Center Of Inertia Research Articles

Enhancing power system stability with adaptive under frequency load shedding using synchrophasor measurements and empirical mode decomposition

This paper introduces an adaptive under frequency load shedding (AUFLS) scheme based on synchrophasor measurements and Empirical Mode Decomposition (EMD) to enhance power system stability during significant disturbances. The traditional UFLS methods, which rely on fixed frequency thresholds, often lead to unnecessary disconnections and a lack of flexibility. The proposed AUFLS scheme dynamically adapts to the magnitude of disturbances, frequency response, and voltage stability index, resulting in a more efficient and responsive system. Various UFLS techniques are reviewed, highlighting the advantages of adaptive strategies. The novelty of this research lies in the innovative application of the EMD algorithm within the AUFLS framework. This method identifies the center of inertia (CoI) of the rate of change of frequency (RoCoF) from frequency signals and calculates the total active power imbalance due to disturbances. Furthermore, EMD is applied to the voltage angle at each bus to identify and form coherent bus groups. These coefficients are subsequently employed to allocate the required active power shedding within each group to maintain system stability. Voltage stability indices are calculated for each group, and load shedding is distributed among the buses based on normalized voltage stability indices, thereby enhancing the precision of load shedding decisions and the overall stability of the power system. Results demonstrate that the proposed scheme provides satisfactory frequency response while requiring less load shedding compared to traditional methods, making it effective for modern power systems with high penetration of renewable energy sources (RES). The performance of the proposed scheme is assessed using the IEEE 39-bus test system, demonstrating its effectiveness in improving system resilience to frequency disturbances. The research concludes that the AUFLS scheme offers a promising approach for enhancing the resilience of power systems to frequency disturbances.

Artificial intelligence-based approach for islanding detection in cyber-physical power systems

Modern power grids, functioning as a cyber-physical system (CPS), accommodate high penetration level of distributed generations (DGs) to ensure sustainability. Achieving sustainability through grid-scale DGs, however, increases the likelihood of islanding occurrences, which jeopardizes a major parameter of CPS implementation: security. This paper proposes an artificial intelligence-based approach for detecting islanding in modern power grids. The method utilizes measured voltage and frequency to develop a fuzzy center of gravity (COG)-based equivalent model of the system. The model is derived by combining data collected from phasor measurement units (PMUs) with fundamental dynamical equations that govern power system dynamics. In this model, the system is represented using a set of fictitious reactances calculated using goal programming, which are then utilized to connect the COG to the local centers of inertia (COIs). By having a set of fictitious reactances for various operating points fed into a fuzzy model, one could develop an online model to calculate the fictitious reactances with high accuracy and speed at specific snapshots. By incorporating the maximum allowable phase differences between areas into the COG model to ensure transient stability, one could enhance the developed model to be robust against cyber-physical contingencies and cyber-attacks, albeit at the expense of a slight reduction in accuracy. The calculated fictitious reactances, represented in terms of local frequencies throughout the system, serve as valuable indicators for detecting islanding. By classifying the calculated fictitious reactances using support vector clustering over a period of time, islanding could be detected with high accuracy. Furthermore, incorporating the COG concept with the clustering based on fictitious reactances makes it possible to detect false data injection in an area of the system. The efficacy of the proposed method is assessed using simulated data from the renewable integrated 73-bus IEEE test system.

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.

Data-driven assessment of center of inertia and regional inertia content considering load contribution

The inertia displacement in power grids, caused by the massive integration of renewable energy resources (RES) and responsive loads, has become one of the biggest challenges to operating and controlling power systems. Locating the centre of inertia (COI) of a region can help identify this inertia displacement. This work proposes a novel fully data-driven disturbance-based methodology to estimate both the COI and the inertia of a region, where the variation of the COI due to RES and load contribution are considered. The methodology uses a recursive form of the typicality-based data analysis (TDA) to find the pilot-bus (TDAp). The TDA methodology approximates the multi-modal distribution of active power and frequency measurements by the typicality property, to detect the COI of each region and the corresponding pilot-bus. A composite metric of correlation and cosine similarities of active power and frequency measurements is used to approximate the measurements’ unknown distribution. The window of measurements necessary for detection is attained by the convergence of the typicality variance. The frequency of the detected pilot-bus of the region and tie-lines active powers deviations are used by an auto-regressive moving average exogenous input (ARMAX) approach to estimate the inertia of a regional equivalent machine. The methodology is capable of identifying RES and load contribution, since the pilot-bus detection through the TDAp is sensible to the COI displacement by these equipments, unlike traditional methods that only consider an average of synchronous machines’ inertia and some heuristics for load contribution. The proposed methodology is tested by using the IEEE 68-bus benchmark test system, an adapted version with aggregated dynamical loads, and also with RES participation through type-3 wind generators, corroborating the effectiveness of the proposal.

