An Adaptive PV Frequency Control Strategy Based On Real-Time Inertia .

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IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 3, MAY 20212355An Adaptive PV Frequency Control StrategyBased on Real-Time Inertia EstimationYu Su , Student Member, IEEE, Hongyu Li, Student Member, IEEE, Yi Cui , Member, IEEE,Shutang You , Member, IEEE, Yiwei Ma, Member, IEEE, Jingxin Wang , Member, IEEE,and Yilu Liu , Fellow, IEEEAbstract—The declining cost of solar Photovoltaics (PV) generation is driving its worldwide deployment. As conventionalgeneration with large rotating masses is being replaced by renewable energy such as PV, the power system’s inertia will beaffected. As a result, the system’s frequency may vary more dramatically in the case of a disturbance, and the frequency nadirmay be low enough to trigger protection relays such as underfrequency load shedding. The existing frequency-watt functionmandated in power inverters cannot provide grid frequencysupport in a loss-of-generation event, as PV plants usually donot have power reserves. In this article, a novel adaptive PVfrequency control strategy is proposed to reserve the minimumpower required for grid frequency support. A machine learning model is trained to predict system frequency response undervarying system conditions, and an adaptive allocation of PV headroom reserves is made based on the machine learning model aswell as real-time system conditions including inertia. Case studies show the proposed control method meets the frequency nadirrequirements using minimal power reserves compared to a fixedheadroom control approach.Index Terms—Adaptive control, frequency response, frequencynadir, machine learning, power system inertia, PV, widearea measurements.I. I NTRODUCTIONENEWABLE energy plays a critical role in energy security and sustainability. As fossil fuels face depletion, theyare being replaced by renewable energy resources worldwide.Solar photovoltaics (PV) has gained a lot of momentum inRManuscript received March 9, 2020; revised August 28, 2020; acceptedDecember 13, 2020. Date of publication December 17, 2020; date of current version April 21, 2021. This work was supported in part by theU.S. Department of Energy under Award 34231; in part by the Departmentof Energy through NSF Award under Grant EEC-1041877; and in part bythe CURENT Industry Partnership Program. Paper no. TSG-00337-2020.(Corresponding author: Yu Su.)Yu Su, Hongyu Li, Shutang You, Yiwei Ma, and Jingxin Wang arewith the Department of Electrical Engineering and Computer Science,University of Tennessee, Knoxville, TN 37996 USA (e-mail: ysu10@utk.edu;hli90@utk.edu; syou3@utk.edu; yma13@utk.edu; jwang78@utk.edu).Yi Cui is with the School of Information Technology and ElectricalEngineering, University of Queensland, Brisbane, QLD 4072, Australia(e-mail: y.cui3@uq.edu.au).Yilu Liu is with the Department of Electrical Engineering and ComputerScience, University of Tennessee, Knoxville, TN 37996 USA, and also withthe Power and Energy Systems Group, Oak Ridge National Laboratory, OakRidge, TN 37830 USA (e-mail: liu@utk.edu).Color versions of one or more figures in this article are available athttps://doi.org/10.1109/TSG.2020.3045626.Digital Object Identifier 10.1109/TSG.2020.3045626deployment, driven by enabling inverter technologies, decreasing solar panel costs, as well as decreasing energy storagesystem costs.The United States has substantial solar resources [1]. TheSunshot Initiative of the U.S. Department of Energy envisionsthat solar PV will generate 14% of the total electrical energyin the U.S. by 2030, and by 2050, solar PV will generate 27%of the total electricity in the U.S. [2].Driven by the continuing trend in solar PV deployment,researchers have been studying the impact of increasing renewable generation on power system stability, especially inverterbased sources such as solar PV and some wind turbines.Without proper control, the inverter-based sources would besimply replacing conventional generators with turbine governors and rotating masses, which would adversely affectthe system’s frequency response. Some preliminary studiesin the U.S. power grids demonstrated that overall frequencyresponse would deteriorate significantly with increased renewable penetration [3]–[5]. Similar studies showed that insufficient inertia would negatively influence the frequency regulation in South Australia power grid with high penetrationof renewable generation [6]. In [7], the Irish power gridfaces challenges in operating at 50% penetration of windgeneration because of reduced inertia. Simulation studies inthe U.S. WECC system [8] reveal vulnerabilities broughtby extremely high wind penetrations and explores potentialmitigating approaches.After reviewing system studies on several power grids withincreasing PV and wind penetrations, the North AmericanElectric Reliability Corporation (NERC) has determined thatadditional control strategies and resources are required tomeet the primary frequency control demand as renewablepenetration increases [9]. As a result, the frequency-wattfunction [10], which is analogous to the governors in conventional generators, has become a standard requirement in NorthAmerican power grids. Moreover, studies show that syntheticinertia control of inverters that emulate the inertia response ofsynchronous generators help regulate the system’s frequencyresponse [11]–[17].The majority of PV inverters online operate in gridfollowing mode, where the inverter regulates the output currentmagnitude and angle [18]. The other control mode is the gridforming mode, where the inverters control the output voltageand frequency. While wind-turbines typically have the abilityto reserve power for frequency response [19], the inverters arec 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.1949-3053 See l for more information.Authorized licensed use limited to: UNIVERSITY OF TENNESSEE LIBRARIES. Downloaded on September 21,2021 at 15:14:20 UTC from IEEE Xplore. Restrictions apply.

