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Transient stability of a power system can be significantly affected by wind power generators due to their stochastic power output and complex dynamic characteristics. This paper proposes a robust optimization approach for coordinating generation dispatch and emergency load shedding against transient instability under uncertain wind power output. The problem is modelled as a two-stage robust optimization (TSRO) model considering transient stability constraints, where the first-stage is to optimize the generation dispatch (preventive control) before a contingency and the second-stage decision is the emergency load shedding (emergency control) after the contingency occurrence under the worst case of wind power variation. To solve this TSRO problem, this paper also proposes a solution algorithm which integrates transient stability assessment and transient stability constraint construction in a column and constraint generation framework. The proposed method is validated on the New-England 39-bus system and the Nordic32 system, which shows high computational efficiency and stability robustness against uncertain wind power.

This paper presents a novel load shedding scheme with consideration of the active power ramping capability of Distributed Energy Resources (DERs) to address the challenges due to low inertia and diverse types of DERs in microgrids. In the paper, it is demonstrated that due to the small inertia in microgrids, even with sufficient reserve power, the frequency could rapidly drop to a low level and trigger the DERs' under frequency protection (thus the total system collapse), if the reserve active power is not ramped up at a sufficient rate. The proposed load shedding scheme addresses this challenge by considering not only the DERs' reserve, but also their speed in injecting active power to the system to determine the amount of load should be shed, so that critical frequency thresholds are not violated. The proposed load shedding scheme is tested using a realistic real time hardware-in-the-loop arrangement. The results show that the proposed scheme can correctly detect the cases when the DERs' responses are too slow and trigger the required load shedding actions, thus effectively containing the frequency above the critical threshold.

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 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.

This paper presents a two-timescale multi-objective coordinated volt/var optimization system for active distribution networks with renewable energy resources (RESs). In the hourly timescale, power loss and the number of control actions of on-load tap changers and (switchable) shunt capacitors for 24 h are minimized by coordinating on-load tap changers, (switchable) shunt capacitors, and reactive power outputs of RESs. A three-step method consisting of global search, user preference, and local search is adopted to solve the corresponding multi-objective mixed-integer nonlinear optimization problem. A rolling volt/var optimization is executed every 6 h, considering the day-ahead RES forecast errors. In the 15-min timescale, the RES reactive powers are optimized with RES uncertainties explicitly taken into consideration to minimize the pilot-bus voltage deviation under all representative scenarios. The pilot buses are those buses whose voltage magnitudes capture the network voltage profile. In this paper, a linear method is applied to quickly identify a set of pilot buses, and the impact of the identified pilot bus on the entire network voltage profile is evaluated. The IEEE 33-bus distribution network is used to evaluate the proposed two-timescale volt/var optimization formulations and methods with promising results.

In this paper, we propose an integral data rectification strategy for phasor measurement units (PMUs) in multi-area power systems, comprising local data processing and central data recovery modules. The local data processing is designed for the purpose of detecting and eliminating false PMU measurements, which is performed in a decentralized manner, based on our previously developed dynamic state estimation technique; whereas the data recovery is performed in a centralized manner at the control center, based on a newly proposed adaptive-phasor approach. The recovered PMU measurements are then utilized in a low-frequency oscillation damping enhancement scheme, which is achieved by a modified proportional-integral (PI) power system stabilizer (PSS) mechanism embedded in the automatic voltage regulator structure of a synchronous generator. Control parameters of the PI-PSS are optimized by maximizing the critical damping ratio of the power system. This paper is intended to make a contribution to the need of high-quality data transmission in modern power grids with contemporary measuring technologies.

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

Optimal placement and sizing of distributed energy resources (DERs) can be performed from various points of view. In this paper, a multiobjective function is employed to determine optimal place and size of DERs including combination of photovoltaic resources and a small-scale synchronous generator (SSSG) with an internal combustion engine as its prime mover. As the objective function, not only minimization of investment costs, operation costs, and system losses are used, but also the voltage of microgrid (μG) busses and current of lines are considered as constraints. In addition, this paper shows mechanical stresses can be imposed on the SSSG caused by generator swings after short circuit fault clearing. Furthermore, it may lead to mechanical fatigue in its associated shaft and prime mover. Meanwhile, it is revealed that the mechanical stresses depend on the DERs placement and size. Thus, a novel index representing the stresses on the SSSG shaft is applied in the multiobjective goal function. This decreases SSSG loss of life in a μG with overhead lines which has high rate of short circuit faults. Optimization studies are performed in a six-bus and four-DER μG using time-based simulations.

