Search

The integration of uncertain photovoltaics (PVs) and flexible loads leads to uncertainties in the power system dynamic simulation results. Furthermore, geographically close PV farms are correlated and may exhibit nonlinear correlations. This article proposes a copula-based sparse polynomial chaos expansion (PCE) framework for quantifying the impacts of uncertain dynamic PVs and loads on power system dynamic simulations and stability. The dynamics include both PV and load stochasticity and those governed by differential and algebraic equations. The copula statistics are utilized to accurately characterize the dependence structure of PVs and further used to develop the copula-PCE for quantifying the impacts of uncertain PVs and loads. A probabilistic TSI is also developed to assess the uncertainties from PVs and loads on the system stability. To address the cases, where both stable and unstable conditions coexist, a preprocessing step via sample classification is proposed. The effects of different dependence structures of PVs and different numbers of uncertain sources are investigated. Comparison results with other methods on the modified IEEE 39- and 118-bus systems, including the Monte Carlo method, Latin hypercube sampling, and traditional PCE without consideration of uncertain input correlations show that the proposed method is able to accurately quantify the uncertain dynamic simulations and transient system stability while being computationally efficient. [ABSTRACT FROM AUTHOR]

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

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

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

The modern power grid is being used under operating conditions of increasing stress, giving rise to grid stability issues. One of these stability issues is the phenomenon of inter-area oscillations. Simulations have demonstrated the advantages of Wide-area Measurement Signals (WAMS)-based Oscillation Damping Controls in achieving improved electromechanical mode damping compared to traditional, local signal-based Power System Stabilizers (PSS). This work takes an existing Phasor-based oscillation damping (POD) algorithm and uses it to implement a proof-of-concept, wide-area, real-time controller on National Instruments hardware. The developed prototype is tested in a real-time Hardware-in-the-loop setup (RT-HIL) using OPAL-RT's eMEGASIM real-time simulation platform and synchrophasor data from actual Phasor Measurement Units (PMUs). The prototype and experiments provide insight into the feasibility and real-world limitations of wide-area controls. Further, it is demonstrated how the proposed control architecture has applications independent of the controlled power system device. Challenges faced, the solutions implemented together with the present prototype's limitations are also discussed.

Reliability and survivability of electric power systems (EPS) depend on transient stability assessment (TSA). One of the most effective way to TSA is time-domain simulation. However, large-scale EPS mathematical model contains a stiff nonlinear system of high-order differential equations. Such system cannot be solved analytically. At the same time, numerical methods are imperfectly applied for such system due to limitation conditions. To make it appropriate, the EPS mathematical model is simplified and additional limitations are used. These simplifications and limitations reduce reliability of simulation results. Consequently, their validation is needed. The most reliable approach to provide it is to compare the simulation results with the field data. However, in practice, there are not enough data for such validation. This paper proposes an alternative approach for validation - the application of a reference model instead of field data. A hardware-software system HRTSim was used as a reference model. This power system simulator has all the necessary properties and capabilities to obtain reliable information required for comprehensive validation of transient stability calculations in EPSs. Main disturbances leading to instability in EPSs are investigated to conduct the validation (processes in cases of faults, single-phase auto-reclosing operation and power system interconnection). Fragments of corresponding experimental studies illustrate the efficiency of the proposed approach. Obtained results confirmed the possibility of the developed approach to identify the causes of numerical calculation errors and to determine disturbances calculated with the significant error. In addition, experimental studies have revealed that numerical calculations error depends on disturbances intensity.

The paper presents accurate and simple dynamic model of a supercapacitor bank system for power system dynamics studies. The proposed model is derived from a detailed RC circuit representation. Furthermore, a complete control system of the supercapacitor bank is also presented. The proposed model is easy to integrate in any power system simulation software and consists of only up to four standard datasheet parameters. The performance of the proposed model in grid frequency control and low-voltage ride through is illustrated on IEEE 14-bus test system in DIgSILENT PowerFactory. It is shown that in case of transient stability simulations the ideal (simplified) model of the supercapacitor can be used while in case of frequency control the ideal representation may not always be appropriate. [ABSTRACT FROM AUTHOR]

