// Numbas version: finer_feedback_settings
{"name": "Fault 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": "Fault Analysis 3 Bus", "extensions": [], "custom_part_types": [], "resources": ["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, "j": false}, "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": "20", "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, "displayAnswer": "", "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": "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": "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": "10", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Fault Analysis 4 Bus", "extensions": [], "custom_part_types": [], "resources": ["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": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"G112": {"name": "G112", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "G10": {"name": "G10", "group": "Ungrouped variables", "definition": "precround(ratio*G112,2)", "description": "", "templateType": "anything", "can_override": false}, "L0": {"name": "L0", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#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}, "T1": {"name": "T1", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "ratio": {"name": "ratio", "group": "Ungrouped variables", "definition": "random(0.1 .. 0.5#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}, "I120": {"name": "I120", "group": "Calculated", "definition": "-i/(2*X12 + X0 + 3*XF)", "description": "", "templateType": "anything", "can_override": false}, "X0": {"name": "X0", "group": "Calculated", "definition": "(G10+T1+L0)*(G20+T2)/(G10+T1+L0+G20+T2)", "description": "", "templateType": "anything", "can_override": false}, "X12": {"name": "X12", "group": "Calculated", "definition": "(G112+T1+L12)*(G212+T2)/(G112+T1+L12+G212+T2)", "description": "", "templateType": "anything", "can_override": false}, "XF": {"name": "XF", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.05#0.01)", "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": "abs((3*I120))", "description": "", "templateType": "anything", "can_override": false}, "T2": {"name": "T2", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "G212": {"name": "G212", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "G20": {"name": "G20", "group": "Ungrouped variables", "definition": "precround(ratio*G212,2)", "description": "", "templateType": "anything", "can_override": false}, "V0": {"name": "V0", "group": "Calculated", "definition": "-i*X0*I120", "description": "", "templateType": "anything", "can_override": false}, "V1": {"name": "V1", "group": "Calculated", "definition": "1-i*X12*I120", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Calculated", "definition": "-i*X12*I120", "description": "", "templateType": "anything", "can_override": false}, "VA": {"name": "VA", "group": "Calculated", "definition": "abs(V0+V1+V2)", "description": "", "templateType": "anything", "can_override": false}, "VB": {"name": "VB", "group": "Calculated", "definition": "abs(1*V0+(a^2)*V1+a*V2)", "description": "", "templateType": "anything", "can_override": false}, "VC": {"name": "VC", "group": "Calculated", "definition": "abs(1*V0+a*V1+(a^2)*V2)", "description": "", "templateType": "anything", "can_override": false}, "deltaA": {"name": "deltaA", "group": "Calculated", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "deltaB": {"name": "deltaB", "group": "Calculated", "definition": "180*arg(1*V0+(a^2)*V1+a*V2)/pi", "description": "", "templateType": "anything", "can_override": false}, "deltaC": {"name": "deltaC", "group": "Calculated", "definition": "180*arg(1*V0+a*V1+(a^2)*V2)/pi", "description": "", "templateType": "anything", "can_override": false}}, "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": "20", "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, "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 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": "4", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "VB", "marks": "4", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "deltaB", "marks": "4", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "VC", "marks": "4", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "deltaC", "marks": "4", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Fault Analysis 5 Bus", "extensions": [], "custom_part_types": [], "resources": ["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, "j": false}, "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": "4", "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": "4", "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": "4", "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": "20", "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": "8", "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"}, {"name": "Protection 4-bus", "extensions": [], "custom_part_types": [], "resources": ["question-resources/Protection4Bus_AF81T62.png", "question-resources/Protection4Bus_OqI6k2p.