Frequency Stability Assessment Research Articles

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.

AI-Based Faster-Than-Real-Time Stability Assessment of Large Power Systems with Applications on WECC System

Achieving clean energy goals will require significant advances in regard to addressing the computational needs for next-generation renewable-dominated power grids. One critical obstacle that lies in the way of transitioning today’s power grid to a renewable-dominated power grid is the lack of a faster-than-real-time stability assessment technology for operating a fast-changing power grid. This paper proposes an artificial intelligence (AI) -based method that predicts the system’s stability margin information (e.g., the frequency nadir in the frequency stability assessment and the critical clearing time (CCT) value in the transient stability assessment) directly from the system operating conditions without performing the conventional time-consuming time-domain simulations over detailed dynamic models. Since the AI method shifts the majority of the computational burden to offline training, the online evaluation is extremely fast. This paper has tested the AI-based stability assessment method using multiple dispatch cases that are converted and tuned from actual dispatch cases of the Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. The results show that the AI-based method could accurately predict the stability margin of such a large power system in less than 0.2 milliseconds using the offline-trained AI agent. Therefore, the proposed method has great potential to achieve faster-than-real-time stability assessment for practical large power systems while preserving sufficient accuracy.

Frequency Stability Assessment of Grid-Forming VSG in Framework of MPME With Feedforward Decoupling Control Strategy

Virtual synchronous generator (VSG), recognized as a grid-friendly control technique, contributes to providing inertia and damping support from the grid-tied power electronic systems. However, similar to the conventional synchronous generator, the VSG is vulnerable to wideband oscillations and can even become unstable when the system is subjected to a variety of disturbances. To tackle this issue, this article proposes a magnitude-phase motion equation (MPME) for grid-forming VSG attached to a weak grid. Besides, a feedback analytical method is introduced to identify the frequency dynamic stability, judged by the sign of ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dω</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dt</i> )/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δω</i> . Besides, the rate of change of frequency (RoCoF) and frequency nadir (FN) are evaluated by the two indices, i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dω</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dt</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δω</i> . In addition, the relationship between the low-inertia-RoCoF-FN-related stability and the weak-damping-oscillation-related stability is illustrated by the feedback analysis. Moreover, in the framework of MPME, a reactive-power feedforward (RPFF) decoupling control strategy is proposed for the enhancement of stability and robustness performance of the VSG system. Finally, the proposed modeling and the RPFF decoupling control strategy are demonstrated with the experiments.

Power system frequency stability using optimal sizing and placement of Battery Energy Storage System under uncertainty

In the literature, a variety of system uncertainty is not included in the frequency stability research. This research demonstrated that employing the probabilistic frequency stability analysis approach which accounts for the uncertainty of system parameters such as loads and generation uncertainty, resulted in a more accurate frequency stability assessment when compared to the deterministic technique. Additionally, this study proposes a framework for determining the optimal size and placement of Battery Energy Storage System (BESS) in power systems while taking into account the uncertainty associated with system generation and demand, as well as intermittent generation sources and contingency locations which have been rarely considered in the literature. The novelty of these methods is that they determine the optimal BESS size and placement based on the amount and location of the critical system loads. The methodologies have been validated using IEEE 39-bus and simplified SE-Australian power systems where the simulations were implemented using DIgSILENT/PowerFactory software with Python interface. The simulation results revealed that the optimal BESS size should not be equal to more than 4.5% from the system loads amount while the optimal BESS placement was acquired when the BESS are placed closer to around 30% of the system loads. Furthermore, by investigating the impact of the contingency and wind farm locations on the optimal BESS size, the contingency location had the greatest impact on the BESS properties, while the wind farm locations provided a negligible impact.

