Grid Frequency Stability Research Articles

Holistic analysis of the dynamic stability of the Southern Cameroon Interconnected grid in contingency situations

The Southern Cameroon Interconnected Network (SIG) is depicted as a large-scale power system that has shown significant instability due to a series of blackouts in recent years. These blackouts are primarily attributed to major disruptions in transmission lines and energy deficits between supply and demand. The imbalance between power supply and demand necessitates the grid to operate near its stability limits, increasing the risk of blackouts. The necessity of investigating the dynamics of SIG behavior in response to observed contingency situations serves as the primary motivation for this study. To achieve this objective, the SIG was modeled using saturated generators with ZIP static loads. Through Newton-Raphson based power flow calculations, voltage magnitude profiles of the grid were obtained for each generation scenario. An N-1 contingency consisting of a standard Newton-based continuation power flow (CPF) analysis has identified line 5–6 as the most frequent worst case of line outage. Additionally, a short-term transient analysis was conducted under three-phase short-circuit, line outage and generator outage scenarios. In the event of a short-circuit, the Mangombe-225 bus experienced the most significant impact. Concerning line outages, line 1–5 had the most adverse effect on the grid's frequency stability. However, generation outages had a lesser impact on frequency stability compared to other disturbances. Lastly, modal analysis revealed that the grid exhibited weak stability with a critical mode identified at a frequency of 4.0267 Hz, exceeding typical values. This underscores the necessity of damping the grid oscillations for enhanced stability.

An Optimized Power-Angle and Excitation Dual Loop Virtual Power System Stabilizer for Enhanced MMC-VSG Control and Low-Frequency Oscillation Suppression

Modular Multilevel Converter Virtual Synchronous Generator (MMC-VSG) technology is gaining widespread attention for its ability to enhance the inertia and frequency stability of the power grid integrated with converter-interfaced renewable energy sources. However, the excitation voltage regulation in the MMC-VSG can generate equivalent negative damping torque and cause low-frequency oscillation problems similar to those in synchronous machines. This article aims to improve the system’s damping torque and minimize low-frequency oscillations by introducing a Virtual Power System Stabilizer (VPSS) into the power control loop. Building on the study of dynamic interactions between various control links of the MMC, this research establishes a reduced-order model (ROM) and a Phillips–Heffron state equation for the MMC-VSG single machine infinite bus system, using a hybrid modeling approach and a zero-pole truncation method. It also analyzes the mechanism of low-frequency oscillations in the MMC-VSG system through the damping torque method. The analysis reveals that the negative damping torque produced during the excitation voltage regulation process causes changes in the virtual power angle, which in turn increases the risk of low-frequency oscillation in the MMC-VSG. To address this issue, the article proposes an optimized control method for the MMC-VSG dual power loop architecture (power-angle/excitation) VPSS. This strategy compensates for the inadequate damping torque of a single loop VPSS and effectively suppresses low-frequency oscillations in the system.

A rheological model analog for assessing the resilience of socio-technical systems across sectors

A rheological model is proposed that captures the performance loss and properties of a potential subsequent recovery of socio-technical systems subject to arbitrary disruptions. The model facilitates the quantitative assessment of such systems’ resilience. While most models known from the literature describe systems that fully recover from aforementioned load events, the proposed model can capture also permanent performance loss or post disruption improvement. To demonstrate the versatility of the approach for a wide range of the socio-technical system spectrum, the model is applied to three systems: the frequency stability of the continental Europe power grid, flight operations of German airports, and the revenue of the German gastronomic sector. Fitting the proposed two-spring, one-damper, single-degree-of-freedom model to the recorded performance data determines relevant parameters which serve as a quantitative measure of the respective system’s resilience. The small set of model parameters can be associated with relevant resilience dimensions. Variation of these parameters allows to quantitively determine the change of the model’s response to the load events, and thus of the resilience predicted by the model. This allows to identify parameter ranges in which the model predicts, e.g., full recovery of a system, instead of permanent performance loss.

Analysis of frequency stability of power grid considering variable speed constant frequency wind motor with local low rotational inertia

Abstract A significant quantity of renewable energy equipment, including photovoltaics and wind turbines, will be connected to the grid instead of traditional synchronous generator sets. However, the significant percentage of renewable energy sources that have been integrated into the power grid will lead to the frequency safety problem of the power system. The decrease in system inertia can adversely affect the stability of the power system’s frequency. Therefore, the influence of the local low moment of inertia on the frequency stability of the power grid is analyzed from the static and dynamic perspectives, and the method of participating in the primary frequency modulation after the wind turbine is connected to the grid is studied by taking the variable speed constant frequency wind turbine as an example.

