Renewable Integrated Power System Stability and Control. Hassan Bevrani

results of authors in Smart/Micro Grids Research Center‐SMGRC, University of Kurdistan (Sanandaj, Iran) and in The Center for Research and Advanced Studies‐CINVESTAV of the National Polytechnic Institute of Mexico (Guadalajara, Mexico). It is a pleasure to acknowledge the received supports from these sources, and the awards from Iran Grid Management Company (IGMC), Iran National Science Foundation (INSF), and Alexander von Humboldt (AvH) Foundation.

      The authors would like to thank their colleagues Prof. J. Raisch and Prof. Bruno Francois for their kind support. Finally, the authors offer their deepest personal gratitude to their families for their patience during the preparation of this book.

      Nomenclature

X,Ydata matricesεKernel bandwidthλeigenvalueσsingular valueξdampingυvector of natural modesψ,φeigenvectorsΨΦmatrices of eigenvectorsΓinflation operatorθphase angleΛdiagonal matrix of eigenvalues∑diagonal matrix of singular valuesδsmechanical rotor angle (rad)δrotor angle position (rad)

rotor angle position of the COI (rad)ωangular speed (rad/s)ωsmechanical rotor angular speed (rad/s)ω rated angular speed (rad/s)Tm(t)mechanical input torque (p.u.)Te(t)electrical output torque (p.u.)Minertia constant of the system (s)

inertia of ESS in area i (s)

minimum required ESS inertia, in compliance with RoCof, in area i (s)

minimum required ESS inertia, in compliance with frequency nadir, in area i (s)Ddamping coefficientI(t)impulse response of the systemP(n)data sequence of interestPininjected power of ESS to the host gridKnumber of sinusoidal components in noiseLlength of P(n)Lx ,Lylatent variablesJmoment of inertiaakmagnitudeΦ kinitial phase angleωkharmonic frequency in radiusAkcomplex magnitude of the kth‐harmonicsieigenvectors associated with the noise subspaceesignal eigenvectoreUcomplex‐conjugate transpose of eCcapcapital costs ($/kW)CPCSpower conversion system costs ($/kW)Cstorstorage section costs ($/kWh)CBOPpower balance costs ($/kW)tchcharging/discharging time (h)CO & Moperation and maintenance costs ($/kW‐year)CR,aannualized replacement costs ($/kW‐year)Ccap,aannualized total capital costs ($/kW‐year)CLCC,aannualized life cycle costs ($/kW‐year)CRFcapital recovery factorCRreplacement costs ($/kWh)CFOM,afixed operation and maintenance costs ($/kW‐year)CVOM,avariable operation and maintenance costs ($/kWh)ncyclenumber of discharge cycles per yearζccharging efficiency of the battery (%)ζddischarging efficiency of the battery (%)ηpower angle‐based stability indexi (j)area (bus) indexffrequency (Hz)

virtual transferred power (pu)

fictitious reactance (pu)TtieCOIi,japplied torques from bus j to COITtieCOIi,COGapplied torques from COG to COIAiarea iΔPisize of disturbance in area iξ−deviations from the target value in negative directionξ+deviations from the target value in positive directionξtarget valuepsprobability of each scenariosscenario counterICinternal combustionSMsynchronous machineMPslope of P‐ꞷ droopKPIintegral control gainKPPproportional control gainFCMDcommand fuel signalECMDexciter control signalPmeasmeasured value of real powerQmeasmeasured value of reactive powerI•line currentKtftorque to fuel conversion ratioηthrthermal constantKcvcalorific valueKfrfuel rate at rated speedKmmechanic losses constantτeexciter machine time constantPMGinjected power of MG to the host gridωMGsangular speed at the point of common couplingζDGs re‐dispatching time (s)υDGs islanding time (s)nnumber of areasβfrequency biasPGensetgeneration of GenstLlevel arm length (m)

conventional synchronous inertia (s)TDdelivery time of primary frequency response (s)Kf(s)transfer function of the phase‐locked loopMMMGmuti‐micro‐grid inerta constant (s)Vinitial values of terminal voltageY HHankel matrix‖.‖norm

      List of Abbreviations and Acronyms

AamplitudeAGCautomatic generation controlAQRautomatic reactive power regulatorAVRautomatic voltage regulatorBresidueBFVbest fitness valueCOGcenter of gravityCOIcenter of inertiaDERdistributed energy resourcesDFIGdoubly‐fed induction generatorDGdistributed generationDMdiffusion mapDMDdynamic mode decompositionEenergyEMTelectromagnetic transientESSenergy storage systemEVelectrical vehicleGAgenetic algorithmHVDChigh‐voltage direct currentKTKumaresan–TuftLCCline commutated converterMCLMarkov clusteringMGmicrogridMMGsmulti‐MGsNERCNorth American Electric Reliability CorporationNYNENew York New EnglandPCprincipal componentPCTVARpercentage of variationPFparticipation factorPIproportional‐integralPLLphase‐locked loopPLSpartial least squares regressionPLSCpartial least squares correlationPMSGpermanent magnet synchronous generatorsPMUphasor measurement unitPOISpoint of interconnection with the systemPSpseudo spectrumPSSpower system stabilizersPVphotovoltaicRESrenewable energy sourceRoCoFrate of change of frequencySCsynchronous condenserSCADAsupervisory control and data acquisitionSGsynchronous generatorSLBstatic load bankSOCstate of chargeSSstatic switchSVCstatic VAR compensatorSVDsingular value decompositionT‐Dtime domainTSOtransmission system operatorUCTEUnion for the Coordination of the Transmission of ElectricityUFLSunderfrequency load sheddingULTCunder load tap changerVARvolt–ampere reactiveVSCvoltage source converterVSGvirtual synchronous generatorV2Gvehicle‐to‐gridV vandVandermonde matrixWAMSwide‐area measurement systemWFwind farmWTwind turbinezcomplex amplitude

1 Introduction

      The term power system stability and control is used to define the application of control theorems and relevant technologies to analyze and enhance the power system functions during normal and abnormal operations. Power system stability and control refers to keep desired performance and stabilizing power system following various disturbances, such as short circuits, loss of generation, and load.

      The capacity of installed inverter‐based distributed generators (DGs) and renewable energy sources (RESs) individually or through the microgrids (MGs) in power systems is rapidly growing, and a high penetration level is targeted for the next few decades. In most countries including developing countries, significant targets are considered for using the distributed microsources and MGs in their power systems for near future. The increase of DGs/RESs in power systems has a significant impact on CO₂ reduction; however, recent studies have shown that relatively high DGs/RESs integration will have some negative impacts on power system dynamics, frequency and voltage regulation, as well as other control and operational issues. Decreasing system inertia and highly variable dynamic nature of DGs/RESs/MGs are known as the main reasons. These impacts may increase for the dynamically weak power systems at the penetration rates that are expected over the next several years.

      In this chapter, a brief discussion on the power system stability and control in modern renewable integrated power systems and the current state of this topic are given. Data‐driven wide‐area power system monitoring and control is emphasized, and the significance of measurement‐based dynamic modeling and parameter estimation is shown.

1.1 Power System Stability and Control

Power system stability and control was first recognized as an important problem in 1920s [1]. Over the years, numerous modeling/simulation programs, synthesis/analysis methodologies, and protection schemes have been developed. Power grid control must provide the ability of an electric power to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables, i.e., frequency, voltage, and angle, bounded so that practically the entire system remains intact. Thus, the main control loops are