Low Frequency Oscillation Analysis and Damping Based on Prony Method and Sparse Eigenvalue Technique

This paper investigates the low frequency (<; 30 Hz) oscillations in isolated microgrids (IMGs) with smart loads (SLs) alongside converter-interfaced distributed generators (CDGs) fuelled by renewable energy resources (e.g. wind, solar) with battery energy storage. In an IMG with normal loads (active or passive), such oscillations are typically associated with the droop control of the CDGs operating in grid forming mode. This paper shows that SLs have marginal influence on these low frequency oscillations but introduce a new oscillatory mode at a slightly higher frequency (> 20 Hz). First, the stability analysis model (linearized state-space model) of an IMG is extended to include the dynamics of a smart load with a series-shunt converter arrangement in its voltage compensator. It is shown that the dynamics of the phase-locked loop (PLL), DC link along with the control loops of the series and shunt converters of the smart load dictates the lower limit of its droop gain for stable operation. This is not apparent from the simplified SL models (i.e. neglecting the dynamics of the shunt converter and DC link) reported previously. Impact of smart loads on low frequency oscillations in IMGs is demonstrated in this paper through stability analysis and time domain simulation.

The interconnected European power system is evolving due to the new extensions and to the systematic integration of Power Park Modules, i.e., unit or ensemble of units generation electricity (Renewable Energy (RE), Distributed Generation (DG), etc), which is connected to the grid by power electronics and FACTS (STATCOM, HVDC,…). As a consequence, the increase of the size and the emergence of the new oscillatory modes which involve distant dynamic devices, i.e., of coupling modes (modes associated to generator/turbine inertia, and modes associated to Power Park Modules), and of modes related to various regulations. In this paper, a full scan of European power system is given. An exhaustive method that determines all oscillatory modes independently of the system’s order, of the topology and without a priori knowledge about the system, is used. The exhaustive method is fully analytic. Indeed, it is based only on the state-space realisation of any given power system and does not require operator manipulation like dynamic simulations. To this end, we quantify and analyse the interaction between the different inputs/outputs of a given system. This leads to the identification of classes of coupled dynamic devices of the power system. Next, starting from a reduced number of classes, a selective modal analysis method is applied to each class to put into evidence a good approximation of all oscillatory modes. Finally, a complete classification of the oscillatory modes found at the previous stage is provided in terms of the types (interarea, electrical,…) and their characteristics (oscillation frequency, damping, participation,…). 2900 oscillatory modes were found for the studied model of the European system.

In this paper, a new method for analyzing low-frequency oscillation between analytic areas based on energy coefficient is proposed. The concept of energy coefficient is proposed by constructing the energy function, and the low-frequency oscillation is analyzed according to the energy coefficient under the current operating conditions; meanwhile, the concept of model energy is proposed to analyze the energy exchange behavior between two generators. Not only does this method provide an explanation of low-frequency oscillation from the energy point of view, but also it helps further reveal the dynamic behavior of complex power systems. The case analysis of four-machine two-area and the power system of Jilin Power Grid proves the correctness and effectiveness of the proposed method in low-frequency oscillation analysis of power system.

Power systems have an increasing demand for operational condition monitoring and safety control aspects. Low-frequency oscillation mode identification is one of the keys to maintain the safe and stable operation of power systems. To address the problems of low accuracy and poor anti-interference of the current low-frequency oscillation mode identification method for power systems, a low-frequency oscillation mode feature identification method combining the adaptive variational modal decomposition and sparse time-domain method is proposed. Firstly, the grey wolf optimization algorithm (GWO) is used to find the optimal number of eigenmodes and penalty factor parameters of the variational modal decomposition (VMD). And the improved method (GWVMD) is used to decompose the measured signal with low-frequency oscillations and then reconstruct the signal to achieve a noise reduction. Next, the processed signal is used as a new input for the identification of the oscillation modes and their parameters using the sparse time-domain method (STD). Finally, the effectiveness of the method is verified by the actual low-frequency oscillation signal identification in the Hengshan power plant and numerical signal simulation experiments. The results show that the proposed method outperforms the conventional methods such as Prony, ITD, and HHT in terms of modal discrimination. Meanwhile, the overall reduction in the frequency error is 34, 44, and 21%, and the overall reduction in the damping error is 37, 41, and 18%, compared with the recently proposed methods such as the EFEMD-HT, RDT-ERA, and TLS-ESPRIT. The effectiveness of the methods in suppressing the modal confusion and noise immunity is demonstrated.

