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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]

Power system inertia is declining and is increasingly variable and uncertain in regions where the penetration of non-synchronous generation and interconnectors is growing. This presents a challenge to power system operators who must take appropriate actions to ensure the stability and security of power systems relying on short-term forecasts of the system’s inertial response. Existing models to forecast inertia fail to quantify uncertainty, which may prevent their utilization given the risk aversion of the system operators when handling stability issues. This paper is the first to develop a model to produce calibrated, data-driven probabilistic forecasts of the inertia contribution of transmission-connected synchronous generators. The model provides a necessary tool for system operators to quantify forecast uncertainty, allowing them to manage the risk of frequency instability cost-effectively. The paper demonstrates that the assumption of a Gaussian distribution of uncertainty applied in existing models is not acceptable to accurately forecast the inertial response and provides a satisfactory forecast model by combining non-parametric density forecasting with parametric tail distributions. Moreover, the paper shows that satisfactory predictive performance can only be achieved by adopting a rolling horizon forecast approach to deal with the rapidly changing characteristics of the inertial response in power systems. [ABSTRACT FROM AUTHOR]

Phase angle measurements from synchrophasors show discontinuities when they roll over from +180 to -180 degrees or vice versa. This paper proposes efficient strategies for unwrapping of the angles in real-time data streams. Examples presented in this paper first show that the phase angle differences across bus voltage phasors can go over 360 degrees in a synchronized power system under stressed conditions. Unwrapped phase angles are shown to be useful in fast reliable islanding detection methodology, and for phase angle arithmetic such as for averaging of phase angles and for phase angle difference calculations. Strategies for handling missing phase angle data in real-time data streams are also discussed. [ABSTRACT FROM PUBLISHER]

After any major blackout, recreating the exact scene is one of the crucial but foundation steps in postmortem analysis. This helps in identifying and understanding the exact causes and sequence of events to avoid such failures in the future. Rather, power system restoration demands critical skills which involves deployment of appropriate strategies based on information about various factors, notably the extent and duration of the blackout, location of black-started units, interconnections with neighbouring systems, generator capabilities, and selecting appropriate restoration paths. The actual execution of the restoration plan consists of many surprises of unique nature and a lot of learning’s to avoid future occurrences of such incidents. The restoration efforts and failure of Mumbai grid failure on October 12, 2020, are highlighted in this paper. The paper first proposes formulating the dynamic models to get a better insight of the restoration process in the event of critical issues during this incident. The various challenges faced in systematic recovery of such a large system and lessons learnt from it forms focus of the paper. The paper also discusses factors not covered in existing literature, such as weather, fuel availability, and water mass oscillations which plays an important role in the restoration. [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]

High-quality generator dynamic models are critical to reliable and accurate power systems studies and planning. With the availability of PMUs, measurement-based approach for model validation has gained significant prominence. In this approach, the quality of a model is analyzed by visually comparing measured generator response with the model-based simulated response for large system disturbances. This paper proposes a new set of performance metrics to assess the model validation results to facilitate automation of the model validation process. In the proposed methodology, first, the slow governor response and comparatively faster oscillatory response are separated, and then a separate set of performance metrics is calculated for each of these two components. These proposed metrics quantify the mismatch between the actual and model-based response in a comprehensive manner without missing any information enabling automation of the process. Furthermore, in this paper, we are also proposing that the sensitivity analysis for model calibration be performed with respect to the proposed metrics for the systematic identification of key parameters. Results obtained using both simulated and real-world case-studies validate the effectiveness of the proposed performance metrics for model validation and their application to the sensitivity analysis for model calibration. [ABSTRACT FROM AUTHOR]

This paper proposes a novel inertia-enhanced distributed control method to complement the inertia of microgrids. The rate of change of frequency (RoCoF) and the rate of change of voltage (RoCoV) are employed in this paper to quantify the frequency inertia and voltage inertia, respectively. Then, a fully distributed algorithm with constrained changing rates is proposed. By bounding the changing rates of frequency and voltage during the consensus control, the algorithm can address the consensus problem while enhancing the inertia of microgrids. Compared with most inertia control methods, the proposed method can utilize the reserve power of scattered DGs to supply inertia. Besides, it performs better under disturbances and delays than conventional distributed control methods. The effectiveness of the proposed method is validated by several cases in MATLAB/Simulation and a hardware experiment. [ABSTRACT FROM AUTHOR]

