Small-signal stability and time-domain analysis of delayed power systems

This chapter describes the impacts that time delays in feedback have on small signal as well as transient stability of power systems. We present a power system model comprising of delay differential-algebraic equations (DDAEs) and describe general techniques to compute the spectrum of DDAE and to integrate such equations in time domain. The focus is on delays arising in measured signals, e.g., remote frequency measurements for power system stabilizers (PSS) of synchronous machines. Several examples based on a benchmark system, the IEEE 14-bus test system, as well as a real-world system are discussed and analysed.

This paper investigates the transient stability of power systems co-dominated\nby different types of grid-forming (GFM) devices. Synchronous generators (SGs\nand VSGs) and droop-controlled inverters are typical GFM devices in modern\npower systems. SGs/VSGs are able to provide inertia while droop-controlled\ninverters are generally inertialess. The transient stability of power systems\ndominated by homogeneous GFM devices has been extensively studied. Regarding\nthe hybrid system jointly dominated by heterogeneous GFM devices, the transient\nstability is rarely reported. This paper aims to fill this gap. It is found\nthat the synchronization behavior of the hybrid system can be described by a\nsecond-order motion equation, resembling the swing equation of SGs. Moreover,\ntwo significant differences from conventional power systems are discovered. The\nfirst is that the droop control dramatically enhances the damping effect,\ngreatly affecting the transient stability region. The second is that the\nfrequency state variable exhibits a jump at the moment of fault disturbances,\nthus impacting the post-fault initial-state location and stability assessment.\nThe underlying mechanism behind the two new characteristics is clarified and\nthe impact on the transient stability performance is analyzed and verified. The\nfindings provide new insights into transient stability of power systems hosting\nheterogeneous devices.\n

Braking resistor is a very powerful tool to improve transient stability in a power system. Usually, a fixed value of the braking resistor is considered for the transient stability analysis. However, when the braking resistor is in operation, temperature of the resistor material rises above ambient temperature which ultimately causes the resistance value to increase. This paper analyzes the effect of the temperature rise of the fuzzy logic-controlled braking resistor on the transient stability in a multimachine power system. The performance of the braking resistor scheme with fuzzy controller is compared to that of with conventional proportional-integral-derivative (PID) controller. Simulation results of both balanced and unbalanced faults at different points in the system indicate that the temperature rise of the fuzzy logic-controlled braking resistors has little or almost no effect on the transient stability of the multimachine power system. Moreover, it is found that the performance of fuzzy logic controller is better than that of conventional PID controller. Thus, the proposed fuzzy control strategy provides a simple and effective method of transient stability enhancement.

With large wind energy integration into power systems, wind farms begin to influence power systems in a much more significant manner. As wind energy systems utilize different generator technologies from the one utilized in the conventional power plants, the steady-state, transient and small-signal dynamics, as well as, power system stability will thus be significantly affected. The impact of wind energy systems on the power system dynamics and stability is thus of practical importance. As there is a significant increase in installation of wind turbines equipped with doubly-fed induction generator (DFIG) in recent years, a dynamic model of the DFIG wind turbine is firstly developed in this thesis. The model is validated against field measurement data, and the validation gives confidence about the accuracy and applicability of the developed model. DFIG wind farms consist of tens to hundreds of identical DFIG wind turbines increasing the complexity of the wind farm model and simulation time. A novel aggregation technique is developed in this thesis that incorporates a multiplication factor, namely mechanical torque compensation factor (MTCF), to the mechanical torque of the full aggregated wind farm model. The MTCF is initially constructed to approximate a Gaussian function by using fuzzy logic method. By optimizing the MTCF on a trial and error basis, less than 10 percent discrepancy is then achieved between the proposed aggregated model and the complete model. The proposed aggregation technique is then applied to a 120 MVA offshore wind farm comprising of 72 DFIG wind turbines and shows higher accuracy in approximating the wind farm dynamics as it appears at the point of common coupling (PCC) as compared to the full aggregated model. The proposed aggregated model computes faster than the complete wind farm model by 90.3 percent during normal operations and 87 percent during grid disturbances. To overcome the adverse effects due to the fluctuating nature of wind, two wind power smoothing methods are proposed using a fuzzy logic pitch angle controller for a smooth performance with a minimum drop in output power. One method performs partial smoothing with only 4.74 percent drop in the output power while the other method offers complete smoothing with a 8.28 percent drop in output power. The impact of wind energy integration on power system transient stability (PSTS) is studied quantitatively with the transient energy margin (TEM), which is calculated through the evaluation of the transient energy function (TEF). This study is carried out in two ways in the thesis. One is to analyse the impact of transient fault on the DFIG wind turbine as compared to SGs for different factors, like the fault clearing time, the grid coupling, the inertia constant and the voltage sag. The study reveals that transient stability of the DFIG wind turbine is hardly affected by the grid coupling, the inertia constant and the generator terminal voltage sag variations indicating its consistent transient performance within a wide range of these factors. The fault clearing time should be almost 11 percent faster for the system with the DFIG than the synchronous generator (SG). The other is to investigate the impact of the DFIG wind farm on the PSTS with the variation of different factors, which are the voltage sag, the fault clearing time, the load and the wind power penetration level. The study reveals that power systems integrated with DFIG wind farms are sensitive to transient events with high voltage sag, high fault clearing time, low load operation and high wind power penetration level. Machines at different locations individually possess distinct fault response and suffer from a large-scale power imbalance. As a result, reliable operation of DFIG wind farm integrated power systems demands upgraded equipment, such as advanced switchgear, fast breakers/isolators, efficient power reserve systems and advanced reactive power compensating device, etc.