2356controlled to output the maximum available power based onMaximum Power Point Tracking (MPPT) to take advantage ofthe low marginal cost of PV generation versus conventionalgeneration, such as gas or coal. However, as the penetration of renewables such as PV increases, there may not beenough primary frequency response resources in an underfrequency event such as loss of generation, if there is no realpower reserve available in the PV inverters. While the powerreserve control strategy is readily available at the inverterlevel [20], and frequency-watt curve has been studied at thesystem level [10], there is a research gap in the determination and scheduling of PV real power reserves. Althoughother grid resources, such as energy storage systems andsupercapacitors can be utilized to improve primary frequencyresponse [21]–[23], they require additional planning, design,and investment. If there is insufficient real power reserve,especially in high renewable penetration scenarios, the systemrisks lower frequency nadirs in severe contingencies, whichmay cause under-frequency tripping of loads and/or inverters. On the other hand, PV real power reserve means lostgeneration with low marginal costs. Therefore, there is greatimportance and economic value from the system’s frequencyresponse standpoint in developing a model that dispatches thePV real power reserves according to system requirements andconditions.The main contributions of this article are twofold: we reducethe error of inertia estimation using ambient PMU measurements from 12% (the state-of-the-art method in the literature)to 5%; based on the real-time system inertia estimation, wepropose a novel PV real power reserve dispatch model leveraging real-time system inertia estimation and conventionalgeneration dispatch signals. The goal of the dispatch is tomeet system frequency response requirements utilizing minimal PV power reserve. A machine learning model is trainedusing time-domain simulation data from a realistic powersystem model, and used to predict the frequency nadir ofa predetermined contingency, given the estimation of systeminertia and dispatch of conventional generators. For each setof system conditions (system inertia, available non-PV generation participating in primary frequency response), a one toone correlation between system PV real power reserve andfrequency response nadir of the predetermined contingencycan be established using the machine learning model. Theminimal PV power reserve that keeps the frequency nadirabove the predefined threshold is selected as the optimal dispatch. Studies on a test system based on the U.S. ElectricReliability Council of Texas (ERCOT) system shows thatthe PV real power reserve dispatch maintains the systemfrequency response nadir above the pre-determined thresholdin the resource contingency criteria (RCC). The dispatch alsogenerates a 50% savings in PV real power reserve compared toa dispatch that fixes the PV real power reserve throughout theday. We also show that the control method performs well usingnoisy measurements on a power electronics converter-basedgrid emulator.The remainder of this article is organized as follows. Thedesign and implementation of our real-time inertia estimation algorithm is introduced in Section II. The adaptive PVIEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 3, MAY 2021Fig. 1.Inertia variations in different levels of PV penetration.1frequency control is proposed and explained in detail inSection III. Section IV shows the validation case study ona realistic large power system simulation model. The controlmethod is tested in a hardware-in-the-loop test platform inSection V. The conclusions are given in Section VI.II. S YSTEM I NERTIA VARIATION ANDR EAL -T IME E STIMATIONPower system inertia consists mostly of the rotatinginertia in synchronous generators, some motor loads, andpotentially future renewable power plants if they provide synthetic inertia, and can vary throughout the day. Fig. 1 showsthe projected daily and yearly inertia variations of the ERCOTsystem at the current and future PV penetration scenarios.The PV penetration is defined as the percentage of PV’soutput power in the system’s total load. With more PV generation during the day, synchronous generators are displaced,and the system inertia will drop, as indicated in Fig. 1 (b).The gap between peak and bottom inertia grows larger as PVpenetration climbs higher.Wide-area measurement systems provide time-synchronizedgrid measurements that can be used to estimate systeminertia [24]–[28]. Although power system inertia estimationhas been heavily investigated in the literature, most usefrequency disturbance data, which suggests that inertia wascalculated offline. In this article, we use ambient frequencymeasurements to estimate the system inertia in real-time,and increase the state-of-the-art accuracy of inertia estimationusing ambient synchrophasor frequency measurements from12% mean absolute