Showing papers in "IEEE Transactions on Power Systems in 2017"

The 2015 Ukraine Blackout: Implications for False Data Injection Attacks

Abstract: In a false data injection attack (FDIA), an adversary stealthily compromises measurements from electricity grid sensors in a coordinated fashion, with a view to evading detection by the power system bad data detection module. A successful FDIA can cause the system operator to perform control actions that compromise either the physical or economic operation of the power system. In this letter, we consider some implications for FDIAs arising from the late 2015 Ukraine Blackout event.

Energy-Sharing Model With Price-Based Demand Response for Microgrids of Peer-to-Peer Prosumers

Abstract: According to the feed-in tariff for encouraging local consumption of photovoltaic (PV) energy, the energy sharing among neighboring PV prosumers in the microgrid could be more economical than the independent operation of prosumers. For microgrids of peer-to-peer PV prosumers, an energy-sharing model with price-based demand response is proposed. First, a dynamical internal pricing model is formulated for the operation of energy-sharing zone, which is defined based on the supply and demand ratio (SDR) of shared PV energy. Moreover, considering the energy consumption flexibility of prosumers, an equivalent cost model is designed in terms of economic cost and users’ willingness. As the internal prices are coupled with SDR in the microgrid, the algorithm and implementation method for solving the model is designed on a distributed iterative way. Finally, through a practical case study, the effectiveness of the method is verified in terms of saving PV prosumers’ costs and improving the sharing of the PV energy.

Grid Structural Characteristics as Validation Criteria for Synthetic Networks

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

Metrics and Quantification of Operational and Infrastructure Resilience in Power Systems

Abstract: Resilience to high impact low probability events is becoming of growing concern, for instance to address the impacts of extreme weather on critical infrastructures worldwide. However, there is, as yet, no clear methodology or set of metrics to quantify resilience in the context of power systems and in terms of both operational and infrastructure integrity. In this paper, the resilience “trapezoid ” is therefore introduced which extends the resilience “triangle” that is traditionally used in existing studies, in order to consider the different phases that a power system may experience during an extreme event. The resilience trapezoid is then quantified using time-dependent resilience metrics that are specifically introduced to help capture the critical system degradation and recovery features associated to the trapezoid for different temporal phases of an event. Further, we introduce the concepts of operational resilience and infrastructure resilience to gain additional insights in the system response. Different structural and operational resilience enhancement strategies are then analyzed using the proposed assessment framework, considering single and multiple severe windstorm events that hit the 29-bus Great Britain transmission network test case. The results clearly highlight the capability of the proposed framework and metrics to quantify power system resilience and relevant enhancement strategies.

A Review on Distribution System State Estimation

Abstract: Transition to a sustainable energy environment results in aggregated generator and load dynamics in the distribution network. State estimation is a key function in building adequate network models for online monitoring and analyzes. The requirements of distribution system state estimation (DSSE) is becoming stringent because of the needs of new system modeling and operation practices associated with integration of distributed energy resources and the adoption of advanced technologies in distribution network. This paper summarizes the state-of-the-art technology, major hurdles, and challenges in DSSE development. The opportunities, paradigm shift, and future research directions that could facilitate the need of DSSE are discussed.

Power System Resilience to Extreme Weather: Fragility Modeling, Probabilistic Impact Assessment, and Adaptation Measures

Abstract: Historical electrical disturbances highlight the impact of extreme weather on power system resilience Even though the occurrence of such events is rare, the severity of their potential impact calls for 1) developing suitable resilience assessment techniques to capture their impacts and 2) assessing relevant strategies to mitigate them This paper aims to provide fundamentals insights on the modeling and quantification of power systems resilience Specifically, a fragility model of individual components and then of the whole transmission system is built for mapping the real-time impact of severe weather, with focus on wind events, on their failure probabilities A probabilistic multitemporal and multiregional resilience assessment methodology, based on optimal power flow and sequential Monte Carlo simulation, is then introduced, allowing the assessment of the spatiotemporal impact of a windstorm moving across a transmission network Different risk-based resilience enhancement (or adaptation) measures are evaluated, which are driven by the resilience achievement worth index of the individual transmission components The methodology is demonstrated using a test version of the Great Britain's system As key outputs, the results demonstrate how, by using a mix of infrastructure and operational indices, it is possible to effectively quantify system resilience to extreme weather, identify and prioritize critical network sections, whose criticality depends on the weather intensity, and assess the technical benefits of different adaptation measures to enhance resilience

Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks

Abstract: Recently, sustained power oscillation at subsynchronous frequency was captured in direct-drive permanent magnetic synchronous generator (PMSG) based wind farms in Xinjiang Uygur Autonomous Region, China. This new type of subsynchronous interaction (SSI) detected in practical systems has never been reported and analyzed before. Therefore, its mechanism and characteristics are not yet clearly clarified. In this paper, a simplified but representative system model with multiple PMSGs interfaced with AC networks is established first based on the actual system and the PMSG model provided by the manufacturer. Then, small-signal eigenanalysis, time-domain simulation, and impedance model analysis are carried out to investigate the interactive dynamics between them. The results show that such interaction between direct-drive PMSG wind farms and weak ac grids characterized by low short-circuit ratio would cause negative-resistance effect for the SSI mode, leading to unstable oscillation. In such cases, the controller of PMSG would saturate soon, resulting in sustained power oscillation in the system. If unfortunately the oscillation frequency matches the torsional mode of any nearby turbogenerator, severe torsional vibration would be excited on the shaft of the latter. The analysis results are finally validated with field measurements of an actual SSI event. To address the problem, a supplementary subsynchronous damping control loop is attached to the controllers of PMSGs to reshape the impedance and thus to stabilize the SSI.

A Robust Iterated Extended Kalman Filter for Power System Dynamic State Estimation

Abstract: This paper develops a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF) for estimating power system state dynamics when subjected to disturbances. The proposed GM-IEKF dynamic state estimator is able to track system transients in a faster and more reliable way than the conventional EKF and the unscented Kalman filter (UKF) thanks to its batch-mode regression form and its robustness to innovation and observation outliers, even in position of leverage. Innovation outliers may be caused by impulsive noise in the dynamic state model while observation outliers may be due to large biases, cyber attacks, or temporary loss of communication links of PMUs. Good robustness and high statistical efficiency under Gaussian noise are achieved via the minimization of the Huber convex cost function of the standardized residuals. The latter is weighted via a function of robust distances of the two-time sequence of the predicted state and innovation vectors and calculated by means of the projection statistics. The state estimation error covariance matrix is derived using the total influence function, resulting in a robust state prediction in the next time step. Simulation results carried out on the IEEE 39-bus test system demonstrate the good performance of the GM-IEKF under Gaussian and non-Gaussian process and observation noise.

Resilient Event-Triggering $H_{\infty }$ Load Frequency Control for Multi-Area Power Systems With Energy-Limited DoS Attacks

Abstract: This paper investigates a resilient event-triggering $H_{\infty }$ load frequency control (LFC) for multi-area power systems with energy-limited Denial-of-Service (DoS) attacks. The LFC design specifically takes the presence of DoS attacks into account. First, an area control error dependent time delay model is delicately constructed for multi-area closed-loop power systems. Second, a resilient event-triggering communication (RETC) scheme is well designed, which allows a degree of packet losses induced by DoS attacks and has the advantage of improving the transaction efficiency. Then, by using the Lyapunov theory, two stability and stabilization criteria for the multi-area power systems are derived under consideration of the energy-limited DoS attacks. In these criteria, the relationship between the allowable DoS attack duration and the resilient event-triggering communication parameters are clearly revealed. Moreover, an algorithm is also provided to obtain the RETC parameters and the LFC gains simultaneously. Finally, a case study shows the effectiveness of the proposed method.

A Distributionally Robust Optimization Model for Unit Commitment Considering Uncertain Wind Power Generation

Abstract: 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.

Distributionally Robust Chance-Constrained Optimal Power Flow With Uncertain Renewables and Uncertain Reserves Provided by Loads

Abstract: Aggregations of electric loads can provide reserves to power systems, but their available reserve capacities are time-varying and not perfectly known when the system operator computes the optimal generation and reserve schedule. In this paper, we formulate a chance constrained optimal power flow problem to procure minimum cost energy, generator reserves, and load reserves given uncertainty in renewable energy production, load consumption, and load reserve capacities. Assuming that uncertainty distributions are not perfectly known, we solve the problem with distributionally robust optimization, which ensures that chance constraints are satisfied for any distribution in an ambiguity set built upon the first two moments. We use two ambiguity sets to reformulate the model as a semidefinite program and a second-order cone program and run computational experiments on the IEEE 9-bus, 39-bus, and 118-bus systems. We compare the solutions to those given by two benchmark reformulations; the first assumes normally distributed uncertainty and the second uses large numbers of uncertainty samples. We find that the use of load reserves, even when load reserve capacities are uncertain, reduces operational costs. Also, the approach is able to meet reliability requirements, unlike the first benchmark approach and with lower computation times than the second benchmark approach.