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;\">The system shown in <strong>Figure 1</strong>, is a subsection of a {Vbase} kV, {Sbase} MVA system with an embedded generator ready to be deployed on bus 3. The generator at bus 1 represents the bulk supply point (BSP) at rated voltage. The per unit sequence impedances of each element on a {Sbase} MVA base are given in <strong>Table 1</strong>.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/Protection4Bus_OqI6k2p.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=\"width: 400px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p style=\"text-align: center;\"><strong>Section&nbsp;</strong></p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p><strong>R</strong></p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p style=\"text-align: center;\"><strong>X</strong></p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p><b>1-2</b></p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p>{R12}</p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p>{X12}</p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p><strong>2-3</strong></p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p>{R23}</p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p>{X23}</p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p><strong>2-4</strong></p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p>{R24}</p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p>{X24}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 1: Intrinsic impedances (p.u. on {SBASE} MVA base)&nbsp; &nbsp;</strong></em></p>\n<p style=\"text-align: left;\"><em><strong>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</strong></em></p>\n<p>The system is protected with overcurrent relays at buses 1 and 2, looking downstream, with inverse-time relationships given by:</p>\n<p>&nbsp;\\[ t = \\frac{TMS \\times K}{{\\left( \\frac{I_F} {I_P}\\right)}^\\alpha - 1} \\]</p>\n<p>The relay settings are shown in <strong>Table 2</strong>.</p>\n<table border=\"1\" cellpadding=\"1\" style=\"width: 800px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 62.7266px;\"><strong>relay</strong></td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>1-2</p>\n</td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>2-3</p>\n</td>\n<td style=\"width: 48.6641px; text-align: center;\">\n<p>2-4</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 62.7266px;\"><strong>Curve Type</strong></td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>{curves[C[0]]}</p>\n</td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>{curves[C[1]]}</p>\n</td>\n<td style=\"width: 48.6641px; text-align: center;\">\n<p>{curves[C[2]]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 62.7266px;\"><strong>TMS</strong></td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>{TMS[0]}</p>\n</td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>{TMS[1]}</p>\n</td>\n<td style=\"width: 48.6641px; text-align: center;\">\n<p>{TMS[2]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 62.7266px;\"><strong>$I_P$ [kA]</strong></td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>{IP[0]}</p>\n</td>\n<td style=\"width: 107.805px; text-align: center;\">\n<p>{IP[1]}</p>\n</td>\n<td style=\"width: 48.6641px; text-align: center;\">\n<p>{IP[2]}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong></strong></em><em><strong>&nbsp;Table 2: Relay parameters</strong></em></p>\n<p>Under normal conditions, the maximum load current to bus 3 is {1000*ILmax[1]} A, to bus 4 is {1000*ILmax[2]} A and from bus 1 is {1000*ILmax[0]} A.</p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": true}, "constants": [], "variables": {"r12": {"name": "r12", "group": "Given", 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"displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "FL4", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*FL4", "maxValue": "1.01*FL4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t12F4", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t12F4", "maxValue": "1.01*t12F4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t24F4", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t24F4", "maxValue": "1.01*t24F4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "m_n_2", "useCustomName": true, "customName": "Relay Suitability", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Plot the inverse time curves for each relay. Are these relays and their settings suitable? (tick as many as apply)</p>", "minMarks": 0, "maxMarks": "6", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "markingMethod": "sum ticked cells", "choices": "suitabilities", "matrix": "suitability_grade"}, {"type": "gapfill", "useCustomName": true, "customName": "Generator