EMT Simulations Research Articles

Physics-informed neural networks for phase locked loop transient stability assessment

A significant increase in renewable energy production is necessary to achieve the UN’s net-zero emission targets for 2050. Using power-electronic controllers, such as Phase Locked Loops (PLLs), to keep grid-tied renewable resources in synchronism with the grid can cause fast transient behavior during grid faults leading to instability. However, assessing all the probable scenarios is impractical, so determining the stability boundary or region of attraction (ROA) is necessary. However, using EMT simulations or Reduced-order models (ROMs) to accurately determine the ROA is computationally expensive. Alternatively, Machine Learning (ML) models have been proposed as an efficient method to predict stability. However, traditional ML algorithms require large amounts of labeled data for training, which is computationally expensive. This paper proposes a Physics-Informed Neural Network (PINN) architecture that accurately predicts the nonlinear transient dynamics of a inverter with a PLL-based controller under fault with less labeled training data. The proposed PINN algorithm can be incorporated into conventional simulations, accelerating EMT simulations or ROMs by over 100 times. The PINN algorithm’s performance is compared against a ROM and an EMT simulation in PSCAD for the CIGRE benchmark model C4.49, demonstrating its ability to accurately approximate trajectories and ROAs of a inverter with a PLL-based controller under varying grid impedance.

Initialization Methods for FPGA-Based EMT Simulations

Initialization Methods for FPGA-Based EMT Simulations

Transient Stability Assessment of Renewable Dominated Power Systems by the Method of Hyperplanes

With continuous increase of penetration of renewable energies and power electronic equipment, power grid stability incidents are emerging frequently worldwide. In this paper, the transient stability assessment of renewable dominated power systems with multiple PLL-based voltage source converters (VSCs) is studied by calculating critical clearing time (CCT). A tangent hyperplane method is developed, which approximates the boundary of basin of attraction near unstable equilibrium point by linear system theory. The detailed algorithm is presented, accompanying with four typical case studies, including a single machine infinite system, two parallel VSCs, modified IEEE 9- bus, and modified 39- bus systems. Broad EMT simulations are performed to verify the accuracy and computational effectiveness of the algorithm. In all these tests, we find that the hyperplane method can give accurate estimations of CCTs. Hence it is expected to be an efficient method. In addition, we find that generally the CCT in renewable dominated power systems is around tens of milliseconds, which is much shorter than that in traditional power systems around hundreds of milliseconds. Therefore, it might be imperative to adopt faster controls and protections for renewable dominated power systems.

Temporary overvoltage assessment and suppression in heterogeneous renewable energy power systems

Temporary overvoltage (TOV) may arise in renewable energy power systems after the fault clearance due to the plant-level delay. It is challenging to evaluate the TOV of a Multi-Infeed Power Electronic System (MIPES) considering the complex interactions among renewable power plants (RPPs). Moreover, the complexity of the evaluation is further increased when the MIPES is heterogeneous, where RPPs have different structures and control parameters. To tackle these challenges, this paper proposes a method to analytically assess TOV in a heterogeneous MIPES based on grid strength analysis. It is derived that different types of RPPs can be equivalent to similar models, i.e., current source parallel reactance. On this basis, it is obtained that the TOV and safety margin of the system can be assessed based on the heterogeneous generalized short-circuit ratio (gSCR-TOVhet) and the critical gSCR (CgSCR). Thereafter, a solution to suppress the TOV based on the configuration of synchronous condensers is proposed, which provides an effective way to improve the voltage safety of the heterogeneous MIPES. EMT simulations based on various test systems are performed to validate the effectiveness of our method.