percentage error [28] to less than 5%.The estimation of inertia is at the system level, which is thesum of the inertia of the generators (and motor loads) in thesystem. This provides a solid basis for the proposed adaptivePV frequency control.A. Multivariate Random Forest Regression (MRFR)In this study, we use the available inertia data, load profile, extracted features in the ambient frequency measurementsat different locations, and weather data (average ambienttemperature) to train a multivariate regression model forsystem inertia estimation. For application with very largeamounts of training data, we use Multivariate Random ForestRegression (MRFR) as the machine learning model to estimate1 Available online: NL.pdf.Authorized licensed use limited to: UNIVERSITY OF TENNESSEE LIBRARIES. Downloaded on September 21,2021 at 15:14:20 UTC from IEEE Xplore. Restrictions apply.

SU et al.: ADAPTIVE PV FREQUENCY CONTROL STRATEGY BASED ON REAL-TIME INERTIA ESTIMATIONFig. 2.2357Data flow of the inertia estimation algorithm.the system inertia. MRFR is an ensemble of regression treestrained by bootstrap sampling and random feature selection.Due to the length restrictions of this article, interested readersare referred to [29].It is worth noting that other machine learning algorithmssuch as neural nets and support vector machines are also applicable to this inertia estimation method. We chose MRFR inthis study due to its high robustness to the input data, its capability to avoid overfitting the training data, and its overall bestperformance in terms of estimation accuracy.We can sum up the data flow of the online inertia estimation algorithm, which is shown Fig. 2. Before application,the MRFR is trained using available offline data. In real-timeapplication, the trained MRFR will receive online measurements and extracted features, and use them to estimate thetotal inertia of the power system. While the inertia data, loadprofile, and weather data are readily available from reliability coordinators and transmission operators, the features fromambient frequency measurements need to be extracted fromthe raw frequency data. It is worth mentioning that by usingthe ambient frequency measurement, we are able to accountfor virtual inertia emulated by inverter-interfaced renewableresources, since its effects on ambient frequency variationscan be captured and converted to equivalent inertia. In thenext section, we will discuss the method to extract featuresfrom ambient frequency data.Fig. 3.Minimum volume enclosing ellipsoids at different inertia levels.part of the system frequency trajectory in the phasor measurement space. We use the frequency measurement matrix θ M ,defined as: θ11 · · · θ1m . , n m.(1)θ M . θn1.θnmwhere n is the number of PMUs, m is the length of the timewindow imposed on the frequency measurements. An ellipsoid (hyper-ellipsoid) that contains the measurements can beexpressed as: HA,C θ n (θ c)T A(θ c) 1(2)where A is a positive definite matrix and θ, c are vectors of ndimensions in the phasor measurement space. The volume ofthe ellipsoid is expressed asnn 2 det (A))(3)Vol(HA,C ) π 2 2B. Ambient Frequency Data Feature Extractionwhere is the gamma function: (n 2) (n 2)!! n/2(n 1)/2 n (n 2) · · · 3 1, n 0, oddn!! n (n 2) · · · 4 2, n 0, even 1,n 1, 0The raw frequency time-series data from multiple PMUs inthe power system is piped through a data pre-processing process, which includes data continuity check, outlier detection,and temporal alignment. We use the processed data to extractthe frequency variations of the frequency time-series data measured from multiple PMUs across the power grid, definedas the frequency deviation from the mean of the frequencymeasurements.Once the variation of the ambient frequency data from eachPMU is calculated, we use a series of time windows with fixedwidth to divide the time series data and use the MinimumVolume Enclosing Ellipsoid (MVEE) [30]–[32] method toconstruct the characteristic ellipsoids and extract the informative features from each data segment for inertia estimation.MVEE provides a novel method to monitor system statusand estimate its dynamic behaviors by interpreting the graphicparameters of a multi-dimensional closed ellipsoid. Such ellipsoid with minimum volume is calculated by enclosing a certainWe obtain the ellipsoid with minimum volume by minimizing ln(det A), using interior-point methods.The correlation between the parameters of the MVEEand the trajectory of the system frequency measurementslies in the volume and shape of the MVEE. We use simulated ambient data from a power system model of the U.S.Eastern Interconnection with randomly varying loads undertwo inertia levels – 100% and 50%. The inertia levels hereare the relative system inertia values, with 100% being thebaseline. It should be noted that the applied load variation isvery small compared to the base load. Two ellipsoids can beconstructed from 60-second frequency data. Due to the difficulties of representing hyper-ellipsoids graphically, we usedfrequency measurements from only three units. The ellipsoidsare shown in Fig. 3. The ellipsoids are constructed in thefrequency space, and the numbers in the figure are per unitvalues. We can observe significant differences in the graphicalparameters of the ellipsoids.(4)(5)Authorized licensed use limited to: UNIVERSITY OF TENNESSEE LIBRARIES. Downloaded on September 21,2021 at 15:14:20 UTC from IEEE Xplore. Restrictions apply.