Installed", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The generator at bus 3 is then deployed, running at full voltage. The generator is protected with an overcurrent relay with the following settings:</p>\n<table border=\"1\" cellpadding=\"1\" style=\"width: 300px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 103.125px;\"><strong>Curve Type</strong></td>\n<td style=\"width: 163.875px;\">\n<p>{curves[C[3]]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 103.125px;\"><strong>TMS</strong></td>\n<td style=\"width: 163.875px;\">\n<p>{TMS[3]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 103.125px;\"><strong>$I_P [kA]$</strong></td>\n<td style=\"width: 163.875px;\">\n<p>{IP[3]}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong></strong></em><em><strong>&nbsp;Table 3: Relay parameters</strong></em></p>\n<p></p>\n<p>The generator has a critical point before instability at a current of {ICCG} kA. It can maintain this current for {tccG} seconds before going unstable. The maximum load current from the generator is {1000*ILmax[3]} A.</p>\n<p>Again, assuming zero fault impedance, calculate the symmetrical Fault Level (in MVA) and Fault Current (in kA) at bus 4 with the generator installed. Calculate the tripping times for this fault at each relay in this case:</p>\n<table style=\"height: 62px; width: 800px; margin-left: auto; margin-right: auto;\" border=\"1\" width=\"800\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 40.375px;\">bus</td>\n<td style=\"height: 18px; width: 79.6328px;\">IF [kA]</td>\n<td style=\"height: 18px; width: 84.6719px;\">FL [MVA]</td>\n<td style=\"width: 101.781px; height: 18px;\">relay 1-2 [s]</td>\n<td style=\"width: 101.781px;\">relay 2-4 [s]</td>\n<td style=\"width: 94.7578px; height: 18px;\">relay EG [s]</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 40.375px;\">4</td>\n<td style=\"height: 22px; width: 79.6328px;\">[[0]]</td>\n<td style=\"height: 22px; width: 84.6719px;\">[[1]]</td>\n<td style=\"width: 101.781px; height: 22px;\">[[2]]</td>\n<td style=\"width: 101.781px;\">[[3]]</td>\n<td style=\"width: 94.7578px; height: 22px;\">[[4]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IF4G", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IF4GkA", "maxValue": "1.01*IF4GkA", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "FL4G", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*FL4G", "maxValue": "1.01*FL4G", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t12F4G", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t12F4G", "maxValue": "1.01*t12F4G", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t24F4G", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t24F4G", "maxValue": "1.01*t24F4G", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "tEGF4", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*tEGF4", "maxValue": "1.01*tEGF4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "m_n_2", "useCustomName": true, "customName": "Relay Suitability", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Add the inverse time curves for bus 3 generator's protection relay to the previous plot. Are these relays and their settings suitable for the scenario with this generator deployed? (tick as many as apply)</p>", "minMarks": 0, "maxMarks": "8", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "markingMethod": "sum ticked cells", "choices": "suitabilitiesG", "matrix": "suitability_gradeG"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Protection 3-bus", "extensions": [], "custom_part_types": [], "resources": ["question-resources/EG3Bus.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 generator is operating at full voltage. The per unit sequence impedances 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/EG3Bus.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=\"width: 400px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p>&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p><strong>Transformer</strong></p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p style=\"text-align: center;\"><strong>Line</strong></p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p><b>R</b></p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p>{RT}</p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p>{RL}</p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 34.1518px;\">\n<p><strong>X</strong></p>\n</td>\n<td style=\"text-align: center; width: 102.183px;\">\n<p>{XT}</p>\n</td>\n<td style=\"text-align: center; width: 51.579px;\">\n<p>{XL}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 1: Intrinsic impedances (p.u. on {SBASE} MVA base)&nbsp; &nbsp;</strong></em></p>\n<table border=\"1\" cellpadding=\"1\" style=\"width: 400px; 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>Generator</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>Transformer</strong></p>\n</td>\n<td width=\"74\" style=\"text-align: center;\">\n<p><strong>Line</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>&nbsp;</strong></em><em><strong>Table 2: Voltage bases (kV)</strong></em></p>\n<p style=\"text-align: left;\"><em><strong>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</strong></em></p>\n<p>The system is protected with overcurrent relays at buses 1 and 2, looking downstream, with inverse-time relationships given by:</p>\n<p>&nbsp;\\[ t = \\frac{TMS \\times K}{{\\left( \\frac{I_F} {I_P}\\right)}^\\alpha - 1} \\]</p>\n<p>The relay settings are shown in <strong>Table 3</strong>.