Nonlinear Time-domain Simulation Research Articles

New Insights Into Coupled Frequency Dynamics of AC Grids in Rectifier and Inverter Sides of LCC-HVDC Interfacing DFIG-Based Wind Farms

Coupling between frequency dynamics of the ac systems on both inverter and rectifier sides of the line-commutated converter HVDC with the rectifier station operating in frequency control is studied, along with the presence of large DFIG-based wind farms on the weak rectifier-side grid. An averaged model with 79 states, which includes dynamic models of grids on the rectifier and inverter sides, phase-locked loop, and the wind farm is derived. To develop a deeper understanding of the frequency dynamics, a simplified four-state nonlinear model is proposed, which, in turn, reveals strong coupling between frequency and ac voltage at the HVDC rectifier terminal. A firing angle correction strategy is proposed to decouple frequency–voltage interactions, thereby improving the frequency dynamics on the rectifier side. The four-state model is linearized to ascertain the interaction between rectifier- and inverter-side frequencies, and an analytical expression for the frequency dynamics in terms of gains of the frequency controller at the rectifier station is derived. Moreover, the proposed reduced-order model shows the implications of frequency droop control of the wind farms in improving frequency dynamics on both rectifier and inverter sides. Expressions for “synchronizing” and “damping torque” contribution from HVDC and wind farm are also established. The analytical expressions and the effectiveness of the proposed strategies are validated through nonlinear time-domain simulations.

Design of Wide-Area Damping Controllers Incorporating Resiliency to Permanent Failure of Remote Communication Links

The synchrophasor data provided by wide-area measurement systems have potential applications in electric power systems such as the use of these measurements as control inputs of wide-area damping controllers (WADCs) for small-signal stability enhancement. However, synchrophasor data are particularly vulnerable to cyber attacks (such as denial-of-service attacks) that can cause communication link failures in a smart grid communication network and, consequently, compromise the power system stability. In order to reduce the impact of communication failures on the performance of a WADC, this paper proposes a method to design a WADC considering robustness to multiple operating points, time delays in the communication channels and possible permanent loss of communication signals in the input and the output of the controller (which may be due, e.g., to denial-of-service cyber attacks). The performance of the designed controller is evaluated using modal analysis and nonlinear time-domain simulations in one of the IEEE benchmark systems to validate the results: the Simplified 14-Generator Model of the Southeastern Australian Power System.

Wide-Area Damping Control Using Multiple DFIG-Based Wind Farms Under Stochastic Data Packet Dropouts

Data dropouts in communication network can have a significant impact on wide-area oscillation damping control of a smart power grid with large-scale deployment of distributed and networked phasor measurement units and wind energy resources. Remote feedback signals sent through communication channels encounter data dropout, which is represented by the Gilbert-Elliott model. An observer-driven reduced copy (ORC) approach is presented, which uses the knowledge of the nominal system dynamics during data dropouts to improve the damping performance where conventional feedback would suffer. An expression for the expectation of the bound on the error norm between the actual and the estimated states relating uncertainties in the cyber system due to data dropout and physical system due to change in operating conditions is also derived. The key contribution comes from the analytical derivation of the impact of coupling between the cyber and the physical layer on ORC performance. Monte Carlo simulation is performed to calculate the dispersion of the error bound. Nonlinear time-domain simulations demonstrate that the ORC produces significantly better performance compared to conventional feedback under higher data drop situations.

Nonlinear analysis of sloshing and floating body coupled motion in the time-domain

