Frequency Response Of System Research Articles

Disturbance size estimation in Great Britain power system including combined cycle gas turbine power stations

With the substantial popularity of combined cycle gas turbine (CCGT) power plants in the nowadays power systems, special care must be taken to regulate frequency due to unique frequency response characteristic of the full-loaded CCGT units. This unique feature is documented in the literature; however, its effect on determining frequency response of the power systems was not addressed in detail. This study proposes a new analytical method to achieve a more accurate estimated size of a loss-of-generation disturbance. This method considers demand-side power deviations and transmission lines power loss as well as unique frequency response of the CCGT units following the event. Firstly, it is exposed that there is an approximately linear relationship between power and frequency deviations of these plants in a real-world power system despite the complexity of the CCGT model. This relationship may be represented by a negative droop gain. Next, the derived CCGT’s linear characteristic is formulated in the disturbance size estimation process. Finally, the effectiveness of the proposed modifications is demonstrated through extensive simulations on a 36-zone Great Britain equivalent test system.

Inertia and Primary Frequency Response Requirement Assessment for High-Penetration Renewable Power Systems Based on Planning Perspective

In order to ensure the sustainable development of energy, the development of new power systems with a high penetration of renewable energy has become a key research direction in the field of power systems. This paper studies the system frequency response process and key indicators from the perspective of high-penetration renewable power systems and proposes an inertia and primary frequency response requirement assessment method for power system planning under high renewable penetration. First, by analyzing the frequency dynamic response process, the key parameters affecting frequency stability are determined, and the evolution trend of system inertia with increasing renewable penetration is analyzed. Second, based on the real-system data, the inertia and primary frequency response parameters for each generator are obtained. With the planning generation mix and load as the goal, whether the synchronous generators in the target system can meet the frequency stability requirements is determined. Finally, with the system inertia demand under the maximum rate of change of frequency (RoCoF) constraint as the starting point, we iteratively increase inertia and the primary frequency response capacity until the minimum matching configuration is found. The simulation results verify the correctness of the proposed assessment method. This method considers various processes in frequency response and multiple influencing factors, providing a practical evaluation tool for the inertia and primary frequency response requirements of high-penetration renewable power systems.

Provision of ramp-rate limitation from distribution networks to transmission systems as preventive action towards frequency disturbances

The high proliferation of Converter-Interfaced Renewable Energy Sources (CIRES) poses several challenges to electric power system operators regarding frequency stability and control. Some of these issues are related with the high active power Ramp Rates (RRs) of CIRES, stemming from their inertia-less and stochastic nature. To deal with such problems, Transmission System Operators (TSOs) often commit excessive amounts of conventional spinning reserves, while in weak Transmission Systems (TSs) regulations are imposed, aiming to mitigate RRs of CIRES. Moreover, several technical studies have proposed control approaches for RR Limitation (RRL). Nevertheless, the influence of RRL on frequency quality and mainly the impact of RRL control capability of small-scale CIRES, connected to Distribution Networks (DNs), on frequency deviations have not been fully explored and quantified. To fill this gap, a detailed investigation is performed in this paper. For this purpose, simulations are conducted on a simplified System Frequency Response (SFR) model as well as on an analytical power system model. The latter is a modified version of the IEEE 9-bus Test System, consisting of three conventional Synchronous Generators (SGs) and three Medium Voltage (MV) DNs, which include CIRES equipped with SuperCapacitors (SCs), thus presenting RRL control capability. To thoroughly evaluate the impact of RRL on frequency dynamics, a set of metrics is introduced and frequency duration curves are created for various scenarios. Finally, the influence of several factors, such as the total system inertia, the RRL target value, the SC size, etc, is quantified by using the proposed indices.

