Inertia Constant Research Articles

A Fast Frequency Control Based on Model Predictive Control Taking Into Account of Optimal Allocation of Power From the Energy Storage System

The displacement of synchronous generators by converter interfaced energy renewable resource essentially reduces the system inertia, which can trigger under-frequency load shedding relay. To support the frequency containment, virtual inertia control (VIC) and fast frequency control (FFC) based on energy storage system (ESS) have been developed. Most of the existing VIC did not take into account the power constraints of the ESS. Although some of the FFC methods account for the ESS constraints, they ignore the intermediate steady-state (ISS) operating point of the primary frequency response (PFR). To counteract these problems, a model predictive control (MPC) based FFC, which considers the power limitations of the ESS, the frequency deviation constraint, and the ISS frequency tracking capability, is proposed in this paper. The proposed MPC only requires few local measurements, and the system parameters including inertia constants, onset time of inertia response and the ISS time of the PFR can be accurately estimated. To achieve the optimal control action and reduce computational burden, quadratic programming (QP) is incorporated in the proposed MPC. The proposed MPC is tested on a real Taiwan power system. The fast response and robustness of the proposed MPC has been justified by comparing with the state-of-the-art method.

Robust Load-Frequency Control in Islanded Microgrids: Virtual Synchronous Generator Concept and Quantitative Feedback Theory

Increasing penetration of renewable energy sources based on power electronic interfaces in traditional power systems reduces the inertia constant and damping coefficient. It also increases uncertainty and the sensitivity of the system to disturbances. The concept of the virtual synchronous generator (VSG) is used to emulate the inertia constant and damping property like a synchronous generator. It can be shown that all given VSG structures have the same dynamics as the proportional-integral-derivative (PID) controller. In this paper, the quantitative feedback theory (QFT) is used to tune the VSG parameters such that robust system stability and performance are guaranteed. Moreover, the desired disturbance attenuation is also taken into account. Through frequency response analysis and time-domain simulations, it is shown that the proposed strategy can be successfully used to solve the load-frequency control problem in islanded microgrids (MGs). In addition, the proposed QFT-based VSG is compared with another robust VSG designed by the well-known <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> technique to illustrate its better performance against disturbances.

주파수응답 성능 기반의 신재생발전기 계통관성 기여도 정량화 방법

The high Penetration of RES could have a negative effect on the power system stability by reducing its system inertia. As one of its measures, the requirements for frequency response performance of RES has been strengthened by revising the grid code for RES in the Korean power system. In this paper, it is confirmed that the frequency response of the RES can contribute even in the system inertia, and a method for quantifying its contribution on the system inertia based on its frequency response is proposed. The effectiveness of the proposed method is verified by comparing the system inertia derived with the calculated inertia constant of RES with the system inertia derived from the simulated frequency response of the RES integrated power system. The Power Simulation Simulator for Engineering (PSS/E) which is a large-scale power system analysis program was used to model Korean power system integrated with RES for the case studies.

A Study on the Power Reserve of Distributed Generators Based on Power Sensitivity Analysis in a Large-Scale Power System

Converter-based generators (CBGs) that use renewable energy sources (RESs) are replacing traditional aging coal and nuclear power generators. Increasing the penetration of CBGs into the entire power generation process reduces both the inertia constant of the power system and the total amount of power reserves. Additionally, RESs are very intermittent and it is difficult to predict changes in them. These problems, due to CBGs using RESs, pose new challenges to net–load balancing. As a solution, this paper proposes a virtual multi-slack (VMS) droop control that secures the stability and efficiency of system operation by controlling the output of CBGs distributed in various regions. The VMS droop control makes it possible to increase the inertia constant of the power system and to respond quickly and appropriately to load changes through the proposed VMS droop control based on power sensitivity. It is also proposed that the process selects proper power reserves of CBGs for stable VMS droop control. To verify the effectiveness of the proposed VMS droop control and the proper power reserve selection method for CBGs, several case studies were performed using a real Korean power system.

