Small-signal Rotor Angle Stability Research Articles

Effect of a Large Proton Exchange Membrane Electrolyser on Power System Small-Signal Angular Stability

The dynamics of electrical systems have changed significantly with the increasing penetration of non-conventional loads such as hydrogen electrolysers. As a result, detailed investigations are required to quantify and characterize these loads’ effects on the dynamic response of interconnected synchronous machines after being subjected to a disturbance. Many studies have focused on the effects of conventional static and dynamic loads. However, the impact of hydrogen electrolysers on the stability of power systems’ rotor angles is rarely studied. This paper assesses the effect of proton exchange membrane (PEM) electrolysers on small-disturbance rotor-angle stability. Dynamic modelling and the control of a PEM electrolyser as a load are first studied to achieve this. Then, the proposed electrolyser model is tested in the Amercoeur plant, which is part of the Belgian power system, to study its effect on the small-signal rotor-angle stability. Two approaches are considered to examine this impact: an analytical approach and time-domain simulations. The analytical approach consists of establishing a state-space model of the Belgian test system through linearisation around an operating point of the non-linear differential and the algebraic equations of the synchronous generators, the PEM electrolyser, the loads, and the network. The obtained state-space model allows for the determination of the eigenvalues, which are useful to evaluate the effect of the PEM electrolyser on the small-signal rotor-angle stability. This impact is investigated by examining the movement of the eigenvalues in the left complex half-plane. The obtained results show that the PEM electrolyser affects the electromechanical modes of synchronous machines by increasing their oscillation frequencies. The results also show that the effect of the electrolyser on these modes can be improved by adjusting the inertial constant and the damping coefficient of the synchronous machines. These results are consolidated through time-domain simulations using the software Matlab/Simscape from the version MatlabR2022a-academic use from Mathworks.

Enhancement of the System Stability of DB-Controlled VSC Links Parallel Operated with a Weak Multi-Machine AC Power System

To allow the large-scale integration of renewable energy sources into the grid, VSC-HVDC is commonly utilized. However, with greater integration, several power system stability issues arise. In this study, we examined the small-signal rotor angle stability of a model of the Australian power system with embedded VSC-based HVDC links. A simplified model of the Australian power network was used to connect the potential geothermal resources in the region of Innamincka using a 1100 km HVDC link. We observed that the introduction of the new source of geothermal power generation had an adverse impact on the damping performance of the system. Therefore, two forms of stabilization are examined here: (i) generator power system stabilizers (PSS) fitted to the synchronous machines, which are used to convert geothermal energy to electrical power; and (ii) power oscillation damping controllers (PODs) fitted to the VSC-HVDC link. In the case of the PODs, two types of stabilizing input signals are considered: (i) local signals such as power flow in adjacent AC lines, and (ii) wide-area signals such as bus voltage angles at key nodes in the various regions of the system. It was concluded that the small-signal rotor angle stability of the interconnected AC/DC system can be greatly enhanced by employing the designed damping controllers.

Frequency Dynamics-Constrained Parameter Design for Fast Frequency Controller of Wind Turbine

During frequency controller design, the system frequency dynamic behavior is normally assessed by a system frequency response (SFR) model, which is a linearized low-order model that can be efficiently handled. Existing SFR models for a system with wind turbines cannot precisely characterize the nonlinear dynamic of fast frequency controllers in these turbines, causing inaccurate evaluation of the system frequency behavior that may lead to undesired design of fast frequency control parameters. To deal with this issue, the linearization error of the SFR model is formally analyzed. A compensation strategy is proposed to guarantee the accuracy of the frequency behavior assessment. Further considering that fast frequency controllers potentially degrade the small-signal rotor angle stability, this paper presents a coordinated parameter optimization model of fast frequency controllers, which guarantees the system frequency behavior while meeting the small-signal rotor angle stability requirement. Case studies validate the effectiveness of the proposed method.

Hierarchical Power Flow Control in Smart Grids: Enhancing Rotor Angle and Frequency Stability with Demand-Side Flexibility

Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of operation, the system must maintain adequate disturbance rejection capability at the time scales of both rotor angle and system frequency dynamics. This calls for flexibility to be exploited on both the generation and demand sides, compensating volatility and ensuring stability at the two separate time scales. This article proposes a hierarchical power flow control architecture that involves both transmission and distribution networks as well as individual buildings to enhance both small-signal rotor angle stability and frequency stability of the transmission network. The proposed architecture consists of a transmission-level optimizer enhancing system damping ratios, a distribution-level controller following transmission commands and providing frequency support, and a building-level scheduler accounting for quality of service and following the distribution-level targets. We validate the feasibility and performance of the whole control architecture through real-time hardware-in-loop tests involving real-world transmission and distribution network models along with real devices at the Stone Edge Farm Microgrid.

