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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.

This paper proposes a systematic and general approach to model correlated stochastic processes in power systems by means of stochastic differential-algebraic equations. The paper discusses the theoretical background of stochastic differential-algebraic equations and provides a variety of examples of correlated stochastic models for power system applications. With this aim, stochastic processes with Normal and Weibull distributions are considered. The case study utilizes the well-known two-area system to demonstrate that the presence of correlation between the stochastic processes can cause instability, despite the fact that the same system is stable if the same processes are uncorrelated. The case study also considers a 1479-bus dynamic model of the all-island Irish transmission system to show the scalability of the proposed technique, and to compare scenarios with different levels of correlation among stochastic processes. Results indicate that correlation has a non-negligible impact on short-term dynamics. A high level of correlation among the processes, in fact, can give raise to instability.

This paper provides an overview of hyperloop technologies, including a brief discussion of key components of a hyperloop system that determine the electric power requirements as a function of time. At-scale hyperloop systems do not yet exist, so a model was used to generate a set of load profiles for conceptual hyperloop realizations at four locations in the United States: two systems in California and one each in Colorado and Ohio. In all four cases, the modeled hyperloop load profiles included pulses in both active and reactive power. Grid modeling was performed to estimate the grid impacts and for discussing grid integration challenges. The paper discusses how energy storage systems might be used to eliminate the pulsating load characteristics or significantly reduce it to accommodate current grid planning guidelines.

This paper investigates the small-signal power oscillations in a VSC-based multi-terminal DC (MTDC) power transmission system. Regarding the DC power oscillation modes (DPOMs), this paper demonstrates that when the master–slave control is adopted for the MTDC power system, there is only one DPOM. In contrast, when the DC voltage droop control is adopted, the DC electric power oscillations (DEPOs) may be multi-modal oscillations as there are multiple DPOMs. Furthermore, a better understanding of DEPOs, which is analogous to low-frequency electric power oscillations (LEPOs) in conventional AC power systems, is obtained, unveiling how the DPOMs determine the power oscillations in AC and MTDC power systems. Moreover, this paper theoretically verifies that the DPOMs determine the behaviors of both DEPOs in MTDC systems and power oscillations between the VSCs (which adopt the DC voltage control or DC voltage droop control) and external AC systems. By analogy to LEPOs, damping torque analysis is applied to examine the stability risk of the MTDC power system. The results indicate that even if VSCs are self-stable, there is a potential risk of growing DEPOs occurring in MTDC power systems under heavy DC loads.

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.

This paper proposes a method to design power system stabilizers (PSSs) based on single-machine infinite-bus system models to mitigate the risk of low-frequency electro- mechanical power oscillations in an N-machine power system. First, models of N fabricated identical-machine power systems are established for the N-machine power system. Analysis in the paper indicates that the electromechanical oscillation mode of fabricated identical-machine power systems with the least damping is of less damping than the electromechanical oscillation modes of N-machine power system. Second, it is proved that models of fabricated identical-machine power systems are dynamically equivalent to the single-machine infinite-bus system models. Finally, it is suggested that the PSSs are designed using single-machine infinite-bus system models to enhance the least damped electromechanical oscillation mode of fabricated identical-machine power systems. This eventually improves the damping of electromechanical oscillation modes of N-machine power system, thus mitigating the risk of low-frequency electromechanical power oscillations. In the paper, the proposed method is demonstrated and evaluated by using three well-known example multi-machine power systems. Effectiveness of PSSs is confirmed by the results of modal computation and simulation.

Solving nonlinear algebraic equations is a core task in many fields of engineering and the sciences. Iterative methods such as Newton's method have been popular in solving power flow equations. Recently, the non-iterative holomorphic embedding (HE) methods that employ polynomial embedded systems have been proposed to solve power flow equations. It is advantageous for the solution functions obtained by the HE method to possess an algebraic property. The present paper points out that algebraic solution functions can have several desired properties for the HE method to work. This paper also exemplifies that the algebraic property cannot be ensured by the elimination process, which corrects an assertion in the literature. It is hence essential to study required conditions for ensuring the existence of algebraic solution functions. The present paper is devoted to the theoretical foundation of HE methods using a polynomial embedded system and develops a novel general theorem and sufficient conditions to ensure the required algebraic property. Examples and numerical results are presented to better explain the derived theoretical results.

This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. The results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties.

This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method.