Data-driven inertia estimation based on frequency gradient for power systems with high penetration of renewable energy sources

The time-dependent inertia can trigger rapid frequency variations, which have become main concerns in power system stability. Prior understanding of the system inertia will help operators to mitigate the stability issues by applying appropriate measures and executing suitable control schemes. Therefore, this paper proposes a data-driven method to estimate the time-dependent inertia in the system based on the frequency gradient of an estimated model of the system. In this approach, phasor measurement units (PMUs) are used for measuring the system data, which is then used to estimate a dynamic model representing the system. Next, a system identification approach is applied to estimate the power system model, from which the inertia will be estimated. The benefits of the proposed method include reduction of the model order to avoid computation burden, extraction of the inertia from the reduced order model using the gradient mapping on RoCoF of the system response and estimation of the inertia constant of the system using normal operating conditions. The use of normal operating conditions to estimate the inertia makes the method unique. The method has been verified using the simulated IEEE 39-bus system in DIgSILENT™ PowerFactory® tool and real data from the New Zealand power system.

Impact of inertia constant on frequency dynamics of a power system

The Ceylon Journal of Science is published by the University of Peradeniya, Sri Lanka. Full text available. The journal also has its own website. The Ceylon Journal of Science is a continuation of the Ceylon Journal of Science (Biological Sciences) which is no longer being published as a separate journal. The history of the journal can be found here.From May 2020, Ceylon Journal of Science is indexed in DOAJ.

A Novel Adaptive Virtual Inertia Control-Based Adaptive Neuro-Fuzzy to Enhance Frequency Stability of a Microgrid with Seamless Transition

A frequency stability improvement of a microgrid with low-inertia constant during severe disturbances remains a challenge using a virtual inertia control to compensate the inertia power to the microgrid, using a battery energy storage system. However, the fixed virtual inertia constant and the low-order model of the battery energy storage system utilized in virtual inertia control can affect the stability behaviors of microgrid and virtual inertia control design. Hence, for solving these issues, this paper proposes a novel adaptive virtual inertia control utilizing an adaptive neuro-fuzzy inference system based on a training data design in order to adjust the controller gain that applies for the direct and the quadrature axis model of the battery energy storage system. In order to investigate the proposed method and to verify the performance, the various case studies are carried out under the high, the low levels existing of renewable energy, and the parameter uncertainties in a microgrid. The simulated results with the proposed scheme are compared with the virtual inertia based-linear quadratic Gaussian synthesis and without the virtual inertia control. The comparative results reveal that the proposed method enhances the frequency stability during the disturbances, reduces the switching transition time from the islanded to the grid-connected mode of the microgrid, seamlessly, with superior performance in comparison with the other methods, satisfying a frequency grid code in Thailand.

Inertial Response Identification Algorithm for the Development of Dynamic Equivalent Model of DFIG-Based Wind Power Plant

As the wind power penetration increases, the frequency stability of the power system is deteriorating. Thus, it is expected that the wind power plants (WPPs) will be required to produce the inertial response during the short-term large-scale frequency disturbances. To study the effects of the inertial response of the WPP, the dynamic equivalent model (DEM) of the WPP should be able to emulate the inertial response of the actual WPP. Otherwise, the simulated system frequency would be different from the actual one. Therefore, the inertial response identification algorithm (IRIA) is proposed in this article. The IRIA is able to identify the gain of the inertial controller and the inertia constants of the WPP according to the actual system frequency and the active power output of the actual WPP. In this article, the actual WPP is represented by the detailed model. In order to prove the effectiveness of the IRIA, three cases with different gains of the inertial controller are studied. The simulation results demonstrate that the proposed IRIA allows the DEM of the WPP to generate similar response of the active power and lead to close response of the system frequency as the actual WPP does in three different scenarios.

Dynamic Inertia Evaluation for type-3 Wind Turbines Based on Inertia Function

Inertia constant is widely used to evaluate the inertia capability for wind turbines (WTs). However, the method fails to reflect the dynamic characteristics of the inertia and neglects the impacts of controllers. For this issue, this article establishes an inertia function to analyze the dynamic inertia for type-3 WTs. Firstly, the consistency of the power transfer mechanisms between the type-3 WT and synchronous generator (SG) is discussed. Then, a new approach to construct the inertia function is offered according to the phase motion model of SG. On this basis, the impacts of the controllers and operating points on the inertia are explored, and the critical factors are revealed. The analysis results help to understand and optimize the inertia capability of the type-3 WT. Moreover, compared with the conventional inertia constant, the presented inertia function can better reveal the dynamic nature and the influence rule of inertia. Finally, the analysis is validated by IEEE 3-bus test system simulation.