A frequency stability assessment framework for renewable energy rich power grids

The worldwide power grid is undergoing a paradigm shift due to the rise of renewable energy sources. Traditional rotating synchronous generators are being replaced by inverter-based renewable energy sources (RESs), and this trend is expected to persist in the years to come. As a result, the grid’s inertia is decreasing gradually, which presents significant obstacles to maintaining grid frequency stability. Moreover, due to the uncertainties associated with the generation of RESs and load demand, grid inertia has become a stochastic quantity. In this paper, considering the stochastic characteristics of the power generation, load demand profile and grid inertia, a framework to assess grid frequency stability with high penetration of RESs has been presented. This framework first quantifies grid frequency characteristics at different levels of RES penetration using Monte-Carlo simulation (MCS) considering the intermittent nature of RESs and load demand. This is followed by assessment of frequency stability of the power grid using proposed matrices that quantifies the amount of deviation in grid frequency and rate of change of frequency (RoCoF) outside the boundary prescribed by the grid operator. In addition, the proposed framework evaluates the sensitivity of grid frequency stability to RES penetration levels and quantifies the resiliency against contingency. Rigorous case studies on modified IEEE 39 bus test system have been presented to demonstrate the effectiveness of the proposed framework in assessing grid frequency stability.

Effects of Battery Energy Storage Systems on the Frequency Stability of Weak Grids with a High-Share of Grid-Connected Converters

To achieve an energy sector independent from fossil fuels, a significant increase in the penetration of variable renewable energy sources, such as solar and wind power, is imperative. However, these sources lack the inertia provided by conventional thermo-electric power stations, which is essential for maintaining grid frequency stability. In this study, a grid resembling Madeira Island’s power generation mix was modeled using the Matlab/Simulink platform. The model included solar, wind, hydro, and thermo-electric generation to accurately represent the energy landscape of Madeira Island. Three scenarios were examined: one reflecting the current power generation on Madeira Island, a future scenario with a substantial rise in the percentage of photovoltaic (PV) generation, and the same future scenario but incorporating a battery energy storage system (BESS). Various analyses were conducted to assess the impact on frequency stability during a ground fault and rapid load/generation changes. In the future scenario without a BESS, the thermoelectric power plant generator desynchronized, leading to system collapse in several simulations. However, with the addition of a BESS, a significant improvement in frequency stability was observed. The thermoelectric power plant generator could return to a steady state after each disturbance. Furthermore, both the maximum frequency deviation and the absolute value of the Rate of Change of Frequency (ROCOF) were reduced, indicating enhanced system performance and stability.

Method of Multi-Energy Complementary System Participating in Auxiliary Frequency Regulation of Power Systems

This research investigates a grid with two areas interconnected by a high-voltage direct-current (DC) link. One of the areas, called the sending-end region, has intermittent renewable generation and frequency stability issues. To address the lack of frequency-regulation (FR) resources in the sending-end region of the interconnected grid, the participation of hydroelectricity–photovoltaics and pumped storage complementary systems (HPPCSs) in auxiliary frequency-regulation (AFR) services is studied in the context of the construction of the electricity market. Firstly, the HPPCS participating in AFR services considering DC modulation is modeled by combining the operational characteristics of the actual power station. Taking the purchase cost of auxiliary service as the objective function, the optimum allocation of FR scheduling demand is achieved by the proposed method. The simulations confirm that the proposed method of HPPCS participation in the AFR service of the sending-end grid can effectively maintain the frequency stability of the regional interconnected grid while ensuring optimal economic efficiency. The proposed method provides the optimal scheduling solution for multiple energy resources participating in the AFR service of the grid.

Assessment and management of frequency stability in low inertia renewable energy rich power grids

AbstractThe integration of the renewable energy sources (RESs) into the power grid, drives a significant transformation in the conventional power generation landscape. This transition from traditional synchronous generators to inverter based RESs introduces unique challenges in maintaining the grid frequency stability due to the reduced system inertia. The inherent stochastic nature of the RES power generation, load demand, and grid inertia includes further complexity in the assessment of frequency stability. Existing studies have limitations, including neglecting the stochastic nature of RES generation and load demand fluctuations, relying on limited metrics, and lacking a comprehensive day‐to‐day assessment. To address these shortcomings of the existing approaches, this paper introduces a novel methodology for assessing frequency stability in power grids with high RES penetration. It proposes three indices for evaluating grid frequency sensitivity, resiliency, and permissibility amidst varying RES integration. Utilizing a stochastic approach, the study incorporates uncertainties in RES generation and load demand, offering a comprehensive framework for day‐to‐day frequency stability analysis. Additionally, it presents a systematic method to ascertain the necessary inertial support for maintaining desired frequency reliability in RES‐dominated grids. The effectiveness of these methodologies is validated through a case study on a modified IEEE 39‐bus test system, demonstrating their applicability in ensuring reliable grid operation under high RES scenarios.

