0885-8950 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2019.2892402, IEEE Transactions on Power Systems IEEE TRANSACTIONS ON POWER SYSTEMS 1 Weather-Dependent Power Flow Algorithm for Accurate Power System Analysis Under Variable Weather Conditions Arif Ahmed, Student Member, IEEE, Fiona J. Stevens McFadden, and Ramesh Rayudu, Senior Member, IEEE Abstract—Accurate power flow analysis is essential to system operators for planning, design, analysis, and control of power networks. The accuracy of power flow analysis can be increased significantly by including the weather-dependent characteristics of the system. In this manuscript, a novel weather-dependent power flow algorithm is proposed and studied in comparison to the very well-known conventional power flow. The weather- dependent power flow algorithm is novel in the sense that it is explicitly parameterised in terms of typically available measured weather parameters (ambient temperature, solar irradiance, wind speed, and wind angle) to perform a fully-coupled weather- dependent power flow analysis. Using this algorithm, the IEEE 30-bus power network was studied utilising real weather data by performing three year-long steady-state time-series power flow analyses. The study demonstrates that the proposed weather- dependent power flow algorithm accurately estimates the branch resistances, the system states (current and voltages), the power losses, the branch flows, and the branch loadings. These are made possible because the proposed algorithm accurately estimates branch conductor temperature due to the coupling of power flow with the nonlinear heat balance model. An analysis of the computational complexity of the proposed algorithm is also presented. Index Terms—Weather effects, Conductor nonlinear heat bal- ance, Power flow algorithm, Weather-Dependent Power Flow (WDPF), Computational complexity of power flow algorithms. I. NOTATION l number of weather-dependent branches. m number of system generators (including slack bus). n number of system buses. P sp k + jQ sp k specified complex power (pu) injection at bus k. P calc k + jQ calc k calculated complex power (pu) injection at bus k. ΔP k + j ΔQ k complex power mismatch (pu) at bus k. E k + jF k complex voltage (pu) at bus k. ΔE k + j ΔF k complex voltage mismatch (pu) at bus k. V k voltage magnitude (pu) at bus k. Arif Ahmed and Ramesh Rayudu are with the Smart Power and Renewable Energy Systems Group (SPRES) and the School of Engineering and Computer Science, Victoria University of Wellington, New Zealand. They are also affiliated with Robinson Research Institute (RRI), Victoria University of Wellington, Wellington 6140, New Zealand. e-mail: (arif.ahmed@vuw.ac.nz, ramesh.rayudu@vuw.ac.nz) Fiona J. Stevens McFadden is with the RRI and is affiliated with SPRES and the School of Engineering and Computer Science, Victo- ria University of Wellington, Wellington 6140, New Zealand. e-mail: (fiona.stevensmcfadden@vuw.ac.nz) R(T c ) conductor resistance per meter (Ω/m) at conductor temperature T c . P lossij real power loss (pu) in a conductor between bus i and j . ΔH ij heat balance mismatch (pu) for the branch conductor connecting bus i to bus j . G ij + jB ij (i, j ) th element of the admittance matrix. g ij + jb ij complex branch admittance (pu) connecting bus i to bus j . T cij temperature ( ◦ C) of the branch conductor connecting bus i to bus j . v iteration number. q c convective heat loss rate (W/m). q r radiative heat loss rate (W/m). q s solar heat gain rate (W/m). q j heat gain rate from Joule losses (W/m). K angle wind direction factor D 0 conductor diameter (m). ρ f air density (kg/m 3 ). μ f dynamic viscosity of air ( kg m·s ) . V w wind speed (m/s). φ wind angle ( ◦ ). T a ambient temperature ( ◦ C). k f thermal conductivity of air at the boundary layer temperature ( W m· ◦ C ) . ε emissivity constant. α solar absorptivity. Q s global solar irradiance (W/m 2 ). Matrices and vectors will be represented in bold in this manuscript. II. I NTRODUCTION P OWER flow analysis (PFA) is an important tool to study the steady-state operation of power systems. Many essen- tial analyses like planning and design, contingency analysis, stability analysis, security analysis, etc. are based on the PFA [1], [2]. It is, therefore, vital to get accurate output from a PFA by performing accurate modelling. The power flows in a power network are not only limited by the amount of load current flowing in the branches, rather they are also dependent on the conductor material, conductor radius, solar irradiance, ambient temperature, wind speed, and wind direction [3]. The conventional PFA [1], [2], however, is based on the assumption of constant network impedance, with no consideration for the impact of changing weather conditions. This introduces a certain degree of inaccuracy in the conventional PFA [3]–[5].