Lab Sheet 6: Performance Analysis of a Three-Phase Induction Motor Objective: Analyze and calculate various performance parameters of a three-phase, 4-pole, 200V, 400Hz induction motor. Understand the effects of electrical properties on motor performance using MATLAB, Python, or Excel. Equipment and Software: MATLAB, Python, or Excel Calculator for manual verification Motor Specifications: Type: Three-phase, 4-pole induction motor Rated Voltage: 200V Frequency: 400Hz Stator Resistance (𝑅𝑠Rs ): 1.71 ohms Stator Reactance (𝑋𝑠Xs ): 0.12 ohms Rotor Resistance (𝑅𝑟Rr ): 0.5 ohms Rotor Reactance (𝑋𝑖′Xi′ ): 0.3 ohms Magnetizing Reactance (𝑋𝑚Xm ): 32 ohms Slip (𝑠s): 2.5% Friction Losses: 100W Negligible Core Losses Tasks: Calculate the Synchronous Speed: Use the formula: 𝑛𝑠=120×𝑓𝑃ns =P120×f Where 𝑓f is the frequency, and 𝑃P is the number of poles. Calculate the Motor Speed at Full Load: Considering the slip (𝑠s), use the formula: 𝑛=𝑛𝑠×(1−𝑠)n=ns ×(1−s) Determine the Total Impedance: Combine stator impedance, rotor impedance referred to the stator, and magnetizing impedance. Use parallel and series combinations as applicable. Calculate the Stator Current and Power Factor: Use Ohm’s law and impedance to find the current: 𝐼𝑠=𝑉𝑝ℎ𝑍𝑡𝑜𝑡𝑎𝑙Is =Ztotal Vph Determine the power factor from the impedance phase angle. Compute Stator and Rotor Copper Losses: 𝑃𝑠𝑐𝑢=3×𝐼𝑠2×𝑅𝑠Pscu =3×Is2 ×Rs 𝑃𝑟𝑐𝑢=3×𝐼𝑟2×𝑅𝑟Prcu =3×Ir2 ×Rr Calculate the Air Gap Power: 𝑃𝑔𝑎𝑝=𝑃𝑟𝑐𝑢/𝑠 Determine the Developed Power and Torque: Subtract rotor copper losses from the air gap power for developed power. Calculate the torque using the developed power and motor speed. Assess Input and Output Power: Input power calculation incorporating power factor. Output power considering friction losses. Evaluate Motor Efficiency: Ratio of output power to input power, expressed as a percentage. Instructions: Students may choose MATLAB, Python, or Excel to perform the calculations. Document all steps, formulas, and intermediate values. Discuss the impact of slip, stator, and rotor resistances on motor performance. Submission: Submit all calculations, code (if applicable) and a discussion on the implications of your findings on motor design and operation. Lab Sheet for Session 5 Objective: Analyse DC motor operations using MATLAB and perform a comprehensive load analysis for an aircraft's electrical system using Excel. Materials: MATLAB software Microsoft Excel Exercise 1: DC Motor Analysis Using MATLAB A DC shunt motor connected to a 460-V supply has an armature resistance of 0.15 Ω. Calculate: (a) The back e.m.f when the armature current is 120 A. (b) The armature current when the back e.m.f. is 447.4 V. A DC shunt motor connected to a 460-V supply takes an armature current of 120 A on full load. Calculate the back e.m.f. at this load given the armature resistance of 0.25 Ω. A 4-pole DC shunt motor takes an armature current of 150 A at 440 V, with an armature resistance of 0.15 Ω. Calculate the back e.m.f. at this load. A 28 V DC motor with an armature resistance of 0.3 ohm, rated at 800 rpm and 5 A, is used to drive a pump. Calculate the no-load speed. Exercise 2: Load Analysis Using Excel Using the provided aircraft electrical data and load profiles, compute the following using Excel: The electrical data for a military aircraft is as follows: Number of generators : 2 (split bus) Number of inverter (for emergency use only) : 1 Number of Transformer Rectifier Unit : 2 Number of battery : 1 Specs: Generator Voltage 115 Frequency 400 Power Factor 0.8 Configuration WYE Max Continuous Power Rating (kVA) 15 Interval Rating (5 s – KVA 24 Interval Rating (5 min – kVA) 18 Inverter Emergency Rating (kVA) 15 Voltage (AC) 115 Frequency 400 Power Factor 0.8 Configuration WYE TRU Rating (amps) 150 Output Voltage (DC) 28 Max Continuous Power Rating (kVA) 150 Interval Rating (5 s – KVA 600 Interval Rating (5 min – kVA) 225 