Inertial frequency response provided by battery energy storage systems: probabilistic assessment

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1 Loughborough University Institutional Repository Inertial frequency response provie by battery energy storage systems: probabilistic assessment This item was submitte to Loughborough University's Institutional Repository by the/an author. Citation: GONZALEZ-LONGATT, F.M.... et al, Inertial frequency response provie by battery energy storage systems: probabilistic assessment. 6th International Conference on Clean Electrical Power (ICCEP), Santa Margherita Ligure, Italy, 27th-29th June 2017, pp Aitional Information: c 2017 IEEE. Personal use of this material is permitte. Permission from IEEE must be obtaine for all other uses, in any current or future meia, incluing reprinting/republishing this material for avertising or promotional purposes, creating new collective works, for resale or reistribution to servers or lists, or reuse of any copyrighte component of this work in other works. Metaata Recor: Version: Accepte for publication Publisher: c IEEE Please cite the publishe version.

2 Inertial Frequency Response provie by Battery Energy Storage Systems: Probabilistic Assessment F Gonzalez-Longatt, S. Alhejaj, A. Bonfiglio, R. Procopio, an J.L. Ruea CREST, Loughborough University, Unite Kingom University of Genoa DITEN, Italy Delft University of Technology, The Netherlans Abstract This paper proposes a methoology for assessment to measure the impact of the inertial frequency response provie by battery energy storage systems (BESS) consiering power system uncertainties. The propose methoology is use to assess the impact of the BESS equippe with sensible frequency controller on the frequency behaviour of the system after a system frequency isturbance consiering the variability coming from power system uncertainties. The propose meteorology is teste in an illustrative power system consiering the integration of a gri-scale BESS equippe with inertial frequency response controller, the uncertainty of the power system is simulate by the variability of the power eman. Monte Carlo simulations an time-omain simulations, using DIgSILENT PowerFactory TM are combine in the implementation of the propose methoology. Simulation results emonstrate the suitability of the propose approach to obtain probabilistic istribution functions (PDF) of the main system frequency response. Inex Terms-- Battery energy storage system, frequency response, Monte-Carlo Simulation, probabilistic assessment. I. INTRODUCTION Power system like other systems that have a real worl phenomenon has a number of possible ranomnesses ue to many events an scenarios that are involve. In orer to moel such as a system, researchers sometimes follow probabilistic or stochastic approaches [1] to preict the results or use these approaches to get a better-optimize esign for the system. In general, probabilistic approaches are use in many risk assessments since they quantify the amount of variation an uncertainty compare to the eterministic methos that provie an only fixe set of values. Therefore, implementing these approaches make it more possible to search for the values of interest within the specifie space of the search. The core principle is to use istributions instea of fixe values to measure an quantify the ata for variables that mostly affect the system behaviour an create the uncertainty. Mainly, istribution efines the range of possible values an shows which value within the expecte range. In turn, this will provie a better founation for making a ecision about the best possible solutions or insecticie risks. Many probabilistic approaches are use in power system analysis to assess the ifferent aspects of the risks [2], reliability [3], security [4] an stability [5]. However, the majority probabilistic assessments publishe researchers for power system stability are written to iscuss mainly small signal transient an voltage stability. However, probabilistic approaches can also be use to analysis frequency stability base on the ranomness of loa an intermittency of power generation supplie by the win an solar with many associate uncertain events. They also provie an outlook for optimisation techniques that are require to control the frequency response for the ancillary services. Therefore, ranom an iscrete events coul be well analyse by the statistical approach an with assistance from the use of stochastic ata moel. This paper proposes a methoology for assessment to measure the impact of the inertial frequency response provie by BESS consiering power systems uncertainties. The paper is organise as the following: Section II introuces the propose methoology of probability assessment an escribes the probabilistic moel use for the power system uncertainties. Section III presents numerical results of the implementation of the propose methoology using a peagogic test system. Finally, Section IV presents the main finings an conclusions. I. MODELLING OF BATTERY ENERGY STORAGE SYSTEM (BESS) There are several technologies available for Electrical Energy Storage System (EESS), some of them use a classical three-step process. The core of the energy storage system is the transformation of electrical energy into some other energy form that coul be reconverte into electricity [6]. In this paper, the EESS consists of a classical battery energy storage system (BESS) see Fig 1. A very generic moel of a BESS consists of two main subsystems [6, 7]: (i) a power conversion system (PCS) an the battery energy system (BES). The power conversion system uses bi-irectional AC/DC converter (inverter/rectifier) as the main interface between the BES an the power gri. The PCS is use to transform the DC-voltage from the BES into AC-voltage conitions require by the power gri [8]. A set of controllers are inclue in the PCS; those control loops are esigne to enable specific functionalities interfacing the BES an the power network. The main moelling etails of those subsystems are presente in the next subsections.

