TAILIEUCHUNG - Electric Circuits, 9th Edition P45

Electric Circuits, 9th Edition P45. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 416 Balanced Three-Phase Circuits ----------- 2 General 3 network W3 J ----------- n Figure A general circuit whose power is supplied by n conductors. Figure A circuit used to analyze the two-wattmeter method of measuring average power delivered to a balanced load. A IaA z Z Z0 B C Applying this general observation we can see that for a three-conductor circuit whether balanced or not we need only two wattmeters to measure the total power. For a four-conductor circuit we need three wattmeters if the three-phase circuit is unbalanced but only two wattmeters if it is balanced because in the latter case there is no current in the neutral line. Thus only two wattmeters are needed to measure the total average power in any balanced three-phase system. The two-wattmeter method reduces to determining the magnitude and algebraic sign of the average power indicated by each wattmeter. We can describe the basic problem in terms of the circuit shown in Fig. where the two wattmeters are indicated by the shaded boxes and labeled Wi and W2. The coil notations cc and pc stand for current coil and potential coil respectively. We have elected to insert the current coils of the wattmeters in lines aA and cC. Thus line bB is the reference line for the two potential coils. The load is connected as a wye and the per-phase load impedance is designated as Z 0. This is a general representation as any A-connected load can be represented by its Y equivalent furthermore for the balanced case the impedance angle 0 is unaffected by the A-to-Y transformation. We now develop general equations for the readings of the two wattmeters. We assume that the current drawn by the potential coil of the wattmeter is negligible compared with the line current measured by the current coil. We further assume that the loads can be modeled by passive circuit elements so that the phase angle of the load impedance 0 in Fig. lies between -90 pure capacitance and 90 pure inductance . Finally we

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