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This paper proposes a Principal Component Analysis (PCA)-based method to construct composite indices to rapidly assess power system transient stability. By assigning appropriate weights to a few selected sub-indicators, a composite index can be constructed to guarantee a better coverage of worst-case stability scenarios of the power system. This paper provides an automatic method to construct a composite index with four sub-indicators calculated by the integral of acceleration, speed deviation and rotor angle of generators over a certain integration period using PCA. The effectiveness of the sub-indicators is validated first, followed by a comprehensive example of process of composite index construction, and the assessment of the influence of the effect of integration period on the performance of the composite index. High accuracy of classification has been demonstrated using composite index with appropriate settings of the integration periods of the sub-indicators. [ABSTRACT FROM AUTHOR]

The stability of power systems can largely limit the power transfer capability limit of transmission lines. The PV generator control is different from synchronous generator control. The impact of PV generator dynamics on the power transfer limit constrained by stability is not well explored in the literature. This paper focuses on improving the stability constrained power transfer capability limit of transmission lines emanating from PV generators. The PV generator is provided with dc link voltage and reactive power control and is equipped with low voltage ride through capability, voltage and frequency support functionalities. In this paper, Lyapunov function analysis based adaptive tuning laws are proposed for PV control parameters to improve the power transfer capability limit (constrained by stability) of transmission lines connecting PV generators to grid. The tuning laws are proposed for Phase Locked Loop (PLL), outer and inner control loop parameters. The proposed tuning laws have inherent robustness towards faults, changes in solar irradiation, changes in grid topology, network impedances, generation and loads in the system. The effectiveness of the proposed method is validated on a Single PV-Synchronous Machine system, modified IEEE-39 and IEEE-118 bus system. The performance of the proposed method is investigated considering various disturbances such as symmetrical and asymmetrical faults on transmission line, switching of a transmission line and change in solar irradiation of PV. Comparison with existing method shows that the proposed tuning method can achieve higher power transfer capability limit considering stability. [ABSTRACT FROM AUTHOR]

Autonomous power systems with a single power station and a high-voltage (HV) network may be susceptible to overvoltage instability, especially during light-load conditions. Moreover, in low inertia systems, considerable frequency excursions may be observed after disturbances. To deal with voltage and frequency stability problems in such isolated power systems, several measures should be taken, such as rules for adequate automatic voltage control of the synchronous generators and load-tap-changers (LTCs), and/or adequate design of actions applied during emergency system conditions such as reactors switching, and redesigning underfrequency load shedding taking into account overvoltage problems. The effectiveness of the proposed countermeasures against overvoltage instability in autonomous power systems is illustrated in this paper. In 2016, the autonomous power system of the Greek island of Rhodes experienced similar voltage/frequency problems leading to a blackout. This event has been accurately reconstructed in this paper. The application of the suggested countermeasures during the simulation of the 2016 blackout event in Rhodes, further highlighted the effectiveness of these measures, providing a guideline for similar cases. [ABSTRACT FROM AUTHOR]

With the increase of photovoltaic penetration, the power-electronic converter (PEC)-interfaced generators with traditional control strategy may cause severe power oscillations after being disturbed due to lack of inertia and damping. The photovoltaic power plant controlled by virtual synchronous generator (VSG) technology, while introducing virtual inertia and virtual damping to improve the stability of the system, will also inherit its oscillation characteristics and cause a new oscillation mode. Aiming at this problem, this paper analyzes the difference between the system low-frequency oscillation (LFO) modes before and after the VSG is connected to the two-area system by the modal analysis. It is pointed out that the PEC-interfaced renewable energy generators based on VSG control technology could change the oscillation mode of the original system. The influence of VSG's main parameters and capacity on system dynamics is analyzed. Finally, a synchrophasor-based inter-area oscillation suppressed comprehensive control strategy is proposed to suppress the LFO of active power on the tie line, and the superiority of the strategy is verified by DIgSILENT /PowerFactory. [ABSTRACT FROM AUTHOR]

The risk of unstable subsynchronous oscillations (SSO) in DFIG-based wind parks radially connected to transmission lines with series capacitive compensation is typically assessed with numerous electromagnetic transient (EMT) simulations, which is a time-consuming process. However, not all operating scenarios present risk of SSO and require such a detailed investigation. This paper proposes two charts based on impedance equivalents of wind generators obtained through frequency scans to quickly map which combinations of parameters can create unstable SSOs and which combinations are risk-free. With the information, engineers can immediately filter out scenarios with no risk of instability and conduct detailed studies on fewer scenarios that are truly critical. These charts can be obtained with simple equations that use only information readily available in practice to engineers, without the need to run any computer simulation. The charts also reveal the key operating conditions that can increase the risk of an unstable SSO and provide real-time quantitative insights into how close a wind park is to an instability. Application examples are provided to illustrate how this approach can help engineers speed up studies to identify the risk of SSO. [ABSTRACT FROM AUTHOR]

Geomagneticallyinduced current (GIC) studies usually focus on transformer response to dc but seldom analyze generator excitation systems. A GIC is driven by an electric field which is induced by a very low-frequency geomagnetic field. It is widely acceptable to model GICs with dc, mostly suitable for static voltage stability analysis, but this does not adequately characterize a power system's dynamic response. Considering this, we studied a multi-machine power system on an OPAL-RT digital real-time simulator (DRTS)-MATLAB/Simulink system. We used real GIC measurement data from high and mid-latitude regions. Wavelet analysis related the frequency components of the GIC to the power system's response. A dynamic generator model with excitation voltage control modelled the source. Our main finding is that excitation system control contributes to reducing the voltage drop caused by increased var demand in saturated transformers with GICs. Measured GICs revealed non-negligible short-term dynamics affecting bus voltages that are not captured with dc-modelling assumptions, yet they are important for voltage stability analysis. This study implies that excitation control creates a buffer for high GICs to flow without violating the grid codes for minimum operating voltages and this paper demonstrates the optimization of this novel approach. [ABSTRACT FROM AUTHOR]

