System Frequency Response Model Research Articles

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.

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.

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.

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.

Inter-regional unit commitment and PV scheduling considering frequency constraints

Unit commitment problem considering renewable uncertainty has received a lot of attention in recent years. The high-level penetration of renewable lowers the system inertia, posing challenges to frequency stability. This work proposes a unit commitment model considering frequency limits. The High Voltage Direct Current (HVDC) tie-line is modeled to transfer PV generation to load centers while providing frequency support. A multi-machine system frequency response model is employed to approximate frequency excursion. PV is considered semi-controllable in the scheduling model. A novel solution approach is proposed to solve the unit commitment problem with nonlinear frequency stability constraints. Case studies demonstrate the benefits and effectiveness of the proposed approach.

An extended SFR model based fast frequency security assessment method for power systems

The large-scale integration of renewable energy and the increasing access to power electronic equipment lead to the low inertia of power grid, which raises severe challenges to frequency security. The low inertia makes power system more sensible to power disturbances, and therefore, evaluating frequency stability is crucial. To address this issue, a fast frequency security assessment method for power grid based on the extended SFR (system frequency response) model is proposed. In this method, an extended SFR model is established based on the characteristics of future new power systems, which are comprised of multiple frequency response sources, including induction motor load, renewable energy, and other asynchronous resources. To obtain the parameters of the proposed model, the principle and applicability of model parameter aggregation methods are explained. Considering the difficulty of obtaining all the required information in real-world situations, the parameters are obtained by parameter identification method through optimization algorithms. Finally, the effectiveness of the proposed extended SFR model is verified in the WSCC-9 bus system and the parameter identification method is validated in a regional power grid. The calculation time is less than 0.03s and the accuracy is more precise than conventional SFR. The results demonstrate that the proposed extended SFR model and parameter identification method show characteristics of both rapidity and accuracy in judging the security of power systems.

An extended modeling of frequency security constraints for unit commitment model

Under the background of high proportion of renewable energy, the frequency security of the power system is facing challenges, which makes it necessary to consider and respond in the optimal dispatching. In this paper, the frequency security constraint is introduced into the basic unit commitment model and the unit commitment model considering the frequency security constraint is proposed. Different from the traditional research, a dynamic modeling method for the unbalanced power of the system is presented. Based on the system frequency response model of primary frequency response, the analytic and linearized frequency safety constraint sets are constructed for the frequency nadir, quasi steady frequency and maximum rate-of-change-of-frequency. The experimental results show that the proposed model not only ensures sufficient frequency security, but also fully considers the actual operation state of the frequency response unit. Compared with the traditional model whose unbalanced power is constant, the proposed model can save operating costs.

The effects of system frequency responses on security constrained unit commitment in presence of wind-hydro-thermal units

PurposeThe purpose of this paper is to present a new system frequency response model with participation of wind-hydro-thermal units to overcome frequency deviations.Design/methodology/approachThe extracted minimum frequency equation is considered as a constraint in security-constrained unit commitment calculations. Because of high-order polynomials in the frequency transfer function and high degree of nonlinearity of minimum frequency constraint, Routh stability criterion method and piecewise linearization technique are used to reduce system order and linearize the system frequency response model, respectively.FindingsThe results of this paper indicate that by using this model, the hourly minimum frequency is improved and is kept within defined range.Originality/valueThis combined model can be used to evaluate the frequency of the power system following unexpected load increase or generation disturbances. It also can be used to investigate the system frequency performance and ensure power system security which are caused by peak load or loss of generation in presence of renewable energies.

Small-Signal System Frequency Stability Analysis of the Power Grid Integrated With Type-II Doubly-Fed Variable Speed Pumped Storage

This article proposes a structurally distinctive doubly-fed variable speed pumped storage (VSPS), denoted as the Type-II VSPS. Where, the speed is controlled by a back-to-back (BTB) converter while the power is controlled by a speed governor, which is the exact opposite of the control method for conventional VSPS. The small-signal frequency stability analysis of a power grid integrated with the Type-II VSPS is carried out to investigate the influence of this type of VSPS on power grid stability. Firstly, the transfer function models of hydraulic and electric subsystems of the Type-II VSPS are established, and the system small-signal stability analysis is carried out based on the obtained models and Nyquist stability criterion. Secondly, an improved system frequency response (SFR) model for the power grid integrated with Type-II VSPS is presented. Such a model is applied to investigate the frequency response of the modern power grid integrated with a large-scale VSPS (the current single unit capacity has reached 450 MW). Furthermore, the small-signal stability of the modern power grid is analyzed based on the Nyquist stability criterion. Finally, time-domain simulations and experiments are conducted to validate the effectiveness of the small-signal stability analysis.