A Predictive Control Method for LCC HVDC Participated Black Start With Commutation Failure Prevention

Line-commutated converter (LCC) based HVDC systems can significantly speed up the restoration of infeed power systems in blackout states. But they are fragile to commutation failure (CF) under the adverse black-start conditions. To improve the adaptability of LCC HVDC systems in such situations, a predictive control method is proposed in this paper. It includes the linear discrete time predictive model, receding horizon regulator, state estimator, and CF prevention (CFPREV) module. The model is based on the quasi-dynamic and transient-state analysis of load disturbances, where the black-start state is forecasted according to voltage sags caused by inrush currents. The regulator operates in real-time to optimize reference inputs for the HVDC controller. In the estimator, process error and measurement noise are modeled and the optimal system state is estimated with a Kalman filter. Moreover, the dc current setting for CFPREV is calculated using the predicted and estimated state variables. The CFPREV module and regulator work in coordination for secure and fast dc power recovery under abnormal conditions. Small-signal stability analysis and EMT simulations are implemented on the CIGRE benchmark model based black start test grid. The results show that the proposed method i) improves dc power response to black start load startups and ii) presents better recovery performance after the fault.

Phasor and EMT models of grid-following and grid-forming converters for short-circuit simulations

Phasor models have been widely used in short-circuit simulations, in which system operators verify the behaviour of the grid over thousands of different contingencies. However, it is still unclear if phasor models can still be used in fault studies in modern or future power grids dominated by renewable generation with power electronics and converters. Therefore, this paper analyses the suitability of phasor models to simulate short-circuit transients in grids with grid-following (GFL) and grid-forming (GFM) voltage-source converters (VSC). Phasor models of GFL and GFM were developed and tested in two test systems, one with 50% of converters in the generation mix and another powered 100% by converters. Asymmetrical and symmetrical faults were applied at different points of the systems and key variables were used to compare the phasor models against EMT models during the transients. The results showed that, despite neglecting transients in the grid, phasor models could be used in a preliminary stage of short-circuit studies as it was capable of tracking the steady-state value of almost all variables analysed. In this case, detailed EMT simulations, although necessary, would be used only at more advanced stages of the studies.

Parallelization of EMT simulations for integration of inverter-based resources

This paper presents a co-simulation tool to link multiple instances of an electromagnetic transient (EMT) simulation tool for parallel and fast computations. The tool exploits the propagation delays of transmission lines and cables to create network decoupling into several smaller sub-networks. These sub-networks are solved in parallel without approximations. A multi-rate option is also incorporated, in which the sub-networks can use different numerical integration time-steps. The Functional Mock-up Interface (FMI) is used for creating the co-simulation interface between multiple instances according to a master-slave communication scheme and the data sharing method is implemented using low-level synchronization primitives called semaphores. The interfaces between each subnetwork are automatically initialized for time-domain simulations using load-flow results.

Impact of an Unsymmetrical Fault on the Controller of the DFIG Wind Farm

Objectives: DFIG-based wind farms are predominant in their performance when compared to other types of generators. In the field study, due to transient events, converters at the machine side and grid side are affected. To protect the converters from an abnormal operation, overcurrent protective relays have to be designed and incorporated. Unsymmetrical fault analysis are help in the design of protective devise and speed sensors. Methods: DFIG-based wind systems are developed using the DIgSILENT power factory software and EMT simulations are executed during the unsymmetrical faults applied near the Machine Side Converter (MSC) and Grid Side Converter(GSC). Findings: During the simulation studies, various parameters are transient time, maximum current, steady-state, and voltage drop identified near the MSC and GSC. The short circuit parameters are attenuated during the unsymmetrical faults and the rotor maximum current increases by 2 to 3 times the rated current per unit, 40% to 50% voltage dip, and the current reach the steady state value after 1.213 sec during the fault. The parameters are affected more when a fault occurs near the GSC when compared to a fault near MSC. Novelty: These research findings will contribute to a better understanding and improvement of sensor sensitivity, as well as the development of control mechanisms, and protection tactics in designing more accurate and appropriate for DFIG-WT. Keywords: DoublyFed Induction Generator; Machine Side Controller; Grid Side Controller; Unsymmetrical Fault; Sensor

