Identification of Coherent Generators Using Fuzzy C-Means ...

From Fig. (2) One can write the matrix form of the excitation system as follows:⎡ 1⎤ ⎡ K ⎤R⎢ − 0 0 ⎥ ⎢ Vt ⎥τRτR⎡V⎤ ⎢ ⎥1 ⎡V1⎤ ⎢ ⎥⎢ KKF A( KKF A A)KF KKF AV⎥ ⎢ + τ ⎥⎢ 3V⎥ ⎢ ⎥⎢ ⎥=− ⎢ − ⎥ 3( VREFVS)ττF AττF Aττ ⎢ ⎥+ ⎢ + ⎥F AττF A⎢E⎥ ⎢ ⎥FDE ⎢ ⎥⎣ ⎦⎢ ⎥FD⎢ KA KA 1 ⎥⎣⎦ ⎢ K ⎥A⎢ − − − ⎥ ⎢ ( VREF+ VS) ⎥⎣ τR τR τR ⎦ ⎣ τA⎦(9)On the other side, by the simplified model of the speed governor transfer function is givenas follows:UmPm1=Gg 1 + ST− ( ) S δωoWhere T g is the governor time constant in sec, G g is the governor gain; P m is the inputmechanical power and U m is the stabilizing signal of speed governor system. Finally; thelinearized form of eqn. (10) is:1 Gg 1Δ P m= ( ) Um−( ) Δω−( ) ΔPm(11)Tg Tgωo TgFrom eqns. 1, 2, 9 and 11, one can get the overall model of one generation unit(synchronous machine, exciter and speed governor) as follows:X = AX + BU(12)Where X =Δ [ δ , Δω, ΔV1, ΔV3, ΔEFD , Δ Pm ], andu = [ Vs , um] , on the other sidefor multi machines system one can get the overall state space model as in eqn. (12) with thefollowing definition:XT= [ x1, x2,..., x6] , x1= [ Δδ1, Δδ 2,..., Δ δn], x2=[ Δω1, Δω 2,..., Δ ωn], x3= [ ΔV 11, ΔV 12,..., ΔV1n],x4= [ ΔV 31, ΔV 32,..., Δ V3n ], x5= [ ΔE FD 1, ΔE FD 2,..., ΔEFDn],x6= [ ΔPm 1, ΔPm 2,..., ΔPmn],BuKR 1KRnKF 1KA 1= [0 : 0 : Vt1,..., Vtn: ( VREFτR 1τRnτF 1τA 1+ Vs),...,KFnKA nKA 1KA n( VREF+ Vs) : ( VREF+ Vs),...,τFnτ A nτA 1τA n1 1TΔPm1,..., ΔPmn]TT( VREF+ Vs) :g 1gng(10)6