To uncover the mechanism by which voltage-dependent loads (VDLs) influence electromechanical dynamics, this paper mathematically deduces the damping torque induced by VDLs based on a single machine infinite bus system. Moreover, by continuously regulating the terminal voltage of a typical large-scale VDL, i.e., the aluminum electrolysis load, this paper proposes a novel load damping control architecture to dynamically modulate the power consumption of controlled loads so as to eliminate interarea oscillations in power systems. Specifically, the decentralized load damping controllers (LDCs) used in this architecture are designed by a proposed multistage mixed ${{{H}}_{2}} / {{{H}}_\infty }$ control approach to guarantee robustness against uncertainties (e.g., tie-line outages and wind generation fluctuations) as well as to ensure reasonable control efforts of controlled VDLs. Simulation results on the modified New England and New York interconnected system validate the method for analysis of VDLs’ effects on interarea oscillations and show the proposed load damping control strategy can satisfactorily damp interarea oscillations over multiple operating points.

This paper extends the dynamic coherency determination (DCD) method by including Type-3 wind power plants (WPPs) models in the coherency evaluation process and quantifies impacts of the high depth of wind power penetration on the coherency phenomena of interconnected power systems. The method is based on frequency-deviation signals, measured at nongenerator buses and terminal buses of WPPs and synchronous generators. Salient features of the presented method are its ability to account for the hybrid nature of enhanced generic models of Type-3 WPPs and expanding notion of the power system coherency beyond the classical definition by including models of Type-3 WPPs. This paper also investigates impacts of the high depth of wind power penetration; i.e., up to 30%, on the coherency structure of the 16-machine/68-bus NPCC equivalent system. The studies are based on time-domain simulations in PSS/E software. The investigations reveal that Type-3 WPPs can introduce new coherent areas, significantly change areas’ boundaries and number of areas, and alter frequencies/dampings of interarea modes.

Frequency deviations of power systems caused by grid-connected wind power fluctuations is one of the key factors which restrains the increase of wind penetration level. This paper examines a combined wind and hybrid energy storage system (HESS, supercapacitor, and battery) to smooth wind power fluctuations. A fuzzy-based wind-HESS system (FWHS) controller is proposed to suppress the wind power fluctuations. The proposed controller takes full advantage of the complimentary characteristics of the supercapacitor and battery with the supercapacitor and battery in charge of high and middle frequency components of wind fluctuations, respectively. A differential evolution (DE)-based optimal sizing method for HESS systems is introduced to evaluate the minimum capacity of HESS as being limited by grid frequency deviation. The efficiency of the proposed scheme in the paper for wind-HESS system is evaluated by a real Chinese power system.

In this paper, a line modal potential energy (LMPE) method is proposed for the interarea oscillation analysis and damping control of doubly fed induction generators (DFIGs). This paper presents a novel attempt to design the damping control loop using the LMPE approach from the network viewpoint. First, an LMPE function containing a DFIG output line is constructed. The distribution characteristics of the LMPE in a network are analyzed in different modes, and the dominant mode of the system is identified. In addition, this approach provides the basis for damping regulation. Second, the wide-area control signals and control locations are selected. Third, a damping controller for DFIGs based on LMPE and extended state observer- ${\rm{H}}_{{\rm{\infty }}}$ control is designed, and this design is shown to have a certain anti-interference ability. The proposed method can be used for submode analysis and oscillation suppression. Finally, the correctness of the LMPE method is verified through the analysis and simulation of a four-generator, two-area system and an actual power system in China .

In this paper, a new device of FACTS family named as amalgam power flow controller (APFC) is proposed. APFC is the amalgamation of electromagnetic and voltage source based converter devices. The key feature of the model is that it inherits the characteristics of both devices. APFC is an economical FACTS device, which not only controls power flow in a network but also increases the reliability and security of power systems. This paper also proposes a new hybrid approach based modeling technique to develop a mathematical model of APFC. Converter losses of APFC are also incorporated in mathematical modeling. The feasibility and convergence characteristics of the proposed APFC are investigated using benchmark IEEE 30-bus and 118-bus test systems.

This paper examines the impact of dynamic interactions between the voltage source converters (VSCs) on the small-signal stability of an AC/MTDC (multiterminal dc) power system. The examination is carried out based on a closed-loop interconnected model consisted of an open-loop VSC subsystem and an open-loop subsystem of the rest of MTDC network (RDCN). Open-loop modal coupling is the modal condition that an oscillation mode of open-loop VSC subsystem is close to an oscillation mode of open-loop subsystem of the RDCN on the complex plane. Analysis indicates that the open-loop modal coupling may very likely degrade the small-signal stability of the AC/MTDC power system. If a VSC uses the active power control, the open-loop VSC subsystem is of no oscillation mode. Hence, open-loop modal coupling between the VSCs cannot occur in the MTDC network implementing the master–slave control. Whilst the open-loop modal coupling may introduce instability risk to the MTDC network using the dc voltage droop control. Therefore, the paper reveals the mechanism about how and why the dynamic interactions between the VSCs may degrade the small-signal stability of the AC/MTDC power system from the perspective of the system modal condition—the open-loop modal coupling.

