS is then employed to rank the nodes and identify the DVI set. VIS is derived analytically in a computationally efficient manner and its efficacy to identify DVI nodes is validated using the IEEE 37-node test system. It is shown through experiments that KL divergence and Bhattacharyya distance are effective indicators of DVI nodes with an identifying accuracy of more than 90%. The computation burden is also reduced by an order of 5, thus providing the foundation for efficient voltage control. [ABSTRACT FROM AUTHOR]

This letter proposes an analytical method to estimate the frequency of buses of transmission grid based on updated generator speed, internal generator voltages, admittance matrix and bus voltages. The proposed method estimates the buses frequency which are much more reliable, accurate and efficient for transient stability studies in contrast to other existing methods. To demonstrate the efficiency of the proposed approach, the method is applied on IEEE 39 bus test system for frequency support and is compared to other existing methods. [ABSTRACT FROM AUTHOR]

The existing research on voltage-source converter HVDC (VSC-HVDC) system stability mostly focuses on small-signal stability analysis methods. However, when large-signal disturbances occur, the intrinsic nonlinearity of the VSC-HVDC system becomes inevitable so that the small-signal studies are no longer valid. In this paper, a large-signal stability analysis method of the VSC-HVDC system is proposed based on the estimation of domain of attraction (DOA). This method can not only analyze the asymptotic stability of the operating point, but also answer the question of how large deviations from the operating point can be tolerated by the system. By using Takagi-Sugeno (T-S) fuzzy model and Lyapunov stability theorem, the DOA of the VSC-HVDC System at the operating point is estimated, and the large-signal stability of VSC-HVDC System is analyzed. On this foundation, the influence of system parameters on the large-signal stability is studied. The results can be used to guide the adjustment of system parameters to solve the problem of system instability. The time-domain simulations conducted in Matlab/Simulink are used to test the stability of the system under large-signal disturbance in the range of DOA. The simulation results verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this work we present a novel technique, based on a trust-region optimization algorithm and second-order trajectory sensitivities, to compute the extreme trajectories of power system dynamic simulations given a bounded set that represents parametric uncertainty. We show how this method, while remaining computationally efficient compared with sampling-based techniques, overcomes the limitations of previous sensitivity-based techniques to approximate the bounds of the trajectories when the local approximation loses validity because of the nonlinearity. We present several numerical experiments that showcase the accuracy and scalability of the technique, including a demonstration on the IEEE New England test system. [ABSTRACT FROM AUTHOR]

It is possible to launch undetectable load-redistribution (LR) attacks against power systems even in systems with protection schemes. Therefore, it is imperative to detect LR attacks in power systems and establish corrective actions to provide secure dispatch points. This paper develops a systematic real-time LR threat analysis (RTLRTA) tool to flag LR attacks and identify all affected transmission assets. Since attackers might introduce some forms of random strategies to create LR attacks, we introduce different optimization models to generate random LR attacks to determine accurate thresholds for our detection index and test the tool’s functionality. Additionally, based on an estimation for the actual loads in the post-attack stage, we design a set of physical line flow security constraints (PLFSCs) that can be added to the existing security-constrained economic dispatch (SCED) models. This leads to appropriate responses to the identified LR attacks and provides secure dispatch points. We generate multiple scenarios of LR attacks and random errors for different target lines in the 2383-bus Polish test system to validate our proposed methods’ accuracy and functionality in detecting LR attacks and responding to them. [ABSTRACT FROM AUTHOR]

Microgrid's voltage regulation is of particular importance during both grid-connected and islanded modes of operation. Especially, during the islanded mode, when the support from the upstream grid is lost, stable voltage regulation is vital for the reliable operation of critical loads. This paper proposes a robust and data-driven control approach for secondary voltage control of AC microgrids in the presence of uncertainties. To this end, unfalsified adaptive control (UAC) is utilized to select the best stabilizing controller from a set of pre-designed controllers with the minimum knowledge required from the microgrid. Two microgrid test systems are simulated in MATLAB to verify the effectiveness of the proposed method under different scenarios like load change and communication link failure. [ABSTRACT FROM AUTHOR]

The nonlinear and nonconvex nature of ac power flow challenges the analysis and optimization of unbalanced distribution networks. To tackle this issue, this paper proposes an online feedback-based linearized power flow model for unbalanced distribution networks with both wye-connected and delta-connected loads. The online feedback-based linearized model is grounded on the first-order Taylor expansion of the branch flow model (BFM), and updates the model parameters via online feedback by leveraging the instantaneous measurements of voltages and load consumption. Exploiting the connection structure of unbalanced radial distribution networks, we also provide a unified matrix-vector compact form of the model. The numerical tests on the IEEE 123-bus test system validate its accuracy and superiority compared with other offline BFM methods. Additionally, we apply the proposed model to the optimal power flow for voltage regulation, which further demonstrates its effectiveness. [ABSTRACT FROM AUTHOR]