Research on frequency regulation strategy of battery energy storage system supporting power system

Due to the large-scale grid connection of new energy, the inertia of the power system has decreased, seriously affecting the frequency stability of the power grid, and there is an urgent need for effective frequency support technology. In response to the above issues, this article proposes a frequency control strategy for battery energy storage systems to support power systems. Firstly, establish a battery equivalent circuit model to simulate the dynamic and static performance as well as external characteristics of the battery; Secondly, two frequency modulation strategies, droop control and accelerated droop control, are used to control the active power emitted by the battery energy storage system. Finally, a four-machine two-zone system with a 25% proportion of wind power was built using MATLAB for simulation analysis in two scenarios: sudden reduction of wind power and rapid fluctuation of wind power. The results showed that the frequency modulation strategy proposed in this paper can effectively improve the lowest and stable point frequencies of the system, and can slow down the rate of frequency decline, thereby improving the frequency stability of the power grid.

Low computational cost convolutional neural network for smart grid frequency stability prediction

In the smart grid, it is critical to collect dynamic and time-dependent information on energy demand and consumption and compare it to current supply conditions. The decentral smart grid control (DSGC) system manages frequency, a Smart grid element. It connects energy costs to grid frequency, allowing access to both consumers and producers. This work proposes a pruning of the convolution layers and neurons of 1-dimensional time-aware convolutional neural network (1D CNN) analysis of grid frequency stability to determine efficient energy costs. The proposed solution evaluated augmented grid stability datasets in addition to two other publicly available datasets to ascertain the approach’s feasibility in various scenarios; the simulation demonstrated a minimal train and prediction time of 124.37 s and 17.67 s efficiency over compared models, with prediction accuracy of 99.79% and 0.01 MFLOPs. Matthew’s correlation coefficient was applied to evaluate further the performance of the proposed 1D CNN to ascertain its applicability in various scenarios.

Interaction Between Grid-Forming Converters With AC Grids and Damping Improvement Based on Loop Shaping

Grid-forming converters (GFC) are a promising technology for improving the grid inertia and frequency stability via voltage source converters (VSC). However, GFCs could make the ac-side oscillations more complicated since it mimics the dynamics of synchronous generators (SG), and the ac-side oscillations could spread to the dc systems. This paper investigates the mechanism of the interactions between GFCs and ac grids, and proposes an enhanced GFC to improve the damping performance on oscillations. By separating the system model into GFC-related transfer functions (TF) and the ac grid-related TFs, the interaction and stability margin can be investigated by the phase difference of these TFs at the cross-gain frequency (CGF). A lead compensator is designed to reshape the phase characteristic of GFC-related TF for enhancing the damping performance of the GFC. The effectiveness of the enhanced GFC is tested according to the simulations on DIgSILENT/PowerFactory.

Vulnerability of the Load Frequency Control Against the Network Parameter Attack

By integrating the communication-enabled high-voltage electronic devices into the supervisory control and data acquisition (SCADA) system, the smart grid achieves flexible, economic, controllable operations of remote and real-time electricity transmission and distribution. However, it has been widely recognized that the SCADA system is vulnerable to unprecedented cyberattacks. In this paper, we propose a novel attack, namely, a network parameter attack (NPA), on the physical parameter of the branch to affect the load frequency control. The idea is to modify the control signal sent to the thyristor-controlled series compensator (TCSC) device to change the reactance of the transmission line, thus, inflicting the grid frequency stability. We first provide a sufficient condition for NPA to cause frequency instability. To further provide more insights, we analyze the impact of NPA on frequency stability based on the eigenvalue sensitivity. The vulnerable transmission lines are screened out based on the error caused by the NPA on the eigenvalues. Furthermore, we develop a least-effort but maximum-impact attack strategy considering the attacker’s limited resources. Finally, we conduct extensive simulations to validate the effectiveness of the attack and evaluate its impact on the system’s operation.

