// Numbas version: exam_results_page_options {"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fault Analysis 4 Bus", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

In the system shown in Figure 1, the transformers are connected star-star with both star points grounded and the generators 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 Table 1.

\n

{image('resources/question-resources/FA4Bus.png')}

\n

Figure 1: A section of the distribution system

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

 

\n
\n

G1

\n
\n

T1

\n
\n

L

\n
\n

T2

\n
\n

G2

\n
\n

X1

\n
\n

{G112}

\n
\n

{T1}

\n
\n

{L12}

\n
\n

{T2}

\n
\n

{G212}

\n
\n

X2

\n
\n

{G112}

\n
\n

{T1}

\n
\n

{L12}

\n
\n

{T2}

\n
\n

{G212}

\n
\n

X0

\n
\n

{G10}

\n
\n

{T1}

\n
\n

{L0}

\n
\n

{T2}

\n
\n

{G20}

\n
\n

 Table 1: Sequence reactances (p.u. on {SBASE} MVA base)

", "advice": "", "rulesets": {}, "extensions": [], "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": "

If a single-phase fault occurs at bus 3 with a fault reactance of {XF} p.u. calculate the fault current flowing at the fault point (in p.u.).

\n

$ I_F $ = -j [[0]]  p.u.

", "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": "

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)

\n

$ V_A $ = [[0]] $\\angle \\ 0 \\ ^o $  p.u.

\n

$ V_B $ = [[1]] $\\angle$  [[2]] p.u.

\n

$ V_C $ =  [[3]] $\\angle$ [[4]] p.u.

", "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", "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}]}]}], "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}]}