This paper develops a supervised learning of overcomplete dictionaries (SLOD) to efficiently perform online analysis and prediction of dynamic stability (DSP) in large power systems. To this end, multiple post-contingency signals with varying faults, load and generator switching are acquired by phasor measurement units (PMUs) based monitoring of all generators to form the training dataset. The SLOD approach then jointly learns a sparse feature dictionary and a stability status classifier using dynamic singular value decomposition (D-KSVD) and orthogonal matching pursuit (OMP). The aim is to learn features of the signals while adding a stability status term to the optimization problem. This enabled stable/unstable classes to be represented. The proposed SLOD manages to improve online DSP shortly after a contingency. It does this without any prior assumptions or signal preprocessing except for dynamic state estimation to get rotor speed from generator terminal PMU data. Test results on the IEEE 2-area 4 machines, 39 and 68 -bus test systems demonstrate that the SLOD gives more than satisfactory performance in all cases (i.e., ∼99.99% accuracy, ∼99.99% reliability, and 100% security) compared to Statistics and Machine Learning Toolbox™ -MATLAB that use time-series-based high-dimensional stability indices as input for DSP. [ABSTRACT FROM AUTHOR]

The increasing complexity of modern AC/DC power systems poses a significant challenge to a fast solution of large-scale transient stability simulation problems. This paper proposes the hybrid parallel-in-time-and-space (PiT+PiS) transient simulation on the CPU-GPU platform to thoroughly exploit the parallelism from time and spatial perspectives, thereby fully utilizing parallel processing hardware. The respective electromechanical and electromagnetic aspects of the AC and DC grids demand a combination of transient stability (TS) simulation and electromagnetic transient (EMT) simulation to reflect both system-level and equipment-level transients. The TS simulation is performed on GPUs in the co-simulation, while the Parareal parallel-in-time (PiT) scheduling and EMT simulation are conducted on CPUs. Therefore, the heterogeneous CPU-GPU scheme can utilize asynchronous computing features to offset the data transfer latency between different processors. Higher scalability and extensibility than GPU-only dynamic parallelism design is achieved by utilizing concurrent GPU streams for coarse-grid and fine-grid computation. A synthetic AC/DC grid based on IEEE-118 Bus and CIGRÉ DCS2 systems showed a good accuracy compared to commercial TSAT software, and a speedup of 165 is achieved with 48 IEEE-118 Bus systems and 192 201-Level detail-modeled MMCs. Furthermore, the proposed method is also applicable to multi-GPU implementation where it demonstrates decent efficacy. [ABSTRACT FROM AUTHOR]

Online transient analysis plays an increasingly important role in dynamic power grids as the renewable generation continues growing. Traditional numerical methods for transient analysis not only are computationally intensive but also require precise contingency information as input, and therefore, are not suitable for online applications. Existing online transient assessment studies focus on the determination of post-contingency system stability or stability margin. This paper develops a novel graph-learning framework, Deep-learning Neural Representation or DNR, for online prediction, of the time-series trajectories of the system states using initial system responses that can be measured by phasor measurement units (PMUs). The proposed DNR framework consists of two sequential modules: a Network Constructor that captures network dependencies among generators, and a Dynamics Predictor that predicts the system trajectories. The key to improved prediction performance is the introduction of the spatio-temporal message-passing operations into graph neural networks with structural knowledge. Its effectiveness and scalability are validated through comparative studies, demonstrating the prediction performance under different contingency scenarios for systems of different sizes. This framework provides a solution to online predicting post-fault system dynamics based on real-time PMU measurements. Additionally, it can also be applied to facilitate the offline transient simulation without simulating the entire trajectories. [ABSTRACT FROM AUTHOR]

Time-domain indirect methods based on Lyapunov stability theory and linear matrix inequality techniques (LMIs) have been applied for delay-dependent stability analysis of large-scale load frequency control (LFC) schemes. This paper aims to enhance the numerical tractability of large-scale LMIs by exploiting the special characteristics of the LFC loops. First, in the typical LFC model, only a few delayed states that are directly influenced by transmission delays are distinguished from other normal system states. Hence, an improved reconstruction model is formed, based on which the delay-dependent stability condition is established with the decreased order of the LMIs and decision variables. Then, to further improve the numerical tractability of the developed stability criterion, all weighting matrices required in the augmented Lyapunov functional are enforced to have structural restrictions by proposing an extended symmetry-exploiting technique. Case studies show that the method proposed in this paper significantly improves the calculation efficiency of stability criterion established for multi-area power systems at the cost of only a minor reduction in computational accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven small-signal stability constrained optimal power flow (SSSC-OPF) method with high computational efficiency. Instead of repeating the computational expense small-signal stability analysis via differential and algebraic equations during the iterative OPF process, a computationally cheap surrogate constraint for small-signal stability is developed. To reduce the learning difficulty for small-signal stability boundaries, an efficient sample generation strategy is proposed with sampling space compression. This allows us to use the support vector machine (SVM) with a kernel function to derive the explicit data-driven surrogate constraint for small-signal stability. Penalty factor optimization is proposed to compensate for the error caused by SVM. The learned small-signal stability constraint is embedded into the OPF model for generator control. An examination strategy is also developed to avoid the small-signal instability of re-dispatch caused by the error of the data-driven surrogate model. Comparison results with other model-based and data-driven methods on the IEEE 39-bus and 118-bus systems demonstrate the high computational efficiency and economic benefits of the proposed method. [ABSTRACT FROM AUTHOR]

