// Numbas version: exam_results_page_options
{"name": "Power Systems Studies", "extensions": [], "custom_part_types": [], "resources": [["question-resources/PSScircuit.png", "/srv/numbas/media/question-resources/PSScircuit.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Power Systems Studies", "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 generator is connected in star with&nbsp;its star points grounded. The per unit&nbsp;impedances of each element on a {SBASE} MVA base are given in <strong>Table 1</strong>&nbsp;and the&nbsp;voltage levels are given in&nbsp;<strong>Table 2</strong>.</p>\n<p style=\"text-align: center;\">{image('resources/question-resources/PSScircuit.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;\" width=\"786\" height=\"79\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 139px;\">\n<p>&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 140px;\">\n<p><strong>Generator</strong></p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p><strong>Transformer T1</strong></p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p style=\"text-align: center;\"><strong>Line</strong></p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p style=\"text-align: center;\"><strong>Transformer T2</strong></p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 139px;\">\n<p><strong>Z&nbsp; &nbsp;[p.u.]</strong></p>\n</td>\n<td style=\"text-align: center; width: 140px;\">\n<p>{RG} + j {XG}&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p>{RT1} + j {XT1}&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p>{RL} + j {XL}&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p>{RT2} + j {XT2}&nbsp;</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 impedances (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; width: 486px;\" height=\"122\">\n<tbody>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 115.5px;\">\n<p>&nbsp;</p>\n</td>\n<td style=\"height: 44px; text-align: center; width: 116.5px;\">\n<p><strong>Generator</strong></p>\n</td>\n<td style=\"height: 44px; text-align: center; width: 93px;\">\n<p><strong>Line</strong></p>\n</td>\n<td style=\"height: 44px; text-align: center; width: 96px;\">\n<p><strong>Load</strong></p>\n</td>\n</tr>\n<tr style=\"height: 52.2118px;\">\n<td style=\"height: 52.2118px; width: 115.5px;\">\n<p><strong>V&nbsp;<sub>BASE</sub></strong>&nbsp;&nbsp;<strong>[kV]</strong></p>\n</td>\n<td style=\"height: 52.2118px; text-align: center; width: 116.5px;\">\n<p>{VG}</p>\n</td>\n<td style=\"width: 93px; text-align: center;\">\n<p>{VLine}</p>\n</td>\n<td style=\"width: 96px; text-align: center;\">\n<p>{VLoad}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 2: Voltage bases&nbsp;</strong></em><strong>(kV)</strong></p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"XG": {"name": "XG", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "XL": {"name": "XL", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "XT1": {"name": "XT1", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "SBASE": {"name": "SBASE", "group": "Ungrouped variables", "definition": "random(10 .. 100#10)", "description": "", "templateType": "randrange", "can_override": false}, "IkA": {"name": "IkA", "group": "Calculated", "definition": "precround(Ipu*IBASE,3)", "description": "", "templateType": "anything", "can_override": false}, "XT2": {"name": "XT2", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "V1": {"name": "V1", "group": "Calculated", "definition": "1-(RG+i*XG)*IL", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Calculated", "definition": "V1-(RT1+i*XT1)*IL", "description": "", "templateType": "anything", "can_override": false}, "V3": {"name": "V3", "group": "Calculated", "definition": "V2-(RL+i*XL)*IL", "description": "", "templateType": "anything", "can_override": false}, "V4": {"name": "V4", "group": "Calculated", "definition": "V3-(RT2+i*XT2)*IL", "description": "", "templateType": "anything", "can_override": false}, "delta1": {"name": "delta1", "group": "Calculated", "definition": "180*arg(V1)/pi", "description": "", "templateType": "anything", "can_override": false}, "delta2": {"name": "delta2", "group": "Calculated", "definition": "180*arg(V2)/pi", "description": "", "templateType": "anything", "can_override": false}, "delta3": {"name": "delta3", "group": "Calculated", "definition": "180*arg(V3)/pi", "description": "", "templateType": "anything", "can_override": false}, "RG": {"name": "RG", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "RT1": {"name": "RT1", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "RL": {"name": "RL", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "RT2": {"name": "RT2", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "VG": {"name": "VG", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "Vline": {"name": "Vline", "group": "Ungrouped variables", "definition": "random(5 .. 