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Krasniqi & Kokabuses 1 and 4 while the loads are indicated at allfour buses. Base values for the transmissionsystem are 100 MVA, 230 KV. The line data of theTable 1 give the per unit series impedance andthe line charging susceptances for theequivalents of the four lines identified by thebuses at which they terminate.The bus data in Table 2 list values of P, Q and V ateach bus. The Q values of load are calculatedfrom the corresponding P values assuming apower factor of 0.85. The net scheduled values P i ,and Q i are negative at the load buses 2 and 3.Generated Q g is not specified where the voltagemagnitude is constant. In the voltage column thevalues for the load buses are flat-start estimates.Figure 3: Bus Branch DiagramSeries Z Series Y=Z -1 Shunt YLine bus toTotal ChargingR per unit X per unit G per unit B per unitbusMvarY/2 per unit1-2 0.01008 0.05040 3.815629 -19.078 10.25 0.051251-3 0.00744 0.03720 5.169561 -25.848 7.75 0.038752-4 0.00744 0.03720 5.169561 -25.848 7.75 0.038753-4 0.01272 0.06360 3.023705 -15.119 12.75 0.06375Table 1: Bus Branch DataGenerationLoadBus P (MW) Q (MW) P (MW) Q (MW) V (per unit) Remarks1 ------------- --------- 50 30.99 1 < 0 Slack bus2 0 0 170 105.35 1 < 0 Load bus (inductive)3 0 0 200 123.94 1 < 0 Load bus (inductive)4 318 --------- 80 49.58 1 < 0 Voltage controlledTable 2: Bus Branch Individual DataBus Number (1) (2) (3) (4)(1) 8.985190 –j.44.83 -3.8156 +j19.07 -5.169 +j25.84 0(2) -3.81562 +j19.078144 8.98 –j44.8359 0 -5.169+j25.84(3) -5.1695 +j25.847 0 8.193 –j40.8693 -3.023+j5.11(4) 0 -5.169 +j25.847 -3.023 +j15.118 8.193-j40.863Table 3: Bus Branch Individual Polar DataDetermining the number of rows and columns inthe Jacobian, and then calculating the initialmismatch e.g. Δp 1 (0) , Δp 2 (0) , Δp 3 (0) and Δp 4 (0) alongwith the initial values of the Jacobian elements ofthe second row, third column, of the second row,second column, and the fifth row fifth column,using all the values in Table 2.Since the slack bus has no rows or columns in theJacobian, a 6x6 matrix would be necessary if Pand Q were specified for the other individualbuses. In fact however the voltage magnitude isAKTET Vol. IV, Nr 2, 2011 181
Krasniqi & Kokaspecified (held constant) at bus 4, and thus theJacobian will be 5x5 matrix. In order to calculatethe power based on the estimated and thespecified voltages of Table 2, we require thepolar form of the off-diagonal entries of Table 3.Y 31 = 26.359695
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Ibrahimi et al.paraqitjen e gëlqer
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Kokalari & Haxhimatematikore, janë
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Lajçi & Metikos-HukovicPbSO 4 /H 2
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Pajaziti et al.Historikisht kontrol
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