Time-of-use (TOU) is an effective price-based demand response strategy. A reasonable design of TOU strategy can effectively reduce the peak-valley difference, and then produce a lot of benefits (such as delaying power grid investment, reducing interruption cost, and improving reliability). However, changing peak-valley period has a great influence on the peak-valley difference and power supply reliability of power system. Therefore, this paper aims to investigate the optimal modification of peak-valley period considering reliability loss under multiple TOU schemes. Firstly, this paper presents a clustering model and algorithm of optimal load curve based on a minimum error iteration method. Secondly, an optimal modification of peak-valley period based on a dynamic load point method is proposed, and the traditional peak-valley difference is replaced by the global peak-valley difference to calculate the objective function. Thirdly, this paper establishes a load–reliability relation fitting model based on the back propagation neural network. Finally, the effectiveness and correctness of the proposed method are investigated by the Roy Billinton test system and reliability test system. [ABSTRACT FROM AUTHOR]

This letter presents a novel sequential black-start restoration model to improve the system resilience after a natural disaster in an active distribution network. Two challenges have been addressed: First, a new set of radiality constraints is designed as the network topology is changing along the restoration paths; Second, a black-start restoration model is proposed where multiple backup black-start units in the system are coordinated to find the best restoration paths. Case studies on two IEEE test systems verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper proposes a machine learning method for the reliability evaluation of integrated power-gas systems (IPGS) under the uncertain component failure probability distributions. The Random Forest (RF) method is designed to select important features to solve the insufficient quantity of data and the curse of dimensionality problems. The Extreme Gradient Boosting (XGBoost) regression algorithm is developed to quantify the relationship between the uncertain parameters and reliability metrics. Moreover, a ten-fold cross-validation method is employed to further improve the accuracy of the regression model. Simulation results on three test systems show that the proposed method can achieve high accuracy for the reliability evaluation. [ABSTRACT FROM AUTHOR]

The paper proposes a technique for the on-line estimation of Thévenin equivalent (TE) which only needs the present phasor measurements. The technique is based on the wide-area measurements including voltage and current phasors of the system loads and synchronous generators, so that it can simultaneously estimate TE of the system seen from the interested buses. The technique has two main steps. In the first step, the conventional impedance matrix $\bar{Z}_{\rm bus}$ is modified to be suitable for TE estimation. In the second step, a correction coefficient based on the sensitivity theory calculated by using two consecutive phasor measurements is applied to correct the diagonal terms of the $\bar{Z}_{\rm bus}$ matrix. Simulation results carried on the IEEE 39-bus and 118-bus test systems show that the proposed technique can accurately estimate the TE for both generation and consumption buses under any load-increase scenario. The comparison scenarios verify the superiority of the proposed technique over others. [ABSTRACT FROM AUTHOR]

A new method for the stability assessment of inverter-based microgrids is presented in this paper. Directly determining stability boundaries by searching the multidimensional space of inverters’ droop gains is a computationally prohibitive task. Instead, we build a certified stability region by utilizing a generalized Laplacian matrix eigenvalues, which are a measure of proximity to stability boundary. We establish an upper threshold for the eigenvalues that determines the stability boundary of the entire system and demonstrate that this value depends only on the network’s R/X ratio but does not depend on the grid topology. We also provide a conservative upper threshold of the eigenvalues that are universal for any systems within a reasonable range of R/X ratios. We then construct approximate certified stability regions representing convex sets in the multidimensional space of droop gains that could be utilized for gains optimization. We show how the certified stability region can be maximized by properly choosing droop gains, and we provide closed-form analytic expressions for the certified stability regions. The computational complexity of our method is almost independent of the number of inverters. The proposed methodology has been tested using IEEE 123 node test system with 10 inverters. [ABSTRACT FROM AUTHOR]

An efficient probabilistic energy flow (PEF) analysis method is proposed for integrated electricity and gas systems (IEGSs) in this letter. A network decoupling based deterministic energy flow (DEF) calculation method is developed. A PEF analysis method is presented based on stochastic response surface method (SRSM). The computational efficiency and convergence performance of DEF and PEF are largely improved. The correctness and effectiveness of the proposed method are verified by using three test systems. [ABSTRACT FROM AUTHOR]