50#5)", "description": "", "templateType": "randrange", "can_override": false}, "Vload": {"name": "Vload", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "IBASE": {"name": "IBASE", "group": "Calculated", "definition": "SBASE/(sqrt(3)*VLoad)", "description": "", "templateType": "anything", "can_override": false}, "Ipu": {"name": "Ipu", "group": "Calculated", "definition": "random(0.1 .. 0.9#0.01)", "description": "<p>percentage of full load on bus 4</p>", "templateType": "randrange", "can_override": false}, "loading": {"name": "loading", "group": "Calculated", "definition": "IkA/IBASE", "description": "", "templateType": "anything", "can_override": false}, "theta_rad": {"name": "theta_rad", "group": "Calculated", "definition": "-arccos(pf/100)", "description": "", "templateType": "anything", "can_override": false}, "pf": {"name": "pf", "group": "Ungrouped variables", "definition": "random(86 .. 99#2)", "description": "", "templateType": "randrange", "can_override": false}, "theta": {"name": "theta", "group": "Calculated", "definition": "180*theta_rad/pi", "description": "", "templateType": "anything", "can_override": false}, "IL": {"name": "IL", "group": "Calculated", "definition": "Ipu*cos(theta_rad)+i*Ipu*sin(theta_rad)", "description": "", "templateType": "anything", "can_override": false}, "delta4": {"name": "delta4", "group": "Calculated", "definition": "180*arg(V4)/pi", "description": "", "templateType": "anything", "can_override": false}, "V1m": {"name": "V1m", "group": "Calculated", "definition": "abs(V1)", "description": "", "templateType": "anything", "can_override": false}, "V4m": {"name": "V4m", "group": "Calculated", "definition": "abs(V4)", "description": "", "templateType": "anything", "can_override": false}, "V2m": {"name": "V2m", "group": "Calculated", "definition": "abs(V2)", "description": "", "templateType": "anything", "can_override": false}, "V3m": {"name": "V3m", "group": "Calculated", "definition": "abs(V3)", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Calculated", "definition": "re(SBASE*1*conj(IL))", "description": "", "templateType": "anything", "can_override": false}, "P4": {"name": "P4", "group": "Calculated", "definition": "re(SBASE*V4*conj(IL))", "description": "", "templateType": "anything", "can_override": false}, "efficiency": {"name": "efficiency", "group": "Calculated", "definition": "100*P4/P1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["XG", "RG", "XT1", "RT1", "XL", "RL", "XT2", "RT2", "VG", "Vline", "Vload", "SBASE", "pf"], "variable_groups": [{"name": "Calculated", "variables": ["IkA", "V1", "V2", "V3", "V4", "delta1", "delta2", "delta3", "delta4", "IBASE", "Ipu", "loading", "theta_rad", "theta", "IL", "V1m", "V2m", "V3m", "V4m", "P1", "P4", "efficiency"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Load 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 load current of {IkA} kA is flowing with a lagging power factor of {pf} %. Convert this to a current vector in per-unit.</p>\n<p>$ I_L $ = [[0]]$\\angle$ [[1]]$^o $&nbsp; &nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ipu", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*Ipu", "maxValue": "1.01*Ipu", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "theta", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*theta", "maxValue": "1.01*theta", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Voltages", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What are the voltages on bus (in p.u.)?</p>\n<p>$ V_1 $ =&nbsp;[[0]]$\\angle$ [[1]]$^o$&nbsp; &nbsp;p.u.</p>\n<p>$ V_2 $ =&nbsp;[[2]]$\\angle$ [[3]]$^o$&nbsp; &nbsp;p.u.</p>\n<p>$ V_3 $ =&nbsp;[[4]]$\\angle$ [[5]]$^o$&nbsp; &nbsp;p.u.</p>\n<p>$ V_4 $ =&nbsp;[[6]]$\\angle$ [[7]]$^o$&nbsp; &nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "V1", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*V1m", "maxValue": "1.01*V1m", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, 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"adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*V2m", "maxValue": "1.01*V2m", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "delta2", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*delta2", "maxValue": "1.01*delta2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "V3", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*V3m", "maxValue": "1.01*V3m", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "delta3", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*delta3", "maxValue": "1.01*delta3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "V4", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*V4m", "maxValue": "1.01*V4m", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "delta4", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*delta4", "maxValue": "1.01*delta4", "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": "Efficiency", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": 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