Optimization for DFIG Fast Frequency Response With Small-Signal Stability Constraint

The increasing penetration of wind power deteriorates the frequency stability of power systems. To address this issue, a fast frequency response (FFR) from wind farms is required to provide frequency support. However, the power point tracking controllers in wind turbines may counteract the effect of droop-based fast frequency controllers during the frequency response, which makes it difficult to estimate the exact contribution of droop-based fast frequency controllers in wind farms to the system frequency behavior. To address this issue, this article proposes a control parameter design method to fully utilize the frequency support potential of wind turbines. To achieve this goal, an explicit expression for the relationship between the droop-based fast frequency control parameters of the wind turbines and the steady-state frequency deviation is derived. Considering that the fast frequency controller may have a negative effect on the small-signal rotor angle stability, we present a coordinated parameter optimization model of droop-based fast frequency controllers, which improves the system frequency behavior while meeting the small-signal rotor angle stability requirement. A sensitivity-based method is presented to solve the proposed optimization model, which efficiently handles violations of the control parameter constraints. Case studies validate the effectiveness of the proposed method.

Qualitative and Quantitative Transient Stability Assessment of Stand-Alone Hybrid Microgrids in a Cluster Environment

Neighboring stand-alone hybrid microgrids with diesel generators (DGs) as well as grid-feeding photovoltaics (PV) and grid-forming battery storage systems (BSS) can be coupled to reduce fuel costs and emissions as well as to enhance the security of supply. In contrast to the research in control and small-signal rotor angle stability of microgrids, there is a significant lack of knowledge regarding the transient stability of off-grid hybrid microgrids in a cluster environment. Therefore, the large-signal rotor angle stability of pooled microgrids was assessed qualitatively and also quantitatively in this research work. Quantitative transient stability assessment (TSA) was carried out with the help of the—recently developed and validated—micro-hybrid method by combining time-domain simulations and transient energy function analyses. For this purpose, three realistic dynamic microgrids were modelled regarding three operating modes (island, interconnection, and cluster) as well as the conventional scenario “classical” and four hybrid scenarios (“storage”, “sun”, “sun & storage”, and “night”) regarding different instants of time on a tropical partly sunny day. It can be inferred that, coupling hybrid microgrids is feasible from the voltage, frequency, and also transient stability point of view. However, the risk of large-signal rotor angle instability in pooled microgrids is relatively higher than in islanded microgrids. Along with critical clearing times, new stability-related indicators such as system stability degree and corrected critical clearing times should be taken into account in the planning phase and in the operation of microgrids. In principle, a general conclusion concerning the best operating mode and scenario of the investigated microgrids cannot be drawn. TSA of pooled hybrid microgrids should be performed—on a regular basis especially in the grid operation—for different loading conditions, tie-line power flows, topologies, operating modes, and scenarios.

A Novel Dynamic Aggregation Modeling Method of Grid-Connected Inverters: Application in Small-Signal Analysis

Converter-control-based generators exhibit different dynamic characteristics compared with traditional synchronous generators, and thus affect the oscillation modes and small-signal stability of power systems in a different manner. Simplified representation of a great number of grid-connected inverters is indispensable for efficient and accurate dynamic analysis of power systems integrated with large-scale renewable energy generation. This paper proposes a novel dynamic aggregation modeling method of grid-connected inverters using coherency-based equivalence, and validates the applicability of the aggregated model for small-signal stability analysis. Modal analysis and dynamic simulation are conducted on the detailed model and aggregated models of the test system. The frequency-domain results and the time-domain results from PSCAD/EMTDC both verify the adequacy of the coherent equivalence practice in the small-signal rotor angle stability analysis.