A Two-Stage Power Distribution Scheme of Multiple Wind Farms Participating in Primary Frequency Regulation

With the increasing penetration rate of renewable energy power generation (RPG) in power system, improving the frequency regulation ability of RPG has become a general trend. The premise of effective participation of RPG in primary frequency regulation (PFR) is to reasonably design the power distribution scheme for RPG devices. In order to effectively evaluate the frequency support capability of wind power generation system, the system frequency response (SFR) model under the joint action of synchronous generators, wind farms (WF) and low frequency load shedding device is established in this paper. According to the time-domain solution of this mathematical model, the influence of the output power of the WF on SFR is mathematically explained. At the same time, the influence of time delay on SFR is further demonstrated. In order to maximize the release of the rotor kinetic energy of the wind turbine and ensure the safe operation of the wind turbine when designing the power distribution scheme, an accurate prediction method of wind turbine rotor speed based on piecewise fitting and Bernoulli equation is proposed. Based on the established SFR model and rotor speed prediction method, a two-stage power distribution scheme for multiple WFs during PFR is proposed, which comprehensively considers the SFR requirements and different power output capabilities of multiple WFs. The effectiveness and superiority of the proposed power distribution scheme are validated with revised IEEE 39-bus test system and revised PG&E 69-bus test system.

Frequency domain identifiability and sloppiness of descriptor systems with an LFT structure

Identifiability and sloppiness are investigated in this paper for the parameters of a descriptor system based on its frequency responses. Two metrics are suggested respectively for measuring absolute and relative sloppiness of the parameter vector. In this descriptor system, system matrices are assumed to depend on its parameters through a linear fractional transformation, which enables it to include a large class of networked dynamic systems as a special case. When an associated transfer function matrix is of full normal row rank, a matrix rank based necessary and sufficient condition is derived for parameter identifiability. This condition can be verified recursively. An algorithm is suggested to find a set of frequencies, at which system frequency responses are capable to uniquely determine its parameter values. An ellipsoid approximation is given for the set consisting of all the parameter values of the descriptor system, whose frequency response deviates within a prescribed distance from that associated with a globally identifiable parameter vector value. Explicit formulas are also derived for the suggested absolute and relative sloppiness metrics for some application significant cases.

Evaluation of the inertia distribution performance for multi-machine power system

Given large-scale modern power systems with inverter-based resources, the frequency stability faces great challenges in the characteristics of the decreasing inertia for the system and the uneven distribution of the inertia. Although several metrics for system inertia performance have been developed, a more generalized inertia evaluation method is still required. This paper proposed an inertia evaluation method for a multi-machine power system considering both the inertia and disturbance distribution. To reflect the dynamic of a more general system, an equivalent homogeneous transformation (EHT) is used in the system frequency response model with heterogeneous parameters. To reveal the inertia distribution under different disturbances scenario, a general inertia (GI) is proposed to evaluate the nodal frequency stability. Finally, the effectiveness of the proposed equivalent homogeneous system and the metric is validated using two test systems: a modified 4-machine 2-area power system and the 5-area 68-bus system. Numerical simulation study reveals that the proposed method can effectively reflect the inertia spatial distribution characteristics.

Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method

AbstractThis work proposes a novel efficient method to track the evolution of amplitude extrema featured by frequency responses of nonlinear systems using the harmonic balance method. Means to compute the amplitude of a Fourier series are first outlined, and a set of equations characterizing a local extremum of a nonlinear frequency response amplitude curve is derived. Efficient numerical procedures are used to evaluate these equations and their derivatives (including second‐order ones) to embed them in a predictor‐corrector continuation framework. The proposed approach is illustrated on three examples of increasing complexity, namely a Helmholtz–Duffing oscillator, a two‐degree‐of‐freedom system with a modal interaction, and a doubly clamped von Kàrmàn beam with a nonlinear tuned vibration absorber.

Externally gapped line arresters placement effect on transmission line lightning performance including the frequency response of the grounding system

AbstractThis paper conducts the frequency‐dependent grounding system impact on externally gapped line arresters (EGLAs) operation and their placement effects on the lightning performance of a transmission line (TL). The study involves placing EGLAs at different phases of a 400‐kV double‐circuit TL with two downstream shield wires and selecting the optimal state with fewer back‐flashover incidents. The results show that using a non‐linear grounding system leads to a higher back return current from insulators or EGLAs, resulting in a higher flashover rate compared to the frequency grounding system (FGS). Installing four EGLAs in the middle and upper phases of the TL provides satisfactory lightning protection, and the flashover probability is zero and 4.2% for the FGS and the non‐linear grounding system, respectively. A sensitivity analysis including soil resistor variation, economic analysis, and grounding electrode configuration has been performed that confirms installing downstream shield wires and EGLAs is an effective and economical technique for lightning protection.