Hybrid state estimation determines the states of systems monitored both by conventional SCADA measurements and PMUs. This paper proposes a decentralization method in order to improve the computational performance of hybrid state estimators with minimum loss of accuracy. The proposed method utilizes sensitivity matrix that relates measurement errors to state estimates in order to form the so-called isolated bus groups and observable subislands. Although the proposed decentralization method can be applied to any state estimator, the paper is developed using a least absolute value (LAV) estimator for demonstration purposes, which is known to be robust against bad data. The high computational burden of LAV estimator compared to the well-known weighted least squares estimator is eliminated, thanks to the proposed decentralization method.

Interarea oscillation is one of the main challenges for the secure and stable operation of a large-scale interconnected power system. To address this problem, this paper presents an adaptive supplementary damping controller (SDC) for voltage source converter based high voltage direct current (VSC-HVDC) by using the goal representation heuristic dynamic programming (GrHDP). Compared with conventional heuristic dynamic programming (HDP), GrHDP adds a new goal representation network to generate an adaptive reward signal to achieve better mapping relationship between the system states and the control action. To compensate phase shift between the output and input signals of a large-scale interconnected AC/DC power system, this paper proposes a parallel phase shift channel for the GrHDP. Moreover, the proposed GrHDP-SDC is a model-free control scheme, which does not need the mathematic model of the power system and has quick online learning ability to adapt to the variation of system operating conditions. Case studies are carried out on the 10-machine 39-bus system and 16-machine 68-bus system, respectively. Compared with the conventional lead-lag SDC (LL-SDC) and HDP-SDC, simulation results show that the proposed GrHDP-SDC can always provide satisfactory damping performance over a wide range of system operating conditions and disturbances.

Online power distribution system time series analyses are typically divided into uniform intervals (e.g., market-driven) ranging from minutes to hours. This paper presents a constraint-driven approach to refining an initial time window structure at critical times within an injection forecast. Implicit temporal load capability (ITLC), which is formalized in this paper, uses forecasted nodal injection characteristics to identify critical times when control actions are necessary in order to maintain feasibility. ITLC and control selection algorithms are presented. Quasi-static time series and ITLC simulation results are presented using a multiphase, 2556-node distribution test circuit. With ITLC, a subset of the initial time windows are subdivided at the analytically-selected critical times. This approach is more efficient than using a large number of short time windows that span the entire forecast horizon.

This paper derives the index of dynamic interactions (IDI), which is the sensitivity of a power system electromechanical oscillation mode (EOM) of concern to the dynamic interactions introduced by a grid-connected double-fed induction generator (DFIG). Based on the IDI, analysis is carried out with the following generally-applicable conclusions obtained: 1) Impact of dynamic interactions introduced by the DFIG increases when wind power penetration increases; 2) as long as the frequency response of an equivalent single DFIG model approximately matches the frequency response of a wind farm around the frequency of electromechanical oscillations of concern, this equivalent dynamic model of single DFIG can be used to represent the wind farm to examine the impact of wind farm on EOMs. Furthermore, an indicator of DFIG control (IDC) is derived for comparing the impact of terminal voltage control and reactive power control implemented by the DFIG. Main merit of the IDC is the computational simplicity without need to know dynamic model of the DFIG to indicate that either the terminal voltage control or the reactive power control is more beneficial to power system stability. An example multi-machine power system with grid-connected DFIGs is presented to demonstrate and validate the analysis and conclusions made in the paper.

This paper establishes a closed-loop interconnected dynamic model of a power system with a doubly fed induction generator (DFIG) for wind power generation, wherein, the DFIG and power system are modeled as two open-loop interconnected subsystems. The established model indicates that the impact of the dynamic interactions introduced by the DFIG on the power system's small-signal angular stability is the difference between the closed-loop and open-loop electromechanical oscillation modes (EOMs). The analysis conducted in this study reveals that when an open-loop DFIG oscillation mode (DOM) is close to an open-loop EOM on the complex plane, the modal coupling of the open-loop EOM and DOM can cause strong dynamic interactions between the DFIG and the power system; thus, the DFIG has a significant impact on the power system's small-signal angular stability. An example multimachine power system with grid-connected DFIGs is presented to demonstrate and validate the analysis and conclusions made in the paper.