Penetration of renewable energy resources (RERs) in the power grid continues to increase as we strive toward a greener environment for the future. While they have many advantages, most RERs possess little or no rotational kinetic energy, thereby threatening the frequency stability of future power grids. Energy storage systems (ESSs) can be used to mitigate this problem, as they are capable of providing virtual inertia to the system. This paper proposes a novel analytical approach for sizing ESSs to provide inertial support to the grid and maintain frequency stability in presence of RERs. This method analytically estimates the total inertia of the system using probability distributions of the outage states of conventional generators and RERs. RERs are modeled as multi-state units, considering the variability of their output power due to changes in weather conditions and also the forced outages of their equipment. The ESS is utilized to provide virtual inertia to the grid in the form of active power once the estimated system inertia falls below the minimum required during a disturbance. The efficacy of the proposed approach is tested on the IEEE 39 bus system and the results obtained by the analytical approach are validated using Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The inertia information of both synchronous generators (SGs)/equivalent SGs and converter interfaced generators (CIGs) are crucial to maintain the frequency stability of modern power grids. This paper proposes a novel data-driven method using ambient measurements, which seems to be the first method that can estimate the inertia constants of SGs/equivalent SGs and the virtual inertia constants of CIGs simultaneously without disturbing the system’s normal operating condition. Numerical studies in the IEEE 68-bus system demonstrate that the developed estimation method can estimate the inertia constants of different generation units accurately and is robust to measurement noises, missing measurements and the variation of operating conditions. [ABSTRACT FROM AUTHOR]

Emergency frequency control is one of the most critical approaches to maintain power system stability after major disturbances. With the increasing number of grid-connected renewable energy sources, existing model-based methods of frequency control are facing up with challenges of computational speed and scalability for large-scale systems. In this paper, the emergency frequency control problem is formulated as a Markov Decision Process and solved through a novel distributional deep reinforcement learning (DRL) method, namely the distributional soft actor critic (DSAC) method. Compared with other reinforcement learning methods that only estimate the mean value, the proposed DSAC model estimates the distribution of value function over returns. This advancement can lead to more insights and knowledge for the agent, with the benefit of a much faster and more stable learning process, and the improved frequency control performance. The simulation results on IEEE 39-bus and IEEE 118-bus systems demonstrate the effectiveness and robustness of proposed models, as well as the advantage compared to other state-of-the-art DRL algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for the design of over-frequency containment schemes in low inertia, high renewable systems. This methodology is demonstrated through the comprehensive redesign of the containment scheme for significant over-frequency events (e.g., the loss of an exporting HVDC interconnector) in the Ireland and Northern Ireland power system (All-Island System). The new scheme allows an existing synchronous generator runback system integrity protection scheme to be replaced with fixed wind tripping and dynamic response from wind. This exploits the capabilities of renewable generation to create effective protection and control resources. The methodology provides the steps required to determine the key parameters of the scheme (e.g., maximum allowable frequency, required volume of tripping, lowest trip frequency). A key consideration of the methodology is the volume of dynamic response from wind that can be deployed before frequency limits are violated (e.g., inertia and wind penetration). Dynamic simulations are performed in DSE Tools for the All-Island system considering a 2020 operational scenario. These simulations support the application of the methodology and demonstrate the effectiveness of the scheme designed for the All-Island system. [ABSTRACT FROM AUTHOR]

Loss of excitation (LOE) is one of the most important issues of synchronous alternators, which may be a source of genuine harms and could lead to power system instability. The principle issue to recognize LOE and stable power swing (SPS) is the time delay, which is a primary segment of the recognition time in all ongoing promise strategies. This paper introduces an effective scheme based on the first derivative of equivalent power factor angle (EPFA) of 3-phase voltage and current quantities in the direct-quadrature axis, to detect the LOE. The new algorithm, based on EPFA, is developed to reduce the required time of LOE recognition scheme. Comprehensive simulation studies are accomplished using MATLAB/Simulink as a robust simulation tool for various generator conditions such as full load and sudden load changes in addition to 3-phase faults with different location and duration times. The relay setting is determined and the algorithm performance is evaluated depending on various scenarios in power system. The simulated study results confirm that the proposed method can discriminate SPS from LOE conditions under different modes of operations. [ABSTRACT FROM AUTHOR]

In this paper, a distributed predefined-time fractional-order sliding mode controller (DPTFOSMC) is proposed for performance improvement of power system. The proposed DPTFOSMC is designed based on the multi-agent framework and distributed control theory, which can reduce the pressure of central controller in communication and calculation, thus obtaining fast and coordinated response. The DPTFOSMC can achieve the advantages of sliding mode control (SMC) with fast response and strong robustness for the power system. In addition, the power system under the proposed DPTFOSMC can be stabilized in stable range within a predefined time which is directly equal to the tunable parameter, thus meeting the high requirement for convergence time of the power system. The prescribed performance function (PPF) is carried out to design the DPTFOSMC, which can ensure that the power system can achieve the expected transient and steady responses. Meanwhile, fractional calculus is implemented to devise the DPTFOSMC to eliminate the chattering phenomenon of conventional SMC. The Lyapunov function is adopted to analysis the predefined-time stability of the power system under the proposed DPTFOSMC. Simulations are taken to validate the effectiveness and superior performance of the proposed DPTFOSMC for the power system. The results show that the DPTFOSMC can ensure the power system to achieve superior performances than the existing control methods. [ABSTRACT FROM AUTHOR]