Frequency regulation scheme in power system using an observer-based waiting event-triggered control with random features

Addressed in this paper is the observer-based waiting event-triggered control issue in multi-area load frequency control (LFC) power system subject to random communication delay and data packet dropout. In order to maintain the grid frequency stability of the multi-area LFC power system in an open communication network, an observer-based waiting event-triggered scheme (WETS) is proposed to deal with frequency fluctuation and extend the life of control equipments. Compared with the existing event-triggered mechanism, the proposed WETS has the merits of continuous event-triggered scheme and the periodic sampling event-triggered scheme in the both of theory and application. Then, by well considering the negative factors of data packet dropout and random time delay in data transmission, a stochastic delay-dependent multi-area LFC model is established, which involves the information of observer-based WETS, random communication delay and packet dropout in a unified structure. Further, an improved Lyapunov–Krasovskii functional (LKF) is constructed by dividing the interval of transmitted delay. Based on the constructed Lyapunov functional, Park’s theorem and Jensen’s integral inequality, some less conservative stabilization criteria are obtained. Finally, the validity of the proposed control method is verified via numerical examples.

Refined Modeling and Dynamic Characteristics of Self-excited Vibration in the Main Inlet Valve of Pumped Storage Power Stations

Self-excited vibration of the main inlet valve poses a great threat to the safe operation of the pumped storage power system, thereby making an indirect hazardous effect on the frequency stability of the power grid. In order to avoid self-excited vibration, this paper focuses on the refined modeling and dynamic characteristics of self-excited vibration. Firstly, the flexible valve model is introduced and the refined pumped storage power system modeling considering self-excited vibration is established. The constructed model is then validated by comparing it with field data in the frequency domain. Secondly, the sensitivity of self-excited vibration to system parameters is investigated by using the modified Morris method. Once the sensitive parameters are found, the effect law of these parameters on the dynamic characteristics of self-excited vibration is studied in depth. Finally, engineering advice is proposed. The result indicates that the self-excited vibration is most sensitive to the length of the diversion pipe, valve clearance of the main inlet valve, and water hammer velocity. Moreover, it is verified by simulation that shorter upstream pipe length, lower water hammer velocity and smaller valve clearance help to restrain the amplitude and deterioration rate of self-excited vibration.

A Storage-Based Fixed-Time Frequency Synchronization Method for Improving Transient Stability and Resilience of Smart Grid

A storage-based distributed fixed-time frequency synchronization method is developed to enhance the frequency and transient stability of smart grid. The multi-agent cyber-physical model of power system is the foundation of the proposed control method which utilizes data on the relative angle and frequency between the local agent and its neighbor agents. The control method mainly consists of frequency control based on energy storage system (ESS), P-ω droop control of synchronous generator (SG), and P-θ droop control of converter-based generator (CBG), which is designed by the backstepping method and Lyapunov theory. In addition, to hasten frequency synchronization, the nonlinear voltage control which is compatible with frequency control is presented. Meanwhile, the control method is not only applied to the homogeneous power systems only include SGs, but also deals with the challenge of heterogeneous bus dynamics introduced by the coexistence of SGs and CBGs. The distributed fixed-time frequency control can achieve self-protecting from denial-of-service (DoS) attacks by transforming into decentralized control. Comparative simulations show that the designed storage-based frequency synchronization method is preferable in improving the transient stability and resilience of smart grid.

Frequency-constrained unit commitment under uncertain PFR of energy storage systems

By increasing the penetration of low-inertia renewable energy systems (RESs) in the power systems, the grid frequency stability becomes even more challenging. It is necessary to emulate the inertia or primary frequency response (PFR) of RESs with power electronic converters (PECs) to have more accurate model. Therefore, frequency constrained unit commitments (FCUCs) are developed based on fully reliable RESs or energy storage systems (ESSs) contribution in frequency control. As, PEC-based resources are not guaranteed to work perfectly in an outage, any sensor, control, or drive system malfunction results in false detection or response. Consequently, if the FCUC relies on the fast, and perfect inertia response of RESs, the frequency may exceed from its standard ranges in the presence of malfunction. To avoid frequency instability, the imperfect PEC-based resource contribution is accounted, here. Thus, the malfunctioned units are removed from the frequency ancillary services. As malfunctioned units are unknown, a distributionally robust optimization is utilized. This paper extracts a robust FCUC model considering the uncertain PFR of PEC-based ESSs. The model proficiency is analyzed under IEEE RTS96 system. It is concluded that the proposed method prevents frequency instability by spending 6.38 % more cost than the FCUC model with perfect operation of converters. In addition, merits of the proposed model get more significance in higher penetration of malfunctioned units.