Real-Time Estimation of Microgrid Inertia and Damping Constant

The displacement of rotational generation and the consequent reduction in system inertia is expected to have major stability and reliability impacts on modern power systems. Fast-frequency support strategies using energy storage systems (ESSs) can be deployed to maintain the inertial response of the system, but information regarding the inertial response of the system is critical for the effective implementation of such control strategies. In this paper, a moving horizon estimation (MHE)-based approach for online estimation of inertia constant of low inertia microgrids is presented. Based on the frequency measurements obtained in response to a non-intrusive excitation signal from an ESS, the inertia constant was estimated using local measurements from the ESS’s phase-locked loop. The proposed MHE formulation was first tested in a linearized power system model, followed by tests in a modified microgrid benchmark from Cordova, Alaska. Even under moderate measurement noise, the technique was able to estimate the inertia constant of the system well within ±20% of the true value. Estimates provided by the proposed method could be utilized for applications such as fast-frequency support, adaptive protection schemes, and planning and procurement of spinning reserves.

Method of integral equations in the polytropic theory of stars with axial rotation. II. Polytropes with indices $n&gt;1$

A new method for finding solutions of the nonlinear equilibrium equations for rotational polytropes was proposed, which is based on a self-consistent description of internal region and periphery using the integral form of equations. Dependencies of geometrical parameters, surface form, mass, moment of inertia and integration constants on angular velocity were calculated for indices $n=2.5$ and $n=3$.

Inertia Emulation Through Supercapacitor for a Weak Grid

Renewable energy sources (RES) have been widely incorporated into the power generation to offset fossil fuels in order to minimize carbon emissions. Typically, RES based power generation integrated into the power grid through the power electronic converters. These power electronic converters decouple the source from the load without providing inertia. As a result, inertia of the power grid decreases, resulting in undesirable load shedding and cascading failures under power imbalances. In order to preserve stability during contingency events, it is important to add inertia support to the grid. This article demonstrates inertia emulation from the supercapacitor (SC) to resolve the low-inertia issue. Inertia emulator based on supercapacitor (IESC) is formulated to generate inertial power by proportionally linking the grid frequency to the active power reference of SC. This article proposes an enhanced emulated inertia control (EIC) technique based on the frequency deviation and frequency derivative to address low inertia. EIC technique controls the inverter associated with IESC to exhibit the equivalent inertia characteristics as the synchronous generator. Further, the selection of the capacitance value of SC is derived to achieve the required inertia constant. The small-signal stability of IESC is demonstrated using the power angle curve. Further, the stability of the EIC is verified through bode plot. Simulation and hardware-in-loop (HIL) results are provided to verify the effectiveness of EIC employed IESC in a weak grid.

A Novel Passive Islanding Detection Scheme for Synchronous-type DG using Load Angle and Mechanical Power Parameters

This paper offers a novel passive islanding detection scheme for synchronous distributed generations (SDGs) based on the combination of (dδ/dt) and (dPm/dt). By the occurrence of islanding and grid-connected events, the load angle (δ) and mechanical power (Pm) of SDGs will change. These signals will oscillate during non-islanding events, while they will reach a stable point without any oscillation during islanding events. However, during some grid-connected disturbances such as high impedance faults and small capacitor switching, the oscillations of δ and Pm may not be significant. Therefore, the swing feature cannot be a reliable index and can lead to an inappropriate operation. Hence, to select the best parameters, a combination of four parameters, including dPm/dt, dδ/dt, dPm/dδ, and dδ/dPm is employed. The sensitivity analysis to discriminate islanding from non-islanding events has been reported in the presence of SDGs with various inertia constants, voltage levels, and loads. Based on the results, the combination of dδ/dt and dPm/dt has high accuracy and speed in clustering the occurred events. The efficiency of the proposed approach is tested on the IEEE 33-bus system. It is proved that the proposed approach decreases the non-detection zone to 0.01 MW and 0.01 MVAr of the powers nonconformity.