This paper analyses the frequency stability of ac grids in the presence of non-dispatchable generation and stochastic loads. Its main goal is to evaluate conditions in which the system is robust to large, persistent active power disturbances without recurring to time-domain simulations. Considering the ongoing energy transition to more renewable sources, defining robustness boundaries is a key topic for power system planning and operation. However, much of the research on long-term studies has not dealt with robust dynamic constraints, while short-term analyses usually depend on time-consuming simulations to evaluate nonlinearities. To bridge this gap, the authors derive an algebraic equation that provides sufficient conditions for robust frequency stability in ac power systems and a relationship among four key quantities: the maximum active power perturbation, the minimum system damping, the steady-state and the transient frequency limits. To achieve this goal, it uses a nonlinear average-model of the ac grid and Lyapunov's direct method extended by perturbation analysis requiring only limited knowledge of the system parameters. The algebraic calculations are validated using time-domain simulations of the IEEE 39-bus test system and results are compared to the traditional Swing Equation model. [ABSTRACT FROM AUTHOR]

The article proposes a computationally efficient and robust method for estimating impulse or frequency response in the context of black-box multiple-input-multiple-output linear model identification of large power systems from simulations. The proposed approach is validated in conjunction with two realization algorithms – ERA method that is based on the established Ho-Kalman procedure for minimal realization, and the relatively new Loewner matrix based method. Practical aspects of identification in presence of numerical noise and nonlinearities are discussed. Study cases presented in the article include a linear model equivalent of a large-scale power system and the full-scale nonlinear transient model of the Eastern Interconnection. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for power system dynamic simulation based on the differential transformation (DT). The DT is introduced to study power systems as high-dimensional nonlinear dynamical systems for the first time, and is able to avoid computations of high-order derivatives with nonlinear differential equations by its transform rules. This paper, first, proposes and proves several new transform rules for generic nonlinear functions that often appear in power system models, and then uses these rules to transform representative power system models such as the synchronous machine model with trigonometric functions and the exciter model with exponential and square root functions. This paper also designs a DT-based simulation scheme that allows significantly prolonged time steps to reduce simulation time compared to a traditional numerical approach. The numerical stability, accuracy, and time performance of the proposed new DT-based simulation approach are compared with widely used numerical methods on the IEEE 39-bus system and Polish 2383-bus system. [ABSTRACT FROM AUTHOR]

Homotopy analysis method (HAM) is a popular semi-analytical method used widely in applied sciences. It stands out from the rest of the semi-analytical methods as it provides a family of solutions to nonlinear equations, including ordinary differential equations (ODEs), partial differential equations, etc. The convergence characteristics of the solutions can be varied by changing an auxiliary parameter ($\hbar$) in HAM. The convergence region of solution of ODEs using HAM can be improved by applying it over multiple intervals of time, which is referred to as multi-stage HAM (MHAM). In this paper, MHAM models for the IEEE Model 2.2 synchronous machine, IEEE Type-1 excitation system, first-order governor and first-order turbine models have been developed. The applicability of MHAM for power system dynamic simulations has been investigated in this paper using seven widely used test systems ranging from 10 generators 39 bus systems to 4092 generators 13 659 bus systems. The effect of number of terms, $\hbar$ and the time step on the accuracy and stability of the solution has been studied. The effectiveness of MHAM has been compared with the modified Euler (ME) and midpoint Trapezoidal (TrapZ) methods. The accuracy of MHAM has been found to be comparable with ME and TrapZ methods for the values of $\hbar$ between $-$ 1.05 and $-$ 0.95. The best accuracy is obtained for $\hbar$ = $-$ 1.0, which is a special case of MHAM called multi-stage homotopy perturbation method (MHPM). In this paper, it is also shown that MHPM is equivalent to multi-stage adomian decomposition method, which has been recently explored for large power system simulations. [ABSTRACT FROM AUTHOR]

