Frequency Stability Of Power System Research Articles

Two-Area Automatic Generation Control for Power Systems with Highly Penetrating Renewable Energy Sources

Currently, renewable energy sources (RESs) are gradually replacing traditional power sources that use fossil fuels. In some countries, such as Vietnam, RESs are developed on a massive scale and are concentrated in some key areas. This causes negative impacts on a power system when its transmission system is not deployed synchronously to release their capacity from these new renewable energy plants. An important challenge today is to ensure frequency stability in power systems with high uncertainty in RES output power. Additionally, the system requires solutions to prevent transmission line overloads during periods when RESs make a substantial contribution to the electricity generation capacity. Therefore, this paper builds an automatic generation control (AGC) system for a two-area power system with high penetration of RESs. This AGC system model aims to maintain system frequency stability amid unpredictable changes in RESs while also ensuring that tie-lines transmit the predetermined power levels to mitigate frequent congestion. By continuously monitoring and adjusting the system’s frequency, the challenges posed by the inherent variability of RESs can be effectively mitigated. The AGC model is simulated on DIgSILENT PowerFactory software and tested with a 106-bus system. The simulation results of this study show that the AGC system operates effectively, ensuring that the frequency returns to the rated value and maintaining the exchange capacity on the tie-lines after occurrences of RES power decrease events.

Frequency stability of new energy power systems based on VSG adaptive energy storage coordinated control strategy

A self-adaptive energy storage coordination control strategy based on virtual synchronous machine technology was studied and designed to address the oscillation problem caused by new energy units. By simulating the characteristics of synchronous generators, the inertia level of the new energy power system was enhanced, and frequency stability optimization was achieved. This strategy is integrated with the frequency response model of the new energy power system to improve the system's frequency regulation capability and achieve more stable and efficient operation. From the results, the damping of the system increased, the oscillation frequency decreased after a duration of about 15 s, and the system stability improved by 76.09%. The proposed strategy based on virtual synchronous generator adaptive energy storage coordination control strategy was improved by 83.25%. In addition, the proposed strategy has improved stability indicators and system completion efficiency by 40.57% and 22.21% respectively, both of which are better than the comparative strategies. As a result, this strategy significantly enhances the frequency regulation capability of the system, which has a positive effect on achieving efficient operation of the new energy power system and maintaining the stability of the power system.

A Multi-Level Operation Method for Improving the Resilience of Power Systems under Extreme Weather through Preventive Control and a Virtual Oscillator.

This paper proposes a multi-level operation method designed to enhance the resilience of power systems under extreme weather conditions by utilizing preventive control and virtual oscillator (VO) technology. Firstly, a novel model for predicting time intervals between successive failures of the power system during extreme weather is introduced. Based on this, this paper proposes a preventive control method considering the system ramping and transmission constraints prior to failures so as to ensure the normal electricity demand within the system. Further, a VO-based adaptive frequency control strategy is designed to accelerate the regulation speed and eliminate the frequency deviation. Finally, the control performance is comprehensively compared under different experimental conditions. The results verify that the method accurately predicted the time of the line fault occurrence, with a maximum error not exceeding 3 min compared to the actual occurrence; also, the virtual oscillator control (VOC) strategy outperformed traditional droop control in frequency stabilization, achieving stability within 2 s compared to the droop control's continued fluctuations beyond 20 s. These results highlight VOC's superior effectiveness in frequency stability and control in power systems.

A simple estimation method of grid‐forming inverter inertia based on rate of change of frequency

AbstractInertia is the core index of the estimation of power system frequency stability; a simple estimation method of grid‐forming inverter inertia based on the rate of change of frequency (RoCoF) is proposed in this paper. The method records and fits the active power curve by applying RoCoF to obtain the value of the grid‐forming inverter inertia, and it is simpler and higher accuracy compared to existing methods. In addition, the inertia and damping are analysed to support the system, and the relationship equation between the grid frequency slope change and the output active power is derived. Considering the theoretical analyses and influencing factors, the inertia and damping are obtained by using the method of function fitting. The test steps show the simplicity of the proposed test method. Finally, the effectiveness of the proposed method is verified in MATLAB/Simulation and two 1.575‐MW parallel grid‐forming electrochemical energy storage power plants.

