MATLAB OBJECTIVESARRAY 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) October 2011 Ertuğrul Eriş 3
EXPERIMENT 3
ENERGY CONSERVATION October 2011 Ertuğrul Eriş 1
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CIRCUIT ANALYSIS TOOLS: MATLAB, PROTEUS
MATLAB Circuit schematic 2ne equations/unknowns MATLAB solutions PROTEUS Circuit schematic Voltage, current probes Voltage current waveforms October 2011 Ertuğrul Eriş 2
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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) October 2011 Ertuğrul Eriş 3
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CIRCUIT EQUATIONS
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 Type Number of equations: KVL+KVC+V/I relations = 2ne Number of unknowns: Elements’ currents and voltages = 2ne ne:number of elements, nd=nımber of nodes October 2011 Ertuğrul Eriş 4
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A X=B MATLAB >> 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 October 2011 Ertuğrul Eriş 6
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POWER (WATT)
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 >> V=[-82.3122;82.3122;82.0635]; >> I=[2.0000;1.7513;0.2487]; >> P=V.*I P = -164.6244 144.1534 20.4092 CALCULATION BY HAND CALCULATION BY MATLAB October 2011 Ertuğrul Eriş 7 Non matrix operarions should have (.) before opration symbol
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ENERGY
CALCULATION BY HAND syms t Es=int(-164.6244,t) Es = -(5792206144500715*t)/35184372088832 CALCULATION BY MATLAB October 2011 Ertuğrul Eriş 8
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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 October 2011 Ertuğrul Eriş 9
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PROBE POLARITY; DIRECTION
Vıs = - Vab Ib ,Vab : Polarity, Direction Passive sign convention Right click on the probe Then Mirror and rotation selection October 2011 Ertuğrul Eriş 10
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MULTIPLICATION: P=V*I
2. Name: Pa 5. Replace (+) with (*) 1. Left click for «add transient trace» 3.Ia probe selection 4.Vab probe selection October 2011 Ertuğrul Eriş 11
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LEFT/RIGHT Y-AXIS
1. Left click for «add transient trace» 2.Left/right y-axis selection October 2011 Ertuğrul Eriş 12
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SEPARATE WINDOWS
2.Click and move «analog» for voltage and current graph 1. Click «graph mode» 3. Again click and move «analog» for power graph October 2011 Ertuğrul Eriş 13
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