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]

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]

Near-optimal unit commitment (UC) scheduling is a practical reality in wholesale electricity markets. This paper revisits previous work that has found that minor differences in cost among near-optimal schedules can result in a large redistribution of market payments (i.e., changes in generator profits and consumer surplus). It has been believed that this instability is unavoidable, but previous studies have only calculated prices using what we call the Restricted pricing model. This paper compares previous results to three additional models that are based on integer relaxation, and which we call the Partial, Tight, and Loose Dispatchable pricing models. Results are presented for a suite of test cases, including four ISO-scale cases. Similar to previous findings, the Restricted and Partial Dispatchable models both result in large payment redistributions among alternative solutions. In contrast, theoretical and experimental results for the Tight and Loose Dispatchable models show that pricing models with unconditional integer relaxation will have bounded payment redistributions, and, further, this bound can become quite small by tightening the UC problem's convex relaxation. In the presence of market power, stable financial outcomes may improve market efficiency by reducing incentives to bid strategically. [ABSTRACT FROM AUTHOR]

This paper introduces a novel methodology of parameter estimation for the power system models using the values of modes and mode shapes extracted from the phasor measurement unit (PMU) measurements. The main idea is to force the state matrix $A$ , which is a function of the unknown parameters, to satisfy as closely as possible the eigenequation linking the state matrix, the modes (eigenvalues of $A$) and the mode shapes (eigenvectors of $A$). The methodology is derived and analyzed for a general case of any model's parameters. The applications to the estimation of generator inertia $M$ coefficients are then discussed in detail. The proposed methodology has been tested using two different system models. The results confirm the efficiency of estimating $M$ using the PMU data, while the estimation of $D$ is shown to be very sensitive to the measurement noise. [ABSTRACT FROM AUTHOR]

This paper proposes a fully data-driven approach for PMU-based pre-fault dynamic security assessment (DSA) with incomplete data measurements. The generative adversarial network (GAN), which is an emerging unsupervised deep learning technique based on two contesting deep neural networks, is used to address the missing data. While the state-of-the-art methods for missing data are dependent on PMU observability, they are limited by the placement of PMU and network topologies. Distinguished from existing methods, the proposed approach is fully data-driven and can fill up incomplete PMU data independent on PMU observability and network topologies. Therefore, it is more generalized and extensible. Simulation results show that, under any PMU missing conditions, the proposed method can maintain a competitively high DSA accuracy with a much less computation complexity. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to obtain dynamic versions of static distribution factors, such as power-transfer, line-outage, and outage-transfer distribution factors. With the proposed dynamic distribution factors (DDFs), one can predict line flows over the post-contingency transient period with the same computational effort as obtaining static distribution factors. Our development centers on deriving closed-form expressions that approximate generator outputs through the post-contingency transient period with a reduced-order aggregate dynamical model to recover dynamic generator participation factors. The full suite of DDFs can then be derived by combining these dynamic generator participation factors with injection shift factors, i.e., static linear sensitivities of line active-power flows with respect to nodal active-power injections, computed at the pre-disturbance steady-state operating point. We illustrate the accuracy and computational benefits of the proposed DDFs via numerical case studies involving the New England test system. [ABSTRACT FROM AUTHOR]

We present a simple method to calculate the marginal capacity credit of energy limited resources with increased penetration. Energy limited resources are defined as any resource with limited hours of dispatch across a day, month, or year. This includes emission limited resources, time-limited demand response, and diurnal energy storage such as batteries and pumped storage. This paper focuses on 4 h energy limited resources with daily dispatch. The method modifies well-established effective load carrying capability methodology by optimally allocating limited capacity to the highest loss of load hours. Subsequent energy limited resources are iteratively stacked upon the prior solution, creating a marginal capacity credit curve with increased penetration of energy limited resources. Two systems are tested using this method. The initial capacity credit depends on system characteristics such as load and renewable penetration. Regardless, the capacity credit for energy limited resources declines steeply with penetration. [ABSTRACT FROM AUTHOR]