Model reduction strategy of doubly-fed induction generator-based wind farms for power system small-signal rotor angle stability analysis

Following the decarbonisation and decentralisation of energy industry, wind energy is becoming a promising generation source to reduce greenhouse emission, and meet future energy demand. Unlike traditional generation using synchronous generators, many wind turbines use induction generators, e.g., doubly-fed induction generators, due to the cost effective design of adjustable-speed operation and flexibility in reactive power control. However, a growing number of doubly-fed induction generator-based wind farms has significantly increased the complexity of system dynamic model, and hence increased the computational burden of power system dynamic study. This becomes a serious concern in the electricity system operation, where a fast power system stability assessment is required to assure the real-time system security during high levels of wind power penetration. In this paper, a novel model reduction strategy of doubly-fed induction generators is derived to improve the efficiency of power system dynamic study, while the study accuracy is still maintained to an acceptable level. To achieve this, a method to assess the modeling adequacy of doubly-fed induction generators for small-signal rotor angle stability analysis is firstly introduced. By evaluating the damping torque contribution to stability margin from different dynamic model components of doubly-fed induction generators, the proposed method provides a quantitative index (i.e., participation level) to show the involvement of each dynamic model component of doubly-fed induction generators in affecting power system damping, and thus can instruct how to reduce the model of doubly-fed induction generators in an efficient and accurate manner. On this basis, five model reduction plans and a model reduction strategy have been proposed according to the previously defined participation levels. The effectiveness of the proposed strategy is demonstrated in the New England test system and a real large power grid in Eastern China respectively. It has been proved that the proposed the model reduction strategy of doubly-fed induction generators for power system dynamic study is undoubtedly useful to the electricity system operator, with a key benefit in reducing model complexity and improving computational efficiency of a large-scale power system with an increasing number of wind power generation.

Real-Time Remedial Action Against Aperiodic Small Signal Rotor Angle Instability

This paper presents a method that in real-time determines remedial actions, which restore stable operation with respect to aperiodic small signal rotor angle stability (ASSRAS) when insecure or unstable operation has been detected. An ASSRAS assessment method is used to monitor the stability boundary for each generator in real-time. The ASSRAS boundary represents the condition when a generator reaches the maximum steady state active power injection. The proposed control method exploits analytically derived expressions for the ASSRAS boundary and other characteristic curves in the injection impedance plane to determine an active power redispatch among selected generators to restore stable and secure operation. Since the method is purely based on analytically derived expression, the computation of the remedial actions is fast and well suited for real-time operation. The method was tested on the IEEE 14-bus and the Nordic32 test systems where results show that the method can efficiently determine the required active power redispatch to avoid an imminent instability.

Prediction of Generators' Participation Factors and Oscillation Types for Dominant Oscillatory Modes of Power System

Small-signal rotor angle stability, also known as small-signal stability, is an important issue for power system operation. This stability is associated with inter-area, local, control, and torsional oscillations. To cope with it, the type and main drivers of the oscillations should be determined. In this way, the system operators can plan more effective preventive and corrective actions, e.g., to transfer power generation from more vulnerable units to less vulnerable ones. However, determining oscillation modes and their participation factors by means of conventional methods (e.g., time-domain simulation and modal analysis) is a challenging and time-consuming task, which is not appropriate for on-line environments, such as dispatching centers of power systems. In this article, a new viewpoint for this problem is proposed through modeling it as a forecast process by which the participation factors of generators for dominant modes as well as the oscillation types are predicted. A new prediction strategy, composed of an information-theoretic feature selection, a probabilistic neural network, and a line search procedure, is also presented to implement the forecast process. The effectiveness of the proposed approach for small-signal stability evaluation is extensively illustrated on the IEEE New England test system.

Wide-Area Assessment of Aperiodic Small Signal Rotor Angle Stability in Real-Time

This paper presents the details of a new real-time stability assessment method. The method assesses a particular mechanism of stability: each generator's capability to generate sufficient steady state electromechanical torque. The lack of sufficient steady state torque causes aperiodic increase in rotor angle and a loss of synchronism, referred to as aperiodic small signal instability. The paper provides the theoretical background of the method and an analytical assessment criterion. Furthermore, a mathematical mapping of the generators' operating points that enables informative visualization of multiple operating points is derived in the paper. Finally, results from time-domain simulation of instability scenarios in the Nordic32 test system are presented and results used for testing the assessment method. The results illustrate the method's capability to efficiently identify the location of the emerging problem and to quantify margins to stability boundary.

An OPF Methodology to Ensure Small-Signal Stability

This paper presents a security redispatching procedure that allows achieving an appropriate security level in terms of small-signal rotor angle stability. The proposed methodology is based on an OPF problem that explicitly considers security limits through stressed loading conditions. The solution of the proposed redispatching procedure yields the optimal preventive control actions to be implemented to ensure a given security level. The New England 39-bus, ten-machine and the IEEE 145-bus, 50-machine systems are used for illustrating, testing, and discussing the proposed technique.