System Frequency Dynamics Research Articles

Primary frequency control considering communication delay for grid-connected offshore wind power systems

Offshore wind farms are becoming increasingly distant from onshore centralized control centers, and the communication delays between them inevitably introduce time delays in the measurement signal of the primary frequency control. This causes a deterioration in the performance of the primary frequency control and, in some cases, may even result in frequency instability within the power system. Therefore, a frequency response model that incorporates communication delays was established for power systems that integrate offshore wind power. The Padé approximation was used to model the time delays, and a linearized frequency response model of the power system was derived to investigate the frequency stability under different time delays. The influences of the wind power proportion and frequency control parameters on the system frequency stability were explored. In addition, a Smith delay compensation control strategy was devised to mitigate the effects of communication delays on the system frequency dynamics. Finally, a power system incorporating offshore wind power was constructed using the MATLAB/Simulink platform. The simulation results demonstrate the effectiveness and robustness of the proposed delay compensation control strategy.

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.

Frequency prediction of a post-disturbance power system using a hybrid ARIMA and DBN model

The online prediction of power system dynamic frequency helps to guide the choice of control measures quickly and accurately after a disturbance, and this then ensures the reliable and stable operations of a power system. However, the prediction performance of the traditional single model is not accurate enough, and the prediction method cannot reflect the dynamic mechanism of the power system. To address these challenges, based on the analysis of the mechanism of the dynamic operation of a power system, a dynamic frequency online prediction method using the autoregressive integrated moving average (ARIMA) model and the deep belief network (DBN) is proposed in this paper. First, according to the mechanism of the dynamic operation of a power system, the dynamic frequency can be regarded as having two stages after the disturbance occurs. In the first stage, the frequency changes monotonously in the short term, which is predicted by the ARIMA model. Furthermore, the second stage is an oscillation phase with changing amplitude, which is predicted by the DBN. The calibration process is used to combine the two predicted results. Second, the three metrics including the frequency nadir (fnadir), the quasi-steady state frequency (fss), and the frequency curve obtained through the prediction are analyzed to measure the accuracy of the prediction results. Finally, to verify the accuracy of the proposed model, the IEEE 10-generator 39-bus benchmark system is used for verification.

Incorporating System Frequency Dynamics Into Real-Time Locational Marginal Pricing of Electricity

Incorporating System Frequency Dynamics Into Real-Time Locational Marginal Pricing of Electricity

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. The comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

Frequency stability control method for multi-energy system considering storage characteristics and transmission inertia of hot and gas pipeline network

The grid-connected capacity of renewable energy generation in multi-energy microgrid is increasing. This leads to a decrease in the inertia level in the microgrid, which has a great impact on the frequency stabilization control. This article proposes an adaptive control method for frequency control of inertia in multi-energy microgrids. Firstly, the system frequency fluctuation problem is addressed. Analyze the response characteristics of virtual inertia and the influence of physical inertia of rotating equipment on system frequency dynamics in multi-energy microgrid. Secondly, study the energy transfer characteristics of electric, thermal and gas systems in multi-energy microgrids. The energy coupling model between the subsystems in the multi-energy microgrid is established. And according to the difference of energy transmission time inertia of electric, heat and gas subsystems, the microgrid inertia response time model of different energy systems is established. Then, according to the energy balance stability criterion of multi-energy microgrid, combined with the current operating state of the system and the state of the higher-level distribution network, the fast response adaptive over-compensation control of multi-energy microgrid cluster is carried out to realize the inertia allocation in multi-energy microgrids. Finally, the proposed advanced frequency control method of multi-energy microgrid considering inertia demand is verified by simulation.

Frequency Dynamics of Power Systems with Inertial Response Support from Wind Generation

Inertial response support from wind turbine generators has become a priority requirement in most grid codes to improve the frequency response and frequency stability margins of power systems. However, the interaction between MPPT and inertial controllers may significantly degrade the power system dynamics. Therefore, there is a need to comprehensively understand the electromechanical dynamics of power systems with high penetration of wind generation. In this context, this work proposes a simplified dynamic model to assess the electromechanical dynamics of modern power systems with inertial response support from wind generation. The proposed simplified model allows simple analyses of the intrinsic and extrinsic aspects of wind generation that directly affect the system frequency dynamics and the dynamics of wind turbine generators. As a secondary contribution, this work also provides a comprehensive assessment of intrinsic and extrinsic aspects of wind generation that significantly affect the electromechanical dynamics of power systems with inertial response support from wind generation.