3 P, ac i P ac V ac i i q V, ac f P ac PQ controllers i p, Charge controler i s, Current controller m Frequency controller i qq, i qs, m q U c I c SOC Battery Moel Fig. 1. A representative block iagram of a Battery Energy Storage System (BESS) [8]. A. Moel of the Power conversion system (PCS) This paper is focuse on the system frequency response, as a consequence, the main attention is on the control behaviour of ac/c PWM-converter instea of switching frequencies, or high frequencies phenomenon. Taking into account the previous consierations, the funamental frequency moel is use in this paper in orer to moel the two-level PWM converter which operate in a stator voltage oriente q reference frame. -axis represents the active an q-axis the reactive component [9]. The line-line AC voltage (rms value) is escribe base on q reference frame as: Vac = V jv q (1) where the an q axis component of the ac voltage are relate to the c voltage (U c ): 3 3 V = mu c Vq = mu (2) q c where m an m q are the real an imaginary part of the moulation inex: m = m jm (3) A. Moel of the Battery Energy System (BES) The BES uses reversible electrochemical reactions to convert/store electricity. There are several batteries technologies commercially available in the market [6]: Lea-aci batteries (Pb-aci), Lithium-ion batteries (Liion), Nickel camium batteries (NiC), molten salt batteries like soium sulfur battery (NaS), aluminiumion (Al-ion), vanaium reox battery (VRB), liqui metal batteries, Soium-ion batteries (SIB). U batt I batt Rin Uin q ( SOC, t ) ( SOC, t ) Fig. 2. Simple equivalent circuit representative of a typical electrochemical battery [8, 10]. f Batteries using Pb-aci provie a scalable technology base for proviing short-term storage, in particular, frequency control. Moelling the battery is one of the most challenging situations in the energy storage system. However, since the battery is an electric bipole, were it linear, its more natural moel woul be constitute by an electromotive force (U in ) in series with an internal impeance (R in ), both function of time (t). In this paper, the simple battery moel is shown in Fig. 2 is use. The state of charge (SOC) is calculate using an integrator which takes into account the current of the battery (I batt ): U = max max ( 1 ) c U SOC U SOC IbattZ i (4) where U min represents the cell voltage ischarge cell (V), U max is the maximum voltage of the battery cell (V). B. Moel of the battery charge controller The charge controller consists of two parts (Fig. 3): (i) Charging logic to achieve the SOC bounary conitions (SOC min SOC SOC max ), an (ii) current limiter to limits the absolute value of the current orer accoring to limits (I min i I max ). The -axis current always has the higher priority than the q-axis current. The signal i is the ifference of the reference -axis current from the PQcontroller an (i,p) the moifie -current from the charging logic (i,s). The feeback of that signal to the PQ-controller prevents a winup of the PI-controller. SOC min Charge Control SOC max Imin Imax i p, i s, i qq, Current Limiter - i i qs, Fig. 3. Block iagram of the battery charge controller [7]. C. Moel of the current controller The input currents to the controller are the converter s AC-currents expresse in a reference q frame (i, i q ). The output signals m an m q are efine in the same reference frame an transforme back to a global reference frame using the same reference angle. A proportional-integral (PI) control loop is use to regulate the an q-axis current components (i, i q ) base on a PI controller regulating the battery charge; these are shown in Fig. 4. i s, i qs, - - K K q m 1 Ts 1Tqs i (a) -axis current i (b) q-axis current q controller controller Fig. 4. Block iagram of the current controllers [8]. D. Moel of the PQ-Controller The controller for the active an reactive power is m q

4 shown in Fig 5. The voltage (or Q) controller has a very slow current controller for set point tracking an a slope with a ea ban for proportional voltage support. P ac - p Pref 1 1 Ts r 1 I,min I,max Vref I q,max - K V U Offset AC p 1 I,ref Deaban Limit Tips 1Trqs Kq (a) Active power controller Vac (b) Reactive power controller Fig. 5. Block iagram of the PQ-Controller. B. Moel of the Frequency Controller During a system frequency isturbance (SFD) the generation/eman power balance is lost, the system frequency will change at a rate initially etermine by the total system inertia (H T ) [11]. Power sources an EESS connecte to the gri using full-rate power converters has the potential to provie a very fast frequency response. Several names have been using in the win turbine inustry to efine the controllers to enable a power converter to mimic the inertial response of a synchronous generator [12]: Artificial, Emulate, Simulate, or Synthetic Inertia. The