The reliable operation of a power distribution system relies on a good prior knowledge of its topology and its system state. Although crucial, due to the lack of direct monitoring devices on the switch statuses, the topology information is often unavailable or outdated for the distribution system operators for real-time applications. Apart from the limited observability of the power distribution system, other challenges are the nonlinearity of the model, the complicated, unbalanced structure of the distribution system, and the scale of the system. To overcome the above challenges, this paper proposes a Bayesian-inference framework that allows us to simultaneously estimate the topology and the state of a three-phase, unbalanced power distribution system. Specifically, by using the very limited number of measurements available that are associated with the forecast load data, we efficiently recover the full Bayesian posterior distributions of the system topology under both normal and outage operation conditions. This is performed through an adaptive importance sampling procedure that greatly alleviates the computational burden of the traditional Monte-Carlo (MC)-sampling-based approach while maintaining a good estimation accuracy. The simulations conducted on the IEEE 123-bus test system and an unbalanced 1282-bus system reveal the excellent performances of the proposed method. [ABSTRACT FROM AUTHOR]

The synchronization requirement is a bottleneck of many distributed optimization algorithms, particularly for solving problems with computationally heterogeneous subproblems and during the occurrence of communication failure/delay. This paper presents a double-loop learning-aided asynchronous alternating direction method of multipliers (LA-ADMM) that has information prediction capability and handles a considerable level of asynchrony between subproblems. A momentum-extrapolation prediction-correction technique is developed to enable subproblems to predict their neighbors missing shared variable information instead of using the latest received values. An online streaming-based anomaly classification is designed to observe the performance of predicted data and control Lagrange multipliers update over the course of iterations. The proposed LA-ADMM reduces under-utilization of computation resources, especially if subproblems are computationally heterogeneous. This algorithm also enhances distributed optimization robustness against communication failure/delay that may result in a considerable level of asynchrony between subproblems. LA-ADMM is applied to solve the optimal power flow problem for several test systems. Promising results are obtained as compared to the classical synchronous ADMM and asynchronous ADMM without the anomaly switch control. [ABSTRACT FROM AUTHOR]

This paper presents a method for controlling the voltage of inverter-based Microgrids by proposing a new scale-free distributed cooperative controller. The main contribution of this paper is that the proposed distributed cooperative controller is scale-free where is independent of any information about the communication system and the number of distributed generators, as such it works for any Microgrids with any size. Moreover, the communication network is modeled by a general time-varying graph which enhances the resilience of the proposed protocol against communication link failure, data packet loss, and arbitrarily fast plug and play operation in the presence of arbitrarily finite communication delays as the protocol does not require the knowledge of the upper bound on the delay. The stability analysis of the proposed protocol is provided. The proposed method is simulated on the CIGRE medium voltage Microgrid test system. The simulation results demonstrate the feasibility of the proposed scale-free distributed nonlinear protocol for regulating voltage of Microgrids in the presence of communication failures, data packet loss, noise, and degradation. [ABSTRACT FROM AUTHOR]

New resource mix, e.g., renewable resources, are imposing operational complexities to modern power systems by intensifying uncertainty and variability in the system net load. This issue has motivated independent system operators (ISOs), e.g., California ISO (CAISO), to add flexible ramping products (FRPs) to their day-ahead (DA) market models. Such structural changes in the DA market formulation require further analyses and detailed design to ensure adequate operational flexibility, market efficiency, and reliability. This paper conducts a comprehensive study to: (a) augment existing DA market models with enhanced FRP design to schedule ramp capabilities that are more adaptive with respect to the real-time (RT) 15-min net load variability and uncertainty, and (b) design corresponding market payment policies that accurately reflect the value of the added flexibility through enhanced FRP design. The proposed FRP design can be implemented in present-day system operations with minimal disruption to existing DA market models. Performance of the proposed DA market model, which includes the enhanced FRP design, is compared against the DA market model with existing FRP design through a validation methodology based on RT unit commitment model. This validation methodology mimics fifteen-minute markets of CAISO. The proposed method is tested on an IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

Weak grid scenarios and low-inertia systems are emerging issues in power systems, which could lead to voltage and frequency instabilities. Synchronous Condensers (SynCons) have recently drawn renewed attention as a promising solution to provide system strength and inertia support. Even though the exciter control of SynCons is a well-established technology, further developments are required to guarantee the stability of post-fault operations, in particular, in weak grids. This paper proposes a data-driven approach for designing higher-order optimized exciter controllers to meet this requirement. A pseudo-random binary sequence (PRBS)-based system identification method is used to obtain frequency response data of the power system, from the exciter point of view, which is then fed into the proposed optimal control design procedure. The proposed exciter controller is tested for voltage ride-through and fault scenarios in a single machine infinite bus (SMIB) case and the IEEE 39-bus test system to assess its performance compared to the conventional AC1A exciter controller. The results obtained through simulation tests carried out using the PSCAD/EMTDC software verify that the proposed exciter controller guarantees the post-fault stability in both strong and weak grids. [ABSTRACT FROM AUTHOR]