Preventing loss of synchronism of droop-based grid-forming converters during frequency excursions

This short communication addresses the risk of synchronisation loss during frequency excursions for droop-based grid-forming converters when active power limitations are considered. The synchronising capability of this control approach is based on the converter’s active power exchange, which is used to generate the internal frequency of the converter control. The power available in the resource or converter ratings can impact the synchronising capability during frequency deviations. The analysis is restricted to droop-based grid-forming converters, but it could be extended to other active-power-based synchronising methods. A droop-based control is proposed to extend the operation frequency range of grid-forming converters. The performance of the suggested method is also compared to alternative ones presented in the literature. Finally, the proposed control is validated in the IEEE 9-bus system with different VSC penetration levels through EMT simulations developed in PSCAD.

An impedance matrix model of DFIG for harmonic power flow analysis considering DC-link dynamics

The doubly-fed induction generator (DFIG) has been increasingly used in modern power systems for interfacing wind energies.Because of the nonlinear characteristics of the DFIG, it is important to properly model the DFIG when conducting harmonic analysis in power systems. This is especially important for low-order harmonics that are routinely encountered by present power systems. Therefore, this paper presents a model of DFIG for harmonic power flow analysis. The harmonic model of the back-to-back converters, i.e., the combined rotor-side converter (RSC) and grid-side converter (GSC) unit, is first established through mathematical derivations, and the result shows that it can be represented by a coupled impedance matrix, which includes the harmonic coupling between the RSC and the GSC and coupling between different harmonics. The studies also show that the coupling between different harmonics is negligible; thus, a simplified 2 × 2 impedance matrix can be practically used with confidence. After integrating with the induction generator model, a full harmonic model of DFIG can be obtained through circuit analyses. The correctness of the developed model has been verified using EMT simulations and lab experiments. The new model fills in a gap in the modeling of renewable energies for harmonic power flow analysis.

Application of Unscented Transform for Efficient Calculation of Statistics for Electromagnetic Transients

Uncertainties in power system studies are typically managed by Monte Carlo methods or by applying some worst case assumptions. As the number ofuncertainties increases, there is a need for methods that can estimate statistical parameters from a limited number of calculations. This paper utilizes a method called the Unscented Transform together with Cornish-Fisher expansion to estimate the 2%-value of switching overvoltages using only about one tenth the number of calculations as a Monte Carlo method, with similar accuracy. The uncertainties considered are the energizing instants of the three phases. The method is illustrated through EMT simulations in PSCAD and it is shown to provide a good approximation of the 2%-value in most of the studied cases.

An Improved Model of Voltage Source Converters for Power System Harmonic Studies

Voltage source converters (VSCs) have been extensively used in power systems for interfacing renewable energies and other modern loads. Because of their nonlinear nature, a proper harmonic model of VSC devices must be established when conducting harmonic analyses in power systems. This is especially true for low-order harmonics, which are routinely encountered in present power systems. To this end, an analytical harmonic model that represents the low-order harmonic characteristics of VSCs is developed in this paper. The new model takes both the control loop and power loop (i.e., DC-link capacitor) of the VSC into account through rigorous mathematical derivations. The final result has shown that the VSC can be represented by a harmonically coupled impedance matrix at harmonic frequencies, which can be easily used for harmonic analyses of large-scale power systems. It also shows that the DC-link capacitor has a more noticeable impact on the harmonic impedance of VSCs with a smaller DC-link capacitance and low-order harmonics. The appropriateness of the new model was verified using EMT simulations and lab experiments. A complete procedure to construct the proposed VSC model is also established based on the research findings.

