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This paper proposes a dynamic valuation framework to determine the opportunity value of battery capacity degradation in grid applications based on the internal degradation mechanism and utilization scenarios. The proposed framework follows a dynamic programming approach and includes a piecewise linear value function approximation solution that solves the optimization problem over a long planning horizon. The paper provides two case studies on price arbitrage and frequency regulation using real market and system data to demonstrate the broad applicability of the proposed framework. Results show that the battery lifetime value is critically dependent on both the external market environment and its internal state of health. On the grid service side, results show that second-life batteries can provide more than 50% of the value compared to new batteries, and frequency regulation provides two times more revenue than price arbitrage throughout the battery lifetime. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new mathematical model for power flow problem based on the linear and nonlinear matrix inequality theory. We start with rectangular model of power flow (PF) problem and then reformulate it as a Bilinear Matrix Inequality (BMI) model. A Theorem is proved which is able to convert this BMI model to a Linear Matrix Inequality (LMI) model along with One Nonconvex Quadratic Constraint (ONQC). Our proposed LMI-ONQC model for PF problem has only one single nonconvex quadratic constraint irrespective of the network size, while in the rectangular and BMI models the number of nonconvex constraints grows as the network size grows. This interesting property leads to reduced complexity level in our LMI-ONQC model which in turn makes it easier to solve for finding a PF solution. The non-conservativeness, iterative LMI solvability, well-defined and easy-to-understand geometry and pathwise connectivity of feasibility region are other important properties of proposed LMI-ONQC model which are discussed in this paper. An illustrative two-bus example is carefully studied to show different properties of our LMI-ONQC model. We have also tested our LMI-ONQC model on 30 different power-system cases including four ill-conditioned systems and compared it with a group of existing approaches. The numerical results show the promising performance of our LMI-ONQC model and its solution algorithm to find a PF solution. [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]

In a wind farm, the interactions between turbines caused by wakes can significantly reduce the power output of the wind farm. Cooperative control among the turbines has the potential to improve the power output. However, existing centralized power optimization methods are computationally expensive and does not scale well for large wind farms, limiting their practical use in real-time control for time-varying wind conditions and turbine configuration (with adding or maintaining of turbines). To address this problem, this paper proposes a fully distributed power optimization method for wind farms using alternating direction method of multipliers (ADMM). The proposed method allows the wind farm power output to be optimized in fully distributed manner with turbine-to-turbine message passing over a mesh network, guarantees the implemented control actions satisfy the control constraints of all turbines, and provably converges to a stationary point of the wind farm power optimization problem. Simulation results demonstrate that the proposed method can significantly reduce the computation time with hardly sacrificing the power gain compared with centralized method and thus is computationally efficient for real-time power optimization of large wind farms. [ABSTRACT FROM AUTHOR]

High renewable energy penetration increases the electricity seasonal imbalance in the long-term timescale. Power system planning needs to consider the optimal configuration of various flexibility resources and electricity balance in different timescales. The coupling of multiple timescales largely increases the computation complexity of the power system planning problem. Thus, this paper presents an efficient source-grid-storage co-planning model which incorporates a year-round hourly operation simulation. To improve the computation efficiency of the planning model, from the temporal scale, a self-adaptive compact panorama time series (CPTS) model is applied, which greatly reduces the number of variables related to short-term decisions. From the spatial scale, a network-constrained relaxed clustered unit commitment (NC-RCUC) model is introduced, which significantly reduces the number of variables related to unit commitment decisions. Case studies on the modified Garver’s 6-node system and HRP-38 system prove the validation and efficiency of the proposed model (“HRP” stands for high renewable penetration). The studies on the China power grid in 2035 demonstrate the future planning results of generation, transmission and storage in China power systems based on the proposed model. [ABSTRACT FROM AUTHOR]

Accurate solar photovoltaic (PV) generation forecast is critical to the reliable and economic operation of a modern power system. In practice, due to various faulty issues in the sensor, communication, or database system, the historical and online measurement data may not be always complete, and the missing data could dramatically degrade the forecasting model's accuracy. To solve this problem, this paper proposes an integrated missing-data tolerant model for probabilistic PV power generation forecasting. Taking historical PV generations as input, this model is based on a recursive long short-term memory network (Rec-LSTM), which can provide multi-step ahead forecasting of the probability distribution of PV generation. The unobserved input data will be imputed recursively based on the model output at the previous time step. During the training process, the imputations and forecasting values are iteratively updated by the negative log-likelihood loss function. As a salient advantage, this method can deal with data missing scenarios at both offline and online stages. Numerical experiments are conducted on two one-year datasets from Australia and Singapore, respectively. Probabilistic forecasting for both large-scale and small-scale building-level PV power generation is tested at the time resolution of 15 mins. Testing results show the proposed method can achieve superior probabilistic prediction accuracy as well as strong robustness under various data missing scenarios, compared to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