A multi‐area design of under frequency load shedding schemes considering energy storage system

AbstractThis paper presents a comprehensive under frequency load shedding (UFLS) model that can be implemented in a multi‐area power system with real network characteristics. Conventional single‐area UFLS models operate on the basis of an equivalent center‐of‐inertia (COI) model, which ignores the local dynamics of system frequency response (SFR) and the impacts of load shedding location. Unlike the single‐SFR model, that is commonly utilized in previous works, the suggested multi‐area or multi‐SFR UFLS plan of this research has the distinct benefit of taking into account the dynamics of power transfer across different electric areas. The proposed multi‐area UFLS design incorporates a flywheel energy storage system (FESS) to support the inertial system frequency response and alleviate more than 30% load shedding while improving the frequency nadir by 25%. In order to investigate the performance of the proposed method under high penetrations of inertia‐free renewables, the inertia of the power network is reduced by around 30%; therefore the proposed UFLS scheme is assessed under a low inertia scenario. The proposed multi‐stage UFLS scheme is formulated as a mixed‐integer linear programming problem, and the optimal settings, including frequency set‐points and load shedding, are then optimized. The efficiency of the proposed model is verified using the IEEE‐118 Bus dynamic test system.

A center-of-gravity-based framework for small- and large-signal frequency analysis of interconnected power systems

In this paper, a unified framework to study small- and large-signal frequency response based on the notion of center-of-gravity (COG)-based dynamic equivalents is presented. The method combines the ability of COG equivalents to capture short-term system response with that of unsupervised probabilistic learning techniques to extract the (slow) dominant oscillation patterns associated with observational data. First, a reduced-order representation is obtained in which the overall system dynamics is represented by the interaction of geographical or coherent areas with a virtual COG at which the total system power equations are at balance. Then, a small-signal representation is derived from which key linear relationships between the frequency of the local centers of inertia (COIs) and the COG are determined. Next, the physical properties of the model are studied, and alternative procedures to compute COG equivalents are explored. Finally, the effectiveness of the developed models is demonstrated through applications to two sample systems, thereby verifying their accuracy.

Active power oscillation suppression and dynamic performance improvement for multi-VSG grids based on consensus control via COI frequency

Virtual synchronous generator (VSG) is deemed to be the key foundation for the future low inertia power system for its superiority to provide flexible inertia support. However, complicated dynamic frequency interaction, active power oscillation, and inappropriate transient active power-sharing will occur when VSGs are widely applied. Center of Inertia (COI) is introduced for solving these problems. But the calculation of COI frequency relies on global communication and a centralized controller, which results in high communication costs and complexity, and reduces the system reliability. This paper proposes a distributed control method via COI frequency for multi-VSG grids. The COI frequency estimator is designed based on dynamic consensus control. Communication between adjacent neighbors is required, which improves reliability and reduces communication costs. The stability of the proposed control method is proved and the feasible range of the control parameter is presented in this paper. Simulations and experiments are carried out to verify the effectiveness and feasibility.

Practical Event Location Estimation Algorithm for Power Transmission System Based on Triangulation and Oscillation Intensity

Event location in power systems is quite essential information for system operators to enhance control-room situational awareness capability. Therefore, it is of great importance to develop an event location estimation algorithm for transmission systems with high accuracy. With the development of wide-area measurement system (WAMS) such as FNET/GridEye, and the synchrophasor measurement devices (SMDs) such as frequency disturbance recorders (FDRs), the synchronous measurement data including frequency, voltage amplitude and phase angle can be collected and used for event location estimation. First, the phase angle and rate of change of frequency (RoCoF) trajectories are respectively used for determining two sets of wave arrival time associated with each FDR. Then, a convolutional neural network (CNN) is utilized to determine the wave arrival order to select the more suitable set of wave arrival times for a given case and to perform corresponding modifications. Next, the oscillation intensity associated with each FDR is determined based on phase angle trajectories in the center of inertia (COI) coordinate system. Finally, the multiple criteria for event location estimation are represented. Case studies and comparisons between the proposed and previous algorithms using actual and confirmed cases in U.S. power systems are performed to demonstrate the effectiveness and improvement of the proposed algorithm in practical applications.