Although distribution grid customers are obliged to share their consumption data with distribution system operators (DSOs), a possible leakage of this data is often disregarded in operational routines of DSOs. This paper introduces a privacy-preserving optimal power flow (OPF) mechanism for distribution grids that secures customer privacy from unauthorised access to OPF solutions, e.g., current and voltage measurements. The mechanism is based on the framework of differential privacy that allows to control the participation risks of individuals in a dataset by applying a carefully calibrated noise to the output of a computation. Unlike existing private mechanisms, this mechanism does not apply the noise to the optimization parameters or its result. Instead, it optimizes OPF variables as affine functions of the random noise, which weakens the correlation between the grid loads and OPF variables. To ensure feasibility of the randomized OPF solution, the mechanism makes use of chance constraints enforced on the grid limits. The mechanism is further extended to control the optimality loss induced by the random noise, as well as the variance of OPF variables. The paper shows that the differentially private OPF solution does not leak customer loads up to specified parameters.

The low-frequency oscillations (LFOs) inherent in power systems will be impacted by the increasing penetration of renewable energy sources (RESs). This paper investigates the impact of virtual synchronous machine (VSM) based RESs on the LFOs in power systems. A detailed two-machine test-bed has been developed to analyze the LFOs which exists when VSMs replace synchronous generators. The characteristics of the LFO modes, and the dominant states have been comprehensively analyzed. Furthermore, this study analyzes the LFO modes which exists in an all-VSM grid. The role of the power system stabilizers in the all-VSM grid has been comprehensively evaluated. The IEEE benchmark two-area four-machine system has been employed to corroborate the results of the small-signal analysis, and observe the transient performance. The analysis in this paper have been performed in MATLAB/SIMULINK environment.

The recent power systems literature has witnessed an intensified interest in state estimation methods that can handle a vast array of measurements from large-scale networks while maintaining performance that is commensurate with real-time requirements. When measurements are from the Supervisory Control and Data Acquisition (SCADA) system and Phasor Measurement Units (PMUs), an elegant formulation of the weighted least squares problem can be cast in complex variables and solved via the Gauss-Newton (GN) method. This paper presents a Perturbed Gauss-Newton (PGN) method in complex variables that is suitable for real-time tracking of the network's state vector. The proposed PGN method is built around an entirely linear measurement model expressed in function of the complex phasor voltages, and its iterative solution scheme requires one factorization of the coefficient matrix followed by repeated forward/backward substitutions. The complex variable PGN method for state estimation can be therefore seen as the counterpart of the classical implicit bus impedance method for power flow. The paper reports numerical results of the PGN method on large-scale transmission networks having up to 9241 nodes and contrasts the proposed method with the equality constrained GN method in complex variables and a recent two-stage estimator also operating in the complex domain.

The modern photovoltaic inverter has an active power-reactive power (Watt-VAr) control curve that is part of its management modes. The Watt-VAr curve, whose settings can be remotely modified, regulates the inverter reactive power output in function of its active power. This paper proposes the optimization of inverter segregated linear decision rules (LDRs), starting from the legacy Volt-VAr optimization in distribution networks. As opposed to classical LDRs that are interfaced with Volt-VAr optimization, the segregated LDRs are piecewise linear continuous curves that directly satisfy the reactive power capability of inverters, and their multiple segments can capture the correlation in solar power variability. The paper presents linear programming formulations for optimizing the segregated linear decision rules using stochastic optimization, robust optimization, and distributionally robust optimization. The optimization schemes are demonstrated on both meshed and radial networks, and their performance is validated via Monte-Carlo simulation.

In this paper, previous theory and results regarding Low-Voltage (LV) distribution losses are validated through power-flow simulation using real load data with standard metering resolution. The validated results are then used to build a generalized loss prediction model for arbitrary grid topologies and metering resolutions. The paper provides the theoretical background to build and generalize a loss prediction model based on load variances together with an approach to estimate such variances. The prediction model uses as explanatory variables the variances of the loads. Yet, such variances are usually unknown for the higher metering resolutions, so the model also proposes a method to predict the higher resolution variances based on the standard metering ones. Results are presented to illustrate the approach proposed and to estimate the increase in losses expected for typical LV grids.

In this paper, we investigate whether and under which conditions jointly owning a variable renewable source of electricity (VRES) and an electricity storage generates economies of scope in competitive electricity markets. Using a simple stochastic optimization model that assumes frictionless markets, we analytically show that no economic benefit arises from combining the two assets. This finding is in contradiction to large parts of the literature, which claim that it is in the economic interest of owners of VRES to additionally own electricity storage. We also identify circumstances where our argument does not hold and the combination of storage and VRES could theoretically make economic sense on the level of individual agents. In the last part of the paper, we demonstrate in a numerical case study of the German market that even in cases where our theoretical results do not hold, tying together storage and VRES may produce suboptimal results.

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.