This paper develops a comprehensive dynamic-phasor-based small-signal model for the modular multilevel converter (MMC) system under unbalanced grid conditions, which takes into consideration the dynamics of the MMC system under a balanced grid condition as well as the other emerging internal harmonics produced by the unbalanced grid components and more complex controllers. The small-signal model is validated by comparing the time-domain responses from a detailed electromagnetic transient (EMT) simulation in PSCAD/EMTDC. Based on the eigen-analysis and PSCAD-based time-domain simulation studies, this paper reveals the poorly damped modes that cause unstable oscillations in MMC system under the unbalanced grid conditions. From the results, more poorly damped modes involved in the internal harmonics are emerging under unbalanced grid conditions compared with the modes under the balanced grid conditions, and can highly impact the system dynamic behaviors by the selection of the control parameters. It is also shown that, under the unbalanced grid conditions, the feasible region of the control parameters of the vector current control gets narrowed indicating the reduction of the stability margin, smaller (larger) value of proportional (integral) gain of the circulating current suppressing controller can enhance the system stability, and larger values of the proportional and integral gains of the negative-sequence current suppressing control can result in the harmonic instability of the MMC system. Besides, the parameters of multiple complex-coefficient filters for positive- and negative-sequence components extraction also have a big impact on the small-signal stability of the MMC system and are required to be properly selected. [ABSTRACT FROM AUTHOR]

Interarea power oscillation damping enhancement in large interconnected power systems is often accomplished using supplementary controls at the synchronous machines involved and with the use of flexible ac transmission system devices. The power system literature has demonstrated that wide area signals could be more effective than the local signals for these controllers. In some cases where phasor measurement units are used, all the required control signals may not be available. To alleviate these cases, control signals are obtained using estimated signals from a “dynamic state estimator,” and a robust supplementary controller is deployed. In this paper, the cited strategy is illustrated using a static var compensator. The feasibility of the proposed method has been demonstrated on the IEEE 50-generator test system. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define and develop an optimal hierarchical demand-side power-system primary-frequency control structure in order to provide a reliable complement to generator inertia and governor response while improving inter-area oscillation damping. This resilient optimal load control strategy utilizes both wide-area and local signals to guarantee that the system remains stable in the case of communication failures. In the device layer, we deal with demand-response and frequency regulation by minimizing the total disutility of consumers subject to power balance and frequency regulation over the network. In the supervisory layer, we handle the power system's electromechanical oscillations using an linear-quadratic regulator (LQR)-based state feedback scheme with sparsity promotion to achieve the necessary tradeoff between complexity and performance. Since the wide-area feedback loops are built on top of an existing decentralized load control strategy, this design approach creates a decentralized/hierarchical demand-side load-control structure with significant advantages in terms of reliability and operational flexibility. Our study clearly shows by simulation that a demand-side hierarchical load-control strategy has a significant potential for improving the dynamic performance of power systems, even when implemented with a limited number of measurement units and controlling less than $1\%$ of the total base load. [ABSTRACT FROM AUTHOR]

POWER plants are subject to introduce disturbances in the power grid, resulting from interactions with the dynamical behavior of the energy source subsystem. In the case of hydropower plants when used to compensate for variations of power generation and consumption, instabilities or undesirable disturbances may arise. They may be caused by phenomena such as part load vortex rope pulsations in the draft tube of Francis turbines. This may affect the dynamical behavior of the power plant and lead to troublesome interactions with the grid. This paper presents a case study of an existing hydropower plant that illustrates the effects of pressure pulsations due to vortex rope precession on the draft tube of Francis turbines. It also showcases possible solutions to the mitigation of the effects of this disturbing hydraulic phenomenon over the operation of the generators and electrical system. The investigated system is a 1-GW hydropower plant (4 × 250 MW units). The assessment of the power swings is performed through modal analysis combined with frequency-domain and time-domain simulations, which are then compared with onsite measurements. [ABSTRACT FROM AUTHOR]

This paper proposes a protection scheme that applies two supervisory zones on each distance relay in the transmission system and timers in order to avoid undesirable Zone 3 operations under voltage-stressed system conditions. The speed at which the apparent impedance trajectory crosses the two supervisory zones is measured by the relay in order to determine the rate of change of the apparent impedance. Zone 3 modifications based on the normalized rate of change of the apparent impedance are applied: 1) Zone 3 operating area is reduced by using circle or straight line blinders when the instability is clearly recognized; 2) Zone 3 is blocked when there is no enough time to identify the cause of the apparent impedance transition; and 3) no measure is applied for a fault or a power swing. Simulations performed in a test power system show the effectiveness of this method in mitigating system blackouts due to cascaded outages. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach in adaptive out-of-step (OOS) protection settings in power systems in real time. The proposed method uses extended equal area criterion (EEAC) to determine the critical clearing time and critical clearing angle of the system, which are vital information for the OOS protection setting calculation. The dynamic model parameters and the coherency groups of the system for EEAC analysis are determined in real time to ensure that the newly calculated settings suit with the prevalent system operating condition. The effectiveness of the method is demonstrated in simulated data from a 16-machine 68-bus system model. [ABSTRACT FROM PUBLISHER]

