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Sensing and measurement systems are quintessential to the safe and reliable operation of electric power grids. Their strategic placement is of ultimate importance because it is not economically viable to install measurement systems on every node and branch of a power grid, though they need to be monitored. An overwhelming number of strategies have been developed to meet oftentimes multiple conflicting objectives. The prime challenge in formulating the problem lies in developing a heuristic or an optimisation model that, though mathematically tractable and constrained in cost, leads to trustworthy technical solutions. Further, large-scale, long-term deployments pose additional challenges because the boundary conditions change as technologies evolve. For instance, the advent of new technologies in sensing and measurement, as well as in communications and networking, might impact the cost and performance of available solutions and shift initially set conditions. Also, the placement strategies developed for transmission grids might not be suitable for distribution grids, and vice versa, because of unique characteristics; therefore, the strategies need to be flexible, to a certain extent, because no two power grids are alike. Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as the optimal placement of measurements to ensure observability in transmission grids. There is a dearth of work providing a comprehensive picture for developing optimal placement strategies. Because of the ongoing efforts on the modernisation of electric power grids, there is a need to consolidate the status quo while exposing its limitations to inform policymakers, industry stakeholders, and researchers on the research-and-development needs to push the boundaries for innovation. Accordingly, this paper first reviews the state-of-the-art considering both transmission and distribution grids. Then, it consolidates the key facto

This paper proposes a novel two-dimensional continuum model that aims to capture the electromechanical wave phenomenon observed in power systems after a disturbance. The model is derived by a homogenization process of the discrete parameters of the conventional, discrete transient analysis model. The implementation of the proposed model is detailed. The paper also demonstrates the accuracy of the proposed model by comparing its results with those obtained from the discrete model. It is observed that the proposed model is able to provide a similar characterization of system electromechanical dynamics as the discrete model from a continuum point of view.

This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions, including heavy-tailed distributions. The proposed RDMD is statistically robust because the outliers in the data set are flagged via projection statistics and suppressed using a Schweppe-type Huber generalized maximum-likelihood estimator that minimizes a convex Huber cost function. The latter is solved using the iteratively reweighted least-squares algorithm that is known to exhibit an excellent convergence property and numerical stability than the Newton algorithms. Several numerical simulations using canonical models of dynamical systems demonstrate the excellent performance of the proposed RDMD method. The results reveal that it outperforms several other methods proposed in the literature.

Emergency services and utilities need appropriate planning tools to analyze and improve infrastructure and community resilience to disasters. Recognized as a key metric of community resilience is the social well-being of a community during a disaster, which is made up of mental and physical social health. Other factors influencing community resilience directly or indirectly are emotional health, emergency services, and the availability of critical infrastructures services, such as food, agriculture, water, transportation, electric power, and communications system. It turns out that in computational social science literature dealing with community resilience, the role of these critical infrastructures along with some important social characteristics is not considered. To address these weaknesses, we develop a new multi-agent based stochastic dynamical model, standardized by overview, design concepts, details, and decision (ODD+D) protocol and derived from neuro-science, psychological and social sciences, to measure community resilience in terms of mental and physical well-being. Using this model, we analyze the micro-macro level dependence between the emergency services and power systems and social characteristics such as fear, risk perception, information-seeking behaviour, cooperation, flexibility, empathy, and experience, in an artificial society. Furthermore, we simulate this model in two case studies and show that a high level of flexibility, experience, and cooperation enhances community resilience. Implications for both theory and practice are discussed.

This paper summarizes the report prepared by an IEEE PES Task Force. Resilience is a fairly new technical concept for power systems, and it is important to precisely delineate this concept for actual applications. As a critical infrastructure, power systems have to be prepared to survive rare but extreme incidents (natural catastrophes, extreme weather events, physical/cyber-attacks, equipment failure cascades, etc.) to guarantee power supply to the electricity-dependent economy and society. Thus, resilience needs to be integrated into planning and operational assessment to design and operate adequately resilient power systems. Quantification of resilience as a key performance indicator is important, together with costs and reliability. Quantification can analyze existing power systems and identify resilience improvements in future power systems. Given that a 100% resilient system is not economic (or even technically achievable), the degree of resilience should be transparent and comprehensible. Several gaps are identified to indicate further needs for research and development.

We propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.

Facing stochastic variations of the loads due to an increasing penetration of renewable energy generation, online decision making under uncertainty in modern power systems is capturing power researchers' attention in recent years. To address this issue while achieving a good balance between system security and economic objectives, we propose a surrogate-enhanced scheme under a joint chance-constrained (JCC) optimal power-flow (OPF) framework. Starting from a stochastic-sampling procedure, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo (MC) method, we propose to use a polynomial-chaos-based surrogate that allows us to efficiently evaluate the power-system model at non-Gaussian distributed sampled values with a negligible computing cost. Learning from the MC simulated samples, we further proposed a hybrid adaptive approach to overcome the conservativeness of the JCC-OPF by utilizing correlation of the system states, which is ignored in the traditional Boole's inequality. The simulations conducted on the modified Illinois test system demonstrate the excellent performance of the proposed method.

Dynamic state estimation (DSE) accurately tracks the dynamics of a power system and provides the evolution of the system state in real-time. This paper focuses on the control and protection applications of DSE, comprehensively presenting different facets of control and protection challenges arising in modern power systems. It is demonstrated how these challenges are effectively addressed with DSE-enabled solutions. As precursors to these solutions, reformulation of DSE considering both synchrophasor and sampled value measurements and comprehensive comparisons of DSE and observers have been presented. The usefulness and necessity of DSE based solutions in ensuring system stability, reliable protection and security, and resilience by revamping of control and protection methods are shown through examples, practical applications, and suggestions for further development.

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

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. Facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.

The observability analysis of a time-varying nonlinear dynamic model has recently attracted the attention of power engineers due to its vital role in power system dynamic state estimation. Generally speaking, due to the nonlinearity of the power system dynamic model, the traditional derivative-based observability analysis approaches either rely on the linear approximation to simplify the problem or require a complicated derivation procedure that ignores the uncertainties of the dynamic system model and of the observations represented by stochastic noises. Facing this challenge, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only brings a low complexity, but also enables us to quantify the degree of observability by considering the stochastic nature of the dynamic systems. The excellent performances of the proposed method is demonstrated using simulations of a decentralized dynamic state estimation performed on a power system using a synchronous generator model with IEEE-DC1A exciter and a TGOV1 turbine-governor.

A modern power system is characterized by a stochastic variation of the loads and an increasing penetration of renewable energy generation, which results in large uncertainties in its states. These uncertainties bring formidable challenges to the power system planning and operation process. To address these challenges, we propose a cost-effective, iterative response-surface-based approach for the chance-constrained AC optimal power-flow problem that aims to ensure the secure operation of the power systems considering dependent uncertainties. Starting from a stochastic-sampling-based framework, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose, instead of using the original complicated power-system model, to rely on a polynomial-chaos-based response surface. This response surface allows us to efficiently evaluate the time-consuming power-system model at arbitrary distributed sampled values with a negligible computational cost. This further enables us to efficiently conduct an online stochastic testing for the system states that not only screens out the statistical active constraints, but also assists in a better design of the tightened bounds without using any Gaussian or symmetric assumption. Finally, an iterative procedure is executed to fine-tune the optimal solution that better satisfies a predefined probability. The simulations conducted in multiple test systems demonstrate the excellent performance of the proposed method.

This paper proposes a new methodology for power system islanding based on Koopman modal coherency (KMC) combined with subgraph theory. Initial system partitioning is determined from the Koopman bus-angle coherency matrix. Then, the technique of subgraph is used to modulate the partitions, yielding to viable islands. Balancing subgraphs are constructed from the clusters pairwise neighboring areas. Overload subgraphs swap to connected over-generation subgraphs. Stable islands satisfy nonlinear dynamic coherency, and minimal power mismatch. The search algorithm substantiates the required bands specified in the frequency operating standards. Under severe disturbances, over-frequency generation shedding and under-frequency load shedding schemes are implemented. The proposed islanding methodology is demonstrated on a realistic 151-bus, 24-machines power system. Results show that the proposed scheme can reduce failure regions in faulted power systems.

