// Numbas version: finer_feedback_settings
{"name": "Fault Analysis 5 Bus", "extensions": [], "custom_part_types": [], "resources": [["question-resources/FA5Bus.png", "/srv/numbas/media/question-resources/FA5Bus.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fault Analysis 5 Bus", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p style=\"text-align: center;\">In the system shown in <strong>Figure 1</strong>, the transformers are connected star-star with both star points grounded and the generators are connected in star with their star points grounded. The system base is {SBASE} MVA. The transformers all have reactances of {Tpu} p.u. on this {SBASE} MVA base. The reactances of all other elements are given in <strong>Table</strong>&nbsp;<strong>1</strong>&nbsp;(in $\\Omega$)<strong>&nbsp;</strong>and the&nbsp;voltage levels are given in&nbsp;<strong>Table 2</strong>.</p>\n<p style=\"text-align: center;\">{image('resources/question-resources/FA5Bus.png')}</p>\n<p style=\"text-align: center;\"><strong><em>Figure 1: A section of the distribution system</em></strong></p>\n<p style=\"text-align: center;\"><strong><em></em></strong></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr style=\"height: 44px;\">\n<td width=\"74\" style=\"text-align: center; height: 44px;\">\n<p>&nbsp;</p>\n</td>\n<td width=\"74\" style=\"text-align: center; height: 44px;\">\n<p><strong>G1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center; height: 44px;\">\n<p style=\"text-align: center;\"><strong>L</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center; height: 44px;\">\n<p style=\"text-align: center;\"><strong>G2</strong></p>\n</td>\n</tr>\n<tr style=\"height: 49.8889px;\">\n<td width=\"74\" style=\"text-align: center; height: 49.8889px;\">\n<p><strong>X</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center; height: 49.8889px;\">\n<p>{G1}</p>\n</td>\n<td width=\"74\" style=\"text-align: center; height: 49.8889px;\">\n<p>{L}</p>\n</td>\n<td width=\"74\" style=\"text-align: center; height: 49.8889px;\">\n<p>{G2}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong></strong></em><em><strong>&nbsp;Table 1: Sequence reactances </strong></em><strong>($\\Omega$)</strong></p>\n<p style=\"text-align: center;\"><strong></strong></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr style=\"height: 44px;\">\n<td width=\"74\" style=\"height: 44px;\">\n<p>&nbsp;</p>\n</td>\n<td width=\"74\" style=\"height: 44px; text-align: center;\">\n<p><strong>G1</strong></p>\n</td>\n<td width=\"74\" style=\"height: 44px; text-align: center;\">\n<p><strong>T1</strong></p>\n</td>\n<td width=\"74\" style=\"height: 44px; text-align: center;\">\n<p><strong>L</strong></p>\n</td>\n<td width=\"74\" style=\"height: 44px; text-align: center;\">\n<p><strong>T2</strong></p>\n</td>\n<td width=\"74\" style=\"height: 44px; text-align: center;\">\n<p><strong>G2</strong></p>\n</td>\n<td width=\"74\" style=\"height: 44px; text-align: center;\">\n<p><strong>T3</strong></p>\n</td>\n</tr>\n<tr style=\"height: 52.2118px;\">\n<td width=\"74\" style=\"height: 52.2118px;\">\n<p><strong>V&nbsp;<sub>BASE</sub></strong></p>\n</td>\n<td width=\"74\" style=\"height: 52.2118px; text-align: center;\">\n<p>{VG1}</p>\n</td>\n<td width=\"74\" style=\"height: 52.2118px; text-align: center;\">\n<p>{VG1}/{VL}</p>\n</td>\n<td width=\"74\" style=\"height: 52.2118px; text-align: center;\">\n<p>{VL}</p>\n</td>\n<td width=\"74\" style=\"height: 52.2118px; text-align: center;\">\n<p>{VL}/{VG2}</p>\n</td>\n<td width=\"74\" style=\"height: 52.2118px; text-align: center;\">\n<p>{VG2}</p>\n</td>\n<td width=\"74\" style=\"height: 52.2118px; text-align: center;\">\n<p>{VL}/{V3}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 2: Voltage bases </strong></em><strong>(kV)</strong></p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"G1": {"name": "G1", "group": "Ungrouped variables", "definition": "precround(0.1*random(1..9)*Xpu*(VG1^2/SBASE),2)", "description": "", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "precround(0.1*random(1..9)*Xpu*(VL^2/SBASE),2)", "description": "", "templateType": "anything", "can_override": false}, "Xpu": {"name": "Xpu", "group": "Ungrouped variables", "definition": "random(0.1 .. 0.25#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "SBASE": {"name": "SBASE", "group": "Ungrouped variables", "definition": "random(5 .. 