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The status of a power network, as well as the techniques for estimating it, are important in assessing the power network's operation and control, as well as determining its future expansion. Power flow analysis, which estimates the magnitudes of the bus voltages as well as the power flowing through the system's lines, may be utilized to identify the state of any distribution network. Power flow analysis of distribution networks necessitates proper mathematical modeling of network components, particularly distribution lines. Typically, single-phase mathematical modeling is used. However, because this mathematical modeling does not reflect the underlying features of the distribution networks, the power flow calculations are insufficiently accurate. In this study, three-phase mathematical modeling was used to analyze the power flow of a practical Nigerian distribution network, and the results were compared to those of a single-phase equivalent. Modified Carson's equations were used to accurately model the lines of the three phases while accounting for mutual inductances between the phases to compute the line impedances. Thereafter, the three-phase bus admittance matrix of the network under study was developed. The three-phase power flow equations of the distribution network were formulated in the phase frame. The Newton-Raphson power flow technique was adopted to solve the network three-phase power flow problems formulated. A MATLAB program was developed to implement the method. The results revealed that the voltage magnitudes, as well as the active and reactive power losses, were not equal in all three phases. This contradicts the results of the power flow simulation using single-phase mathematical modeling. Therefore, three-phase power flow analysis better matched the actual distribution network operating circumstances than single-phase power flow analysis. [ABSTRACT FROM AUTHOR]