// Numbas version: finer_feedback_settings
{"name": "Fault Analysis - Practice", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "40", "showQuestionGroupNames": false, "showstudentname": false, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Fault Analysis 3 Bus", "extensions": [], "custom_part_types": [], "resources": [["question-resources/FA3Bus.png", "/srv/numbas/media/question-resources/FA3Bus.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: center;\">In the system shown in <strong>Figure 1</strong>, the transformer is connected star-star with both star points grounded and the generator is connected in star with its star point grounded. The per unit sequence reactances of each element on a {SBASE} MVA base are given in <strong>Table 1</strong> and the voltage levels are given in <strong>Table 2</strong>.</p>\n<p style=\"text-align: center;\">{image('resources/question-resources/FA3Bus.png')}</p>\n<p style=\"text-align: center;\"><strong><em>Figure 1: A section of the distribution system</em></strong></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p>&nbsp;</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>G1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>T1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p style=\"text-align: center;\"><strong>L</strong></p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>X<sub>1</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G12}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T120}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{L12}</p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>X<sub>2</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G12}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T120}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{L12}</p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>X<sub>0</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G0}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T120}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{L0}</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 (p.u. on {SBASE} MVA base)</strong></em></p>\n<p style=\"text-align: center;\"><em><strong></strong></em></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p>&nbsp;</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>G1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>T1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>L</strong></p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>V&nbsp;<sub>BASE</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{VG}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{VG}/{VL}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{VL}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 1: Voltage bases (kV)</strong></em></p>\n<p style=\"text-align: center;\"><strong><em></em></strong></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"VL": {"name": "VL", "group": "Ungrouped variables", "definition": "random(20 .. 50#2)", "description": "", "templateType": "randrange", "can_override": false}, "G12": {"name": "G12", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.15#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "G0": {"name": "G0", "group": "Ungrouped variables", "definition": "precround(ratio*G12,2)", "description": "", "templateType": "anything", "can_override": false}, "L0": {"name": "L0", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.15#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "L12": {"name": "L12", "group": "Ungrouped variables", "definition": "precround(ratio*L0,2)", "description": "", "templateType": "anything", "can_override": false}, "T120": {"name": "T120", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.15#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "VG": {"name": "VG", "group": "Ungrouped variables", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "ratio": {"name": "ratio", "group": "Ungrouped variables", "definition": "random(0.5 .. 0.9#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "SBASE": {"name": "SBASE", "group": "Ungrouped variables", "definition": "random(10 .. 100#10)", "description": "", "templateType": "randrange", "can_override": false}, "I1": {"name": "I1", "group": "Calculated", "definition": "-i/(2*X12)", "description": "", "templateType": "anything", "can_override": false}, "IFkA": {"name": "IFkA", "group": "Calculated", "definition": "IFpu*SBASE/(sqrt(3)*VL)", "description": "", "templateType": "anything", "can_override": false}, "IGkA": {"name": "IGkA", "group": "Calculated", "definition": "IFpu*SBASE/(sqrt(3)*VG)", "description": "", "templateType": "anything", "can_override": false}, "X0": {"name": "X0", "group": "Calculated", "definition": "G0+T120+L0", "description": "", "templateType": "anything", "can_override": false}, "X12": {"name": "X12", "group": "Calculated", "definition": "G12+T120+L12", "description": "", "templateType": "anything", "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": "abs((a^2-a)*I1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["VG", "VL", "G12", "G0", "T120", "L12", "L0", "ratio", "SBASE"], "variable_groups": [{"name": "Calculated", "variables": ["I1", "IFkA", "IGkA", "X0", "X12", "AMatrix", "a", "IFpu"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Fault Current (p.u.)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If a&nbsp;line-line fault occurs at bus&nbsp;3 with zero fault impedance, calculate the magnitude of the fault current flowing between phases at the fault point (in p.u.).</p>\n<p>$ I $ =&nbsp;&nbsp;[[0]] &nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IFpu", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IFpu", "maxValue": "1.01*IFpu", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Fault Current (kA)", "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 fault current at the fault point in kA?</p>\n<p>$ I $ =&nbsp; [[0]] kA</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IFkA", "marks": "5", "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, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Generator Current (kA)", "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 fault current flowing from the generator in kA?</p>\n<p>$ I $ =&nbsp; [[0]] kA</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IGkA", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IGkA", "maxValue": "1.01*IGkA", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Fault Analysis 4 Bus", "extensions": [], "custom_part_types": [], "resources": [["question-resources/FA4Bus.png", "/srv/numbas/media/question-resources/FA4Bus.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: center;\">In the system shown in <strong>Figure 1</strong>, the transformers&nbsp;are connected star-star with both star points grounded and the generators&nbsp;are connected in star with thier star points grounded. The per unit sequence reactances of each element on a {SBASE} MVA base are given in <strong>Table 1</strong>.