This paper presents a unified control strategy for parallel LCC-VSCs interlinking converters (IC)s in hybrid AC/DC grids. The parallel LCC-VSCs configuration takes advantage of the low cost of the LCC system as well as the bidirectional power flow capability of VSCs and offers an excellent option for lowering system costs with high performance. Moreover, drawbacks of the LCCs such as low power quality, reactive power consumption, and commutation failure can be addressed by using the parallel LCC-VSCs configuration with proper control and coordination. The proposed unified control system is developed by modifying the LCC's V-I graph to create a droop equivalent along with droop-based control of the VSCs. As a result, it provides voltage/frequency support for the AC and voltage support for the DC sub-grids in various operating conditions. In this paper, the performance of the proposed control strategy under different operation conditions is investigated. Case study results, with a realtime simulator, are provided to verify the effectiveness of the proposed control strategy.

As the penetration of utility-scale solar photovoltaic (PV) power plants increases, the inertia in the system is reduced and there will be increased primary frequency response requirements. To increase inertia and improve the primary frequency response, grid-forming inverters connecting PV to grid and energy storage systems (ESSs) may play an important role. Moreover, high-voltage direct current (HVdc) links can also be an enabler to transfer remote PV power generation and to improve grid stability. That is, with increased penetration of PV, discrete development of PV and ESS connecting to transmission ac grid and HVdc links is one of the solutions for stable operation of the grid. In this paper, an integrated concept for integration of PV and ESS to transmission ac grid and HVdc links is proposed that is named as multi-port autonomous reconfigurable solar power plant (MARS). The integrated development incorporates advanced control methods to provide inertial and primary frequency response, reactive power support, and transient stability to manage PV and ESS resources. In this paper, high-fidelity switched system model of the integrated system and grids are developed and detailed simulation results are provided to showcase the stable operation of the integrated system and provision of grid support functions.

Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address these challenges, recent research has applied various convex relaxation approaches to OPF problems. The QC relaxation is a promising approach that convexifies the trigonometric and product terms in the OPF problem by enclosing these terms in convex envelopes. The accuracy of the QC relaxation strongly depends on the tightness of these envelopes. This paper presents two improvements to these envelopes. The first improvement leverages a polar representation of the branch admittances in addition to the rectangular representation used previously. The second improvement is based on a coordinate transformation via a complex per unit base power normalization that rotates the power flow equations. The trigonometric envelopes resulting from this rotation can be tighter than the corresponding envelopes in previous QC relaxation formulations. Using an empirical analysis with a variety of test cases, this paper suggests an appropriate value for the angle of the complex base power. Comparing the results with a state-of-the-art QC formulation reveals the advantages of the proposed improvements.

With more variable and uncertain patterns of electricity production and consumption, the need for flexibility in the power grid is becoming increasingly crucial. Industrial energy systems have the potential to contribute to providing such flexibility. Yet, there is still a lack of effective methods to quantify the magnitude of available flexibility from industrial energy systems that can be optimally dispatched to support the operation of the power grid. This paper studies the flexibility provision from steam systems, which exist in many energy-intensive industries. A generic model of industrial steam systems with turbine-generators is presented to reflect its interactions with the power grid. Then, a hybrid physics-based and data-driven approach is developed to approximate the boundaries of the flexibility domain at different operating conditions of the steam systems. The proposed flexibility quantification method is applied to two real industrial steam systems in a paper mill and a steel mill. The results show that the proposed method can approximate the flexibility boundaries under uncertainty steam states and reflect key factors that affect the boundaries. Also, it is shown that neglecting the limits imposed by the steam network leads to an overestimation of flexibility boundaries at certain operating conditions.

State Estimation (SE) is the backbone of modern Energy Management System (EMS) due its capability of processing real time measurements and provide reliable information to system operators. Since its introduction to power systems in the 70's, SE has been widely used in transmission networks. Distribution grids on the other hand lack sufficient number of real time measurements, and for that reason SE has not been widely implemented on these systems. The recent increase in the number of renewable energy sources connected to the grid at lower voltage levels, the advent of Distribution Automation (DA) and Smart Grids necessitate closer monitoring of distribution networks and thus forcing utilities to upgrade their operations and deploy Advanced Distribution Management Sytems (ADMS). Therefore, Distribution System State Estimation (DSE) is paramount to provide real time monitoring of active distribution grids. This papers investigates the formulation of the three-phase distribution state estimation where in the most general case, none of the system buses may have balanced three phase voltages. In such a case, the choice and definition of the slack bus need to be revisited. Most of the existing work arbitrarily assign the root bus of the distribution feeder as the balanced three-phase reference which may not be realistic for today's active distribution systems. This paper addresses this shortcoming of the existing SE formulations by introducing a virtual reference bus. The proposed approach is effectively validated by simulations carried out on distribution test systems.