Increasing renewable penetration in distribution grids calls for improved monitoring and control, where power flow (PF) model is the basis for many advanced functionalities. However, unobservability makes the traditional way infeasible to construct PF analysis via admittance matrix for many distribution grids. While data-driven approaches can approximate PF mapping, direct machine learning (ML) applications may suffer from several drawbacks. First, complex ML models like deep neural networks lack the degradability and explainability to the true system model, leading to overfitting. There are also asynchronization issues among different meters without GPS chips. Last but not least, bad data is quite common in the distribution grids. To resolve these problems all at once, we propose a variational support matrix regression (SMR). It provides structural learning to (1) embed kernels to regularize physical form in observable area while achieving good approximation at unobservable area, (2) integrate temporal information into matrix regression for asynchronized data imputation, and (3) define support matrix for margins to be robust against bad data. We test the performance for mapping rule learning via IEEE test systems and a utility distribution grid. Simulation results show high accuracy, degradability from data-driven model to physical model, and robustness to data quality issues. [ABSTRACT FROM AUTHOR]

This paper proposes a novel real-time adaptive under voltage load shedding (UVLS) method by using optimized fuzzy logic controllers to address fault-induced delayed voltage recovery (FIDVR) and short-term voltage instability (STVIS) problems. An intelligent multi-input multi-output fuzzy logic load shedding controller is developed based on a short-term voltage recovery criterion (STVRC). For the controller, the magnitude deviation and the recovery time deviation of voltage trajectory are extracted as inputs, while the load shedding amount at the current load shedding stage and the time delay of the next stage are taken as outputs. Particle swarm optimization (PSO) technique is further employed for the tuning of the controller parameters to realize the voltage recovery requirement at the lowest cost of load shedding. The proposed UVLS method is formed by a group of the fuzzy logic controllers deployed at the load buses, each monitoring its own bus voltage and shedding load in closed-loop. Responding to the severity of voltage variations, the proposed method is able to adaptively determine the location, time and amount of load shedding in real-time to make the voltage satisfy the STVRC. The effectiveness of the proposed method compared to other methods is testified by simulations on the Nordic test system. [ABSTRACT FROM AUTHOR]

A distribution service restoration algorithm as a fundamental resilient paradigm for system operators provides an optimally coordinated, resilient solution to enhance the restoration performance. The restoration problem is formulated to coordinate distribution generators and controllable switches optimally. A model-based control scheme is usually designed to solve this problem, relying on a precise model and resulting in low scalability. To tackle these limitations, this work proposes a graph-reinforcement learning framework for the restoration problem. We link the power system topology with a graph convolutional network, which captures the complex mechanism of network restoration in power networks and understands the mutual interactions among controllable devices. Latent features over graphical power networks produced by graph convolutional layers are exploited to learn the control policy for network restoration using deep reinforcement learning. The solution scalability is guaranteed by modeling distributed generators as agents in a multi-agent environment and a proper pre-training paradigm. Comparative studies on IEEE 123-node and 8500-node test systems demonstrate the performance of the proposed solution. [ABSTRACT FROM AUTHOR]

Fundamental sensor feedback limitations for improving rotor angle stability using local frequency or phase angle measurement are derived. Using a two-machine power system model, it is shown that improved damping of inter-area oscillations must come at the cost of reduced transient stability margins, regardless of the control design method. The control limitations stem from that the excitation of an inter-area mode by external disturbances cannot be estimated with certainty using local frequency information. The results are validated on a modified Kundur four-machine two-area test system where the active power is modulated on an embedded high-voltage dc link. Damping control using local phase angle measurements, unavoidably leads to an increased rotor angle deviation following certain load disturbances. For a highly stressed system, it is shown that this may lead to transient instability. The limitations derived in the paper may motivate the need for wide-area measurements in power oscillation damping control. [ABSTRACT FROM AUTHOR]

The power and natural-gas industries have narrowed the time differences between daily power market clearing and natural-gas market clearing. This facilitates the gas-power coordination in day-ahead scheduling. However, using natural-gas-fired power units to balance the variability of renewable energy production may cause fluctuations in natural-gas demand, which result in risks to the natural-gas system in actual operation. As such, gas-power coordination at all time is highly desirable. We analyze the coordinated operation of power and natural-gas systems at the scheduling stage and in actual operation. We assume that the two systems are operated independently, but with information interchange. We use a Lagrangian decomposition approach to identify an operational equilibrium involving the two systems. Numerical results on two test systems verify the value of gas-power coordination in actual operation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parallel dual dynamic programming (PDDP)-based decentralized algorithm for the multi-area optimal power flow (MAOPF), which can preserve the information privacy and operational independence of each area. The MAOPF problem is decomposed into a series of subproblems for individual areas by the dual dynamic programming (DDP) algorithm, and the Benders cut-based value functions are used to reflect the impacts of one area’s decisions to the subsequent areas. The optimal solution of MAOPF can be obtained in a decentralized fashion, requiring only a limited amount of information exchange among neighbor areas. Moreover, a parallel processing technique is designed to avoid the waiting process of the basic DDP algorithm, thus accelerating the computing speed of the proposed decentralized algorithm. Compared with the existing decentralized algorithms, the proposed algorithm has better performance in terms of convergence and computational efficiency. In addition, there is no need for parameter tuning. Case studies on several IEEE test systems and a real 2298-bus system demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