Analysis of Frequency Regulation Capability of Doubly Fed Induction Generator and Supercapacitor Energy Storage Based on Dynamic Power Flow

The grid-integrated doubly fed induction generator (DFIG) is required to participate in the frequency regulation of the power system. The supercapacitor energy storage (SES) is capable of enhancing the frequency regulation capability of the DFIG in a coupled manner. The SES is connected to the DC capacitor of the DFIG and provides active power response through the droop control. The dynamic power flow (DPF) model is established to quantify the frequency response of the power system when the DFIG-SES system participates in the frequency regulation. The integration of the SES affects the internal power flow distribution of the DFIG; thus, the detailed model of the DFIG is incorporated into the DPF analysis. Considering the different response speeds of the synchronous generator (SG), the SES, and the DFIG to the frequency regulation, the first-order inertia delay in the governor control of the SG is included in the DPF model. The impact of the delay time constant on the continued operation time of the SES is analyzed. With the same deloading percentage, the output power of the DFIG is adjusted based on a variable droop coefficient scheme to fully utilize its active power reserve. The feasibility and effectiveness of the DFIG-SES scheme to participate in the frequency regulation are analyzed based on the DPF and verified through numerical analysis.

Experimental investigation on the effects of a mesh in the downstream region of a combustion-driven Rijke tube on self-excited thermoacoustic oscillations

Self-excited thermoacoustic oscillations are undesirable in most combustion systems due to their negative influence on combustion efficiency and structural vibration. Nonlinear thermoacoustic oscillations driven by combustion can be sensitive to changes in the heat and flow conditions. Therefore, a comprehensive study on self-excited thermoacoustic oscillations was conducted to investigate the effect of incorporating a woven mesh with varying mesh numbers and positions into the downstream region of a Rijke tube. This study determined system frequency and amplitude response and revealed dynamic properties of the system by applying recurrence analysis. To obtain temperature distributions, a thermal imaging system was employed, comprising a short wavelength infrared (SWIR) camera for the mesh and a long wavelength infrared (LWIR) camera for the tube wall. A high-speed schlieren imaging system was utilised for visualising heat and flow conditions at the tube end. The study demonstrated the effect of including a mesh in changing the oscillation eigenfrequency, suppressing the oscillation amplitude by up to 50 % and influencing the system dynamics. Higher mesh number demonstrated greater effectiveness. The captured thermal and schlieren images clearly evidenced the mesh’s significant influence on the downstream heat and flow conditions. The insights gained from this work provide a potential control method of self-excited, nonlinear thermoacoustic oscillations.

A novel method to estimate maximum wind energy penetration level considering potential frequency support of wind power plants

Wind turbines’ installed capacity is expected to increase significantly in future power grids due to environmental concerns. Reductions in the power system inertia and frequency response due to increasing penetration levels of wind energy lead to a decrement in the frequency stability margin. This paper focuses on the frequency stability issue in power grids with high penetration level of wind turbines. The maximum allowable wind generation penetration level is first formulated as a function of primary frequency response and system inertia with/without considering operating reserve limits. Following that, the possibility of participation of wind turbines in the frequency stability improvement is investigated and the minimum required wind turbine participation is estimated as a function of wind energy penetration level. In this trend, a time-independent formulation for power system frequency response is utilized to increase the accuracy and reduce the computational complexity. A comprehensive analysis is performed on IEEE 39-bus test system to investigate the proposed methodologies. As results confirm, participation of wind turbines in the frequency control task leads to more secure operation of the power system.

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.