Simulation and Characteristics Analysis of Multiple Wind Generators in Large-Scale Wind Farms Based on Simplified Model

In the view of the high complexity and a large amount of data of the electromagnetic transient model for the single wind generator, it is difficult to realize the multi-unit simulation modeling of large-scale wind farms by power system simulation software. In this paper, the simplified models of single direct drive and doubly-fed wind generator system are proposed, respectively. In order to study the output characteristics of the wind generator system, the components with small inertia constant in the electromagnetic transient model are neglected, and the shafting model, the converter model, and the control loops are simplified and reduced, respectively. Based on the study of the single electromagnetic transient model of wind generators, the simplified simulation models are built by the PSCAD (Power Systems Computer Aided Design) simulation platform, which are carried out under the conditions of constant wind speed, step wind speed, and fault. The output characteristics of the simplified models under different working conditions are compared in detail models. The simulation results show that, within the allowable calculation accuracy range, the dynamic response curves of the single simplified model and the electromagnetic transient model are consistent. The simulation speed can be significantly improved, the time consumption can be reduced, and the simulation speed can be increased more obviously when the number of simulation models increases. Therefore, it can be applied to the simulation research of multi-wind generators in large-scale wind farms.

Double stage controller optimization for load frequency stabilization in hybrid wind-ocean wave energy based maritime microgrid system

The momentum towards reduction of greenhouse gas emissions by reduced use of conventional source in marine power networks as well as significant development of renewable energy resources (RRs) have been the motivating factors for inclusion RRs in hybrid maritime microgrid system (HMμGS) and investigation of consequent frequent control mechanism. This article presents an approach of load frequency control in an independent HMμGS consisting of wind driven generation (WDG), Archimedes wave power generation (AWPG), marine biodiesel generator (MBG), solid-oxide fuel cell (SOFC) energy units, heat pump (HP) and freezer (FZR). The stability of the HMμGS model have been evaluated through the rigorous tests considering non-availability of renewable resources, concurrent random generation of AWPG, load demand, real recorded data of WDG. Comparative performance of several controllers such as PID, PID with filter (PIDN) and PI-(1 + PD) controller are presented with their parameters optimized using genetic algorithmic technique (GA), particle swarm technique (PSO), firefly algorithmic technique (FA), cultural algorithmic technique (CA) and the recent metaheuristic grasshopper algorithmic technique (GOA). The proposed frequency control strategy of HMμGS model is benchmarked by comparative statistical assessment and decision indicators. Finally, sensitivity assessment of GOA tuned PI-(1 + PD) controller under uncertain parametric variations such as; variation of WDG gain, droop factor (R), inertia constant (M) and loading without reoptimizing the optimal base condition values is conducted as an evidence of the sturdiness of the proposed frequency control strategy. The analysis of the results shows that the proposed GOA optimized PI-(1 + PD) control strategy perform much better than other control schemes.

Extensive frequency response and inertia analysis under high renewable energy source integration scenarios: application to the European interconnected power system

Traditionally, power system's inertia has been estimated according to the rotating masses directly connected to the grid. However, a new generation mix scenario is currently identified, where conventional supply-side is gradually replaced by renewable sources decoupled from the grid by electronic converters (i.e., wind and photovoltaic power plants). Due to the significant penetration of such renewable generation units, the conventional grid inertia is decreasing, subsequently affecting both reliability analysis and grid stability. As a result, concepts such as 'synthetic inertia', 'hidden inertia' or 'virtual inertia', together with alternative spinning reserves, are currently under discussion to ensure power system stability and reliability. Under this new framework, an algorithm to estimate the minimum inertia needed to fulfil the ENTSO-E requirements for ROCOF values is proposed and assessed under a relevant variety of imbalanced conditions. The additional active power needed to be within the frequency dynamic range is also estimated and determined. Both inertia and additional active power can come from different sources, such as storage solutions, renewable sources decoupled from the grid including some frequency control strategies, interconnections with other grids, or a combination of them. The power system under consideration includes thermal, hydro-power plants, and renewable generation units, in line with most current and future European supply-side power systems. More than 700 generation mix scenarios are identified and simulated, varying the renewable integration, the power imbalance, and the inertia constant of conventional power plants. In fact, the solutions studied here provide important information to ease the massive integration of renewable resources, without reducing the capacity of the grid in terms of stability and response to contingencies.

