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This paper gives an experimentally supported review and comparison of several indices based on the conventional K-means inertia criterion for determining the number of clusters, $K$ , in datasets, using the popular Silhouette width index as a benchmark. Our experiments involve a novel version of the Elbow index, defined using values of $K$ two or three steps apart. We also discuss alternative ways of computing the inertia and summarizing its values. Even though there are no overall winners in our experiments, some of our results are very conclusive and can be used as a guide for indices determining the number of clusters in K-means.

With the increasing proliferation of photovoltaic (PV) and wind power globally, frequency regulation by balancing generation and load in power systems is becoming increasingly difficult owing to reductions in dispatchable power and inertia. One countermeasure is autonomous load control, in which thermostatic loads and electric vehicle chargers quickly adjust the power consumption based on the grid frequency monitored by themselves without communication. However, testing the impact of such load controls on the frequency in actual power systems is too expensive. Therefore, a laboratory-scale isolated power system was prepared as a test bed to examine autonomous load control based on the rate of change of frequency (RoCoF) and the frequency deviation to cope with steep frequency fluctuations. Moreover, the experimental system was simulated numerically using MATLAB/Simulink. The experimental and simulation results are comparable, indicating that the simulation can be used to determine the total capacity and threshold when planning the introduction of autonomous control loads. The experimental and simulation results also show that frequency fluctuations can be mitigated by introducing autonomous control loads to the grid, and the response time can be improved by approximately 1 s by controlling the load based on the RoCoF.

Matrix converters (MC) have been considered for applications in renewable power generation and microgrids. However, similar to other power electronic converter-interfaced power generation systems, the MC-interfaced system cannot provide inertia or damping effect to support the grid’s frequency or voltage. To improve the inertia and damping effect of the MC-interfaced distributed generation system and realize the grid-friendly connection of new energy power generation, a virtual synchronous generator (VSG) control strategy suitable for the MC-interfaced system is proposed. Aiming at the problem that the system frequency in the traditional VSG cannot be restored to the nominal value after the load power fluctuations, the VSG secondary frequency control strategy is introduced. To ensure a smooth grid connection, a synchronization control strategy based on virtual power has been designed. An experimental validation platform was built and the experimental results verify the correctness and effectiveness of the proposed control strategies for a grid-forming MC.

This paper investigates the use of a battery energy storage system (BESS) to enhance the frequency response characteristics of a low-inertia power system following a disturbance or active power mismatch. A simple control strategy of the BESS is proposed to improve the inertia response and primary frequency response of the system. The effectiveness of the proposed control strategy is evaluated on two test systems, which have been modified by replacing some fossil fuel-based generators with solar photovoltaic (PV) systems to create low inertia systems. A BESS is then added to provide additional system inertia. The DigSILENT PowerFactory software is used to model these modified systems with the BESS and to generate the corresponding frequency response characteristics under various power imbalanced conditions. Simulation results indicate that the BESS, with the proposed control strategy, can improve the system rate-of-change of frequency (ROCOF), frequency nadir (minimum frequency), and final steady-state frequency. In the 3-machine system, replacing a traditional power plant with a solar PV farm decreases the frequency nadir from 49.34 Hz to 48.69 Hz following a sudden load increase of 60 MW. However, adding a 30 MW BESS improves the frequency nadir to 49.48 Hz, which is better than the original system. In the 4-machine system, replacing two traditional power plants with solar farms increases the initial ROCOF to 0.55 Hz/s, exceeding the acceptable limit of 0.50 Hz/s for a severe disturbance. However, incorporating a BESS reduces the initial ROCOF to 0.44 Hz/s.

DC microgrids are gaining more attention with the increased penetration of various DC sources such as solar photovoltaic systems, fuel cells, batteries, etc., and DC loads. Due to the rapid integration of these components into the existing power system, the importance of DC microgrids has reached a salient point. Compared with conventional AC systems, DC systems are free from synchronization issues, reactive power control, frequency control, etc., and are more reliable and efficient. However, many challenges need to be addressed for utilizing DC power to its full potential. The absence of natural current zero is a significant issue in protecting DC systems. In addition, the stability of the DC microgrid, which relies on inertia, needs to be considered during system design. Moreover, power quality and communication issues are also significant challenges in DC microgrids. This paper presents a review of various value streams of DC microgrids including architectures, protection schemes, power quality, inertia, communication, and economic operation. In addition, comparisons between different microgrid configurations, the state-of-the-art projects of DC microgrid, and future trends are also set forth for further studies.

The virtual synchronous generator (VSG) control is a promising solution for the grid-forming converters to enhance the inertia of the converter-based power grid. The virtual inertia and output impedance of the VSG are the important behaviors to be focused. However, the virtual inertia of grid-forming converters may cause active power oscillation due to the interaction with the power inertia of grid through the low-frequency band grid impedance. Besides, the resonance can be also triggered by the interaction between middle-frequency impedance of power grid and output impedance of converter. In order to test the stability of grid-forming converter, accurate emulation of grid behaviors from more aspects, including inertia and impedance under wider frequency ranges, is becoming critical. This article proposes a grid emulation method to mimic the inertia and impedance characteristics of power grid, targeting for the stability test of grid-forming converter under multifrequency bands. A high-switching-frequency converter and a low-switching-frequency converter are adopted in the proposed emulator structure to achieve both high capability in respect to control bandwidth and power level. Moreover, the virtual impedance control is integrated with the VSG control to emulate the line impedance and inertia within relatively wider frequency ranges. The realization of virtual impedance is achieved without derivation terms nor low pass filter. Finally, the performance of the proposed emulator is verified by various simulations and experimental measurements. [ABSTRACT FROM AUTHOR]

An ambient modal framework for inertia estimation using synchrophasor data is proposed in this letter. Specifically, an analytical formulation is developed for the estimation of inertia based on the frequency and damping ratio modes extracted from ambient data. An advantage of the proposed framework is that it can rely on synchronized ambient data under non-disturbed conditions for online estimation and tracking of inertia. Ultimately, numerical simulation studies and physical experiments demonstrate the feasibility of the proposed approach.

