Virtual Synchronous Machine VSG 36 Virtual Synchronous Machine ❑ To make the interaction between grid and generator as in a remote power dispatch. ❑ To make the reaction to transients as well as the full electrical effects of a rotating mass ❑ To provide primary reserve ❑ From the grid point of view, to make wind and PV conversion systems to be regarded as conventional power stations ❑ To make the inverter based DER to exhibit inertia and damping properties similar of conventional synchronous machines for short time interval 37 Synchronous Machine v = rs i + 1 2 Ks = 0 3 1 2 1 2 3 2 1 2 − 1 2 3 − 2 1 2 − dλ dt λ = L s i l sr id Ls Ls = 0 0 Ls v = rs i + L s e Lsfd sin(r ) l sr = − L cos( ) r sfd di + e dt cos(r ) = d r sin( ) r Te = i T l sr id = d i T r d = Lsfd id cos(r ) sin( ) r 38 Synchronous Machine v = rs i + L s e di + e dt cos(r ) = d r sin( ) r Te = d i T cos(r ) sin( ) r 39 Synchronous Generator v = −rs i − L s e di dt cos(r ) = d r sin( ) r Te = d i T + e cos(r ) sin( ) r d r 1 = (TI − Te − D p r ) dt J Qgap = d r i T d r = r dt − sin(r ) cos( ) r T QPOC 0 1 = v i −1 0 40 Virtual Synchronous Generator 41 Dynamic model – Single phase equivalent VSG connected to a stiff grid ❑ The non-linear dynamic equation that describes the behavior of the frequency, power angle, and flux is: d 1 V sin() Po = − Dp − + + D p o dt J XL o d = − g dt d 1 2 2 V = − DqV + Qo − + cos() + Dq Eo dt K XL XL 42 Dynamic model – VSG connected to a Stiff Grid ❑ The non-linear dynamic equation that describe the behavior of the, frequency, power angle, and flux of the VSG is: d = a11 + a12 sin() + b11 dt d = + b12 dt d = a32 2 2 + a33 cos() + b31 dt a11 = − Dp J −V a12 = JX L a32 = −1 KX L a33 = V KX L b11 = 1 Po ( + D p o ) J o b21 = −g b31 = 1 (Qo + Dq ( Eo − V )) K 43 Dynamic model – VSG connected to the Grid 0 = a11 + a12 sin() + b11 0 = + b12 0 = a322 2 + a33 cos() + b31 This algebraic equation has an solutions: (o , o , o ) The local qualitative behavior of the VSG can be analyzed from the eigenvalues of: 44 Example Let us consider again a 33kVA single phase inverter connected to a 220V 60Hz grid where: First, the droop coefficients can be found as: Dp = T P 33000 = = = 4.64 g (260)(23) Dq = Q 33000 = = 1500 E 0.1(220) 45 Example Let us consider again a 33kVA single phase inverter connected to a 220V 60Hz grid where: First, the droop coefficients can be found as: Dp = T P 33000 = = = 4.64 g (2 60)(2 3) Dq = Q 33000 = = 1500 E 0.1(220) 46 Example The time constants associated with the frequency and the voltage are: J f = Dp K v = g Dq J = f Dp K = v g Dq By selecting f = 0.1 v = 0.5 47 Qualitative Behavior D p = 4.64 Dq = 1500 J = 0.464 K = 113110 X L = 0.257(pu) 48 Example The relation between the states and the modes can be revealed from the participation factors. 1 -5.01 + j15.47 = -5.01- j15.47 2 3 -0.41 1 2 3 0.525 0.525 0 0.525 0.525 0 0 0 0.999 49 Simulation 50 Damping Correction Action d Te D f ( ) ( − g ) dt d S. Dong and C. Chen, "Adjusting Synchronverter Dynamic Response Speed via Damping Correction Loop,“ publishied in 2018 IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, 2018, pp. 1-1” 51 Damping Correction Action 52 Simulation 53