Transactive Control of Commercial Buildings for Demand Response

Abstract: Transactive control is a type of distributed control strategy that uses market mechanisms to engage self-interested responsive loads to achieve power balance in the electrical power grid. In this paper, we propose a transactive control approach of commercial building heating, ventilation, and air-conditioning (HVAC) systems for demand response. We first describe the system models, and identify their model parameters using data collected from systems engineering building (SEB) located on our Pacific Northwest National Laboratory campus. We next present a transactive control market structure for commercial building HVAC systems, and describe its agent bidding and market clearing strategies. Several case studies are performed in a simulation environment using building controls virtual test bed (BCVTB) and calibrated SEB EnergyPlus model. We show that the proposed transactive control approach is very effective at peak shaving, load shifting, and strategic conservation for commercial building HVAC systems.

Selecting Representative Days for Capturing the Implications of Integrating Intermittent Renewables in Generation Expansion Planning Problems

Abstract: Due to computational restrictions, energy-system optimization models (ESOMs) and generation expansion planning models (GEPMs) frequently represent intraannual variations in demand and supply by using the data of a limited number of representative historical days. The vast majority of the current approaches to select a representative set of days relies on either simple heuristics or clustering algorithms and comparison of different approaches is restricted to different clustering algorithms. This paper contributes by: i) proposing criteria and metrics for evaluating representativeness, ii) providing a novel optimization-based approach to select a representative set of days, and iii) evaluating and comparing the developed approach to multiple approaches available from the literature. The developed optimization-based approach is shown to achieve more accurate results than the approaches available from the literature. As a consequence, by applying this approach to select a representative set of days, the accuracy of ESOMs/GEPMs can be improved without increasing the computational cost. The main disadvantage is that the approach is computationally costly and requires an implementation effort.

Integrated Planning of Electricity and Natural Gas Transportation Systems for Enhancing the Power Grid Resilience

Abstract: Power systems are exceedingly faced with extreme events such as natural disasters and deliberate attacks. In comparison, the underground natural gas system is considered less vulnerable to such extreme events. We consider that the overhead power grid can be hardened by replacing segments of electric power grid with underground natural gas pipelines as an energy transportation system to countereffect extreme events which can damage interdependent infrastructures severely. In this paper, an integrated electricity and natural gas transportation system planning algorithm is proposed for enhancing the power grid resilience in extreme conditions. A variable uncertainty set is developed to describe the interactions among power grid expansion states and extreme events. The proposed planning problem is formulated as a two-stage robust optimization problem. First, the influence of extreme events representing natural disasters is described by the proposed variable uncertainty set and the proposed robust model for the integrated planning is solved with the grid resilience represented by a set of constraints. Second, the investment decisions are evaluated iteratively using the conditional events. The integrated electricity and natural gas planning options are analyzed using the modified IEEE-RTS 1979 for enhancing the power grid resilience. The numerical results point out that the proposed integrated planning is an effective approach to improving the power grid resilience.

Quantitative SSR Analysis of Series-Compensated DFIG-Based Wind Farms Using Aggregated RLC Circuit Model

Abstract: A new type of subsynchronous resonance (SSR), namely, subsynchronous control interaction (SSCI), was recently observed in doubly-fed induction generators (DFIGs) interfaced with series-compensated power networks. In this paper, a more accurate method based on aggregated RLC circuit model is proposed to intuitively explain and quantitatively evaluate this type of SSR. For a practical power system containing multiple DFIGs and fixed series compensation, an improved impedance model (IM) is derived, which incorporates DFIG's full-scale control system. Around the series-resonant frequency, IM can be further represented with an aggregated RLC circuit model. Its equivalent parameters are worked out and then used for the quantitative assessment of potential SSR risk. The proposed method is applied for SSR analysis of a practical wind farm system in North China that experienced actual SSR incidents. The consistence between the obtained results and field measured data verifies its effectiveness very well. Further, its advantage in accuracy over existing impedance-based approaches is validated by both eigenvalue analysis and time-domain simulations. The method is also used to quantitatively investigate the impact on SSR stability from the various factors, including wind speed, number of online DFIGs and their control parameters.