Enhanced Frequency-Constrained Unit Commitment Considering Variable-Droop Frequency Control From Converter-Based Generator

To improve the frequency stability of power systems with a high penetration of converter-based generators, this paper proposes an Enhanced Frequency-Constrained Unit Commitment (E-FCUC) considering variable-droop-controlled Frequency Control (FC) from converter-based generators. Unlike previous studies emphasizing conventional and fix-droop converter-based generators participating in primary frequency response, the impact of converter-based generators with variable-droop FC (VD-FC) is investigated, modeled, and then incorporated into the UC problems. Firstly, the transfer function of variable-droop-controlled converter-based generators is modeled; the available primary power reserves bounding provided by converter-based generators is analyzed. Secondly, the frequency dynamic of power systems considering joint frequency control from conventional generators and variable-droop-controlled converter-based generators is derived based on an analytical aggregated System Frequency Response (SFR) model. Since the nonlinear non-smooth feature of obtained frequency dynamic function, the “max-affine” Piece-Wise-Linearization method (PWL) is adopted here to fit the calculated frequency function. The fitting function is subsequently reformulated into mix-integer linearized constraints participating in UC studies. Case studies based on a modified IEEE 6 bus test system and a modified IEEE 118 bus test system are carried out to verify the effectiveness of the proposed E-FCUC through comparisons of results with existing empirical models.

Aggregated SFR model for VSC HVDC interconnected power systems with high penetration of wind power

This letter proposes a novel aggregated system frequency response (ASFR) model, which can fully capture the frequency characteristics of the voltage source converter-based high voltage direct current (VSCHVDC) interconnected power system with high penetration of wind power. First, a multi-machine SFR model is presented, considering the inertia and frequency control processes of VSCHVDC and wind turbines (WTs). Then, a novel aggregation approach is proposed to transform the multi-machine SFR model into a single-machine SFR model on the basis of different control modes of the VSCHVDCs and WTs. Finally, simulation studies are conducted to validate the performance of the proposed ASFR model and its application in frequency response analysis.

A sliding mode frequency control scheme for wind turbines participating in frequency regulation support in power systems

With high penetration of wind power, the apparent inertia of power systems is decreased, which seriously affects the safety and stability of the system frequency. Therefore, a novel sliding mode frequency control (SMFC) scheme is proposed for the wind turbines participating in frequency regulation support (FRS) in power systems, which can significantly improve the dynamic characteristics of the system frequency. At first, a power system frequency response model considering wind turbines participation in FRS is derived. In this model, the load disturbance, wind power disturbance and synchronous generator frequency regulation dynamics are combined as a lumped disturbance. Then, the design of the proposed SMFC scheme, which combines the super-twisting sliding-mode disturbance observer (STSMDO) with the super-twisting sliding-mode frequency controller (STSMFC), is introduced. The proposed STSMFC has ability to tune the system dynamics easily by choosing suitable sliding surface matrix via eigenvalue assignment method or optimal sliding manifold design. In such a frequency control scheme, the stability of the system frequency is guaranteed by the STSMFC, whereas the STSMDO is employed to estimate the lumped disturbance. Finally, numerical simulations verify the effectiveness and superiority of the proposed SMFC scheme.

Online Prediction Method for Power System Frequency Response Analysis Based on Swarm Intelligence Fusion Model

Instability at transient frequency caused by faults in complex power systems is one of the greatest threats to operational safety. By analyzing the frequency response of power system in real-time and adopting control strategies promptly, power system accidents can be efficiently prevented. While existing online analysis methods integrate physical-driven and data-driven methodologies, they do not effectively utilize frequency timing characteristics. Consequently, a swarm intelligence fusion model, which integrates physical-driven and data-driven methods, is proposed as an improved frequency response analysis method. The transient frequency affecting components are separated into primary state variables and system time series data based on the properties of the time sequence. To preserve the actual relationship of the electrical mechanism model, the system frequency response (SFR) model is used as the physical-driven method for the primary state variables of the system. The Long Short Term Memory (LSTM) network was used as the data-driven method to extract timing features and correct the SFR model’s prediction using the system time series data as input. The two methods are combined using the bootstrap mode to form the fusion model, and the structure of the model is optimized using an improved sparrow search algorithm (ISSA), a swarm intelligence optimization algorithm. The model structure is adapted autonomously, implementing a method for online frequency response analysis. The simulation on the New England 39-bus system has verified that the method can quickly and accurately calculate the dynamic process of frequency response after a large-scale disturbance.

A Novel Approach to Extended System Frequency Response Model for Complex Power Systems (ESFR)

A Novel Approach to Extended System Frequency Response Model for Complex Power Systems (ESFR)

Minimum inertia demand estimation of new power system considering diverse inertial resources based on deep neural network

AbstractWith the high‐proportion integration of renewable energy and power electronic equipment, the inertia supporting ability of new power system continues to decline, which seriously threatens the frequency stability of power grids. In order to clarify the operation boundary, and realise the rapid analysis and prediction of the minimum inertia demand of new power systems, this study proposes a minimum inertia demand estimation method based on deep neural network (DNN). Firstly, this study establishes the system frequency response model of new power systems containing diverse inertia resources including renewable energy, induction machine and so on. Considering the constraints of rate of change of frequency and maximum frequency deviation, the minimum inertia demand estimation model is established to ensure the system frequency stability. DNN is introduced to effectively map non‐linear relations in complex situations, which can quickly estimate and predict the minimum inertia of new power systems. Adam algorithm is utilised to optimise the input weight matrix and hidden layer feature vector of the network to improve accuracy. Finally, the simulations and analysis are conducted in IEEE‐39 system to verify the accuracy and generalisation ability of the proposed method in this paper.