Fast Voltage Boosters to Improve Transient Stability of Power Systems With 100% of Grid-Forming VSC-Based Generation

Grid-forming voltage source converter (GF-VSC) has been identified as the key technology for the operation of future converter-dominated power systems. Among many other issues, transient stability of these types of power systems remains an open topic of research because it is still a key limiting factor for stressed power systems. Previous studies have proposed control strategies for GF-VSCs to improve the transient stability of systems of this type by suitable current-limitation algorithms and/or control of active-power injections. As an alternative, this paper proposes two fast voltage boosters to improve the transient stability of power systems with 100% of GF-VSC-based generation with virtual synchronous machine (VSM). One control strategy uses local measurements, whereas the other one uses global measurements of the frequency of the centre of inertia (COI). Both strategies improve transient stability of these types of systems significantly. The advantage of using fast voltage boosters for this purpose is that the set points linked to frequency/active-power injection (i.e., set points linked to the primary energy source of the VSCs) will not be modified. Furthermore, strategies such as current-limitation, active-power control and fast voltage controllers for transient stability improvement are compatible and complementary.

A control strategy for improving power system resilience in N-k contingency

With the global climate change, the frequency of extreme weather is getting higher and higher, and the threat to the safe operation of the power system is gradually increasing, which is likely to cause large-scale power outages and then result in N-k contingencies. Meanwhile, the Modular Multi-level Converter (MMC) based Multi-Terminal High Voltage Direct Current (MTDC) power system has been confirmed that can provide the possibility for the network interconnection between regional power systems and various renewable energy resources to boost supply reliability and economy. To enhance the resilience of the power grid, a generation rescheduling scheme by optimal emergency control that considers the risk-based dynamic security constraint and reactive power constraints is proposed. Based on the transient stability criterion of the rotor angle speed of the center of inertia (COI), the active power is adjusted to improve the transient stability of the system. The usefulness of the proposed control strategy is highlighted on a 10-machine-39-bus hybrid power system built on MATMTDC, a MATLAB-based open-source software. The obtained results demonstrate that the state optimization control strategy is capable of enhancing the resilience of hybrid power systems and improving the transient stability when suffering N-k contingencies.

Can Center-of-Inertia Model be Identified From Ambient Frequency Measurements?

This letter analyzes the difficulty of estimating power system inertia under ambient conditions using the Center-of-Inertia (CoI) system model. We show that the main obstacle to doing this is a difficulty in detecting a peak in the Power Spectral Density (PSD) of the frequency trace. This is due to a combination of two factors: (i) the Ornstein-Uhlenbeck (OU) process with a high mean-reversion time, which models the load disturbance and is mathematically equivalent to a low-pass filter with a high time constant; (ii) the CoI dominant mode is highly damped. This observation also explains why it is possible to estimate system inertia under ambient conditions using wide-area PMU measurements by exploiting information about inter-area oscillations which have lower damping than the dominant mode of the CoI model. We validated those findings by using the PSD of the actual 2-hour frequency trace for Great Britain from 00:00 to 02:00 of January 01, 2019.

A Stability Result for Network Reduced Power Systems Using Virtual Friction and Inertia

We prove that virtual friction can stabilize a power grid containing several virtual synchronous machines (VSMs), connecting line impedances and loads. Virtual friction is a torque added to the swing equation of each VSM, proportional to the deviation of its frequency from the overall center of inertia (COI) frequency. Our analysis is based on the network reduced power system (NRPS) model. We support our results with simulations for a two-area network of four VSMs, looking at the transients induced by a change of tie-line impedance and an asymmetric load change. We compare the results for the NRPS model with the corresponding results using detailed models of synchronverters and line impedances. We find that virtual friction has a strong stabilizing effect both for the NRPS model and for the detailed model. Furthermore we show simulation results on the influence of time delays in the communication between the inverters. This communication is used to compute the COI frequency. It turns out that communication delays of less than 100ms have practically no effect on the overall system.

