// Numbas version: exam_results_page_options
{"name": "Load Flow Analysis - Practice", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "40", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": false, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Load Flow Analysis - 2bus", "extensions": [], "custom_part_types": [], "resources": [["question-resources/LF2bus.png", "/srv/numbas/media/question-resources/LF2bus.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>For the following 2-bus system, bus 1 is the swing bus. Values are given in per-unit on a 10 MVA base:</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/LF2bus.png\"/></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>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>{P2} + j {Q2}</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>\n<p style=\"text-align: center;\"><em><strong></strong></em></p>\n<table border=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr style=\"height: 43px;\">\n<td style=\"text-align: center; height: 43px;\">\n<p><strong>Section</strong></p>\n</td>\n<td style=\"text-align: center; height: 43px;\">\n<p><strong>Series Impedance</strong></p>\n</td>\n</tr>\n<tr style=\"height: 43px;\">\n<td style=\"text-align: center; height: 43px;\">\n<p>1-2</p>\n</td>\n<td style=\"text-align: center; height: 43px;\">\n<p>{R12} + j {X12}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 2: Line information</strong></em></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Y": {"name": "Y", "group": "Computed", "definition": "matrix([y12,-y12],[-y12,y12])", "description": "", "templateType": "anything", "can_override": false}, "R12": {"name": "R12", "group": "Given", "definition": "random(0.005 .. 0.02#0.001)", "description": "", "templateType": "randrange", "can_override": false}, "X12": {"name": "X12", "group": "Given", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Z12": {"name": "Z12", "group": "Given", "definition": "R12+X12*i", "description": "", "templateType": "anything", "can_override": false}, "P2": {"name": "P2", "group": "Given", "definition": "random(0.5 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "Q2": {"name": "Q2", "group": "Given", "definition": "random(0 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "S2": {"name": "S2", "group": "Given", "definition": "-P2 - Q2*i", "description": "", "templateType": "anything", "can_override": false}, "y12": {"name": "y12", "group": "Computed", "definition": "1/Z12", "description": "", "templateType": "anything", "can_override": false}, "delta2": {"name": "delta2", "group": "Computed", "definition": "180*arg(V2g)/pi", "description": "", "templateType": "anything", "can_override": false}, "V2a": {"name": "V2a", "group": "Computed", "definition": "Z12*conj(S2)+1", "description": "", "templateType": "anything", "can_override": false}, "V2b": {"name": "V2b", "group": "Computed", "definition": "Z12*conj(S2)/conj(V2a)+1", "description": "", "templateType": "anything", "can_override": false}, "V2c": {"name": "V2c", "group": "Computed", "definition": "Z12*conj(S2)/conj(V2b)+1", "description": "", "templateType": "anything", "can_override": false}, "V2d": {"name": "V2d", "group": "Computed", "definition": "Z12*conj(S2)/conj(V2c)+1", "description": "", "templateType": "anything", "can_override": false}, "V2e": {"name": "V2e", "group": "Computed", "definition": "Z12*conj(S2)/conj(V2d)+1", "description": "", "templateType": "anything", "can_override": false}, "V2f": {"name": "V2f", "group": "Computed", "definition": "Z12*conj(S2)/conj(V2e)+1", "description": "", "templateType": "anything", "can_override": false}, "V2g": {"name": "V2g", "group": "Computed", "definition": "Z12*conj(S2)/conj(V2f)+1", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Computed", "definition": "abs(V2g)", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Computed", "definition": "re(S1)", "description": "", "templateType": "anything", "can_override": false}, "Q1": {"name": "Q1", "group": "Computed", "definition": "im(S1)", "description": "", "templateType": "anything", "can_override": false}, "S1": {"name": "S1", "group": "Computed", "definition": "conj((1-V2g)/Z12)", "description": "", "templateType": "anything", "can_override": false}, "Ploss": {"name": "Ploss", "group": "Computed", "definition": "re(S1+S2)", "description": "", "templateType": "anything", "can_override": false}, "PlossTest": {"name": "PlossTest", "group": "Ungrouped variables", "definition": "-re((1-V2g)*conj((1-V2g)*(-Y12)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "precround(Ploss,2)=precround(PlossTest,2)", "maxRuns": "1000"}, "ungrouped_variables": ["PlossTest"], "variable_groups": [{"name": "Given", "variables": ["R12", "X12", "Z12", "P2", "Q2", "S2"]}, {"name": "Computed", "variables": ["y12", "Y", "V2a", "V2b", "V2c", "V2d", "V2e", "V2f", "V2g", "V2", "delta2", "S1", "P1", "Q1", "Ploss"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Y-Matrix", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the Y-matrix in