The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequency’s nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of thermal plants that are needed to provide frequency response (FR) and inertia. Additional consideration of fast FR, a dynamically reduced largest loss and under frequency load shedding (UFLS) allows frequency security to be achieved more cost effectively. This paper derives a novel constraint from the swing equation to contain the frequency nadir using all of these services. The expected cost of UFLS is found probabilistically to facilitate its comparison to the other frequency services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone (SOC), resulting in highly tractable convex problems. Case studies performed on a Great Britain 2030 system demonstrate that UFLS as an option to contain single plant outages can reduce annual operational costs by up to $\pounds $ 559 m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for the design of over-frequency containment schemes in low inertia, high renewable systems. This methodology is demonstrated through the comprehensive redesign of the containment scheme for significant over-frequency events (e.g., the loss of an exporting HVDC interconnector) in the Ireland and Northern Ireland power system (All-Island System). The new scheme allows an existing synchronous generator runback system integrity protection scheme to be replaced with fixed wind tripping and dynamic response from wind. This exploits the capabilities of renewable generation to create effective protection and control resources. The methodology provides the steps required to determine the key parameters of the scheme (e.g., maximum allowable frequency, required volume of tripping, lowest trip frequency). A key consideration of the methodology is the volume of dynamic response from wind that can be deployed before frequency limits are violated (e.g., inertia and wind penetration). Dynamic simulations are performed in DSE Tools for the All-Island system considering a 2020 operational scenario. These simulations support the application of the methodology and demonstrate the effectiveness of the scheme designed for the All-Island system. [ABSTRACT FROM AUTHOR]

Light-duty offshore wind power system has been a research hotspot in recent years. The diode rectifier based HVDC scheme is a promising solution and has attracted more and more attention. In this paper, a self-synchronizing control for offshore wind farms connected to diode rectifier based HVDC system is proposed. The active power of each wind turbine is controlled by regulating the amplitude of the AC voltage, while the reactive power is used to adjust the offshore frequency. The proposed control is a decentralized scheme. Thus, no communication network or GPS is required and only the local information is used in the control system. The synchronization of wind turbines is achieved by the proposed self-synchronizing frequency control instead of using phase-lock loop. Besides, in order to make offshore wind farms provide necessary frequency support to the onshore power system, a communication-less frequency regulation scheme with artificial coupling method is proposed. The feasibility and effectiveness of the proposed self-synchronizing control and frequency regulation scheme are verified through simulation studies in PSCAD/EMTDC platform. [ABSTRACT FROM AUTHOR]

This article proposes new control architecture to improve the dynamic performance of DC microgrid by enhancing system inertia. The DC microgrids are gaining more importance due to the controlled and combined operation of multiple distributed energy resources (DERs). The DC microgrid is dominated by controlled power electronics converters. These converters are not having inbuilt inertia like rotating generators. Therefore, the DC microgrid has a fast rate of change of bus voltage under fluctuations of load, change in available power capacity of sources due to their randomness, etc. This affects the voltage profile and stability of the system under dynamic variation. The proposed closed loop control scheme estimates the amount of inertia required in the DC microgrid to minimize the voltage variation. The new power references are given to sources based on virtual generation to improve the inertia in the system. The proposed control scheme maintains the stability of DC microgrid. It also achieves effective power management based on available power in DERs with a minimum burden on the energy storage system (ESS). The bus voltages are regulated at reference value. The stability analysis of the system is carried out for DC microgrid under different operating conditions. The proposed control method is tested experimentally under diverse operating conditions.

In modern power systems, the increasing penetration of renewable energy resources has reduced the overall system inertia. However, the intermittent nature of wind power generation reduces frequency stability, which is a crucial issue. Consequently, modern power systems require that renewable energy sources, such as offshore wind farms, support the frequency regulation. High voltage direct current (HVDC) systems based on voltage source converters (VSCs) are currently being used to connect wind farms with the main grid. By adjusting the DC-link voltage of the VSC-HVDC, a capacitor can absorb or release energy to provide frequency support. In addition, the VSC-HVDC system can coordinate wind farms to support frequency regulation and thereby achieve better performance. Thus, this paper reviews and compares various frequency-control strategies for a VSC-HVDC-connected wind farm. This work implements in PSCAD/EMTDC a simulation of typical frequency-control techniques to verify their effectiveness and robustness. Furthermore, this paper shows the advantages and drawbacks of each frequency regulation method. Other auxiliary services for supporting frequency regulation, such as by energy storage systems, are also discussed. Finally, this paper provides complete recommendations for frequency regulation techniques for VSC-HVDC-integrated wind farms.