Evaluation of Achievable Vehicle-to-Grid Capacity Using Aggregate PEV Model

Abstract: Large-scale plug-in electric vehicles (PEVs) utilizing vehicle-to-grid (V2G) technology can collectively behave as a storage system under the control of an aggregator, e.g., arbitraging in the energy market and providing ancillary services to the grid. Quantitatively evaluating V2G capacity, i.e., charging and discharging power ranges, for a PEV fleet utilizing V2G technology (which is referred to as a V2G fleet in this paper) ahead of time is of fundamental importance for V2G implementation. However, because of the stochastic characteristics of PEV driving behaviors, charging demands are difficult to forecast, which makes evaluating V2G capacity technically difficult. This paper first establishes an aggregate model of a V2G fleet that employs aggregated parameters to represent energy and power constraints of the entire V2G fleet and, therefore, reduces the difficulty of forecasting. Then, an evaluation method for V2G capacity of large-scale PEVs is developed based on the proposed aggregate model. To make the V2G capacity evaluated in advance achievable while guaranteeing charging demands during real-time operation, a heuristic smart charging strategy is designed. The application of the evaluation method in optimal charge and discharge scheduling for a V2G fleet providing power reserves is illustrated. Numerical simulations are conducted to validate the proposed method.

A State-Independent Linear Power Flow Model With Accurate Estimation of Voltage Magnitude

Abstract: Linearized power flow models are of great interest in power system studies such as contingency analyses and reliability assessments, especially for large-scale systems. One of the most popular models—the classical DC power flow model—is widely used and praised for its state independence, robustness, and computational efficiency. Despite its advantages, however, the DC power flow model fails to consider reactive power or bus voltage magnitude. This paper closes this gap by proposing a decoupled linearized power flow (DLPF) model with respect to voltage magnitude and phase angle. The model is state independent but is distinguished by its high accuracy in voltage magnitude. Moreover, this paper presents an in-depth analysis of the DLPF model with the purpose of accelerating its computation speed, leading to the fast DLPF (FDLPF) model. The approximation that is applied to obtain the FDLPF model from the DLPF model is justified by a theoretical derivation and numerical tests. The proposed methods are provably accurate and robust for several cases, including radial distribution systems, meshed large-scale transmission systems and ill-conditioned systems. Finally, expressions for sensitivity with regard to MW flow and bus voltage are provided as a potential application.

Modeling of Grid-Connected VSCs for Power System Small-Signal Stability Analysis in DC-Link Voltage Control Timescale

Abstract: 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.

Integration of Preventive and Emergency Responses for Power Grid Resilience Enhancement

Abstract: Boosting the resilience of power systems is one of the core requirements of smart grid. In this paper, an integrated resilience response framework is proposed, which not only links the situational awareness with resilience enhancement, but also provides effective and efficient responses in both preventive and emergency states. The core of the proposed framework is a two-stage robust mixed-integer optimization model, whose mathematical formulation is presented in this paper as well. To solve the above model, an algorithm based on the nested column-and-constraint generation decomposition is provided, and computational efficiency improvement techniques are proposed. Preventive response in this paper considers generator re-dispatch and topology switching, while emergency response includes generator re-dispatch, topology switching and load shedding. Several numerical simulations validate the effectiveness of the proposed framework and the efficiency of the solution methodology. Key findings include the following: 1) in terms of enhancing power grid resilience, the integrated resilience response is preferable to both independent preventive response and independent emergency response; 2) the power grid resilience could be further enhanced by utilizing topology switching in the integrated resilience response.

Multi-Timescale Coordinated Voltage/Var Control of High Renewable-Penetrated Distribution Systems

Abstract: This paper proposes a multi-timescale coordinated stochastic voltage/var control method for high renewable-penetrated distribution networks. It aims to utilize multiple devices to counteract uncertain voltage fluctuation and deviation. In the hourly timescale (first stage), capacitor banks and transformer tap changers are scheduled before stochastic renewable output and load variations are realized. In the 15-min timescale (second stage), inverters that interface the renewable energy resources provide var support to supplement the first-stage decision after uncertainty is observed. The coordination is model as a two-stage stochastic programming problem with scenario reduction. It is then converted to a deterministic mixed-integer quadratic programming equivalence model and solved by commercial solvers combined. Compared with existing methods, the proposed volt/var control can achieve lower expected energy loss and can sustain a secure voltage level under random load demand and renewable power injection. The proposed method is verified on the IEEE 33-bus distribution network and compared with existing practices.