synthetic inertia concept allows a controller to the take the kinetic energy from the rotating mass in a win turbine generator (WTG) [13]. This concept can be perfectly applie to BESS, but instea of taking kinetic energy from the rotating masses, the controller enables to ischarge the battery in a controlle way proucing an aitional power in the form of inertial power. The synthetic inertia controller can be unerstoo as a simple loop that increases the electric power output of the PCS uring the initial stages of a significant ownwar frequency event. The inertial power or power prouce uring the system frequency isturbance is calculate using the equivalent to the swing equation of a synchronous generator [14]: f P = 2 fh syn (5) t where H syn represent the value of the synthetic inertia (sec) an f is system frequency (p.u). Implementation of synthetic inertia controller is epicte in Fig. 6, where P ac = P. f t f t Π 2H syn I q,min I q,min I q,max 1 T iq Π ac Fig. 6. Block iagram of the of the frequency controller [15]. It is important to point out the synthetic inertia H syn, represent the gain of the proportional controller in the frequency controller. The gain of the frequency controller coul be any value when the inertia controller is installe in WTG; the gain takes values relate with the physical inertia constant of the rotating components. However, when the concept of inertia controller is applie to BESS, Iq,ref the physical unerstaning is lost, an as a consequence, any value coul be use but consieration about the rate of ischarge of the battery must be taken into account. A suen high ischarge current coul lea to excessive heat buil-up an thermal runaway. II. PROPOSED PROBABILISTIC ASSESSMENT The appropriate analysis of power system consiere increase number of uncertainties requires a ifferent approach to the classical eterministic. Moelling the uncertainties using stochastics moels has been the roots of the probabilistic approaches. The Stochastic Power Flow (SPF) analysis is one successful example of that. In the SPF the power generation an the gri configurations are both consiere as iscrete ranom variables, while the loa eman is consiere as a continuous ranom variable [16]. The aim of the PSF is to create Probabilistic Density Functions (PDF) to escribe the performance of the power system. The increase levels of uncertainties in power system has special impact on the power system ynamic, as a consequence, the probabilistic assessment has been a tenency in recent years. However, power system ynamic is a complex problem in terms of size an nonlinearity an coping with them require ingenious approaches. This paper proposes a methoology for assessment to measure the impact of the inertial frequency response provie by BESS consiering power systems uncertainties. The core of the propose methoology is the use of robust uncertainties moelling consiering stochastic properties an scenarios generation an the use of a wiely use numerical approach of probabilistic assessment, the Monte Carlo (MC) metho. The propose methoology consists of the following sequence of steps: (i) Uncertainties moelling, (ii) Scenarios creation, (iii) Monte Carlo Simulation, (iv) Probabilistic analysis of the results. C. Uncertainties Moelling Uncertainty is a very complex concept; however, it can be escribe as a lack of knowlege regaring the true value of a parameter. The mathematical moel that escribe the uncertainties is a elicate component of the propose methoology. A stochastic moel can be use to represent uncertainties, the moel use for each uncertainty is critical for the propose approach. The uncertainty moel shoul be able to reprouce the associate variability systematically. The uncertainties in the future electrical power system can come from so many ifferent sources: generation, eman, etc. The first step is to select the relevant uncertainties relate to the phenomenon of interest. This methoology is intereste in the ynamic system frequency response, as a consequence, any source of power imbalance is consiere the universe of potential uncertainties. The stochastic moel of the uncertainties can be efine by a continuous of iscrete probabilistic istribution with