Droop control is a viable method for the operation of island DC microgrids in a decentralized architecture. This paper presents a mixed-integer conic optimization formulation for the design of generator droop control, comprising the parameters of a piecewise linear droop curve. The mixed-integer formulation originates from a stochastic optimization framework that considers several operating scenarios for finding the optimal design. The convexity of the mixed-integer problem continuous relaxation gives global optimality guarantees for the design problem. The paper presents computational results using a tight polyhedral approximation of the conic program, leading to a mixed-integer linear programming (MILP) problem that is solved using a state-of-the-art commercial solver. The results from the proposed approach are contrasted with both a classic linear droop control design and a recent piecewise linear formulation. The Monte-Carlo simulation results quantify the extent to which the MILP solution is superior in reducing voltage violations and power loss, and the degree to which the loss is close to that from a conic optimal power flow solution. [ABSTRACT FROM AUTHOR]

Pricing multi-interval economic dispatch of electric power under operational uncertainty is considered in this two-part paper. Part I investigates dispatch-following incentives of profit-maximizing generators and shows that, under mild conditions, no uniform-pricing scheme for the rolling-window economic dispatch provides dispatch-following incentives that avoid discriminative out-of-the-market uplifts. A nonuniform pricing mechanism, referred to as the temporal locational marginal pricing (TLMP), is proposed. As an extension of the standard locational marginal pricing (LMP), TLMP takes into account both generation and ramping-induced opportunity costs. It eliminates the need for the out-of-the-market uplifts and guarantees full dispatch-following incentives regardless of the accuracy of the demand forecasts used in the dispatch. It is also shown that, under TLMP, a price-taking market participant has incentives to bid truthfully with its marginal cost of generation. Part II of the paper extends the theoretical results developed in Part I to more general network settings. It investigates a broader set of performance measures, including the incentives of the truthful revelation of ramping limits, revenue adequacy of the operator, consumer payments, generator profits, and price volatility under the rolling-window dispatch model with demand forecast errors. [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]

Unified power flow controller (UPFC) gains growing application in power systems due to its power flow regulation ability. However, there is still a dilemma in the incorporation of UPFC into security-constrained economic dispatch (SCED). The modeling of UPFC involves nonlinear and nonconvex operational constraints, which is difficult to solve efficiently and accurately. Conventional methods adopted Taylor expansion or sensitivity analysis to realize the convexification of UPFC models, which leads to a loop structure and is subject to initial point choice. In this paper, a novel three-terminal injected UPFC model is proposed. In the proposed model, the voltage source variables are eliminated completely. Instead, only power injection variables are introduced to equivalently describe physical characteristics and constraints of UPFC. The nonlinear and nonconvex operational constraints of UPFC are transformed into mixed integer second-order cone form. Moreover, compared with conventional UPFC models, the control characteristic of UPFC is considered in a more accurate and practical manner in the proposed SCED, which helps to prevent potential risks of power flow over-limit under N-1 contingencies. Simulation results show the effectiveness and efficiency of the established solution. [ABSTRACT FROM AUTHOR]

Achieving the low-carbon transition of power systems requires the coordination of renewable energy generation and other emerging electricity technologies. Their technical indicators are changing rapidly since these technologies are in the initial stages of development. Determining the technical and policy targets for achieving the low-carbon transition is critical for regulators and power system planners. This paper defines this problem as a backcasting problem, whose concept is derived from environmental science research. We introduce it into the power system planning field and innovatively model it as a bi-level optimization problem. According to the characteristics of the backcasting problem, an improved barrier method is proposed to solve it efficiently. The effectiveness of the proposed model and algorithm are verified through case studies on a modified Garver’s 6-bus system and a realistic Northwest China power system, and they are compared with state-of-the-art solution techniques. The results of the backcasting problem provide a new perspective on the economic impacts of the low-carbon transition and are helpful in energy policy formulation for power systems. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of network connectedness (NC) in security-constrained optimal transmission switching problems, which is complicated by branch contingencies and corrective line switching. Two criteria are firstly proposed with the principle of preserving NC as much as possible within reasonable limits. By extending the electrical flow based NC constraints, a proposition is derived to associate different cases of NC with the optimum of a linear program, yielding the mathematical formulation of the NC criteria. By Karush-Kuhn-Tucker conditions, this formulation is further transformed into a tractable version which can be incorporated with existing SCOTS models without affecting the applicability of original solution approaches. Finally, case studies on various networks and SCOTS models demonstrate the efficacy of the proposed approach. [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]