This paper aims at improving the excitation control system for the doubly fed induction generator-based wind farm (WF). The proposed decentralized coordinated neural control is consisted of two controllers, i.e., a multiple model predictive controller (MPC) and an artificial neural network (ANN) controller. The MPC is based on the interaction measurement model and designed to guarantee the performance of system-wide optimization around the chosen operating points, while the ANN controller is used to calculate the weights of MPC controllers and trained to guarantee the control performance over the full operating region. The proposed control strategy allows to reduce the computational cost, and at the same time to take advantage of the distributed nature of the power system. Moreover, a simple, generic hybrid power system is used to demonstrate transient stability contributions. The problems of large-scale WF integration and its impact on transient stabilities of power systems are discussed through the eigenvalue analysis and time domain simulation. The results show that system damping and transient stability of hybrid power system are considerably improved.

This paper proposes a method to control the output power of a wind farm with the aim of improving the transient stability of a multi-machine power system. Doubly fed induction generators (DFIG) are considered for the variable speed wind farms. The variation of the frequency of the DFIG terminal bus is used to modulate the torque reference and thus the output power of the DFIG in the post-disturbance condition. This in turn modifies the electrical power of the nearby alternators and causes improvement of stability. The proposed control technique is validated in WSCC 3-machine 9-bus system and IEEE 16-machine 68-bus system. The study is carried out in PSCAD/EMTDC as well as in MATLAB platforms.

A new measure of the relative transient stability of a multimachine power system based on the Lyapunov stability theory is introduced. Techniques of sensitivity analysis are used to determine numerically the influence of variations or errors in the estimation of the system parameters on the transient stability of a power system. In particular, data is presented for an application of these ideas to a one machine infinite bus system.

In this paper we present a robust nonlinear excitation controller of synchronous generator connected through one transmission line to an infinite bus (SMIB) to enhance transient stability. Simulation results show that transient stability of a single machine infinite bus power system under a large sudden fault can be improved.

As the increasing capacity of renewable energy sources (RESs), power system with high RES penetration urgently need virtual inertia support from RESs. Current research has found that, due to inherent time delay, providing excessive virtual inertia from RESs may instead cause small-signal instability in the power system. Therefore, determining the upper limit of virtual inertia from RESs is critical to ensuring small-signal stability. However, current studies have only proposed methods for determining small-signal stability in power systems that consider VIC time delay, with limited discussion of the upper limit of virtual inertia. Therefore, a discrete system frequency response (SFR) model considering VIC time delay is established in this paper. It is found through analysis that the frequency sampling period affects the critical stability condition much more sensitively than the time delay length. Furthermore, a sufficient condition for small-signal stability is proposed, which describes the upper limit of the virtual inertia of RESs by the frequency sampling period and the system inertia time constant. Although this condition is a conservative estimation of the upper limit of virtual inertia, but the experiment on the test bench of wind-integrated power systems verifies that the sufficient condition is close to the critical condition. The sufficient condition is independent of the time delay length, making it more suitable for guiding practical engineering applications.