2358IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 3, MAY 2021Based on the above analyses, we can use the graphicalparameters of the MVEE, including volume, center vectors,projections of the longest semi-axis along each dimension,and the eccentricity as descriptive features to estimate thesystem inertia. Based on the reporting rate of the availablesystem inertia data used for training, we divide the ambientfrequency measurements into the number of segments equalto the number of inertia data points. In our case, we haveinertia data reported at 10-minute intervals. This means wehave 144 segments in one day. For each of the 144 frequencysegments, we use a 5-minute sliding window with a 10-secondstep to step through the segments and calculate the characteristic ellipsoids. For each segment the descriptive features fromthe characteristic ellipsoids are averaged and used as inputs tothe MRFR. More description on the inertia estimation methodcan be found in [40].Fig. 4. Estimated and measured inertia in WECC during heavy and lightload seasons.C. Performance EvaluationTo evaluate the performance of the MRFR based real-timeinertia estimation algorithm, we use a testing dataset that’sindependent from the training dataset. The testing datasetspans a whole year and includes system inertia data, synchrophasor measurements of the U.S. WECC system fromGridEye [35], actual weather data (average ambient temperature of six cities in WECC system, including Los Angeles,Phoenix, Salt Lake City, Denver, Las Vegas, and Seattle), andsystem generation and load data. We used measurements from20 Frequency Disturbance Recorders (FDRs) [35] deployedin the WECC system. More details on their geographicaldistribution can be found online.2During the training process, we used a 5-minute time window and a 10-second step size. Since the reporting interval ofthe inertia data is 10 minutes, 30 sets of MVEEs are generated for each 10-minute interval and each measurement. Thegraphical features of the MVEEs are averaged within the same10-minute window and used to train the MRFR.The metrics used for performance evaluation are absolute percentage error (APE) and mean absolute percentageerror (MAPE), defined as: Mi Mi 100%APEi Mi(6)1 APEim(7)mMAPE i 1 where Mi and Mi denote the i-th estimated and measuredinertia, respectively, and m is the total number of pointsestimated.An example of inertia estimation result is given in Fig. 4.The MAPE for the heavy load season day is 1.2%, and theMAPE for the light load season day is 0.8%. We performeddaily inertia estimations for a whole year and evaluated theAPE of each estimation point (Fig. 5). The maximum APE ofthe whole year is 8.7%, and the mean is 3.1%. (It is also foundthat the estimation errors are on similar levels as load changes2 Available online: http://fnetpublic.utk.edu/.Fig. 5.Inertia estimation error distribution over one year.and the MAPE does not show significant correlation with theload levels.) Compared to the estimation performance of 12%MAPE in [28], we have reduced the errors dramatically. It isworth mentioning that although the present work and [28] usedifferent test systems, both studies used actual system data intesting.In this section, we discussed the system inertia estimationusing labeled data. In the case inertia information is not available or inaccurate (for example, uncertainties in load inertiaand virtual inertia emulation), we can first classify the system’soperation status using the characteristics from the ambientfrequency measurements. Then frequency event (generationdrop, load trip, etc.) can be utilized to benchmark the systeminertia level. As frequency events only happen occasionally inthe system, the machine learning-based inertia estimation willrequire longer time to gather enough measurements to includesufficient frequency event data.The accuracies of the PMUs that are used to measure theambient frequency will be affected by the grid transients.However, since our proposed method is based on ambientfrequency measurement, which usually does not have anymajor events or phase jumps, the impacts should be minimal.In addition, the work proposed in [41] developed a frequencymeasurement technology that is immune to phase jumps in gridtransient conditions, which could be used to further mitigateits impact.Authorized licensed use limited to: UNIVERSITY OF TENNESSEE LIBRARIES. Downloaded on September 21,2021 at 15:14:20 UTC from IEEE Xplore. Restrictions apply.

