# Conventional small signal model developed here consists of

Conventional power system has fully dispatchable andcontrolled generation. The system’s frequency dynamics andstability is taken care by the inertial response of SGs. Withthe electro-mechanical coupling of SG with grid, the rotatingmass of SG provides kinetic energy required by grid duringfrequency deviation. This kinetic energy is directly proportionalto rate of frequency change. It is given as:EK:E=12J(2fm)2(1)where J is moment of inertia of SG, frotating frequency.Owing to any disturbance that leads to power imbalance andmhence frequency deviation, the kinetic energy of SG is releasedmake the frequency deviation slower and easy to regulate.The swing equation clearly re?ects the inertial response of SG with respect to change in its rotational speed following a powerimbalance. Swing equation or dynamic model of rotating massis given as:Jd2dt2(m) + Dd(2)where J is total moment of inertia, D is damping factor, dt(m) = Tmis the angular position of rotor w.r.t stationary axis, T Teis themechanical torque, Tis the electrical torque. Converting thisto per unit system and rationalizing the swing equation weget:Md2dt2(esg) + Dd(3)where M is inertia constant de?ned as M = J!dt(sg) = Pm Peisangular speed of rotor, sgis the power angle, Pis themechanical power, Pis the electrical powerIf there is a high share of SGs in the power system, theneoverall system inertia will be high and system can meetup the stability challenges. But with increasing penetrationof inverter interfaced DGs, rotational inertia of the systemis considerably reducing and becoming time variant. Hencefrequency stabilization becomes dif?cult and system can sufferinstability issues. The impact of RES on system inertia can beseen in Fig.1.smm, !smThe system considered here basically consists of two DGs.Both DGs are considered to be inverter interfaced, irrespectiveof the type of microsource. Voltage source based droop control(VSC) is used as the control strategy. For the purpose ofmodelling only grid side converter and its control is considered.The system structure is shown in Fig.2. The systematicmodelling approach is adopted from 18.For developing the small signal model the system is as-sumed to be operating in a balanced condition and eachcomponent of the system is represented in dq reference frame.The small signal model developed here consists of three subsystems- inverter, network and load model. Each subsystem ismodeled in its local d-q frame. 18. One of the inverter’s dqframe is taken as the global reference frame (DQ), that rotates at frequency !refand others are translated to this referenceframe according to transformation technique mentioned in19. The rest of the dq reference frame are denoted as (dq)that rotates at !frequency. The transformation equation isgiven asiiglobal reference frame and Fdq=FqFdis the vectorcomponent of F for n other subsystems. Tis called thetransformation matrix. iiis the angle between d axis of globalreference frame and d axis of ilocal reference frame.thnverter modeling in-thvolves the modeling of voltage source inverters (VSI) in itslocal dq reference frame. To model the inverter sub systemwe have to model its controller block, output LC ?lter and thecoupling inductor. The controller consists of power controller,voltage controller and current controller. 18. In this modelingswitching sequence of inverter is neglected, considering highswitching frequency.

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