Frequency Nadir Estimation Using the Linear Characteristics of Frequency Control in Power Systems

With the increasing integration of inverter-based resources, the contribution of synchronous generators to power grids has decreased, resulting in a reduction in system inertia. Currently, acquiring the reserve power to mitigate the volatility associated with renewable-energy sources are difficult. Hence, evaluating the frequency stability of power systems and formulating operational and planning strategies based on these evaluations are becoming increasingly important. In this paper, we propose the definition and formalization of the frequency nadir index (FNI) by identifying the linear characteristics of inertia, frequency regulating reserve space (FRRS), and governor free (G/F) reserve in relation to frequency nadir, particularly under assumed contingencies such as generator dropout and sudden load fluctuation. Furthermore, we present an effective methodology for evaluating frequency stability using the FNI equation by extracting inertia, FRRS, and G/F reserve information from the power-system data. This approach is straightforward and efficiently computes the frequency nadir based on the size of the generator failure using readily available power-system data within a short timeframe.

Inertial Estimation in Power Grids Considering Load Contribution Based on FF-UKF

Abstract In modern power systems, the extensive integration of renewable energy sources leads to a reduction in system inertia, thereby affecting grid stability. This study proposes a novel method for estimating grid inertia, which, under quasi-steady state conditions, effectively incorporates load contribution by combining class noise signals collected by PMUs (Phasor Measurement Units) with the Forgetting Factor Unscented Kalman Filter algorithm (FF-UKF). The research initially analyzes the characteristics of various inertia sources in power systems dominated by renewable energy. Building on this, we propose a grid node equivalent inertia estimation model based on node equivalent frequency response, developing an FF-UKF-based algorithm that allows for the continuous dynamic estimation of inertia at various grid nodes. Simulation experiments conducted within the IEEE 39 bus system validate the method’s effectiveness and demonstrate the spatiotemporal distribution of grid inertia under varying levels of renewable energy penetration. This study is significant for understanding and enhancing frequency control and stability in power systems, providing key technical support for the modernization of the power system and the efficient integration of renewable energy.

RoCoF Constrained Unit Commitment Considering Spatial Difference in Frequency Dynamics

The post-disturbance rate of change of frequency (RoCoF) is a critical index for low-inertia power system frequency stability. This paper proposes a RoCoF constrained unit commitment model so as to enhance the frequency stability in operation time-scale, where the spatial difference in frequency dynamics is considered and the RoCoF constraint is enforced for each node. The maximum of node RoCoF is approximated by two terms, i.e., the initial post-disturbance node RoCoF and the maximum of the center of inertia (COI) RoCoF. Analytical expressions of the node initial RoCoF under typical disturbances are derived. Then, a tractable relationship between the node initial RoCoF and the working status of generators is obtained by the piecewise linearization approach. Simulation results carried out on the IEEE 39-bus system demonstrate the proposed model can limit the node RoCoF in an economic and accurate manner. The adaptability to renewable power generation and online application are also discussed.

Frequency Stability of Multi-source Power System using Whale Optimization Algorithm

The Whale Optimization Algorithm (WOA), an evolutionary computing approach, is presented in this study and is used to auto regulated frequency of many composed power systems including thermoelectric power station, hydroelectric, and gas power plants. The purpose of this process follows the concept of a hunting mechanism of fish through water bubbles. The WOA is first applied to a single region with a multi-source power system for optimal gain adjustment of proportional integral controllers (PID). This approach is then applied to two areas, each having six generating sources with AC and AC-DC links. The credible achievements of the WOA-based PID controller are compared with previously constructed optimization approaches like Teaching Learning Based Optimization (TLBO), Differential evolution (DE) and Optimal Controller (OC), which is demonstrated in terms of frequency error, settling time and damping ratio. The performance indices of the purposed controller are analyzed through different objective functions like integral square error (ISE), integral time absolute error (ITAE), integral absolute error (IAE) and integral time squared error (ITSE). By using step load agitation, the simulation results indicate that the suggested technique is computationally stable.

