// Numbas version: finer_feedback_settings
{"name": "Load Flow Analysis - 3bus", "extensions": [], "custom_part_types": [], "resources": [["question-resources/LF1Circuit_3wHSQnZ.png", "/srv/numbas/media/question-resources/LF1Circuit_3wHSQnZ.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Load Flow Analysis - 3bus", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>For the 3-bus system shown in <strong>Figure 1</strong>, bus 1 is the swing bus. The lines all have impedance j {X} p.u.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/LF1Circuit_3wHSQnZ.png\"/></p>\n<p style=\"text-align: center;\"><em><strong>Figure 1: A 3-bus system</strong></em></p>\n<table border=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">\n<p><strong>Bus</strong></p>\n</td>\n<td style=\"text-align: center;\">\n<p><strong>Power In</strong></p>\n</td>\n<td style=\"text-align: center;\">\n<p><strong>Power&nbsp;Out</strong></p>\n</td>\n<td style=\"text-align: center;\">\n<p><strong>Voltage</strong></p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">\n<p>1</p>\n</td>\n<td style=\"text-align: center;\">\n<p>?</p>\n</td>\n<td style=\"text-align: center;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>1&nbsp;$\\angle $0</p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">\n<p>2</p>\n</td>\n<td style=\"text-align: center;\">\n<p>{PG2} + j&nbsp;?</p>\n</td>\n<td style=\"text-align: center;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>{V2} $\\angle $&nbsp;?</p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">\n<p>3</p>\n</td>\n<td style=\"text-align: center;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>{P3}&nbsp;+ j {Q3}</p>\n</td>\n<td style=\"text-align: center;\">\n<p>?</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>&nbsp;Table 1: Bus information</strong></em></p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"X": {"name": "X", "group": "Given", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Y": {"name": "Y", "group": "Computed", "definition": "1/(X*i)", "description": "", "templateType": "anything", "can_override": false}, "P3": {"name": "P3", "group": "Given", "definition": 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false}, "V3a": {"name": "V3a", "group": "Computed", "definition": "(conj(S3) + Y + Y*V2a)/(2*Y)", "description": "", "templateType": "anything", "can_override": false}, "Q2a": {"name": "Q2a", "group": "Computed", "definition": "-im(conj(V20)*(-Y + (2*Y)*V20 -Y))", "description": "", "templateType": "anything", "can_override": false}, "V3b": {"name": "V3b", "group": "Computed", "definition": "(conj(S3)/conj(V3a) + Y + Y*V2b)/(2*Y) ", "description": "", "templateType": "anything", "can_override": false}, "Q2b": {"name": "Q2b", "group": "Computed", "definition": "-im(conj(V2a)*(-Y + (2*Y)*V2a -Y*V3a))", "description": "", "templateType": "anything", "can_override": false}, "V3": {"name": "V3", "group": "Outputs", "definition": "abs(V3c)", "description": "", "templateType": "anything", "can_override": false}, "delta3": {"name": "delta3", "group": "Outputs", "definition": "180*arg(V3c)/pi", "description": "", "templateType": "anything", "can_override": false}, "PG2percentage": {"name": "PG2percentage", "group": "Given", "definition": "random(0 .. 0.9#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "V20": {"name": "V20", "group": "Given", "definition": "random(1.01 .. 1.07#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "delta2a": {"name": "delta2a", "group": "Computed", "definition": "arg((conj(S2a)/conj(V20) + Y + Y)/(2*Y))", "description": "", "templateType": "anything", "can_override": false}, "S2a": {"name": "S2a", "group": "Computed", "definition": "PG2 + Q2a*i", "description": "", "templateType": "anything", "can_override": false}, "delta2b": {"name": "delta2b", "group": "Computed", "definition": "arg((conj(S2b)/conj(V2a) + Y + Y*V3a)/(2*Y))", "description": "", "templateType": "anything", "can_override": false}, "S2b": {"name": "S2b", "group": "Computed", "definition": "PG2 + Q2b*i", "description": "", "templateType": "anything", "can_override": false}, "V2b": {"name": "V2b", "group": "Computed", 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[], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the Y-matrix in per-unit:</p>\n<p></p>\n<p>j&nbsp;*&nbsp;</p>", "correctAnswer": "matrix([im(2*Y),-im(Y),-im(Y)],[-im(Y),im(2*Y),-im(Y)],[-im(Y),-im(Y),im(2*Y)]) ", "correctAnswerFractions": false, "numRows": "3", "numColumns": "3", "allowResize": false, "tolerance": "0.01", "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}, {"type": "gapfill", "useCustomName": true, "customName": "Voltage", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the voltage at bus 3 after three iterations of the Gauss-Seidel method?</p>\n<p>$V_3$&nbsp;=&nbsp;[[0]]&nbsp; $\\angle$ [[1]]$^o \\ p.u.$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "V3", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "V3*0.99", "maxValue": "V3*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "delta3", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", 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"<p>Calculate the reactive power produced at bus 2:*</p>\n<p>$Q_2$&nbsp;=&nbsp;[[0]]&nbsp;&nbsp;p.u.</p>\n<p>As a result, approximate the reactive power flow at bus 1:*</p>\n<p>$Q_1$ =&nbsp;[[1]]&nbsp;p.u.</p>\n<p>*note: in both cases enter a positive value</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Q2", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Q2*0.99", "maxValue": "Q2*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, 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