System Frequency Response Model Research Articles

Study on Primary Frequency Regulation Reserve Configuration of High Wind Power System Considering Governor Limiting Links

With the large-scale use of wind turbines, the ability of the power system to resist frequency fluctuations has been greatly weakened, making the contradiction between frequency regulation supply and demand in the power system increasingly prominent. In order to ensure the frequency security of the power system, this paper conducts research on the primary frequency regulation (PR) backup configuration problem of a power system containing a high proportion of wind power. First, according to the dynamic properties of the speed regulator, a system frequency response model considering the limiting link is established. And the system frequency response model is transformed into a time-domain analytical function of PR reserve capacity and frequency maximum value. On this basis, a PR backup configuration model of a power system containing a high proportion of wind power is constructed with the optimization goal of minimizing system operating costs and taking into account the limiting link constraints. It is proposed to use the L-shape algorithm to decompose the model into main problems and sub-problems, which effectively reduces the solution complexity of the model. Finally, the correctness and effectiveness of this model are verified based on the improved IEEE 39-bus system.

Multi-segment droop control and optimal parameter setting strategy of wind turbine for frequency regulation

Traditionally, virtual inertia is used as the control strategy for wind turbines when participating in frequency regulation. However, it has inherent defects in measurement error amplification due to the frequency differential. Also, when control delay of wind turbines is taken into consideration, virtual inertia is essentially a fast power response, just the same as droop control. Hence, considering the adaptability of droop control, it is valuable to explore a novel droop control method without virtual inertia, as the frequency response model of wind turbines. For this reason, a multi-segment droop control strategy is proposed to provide a reliable frequency regulation model for wind turbines that can be broadly applied to other inverter-based power sources. Firstly, based on the extended system frequency response model, a differential equation including piecewise time-varying coefficients is established, and the analytical expression of the frequency response is obtained using the impulse function balancing principle and the integration by parts algorithm. Subsequently, based on analytical expression, the performance of the presented strategy is theoretically analyzed via comparison with virtual inertia control, and the conclusion that the presented multi-segment droop control has better frequency regulation performance can be got. Furthermore, to achieve optimal frequency regulation performance, a Lagrangian function is established to determine the optimal parameters of the proposed control strategy. Finally, the performance of the proposed strategy was verified in a two-area system model constructed on MATLAB/Simulink. Results show that the proposed multi-segment droop control has better frequency regulation performance.

Multi-objective configuration and evaluation of dynamic virtual inertia from DFIG based wind farm for frequency regulation

Modern power systems are gradually evolving into low-inertia systems due to the integration of high penetration of renewable energy and power electronic equipment. For the natural inertia on the rotor, doubly-fed induction generator (DFIG) based wind farms are expected to provide inertia support for systems. The paper proposed an analytical model of DFIG with df/dt inertia control for studying frequency dynamics, and investigates the optimal design of virtual inertia from wind farms, as well as its equivalent inertia contribution to system. The inertia response differences between DFIG and synchronous generator (SG) are discussed and analyzed for the first time, and then to accurately describe the frequency response with low cost, an analytical model of DFIG with inertia control is developed considering wind turbine aerodynamic characteristics. The explicit expression of virtual inertia provided by DFIG is derived according to the kinetic energy equilibrium, and the key factors that dominate the magnitude of virtual inertia are illustrated. Based on the system frequency response model including wind farms, taking the system frequency nadir (SFN) and the time of reaching nadir (ToN) as targets, a multi-objective optimal configuration model of virtual inertia is constructed and solved through MOPSO. The time domain simulations of a generic two machine four bus system and modified IEEE 9-bus test system are both performed in MATLAB/Simulink, the accuracy and efficiency of our proposed DFIG model on system frequency dynamics research are demonstrated, the pareto frontiers of virtual inertia configuration under different working conditions are optimized and analyzed as well as the impacts of different parameters on inertia evaluation.