Advantage of battery energy storage systems for assisting hydropower units to suppress the frequency fluctuations caused by wind power variations

The integration of renewable energy sources into power grids has led to new challenges for maintaining the frequency stability of power systems. Hydropower has traditionally played a key role in frequency regulation due to its flexibility in output power. However, the water hammer effect can lead to the phenomenon of inverse regulation, which can degrade the transient characteristics of power systems, particularly in hydropower-dominant systems, such as the Southwest China Power Grid. On the other hand, battery energy storage systems (BESSs) are well-suited for frequency regulation due to their fast response speed, high response accuracy, and flexible control capabilities. Hence, it is a meaningful topic to evaluate the advantage of integrated battery energy storage systems for assisting hydropower units (HPUs) in frequency regulation. First, the frequency dynamic response model of power system with BESSs assisting HPUs to participate in frequency regulation is established. Then, a two-part strategy is presented. The primary frequency regulation strategy for BESSs uses droop control with a variable regulation coefficient and the secondary frequency regulation strategy considers the costs associated with both HPUs and BESSs. Last, a performance assessment is carried out based on the management rules for auxiliary services of power plants in China and the USA. The results of this study demonstrate that the incorporation of the BESS into the HPU can significantly improve the regulating performance, and can provide important economic and technical benefits for the power system. Specifically, the maximum ratio of HPU with BESS to conventional HPU is 33.13 %, 33.85 %, 7.60 % and 41.52 % for the different indicators (difference, delay, distance, and cost). Notably, the implementation of BESS in the HPU not only contributes to the stability of the power system, but it also provides considerable economic benefits by achieving higher evaluations for auxiliary services in the power market. These findings are critical in supporting the transformation and development of conventional HPUs under large-scale new energy grid connection conditions.

Analysis of Minimum Rotational Inertia Requirements for Power System Frequency Stability

With the advancement of energy transformation and new power systems, large-scale integration of new energy to replace synchronous generators is leading to insufficient inertia in the system, threatening stable frequency operation. Evaluating the minimum inertia requirements of power systems is beneficial for improving the integration capacity of new energy and ensuring secure and stable operation. This paper establishes a mathematical model of frequency dynamics after a fault and advances an approach to assess the minimum rotational inertia requirements. The proposed approach is tested on the modified WSCC-9 bus system to validate its efficacy.

A New Fractional-Order Virtual Inertia Support Based on Battery Energy Storage for Enhancing Microgrid Frequency Stability

Microgrids have a low inertia constant due to the high penetration of renewable energy sources and the limited penetration of conventional generation with rotating mass. This makes microgrids more susceptible to frequency stability challenges. Virtual inertia control (VIC) is one of the most effective approaches to improving microgrid frequency stability. Therefore, this study proposes a new model to precisely mimic inertia power based on an energy storage system (ESS) that supports low-inertia power systems. The developed VIC model considers the effect of both the DC-DC converter and the DC-AC inverter on the power of the ESS used. This allows for more precise and accurate modeling of the VIC compared to conventional models. Moreover, this study proposes a fractional-order derivative control for the proposed VIC model to provide greater flexibility in dealing with different perturbations that occur in the system. Furthermore, the effectiveness of the proposed fractional-order VIC (FOVIC) is verified through an islanded microgrid that includes heterogeneous sources: a small thermal power plant, wind and solar power plants, and ESSs. The simulation results performed using MATLAB software indicate that the proposed VIC scheme provides fast stabilization times and slight deviations in system frequency compared to the conventional VIC schemes. The proposed VIC outperforms the conventional load frequency control by about 80% and the conventional VIC model by about 45% in tackling load/RESs fluctuations and system uncertainty. Additionally, the studied microgrid with the proposed FOVIC scheme is noticeably more stable and responds faster than that designed with integer-order derivative control. Thus, the proposed FOVIC scheme gives better performance for frequency stability of low-inertia power systems compared to conventional VIC schemes used in the literature.