This paper applies a new technique for modal decomposition based solely on measurements to test systems and demonstrates the technique's capability for partitioning a power network, which determines the points of separation in an islanding strategy. The mathematical technique is called the Koopman mode analysis (KMA) and stems from a spectral analysis of the so-called Koopman operator. Here, KMA is numerically approximated by applying an Arnoldi-like algorithm recently first applied to power system dynamics. In this paper we propose a practical data-driven algorithm incorporating KMA for network partitioning. Comparisons are made with two techniques previously applied for the network partitioning: spectral graph theory which is based on the eigenstructure of the graph Laplacian, and slow-coherency which identifies coherent groups of generators for a specified number of low-frequency modes. The partitioning results share common features with results obtained with graph theory and slow-coherency-based techniques. The suggested partitioning method is evaluated with two test systems, and similarities between Koopman modes and Laplacian eigenvectors are showed numerically and elaborated theoretically. [ABSTRACT FROM PUBLISHER]

This paper proposes a framework for online monitoring of subsynchronous oscillations using ambient sensor data from high speed sampling devices such as digital fault recorders (DFRs). Ambient data is continuously available in the form of routine system responses to random load fluctuations. This paper shows the usefulness of ambient data for tracking the frequency, damping ratio and mode shape of torsional modes related to subsynchronous resonance (SSR). Frequency domain decomposition (FDD) and recursive least square (RLS) algorithms are tested for ambient monitoring of SSR modes. IEEE second SSR benchmark model is used as the study system. Nonlinear and linearized equations of this system are analyzed for testing the performance of measurement based methods and to compare their results with respective linearized system modes. It is shown that both electrical and mechanical signals can be used for the SSR monitoring while the torsional modes are more observable in mechanical signals such as generator speeds. In addition to estimating the frequency and damping ratio, torsional mode shapes can be identified by implementing FDD as a multi-dimensional method on the speeds of the masses of the turbine shaft. The algorithms are tested on an archived real system data set from a DFR. [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]

The identification of generator coherency is crucial to design intentional controlled power system islanding. Due to high penetration of nonsynchronous generation, power system inertia changes both temporally and spatially. Thus, the dynamics in system oscillations and associated slow coherency of generators are directly affected by this. Therefore, their sensitivity deserves investigation. In this paper, the slow coherency with variable inertia is systematically discussed by incremental analysis. Specifically, the approach to study the impacts of variable inertia, based on the matrix perturbation theory, is deployed to provide the explicit eigen-solution sensitivity of slow coherency. To investigate the dependency of coherency grouping on inertia, the changing trends of eigenvector and possible alteration of coherency grouping are estimated. The unusual and abrupt alteration of slow coherency is observed in special scenarios near to modal resonance, i.e. close eigenvalue. The analysis in such scenarios was hardly found in the previous work of coherency sensitivity. Since close eigenvalue can make the traditional matrix perturbation inapplicable, the feasible perturbation in such special scenarios is proposed in this paper. The proposed approach has been thoroughly tested using the classic IEEE 118-bus system. The quantitative results are compared with those obtained analytically. [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]