20#5)", "description": "", "templateType": "randrange", "can_override": false}, "AMatrix": {"name": "AMatrix", "group": "Calculated", "definition": "matrix([1,1,1],[1,a^2,a],[1,a,a^2])", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Calculated", "definition": "cos(pi*120/180)+i*sin(pi*120/180)", "description": "", "templateType": "anything", "can_override": false}, "IFpu": {"name": "IFpu", "group": "Calculated", "definition": "1/XTH", "description": "", "templateType": "anything", "can_override": false}, "G2": {"name": "G2", "group": "Ungrouped variables", "definition": "precround(0.1*random(1..9)*Xpu*(VG2^2/SBASE),2)", "description": "", "templateType": "anything", "can_override": false}, "Tpu": {"name": "Tpu", "group": "Ungrouped variables", "definition": "precround(0.1*random(1..9)*Xpu,2)", "description": "", "templateType": "anything", "can_override": false}, "VG1": {"name": "VG1", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "VG2": {"name": "VG2", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "VL": {"name": "VL", "group": "Ungrouped variables", "definition": "random(10 .. 50#5)", "description": "", "templateType": "randrange", "can_override": false}, "V3": {"name": "V3", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "G1pu": {"name": "G1pu", "group": "Calculated", "definition": "G1/(VG1^2/SBASE)", "description": "", "templateType": "anything", "can_override": false}, "G2pu": {"name": "G2pu", "group": "Calculated", "definition": "G2/(VG2^2/SBASE)", "description": "", "templateType": "anything", "can_override": false}, "Lpu": {"name": "Lpu", "group": "Calculated", "definition": "L/(VL^2/SBASE)", "description": "", "templateType": "anything", "can_override": false}, "IFkA": {"name": "IFkA", "group": "Calculated", "definition": "IFpu*IFBASE", "description": "", "templateType": "anything", "can_override": false}, "IFBASE": {"name": "IFBASE", "group": "Calculated", "definition": "SBASE/(V3*sqrt(3))", "description": "", "templateType": "anything", "can_override": false}, "XFpu": {"name": "XFpu", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.05#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "XTH": {"name": "XTH", "group": "Calculated", "definition": "XFpu+Tpu+((G1pu+Tpu)*(G2pu+Tpu+Lpu)/(G1pu+Tpu+Lpu+G2pu+Tpu))", "description": "", "templateType": "anything", "can_override": false}, "VFpu": {"name": "VFpu", "group": "Calculated", "definition": "XFpu*IFpu", "description": "", "templateType": "anything", "can_override": false}, "VF": {"name": "VF", "group": "Calculated", "definition": "1000*VFpu*V3", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["XFpu", "G1", "L", "Xpu", "SBASE", "G2", "Tpu", "VG1", "VG2", "VL", "V3"], "variable_groups": [{"name": "Calculated", "variables": ["a", "AMatrix", "G1pu", "G2pu", "IFBASE", "IFkA", "IFpu", "Lpu", "VF", "VFpu", "XTH"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Per-Unit", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Convert all values to p.u. on a {SBASE} MVA base.</p>\n<p>$ X_{G1} $ =&nbsp;[[0]]&nbsp;p.u.</p>\n<p>$ X_{G2} $ =&nbsp;[[1]]&nbsp;p.u.</p>\n<p>$X_L $ =&nbsp;[[2]]&nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "G1pu", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*G1pu", "maxValue": "1.01*G1pu", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "G2pu", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*G2pu", "maxValue": "1.01*G2pu", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Lpu", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*Lpu", "maxValue": "1.01*Lpu", "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": "Fault Current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A three-phase fault with a fault reactance of {XFpu}&nbsp;p.u. occurs at bus 3. Calculate the fault current flowing&nbsp;at the fault point in kA.</p>\n<p>$ I_F $ = -j&nbsp;[[0]]&nbsp; kA</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IFkA", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IFkA", "maxValue": "1.01*IFkA", "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": "Fault 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 3 (in Volts) after the fault has occurred?</p>\n<p>$V_F$ =&nbsp;[[0]] V</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "VF", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*VF", "maxValue": "1.01*VF", "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", "type": "question", "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}]}]}], "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}]}