EE587_HW Part2

# EE587_HW Part2 - 9.7.6 Normal flow of harmonic currents...

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9.7.6 Normal flow of harmonic currents Harmonic currents tend to flow from the nonlinear loads (harmonic sources) toward the point of lowest impedance, usually the utility source, figure 9-7. The impedance of the utility source is usually much lower than parallel paths offered by loads. However, the harmonic current will split depending on the impedance ratios of available paths. Higher harmonic currents will, therefore, flow to capacitors that offer low impedance to high frequencies. Figure 9-7 Normal flow of harmonic currents 9.7.7 Parallel resonance Parallel resonance (figure 9-8) occurs when the system inductive reactance and capacitive reactances are equal at some frequency. It can also occur where is connected to the same bus - bar as a harmonic source. Parallel resonance will then occur between the system impedance and the capacitor. If the combination of capacitor banks and system inductance result in a parallel resonance near one of the characteristic harmonics generated by a nonlinear load, that harmonic current will excite the “tank” circuit, causing an amplified current to oscillate between the energy storage in the inductance and the energy storage in the capacitance. This high oscillating current can cause excessive voltage distortion. Figure 9-8 Parallel resonance conditions Frequency at which parallel resonance occurs can be estimated by the following simple equation:

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where H is the harmonic order. X C and X L are reactances at the fundamental frequency. 9.7.8 Series resonance Series resonance occurs when an inductive reactance and capacitive reactance that are in series are equal at some frequency. This condition occurs as a result of the series combination of capacitor banks and line or transformer inductances. Series resonance presents a low impedance path to harmonic currents and tends to draw in, or “trap,” any harmonic current to which it is tuned. Series resonance can result in high voltage distortion levels between the inductive and the capacitive elements in the series circuit. Another concern with series resonance is that high capacitor currents can flow for relatively small harmonic voltages. The actual current that will actually flow will depend on the quality factor, Q, of the circuit. One example of a possible series resonance circuit is a load center transformer that has capacitors connected to its secondary bus (figure 9-9). This circuit appears as a series circuit when viewed from the primary side of the transformer. In general, t o determine which resonance condition exists, it is necessary to measure the harmonic currents in the load and supply, together with harmonic voltage at the bus s . If the current flowing into the power system from the bus is small, while the harmonic voltage is high, resonance within the power system is indicated. 9.7.9 Effect of system loading
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## This note was uploaded on 02/04/2011 for the course EE 587 taught by Professor Dr.mohammedsafiuddin during the Spring '11 term at SUNY Buffalo.

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EE587_HW Part2 - 9.7.6 Normal flow of harmonic currents...

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