### Problem 7.8: Harmonic Power Flow with one Nonlinear Bus and Two Sets of Harmonic Nonlinear Device Currents

To the three-bus system of Fig. P7.8 apply the Newton–Raphson harmonic load flow analysis technique. Assume that bus 1 is the swing or slack bus, bus 2 is a linear PQ bus, and bus 3 is a nonlinear bus, where the fundamental real and reactive powers are specified. In addition, at bus 3 the real and imaginary harmonic nonlinear device currents are given as

${g}_{r,3}^{\left(5\right)}=|{\stackrel{~}{V}}_{3}^{\left(1\right)}|\mathrm{cos}\left({\delta }_{3}^{\left(1\right)}\right)+|{\stackrel{~}{V}}_{3}^{\left(5\right)}|{2}^{}\mathrm{cos}\left(2{\delta }_{3}^{\left(5\right)}\right)+|{\stackrel{~}{V}}_{3}^{\left(7\right)}|cos\left({\delta }_{3}^{\left(7\right)}\right)\text{,}$ (P8-1a)

${g}_{i,3}^{\left(5\right)}=|{\stackrel{~}{V}}_{3}^{\left(1\right)}|\mathrm{sin}\left({\delta }_{3}^{\left(1\right)}\right)+|{\stackrel{~}{V}}_{3}^{\left(5\right)}|{2}^{}\mathrm{sin}\left(2{\delta }_{3}^{\left(5\right)}\right)+|{\stackrel{~}{V}}_{3}^{\left(7\right)}|sin\left({\delta }_{3}^{\left(7\right)}\right)\text{,}$

(P8-1b)

${g}_{i,3}^{\left(7\right)}=|{\stackrel{~}{V}}_{3}^{\left(1\right)}|\mathrm{cos}\left({\delta }_{3}^{\left(1\right)}\right)+|{\stackrel{~}{V}}_{3}^{\left(5\right)}|\mathrm{cos}\left({\delta }_{3}^{\left(5\right)}\right)+|{\stackrel{~}{V}}_{3}^{\left(7\right)}|{2}^{}cos\left(2{\delta }_{3}^{\left(7\right)}\right)\text{,}$

(P8-2a)

${g}_{i,3}^{\left(7\right)}=$

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