The aim of this paper is to develop a coupled nonlinear time-domain simulation scheme for nonlinear interactions among sloshing flows and floating body motion for both regular and irregular wave excitation. The contributions of a variety of nonlinear factors, outside waves and inside sloshing induced forces, as well as their influences on body coupled sway and roll motion were investigated. The induced forces are due to the changes in the transient wet surface of the floating body and full nonlinear sloshing. The effects of tank fill ratio and excitation wave height on the nonlinear coupled motion, as well as the relationship between sloshing and floating body nonlinear coupled motion under large wave amplitudes and severe sea conditions were also investigated and the results are presented. Finally, the numerical solutions are compared with existing experimental result. The fully nonlinear sloshing and floating body coupled motion are simulated based on the potential flow theory, with the transient position hydrodynamic assumption. The boundary value problem is solved by the B-spline higher-order panel method. The ISITIMFB (iterative semi-implicit time integration method for floating bodies) is applied to solve for the body's velocity and displacements. The sloshing energy dissipation is modeled by changing the boundary condition on the tank's solid boundaries. An extended principle to determine the energy dissipation coefficient for both regular and irregular cases is extracted. Then, the sloshing and floating body nonlinear coupled motion under large wave amplitudes and severe sea conditions are investigated, and the numerical solutions are compared with existing experimental results. The effects of tank fill ratio and excitation wave height on the nonlinear coupled motion is also investigated.

Fractional‐order lead‐lag compensator‐based multi‐band power system stabiliser design using a hybrid dynamic GA‐PSO algorithm

Power system stabilisers (PSSs) are supplementary controllers connected to the excitation system of synchronous generators to damp electromechanical oscillations. Multi-band PSSs are reported as advanced PSSs with the ability to damp out all oscillation modes present in the power systems. This study presents the design of a robust fractional-order multi-band power system stabiliser (Fo-MBPSS) using a meta-heuristic hybrid algorithm for dynamic stability improvement of multi-machine power systems. The large bandwidth, memory effect and flat phase contribution in the frequency response of fractional-order controllers are exploited to make the Fo-MBPSS perform well against a wide range of system uncertainties. The parameter tuning problem of Fo-MBPSS is transformed to an optimisation problem that is solved using a hybrid algorithm by combining a dynamic genetic algorithm (DGA) with a standard particle swarm optimisation (PSO) algorithm. The performance of the proposed DGA-PSO-Fo-MBPSS is evaluated through eigenvalue analysis, non-linear time-domain simulations and some performance indices, in two different multi-machine systems under different loading conditions and disturbances. The results are compared with PSO-based conventional MBPSS and PSO based Fo-MBPSS (PSO-Fo-MBPSS) to establish the fractional parameter effect on the improvement of the system dynamic response and the relevance of the proposed hybrid optimisation technique in achieving robustness.

Decentralized frequency-voltage control and stability enhancement of standalone wind turbine-load-battery

This paper simulates an islanding network including wind turbine, battery energy storage systems (BESS), and load. The purpose is to control voltage and frequency of the load following wind speed variations by proper control of BESS. A decentralized control scheme including two control loops is designed on BESS. One control loop is implemented for voltage regulation and the other loop is designed for frequency control. Both loops are equipped with PI (Proportional–Integral) type controllers as internal controllers. Furthermore, both loops are equipped with supplementary stabilizers as external controllers. The internal controllers regulate frequency and voltage and the external stabilizers enhance stability. This paper optimally tunes all the parameters of internal controllers and external stabilizers at the same time. The problem for tuning a large number of the design variables is mathematically expressed as a mixed integer nonlinear optimization programming and solved by modified-adaptive PSO technique. The proposed methodology is simulated on a typical standalone network including wind turbine, BESS, and load. The accurate model of BESS and wind turbine is incorporated to cope with real conditions. Moreover, in order to demonstrate the real-world results, non-linear time domain simulations are carried out in MATLAB software. The results verify that the proposed control scheme can efficiently utilize BESS to control voltage, regulate frequency, and damp out oscillations under wind and load variations.

Identification of the Most Effective Point of Connection for Battery Energy Storage Systems Focusing on Power System Frequency Response Improvement

With the massive penetration of intermittent generation (wind and solar), the reduction of Electrical Power Systems’ (EPSs) inertial frequency response represents a new challenge. One alternative to deal with this scenario may be the application of a Battery Energy Storage System (BESS). However, the main constraint for the massive deployment of BESSs is the high acquisition cost of these storage systems which in some situations, can preclude their use in transmission systems. The main goal of this paper is to propose a systematic procedure to include BESSs in power system aiming to improve the power system frequency response using full linear models and geometric measures. In this work, a generic battery model is developed in a two-area test system with assumed high wind penetration and full conventional generators models. The full power system is linearized, and the geometric measures of controllability associated with of the frequency regulation mode are estimated. Then, these results are used to identify the most effective point of connection for a BESS aiming at the improvement of the power system frequency response. Nonlinear time-domain simulations are carried out to evaluate and validate the results.