Regarding the continuing increase of anthropogenic carbon emissions in the power system with growing energy consumption, researchers have focused on managing the demand side to achieve low-carbon transition. However, such a low-carbon transition cannot be achieved effectively without the proper incentive scheme. Moreover, it is desired to improve the computation quality of carbon tracing tools and extend their applications by state-of-art techniques. To fulfil these existing research gaps, this paper proposes a low-carbon optimal scheduling model with demand response (DR) based carbon intensity control. It aims to reduce the dependence of customers on energy sources with high carbon intensities while decreasing reasonable energy consumption. Likewise, a data-driven approach conducted with the Bayesian interfere regression is proposed to carry out the carbon emission flow (CEF) model to cope with the drawbacks of the conventional emission calculation. Moreover, the storage emission and relevant dynamic impacts to the system are fully considered. The proposed data-driven approach is tested on a series of IEEE systems with different sizes, its high accuracy and efficiency are proved by the simulation results. Further, simulation results indicate that the proposed scheduling model can effectively achieve carbon emission mitigation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel machine-learning approach for predicting AC-OPF solutions that features a fast and scalable training. It is motivated by the significant training time needed by existing machine-learning approaches for predicting AC-OPF. The proposed approach is a 2-stage methodology that exploits a spatial decomposition of the power network that is viewed as a set of regions. The first stage learns to predict the flows and voltages on the buses and lines coupling the regions, and the second stage trains, in parallel, the machine-learning models for each region. The predictions can then seed a power flow to eliminate the physical constraint violations, resulting in minor violations only for the operational bound constraints. Experimental results on the French transmission system (up to 6,700 buses) and large test cases from the pglib library (up to 9,000 buses) demonstrate the potential of the approach. Within a short training time, the approach predicts AC-OPF solutions with very high fidelity, producing significant improvements over the state-of-the-art. The proposed approach thus opens the possibility of training machine-learning models quickly to respond to changes in operating conditions. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy, accurate and efficient probabilistic optimal power flow (POPF) calculation becomes more and more important to provide decision support for secure and economic operation of power systems. This paper develops a novel nonparametric probabilistic optimal power flow (N-POPF) model describing the probabilistic information by quantiles, which avoids any parametric probability distribution assumptions of random variables. A novel critical region integral method (CRIM) which combines the multiparametric programming theory and discrete integral is proposed to efficiently solve the N-POPF problem. In the CRIM, the critical region partitioning algorithm is firstly introduced into the POPF model to directly establish the mapping relationship from wind power to optimal solutions of the POPF problem. Besides, a discrete integral method is developed in the CRIM to achieve the probability convolution calculation based on quantiles. Comprehensive numerical experiments verify the superior performance of the proposed CRIM in estimation accuracy and computational efficiency, and demonstrate that N-POPF model significantly improves the accuracy of uncertainty analysis. In general, the proposed N-POPF model and CRIM form a new framework of POPF problem for power system analysis and operation. [ABSTRACT FROM AUTHOR]

The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequency’s nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of thermal plants that are needed to provide frequency response (FR) and inertia. Additional consideration of fast FR, a dynamically reduced largest loss and under frequency load shedding (UFLS) allows frequency security to be achieved more cost effectively. This paper derives a novel constraint from the swing equation to contain the frequency nadir using all of these services. The expected cost of UFLS is found probabilistically to facilitate its comparison to the other frequency services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone (SOC), resulting in highly tractable convex problems. Case studies performed on a Great Britain 2030 system demonstrate that UFLS as an option to contain single plant outages can reduce annual operational costs by up to $\pounds $ 559 m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored. [ABSTRACT FROM AUTHOR]

This paper proposes a novel modeling framework and decomposition-based solution strategy combining stochastic programming (SP) and robust optimization (RO) to deal with multiplex uncertainties in coordinated mid- and long-term power system planning. The problem is formulated as a multi-year generation and transmission planning problem from an independent system operator (ISO)’s perspective to minimize both expansion and operational costs under binary and continuous uncertainties, ${\bf i.e.}$ , system component contingency and load/generation variation. N- $\bf {k}$ contingencies are captured in RO using the reformulated contingency criteria, while the load/generation uncertainty is considered in SP embedded with RO using operating scenarios generated from the historical data with spatiotemporal correlations. The original hybrid model is highly intractable, but the intractability can be relieved by the proposed decomposition strategy based on the column-and-constraint generation and L-shaped algorithms. We apply our model to perform long-term system planning under extremely high renewable penetration and investigate the case of 100% renewables in long-term planning. Numerical experiments on multi-scale test systems verify the efficacy of the proposed approach. [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]