Wide-area time-synchronized measurements have recently revealed troublesome forced oscillations (FOs) within modern synchronized power grids. In some cases, these FOs represent a dangerous hazard to the system. Recent research has focused on locating the source of FOs to provide operators with knowledge for mitigating their impact locally. This paper presents a complementary mitigation strategy, which is to purposely induce a second oscillation into the grid which cancels the impact of the FO. Such a strategy is complementary in that it may provide valuable time to operators attempting to locate the FOs source and to determine how to rectify it. This paper presents a suppression control strategy which modulates controllable devices to automatically cancel the impact of the FO without the need for locating the source of the original FO. The strategy is based upon tuned feedback control. The approach is demonstrated on a simulation system via modulation of inverter-based generation.

The conductor temperature is a critical state variable that should be considered in power flow calculations to improve the calculation accuracy and reveal the potential thermal loadability of transmission components. This paper proposes a calculation method for time-process power flow considering the thermal behavior (TPPFCTB) of transmission components to calculate the temperature dynamics of overhead lines, power cables, and transformers under anticipated system operation scenarios. The TPPFCTB model is represented by differential-algebraic equations, which can be solved as a sequence of extended power flow problems at discretization time intervals. Based on the Newton method, incomplete and complete decoupling methods are proposed to decouple the correction equations into several independent groups with constant coefficient matrices, thus improving computational efficiency. The work presented in this paper provides an effective method for the detection of potential power transfer capability problems associated with transmission components, thus guiding operators to make more economical decisions. Numerical simulations were conducted to verify the effectiveness of the proposed method.

In the absence of demand-side bids for certain reliability products in the wholesale electricity markets, Independent System Operators (ISOs) traditionally use fixed demand requirements with penalty factors to clear the market. This approach does not allow proper tradeoffs between cost and reliability due to the inelasticity of the fixed requirements. Therefore, ISOs have been replacing the fixed requirements with sloped demand curves. However, the economic interpretation of demand curves, especially for multiple coupled products, is largely missing in both theory and practice. This could lead to the misrepresentation of the demand benefit in the market clearing objective. Using a two-product market model, Part I of this paper reveals two distinct interpretations of demand curves, each associated with a specific form of the market clearing problem. This implies that the construction of demand curves and the use of them in market clearing must be consistent with their economic interpretation. In Part II of this paper, we analyze the sequential and iterative market clearing processes currently implemented in some markets to demonstrate their solution sub-optimality. The root cause of the problem is the lack of a clear representation of the demand benefit. The social surplus optimization based on the proper interpretation of demand curves is proposed.

This paper addresses the problem of hybrid state estimation, which relies on data provided by both conventional SCADA systems and phasor measurement units. A previously proposed cascaded architecture is employed, whose first estimation module processes the asynchronous measurements through a conventional, nonlinear state estimator. The focus, however, is on the second estimation module, where the SCADA-based estimates are combined with synchrophasor data in order to enhance the quality of the state estimates. For the benefit of computational performance, that task must be performed by a non-iterative and numerically robust algorithm. It is equally important to avoid awkward uncorrelatedness assumptions while defining measurement weighting factors, since they may severely compromise the statistical characterization of the final solution. To accomplish both objectives, a generalized $2\times 2$ block version of the 3-multiplier Givens rotations has been developed and is introduced in this paper. This leads to numerically stable solutions, whose statistical properties are preserved. The features and advantages of the proposed two-stage hybrid state estimator are illustrated through case studies conducted on the IEEE 14-bus, 30-bus, 57-bus, and 300-bus test systems.

Renewables, such as solar and wind generation, combined with storage are becoming a key part of modern grid. This paper develops probabilistic tools for analysis of grid reliability with such variable generation resources. The developed tools improve speed and accuracy of the reliability analysis compared to usual Monte Carlo methods. This is achieved by using an extension of well known convolution method applicable to interdependent variables. The interdependent distributions are obtained from historical data using Machine Learning of quantile models. The paper presents a novel approach to the analysis of reliability contribution of storage based on these models and related to Information Theory. The developed tools are demonstrated in several example scenarios for ISO-New England service area.