A new smooth model is proposed in this paper to eliminate the non-differentiability of several types of limits in power flow models. The proposed smooth model accurately represents power system static models with limits as a continuously differentiable function. Analytic results are developed to show that each solution of the proposed smooth model is arbitrarily close to a solution of the corresponding original power flow model with limits. The proposed smooth model includes a wide range of devices with physical limits, such as generators, transformers, HVDCs, phase shifters, and shunts. In addition, it is shown that every generic static bifurcation in the original model is transformed into a saddle-node bifurcation in the smoothed model. Hence, the search for bifurcations in voltage stability assessment can be greatly simplified. Several numerical studies of the proposed smooth model on a 9241-bus power system and on a 13659-bus power system have shown promising results. [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]

Service restoration is one of the critical functions to enable the future self-healing distribution system. To restore the distribution system in a timely and reliable manner, the realistic system operating conditions need to be accurately characterized. In this paper, two main factors that have great impacts on distribution system restoration (DSR) in practice are investigated. First, cold load pickup (CLPU), generally caused by thermostatically controlled loads (TCLs), is a common phenomenon after an outage and shaped by the outage duration. However, the time-dependent behaviors of CLPU are rarely considered in literature. In this paper, the operating state evolution of TCLs after an outage is analyzed to characterize time-dependent CLPU. And the time-dependent CLPU is analytically embedded in DSR to accurately represent the actual behaviors of the restored loads. Second, it is difficult to predict loads that fluctuate during DSR due to the lack of real-time measurement data. Accordingly, a robust DSR based on the information gap decision theory (IGDT) is proposed to address this challenge, fully considering the uncertainty of CLPU. The proposed models are tested in IEEE 13-node and 123-node test feeders. Simulation results demonstrate that the time-dependent CLPU model and the uncertainty modeling of CLPU can accurately capture the actual behaviors of loads with TCLs after an outage, which greatly improves DSR decisions in practice. [ABSTRACT FROM AUTHOR]

It is found from actual data that due to generation dispatch and uncertain renewable generations and loads with complicated correlations, inferring the probabilistic distributions for uncertain inputs is challenging. Many probabilistic power flow approaches have been developed in the literature but their validations using realistic systems and data are lacking. This paper proposes a data-driven probabilistic analysis approach for system risk assessment of the miniWECC system using actual data. The sparse Gaussian process (SGP) is advocated to quantify the impacts of uncertain inputs on voltage security. SGP does not need the probability distribution function of uncertain inputs, can handle correlations and is highly computationally efficient. Results on the miniWECC system using realistic data show that SGP outperforms existing approaches and is able to quantify the voltage violation risks. [ABSTRACT FROM AUTHOR]

In this paper, we propose a data-driven approach for uncertainty moment propagation through the non-linear power system dynamics. The proposed approach relies on the linear representation of a nonlinear system using the Perron-Frobenius & Koopman operators for propagating the moments. Data from non-linear simulations is used to approximate the linear operators by matrices, thereby enabling moment propagation by matrix multiplication. Results for a large-scale system are presented to demonstrate the accuracy and speed-up of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an approximate aggregated impedance model (AAIM) of a grid-connected wind farm with multiple wind turbine generators (WTGs) for the small-signal stability study is derived. The derivation is conducted under the condition that the WTGs inside the wind farm are of the same type and from the same manufacturer. The AAIM derived can be seen as the impedance model (IM) of a grid-connected aggregated WTG. The IM of the aggregated WTG is the weighted average of the IMs of the individual WTGs in the wind farm and hence is simple to be built. The reactance of the line connecting the aggregated WTG to the external AC grid is the maximum eigenvalue of the network reactance matrix of the grid-connected wind farm. In addition, the derivation justifies the representation of a wind farm by an aggregated WTG in the IM-based small-signal stability analysis. Finally, two example grid-connected wind farms are used to evaluate and demonstrate the effectiveness of the AAIM proposed in the small-signal stability analysis. It is also shown that the computational burden of the stability analysis of a large-scale wind farm could be effectively reduced when the AAIM is used. [ABSTRACT FROM AUTHOR]

