Frequency Response Model Research Articles

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.

Optimal Strategy of Primary Frequency Regulation for Wind-Storage System Considering Adaptive Parameter Control

For the problem that the power system has different demands on the frequency response characteristics in different segments of dynamic frequency response, this paper proposes an optimal primary frequency regulation strategy for the wind-storage system considering adaptive parameter control. Firstly, the dynamic frequency response processes of the system under single, continuous disturbances are analyzed to obtain the frequency regulation demand of the system in different segments. Secondly, the frequency response model of the power system is established to obtain the transfer function of the system’s primary frequency regulation. Finally, the adaptive parameter adjustment strategy of the wind-storage system is proposed, and the optimal primary regulation strategy of the wind-storage system is established. The result of the case study indicates that the proposed optimal primary frequency regulation strategy can effectively improve the performance of the power system in the dynamic frequency response process, especially when a continuous disturbance occurs.

An online identification method for establishing a microgrid equivalent model based on the hybrid particle swarm optimization butterfly algorithm

AbstractThe frequency response model of a microgrid system is an indispensable tool for designing secondary frequency controllers and analyzing system frequency stability. Owing to the complexity of a microgrid system structure, time‐varying operation state, and difficulty in obtaining the inverter parameters, it is difficult to model the microgrid system. To address the abovementioned problems, this study constructs the equivalent model of a microgrid system based on mechanism analysis and then identifies the equivalent model parameters using an online identification method based on a hybrid particle swarm optimization butterfly algorithm according to the sampled operation data to obtain the specific equivalent model of a microgrid for the controller. This modeling method has strong adaptability and can yield accurate identification modeling when the operational structure of the microgrid changes.

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.

Frequency Response Model of Power System in Presence of Thermal, Wind and Hydroelectric Units

Frequency Response Model of Power System in Presence of Thermal, Wind and Hydroelectric Units

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.

Research on generation of stable mid-infrared lasers with narrow linewidths based on optical feedback locking

Mid-infrared precision spectroscopy has important applications in the fields of trace gas detection and the determination of fundamental physical constants. However, due to the limited commercialization of related technologies, there is a lack of narrow linewidth laser sources or linewidth narrowing approaches in the mid-infrared region, as well as stable mid-infrared frequency standards. The most commercialized and widely used mid-infrared laser source is the quantum cascade laser (QCL). But its free-running linewidth is more than MHz scale due to the influence of laser drive current noise and temperature fluctuation. This impedes the development of precision spectroscopy in this region. In this work, we introduce a technique for generating a narrow linewidth, stable mid-infrared laser by using optical feedback frequency locking, with a high-finesse mid-infrared ultrastable Fabry-Pérot cavity as the frequency reference. The optical cavity consists of two high reflectivity mirrors separated by ultra-low expansion (ULE) material with a low temperature expansion coefficient, and its temperature is precisely controlled. And the cavity is also surrounded in a vaccum cavity made of stainless steel. All these measures ensure the cavity length and its longitudinal mode stability. By using optical feecback, a QCL is locked to the cavity, which stabilizes the laser frequency and narrows the laser linewidth. In order to improve the long-term stability of the optical feedback, an active servo is leveraged to control the feedback phase. The error signal for the servo is obtained by using the method similar to the Pound-Derver-Hall locking. In this work, we first theoretically analyze the feasibility of laser to F-P cavity frequency locking by optical feedback. We propose the laser frequency response model with a linear F-P cavity under optical feedback, and analyze the influence of the direct cavity reflection on the laser frequency. Then the experimental demonstration is conducted. Firstly, we measure the reflectivity of the cavity mirror by using cavity ring-down spectroscopy, resulting in a cavity finesse of 30200 and a cavity mode linewidth of 49.7 kHz. After that, we successfully achieve optical feedback frequency locking, and consecutive cavity transmission is observed. The error signal for the control of the optical feedback phase is used to evaluate the locking performance by converting it into the laser frequency noise. By analyzing the noise spectral density, the QCL linewidth is narrowed to 0.3 Hz on a short timescale (< 10 ms). And the long-term stability is suspected to be dedicated by the temperature variation of the optical cavity, resulting in a laser frequency drift 20 kHz/12 h. The narrow linewidth stabilized mid-infrared laser source obtained with this technique is expected to serve as an effective frequency reference source for mid-infrared precision spectroscopic measurements.

Reliability Assessment of Interconnected Power Systems with HVDC Links Considering Frequency Regulation Process

With various components and complex topologies, the applications of high-voltage direct current (HVDC) links bring new challenges to the interconnected power systems in the aspect of frequency security, which further influence their reliability performances. Consequently, this paper presents an approach to evaluate the impacts of the HVDC link outage on the reliability of interconnected power system considering the frequency regulation process during system contingencies. Firstly, a multi-state model of an HVDC link with different available loading rates (ALRs) is established based on its reliability network. Then, dynamic frequency response models of the inter- connected power system are presented and integrated with a novel frequency regulation scheme enabled by the HVDC link. The proposed scheme exploits the temporary overload capability of normal converters to compensate for the imbalanced power during system contingencies. Moreover, it offers frequency support that enables the frequency regulation reserves of the sending-end and receiving-end power systems to be mutually available. Several indices are established to measure the system reliability based on the given models in terms of abnormal frequency duration, frequency deviation, and energy losses of the frequency regulation process during system contingencies. Finally, a modified two-area reliability test system (RTS) with an HVDC link is adopted to verify the proposed approach.