Modeling of Non-Characteristic Third Harmonics Produced by Voltage Source Converter under Unbalanced Condition

A three-phase three-wire voltage source converter (VSC) can produce third harmonics when it is operated under an unbalanced condition. It is essential to understand the mechanism of the production of this third harmonic and to assess its impact on power systems. Therefore, this paper presents an analytical model of the VSC under the unbalanced condition through mathematical derivations, and the final model is a coupled Thevenin circuit. The proposed model allows for direct computation of the non-characteristic third harmonics through harmonic power flow studies. The results show that VSC under unbalanced conditions emits both positive-sequence and negative-sequence third harmonics, and that the positive-sequence third harmonic is much larger than the negative-sequence third harmonic. It also shows that the unbalanced level and the size of the dc-link capacitor are critical to the level of non-characteristic third harmonics. The correctness of the proposed model and its application on noncharacteristic third harmonic evaluations have been verified using EMT simulations.

Adaptive Damping Control of Subsynchronous Oscillation in DFIG-Based Wind Farms Connected to Series-Compensated Network

The frequency of subsynchronous oscillation (SSO) in doubly-fed induction generator (DFIG)-based wind farms connected to series-compensated networks is determined by system-wide operating conditions, including the wind speed, number of in-service wind turbines, and degree of series-compensation. This paper proposes an adaptive mitigation scheme to damp the SSO for a full range of subsynchronous frequency variations due to different operating conditions. The proposed scheme comprises 1) a subsynchronous frequency estimator (SSFE) and 2) an adaptive subsynchronous damping controller (ASDC). The SSFE detects the SSO mode and tracks its subsynchronous frequency accurately. The ASDC utilizes voltage signals to extract the SSO at the estimated subsynchronous frequency, generates appropriate current signals, and injects them into the grid through a shunt-voltage sourced converter (SVSC). The ASDC behaves like a variable impedance, which essentially reshapes the system's impedance response by adding a positive resistance at the estimated subsynchronous frequency. The parameters of the phase-shifters are computed using Brent's root-finding method such that the desired phase-shift at the estimated subsynchronous frequency is always maintained. The control's adaptiveness and damping performance under different operating scenarios is verified through extensive EMT simulations on a real-world wind power system facing SSO using PSCAD.

Phase-Unsynchronized Power Decoupling Control of MMC Based on Feedback Linearization

The traditional power decoupling control of modular multilevel converter (MMC) is based on the phase synchronization achieved by the phase-locked loop (PLL), and MMC intricate inner dynamics are ignored, which jeopardizes the system stability and power decoupling. To improve the performance, a nonlinear phase-unsynchronized power decoupling control for MMC is proposed without PLL. At first, the MMC model as a nonlinear multi-input multi-output system is developed. The developed model illustrates that the MMC power coupling is caused by the ac current as well as the MMC capacitor voltages. Then, through the input–output linearization method, the proposed method decouples the MMC output powers without the phase synchronization. Involving integral control, the dynamics of MMC output powers are designed as second-order systems so that the control parameters can be easily determined based on the required transient performance. To verify the accuracy and correctness of the developed model, a comparison of MMC dynamics with the proposed control is conducted between the numerical solution in MATLAB and the EMT simulation in PSCAD/EMTDC. Moreover, seven cases in the EMT simulations and four cases in the experimental results demonstrate the desired phase asynchronization and power decoupling performance of the proposed method compared with the conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> control. At last, the system zero dynamic stability is investigated and the influences of MMC control parameters, ac-side voltage, dc-side voltage and equilibrium points are analyzed to evaluate the stability performance of the proposed method.

Comparison and Selection of Grid-Tied Inverter Models for Accurate and Efficient EMT Simulations

This article compares five modeling methods of grid-tied inverters for the electromagnetic transient simulation of power system, clarifies their differences, and discusses the suitable model for each simulation purpose. The comparison was made under the same conditions between the conventional switching model, and four simplified models—voltage interpolation, average-value, controlled current-injection, and simplified current-injection model. The comparison of the simulated waveforms clarifies the behaviors that can be simulated and cannot be simulated by each simplified model. The comparison of the computing time reveals the significant decrease of the computing time by selecting the proper simplified modeling method. Based on these comparisons, this article discusses the selection of the modeling methods for each simulation purpose to perform simulations accurately and efficiently.