AC optimal power flow (AC-OPF) problems need to be solved more frequently in the future to maintain stable and economic power system operation. To tackle this challenge, a deep neural network-based voltage-constrained approach (DeepOPF-V) is proposed to solve AC-OPF problems with high computational efficiency. Its unique design predicts voltages of all buses and then uses them to reconstruct the remaining variables without solving non-linear AC power flow equations. A fast post-processing process is also developed to enforce the box constraints. The effectiveness of DeepOPF-V is validated by simulations on IEEE 118/300-bus systems and a 2000-bus test system. Compared with existing studies, DeepOPF-V achieves decent computation speedup up to four orders of magnitude and comparable performance in optimality gap, while preserving feasibility of the solution. [ABSTRACT FROM AUTHOR]

Pumped storage hydro units (PSHU) can provide flexibility to power systems. This becomes particularly valuable in recent years with the increasing shares of intermittent renewable resources. However, due to emphasis on thermal generation in the current market practices, the flexibility from PSHUs has not been fully explored and utilized. This paper proposes a configuration based pumped storage hydro (PSH) model for the day-ahead market, in order to enhance the use of PSH resources in the system. A strategic design of incorporating and fully optimizing PSHUs in the day-ahead market is presented. We show the compactness of the proposed model. Numerical studies are presented in an illustrative test system and the Midcontinent Independent System Operator (MISO) system. [ABSTRACT FROM AUTHOR]

Harnessing flexibility from distributed energy resources (DER) to participate in various markets while accounting for relevant technical and commercial constraints is essential for the development of low-carbon grids. However, there is no clear definition or even description of the salient features of aggregated DER flexibility, including its steady-state and dynamic features and how these are impacted by network constraints and market requirements. This paper proposes a comprehensive DER flexibility modelling and characterisation framework that is based on the concept of nodal operating envelope (NOE). In particular, capacity, ramp, duration and cost are identified as key flexibility metrics and associated with different but consistent NOEs describing capability, feasibility, ramp, duration, economic, technical and commercial flexibility features. These NOEs, which conceptually arise from a Venn diagram, can be built via optimal power flow (OPF) analysis, visualised in the active-reactive power space, and used by different stakeholders. Results from a canonical test system and a real distribution system illustrate the value and applicability of the proposed framework to model and characterise provision of flexibility and market services from DER for different use cases. [ABSTRACT FROM AUTHOR]

Generation expansion planning (GEP) can be a challenging problem when short-circuit (SC) levels and transient stability constraints are considered. We propose a multi-period GEP model in which resistive superconducting fault current limiters (SFCLs) are deployed to limit SC levels, which may be elevated by new generators, and to enhance transient stability at the same time. Through investigating the effect of SFCLs on transient stability and SC levels, efficient linear regions of SFCL deployment are identified and employed to achieve a more cost-effective solution and enhance problem tractability. An effective solution method is also presented by decomposing the main problem into smaller ones. We also propose a linearized AC network framework incorporating bilinear terms based on McCormick envelopes. Relaxation errors are minimized by an exactness loop until the linearized model solution sufficiently matches the original nonlinear model solution. The methodology is illustrated and discussed using the IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

In the steady-state contingency analysis, the traditional Newton-Raphson method suffers from non-convergence issues when solving post-outage power flow problems, which hinders the integrity and accuracy of security assessment. In this paper, we propose a novel robust contingency analysis approach based on holomorphic embedding (HE). The HE-based simulator provides theoretical convergence guarantee, which is desirable because it avoids the influence of numerical issues and provides a credible security assessment conclusion. In addition, based on the multi-area characteristics of real-world power systems, a partitioned HE (PHE) method is proposed with an interface-based partitioning of HE formulation. The PHE method does not undermine the numerical robustness of HE and significantly reduces the computation burden in large-scale contingency analysis. The PHE method is further enhanced by parallel or distributed computation to become parallel PHE (P2HE). Tests on a 458-bus system, a synthetic 419-bus system and a large-scale 21 447-bus system demonstrate the advantages of the proposed methods in robustness and efficiency. [ABSTRACT FROM AUTHOR]

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model. [ABSTRACT FROM AUTHOR]