Frequency Stability Assessment of Multiple Virtual Synchronous Generators for Interconnected Power System

Virtual inertia (VI) control is a promising concept to ensure the frequency stability of systems dominated by high renewable energy. Supply of VI is established by an inverter-based energy storage system, which can emulate a necessary behavior of synchronous generation in terms of inertia and damping properties, enhancing the entire system stability. This work investigates the dynamic behavior of multiple-VI in an interconnected system. A frequency control model of a three-area interconnected system with multiple-VI control is presented. Then, contrastive test scenarios are conducted to evaluate the necessity of the VI control in both islanded and grid-connected modes. The obtained results show that the genuine dynamic behavior of a grid-connected mode can lead to critical frequency issues with damping insufficiency. The instability in a grid-connected mode can be resolved by the development of multiple-VI control. The promising results will be useful and essential for further research on an interconnected system in respect to a detailed model-based frequency and inertia power response.

Reintegration-based controlled islanding considering fast and slow active/reactive corrective actions to enhance frequency and transient voltage stabilities

In this paper, a reintegration-based multi-objective intentional controlled islanding (ICI) model is proposed to enhance resiliency of electrical power systems under catastrophic events. This remedial measure plan relies on a mixed-integer linear programming model with two objective functions including reintegration risk and total load shedding value. While ensuring that each island includes only coherent generators, the proposed multi-objective model solves the controlled islanding problem using lexicographic optimization approach. To ease the islands’ reintegration, charging reactive power, reliability, capacity, and power flow disruption of transmission lines are considered in the model. After implementation of controlled islanding, each resulted island may face temporary active/reactive load-generation imbalance, which may put the islands at the risk of frequency instability, transient voltage instability or a combination of both. The proposed model reduces these risks by modeling energy storage systems (ESSs) and static VAR compensators (SVCs) as fast corrective control actions. In addition to modeling voltage dependent loads in the controlled islanding problem, a linear island frequency response (IFR) model is proposed for frequency stability assessment. The test results of the proposed ICI model on the IEEE 39-bus and IEEE 118-bus test systems demonstrate its performance.

A Transfer and Deep Learning-Based Method for Online Frequency Stability Assessment and Control

Fast and accurate prediction and control of power system dynamic frequency after disturbance is essential to enhance power system stability. Machine learning methods have great potential in harnessing data for online application with accurate predictions. This paper proposes a two-stage novel transfer and deep learning-based method to predict power system dynamic frequency after disturbance and provide optimal event-based load shedding strategy to maintain system frequency. The proposed deep learning model combines convolutional neural network (CNN) and long short-term memory (LSTM) network to harness both spatial and temporal measurements in the input data, through a four-dimensional (4-D) tensor input construction process including, 1) capture system network topology information and critical measurements from different time intervals; 2) compute a multi-dimensional electric distance matrix and reduce to a 2-D plane which can describe the system nodal distribution; 3) construct 3-D tensors based on state variables at different sample times; and 4) integrate into 4-D tensor inputs. Moreover, a transfer learning process is employed to overcome the challenge of insufficient data and operating condition changes in real power systems for new prediction tasks. Simulation results in IEEE 118-bus system verify that the CNN-LSTM method not only greatly improves the timeliness of online frequency control, but also presents good accuracy and effectiveness. Test cases in the New England 39-bus system and the South Carolina 500-bus system validate that the transfer learning process can provide accurate results even with insufficient training data.

Data‐driven transient frequency stability assessment: A deep learning method with combined estimation‐correction framework

Data‐driven transient frequency stability assessment: A deep learning method with combined estimation‐correction framework

Frequency stability assessment of modern power systems: Models definition and parameters identification

One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context, the paper proposes a framework that, by making use of linear models of the frequency response of different types of power plants, including also grid--forming and grid-following converters, is capable to infer a numerically tractable dynamical model to be used in frequency stability assessment. Furthermore, the proposed framework makes use of models defined in a way such that their parameters can be inferred from real-time measurements feeding a classical least squares estimator. The paper validates the proposed framework using a full-replica of the dynamical model of the IEEE 39 bus system simulated in a real-time platform.

Frequency Stability Assessment of Power System Using Frequency Stability Indices and Artificial Neural Newwork

Frequency stability assessment (FSA) is an evaluation of a dynamic behavior in power system under severe contingency. One of the significant approach in FSA is using frequency stability indices (FSI) to evaluate the performance of the power system and identify the stability status of the power system. Many methods for frequency stability assessment is Time Domain Simulation, Frequency Stability Index and Individual Generator’s Frequency referred to Slack Generator’s Frequency.