Wind power, photovoltaics and other new energy sources are connected to the grid on a large scale. The power electronic interface cannot provide inertia and damping support for the microgrid. The virtual synchronous generator technology is introduced into the inverter control system. Unlike the synchronous generator, its parameters are flexible and adjustable, which can enhance the robustness of the microgrid. This paper firstly analyzes the influence of the moment of inertia and damping on the system, it is based on the equivalent relationship between the three-phase inverter and the synchronous machine, combined with the VSG rotor motion equation, and conducts stability analysis based on the small signal model and root locus. Based on the existing control strategy, a virtual synchronous generator cooperative control strategy based on the optimal damping ratio is proposed. Finally, the VSG collaborative control model is built in MATLAB/Simlink, the experimental results show that the proposed control strategy effectively improves the transient performance of the VSG, the system active power overshoot is reduced from 5% to 0, and the frequency deviation peak is lowered from 0.174 Hz to 0.115 Hz, which confirms the effectiveness of the proposed control strategy.

The synchronverter algorithm is a way to control a switched mode power converter that connects a DC energy source to the AC power grid. The main features of this algorithm are frequency and voltage droops as well as synthetic inertia, so that the inverter resembles a synchronous generator (SG). Many versions of this algorithm have been proposed and tested, but all share the same “basic control algorithm”, which is based on the equations of a SG. We analyze the sensitivity of the output currents of a synchronverter, with respect to the measurement errors. We show that some of the sensitivity functions exhibit high gains at the relevant frequencies, leading to distorted grid currents, which makes the use of this inverter control algorithm problematic. We then do a similar analysis assuming that we have controlled current sources available at the grid output of the converter, that we control using virtual currents generated in the algorithm. The virtual currents are flowing through virtual output inductors, that we can choose to be significantly larger than the actual output inductors. We show that using the current sources reduces the sensitivity considerably, thus indicating a better approach to synchronverter design.

We prove that virtual friction can stabilize a power grid containing several virtual synchronous machines (VSMs), connecting line impedances and loads. Virtual friction is a torque added to the swing equation of each VSM, proportional to the deviation of its frequency from the overall center of inertia (COI) frequency. Our analysis is based on the network reduced power system (NRPS) model. We support our results with simulations for a two-area network of four VSMs, looking at the transients induced by a change of tie-line impedance and an asymmetric load change. We compare the results for the NRPS model with the corresponding results using detailed models of synchronverters and line impedances. We find that virtual friction has a strong stabilizing effect both for the NRPS model and for the detailed model. Furthermore we show simulation results on the influence of time delays in the communication between the inverters. This communication is used to compute the COI frequency. It turns out that communication delays of less than 100ms have practically no effect on the overall system. [ABSTRACT FROM AUTHOR]

Kinetic energy available from the turbomachinery may boost short-term ramp rates during load shifting between generator and fuel cell that may be exploited to optimize the performance of turbine-fuel cell hybrid systems during load following. The paper starts with modeling a gas turbine, gearbox, and generator sitting on the rigid shafts as a two-mass model primarily for estimating the rotational inertia available from the turbogenerator. The gas turbine and its environment impose constraints of available space allowances, measurements from high-speed rotating parts, lack of accessibility to the shaft of measure, making replacements and/or required installation adjustments of the torque transducer difficult. It is demonstrated that in the absence of torque measurement, the data containing only a slow excursion of the rotor motion in response to a slight load change is sufficient to determine inertia and damping coefficients from the model. Furthermore, the generator's reactive power capability was investigated because it serves as an asset in integrated hybrid systems to meet dynamic reactive power demands, reducing the burden on the fuel cell's power electronics control in generating reactive power. [ABSTRACT FROM AUTHOR]

Collective self-consumption is driving the transformation of distribution networks towards independently controllable community microgrids. The objective of this work is to utilize limited heterogeneous flexibilities in the system to perform grid-support functions to evade additional investment on dedicated storage facilities. We propose a cooperative receding horizon control that allows optimal use of the collective resources over the prediction horizon. The conventional linear state-space model employed in the predictive control is replaced by a novel rate-based model that propagates state derivatives rather than the states across the prediction horizon, thus eliminating offset errors. The proposed cooperative predictive control strategy with rate-based model has been applied to the microgrid frequency control problem. The proposed control strategy has been illustrated on a power hardware-in-the loop platform by modeling a microgrid system with grid-supporting ders. The simulations reveal the effectiveness of the proposed strategy by comparing the control solution with a dedicated storage facility and its replacement distributed flexible resources. [ABSTRACT FROM AUTHOR]

This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are discussed, demonstrating that the post-fault frequency evolution in any given region is equal to the frequency evolution of the Centre Of Inertia plus certain inter-area oscillations. This finding leads to the deduction of conditions for guaranteeing frequency stability in all regions of a power system, a deduction performed using a mixed analytical-numerical approach that combines mathematical analysis with regression methods on simulation samples. The proposed stability conditions are linear inequalities that can be implemented in any optimisation routine allowing the co-optimisation of all existing ancillary services for frequency support: inertia, multi-speed frequency response, load damping and an optimised largest power infeed. This is the first reported mathematical framework with explicit conditions to maintain frequency stability in a power system exhibiting inter-area oscillations in frequency. [ABSTRACT FROM AUTHOR]

In Part I of this paper we have introduced the closed-form conditions for guaranteeing regional frequency stability in a power system. Here we propose a methodology to represent these conditions in the form of linear constraints and demonstrate their applicability by implementing them in a generation-scheduling model. This model simultaneously optimises energy production and ancillary services for maintaining frequency stability in the event of a generation outage, by solving a frequency-secured Stochastic Unit Commitment (SUC). We consider the Great Britain system, characterised by two regions that create a non-uniform distribution of inertia: England in the South, where most of the load is located, and Scotland in the North, containing significant wind resources. Through several case studies, it is shown that inertia and frequency response cannot be considered as system-wide magnitudes in power systems that exhibit inter-area oscillations in frequency, as their location in a particular region is key to guarantee stability. In addition, securing against a medium-sized loss in the low-inertia region proves to cause significant wind curtailment, which could be alleviated through reinforced transmission corridors. In this context, the proposed constraints allow to find the optimal volume of ancillary services to be procured in each region. [ABSTRACT FROM AUTHOR]