Online purely data-driven estimation of inertia and center-of-inertia frequency for power systems with VSC-interfaced energy sources

The paper proposes a novel online purely data-driven method to estimate the power system inertia and the center-of-inertia (COI) frequency by considering integration of VSC-interfaced energy sources. Without interrupting the normal operation of the grid, the proposed algorithm utilizes ambient phasor measurement unit (PMU) data to provide accurate estimation for the inertia constants of all generators/equivalent areas and the COI frequency simultaneously and efficiently. The estimated system inertia and the COI frequency can be further used to monitor the generation-demand power mismatch early in the disturbance events, providing crucial information to the design of online frequency control measures. The accuracy and efficiency of the method as well as its application in monitoring the power mismatch have been demonstrated in comprehensive numerical studies in the IEEE 68-bus system.

Power system inertia estimation method based on maximum frequency deviation

In order to solve the problem that the inertia estimation method based on the rate of change of frequency (RoCoF) is only applicable to the centre of inertia (COI) frequency, a novel inertia estimation method is proposed based on the maximum frequency deviation. This method utilizes the property that the maximum frequency deviation of each generator is basically consistent and easy to obtain. Firstly, the inertia support power of the system is quantified according to the disturbance power and frequency, and then the inertia support energy of the disturbance process is obtained. Finally, the system inertia is estimated by the ratio of the inertia support energy to the maximum frequency deviation. The proposed estimation method is suitable for non-COI frequency, which makes it unnecessary to obtain the COI frequency and RoCoF. On this basis, a simplified estimation method is proposed based on the linearization of regulation power, which improves the estimation accuracy and simplifies the estimation process. According to the proposed method, the governor test data is used to estimate, which increases the estimation times and provides more information for system stable operation. The effectiveness and accuracy of the proposed method are validated by some cases.

A new optimal design of ACD-based UPFC supplementary controller for interconnected power systems

This study presents a new optimal supplementary neuro-controller design for unified power flow controllers (UPFCs) using wide-area signals. The new design is oriented by the dual heuristic programming (DHP) method, which is a powerful adaptive critic procedure. The proposed controller injects additional signals to the UPFC series inverter to enhance power system stability. A model, action and critic neural networks are also designed for optimizing the neuro-controller. To have an accurate dynamic response of multi-machine power systems, the concepts of two-machine equivalent model (TMEM) and center of inertia (COI) are used to train the adaptive critic design (ACD) neural networks. The ANFIS structure is applied to the suggested DHP technique based on the selected input signals to improve the dynamic performance of the applied DHP controller. The designed optimal controller is applied on a real interconnected power system between Tehran and Khuzestan regions in Iran power grid. The proposed ANFIS-DHP controller performance is compared with various controllers, such as PI-Genetic, PI-Lyapunov and other intelligent approaches. The dynamic responses of the proposed controller are found to be the most effective in increasing system stability and damping out system inter-area oscillations.

Dynamic clustering-based model reduction scheme for damping control of large power systems using series compensators from wide area signals

This paper presents a new scheme of thyristor controlled series compensators (TCSC)-based damping controller for damping inter-area oscillations in bulk power systems based on a wide area measurement system (WAMS). In this regard, the proposed scheme provides an adaptive three-phase step through real-time working mode. In the first step, by proposing dynamic clustering-based technique, wide area signals evaluate the inter-area oscillations of the system which in a real-time procedure identify the corresponding oscillating areas. In the case of reducing the order of power systems through a set of aggregated coherent areas, the proposed scheme implements through the second step which utilizes as a damping controller for damping the inter-area oscillations. In this step, the wide area electromechanical signals use as input data through the proposed TCSC-based damping controller. The corresponding controlling signals consist of inter-area rotor angle (ΔδCOI) and inter-area speed deviation (ΔωCOI) evaluated through center of inertia (COI) frame. In the third step, at each time window (ΔT) through real-time working mode, the proposed scheme examines through a set of fault occurrences which based on online evaluations of the system dynamic responses, the controller parameters adjust adaptively. The proposed controller is an online and non-model-based scheme which properly reduces the system order through a set of coherent areas to provide proper damping performances of inter-area oscillations. The effectiveness of the proposed scheme evaluates through the Iran National Power Grid with the potential of two oscillating areas with proper damping performances for damping the unstable inter-area oscillations.