The increasing penetrations of renewable energy in the electricity sector and plug-in electric vehicles (PEVs) in the transportation sector have increased the interests in introducing new methods to deal with uncertainties in power system studies. In this paper, a new distributionally robust optimization (DRO) via scenario wise ambiguity set is proposed to develop a collaborative bidding strategy for intermittent resources such as hydroelectric generation, wind farms, solar farms and electric vehicle aggregator in the day-ahead energy market. The proposed scenario wise ambiguity set is based on Wasserstein distance and is capable of considering both distributional information and statistical distance metric information in the ambiguity set. In this context, the robust counterpart of proposed DRO applying scenario based affine recourse approximation is developed in this paper. The proposed methodology is applied on a 3-bus test system as well as IEEE 118-bus test system to corroborate the effectiveness of the novel DRO model.

The increasingly wide application of technologies such as combined heat and power (CHP) systems and micro energy management systems has enhanced the coupling of various types of energy. In this paper, a generalized Nash game model is built in this paper to simulate the multi-round auction in combined heat and power market (CHPM). In this model, the consumer demand curves are deduced from the partial derivatives of their payoff functions, and the thermal comfort of the consumers is considered in their payoff functions. The integrated energy suppliers (IES) compete with each other in the CHPM. The generalized Nash game model is applied to describe their rational economic behavior. First, the existence and uniqueness of the generalized Nash equilibrium is proven in detail. Subsequently, a distributed algorithm based on the augmented Lagrangian approach is designed to solve this generalized Nash game model. Through the distributed algorithm, the participants can protect their privacy without revealing their generation parameters or energy consumption schedule to other participants. Finally, by simulating the multi-round auction, it was found that the proposed method has faster convergence than standard Lagrangian approaches.

Eigen-analysis is widely used in the studies of power system oscillation and small-signal stability. However, it may give inaccurate analyses on subsynchronous oscillation (SSO) when nonlinearity is not negligible. In this paper, a nonlinear analytical approach based on the describing function and generalized Nyquist criterion is proposed to analyze the characteristics of SSO with wind farms. The paper first presents describing function-based model reduction considering key nonlinear elements involved in SSO, and then uses a generalized Nyquist criterion for accurate estimation of SSO amplitude and frequency. The results are verified by time-domain simulations on a detailed model with different scenarios considering variations of the system condition and controller parameters.

This paper describes a simple and practical reliability model based on a stationary Markov process for assessing the number of spare parts required for a group of bundles of similar component parts. The proposed model accounts for a number of factors that affect the number of spare parts. The factors include the number of bundles, bundle size, bundle failure rate, time required to repair the failed part or to acquire a new spare part, time needed to install the spare part and any redundancy in the bundle. In addition, the proposed model is capable of handling bundles of different sizes. Two performance criteria namely the group availability criterion and the system total minimum cost criterion can be used in the spare part assessment. The purpose of this paper is to present the new reliability model and to compare its results with other existing probability models.

This paper introduces a novel application of a stochastic filtering algorithm–unscented particle filter (UPF)–to estimate the inaccessible state variables of doubly fed induction generator (DFIG) connected to a multi-area power system with local phasor measurement units (PMUs). This dynamic estimation implementation bears more advanced features than the particle filter (PF) method since it can not only track the dynamic states more accurately and smoothly when the power system experiences sudden disturbances, but also manage to resolve the particle degeneration problem that exists in the PF algorithm. Moreover, the proposed UPF-based dynamic state estimation method is achieved in a decentralized manner and only uses local PMU measurements of voltage and current. Through a comparison study where popular stochastic filtering methods, unscented Kalman filter (UKF) and PF, are employed to achieve the same estimation purpose, this paper shows the superiority of the UPF algorithm particularly designed for state estimation over the other two existing algorithms in terms of accuracy and error tolerance.

This paper studies the convex hull pricing problem in electricity markets using a network-flow-based formulation. The network represents the feasible operating region of a generating unit, and the associated flow constraints define a polyhedron with an integrality property. These facts provide modeling flexibility with respect to the inclusion of unit features and allow to obtain convex hull prices from a linear programming problem. The formulation is solved using a primal-dual approach based on the algorithm developed by Bienstock and Zuckerberg. The algorithm, together with the implemented pre-processing and initialization techniques, allows achieving lower solution times than those obtained by state-of-the-art algorithms available in commercial solvers, e.g., barrier and dual simplex. Furthermore, results suggest that the proposed formulation obtains the minimum uplift payments even when time-dependent start-up costs are included, making the approach more robust than the best documented compact formulation. The paper also discusses the effect of sub-optimal prices on uplift payments by relaxing the optimality criterion of the algorithm, observing a significant impact on lost opportunity costs.

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.