Using Particle Swarm Optimization for Power System Stabilizer and energy storage in the SMIB system under load shedding conditions

Generator instability, which manifests as oscillations in frequency and rotor angle, is brought on by sudden disruptions in the power supply. Power System Stabilizer (PSS) and Energy Storage are additional controllers that enhance generator stability. Energy storage types include superconducting magnetic (SMES) and capacitive (CES) storage. If the correct settings are employed, PSS, SMES, and CES coordination can boost system performance. It is necessary to use accurate and effective PSS, SMES, and CES tuning techniques. Artificial intelligence techniques can replace traditional trial-and-error tuning techniques and assist in adjusting controller parameters. According to this study, the PSS, SMES, and CES parameters can be optimized using a method based on particle swarm optimization (PSO). Based on the investigation's findings, PSO executes quick and accurate calculations in the fifth iteration with a fitness function value of 0.007813. The PSO aims to reduce the integral time absolute error (ITAE). With the addition of a load-shedding instance, the case study utilized the Single Machine Infinite Bus (SMIB) technology. The frequency response and rotor angle of the SMIB system are shown via time domain simulation. The analysis's findings demonstrate that the controller combination can offer stability, reducing overshoot oscillations and enabling quick settling times.

Configuration and control strategy for an integrated system of wind turbine generator and supercapacitor to provide frequency support

Wind turbine generators (WTGs) can provide fast frequency support to power systems through inertial control via the release of kinetic energy stored in rotating masses. However, because the kinetic energy is limited, the frequency support from WTGs based on inertial control cannot last until the system frequency recovers to the nominal value. Thus, it must be terminated during system frequency control, which results in adverse effects on the system frequency response. To guarantee sufficient energy and fast response for the frequency support of a permanent magnet synchronous generator based WTG, this study proposed the integration of a DC/DC converter-interfaced supercapacitor (SC) at the DC link of the WTG and consequently formed an integrated system of WTG and SC (WTG-SC system). First, the configuration of the SC was proposed based on the evaluation of the energy consumption of the WTG-SC system for frequency support and the available kinetic energy of the WTG. Second, a control structure that coordinates the machine-side converter (MSC), grid-side converter (GSC), and DC/DC converter of the SC was proposed. Finally, a “dual-droop” frequency support control scheme for the WTG was proposed to enhance the WTG-SC system’s frequency support capability and the efficiency of energy utilisation during frequency support. The efficacy of the proposed approach was validated using a modified IEEE 39 bus system with a wind farm comprising 100 WTG-SC systems under different operating conditions.

Incentivizing Frequency Provision of Power-to-Hydrogen Toward Grid Resiliency Enhancement

As a most promising alternative carrier of energy in the future low-carbon energy system, the possibility of power-to-hydrogen (P2H) generally proton exchange membrane (PEM)-based water electrolyzers, has been explored for frequency response provision. However, there remains an open question as to how to capture the interaction of P2H operation and frequency response provision, and incentivize such behaviors to enhance system resiliency. In this paper, we propose a marginal pricing mechanism for frequency response service provision to enhance grid resilience considering the participation of P2H. To depict the interaction between P2H operation and frequency response provision, a dynamic model of P2H is partially simplified to be incorporated into the system frequency response process. Case studies based on the IEEE RTS-24 system and a realistic Northwest power grid of China show that P2H can significantly improve the frequency response ability, especially reduce the startup of conventional units, so as to reduce carbon emissions. This effect is extremely appealing in the renewable-dominated cases.

Coordinating Multiple Resources for Emergency Frequency Control in the Energy Receiving-End Power System With HVDCs

High voltage transmission lines, especially high-voltage direct-current (HVDC) lines, have been built around the world linking the populated load centers with major green energy resources at a far distance or offshore. Any major faults on these long-distance point-to-point connections may lead to large power unbalances and cause frequency security problems in the regional grid at the energy receiving end. In this work, an emergence frequency control strategy is proposed, utilizing available frequency response resources at the receiving end, including synchronous generators, local wind farms, battery-based energy storage systems, pumped hydro storages, etc. First, a system frequency response model consisting of multiple resources is formulated, including the secondary frequency drop caused by wind farms. Then, the order of the model is reduced to derive the analytical expressions of the frequency nadirs and the quasi-steady-state frequency. Finally, the emergency frequency control decision method is proposed with the consideration of the system frequency security constraints. The proposed strategy is studied and analyzed with simulations on a generalized model of Huadong regional grid in eastern China.