Distributed energy resources (DERs) offer a promising solution for enhancing the resilience and efficiency of modern power systems. However, the inherent time delays in their communication and control systems can degrade their small signal stability, affecting reliable operation. This paper presents an Adaptive Step Size Linear Multistep Method (AS-LMS), for analyzing small signal stability of the system in the presence of time delays. The AS-LMS automatically adjusts the step size based on the computed solution behavior, achieving a balance between accuracy and computational efficiency. The essential idea is to use smaller steps in regions where the dynamic is changing rapidly and larger steps in regions where it is relatively smooth. Two adaptive step size strategies are proposed. The first strategy compares the current step size to the initial step size, ensuring consistency across iterations. The second strategy compares the current step size with the previous step size, allowing for more local adjustments throughout the numerical integration process. We evaluate the performance of the proposed AS-LMS method on two standard testing systems, i.e., the IEEE 9-bus and IEEE 30-bus systems. Both systems are modified to converter-interfaced DER units and different delays are applied to each testing system. The results show that the proposed AS-LMS method improves computational efficiency while maintaining accuracy in stability assessments. By balancing the accuracy and computational efficiency, the AS-LMS method provides a potent tool to analyze the stability of power systems with time delay.

Guest Editorial: Situational awareness of integrated energy systems

To ensure stable operation of a power system, it is necessary to analyse the power system performance under various operating conditions. Analysis includes studies such as power flow and both steady-state and transient stability. To perform such studies requires knowledge about the models used to represent the various components that constitute an integrated power system. In situations where there is a risk of loss of stability, it is necessary to apply controls that can ensure stable and uninterrupted supply of electricity following a disturbance. The subject of stability thus encompasses modelling, computation of load flow in the transmission grid, stability analysis under both steady-state and disturbed conditions, and appropriate controls to enhance stability. All these topics are covered in this book, providing a comprehensive treatment of the overall subject of stability of power systems. Topics covered include modelling of the synchronous machine; the synchronous machine connected to power systems; modelling of transformers, transmission lines and loads; power flow analysis; optimal power flow; small signal stability; transient stability; transient energy function methods; artificial intelligent techniques; power system stabilizers; series compensation; shunt compensation; compensation devices; and recent technologies. The subject matter is covered at a level that is suitable for students, scientists and engineers involved in the study, design, analysis and control of power systems.

This paper reports a new technique for achieving optimized design for power system stabilizers. In any large scale interconnected systems, disturbances of small magnitudes are very common and low frequency oscillations pose a major problem. Hence small signal stability analysis is very important for analyzing system stability and performance. Power System Stabilizers (PSS) are used in these large interconnected systems for damping out low-frequency oscillations by providing auxiliary control signals to the generator excitation input. In this paper, collective decision optimization (CDO) algorithm, a meta-heuristic approach based on the decision making approach of human beings, has been applied for the optimal design of PSS. PSS parameters are tuned for the objective function, involving eigenvalues and damping ratios of the lightly damped electromechanical modes over a wide range of operating conditions. Also, optimal locations for PSS placement have been derived. Comparative study of the results obtained using CDO with those of grey wolf optimizer (GWO), differential Evolution (DE), Whale Optimization Algorithm (WOA) and crow search algorithm (CSA) methods, established the robustness of the algorithm in designing PSS under different operating conditions.

Wind generation is increasing rapidly in the grid, which has greater impacts on the power system than ever. The impacts are more serious under grid fault. The low‐voltage ride through (LVRT) controls of doubly fed induction generators (DFIGs) may change characteristics of synchronous generators (SGs) and threaten the transient stability of power system. However, the influence on the transient stability and even the controllable powers of a DFIG has not been considered in the existing LVRT method. The contributions of the reactive power supplied by a DFIG in the oscillation process of power angle of SG were analysed. The controllable range of powers of a DFIG was researched with consideration of the rotor speed limit. An LVRT control method of a DFIG based on the controllable range was proposed to improve the transient stability of power system. Simulations show that the proposed method could enhance the power angle stability of power system under the condition of avoiding overspeed and out of service of DFIG.

Due to power system oscillations induced by complex interconnections, power system stability has been a major concern and will continue to be a major concern in power system operations. For improving power system stability, efforts have been directed toward damping power system oscillations. The small signal stability is the instability that has been influenced by complex interconnections. Small signal stability can be dampened with power system stabilisers (PSS). PSS, on the other hand, have certain disadvantages, such as significant variations in voltage profiles and the potential for leading power factor operations, which may reduce system stability in the face of severe disturbances. In wide multi machine power systems, using only traditional PSS can not be enough to dampen inter-area oscillations and the effect of voltage profile variation. Power electronic devices known as Flexible Alternating Current Transmission System (FACTS) devices, on the other hand, are good at damping inter-area oscillations and can handle voltage variations. As a result, based on computational intelligence techniques, this paper provides a thorough analysis and evaluation of PSS and FACTS power oscillation damping (POD) controllers in reducing low frequency oscillations. The importance of technical paper publications on PSS and FACTS-based controller design, optimum location, and parameter tuning is highlighted. Finally, the potential future research directions for novel PSS and FACTS devices is proposed as a reference for interested researchers.