Underfrequency Load Shedding Using Locally Estimated RoCoF of the Center of Inertia

The conventional Under Frequency Load Shedding (UFLS) scheme could result in unacceptably low frequency nadirs or overshedding in power systems with volatile inertia. This paper proposes a novel UFLS scheme for modern power systems whose inertia may vary in a wide range due to high penetration of renewable energy sources (RESs). The proposed scheme estimates the rate of change of frequency (RoCoF) of the center of inertia (CoI), and consequently, the loss of generation (LoG) size, using local frequency measurements only. An innovative inflection point detector technique is presented to remove the effect of local frequency oscillations. This enables fast and accurate LoG size calculation, thereby more effective load shedding. The proposed UFLS scheme also accounts for the effect of the inertia change resulting from LoG events. The performance of the proposed scheme is validated by conducting extensive dynamic simulations on the IEEE 39-bus test system using Real Time Digital Simulator (RTDS). Simulation results confirm that the proposed UFLS scheme outperforms the conventional UFLS scheme in terms of both arresting frequency deviations and the amount of load shed.

Average dynamical frequency behaviour for multi-area islanded micro-grid networks

A micro-grid is a part of power system which able to operates in grid or islanding mode. The most important variable that able to give us information about the stability in islanded micro-grid network is the frequency dynamical responses. The frequency analysis for multi-area micro-grid network model may involve a complicated of mathematical equations. This makes the researcher intending to omit several unnecessary parameters in order to simplify the equations. The purpose of this paper is to show an approach to derive the mathematical equations to represent the average behavior of frequency dynamical responses for two different micro-grid areas. Both of networks are assumed to have non-identical distributed generator behavior with different parameters. The prime mover and speed governor systems are augmented with the general swing equation. The tie line model and the information of rotor angle was considered. Then, in the last section, the comparison between this technique with the conventional approach using centre of inertia (COI) technique was defined.

Wind Inertial Response Based on the Center of Inertia Frequency of a Control Area

As a result of the increased integration of power converter-connected variable speed wind generators (VSWG), which do not provide rotational inertia, concerns about the frequency stability of interconnected power systems permanently arise. If the inertia of a power system is insufficient, wind power plants’ participation in the inertial response should be required. A trendy solution for the frequency stability improvement in low inertia systems is based on utilizing so-called “synthetic” or “virtual” inertia from modern VSWG. This paper presents a control scheme for the virtual inertia response of wind power plants based on the center of inertia (COI) frequency of a control area. The PSS/E user written wind inertial controller based on COI frequency is developed using FORTRAN. The efficiency of the controller is tested and applied to the real interconnected power system of Southeast Europe. The performed simulations show certain conceptual advantages of the proposed controller in comparison to traditional schemes that use the local frequency to trigger the wind inertial response. The frequency response metrics, COI frequency calculation and graphical plots are obtained using Python.

Inertia Emulation Uncorrelated With Electromechanical Dynamics to Improve Frequency Transients Using Center of Inertia (COI) Frequency Signal

This paper proposes an inertia emulation method that uses the frequency of the center of inertia (COI) as the feedback signal, aiming to slow the frequency change rate and raise the frequency nadir during frequency-dropping events. An approximated model depicting the COI frequency dynamics is first introduced, which shows the COI frequency signal has low observabilities of electromechanical modes. Thus, this feature enables the proposed inertia emulation to react quickly to steep frequency changes without suffering any adverse impacts caused by electromechanical dynamics, such as excessively saturating the controlled objects. Moreover, the electromechanical dynamics associated with small-signal stability properties will not be interrupted by the proposed inertia emulation. In addition, a simple yet effective computing procedure is proposed to configure the critical parameters, as the inertia emulation is implemented with multiple flywheel-based energy storage systems. Simulation results obtained based on two large interconnected systems verify the effectiveness of the proposed inertia emulation in terms of improving the frequency transients as well as its limited correlation with the electromechanical dynamics of the system. The signal transmission latency's impacts on the proposed inertia emulation are also investigated and discussed.