Concerning the stochastic excitation caused by wind power fluctuation and the stochastic parameter of virtual inertia caused by wind speed uncertainty, a power system stability analysis method considering the Wiener noise is proposed in this paper. First, based on the reduced-order model of DFIG retaining virtual inertia control and phase-locked loop (phase-locked loop) dynamics, the analytic function relationship between stochastic parameters and elements in the state matrix is derived using the sensitivity analysis method; thus, the model of interconnected system with stochastic parameters considering the Wiener noise is established. And by constructing the Lyapunov functional containing the model of stochastic parameters, the linear matrix inequality (LMI) that satisfies the robust stochastic stability criterion is derived. Furthermore, by transforming the solving of LMI to a feasibility problem, the stability of system is identified. And then, by calculating online system instability probability under the current operating condition, the probability stability analysis method is proposed. On this basis, a system stochastic stability degree index is defined in this paper, which quantifies the effect of stochastic parameters on system small-signal stability, and could provide more effective information for the safe and stable operation of power system. Simulation tests on the IEEE four-generator two-area system and the New England 10-machine 39-bus system verify that the proposed method could effectively identify the small-signal stability of power system under the joint influence of stochastic parameter and stochastic external excitation, and is applicable to complex system with multiple generators.

This paper presents a distributed, robust, finite-time secondary control for both voltage and frequency restoration of an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). The distributed cooperative secondary control is fully distributed (i.e., uses only the information of neighboring DGs that can communicate with one another through a sparse communication network). In contrast to existing distributed methods that require a detailed model of the system (such as line impedances, loads, other DG units parameters, and even the microgrid configuration, which are practically unknown), the proposed protocols are synthesized by considering the unmodeled dynamics, unknown disturbances, and uncertainties in their models. The other novel idea in this paper is that the consensus-based distributed controllers restore the islanded microgrid's voltage magnitudes and frequency to their reference values for all DGs within finite time, irrespective of parametric uncertainties, unmodeled dynamics, and disturbances, while providing accurate real-power sharing. Moreover, the proposed method considers the coupling between the frequency and voltage of the islanded microgrid. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we verify the proposed control strategy's performance using the MATLAB/SimPowerSystems toolbox.

This paper investigates the impacts of transient instability on power system reliability. Traditionally, composite system reliability evaluation has been performed based on steady-state estimation of load curtailments; system dynamics have often been ignored, mostly due to computational complexity. In this paper, three probabilistic transient stability indices are proposed to assess system robustness against dynamic contingencies and to account for system instability in computing reliability indices. A direct method is utilized for transient stability assessment based on computing the energy margin of the system under fault events (energy margins measure the ability of a system to withstand contingencies). Energy margins along with the probability of occurrences of the events are used to update the probabilistic transient stability indices. The dependencies of reliability and stability indices on the fault clearing time are also evaluated. This method is applied on the reduced Western Electricity Coordinating Council and the New England 39 bus test systems. The results indicate the importance of considering the effect of stability in reliability evaluation.

With the increasing use of voltage source converters (VSCs) in power electronics dominated power systems, oscillation phenomena in DC-link voltage control (DVC) timescale (around 10 Hz) among multiple VSCs have occurred. Several studies have tried to analyze these oscillation problems, but all associated with the single VSC situation. To consider the dynamic interactions between VSCs in DVC timescale, especially in the weak grid condition, this paper presents a small-signal model to understand VSC external characteristics based on motion equation concept also featured in synchronous generator (SG). Comparisons of time-domain simulation responses and eigenvalues show that the proposed model can hold the main behaviors of concern. The form of the model is very similar to the rotor motion equation in SG, with which power engineers have been very familiar. In addition, by establishing the relationship between the unbalanced powers and state variables of internal voltage (viz., VSC output voltage), the modeling idea introduced in this paper can be applied to other power electronic devices.

This paper develops enhanced hybrid generic (nonlinear) models of Type-3 and Type-4 wind power plants (WPPs) and extracts the corresponding linear (small-signal) dynamic models for power system transient stability analysis. The models are hybrid in nature since they consider both continuous states and discrete logic-controlled variables. The introduced enhancements include (i) a freezing function to reactivate reactive power emulator of Type-3 and Type-4 WPPs, (ii) active-current command recalculation step for Type-3 WPP and (iii) elimination of an activating logic of PI-controller limits in real current control path. The main feature of the enhanced models is that they can replicate the field-verified responses of the built-in PSS/E software models in any adopted software platform. It should be noted that the generic models described in the technical literature do not necessarily provide such replication. The paper also deduces small-signal dynamic models of Type-3 and Type-4 WPPs and addresses the multiple eigen structures of the linearized enhanced generic model of Type-3 WPP, which has not been comprehensively discussed in the technical literature. The enhanced nonlinear hybrid models and the corresponding linearized models are evaluated and verified based on time-domain simulation studies in PSS/E and MATLAB platforms, using NPCC system as the test bed.