Long-Term Frequency Stability Assessment Based on Extended Frequency Response Model

Large frequency deviation degrades the operation performance of the boiler and its auxiliaries. It affects the output of thermal power units. A significant change in power generation leads to a great frequency deviation. An extended frequency response model for long-term frequency stability assessment is constructed to consider the effects of frequency deviations on boiler auxiliaries. The static power-frequency characteristic of the thermal power unit within an extensive frequency variation range is analyzed. It reveals that the active power output of the generating unit is not monotonically increasing with frequency dropping. An inflection point is observed on the static power-frequency characteristic curve when considering boiler auxiliary frequency characteristics. In the range of greater frequency deviation, the output power decreases rapidly with frequency declination, and an unstable equilibrium point (UEP) of frequency stability is identified. A quantitative index is proposed for frequency stability assessment based on UEP. The stability characteristic and the frequency stability quantitative index based on UEP are analyzed. The frequency dynamic behaviors of the extended model are demonstrated to analyze frequency stability characteristics within an extensive frequency variation range by a single machine system and the IEEE 39-bus system with considering boilers and its auxiliaries.

Integrating Model-Driven and Data-Driven Methods for Power System Frequency Stability Assessment and Control

With increase of practical power system complexity, power system online stability assessment and control is more and more important. Application of the traditional model-driven methods is always limited by contradiction between accuracy and efficiency, while data-driven methods demonstrate strong abilities for the online decision-making support with advancement of various data mining techniques. Instead of direct application of data-driven methods in the power system, this paper first discusses feasible integration approaches for the model-driven and data-driven methods based on the existing achievements, and then, proposes to integrate both methods for the power system online frequency stability assessment and control. The integrated method consists of frequency dynamics prediction and load shedding procedure. In frequency dynamics prediction procedure, integration of system frequency response (SFR) model and the extreme learning machine (ELM)-based learning model is applied, where basic physical causality is kept in the SFR model and ELM is used to fit and correct error of the SFR. The ELM also plays a part in load shedding prediction model construction by digging out mapping relationship from samples. Finally, the proposed prediction and control scheme for the frequency stability is verified by simulations on WSCC 9-bus, New England 39-bus, and NPCC 140-bus system. Results show that the reliability, time efficiency, and accuracy are enhanced with the proposed method.

Bulk power system frequency stability assessment in presence of microgrids

An attempt is made in this paper to propose an analytical approach to mathematically assess the impact of MGs penetration level on power system frequency stability. Firstly, experimental-based model of constitute DGs of the University of Kurdistan-MG (UOK-MG) in islanded mode may be derived. Afterwards, realistic model of the MG in grid connected mode may be derived to realize penetrated system for future studies. Finally, some simple algebraic equations are derived to predict frequency dynamics of interest in penetrated system. The method interprets the frequency dynamic behavior of the penetrated system based on the conventional system in terms of frequency nadir, Rate of Change of Frequency (RoCoF), steady state deviation and a rolling window. Simulation results demonstrate high efficiency of the proposed approach for dynamical modeling and stability analysis of penetrated power systems.

A Key Performance Indicator to Assess the Frequency Stability of Wind Generation Dominated Power System

High penetration of power electronic interfaced generation, like wind power, has an essential impact on the inertia of the interconnected power system. It can pose a significant threat to the frequency stability. This paper introduces the notion of the key performance indicator (KPI) and illustrates its application on large scale power systems, including Fast Frequency Response (FFR) and a high share of wind power, to measure the possible distance to the frequency stability limit. The proposed KPI estimates the change of frequency performance (e,g., ROCOF, NADIR) in the frequency containment period. The effect of FFR is analyzed by introducing a droop based controller for wind power plants. The FFR controller responds to a drop in grid frequency with a temporary increase of the wind active power. The proposed KPI maps a change in key system variables (e.g., system kinetic energy, aggregated generation output) onto the change of frequency performance. A comprehensive analysis using DIgSILENT, Matlab, and Python is performed for GB reduced size system. According to the obtained results, the FFR capability of wind generator leads to improvements of NADIR especially in cases with high penetration levels of wind power. The proposed KPI is a valuable tool for the frequency stability assessment in power system planning studies. It can be determined based on off-line simulations, and it can assist the system operators for frequency stability assessment in intra-day operational planning.