Analysis and Mitigation of Interaction Dynamics in Active DC Distribution Systems With Positive Feedback Islanding Detection Schemes

The direct current (DC) technology has gained significant momentum in modern distribution systems due to the high penetration levels of dc loads and dc-based distributed generators (DGs). Unlike conventional ac distribution systems, dc distribution systems have the following distinct features that challenge the system stability. 1) The high penetration level of tightly regulated converters used to interface both DGs and loads yields a destabilizing constant power load (CPL) effect in a considerable range of frequencies. 2) The filtering inductors and capacitors form poorly damped LC networks that interact negatively with the CPLs leading to further deterioration of the system stability. 3) Because islanding in a dc system can be hardly detected with passive methods due the absence of the frequency and reactive power terms, DGs are usually equipped with active islanding detection methods to detect the grid disconnection state; however, the islanding detection schemes could negatively impact the distribution system stability. The analysis and mitigation of undesirable interaction dynamics in a dc distribution system considering the aforementioned practical characteristics are not reported in the current literature. In this paper, the interaction dynamics of a dc distribution system characterized by a high penetration level of CPLs, and DGs equipped with positive feedback islanding detection scheme are investigated. The factors affecting the system stability with a single and multiple DGs are thoroughly addressed. Further, a stabilizing compensation loop is proposed to mitigate the stability problems and poor damping capability. Detailed time-domain nonlinear simulations and experimental results validate the analytical results.

Fully nonlinear simulation of wave interaction with a cylindrical wave energy converter in a numerical wave tank

Convergence and accuracy of fully nonlinear time-domain simulation of wave interaction with a submerged cylindrical wave energy converter oscillating about an off-center axis which was conducted using a two-dimensional numerical wave tank are examined in this study. A high-order boundary element method is used to compute the fluid flow in the Eulerian frame. Fully nonlinear boundary conditions are applied to achieve the unique solution of the boundary value problem. Hence, kinematics of the fluid particles on the exact free surface boundary is calculated using the material node approach in the Lagrangian frame. Runge-Kutta time integration is employed to update the boundary values and the computational control volume. To implement the body condition, the time derivative of the velocity potential is computed implicitly using the acceleration potential. An artificial wave maker and two artificial sponge layers are provided to retain the open water condition. The power absorption efficiency of the submerged Bristol cylinder is compared with experimental data and numerical solutions for different incident waves to verify the present numerical model and the accuracy of the solution is also investigated. The convergence of the present fully nonlinear model in the simulation of the freely rotating cylinder about the off-centered axis as a wave energy converter is evaluated for different submergence depths, off-center distances, and a robust nonlinear incident wave.

Nonlinear Robust Approaches to Study Stability and Postcritical Behavior of an Aeroelastic Plant

Two approaches to tackle the nonlinear robust stability problem of an aerospace system are compared. The first employs a combination of the describing function method and $\mu $ analysis, while the second makes use of integral quadratic constraints (IQCs). The model analyzed consists of an open-loop wing’s airfoil subject to freeplay and linear time-invariant parametric uncertainties. The key steps entailed by the application of the two methodologies and their main features are critically discussed. Emphasis is put on the available insight on the nonlinear postcritical behavior known as limit cycle oscillation. It is proposed a strategy to apply IQCs, typically used to find absolute stability certificates, in this scenario, based on a restricted sector bound condition for the nonlinearity. Another contribution of this paper is to understand how the conservatism usually associated with the IQCs multipliers selection can be overcome by using information coming from the first approach. Nonlinear time-domain simulations showcase the prowess of these approaches in estimating qualitative trends and quantitative response’s features.