This paper proposes a delta-connected Modular Multilevel STATCOM with partially rated storage (PRS-STATCOM), capable of providing both reactive, and active power support. The purpose is to provide short-term energy storage enabled grid support services such as inertial, and frequency response, either alongside or temporarily instead of standard STATCOM voltage support. The topology proposed here contains two types of sub-modules (SM) in each phase-leg: standard sub-modules (STD-SMs), and energy storage element sub-modules (ESE-SMs) with a dc-dc interface converter between the SM capacitor, and the ESE. A control structure has been developed that allows energy transfer between the SM capacitor, and the ESE resulting in active power exchange between the converter, and the grid. Injecting $\text{3}^{rd}$ harmonic current into the converter waveforms can be used to increase the amount of power that can be extracted from the ESE-SMs, and so reduce the required ESE-SMs fraction in each phase-leg. Simulation results demonstrate that for three selected active power ratings, 1 pu, $\frac{2}{3}$ pu, and $\frac{1}{3}$ pu, the fraction of SMs that need be converted to ESE-SMs are only 69%, 59% & 38%. Thus, the proposed topology is effective in adding real power capability to a STATCOM without a large increase in equipment cost. [ABSTRACT FROM AUTHOR]

As more and more power electronic based generation units are integrated into power systems, the stable operation of power systems has been challenged due to the lack of system inertia. In order to solve this issue, the virtual synchronous generator (VSG), in which the power electronic inverter is controlled to mimic the characteristics of traditional synchronous generators, is a promising strategy. In this paper, the representation of the synchronous generator in power systems is firstly presented as the basis for the VSG. Then the modelling methods of VSG are comprehensively reviewed and compared. Applications of the VSG in power systems are summarized as well. Finally, the challenges and future trends of the VSG implementation are discussed.

In recent years, the expansion of renewable energy in electric power systems has been increasing at such a rapid pace that it has started affecting frequency stability. Renewable generators connected to the grid produce variable amounts of power, and in most cases have no inherent inertia response (IR) to the system frequency. Therefore, the high penetration of renewable generators in the system results in low inertia and frequency distortion. If renewable generators account for a high proportion of the supply in a power system, the use of energy storage systems (ESSs) with frequency-support algorithms (in the place of synchronous generators) can stabilize the network. The participation of ESSs in frequency support must be organized precisely, so that they are fully devoted to their own purpose. In this paper, the frequency-support parameters of ESSs are calculated for achieving stable frequency response from a network. An estimation and calibration process is conducted during the active power-order change of the ESSs in the substation, and is verified through electromagnetic-transients-including-DC (EMTDC)-based simulations.

Typical handheld controllers for interaction in virtual reality (VR) have fixed shapes and sizes, regardless of what visual objects they represent. Resolving this crossmodal incongruence with a shape-changing interface is our long-term goal. In this paper, we seek to find a length perception model that considers the moment of inertia (MOI) and diameter of a handheld object based on the concept of dynamic touch. Such models serve as a basis for computational algorithms for shape changing. We carried out two perceptual experiments. In Experiment 1, we measured the perceived lengths of 24 physical objects with different MOIs and diameters. Then we obtained a length perception model to reproduce the desired perceived length with a handheld controller. In Experiment 2, we validated our model in a crossmodal matching scenario, where a visual rod was matched to a haptic rod in terms of the perceived length. Our results contribute to understanding the relationship between the perceived length and physical properties of a handheld object and designing shape-changing algorithms to render equivalent visual and haptic sensory cues for length perception in VR. [ABSTRACT FROM AUTHOR]

The virtual synchronous generator (VSG) control, which enables inverter-interfaced distributed generators to possess inertia like synchronous generators, provides a promising solution to the lack of inertia of a future power grid. The energy buffer emulating the kinetic energy variation is essential to this technique. In this article, we propose a new control scheme for a smart motor, i.e., a back-to-back motor drive system which temporarily utilizes the kinetic energy stored in rotating loads. With this system, significant frequency regulation support can be achieved through merely a control mechanism update, and without any dedicated energy storage system. To achieve it, the VSG control is applied to the grid-side converter of the back-to-back motor drive system, and a coordinated control between the VSG control and the motor speed control is proposed. The proposed coordinated control has a faster frequency support response and a lower sensitivity to grid voltage unbalance and distortion than previous control schemes based on frequency measurement. The parameter tuning of the proposed control is discussed based on stability analyses and verified by simulation studies. The effectiveness of suppression of grid frequency fluctuation by the proposed system is verified through experimental results obtained with a commercial blower. [ABSTRACT FROM AUTHOR]

The existing microgrid operation schemes do not consider the dynamic performance of frequency in the islanded operation of microgrids. When an islanded microgrid encounters a disturbance, the sudden power mismatch could impose security risks or even a system collapse. To address such a challenge, this paper proposes the primary frequency response rescheduling (PFRR) approach. For a certain operation interval, the PFRR will optimally reschedule the distributed generators (DGs) with non-zero mechanical inertia and adjust the battery power. And the objective is to limit the rate-of-change-of-frequency (ROCOF) and to maintain the post-disturbance frequency nadir above a prescribed threshold. The effectiveness of the proposed strategy is verified by a case study on the IEEE 123-node test feeder system and the time-domain simulation in MATLAB Simulink.