The Effect of the Fast Frequency Response of the Solar Energy System on the Power System Dynamic Frequency Evolution

The existence of a large-scale photovoltaic power generation system without any rotational inertia can deteriorate the frequency stability of the power system. The solar energy storage system consisted of photovoltaic power generation and the energy storage device with fast charge and discharge can provide fast frequency responses to the grid through the power electronics controls, and therefore improve the dynamic frequency security of the low-inertia system. This paper discusses the modeling and fast frequency controls, namely virtual inertia and droop control. The modified WSCC 9-bus system with high photovoltaic power penetration and low inertia serves to show the effects of the solar energy storage system’s fast frequency responses on the frequency evolutions of the new power system. The results show that in the low inertia system with large-scale photovoltaic power generation, the active power droop control of the solar energy storage system can decrease the frequency deviations, but may introduce low-frequency oscillations during the frequency evolution following a contingency; the virtual inertia control can depress both the rate of change of frequency as well as the oscillations during the frequency evaluation.

Optimal Reset-Control-Based Load Frequency Regulation in Isolated Microgrids

In isolated ac microgrids, multiple controllable distributed energy resources (DERs) may simultaneously participate in load frequency control (LFC). To improve system frequency dynamics and reduce the frequency deviation for such a multiple-DER microgrid,this paper presents a novel LFC method based on an optimal reset control (ORC) scheme. The proposed ORC comprises a baseline linear controller and resetting elements, i.e., the integrator outputs, determined by a linear quadratic regulation problem. The overshoot in frequency regulation induced by integral control is reduced, and the settling time is shortened. Besides, the simple structure facilitates its real-time application, making ORC a simple yet effective solution for the LFC of microgrids. By coordinating the reset controllers of all controllable DERs, the ORC further improves the overall frequency control performance. The asymptotic stability of the closed-loop system is theoretically proved. Finally, the effectiveness of the presented LFC method is validated by switch-level simulation studies.

Frequency dynamics-aware real-time marginal pricing of electricity

This paper presents a frequency dynamics-aware marginal pricing method for real-time electricity markets. The proposed method captures the impact of system frequency dynamics on the marginal price of electricity in the presence of aggressive net-load variations made more likely by greater renewable integration. We formulate a dynamics-aware economic dispatch (ED) by augmenting the traditional single-snapshot ED with constraints pertaining to system frequency dynamics, and frequency deviations from the synchronous speed are penalized in the modified objective function. The resulting ED embeds two distinct time steps to optimize over fast system dynamics and slower decisions on generator set-points. We prove that the dynamics-aware marginal price is the (suitably scaled) Lagrange multiplier of the power balance constraint and that it converges in steady state to the marginal price obtained from traditional ED solved with comparable system load. Numerical case studies involving the Western System Coordinating Council test system validate our findings and confirm added revenue opportunities for generators contributing to frequency regulation.

Modelling of water conduit dynamics using the electromagnetic transient program line model

Almost all electrical power systems literature assumes that the shaft mechanical torque of a water turbine is linearly proportional to the wicket gate position and ignores the dynamics in the shaft torque due to the propagation of the water from the reservoir to the turbine. This propagation is usually modelled very simply using the water start-time equation and ignoring the travelling wave dynamics along possibly long conduits. This simplified modelling may introduce significant errors in the frequencies of oscillation which are in the range of 0.5–2 Hz and often fall within the range of slow oscillations in power system dynamics. This paper introduces the EMTP-H model for water dynamics based on the analogy between the hydraulic equations and the EMTP transmission line equations. The proposed model is validated with a field test and is applied to a simple power system frequency dynamics case.

Data-Driven, Web-Based Parameter Identification for a Reduced-Order Model of the Chilean Power System

The current need for power-system control-room operational tools to increase real-time situational awareness has led to various proposals on data analytics algorithms to obtain operational information from SCADA and PMU power system networks. Most of the proposals are implemented in simulation, with reduced practical significance for system operators. This work proposes a web-based simple algorithm to identify the dynamic parameters of a reduced-order model of power system frequency dynamics that is implemented with industrial hardware on a PMU network in the Chilean power system. To demonstrate the applicability of the proposed tool, the algorithm is implemented in a web page with real-time monitoring of the frequency of the Chilean power system, so that utilities and academic institutions with access to PMU measurements can apply the proposed concepts regardless of the topology of the monitored system.