</p>\n<table border=\"1\" cellpadding=\"1\" style=\"width: 600px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>relay bus</strong></td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>1</p>\n</td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>2</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>Curve Type</strong></td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>{curves[C[0]]}</p>\n</td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>{curves[C[1]]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>TMS</strong></td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>{TMS[0]}</p>\n</td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>{TMS[1]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>$I_P [kA]$</strong></td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>{IP[0]}</p>\n</td>\n<td style=\"width: 107.804px; text-align: center;\">\n<p>{IP[1]}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong></strong></em><em><strong>&nbsp;Table 3: Relay parameters</strong></em></p>\n<p>The generator has a critical point before instability at a current of {ICC[0]} kA. It can maintain this current for {tcc} s before going unstable. The maximum load current from this generator is {1000*ILmax[0]} A.</p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"VL": {"name": "VL", "group": "Given", "definition": "random([10,11,20])", "description": "", "templateType": "anything", "can_override": false}, "VG": {"name": "VG", "group": "Given", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "SBASE": {"name": "SBASE", "group": "Given", "definition": "random(3 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "rt": {"name": "rt", "group": "Given", "definition": "0.1*random(1..2)*xt", "description": "", "templateType": "anything", "can_override": false}, "rl": {"name": "rl", "group": "Given", "definition": "0.1*random(1..2)*xl", "description": "", "templateType": "anything", "can_override": false}, "xt": {"name": "xt", "group": "Given", "definition": "0.01*random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "xl": {"name": "xl", "group": "Given", "definition": "0.01*random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "IBASE": {"name": "IBASE", "group": "Given", "definition": "[SBASE/(sqrt(3)*VG),SBASE/(sqrt(3)*VL)]", "description": "", "templateType": "anything", "can_override": false}, "icc": {"name": "icc", "group": "Given", "definition": "[precround(random(10..50)*IBASE[0],2),precround(random(10..50)*IBASE[1],2)]", "description": "", "templateType": "anything", "can_override": false}, "tcc": {"name": "tcc", "group": "Given", "definition": "precround(0.01*random(90..120 except 100)*trip12CC,3)", "description": "", "templateType": "anything", "can_override": false}, "ILmax": {"name": "ILmax", "group": "Given", "definition": "[precround(0.01*random(80..120 except 100)*IBASE[0],2),precround(0.01*random(80..120 except 100)*IBASE[1],2)]", "description": "", "templateType": "anything", "can_override": false}, "if2ka": {"name": "if2ka", "group": "Ungrouped variables", "definition": "[IBASE[0]*abs(IF2),IBASE[1]*abs(IF2)]", "description": "", "templateType": "anything", "can_override": false}, "fl2": {"name": "fl2", "group": "Ungrouped variables", "definition": "SBASE*abs(IF2)", "description": "", "templateType": "anything", "can_override": false}, "if3ka": {"name": "if3ka", "group": "Ungrouped variables", "definition": "[IBASE[0]*abs(IF3),IBASE[1]*abs(IF3)]", "description": "", "templateType": "anything", "can_override": false}, "fl3": {"name": "fl3", "group": "Ungrouped variables", "definition": "SBASE*abs(IF3)", "description": "", "templateType": "anything", "can_override": false}, "suitabilities": {"name": "suitabilities", "group": "Ungrouped variables", "definition": "[ 'No, a relay trips for normal current flow',\n  'No, the generator goes unstable before the relay trips',\n  'No, the protection coordination is bad',\n  'Yes, this relay is suitable']", "description": "", "templateType": "anything", "can_override": false}, "t12f2": {"name": "t12f2", "group": "Ungrouped variables", "definition": "TMS[0]*K[0]/((IF2kA[0]/IP[0])^alpha[0]-1)", "description": "", "templateType": "anything", "can_override": false}, "t12f3": {"name": "t12f3", "group": "Ungrouped