Due to the increasing integration of distributed energy resources (DERs) into the national grid, research is needed to understand high DER penetration in relation to grid reliability and stability. Emulation-based research is a viable option to consider hardware intensive investigations. Indeed, DER emulation-based research has advantages over DER software-based simulation and real DER implementation research. Some of these advantages are more realistic performance and boundaries and considerably less expense, higher safety, and modularity. While the downside of DER emulation-based research is the complexity of modeling large scale grid systems. This paper provides a rationalization for the selection of an emulation-based DER laboratory and description of the DER laboratory’s capabilities. Additionally, guidelines for running experiments are discussed and two approaches, power scaling using rescaling coefficients and system sizing using Multi-Port Thevenin Equivalence (MPTE), are proposed to emulate realistic complex interconnected DER grid connected systems. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy, frequency response and its security are of significant concerns for reliable power system operations. Frequency-constrained unit commitment (FCUC) is proposed to address this challenge. Despite existing efforts in modeling frequency characteristics in unit commitment (UC), current strategies can only handle oversimplified low-order frequency response models and do not consider wide-range operating conditions. This paper presents a generic data-driven framework for FCUC under high renewable penetration. Deep neural networks (DNNs) are trained to predict the frequency response using real data or high-fidelity simulation data. Next, the DNN is reformulated as a set of mixed-integer linear constraints to be incorporated into the ordinary UC formulation. In the data generation phase, all possible power injections are considered, and a region-of-interest active sampling is proposed to include power injection samples with frequency nadirs closer to the UFLC threshold, which enhances the accuracy of frequency constraints in FCUC. The proposed FCUC is investigated on the IEEE 39-bus system. Then, a full-order dynamic model simulation using PSS/E verifies the effectiveness of FCUC in frequency-secure generator commitments. [ABSTRACT FROM AUTHOR]

Accurate models of power plants play an important role in maintaining the reliable and secure grid operations. In this paper, we propose a synchrophasor measurement-based generator parameter calibration method by a novel deep learning method with high computational efficiency. An elementary effects-based approach is developed to identify the critical parameters from a nonlinear system with much better performance than the widely used trajectory sensitivity-based method. Then, synchrophasor measurement-based conditional variational autoencoder is developed to estimate the parameters’ posterior distributions even in the presence of a high-dimensional case with eighteen critical parameters to be calibrated. The effectiveness of the proposed method is validated for a hydro generator with a very detailed model. The results show that the proposed approach can accurately and efficiently estimate the generator parameters’ posterior distributions even when the parameters true values are not in support of the prior distribution. [ABSTRACT FROM AUTHOR]

In this paper, a novel energy flow analysis (EFA) is proposed based on the signal reconstruction and decomposition to investigate the electromechanical oscillations. In contrast to the conventional EFA, the connection between the proposed EFA and modal analysis (MA) can be quantitatively revealed for arbitrary models of synchronous generators in multi-machine power systems. Firstly, the time-domain implementation (TDI) of the proposed EFA is designed. Specifically, the measurements at the terminal of a local generator are reconstructed through an exponential operator and then decomposed with respect to an angular frequency. Then, the mode-screened damping torque coefficient is defined to extract the damping feature with respect to an electromechanical oscillation mode. After that, the frequency-domain implementation (FDI) is derived. Specifically, the Parseval's Theorem is applied to transform the proposed EFA from the time domain to frequency domain. On this basis, the consistency between the proposed EFA and MA is strictly proved, which is applicable for arbitrary models of synchronous generators in multi-machine power systems. Additionally, the application procedure of the proposed EFA in investigating electromechanical oscillations is given. Finally, the proposed EFA are substantially demonstrated in multiple case studies. [ABSTRACT FROM AUTHOR]

Security-constrained unit commitment (SCUC) model is used for power system day-ahead scheduling. However, current SCUC model uses a static network to deliver power and meet demand optimally. A dynamic network can provide a lower optimal cost and alleviate network congestion. However, due to the computational complexity and the lack of effective algorithms, network reconfiguration has not been included in the SCUC model yet. This paper presents a novel approach to handle the computational complexity in security-constrained unit commitment (SCUC) with corrective network reconfiguration (CNR) while considering the scalability through accelerated-decomposition approach with fast screening non-critical sub-problems of SCUC-CNR. The proposed approach provides substantial computational benefits and is also applicable to SCUC. Simulation results on the IEEE 24-bus system show that the proposed methods are substantially faster without the loss in solution quality while the scalability benefits are demonstrated using larger cases: the IEEE 73-bus system, IEEE 118-bus system and Polish system. [ABSTRACT FROM AUTHOR]

Low frequency electromechanical oscillations can pose a threat to the stability of power systems if not properly addressed. This paper proposes a novel methodology to damp these inter-area oscillations using loads, the demand side of the system. In the proposed methodology, loads are assigned to an aggregated cluster whose demand is modulated for oscillation damping. The load cluster control action is obtained from an optimal output feedback control (OOFC) strategy. The paper presents an extension to the regular OOFC formulation by imposing a constraint on the sum of the rows in the optimal gain matrix. This constraint is useful when the feedback signals are generator speeds. In this case, the sum of the rows of the optimal gain matrix is the droop gain of each load actuator. Time-domain simulations of a large-scale power system are used to demonstrate the efficacy of the proposed control algorithm. Two different cases are considered: a power imbalance and a line fault. The simulation results show that the proposed controllers successfully damp inter-area oscillations under different operating conditions and with different clustering for the events considered. In addition, the simulations illustrate the benefit of the proposed extension to the OOFC that enable load to provide a combination of droop control and small signal stability augmentation. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for advanced demand side management (DSM) in the distribution network (DN), catering at the same time for the requirements of the network operator, transmission or distribution, the available flexibility of the demand side, and the preservation of network performance. The basic premise of the study is that the distribution network operator is providing flexibility to the transmission system operator through load shaping. Different, one or more, indicators can be chosen to assess preservation of network performance. In this paper, for illustrative purposes of the methodology, the steady state voltage stability index, namely the load margin, is chosen as the network performance indicator. This is evaluated before and after a DSM action, in order to analyse the possible effect of DSM on network loadability. Load at each DN bus is represented using a realistic composite load model comprising controllable and uncontrollable loads. The DSM is initially performed based on optimal power flow calculation to ensure that the distribution system load profile at the grid supply point follows the required (pre-specified) load profile during a 24 hour period. Following this, a particle swarm optimisation is used to modify DSM program in those time steps of the planning horizon where load margin is reduced. The methodology is illustrated on a number of case studies using modified IEEE 33 bus distribution network model. The results illustrate the extent to which the available flexibility of demand can be used in support of transmission network operation when the preservation of network performance and appropriate load modeling are considered. [ABSTRACT FROM AUTHOR]