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.

A predictive tool for power system operators to ensure frequency stability for power grids with renewable energy integration

The increased penetration levels of renewable energy resources (RESs) transform the power generation schema into one that is more susceptible to changes due to weather conditions, complicated load profiles, and reduced inertia levels. One of the main challenges that power grids can encounter under varying and low system inertia (SI) is poor frequency response (FR). Therefore, this paper proposes a novel online tool for assessing, predicting, and enhancing the frequency stability (FS) of power systems with renewable power generation and energy storage systems (ESS). Firstly, the tool provides accurate tracking of the SI in real-time settings using recursive least square identification and Kalman filtering to provide accurate and computationally efficient results. Secondly, the tool estimates the FR of the whole system in a virtual environment for different contingencies and inertia levels. The accuracy of the FR is improved by classifying the frequency response models (FRMs) based on the SI levels. Lastly, the proposed tool computes the optimal additional estimated reserve power (ERP) required from PV and battery energy storage systems (BESS) to provide inertial and primary frequency support to the power grid at the onset of a contingency. In addition, a reserve power allocation and load-shedding strategies are proposed and implemented to dynamically adjust the reserve power of PV power plants. This dynamic control of the PV power plant reserve capacity guarantees the availability of adequate reserves for addressing unforeseen systems contingencies. Moreover, dedicated FR controllers for PV and BESS are employed to emulate the synchronous machine’s inertial response (IR) and primary frequency control (PFC). The performance of the proposed tool and the FR controllers are tested and validated on a generic power grid and the IEEE 39 bus system using MATLAB Simulink and the OPAL-RT real-time simulation software.

Minimum inertial demand estimation of renewable energy considering new power system frequency constraints using sparrow search algorithm

With the proposal of a "dual carbon strategy " and the rising share of renewable energy sources, the resulting low-inertia problem has seriously affected the frequency stability of new power systems. This paper proposes a minimum inertial demand estimation of renewable energy considering new power system frequency constraints to enhance the power system inertia situational awareness and clarify the system operation boundary. Firstly, the frequency response model with multi-source renewable energy units and the time-domain mathematical expressions are established, and the frequency constraints and inertial demand of new power systems are given. The minimum inertial demand estimation model is constructed on this basis, which can be solved by the sparrow search algorithm (SSA). Ultimately, the applicability and practicality of the suggested approach are demonstrated and verified in IEEE 39-bus system. The case study results demonstrate the process can accurately calculate the inertial demand of renewable energy side considering system frequency constraints and give guidance for the stable operation of new power systems.

Analysis of the cause of power system inertia generation and decline

Variable renewable energy sources (RES) are becoming more and more common, and traditional power generation plants are rapidly being replaced by them. As RES are used more frequently, power electronics are also utilized more frequently, both to connect RES and as drives for electric motors. As a result, the inertia level of the power system is continuously decreasing, and the frequency stability of the power system is facing severe challenges. Traditional power-generating methods such as thermal, hydroelectric, nuclear, and natural gas use generators to produce electric energy. By utilizing the rotational inertia of the steam turbine unit, the frequency fluctuation trend that occurs in the power grid can be delayed. However, photovoltaic power generation lacks rotating machinery and has no rotational inertia, whereas wind turbines operate at a modest speed and have negligible rotational inertia. The response capability is reduced significantly when the power grid's frequency changes. Any electric power system tends to rely on rotational inertia. The relevant factors impacting the inertia level of the power system are introduced based on the concept of inertia of the power system. The power system experiences inertia from the synchronous grid-connected generation side, the load side, and the grid-connected generation side of the converter. These three sources make up the majority of the inertia in the system. From the aspects of the power generating side, grid side, and load side, approaches and strategies to increase the frequency stability of power systems are introduced.