This paper presents a novel distributed voltage control method for multi-terminal direct current (MTDC) systems based on the average consensus algorithm. The proposed method combines the idea of secondary integral voltage control and regulator synchronization problem. It realizes adjustable tradeoff between two conflicting control objectives, that is, voltage regulation and power sharing. The proposed control algorithm only needs a low-bandwidth communication between two adjacent voltage source converters (VSCs) and local information to work effectively. Moreover, regarding the system dynamic response, a parameter tuning method for the proposed controller is provided to achieve the fastest convergence of the distributed control algorithm. This paper also develops a small-signal dynamic model for VSC-MTDC systems with distributed controllers to evaluate the system dynamic performance. The proposed method is validated by time-domain simulation of a 4-terminal VSC-MTDC system. The simulation results show that flexible tradeoff between voltage regulation and power sharing can be achieved under necessary constraints on the DC bus voltages and power sharing ratio.

This paper proposes a temporal decomposition strategy to reduce the computation time of security-constrained unit commitment (SCUC). The novelty of this paper is twofold. The scheduling horizon is decomposed into multiple subhorizons. The concept of coupling intervals is introduced, and a set of auxiliary counting variables and logical expressions along with their equivalent linear models are formulated to handle intertemporal ramp constraints and minimum on/off times between consecutive subhorizons. An accelerated analytical target cascading (A-ATC) algorithm is developed to coordinate SCUC subproblems and find the optimal solution for the whole operation horizon in a distributed manner. An initialization strategy is presented to enhance the convergence performance of A-ATC. The proposed algorithm is tested on four test systems.

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

Truck-mounted mobile emergency resources (MERs) play a significant role in microgrid formation and regulation for power system resilience enhancement. This paper proposes a distributed fixed-time secondary control (DFSC) scheme to regulate the frequency and active power sharing in islanded microgrids with MERs. The proposed DFSC scheme is designed based on a general directed communication graph which considers MER characteristics (e.g., mobility, flexibility, and potential cyber threats). Each DER receives data from its neighbors through directional communication links. The proposed pinning control strategy selects only a small number of DERs for pinning, which have access to the reference frequency information and would guide the operation of remaining local DERs and MERs. In addition, the guaranteed convergence time is determined by control parameters and communication graph without applying the initial operation states. The paper demonstrates that the desired control performances (i.e., frequency restoration and accurate active power sharing) are realized in a timely fashion considering frequent operations of MERs. Case studies are tested and discussed for load variations, different control parameters, communication link failures, and MER operations through time-domain simulations in PSCAD/EMTDC platform.

This paper introduces an alternative description of autonomous dynamical systems as a sum of individual vector fields. This structure of a dynamical system gives us the opportunity to construct individual Lyapunov-like functions to certify stability of an equilibrium point. A theorem on individual functions is developed in a quadratic form to maintain computational efficiency. As a corollary to the developed theory, we conclude that regions of attraction can be estimated by sub-level sets of individual quadratic functions, and through geometric programs they can easily be maximized efficiently. Theoretical findings in this paper are examined on transient stability problem in power systems for both single machine to infinite bus and multi-machine systems with promising results for critical clearing time estimation compared to the values obtained from time domain simulations.

This paper considers the problem of releasing optimal power flow (OPF) test cases that preserve the privacy of customers (loads) using the notion of Differential Privacy . It is motivated by the observation that traditional differential privacy algorithms are not suitable for releasing privacy preserving OPF test cases: The added noise fundamentally changes the nature of the underlying optimization and often leads to test cases with no solutions. To remedy this limitation, the paper introduces the OPF Load Indistinguishability (OLI) problem, which guarantees load privacy while satisfying the OPF constraints and remaining close to the optimal dispatch cost. The paper introduces an exact mechanism, based on bilevel optimization, as well as three mechanisms that approximate the OLI problem accurately. These mechanisms enjoy desirable theoretical properties, and the computational experiments show that they produce orders of magnitude improvements over standard approaches on an extensive collection of test cases.

In this paper, we propose a novel Newton method-based distributed algorithm (NMDA), which is also effective in solving the general single-area EDP (SAEDP), to deal with the multi-area economic dispatch problem (MAEDP), of which the focus is to minimize the total generation cost in the presence of system and generator constraints. To develop the NMDA, we first introduce a virtual SAEDP formulation to fit the framework of Newton method (NM), and then employ the average consensus protocol to obtain the global information needed to execute the NM and backtracking line search algorithm in a distributed manner. Compared with the centralized methods that can yield the optimal solution, the proposed NMDA provides a suboptimal solution with a very small relative error. The NMDA ensures the instantaneous system power balance throughout the iteration process while the centralized methods compared in this paper cannot do so. We also provide a rigorous theoretical analysis for the convergence of NMDA. Moreover, the advantage of NMDA in terms of the convergence speed is validated by comparing with other distributed methods such as the gradient-based ADMM (G-ADMM) and quasi Newton-based primal dual interior point (QN-PDIP) method. Finally, case studies demonstrate the effectiveness and scalability of the proposed distributed algorithm.