Wind power generators will become increasingly useful in modern power systems; therefore, they should be able to support the system frequency in a way similar to that of conventional generators. Droop and virtual inertia are the most reported methods in the literature. However, their impact on the generator and system frequency stability, when the double-mass mechanical dynamics of a wind power generator are considered, has not been addressed thoroughly. In this paper, small-signal modeling, analysis, and eigenvalues studies are used to show that incorporating a wind power generator in the frequency regulation can expose its shaft to forces stimulating its natural resonance frequency dynamics and lead to instability. This paper shows that the mechanical resonance of frequency-regulating wind generators must be studied and enhanced not individually but as a part of the whole power system stability analyses. To overcome the stability problem caused by implementing frequency regulation in wind generators, this paper investigates different alternatives to stabilize the generator dynamics and, at the same time, minimize undesirable interference in the conventional wind power generator controllers. Time-domain simulation results validate the analytical results and discussions.

The PMU data is increasingly used in the grid monitoring system SCADA. As the DFT algorithm used in PMUs fails to distinguish the fundamental frequency signal with low-frequency interference, the low-frequency disturbance (LFD) included in fundamental frequency variable data, which are collected from PMUs, will affect the correctness of calculation and analysis of the power system's steady state. In order to extract the fundamental frequency variable from PMU data, taking low-frequency forced oscillation as an example, a method for filtering LFD in PMU data is proposed. First, the effect of low-frequency oscillation to the fundamental frequency variable is analyzed in this paper. Then, the component of LFD in PMU data is explained. By finding the maximum value and minimum value of voltage or current in PMU data to draw the envelopes and add them together, the mean value or fundamental frequency variable of voltage and current is obtained. The mechanism of error in calculating active power is analyzed when low-frequency oscillation occurs in the power grid. The results of analyzing actual PMU data under low-frequency oscillation verify the correctness of the method proposed in this paper. This method is of great significance to improve the accuracy of calculation in SCADA.

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second-order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter semidefinite programming (SDP) relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder.

This paper describes the modeling and formulation of a variety of deterministic techniques for energy storage devices, namely the PI, H-infinity, and sliding mode controllers. These techniques are defined based on a general, yet detailed, energy storage device model, which is accurate for transient stability analysis. The paper also presents a thorough statistical comparison of the performance and robustness of the considered control techniques, using stochastic dynamic models and a variety of disturbances and scenarios. The case study is based on a 1479-bus model of the all-island Irish transmission system and an energy storage device actually installed in the system. European Commission Horizon 2020 Science Foundation Ireland

This paper proposes a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation. The uncertainty of wind power is captured by an ambiguity set that defines a family of wind power distributions, and the expected total cost under the worst-case distribution is minimized. Compared with stochastic programming, this method may have less dependence on the data of exact probability distributions. It should also outperform the conventional robust optimization methods because some distribution information can be incorporated into the ambiguity sets to generate less conservative results. In this paper, the UC model is formulated based on the typical two-stage framework, where the UC decisions are determined in a here-and-now manner, and the economic dispatch decisions are assumed to be wait-and-see , made after the observation of wind power outcomes. For computational tractability, the wait-and-see decisions are addressed by linear decision rule approximation, assuming that the economic dispatch decisions affinely depend on uncertain parameters as well as auxiliary random variables introduced to describe distributional characteristics of wind power generation. It is shown in case studies that this decision rule model tends to provide a tight approximation to the original two-stage problem, and the performance of UC solutions may be greatly improved by incorporating information on wind power distributions into the robust model.

In a recent paper, we proposed a system identification method for constructing reduced-order models for the electro-mechanical dynamics of large power systems, divided into multiple coherent clusters, using Synchrophasors. Every cluster in the actual model was represented as an aggregate generator in the reduced-order model. An aggregate network graph connected one aggregate generator to another. In this paper, we extend this identification approach to differential-algebraic (DAE) models. First, every cluster is associated with a unique terminal bus, referred to as the pilot bus, that couples its internal network to the rest of the system. The proposed algorithm uses Synchrophasor measurements from the pilot buses to identify the dynamic model of the aggregate generator for each cluster using nonlinear least squares while retaining the identity of all the pilot buses. The resulting reduced-order model is in the form of a nonlinear electric circuit described by aggregate differential and algebraic equations. We illustrate our results using two case studies, one for the IEEE 9-bus power system and another for the IEEE 39-bus power system. We also discuss how these reduced-order DAE models may be useful for designing shunt controllers at the pilot buses by using Synchrophasor feedback.