5 known or unknown parameters. Many istribution moels are propose to create probabilistic moels base on the istribution function an the type of ata that are neee. The most popular of these istribution moels are uniform, binomial, Passion an Gaussian istribution. In this paper, the uncertainty of the system inputs are moelle consiering stochastic nature of the system loas. The uncertainty coming from changes in the electricity eman can be moelle using a stochastics moel where the power eman is assume to be the ranom variable (P L ). The literature is well-ocumente with scientific ocuments ealing with the specific etails of the loa moel, but the majority agrees the uncertainty relate to the loas can be assume normally istribute, as a consequence, a simple two-parameter Gaussian istribution can be use. The loa is assume to be a ranom variable (P L,i ) normally istribute within each hour for a given time perio [17]. Then, the probability istribution function (PDF) of the power eman of the i th loa (P L,i ) is given by the following expression: ( P ) 2 Li, µ Li, 1 2 2σ i fp ( P ),, = Li Li e (6) σ 2π i where µ L,i is the mean value of the electric eman an σ i is the stanar eviation. Using this approach, the uncertainty relate to a power eman is efine by two main parameters: µ L,i an σ i. Assuming the power eman follow a Gaussian istribution in a typical loa is a reasonable assumption that makes sense base on the bets citify knowlege. This approach can be easy extene to represents any other source of uncertainty in future power systems. The main ifference on moelling other sources of uncertainties come from the moel assumptions, e.g. probabilistic istribution an number of parameters. In general sense, the best uncertainty moel has the following characteristics: simple, realistic, efficient, useful, reliable, vali, etc. Literature is rich in more etaile moels for some other sources of uncertainties as win spee [16] an win power [18], classical generation, more complex loas [19] D. Scenarios creation The ranom variables are use to represent variables whose values cannot be preicte with certainty. If a ranom process is consiere stationary that means the statistical attributes of the process are not changing an if there is no serial correlation in the spatial or temporal sequence of observe values. Single probability istributions can escribe the previously escribe ranom processes as the uncertainties moel presente in the previous subsection. The use of parametric PDFs escription of the uncertainties allows the creation of scenarios base on ranom sampling; the create scenarios then are use by the Monte Carlo metho to obtain numerical results. The stochastic moels, for the consiere uncertainties, are use to create a set of scenarios. Ranom numbers are use in the stochastics moels in orer to create samples for each uncertainty, an then the samples of the forecaste uncertainties are combine together to create scenarios. The inverse transform sampling (also known as Smirnov transform) is use in this paper for scenarios creations. The power eman uncertainty is represente by the ranom variable p L,i, whose probabilistic istribution can be characterise by the cumulative istribution function (cf) F pli. Now, in orer to generate values of p L,i which are istribute accoring to cf, the inverse transform sampling metho is use: (i) generate a ranom number p from the stanar uniform istribution in the interval p [0,1]; (ii) compute the value p such that F PLi (p) = u; (iii) take p to be the ranom number rawn from the istribution escribe by F pli. E. Monte Carlo Simulations (MSC) The Monte Carlo methos or Monte Carlo experiments are the core of the propose methoology. MSC uses the eterministic moel of the system an systematically solve it consiering each scenario. In this paper, the main interest is the system frequency response. The best way to obtain the eterministic system frequency response of the power system after a isturbance is by using time-omain simulations. This approach also, allows an easy implementation of the propose methoology by using a commercially available power system analysis software for to obtain the system frequency response. The Monte Carlo metho uses time-omain simulation consiering each scenario, an then collect the eterministic ata of each scenario for the most relevant variables of the system frequency response are collecte. Several performance inicators are available to evaluate the performance of the system frequency response (SFR): (i) Maximum frequency graient ([f/t] max ) as observe by ROCOF (Rate-Of-Change-Of- Frequency) relays; (ii) Maximum frequency eviation (f max ) as observe by uner-frequency relays. It is efine as the absolute frequency eviation from the nominal frequency (f n ). (iii) Frequency nair (f min ) measures the minimum post-contingency frequency; (iv) Frequency nair time (t min ) is the time it takes for the response to reach f min ; (v) Quasi-steay-state eviation ( f ss ) is the eviation between f n an the final value (f ss ). In this paper, the main inicators use are f min an ROCOF. The time-omain simulation is a time-consuming process, an it generates a consierable volume of result ata, it must be post-processe in orer to extract the appropriate information for the probabilistic assessment an the impact of the inertial frequency response provie by battery energy storage systems (BESS) consiering power system uncertainties.