The reduction in bus voltage magnitudes as the load demand grows may lead to sudden disconnection of loads and/or distributed generation units, in distribution grids, caused by undervoltage protection schemes. As proposed in this paper, this discontinuous behavior of distribution grids can be modeled as a sudden load variation in traditional static voltage stability assessment methods, such as the continuation power flow (CPFLOW). A discussion on the impacts of these discontinuities on the equilibrium diagram of the system is presented in this paper, as well as a set of numerical simulations showing that the traditional CPFLOW algorithm presents convergence problems caused by the discontinuities under analysis. From this perspective, this paper proposes an algorithm based on novel predictor/corrector and identification schemes, which are capable of successively calculating the discontinuities that exist in the equilibrium loci of the system under analysis, as well as the maximum loadability point and the type of bifurcation. A simplified modeling approach that eliminates the need for a complex (and computationally expensive), detailed description of distribution grids is also elaborated and incorporated into the proposed algorithm. The simulated examples show that the proposed algorithm adequately handles the problem, yelding more accurate results than the traditional CPFLOW algorithm. [ABSTRACT FROM AUTHOR]

As renewable energy penetration increases and system inertia levels drop, primary frequency control is becoming a critical concern in relatively small interconnections such as the Electric Reliability Council of Texas (ERCOT). To address this problem ERCOT is implementing a number of market rule changes including the introduction of a new Fast Frequency Response (FFR) reserve type to the electricity market. This FFR reserve type aims to help the traditional Primary Frequency Response (PFR) reserve type in arresting frequency decline in the event of a large generator outage. This paper derives reserve requirements to ensure sufficient reserve to arrest frequency decline before reaching the critical frequency threshold while coupling PFR reserve, FFR reserve, and system inertia. The general reserve requirement places limits on the amount of PFR reserve that can be provided by each unit based on its ramping capabilities. Two such limits are derived from first principles and another is proposed that is capable of accommodating the equivalency ratio introduced in previous work. These PFR reserve limits also provide first principles insight into equivalency ratios, which have only been studied empirically in the past. High-level insights are provided on a large Texas test case. [ABSTRACT FROM AUTHOR]

This paper proposes the design of two coordinated wide-area damping controllers (CWADCs) for damping low frequency oscillations (LFOs), while accounting for the uncertainties present in the power system. The controllers based on Deep Neural Network (DNN) and Deep Reinforcement Learning (DRL), respectively, coordinate the operation of different local damping controls such as power system stabilizers (PSSs), static VAr compensators (SVCs), and supplementary damping controllers for DC lines (DC-SDCs). The DNN-CWADC learns to make control decisions using supervised learning; the training dataset consisting of polytopic controllers designed with the help of linear matrix inequality (LMI)-based mixed $H_2/H_\infty$ optimization. The DRL-CWADC learns to adapt to the system uncertainties based on its continuous interaction with the power system environment by employing an advanced version of the state-of-the-art deep deterministic policy gradient (DDPG) algorithm referred to as bounded exploratory control-based DDPG (BEC-DDPG). The studies performed on a 33 machine, 127 bus equivalent model of the Western Electricity Coordinating Council (WECC) system-embedded with different types of damping controls demonstrate the effectiveness of the proposed CWADCs. [ABSTRACT FROM AUTHOR]

Out-of-Step (OOS) protection against severe grid disturbances is one of the most serious concerns of the power industry. Many methods have been proposed to identify the OOS condition in which impedance-based relays are one of the most widely used ones. However, some problems have been reported associated with the performance and application of these techniques. Therefore, to alleviate some of these problems, this paper presents a new real-time approach based on the active power deviation to estimate the instability of a single synchronous generator in the multi-machine power system. The angular velocity and acceleration data obtained from the instantaneous active power are continuously calculated to determine whether or not the generator experiences an unstable condition. The instability can be distinguished by monitoring the polarity of extracted angular velocity and acceleration data during the power swing. The instantaneous active power is computed locally using voltages and currents measured at the terminals of each generator. Additionally, this method does not require such information as fault clearing time and network parameters. The reliability of the presented approach and its independence from the network configuration are successfully investigated by simulating various scenarios. Furthermore, simulation results demonstrate the straightforward and satisfactory application of this method. [ABSTRACT FROM AUTHOR]

Interactions of identical inverters in weak grids have received wide attentions. However, in a practical wind farm, parameters of grid-side inverters and lengths of collecting lines are not completely the same. In this case, a multi-inverter system is not symmetric, and thus the interaction mechanism could be more complicated than that of identical inverters. To investigate the interaction mechanism of differently parameterized inverters, this paper proposes a clustering-based modeling method, in which inverters with identical parameters are classified as one group. The clustering-based model allows for efficient stability assessment using three low-order transfer function matrices, instead of a full-order dynamic model. The root locus analysis is applied in the clustering-based model for stability analysis. Results show that the interconnection of distinct groups of inverters deteriorates common current stability, but has no impact on interactive current stability. The simulation and rtlab-based experimental results validate the effectiveness of the proposed model and the interaction mechanism of differently parameterized inverters. [ABSTRACT FROM AUTHOR]