A Comparative Study of Electromagnetic Transient Simulations using Companion Circuits, and Descriptor State-space Equations

This paper investigates an alternative method for EMT simulation of power networks, which uses Descriptor State-space Equations (DSE) to represent the dynamical equations of the circuit. An automated procedure to formulate the DSEs directly from the circuit's netlist is presented. Once formulated, the DSEs can be discretized using the trapezoidal integration method, and subsequently used for EMT simulations. This approach is compared with the widely used Companion Circuit (CC) approach. Advantages and disadvantages of each approach are discussed. Finally, a procedure for interfacing a DSE-based formulation with a CC-based EMT simulator is also presented. This procedure enables interfacing of arbitrary power networks with a commercial CC-based EMT simulation package and can also be used to speed up the simulation using parallel processing.

Simulation of Low Inertia Power Systems Based on Shifted Frequency Analysis

New types of power system transients with lower time constants are emerging due to the replacement of synchronous generation with converter interfaced generation and are challenging the modeling approaches conventionally applied in power system simulation. Quasi-stationary simulations are based on classical phasor models, whereas EMT simulations calculate the instantaneous values of models in the time domain. In addition to these conventional modeling approaches, this paper investigates simulation based on dynamic phasor models, as has been proposed by the Shifted Frequency Analysis. The simulation accuracy of the three modeling approaches was analyzed for characteristic transients from the electromagnetic to the electromechanical phenomena range, including converter control as well as low inertia transients. The analysis was carried out for systems with converter interfaced and synchronous generation whilst considering the simulation step size as a crucial influence parameter. The results show that simulations based on dynamic phasors allow for larger step sizes than simulations that calculate the instantaneous values in the time domain. This can facilitate the simulation of more complex component models and larger grid sizes. In addition, with dynamic phasors, more accurate simulation results were obtained than with classical phasors, in particular—but not exclusively—in a low inertia case. Overall, the presented work demonstrates that dynamic phasors can enable fast and accurate simulations during the transition to low inertia power systems.

Over- and Under-Voltage Containment Reserves for Droop-Based Primary Voltage Control of MTDC Grids

This paper proposes a comprehensive methodology for determining the converter droop settings to ensure the voltage security in multi-terminal direct current (MTDC) grid. The novelty lies in the introduction of the concept of over- and under-voltage containment reserves in analogy to the frequency containment reserves in AC systems. This not only gives a distinction of the contribution between the converters in rectifying and inverting modes, but also significantly facilitates the sizing of necessary amount of reserves within their available headroom capacity of power. In particular, the constraints of converters outages, converter rating, and DC voltage deviations are all taken into account in the design of reserves. The effectiveness of the proposed approach is demonstrated by a contingency power flow analysis algorithm and EMT simulations of a four-terminal MTDC grid.

A Novel Distributed Supplementary Control of Multi-Terminal VSC-HVDC Grids for Rotor Angle Stability Enhancement of AC/DC Systems

This paper presents a distributed supplementary control for embedded Multi-Terminal VSC-HVDC (MTDC) grids to enhance the transient stability of the surrounding AC grid. Firstly, the need of supplementary controllers for embedded MTDC grids is demonstrated via the study of the Transient Energy Functions (TEF) of a simple hybrid AC/DC power system. Then, the proposed control structure is presented. This control aims to enhance the angle stability of the surrounding AC system via the modulation of the active power references of the converters. The objective of the control is to enhance AC transient stability while keeping the power balance of the DC grid even if converters reach their active power limits. The proposed control uses frequency, and angle measurements at the Point of Common Coupling (PCC) of the converters. The idea behind the proposed strategy is to match the control actions, and limits of each pair (i, j) of converters. If converter i modulates its power, converter j modulates the same amount of power in the opposite direction. The concept of virtual links is used in this paper to represent this matching. Finally, the proposed controller is tested on a modified version of the IEEE 39 bus system using EMT simulations.