6 F. Probabilistic Analysis of the Results The solution of the eterministic moel is performe per each scenario, the solution of the time-omain simulation is a set of time-series for each variable of interest. The MCS will solve the eterministic moel for each sample, creating at the en a massive volume of information to be processe. In this paper the main interest is the system frequency response, as a consequence, specific inicators are efine an collecte for each time-series: f min an ROCOF. In the propose approach the collecte ata is collecte from the time-omain simulation, an it is use to create a set of time series of the generator s frequency. The frequency of centre inertia is use to combines the generator s frequency in a single time-series, an it coul be processe to obtain frequency inicators as minimum frequency, the maximum rate of change of frequency ([f/t] max ), steay-state frequency eviation, etc. The set of inicators obtaine consiering all the scenarios are use to create probability istributions for each variable. The process of creating the PDF s from the set of inicators is explaine in the final paper. III. SIMULATION AND RESULTS The propose a methoology for assessment to measure the impact of the inertial frequency response provie by BESS consiering power systems uncertainties is teste in this section. The propose methoology is teste an illustrate using a numerical example. A simple test system is use (see Fig. 1). It consists of two synchronous generators (P n = 400 MVW, H = 5.0 sec) connecte to an equivalent transmission system, where a 50 MW BESS in connecte. The synchronous generator is equippe with GAST governor an IEEE Type I AVR [20]. The full moel of the BESS has been evelope using DigSILENT Simulation Language (DSL) consier the previous section moels, an the BESS has been enable to provie system frequency response using an inertia frequency response controller. Fig. 7. Illustrative two-machinesbess test system. For illustrative purposes, a single source of power system uncertainty is consiere. The uncertainties coming from the eman are moelle using a Gaussian istribution (µ PL = 100 MW, σ PL = ±10%). Details of the iscrete probability istribution of a 1,000 samples power eman are shown in Fig. 8. Fig. 8. The probability istribution of the simulate loa in MW. The system frequency response of the test system is analyse using time-omain simulations. The power system analysis software DIgSILENT PowerFactory is use to obtain the system frequency response, controls moel of all components are inclue, an the user efine moel is use in the BESS. The system frequency isturbance consists of suen isconnection of Generator G2 (see Fig. 7). Previous to the isturbance the G1 is consiere as reference machine an the G2 is ispatche to cover 50% of the total system loa (P L ). Two main simulation cases are stuie in this section: Case I: Without BESS an Case II: With BESS. The Case I is selecte as reference an Case II is esigne to measure the impact of using BESS for inertial frequency response. A DIgSILENT Simulation Programming (DPL) script is evelope to automatize the time-omain simulations. The DPL script rea the power eman samples from a MS Excel file an run the RMS time-omain simulation, an time series of relevant variables are exporte in text format for later post-processing. The DPL script runs 1,000 time-omain simulations; it is a time-consuming process. A MATLAB script was evelope to post-processing the results of the Monte Carlo simulations. The MATLAB program rea the text files an extract the relevant information an calculates the inexes for frequency response: ROCOF an f min. Table I shows the main statistic inicators for the frequency inicator are the stuie cases. Fig. 9 an 10 show the iscrete probabilistic istribution function of the minimum frequency an ROCOF for the Case I an II respectively. The suen isconnection of G2 prouces a power imbalance ( P = 50%P L ); the BESS is able of proviing