Extreme events can cause severe power system damage. Resilience-driven operation of networked microgrids (MGs) has been heavily studied in literature. There is, though, little research considering the influence of resilience on decision making for planning. In this paper, a three-level model is suggested to solve the optimal sizing problem of networked MGs considering both resilience and cost. In the first level, a meta-heuristic technique based on an adaptive genetic algorithm (AGA) is utilized to tackle the normal sizing problem, while a time-coupled AC OPF is utilized to capture stability properties for accurate decision-making. The second and third levels are combined as a defender-attacker-defender model. In the former, the suggested AGA is utilized to generate attacking plans capturing load profile uncertainty and contingencies for load shedding maximization, while a multi-objective optimization problem is suggested for the latter to obtain a trade-off between cost and resilience. Simulations considering meshed networks and load distinction into critical and non-critical are developed to demonstrate algorithm effectiveness on capturing resilience at the planning stage and optimally sizing multiple parameters. The results indicate that higher resilience levels lead to higher investment cost, while sizing networked MGs leads to decreased investment in comparison with standalone MGs sizing. [ABSTRACT FROM AUTHOR]

This paper presents an optimal transient-stability control strategy that modulates the real power injected and absorbed by distributed energy-storage devices. These devices are located at the high-voltage bus of several generators in a synchronous power system. The system is broken into areas based upon groupings of generators. The control strategy consists of two parallel feedback loops. One loop focuses on preserving the synchronism of the generator to its own area. The second loop focuses on preserving the synchronism of a given area to the other areas. Each control loop strategy is based upon local and center-of-inertia frequency measurements. The strategy is derived from two perspectives. With the first, the goal is to remove as much kinetic energy gained during a disturbance as quickly as possible before it is converted to potential energy. With the second perspective, an optimal transient control cost-function is minimized. Both perspectives result in the same strategy. The performance of the control strategy is evaluated on a four-machine power system model and on a 34-generator reduced-order model of the western North-American grid. The results show that this control approach significantly improves the transient stability of power systems. [ABSTRACT FROM AUTHOR]

Distance relays are quite vulnerable to maloperation during dynamic stressed situations. The apparent impedance seen by the relay encroaches the zone-3 resulting in distance relay maloperation that can initiate cascading failures. This paper presents an enhanced scheme for wide area backup protection which implements improved protection algorithms to decide final relaying status. A machine learning tool namely Deep Neural Network is utilized to build those protective relaying decision logics: RDL-1 and RDL-2. Wide area information retrieved from phasor measurement units (PMU) is used to take real time decisions. RDL-1 is designed to detect if the system is operating in normal or stressed condition. During normal state, traditional zone-3 relay undertakes the relaying decision. However, under stressed situations, RDL-1 switches the decision-taking to RDL-2. RDL-1 also predicts whether the system is progressing towards an out-of-step situation so that appropriate remedial action can be undertaken. Proposed scheme was studied on IEEE-39 bus New England system using MATLAB/SIMULINK and validated on Real Time Digital Simulator platform and third zone mal-tripping are avoided. Performance of the proposed algorithm was compared with the conventional blinder and other data-mining techniques which show considerably high classification accuracy. [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]

This paper presents a comprehensive analysis of the impact that supplementary power control of an HVDC link has on the electromechanical dynamics of power systems. The presented work addresses an interesting phenomenon that may occur when an HVDC power controller is installed to support frequency stability. In specific cases, a high gain HVDC frequency controller could deteriorate system damping. The given analytical study is the first of its kind that addresses this issue by including both: (i) the important higher-order generator dynamics that affect small signal stability simultaneously with an HVDC control as well as (ii) the available local angle/frequency input signals of the controller. The methodological approach here analytically formulates the impact an HVDC control has on the single generator dynamics. Furthermore, the relationship between the damping/synchronizing coefficients and the HVDC gain is explicitly derived when a frequency proportional HVDC controller is installed. The derived expressions confirm that, indeed, there is an optimal HVDC gain with respect to the damping coefficient and a typically positive impact of the HVDC controller on the synchronizing component. Finally, the developed theoretical foundation is demonstrated by the tools of linear and nonlinear analysis in a one-machine system case study. [ABSTRACT FROM AUTHOR]

This paper proposes a transient stability constrained controlled islanding (TSC-CI) approach against cascading events in power systems. Using the wide area measurements, the proposed islanding algorithm is implemented regarding the actual dynamic conditions of the resulted islands. Since the main concern, right after the execution of controlled network splitting, is the transient stability of synchronous machines, a transient energy function is utilized for proper network partitioning. The proposed transient stability criterion is expressed as a function of the transfer impedance between each pair of generators in the resulted islands. Transfer impedance between each pair of coherent generators determines the direction of network splitting for transient stability improvement. A multi-objective function is then introduced to provide the transient stability with least possible power imbalance, as a resilience measure, over the created islands considering operational and structural constraints. Based on the wide-area measurements, a proper weighting procedure is utilized to prioritize the critical islands, avoiding the unnecessary power imbalance in favor of transient stability improvement. The proposed TSC-CI model is formulated as a mixed integer linear programming (MILP) multi-objective model and is solved using CPLEX in GAMS. The obtained results are compared with the conventional islanding scheme using the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