Benchmark Models for the Analysis and Control of Small-Signal Oscillatory Dynamics in Power Systems

Abstract: This paper summarizes a set of six benchmark systems for the analysis and control of electromechanical oscillations in power systems, recommended by the IEEE Task Force on Benchmark Systems for Stability Controls of the Power System Dynamic Performance Committee. The benchmark systems were chosen for their tutorial value and particular characteristics leading to control the system design problems relevant to the research community. For each benchmark, the modeling guidelines are provided, along with eigenvalues and time-domain results produced with at least two simulation softwares, and one possible control approach is provided for each system as well. Researchers and practicing engineers are encouraged to use these benchmark systems when assessing new oscillation damping control strategies.

Distributed Robust Finite-Time Secondary Voltage and Frequency Control of Islanded Microgrids

Abstract: 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.

Direct Quantile Regression for Nonparametric Probabilistic Forecasting of Wind Power Generation

Abstract: The fluctuation and uncertainty of wind power generation bring severe challenges to secure and economic operation of power systems. Because wind power forecasting error is unavoidable, probabilistic forecasting becomes critical to accurately quantifying the uncertainty involved in traditional point forecasts of wind power and to providing meaningful information to conduct risk management in power system operation. This paper proposes a novel direct quantile regression approach to efficiently generate nonparametric probabilistic forecasting of wind power generation combining extreme learning machine and quantile regression. Quantiles with different proportions can be directly produced via an innovatively formulated linear programming optimization model, without dependency on point forecasts. Multistep probabilistic forecasting of 10-min wind power is newly carried out based on real wind farm data from Bornholm Island in Denmark. The superiority of the proposed approach is verified through comparisons with other well-established benchmarks. The proposed approach forms a new artificial neural network-based nonparametric forecasting framework for wind power with high efficiency, reliability, and flexibility, which can be beneficial to various decision-making activities in power systems.

Robust Operation of Microgrids via Two-Stage Coordinated Energy Storage and Direct Load Control

Abstract: This paper proposes a robust optimization approach for optimal operation of microgrids. The uncertain output variation of renewable energy sources (RESs) is addressed by collaboratively scheduling of energy storage (ES) and direct load control (DLC) through a two-stage complementary framework: an hour-ahead charging/discharging of ES and a quarter-hour-ahead activation of DLC. The objective is to maximize the total profit of the microgrid considering operation and maintenance costs of ES units, wind turbines and photovoltaics, and transaction with main grid and customer loads. Assuming the power output of RES randomly varies within a bounded uncertainty set, the problem is modeled to a two-stage robust optimization model and solved by a column-and-constraint generation algorithm. Compared with conventional operation methods, the ES and DLC are coordinated in different time-scales, and RES uncertainties are fully addressed during operation decision-making, ensuring the solutions to be optimal and robust for any realization of uncertainty. The proposed methodology is verified on the IEEE 33-bus distribution system through a wide range of different tests.

A New Feature Selection Technique for Load and Price Forecast of Electrical Power Systems

Abstract: Load and price forecasts are necessary for optimal operation planning in competitive electricity markets. However, most of the load and price forecast methods suffer from lack of an efficient feature selection technique with the ability of modeling the nonlinearities and interacting features of the forecast processes. In this paper, a new feature selection method is presented. An important contribution of the proposed method is modeling interaction in addition to relevancy and redundancy, based on information-theoretic criteria, for feature selection. Another main contribution of the paper is proposing a hybrid filter-wrapper approach. The filter part selects a minimum subset of the most informative features by considering relevancy, redundancy, and interaction of the candidate inputs in a coordinated manner. The wrapper part fine-tunes the settings of the composite filter.