Polynomial approximation based on collocation method is an emerging technique to establish the relationship between changeable parameters and interested transient trajectory in a given parameter space. If transient stability region boundary (TSRB) exists in the parameter space, the approximation may have low accuracy due to the high sensitivity of the real trajectory with respect to parameters on TSRB. Utilizing the approximated trajectory and the high sensitivity characteristic, this letter proposes a complementary method to obtain TSRB by calculating the local maxima of a sensitivity-based index. The effectiveness of the method is verified in IEEE 39-bus test system. [ABSTRACT FROM AUTHOR]

This paper introduces a network topology identification (TI) method based on deep neural networks (DNNs) for online applications. The proposed TI DNN utilizes the set of measurements used for state estimation to predict the actual network topology and offers low computational times along with high accuracy under a wide variety of testing scenarios. The training process of the TI DNN is duly discussed, and several deep learning heuristics that may be useful for similar implementations are provided. Simulations on the IEEE 14-bus and IEEE 39-bus test systems are reported to demonstrate the effectiveness and the small computational cost of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper presents a distributionally robust network-constrained unit commitment (DR-NCUC) model considering AC network modeling and uncertainties of demands and renewable productions. The proposed model characterizes uncertain parameters using a data-driven ambiguity set constructed by training samples. The non-convex AC power flow equations are approximated by convex quadratic and McCormick relaxations. Since the proposed min-max-min DR-NCUC problem cannot be solved directly by available solvers, a new decomposition algorithm with proof of convergence is reported in this paper. The master problem of this algorithm is solved using both primal and dual cuts, while the max-min sub-problem is solved using the primal-dual hybrid gradient method, obviating the need for using duality theory. Also, an active set strategy is proposed to enhance the tractability of the decomposition algorithm by ignoring the subset of inactive constraints. The proposed model is applied to a 6-bus test system and the IEEE 118-bus test system under different conditions. These case studies illustrate the performance of the proposed DR-NCUC model to characterize uncertainties and the superiority of the proposed decomposition algorithm over other decomposition approaches using either primal or dual cuts. [ABSTRACT FROM AUTHOR]

This paper proposes a real-time coordinated scheduling method for active distribution networks (ADNs) with soft open points (SOPs) and plug-in electric vehicles (PEVs) via multi-timescale framework under uncertainties. Specifically, this method is achieved with day-ahead pre-scheduling and intra-day corrective control stages by coordinating various flexible resources at different timescales. The day-ahead stage is designed to reduce operational cost, regulate voltage profile and avoid risk exposure through joint scheduling of traditional devices, SOPs and PEVs on hourly basis. In intra-day corrective control stage, an hour is further divided into two timescales. The slow-timescale scheduling (STS) aims to corrective coordination of SOPs and across-time-and-space energy transmission of PEVs, and nested within the STS, the fast-timescale scheduling optimally coordinates the active & reactive power of SOPs and PV inverters to handle fast voltage fluctuations as well as against real-time uncertainties. The formulated three models are all transformed into second-order cone programming problems via sample weighted average approximation (SWAA), linearization and conic relaxation, which can be thus efficiently solved. Case studies based on three modified distribution systems (including two IEEE test systems and one actual distribution network) are performed to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Robust look-ahead dispatch (RLAD) is essential to manage uncertainties in power systems. As its key step, the worst-case scenario identification (WCSI) problem is cast to a max-min program. This computationally intensive procedure has to be performed repeatedly, impairing the computational efficiency of RLAD. To address this issue, an efficient RLAD scheme incorporating critical region preparation in gap time is proposed. The computation burden is mostly transferred from the online decision stage to the gap time via a customized technique based on multi-parametric programming. The accuracy of computing the critical regions is validated by the test in a six-bus system, and the proposed method is shown to cut down 21% of total iterations and save computational time dramatically by the test in a practical-scale system in Northeastern China. [ABSTRACT FROM AUTHOR]

This letter proposes an integrated transfer learning (TL) method for pre-fault dynamic security assessment (DSA) of power systems, which aims to simultaneously achieve fault transfer and address missing data issue for unlearned faults. Moreover, this letter provides the tight mathematic proof for the guaranteed DSA performance of the proposed integrated TL method. Comprehensive simulation results on the benchmark testing system have shown that the proposed integrated TL method can achieve a high DSA accuracy for unknown faults with complete data and can also maintain a satisfactory DSA accuracy for unknown faults even with incomplete data inputs. [ABSTRACT FROM AUTHOR]