The quantification of heating, ventilation, and air condition (HVAC) system flexibility is critical to the operations of both the grid and buildings in demand response (DR) programs. However, the flexibility quantification is challenging due to the non-linearity and non-convexity of thermal dynamics associated with HVAC components. This paper proposes a novel HVAC flexibility quantification method based on a semidefinite programming (SDP) formulation. The SDP is reformulated from the non-convex problem of HVAC power optimization, and can be solved efficiently in real-time. The physics-based HVAC model is incorporated to ensure the reliability and accuracy of solutions. The quantification results are organized into an HVAC flexibility table that can provide response strategies on adjusting HVAC setpoints in response to the grid signals received. The developed response strategies minimize occupant discomfort while satisfying grid requirements. A case study of a test building model is carried out to illustrate the flexibility quantification framework and compares the performance of two DR strategies. [ABSTRACT FROM AUTHOR]

The paper establishes convergence properties of decentralized and distributed control strategies that use a Steinmetz-based technique for mitigating voltage unbalance on distribution feeders. Reactive power from distributed energy resources (DERs), such as solar photovoltaic (PV), is used to balance voltages at critical nodes in the distribution network. Interactions between controllers are analyzed and a theoretical guarantee is derived for stability of the control algorithms. This is achieved using Banach fixed-point theory. Providing such convergence results ensures robustness of the proposed control algorithms in realistic settings where parameters are uncertain and/or slowly varying, disturbances are prevalent, and control and measurement signals are prone to delays. The convergence results are evaluated on three test distribution networks. [ABSTRACT FROM AUTHOR]

Deep learning (DL) techniques have shown promising performance for designing data-driven power system transient stability assessment (TSA) models. However, due to the deep structure of the DL, the resulting model is always a black-box and hard to explain, which hinders its practical adoption by the industry. This paper proposes an interpretable DL-based TSA model to balance the TSA accuracy and transparency. The proposed method combines the strong nonlinear modelling capability of a deep neural network and the interpretability of a decision tree (DT). Through regularizing DL-based model with the average DT path length in the training process, the proposed interpretable DL-based TSA method can visually explain the TSA decision-making process. Simulation results have shown that the proposed method can deliver highly accurate TSA results and interpretable TSA decision-making rules, which can be used for designing preventive control actions. [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]

The increase in distributed energy resources and flexible electricity consumers has turned TSO-DSO coordination strategies into a challenging problem. Existing decomposition/decentralized methods apply divide-and-conquer strategies to trim down the computational burden of this complex problem, but rely on access to proprietary information or fail-safe real-time communication infrastructures. To overcome these drawbacks, we propose in this paper a TSO-DSO coordination strategy that only needs a series of observations of the nodal price and the power intake at the substations connecting the transmission and distribution networks. Using this information, we learn the price response of active distribution networks (DN) using a decreasing step-wise function that can also adapt to some contextual information. The learning task can be carried out in a computationally efficient manner and the curve it produces can be interpreted as a market bid, thus averting the need to revise the current operational procedures for the transmission network. Inaccuracies derived from the learning task may lead to suboptimal decisions. However, results from a realistic case study show that the proposed methodology yields operating decisions very close to those obtained by a fully centralized coordination of transmission and distribution. [ABSTRACT FROM AUTHOR]

Block orders are increasingly adopted in many electricity markets as they enable power producers to implicitly express their unit commitment characteristics and address price volatility risks. However, previous work on the optimal offering problem of a price-taking producer participating in such markets has only considered the simplest type of block orders (regular block orders-RBO) and has neglected relevant realistic market regulations. This paper addresses these simplifications by proposing a new optimal offering model which also considers the more complex profile block orders (PBO) and linked block orders (LBO). This model is generic in that it can treat the block orders’ time spans either as fixed parameters (following the modelling approach of previous work) or as endogenous decision variables, which constitutes a completely novel modeling approach. The presented case studies demonstrate that this novel approach yields a tremendously lower number of binary variables and more efficient computational performance, when PBO and LBO are considered. Furthermore, the case studies analyze the physical conditions under which the introduction of different types of block orders increases the examined producer’s profit. [ABSTRACT FROM AUTHOR]

False data injection attack (FDIA) is a major threat in wide-area monitoring systems. Being able to differentiate FDIA from normal grid contingencies is a paramount necessity for a grid operator to decide the correct response on a critical prompt basis as well as reduce the overall FDIA's false alarms. Two FDIA's characterization algorithms are developed in this paper. The first is based on the principal component analysis (PCA) while the second is based on the canonical correlation analysis (CCA). Both algorithms are developed in an online platform to reduce the computational complexity. The various designed test cases demonstrate a promising FDIA characterization performance utilizing both algorithms. The testing results of three machine learning-based classifiers indicate that the proposed FDIA's characterization algorithms provide better classification models than conventional PCA-based characterization algorithm with CCA illustrating advanced characterization and detection results. [ABSTRACT FROM AUTHOR]