Inverter Based Generators (IBGs) have been increasing significantly in power systems. Due to the demanding thermal rating of Power Electronics (PE), their contribution to the system Short Circuit Current (SCC) is much less than that from the conventional Synchronous Generators (SGs) thus reducing the system strength and posing challenges to system protection and stability. This paper proposes a Unit Commitment (UC) model with SCC constraint in high IBG-penetrated systems to ensure minimum operation cost while maintaining the SCC level at each bus in the system. The SCC from synchronous generators as well as the IBGs are explicitly modeled in the formulation leading to an SCC constraint involving decision-dependent matrix inverse. This highly nonlinear constraint is further reformulated into linear form conservatively. The influence of the SCC constraint on the system operation and its interaction with the frequency regulation are demonstrated through simulations on IEEE 30- and 118-bus systems. [ABSTRACT FROM AUTHOR]

In multi-infeed hybrid AC-DC (MIDC) systems, the asynchronous interconnection between regional grids, complicated system dynamics and possible emergency faults have enormous effects on the frequency stability. To address the frequency instability problems in emergency situations, this paper proposes a decentralized emergency frequency control (EFC) strategy based on coordinated droop for the MIDC system. First, a P-f droop control for LCC-HVDC systems is introduced, and the coordinated droop mechanism among LCC-HVDC systems and generators is designed. Then, to appropriately allocate the power imbalance among the LCC-HVDC systems and generators, an optimal emergency frequency control (OEFC) problem is formulated, and the optimal droop coefficients are selected in a decentralized way, which can deal with various control objectives. A Lyapunov stability analysis shows that the closed-loop equilibrium is locally asymptotically stable considering the LCC-HVDC dynamics. The effectiveness of the proposed emergency control strategy is verified through simulations. [ABSTRACT FROM AUTHOR]

Hybrid storage system composed of battery energy storage systems (BESSs) and supercapacitors is a promising solution to mitigate the high frequency power fluctuations of pulsed power loads (PPLs) in medium voltage DC (MVDC) shipboard power systems. Due to the presence of multiple storage units, a power sharing algorithm needs to be considered within the energy management system (EMS) in the shipboard power system. In this paper, an optimal power flow problem is formulated for MVDC shipboard power systems with hybrid energy storage systems. Battery energy storage systems (BESSs) and conventional generation units are enhanced with virtual resistive droop controllers to share the steady-state power fluctuations. Supercapacitors are enhanced with virtual capacitive droop controllers to share the high frequency fluctuations in the load. The optimal flow accounts for minimizing the operational cost of the generation units in the shipboard power system considering the constraints of network, load balance, voltage profile, and power/energy limits. Second-order cone programming (SOCP) relaxation is used to approximate the nonconvexity of the optimal flow formulation and necessary conditions for global optimality of the solution are discussed. Results confirm the effectiveness of the proposed formulation in load support and managing the energy between storage units. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology for the construction of a transient stability boundary (TSB) that overcomes the lack of TSB analytical description for multiple operating states and contingencies in power systems. The proposed approach models the TSB as a nonlinear mapping between the system parameters of interest and the corresponding critical clearing time (CCT). This compact mathematical expression is built based on an efficient discriminative network, broad learning system (BLS). While keeping a high accuracy and generalization ability, the newly introduced construction method provides an efficient update strategy that does not require an entire retraining cycle. These properties make this method suitable for online transient stability assessment (TSA). The prospects of the developed method are verified via case studies by employing the IEEE 9-bus, IEEE 39-bus (New England) test systems and a real system of China Southern Power Grid. In comparison with existing methods, the newly introduced algorithm has a higher prediction accuracy and improved robustness. The demonstrated characteristics indicate that the proposed method may serve as a valuable tool in the framework of online TSA. [ABSTRACT FROM AUTHOR]

The increased penetration of wind power introduces more operational changes of critical corridors and the traditional time-consuming transient stability constrained total transfer capability (TTC) operational planning is unable to meet the real-time monitoring need. This paper develops a more computationally efficient approach to address that challenge via the analytical deep learning-based surrogate model. The key idea is to resort to deep learning for developing a computationally cheap surrogate model to replace the original time-consuming differential-algebraic constraints related to TTC. However, the deep learning-based surrogate model introduces implicit rules that are difficult to handle in the optimization process. To this end, we derive the Jacobian and Hessian matrices of the implicit surrogate models and finally transfer them into an analytical formulation that can be easily solved by the interior point method. Surrogate modeling and problem reformulation allow us to achieve significantly improved computational efficiency and the yielded solutions can be used for operational planning. Numerical results carried out on the modified IEEE 39-bus and 68-bus systems demonstrate the effectiveness of the proposed method in dealing with complicated TTC constraints while balancing the computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Convex hull pricing has been introduced recently to increase transparency and reduce uplift payments for the U.S. wholesale markets. A convex primal formulation approach is one of the most efficient methods to obtain a high-quality convex hull price. Even though significant progress has been made, the co-optimization of energy and ancillary services is much more challenging due to the discrete nature in formulating ancillary services, for example, the regulating reserve commitment variables, which are binary introduced by some Independent System Operators (ISOs), such as Midcontinent ISO (MISO), to capture the special characteristics of certain generators, such as combined-cycle units. In this paper, we propose convex primal formulations for convex hull pricing considering regulating, spinning, and online/offline-supplemental reserves, in which the regulating reserve commitment variables are considered. Accordingly, we can solve a linear program, instead of a mixed-integer program, which is much harder to solve, to derive the minimum uplift payments and exact convex hull price for the case without general ramping constraints. For the case with general ramping constraints, an upper bound of the minimum uplift payment can also be derived. The final computational experiments on MISO cases verify the effectiveness of our approach in solution quality and computational time. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for enhancing the power system flexibility, which can respond properly to contingencies in real-time operations. The proposed approach introduces a unified power flow controller (UPFC) in a three-stage security-constrained optimal power flow (SCOPF). The pre- and post-contingency system operation states are divided into three stages including the base case, post-contingency short-term, and post-contingency long-term periods. The UPFC applications re-route active power flow and provide reactive power to mitigate overloads and voltage violations when line outages occur in power systems. UPFC is adopted as a fast-response corrective control device during the post-contingency short-term period, which is coordinated with the conventional slow-response corrective control system during the post-contingency long-term period. A convex approach is applied to reformulate the original nonlinear nonconvex SCOPF problem into a second-order cone programming (SOCP) problem. A two-level algorithm using Benders decomposition and sequential cone programming (SCP) is applied to solve the large-scale SOCP problem. An improved covering cut bundle (CCB) strategy is proposed to accelerate the convergence of the Benders decomposition algorithm. Numerical results show the effectiveness of the proposed model and its solution technique for enhancing the power system flexibility. [ABSTRACT FROM AUTHOR]