Optimal Location of STATCOM based Dynamic Stability Analysis tuning of PSS using Particle Swarm Optimization

Recent days in the field of power electronics are provided an appropriate place in order to using of Flexible AC transmission system in power system network. The FACTS devices have an ability to preserve the synchronism of generators under all kind of disturbance. The FACTS i.e static synchronous compensation (STATCOM) can play vital role to enhance dynamic stability in power system. In this paper introduces the concept of voltage stability and rotor angle improvement through tuning of PSS and optimal location of STATCOM is investigated. The performance of PSS with STATCOM has been carried out for Western Science Coordinated Council (WSCC) 9 bus system for the enhancement of dynamic stability using power system analysis tool box (PSAT) software. The effect of PSS with STATCOM is implemented in non-linear time domain simulation. The particle swarm optimization algorithm is developed for optimal location of STATCOM to improve voltage profile in the system.

Stability Analysis of Wide Area Damping Controllers with Multiple Time Delays

Abstract The paper discusses the impact of multiple time delays on the stability of centralized wide area damping controllers (WADCs). These controllers are utilized in electric power systems to damp the interarea oscillations. With this aim, an ideal WADC is first designed based on the well-known H∞ control scheme. Then delays are included for all remote signals of the WADC and different delay models, namely, constant, stochastic and periodic delays with dropout, are considered and compared. Both nonlinear time domain simulations and closed-loop eigenvalue analysis based on the 2-area test system are carried out. Finally, a probabilistic method to evaluate the impact of stochastic communication delays on small-signal stability is discussed.

An Improved LMI-based Approach for the Design of Power System Damping Controllers

Abstract This paper presents a less conservative LMI-based method for the coordinated design of robust decentralized damping controllers in the power systems context. The algorithm results from modifications made in a previous LMI design procedure widely explored in the literature. More precisely, slack variables are introduced in the synthesis procedures to remove structural constraints on the Lyapunov matrix, potentially reducing the conservativeness inherent in this type of approach. The advantage of the proposed technique is verified in an IEEE benchmark power system application and the designed controller performance is observed with eigenvalue analyses and non-linear time domain simulations.

Stability of Renewable Energy based Microgrid in Autonomous Operation

Abstract This paper develops a comprehensive small-signal model of hybrid renewable-energy-based microgrid (MG) in an attempt to perceive oscillatory stability performance and capture the potential interaction between low-frequency critical modes within the MG. Trajectories of sensitive modes due to controller gain variations were evaluated in order to determine the stability boundaries. It was noticeable that various power-sharing schemes significantly influenced the small-signal stability of MG. Moreover, modal interaction emerged due to the proximity of RES-based DG units and non-linear dynamic behaviour of the sensitive modes. The interaction may result in a more oscillatory situation which potentially leads to instability of MG. The low-frequency critical modes obtained from eigenvalues analysis were then verified with the help of nonlinear time domain simulations. The presented work contributes to enhance the design and tuning of controller gain and propose appropriate power-sharing scheme within MG.

Volterra approach – a new method to accurately calculate the non-linear and time-varying roll restoring arm of ships in irregular longitudinal seas

ABSTRACTWith several incidents of large amplitude roll motion of ships observed at sea over the past two decades, the dynamic stability of modern ship types has assumed significant importance. The move by the International Maritime Organization to develop a second generation level-2 criteria has resulted in considerable attention to the development of simplified analytical models for roll motion. Especially for the problem of parametric roll, there is still no analytical model which accurately captures the non-linear roll restoring stiffness taking into account the combined effect of incident waves and dynamic heave and pitch motions of the vessel. This paper extends our previous work to accurately capture both the linear and higher-order time-varying roll stiffness coefficients through an analytical model while taking into account incident waves and dynamic motion of the vessel. This approach called the Volterra method is compared against the existing simplified models and a non-linear time-domain simulation program to demonstrate better agreement of the proposed approach.