SFR Modeling for Hybrid Power Systems Based on Deep Transfer Learning

A deep transfer learning method is presented for establishing the aggregated system frequency response (SFR) model of wind-thermal hybrid power systems (HPSs). In order to deal with nonlinearities and non-Gaussian disturbances, the quadratic survival information potential (QSIP) of the squared identification error is employed to construct the performance index when training recurrent neural networks (RNNs). A pre-trained SFR model is then obtained by the improved RNNs using the source domain data collected from the HPS in historical scenarios. Subsequently, the maximum mean difference is utilized to test the similarity of the HPS in historical and current scenarios. After that, the pre-trained SFR model is fine-tuned by adding some nodes to the recurrent layer and a functional link to the input layer. The SFR model of the HPS operating in current scenario can then be built based on the transferred source domain pre-trained SFR model. Simulation results illustrate that the proposed data driven modelling method can obtain accurate, effective and timely SFR model for a wind-thermal HPS with different wind speeds and load disturbances.

Integrating Physical and Data-Driven System Frequency Response Modelling for Wind-PV-Thermal Power Systems

This paper presents an integrated system frequency response (SFR) modelling method for wind-PV-thermal power systems (WPTPSs) by combining both physical model-based and data-driven modelling methods. The SFR physical model is built and simplified by the balanced truncation (BT) method. Based on the physical model, an improved radial basis function neural networks (RBFNNs) is then employed to establish an off-line SFR model using source data. Following the transfer learning principle, the transferred data from the source data set is determined by the maximum mean discrepancy (MMD) criterion. The RBFNN-based SFR model is then fine-tuned using both the transferred source data and target data. Finally, the fine-tuned RBFNNs is applied to investigate real-time SFR of WPTPSs. Simulation results confirm the effectiveness of the proposed SFR modelling strategy with an illustrative WPTPS.

A Coordinated Consensus Control Strategy for Distributed Battery Energy Storages Considering Different Frequency Control Demands

With the increasing penetration of renewable energy sources (RESs), ensuring frequency stability is becoming urgent for the power system. The distributed battery energy storage systems (DBESs) is one of the promising solutions to this problem. In this paper, a consensus control-based strategy is proposed for coordinating the DBESs to participate in the frequency regulation. Firstly, the system frequency response (SFR) model with the DBESs is introduced, and different frequency control demands are analyzed in detail, based on which the designing principles of the strategy are elaborated. Then, a revised dead band of frequency response is proposed to improve the frequency control performance under severer and more frequent RESs power fluctuation, reduce the possibility of frequency variation crossing the thresholds, and fully utilizes the DBESs' frequency regulation capability. Further, a developed consensus strategy derived from droop control is proposed, which enables the DBESs to participate in different frequency control demands simultaneously. The proposed strategy can prolong the service time when DBESs involved in frequency control as an aggregator, avoid unexpected energy exhaustion during frequency regulation, and reduce the frequency variation. The performance of the proposed control strategy is validated by the simulation cases with different operating scenarios.

Frequency-constrained expansion planning for wind and photovoltaic power in wind-photovoltaic-hydro-thermal multi-power system

Frequency security is one of the most critical factors for ensuring the safe and stable operation of power systems. In wind-photovoltaic-hydro-thermal multi-power systems (WPHTMPS), the increase in new energy share and the water hammer effect weaken the frequency modulation (FM) capability, threatening the frequency security of the power system. To address this issue and ensure the frequency security of WPHTMPS under the trend of large-scale development of wind and photovoltaic (PV) power, this paper proposes a novel expansion planning method for wind and PV power in WPHTMPS that considers FM capability in the planning stage. The method realizes the coordinated optimization of long-term planning and short-term operation while adhering to the frequency security constraints. The constraints are derived from the multi-power system frequency response model (MPSFR) which integrates virtual inertia, synchronous inertia, and the water hammer effect. However, due to the high-order characteristic of the MPSFR model, the frequency security constraints cannot be expressed explicitly to be embedded in the planning model by current study. Therefore, the boundary equivalence method is proposed to deal with this problem, which is effective to convert the frequency security constraints into inertia constraints and embed them in the planning model according to their relationship with installed capacity and unit commitment. Finally, simulation for a power system in Southwest China validates the proposed method, with results indicating that around 13% more capacity of new energy is needed to provide adequate FM reserve and power supply. Furthermore, it is demonstrated that the FM capability of new energy can improve the installed share of new energy from 46.5% to 70% while effectively ensuring frequency security.

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.

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.