There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinite-dimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty. [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]

The novel cascade-mitigation scheme developed in Part I of this paper is implemented within a receding-horizon model predictive control (MPC) scheme with a linear controller model. This present paper illustrates the MPC strategy with a case-study that is based on the IEEE RTS-96 network, though with energy storage and renewable generation added. It is shown that the MPC strategy alleviates temperature overloads on transmission lines by rescheduling generation, energy storage, and other network elements, while taking into account ramp-rate limits and network limitations. Resilient performance is achieved despite the use of a simplified linear controller model. The MPC scheme is compared against a base-case that seeks to emulate human operator behavior. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the optimal power flow (OPF) problem. We have recently shown that a convex relaxation based on semidefinite programming (SDP) is able to find a global solution of OPF for IEEE benchmark systems, and moreover this technique is guaranteed to work over acyclic (distribution) networks. The present work studies the potential of the SDP relaxation for OPF over mesh (transmission) networks. First, we consider a simple class of cyclic systems, namely weakly-cyclic networks with cycles of size 3. We show that the success of the SDP relaxation depends on how the line capacities are modeled mathematically. More precisely, the SDP relaxation is proven to succeed if the capacity of each line is modeled in terms of bus voltage difference, as opposed to line active power, apparent power or angle difference. This result elucidates the role of the problem formulation. Our second contribution is to relate the rank of the minimum-rank solution of the SDP relaxation to the network topology. The goal is to understand how the computational complexity of OPF is related to the underlying topology of the power network. To this end, an upper bound is derived on the rank of the SDP solution, which is expected to be small in practice. A penalization method is then applied to the SDP relaxation to enforce the rank of its solution to become 1, leading to a near-optimal solution for OPF with a guaranteed optimality degree. The remarkable performance of this technique is demonstrated on IEEE systems with more than 7000 different cost functions. [ABSTRACT FROM PUBLISHER]

This paper studies the feasibility of utilizing the reactive power of grid-connected variable-speed wind generators to enhance the steady-state voltage stability margin of the system. Allowing wind generators to work at maximum reactive power limit may cause the system to operate near the steady-state stability limit, which is undesirable. This necessitates proper coordination of reactive power output of wind generators with other reactive power controllers in the grid. This paper presents a trust region framework for coordinating reactive output of wind generators with other reactive sources for voltage stability enhancement. Case studies on 418-bus equivalent system of Indian southern grid indicates the effectiveness of proposed methodology in enhancing the steady-state voltage stability margin. [ABSTRACT FROM PUBLISHER]

This paper presents a methodology and set of validation criteria for the systematic creation of synthetic power system test cases. The synthesized grids do not correspond to any real grid and are, thus, free from confidentiality requirements. The cases are built to match statistical characteristics found in actual power grids. First, substations are geographically placed on a selected territory, synthesized from public information about the underlying population and generation plants. A clustering technique is employed, which ensures the synthetic substations meet realistic proportions of load and generation, among other constraints. Next, a network of transmission lines is added. This paper describes several structural statistics to be used in characterizing real power system networks, including connectivity, Delaunay triangulation overlap, dc power flow analysis, and line intersection rate. The paper presents a methodology to generate synthetic line topologies with realistic parameters that satisfy these criteria. Then, the test cases can be augmented with additional complexities to build large, realistic cases. The methodology is illustrated in building a 2000 bus public test case that meets the criteria specified. [ABSTRACT FROM AUTHOR]

This paper presents a new method for studying electromechanical transients in power systems using three phase, combined transmission and distribution models (hybrid models). The methodology models individual phases of an electric network and associated unbalance in load and generation. Therefore, the impacts of load unbalance, single phase distributed generation and line impedance unbalance on electromechanical transients can be studied without using electromagnetic transient simulation (EMTP) programs. The implementation of this methodology in software is called the Three Phase Dynamics Analyzer (TPDA). Case studies included in the paper demonstrate the accuracy of TPDA and its ability to simulate electromechanical transients in hybrid models. TPDA has the potential for providing electric utilities and power system planners with more accurate assessment of system stability than traditional dynamic simulation software that assume balanced network topology. [ABSTRACT FROM PUBLISHER]