variables", "definition": "TMS[0]*K[0]/((IF3kA[0]/IP[0])^alpha[0]-1)", "description": "", "templateType": "anything", "can_override": false}, "t23f3": {"name": "t23f3", "group": "Ungrouped variables", "definition": "TMS[1]*K[1]/((IF3kA[1]/IP[1])^alpha[1]-1)", "description": "", "templateType": "anything", "can_override": false}, "TMS": {"name": "TMS", "group": "Ungrouped variables", "definition": "[0.1*random(1..10),0.1*random(1..10),0.1*random(1..10)]", "description": "", "templateType": "anything", "can_override": false}, "IP": {"name": "IP", "group": "Ungrouped variables", "definition": "[precround(0.01*random(90..120 except 100)*ILmax[0],2),precround(0.01*random(80..120 except 100)*ILmax[1],2),precround(0.01*random(80..120 except 100)*ILmaxG,2)]", "description": "", "templateType": "anything", "can_override": false}, "if2kag": {"name": "if2kag", "group": "Ungrouped variables", "definition": "[IBASE[0]*abs(I12G+IEG),IBASE[1]*abs(I12G+IEG)]", "description": "", "templateType": "anything", "can_override": false}, "fl2g": {"name": "fl2g", "group": "Ungrouped variables", "definition": "SBASE*abs(I12G+IEG)", "description": "", "templateType": "anything", "can_override": false}, "t12f2g": {"name": "t12f2g", "group": "Ungrouped variables", "definition": "TMS[0]*K[0]/((I12GkA/IP[0])^alpha[0]-1)", "description": "", "templateType": "anything", "can_override": false}, "tEGf2": {"name": "tEGf2", "group": "Ungrouped variables", "definition": "TMS[2]*K[2]/((IEGkA/IP[2])^alpha[2]-1)", "description": "", "templateType": "anything", "can_override": false}, "curves": {"name": "curves", "group": "Ungrouped variables", "definition": "['standard inverse','very inverse','extremely inverse']", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "[random(0..2),random(0..2),random(0..2)]", "description": "<p>Curve Type: 0 = standard, 1 = very, 2 = extremely</p>", "templateType": "anything", "can_override": false}, "Ks": {"name": "Ks", "group": "Ungrouped variables", "definition": "[0.14,13.5,80]", "description": "", "templateType": "anything", "can_override": false}, "alphas": {"name": "alphas", "group": "Ungrouped variables", "definition": "[0.02,1,2]", "description": "", "templateType": "anything", "can_override": false}, "K": {"name": "K", "group": "Ungrouped variables", "definition": "[Ks[C[0]],Ks[C[1]],Ks[C[2]]]", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "[alphas[C[0]],alphas[C[1]],alphas[C[2]]]", "description": "", "templateType": "anything", "can_override": false}, "suitability_grade": {"name": "suitability_grade", "group": "Ungrouped variables", "definition": "[10*if(trippy>0,1,-1)/SUITABILITY_TOTAL_GRADE,10*if(Unstable>0,1,-1)/SUITABILITY_TOTAL_GRADE,10*if(Uncoordinated>0,1,-1)/SUITABILITY_TOTAL_GRADE,10*if(Suitable>0,1,-1)/SUITABILITY_TOTAL_GRADE]", "description": "", "templateType": "anything", "can_override": false}, "suitability_gradeG": {"name": "suitability_gradeG", "group": "Ungrouped variables", "definition": "[8*if(TrippyG>0,1,-1)/SUITABILITY_TOTAL_GRADE_G,8*if(UnstableG>0,1,-1)/SUITABILITY_TOTAL_GRADE_G,8*if(SuitableG>0,1,-1)/SUITABILITY_TOTAL_GRADE_G]", "description": "", "templateType": "anything", "can_override": false}, "Trippy": {"name": "Trippy", "group": "Ungrouped variables", "definition": "award(1, ILmax[0]>IP[0] || ILmax[1]>IP[1])", "description": "", "templateType": "anything", "can_override": false}, "Unstable": {"name": "Unstable", "group": "Ungrouped variables", "definition": "award(1, (TMS[0]*K[0]/((ICC[0]/IP[0])^alpha[0]-1) > tCC) || (TMS[1]*K[1]/((ICC[1]/IP[1])^alpha[1]-1) > tCC))", "description": "", "templateType": "anything", "can_override": false}, "Uncoordinated": {"name": "Uncoordinated", "group": "Ungrouped variables", "definition": "award(1, t23f3>t12f3)", "description": "", "templateType": "anything", "can_override": false}, "Suitable": {"name": "Suitable", "group": "Ungrouped variables", "definition": "award(1, (Trippy+Unstable+Uncoordinated) = 0)", "description": "", "templateType": "anything", "can_override": false}, "TrippyG": {"name": "TrippyG", "group": "Ungrouped variables", "definition": "award(1, ILmaxG>IP[0] || ILmaxG>IP[2])", "description": "", "templateType": "anything", "can_override": false}, "UnstableG": {"name": "UnstableG", "group": "Ungrouped variables", "definition": "award(1, (trip12CC>tCC) || (tripEGCC > tCCG))", "description": "", "templateType": "anything", "can_override": false}, "I12GkA": {"name": "I12GkA", 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Calculate the tripping times for these faults at each relay:</p>\n<table style=\"height: 62px; width: 600px; margin-left: auto; margin-right: auto;\" border=\"1\" width=\"600\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 54.6048px;\">Fault Bus</td>\n<td