The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges, this paper proposes a cost-effective, nonparametric method to quantity the impact of uncertain power injections on the load margins. First, we propose to generate system uncertain inputs via a novel vine copula due to its capability in simulating complex multivariate highly dependent model inputs. Furthermore, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. The simulations conducted on the IEEE 57-bus system, to which correlated renewable generation are attached, reveal the excellent performance of the proposed method.

Risk assessment of power system failures induced by low-frequency, high-impact rare events is of paramount importance to power system planners and operators. In this paper, we develop a cost-effective multi-surrogate method based on multifidelity model for assessing risks in probabilistic power-flow analysis under rare events. Specifically, multiple polynomial-chaos-expansion-based surrogate models are constructed to reproduce power system responses to the stochastic changes of the load and the random occurrence of component outages. These surrogates then propagate a large number of samples at negligible computation cost and thus efficiently screen out the samples associated with high-risk rare events. The results generated by the surrogates, however, may be biased for the samples located in the low-probability tail regions that are critical to power system risk assessment. To resolve this issue, the original high-fidelity power system model is adopted to fine-tune the estimation results of low-fidelity surrogates by reevaluating only a small portion of the samples. This multifidelity model approach greatly improves the computational efficiency of the traditional Monte Carlo method used in computing the risk-event probabilities under rare events without sacrificing computational accuracy.

Due to the lack of sufficient online measurements for distribution system observability, pseudo-measurements from short-term load or distributed renewable energy resources (DERs) forecasting are used. However, the accuracy of them is low and thus significantly limits the performance of distribution system state estimation (DSSE). In this paper, a robust DSSE that integrates multi-source measurement data is proposed. Specifically, the historical low-voltage (LV) side smart meters are used to forecast load and DERs injections via the support vector machine (SVM) with optimally tuned parameters. By contrast, the online smart meters at LV side are utilized to derive equivalent power injections at the MV/LV transformers, yielding more accurate pseudo-measurements compared to the forecasted injections. Furthermore, to deal with bad data caused by communication loss, instrumental errors and cyber attacks, robust DSSE that relies on generalized maximum-likelihood (GM)-estimation criterion is developed. The projection statistics are developed to adjust the weights of each measurement, leading to better balance between pseudo- and real-time measurements. Numerical results conducted on modified IEEE 33-bus system with DG integration demonstrate the effectiveness and robustness of the proposed method.

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To solve this stochastic economic dispatch, the conventional Monte Carlo method is prohibitively time consuming for medium- and large-scale power systems. To overcome this problem, we propose in this paper a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Based on the dimension-reduction results obtained by the Karhunen-Loeve expansion, a Gaussian-process emulator is constructed. This surrogate allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus system reveal that the proposed method has an excellent performance as compared to the traditional Monte Carlo method.

Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time-synchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving the way for developing the next generation of energy management systems and novel system monitoring, control and protection tools to achieve better reliability and resiliency.

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in the stochastic economic dispatch (SED) problem for the purpose of forecasting, the conventional Monte-Carlo (MC) method is prohibitively time-consuming for practical applications. To overcome this problem, we propose a novel Gaussian-process-emulator (GPE)-based approach to quantify the uncertainty in SED considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling (LHS) as the computer experimental design, a GPE is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated SED model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

Details are presented of the development and incorporation of a generation and transmission reliability approach in an upper-level sustainability assessment framework for power system planning. This application represents a quasi-stationary, multiobjective optimization problem with nonlinear constraints, load uncertainties, stochastic effects for renewable energy producers, and the propagation of uncertainties along the transmission lines. The Expected Energy Not Supplied (EENS) accounts for generation and transmission reliability and is based on a probabilistic as opposed to deterministic approach. The optimization is developed for three scenarios. The first excludes uncertainties in the load demand, while the second includes them. The third scenario accounts not only for these uncertainties, but also for the stochastic effects related to wind and photovoltaic producers. The sustainability-reliability approach is applied to the standard IEEE Reliability Test System. Results show that using a Mixture of Normals Approximation (MONA) for the EENS formulation makes the reliability analysis simpler, as well as possible within a large-scale optimization. In addition, results show that the inclusion of renewable energy producers has some positive impact on the optimal synthesis/design of power networks under sustainability considerations. Also shown is the negative impact of renewable energy producers on the reliability of the power network.