A latencies tolerant model predictive control approach to damp Inter-area oscillations in delayed power systems

Automatic voltage regulators and power system stabilizers have been employed successfully to deal with fast dynamics associated to local oscillations phenomena. Whereas, inter-area oscillations damping in large power systems requires remote feedback controllers fed by Wide Area Monitoring Systems (WAMS). Although these improvements in the inter-area oscillations behavior have been effective, a new challenge emerges: reaching stability with a closed loop control despite latencies due to measurements taken far away from the control centre. The research was motivated by the need for modernization of power systems capable of dealing with control difficulties in centralised WAMS for damping inter-area oscillations in power systems caused by delays in the communication system. Herein, time delay and control problems are addressed separately. The time delay problem is solved by a database based time compensation solution relying on the most updated available state of the system. The control problem is solved by a Model Predictive Control (MPC) with terminal cost and constraint set to handle complexities due to nonlinearities of the power system, the large scale of the problem and the parametric variations. Both solutions work in a coordinated way with local controllers to implement a decentralised coordinated strategy that manages slow global dynamics and fast local dynamics as well. The integrated proposed approach is called Time-Delay-Tolerant Model Predictive Control (TDT-MPC). Coordinated and coherent performance of the two TDT-MPC components (Kalman compensator and MPC) is achieved thanks to unifying power system reference models for both strategies. The approach has been tested on the IEEE 39 system and validated with time domain nonlinear simulations, obtaining post-fault damped oscillations and a good tracking of new power references when tripping tie lines.

Estimation of Short-and Long-Term Probability Distributions of Wave-Induced Loads Acting on a Cruise Vessel in Extreme Seas

A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude–Krylov forces, hydrostatic forces, and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses, and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces. The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The short-term nonlinear responses are represented by empirical probability distributions, obtained from the nonlinear time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data. Finally, the long-term value of the bending moment is calculated from the short-term distribution of the nonlinear loads in a few extreme sea states selected based on coefficient of contribution method, and the results are compared with the International Association of Classification Societies (IACS) rule bending moment.

An optimization methodology of susceptance variation using lead-lag controller for grid connected FSIG based wind generator system

In wind power system, low frequency oscillations are observed due to imbalance between mechanical input and electrical output. Hence, variable susceptance controllers are being adopted to mitigate these oscillations. However, improper modulation of control parameters also leads to system instability. Therefore, we propose an optimization methodology for mitigating low frequency oscillations in wind power generation system. To visualize our methodology, we use a lead-lag type variable susceptance controller for fixed speed induction generator (FSIG) based wind generation system. Then, we optimize gain and time constants of lead-lag controller using three optimization algorithms: particle swarm optimization (PSO), genetic algorithm (GA), and flower pollination algorithm (FPA). Later, we perform non-linear time domain simulation and quantitative analysis to find average fitness, standard deviation, run time, and iteration number for these optimization algorithms. Moreover, non-parametric statistical analysis, such as Kolmogorov–Smirnov and Wilcoxon signed-rank tests are employed for identifying statistically significant differences among these algorithms.

Optimal Fuzzy Controller Based on Chaotic Invasive Weed Optimization for Damping Power System Oscillation

This paper proposed an optimal fuzzy controller for damping the power system oscillation in multi-machine environment. In this strategy, the proposed controller is optimized by new chaotic invasive weed optimization algorithm. Furthermore, a new objective function has been considered to test the proposed controller in different load conditions which increase the stability of system after disturbances. For this purpose, the damping factor, damping ratio, and a combination of the damping factor and damping ratio were analyzed and compared with the proposed objective function. The effectiveness of the proposed strategy has been applied in two multi-machine power system test cases as three machine 9-bus IEEE standard and 10-machine 39-bus New England power systems. The eigenvalue analysis and nonlinear time-domain simulation results proof the effectiveness of the proposed strategy.

Design of Coordinated Decentralized Damping Controllers for Power Systems Considering Uncertainties

This paper presents an analytical method based on the solution of the nonlinear Riccati equation for the design of coordinated, decentralized damping controllers for power systems. While other approaches use analytical methods that ensure robustness with respect to uncertainties in the system operating conditions by considering a controller of the same order as the plant, which results in high-order controller structures, the proposed method has the advantage of providing robust and decentralized low-order controllers. The method is applied to two IEEE benchmarks, and the designed controllers are assessed by modal analysis and nonlinear time-domain simulation.