style=\"height: 18px; width: 86.6567px;\">IF [kA]</td>\n<td style=\"height: 18px; width: 110.913px;\">FL [MVA]</td>\n<td style=\"width: 97.3462px; height: 18px;\">relay 1-2 [s]</td>\n<td style=\"width: 97.3628px; height: 18px;\">relay 2-3 [s]</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 54.6048px;\">2</td>\n<td style=\"height: 22px; width: 86.6567px;\">[[0]]</td>\n<td style=\"height: 22px; width: 110.913px;\">[[1]]</td>\n<td style=\"width: 97.3462px; height: 22px;\">[[4]]</td>\n<td style=\"width: 97.3628px; height: 22px;\">X</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 54.6048px;\">3</td>\n<td style=\"height: 22px; width: 86.6567px;\">[[2]]</td>\n<td style=\"height: 22px; width: 110.913px;\">[[3]]</td>\n<td style=\"width: 97.3462px; height: 22px;\">[[5]]</td>\n<td style=\"width: 97.3628px; height: 22px;\">[[6]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IF2", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IF2kA[1]", "maxValue": "1.01*IF2kA[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": 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"nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t12F3", "maxValue": "1.01*t12F3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t23F3", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t23F3", "maxValue": "1.01*t23F3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "m_n_2", "useCustomName": true, "customName": "Relay Suitability", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Plot the inverse time curves for each relay. Are these relays and their settings suitable? (tick as many as apply)</p>", "minMarks": 0, "maxMarks": "10", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "markingMethod": "sum ticked cells", "choices": "suitabilities", "matrix": "suitability_grade"}, {"type": "gapfill", "useCustomName": true, "customName": "Generator Installed", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A generator is installed at bus 3, running at full voltage. The generator is protected with an overcurrent relay with the following settings:</p>\n<table border=\"1\" cellpadding=\"1\" style=\"width: 300px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>Curve Type</strong></td>\n<td style=\"width: 107.804px;\">\n<p>{curves[C[2]]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>TMS</strong></td>\n<td style=\"width: 107.804px;\">\n<p>{TMS[2]}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 45.4613px;\"><strong>$I_P [kA]$</strong></td>\n<td style=\"width: 107.804px;\">\n<p>{IP[2]}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong></strong></em><em><strong>&nbsp;Table 3: Relay parameters</strong></em></p>\n<p></p>\n<p>The generator has a critical point before instability at a current of {ICCG} kA. It can maintain this current for {tccG} seconds before going unstable. The maximum load current from the new generator is {1000*ILmaxG} A.</p>\n<p>Again, assuming zero fault impedance, calculate the symmetrical Fault Level (in MVA) and Fault Current (in kA) at bus 2 with the generator installed. Calculate the tripping times for this fault at each relay in this case:</p>\n<table style=\"height: 62px; width: 600px; margin-left: auto; margin-right: auto;\" border=\"1\" width=\"600\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 54.6048px;\">bus</td>\n<td style=\"height: 18px; width: 86.6567px;\">IF [kA]</td>\n<td style=\"height: 18px; width: 110.913px;\">FL [MVA]</td>\n<td style=\"width: 97.3462px; height: 18px;\">relay 1-2 [s]</td>\n<td style=\"width: 97.3628px; height: 18px;\">relay EG [s]</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 54.6048px;\">2</td>\n<td style=\"height: 22px; width: 86.6567px;\">[[0]]</td>\n<td style=\"height: 22px; width: 110.913px;\">[[1]]</td>\n<td style=\"width: 97.3462px; height: 22px;\">[[2]]</td>\n<td style=\"width: 97.3628px; height: 22px;\">[[3]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IF2G", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IF2kAG[1]", "maxValue": "1.01*IF2kAG[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "FL2G", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*FL2G", "maxValue": "1.01*FL2G", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t12F2G", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*t12F2G", "maxValue": "1.01*t12F2G", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "tEGF2", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*tEGF2", "maxValue": "1.01*tEGF2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "m_n_2", "useCustomName": true, "customName": "Relay Suitability", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Add the inverse time curves for bus 3 generator's protection relay to the previous plot. Are these relays and their settings suitable for the scenario with the new generator installed? 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