SU et al.: ADAPTIVE PV FREQUENCY CONTROL STRATEGY BASED ON REAL-TIME INERTIA ESTIMATIONFig. 6.Fig. 7.Inputs and output of the machine learning model.Fig. 8.Real-time PV headroom requirement estimation.2359PV frequency control based on real-time inertia estimation.III. A DAPTIVE PV F REQUENCY C ONTROL BASED ONR EAL -T IME S YSTEM I NERTIA E STIMATIONA. Control ArchitectureSeveral system conditions, including system inertia andsystem governor capacity affect the system’s frequencyresponse. It is well-established that the relation between varioussystem conditions and frequency nadir is nonlinear. The systemconditions also vary throughout the day, especially in futurehigh renewable penetration scenarios. To handle the variabilities in the system conditions and the nonlinearity of the controlsystem, we propose an adaptive PV frequency control method,shown in Fig. 6. There are four steps in this control.1) Wide-area synchrophasor data and weather informationare used for system inertia estimation.2) System conditions including system inertia and governor capacity are used to estimate the PV headroomrequirements.3) The PV headroom requirements are distributed to thePV plants through communication.4) PV plants execute headroom setpoints to ensure adequate system frequency response. If a PV plant cannotmeet the headroom requirement, the difference will becompensated by other PV plants.We propose using two machine learning models back-toback to achieve the adaptive PV frequency control instead ofusing the end-to-end model that maps the frequency measurements directly to the PV headroom requirement. Althoughdoing so will introduce additional uncertainty to the model,the uncertainty can be regulated by increasing the trainingdataset. On the other hand, the benefit of this setup is that itcan provide the system inertia information as an extra output.The system inertia itself is a very important system metricto ensure system stability and can be utilized by the systemoperator.According to the NERC requirements, the PV plants shouldalready have the frequency-watt function, and are monitoring the local frequency. The adaptive controller can beimplemented on top of the existing controller with some modifications. The assigned headroom setpoint is transmitted tothe local PV plant via Inter-Control Center CommunicationsProtocol (ICCP). Then the PV inverter will regulate its outputpower based on the headroom setpoint through a power reservecontrol strategy. An example of such control is presentedin [20]. The distribution of PV headroom to multiple PVplants can be integrated into the security-constrained economic dispatch (SCED). For simplicity, we assumed that theheadroom is distributed to multiple PV plants according toa fixed percentage (of their real-time dispatch).The main control target is the frequency nadir duringa pre-determined large contingency, such as the RCC inERCOT. This criterion gives operators relatively sufficientresources to respond to an emergency without being overlyconservative and inefficient. The control is designed to runcontinuously with headroom setpoints updated periodicallybased on real-time system conditions.B. PV Headroom Estimation ModelOne crucial process in the adaptive PV frequency control isto have an accurate estimate of the required PV headroomgiven the system inertia, governor capacity, and frequencyresponse target. Since the relationship between system conditions and frequency response nadir is nonlinear, machinelearning methods such as neural networks and random forestscan be used to accurately model the relationship betweensystem inertia, system governor capacity, PV frequency control headroom, and system frequency nadir. Fig. 7 shows theinputs and output of the machine learning model. It should benoted that in a realistic large system, there are multiple types ofgovernors for different synchronous generators with differentcontrol parameters such as droop and time delay. A clusteringstep on the different governors helps reduce the dimension ofthe inputs.For a given system, the machine learning model can betrained using simulation data or historical data. The trainedmachine learning model is an adaptive model that predictsthe frequency nadir of the RCC. Using the pre-trained model,system inertia, and system governor capacity information,the PV headroom requirement can be estimated for a givenfrequency nadir target using the bisection method, as shownin Fig. 8.C. PV Headroom DistributionAfter the PV headroom requirement is estimated, it is distributed among the PV plants based on their forecast MPPTpower. Currently, the power reserve market for PV generationhas not yet been established [33]. Therefore, the distributionof the PV headroom can be as simple as each PV plant contributing the same percentage of PV headroom. Conversely, thePV headroom distribution can be integrated into the securityconstrained economic dispatch model where the PV headroomrequirement is a constraint on the PV generation dispatch. DueAuthorized licensed use limited to: UNIVERSITY OF TENNESSEE LIBRARIES. Downloaded on September 21,2021 at 15:14:20 UTC from IEEE Xplore. Restrictions apply.