7 an inertial response, an however, the effect on the minimum frequency (f min ) is minimum. It is an expecte conclusion because the inertial controller aims to improve the ROCOF. However, this results shows how the initial state of the power system (generation/eman) affect the minimum frequency. The average minimum frequency is Hz, an the minimum frequency is below Hz in 67% of the cases. TABLE I. BATTERY MODELS PARAMETERS Statistic Case I: Without Case II: With BESS BESS ROCOF ROCOF f Max min f min Max Mean St. Error of Mean Meian Moe a a St. Deviation Variance Skewness St. Error of Skewness Kurtosis St. Error of Kurtosis Range Minimum Maximum Sum Percentiles a. Multiple moes exist. The smallest value is shown help to control the system frequency, an it is evient with the reuction in the stanar eviation of the ROCOF on the 1,000 simulate cases. Fig. 10. PDF of f min an ROCOF: Case II: With BESS. IV. CONCLUSIONS This paper proposes a methoology for assessment to measure the impact of the inertial frequency response provie by battery energy storage systems (BESS) consiering power system uncertainties. The core of the methoology is the combination of Monte Carlo simulations an time-omains simulations. The propose methoology is use to assess the impact of the BESS equippe with sensible frequency controller on the frequency behaviour of the system after a system frequency isturbance consiering the variability coming from power system uncertainties. Simulations results emonstrate the suitability of the propose approach. APPENDIX Fig. 9. PDF of f min an ROCOF: Case I: Without BESS. The main impact of using BESS to provie inertial response, as expecte, is on the ROCOF. Case I shows a high average ROCOF of pu/sec, but when the BESS is enable to provie frequency support the ROCOF is reuce to pu/sec. Also, the BESS TABLE A. BATTERY MODELS PARAMETERS Description Parameter Unit Value State of change SOC Single Cell Capacity W n Ah 1.2 Min. Voltage of empty cell U min V max. Voltage of full cell U max V Number of parallel connecte cells N p - 60 Number of parallel connecte cells N s - 65 Nominal BESS Voltage U n V 900 Internal Resistance per cell Z i Ω TABLE B. BATTERY CHARGER CONTROLLER PARAMETERS Description Parameter Unit Value Min charge current Imin p.u. 0.1 Min state of charge SOC min p.u. 0.0 Max state of charge SOC max p.u. 1.0 Max absolute current I max p.u 1.0

8 TABLE C. CURRENT CONTROLLER PARAMETERS Description Parameter Unit Value Proportional gain, -axis K Integration time constant, -axis T sec Proportional gain, q-axis K q Integration time constant, q-axis T q sec TABLE D. CURRENT CONTROLLER PARAMETERS Description Parameter Unit Value Filter time constant, -axis T r sec 0.05 Filter time contact, q-axis T rq sec 0.01 Proportional gain, -axis K p Integration time constant, -axis T sec 0.10 Deaban for proportional gain K b Proportional gain, q-axis K q Integrator time constant, q-axis T q sec 1.00 Min. current, -axis I min p.u Min. current, q-axis I qmin p.u Max. current, -axis I max p.u Min. current, q-axis I qmax p.u REFERENCES [1] R. Allan an R. Billinton, "Probabilistic assessment of power systems," Proceeings of the IEEE, vol. 88, no. 2, pp , [2] W. Li, Risk Assessment of Power Systems:Moels, Methos, an Applications. Wiley-IEEE Press, [3] M. T. Schilling, J. C. S.. Souza, an M. B. D. C. Filho, "Power System Probabilistic Reliability Assessment: Current Proceures in