In recent years, machine learning (ML) tools have gained tremendous momentum and received wide-spread attention in different segments of modern-day life. As part of digital transformation, the power system industry is one of the pioneers in adopting such attractive and efficient tools for various applications. Apparently, a nonthreatening, but slow-burning issue of the electric power systems is the low-frequency oscillations (LFO), which, if not dealt with appropriately and on time, could result in complete network failure. This paper addresses the role of a prominent ML family member, particle swarm optimization (PSO) tuned adaptive neuro-fuzzy inference system (ANFIS) for real-time enhancement of LFO damping in electric power system networks. It adopts and models two power system networks where in the first network, the synchronous machine is equipped with only a power system stabilizer (PSS), and in the other, the PSS of the synchronous machine is coordinated with the unified power flow controller (UPFC), a second-generation flexible alternating current transmission system (FACTS) device. Then, it develops the proposed ML approach to enhance LFO damping for both adopted networks based on the customary practices of statistical judgment. The performance measuring metrics of power system stability, including the minimum damping ratio (MDR), eigenvalue, and time-domain simulation, were used to analyze the developed approach. Moreover, the paper presents a comparative analysis and discussion with the referenced works’ achieved results to conclude the proposed PSO-ANFIS technique’s ability to enhance power system stability in real-time by damping out the unwanted LFO.

Flexible AC Transmission System (FACTS) controllers are advanced power electronic devices employed in electrical power systems to enhance system stability, reliability, and power transfer capabilities. These controllers enable dynamic and flexible control of various transmission parameters such as voltage, current, impedance, and phase angle, thereby improving the overall power system performance. FACTS devices are broadly classified into series, shunt, series- series, and series-shunt configurations, each designed to manage reactive power and regulate voltage either by injecting voltage in series or current in shunt with the transmission line. Well-known FACTS devices include Static Var Compensators (SVC), Static Synchronous Compensators (STATCOM), Thyristor Controlled Series Capacitors (TCSC), Static Synchronous Series Compensators (SSSC), and Unified Power Flow Controllers (UPFC), each serving specific roles in power flow control, voltage regulation, and transient stability enhancement. The integration of these controllers provides significant benefits such as increased transmission line capacity, improved voltage stability, minimized transmission losses, and damping of power system oscillations. They are capable of rapid response during transient disturbances, effectively mitigating voltage collapses and enhancing system resilience against faults and contingencies. FACTS controllers not only improve steady-state operational parameters but also address dynamic stability and transient conditions, enabling power systems to operate closer to their stability limits while maintaining security. Their deployment helps avoid costly infrastructural expansions by optimizing existing transmission assets, which is critical given environmental and economic constraints. Recent advances in semiconductor technologies and control algorithms have made FACTS devices more reliable, efficient, and adaptable to modern grids, including renewable integration and deregulated power markets. In summary, FACTS controllers play a vital role in modern power systems by providing flexible, efficient, and reliable solutions for power flow management, voltage control, and system stability enhancement, thereby supporting the evolving demands of today's complex electrical networks.