Voltage source converter (VSC)-based high-voltage direct current (HVDC) transmission systems have been employed widely in recent years. However, connecting a VSC-HVDC link to a very weak grid (a high-impedance grid) is challenging. A vector-controlled VSC is incapable of injecting/absorbing its maximum theoretical active power in such grids. A simple yet effective control system for a standard vector-controlled VSC in a very weak grid condition has not been reported in the literature. This paper, benefiting from a comprehensive small-signal model, presents a detailed analysis of the VSC dynamics and shows how the assumptions made for designing VSC regulators in strong grids are no longer valid in very weak grids. The paper then proposes and compares two straightforward solutions: retuning the control parameters and using an artificial bus for converter-grid synchronization. Both methods enable the VSC to operate at the maximum theoretical active power at a very weak grid condition (i.e., at unity short-circuit ratio) by minimal modification in the widely accepted vector control method. The advantages and disadvantages of each method are discussed. The analytical results are verified by detailed nonlinear time-domain simulation results.

This paper introduces a framework of transient stability assessment for future distribution systems that are comprised of multiple microgrids. Enabled by the advances in power electronics and synchrophasor technologies, an angle droop method is introduced for autonomous real power sharing among coupling-operated microgrids. In our previous work, the small-signal stability criterion are derived. It is well-known that only regional transient stability can be established for conventional multi-machine systems interfaced with synchronous generators. In contrast, we show in this paper that asymptotical stability in the large can be achieved if angle droop method is adopted for real power sharing among coupled microgrids. Transient stability criterion is derived by formulating the linear matrix inequality (LMI) version of the Kalman-Yakubovich-Popov (KYP) conditions corresponding to the multi-variable Popov criterion. Numerical studies show the effectiveness of the proposed transient stability assessment framework for future power electronic-interfaced distribution systems.

Multi-terminal High Voltage Direct Current (HVDC) using Voltage Source Converters (VSC-HVDC) is a promising technology which provides flexible control of active and reactive power and facilitates remote renewable energy integration, above all using long cables. This paper analyses an active power control strategy for multi-terminal VSC-HVDC systems tailored to enhance transient stability of hybrid AC/DC grids. The proposed strategy controls each VSC using frequency measurements of all terminals. Its performance is compared to a strategy in which each VSC is controlled using only local frequency measurements of the AC side, proving that the proposed strategy shows better performance, even taking into account reasonable communication delays. The paper also shows that the proposed strategy generally gives similar results to those obtained when each VSC is controlled using the speed of the centre of inertia (COI). The speed of the COI is a more comprehensive and richer figure than the one proposed in this paper but it is also much more complex to obtain. Simulation results with PSS/E of a test system have been used to illustrate the comparisons and the main contributions of the proposal.

The method of symmetrical components is not effective for fault location in the case of untransposed lines, due to potential couplings between the sequence circuits. This paper proposes a non-iterative algorithm in the phase-coordinates for wide-area fault location on untransposed transmission networks. In doing so, first, an improved two-terminal method is suggested to accurately locate faults on untransposed lines. Next, an algorithm is proposed to infer voltage and current phasors at the faulted line ends without direct measurements, by taking advantage of the data provided by phasor measurement units (PMUs). Accordingly, the adverse effect of close instrument transformers transients on the estimation accuracy is minimized. Being highly nonlinear in terms of fault distance and impedance, the fault equations are derived and made linear in this paper by defining six suitable auxiliary variables. The resulting system of equations is solved using the least-squares method to obtain three-phase voltages and currents at the faulted line ends. A main feature of the proposed algorithm is that it only requires a limited number of current and voltage synchrophasors. An additional advantage of the proposed algorithm is that the faulted line is not required to be known a-priori. The proposed algorithm is validated using extensive simulation studies on the New England 39-bus test system, accounting for different fault locations, types and resistances.

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

Increasing wind penetration in non-interconnected power systems represents a techno-economic challenge for system operators. To accommodate the increased variability and uncertainty adequate reserve levels and advanced solutions that increase the controllability of wind power output, such as hybrid power stations, are used to ensure system stability. This paper presents a two-stage stochastic optimization model for the joint scheduling of energy and reserves of conventional units and hybrid power stations in insular power systems. The proposed methodology is based, in general, on the recently established regulatory framework for the non-interconnected island systems of Greece. The main scope of the paper is to analyze wind and pumped-storage solutions for the normal operation of saturated insular power systems. In this context, the introduction of hypothetical hybrid power stations in a real-life system, the insular power system of Crete, Greece is examined. Test results are analytically presented and thoroughly discussed.

In order to provide the ancillary service for smart grid, this paper proposes a modelling and control protocol design approach for the aggregation of heterogeneous thermostatically controlled loads (TCLs). A 2-D state bin is proposed to model the second-order TCL dynamics in a population model. Detailed procedure of calculating the transition probability in the system matrix is provided. In the controller design, a model predictive control (MPC) scheme is proposed to obtain the optimal control actions along the prediction horizon. In addition, implementation of the control signal for adjusting TCLs' statuses are also investigated with practical situations considered. Simulation results reveal the feasibility and efficacy of the proposed modelling and control approach when applied on a large population of TCLs. Some factors that may affect the service performance are also discussed in this paper.