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.

A novel two-stage energy management of hybrid AC/DC microgrid considering frequency security constraints

The increasing penetration of renewable energy in the hybrid AC/DC microgrid (MG) reduces the inertia and further threatens the frequency security. Furthermore, the stochastic and intermittent characteristics of the renewable energy challenge the optimal scheduling of MG. To deal with these issues, this paper proposes a novel two-stage energy management strategy to minimize the operating cost of the hybrid AC/DC MG while ensuring frequency security by considering the uncertainties in both the renewable energy resources (RES) and load demand. Firstly, the relation between the maximal frequency deviation and the power reserve is derived by analyzing the dynamic frequency response model. Secondly, scenario generation and scenario reduction based on Monte Carlo simulation (MCS) are carried out to simulate the unbalanced system power. Thirdly, the day-ahead scheduling stage determines the optimal power reservation of the distributed generators (DGs) for primary and secondary frequency regulation. Then, in the intraday scheduling stage, the day-ahead power reservation plan is adjusted to meet the frequency security constraints by using the real-time updated forecasting information. Finally, the proposed energy management system (EMS) is formulated and solved. The simulation results demonstrate that the proposed method can significantly reduce the operating cost, the maximal frequency deviation, and load shedding.

Impact of inertia response control strategy based doubly fed induction generator on frequency stability of power system

While the doubly fed induction generator (DFIG) is widely applied in the new power system, its decoupled control and fluctuation of output power have led to serious problems in frequency stability. Inertia response control (IRC) of DFIG has attracted significant attention, while its impact has not been clearly researched. In this study, a low-order model of DFIG focusing on frequency stability is proposed. Firstly, the simplified model of DFIG considering the IRC is introduced through Taylor series expansion. The frequency response model considering the energy storage system (ESS) is proposed. Taking the rate of change of frequency (RoCoF) and steady-state frequency deviation (SFD) as the constraint, an analytical solution for the maximum proportion of DFIGs is deduced to reflect the impact of IRC on the system frequency stability. Finally, the accuracy of the proposed method and the effectiveness of IRC is verified on the modified IEEE-9 system.

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.

A gas-thermal inertia-based frequency response strategy considering the suppression of a second frequency dip in an integrated energy system

Increasing access to intermittent new energy in the power grid reduces system inertia and exposes the power system to severe frequency stability problems. To address this issue, this study fully exploits the slow-dynamic characteristics in gas-thermal systems of the integrated energy system to provide frequency response. Given the characteristics of both being able to provide buffer space for energy fluctuations, this study gives definitions of gas-thermal inertia and explores their similar power shortage support potential. Then given the necessity of thermal recovery on the load side, a gas-thermal inertia-based frequency response strategy is proposed with help of gas inertia to suppress the second frequency dip. The frequency response model presented in the paper also offers an opportunity to weigh the frequency response effect against the total economic benefit. The proposed strategy is tested in an actual scenario, and the effectiveness of second frequency dip suppression is tested.

Automatic Generation Control Considering Uncertainties of the Key Parameters in the Frequency Response Model

The highly fluctuated renewable generations and electric vehicles have undergone tremendous growth in recent years. Most of them are connected to the grid via power electronic devices, resulting in wide variation ranges for several key parameters in the frequency response model (FRM), such as system inertia and load damping factors. This paper proposes an automatic generation control (AGC) method considering the uncertainties of these key parameters. First, the historical power system operation data following large power disturbances are used to identify the FRM key parameters offline. Second, the offline identification results and the normal operation data right before the large power disturbance are used to train the online probability estimation model of the FRM key parameters. Third, the online estimation results of the FRM key parameters are used as the input, and the model predictive-based AGC optimization method is developed based on distributionally robust optimization (DRO) theory. Case studies conducted on the IEEE 118-bus system show that the proposed AGC method outperforms the widely utilized PI-based and PID-based control methods in terms of performance and efficiency.

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.

Solution to the problem of bridge structure damage identification by a response surface method and an imperialist competitive algorithm

To increase the efficiency of structural damage identification (SDI) methods and timeously and accurately detect initial structural damage, this research develops an SDI method based on a response surface method (RSM) and an imperialist competitive algorithm (ICA). At first, a Latin hypercube design method is used for experimental design and selection of sample points based on RSM. Then, a high-order response surface surrogate model for the target frequency response and stiffness reduction factor is established. Finally, analysis of variance is performed to assess the overall goodness-of-fit and prediction accuracy of the established model. Then the results obtained are combined with structural dynamic response data to construct objective functions; furthermore, the optimal solution of parameter vector in the objective function is solved based on the ICA. Then damage positioning and quantification can be achieved according to location and degree of change in each parameter; finally, the RSM-ICA-based SDI method proposed is applied to damage identification of high-dimensional damaged simply-supported beam models. To verify the effectiveness of the proposed method, the damage identification results are compared with the results obtained from traditional optimization algorithms. The results indicate that: average errors in the structural stiffness parameters and natural frequency that are identified by the proposed method are 6.104% and 0.134% respectively. The RSM-ICA-based SDI method can more accurately identify the location and degree of damages with more significantly increased identification efficiency and better precision compared to traditional algorithms. This approach provides a novel means of solving SDI problems.