Battery Rating (AH) 40 Output Voltage (DC) 28 There are seven flight profiles. G1 : Start-Up G2 : Taxi G3 : Take Off and Climb G4: Cruise G5 : Landing G6: Ground Alert G7: Double Gen Failure The various AC Loads are as follows: LRU Consumption (VA) Profiles Used Operating Time Fuel Booster Pump 1800 G1, G6 Continuous Fuel Transfer Pump 1628 G1, G6,G7 Continuous Amplifier 10 G1, G3,G7 Continuous Oxygen 9 G2, G3,G4,G7 Continuous Cabin Control 23 G2, G3,G5,G6 Continuous Cockpit Lighting 167 G2, G4,G5,G6 Continuous Heat 270 G1, G2, G5,G6 Continuous Radar 2500 G1, G4, G6 Continuous Avionics Computer 170 G1,G3, G4,G6,G7 Continuous Avionics Sys 1 2700 G3, G7 Continuous Avionics Sys 2 870 G5,G7 Continuous HUD 235 G3,G4,G5 Continuous Fuel Measurement 28 G4,G5 Continuous Weapon System 400 G2, G6 Continuous EW System 3410 G1,G2, G6,G7 Continuous Nav 1` 132 G1,G2, G4,G6,G7 Continuous Nav 2 85.7 G1,G5, G4,G6,G7 Continuous GPS 98.9 G5,G6,G7 Continuous 26 V transformer 82 G2,G5 Continuous Others 4300 G3 Continuous The various DC Loads are as follows: LRU Consumption (Amps) Profiles Used Operating Time VOR/ILS 2 G1, G7 Continuous EW1 5.5 G5, G7 Continuous EW2 1.52 G2, G5,G7 Continuous Controller 0.1 G2, G5, G6 Continuous J Box 0.5 G2, G4,G5,G6 Continuous Air Con 1.8 G3, G4,G5 Continuous Cockpit Lights 4.7 G2, G3,G5,G6,G7 Continuous Anti-Collision Lights 3.4 G1, G4, G3 Continuous Formation Light 0.2 G7, G4, G3 Continuous Landing Light 16.1 G6 Continuous EFIS 2.33 G6,G7 Continuous ADAHRS 0.6 G2 Continuous Transmitter 14.28 G4,G5,G6,G7 Continuous Receiver 3.57 G2, G3,G5,G6,G7 Continuous Standby 4 G3,G5,G6,G4 Continuous Comms Panel 0.3 G4, G3,G5,G6,G7 Continuous AWS 6.9 G2, G5,G7 Continuous SMD 5 G7 Continuous Master Comp 1 G7 Continuous Others 122 G1 Continuous AC Load Analysis: For each flight profile, compute the total consumption in VA. DC Load Analysis: For each flight profile, compute the total consumption in Amps. Evaluate whether the provided generators, inverter, and TRU can cater to these loads under different flight profiles. Questions: How does the back e.m.f. affect the performance of a DC motor? What is the impact of varying the load conditions on the electrical system of an aircraft? Can the aircraft's electrical system handle all operational scenarios without overloading any component? Lab Sheet for Session 4 Objective: Explore the Fourier series representation of square waves and perform detailed harmonic power analysis for inverters in electrical circuits. Materials: Microsoft Excel software Exercise 1: Fourier Series Analysis of a Square Wave Given a square wave of amplitude 3 V and frequency 50 Hz, use MATLAB to compute the Fourier series coefficients up to the 25th harmonic. Sum up to 12th harmonics and up to 2th 5 harmonics plot the two resulting waveform. Observe which waveform (12 vs 25 harmonics) looks more like the original square wave. Questions: Which waveform resembles the original square wave more closely, and why? How does increasing the number of harmonics affect the approximation of the square wave? Exercise 2: Power Analysis for Inverter Circuits Using Excel Using Microsoft Excel, perform a detailed power analysis for a half-bridge and a full-bridge inverter under the following conditions: Load = 20 ohms, DC voltage = 20V, frequency of switching = 200 Hz. Calculate up to the 100th harmonic. Columns: Harmonic Number, Frequency, Voltage at the Harmonic, Resistance, Inductive Reactance, Impedance, Current, Power Factor, and Power. Compute Total Power, Fundamental Power, Total Harmonic Power, and Total Harmonic Distortion (THD). Repeat for the two inverters for Load = 20 ohms, L = 159 mH, DC voltage = 20V, frequency of switching = 200 Hz. Questions: How does the addition of inductance affect the power distribution across the harmonics? What implications do your findings have for the design and operation of inverter systems?