We study the equilibria reached in electricity, natural-gas, and carbon-emission markets, where power producers simultaneously participate in these three markets. We use a conjectural-variations equilibrium model to represent both electricity and natural-gas markets, in which power/natural gas-producers play a quantity game and adjust their production decisions in reaction to the production levels of their rivals. We use a cap-and-trade mechanism to model the carbon-emission market. We develop a direct approach to identify equilibria involving the three markets, in which the optimality conditions of all players and market clearing conditions are gathered and solved jointly. Numerical results from two test systems illustrate the impact of carbon-emission trading and transmission constraints on the equilibria reached. Additionally, we compare equilibrium results under different types of competition. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven chance-constrained optimal gas-power flow (OGPF) calculation method without any prior assumption on the distribution of uncertainties of wind power generation. The Gaussian mixture model is employed to fit the uncertainty distribution, where the Bayesian nonparametric Dirichlet process is adopted to tune the component number. To facilitate the online application of the proposed methods, an online-offline double-track distribution construction approach is established, where the frequency of training the relatively time-consuming Dirichlet process Gaussian mixture model can be reduced. On account of the quadratic gas consumption expression of gas-fired generators as well as the linear decision rule based uncertainty mitigation mechanism, the chance constraints would become quadratic ones with quadratic terms of uncertainties, which makes the proposed model more intractable. An equivalent linear separable counterpart is then provided for the quadratic chance constraints, after which the intractable chance constraints could be converted into traditional linear ones. The convex-concave procedure is used to crack the nonconvex Weymouth equation in the gas network and the auxiliary quadratic equalities. Simulation results on two test systems validate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Transmission line failure in power systems prop-agate non-locally, making the control of the resulting outages extremely difficult. In Part II of this paper, we continue the study of line failure localizability in transmission networks and characterize the impact of cut set outages. We establish a Simple Path Criterion, showing that the propagation pattern due to bridge outages, a special case of cut set failures, are fully determined by the positions in the network of the buses that participate in load balancing. We then extend our results to general cut set outages. In contrast to non-cut outages discussed in Part I whose subsequent line failures are contained within the original blocks, cut set outages typically impact the whole network, affecting the power flows on all remaining lines. We corroborate our analytical results in both parts using the IEEE 118-bus test system, in which the failure propagation patterns exhibit a clear block-diagonal structure predicted by our theory, even when using full AC power flow equations. [ABSTRACT FROM AUTHOR]

The automatic generation control (AGC) system is temporally situated between economic dispatch and synchronous generator dynamics, and its primary role is to regulate frequency within and tie-line flows between control areas. Given appropriate choice of participation factors (feed-forward controller gains that govern the disaggregation of the area-level power requirement to individual generators), the AGC can be engineered to nudge system dynamics toward a steady-state operating point corresponding to economic optimality. This paper establishes necessary and sufficient conditions under which a widely accepted choice of participation factors guarantees the alignment of steady-state synchronous generator outputs with a global minimum of a prototypical economic dispatch problem. In so doing, it resolves several ambiguities and formalizes technical assumptions governing the role of the standard AGC architecture in the context of economic dispatch and steady-state operation. Numerical case studies tailored to a modified version of the New England 39-bus 10-machine test system validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a two-stage stochastic planning model for transmission systems and distributed energy resources (DERs) considering power system resiliency. The model takes into account both normal and emergency conditions as well as the duration of each condition. The proposed model is formulated as a mixed-integer linear program to minimize the total investment cost of transmission lines and DERs, expected values of generators’ operation cost in normal and emergency situations, and load shedding cost in emergency condition. The emergency scenarios are considered as moderate, severe, and complete damage states, which have different recovery times for transmission assets. The Benders decomposition technique is utilized to solve the optimization problem. Numerical results are demonstrated based on the IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

In transient stability simulators such as PSS/E, the bus frequency is estimated using a window of (positive-sequence) phasor angle measurements. A digital filter is often used to account for the filtering effect in actual measurement devices and to eliminate sudden changes during frequency computations. Although transient stability simulators label the filtered angle derivative as the “frequency,” the frequency provided by such programs does not match actual measurements reported by phasor measurement units (PMUs), which makes it difficult to gauge the validity of studies (e.g., wide-area event detection and control applications) that are based on such simulations. In this paper, we implement a frequency computation method directly using positive phasor angles provided by simulators. The proposed method is tested on two systems extensively and validated against the measurements of an actual PMU. The improved frequency measurements closely match PMU responses. Cross-validation results also suggest the method may be used for other systems without conducting full time-domain simulations. [ABSTRACT FROM AUTHOR]