This paper proposes a new method for measurement-based modeling of nonlinear loads in power systems. The proposed method includes a combination of a binary tree algorithm with nonlinear autoregressive with exogenous input (NARX) identification. This paper demonstrates that the new method performs well without any prior knowledge of the system structure. In contrast to other load modeling methods, which are typically aimed for particular studies or load types, the proposed method can be used with any load type and for any study. Accurate load modeling is particularly important for studies of industrial networks and grids. In the study described, a field data set was collected at a mine site from a large electrical rope shovel. This data set has been used to develop a model of the rope shovel based on the proposed binary tree—NARX algorithm. When compared to other known methods, such as wavelet and sigmoid networks, the proposed method has shown the fastest training time and the highest accuracy. Finally, the modeling results have been verified against another set of field measurements from an existing network and have shown a very good agreement. [ABSTRACT FROM PUBLISHER]

Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical “robust stability” criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of robust stability assessment (RSA), that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies. [ABSTRACT FROM PUBLISHER]

Short-term voltage stability is an increasing concern in today's power systems due to the growing penetration of induction motors. This paper proposes a systematic method for optimal placement of dynamic VAR support against short-term voltage instability. The problem is formulated as a multi-objective optimization model minimizing two conflicting objectives: 1) the total investment cost and 2) the expected unacceptable short-term voltage performance subject to a set of probable contingencies. STATCOM is employed for its stronger dynamic VAR support capability. Indices for quantifying the short-term voltage stability and the related risk level are proposed for problem modeling. Candidate buses are selected based on the concept of trajectory sensitivity. Load dynamics are fully considered using a composite load model containing induction motor and other typical components. A relatively new and superior multi-objective evolutionary algorithm called MOEA/D is introduced and employed to find the Pareto optimal solutions of the model. The proposed method is verified on the New England 39-bus system using industry-grade models and simulation tool. [ABSTRACT FROM AUTHOR]

This paper presents an ultra-high speed hardware platform dedicated to power system dynamic (small signal) and transient (large signal) stability. It is based on an intrinsic parallel architecture which contains hybrid mixed-signal (analog and digital) circuits. For a given model, this architecture overcomes the speed of the numerical simulators by means of the so-called emulation approach. Indeed, the emulation speed does not depend on the power system size. This approach is nevertheless not competing against high-performance numerical simulators in term of accuracy and model complexity. It targets to complement the numerical simulators with the advantage of speed, portability, low cost and autonomous functioning. The proof of concept is a flexible and modular 96-node hardware platform. It is based on a reconfigurable array of power system buses called Field Programmable Power Network System (FPPNS). Details on this hardware are given. Two benchmark topologies with, respectively, 17 nodes and 57 nodes are provided. Comparisons with a digital simulator are done in terms of speed and accuracy. The calibration of the system is explained and different applications are proposed and discussed. The promising results of this hardware platform show that the design of a fully integrated solution containing hundreds of power system buses can be achieved in order to provide a low cost solution. [ABSTRACT FROM PUBLISHER]

Electromagnetic Transients Program (EMTP) is widely used in power system dynamics studies. However, in most cases EMTP is found inadequate for dealing with the realistic size power systems due to the small time step resulting in relatively slow simulation speeds. To accelerate the EMTP simulations of power system dynamics, a novel frequency-adaptive methodology is proposed. In this method, a new transformation is presented. The properties of the transformation and the numerical solutions based on the transformation are discussed. The component models obtained by discretizing the differential equations at the branch level are also given which are convenient for EMTP implementation. The proposed method allows using large time steps without sacrificing accuracy, which greatly improves the simulation speed. To validate the proposed methodology, a general program has been developed. Furthermore, various case studies substantiate the claims and demonstrate the application of the method. [ABSTRACT FROM PUBLISHER]

Repeated simulations have been most widely applied in analyzing the sensitivities of the power system dynamics with respect to controller inputs. This approach is computationally intensive and it does not explicitly show the physical insights. A transfer function matrix based approach is proposed in this letter for control input sensitivity analysis. A bottom up method is also presented to build the respective transfer function matrix. The effectiveness of the method is demonstrated through case studies. [ABSTRACT FROM AUTHOR]