Brazil," IEEE Transactions on Power Systems, vol. 23, no. 3, pp , [4] K. Morison, W. Lei, an P. Kunur, "Power system security assessment," IEEE Power an Energy Magazine, vol. 2, no. 5, pp , [5] P. M. Anerson an A. Bose, "A Probabilistic Approach to Power System Stability Analysis," IEEE Transactions on Power Apparatus an Systems, vol. PAS-102, no. 8, pp , [6] F. M. Gonzalez-Longatt an S. M. Alhejaj, "Enabling inertial response in utility-scale battery energy storage system," in 2016 IEEE Innovative Smart Gri Technologies - Asia (ISGT-Asia), 2016, pp [7] S. M. Alhejaj an F. M. Gonzalez-Longatt, "Impact of inertia emulation control of gri-scale BESS on power system frequency response," in 2016 International Conference for Stuents on Applie Engineering (ICSAE), 2016, pp [8] S. Alhejaj an F. Gonzalez-Longatt, "Investigation on griscale BESS proviing Inertial Response Support," presente at the IEEE PES POWERCON 2016, Wollongong Australia, 28 September 1 October 2016, [9] M. Deepak, R. J. Abraham, F. M. Gonzalez-Longatt, D. M. Greenwoo, an H.-S. Rajamani, "A novel approach to frequency support in a win integrate power system," Renewable Energy, vol. 108, pp , 8// [10] M. Ceraolo, "New ynamical moels of lea-aci batteries," IEEE Transactions on Power Systems, vol. 15, no. 4, pp , [11] A. Bonfiglio, F. Gonzalez-Longatt, an R. Procopio, "Integrate Inertial an Droop Frequency Controller for Variable Spee Win Generators," WSEAS Transactions on Environment an Development, vol. 12, no. 18, pp , [12] F. Gonzalez-Longatt, "Impact of emulate inertia from win power on uner-frequency protection schemes of future power systems," (in English), Journal of Moern Power Systems an Clean Energy, pp. 1-8, 2015/08/ [13] A. Bonfiglio, F. Delfino, F. Gonzalez-Longatt, an R. Procopio, "Steay-state assessments of PMSGs in win generating units," International Journal of Electrical Power & Energy Systems, vol. 90, pp , 9// [14] F. Gonzalez-Longatt, "Frequency Control an Inertial Response Schemes for the Future Power Networks," in Large Scale Renewable Power Generation, J. Hossain an A. Mahmu, Es. (Green Energy an Technology: Springer Singapore, 2014, pp [15] F. Gonzalez-Longatt, A. A. Bonfiglio, R. Procopio, an B. Veruci, "Evaluation of Inertial Response Controllers for Full-Rate Power Converter Win Turbine (Type 4)," presente at the IEEE PES General Meeting 2016, Boston, USA, July 2016, [16] F. Gonzalez-Longatt, J. L. Ruea, an D. Doganov, "Assessment of the Variability on the Electricity Prouction of Win Turbines Technologies consiering Time-Series of Win Spee," presente at the Efficacité énergétique sources énergies renouvelables protection e l environnement COFRET 12, Sozopol, Bulgaria, 6-8 September 2013, [17] N. D. Hatziargyriou, T. S. Karakatsanis, an M. Papaopoulos, "Probabilistic loa flow in istribution systems containing isperse win power generation," Power Systems, IEEE Transactions on, vol. 8, no. 1, pp , [18] F. Gonzalez-Longatt, J. L. Ruea, an D. Boganov, "Probabilistic assessment of operational risk consiering ifferent win turbine technologies," in 3r IEEE PES International Conference an Exhibition on Innovative Smart Gri Technologies (ISGT Europe 2012), 2012, pp [19] F. M. Gonzalez-Longatt, J. L. Ruea, I. Erlich, D. Boganov, an W. Villa, "Ientification of Gaussian mixture moel using Mean Variance Mapping Optimization: Venezuelan case," in 3r IEEE PES International Conference an Exhibition on Innovative Smart Gri Technologies (ISGT Europe 2012) 2012, pp [20] A. Bonfiglio, F. Delfino, M. Invernizzi, A. Perfumo, an R. Procopio, "A Feeback Linearization Scheme for the Control of Synchronous Generators," Electric Power Components an Systems, vol. 40, no. 16, pp , 2012/10/