barcode in vb.net 2010 True Power, VA Power, and Reactive Power in Software

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True Power, VA Power, and Reactive Power
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In an ac circuit or system containing nonzero resistance and nonzero reactance, the relationships among true power PT, apparent (VA) power PVA, and imaginary (reactive) power PX are as follows: PV A2 = P T2 + PX2 PT < PV A PX < PV A
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True Power, VA Power, and Reactive Power 269
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If there is no reactance in the circuit or system, then PVA = P T, and P X = 0. Engineers strive to minimize, and if possible eliminate, the reactance in power-transmission systems.
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Power Factor In an ac circuit, the ratio of the true power to the VA power, PT/PVA, is called the power factor. If there is no reactance, the ideal case, then PT = PVA, and the power factor (PF ) is equal to 1. If the circuit contains all reactance and no resistance of any significance (that is, zero or infinite resistance), then PT = 0, and therefore PF = 0. When a load, or a circuit in which you want power to be dissipated, contains resistance and reactance, then PF is between 0 and 1. That is, 0 < PF < 1. The power factor can also be expressed as a percentage between 0 and 100, written PF%. Mathematically, we have these formulas for the power factor:
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PF = PT/PVA PF% = 100PT/PVA When a load has some resistance and some reactance, then some of the power is dissipated as true power, and some is rejected by the load as imaginary power. In a sense, this imaginary power is sent back to the power source. There are two ways to determine the power factor in an ac circuit that contains reactance and resistance. One method is to find the cosine of the phase angle. The other method involves the ratio of the resistance to the absolute-value impedance.
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Cosine of Phase Angle Recall that in a circuit having reactance and resistance, the current and the voltage are not in phase. The phase angle ( ) is the extent, expressed in degrees, to which the current and the voltage differ in phase. If there is no reactance, then = 0 . If there is a pure reactance, then either = +90 (if the reactance is inductive) or else = 90 (if the reactance is capacitive). The power factor is equal to the cosine of the phase angle:
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PF = cos
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Problem 17-1 Suppose a circuit contains no reactance, but a pure resistance of 600 . What is the power factor Without doing any calculations, it is evident that PF = 1, because PVA = PT in a pure resistance. That means PT/PVA = 1. But you can also look at this by noting that the phase angle is 0 , because the current is in phase with the voltage. Using your calculator, you can see that cos 0 = 1. Therefore, PF = 1 = 100%. The vector for this case is shown in Fig. 17-5. Problem 17-2 Suppose a circuit contains a pure capacitive reactance of 40 , but no resistance. What is the power factor Here, the phase angle is 90 (Fig. 17-6). A calculator will tell you that cos 90 = 0. Therefore, PF = 0, and PT/PVA = 0 = 0%. None of the power is true; all of it is reactive.
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270 Power and Resonance in Alternating-Current Circuits
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17-5 Vector diagram
showing the phase angle for a purely resistive impedance of 600 + j0. The R and jX scales are relative.
Problem 17-3 Suppose a circuit contains a resistance of 50 and an inductive reactance of 50 in series. What is the power factor The phase angle in this case is 45 (Fig. 17-7). The resistance and reactance vectors have equal lengths and form two sides of a right triangle, with the complex impedance vector forming the hypotenuse. To determine the power factor, you can use a calculator to find cos 45 = 0.707. This means that PT/PVA = 0.707 = 70.7%. The Ratio R/Z The second way to calculate the power factor is to find the ratio of the resistance R to the absolutevalue impedance Z. In Fig. 17-7, this is visually apparent. A right triangle is formed by the resistance vector R (the base), the reactance vector jX (the height), and the absolute-value impedance Z (the hypotenuse). The cosine of the phase angle is equal to the ratio of the base length to the hypotenuse length; this represents R/Z.
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