Synchronized phasor measurement unit (PMU) data contain rich information about power systems, hence the quality of estimates is of utmost concern. The existing methodologies for estimation rely on certain assumptions regarding the error in the measurement data. This paper revisits a key assumption specifically the Gaussian character of the error. A quantification of the PMU error yields its nature and statistical properties including its dependence on various sections of the PMU instrumentation channel (supposedly the major source of error in the PMU data). The non Gaussian nature of the error is asserted using various null hypotheses tests and a novel Gaussian mixture model based clustering technique is proposed to characterize and relate the errors present in PMU measurement data to the saturation in current transformer, cable length and the PMU burden. The proposed approach is tested using both real and synthetic PMU datasets. The ultimate goal of the paper is towards creating a PMU error emulator for testing and research of data analytic algorithms focused on crucial WAMS based applications.

This document is a summary of a report prepared by the IEEE PES Task Force (TF) on Microgrid Stability Definitions, Analysis, and Modeling, IEEE Power and Energy Society, Piscataway, NJ, USA, Tech. Rep. PES-TR66, Apr. 2018, which defines concepts and identifies relevant issues related to stability in microgrids. In this paper, definitions and classification of microgrid stability are presented and discussed, considering pertinent microgrid features such as voltage-frequency dependence, unbalancing, low inertia, and generation intermittency. A few examples are also presented, highlighting some of the stability classes defined in this paper. Further examples, along with discussions on microgrid components modeling and stability analysis tools can be found in the TF report.

This paper presents a market-based resource adequacy assessment framework to analyze the system generation portfolio that results in a competitive market environment. In particular, we apply the modeling framework to investigate the impact of high penetration levels of variable renewable energy resources and different market designs on achieving resource adequacy. The model captures the strategic capacity investment and retirement decision-making of profit-maximizing generation companies. In contrast to many previous studies, this paper considers markets for capacity, energy, and reserve products in detail; thus, the modeling framework allows improved analysis of generation expansion and revenue sufficiency in a competitive market environment. The modeling framework is based on Stackelberg leader–follower games and is formulated as a bi-level optimization problem, which is then transformed into a mathematical program with equilibrium constraints. Furthermore, we employ a Lagrangian decomposition algorithm to enhance computational performance. In a case study of the electric reliability council of texas (ERCOT) system, we compare the results from the proposed model with those obtained from a traditional centralized least-cost planning model. The results demonstrate the effectiveness of the proposed modeling framework and highlight the importance of considering strategic behavior in a competitive market framework when assessing resource adequacy.

This paper proposes an approach to determine the participation of algebraic variables in power system modes. The approach is based on a new interpretation of the classical participation factors, as well as on the definition of adequate output variables of the system’s state-space representation. The paper considers both the linear and generalized eigenvalue problems for the calculation of the participation factors and presents a theorem to cope with eigenvalue multiplicities. An illustrative example on the two-area system, as well as a study on a 1,479-bus dynamic model of the all-Irish transmission system are carried out to support the theory and illustrate the features of the proposed approach.

This paper is concerned with a fuzzy analysis of power-flow (PF) involving uncertainties of load demands and network parameters. The crux of this paper is to propose an advanced fuzzy arithmetic. Fuzzy transformation method merges with backward–forward sweep in order to evaluate the contribution and propagation of uncertainty in IEEE 33-bus and 69-bus distribution systems. Results are validated by true intervals and random ranges. To determine true intervals, Global Optimization Problems (GOPs) are defined and solved through derivative-based and free techniques. To estimate random ranges, Monte-Carlo Simulations (MCSs) are employed. Our findings confirm that the sharpness of fuzzy intervals, tractability of computations, and applicability of possibility distributions. Following scenario-based evaluations, this paper discusses new implications of power losses, voltage profiles, optimal re-configuration, feeder extension, and reactive power compensation so that results would be beneficial to system planners and operators. Altogether, this paper provides a blueprint for a new way to handle uncertainties in a wide variety of power system problems without global optimization, linearization, and randomized simulations.