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.

PID and compliance control-based anti-sticking of drill rod in underground mining

PurposeDuring drilling in coal mines, sticking of drill rod (referred to as SDR in this work) is a potential threat to underground safety. However, no practical measures to deter SDR have been developed yet. The purpose of this study is to develop an anti-SDR strategy using proportional-integral-derivative (PID) and compliance control (PIDC). The proposed strategy is compatible with the drilling process currently used in underground coal mines using drill rigs. Therefore, this study aims to contribute to the PIDC strategy for solving SDR.Design/methodology/approachA hydraulic circuit to reduce SDR was built based on a load-independent flow distribution system, a PID controller was designed to control the inlet hydraulic pressure of the rotation motor and a typical compliance control approach was adopted to control the feed force and displacement. Moreover, the weight and optimal combination of the alternative admittance control parameters for the feed cylinder were obtained by adopting the orthogonal experiment approach. Furthermore, a fuzzy admittance control approach was proposed to control the feed displacement. Experiments were conducted to test the effectiveness of the proposed method.FindingsThe experimental results indicated that the PIDC strategy was appropriate and effective for controlling the rotation motor and feed cylinder; thus, the proposed method significantly reduces the SDR during drilling operations in underground coal mines.Research limitations/implicationsAs the PIDC strategy solves the SDR problem in underground coal mines, it greatly improves the safety of coal mine operation and decreases the power cost. Consequently, it brings the considerable benefits of coal mine production and vast application prospects in other corresponding fields. Actual drilling conditions are difficult to accurately simulate in a laboratory; thus, for future work, drilling experiments can be conducted in actual underground coal mines.Originality/valueThe PIDC-based anti-SDR strategy proposed in this study satisfactorily controls the rotation motor and feed cylinder and facilitates the feed and rotation movements. Furthermore, the tangible novelty of this study results is that it improves the frequency response of the entire drilling system. The drilling process with PIDC decreased the occurrence of SDR by 50%; therefore, the anti-SDR strategy can significantly improve the safety and efficiency of underground coal mining.

A Novel Allocation Strategy Based on the Model Predictive Control of Primary Frequency Regulation Power for Multiple Distributed Energy Storage Aggregators

As the amount of distributed energy storage (DES) in a power system continues to increase, it will not be long before there are multiple DES aggregators participating in frequency regulation, and the realization of their coordinated control is a critical topic of current research. This study focused on the primary frequency regulation (PFR) power allocation strategy among multiple DES aggregators participating in PFR. This study first calculated the PFR demand according to a system frequency response model of the power system with DESs. Next, a PFR power allocation model of DES aggregators was developed based on model predictive control. The objective of this model was to minimize the overall frequency regulation cost while satisfying all of the constraints of DESs. Finally, the distributed interior point method was used to solve the model rapidly. The correctness and effectiveness of the proposed model and algorithm were verified on two unified transmission and distribution systems with DES aggregators used to supply the PFR service. The results revealed that the proposed model could effectively allocate PFR power to the various types of energy storage, with the additional benefits of slowing down the shift in the state of charge for energy storage units and ensuring the continuity of energy storage participation in frequency regulation.

Achieve hybrid energy harvesting based on the internal resonance of a two-degree-of-freedom cantilever beam

Taking a cantilever beam with two-degree-of-freedom (DOF) as an example, this paper studies the energy transfer mechanism between the vibration DOF and the rotation DOF, proposes a hybrid energy harvesting scheme, establishes the dynamic equation and solves it. Through the simulation of the analytical equation, it is found that under the condition of internal resonance of two DOFs, the two nonlinear peaks on the rotation DOF are very conducive to energy harvesting in the wide frequency domain. Furthermore, the influence of excitation amplitude, electromechanical coupling coefficient, time domain constant and other parameters on the resonance frequency and amplitude response of the energy harvesting system is studied.