Improved Control Strategy of MMC–HVDC to Improve Frequency Support of AC System

With the continuous development of power electronics technology, variable-speed offshore wind turbines that penetrated the grid system caused the problem of inertia reduction. This study investigates the frequency stability of synchronous, offshore wind-farm integration through a modular-multilevel-converter high-voltage direct-current (MMC–HVDC) transmission system. When full-scale converter wind turbines (type 4) penetrate the AC grid, the AC system debilitates, and it becomes difficult to maintain the AC system frequency stability. In this paper, we present an improved inertial-response-control method to solve this problem. The mathematical model of the synchronous generator is based on the swing equation and is theoretically derived by establishing a MMC–HVDC. Based on the above model, the inertia constant is analyzed using a model that integrates the MMC–HVDC and offshore synchronous generator. With the new improved control method, a more sensitive and accurate inertia index can be obtained using the formula related to the effective short-circuit ratio of the AC system. Moreover, it is advantageous to provide a more accurate inertial control evaluation for AC systems under various conditions. Furthermore, the impact of the MMC–HVDC on system safety is assessed based on the capacitor time constant. This simulation was implemented using the PSCAD/EMTDC platform.

Impact of Synchronous Condenser on Sub/Super-Synchronous Oscillations in Wind Farms

Sub/Super-synchronous oscillations have occurred in wind farms consisting of doubly-fed induction generators (DFIGs) or permanent magnet synchronous generators (PMSGs). This paper investigates the impact of synchronous condenser (SC) on sub/super-synchronous oscillations in wind farms with different types of generator and compares it with STATCOM. Impedance model is adopted in this paper to explain the mechanism of oscillations in wind farms and its mitigation using SC. Compared to STATCOM, SC is more effective in oscillation mitigations of the two types of wind farms. Eigenvalue analysis and time domain simulations in PSCAD/EMTDC are used to check the influence on sub/super-synchronous oscillations from different parameters of SC, such as its capacity, leakage reactance and inertia constant. The results indicate that SC would improve the system stability while a larger capacity will induce a greater improvement. A smaller leakage reactance of SC also benefits the mitigation of oscillations while its inertia constant can hardly influence system stability.

Demand Management of Active Distribution Network Using Coordination of Virtual Synchronous Generators

This article proposes a hierarchical control structure to address two major issues in power systems: 1) power imbalance during events when output power from distributed generations (DGs) is not fully consumed; 2) reduction of inertia constant and damping effect in overall power systems due to integration of DGs. To address these issues, a hierarchical control structure for a virtual synchronous generator (VSG) based active distribution network (ADN) is proposed to achieve three objectives; 1) to regulate the point of common coupling (PCC) of ADN according to demand; 2) to coordinate all VSGs to share active and reactive power proportionately; 3) to ensure that the error in reactive power sharing caused by the unequal line impedances will not disturb the demand at PCC. The uniqueness of this study lies in the fact that the VSG coordination of the PCC demand management for ADN has never been implemented. Furthermore, the proposed method does not require a large battery energy storage (BES) system to balance the output voltages of all DGs. This strategy will not only increase the revenue of distribution companies but will also provide power to the customers with enhanced quality and lower rate of change of frequency (RoCoF).

Implementation of Dynamic Virtual Inertia Control of Supercapacitors for Multi-Area PV-Based Microgrid Clusters

In order to improve the dynamic stability of multi-area microgrid (MG) clusters in the autonomous mode, this study proposes a novel fuzzy-based dynamic inertia control strategy for supercapacitors in multi-area autonomous MG clusters. By virtue of the integral manifold theory, the interactive influence of inertia on dynamic stability for multi-area MG clusters is explored in detail. The energy function of multi-area MG clusters is constructed to further analyze the inertia constant. Based on the analysis of the mechanism, a control strategy for the fuzzy-based dynamic inertia control of supercapacitors for multi-area MG clusters is further proposed. For each sub-microgrid (sub-MG), the gain of the fuzzy-based dynamic inertia control is self-tuned dynamically, with system events being triggered, so as to flexibly and robustly enhance the dynamic performance of the multi-area MG clusters in the autonomous mode. To verify the effectiveness of the proposed control scheme, a three-area photovoltaic (PV)-based MG cluster is designed and simulated on the MATLAB/Simulink platform. Moreover, a comparison between the dynamic fuzzy-based inertial control method and an additional droop control method is finally presented to validate the advantages of the fuzzy-based dynamic inertial control approach.