A balanced, three phase, {VLINE} V system is supplying a load connected in {type}.
\n{image('resources/question-resources/'+Circuit)}
\n\nThe loads are:
\n$Z_1 = \\var{R1}+i\\ \\var{X1}\\ \\Omega $
\n$Z_2 = \\var{R2}+i\\ \\var{X2}\\ \\Omega $
\n$Z_3 = \\var{R3}+i\\ \\var{X3}\\ \\Omega $
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\n0 = star with a neutral
\n1 = delta
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\nUsing $V_A$ as the reference voltage, calculate the currents in each load:
\n$I_1 = $[[1]]$\\angle$ [[2]]$^o$ A
\n$I_2 = $[[3]]$\\angle$ [[4]]$^o$ A
\n$I_3 = $[[5]]$\\angle$ [[6]]$^o$ A
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\n$I_A = $[[0]]$\\angle$ [[1]]$^o$ A
\n$I_B = $[[2]]$\\angle$ [[3]]$^o$ A
\n$I_C = $[[4]]$\\angle$ [[5]]$^o$ A
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\n$P_A = $[[0]]W
\n$P_B = $[[1]]W
\n$P_C = $[[2]]W
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\n$P_1 = $[[0]]W
\n$P_2 = $[[1]]W
\n$P_3 = $[[2]]W
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "In the system shown in Figure 1, the transformers are connected star-star with both star points grounded and the generator is connected in star with its star points grounded. The per unit impedances of each element on a {SBASE} MVA base are given in Table 1 and the voltage levels are given in Table 2.
\n{image('resources/question-resources/PSScircuit.png')}
\nFigure 1: A section of the distribution system
\n| \n \n | \n\n Generator \n | \n\n Transformer T1 \n | \n\n Line \n | \n\n Transformer T2 \n | \n
| \n Z [p.u.] \n | \n\n {RG} + j {XG} \n | \n\n {RT1} + j {XT1} \n | \n\n {RL} + j {XL} \n | \n\n {RT2} + j {XT2} \n | \n
Table 1: Sequence impedances (p.u. on {SBASE} MVA base)
\n\n
| \n \n | \n\n Generator \n | \n\n Line \n | \n\n Load \n | \n
| \n V BASE [kV] \n | \n\n {VG} \n | \n\n {VLine} \n | \n\n {VLoad} \n | \n
Table 2: Voltage bases (kV)
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\n$ I_L $ = [[0]]$\\angle$ [[1]]$^o $ p.u.
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\n$ V_1 $ = [[0]]$\\angle$ [[1]]$^o$ p.u.
\n$ V_2 $ = [[2]]$\\angle$ [[3]]$^o$ p.u.
\n$ V_3 $ = [[4]]$\\angle$ [[5]]$^o$ p.u.
\n$ V_4 $ = [[6]]$\\angle$ [[7]]$^o$ p.u.
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\n$ P_{OUT} $ = [[0]] MW
\nCalcuate the input power to the generator in MW.
\n$ P_{IN} $ = [[1]] MW
\nCalculate the overall efficiency of the sytem.
\n$ \\eta $ = [[2]] %
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