Abstract Longest geographically connected Australian power system is undergoing an unprecedented transition, under the effect of increased integration of renewable energy systems. This change in generation mix has implications for the whole interconnected system designs, its operational strategies and the regulatory framework. Frequency control policies about real-time balancing of demand and supply is one of the prominent and priority operational challenge requiring urgent attention. This paper reviews the Australian electricity market structure in presence of wind energy and its governance. Various issues related to increased wind generation systems integration are discussed in detail. Currently applied mitigations along with prospective mitigation methods requiring new or improved policies are also discussed. It is concluded that developing prospective frequency regulation ancillary services market desires further encouraging policies from governing authority to keep pace with current grid transition and maintain its security.

Abstract Along with the increasing penetration of distributed generation with voltage-source converters (VSCs), there are extensive concerns over the potential virtual rotor angle stability, which is characterized by oscillations of power and frequency during the dynamic process of synchronization in the grid. Several control strategies have been developed for VSCs to emulate rotating inertia as well as damping of oscillations. This paper classifies these strategies and provides a small-signal modeling framework including all kinds of VSCs in different applications for virtual rotor angle stability. A unified perspective based on the famous Phillips–Heffron model is established for various VSCs. Thus, the concepts of equivalent inertia and the synchronizing and damping coefficients in different VSCs are highlighted, based on the similarities with the synchronous generator (SG) system in both physical mechanisms and mathematical models. It revealed the potentiality of various VSCs to achieve equivalence with the SG. This study helps promote the unity of VSCs and traditional SGs in both theories and methods for analyzing the dynamic behavior and enhancing the stability. Finally, future research needs and new perspectives are addressed.

The increasing penetration of renewable energy resources (RESs) leads to a continuous displacement of synchronous generators. Since the grid integration of RESs is usually achieved through inertialess power converters, the system inertia reduces and the power system frequency stability is compromised. Consequently, unexpected generator tripping, load shedding, and even blackouts may occur and pose a great threat to the system normal operation. In view of these challenges, this article explores the possibility of providing the inertia support from power-electronics interfaced smart loads. Specifically, a transformerless electric spring topology and the associated control strategy have been developed to provide a substantial inertia support from the noncritical load. As compared with existing inertia enhancement techniques, the proposed solution is cost-effective without the need of additional energy storage units. The smart load inertia provision capability is quantitatively analyzed and experimentally verified on a laboratory-scale test. In the testing results, 40% and 18% reductions of the rate of change of frequency and the maximum frequency deviation are, respectively, observed with a 12% smart load penetration ratio. [ABSTRACT FROM AUTHOR]

Conventional load frequency control primarily relies on large synchronous generation units to ensure regulation of the system frequency. However, its performance deteriorates as the system parameters, including inertia and droop coefficients, deviate from original system design. This letter proposes an augmented load frequency control (ALFC) to ensure robust frequency regulation under diurnal variations in system parameters that are expected in the future, renewables-rich power system. The superior performance of ALFC is demonstrated by several case studies, and its stability is assessed by small-signal analysis. [ABSTRACT FROM AUTHOR]

A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper a closed-form solution to the differential equation describing frequency dynamics is proposed, which allows to obtain frequency-security algebraic constraints to be implemented in optimization routines. This is done while considering any finite number of FR services with distinguished characteristics, such as different delivery times and activation delays. The problem defined by these frequency-security constraints can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), which can be efficiently handled by off-the-shelf conic optimization solvers. This paper also takes into account the uncertainty in inertia contribution from the demand side by formulating the frequency-security conditions as chance constraints, for which an exact convex reformulation is provided. Finally, case studies highlighting the effectiveness of this frequency-secured formulation are presented. [ABSTRACT FROM AUTHOR]

Recent analyses have shown that the grid-integration of offshore wind farms through MTDC systems has brought low inertia and small-signal stability issues, in which the dynamics of phase-locked-loop (PLL) play a crucial role. To address this issue, this article proposes a control strategy for the multi-terminal VSCs aiming at PLL-less synchronization and autonomous frequency response of the MTDC system. One of the significant features of the proposed control is that the deviation of the grid frequency can be instantaneously reflected on the deviation of the DC voltage without ancillary control. Based on this feature, a fast inertia response and primary frequency regulation among wind farms and AC systems interconnected by the MTDC system can be achieved. A small-signal model is established to evaluate the overall system stability using the proposed control. Finally, comparative studies of this proposed control with the conventional PLL-based vector control are conducted in PSCAD/EMTDC based on a practical MTDC system in China, the Zhangbei four-terminal HVDC transmission system. The analysis shows that the proposed control exhibits advantages in weak grid operation and autonomous frequency response. [ABSTRACT FROM AUTHOR]

System strength and inertia inherently provided by synchronous generators (SGs) empower a power system to ride through voltage and frequency disturbances. The requirements of system strength and inertia were not enforced in the National Electricity Market (NEM) of Australia since SGs dominated the generation fleet in the past. However, the increasing wind and solar generation continuously displaces SGs and consequently reduces system strength and inertia in the NEM. This paper proposes a formulation of system strength and inertia constrained generator dispatch to reassure NEM operational security in light of emerging high renewable penetration. A fault current iterative solver is developed to evaluate system strength, in which the current limitation and voltage control logic of inverter-based generators, and the fault current contribution from VAR compensators are properly modelled in the phasor domain. The system strength contribution factor of an SG is defined to linearize system strength constraint for unit commitment (UC). System and sub-network inertia constraints are also formulated for the UC to limit the rate of change of frequency (RoCoF) in the event of generator/interconnector trip. The proposed generator dispatch formulation can fully meet system strength and inertia requirements in the NEM. [ABSTRACT FROM AUTHOR]

