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EXPERIMENT 3

EXPERIMENT 3. ENERGY CONSERVATION. CIRCUIT ANALYSIS TOOLS: MATLAB, PROTEUS. MATLAB Circuit schematic 2n e equations/unknowns MATLAB solutions PROTEUS Circuit schematic Voltage, current probes Voltage current waveforms. MATLAB OBJECTIVES. ARRAY MULTIPLICATION: P(t)=V(t)*I(t)

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EXPERIMENT 3

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  1. EXPERIMENT 3 ENERGY CONSERVATION Ertuğrul Eriş

  2. CIRCUIT ANALYSIS TOOLS: MATLAB, PROTEUS • MATLAB • Circuit schematic • 2ne equations/unknowns • MATLAB solutions • PROTEUS • Circuit schematic • Voltage, current probes • Voltage current waveforms Ertuğrul Eriş

  3. MATLAB OBJECTIVES • ARRAY MULTIPLICATION: P(t)=V(t)*I(t) • V= Element voltages’ array, • I= Element currents’ array • MATLAB: P=V.*I • SYMBOLIC INTEGRATION: • E(t) energy function • P(t) power function • MATLAB: syms t; int(p,t) Ertuğrul Eriş

  4. CIRCUIT EQUATIONS ne:number of elements, nd=nımber of nodes ne=3; nd=2; 2ne=6 KVL equations: ne-nd +1=2 • Va+Vs=0 • Vb -Va=0 KCL equation: nd-1=1 • -I+ia+ib=0 V-I/definition Relations: ne=3 • I=2 • Va-47ia =0 • Vb-330ib =0 Topology Number of equations: KVL+KVC+V/I relations = 2ne Number of unknowns: Elements’ currents and voltages = 2ne Type Ertuğrul Eriş

  5. CIRCUIT EQUATIONS A X=B • KVL: Vs+Va=0 • KVL: Va- Vb=0 • KCL: ia+ib-I=0 • V-I: I=2; • V-I : Va-47ia =0; • V-I : Vb-330ib=0 Ertuğrul Eriş

  6. CIRCUIT EQUATIONS:ALGEBRIAC LINEAR MATLAB A X=B >> A=[1,1,0,0,0,0; 0,1,-1,0,0,0; 0,0,0,-1,1,1; 0,0,0,1,0,0; 0,1,0,0, -47,0; 0,0,1,0,0,-330]; B=[0;0;0;2;0;0]; X=A\B X = -82.3122 = Vs 82.3122= Va 82.0635 = Vb 2.0000 = I 1.7513 = Ia 0.2487 = Ib Ertuğrul Eriş

  7. POWER (WATT) CALCULATION BY HAND 2.0000=I -82.3122=Vs Ps= I* Vs = 2.0000*-82.3122 =-164W 82.3122=Va 1.7513=Ia Pa= Ia* Va = 1.7513 * 82.3122 =144W 82.0635=Vb 0.2487=Ib Pb= Ib* Vb = 0.2487 * 82.3122 = 20W Σ Pi= 0 CALCULATION BY MATLAB >> V=[-82.3122;82.3122;82.0635]; >> I=[2.0000;1.7513;0.2487]; >> P=V.*I P = -164.6244 144.1534 20.4092 Non matrix operarions should have (.) before opration symbol Ertuğrul Eriş

  8. ENERGY CALCULATION BY HAND CALCULATION BY MATLAB syms t Es=int(-164.6244,t) Es = -(5792206144500715*t)/35184372088832 Ertuğrul Eriş

  9. PROTEUS OBJECTIVES • Appropriate probe (polarity, direction) selection for the right power sign • Passive sign convention • Multiplication: P=v*i • Different Right/left y-axis selection for voltage and current waveforms • Separate windows selection for voltage(current) and Power waveforms Ertuğrul Eriş

  10. PROBE POLARITY; DIRECTION Right click on the probe Then Mirror and rotation selection • Ib ,Vab : • Polarity, • Direction • Passive sign • convention Vıs = - Vab Ertuğrul Eriş

  11. 1. Left click for «add transient trace» MULTIPLICATION: P=V*I 2. Name: Pa 3.Ia probe selection 4.Vab probe selection 5. Replace (+) with (*) Ertuğrul Eriş

  12. 1. Left click for «add transient trace» LEFT/RIGHT Y-AXIS 2.Left/right y-axis selection Ertuğrul Eriş

  13. SEPARATE WINDOWS 1. Click «graph mode» 2.Click and move «analog» for voltage and current graph 3. Again click and move «analog» for power graph Ertuğrul Eriş

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