</p>\n<p style=\"text-align: center;\">{image('resources/question-resources/FA4Bus.png')}</p>\n<p style=\"text-align: center;\"><strong><em>Figure 1: A section of the distribution system</em></strong></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p>&nbsp;</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>G1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>T1</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p style=\"text-align: center;\"><strong>L</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p style=\"text-align: center;\"><strong>T2</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p style=\"text-align: center;\"><strong>G2</strong></p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>X<sub>1</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G112}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T1}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{L12}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T2}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G212}</p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>X<sub>2</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G112}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T1}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{L12}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T2}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G212}</p>\n</td>\n</tr>\n<tr>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>X<sub>0</sub></strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G10}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T1}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{L0}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{T2}</p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p>{G20}</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 (p.u. on {SBASE} MVA base)</strong></em></p>", "advice": "", "rulesets": {}, "variables": {"G112": {"name": "G112", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange"}, "G10": {"name": "G10", "group": "Ungrouped variables", "definition": "precround(ratio*G112,2)", "description": "", "templateType": "anything"}, "L0": {"name": "L0", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange"}, "L12": {"name": "L12", "group": "Ungrouped variables", "definition": "precround(ratio*L0,2)", "description": "", "templateType": "anything"}, "T1": {"name": "T1", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange"}, "ratio": {"name": "ratio", "group": "Ungrouped variables", "definition": "random(0.1 .. 0.5#0.1)", "description": "", "templateType": "randrange"}, "SBASE": {"name": "SBASE", "group": "Ungrouped variables", "definition": "random(10 .. 100#10)", "description": "", "templateType": "randrange"}, "I120": {"name": "I120", "group": "Calculated", "definition": "-i/(2*X12 + X0 + 3*XF)", "description": "", "templateType": "anything"}, "X0": {"name": "X0", "group": "Calculated", "definition": "(G10+T1+L0)*(G20+T2)/(G10+T1+L0+G20+T2)", "description": "", "templateType": "anything"}, "X12": {"name": "X12", "group": "Calculated", "definition": "(G112+T1+L12)*(G212+T2)/(G112+T1+L12+G212+T2)", "description": "", "templateType": "anything"}, "XF": {"name": "XF", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.05#0.01)", "description": "", "templateType": "randrange"}, "AMatrix": {"name": "AMatrix", "group": "Calculated", "definition": "matrix([1,1,1],[1,a^2,a],[1,a,a^2])", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Calculated", "definition": "cos(pi*120/180)+i*sin(pi*120/180)", "description": "", "templateType": "anything"}, "IFpu": {"name": "IFpu", "group": "Calculated", "definition": "abs((3*I120))", "description": "", "templateType": "anything"}, "T2": {"name": "T2", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange"}, "G212": {"name": "G212", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange"}, "G20": {"name": "G20", "group": "Ungrouped variables", "definition": "precround(ratio*G212,2)", "description": "", "templateType": "anything"}, "V0": {"name": "V0", "group": "Calculated", "definition": "-i*X0*I120", "description": "", "templateType": "anything"}, "V1": {"name": "V1", "group": "Calculated", "definition": "1-i*X12*I120", "description": "", "templateType": "anything"}, "V2": {"name": "V2", "group": "Calculated", "definition": "-i*X12*I120", "description": "", "templateType": "anything"}, "VA": {"name": "VA", "group": "Calculated", "definition": "abs(V0+V1+V2)", "description": "", "templateType": "anything"}, "VB": {"name": "VB", "group": "Calculated", "definition": "abs(1*V0+(a^2)*V1+a*V2)", "description": "", "templateType": "anything"}, "VC": {"name": "VC", "group": "Calculated", "definition": "abs(1*V0+a*V1+(a^2)*V2)", "description": "", "templateType": "anything"}, "deltaA": {"name": "deltaA", "group": "Calculated", "definition": "0", "description": "", "templateType": "anything"}, "deltaB": {"name": "deltaB", "group": "Calculated", "definition": "180*arg(1*V0+(a^2)*V1+a*V2)/pi", "description": "", "templateType": "anything"}, "deltaC": {"name": "deltaC", "group": "Calculated", "definition": "180*arg(1*V0+a*V1+(a^2)*V2)/pi", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["XF", "G112", "G10", "T1", "L12", "L0", "ratio", "SBASE", "T2", "G212", "G20"], "variable_groups": [{"name": "Calculated", "variables": ["I120", "X0", "X12", "AMatrix", "a", "IFpu", "V0", "V1", "V2", "VA", "VB", "VC", "deltaA", "deltaB", "deltaC"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>If a&nbsp;single-phase fault occurs at bus&nbsp;3 with a fault reactance of {XF} p.u. calculate the fault current flowing&nbsp;at the fault point (in p.u.).</p>\n<p>$ I_F $ = -j&nbsp;[[0]] &nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IFpu", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.999*IFpu", "maxValue": "1.001*IFpu", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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 are the voltages on each phase at the fault point (in p.u.) after the fault occurs? (Assume the fault is on the A-phase)</p>\n<p>$ V_A $ =&nbsp;[[0]] $\\angle \\ 0 \\ ^o $&nbsp;&nbsp;p.u.</p>\n<p>$ V_B $ =&nbsp;[[1]]&nbsp;$\\angle$&nbsp; [[2]]&nbsp;p.u.</p>\n<p>$ V_C $ =&nbsp; [[3]]&nbsp;$\\angle$&nbsp;[[4]]&nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "VA", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.999*VA", "maxValue": "1.001*VA", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "VB", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.999*VB", "maxValue": "1.001*VB", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "deltaB", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*deltaB", "maxValue": "1.01*deltaB", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "VC", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.999*VC", "maxValue": "1.001*VC", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "deltaC", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*deltaC", "maxValue": "1.01*deltaC", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"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}, "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: 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": {}, "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"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": false, "browse": false, "allowsteps": false, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": false, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": false, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": false, "reviewshowexpectedanswer": true, "reviewshowadvice": false, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "never", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "type": "exam", "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/FA3Bus.png", "/srv/numbas/media/question-resources/FA3Bus.png"], ["question-resources/FA4Bus.png", "/srv/numbas/media/question-resources/FA4Bus.png"], ["question-resources/FA5Bus.png", "/srv/numbas/media/question-resources/FA5Bus.png"]]}