Depleting fossil fuels and concerns about global warming have forced a paradigm shift toward renewable energy resources in meeting our energy requirements. Wind energy utilization has been growing at a rapid rate fuelling research and development in high power wind turbines (WTs). To advance research and education in wind energy conversion systems, a controlled test bed is necessary that does not depend on wind availability. Majority of the existing WT emulation schemes employ a torque compensation loop to account for the inertia difference between the WT and motor used for emulation. However, the loop suffers from noise and instability issues. Also, the torque compensation term is sensitive to parameter estimates. This article proposes one degree of freedom (1-DOF) and 2-DOF control structures for WT emulation. It first illustrates the design and performance of 1-DOF control structure. It further proposes two controllers along with their prefilters in 2-DOF structure, which has superior performance than 1-DOF structure. The design of the controllers and prefilters is explained with the help of root locus. The performance of the WT emulator with the proposed control structures is demonstrated through simulations and experiments on a 7.5 kW doubly fed induction generator driven by a 5.5 kW squirrel cage induction motor, where the dynamics and steady-state operation of a WT–generator system are emulated. [ABSTRACT FROM AUTHOR]

Synchronous generators are operating for less time than before or being decommissioned in the National Electricity Market (NEM) of Australia, due to the proliferation of asynchronous wind and solar generation. Sub-networks of the NEM will face inertia shortages in the near future. This paper develops a formulation of zonal inertia constrained generator dispatch for power systems with a diversified generator portfolio including synchronous generators, synchronous condensers, inverter-interfaced generators and energy storages. Zonal inertia constraints are formulated in unit commitment and optimal power flow to limit the rate of change of frequency (RoCoF) in the event of network separation. Load frequency relief is also considered to reduce the ramp rate requirement of primary reserve. The proposed formulation can reduce the average cost of primary reserve and maintain zonal inertia adequacy to constrain RoCoF in case of the trip of the interconnector(s). [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) minimizes the production cost, while satisfying the constraints on the system, such as real and reactive power balance, equipment capability constraints, and voltage limits. This article presents a method of incorporating a frequency security constraint within the framework of the OPF problem. Increasing displacement of conventional generation by renewable resources that contribute little or no frequency regulation capability may necessitate the enforcement of such a constraint to meet frequency security requirements. The system frequency is required to be maintained within a safe limit, thus indicating the balance between generation and consumption. Hence, the solution for optimization of power flow should not only present a minimum cost of generation within the operating conditions, but also ensure frequency stability. In order to obtain this solution, the requirement of frequency stability is introduced as a new constraint of the power dispatch problem and is represented by the maximum frequency deviation limit. This new constraint is constructed as a nonlinear function of system inertia and the frequency regulation constant, since frequency deviation is highly sensitive to these factors. It is shown that the inclusion of this constraint causes the OPF to preferentially select higher inertia generators as necessary, to satisfy the frequency security requirement. A genetic algorithm is utilized as the optimization tool in this article. The IEEE RTS-79 test system is used to demonstrate efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

The short circuit response of voltage source converters (VSCs) could be significantly different from that of synchronous condensers (SCs) under unbalanced faults. This paper investigates the combined effect of VSC-based sources and synchronous condensers under grid unbalanced faults considering two groups of VSC fault-ride-through control strategies. It aims to provide an evaluation of typical control strategies and to explore the impact of equipping a synchronous condenser at the point of common coupling (PCC). By examining the combined short-circuit currents, PCC voltages, DC-side voltages, and system frequency responses, this study points out the merits and demerits of the examined control strategies, illustrates the benefits of synchronous condensers on mitigating the disadvantages of certain control strategies, and provides suggestions on selecting the control strategies for the VSC when incorporating a synchronous condenser at the PCC. [ABSTRACT FROM AUTHOR]

This paper presents a practical procedure regarding inertia estimation and speed loop auto-tuning for sensorless interior permanent-magnet synchronous motor (IPMSM) drives. In many applications, well-tuned speed controller is essential to enable dynamic and stable drive operations. However, high-performance speed controller design requires system parameters such as inertia which are unknown at the beginning of drive commissioning. Manual trial-and-error tuning is unattractive due to its blind, lengthy, non-optimal, and potentially unsafe nature. On the other hand, model-based tuning through inertia estimation has unique challenges at this step of self-commissioning. Determining the test torque for a safe and reasonably short test in inertia estimation is a real practical problem because the total inertia can be in wide range in different mechanical systems. Furthermore, feedback controllers are not usable to automatically determine the test torque due to unknown motor parameters. As a solution, this paper proposes an automated test torque selection procedure. Then it identifies the inertia and lastly tunes the speed controller using the identified parameter. Overall, a fully automated speed-loop auto-tuning method is proposed which aims minimal operator involvement. The findings are experimentally verified on an IPMSM drive. In addition, the proposed method can easily be extended to different motor types and sensored or sensorless vector control strategies. [ABSTRACT FROM AUTHOR]

