// Numbas version: finer_feedback_settings
{"name": "Calculating stationary frame components from three-phase quantities", "extensions": ["eukleides"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Calculating stationary frame components from three-phase quantities", "tags": [], "metadata": {"description": "<p>Question 1 of&nbsp;Electric Drives Tutorial Sheet 2019/20 &ndash; AC Questions</p>", "licence": "All rights reserved"}, "statement": "<p>The stator winding of an AC machine carries the following instantaneous currents:</p>\n<p>\\(i_{sa} = \\) {ia}A, \\(i_{sb} = \\) {ib}A, \\(i_{sc} = \\) {ic}A</p>\n<p></p>\n<p>Calculate:</p>", "advice": "<p>Recall the transformation to convert three phase quantities to equivalent two-phase ones. Use the first row of trasnformation matrix to get \\(i_{s\\alpha}\\) and the second row for \\(i_{s\\beta}\\) as:</p>\n<p>\\(i_{s\\alpha} = \\frac{2}{3} i_{sa} - \\frac{1}{3} i_{sb} - \\frac{1}{3} i_{sc} = \\frac{2}{3}\\) ({ia}) \\(-\\frac{1}{3}\\) ({ib}) \\(-\\frac{1}{3}\\) ({ic}) = {precround({ial}, 3)}</p>\n<p>\\(i_{s\\beta} = \\frac{1}{\\sqrt3} (i_{sb} - i_{sc}) = \\frac{1}{\\sqrt3}\\) ({ib - ic}) = {precround({ibe}, 3)}</p>\n<p></p>\n<p>Now calculate the magnitude and angle of the current vector as:</p>\n<p>\\(\\lvert\\bar{i}_s\\rvert = \\sqrt{i_{s\\alpha}^2 + i_{s\\beta}^2} = \\) {precround({i_mag}, 3)}</p>\n<p></p>\n<p>\\(\\vartheta = \\tan^{-1}\\left(\\frac{i_{s\\beta}}{i_{s\\alpha}}\\right) =\\) {precround({i_arg}, 3)}\\(^\\circ\\)</p>\n<p></p>\n<p>The vector on the two-dimensional plane is drawn here.</p>\n<p>{vector_drawn}</p>\n<p></p>", "rulesets": {}, "extensions": ["eukleides"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ia": {"name": "ia", "group": "Ungrouped variables", "definition": "-4.5", "description": "", "templateType": "anything", "can_override": false}, "ib": {"name": "ib", "group": "Ungrouped variables", "definition": "-2.5", "description": "", "templateType": "anything", "can_override": false}, "ic": {"name": "ic", "group": "Ungrouped variables", "definition": "-ia-ib", "description": "", "templateType": "anything", "can_override": false}, "ial": {"name": "ial", "group": "Ungrouped variables", "definition": "(2*ia - ib - ic)/3", "description": "", "templateType": "anything", "can_override": false}, "ibe": {"name": "ibe", "group": "Ungrouped variables", "definition": "(ib - ic)/sqrt(3)", "description": "", "templateType": "anything", "can_override": false}, "i_mag": {"name": "i_mag", "group": "Ungrouped variables", "definition": "sqrt(ial*ial + ibe*ibe)", "description": "", "templateType": "anything", "can_override": false}, "i_arg": {"name": "i_arg", "group": "Ungrouped variables", "definition": "sign(ibe)*arccos(ial/i_mag)*180/pi", "description": "", "templateType": "anything", "can_override": false}, "vector_drawn": {"name": "vector_drawn", "group": "Ungrouped variables", "definition": "eukleides(\"Vector\", [\n    line(point(0, 0)..point(1, 0)),\n    line(point(0, 0)..point(0, 1)),\n    point(0, 0)..point(ial, ibe) arrow\n])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ia", "ib", "ic", "ial", "ibe", "i_mag", "i_arg", "vector_drawn"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "is_alpha", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\(i_{s\\alpha}\\)</p>", "minValue": "0.99*ial", "maxValue": "1.01*ial", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "is_beta", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\(i_{s\\beta}\\)</p>", "minValue": "0.99*ibe", "maxValue": "1.01*ibe", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "imag", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "ia", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\(\\lvert \\bar {i}_s\\rvert\\)</p>", "minValue": "0.99*i_mag", "maxValue": "1.01*i_mag", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "theta", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\(\\vartheta\\) in degrees (\\(-180^\\circ \\le \\vartheta \\le 180^\\circ\\))</p>", "minValue": "0.99*i_arg", "maxValue": "1.01*i_arg", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Shafiq Odhano", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5160/"}], "resources": []}]}], "contributors": [{"name": "Shafiq Odhano", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5160/"}]}