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

The fast development of renewable energies leads to an increase in the power electronics penetration in transmission systems. This is particularly true if one considers a 100% renewable energies power system, where wind and solar photovoltaic energies, which make most of the renewable energies connections today, are connected to the grid through power electronics converters. Because power electronics-based generators and synchronous machines-based generators have very different dynamic behaviours, some approximations usually used to run transient simulations of transmission systems might not be optimal for future grids. The systematic use of the phasor approximation applied to the power lines, implemented in most of the Transient Simulation Programs, is indeed not relevant any more. To avoid the use of Electromagnetic Transient simulations, that are resource-demanding and time-consuming, this paper presents a novel Model Order Reduction technique for large grids with a high penetration of power electronic devices. Compared to the classical phasor approximation, this event-based state residualization approximation allows accurate transient simulations and at the same time an optimal reduction of the number of the system’s state variables depending on the observed variables, the considered events and the tolerated approximation error. [ABSTRACT FROM AUTHOR]

A rapid deployment of renewable generation has led to significant reduction in the rotational system inertia and damping, thus making frequency control in power systems more challenging. This paper proposes a novel control scheme based on Model Predictive Control (MPC) for converter-interfaced generators operating in a grid-forming mode, with the goal of exploiting their fast response capabilities to provide fast frequency control service to the system. The controller manipulates converter power injections to limit the frequency nadir and rate-of-change-of-frequency after a disturbance. Both centralized and decentralized MPC approaches are considered and compared in terms of performance and practical implementation. Special attention is given to the decentralized controller by generating an explicit MPC solution to enhance computational efficiency and reduce hardware requirements. Simulation results obtained from a detailed dynamic model of the IEEE 39-bus system demonstrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper develops a computationally efficient algorithm which speeds up the probabilistic power flow (PPF) problem by exploiting the inherently low-rank nature of the voltage profile in electrical power distribution networks. The algorithm is accordingly termed the Accelerated-PPF (APPF), since it can accelerate “any” sampling-based PPF solver. As the APPF runs, it concurrently generates a low-dimensional subspace of orthonormalized solution vectors. This subspace is used to construct and update a reduced order model (ROM) of the full nonlinear system, resulting in a highly efficient simulation for future voltage profiles. When constructing and updating the subspace, the power flow problem must still be solved on the full nonlinear system. In order to accelerate the computation of these solutions, a Neumann expansion of a modified power flow Jacobian is implemented. Applicable when load bus injections are small, this Neumann expansion allows for a considerable speed up of Jacobian system solves during the standard Newton iterations. APPF test results, from experiments run on the full IEEE 8500-node test feeder, are finally presented. [ABSTRACT FROM AUTHOR]

Machine learning approaches have exhibited high potential in power system transient stability assessment (TSA), yet their initial preparation stages of stability knowledge base generation (SKBG) based on time-domain simulations often undergo high computational costs. In fact, how to ease the heavy computational burden of SKBG without sacrificing the reliability is still a significant challenge. To address this problem, this paper develops a semi-supervised ensemble learning (SSEL) framework for reliable SKBG acceleration, without additional need for computing hardware upgrading. In particular, it performs detailed simulations for a minority of cases and fast simulations for the majority ones to reduce the total computation time. Considering the absence of stability status information of those fast simulated cases, an SSEL scheme is systematically designed to reliably label their stability status. Before implementing SSEL, two concise feature descriptors are first introduced to efficiently extract transient features from multiplex system trajectories. Then, all the cases are characterized in a unified feature space, whereby a series of semi-supervised support vector machines are trained in randomly formed subspaces. Afterward, these single machines are systematically combined to derive an enhanced SSEL model, which is able to make reliable and robust labeling decisions. Further, a backtrace strategy is carefully devised for SSEL, so as to maintain the high reliability of SKBG. Test results on the IEEE 39-bus system and the realistic GD Power Grid in South China illustrate the excellent performances of the proposed framework on SKBG acceleration. [ABSTRACT FROM AUTHOR]

This paper presents a distribution system operator (DSO) framework for wholesale and retail market participation of distributed energy resources (DERs) aggregators. The DSO coordinates aggregators’ energy and regulation offers as well as end-users’ energy consumption through the unbalanced retail market and submits balanced energy and regulation offers to the wholesale market on behalf of all the aggregators and end-users within its territory. Various kinds of DER aggregators including demand response aggregators (DRAGs), energy storage aggregators (ESAGs), electric vehicle (EV) charging stations (EVCSs), dispatchable distributed generation aggregators (DDGAGs), and renewable energy aggregators (REAGs) are modeled. To handle unbalanced distribution grids with single-phase aggregators, a linearized unbalanced power flow is tailored to model operating constraints of the distribution grid with various aggregators. A market settlement approach is proposed for the DSO, which coordinates with wholesale market clearing process and ensures the DSO’s non-profit characteristic. It is proved that at the wholesale-DSO coupling substation, the total payment received/compensated by the DSO under the wholesale price is identical to that under three single-phase retail prices for each phase at the substation. Case studies are performed on the modified IEEE 33-node and 240-node distribution test systems to investigate the market outcomes of the proposed DSO. [ABSTRACT FROM AUTHOR]