Renewable energy sources (RESs) have been extensively employed to replace fossil fuels for reducing carbon footprints. Since RESs are normally coupled to the power grid by fast-response power converters without providing any inertia, the power system inertia generated by synchronous generators continues to decrease, making modern power systems sensitive to frequency events. As a result, undesirable load-shedding, cascading failures, or even large-scale blackouts may occur under severe frequency events. To address the lack of inertia concern, this paper presents a frequency derivative-based inertia enhancement method for battery storage systems. Specifically, the method achieves inertia emulation by proportionally linking the time derivative of the grid frequency and active power references of power converters. The main contribution is to use a frequency-locked-loop to accurately estimate the frequency derivative signal, which avoids the high frequency noises introduced by differential operators. Simulation and experimental results are finally presented to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Following an unintended disconnection of a synchronous generator from the power system, what is also known as a loss of generation (LoG), it is not trivial to precisely estimate the post-event power system's inertia and the LoG size. One of the reasons for that is that both of them are a function of the unknown inertia reduction. To solve this challenging problem, this paper presents an analytical method based on the rate-of-change-of-frequency (RoCoF). The method relies on a modified swing equation, allowing a simultaneous estimation of both unknowns. To this end, the values of mechanical starting time, apparent power, and loading of lost generator are formulated for the power system under study. In a practical application, the method can use RoCoF measured by phasor measurement units. The paper discusses the impact of various frequency estimation approaches to the proposed LoG estimation. Furthermore, a new method for LoG size estimation, based on the interpolated estimated inertial response, is proposed. The efficiency of the proposed approach is validated through extensive simulations with Matlab/Simulink using a simple power system and the IEEE 39-bus test network. [ABSTRACT FROM AUTHOR]

Power grid primary frequency response will be significantly impaired by photovoltaic (PV) penetration increase because of the decrease in inertia and governor response. PV inertia and governor emulation requires reserving PV output and leads to solar energy waste. This paper exploits current grid resources and explores energy storage for primary frequency response under high PV penetration at the interconnection level. Based on the actual models of the U.S. Eastern Interconnection grid and the Texas grid, effects of multiple factors associated with primary frequency response, including the governor ratio, governor deadband, droop rate, and fast load response, are assessed under high PV penetration scenarios. In addition, performance of batteries and supercapacitors using different control strategies is studied in the two interconnections. This paper quantifies the potential of various resources to improve interconnection-level primary frequency response under high PV penetration without curtailing solar output. [ABSTRACT FROM AUTHOR]

Reduced system inertia decreases the time available for control actions to prevent the system frequency from violating security limits after a disturbance. Therefore, as system inertia is reduced by the shift toward renewable generation that provides little or no inertia, system operators must deploy faster frequency control actions if they are to preserve security and quality of supply. Realising methods for the fast and accurate detection, localization and sizing of an active power disturbance (e.g., the loss/connection of a large generator or load) will be a crucial enabler for the successful implementation of these faster actions. This paper presents a novel method that can simultaneously estimate the time, size, and location of a disturbance using PMU measurements of the active power output of a limited number of generators and the impedance matrix of the system. The immediate power change at the remote generator terminals is combined with the synchronizing power coefficient matrix in a two-stage process. Stage one uses a decision tree to determine that a disturbance has occurred, which then initiates stage two that estimates the size and location of the disturbance. This is based on the level of agreement between the monitored generators. Case studies and sensitivity analysis for the IEEE 39 bus test network are presented to verify the accuracy of the proposed method for varied levels of measurement noise, impedance matrix errors, and topology errors for various disturbance sizes and locations. [ABSTRACT FROM AUTHOR]

This paper proposes a computationally efficient electricity market simulation tool (MST) suitable for future grid scenario analysis. The market model is based on a unit commitment (UC) problem and takes into account the uptake of emerging technologies, like demand response, battery storage, concentrated solar thermal generation, and HVDC transmission. To allow for a subsequent stability assessment, the MST requires an explicit representation of the number of online generation units, which affects power system inertia and reactive power support capability. These requirements render a full-fledged UC model computationally intractable, so we propose unit clustering, a rolling horizon approach, and constraint clipping to increase the computational efficiency. To showcase the capability of the proposed tool, we use a simplified model of the Australian National Electricity Market with different penetrations of renewable generation. The results are verified by a comparison to a more expressive and computationally intensive binary UC, which confirm the validity of the approach for long term future grid studies. [ABSTRACT FROM AUTHOR]

This study explores the impact of high-photovoltaic (PV) penetration on the inter-area oscillation modes of large-scale power grids. A series of dynamic models with various PV penetration levels are developed based on a detailed model representing the U.S. Eastern Interconnection (EI). Transient simulations are performed to investigate the change of inter-area oscillation modes with PV penetration. The impact of PV control strategies and parameter settings on inter-area oscillations is studied. This paper finds that as PV increases, the damping of the dominant oscillation mode decreases monotonically. It is also observed that the mode shape varies with the PV control strategy and new oscillation modes may emerge under inappropriate parameter settings in PV plant controls.