In recent year, renewable energy sources like wind and solar photovoltaic (PV) are rapidly evolving worldwide. Accordingly, fossil energy based conventional generators are being replaced by renewable energy sources for powering electric production in smart grid. Some low inertia issues will be brought in future smart grid and will affect system frequency stability. An estimation method of dominant electromechanical oscillation (EMO) mode based on synchrophasor data of low inertia power system is proposed. A power system with a lot of renewable energy sources tends to have low inertia power system, an accurate estimated model is difficult to achieve by existing methods, i.e., Simplified Oscillation mode (SOM) and Prony methods, because of high fluctuation of system frequency. The proposed method is developed by observing decaying signal period. Then, a dominant oscillation mode is evaluated based on the proposed method to obtain dominant frequency and damping factor. Finally, the effectiveness of proposed method is examined via traditional and low inertia power systems based on simulated synchrophasor data of a two-area smart grid, and comparisons between proposed method and existing method is also discussed.

This paper presents a dynamic model of the equivalent Great Britain (GB) 36-zone power system, which can be used for reliable and realistic assessment of emerging load frequency control mechanisms. Flexible architecture of the presented dynamic test system permits a broad range of security of supply and small-signal stability studies for design of future power grids. It can be particularly useful for academic research, but also for undertaking feasibility studies in power industries. The proposed dynamic test system, which is obtained through network reduction of the original full-scale GB transmission power system developed by National Grid Electricity System Operator (NGESO) Company, provides detailed information about the GB power system. In this regard, the required data and modelling approaches to develop the 36-zone system are provided in detail. The presented dynamic test system represents the system topology, impedance characteristics and electromechanical oscillations of the original GB power system however, it is not an exact equivalent of the master GB system. Illustrative dynamic models of the key system components, including synchronous generators, automatic voltage regulators, power system stabilizers, hydro and steam turbines models along with speed governing systems are presented. Dynamic behavior of 36-zone test system in response to infeed loss contingencies is investigated. Particularly, the impact of changes in the system inertia on the system electromechanical modes is examined using the modal analysis approach. In this context, the mode shape concept is employed to determine dominant generators and contribution of different zones in the low frequency oscillations. Moreover, time-domain simulations are undertaken to validate the modal analysis results. Additionally, the condition of different zones from the viewpoint of frequency nadir and maximum rate of change of frequency for various contingencies and extreme cases are examined.

Traditionally, the linear analysis of a power system is performed by first computing a state space model, followed by the application of a suitable analysis method. However, the applicability of this approach is restricted by several practical limitations: typical power systems are represented by very large state matrices that require specialized large-scale eigen analysis programs; the program where the power system models reside does not include linearization capabilities; only time domain data is available. This article illustrates the applicability of a new system identification software program, SYSID, developed to circumvent these limitations. The program incorporates several identification techniques that allow for the computation of equivalent linear models, suitable for control design applications, from time domain simulation data. The program has been used to calculate equivalent models from simulations performed with standard stability programs, as well as from the Electromagnetic Transient Program (EMTP) simulations of detailed three-phase power systems. The equivalent systems are small and retain the modal characteristics of the original system. The identification techniques are based on various algorithms including Prony's method, transfer function fitting, and Hankel matrices. In addition to the identification algorithms, the program also includes signal processing, plotting, modal analysis functions, and basic control design capabilities to assess closed loop system performance.

A novel tool for transient stability analysis of large-scale power systems: Its application to the KEPCO system

This paper presents a new method to suppress low frequency oscillation based on wide-area measurement. Since negative damping low frequency oscillation is usually caused by large disturbance that deteriorates system damping, relationships between oscillation modes and fault components are established through time-domain simulation. Then, abrupt change in electrical quantity of related components will be detected to distinguish negative damping low frequency oscillation and forced power oscillation. Forced power oscillation can be suppressed by isolating the disturbance source. However, direction of the oscillation energy flow can only identify multiple suspected areas when wide-area measurement is limited. Phase of tie-line active power for each suspected area is calculated during propagation stage to determine the area containing disturbance source. Dispatching actions should be given to enhance the system damping to secure value for low frequency oscillation. Therefore, control strategy is calculated to improve the damping of weakly damped modes to different values through online small signal stability analysis. Appropriate actions can be selected based on real-time measured dominant oscillation mode. Real engineering applications have fully confirmed the validity and practicability of this method.