This paper presents a new formulation for the preventive security-constrained unit commitment problem modeling N-k line outages and transmission losses. The pre- and post-contingency transmission constraints, representing N-k line outages, are explicitly included by using generalized generation distribution factors. To account for security, a contingency selection procedure based on line outage distribution factors finds a list of worst-case contingencies. Transmission losses are incorporated using piecewise linear expressions. The proposed model is formulated as an instance of mixed-integer linear programming. The effectiveness of the proposed approach is illustrated with the IEEE 57-bus system and the 1,354-bus portion of the European transmission system. As empirically evidenced, the explicit consideration of N-k line outages and transmission losses leads to different decisions in the generation scheduling and dispatch, ensuring secure power system operation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel high-performance deep learning framework for load recognition. The framework consists of a deep-shallow model and a fast backpropagation (FBP) algorithm. In the deep-shallow model, power-related wave patterns are perceived by a convolutional neural network (CNN), and feature statistics of the power consumption data are analyzed by a sparse feed-forward neural network. The new architecture improves model interpretability and prevents information loss problems in CNNs. The architecture also greatly boosts the convergence speed and significantly enhances the test set accuracy of a neural network. Compared with conventional CNN models utilized by many load recognition applications, the FBP algorithm consisting of four sub-algorithms converges faster at the start of the training process and reduces at least 87.5% of the filter gradient computations on average. The deep-shallow-fast model that combines the deep-shallow model and the FBP algorithm attains 97.62% accuracy on the test set in the load recognition task. To fully utilize the training data, a data augmentation technique is invented that transforms the voltage and current time series into an image-like 4-D tensor. Experiments illustrate that the proposed framework is much more accurate and converges considerably faster than the conventional CNN model that many deep-learning-based load recognition applications are based upon. [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]

Given its physical characteristics and the range of services that it can provide, energy storage raises unique modeling challenges. This paper summarizes capabilities that operational, planning, and resource-adequacy models that include energy storage should have and surveys gaps in extant models. Existing models that represent energy storage differ in fidelity of representing the balance of the power system and energy-storage applications. Modeling results are sensitive to these differences. The importance of capturing chronology can raise challenges in energy-storage modeling. Some models ‘decouple’ individual operating periods from one another, allowing for natural decomposition and rendering the models relatively computationally tractable. Energy storage complicates such a modeling approach. Improving the representation of the balance of the system can have major effects in capturing energy-storage costs and benefits. [ABSTRACT FROM AUTHOR]

This paper proposes a new model for the optimal partitioning of active distribution networks into a number of islanded microgrids. The objective of the developed model is to maximize the minimum value of maximum loadability amongst formed islands to create resilient islanded microgrids against unexpected local disturbances and power mismatches. The model takes key aspects such as the operation of islanded microgrids using droop control, system tie-lines, and line capacity limit into consideration. An ear decomposition-based method is proposed in order to preserve the radiality of formed islands. Besides the formulated exact optimization model, which is a nonconvex formulation, two convex mixed-integer models are introduced to achieve a trade-off between solution accuracy and computational time. The numerical results demonstrate the effectiveness and robustness of the proposed models in forming droop-controlled islanded microgrids with optimum loadability. [ABSTRACT FROM AUTHOR]