A robust control approach integrating with optimal fuel cells to strengthen the frequency stability of a diverse-sources power system including renewables

In the current power landscape, renewable energy sources (RESs) have assumed a crucial role in satisfying consumer demand. However, as the deployment of renewables increases, certain challenges arise, including issues with system frequency stability, inertia, and damping reduction. To address these concerns, an innovative approach is suggested in this study. The proposed strategy aims to maintain frequency stability in a diverse-source power system that encompasses two interconnected regions incorporating RESs. The proposed strategy comprises a new multi-degree of freedom FOTID controller known as the MDOF-TIλDμN controller in the secondary control loop (SCL) and optimally controlled fuel cells (OFCL) to enhance the system’s stability under the effect of renewable energy (RESs) fluctuations. In this context, the gains of the considered strategy (optimal MDOF-TIλDμN in addition to OFCL) have been picked out by using an innovative optimization approach known as the Capuchin search algorithm (CapSA). The statistical tests are used to examine the efficacy of the considered CapSA compared to those of other optimization strategies utilized in previous studies. Furthermore, the performance of the proposed controller in the SCL is verified by contrasting its performance with that of another suggested controller known as MDOF-PIDN as well as other controllers such as PD-IT, PDμN-IλT, 2DOF-TIλDμN, 3DOF-PIDN, 3DOF-TIDN, and 3DOF-PIλDμN. Additionally, grid nonlinearities, including Boiler Dynamics, Generation Rate Constraint, Governor Dead Band, and random communication time delay (CTD), are considered. Moreover, the proposed strategy’s performance is verified in the face of system constraints and nonlinearities. Different scenarios are implemented, and the simulation outcomes emphasize the superior performance of the suggested strategy. Therefore, the suggested strategy provides consistent power system adoption wherever it is implemented.

Enhancing frequency stability in diverse power systems with conventional and renewable energy sources based on an innovative LFC and controlled energy storage integration

The rapid advancement of renewable energy sources (RESs) has led to a decrease in system inertia and an exacerbation of the instability issue. Hence, this study puts forward an approach to bolster the stability of the power grid amidst the presence of RESs and disturbances in load conditions. The strategy utilizes controlled energy storage systems, including plug-in electric vehicles and fuel cell systems, along with a secondary controller (SC). To improve the strategy's performance, novel controllers and an enhanced optimization technique are employed. The proposed controller combines proportional-integral-derivative (PID) and fractional order control methods, resulting in a new arrangement. The parameters of the controller are tuned using an improved optimization technique called an Enhanced Runge Kutta Optimizer. The effectiveness of the proposed algorithm is demonstrated through a performance comparison with conventional optimizers, using well-established mathematical equations. Additionally, the proposed controller's effectiveness is verified by comparing its performance with other controller arrangements, such as PID, combining TD-TI, and cascaded (1 + PD)-PID controllers. The performance of the system is enhanced by 66 % more with the proposed controller in SC compared to the (1 + PD)-PID controller, which is regarded as the most optimal among the controllers examined in this study. Additionally, the system's performance is improved by 44 % when the proposed strategy is implemented, as compared to the system's performance without the proposed strategy. Totally, the effectiveness of the proposed strategy is validated across various scenarios, including high penetration of RESs, significant load fluctuations, and system non-linearity.