The conventional Under Frequency Load Shedding (UFLS) scheme could result in unacceptably low frequency nadirs or overshedding in power systems with volatile inertia. This paper proposes a novel UFLS scheme for modern power systems whose inertia may vary in a wide range due to high penetration of renewable energy sources (RESs). The proposed scheme estimates the rate of change of frequency (RoCoF) of the center of inertia (CoI), and consequently, the loss of generation (LoG) size, using local frequency measurements only. An innovative inflection point detector technique is presented to remove the effect of local frequency oscillations. This enables fast and accurate LoG size calculation, thereby more effective load shedding. The proposed UFLS scheme also accounts for the effect of the inertia change resulting from LoG events. The performance of the proposed scheme is validated by conducting extensive dynamic simulations on the IEEE 39-bus test system using Real Time Digital Simulator (RTDS). Simulation results confirm that the proposed UFLS scheme outperforms the conventional UFLS scheme in terms of both arresting frequency deviations and the amount of load shed. [ABSTRACT FROM AUTHOR]

To analyze the grid integration effect of a virtual synchronous generator (VSG), this paper proposes a simple power system modeling method. It is shown that for a specific disturbance, by simplifying the original network to a radical n generators single-load model, its state-space small-signal model can be obtained using a unified formula, as long as the single generator infinite bus model of each generator is given. Case studies based on the IEEE 9-bus test system as well as the New York New England test system show high efficiency of the proposed modeling to represent slow power and frequency deviations. Modal analyses give insight into how system poles are synthesized by individual generator poles, and how different designs of VSGs affect the system oscillation modes. Potential errors due to the topology simplification and the measures to avoid them are discussed. The time-domain results and modal analyses highlight some important features of VSG, which are overlooked in previous studies. [ABSTRACT FROM AUTHOR]

With the increasing integration of renewable energy sources (RESs) and the implementation of dynamic line rating (DLR), the accompanying uncertainties in power systems require intensive management to ensure reliable and secure operational planning. However, while numerous approaches and methods in the literature deal with uncertainties, they have not been analyzed axiomatically. This paper presents an analysis of risk in power system operation using coherent risk measures, elaborating on the origin of risk and the mechanisms of its management in the presence of various sources of uncertainty. To illustrate the practicality and benefits of coherent risk measures, a risk-averse asymmetry robust unit commitment (UC) model is established. It is based on coherent reformulations of the uncertain reserve and line flow constraints and is formulated in the form of a compact computationally efficient mixed-integer second-order conic program (SOCP). The overall performance of the proposed framework is verified using the updated 2019 IEEE Reliability Test System and the ACTIVSg2000 test system over a year-long period. [ABSTRACT FROM AUTHOR]

Non-negligible amounts of Distributed Generating Units (DGUs) are already connected to power systems, predominantly to medium- and low-voltage networks. The interaction between distribution and transmission systems is gaining the attention of system operators. Given the high controlability of DGUs, the active distribution networks can potentially support the transmission system during emergency situations. Previously proposed voltage emergency controls involving distribution network assets focused on preserving the transmission system integrity, even if it implies affecting the distribution system operation (intrusive schemes). More attention needs to be devoted to supporting transmission voltages, while preserving the distribution network operation (non-intrusive schemes). This paper introduces a new adaptive and non-intrusive voltage emergency control scheme based on the synchronization of DGUs and the load tap changer of the corresponding distribution transformer. The conclusions are derived from time-domain simulations using an extended version of the IEEE Nordic test system for voltage stability assessment. [ABSTRACT FROM AUTHOR]

Extreme weather events pose a serious threat to energy distribution systems. We propose a distributionally robust optimization model for the resilient operation of the integrated electricity and heat energy distribution systems in extreme weather events. We develop a strengthened ambiguity set that incorporates both moment and Wasserstein metric information of uncertain contingencies, which provides a more accurate characterization of the true probability distribution. We first recast the proposed model into an equivalent framework which is similar to a conventional two-stage robust model and then utilize a modified column-and-constraint generation algorithm to solve the recast model. Numerical results from three test systems validate the enhanced resilience of the distributionally robust approach, the reduced conservatism of the strengthened ambiguity set, and the computational efficiency of the proposed solution algorithm. [ABSTRACT FROM AUTHOR]

The limitations of centralized optimization methods for power systems operation have led to the distributed computing paradigm, particularly in power distribution systems. The existing techniques reported in recent literature for solving distributed optimization problems are not viable for power distribution systems applications. The essential drawback remains a large number of required communication rounds, i.e., macro-iterations among the computing agents to solve one instance of the optimization problem; the typical number of macro-iterations are in the order of $10^2\sim 10^3$. In this paper, a new and scalable distributed optimization method based on Equivalent Network Approximation (ENApp) is proposed to solve optimal power flow (OPF) for a balanced radial distribution system. Specifically, the distribution system's radial topology is leveraged to reduce the decomposed systems into upstream and downstream network equivalents. The proposed innovations reduce the required number of macro-iterations/communication-rounds for convergence by order of magnitude. The approach is validated using IEEE 123-bus and IEEE 8500-node test systems and is shown to converge to the same optimal solution as obtained using an equivalent centralized OPF (C-OPF) model. [ABSTRACT FROM AUTHOR]