Accurate load modeling is critical for credible power system stability analysis. Because of the increasing complexity in modern system load, establishing a more comprehensive load model and performing accurate parameter estimation are the two biggest challenges in composite load modeling. In this paper, an induction motor with variable frequency drive (IM-VFD) together with the traditional ZIP+IM model is utilized to describe the dynamic characteristics of the system load. We estimate the time-varying probabilistic distributions of all states and parameters to describe their stochastic characteristics, thereby representing the real-time varying features of an actual load. The Fokker-Planck operator is applied to linearize the updated load model in tensor format. We then use tensor decomposition to reduce the computational and storage costs for calculating load model parameters. A sensitivity indicator is used to analyze the sensitivities of the estimated parameter distributions for subsequent model reduction. Simulations demonstrate that the updated load model has better performance than the traditional ZIP+IM model. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm based on the partial least square (PLS) techniques and the arbitrary polynomial chaos expansion (aPCE) for the probabilistic power flow (PPF) analysis of a power system having many uncertain variables. The proposed method uses the nonlinear PLS to transform a set of random input variables to a smaller number of de-correlated random variables. Then, the aPCE technique is applied to generate the basis polynomial functions and build a surrogate model of the power system response. The algorithm has been implemented and tested with the modified IEEE 118-bus and European 1354-bus systems. The numerical results indicate that, similar to the sparse PCE method and the low-rank approximation technique, the proposed method can be applied to high-dimensional PPF problems. Nonetheless, the proposed approach uses smaller computation time, and estimates statistical characteristics of the response with higher accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to dynamic phasor-based transient stability simulation. The proposed method is based on the modified nodal analysis (MNA) approach to circuit simulation, which is used to construct continuous differential-algebraic equations (DAEs). The proposed method makes use of the stamp technique, which makes it possible to construct a general purpose MNA-based simulator. Stamp-based models for common power system components are derived in this work. A new MNA-based synchronous machine model is presented, which represents machines as nonlinear inductances instead of subtransient equivalents. The resultant continuous DAEs are numerically solved using the general purpose variable step and variable order library IDA. Simulation results from the IEEE 68 bus test system, a real 400 bus power system, and the IEEE 39 bus test system with an embedded HVdc transmission system demonstrate that the proposed method is suitable for large ac networks with power electronic devices. The results demonstrate good agreement between the proposed method and electromagnetic transient (EMT) simulation. The results also demonstrate that the proposed method is fast and scalable with CPU times that are up to 200 times faster than EMT simulation. [ABSTRACT FROM AUTHOR]

In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, automatically tuned, parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes and halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate steering procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality feasible solutions in computation times at least two orders of magnitude faster than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the real electricity and gas transmission networks of the state of Victoria with actual linepack and demand profiles. [ABSTRACT FROM AUTHOR]

This paper presents a procedure for estimating the systems state when considerable Information and Communication Technology (ICT) component outages occur, leaving entire system areas unobservable. For this task, a novel method for analyzing system observability is proposed based on the Manifold Boundary Approximation Method (MBAM). By utilizing information geometry, MBAM analyzes boundaries of models in data space, thus detecting unidentifiable system parameters and states based on available data. This approach extends local, matrix-based methods to a global perspective, making it capable of detecting both structurally unidentifiable parameters as well as practically unidentifiable parameters (i.e., identifiable with low accuracy). Beyond partitioning identifiable/unidentifiable states, MBAM also reduces the model to remove reference to the unidentifiable state variables. To test this procedure, cyber-physical system (CPS) simulation environments are constructed by co-simulating the physical and cyber system layers. [ABSTRACT FROM AUTHOR]

To design a reliable and secure power system, it is necessary to have enough transmission capacity. The solution of transmission expansion planning (TEP) problem determines cost-optimal investment in future transmission equipment. In this paper, we propose a new global solver, named Global-TEP, for the TEP problem with an AC network representation (ACTEP), which is a mixed-integer nonlinear programming problem. The proposed solver is based on second-order cone relaxation, enhanced relaxation tightening constraints, and optimization-based/feasibility-based bound tightening techniques. Multiple enhanced relaxation tightening constraints are incorporated into the mixed-integer second-order cone relaxation of TEP in order to obtain a very strong relaxation as the lower bounding problem. In addition, a novel feasibility-based bound tightening technique is proposed to tighten the bounds of decision variables in a considerably short runtime. Finally, introducing a novel application of optimization-based bound tightening technique, Global-TEP is constructed that can solve the ACTEP problem efficiently with a guaranteed optimality gap. As illustrated by numerical case studies, Global-TEP is more scalable, more flexible, and much faster than the available global solvers. [ABSTRACT FROM AUTHOR]

For the popular second-order conic program (SOCP) formulation of AC optimal power flow (OPF) in a radial network, this paper first shows that it does not have the strong duality property in general. Then, through a series of restrictive reformulations, we derive a set of closed-form sufficient conditions on network parameters that ensure its strong duality. Numerical studies on IEEE 33-bus, 69-bus test networks and two real-world distribution systems confirm that non-negligible duality gaps do exist in this SOCP formulation, and also demonstrate the validity of the proposed sufficient conditions on closing the duality gap. Our results provide an analytical tool to ensure the strong duality of the SOCP power flow formulation and to support algorithm developments for its complex extensions. [ABSTRACT FROM AUTHOR]

