Basic Engineering Circuit Analysis 11th Edition by David Irwin ,Robert Nelms

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A standard practice for utility companies is to divide customers into single-phase users and three-phase users. The utility must provide three-phase users, typically industries, with all three phases. However, single-phase users, residential and light commercial, are connected to only one phase. To reduce cable costs, all single-phase users in a neighborhood are connected together. This means that even if the three-phase users present perfectly balanced loads to the power grid, the single-phase loads will never be in balance, resulting in current flow in the neutral connection. Consider the 60-Hz, abc-sequence network in Fig. P11.94. With a line voltage of 416 30° V rms, phase a supplies the single-phase users on A Street, phase b supplies B Street, and phase c supplies C Street. Furthermore, the three-phase industrial load, which is connected in delta, is balanced. Find the neutral current.

Figure P11.94