Frequency Response From Aggregated V2G Chargers With Uncertain EV Connections

Fast frequency response (FR) is highly effective at securing frequency dynamics after a generator outage in low inertia systems. Electric vehicles (EVs) equipped with vehicle to grid (V2G) chargers could offer an abundant source of FR in future. However, the uncertainty associated with V2G aggregation, driven by the uncertain number of connected EVs at the time of an outage, has not been fully understood and prevents its participation in the existing service provision framework. To tackle this limitation, this paper, for the first time, incorporates such uncertainty into system frequency dynamics, from which probabilistic nadir and steady state frequency requirements are enforced via a derived moment-based distributionally-robust chance constraint. Field data from over 25,000 chargers is analysed to provide realistic parameters and connection forecasts to examine the value of FR from V2G chargers in annual operation of the GB 2030 system. The case study demonstrates that uncertainty of EV connections can be effectively managed through the proposed scheduling framework, which results in annual savings of <inline-formula><tex-math notation="LaTeX">$&amp;pound;$</tex-math></inline-formula>6,300 or 37.4&#x00A0;tCO<inline-formula><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula> per charger. The sensitivity of this value to renewable capacity and FR delays is explored, with V2G capacity shown to be a third as valuable as the same grid battery capacity.

Predictive Control-Based NADIR-Minimizing Algorithm for Solid-State Transformer

Solid-state transformers (SSTs) are becoming an important solution to control active distribution systems. Their significant flexibility in comparison with traditional magnetic transformers is essential to ensure power quality and protection coordination at the distribution level in scenarios of large penetration of distributed energy resources such as renewables, electric vehicles and energy storage. However, the power electronic interface of SSTs decouples the nature of the inertial and frequency responses of distribution loads, deteriorating the frequency stability, especially under the integration of large-scale solar and wind power plants. Despite the virtual inertia/voltage sensitivity-based algorithms that have been proposed, the frequency sensitivity of loads and the capability of guaranteeing optimal control, considering the operating restrictions, have been overlooked. To counteract this specific issue, this work proposes a predictive control-driven approach to provide SSTs with frequency response actions by a strategy that harnesses the voltage and frequency sensibility of distribution loads and considers the limitations of voltage and frequency given by grid codes at distribution grids. In particular, the control strategy is centered in minimizing the NADIR of frequency transients. Numerical results are attained employing an empirically-validated model of the power system frequency dynamics and a dynamic model of distribution loads. Through proportional frequency control, the results of the proposed algorithm are contrasted. It is demonstrated that the NADIR improved about 0.1 Hz for 30% of SST penetration.

Frequency-Constrained Resilient Scheduling of Microgrid: A Distributionally Robust Approach

In order to prevent the potential frequency instability due to the high Power Electronics (PE) penetration under an unintentional islanding event, this paper presents a novel microgrid scheduling approach which includes the system frequency dynamics as well as the uncertainty associated with renewable energy resources and load. Synthetic Inertia (SI) control is applied to regulating the active power output of the Inverter-Based Generators (IBGs) to support the post-islanding frequency evaluation. The uncertainty associated with the noncritical load shedding is explicitly modeled based on the distributionally robust formulation to ensure resilient operation during islanding events. The resulted frequency constraints are derived analytically and reformulated into Second-Order Cone (SOC) form, which are further incorporated into the microgrid scheduling model, enabling optimal frequency services provision from the micorgrid perspective. With the SOC relaxation of the AC power flow constraints, the overall problem is constructed as a mixed-integer SOC Programming (MISOCP). The effectiveness of the proposed model is demonstrated based on modified IEEE 14-bus system.

Hierarchical Coordinated Fast Frequency Control Using Inverter-Based Resources

The share of inverter-connected renewable energy resources (RESs) is increasing in the grid, with these resources partially displacing conventional synchronous generators. This has resulted in increased variability of active power supply, reduced overall inertia, and increased spatial heterogeneity of inertia, leading to faster system frequency dynamics along with larger and more frequent frequency control events. These effects are expected to become increasingly more important in power system control in next-generation grids, which may conceivably be made up entirely of RESs. To mitigate these challenges, a fast, area-based hierarchical control strategy is proposed. This scheme partitions the power system into small areas, estimates local power imbalances, and corrects them by utilizing local inverter-based resources (IBRs). In cases where sufficient resources are not available locally, power is preferentially sourced from electrically close neighbours using an iterative distributed optimization scheme which preserves information privacy between areas. The proposed frequency control architecture can be retrofit onto existing control systems, and allows for flexibility in the amount of model information available to the designer. The control strategy is validated on two detailed multi-area power system models. Simulation results show that the strategy provides fast and localized frequency control.

Hierarchical Power Flow Control in Smart Grids: Enhancing Rotor Angle and Frequency Stability with Demand-Side Flexibility

Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of operation, the system must maintain adequate disturbance rejection capability at the time scales of both rotor angle and system frequency dynamics. This calls for flexibility to be exploited on both the generation and demand sides, compensating volatility and ensuring stability at the two separate time scales. This article proposes a hierarchical power flow control architecture that involves both transmission and distribution networks as well as individual buildings to enhance both small-signal rotor angle stability and frequency stability of the transmission network. The proposed architecture consists of a transmission-level optimizer enhancing system damping ratios, a distribution-level controller following transmission commands and providing frequency support, and a building-level scheduler accounting for quality of service and following the distribution-level targets. We validate the feasibility and performance of the whole control architecture through real-time hardware-in-loop tests involving real-world transmission and distribution network models along with real devices at the Stone Edge Farm Microgrid.