Bulk integrated electricity and gas systems (IEGSs) introduce complex coupling relations and induce synergistic operation challenges. The growing uncertainty arising from the renewable power generation in the IEGS further aggravates the synergistic problems. Considering the availability of historical wind power generation data, this paper adopts a two-stage sample robust optimization (SRO) model, which is equivalent to the two-stage distributionally robust optimization (DRO) model with a ${\text{type}} - \infty $ Wasserstein ambiguity set, to address the wind power penetrated unit commitment optimal energy flow (UC-OEF) problem for the IEGS. Compared to the equivalent DRO model, the two-stage SRO model can be approximately transformed into a computationally efficient form. Specifically, we employ linear decision rules to simplify the proposed UC-OEF model. Moreover, we further enhance the tractability of the simplified model by exploring its structural features and, accordingly, develop a solution method. Simulation results on two IEGSs validate the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

Over the past decades, the increasing penetration of distributed energy resources (DERs) has dramatically changed the power load composition in the distribution networks. The traditional static and dynamic load models can hardly capture the dynamic behavior of modern loads especially for fault-induced delayed voltage recovery (FIDVR) events. Thus, a more comprehensive composite load model with combination of static load, different types of induction motors, single-phase A/C motor, electronic load and DERs has been proposed by Western Electricity Coordinating Council (WECC). However, due to the large number of parameters and model complexity, the WECC composite load model (WECC CMLD) raises new challenges to power system studies. To overcome these challenges, in this paper, a cutting-edge parameter reduction (PR) approach for WECC CMLD based on active subspace method (ASM) is proposed. Firstly, the WECC CMLD is parameterized in a discrete-time manner for the application of the proposed method. Then, parameter sensitivities are calculated by discovering the active subspace, which is a lower-dimensional linear subspace of the parameter space of WECC CMLD in which the dynamic response is most sensitive. The interdependency among parameters can be taken into consideration by our approach. Finally, the numerical experiments validate the effectiveness and advantages of the proposed approach for WECC CMLD model. [ABSTRACT FROM AUTHOR]

The approach of ambient signals-based load modeling (ASLM) was recently proposed to better track the time-varying changes of load models. To improve computation efficiency and model structure complexity, a hierarchical framework for ASLM is proposed in this paper. Through this framework, the hidden quasi-convexity of the load modeling problem is explored for the first time. This allows more complicated static load model structures and gradient or Hessian-based optimization algorithms to be used. In the upper level, the identification of dynamic load parameters is regarded as an optimization problem. In the lower level, the optimal static load parameters are obtained through linear regression for a given group of dynamic load parameters. Afterward, the regression residuals are regarded as the objective function (OF) of the upper level optimization problem. The proposed method is validated by the case study results on the Guangdong Power Grid. The results show that the OF is mostly quasi-convex after the transformation of the induction motor model, which provides the basis for the application of gradient or Hessian-based optimization algorithms. The case study results also validate that the proposed approach has better computation efficiency and model structure complexity compared with the previous ASLM approaches. [ABSTRACT FROM AUTHOR]

Stochastic unit commitment is an efficient method for grid operation in the presence of significant uncertainties. An example is an operation during a predicted hurricane with uncertain line out-ages. However, the solution quality comes at the cost of substantial computational burden, which makes its adoption challenging. This paper evaluates some possible ways that machine learning can be used to reduce this computational burden. First, a set of feasibility studies is conducted. Results suggest that using machine learning as an assistant to the stochastic unit commitment solver is more advantageous than using it as a standalone solver. In particular, the machine learning model is trained to facilitate solving the problem by determining the unnecessary constraints that can be removed from the original problem without affecting the final accuracy. The variables that can be used as input features/predictors or outputs for the machine learning model are determined through feasibility studies. Then, an algorithm to train and utilize a machine learning model is proposed. The method is tested on a 500-bus synthetic South Carolina system. Various test cases show an average reduction in solution time by more than 90% by using the trained machine learning model to assist the stochastic unit commitment solver. [ABSTRACT FROM AUTHOR]

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. The selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) of voltage to uncertain power injection variations plays an important role for appropriate Volt-VAR optimization. This paper proposes a data-driven GSA method for large-scale distribution systems with a large number of uncertain sources. Specifically, the deep Gaussian process is used to identify the mapping relationship between uncertain power injections and voltages. This allows resorting to the analysis of variance framework to calculate the Sobol indices for GSA. Unlike the existing polynomial chaos expansion and Gaussian process-based approaches, our proposed method has much better scalability. Test results on the EPRI 1747-node K1 circuit with different numbers of uncertain sources with various uncertain levels and different PV distributions demonstrate that the proposed method can achieve accurate GSA. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution system. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of load and PV power injections. The sampling-based method estimates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-bus distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework. [ABSTRACT FROM AUTHOR]