This paper proposes a method for the optimal deployment of Corrective Control Measures (CCMs) for the improvement of transient stability in uncertain power systems. First, the critical oscillation patterns of the disturbed system are identified using Hierarchical Clustering (HC) with statistically defined algorithm parameters. This is followed by the identification of critical generators where the application of CCMs will have maximum impact. The results show that a significant reduction in multi-machine unstable events can be achieved by the strategic deployment of CCMs. The proposed method is demonstrated on a modified IEEE 68 bus NETS-NYPS test network with Renewable Energy Sources (RES) and realistically modelled system uncertainties. [ABSTRACT FROM AUTHOR]

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

This paper provides the concept of design, implementation, and system integration of energy efficient power management solution for a fault-tolerant more electric engine/aircraft (MEE/MEA). The power management solution consists of three components, i.e., the power management system (PMS), the stability analysis module, and the condition-based control (CBC) module. The PMS is to optimize the electrical power system (EPS) level efficiency based on constraints with consideration of power limits of the dc system in the MEE/MEA architecture, which are calculated by the stability analysis module, and system reconfiguration, which is provided by the CBC module. This paper focuses on the design and implementation of PMS algorithm for EPS of a fault-tolerant MEE/MEA architecture. A PMS solution to optimize EPS level efficiency optimization is proposed, which is based on multiple objective optimization problem (MOOP). The proposed MOOP is solved with a modified nondominated genetic algorithm with local search mechanisms. The proposed power management solution are implemented in the MEE/MEA simulation model as well as hardware-in-loop virtual testbed and results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Homotopy analysis method (HAM) is a popular semi-analytical method used widely in applied sciences. It stands out from the rest of the semi-analytical methods as it provides a family of solutions to nonlinear equations, including ordinary differential equations (ODEs), partial differential equations, etc. The convergence characteristics of the solutions can be varied by changing an auxiliary parameter ($\hbar$) in HAM. The convergence region of solution of ODEs using HAM can be improved by applying it over multiple intervals of time, which is referred to as multi-stage HAM (MHAM). In this paper, MHAM models for the IEEE Model 2.2 synchronous machine, IEEE Type-1 excitation system, first-order governor and first-order turbine models have been developed. The applicability of MHAM for power system dynamic simulations has been investigated in this paper using seven widely used test systems ranging from 10 generators 39 bus systems to 4092 generators 13 659 bus systems. The effect of number of terms, $\hbar$ and the time step on the accuracy and stability of the solution has been studied. The effectiveness of MHAM has been compared with the modified Euler (ME) and midpoint Trapezoidal (TrapZ) methods. The accuracy of MHAM has been found to be comparable with ME and TrapZ methods for the values of $\hbar$ between $-$ 1.05 and $-$ 0.95. The best accuracy is obtained for $\hbar$ = $-$ 1.0, which is a special case of MHAM called multi-stage homotopy perturbation method (MHPM). In this paper, it is also shown that MHPM is equivalent to multi-stage adomian decomposition method, which has been recently explored for large power system simulations. [ABSTRACT FROM AUTHOR]

A continuous Online Monitoring System (OMS) for power system stability based on Phasor Measurements (PMU measurements) at all the generator buses is proposed in this paper. Unlike the state-of-the-art methods, the proposed OMS does not require information about fault clearance. This paper proposes a convolutional neural network, whose input is the heatmap representation of the measurements, for instability prediction. Through extensive simulations on standard IEEE 118-bus and IEEE 145-bus systems, the effectiveness of the proposed OMS is demonstrated under varying loading conditions, fault scenarios, topology changes, and generator parameter variations. Two different methods are also proposed to identify the set of critical generators that are most impacted in the unstable cases. [ABSTRACT FROM AUTHOR]

This paper investigates the torsional subsynchronous oscillations (SSOs) of synchronous generators caused by the grid-connected wind farms. The investigation does not rely on the representation of a wind farm by an aggregated wind generator and is based on a multi-input and multi-output closed-loop model. The model is comprised of the wind farm subsystem, which includes all the wind farms, and the subsystem of rest of power system (ROPS). Theoretical analysis proves that the open-loop SSO modal coupling of wind farm subsystem and ROPS subsystem results in the closed-loop SSO modal repulsion on the complex plane. Subsequently, damping of torsional SSOs decreases and growing SSOs may occur when the closed-loop modal repulsion is strong. Hence, closed-loop modal repulsion explains and reveals the mechanism about why the wind farms may cause the torsional SSOs in the power system. In addition, a method of open-loop modal analysis is proposed to detect the SSO instability risk brought about by the wind farms. The detection is based on the estimation of degree of closed-loop modal repulsion and only needs the modal information of open-loop subsystems. An example power system with wind farms is presented to demonstrate analysis and conclusions made in the paper. [ABSTRACT FROM AUTHOR]