per-unit:</p>\n<p>[[0]]+i&nbsp;[[1]]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[2]]+i&nbsp;[[3]]</p>\n<p></p>\n<p>[[4]]+i&nbsp;[[5]]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[6]]+i&nbsp;[[7]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "R11", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "re(y12)*0.99", "maxValue": "re(y12)*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": "X11", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "im(y12)*0.99", "maxValue": "im(y12)*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": "R12", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-re(y12)*0.99", "maxValue": "-re(y12)*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": "X12", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-im(y12)*0.99", "maxValue": "-im(y12)*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": "R21", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-re(y12)*0.99", "maxValue": "-re(y12)*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": "X21", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-im(y12)*0.99", "maxValue": "-im(y12)*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": "R22", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "re(y12)*0.99", "maxValue": "re(y12)*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": "X22", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "im(y12)*0.99", "maxValue": "im(y12)*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Voltage", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the voltage at bus 2?</p>\n<p>$V_2$&nbsp;=&nbsp;[[0]]&nbsp; $\\angle$ [[1]]&nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Voltage", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "V2*0.99", "maxValue": "V2*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": "Delta", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "delta2*0.99", "maxValue": "delta2*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Power", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the power in at bus 1:</p>\n<p>$S_1$&nbsp;=&nbsp;[[0]]&nbsp;+ i&nbsp;[[1]]&nbsp; p.u.</p>\n<p>Calculate the real power lost in the system in per-unit and verify this:</p>\n<p>$P_{LOSS}$ =&nbsp;[[2]] p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "P1", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P1*0.99", "maxValue": "P1*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": "Q1", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Q1*0.99", "maxValue": "Q1*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": "Ploss", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Ploss*0.99", "maxValue": "Ploss*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"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}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "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": {}, "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": "random(0.5 .. 2#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "Q3": {"name": "Q3", "group": "Given", "definition": "random(0.1 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "S3": {"name": "S3", "group": "Computed", "definition": "-P3 - Q3*i", "description": "", "templateType": "anything", "can_override": false}, "delta2": {"name": "delta2", "group": "Outputs", "definition": "180*arg(V2c)/pi", "description": "", "templateType": "anything", "can_override": false}, "V2a": {"name": "V2a", "group": "Computed", "definition": "V20*cos(delta2a)+V20*sin(delta2a)*i", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Outputs", "definition": "abs(V2c)", "description": "", "templateType": "anything", "can_override": false}, "PG2": {"name": "PG2", "group": "Given", "definition": "precround(PG2percentage*P3,1)", "description": "", "templateType": "anything", "can_override": 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", "definition": "V20*cos(delta2b)+V20*sin(delta2b)*i", "description": "", "templateType": "anything", "can_override": false}, "delta2c": {"name": "delta2c", "group": "Computed", "definition": "arg((conj(S2c)/conj(V2b) + Y + Y*V3b)/(2*Y))", "description": "", "templateType": "anything", "can_override": false}, "Q2c": {"name": "Q2c", "group": "Computed", "definition": "-im(conj(V2b)*(-Y + (2*Y)*V2b -Y*V3b))", "description": "", "templateType": "anything", "can_override": false}, "V2c": {"name": "V2c", "group": "Computed", "definition": "V20*cos(delta2c)+V20*sin(delta2c)*i", "description": "", "templateType": "anything", "can_override": false}, "S2c": {"name": "S2c", "group": "Computed", "definition": "PG2 + Q2c*i", "description": "", "templateType": "anything", "can_override": false}, "V3c": {"name": "V3c", "group": "Computed", "definition": "(conj(S3)/conj(V3b) + Y + Y*V2c)/(2*Y) ", "description": "", "templateType": "anything", "can_override": false}, "Q2": {"name": "Q2", "group": "Outputs", "definition": "abs(Q2c)", "description": "", "templateType": "anything", "can_override": false}, "Q1": {"name": "Q1", "group": "Outputs", "definition": "abs(Q2c-Q3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": [], "variable_groups": [{"name": "Given", "variables": ["X", "P3", "Q3", "PG2percentage", "PG2", "V20"]}, {"name": "Computed", "variables": ["Y", "S3", "Q2a", "S2a", "delta2a", "V2a", "V3a", "Q2b", "S2b", "delta2b", "V2b", "V3b", "Q2c", "S2c", "delta2c", "V2c", "V3c"]}, {"name": "Outputs", "variables": ["V2", "delta2", "V3", "delta3", "Q2", "Q1"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": true, "customName": "Y