In this paper, we consider a distributed energy storage system (ESS)-based control paradigm for transient stability of power systems. Utilizing a multi-agent control framework, we propose an effective virtual inertia measure for cyber-physical agents that includes both traditional synchronous generators and actuated ESSs. We derive the effective virtual inertia analytically for the case of general ESS-based control. We further consider the case of parametric feedback linearization control (PFL) as an application and investigate the proposed inertia measures after applying the PFL control. The utility of the proposed inertia measures is studied using the IEEE 68-bus test power system. Numerical results demonstrate the impact of storage limits, control scheme aggressiveness, and delay on the proposed inertia measures during a disturbance in the power system. [ABSTRACT FROM AUTHOR]

The integration of wind power into the grid causes numerous stability and reliability issues due to its low inertia and intermittent nature. To ensure system stability, wind power production has to be restricted, which implies that the system cannot absorb the entire output available from wind generation, especially if the output is high. Consequently, the reliability of the integrated system is adversely affected. In order to improve the system reliability, energy storage can be used, which is emerging as a prominent solution for enhancing supply continuity. Complete utilization of an energy storage device can be achieved if it is properly coordinated with wind and conventional generation. This paper proposes a new method to coordinate energy storage with the existing system to improve the system reliability while maintaining the system frequency security. The effectiveness of the model is demonstrated on the IEEE RTS-79 system. [ABSTRACT FROM AUTHOR]

This paper investigates how the operation of the onshore AC grid and the offshore voltage source converter-based multiterminal dc (VSC-MTDC) grid can be cooptimized within the unit commitment (UC) framework to enhance system frequency stability following various contingencies. Frequency dynamic constraints corresponding to three typical types of outages (i.e., loss of a synchronous unit, loss of a grid-side VSC, and loss of a wind farm-side VSC) are established. A novel frequency dynamics constrained UC for integrated AC/VSC-MTDC systems is then proposed. Case studies on three integrated AC/VSC-MTDC systems demonstrate that major frequency disturbances caused by credible contingencies occurring in either the AC grid or VSC-MTDC grid can be effectively stabilized by the proposed approach. [ABSTRACT FROM AUTHOR]

Coupling between frequency dynamics of the ac systems on both inverter and rectifier sides of the line-commutated converter HVDC with the rectifier station operating in frequency control is studied, along with the presence of large DFIG-based wind farms on the weak rectifier-side grid. An averaged model with 79 states, which includes dynamic models of grids on the rectifier and inverter sides, phase-locked loop, and the wind farm is derived. To develop a deeper understanding of the frequency dynamics, a simplified four-state nonlinear model is proposed, which, in turn, reveals strong coupling between frequency and ac voltage at the HVDC rectifier terminal. A firing angle correction strategy is proposed to decouple frequency–voltage interactions, thereby improving the frequency dynamics on the rectifier side. The four-state model is linearized to ascertain the interaction between rectifier- and inverter-side frequencies, and an analytical expression for the frequency dynamics in terms of gains of the frequency controller at the rectifier station is derived. Moreover, the proposed reduced-order model shows the implications of frequency droop control of the wind farms in improving frequency dynamics on both rectifier and inverter sides. Expressions for “synchronizing” and “damping torque” contribution from HVDC and wind farm are also established. The analytical expressions and the effectiveness of the proposed strategies are validated through nonlinear time-domain simulations. [ABSTRACT FROM PUBLISHER]

A novel droop control with coupling compensation and inertia is proposed for a microgrid to achieve high dynamic performance and stability of distributed generation units. The coupling compensation scheme consists of angular frequency deviation compensation and voltage deviation compensation. They can reduce the influence of uncontrolled power coupling. The inertia scheme consists of angular frequency inertia and voltage inertia. They can slow down the change rates of the angular frequency and voltage and reduce their fluctuation magnitudes. The combination of this novel droop control method and virtual impedance can help achieve accurate power sharing. An improved particle swarm optimization (PSO) algorithm with multiswarm and multivelocity (MMPSO) is also proposed to optimize the parameters of the coupling compensation and inertia with high precision and high reliability. A simulated model and experiment platform of a microgrid are set up for testing, and the simulation and experimental results validate the excellent performance of the MMPSO and the effectiveness of the novel droop control method. [ABSTRACT FROM AUTHOR]

Nonsynchronous generators such as photovoltaics (PVs) are expected to undermine bulk power systems (BPSs)’ frequency response at high penetration levels. Though the underlying mechanism has been relatively well understood, the accurate assessment and effective enhancement of the U.S. interconnections’ frequency response under extra-high PV penetration conditions remains an issue. In this paper, the industry-provided full-detail interconnection models were further validated by synchrophasor frequency measurements and realistically-projected PV geographic distribution information were used to develop extra-high PV penetration scenarios and dynamic models for the three main U.S. interconnections, including Eastern Interconnection (EI), Western Electricity Coordinating Council (WECC), and Electric Reliability Council of Texas (ERCOT). Up to 65% instantaneous PV and 15% wind penetration were simulated and the frequency response change trend of each U.S. interconnection due to the increasing PV penetration level were examined. Most importantly, the practical solutions to address the declining frequency response were discussed. This paper will provide valuable guidance for policy makers, utility operators and academic researchers not only in the U.S. but also other countries in the world. [ABSTRACT FROM PUBLISHER]

Frequency stability management of asynchronously interconnected grids is becoming a great challenge. This paper investigates how asynchronous sending- and receiving-end grids can be operated in a synergistic and interactive manner to guarantee frequency stability following the worst case HVDC bipole block while still ensuring operational economy. A novel enhanced frequency stability constrained multiperiod optimal power flow model (EFOPF) with flexible fast-acting HVDC corrective control is proposed. EFOPF dynamically schedules the distribution of primary reserves and HVDC corrective actions to simultaneously handle postcontingency over- and under-frequency disturbances occurring in the sending- and receiving-end grids, respectively. An alternating direction method of multipliers based distributed algorithm was developed to solve this problem. A case study of a modified two-area RTS-96 system demonstrates the effectiveness of the proposed EFOPF. [ABSTRACT FROM PUBLISHER]