A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads

Abstract: Coordinated aggregation of a large population of thermostatically controlled loads (TCLs) presents a great potential to provide various ancillary services to the grid. One of the key challenges of integrating TCLs into system-level operation and control is developing a simple and portable model to accurately capture their aggregate flexibility. In this paper, we propose a geometric approach to model the aggregate flexibility of TCLs. We show that the set of admissible power profiles of an individual TCL is a polytope, and their aggregate flexibility is the Minkowski sum of the individual polytopes. In order to represent their aggregate flexibility in an intuitive way and achieve a tractable approximation, we develop optimization-based algorithms to approximate the polytopes by the homothets of a given convex set. As a special application, this set is chosen as a virtual battery model, and the corresponding optimal approximations are solved efficiently by equivalent linear programming problems. Numerical results show that our algorithms yield significant improvement in characterizing the aggregate flexibility over existing modeling methods. We also conduct case studies to demonstrate the efficacy of our approaches by coordinating TCLs to track a frequency regulation signal from the Pennsylvania-New Jersey-Maryland Interconnection.

A Pole-to-Pole Short-Circuit Fault Current Calculation Method for DC Grids

Abstract: This paper proposes a generic pole-to-pole short-circuit fault current calculation method for dc grids. The calculation procedure begins from the simplified RLC equivalent model of a single modular multilevel converter, and then the prefault matrices and faulted matrices are established and modified to calculate the dc fault currents of all the branches. The proposed approaches are validated by comparing with the electromagnetic transient (EMT) simulation results on PSCAD/EMTDC. Besides, two case studies showed that the calculation method can be easily used to evaluate the severity of a dc fault. Moreover, the calculation can be applied to select the parameters of a fault current limiter (to match the circuit breaker capacity. The main contributions of the proposed numerical calculation method are: 1) The proposed method is accurate and much more time efficient than the EMT simulations; 2) the proposed method can handle all kinds of dc grid networks including the ring, radial, and meshed topologies; and 3) the proposed method is applicable to dc grid with multiple dc voltage level areas connected with dc/dc converters.

Fast-Frequency Response Provided by DFIG-Wind Turbines and its Impact on the Grid

Abstract: This paper presents a methodology for the analysis of frequency dynamics in large-scale power systems with high level of wind energy penetration by means of a simplified model for DFIG-based wind turbines. In addition, a virtual inertia controller version of the optimized power point tracking (OPPT) method is implemented for this kind of wind turbines, where the maximum power point tracking curve is shifted to drive variations in the active power injection as a function of both the grid frequency deviation and its time derivative. The proposed methodology integrates the model in a primary frequency control scheme to analyze the interaction with the rest of the plants in the power system. It is also proven that, under real wind conditions, the proposed version of the OPPT method allows us to smooth the wind power injected into the grid, thereby reducing frequency fluctuations.

Inertia Emulation in AC/DC Interconnected Power Systems Using Derivative Technique Considering Frequency Measurement Effects

Abstract: Virtual inertia is known as an inevitable part of the modern power systems with high penetration of renewable energy. Recent trend of research is oriented in different methods of emulating the inertia to increase the sustainability of the system. In the case of dynamic performance of power systems especially in Automatic Generation Control (AGC) issue, there are concerns considering the matter of virtual inertia. This paper proposes an approach for analyzing the dynamic effects of virtual inertia in two-area AC/DC interconnected AGC power systems. Derivative control technique is used for higher level control application of inertia emulation. This method of inertia emulation is developed for two-area AGC system, which is connected by parallel AC/DC transmission systems. Based on the proposed technique, the dynamic effect of inertia emulated by storage devices for frequency and active power control are evaluated. The effects of frequency measurement delay and phase-locked loop effect are also considered by introducing a second-order function. Simulations performed by MATLAB software demonstrate how virtual inertia emulation can effectively improve the performance of the power system. A detailed eigenvalue analysis is also performed to support the positive effects of the proposed method.

A New Model for Resilient Distribution Systems by Microgrids Formation

Abstract: Forming multiple micorgrids with distributed generators offers a resilient solution to restore critical loads from natural disasters in distribution systems. However, more dummy binary and continuous variables are needed with the increase of the number of microgrids, which will therefore increase the complexity of this model. To address this issue, this letter presents a new model to reformulate the micorgrid formulation problem in resilient distribution networks. Compared with the traditional model, the number of both binary and continuous variables is greatly reduced, such that the computational performance is significantly improved. Numerical results on IEEE test systems verify the effectiveness of the proposed model.