Equivalent Inertia Estimation of Asynchronous Motor and Its Effect on Power System Frequency Response

With the increase in renewable energy penetration, the traditional synchronous generator is gradually replaced, resulting in the decrease in system inertia level and the weakening of frequency modulation capability. In addition to synchronous inertia, load inertia of asynchronous motors also widely exists in power systems, but its effect on system frequency stability has not been fully studied. To this end, based on the detailed model of asynchronous motor, the amplitude–phase motion equation based on potential after transient reactance is proposed, and then the phase motion equation of potential after transient reactance is derived to evaluate the equivalent inertia of asynchronous motor under electromechanical time scale. The equivalent inertia of asynchronous motor is studied theoretically by building the system frequency response model. The results show that the equivalent inertia of asynchronous motor can essentially improve the system frequency stability, while showing time-varying characteristics due to the combined effect of slip frequency and rotor speed. The analyses are validated with time-domain simulation results. The proposed method lays a foundation for mechanistic understanding of the frequency characteristics of the equivalent inertia of asynchronous motors affected by active and reactive power and its influence on the system frequency characteristics.

Stability Analysis and Performance Improvement of Power Sharing Control in Islanded Microgrids

Due to the requirement of synchronism and power sharing, droop control and its variations have become one essential component for distributed generator (DG)-powered microgrids. However, the power sharing accuracy and system stability margin may be threatened by the randomness from the load demand and renewable generation. In this paper, a dynamic stability analysis is first performed on a DG-powered microgrid through a produced system frequency response model (SFR). The results point out that (i) the critical system eigenvalues directly vary with the system operating condition; (ii) a fixed-gain power sharing control is prone to be less damped and loses stability easily under some operating conditions. Then, the heuristic adaptive dynamic programming (HDP) strategy is used for power sharing control with the benefit of adapting to real-time disturbances and uncertainties. Through Lyapunov theorem, stability analysis is provided to demonstrate the reliability of the HDP-based power sharing control in islanded microgrids. Finally, simulation tests verify the analysis results and demonstrate the favorable performance of the HDP-based power sharing control under uncertain load disturbances.

Reduced-Order System Frequency Response Modeling for the Power Grid Integrated With the Type-II Doubly-Fed Variable Speed Pumped Storage Units

The traditional system frequency response (SFR) model is not applicable to the study of the frequency response of contemporary power grid due to the response of the large capacity (single unit up to 500 MW) type-II doubly-fed variable speed pumped storage (VSPS) unit is not considered. This article proposes an improved reduced-order SFR model for the power grid integrated with the large-scale type-II VSPS. proposed models Compared with the traditional SFR model, this model takes into account the active power coupling effect of this type of VSPS, and the computational burden increase of the model is small due to the model of VSPS has been reduced to the greatest extent. Therefore, the SFR model can be used by the system operators to rapidly calculate and evaluate the frequency response of contemporary power grid. Firstly, a reduced-order frequency response transfer function model of the Type-II VSPS is established by using the state-space model and small-signal incremental method. Compared with the higher-order nonlinear model of the Type-II VSPS, the state variables and computation burden of the established model is dramatically decreased. Secondly, an improved SFR model for the power grid integrated with the type-II VSPS is presented, and then the reduced-order analytical solution for the frequency response of the grid is put forward based on the parameter weighted aggregation method. The improved SFR model is more realistic and can better express the frequency response characteristics of the contemporary power grid. The proposed SFR model have demonstrated advantages in solving speed and efficiency when contrast it with the higher-order nonlinear model of the grid. Finally, the simulation and experimental results are respectively compared with the analytical solution of the reduced-order models, and the results have demonstrated the effectiveness of the.

A novel frequency response analysis model applicable to high-penetration wind power grid

The decoupling relationship and low inertia characteristics of wind turbine generator system (WTGS) make the system frequency response more complex. In order to evaluate the frequency stability of high-penetration wind power grid, it is significant to establish an exactly frequency response analysis model. Due to the features of wide spatial distribution and large number of WTGS in the power grid, the wind speed and actual operating state faced by WTGS in different regions have obvious discrepancy, which makes the traditional frequency response models that merely considers the single operating state of WTGS have evident limitations. Therefore, in order to consider the discrepancy of frequency regulation characteristics caused by the spatial dispersion of WTGS, an improved frequency response modeling method which can take into account the frequency regulation characteristics of multiple wind speeds is proposed. This method uses small signal analysis theory and fuzzy control method to construct an improved equivalent aggregation model of WTGS. Combining this model with the typical system frequency response (SFR) model, a novel frequency response model considering different wind conditions and different frequency regulation characteristics of WTGSs is established. Finally, an improved IEEE-118 bus system is used for case analysis to verify the correctness and superiority of the proposed method for high-penetration wind power grid.