Matrix", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "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": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "delta3*0.99", "maxValue": "delta3*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Power", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<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, "customName": "Q1", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Q1*0.6", "maxValue": "Q1*1.4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Load Flow Analysis - 4bus", "extensions": [], "custom_part_types": [], "resources": [["question-resources/LF2Circuit_GJ385fH.png", "/srv/numbas/media/question-resources/LF2Circuit_GJ385fH.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p style=\"text-align: left;\">For the following 4-bus system, bus 1 is the swing bus. Values are given in per-unit on a 10 MVA base:</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/LF2Circuit_GJ385fH.png\"/></p>\n<p></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>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>?</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<tr>\n<td style=\"text-align: center;\">\n<p>4</p>\n</td>\n<td style=\"text-align: center;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center;\">\n<p>{P4}&nbsp;+ j {Q4}</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>\n<p style=\"text-align: center;\"><em><strong></strong></em></p>\n<table border=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr style=\"height: 43px;\">\n<td style=\"text-align: center; height: 43px;\">\n<p><strong>Section</strong></p>\n</td>\n<td style=\"text-align: center; height: 43px;\">\n<p><strong>Series Impedance</strong></p>\n</td>\n</tr>\n<tr style=\"height: 43px;\">\n<td style=\"text-align: center; height: 43px;\">\n<p>1-2</p>\n</td>\n<td style=\"text-align: center; height: 43px;\">\n<p>j {X12}</p>\n</td>\n</tr>\n<tr style=\"height: 43px;\">\n<td style=\"text-align: center; height: 43px;\">\n<p>2-3</p>\n</td>\n<td style=\"text-align: center; height: 43px;\">\n<p>j {X23}</p>\n</td>\n</tr>\n<tr style=\"height: 37.5742px;\">\n<td style=\"text-align: center; height: 37.5742px;\">2-4</td>\n<td style=\"text-align: center; height: 37.5742px;\">j {X24}</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 2: Line information</strong></em></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Y": {"name": "Y", "group": "Computed", "definition": "matrix([Y12,-Y12,0,0],[-Y12,Y12+Y23+Y24,-Y23,-Y24],[0,-Y23,Y23,0],[0,-Y24,0,Y24])", "description": "", "templateType": "anything", 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"description": "", "templateType": "anything", "can_override": false}, "V2b": {"name": "V2b", "group": "Computed", "definition": "(Y12 + Y23*V3a + Y24*V4a)/(Y12 + Y23 + Y24)", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Computed", "definition": "abs(V2b)", "description": "", "templateType": "anything", "can_override": false}, "X24": {"name": "X24", "group": "Given", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Y24": {"name": "Y24", "group": "Computed", "definition": "1/(X24*i)", "description": "", "templateType": "anything", "can_override": false}, "Y23": {"name": "Y23", "group": "Computed", "definition": "1/(X23*i)", "description": "", "templateType": "anything", "can_override": false}, "P4": {"name": "P4", "group": "Given", "definition": "random(0 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "Q4": {"name": "Q4", "group": "Given", "definition": "random(0 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "S4": {"name": "S4", "group": "Computed", "definition": "-P4 - Q4*i", "description": "", "templateType": "anything", "can_override": false}, "V3a": {"name": "V3a", "group": "Computed", "definition": "(conj(S3) + Y23)/Y23", "description": "", "templateType": "anything", "can_override": false}, "V4a": {"name": "V4a", "group": "Computed", "definition": "(conj(S4) + Y24)/Y24", "description": "", "templateType": "anything", "can_override": false}, "V3b": {"name": "V3b", "group": "Computed", "definition": "((conj(S3)/conj(V3a)) + Y23*V2b)/Y23", "description": "", "templateType": "anything", "can_override": false}, "V4b": {"name": "V4b", "group": "Computed", "definition": "((conj(S4)/conj(V4a)) + Y24*V2b)/Y24", "description": "", "templateType": "anything", "can_override": false}, "V3": {"name": "V3", "group": "Computed", "definition": "abs(V3b)", "description": "", 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{}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "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(Y12),-im(Y12),0,0],[-im(Y12),im(Y12+Y23+Y24),-im(Y23),-im(Y24)],[0,-im(Y23),im(Y23),0],[0,-im(Y24),0,im(Y24)])", "correctAnswerFractions": false, "numRows": "4", "numColumns": "4", "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, 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