2360IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 3, MAY 2021Fig. 10. PV headroom requirement using adaptive PV frequency control andfixed headroom control.Fig. 9. Frequency response of the ERCOT system under different renewablepenetrations.to the study scope limitation, the method that distributes headroom reserve according to a certain percentage is applied inthis study.IV. S IMULATION C ASE S TUDYA. Simulation System OverviewTo evaluate the performance of the proposed adaptive PVfrequency control, a series of dynamic simulation is performed on a 6,102-bus power system representing the ERCOTsystem. The test system is a power system with extra-highinstantaneous PV power penetration capabilities, developedand validated in [34]. The frequency response of the ERCOTtest system has been validated using both synchrophasor measurements from FNET/GridEye [35] and information of actualevents provided by utilities. The model can be adjusted torepresent different renewable penetration levels by displacing traditional synchronous generators and/or reducing thesystem inertia. Fig. 9 shows the frequency response of the testsystem under different renewable penetrations. When creatingthe training cases, the effect of varying renewable penetrationsis approximated by varying system inertia as well as changingthe amount of system turbine governor resources.The PV frequency control is implemented in the modelwith the control gain set to 40. The PV headroom is alsoa parameter that can be modified in the simulation model.B. PV Headroom Estimation ModelMore than 13,000 training cases are created by varying theamount of responsive generation capacity, system inertia, andPV headroom. In each simulation case, the RCC, which isa tripping of 2,750 MW generation in the South Texas ProjectNuclear Plant, is simulated, and the frequency response of thesystem is recorded. A dataset containing governor capacity,system inertia, and PV headroom as inputs and frequency nadiras output is extracted from the simulation cases. A vanillafeedforward neural network is selected as the machine learningalgorithm for this study. While other machine learning algorithms are available, the neural network is selected for its widearray of applications backed by a mature theoretical background. Namely, the Universal Approximation Theorem [36]states that a feedforward multilayer neural network is capable of approximating any continuous function, and providesa solid theoretical ground for applying the bisection method.Another consideration when choosing neural networks overother machine learning methods is its ease of tuning andbetter performance in the training set. Interested readers arereferred to [37] for more information on neural networks andits training using backpropagation.After tuning the hyper-parameters such as the number ofthe hidden neurons, the number of hidden layers, activationfunction, we can achieve very high prediction accuracies. Theerrors on the testing set are in the order of 1 mHz, indicatinggood performance.C. Adaptive PV Frequency Control PerformanceAfter the machine learning model is trained, a realistic oneday scenario in ERCOT is created to evaluate the performanceof the adaptive PV frequency control. The frequency nadirtarget is set to 59.5 Hz, which is 0.2 Hz above the UnderFrequency Load Shedding threshold specified by ERCOT. ThePV headroom required by the adaptive PV frequency controlalgorithm is shown in Fig. 10. For reference, a more conservative control strategy where the PV reserves a fixed amount ofpower for primary frequency response is also shown in Fig. 10.The control effect of the adaptive PV frequency controlis tested against

IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 3, MAY 2021 2355 An Adaptive PV Frequency Control Strategy Based on Real-Time Inertia Estimation Yu Su , Student Member, IEEE, Hongyu Li, Student Member, IEEE,YiCui, Member, IEEE, Shutang You , Member, IEEE, Yiwei Ma, Member, IEEE, Jingxin Wang , Member, IEEE, and Yilu Liu , Fellow, IEEE Abstract—The declining cost of solar Photovoltaics (PV) gen-

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