Author's copy of this paper for IEEE Transactions on Power SystemsAbstract: This paper proposes a new technique to identify sets of branches that form heavily loaded and potentially vulnerable flowgates within power grids. To this end, a directed acyclic graph is used to model the instantaneous state of power grids. One of the advantages of directed acyclic graphs is they allow the identification of where power flows are coherent e.g where power flows in a uniform direction along a set of branches that partition the network into two islands. This paper uses topological sorts to identify many sets of branches having this property. Definitions are provided for two new concepts, termed coherent cut-sets and coherent crack-sets, which are particular sets of branches extracted from a specific topological sort. Notably, there are numerous possible topological sorts for a directed acyclic graph and calculating distinctive topological sorts is challenging. In this paper a novel optimization algorithm is proposed to find multiple, diverse topological sorts each of which implies many cut-sets. The effectiveness of the proposed methods for enhancing grid observability and situational awareness is demonstrated using two standard test networks.

It is possible to launch undetectable load-redistribution (LR) attacks against power systems, even in systems with protection schemes. Therefore, detecting LR attacks in power systems and establishing a corrective action to provide secured operating points are imperative. In this paper, we develop a systematic real-time LR threat analysis (RTLRTA) tool, which can flag LR attacks and identify all affected transmission assets. Since attackers might use random deviations to create LR attacks, we introduce an optimization model to generate random LR attacks. Hence, we can determine accurate thresholds for our detection index and test the tool's functionality when there are random LR attacks. Additionally, based on an estimation for the actual loads in the post-attack stage, we design a set of physical line flow security constraints (PLFSCs) and add it to the security-constrained economic dispatch (SCED) model. We call the new model cyber-physical SCED (CPSCED), which can appropriately respond to the identified LR attacks and provide secured dispatch points. We generate multiple scenarios of random LR attacks and noise errors for different target lines in the $2383$-bus Polish test system to validate our proposed methods' accuracy and functionality in detecting LR attacks and responding to them.

This paper examines the dynamic aggregation of a group of M same wind turbine generators (WTGs) in a parallel connection. The group of WTGs could either be a part of a grid-connected wind farm or constitute the entire wind farm. Analytical derivation in this paper indicates that the group of M same WTGs is equivalent to M dynamically independent subsystems. Each of the subsystems is comprised of a single WTG. Hence, the dynamic aggregation of a grid-connected group of same WTGs in a parallel connection can be represented by grid-connected single-WTG subsystems for studying the oscillation stability. Further analysis in this paper reveals that when the number of WTGs in a parallel connection increases, it is possible that oscillation modes of the group of WTGs may move into the right half of a complex plane. Thus, the dynamic coupling of the increasing number of WTGs in a parallel connection may likely cause growing oscillations in the wind farm. An example grid-connected DFIG wind farm is used to demonstrate and evaluate the analysis and conclusions made in this paper. The oscillation stability of the example wind farm was examined when the dynamic models of a group of DFIGs in a parallel connection in the example wind farm were identical and different.

This paper is committed to developing a thorough analysis on the electromechanical oscillations (EOs) of doubly-fed induction generator (DFIG) wind turbines (WTs), taking into consideration the implemented frequency control and drivetrain dynamics of the mechanical system. Some basic recommendations for mitigating EOs would be hence attained. To this end, a linearized model of DFIG WT is proposed to present the interplay between frequency control and the dynamics of WT's drivetrain and electrical system. Then, the conventional torque analysis method is used to establish the basic effects of the frequency control on the damping of the drivetrain and electrical system frequency dynamics. Therein, the adverse effects could incur detrimental EOs, viz., drivetrain torsional oscillations (TOs) and electrical system low-frequency oscillations (LFOs). To mitigate such TOs and LFOs, this paper proceeds with an investigation of different alternatives to stabilize the torsional dynamics of drivetrain and the frequency dynamics of electrical system, meanwhile, to minimize undesired impacts caused by their interactions. Simulation studies on two test systems validate: the basic concepts obtained from theoretical analysis and that the findings can be generalized to multi-machine systems.

Traditional power flow algorithms assume that a slack bus is present and that the frequency is not fluctuating. In islanded industrial systems and microgrids, however, these assumptions are not valid because such systems usually do not have a strong source performing as the slack bus and the system frequency is more prone to vary near nominal frequency. Considering these characteristics, this paper presents a novel universal power flow (UPF) algorithm for industrial systems and microgrids as well as traditional systems, with a focus on active power. Development of a reactive power UPF algorithm will be presented in a subsequent paper. The proposed UPF model has the following merits: first, it can handle islanded and grid-connected systems at nominal or off-nominal frequency; second, it can handle the active control strategies of distributed generators (DGs), such as isochronous (ISOC) control, droop control, or constant power control; third, it can handle the megawatt and megavolt-ampere reactive limitations of ISOC or droop DG units; fourth, it can evaluate system frequency; and finally, it can handle frequency-dependent active and reactive power loads. The proposed UPF model is validated by comparing the results with those obtained from a real-time simulator.