This paper presents a design of a power system damping controller using partial right eigenstructure assignment. The eigenstructure assignment technique selects a set of closed-loop eigenvalues along with their right or left eigenvectors. The selection of eigenvectors offers extra flexibility which is exploited in this paper by designing a robust damping controller which provides the required damping under multiple operating conditions. A multi-input controller is used to increase the degrees of freedom available for the design. Remote measurements available from synchronised phasor measurements are also considered. The problem is formulated as a multi-objective nonlinear optimization problem and solved using the nonlinear simplex function in MATLAB. The proposed technique is used to design a robust power system stabilizer for the interconnected New England New York simplified power system model. Four contingencies are selected as additional operating conditions. The designed controller is validated using a nonlinear simulation.

The financial value of security service provided by dual-branch controller of a large-scale photovoltaic system (LPS) has been investigated in this paper. To perform this task, it is necessary to investigate the impact of LPS on small-signal stability of power network. To study the impact and performance of LPS on low-frequency oscillatory modes, a systematic scheme is developed to achieve an accurate model of multi-machine power network including of the LPS technology. A fully-described LPS model with all network-relevant control functions will be obtained. The proposed model has been then employed in the study of financial compensation strategy of security service provided by the LPS controller. The proposed compensation strategy in this paper is based on correlation of swing damping rate (SDR) criterion with generation cost (GC) criterion as dynamic and pecuniary indices, respectively. A weighted sum of performance and robustness indices is considered for SDR. The financial profit created by dual-branch controller of LPS as ancillary service (AS) is evaluated by a two-purpose optimization based on SDR and GC indices. The proposed strategy is tested on a modified 6-machine 3-area power system. Comprehensive discussion is provided to describe the performance of the presented method.

The integration of the dynamic line rating (DLR) of overhead transmission lines (OTLs) in power systems secu- rity constrained unit commitment (SCUC) potentially enhances the overall system security as well as its technical/economic performances. This paper proposes a scalable and computation- ally efficient approach aimed at integrating the DLR in SCUC problem. The paper analyzes the case of the SCUC with AC load flow constraints. The AC-optimal power flow (AC-OPF) is linearized and incorporated into the problem. The proposed multi-period formulation takes into account a realistic model to represent the different terms appearing in the Heat-Balance Equation (HBE) of the OTL conductors. In order to include the HBE in the OPF, a relaxation is proposed for the heat gain associ- ated to resistive losses while the inclusion of linear approximations are investigated for both convection and radiation heat losses. A decomposition process relying on the Benders decomposition is used in order to breakdown the problem and incorporate a set of contingencies representing both generators and line outages. The effects of different linearization, as well as time step discretization of HBE, are investigated. The scalability of the proposed method is verified using IEEE 118-bus test system.

A modified fruit fly optimization algorithm (MFOA) combined with a probabilistic approach are proposed in this paper to coordinate and optimize the parameters of power system stabilizers (PSSs) and static VAR compensator (SVC) damping controller for improving the probabilistic small-signal stability of power systems with large-scale wind generation, taking into consideration the stochastic uncertainty of system operating conditions. It is generally accepted that there is a threat to the stability of power system with penetration of wind farm. In addition, the stochastic fluctuations of wind generation make PSSs tuning more difficult. In this paper, PSSs and SVC damping controller are employed for suppressing local and inter-area low frequency oscillation. In order to eliminate the adverse effect between PSSs and SVC damping controller, the MFOA based on the probabilistic eigenvalue is applied to coordinate and optimize their parameters. The effectiveness of the proposed approach is verified on two test systems.

The paper proposes a framework for the selection of optimal configuration of line compensation devices, thyristor controlled series capacitors (TCSC) and conventional fixed series capacitors, for reducing the risk of subsynchronous resonance (SSR) in the network while maintaining required power transfer. The methodology developed in the paper is based on the robust risk evaluation of SSR that takes into consideration the severity of subsynchronous resonance and probability of its occurrence. The subsynchronous resonance risk index developed previously is used to assess the severity of subsynchronous resonance. The line outage model is employed to determine the probability of contingencies potentially leading to subsynchronous resonance. It is demonstrated that with relatively small participation of TCSC, even with the most basic control, in series compensation of lines, the risk of SSR can be successfully managed.

Load-damping characteristic models the load response to the frequency deviation, which has important impact on system frequency response. The load-damping coefficient is normally considered as a constant, obtained from operational experiences in large-scale power systems or from detailed load models in isolated power systems. An industrial isolated power system for aluminum production driven by coal-fired power and large scale wind power is studied in this paper. Since the electrolytic aluminum load is driven by direct current, it is one type of voltage-sensitive load and does not respond to the frequency deviation. This paper proposes a load-damping characteristic control method for such isolated industrial power system with voltage-sensitive load. To decrease the maximum frequency deviation during transient process, a time-varying load-damping coefficient control scheme is presented. Simulation is done on real-time digital simulator (RTDS) and the results verify the effectiveness of the proposed control method.