Optimal deloading of PV power plants for frequency control: A techno-economic assessment

Due to the lack of inertial support from photovoltaic (PV) systems, large-scale PV integration into the existing grid poses a major threat to frequency stability. To address this, numerous techniques for incorporating energy storage systems have been proposed in the existing literature, but they incur significant operational costs. PV systems with deloading mechanisms have been researched as an alternative efficient strategy in many studies as a key frequency response support after a disturbance. However, deloaded PV systems incur a cost burden due to idle reserve capacity during regular operation. Consequently, an optimum deloading of PV systems is required to enhance the grid's frequency stability while minimizing its total operating cost. To that aim, this paper proposes a gradient descent-based optimization method to determine the optimum deloading of PV systems. The optimization considers both frequency response constraints (frequency nadir and rate of change of frequency – ROCOF) and operating cost constraints (generation, up-regulation, and value of lost load cost). The proposed technique is employed in a modified IEEE 39 bus New England System for varying levels of PV integration under two distinct cases. The optimization and relevant simulations are performed in Python and DIgSILENT PowerFactory platforms. In the case of a major generator outage with PV penetrations of 30%, 40%, and 50%, the optimal deloading percentages are 6.96%, 5.931%, and 4.968%, respectively, with no load shedding. Moreover, in the interconnection outage case, the optimal deloading percentages increase to 14.92%, 13.3%, and 12.42%, respectively, with load shedding. Nevertheless, in each case, deloaded PV systems consistently preserve frequency stability in the grid while incurring minimized operating costs. Furthermore, the performance and cost of the proposed solution are compared to two other primary frequency response support systems, viz. Battery Energy Storage System (BESS) and Synchronous Condenser (SC). The optimally deloaded PV system outperforms both these devices considering both technical and economic aspects.

Impact of electric vehicles fast frequency regulation and charging strategies on grid frequency stability

With the gradual reduction of grid inertia, system sensitivity to load unbalances is increasing, compromising frequency stability. To face this problem, faster frequency regulation resources are required. In this context, vehicle-to-grid (V2G) is one of the concepts that is suggested for this purpose. When electric vehicles (EVs) are parked, their batteries can be used as distributed energy storage systems (EESs), injecting and absorbing power faster than conventional generation units (CGUs). The goal of this paper is to analyse the impact of fast frequency regulation of EVs in a small-scale grid, under sudden load variations. In this paper, the effect of charging strategies (CSs) is addressed, as they have a direct impact on the magnitude of the EV fleet regulation. In this way, different CSs can be used to achieve symmetrical up and down regulation, or to maximize one of them. The effect of the EV fleet dynamics in the frequency transient is also studied. The speed of response, and hence, the frequency transient, are influenced by these dynamics. The focus of the analysis will be the communication delay between the EV fleet and the central controller.

Security assessment method for inertia and frequency stability of high proportional renewable energy system

With the increase in large-scale renewable energy and DC transmission, synchronous generators in power grids are gradually being replaced, resulting in a continuous reduction in inertia. The resulting low-inertia system influenced the frequency stability of the power grid. On the one hand, knowledge of the inertia level of the system is relevant to evaluate the frequency stability of the power system. On the other hand, knowledge of the anti-interference ability of the system is also relevant. Based on the frequency response mechanism of a conventional synchronous system, this study extended the concept of inertia of a synchronous generator by introducing virtual inertia and proposed an inertia evaluation method for power grids with high-penetration electronic devices. Subsequently, a minimum inertia estimation method considering fast frequency response was proposed based on the virtual inertia technology of grid-connected inverters. Finally, the effectiveness of the proposed model was illustrated using a case study based on the South-East Australian system.

Overview of frequency control techniques in power systems with high inverter‐based resources: Challenges and mitigation measures

AbstractPower systems are rapidly transitioning towards having an increasing proportion of electricity from inverter‐based resources (IBR) such as wind and solar. An inevitable consequence of a power system transition towards 100% IBR is the loss of synchronous generators with their associated inertia, frequency, and voltage control mechanisms. To ensure future grid needs can be met, the source of system services to meet these needs must change from synchronous plants to IBR. Under this context, the main objective is to extensively review grid frequency stability challenges concerning the massive integration of IBR from the perspective of system operators. Following that, the newly established international fast frequency response services in different renewable dominant power systems to address low inertia challenges are compared from various perspectives. Finally, potential solutions based on various renewable enabling technologies and renewable sources are investigated from the standpoint of their expectation to play an active role in the energy system and to provide a wide range of system frequency services. The findings of this study provide a deep understanding of prospective frequency control solutions and an actionable dataset that will support various research and policy needs as we approach net‐zero targets.