Economic Analysis of Li-Ion Battery–Supercapacitor Hybrid Energy Storage System Considering Multitype Frequency Response Benefits in Power Systems

With the promotion of carbon peaking and carbon neutrality goals and the construction of renewable-dominated electric power systems, renewable energy will become the main power source of power systems in China. Therefore, ensuring frequency stability and system security will emerge as pivotal challenges in the future development process. Created by combining a Li-ion battery and a supercapacitor, a hybrid energy storage system (HESS), which possesses robust power regulation capabilities and rapid response capabilities, holds promise for supporting the frequency stability of power systems. In this context, the assessment of the economic viability of HESSs providing multitype frequency response services becomes a critical factor in their deployment and promotion. In this paper, an economic analysis approach for a Li-ion battery–supercapacitor HESS towards a multitype frequency response is presented. First, a multitype frequency response-oriented operational mode for the HESS is designed, outlining the roles and functions of the Li-ion battery and the supercapacitor in delivering distinct services. Moreover, building upon the analysis of the power trajectory of Li-ion batteries, a lifetime model for the HESS is proposed based on the rain-flow counting method. Furthermore, considering the competitive landscape for the HESS in the frequency regulation ancillary service market, a full lifecycle economic assessment model is proposed. Finally, case studies on actual power system frequency data and PJM market data are performed to verify the effectiveness of the proposed method, and the simulation results confirm that the HESS exhibits robust performance and a competitive advantage in providing multitype frequency response services. Additionally, it demonstrates commendable economic benefits, establishing its potential as a valuable contributor to frequency response services.

A Two-Stage Data-Driven Method for Estimating the System Inertia Utilizing Event-Driven PMU Measurements

With the increasing penetration level of renewable energy resources with less system inertia, accurate estimation of the power system inertia has become a critical issue for maintaining the frequency stability of the entire power system. To tackle out this challenging task, a two-stage data-driven method is proposed in this paper for estimating the system inertia from disturbed PMU measurements. First, by integrating its low-order system frequency response model with the first-order turbine model, analytical expressions of the frequency response under the steady-state and these transient oscillatory components are derived. Then, based on this parametric model, a two-stage estimation algorithm will be developed. At the first stage, system parameters of oscillatory components can be extracted from PMU measurements by Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). By utilizing frequency measurement data from PMUs and those estimated parameters from the ESPRIT algorithm, a weighted nonlinear least square approach is applied at the second stage to estimate physical parameters such as system inertia, damping coefficient, turbine time constant, and regulation coefficient. To validate the effectiveness of the proposed method, simulation studies of IEEE 39- bus system is investigated. Historical PMU measurements from various contingencies of Taiwan Power System will also be explored. All of these results demonstrated that the proposed method provides satisfactory performances with the mean relative error less than 10%. Comparisons with other existing methods are performed to demonstrate the advantage of the proposed method.

A robustness-enhanced frequency regulation scheme for power system against multiple cyber and physical emergency events

Emergency events, e.g., accidental generator outages and abrupt steeps in electric load in physical layer, and unexpected communication time delays in cyber layer, are raising increasing concerns in modern power systems, and can cause system frequency deterioration, thus threatening power energy security. However, currently there is few discussions on dealing with multiple emergency events in power system comprehensively and simultaneously. In order to counter the adverse effects caused by these various emergency events and maintain the system frequency, a robustness-enhanced frequency regulation scheme is proposed in this article based on the coordinate transformation technique and Lyapunov theorem. First, to analyze the dynamic process of the power system in contingency conditions, the model of the power system frequency regulation is reconstructed considering multiple emergency events. Furthermore, to guarantee the power system frequency stability, a virtual auxiliary surface is constructed based on the coordinate transformation technique, which can provide the control reference for frequency regulation. On this basis, a robust controller is developed to drive the system’s trajectory to the proposed virtual auxiliary surface, thus guaranteeing the robustness of power system frequency, e.g., minor frequency deviation and faster recovery speed, even with emergency events. In addition, the stability of the system with the proposed controller is rigorously proved by Lyapunov theorem. Finally, the effectiveness of the proposed scheme is verified by case studies. The results show that by using the proposed scheme, the maximum frequency deviation and recovery time can be improved to about 61.11% and 46.40% of the original value under multiple emergency events, respectively. Therefore, the proposed scheme can counter well against emergency events and contribute to the power system’s frequency regulation and energy security.