The problem of low-frequency power swings is a matter of concern for power systems engineers in the operation and planning of power systems. Therefore, this paper is an investigation of the use of unified power flow controller (UPFC) that is suitably tuned to improve the damping of low frequency power oscillations present in Nigerian grid system. A large disturbance is initiated, during simulation in PSAT, in the network to induce nonlinear oscillations of the power system in order to ascertain the damping effect of UPFC. The dynamic responses of the system simulated show that the system is well damped and is stabilized at minimal time which confirms the robustness of the UPFC. Finally, a comparative study in a typical transient stability problem on IEEE 14-bus system using a UPFC model and the Nigerian high voltage interconnected system is used to illustrate the concepts presented in this paper. Key words: Power oscillation damping, power systems, unified power flow controller (UPFC), flexible AC transmission system (FACTS) devices, low frequency oscillation

In this paper, an investigation into the use of Flexible ac Transmission Systems (FACTS) devices to aid damping of low-frequency inter-area oscillations in longitudinal power systems is presented. A linear model of VSC-based FACTS devices that takes into account the dynamics of dc links is developed and incorporated into a production-grade software for small signal analysis of large power systems. Based on this representation, a unified framework for modal power oscillation flow studies is then developed to analyze the sensitivity of modal behavior to FACTS control action. With this method, the transmission corridors and system parameters having a large contribution to critical system oscillations modes are determined. The method is particularly well suited for investigating inter-system oscillations in large-scale power systems with embedded FACTS controllers The utilized methodology is tested on a practical 45-machine Mexican system that includes several major static VAR compensators. Control mode implementations are discussed and tested and comparisons with existing technologies are presented.

In this paper, a robust method for the simultaneous coordinated design of the interline power flow controller (IPFC) and power system stabilizer (PSS) based on output feedback controllers in a single-machine infinite-bus power system for the enhancement of power systems low-frequency oscillations damping is presented. The Honey Bee Algorithm, which has a strong ability to find the most optimistic results, is employed to search for optimal IPFC and PSS output feedback controller parameters. A singular value decomposition method is utilized to select the most effective damping control signal of the IPFC output feedback controller. To assess the effectiveness and robustness of the proposed method, simulation studies are carried out for three operating conditions. Analysis of the results shows that the combined design has an excellent capability for damping a power system’s low-frequency oscillations. Moreover, system performance analysis under different operating conditions and performance indices shows the effectiveness of the proposed method even when a severe fault is applied.

Low frequency oscillations (LFOs) in interconnected multi-machine power systems is a major concern in viewpoint of power system dynamic stability. Proposing high performance power system stabilizers (PSSs) to mitigate efficiently the LFOs is an attractive subject which has found remarkable consideration in latter literature. Owing to high potential of fractional order controllers (FOCs), a tilt-integral-derivative (TID) assisted stabilizer is proposed here. In doing so, IEEE type PSS2B is modified to establish a TID-based PSS2B stabilizer. The dynamic performance of the suggested TID-PSS2B is investigated in comparison with an ingeter order proportional integral derivative (PID) based PSS2B counterpart and a former TID-PSS. The objective of this paper is to improve the small-signal stability of an interconnected power system via preparing further damping torque to suppress the LFOs. The design procedure of the TID-PSS2B is mathematically formulated as a minimization problem with the aim of decreasing the machines speed deviations. An improved particle swarm optimization (IPSO) algorithm is used to find optimal parameters of the presented stabilizer. The time domain simulation results reveal that by employing the suggested TID-PSS2B, the speed oscillations are suppressed effectively. Furthermore, to evaluate the robustness behavior of the presented controller, sensitivity analysis is carried out.