Frequency and Voltage Stability Assessment Applied to Load Shedding

Under voltage load shedding (UVLS) and under frequency load shedding (UFLS) is plays vital role in the power system operation. As large disturbances are occur frequently in previous days. Generally these two methods are work independently from each other, and are not designed to integrated way to use their combined effect on load shedding. The reactive power hardly consider in load shedding process. To fill this gap, we froth put in this paper a new concentration about adaptive load shedding algorithm. The phasor measurement unit can gives both voltage and frequency information. The main concept of the new method is consideration of reactive power combined with active power in load shedding strategy. This method is gives information about the combined voltage and frequency stability issues is better than the independent approaches. The new method is tested on the IEEE 39-Bus system, in order to compare with other methods. By applying this new method to the system, that system will be back to new stable steady state that is better from the perspective of voltage and frequency and loadability.

Event‐based remedial action scheme against super‐component contingencies to avert frequency and voltage instabilities

Frequency instability, voltage instability or a combination of both have been the cause of several power system breakdowns throughout the world in the recent decades. Occurrence of a super-component contingency (SCC) that refers to multiple and simultaneous outages of grid facilities like a power plant or substation may lead to blackout if no remedial action schemes (RAS) are implemented. This study proposes a new event-based RAS to overcome the frequency and voltage instabilities caused by SCCs through optimal load shedding. To do this, a new multi-objective framework is presented simultaneously optimising the competing objective functions of long-term voltage stability margin, steady-state frequency deviation, maximum transient frequency deviation and load shed amount. A modified system frequency response model is also proposed for frequency stability assessment. Multi-objective decision making (MODM) is performed using a combination of analytical hierarchy process, modified augmented e-constraint method and technique for order preference by similarity to ideal solution. The effectiveness of both the proposed model and MODM solution approach is extensively illustrated on a simulated model of Iran's power system in 2012.

Adaptive load shedding based on combined frequency and voltage stability assessment using synchrophasor measurements

Under frequency load shedding (UFLS) and under voltage load shedding (UVLS) are attracting more attention, as large disturbances occur more frequently than in the past. Usually, these two schemes work independently from each other, and are not designed in an integrated way to exploit their combined effect on load shedding. Besides, reactive power is seldom considered in the load shedding process. To fill this gap, we propose in this paper a new centralized, adaptive load shedding algorithm, which uses both voltage and frequency information provided by phasor measurement units (PMUs). The main contribution of the new method is the consideration of reactive power together with active power in the load shedding strategy. Therefore, this method addresses the combined voltage and frequency stability issues better than the independent approaches. The new method is tested on the IEEE 39-Bus system, in order to compare it with other methods. Simulation results show that, after large disturbance, this method can bring the system back to a new stable steady state that is better from the point of view of frequency and voltage stability, and loadability.

Extreme learning machine-based predictor for real-time frequency stability assessment of electric power systems

As a novel and promising learning technology, extreme learning machine (ELM) is featured by its much faster training speed and better generalization performance over traditional learning techniques. ELM has found applications in solving many real-world engineering problems, including those in electric power systems. Maintaining frequency stability is one of the essential requirements for secure and reliable operations of a power system. Conventionally, its assessment involves solving a large set of nonlinear differential–algebraic equations, which is very time-consuming and can be only carried out off-line. This paper firstly reviews the ELM’s applications in power engineering and then develops an ELM-based predictor for real-time frequency stability assessment (FSA) of power systems. The inputs of the predictor are power system operational parameters, and the output is the frequency stability margin that measures the stability degree of the power system subject to a contingency. By off-line training with a frequency stability database, the predictor can be online applied for real-time FSA. Benefiting from the very fast speed of ELM, the predictor can be online updated for enhanced robustness and reliability. The developed predictor is examined on the New England 10-generator 39-bus test system, and the simulation results show that it can exactly (within acceptable errors) and rapidly (within very small computing time) predict the frequency stability.