Comparative study of SBOAs on the tuning procedure of the designed SMPI controller for MIMO VSP/HVDC interconnected model

This paper presents a new application of advanced SMPI controller for a newly introduced interconnected dynamic system with VSP based HVDC links for frequency control problem. This work presents an outgrowth of analysis about the Swarm – Based Optimization Algorithms (SBOAs) in the tuning process of Multivariable Proportional – Integral (MPI) controller, which is called swarm – based MPI (SMPI). PSO, GOA and GWO algorithms are used for tuning process of the designed SMPI. The VSP based HVDC model is added for mitigation of system frequency dynamics with emulating virtual inertia. The proposed SMPI controller are designed for enhancing the dynamic performance of this system’s states during contingencies and they are compared with the conventional designed MPI controller. Deviation characteristics of the step function in MIMO transfer function of the VSP based HVDC model is considered as the common performance index in the proposed algorithms. On the other hand, the role of the proposed SMPI controller is to stabilize such interconnected system while minimizing the associated cost function. Matlab simulations next to the performed Nyquist’s stability anslysis demonstrate how the tuned SMPI can remarkably improve the frequency deviations and the damping of the inter-area oscillations excited during a fault. This enhancement is more obvious especially when SMPI controller for a VSP based virtual inertia emulation is tuned using GWO method.

A Quasi-Oppositional Method for Output Tracking Control by Swarm-Based MPID Controller on AC/HVDC Interconnected Systems With Virtual Inertia Emulation

This paper presents a comprehensive evaluation of the effect of quasi oppositional - based learning method utilization in output tracking control through a swarm-based multivariable Proportional-Integral-Derivative (SMPID) controller, which is tuned by a novel performance index based on the step response characteristics in multi-input multi-output (MIMO) system. The role of the proposed quasi oppositional based SMPID controller is to modify the tracking strategy on AC/HVDC interconnected systems while reducing the related cost function. The proposed analysis is established considering the most highly cited, well-known tested and newly expanded swarm-based optimization algorithms (SBOAs), such as Grasshopper Optimization Algorithm (GOA), Grey Wolf Optimization (GWO), Artificial Fish Swarm Algorithm (AFSA), Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO). These methods are used in the tuning process of multivariable PID (MPID) controller for output tracking control of an interconnected AC/DC system with virtual inertia emulation-based HVDC capabilities. The virtual inertia-based HVDC model, which is using a derivative technique, is attached for enhancing the system frequency dynamics with fast power injection during the contingency. The potential possibility for achieving a suitable assessment about the velocity reaction, the flexibility response, and the accuracy of the tracking process is provided by four different scenarios which are operated by step load changes as essential inputs in AC/HVDC interconnected MIMO system. Also the proposed fitness function, as deviation characteristics of the step response in MIMO transfer function in virtual inertia emulation based HVDC model, is compared with integral time absolute error (ITAE), as the standard performance index in the optimization process. The results are compared with the conventional tuned MPID (C - MPID) controller using MATLAB software. The obtained analysis emphasizes how the tuned SMPID can significantly increase the capability of tracking control on the proposed AC/HVDC interconnected model.

A Transfer and Deep Learning-Based Method for Online Frequency Stability Assessment and Control

Fast and accurate prediction and control of power system dynamic frequency after disturbance is essential to enhance power system stability. Machine learning methods have great potential in harnessing data for online application with accurate predictions. This paper proposes a two-stage novel transfer and deep learning-based method to predict power system dynamic frequency after disturbance and provide optimal event-based load shedding strategy to maintain system frequency. The proposed deep learning model combines convolutional neural network (CNN) and long short-term memory (LSTM) network to harness both spatial and temporal measurements in the input data, through a four-dimensional (4-D) tensor input construction process including, 1) capture system network topology information and critical measurements from different time intervals; 2) compute a multi-dimensional electric distance matrix and reduce to a 2-D plane which can describe the system nodal distribution; 3) construct 3-D tensors based on state variables at different sample times; and 4) integrate into 4-D tensor inputs. Moreover, a transfer learning process is employed to overcome the challenge of insufficient data and operating condition changes in real power systems for new prediction tasks. Simulation results in IEEE 118-bus system verify that the CNN-LSTM method not only greatly improves the timeliness of online frequency control, but also presents good accuracy and effectiveness. Test cases in the New England 39-bus system and the South Carolina 500-bus system validate that the transfer learning process can provide accurate results even with insufficient training data.