This paper proposes a cascading failure simulation (CFS) method and a hybrid machine learning method for vulnerability analysis of integrated power-gas systems (IPGSs). The CFS method is designed to study the propagating process of cascading failures between the two systems, generating data for machine learning with initial states randomly sampled. The proposed method considers generator and gas well ramping, transmission line and gas pipeline tripping, island issue handling and load shedding strategies. Then, a hybrid machine learning model with a combined random forest (RF) classification and regression algorithms is proposed to investigate the impact of random initial states on the vulnerability metrics of IPGSs. Extensive case studies are carried out on three test IPGSs to verify the proposed models and algorithms. Simulation results show that the proposed models and algorithms can achieve high accuracy for the vulnerability analysis of IPGSs. [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]

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]

This paper presents an algorithm for solving the AC basic power flow based on some enrichments provided in the bus admittance matrix methods findable in the literature. In particular, the interpretation of the slack bus generator as a current source rather than a voltage one and its inclusion inside an “all-inclusive” admittance matrix allows obtaining strong performances of the algorithm. In fact, this method gives both a well conditioning of the admittance matrix and the reduction of matrix partitioning for each iteration. As a result, a greater precision of the solution, a shorter execution time compared to classical commercial methods, a decreasing number of iterations and optimal convergence properties are obtained. Eventually, in order to show the efficiency of the method, real and fictious networks are tested, by comparing its results and performances with robust open source/commercial software packages that use well-known methods (i.e., Newton-Raphson and Fast Decoupled Load Flow methods). [ABSTRACT FROM AUTHOR]

As the installation of electronically interconnected renewable energy resources grows rapidly in power systems, system frequency maintenance and control become challenging problems to maintain the system reliability in bulk power systems. As two of the most important frequency control actions in the control centers of independent system operators (ISOs) and utilities, the interaction between Economic Dispatch (ED) and Automatic Generation Control (AGC) attracts more and more attention. In this paper, we propose a robust optimization based framework to measure the system flexibility by considering the interaction between two hierarchical processes (i.e., ED and AGC). We propose a cutting plane algorithm with the reformulation technique to obtain seven different indices of the system. In addition, we study the impacts of several system factors (i.e., the budget of operational cost, ramping capability, and transmission line capacity) and show numerically how these factors can influence the system flexibility. [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]

To increase market transparency, independent system operators (ISOs) have been working on minimizing uplift payments based on convex hull pricing theorems. Along this direction, in this paper, based on the analysis of specific generator features in the Midcontinent ISO (MISO) system, besides reviewing integral formulations for several special cases, we develop two integral formulations of a single generator that can capture these features. We then build a compact convex hull pricing formulation based on these integral formulations, which guarantees to obtain an exact convex hull price by solving a large-scale linear program. Meanwhile, to address the computational challenges caused by the large-scale MISO system, we propose innovative iterative algorithms with convergence properties, plus a complementary algorithm, to obtain an approximated convex hull price. The case studies on MISO instances with and without transmission constraints indicate that our algorithms lead to an exact convex hull price for all numerical studies and, the solutions can be obtained within 20 minutes. [ABSTRACT FROM AUTHOR]

This is the second part of a two-part paper on a new adaptive coordinated voltage control (ACVC) strategy. The overall basic scheme and the online control for prepared faults have been presented in Part I. In this paper, learning control is explored to accumulate knowledge, so that the online control performances can be improved for unknown emergencies. For unknown situations where no past experiences can be exploited, a learning scheme is used by which the control knowledge can be acquired gradually. The learnt knowledge goes into the database and is improved the next time a related situation happens. After full knowledge is acquired, the unknown fault becomes a prepared fault with prepared knowledge. With the learning scheme, control for any emergency can be realized in a rapid and effective response. The learning process is demonstrated by providing control for an unknown emergency in the New England 39-bus power system. The ACVC performance for a sequence of randomly generated fault and load event emergencies is presented at the end of this paper. [ABSTRACT FROM PUBLISHER]