This paper presents a modified method for power system transient stability analysis, allowing the reduction of the computational requirements while retaining important system dynamics. The approach formulates the power balance equations depending on the area of interest. The detailed ac model, including full real and reactive power equations, is used for the area in which high accuracy is required, while the simpler dc model, including linear real power equation, is used for more remote areas where real power dynamics dominate. A high level of accuracy can be achieved using the ac model in the area of interest, and computational complexity can be reduced with the less detailed dc model in the remainder of the system. In order to prevent the loss of simulation accuracy, this paper proposes a way to compensate line losses neglected using the dc model. Case studies with the IEEE 118-bus system are provided to validate the performance of the proposed method.

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

Small isolated power systems often experience generator outages, which are responsible for the activation of the under-frequency load shedding scheme with the corresponding negative impact on electricity consumers and, hence, market loss. There are three main causes of this problem: the power system's low inertia, the speed governors' low capacity, and a poor size-ratio between generator and system. The most extensive research line in this area is focused on the optimization of the load shedding scheme, which is a partial solution. Another research line is presented to solve the problem from the point of view of the system operator. This paper proposes an online method to predict and correct possible load shedding by redistributing load dispatching. This proposal uses artificial intelligence techniques, in particular neural networks, and a special-purpose power system simulator. In order to evaluate the proposal, the achieved solution is applied to a real case study: the island of Gran Canaria. This application shows the improvement that might be achieved by implementing this simple method. The method proposed in this paper is strongly recommended for regions that have suitable geographical sites as well as energy problems similar to those of the Canary Islands (see tech. rep. “Map of the Canary Islands Power Systems” by Red Electrica de Espana).

In this paper, we propose a novel control algorithm for improving steady-state (quasi-static) voltage stability by use of an embedded voltage source converter (VSC) based high voltage direct current (HVDC) system. In this paper, the terms “steady-state” and “quasi-static” are used interchangeably. By embedded HVDC, we refer to a meshed AC system with all HVDC terminals connected within the same AC grid. The sensitivity between VSC control input and the voltage stability margin is introduced. Based on this sensitivity, the proposed control algorithm jointly satisfies system-wide voltage stability margin as well as local voltage magnitude requirements. The proposed approach is to first migrate the entire system to have sufficient voltage stability margin, and then to correct any voltage magnitude violation while keeping that stability margin. A contour-based visualization of the VSC capability space for maintaining system voltage stability is introduced, which can effectively illustrate how the singular value sensitivity (SVS) based control achieves both the local and global voltage stability requirements. The efficacy of the proposed algorithm is shown via case studies on a 6-bus and 118-bus system with and without static VAR compensation.

This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems.

This paper proposes a control method to coordinate multiple energy storage systems (ESS) spread across an AC microgrid. Each storage unit controls its own local node voltage (i.e., where the storage is connected in the network) as well as a global node voltage (i.e., a remote location in the network) that is controlled by all ESSs together. The storage power output is controlled in a way that the node voltage is restored and maintained in case it drops or rises outside the predefined limits. This can occur due to disturbances, such as load changes, loss of distributed generators (DGs), or power limitations in the DGs. In order to determine the power reference for each storage unit, a state of charge (SoC) based adaptive deadband droop control is used. In this decentralized control, the storage power output is inversely proportional to its SoC. By using this approach, the ESS with higher SoC will inject more power whereas storage units with lower SoC will inject less power, leading to more balanced SoC levels among the ESSs. The controller is tested in a microgrid in both island- and grid-connected modes in different scenarios. The microgrid includes several DGs that operate in different control modes depending on the microgrid operation. The storage unit configurations differ in their response time and capacity. This has significant implication in dynamic response of the storage units which is scrutinized in this paper with time-domain simulation.

This paper proposes a novel contribution factor (CF) approach to predict diversified daily peak load of low voltage (LV) substations. The CF for each LV template developed in part I of the paper is determined by a novel method—clusterwise weighted constrained regression (CWCR). It takes into account the contribution from different customer classes to substation peaks, respecting the natural difference in time and magnitude between LV substation peaks and the variance within the templates. In CWCR, intercept and coefficients are constrained to ensure that the resultant coefficients do not lead to reverse load flow and can respect zero-load substations. Cross validation is developed to validate the stability of the proposed method and prevent over fitting. The proposed method shows significant improvement in the accuracy of peak estimation over the current status quo across 800 substations of different mixes of domestic, industrial and commercial (I&C) customers. The work in the two parts of the paper is particularly useful for understanding the capabilities of LV networks to accommodate the increasing penetration of low carbon technologies without large-scale monitoring.