Large blackouts in power grids are often the consequence of uncontrolled failure cascades. The ability to predict the failure cascade process in an efficient and accurate manner is important for power system contingency analysis. In this paper, we propose to apply the influence model for the prediction and screening of failure cascades in large scale DC and AC power networks. Then, the trained influence model is applied to some large power grids with thousands of buses and transmission lines. The prediction performance is evaluated in four different aspects, from the global perspective of the overall failure size to the individual information regarding the link failure time. The results show that under limited training samples, the proposed framework is capable of predicting the failure cascade size with a 7% error rate, the final state of links with a 10% error rate, and the failure time within 1 time unit for both the DC and AC model. One major advantage of the proposed method is that it can reduce the computational time of the failure cascade prediction by a few orders of magnitude with limited compromise in accuracy, as compared to the power flow based contingency analysis. Another important feature of the proposed method is that the trained influence parameters can reveal the critical initial contingencies. This information is very helpful for identifying the worst contingency scenarios for system operators. [ABSTRACT FROM AUTHOR]

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. It is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLP D-OPF model for the same distribution system. [ABSTRACT FROM AUTHOR]

In this paper, a coupled interaction matrix is proposed to describe the interactions between line outages and the load shed at buses. The coupled interaction matrix is effectively estimated by the Expectation Maximization algorithm. A highly probabilistic coupled interaction model is further proposed to efficiently generate cascades with both line outages and the load shed based on the coupled interaction matrix and the distribution of initial outages. To mitigate cascading failures, critical links are identified based on the coupled interaction matrix by calculating a comprehensive severity index that considers the consequences of both line outages and the load shed. Simulation results on the IEEE 300-bus system verify the effectiveness of the proposed approach. The cascades generated from the coupled interaction model match the statistics of the original cascades very well. The identified critical links based on the comprehensive severity index enable a proper tradeoff between reducing line outages and reducing the load shed, leading to a better mitigation effect than only considering either line outages or the load shed. [ABSTRACT FROM AUTHOR]

A state estimation framework that eliminates the need for a topology processor is presented in this paper. By retaining switching devices (SDs) in the network model, this approach allows estimation of their statuses. Consequently, topology error detection becomes part of the SE process. Since this approach requires expansion of bus-branch models with SDs, the conventional state estimation formulation is accordingly modified to avoid numerical issues due to extremely small (large) impedance values of open (closed) switching devices. The scalability of the proposed framework is achieved by parallel processing, which is implemented after partitioning the system into zones. The measurement overhead is kept minimal by utilizing two optimal measurement placement algorithms and taking advantage of KCL-based virtual measurements. Case studies presented show that the proposed method can identify concurrent bad data and topology errors. The improvements in computation times due to parallel processing are demonstrated through simulations on the IEEE 300-bus system with and without zone-partitioning. [ABSTRACT FROM AUTHOR]

The Virtual Power Plant (VPP) has been proposed to aggregate Distributed Generations (DGs) to act like a single power plant, thus, also has functions on the frequency and voltage support. The previous models of the VPP are static and focus on the energy trading and management. For the system transient response analysis, a dynamic VPP model must be needed. The paper proposes a reduced-order yet accurate aggregated model to represent VPP transients for the stability analysis of power systems. The goal is to provide a model that is adequate for system studies and can serve to the Transmission System Operator (TSO) to evaluate the impact of VPPs on the overall grid. The proposed model can accommodate the transient response of the most relevant controllers included in the distributed generators that compose the VPP. Using a comparison with a real-time detailed Electro-Magnetic Transients (EMT) models of the VPP confirms the validity of the proposed aggregated model. The case studies based on the IEEE 39-bus system verifies the accuracy of the proposed aggregated model on the system stability analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a new decentralized data-driven load restoration (DDLR) scheme for transmission and distribution (TD) systems with high penetration of wind power. Robust DDLR models are constructed in order to handle uncertainties and ensure the feasibility of decentralized schemes. The Wasserstein metric is used to describe the ambiguity sets of probability distributions in order to build the complete DDLR model and realize computationally tractable formulation. A data-driven model-nested analytical target cascading (DATC) algorithm is developed to obtain the final load restoration result by iteratively solving small-scale mathematical models. The proposed DDLR scheme provides load restoration results with adjustable robustness, and performance efficiency is independent from the amount of data. The DDLR scheme makes full use of the available data while respecting information privacy requirements of independent operated systems, and ensures the feasibility of a decentralized load restoration strategy even in the worst-case condition. The effectiveness of the proposed method is validated using a small-scale TD system and a large-scale system with the IEEE 118-bus TS and thirty IEEE-33 DSs, showing high computational efficiency and superior restoration performance. [ABSTRACT FROM AUTHOR]